Properties

Label 405.2.r.a.197.8
Level $405$
Weight $2$
Character 405.197
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 197.8
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0152086 - 0.00133058i) q^{2} +(-1.96939 + 0.347256i) q^{4} +(1.79388 - 1.33492i) q^{5} +(0.211408 - 0.148030i) q^{7} +(-0.0589827 + 0.0158044i) q^{8} +O(q^{10})\) \(q+(0.0152086 - 0.00133058i) q^{2} +(-1.96939 + 0.347256i) q^{4} +(1.79388 - 1.33492i) q^{5} +(0.211408 - 0.148030i) q^{7} +(-0.0589827 + 0.0158044i) q^{8} +(0.0255062 - 0.0226891i) q^{10} +(-1.49616 - 4.11066i) q^{11} +(0.187451 - 2.14258i) q^{13} +(0.00301826 - 0.00253263i) q^{14} +(3.75746 - 1.36760i) q^{16} +(-1.70216 - 0.456091i) q^{17} +(4.91894 + 2.83995i) q^{19} +(-3.06928 + 3.25190i) q^{20} +(-0.0282241 - 0.0605267i) q^{22} +(3.32360 - 4.74660i) q^{23} +(1.43600 - 4.78935i) q^{25} -0.0328351i q^{26} +(-0.364940 + 0.364940i) q^{28} +(-3.59567 - 3.01712i) q^{29} +(-0.912568 - 5.17543i) q^{31} +(0.166010 - 0.0774120i) q^{32} +(-0.0264943 - 0.00467167i) q^{34} +(0.181634 - 0.547759i) q^{35} +(-0.837479 + 3.12552i) q^{37} +(0.0785891 + 0.0366467i) q^{38} +(-0.0847103 + 0.107088i) q^{40} +(-0.241984 - 0.288386i) q^{41} +(3.84888 - 8.25395i) q^{43} +(4.37396 + 7.57592i) q^{44} +(0.0442317 - 0.0766116i) q^{46} +(2.29910 + 3.28345i) q^{47} +(-2.37136 + 6.51526i) q^{49} +(0.0154670 - 0.0747502i) q^{50} +(0.374859 + 4.28465i) q^{52} +(8.15900 + 8.15900i) q^{53} +(-8.17131 - 5.37678i) q^{55} +(-0.0101299 + 0.0120724i) q^{56} +(-0.0586997 - 0.0411020i) q^{58} +(-10.6146 - 3.86341i) q^{59} +(-2.10712 + 11.9501i) q^{61} +(-0.0207652 - 0.0774969i) q^{62} +(-6.92336 + 3.99720i) q^{64} +(-2.52389 - 4.09375i) q^{65} +(1.82940 + 0.160052i) q^{67} +(3.51058 + 0.307136i) q^{68} +(0.00203356 - 0.00857235i) q^{70} +(-4.44360 + 2.56551i) q^{71} +(3.71651 + 13.8702i) q^{73} +(-0.00857816 + 0.0486492i) q^{74} +(-10.6735 - 3.88483i) q^{76} +(-0.924799 - 0.647552i) q^{77} +(1.98949 - 2.37099i) q^{79} +(4.91479 - 7.46920i) q^{80} +(-0.00406398 - 0.00406398i) q^{82} +(0.432904 + 4.94812i) q^{83} +(-3.66230 + 1.45406i) q^{85} +(0.0475536 - 0.130653i) q^{86} +(0.153214 + 0.218812i) q^{88} +(1.44584 - 2.50426i) q^{89} +(-0.277536 - 0.480707i) q^{91} +(-4.89717 + 10.5020i) q^{92} +(0.0393351 + 0.0468777i) q^{94} +(12.6151 - 1.47184i) q^{95} +(-4.27105 - 1.99162i) q^{97} +(-0.0273961 + 0.102243i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0152086 0.00133058i 0.0107541 0.000940864i −0.0817774 0.996651i \(-0.526060\pi\)
0.0925315 + 0.995710i \(0.470504\pi\)
\(3\) 0 0
\(4\) −1.96939 + 0.347256i −0.984693 + 0.173628i
\(5\) 1.79388 1.33492i 0.802247 0.596992i
\(6\) 0 0
\(7\) 0.211408 0.148030i 0.0799048 0.0559499i −0.532941 0.846152i \(-0.678913\pi\)
0.612846 + 0.790202i \(0.290025\pi\)
\(8\) −0.0589827 + 0.0158044i −0.0208535 + 0.00558769i
\(9\) 0 0
\(10\) 0.0255062 0.0226891i 0.00806578 0.00717494i
\(11\) −1.49616 4.11066i −0.451108 1.23941i −0.931945 0.362600i \(-0.881889\pi\)
0.480836 0.876810i \(-0.340333\pi\)
\(12\) 0 0
\(13\) 0.187451 2.14258i 0.0519896 0.594244i −0.924859 0.380311i \(-0.875817\pi\)
0.976848 0.213933i \(-0.0686274\pi\)
\(14\) 0.00301826 0.00253263i 0.000806665 0.000676873i
\(15\) 0 0
\(16\) 3.75746 1.36760i 0.939364 0.341901i
\(17\) −1.70216 0.456091i −0.412833 0.110618i 0.0464236 0.998922i \(-0.485218\pi\)
−0.459257 + 0.888303i \(0.651884\pi\)
\(18\) 0 0
\(19\) 4.91894 + 2.83995i 1.12848 + 0.651529i 0.943553 0.331222i \(-0.107461\pi\)
0.184929 + 0.982752i \(0.440794\pi\)
\(20\) −3.06928 + 3.25190i −0.686312 + 0.727147i
\(21\) 0 0
\(22\) −0.0282241 0.0605267i −0.00601740 0.0129043i
\(23\) 3.32360 4.74660i 0.693019 0.989734i −0.306267 0.951946i \(-0.599080\pi\)
0.999286 0.0377879i \(-0.0120311\pi\)
\(24\) 0 0
\(25\) 1.43600 4.78935i 0.287200 0.957871i
\(26\) 0.0328351i 0.00643949i
\(27\) 0 0
\(28\) −0.364940 + 0.364940i −0.0689672 + 0.0689672i
\(29\) −3.59567 3.01712i −0.667699 0.560266i 0.244685 0.969603i \(-0.421316\pi\)
−0.912383 + 0.409337i \(0.865760\pi\)
\(30\) 0 0
\(31\) −0.912568 5.17543i −0.163902 0.929534i −0.950189 0.311673i \(-0.899111\pi\)
0.786287 0.617861i \(-0.212001\pi\)
\(32\) 0.166010 0.0774120i 0.0293468 0.0136846i
\(33\) 0 0
\(34\) −0.0264943 0.00467167i −0.00454374 0.000801184i
\(35\) 0.181634 0.547759i 0.0307017 0.0925882i
\(36\) 0 0
\(37\) −0.837479 + 3.12552i −0.137681 + 0.513832i 0.862292 + 0.506412i \(0.169028\pi\)
−0.999972 + 0.00741968i \(0.997638\pi\)
\(38\) 0.0785891 + 0.0366467i 0.0127488 + 0.00594488i
\(39\) 0 0
\(40\) −0.0847103 + 0.107088i −0.0133939 + 0.0169321i
\(41\) −0.241984 0.288386i −0.0377916 0.0450383i 0.746818 0.665029i \(-0.231581\pi\)
−0.784609 + 0.619991i \(0.787136\pi\)
\(42\) 0 0
\(43\) 3.84888 8.25395i 0.586948 1.25872i −0.358678 0.933461i \(-0.616772\pi\)
0.945627 0.325254i \(-0.105450\pi\)
\(44\) 4.37396 + 7.57592i 0.659400 + 1.14211i
\(45\) 0 0
\(46\) 0.0442317 0.0766116i 0.00652161 0.0112958i
\(47\) 2.29910 + 3.28345i 0.335358 + 0.478941i 0.951046 0.309049i \(-0.100011\pi\)
−0.615688 + 0.787990i \(0.711122\pi\)
\(48\) 0 0
\(49\) −2.37136 + 6.51526i −0.338766 + 0.930751i
\(50\) 0.0154670 0.0747502i 0.00218736 0.0105713i
\(51\) 0 0
