Properties

Label 1183.2.e.j.508.2
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.2
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.j.170.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.15163 - 1.99469i) q^{2} +(0.736680 - 1.27597i) q^{3} +(-1.65252 + 2.86225i) q^{4} +(-0.423646 - 0.733776i) q^{5} -3.39354 q^{6} +(-1.00088 + 2.44913i) q^{7} +3.00585 q^{8} +(0.414604 + 0.718115i) q^{9} +O(q^{10})\) \(q+(-1.15163 - 1.99469i) q^{2} +(0.736680 - 1.27597i) q^{3} +(-1.65252 + 2.86225i) q^{4} +(-0.423646 - 0.733776i) q^{5} -3.39354 q^{6} +(-1.00088 + 2.44913i) q^{7} +3.00585 q^{8} +(0.414604 + 0.718115i) q^{9} +(-0.975769 + 1.69008i) q^{10} +(0.751701 - 1.30198i) q^{11} +(2.43476 + 4.21712i) q^{12} +(6.03790 - 0.824057i) q^{14} -1.24837 q^{15} +(-0.156597 - 0.271234i) q^{16} +(-1.03570 + 1.79389i) q^{17} +(0.954943 - 1.65401i) q^{18} +(0.0237136 + 0.0410731i) q^{19} +2.80033 q^{20} +(2.38768 + 3.08132i) q^{21} -3.46274 q^{22} +(3.90935 + 6.77119i) q^{23} +(2.21435 - 3.83536i) q^{24} +(2.14105 - 3.70840i) q^{25} +5.64180 q^{27} +(-5.35604 - 6.91200i) q^{28} +1.35971 q^{29} +(1.43766 + 2.49010i) q^{30} +(-3.93052 + 6.80787i) q^{31} +(2.64516 - 4.58156i) q^{32} +(-1.10753 - 1.91829i) q^{33} +4.77099 q^{34} +(2.22113 - 0.303142i) q^{35} -2.74056 q^{36} +(-3.35110 - 5.80427i) q^{37} +(0.0546187 - 0.0946024i) q^{38} +(-1.27341 - 2.20562i) q^{40} +10.0184 q^{41} +(3.39653 - 8.31123i) q^{42} +9.26566 q^{43} +(2.48440 + 4.30311i) q^{44} +(0.351290 - 0.608453i) q^{45} +(9.00428 - 15.5959i) q^{46} +(-0.180007 - 0.311781i) q^{47} -0.461448 q^{48} +(-4.99648 - 4.90257i) q^{49} -9.86281 q^{50} +(1.52596 + 2.64304i) q^{51} +(-1.35591 + 2.34850i) q^{53} +(-6.49729 - 11.2536i) q^{54} -1.27382 q^{55} +(-3.00849 + 7.36171i) q^{56} +0.0698773 q^{57} +(-1.56588 - 2.71219i) q^{58} +(-0.820598 + 1.42132i) q^{59} +(2.06295 - 3.57313i) q^{60} +(-2.26097 - 3.91612i) q^{61} +18.1061 q^{62} +(-2.17373 + 0.296672i) q^{63} -12.8114 q^{64} +(-2.55093 + 4.41834i) q^{66} +(1.02133 - 1.76900i) q^{67} +(-3.42303 - 5.92886i) q^{68} +11.5198 q^{69} +(-3.16260 - 4.08136i) q^{70} +14.2139 q^{71} +(1.24624 + 2.15854i) q^{72} +(-3.38075 + 5.85563i) q^{73} +(-7.71847 + 13.3688i) q^{74} +(-3.15454 - 5.46382i) q^{75} -0.156749 q^{76} +(2.43637 + 3.14414i) q^{77} +(-5.82952 - 10.0970i) q^{79} +(-0.132683 + 0.229814i) q^{80} +(2.91240 - 5.04442i) q^{81} +(-11.5376 - 19.9837i) q^{82} +11.5362 q^{83} +(-12.7652 + 1.74220i) q^{84} +1.75508 q^{85} +(-10.6706 - 18.4821i) q^{86} +(1.00167 - 1.73494i) q^{87} +(2.25950 - 3.91357i) q^{88} +(8.75561 + 15.1652i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(5.79108 + 10.0304i) q^{93} +(-0.414604 + 0.718115i) q^{94} +(0.0200923 - 0.0348009i) q^{95} +(-3.89728 - 6.75029i) q^{96} +0.426229 q^{97} +(-4.02499 + 15.6124i) q^{98} +1.24663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15163 1.99469i −0.814328 1.41046i −0.909810 0.415026i \(-0.863773\pi\)
0.0954820 0.995431i \(-0.469561\pi\)
\(3\) 0.736680 1.27597i 0.425323 0.736680i −0.571128 0.820861i \(-0.693494\pi\)
0.996451 + 0.0841807i \(0.0268273\pi\)
\(4\) −1.65252 + 2.86225i −0.826259 + 1.43112i
\(5\) −0.423646 0.733776i −0.189460 0.328155i 0.755610 0.655022i \(-0.227340\pi\)
−0.945070 + 0.326867i \(0.894007\pi\)
\(6\) −3.39354 −1.38541
\(7\) −1.00088 + 2.44913i −0.378297 + 0.925684i
\(8\) 3.00585 1.06273
\(9\) 0.414604 + 0.718115i 0.138201 + 0.239372i
\(10\) −0.975769 + 1.69008i −0.308565 + 0.534451i
\(11\) 0.751701 1.30198i 0.226646 0.392563i −0.730166 0.683270i \(-0.760557\pi\)
0.956812 + 0.290707i \(0.0938905\pi\)
\(12\) 2.43476 + 4.21712i 0.702853 + 1.21738i
\(13\) 0 0
\(14\) 6.03790 0.824057i 1.61370 0.220238i
\(15\) −1.24837 −0.322327
\(16\) −0.156597 0.271234i −0.0391492 0.0678085i