\(52\) 0.374859 + 4.28465i 0.0519835 + 0.594174i
\(53\) 8.15900 + 8.15900i 1.12072 + 1.12072i 0.991633 + 0.129092i \(0.0412062\pi\)
0.129092 + 0.991633i \(0.458794\pi\)
\(54\) 0 0
\(55\) −8.17131 5.37678i −1.10182 0.725005i
\(56\) −0.0101299 + 0.0120724i −0.00135367 + 0.00161324i
\(57\) 0 0
\(58\) −0.0586997 0.0411020i −0.00770765 0.00539696i
\(59\) −10.6146 3.86341i −1.38191 0.502973i −0.459152 0.888358i \(-0.651847\pi\)
−0.922756 + 0.385385i \(0.874069\pi\)
\(60\) 0 0
\(61\) −2.10712 + 11.9501i −0.269790 + 1.53005i 0.485251 + 0.874375i \(0.338728\pi\)
−0.755040 + 0.655678i \(0.772383\pi\)
\(62\) −0.0207652 0.0774969i −0.00263719 0.00984212i
\(63\) 0 0
\(64\) −6.92336 + 3.99720i −0.865420 + 0.499650i
\(65\) −2.52389 4.09375i −0.313050 0.507768i
\(66\) 0 0
\(67\) 1.82940 + 0.160052i 0.223497 + 0.0195534i 0.198354 0.980130i \(-0.436440\pi\)
0.0251426 + 0.999684i \(0.491996\pi\)
\(68\) 3.51058 + 0.307136i 0.425721 + 0.0372457i
\(69\) 0 0
\(70\) 0.00203356 0.00857235i 0.000243057 0.00102459i
\(71\) −4.44360 + 2.56551i −0.527358 + 0.304471i −0.739940 0.672673i \(-0.765146\pi\)
0.212582 + 0.977143i \(0.431813\pi\)
\(72\) 0 0
\(73\) 3.71651 + 13.8702i 0.434984 + 1.62338i 0.741104 + 0.671390i \(0.234303\pi\)
−0.306120 + 0.951993i \(0.599031\pi\)
\(74\) −0.00857816 + 0.0486492i −0.000997191 + 0.00565535i
\(75\) 0 0
\(76\) −10.6735 3.88483i −1.22433 0.445620i
\(77\) −0.924799 0.647552i −0.105391 0.0737953i
\(78\) 0 0
\(79\) 1.98949 2.37099i 0.223835 0.266757i −0.642426 0.766348i \(-0.722072\pi\)
0.866261 + 0.499591i \(0.166516\pi\)
\(80\) 4.91479 7.46920i 0.549490 0.835082i
\(81\) 0 0
\(82\) −0.00406398 0.00406398i −0.000448791 0.000448791i
\(83\) 0.432904 + 4.94812i 0.0475174 + 0.543127i 0.982225 + 0.187708i \(0.0601060\pi\)
−0.934707 + 0.355418i \(0.884338\pi\)
\(84\) 0 0
\(85\) −3.66230 + 1.45406i −0.397233 + 0.157715i
\(86\) 0.0475536 0.130653i 0.00512784 0.0140886i
\(87\) 0 0
\(88\) 0.153214 + 0.218812i 0.0163326 + 0.0233254i
\(89\) 1.44584 2.50426i 0.153259 0.265452i −0.779165 0.626819i \(-0.784357\pi\)
0.932424 + 0.361367i \(0.117690\pi\)
\(90\) 0 0
\(91\) −0.277536 0.480707i −0.0290937 0.0503917i
\(92\) −4.89717 + 10.5020i −0.510565 + 1.09491i
\(93\) 0 0
\(94\) 0.0393351 + 0.0468777i 0.00405710 + 0.00483507i
\(95\) 12.6151 1.47184i 1.29428 0.151008i
\(96\) 0 0
\(97\) −4.27105 1.99162i −0.433659 0.202219i 0.193516 0.981097i \(-0.438011\pi\)
−0.627175 + 0.778879i \(0.715789\pi\)
\(98\) −0.0273961 + 0.102243i −0.00276742 + 0.0103282i
\(99\) 0 0
\(100\) −1.16491 + 9.93074i −0.116491 + 0.993074i
\(101\) −2.84523 0.501690i −0.283110 0.0499200i 0.0302897 0.999541i \(-0.490357\pi\)
−0.313400 + 0.949621i \(0.601468\pi\)
\(102\) 0 0
\(103\) 9.15274 4.26799i 0.901846 0.420538i 0.0843263 0.996438i \(-0.473126\pi\)
0.817520 + 0.575900i \(0.195348\pi\)
\(104\) 0.0228057 + 0.129337i 0.00223628 + 0.0126826i
\(105\) 0 0
\(106\) 0.134943 + 0.113231i 0.0131069 + 0.0109980i
\(107\) −10.6261 + 10.6261i −1.02727 + 1.02727i −0.0276498 + 0.999618i \(0.508802\pi\)
−0.999618 + 0.0276498i \(0.991198\pi\)
\(108\) 0 0
\(109\) 12.0030i 1.14968i −0.818265 0.574841i \(-0.805064\pi\)
0.818265 0.574841i \(-0.194936\pi\)
\(110\) −0.131429 0.0709009i −0.0125312 0.00676013i
\(111\) 0 0
\(112\) 0.591912 0.845337i 0.0559304 0.0798769i
\(113\) 3.92562 + 8.41851i 0.369291 + 0.791947i 0.999875 + 0.0158260i \(0.00503778\pi\)
−0.630584 + 0.776121i \(0.717184\pi\)
\(114\) 0 0
\(115\) −0.374165 12.9515i −0.0348911 1.20774i
\(116\) 8.12897 + 4.69326i 0.754756 + 0.435759i
\(117\) 0 0
\(118\) −0.166575 0.0446336i −0.0153344 0.00410885i
\(119\) −0.427365 + 0.155548i −0.0391765 + 0.0142591i
\(120\) 0 0
\(121\) −6.23254 + 5.22972i −0.566595 + 0.475429i
\(122\) −0.0161459 + 0.184548i −0.00146178 + 0.0167082i
\(123\) 0 0
\(124\) 3.59440 + 9.87552i 0.322786 + 0.886848i
\(125\) −3.81737 10.5085i −0.341436 0.939905i
\(126\) 0 0
\(127\) 18.7735 5.03035i 1.66588 0.446371i 0.701885 0.712290i \(-0.252342\pi\)
0.963996 + 0.265918i \(0.0856752\pi\)
\(128\) −0.400068 + 0.280131i −0.0353614 + 0.0247603i
\(129\) 0 0
\(130\) −0.0438320 0.0589021i −0.00384433 0.00516606i
\(131\) 4.49710 0.792959i 0.392913 0.0692812i 0.0262986 0.999654i \(-0.491628\pi\)
0.366614 + 0.930373i \(0.380517\pi\)
\(132\) 0 0
\(133\) 1.46030 0.127760i 0.126624 0.0110782i
\(134\) 0.0280356 0.00242191
\(135\) 0 0
\(136\) 0.107606 0.00922713
\(137\) 6.96948 0.609750i 0.595443 0.0520945i 0.214549 0.976713i \(-0.431172\pi\)
0.380894 + 0.924619i \(0.375616\pi\)
\(138\) 0 0
\(139\) −8.03836 + 1.41738i −0.681805 + 0.120221i −0.503815 0.863812i \(-0.668071\pi\)
−0.177990 + 0.984032i \(0.556959\pi\)
\(140\) −0.167494 + 1.14182i −0.0141558 + 0.0965017i
\(141\) 0 0
\(142\) −0.0641675 + 0.0449306i −0.00538482 + 0.00377049i
\(143\) −9.08786 + 2.43508i −0.759965 + 0.203632i
\(144\) 0 0
\(145\) −10.4778 0.612441i −0.870133 0.0508605i
\(146\) 0.0749784 + 0.206002i 0.00620526 + 0.0170488i
\(147\) 0 0
\(148\) 0.563966 6.44617i 0.0463578 0.529872i
\(149\) −14.7726 + 12.3956i −1.21021 + 1.01549i −0.210937 + 0.977500i \(0.567651\pi\)
−0.999278 + 0.0379911i \(0.987904\pi\)
\(150\) 0 0
\(151\) −14.1147 + 5.13734i −1.14864 + 0.418070i −0.845026 0.534725i \(-0.820415\pi\)
−0.303613 + 0.952795i \(0.598193\pi\)
\(152\) −0.335016 0.0897672i −0.0271734 0.00728108i
\(153\) 0 0
\(154\) −0.0149266 0.00861785i −0.00120282 0.000694446i
\(155\) −8.54579 8.06589i −0.686415 0.647868i
\(156\) 0 0
\(157\) 0.987420 + 2.11753i 0.0788047 + 0.168997i 0.941762 0.336279i \(-0.109168\pi\)
−0.862958 + 0.505276i \(0.831391\pi\)
\(158\) 0.0271027 0.0387066i 0.00215617 0.00307933i
\(159\) 0 0
\(160\) 0.194464 0.360478i 0.0153737 0.0284983i
\(161\) 1.49546i 0.117859i
\(162\) 0 0
\(163\) 10.7302 10.7302i 0.840451 0.840451i −0.148467 0.988917i \(-0.547434\pi\)
0.988917 + 0.148467i \(0.0474338\pi\)
\(164\) 0.576705 + 0.483913i 0.0450331 + 0.0377872i
\(165\) 0 0
\(166\) 0.0131678 + 0.0746781i 0.00102202 + 0.00579615i
\(167\) 17.5852 8.20013i 1.36079 0.634545i 0.401208 0.915987i \(-0.368590\pi\)
0.959578 + 0.281442i \(0.0908126\pi\)
\(168\) 0 0
\(169\) 8.24701 + 1.45417i 0.634385 + 0.111859i
\(170\) −0.0537639 + 0.0269873i −0.00412350 + 0.00206983i
\(171\) 0 0
\(172\) −4.71370 + 17.5918i −0.359416 + 1.34136i
\(173\) 5.26921 + 2.45707i 0.400610 + 0.186808i 0.612472 0.790492i \(-0.290175\pi\)
−0.211862 + 0.977300i \(0.567953\pi\)
\(174\) 0 0
\(175\) −0.405384 1.22508i −0.0306441 0.0926073i
\(176\) −11.2435 13.3995i −0.847510 1.01002i
\(177\) 0 0
\(178\) 0.0186571 0.0400103i 0.00139841 0.00299890i
\(179\) 4.77974 + 8.27875i 0.357254 + 0.618783i 0.987501 0.157612i \(-0.0503796\pi\)
−0.630247 + 0.776395i \(0.717046\pi\)
\(180\) 0 0
\(181\) 6.93879 12.0183i 0.515756 0.893315i −0.484077 0.875026i \(-0.660844\pi\)
0.999833 0.0182899i \(-0.00582219\pi\)
\(182\) −0.00486056 0.00694161i −0.000360289 0.000514546i
\(183\) 0 0
\(184\) −0.121018 + 0.332494i −0.00892157 + 0.0245118i
\(185\) 2.66996 + 6.72476i 0.196300 + 0.494414i
\(186\) 0 0
\(187\) 0.671857 + 7.67937i 0.0491311 + 0.561571i
\(188\) −5.66801 5.66801i −0.413382 0.413382i
\(189\) 0 0
\(190\) 0.189900 0.0391701i 0.0137768 0.00284170i
\(191\) 7.63489 9.09890i 0.552441 0.658374i −0.415488 0.909599i \(-0.636389\pi\)
0.967929 + 0.251225i \(0.0808335\pi\)
\(192\) 0 0
\(193\) 9.91741 + 6.94425i 0.713871 + 0.499858i 0.873197 0.487368i \(-0.162043\pi\)
−0.159325 + 0.987226i \(0.550932\pi\)
\(194\) −0.0676068 0.0246069i −0.00485389 0.00176667i
\(195\) 0 0
\(196\) 2.40766 13.6545i 0.171976 0.975323i
\(197\) −1.53862 5.74222i −0.109622 0.409116i 0.889206 0.457507i \(-0.151257\pi\)
−0.998828 + 0.0483907i \(0.984591\pi\)
\(198\) 0 0
\(199\) −4.84519 + 2.79737i −0.343466 + 0.198300i −0.661804 0.749677i \(-0.730209\pi\)
0.318337 + 0.947977i \(0.396876\pi\)
\(200\) −0.00900656 + 0.305184i −0.000636860 + 0.0215798i
\(201\) 0 0
\(202\) −0.0439395 0.00384421i −0.00309157 0.000270478i
\(203\) −1.20678 0.105579i −0.0846992 0.00741022i
\(204\) 0 0
\(205\) −0.819062 0.194300i −0.0572057 0.0135705i
\(206\) 0.133522 0.0770888i 0.00930290 0.00537103i
\(207\) 0 0
\(208\) −2.22585 8.30699i −0.154335 0.575986i
\(209\) 4.31456 24.4691i 0.298444 1.69256i
\(210\) 0 0
\(211\) 5.33826 + 1.94297i 0.367501 + 0.133759i 0.519168 0.854672i \(-0.326242\pi\)
−0.151667 + 0.988432i \(0.548464\pi\)
\(212\) −18.9015 13.2350i −1.29816 0.908980i
\(213\) 0 0
\(214\) −0.147470 + 0.175748i −0.0100808 + 0.0120139i
\(215\) −4.11390 19.9445i −0.280566 1.36020i
\(216\) 0 0
\(217\) −0.959041 0.959041i −0.0651039 0.0651039i
\(218\) −0.0159710 0.182550i −0.00108169 0.0123638i
\(219\) 0 0
\(220\) 17.9596 + 7.75142i 1.21083 + 0.522601i
\(221\) −1.29628 + 3.56150i −0.0871973 + 0.239573i
\(222\) 0 0
\(223\) −7.56295 10.8010i −0.506452 0.723289i 0.481773 0.876296i \(-0.339993\pi\)
−0.988225 + 0.153007i \(0.951104\pi\)
\(224\) 0.0236367 0.0409400i 0.00157929 0.00273542i
\(225\) 0 0
\(226\) 0.0709048 + 0.122811i 0.00471652 + 0.00816925i
\(227\) 6.15899 13.2080i 0.408787 0.876646i −0.588870 0.808228i \(-0.700427\pi\)
0.997657 0.0684181i \(-0.0217952\pi\)
\(228\) 0 0
\(229\) 5.35302 + 6.37948i 0.353738 + 0.421568i 0.913343 0.407191i \(-0.133492\pi\)
−0.559605 + 0.828759i \(0.689047\pi\)
\(230\) −0.0229236 0.196477i −0.00151154 0.0129553i
\(231\) 0 0
\(232\) 0.259766 + 0.121131i 0.0170545 + 0.00795262i
\(233\) 7.15675 26.7094i 0.468854 1.74979i −0.174930 0.984581i \(-0.555970\pi\)
0.643784 0.765207i \(-0.277363\pi\)
\(234\) 0 0
\(235\) 8.50744 + 2.82101i 0.554964 + 0.184023i
\(236\) 22.2459 + 3.92255i 1.44808 + 0.255336i
\(237\) 0 0
\(238\) −0.00629266 + 0.00293432i −0.000407893 + 0.000190204i
\(239\) 3.76477 + 21.3510i 0.243522 + 1.38108i 0.823899 + 0.566736i \(0.191794\pi\)
−0.580377 + 0.814348i \(0.697095\pi\)
\(240\) 0 0
\(241\) 3.99926 + 3.35578i 0.257615 + 0.216165i 0.762443 0.647055i \(-0.224000\pi\)
−0.504828 + 0.863220i \(0.668444\pi\)
\(242\) −0.0878299 + 0.0878299i −0.00564592 + 0.00564592i
\(243\) 0 0
\(244\) 24.2661i 1.55348i
\(245\) 4.44339 + 14.8531i 0.283878 + 0.948933i
\(246\) 0 0
\(247\) 7.00687 10.0068i 0.445837 0.636721i
\(248\) 0.135620 + 0.290838i 0.00861188 + 0.0184682i
\(249\) 0 0
\(250\) −0.0720393 0.154740i −0.00455617 0.00978662i
\(251\) −12.0778 6.97313i −0.762345 0.440140i 0.0677923 0.997699i \(-0.478404\pi\)
−0.830137 + 0.557560i \(0.811738\pi\)
\(252\) 0 0
\(253\) −24.4843 6.56054i −1.53931 0.412458i