\(17\) −1.03570 + 1.79389i −0.251194 + 0.435081i −0.963855 0.266428i \(-0.914157\pi\)
0.712661 + 0.701509i \(0.247490\pi\)
\(18\) 0.954943 1.65401i 0.225082 0.389854i
\(19\) 0.0237136 + 0.0410731i 0.00544027 + 0.00942282i 0.868733 0.495281i \(-0.164935\pi\)
−0.863292 + 0.504704i \(0.831602\pi\)
\(20\) 2.80033 0.626173
\(21\) 2.38768 + 3.08132i 0.521035 + 0.672399i
\(22\) −3.46274 −0.738258
\(23\) 3.90935 + 6.77119i 0.815156 + 1.41189i 0.909216 + 0.416325i \(0.136682\pi\)
−0.0940598 + 0.995567i \(0.529984\pi\)
\(24\) 2.21435 3.83536i 0.452002 0.782891i
\(25\) 2.14105 3.70840i 0.428210 0.741681i
\(26\) 0 0
\(27\) 5.64180 1.08577
\(28\) −5.35604 6.91200i −1.01220 1.30624i
\(29\) 1.35971 0.252491 0.126246 0.991999i \(-0.459707\pi\)
0.126246 + 0.991999i \(0.459707\pi\)
\(30\) 1.43766 + 2.49010i 0.262480 + 0.454628i
\(31\) −3.93052 + 6.80787i −0.705943 + 1.22273i 0.260407 + 0.965499i \(0.416143\pi\)
−0.966350 + 0.257230i \(0.917190\pi\)
\(32\) 2.64516 4.58156i 0.467603 0.809912i
\(33\) −1.10753 1.91829i −0.192796 0.333932i
\(34\) 4.77099 0.818218
\(35\) 2.22113 0.303142i 0.375440 0.0512403i
\(36\) −2.74056 −0.456760
\(37\) −3.35110 5.80427i −0.550917 0.954216i −0.998209 0.0598278i \(-0.980945\pi\)
0.447292 0.894388i \(-0.352388\pi\)
\(38\) 0.0546187 0.0946024i 0.00886032 0.0153465i
\(39\) 0 0
\(40\) −1.27341 2.20562i −0.201345 0.348739i
\(41\) 10.0184 1.56462 0.782309 0.622891i \(-0.214042\pi\)
0.782309 + 0.622891i \(0.214042\pi\)
\(42\) 3.39653 8.31123i 0.524096 1.28245i
\(43\) 9.26566 1.41300 0.706500 0.707713i \(-0.250273\pi\)
0.706500 + 0.707713i \(0.250273\pi\)
\(44\) 2.48440 + 4.30311i 0.374537 + 0.648718i
\(45\) 0.351290 0.608453i 0.0523673 0.0907028i
\(46\) 9.00428 15.5959i 1.32761 2.29948i
\(47\) −0.180007 0.311781i −0.0262567 0.0454779i 0.852598 0.522567i \(-0.175025\pi\)
−0.878855 + 0.477089i \(0.841692\pi\)
\(48\) −0.461448 −0.0666042
\(49\) −4.99648 4.90257i −0.713782 0.700367i
\(50\) −9.86281 −1.39481
\(51\) 1.52596 + 2.64304i 0.213677 + 0.370100i
\(52\) 0 0
\(53\) −1.35591 + 2.34850i −0.186248 + 0.322591i −0.943996 0.329956i \(-0.892966\pi\)
0.757748 + 0.652547i \(0.226299\pi\)
\(54\) −6.49729 11.2536i −0.884169 1.53143i
\(55\) −1.27382 −0.171762
\(56\) −3.00849 + 7.36171i −0.402027 + 0.983750i
\(57\) 0.0698773 0.00925548
\(58\) −1.56588 2.71219i −0.205611 0.356128i
\(59\) −0.820598 + 1.42132i −0.106833 + 0.185040i −0.914486 0.404619i \(-0.867404\pi\)
0.807653 + 0.589658i \(0.200738\pi\)
\(60\) 2.06295 3.57313i 0.266325 0.461289i
\(61\) −2.26097 3.91612i −0.289488 0.501407i 0.684200 0.729295i \(-0.260152\pi\)
−0.973688 + 0.227887i \(0.926818\pi\)
\(62\) 18.1061 2.29948
\(63\) −2.17373 + 0.296672i −0.273864 + 0.0373771i
\(64\) −12.8114 −1.60143
\(65\) 0 0
\(66\) −2.55093 + 4.41834i −0.313998 + 0.543860i
\(67\) 1.02133 1.76900i 0.124775 0.216117i −0.796870 0.604151i \(-0.793512\pi\)
0.921645 + 0.388034i \(0.126846\pi\)
\(68\) −3.42303 5.92886i −0.415103 0.718980i
\(69\) 11.5198 1.38682
\(70\) −3.16260 4.08136i −0.378003 0.487815i
\(71\) 14.2139 1.68688 0.843442 0.537220i \(-0.180526\pi\)
0.843442 + 0.537220i \(0.180526\pi\)
\(72\) 1.24624 + 2.15854i 0.146870 + 0.254387i
\(73\) −3.38075 + 5.85563i −0.395687 + 0.685349i −0.993189 0.116518i \(-0.962827\pi\)
0.597502 + 0.801867i \(0.296160\pi\)
\(74\) −7.71847 + 13.3688i −0.897253 + 1.55409i
\(75\) −3.15454 5.46382i −0.364255 0.630907i
\(76\) −0.156749 −0.0179803
\(77\) 2.43637 + 3.14414i 0.277650 + 0.358308i
\(78\) 0 0
\(79\) −5.82952 10.0970i −0.655873 1.13600i −0.981674 0.190567i \(-0.938967\pi\)
0.325801 0.945438i \(-0.394366\pi\)
\(80\) −0.132683 + 0.229814i −0.0148344 + 0.0256940i
\(81\) 2.91240 5.04442i 0.323600 0.560491i
\(82\) −11.5376 19.9837i −1.27411 2.20683i
\(83\) 11.5362 1.26627 0.633133 0.774043i \(-0.281768\pi\)
0.633133 + 0.774043i \(0.281768\pi\)
\(84\) −12.7652 + 1.74220i −1.39280 + 0.190090i
\(85\) 1.75508 0.190365
\(86\) −10.6706 18.4821i −1.15065 1.99298i
\(87\) 1.00167 1.73494i 0.107390 0.186006i
\(88\) 2.25950 3.91357i 0.240863 0.417188i
\(89\) 8.75561 + 15.1652i 0.928093 + 1.60750i 0.786510 + 0.617577i \(0.211886\pi\)
0.141582 + 0.989927i \(0.454781\pi\)
\(90\) −1.61823 −0.170576
\(91\) 0 0
\(92\) −25.8411 −2.69412
\(93\) 5.79108 + 10.0304i 0.600507 + 1.04011i
\(94\) −0.414604 + 0.718115i −0.0427631 + 0.0740679i
\(95\) 0.0200923 0.0348009i 0.00206143 0.00357050i
\(96\) −3.89728 6.75029i −0.397764 0.688948i
\(97\) 0.426229 0.0432770 0.0216385 0.999766i \(-0.493112\pi\)
0.0216385 + 0.999766i \(0.493112\pi\)
\(98\) −4.02499 + 15.6124i −0.406585 + 1.57709i
\(99\) 1.24663 0.125291
\(100\) 7.07624 + 12.2564i 0.707624 + 1.22564i
\(101\) −4.83499 + 8.37444i −0.481099 + 0.833288i −0.999765 0.0216891i \(-0.993096\pi\)
0.518666 + 0.854977i \(0.326429\pi\)
\(102\) 3.51469 6.08763i 0.348007 0.602765i
\(103\) 4.98912 + 8.64140i 0.491592 + 0.851463i 0.999953 0.00968129i \(-0.00308170\pi\)
−0.508361 + 0.861144i \(0.669748\pi\)
\(104\) 0 0
\(105\) 1.24947 3.05741i 0.121935 0.298373i
\(106\) 6.24603 0.606668
\(107\) −4.93111 8.54094i −0.476709 0.825684i 0.522935 0.852373i \(-0.324837\pi\)
−0.999644 + 0.0266888i \(0.991504\pi\)
\(108\) −9.32319 + 16.1482i −0.897124 + 1.55386i
\(109\) −5.80275 + 10.0507i −0.555803 + 0.962679i 0.442038 + 0.896996i \(0.354256\pi\)
−0.997841 + 0.0656822i \(0.979078\pi\)
\(110\) 1.46697 + 2.54087i 0.139870 + 0.242263i
\(111\) −9.87475 −0.937269
\(112\) 0.821022 0.112054i 0.0775793 0.0105881i
\(113\) −3.47758 −0.327143 −0.163572 0.986531i \(-0.552301\pi\)
−0.163572 + 0.986531i \(0.552301\pi\)
\(114\) −0.0804731 0.139383i −0.00753699 0.0130545i
\(115\) 3.31236 5.73718i 0.308879 0.534994i
\(116\) −2.24694 + 3.89182i −0.208623 + 0.361346i
\(117\) 0 0
\(118\) 3.78011 0.347987
\(119\) −3.35685 4.33203i −0.307722 0.397117i
\(120\) −3.75240 −0.342546
\(121\) 4.36989 + 7.56887i 0.397263 + 0.688079i
\(122\) −5.20762 + 9.01986i −0.471476 + 0.816620i
\(123\) 7.38039 12.7832i 0.665467 1.15262i
\(124\) −12.9905 22.5003i −1.16658 2.02058i
\(125\) −7.86464 −0.703435
\(126\) 3.09510 + 3.99425i 0.275734 + 0.355836i
\(127\) −15.6998 −1.39313 −0.696567 0.717491i \(-0.745290\pi\)
−0.696567 + 0.717491i \(0.745290\pi\)
\(128\) 9.46373 + 16.3917i 0.836483 + 1.44883i
\(129\) 6.82583 11.8227i 0.600981 1.04093i
\(130\) 0 0
\(131\) 1.27259 + 2.20418i 0.111186 + 0.192580i 0.916249 0.400610i \(-0.131202\pi\)
−0.805063 + 0.593190i \(0.797868\pi\)
\(132\) 7.32083 0.637197
\(133\) −0.124328 + 0.0169684i −0.0107806 + 0.00147134i
\(134\) −4.70479 −0.406432
\(135\) −2.39013 4.13982i −0.205709 0.356299i
\(136\) −3.11316 + 5.39215i −0.266951 + 0.462373i
\(137\) 0.932362 1.61490i 0.0796571 0.137970i −0.823445 0.567396i \(-0.807951\pi\)
0.903102 + 0.429426i \(0.141284\pi\)
\(138\) −13.2665 22.9783i −1.12932 1.95605i
\(139\) 15.6092 1.32396 0.661979 0.749522i \(-0.269717\pi\)
0.661979 + 0.749522i \(0.269717\pi\)
\(140\) −2.80280 + 6.85837i −0.236879 + 0.579638i
\(141\) −0.530430 −0.0446703
\(142\) −16.3692 28.3524i −1.37368 2.37928i
\(143\) 0 0
\(144\) 0.129851 0.224909i 0.0108209 0.0187424i
\(145\) −0.576035 0.997721i −0.0478371 0.0828562i
\(146\) 15.5735 1.28887
\(147\) −9.93633 + 2.76372i −0.819535 + 0.227947i
\(148\) 22.1510 1.82080
\(149\) 3.18181 + 5.51106i 0.260664 + 0.451484i 0.966419 0.256973i \(-0.0827251\pi\)
−0.705754 + 0.708457i \(0.749392\pi\)
\(150\) −7.26574 + 12.5846i −0.593245 + 1.02753i
\(151\) −0.332047 + 0.575122i −0.0270216 + 0.0468028i −0.879220 0.476416i \(-0.841936\pi\)
0.852198 + 0.523219i \(0.175269\pi\)