\(254\) 0.278826 0.101484i 0.0174951 0.00636770i
\(255\) 0 0
\(256\) 12.2424 10.2726i 0.765152 0.642039i
\(257\) −0.816897 + 9.33717i −0.0509566 + 0.582437i 0.927200 + 0.374567i \(0.122209\pi\)
−0.978156 + 0.207870i \(0.933347\pi\)
\(258\) 0 0
\(259\) 0.285619 + 0.784731i 0.0177475 + 0.0487608i
\(260\) 6.39210 + 7.18574i 0.396421 + 0.445641i
\(261\) 0 0
\(262\) 0.0673396 0.0180436i 0.00416025 0.00111474i
\(263\) −8.22122 + 5.75656i −0.506942 + 0.354965i −0.798897 0.601467i \(-0.794583\pi\)
0.291955 + 0.956432i \(0.405694\pi\)
\(264\) 0 0
\(265\) 25.5278 + 3.74468i 1.56816 + 0.230034i
\(266\) 0.0220392 0.00388610i 0.00135131 0.000238272i
\(267\) 0 0
\(268\) −3.65837 + 0.320066i −0.223470 + 0.0195511i
\(269\) 1.84882 0.112724 0.0563622 0.998410i \(-0.482050\pi\)
0.0563622 + 0.998410i \(0.482050\pi\)
\(270\) 0 0
\(271\) 14.0068 0.850851 0.425426 0.904993i \(-0.360124\pi\)
0.425426 + 0.904993i \(0.360124\pi\)
\(272\) −7.01953 + 0.614129i −0.425621 + 0.0372370i
\(273\) 0 0
\(274\) 0.105185 0.0185469i 0.00635445 0.00112046i
\(275\) −21.8359 + 1.26271i −1.31675 + 0.0761445i
\(276\) 0 0
\(277\) −14.8975 + 10.4313i −0.895103 + 0.626758i −0.927951 0.372703i \(-0.878431\pi\)
0.0328481 + 0.999460i \(0.489542\pi\)
\(278\) −0.120367 + 0.0322521i −0.00721911 + 0.00193435i
\(279\) 0 0
\(280\) −0.00205625 + 0.0351789i −0.000122885 + 0.00210234i
\(281\) 8.98091 + 24.6748i 0.535756 + 1.47198i 0.852124 + 0.523341i \(0.175314\pi\)
−0.316368 + 0.948637i \(0.602463\pi\)
\(282\) 0 0
\(283\) −1.59875 + 18.2738i −0.0950360 + 1.08627i 0.787593 + 0.616196i \(0.211327\pi\)
−0.882629 + 0.470071i \(0.844228\pi\)
\(284\) 7.86028 6.59556i 0.466422 0.391374i
\(285\) 0 0
\(286\) −0.134974 + 0.0491264i −0.00798117 + 0.00290491i
\(287\) −0.0938472 0.0251463i −0.00553962 0.00148434i
\(288\) 0 0
\(289\) −12.0331 6.94732i −0.707830 0.408666i
\(290\) −0.160168 + 0.00462718i −0.00940538 + 0.000271718i
\(291\) 0 0
\(292\) −12.1357 26.0252i −0.710191 1.52301i
\(293\) −6.02781 + 8.60861i −0.352149 + 0.502920i −0.955675 0.294422i \(-0.904873\pi\)
0.603527 + 0.797343i \(0.293762\pi\)
\(294\) 0 0
\(295\) −24.1987 + 7.23915i −1.40890 + 0.421480i
\(296\) 0.197587i 0.0114845i
\(297\) 0 0
\(298\) −0.208177 + 0.208177i −0.0120594 + 0.0120594i
\(299\) −9.54693 8.01082i −0.552113 0.463278i
\(300\) 0 0
\(301\) −0.408144 2.31470i −0.0235250 0.133417i
\(302\) −0.207830 + 0.0969127i −0.0119593 + 0.00557670i
\(303\) 0 0
\(304\) 22.3666 + 3.94384i 1.28281 + 0.226195i
\(305\) 12.1724 + 24.2499i 0.696992 + 1.38854i
\(306\) 0 0
\(307\) 3.31491 12.3714i 0.189192 0.706074i −0.804502 0.593949i \(-0.797568\pi\)
0.993694 0.112124i \(-0.0357654\pi\)
\(308\) 2.04615 + 0.954137i 0.116590 + 0.0543670i
\(309\) 0 0
\(310\) −0.140702 0.111300i −0.00799135 0.00632143i
\(311\) −13.5014 16.0903i −0.765592 0.912397i 0.232596 0.972573i \(-0.425278\pi\)
−0.998188 + 0.0601768i \(0.980834\pi\)
\(312\) 0 0
\(313\) −12.4918 + 26.7887i −0.706078 + 1.51419i 0.145159 + 0.989408i \(0.453631\pi\)
−0.851237 + 0.524781i \(0.824147\pi\)
\(314\) 0.0178349 + 0.0308909i 0.00100648 + 0.00174327i
\(315\) 0 0
\(316\) −3.09474 + 5.36025i −0.174093 + 0.301538i
\(317\) 15.2311 + 21.7523i 0.855465 + 1.22173i 0.973492 + 0.228720i \(0.0734540\pi\)
−0.118027 + 0.993010i \(0.537657\pi\)
\(318\) 0 0
\(319\) −7.02268 + 19.2947i −0.393195 + 1.08029i
\(320\) −7.08374 + 16.4126i −0.395993 + 0.917492i
\(321\) 0 0
\(322\) −0.00198984 0.0227439i −0.000110889 0.00126747i
\(323\) −7.07752 7.07752i −0.393804 0.393804i
\(324\) 0 0
\(325\) −9.99237 3.97451i −0.554277 0.220466i
\(326\) 0.148914 0.177468i 0.00824756 0.00982906i
\(327\) 0 0
\(328\) 0.0188306 + 0.0131854i 0.00103975 + 0.000728040i
\(329\) 0.972097 + 0.353814i 0.0535934 + 0.0195064i
\(330\) 0 0
\(331\) −1.72647 + 9.79132i −0.0948956 + 0.538179i 0.899884 + 0.436130i \(0.143651\pi\)
−0.994779 + 0.102050i \(0.967460\pi\)
\(332\) −2.57082 9.59443i −0.141092 0.526563i
\(333\) 0 0
\(334\) 0.256536 0.148111i 0.0140371 0.00810430i
\(335\) 3.49537 2.15498i 0.190973 0.117739i
\(336\) 0 0
\(337\) −13.9748 1.22264i −0.761258 0.0666015i −0.300086 0.953912i \(-0.597015\pi\)
−0.461172 + 0.887311i \(0.652571\pi\)
\(338\) 0.127361 + 0.0111426i 0.00692750 + 0.000606078i
\(339\) 0 0
\(340\) 6.70756 4.13536i 0.363768 0.224272i
\(341\) −19.9091 + 11.4945i −1.07814 + 0.622463i
\(342\) 0 0
\(343\) 0.930702 + 3.47343i 0.0502532 + 0.187547i
\(344\) −0.0965688 + 0.547669i −0.00520664 + 0.0295283i
\(345\) 0 0
\(346\) 0.0834068 + 0.0303576i 0.00448397 + 0.00163203i
\(347\) −5.00149 3.50208i −0.268494 0.188001i 0.431574 0.902077i \(-0.357958\pi\)
−0.700068 + 0.714076i \(0.746847\pi\)
\(348\) 0 0
\(349\) 2.45708 2.92823i 0.131524 0.156745i −0.696263 0.717787i \(-0.745155\pi\)
0.827787 + 0.561042i \(0.189600\pi\)
\(350\) −0.00779540 0.0180924i −0.000416682 0.000967079i
\(351\) 0 0
\(352\) −0.566592 0.566592i −0.0301995 0.0301995i
\(353\) −0.194119 2.21879i −0.0103319 0.118094i 0.989277 0.146050i \(-0.0466559\pi\)
−0.999609 + 0.0279554i \(0.991100\pi\)
\(354\) 0 0
\(355\) −4.54654 + 10.5341i −0.241305 + 0.559090i
\(356\) −1.97779 + 5.43394i −0.104823 + 0.287998i
\(357\) 0 0
\(358\) 0.0837088 + 0.119549i 0.00442415 + 0.00631834i