\(152\) 0.0712794 + 0.123460i 0.00578152 + 0.0100139i
\(153\) −1.71762 −0.138861
\(154\) 3.46578 8.48069i 0.279281 0.683393i
\(155\) 6.66060 0.534992
\(156\) 0 0
\(157\) 8.28798 14.3552i 0.661453 1.14567i −0.318781 0.947828i \(-0.603273\pi\)
0.980234 0.197842i \(-0.0633933\pi\)
\(158\) −13.4269 + 23.2562i −1.06819 + 1.85016i
\(159\) 1.99774 + 3.46019i 0.158431 + 0.274411i
\(160\) −4.48245 −0.354369
\(161\) −20.4963 + 2.79735i −1.61534 + 0.220462i
\(162\) −13.4160 −1.05406
\(163\) −4.52563 7.83863i −0.354475 0.613969i 0.632553 0.774517i \(-0.282007\pi\)
−0.987028 + 0.160548i \(0.948674\pi\)
\(164\) −16.5557 + 28.6752i −1.29278 + 2.23916i
\(165\) −0.938398 + 1.62535i −0.0730542 + 0.126534i
\(166\) −13.2855 23.0112i −1.03116 1.78601i
\(167\) −2.65761 −0.205652 −0.102826 0.994699i \(-0.532788\pi\)
−0.102826 + 0.994699i \(0.532788\pi\)
\(168\) 7.17701 + 9.26197i 0.553718 + 0.714576i
\(169\) 0 0
\(170\) −2.02121 3.50084i −0.155020 0.268502i
\(171\) −0.0196635 + 0.0340582i −0.00150370 + 0.00260449i
\(172\) −15.3117 + 26.5206i −1.16750 + 2.02218i
\(173\) −9.79352 16.9629i −0.744588 1.28966i −0.950387 0.311070i \(-0.899313\pi\)
0.205799 0.978594i \(-0.434021\pi\)
\(174\) −4.61423 −0.349804
\(175\) 6.93943 + 8.95538i 0.524572 + 0.676963i
\(176\) −0.470856 −0.0354921
\(177\) 1.20904 + 2.09411i 0.0908768 + 0.157403i
\(178\) 20.1665 34.9294i 1.51154 2.61807i
\(179\) 1.44666 2.50569i 0.108129 0.187284i −0.806884 0.590711i \(-0.798848\pi\)
0.915012 + 0.403426i \(0.132181\pi\)
\(180\) 1.16103 + 2.01096i 0.0865379 + 0.149888i
\(181\) 1.36804 0.101686 0.0508429 0.998707i \(-0.483809\pi\)
0.0508429 + 0.998707i \(0.483809\pi\)
\(182\) 0 0
\(183\) −6.66245 −0.492503
\(184\) 11.7509 + 20.3532i 0.866289 + 1.50046i
\(185\) −2.83936 + 4.91791i −0.208754 + 0.361572i
\(186\) 13.3384 23.1028i 0.978019 1.69398i
\(187\) 1.55707 + 2.69693i 0.113865 + 0.197219i
\(188\) 1.18986 0.0867794
\(189\) −5.64677 + 13.8175i −0.410742 + 1.00508i
\(190\) −0.0925559 −0.00671471
\(191\) 0.756625 + 1.31051i 0.0547475 + 0.0948254i 0.892100 0.451837i \(-0.149231\pi\)
−0.837353 + 0.546663i \(0.815898\pi\)
\(192\) −9.43792 + 16.3470i −0.681123 + 1.17974i
\(193\) −3.47697 + 6.02229i −0.250278 + 0.433494i −0.963602 0.267340i \(-0.913855\pi\)
0.713324 + 0.700834i \(0.247189\pi\)
\(194\) −0.490860 0.850194i −0.0352417 0.0610404i
\(195\) 0 0
\(196\) 22.2891 6.19955i 1.59208 0.442825i
\(197\) 15.4772 1.10271 0.551353 0.834272i \(-0.314112\pi\)
0.551353 + 0.834272i \(0.314112\pi\)
\(198\) −1.43566 2.48664i −0.102028 0.176718i
\(199\) −3.30764 + 5.72901i −0.234473 + 0.406118i −0.959119 0.283002i \(-0.908670\pi\)
0.724647 + 0.689121i \(0.242003\pi\)
\(200\) 6.43566 11.1469i 0.455070 0.788205i
\(201\) −1.50479 2.60637i −0.106140 0.183839i
\(202\) 22.2725 1.56709
\(203\) −1.36090 + 3.33010i −0.0955168 + 0.233727i
\(204\) −10.0867 −0.706211
\(205\) −4.24427 7.35129i −0.296433 0.513436i
\(206\) 11.4913 19.9035i 0.800634 1.38674i
\(207\) −3.24166 + 5.61473i −0.225311 + 0.390250i
\(208\) 0 0
\(209\) 0.0713021 0.00493207
\(210\) −7.53751 + 1.02872i −0.520137 + 0.0709887i
\(211\) −8.09428 −0.557234 −0.278617 0.960402i \(-0.589876\pi\)
−0.278617 + 0.960402i \(0.589876\pi\)
\(212\) −4.48132 7.76187i −0.307778 0.533088i
\(213\) 10.4711 18.1365i 0.717470 1.24269i
\(214\) −11.3577 + 19.6721i −0.776394 + 1.34475i
\(215\) −3.92536 6.79892i −0.267707 0.463683i
\(216\) 16.9584 1.15387
\(217\) −12.7394 16.4402i −0.864805 1.11604i
\(218\) 26.7306 1.81042
\(219\) 4.98106 + 8.62745i 0.336589 + 0.582989i
\(220\) 2.10501 3.64599i 0.141920 0.245812i
\(221\) 0 0
\(222\) 11.3721 + 19.6970i 0.763244 + 1.32198i
\(223\) −16.0581 −1.07533 −0.537664 0.843159i \(-0.680693\pi\)
−0.537664 + 0.843159i \(0.680693\pi\)
\(224\) 8.57334 + 11.0639i 0.572830 + 0.739240i
\(225\) 3.55075 0.236716
\(226\) 4.00490 + 6.93668i 0.266402 + 0.461421i
\(227\) −0.647903 + 1.12220i −0.0430029 + 0.0744831i −0.886726 0.462296i \(-0.847026\pi\)
0.843723 + 0.536779i \(0.180359\pi\)
\(228\) −0.115474 + 0.200006i −0.00764742 + 0.0132457i
\(229\) 10.4088 + 18.0285i 0.687831 + 1.19136i 0.972538 + 0.232743i \(0.0747702\pi\)
−0.284707 + 0.958614i \(0.591896\pi\)
\(230\) −15.2585 −1.00612
\(231\) 5.80665 0.792496i 0.382050 0.0521424i
\(232\) 4.08707 0.268330
\(233\) 6.65213 + 11.5218i 0.435796 + 0.754820i 0.997360 0.0726127i \(-0.0231337\pi\)
−0.561565 + 0.827433i \(0.689800\pi\)
\(234\) 0 0
\(235\) −0.152518 + 0.264169i −0.00994920 + 0.0172325i
\(236\) −2.71211 4.69751i −0.176543 0.305782i
\(237\) −17.1780 −1.11583
\(238\) −4.77519 + 11.6848i −0.309530 + 0.757411i
\(239\) 13.3652 0.864525 0.432263 0.901748i \(-0.357715\pi\)
0.432263 + 0.901748i \(0.357715\pi\)
\(240\) 0.195490 + 0.338599i 0.0126188 + 0.0218565i
\(241\) 0.417076 0.722398i 0.0268663 0.0465337i −0.852280 0.523086i \(-0.824781\pi\)
0.879146 + 0.476553i \(0.158114\pi\)
\(242\) 10.0650 17.4331i 0.647004 1.12064i
\(243\) 4.17170 + 7.22559i 0.267614 + 0.463522i
\(244\) 14.9452 0.956767
\(245\) −1.48065 + 5.74325i −0.0945955 + 0.366923i
\(246\) −33.9980 −2.16763
\(247\) 0 0
\(248\) −11.8146 + 20.4634i −0.750225 + 1.29943i
\(249\) 8.49852 14.7199i 0.538572 0.932834i
\(250\) 9.05718 + 15.6875i 0.572827 + 0.992165i
\(251\) 27.2721 1.72140 0.860699 0.509114i \(-0.170027\pi\)
0.860699 + 0.509114i \(0.170027\pi\)
\(252\) 2.74297 6.71199i 0.172791 0.422816i
\(253\) 11.7547 0.739009
\(254\) 18.0804 + 31.3163i 1.13447 + 1.96496i
\(255\) 1.29293 2.23943i 0.0809667 0.140238i
\(256\) 8.98607 15.5643i 0.561630 0.972771i
\(257\) −3.27594 5.67409i −0.204348 0.353940i 0.745577 0.666419i \(-0.232174\pi\)
−0.949925 + 0.312479i \(0.898841\pi\)
\(258\) −31.4434 −1.95758
\(259\) 17.5695 2.39789i 1.09171 0.148998i
\(260\) 0 0
\(261\) 0.563740 + 0.976426i 0.0348946 + 0.0604393i
\(262\) 2.93110 5.07682i 0.181084 0.313647i
\(263\) 11.2945 19.5627i 0.696450 1.20629i −0.273239 0.961946i \(-0.588095\pi\)
0.969689 0.244341i \(-0.0785717\pi\)
\(264\) −3.32906 5.76610i −0.204889 0.354879i
\(265\) 2.29770 0.141146
\(266\) 0.177027 + 0.228454i 0.0108542 + 0.0140074i
\(267\) 25.8003 1.57896
\(268\) 3.37553 + 5.84660i 0.206194 + 0.357138i
\(269\) −8.00065 + 13.8575i −0.487808 + 0.844909i −0.999902 0.0140210i \(-0.995537\pi\)
0.512093 + 0.858930i \(0.328870\pi\)
\(270\) −5.50510 + 9.53511i −0.335030 + 0.580288i
\(271\) −4.37967 7.58582i −0.266046 0.460806i 0.701791 0.712383i \(-0.252384\pi\)
−0.967837 + 0.251577i \(0.919051\pi\)
\(272\) 0.648750 0.0393363
\(273\) 0 0
\(274\) −4.29496 −0.259468
\(275\) −3.21886 5.57522i −0.194104 0.336199i
\(276\) −19.0366 + 32.9724i −1.14587 + 1.98471i
\(277\) 9.95914 17.2497i 0.598387 1.03644i −0.394673 0.918822i \(-0.629142\pi\)
0.993059 0.117614i \(-0.0375246\pi\)
\(278\) −17.9761 31.1355i −1.07814 1.86739i
\(279\) −6.51844 −0.390249
\(280\) 6.67638 0.911198i 0.398990 0.0544545i
\(281\) 14.0234 0.836566 0.418283 0.908317i \(-0.362632\pi\)
0.418283 + 0.908317i \(0.362632\pi\)
\(282\) 0.610861 + 1.05804i 0.0363762 + 0.0630055i
\(283\) −0.506295 + 0.876929i −0.0300961 + 0.0521280i −0.880681 0.473710i \(-0.842915\pi\)
0.850585 + 0.525838i \(0.176248\pi\)
\(284\) −23.4888 + 40.6838i −1.39380 + 2.41414i
\(285\) −0.0296032 0.0512743i −0.00175354 0.00303723i
\(286\) 0 0
\(287\) −10.0273 + 24.5365i −0.591890 + 1.44834i
\(288\) 4.38678 0.258493
\(289\) 6.35465 + 11.0066i 0.373803 + 0.647446i
\(290\) −1.32676 + 2.29802i −0.0779101 + 0.134944i
\(291\) 0.313995 0.543855i 0.0184067 0.0318813i
\(292\) −11.1735 19.3531i −0.653879 1.13255i