\(359\) 5.90045 10.2199i 0.311414 0.539385i −0.667255 0.744829i \(-0.732531\pi\)
0.978669 + 0.205445i \(0.0658641\pi\)
\(360\) 0 0
\(361\) 6.63064 + 11.4846i 0.348981 + 0.604453i
\(362\) 0.0895381 0.192015i 0.00470602 0.0100921i
\(363\) 0 0
\(364\) 0.713504 + 0.850321i 0.0373978 + 0.0445689i
\(365\) 25.1825 + 19.9202i 1.31811 + 1.04267i
\(366\) 0 0
\(367\) −1.92158 0.896047i −0.100306 0.0467733i 0.371818 0.928306i \(-0.378735\pi\)
−0.472123 + 0.881532i \(0.656512\pi\)
\(368\) 5.99683 22.3805i 0.312607 1.16666i
\(369\) 0 0
\(370\) 0.0495543 + 0.0987218i 0.00257621 + 0.00513230i
\(371\) 2.93265 + 0.517106i 0.152256 + 0.0268468i
\(372\) 0 0
\(373\) 3.00825 1.40277i 0.155762 0.0726328i −0.343174 0.939272i \(-0.611502\pi\)
0.498936 + 0.866639i \(0.333724\pi\)
\(374\) 0.0204361 + 0.115899i 0.00105672 + 0.00599298i
\(375\) 0 0
\(376\) −0.187500 0.157331i −0.00966957 0.00811373i
\(377\) −7.13843 + 7.13843i −0.367648 + 0.367648i
\(378\) 0 0
\(379\) 15.7634i 0.809713i −0.914380 0.404856i \(-0.867322\pi\)
0.914380 0.404856i \(-0.132678\pi\)
\(380\) −24.3328 + 7.27928i −1.24825 + 0.373419i
\(381\) 0 0
\(382\) 0.104009 0.148541i 0.00532158 0.00760001i
\(383\) 11.6401 + 24.9622i 0.594781 + 1.27551i 0.941333 + 0.337480i \(0.109575\pi\)
−0.346552 + 0.938031i \(0.612648\pi\)
\(384\) 0 0
\(385\) −2.52340 + 0.0729001i −0.128605 + 0.00371533i
\(386\) 0.160070 + 0.0924166i 0.00814736 + 0.00470388i
\(387\) 0 0
\(388\) 9.10294 + 2.43913i 0.462132 + 0.123828i
\(389\) 28.2091 10.2673i 1.43026 0.520571i 0.493252 0.869886i \(-0.335808\pi\)
0.937005 + 0.349315i \(0.113586\pi\)
\(390\) 0 0
\(391\) −7.82217 + 6.56358i −0.395584 + 0.331934i
\(392\) 0.0368997 0.421765i 0.00186372 0.0213024i
\(393\) 0 0
\(394\) −0.0310408 0.0852840i −0.00156382 0.00429655i
\(395\) 0.403844 6.90906i 0.0203196 0.347633i
\(396\) 0 0
\(397\) 4.62074 1.23812i 0.231908 0.0621397i −0.140993 0.990011i \(-0.545030\pi\)
0.372902 + 0.927871i \(0.378363\pi\)
\(398\) −0.0699666 + 0.0489911i −0.00350711 + 0.00245570i
\(399\) 0 0
\(400\) −1.15422 19.9597i −0.0577108 0.997983i
\(401\) 8.47214 1.49387i 0.423078 0.0746001i 0.0419444 0.999120i \(-0.486645\pi\)
0.381134 + 0.924520i \(0.375534\pi\)
\(402\) 0 0
\(403\) −11.2598 + 0.985106i −0.560891 + 0.0490716i
\(404\) 5.77756 0.287444
\(405\) 0 0
\(406\) −0.0184939 −0.000917838
\(407\) 14.1009 1.23367i 0.698957 0.0611508i
\(408\) 0 0
\(409\) −8.33076 + 1.46894i −0.411930 + 0.0726343i −0.375773 0.926712i \(-0.622623\pi\)
−0.0361568 + 0.999346i \(0.511512\pi\)
\(410\) −0.0127153 0.00186522i −0.000627966 9.21164e-5i
\(411\) 0 0
\(412\) −16.5432 + 11.5837i −0.815024 + 0.570686i
\(413\) −2.81592 + 0.754524i −0.138562 + 0.0371277i
\(414\) 0 0
\(415\) 7.38190 + 8.29843i 0.362363 + 0.407354i
\(416\) −0.134742 0.370201i −0.00660628 0.0181506i
\(417\) 0 0
\(418\) 0.0330604 0.377882i 0.00161704 0.0184828i
\(419\) 6.72816 5.64560i 0.328692 0.275806i −0.463475 0.886110i \(-0.653397\pi\)
0.792167 + 0.610305i \(0.208953\pi\)
\(420\) 0 0
\(421\) 0.538899 0.196143i 0.0262643 0.00955944i −0.328855 0.944381i \(-0.606663\pi\)
0.355119 + 0.934821i \(0.384440\pi\)
\(422\) 0.0837730 + 0.0224469i 0.00407800 + 0.00109270i
\(423\) 0 0
\(424\) −0.610187 0.352292i −0.0296333 0.0171088i
\(425\) −4.62868 + 7.49728i −0.224524 + 0.363671i
\(426\) 0 0
\(427\) 1.32351 + 2.83827i 0.0640489 + 0.137353i
\(428\) 17.2370 24.6170i 0.833181 1.18991i
\(429\) 0 0
\(430\) −0.0891046 0.297855i −0.00429701 0.0143638i
\(431\) 25.0117i 1.20477i 0.798205 + 0.602386i \(0.205783\pi\)
−0.798205 + 0.602386i \(0.794217\pi\)
\(432\) 0 0
\(433\) −24.9892 + 24.9892i −1.20090 + 1.20090i −0.227011 + 0.973892i \(0.572895\pi\)
−0.973892 + 0.227011i \(0.927105\pi\)
\(434\) −0.0158618 0.0133096i −0.000761390 0.000638882i
\(435\) 0 0
\(436\) 4.16812 + 23.6386i 0.199617 + 1.13208i
\(437\) 29.8287 13.9093i 1.42690 0.665374i
\(438\) 0 0
\(439\) 4.64923 + 0.819785i 0.221896 + 0.0391262i 0.283491 0.958975i \(-0.408508\pi\)
−0.0615948 + 0.998101i \(0.519619\pi\)
\(440\) 0.566942 + 0.187995i 0.0270279 + 0.00896229i
\(441\) 0 0
\(442\) −0.0149758 + 0.0558904i −0.000712326 + 0.00265844i
\(443\) −26.7976 12.4959i −1.27319 0.593700i −0.335787 0.941938i \(-0.609002\pi\)
−0.937406 + 0.348238i \(0.886780\pi\)
\(444\) 0 0
\(445\) −0.749324 6.42242i −0.0355214 0.304452i
\(446\) −0.129394 0.154205i −0.00612697 0.00730184i
\(447\) 0 0
\(448\) −0.871951 + 1.86990i −0.0411958 + 0.0883447i
\(449\) 3.36725 + 5.83225i 0.158910 + 0.275241i 0.934476 0.356026i \(-0.115869\pi\)
−0.775566 + 0.631267i \(0.782535\pi\)
\(450\) 0 0
\(451\) −0.823409 + 1.42619i −0.0387728 + 0.0671565i
\(452\) −10.6544 15.2161i −0.501142 0.715706i
\(453\) 0 0
\(454\) 0.0760955 0.209071i 0.00357134 0.00981217i
\(455\) −1.13957 0.491842i −0.0534238 0.0230579i
\(456\) 0 0
\(457\) −3.16016 36.1208i −0.147826 1.68966i −0.601800 0.798647i \(-0.705550\pi\)
0.453974 0.891015i \(-0.350006\pi\)
\(458\) 0.0899006 + 0.0899006i 0.00420078 + 0.00420078i
\(459\) 0 0
\(460\) 5.23438 + 25.3767i 0.244054 + 1.18319i
\(461\) −16.9825 + 20.2390i −0.790956 + 0.942625i −0.999373 0.0354156i \(-0.988725\pi\)
0.208417 + 0.978040i \(0.433169\pi\)
\(462\) 0 0