\(293\) 0.199235 0.0116394 0.00581972 0.999983i \(-0.498148\pi\)
0.00581972 + 0.999983i \(0.498148\pi\)
\(294\) 16.9558 + 16.6371i 0.988880 + 0.970295i
\(295\) 1.39057 0.0809622
\(296\) −10.0729 17.4467i −0.585474 1.01407i
\(297\) 4.24095 7.34554i 0.246085 0.426232i
\(298\) 7.32857 12.6935i 0.424532 0.735312i
\(299\) 0 0
\(300\) 20.8517 1.20387
\(301\) −9.27382 + 22.6928i −0.534534 + 1.30799i
\(302\) 1.52958 0.0880177
\(303\) 7.12368 + 12.3386i 0.409245 + 0.708833i
\(304\) 0.00742695 0.0128639i 0.000425965 0.000737793i
\(305\) −1.91570 + 3.31809i −0.109693 + 0.189993i
\(306\) 1.97807 + 3.42612i 0.113079 + 0.195858i
\(307\) 27.2004 1.55241 0.776204 0.630482i \(-0.217143\pi\)
0.776204 + 0.630482i \(0.217143\pi\)
\(308\) −13.0255 + 1.77772i −0.742194 + 0.101295i
\(309\) 14.7015 0.836341
\(310\) −7.67057 13.2858i −0.435659 0.754584i
\(311\) −13.5505 + 23.4701i −0.768376 + 1.33087i 0.170067 + 0.985432i \(0.445602\pi\)
−0.938443 + 0.345434i \(0.887732\pi\)
\(312\) 0 0
\(313\) 11.0392 + 19.1205i 0.623975 + 1.08076i 0.988738 + 0.149656i \(0.0478165\pi\)
−0.364763 + 0.931100i \(0.618850\pi\)
\(314\) −38.1789 −2.15456
\(315\) 1.13858 + 1.46934i 0.0641517 + 0.0827882i
\(316\) 38.5336 2.16768
\(317\) 3.53411 + 6.12126i 0.198496 + 0.343804i 0.948041 0.318149i \(-0.103061\pi\)
−0.749545 + 0.661953i \(0.769728\pi\)
\(318\) 4.60133 7.96973i 0.258030 0.446920i
\(319\) 1.02209 1.77032i 0.0572263 0.0991188i
\(320\) 5.42750 + 9.40071i 0.303407 + 0.525516i
\(321\) −14.5306 −0.811020
\(322\) 29.1841 + 37.6622i 1.62637 + 2.09883i
\(323\) −0.0982407 −0.00546626
\(324\) 9.62558 + 16.6720i 0.534754 + 0.926221i
\(325\) 0 0
\(326\) −10.4237 + 18.0544i −0.577318 + 0.999943i
\(327\) 8.54955 + 14.8082i 0.472791 + 0.818898i
\(328\) 30.1139 1.66276
\(329\) 0.943758 0.128805i 0.0520310 0.00710124i
\(330\) 4.32276 0.237960
\(331\) 3.29429 + 5.70588i 0.181071 + 0.313623i 0.942245 0.334923i \(-0.108710\pi\)
−0.761175 + 0.648547i \(0.775377\pi\)
\(332\) −19.0638 + 33.0195i −1.04626 + 1.81218i
\(333\) 2.77875 4.81294i 0.152275 0.263748i
\(334\) 3.06059 + 5.30110i 0.167468 + 0.290063i
\(335\) −1.73073 −0.0945599
\(336\) 0.461854 1.13015i 0.0251962 0.0616545i
\(337\) 4.22290 0.230036 0.115018 0.993363i \(-0.463307\pi\)
0.115018 + 0.993363i \(0.463307\pi\)
\(338\) 0 0
\(339\) −2.56187 + 4.43728i −0.139141 + 0.241000i
\(340\) −2.90030 + 5.02347i −0.157291 + 0.272436i
\(341\) 5.90916 + 10.2350i 0.319999 + 0.554254i
\(342\) 0.0905805 0.00489803
\(343\) 17.0079 7.33014i 0.918341 0.395790i
\(344\) 27.8512 1.50163
\(345\) −4.88030 8.45293i −0.262747 0.455091i
\(346\) −22.5571 + 39.0700i −1.21268 + 2.10042i
\(347\) 4.54739 7.87631i 0.244117 0.422822i −0.717766 0.696284i \(-0.754835\pi\)
0.961883 + 0.273462i \(0.0881687\pi\)
\(348\) 3.31056 + 5.73405i 0.177464 + 0.307378i
\(349\) 9.22053 0.493564 0.246782 0.969071i \(-0.420627\pi\)
0.246782 + 0.969071i \(0.420627\pi\)
\(350\) 9.87149 24.1553i 0.527653 1.29116i
\(351\) 0 0
\(352\) −3.97674 6.88792i −0.211961 0.367127i
\(353\) −1.07724 + 1.86584i −0.0573359 + 0.0993087i −0.893269 0.449523i \(-0.851594\pi\)
0.835933 + 0.548832i \(0.184927\pi\)
\(354\) 2.78473 4.82330i 0.148007 0.256356i
\(355\) −6.02167 10.4298i −0.319597 0.553559i
\(356\) −57.8752 −3.06738
\(357\) −8.00046 + 1.09191i −0.423429 + 0.0577899i
\(358\) −6.66410 −0.352208
\(359\) −4.27878 7.41107i −0.225825 0.391141i 0.730741 0.682654i \(-0.239175\pi\)
−0.956567 + 0.291513i \(0.905841\pi\)
\(360\) 1.05593 1.82892i 0.0556521 0.0963923i
\(361\) 9.49888 16.4525i 0.499941 0.865923i
\(362\) −1.57548 2.72881i −0.0828055 0.143423i
\(363\) 12.8769 0.675860
\(364\) 0 0
\(365\) 5.72896 0.299867
\(366\) 7.67270 + 13.2895i 0.401059 + 0.694654i
\(367\) −1.14912 + 1.99033i −0.0599833 + 0.103894i −0.894458 0.447153i \(-0.852438\pi\)