\(463\) −9.85172 6.89825i −0.457848 0.320589i 0.321799 0.946808i \(-0.395713\pi\)
−0.779647 + 0.626219i \(0.784601\pi\)
\(464\) −17.6368 6.41927i −0.818767 0.298007i
\(465\) 0 0
\(466\) 0.0733054 0.415735i 0.00339581 0.0192586i
\(467\) 2.86104 + 10.6775i 0.132393 + 0.494098i 0.999995 0.00316149i \(-0.00100633\pi\)
−0.867602 + 0.497260i \(0.834340\pi\)
\(468\) 0 0
\(469\) 0.410442 0.236969i 0.0189525 0.0109422i
\(470\) 0.133140 + 0.0315839i 0.00614129 + 0.00145686i
\(471\) 0 0
\(472\) 0.687138 + 0.0601168i 0.0316281 + 0.00276710i
\(473\) −39.6877 3.47222i −1.82484 0.159653i
\(474\) 0 0
\(475\) 20.6651 19.4804i 0.948181 0.893820i
\(476\) 0.787631 0.454739i 0.0361010 0.0208429i
\(477\) 0 0
\(478\) 0.0856663 + 0.319711i 0.00391828 + 0.0146232i
\(479\) −0.735877 + 4.17337i −0.0336231 + 0.190686i −0.996993 0.0774895i \(-0.975310\pi\)
0.963370 + 0.268175i \(0.0864207\pi\)
\(480\) 0 0
\(481\) 6.53967 + 2.38024i 0.298183 + 0.108530i
\(482\) 0.0652884 + 0.0457155i 0.00297381 + 0.00208228i
\(483\) 0 0
\(484\) 10.4582 12.4636i 0.475374 0.566529i
\(485\) −10.3204 + 2.12876i −0.468625 + 0.0966619i
\(486\) 0 0
\(487\) 16.7646 + 16.7646i 0.759676 + 0.759676i 0.976263 0.216587i \(-0.0694925\pi\)
−0.216587 + 0.976263i \(0.569493\pi\)
\(488\) −0.0645798 0.738151i −0.00292339 0.0334145i
\(489\) 0 0
\(490\) 0.0873412 + 0.219984i 0.00394567 + 0.00993786i
\(491\) −0.697417 + 1.91614i −0.0314740 + 0.0864740i −0.954434 0.298421i \(-0.903540\pi\)
0.922960 + 0.384895i \(0.125762\pi\)
\(492\) 0 0
\(493\) 4.74430 + 6.77556i 0.213673 + 0.305156i
\(494\) 0.0932500 0.161514i 0.00419552 0.00726685i
\(495\) 0 0
\(496\) −10.5069 18.1984i −0.471772 0.817133i
\(497\) −0.559642 + 1.20016i −0.0251034 + 0.0538343i
\(498\) 0 0
\(499\) −8.77600 10.4588i −0.392868 0.468202i 0.532964 0.846138i \(-0.321078\pi\)
−0.925832 + 0.377937i \(0.876634\pi\)
\(500\) 11.1670 + 19.3696i 0.499403 + 0.866235i
\(501\) 0 0
\(502\) −0.192965 0.0899812i −0.00861246 0.00401606i
\(503\) −11.4964 + 42.9050i −0.512597 + 1.91304i −0.121825 + 0.992552i \(0.538875\pi\)
−0.390772 + 0.920487i \(0.627792\pi\)
\(504\) 0 0
\(505\) −5.77370 + 2.89816i −0.256926 + 0.128967i
\(506\) −0.381102 0.0671985i −0.0169420 0.00298734i
\(507\) 0 0
\(508\) −35.2255 + 16.4259i −1.56288 + 0.728782i
\(509\) 0.883595 + 5.01112i 0.0391647 + 0.222114i 0.998108 0.0614836i \(-0.0195832\pi\)
−0.958943 + 0.283597i \(0.908472\pi\)
\(510\) 0 0
\(511\) 2.83890 + 2.38212i 0.125586 + 0.105379i
\(512\) 0.863214 0.863214i 0.0381490 0.0381490i
\(513\) 0 0
\(514\) 0.143093i 0.00631155i
\(515\) 10.7215 19.8744i 0.472445 0.875770i
\(516\) 0 0
\(517\) 10.0573 14.3634i 0.442321 0.631700i
\(518\) 0.00538802 + 0.0115547i 0.000236736 + 0.000507682i
\(519\) 0 0
\(520\) 0.213565 + 0.201572i 0.00936545 + 0.00883952i
\(521\) 14.9219 + 8.61518i 0.653742 + 0.377438i 0.789888 0.613251i \(-0.210138\pi\)
−0.136146 + 0.990689i \(0.543472\pi\)
\(522\) 0 0
\(523\) 12.9054 + 3.45799i 0.564314 + 0.151207i 0.529688 0.848193i \(-0.322309\pi\)
0.0346265 + 0.999400i \(0.488976\pi\)
\(524\) −8.58116 + 3.12329i −0.374870 + 0.136441i
\(525\) 0 0
\(526\) −0.117374 + 0.0984884i −0.00511775 + 0.00429430i
\(527\) −0.807135 + 9.22560i −0.0351594 + 0.401873i
\(528\) 0 0
\(529\) −3.61738 9.93866i −0.157277 0.432116i
\(530\) 0.393226 + 0.0229846i 0.0170806 + 0.000998386i
\(531\) 0 0
\(532\) −2.83153 + 0.758707i −0.122762 + 0.0328941i
\(533\) −0.663249 + 0.464412i −0.0287285 + 0.0201159i
\(534\) 0 0
\(535\) −4.87701 + 33.2470i −0.210851 + 1.43739i
\(536\) −0.110432 + 0.0194722i −0.00476995 + 0.000841071i
\(537\) 0 0
\(538\) 0.0281180 0.00246001i 0.00121225 0.000106058i
\(539\) 30.3299 1.30640
\(540\) 0 0
\(541\) 7.10549 0.305489 0.152745 0.988266i \(-0.451189\pi\)
0.152745 + 0.988266i \(0.451189\pi\)
\(542\) 0.213024 0.0186372i 0.00915016 0.000800535i
\(543\) 0 0
\(544\) −0.317883 + 0.0560513i −0.0136291 + 0.00240318i
\(545\) −16.0230 21.5320i −0.686351 0.922328i
\(546\) 0 0
\(547\) 8.41425 5.89172i 0.359767 0.251912i −0.379692 0.925113i \(-0.623970\pi\)
0.739459 + 0.673201i \(0.235081\pi\)
\(548\) −13.5139 + 3.62103i −0.577283 + 0.154683i
\(549\) 0 0
\(550\) −0.330414 + 0.0482586i −0.0140889 + 0.00205775i
\(551\) −9.11839 25.0526i −0.388456 1.06728i
\(552\) 0 0
\(553\) 0.0696191 0.795750i 0.00296050 0.0338387i
\(554\) −0.212691 + 0.178469i −0.00903636 + 0.00758240i
\(555\) 0 0
\(556\) 15.3384 5.58274i 0.650495 0.236761i
\(557\) 5.55174 + 1.48759i 0.235235 + 0.0630310i 0.374511 0.927223i \(-0.377811\pi\)
−0.139276 + 0.990254i \(0.544477\pi\)
\(558\) 0 0
\(559\) −16.9632 9.79373i −0.717468 0.414230i
\(560\) −0.0666363 2.30658i −0.00281590 0.0974710i
\(561\) 0 0
\(562\) 0.169419 + 0.363321i 0.00714652 + 0.0153258i
\(563\) 14.1548 20.2152i 0.596555 0.851969i −0.401399 0.915903i \(-0.631476\pi\)
0.997954 + 0.0639343i \(0.0203648\pi\)
\(564\) 0 0
\(565\) 18.2801 + 9.86143i 0.769049 + 0.414873i
\(566\) 0.280047i 0.0117713i
\(567\) 0 0
\(568\) 0.221549 0.221549i 0.00929600 0.00929600i
\(569\) −1.46173 1.22654i −0.0612790 0.0514192i 0.611634 0.791141i \(-0.290513\pi\)
−0.672913 + 0.739722i \(0.734957\pi\)
\(570\) 0 0
\(571\) −7.82276 44.3651i −0.327372 1.85662i −0.492452 0.870340i \(-0.663899\pi\)