0.834474 + 0.551047i \(0.185771\pi\)
\(368\) 1.22438 2.12070i 0.0638255 0.110549i
\(369\) 4.15368 + 7.19439i 0.216232 + 0.374525i
\(370\) 13.0796 0.679975
\(371\) −4.39468 5.67136i −0.228160 0.294442i
\(372\) −38.2795 −1.98470
\(373\) −5.88418 10.1917i −0.304672 0.527707i 0.672517 0.740082i \(-0.265213\pi\)
−0.977188 + 0.212375i \(0.931880\pi\)
\(374\) 3.58636 6.21175i 0.185446 0.321202i
\(375\) −5.79373 + 10.0350i −0.299187 + 0.518207i
\(376\) −0.541073 0.937166i −0.0279037 0.0483307i
\(377\) 0 0
\(378\) 34.0646 4.64917i 1.75210 0.239127i
\(379\) 7.99093 0.410466 0.205233 0.978713i \(-0.434205\pi\)
0.205233 + 0.978713i \(0.434205\pi\)
\(380\) 0.0664059 + 0.115018i 0.00340655 + 0.00590032i
\(381\) −11.5658 + 20.0325i −0.592532 + 1.02630i
\(382\) 1.74271 3.01846i 0.0891647 0.154438i
\(383\) −14.1223 24.4605i −0.721616 1.24988i −0.960352 0.278791i \(-0.910066\pi\)
0.238736 0.971084i \(-0.423267\pi\)
\(384\) 27.8870 1.42310
\(385\) 1.27494 3.11975i 0.0649770 0.158997i
\(386\) 16.0168 0.815233
\(387\) 3.84158 + 6.65381i 0.195278 + 0.338232i
\(388\) −0.704352 + 1.21997i −0.0357580 + 0.0619347i
\(389\) −3.84043 + 6.65182i −0.194717 + 0.337261i −0.946808 0.321799i \(-0.895712\pi\)
0.752090 + 0.659060i \(0.229046\pi\)
\(390\) 0 0
\(391\) −16.1957 −0.819050
\(392\) −15.0186 14.7364i −0.758556 0.744300i
\(393\) 3.74996 0.189160
\(394\) −17.8241 30.8722i −0.897964 1.55532i
\(395\) −4.93931 + 8.55513i −0.248524 + 0.430455i
\(396\) −2.06008 + 3.56817i −0.103523 + 0.179307i
\(397\) −3.72641 6.45433i −0.187023 0.323933i 0.757233 0.653144i \(-0.226551\pi\)
−0.944256 + 0.329211i \(0.893217\pi\)
\(398\) 15.2368 0.763750
\(399\) −0.0699389 + 0.171139i −0.00350132 + 0.00856765i
\(400\) −1.34113 −0.0670563
\(401\) −9.09912 15.7601i −0.454389 0.787024i 0.544264 0.838914i \(-0.316809\pi\)
−0.998653 + 0.0518898i \(0.983476\pi\)
\(402\) −3.46593 + 6.00316i −0.172865 + 0.299411i
\(403\) 0 0
\(404\) −15.9798 27.6778i −0.795025 1.37702i
\(405\) −4.93530 −0.245237
\(406\) 8.20978 1.12048i 0.407444 0.0556083i
\(407\) −10.0761 −0.499453
\(408\) 4.58681 + 7.94458i 0.227081 + 0.393315i
\(409\) −14.6413 + 25.3594i −0.723964 + 1.25394i 0.235435 + 0.971890i \(0.424349\pi\)
−0.959399 + 0.282053i \(0.908985\pi\)
\(410\) −9.77568 + 16.9320i −0.482787 + 0.836211i
\(411\) −1.37371 2.37933i −0.0677599 0.117364i
\(412\) −32.9784 −1.62473
\(413\) −2.65967 3.43232i −0.130874 0.168893i
\(414\) 14.9328 0.733909
\(415\) −4.88728 8.46502i −0.239907 0.415531i
\(416\) 0 0
\(417\) 11.4990 19.9169i 0.563109 0.975334i
\(418\) −0.0821139 0.142225i −0.00401632 0.00695647i
\(419\) −20.7393 −1.01318 −0.506591 0.862187i \(-0.669095\pi\)
−0.506591 + 0.862187i \(0.669095\pi\)
\(420\) 6.68630 + 8.62871i 0.326258 + 0.421038i
\(421\) −24.8696 −1.21207 −0.606036 0.795437i \(-0.707241\pi\)
−0.606036 + 0.795437i \(0.707241\pi\)
\(422\) 9.32165 + 16.1456i 0.453771 + 0.785954i
\(423\) 0.149263 0.258531i 0.00725742 0.0125702i
\(424\) −4.07565 + 7.05923i −0.197931 + 0.342826i
\(425\) 4.43497 + 7.68159i 0.215128 + 0.372612i
\(426\) −48.2356 −2.33702
\(427\) 11.8540 1.61785i 0.573657 0.0782932i
\(428\) 32.5950 1.57554
\(429\) 0 0
\(430\) −9.04115 + 15.6597i −0.436003 + 0.755179i
\(431\) 10.5844 18.3327i 0.509832 0.883055i −0.490103 0.871665i \(-0.663041\pi\)
0.999935 0.0113906i \(-0.00362583\pi\)
\(432\) −0.883489 1.53025i −0.0425069 0.0736241i
\(433\) −23.4296 −1.12595 −0.562977 0.826472i \(-0.690344\pi\)
−0.562977 + 0.826472i \(0.690344\pi\)
\(434\) −18.1220 + 44.3442i −0.869885 + 2.12859i
\(435\) −1.69741 −0.0813848
\(436\) −19.1783 33.2178i −0.918474 1.59084i
\(437\) −0.185409 + 0.321139i −0.00886934 + 0.0153621i
\(438\) 11.4727 19.8713i 0.548187 0.949488i
\(439\) 6.01919 + 10.4256i 0.287280 + 0.497584i 0.973160 0.230131i \(-0.0739155\pi\)