0.165080 0.986280i \(-0.447212\pi\)
\(572\) 17.0519 7.95143i 0.712976 0.332466i
\(573\) 0 0
\(574\) −0.00146075 0.000257569i −6.09704e−5 1.07507e-5i
\(575\) −17.9604 22.7340i −0.749001 0.948074i
\(576\) 0 0
\(577\) 5.87132 21.9121i 0.244426 0.912211i −0.729245 0.684253i \(-0.760128\pi\)
0.973671 0.227958i \(-0.0732049\pi\)
\(578\) −0.192251 0.0896482i −0.00799660 0.00372888i
\(579\) 0 0
\(580\) 20.8475 2.43234i 0.865645 0.100998i
\(581\) 0.823988 + 0.981990i 0.0341848 + 0.0407398i
\(582\) 0 0
\(583\) 21.3317 45.7460i 0.883469 1.89461i
\(584\) −0.438419 0.759364i −0.0181419 0.0314227i
\(585\) 0 0
\(586\) −0.0802204 + 0.138946i −0.00331387 + 0.00573980i
\(587\) −4.91190 7.01492i −0.202736 0.289537i 0.704890 0.709316i \(-0.250996\pi\)
−0.907626 + 0.419780i \(0.862107\pi\)
\(588\) 0 0
\(589\) 10.2091 28.0493i 0.420659 1.15575i
\(590\) −0.358397 + 0.142296i −0.0147550 + 0.00585823i
\(591\) 0 0
\(592\) 1.12767 + 12.8893i 0.0463469 + 0.529748i
\(593\) −4.26261 4.26261i −0.175044 0.175044i 0.614147 0.789192i \(-0.289500\pi\)
−0.789192 + 0.614147i \(0.789500\pi\)
\(594\) 0 0
\(595\) −0.558997 + 0.849530i −0.0229166 + 0.0348273i
\(596\) 24.7884 29.5417i 1.01537 1.21007i
\(597\) 0 0
\(598\) −0.155855 0.109131i −0.00637338 0.00446269i
\(599\) −13.5981 4.94929i −0.555602 0.202223i 0.0489318 0.998802i \(-0.484418\pi\)
−0.604534 + 0.796580i \(0.706641\pi\)
\(600\) 0 0
\(601\) −2.11215 + 11.9786i −0.0861565 + 0.488618i 0.910944 + 0.412529i \(0.135354\pi\)
−0.997101 + 0.0760891i \(0.975757\pi\)
\(602\) −0.00928722 0.0346604i −0.000378519 0.00141265i
\(603\) 0 0
\(604\) 26.0133 15.0188i 1.05847 0.611107i
\(605\) −4.19918 + 17.7014i −0.170721 + 0.719664i
\(606\) 0 0
\(607\) 19.3845 + 1.69592i 0.786792 + 0.0688354i 0.473468 0.880811i \(-0.343002\pi\)
0.313324 + 0.949646i \(0.398557\pi\)
\(608\) 1.03644 + 0.0906769i 0.0420333 + 0.00367743i
\(609\) 0 0
\(610\) 0.217393 + 0.352611i 0.00880197 + 0.0142768i
\(611\) 7.46602 4.31051i 0.302043 0.174384i
\(612\) 0 0
\(613\) 3.48768 + 13.0162i 0.140866 + 0.525720i 0.999905 + 0.0138088i \(0.00439561\pi\)
−0.859038 + 0.511911i \(0.828938\pi\)
\(614\) 0.0339541 0.192563i 0.00137027 0.00777121i
\(615\) 0 0
\(616\) 0.0647813 + 0.0235785i 0.00261011 + 0.000950003i
\(617\) −37.1967 26.0454i −1.49748 1.04855i −0.981392 0.192014i \(-0.938498\pi\)
−0.516090 0.856535i \(-0.672613\pi\)
\(618\) 0 0
\(619\) −0.765342 + 0.912099i −0.0307617 + 0.0366604i −0.781206 0.624273i \(-0.785395\pi\)
0.750444 + 0.660934i \(0.229840\pi\)
\(620\) 19.6309 + 12.9173i 0.788396 + 0.518770i
\(621\) 0 0
\(622\) −0.226747 0.226747i −0.00909171 0.00909171i
\(623\) −0.0650434 0.743449i −0.00260591 0.0297857i
\(624\) 0 0
\(625\) −20.8758 13.7550i −0.835032 0.550201i
\(626\) −0.154339 + 0.424042i −0.00616861 + 0.0169481i
\(627\) 0 0
\(628\) −2.67993 3.82734i −0.106941 0.152728i
\(629\) 2.85104 4.93815i 0.113678 0.196897i
\(630\) 0 0
\(631\) 10.8669 + 18.8220i 0.432605 + 0.749293i 0.997097 0.0761454i \(-0.0242613\pi\)
−0.564492 + 0.825438i \(0.690928\pi\)
\(632\) −0.0798737 + 0.171290i −0.00317721 + 0.00681354i
\(633\) 0 0
\(634\) 0.260588 + 0.310556i 0.0103493 + 0.0123338i
\(635\) 26.9623 34.0849i 1.06997 1.35262i
\(636\) 0 0
\(637\) 13.5149 + 6.30211i 0.535481 + 0.249699i
\(638\) −0.0811322 + 0.302790i −0.00321206 + 0.0119876i
\(639\) 0 0
\(640\) −0.343723 + 1.03658i −0.0135868 + 0.0409743i
\(641\) −11.0540 1.94912i −0.436606 0.0769855i −0.0489751 0.998800i \(-0.515595\pi\)
−0.387631 + 0.921815i \(0.626707\pi\)
\(642\) 0 0
\(643\) 21.6198 10.0815i 0.852602 0.397575i 0.0533535 0.998576i \(-0.483009\pi\)
0.799248 + 0.601001i \(0.205231\pi\)
\(644\) 0.519308 + 2.94514i 0.0204636 + 0.116055i
\(645\) 0 0
\(646\) −0.117057 0.0982222i −0.00460553 0.00386450i
\(647\) 17.7336 17.7336i 0.697179 0.697179i −0.266622 0.963801i \(-0.585908\pi\)
0.963801 + 0.266622i \(0.0859076\pi\)
\(648\) 0 0
\(649\) 49.4134i 1.93965i
\(650\) −0.157259 0.0471512i −0.00616820 0.00184942i
\(651\) 0 0
\(652\) −17.4057 + 24.8579i −0.681660 + 0.973511i
\(653\) −7.70684 16.5274i −0.301592 0.646766i 0.695855 0.718183i \(-0.255026\pi\)
−0.997447 + 0.0714165i \(0.977248\pi\)
\(654\) 0 0
\(655\) 7.00871 7.42571i 0.273853 0.290147i
\(656\) −1.30364 0.752659i −0.0508987 0.0293864i
\(657\) 0 0
\(658\) 0.0152550 + 0.00408758i 0.000594704 + 0.000159350i
\(659\) −32.1808 + 11.7129i −1.25359 + 0.456269i −0.881612 0.471974i \(-0.843542\pi\)
−0.371975 + 0.928243i \(0.621319\pi\)
\(660\) 0 0
\(661\) 3.43935 2.88596i 0.133775 0.112251i −0.573445 0.819244i \(-0.694393\pi\)
0.707220 + 0.706993i \(0.249949\pi\)
\(662\) −0.0132291 + 0.151210i −0.000514165 + 0.00587693i
\(663\) 0 0
\(664\) −0.103736 0.285012i −0.00402573 0.0110606i
\(665\) 2.44905 2.17856i 0.0949703 0.0844811i
\(666\) 0 0
\(667\) −26.2716 + 7.03946i −1.01724 + 0.272569i
\(668\) −31.7846 + 22.2558i −1.22978 + 0.861103i
\(669\) 0 0
\(670\) 0.0502925 0.0374252i 0.00194297 0.00144586i
\(671\) 52.2754 9.21756i 2.01807 0.355840i
\(672\) 0 0
\(673\) 15.0821 1.31952i 0.581374 0.0508636i 0.207324 0.978272i \(-0.433525\pi\)
0.374050 + 0.927409i \(0.377969\pi\)
\(674\) −0.214165 −0.00824933
\(675\) 0 0
\(676\) −16.7465 −0.644096
\(677\) 9.69800 0.848465i 0.372724 0.0326092i 0.100745 0.994912i \(-0.467877\pi\)
0.271979 + 0.962303i \(0.412322\pi\)
\(678\) 0 0
\(679\) −1.19775 + 0.211196i −0.0459656 + 0.00810497i
\(680\) 0.193032 0.143645i 0.00740244 0.00550853i
\(681\) 0 0
\(682\) −0.287495 + 0.201306i −0.0110088 + 0.00770842i
\(683\) 22.4891 6.02595i 0.860523 0.230577i 0.198538 0.980093i \(-0.436381\pi\)
0.661985 + 0.749517i \(0.269714\pi\)
\(684\) 0 0
\(685\) 11.6884 10.3975i 0.446592 0.397267i
\(686\) 0.0187764 + 0.0515877i 0.000716886 + 0.00196963i
\(687\) 0 0
\(688\) 3.17388 36.2776i 0.121003 1.38307i
\(689\) 19.0107 15.9519i 0.724249 0.607717i
\(690\) 0 0
\(691\) −4.24724 + 1.54587i −0.161573 + 0.0588077i −0.421540 0.906810i \(-0.638510\pi\)
0.259968 + 0.965617i \(0.416288\pi\)
\(692\) −11.2303 3.00916i −0.426913 0.114391i
\(693\) 0 0
\(694\) −0.0807256 0.0466069i −0.00306430 0.00176918i
\(695\) −12.5278 + 13.2731i −0.475205 + 0.503479i
\(696\) 0 0
\(697\) 0.280365 + 0.601245i 0.0106196 + 0.0227738i
\(698\) 0.0334725 0.0478038i 0.00126695 0.00180940i
\(699\) 0 0
\(700\) 1.22377 + 2.27188i 0.0462543 + 0.0858691i
\(701\) 28.3612i 1.07119i −0.844476 0.535593i \(-0.820088\pi\)
0.844476 0.535593i \(-0.179912\pi\)
\(702\) 0 0
\(703\) −12.9958 + 12.9958i −0.490147 + 0.490147i
\(704\) 26.7896 + 22.4791i 1.00967 + 0.847214i
\(705\) 0 0
\(706\) −0.00590457 0.0334865i −0.000222221 0.00126028i
\(707\) −0.675769 + 0.315116i −0.0254149 + 0.0118512i
\(708\) 0 0
\(709\) −27.9978 4.93677i −1.05148 0.185404i −0.378907 0.925435i \(-0.623700\pi\)
−0.672574 + 0.740030i \(0.734811\pi\)
\(710\) −0.0551302 + 0.166258i −0.00206900 + 0.00623956i
\(711\) 0 0
\(712\) −0.0457011 + 0.170559i −0.00171272 + 0.00639196i
\(713\) −27.5987 12.8695i −1.03358 0.481966i
\(714\) 0 0
\(715\) −13.0519 + 16.4998i −0.488113 + 0.617056i
\(716\) −12.2880 14.6443i −0.459224 0.547282i
\(717\) 0 0
\(718\) 0.0761394 0.163281i 0.00284150 0.00609361i
\(719\) 8.97949 + 15.5529i 0.334878 + 0.580026i 0.983461 0.181118i \(-0.0579714\pi\)
−0.648583 + 0.761144i \(0.724638\pi\)
\(720\) 0 0
\(721\) 1.30318 2.25717i 0.0485328 0.0840612i
\(722\) 0.116124 + 0.165843i 0.00432170 + 0.00617202i
\(723\) 0 0
\(724\) −9.49171 + 26.0783i −0.352757 + 0.969191i
\(725\) −19.6134 + 12.8883i −0.728425 + 0.478660i
\(726\) 0 0
\(727\) 2.47494 + 28.2887i 0.0917905 + 1.04917i 0.892780 + 0.450492i \(0.148751\pi\)
−0.800990 + 0.598678i \(0.795693\pi\)
\(728\) 0.0239671 + 0.0239671i 0.000888279 + 0.000888279i
\(729\) 0 0
\(730\) 0.409497 + 0.269452i 0.0151562 + 0.00997286i
\(731\) −10.3159 + 12.2941i −0.381549 + 0.454712i
\(732\) 0 0
\(733\) −8.28966 5.80448i −0.306185 0.214393i 0.410378 0.911916i \(-0.365397\pi\)
−0.716563 + 0.697522i \(0.754286\pi\)
\(734\) −0.0304169 0.0110708i −0.00112271 0.000408632i
\(735\) 0 0
\(736\) 0.184310 1.04527i 0.00679374 0.0385292i
\(737\) −2.07915 7.75949i −0.0765865 0.285825i
\(738\) 0 0
\(739\) 35.8294 20.6861i 1.31801 0.760951i 0.334598 0.942361i \(-0.391399\pi\)
0.983408 + 0.181410i \(0.0580660\pi\)
\(740\) −7.59340 12.3165i −0.279139 0.452763i
\(741\) 0 0
\(742\) 0.0452897 + 0.00396233i 0.00166264 + 0.000145462i
\(743\) 7.70953 + 0.674496i 0.282835 + 0.0247449i 0.227691 0.973734i \(-0.426882\pi\)
0.0551445 + 0.998478i \(0.482438\pi\)
\(744\) 0 0
\(745\) −9.95303 + 41.9564i −0.364651 + 1.53716i
\(746\) 0.0438849 0.0253370i 0.00160674 0.000927653i
\(747\) 0 0
\(748\) −3.98985 14.8903i −0.145883 0.544444i
\(749\) −0.673470 + 3.81944i −0.0246080 + 0.139559i
\(750\) 0 0
\(751\) −38.8916 14.1554i −1.41918 0.516537i −0.485367 0.874311i \(-0.661314\pi\)
−0.933808 + 0.357773i \(0.883536\pi\)
\(752\) 13.1292 + 9.19318i 0.478773 + 0.335241i
\(753\) 0 0
\(754\) −0.0990675 + 0.118064i −0.00360782 + 0.00429964i
\(755\) −18.4622 + 28.0577i −0.671907 + 1.02112i
\(756\) 0 0
\(757\) −10.7021 10.7021i −0.388975 0.388975i 0.485347 0.874322i \(-0.338693\pi\)
−0.874322 + 0.485347i \(0.838693\pi\)
\(758\) −0.0209745 0.239740i −0.000761830 0.00870775i
\(759\) 0 0
\(760\) −0.720809 + 0.286186i −0.0261465 + 0.0103811i
\(761\) −16.8761 + 46.3666i −0.611756 + 1.68079i 0.114551 + 0.993417i \(0.463457\pi\)
−0.726308 + 0.687370i \(0.758765\pi\)
\(762\) 0 0
\(763\) −1.77680 2.53754i −0.0643246 0.0918651i
\(764\) −11.8764 + 20.5705i −0.429673 + 0.744215i
\(765\) 0 0
\(766\) 0.210244 + 0.364154i 0.00759643 + 0.0131574i
\(767\) −10.2674 + 22.0185i −0.370733 + 0.795040i
\(768\) 0 0
\(769\) −4.55804 5.43206i −0.164367 0.195885i 0.677574 0.735455i \(-0.263031\pi\)
−0.841941 + 0.539570i \(0.818587\pi\)
\(770\) −0.0382805 + 0.00446631i −0.00137953 + 0.000160955i
\(771\) 0 0
\(772\) −21.9426 10.2320i −0.789733 0.368259i
\(773\) −2.31145 + 8.62644i −0.0831370 + 0.310272i −0.994955 0.100323i \(-0.968012\pi\)
0.911818 + 0.410595i \(0.134679\pi\)
\(774\) 0 0
\(775\) −26.0974 3.06131i −0.937446 0.109966i
\(776\) 0.283394 + 0.0499700i 0.0101733 + 0.00179382i
\(777\) 0 0
\(778\) 0.415360 0.193686i 0.0148914 0.00694397i
\(779\) −0.371305 2.10578i −0.0133034 0.0754473i
\(780\) 0 0
\(781\) 17.1943 + 14.4277i 0.615260 + 0.516264i
\(782\) −0.110231 + 0.110231i −0.00394186 + 0.00394186i
\(783\) 0 0
\(784\) 27.7239i 0.990139i
\(785\) 4.59803 + 2.48047i 0.164111 + 0.0885317i