−0.685879 + 0.727715i \(0.740582\pi\)
\(440\) −3.82891 −0.182536
\(441\) 1.44905 5.62067i 0.0690025 0.267651i
\(442\) 0 0
\(443\) −7.86656 13.6253i −0.373752 0.647357i 0.616388 0.787443i \(-0.288595\pi\)
−0.990139 + 0.140086i \(0.955262\pi\)
\(444\) 16.3182 28.2640i 0.774427 1.34135i
\(445\) 7.41855 12.8493i 0.351673 0.609116i
\(446\) 18.4930 + 32.0308i 0.875669 + 1.51670i
\(447\) 9.37592 0.443466
\(448\) 12.8227 31.3768i 0.605815 1.48242i
\(449\) −26.0012 −1.22707 −0.613536 0.789667i \(-0.710253\pi\)
−0.613536 + 0.789667i \(0.710253\pi\)
\(450\) −4.08916 7.08263i −0.192765 0.333878i
\(451\) 7.53087 13.0438i 0.354615 0.614211i
\(452\) 5.74676 9.95369i 0.270305 0.468182i
\(453\) 0.489225 + 0.847362i 0.0229858 + 0.0398125i
\(454\) 2.98459 0.140074
\(455\) 0 0
\(456\) 0.210041 0.00983605
\(457\) −15.3979 26.6700i −0.720284 1.24757i −0.960886 0.276945i \(-0.910678\pi\)
0.240602 0.970624i \(-0.422655\pi\)
\(458\) 23.9742 41.5245i 1.12024 1.94031i
\(459\) −5.84322 + 10.1208i −0.272738 + 0.472396i
\(460\) 10.9475 + 18.9616i 0.510429 + 0.884088i
\(461\) −34.0958 −1.58800 −0.794000 0.607918i \(-0.792005\pi\)
−0.794000 + 0.607918i \(0.792005\pi\)
\(462\) −8.26791 10.6698i −0.384658 0.496403i
\(463\) −1.69184 −0.0786263 −0.0393131 0.999227i \(-0.512517\pi\)
−0.0393131 + 0.999227i \(0.512517\pi\)
\(464\) −0.212926 0.368799i −0.00988485 0.0171211i
\(465\) 4.90674 8.49871i 0.227544 0.394118i
\(466\) 15.3216 26.5378i 0.709761 1.22934i
\(467\) −14.1762 24.5539i −0.655996 1.13622i −0.981643 0.190727i \(-0.938916\pi\)
0.325647 0.945491i \(-0.394418\pi\)
\(468\) 0 0
\(469\) 3.31027 + 4.27192i 0.152854 + 0.197259i
\(470\) 0.702581 0.0324076
\(471\) −12.2112 21.1504i −0.562662 0.974559i
\(472\) −2.46659 + 4.27226i −0.113534 + 0.196647i
\(473\) 6.96501 12.0637i 0.320251 0.554692i
\(474\) 19.7827 + 34.2647i 0.908651 + 1.57383i
\(475\) 0.203088 0.00931830
\(476\) 17.9466 2.44936i 0.822581 0.112266i
\(477\) −2.24866 −0.102959
\(478\) −15.3918 26.6595i −0.704007 1.21938i
\(479\) 3.14123 5.44077i 0.143526 0.248595i −0.785296 0.619121i \(-0.787489\pi\)
0.928822 + 0.370526i \(0.120822\pi\)
\(480\) −3.30213 + 5.71946i −0.150721 + 0.261056i
\(481\) 0 0
\(482\) −1.92128 −0.0875117
\(483\) −11.5299 + 28.2134i −0.524629 + 1.28375i
\(484\) −28.8853 −1.31297
\(485\) −0.180570 0.312757i −0.00819927 0.0142016i
\(486\) 9.60853 16.6425i 0.435852 0.754917i
\(487\) −6.50879 + 11.2736i −0.294942 + 0.510854i −0.974971 0.222331i \(-0.928634\pi\)
0.680030 + 0.733185i \(0.261967\pi\)
\(488\) −6.79613 11.7712i −0.307647 0.532859i
\(489\) −13.3358 −0.603065
\(490\) 13.1612 3.66068i 0.594560 0.165373i
\(491\) −12.3523 −0.557453 −0.278726 0.960371i \(-0.589912\pi\)
−0.278726 + 0.960371i \(0.589912\pi\)
\(492\) 24.3925 + 42.2490i 1.09970 + 1.90473i
\(493\) −1.40825 + 2.43916i −0.0634244 + 0.109854i
\(494\) 0 0
\(495\) −0.528131 0.914749i −0.0237377 0.0411149i
\(496\) 2.46203 0.110549
\(497\) −14.2264 + 34.8118i −0.638143 + 1.56152i
\(498\) −39.1487 −1.75430
\(499\) −4.57670 7.92708i −0.204881 0.354865i 0.745214 0.666826i \(-0.232348\pi\)
−0.950095 + 0.311961i \(0.899014\pi\)
\(500\) 12.9965 22.5105i 0.581220 1.00670i
\(501\) −1.95781 + 3.39102i −0.0874684 + 0.151500i
\(502\) −31.4074 54.3993i −1.40178 2.42796i
\(503\) 22.5037 1.00339 0.501696 0.865044i \(-0.332710\pi\)
0.501696 + 0.865044i \(0.332710\pi\)
\(504\) −6.53389 + 0.891750i −0.291042 + 0.0397217i
\(505\) 8.19329 0.364596
\(506\) −13.5370 23.4469i −0.601795 1.04234i
\(507\) 0 0
\(508\) 25.9443 44.9368i 1.15109 1.99375i
\(509\) 19.3303 + 33.4811i 0.856800 + 1.48402i 0.874965 + 0.484187i \(0.160884\pi\)
−0.0181646 + 0.999835i \(0.505782\pi\)
\(510\) −5.95594 −0.263734
\(511\) −10.9575 14.1407i −0.484730 0.625546i
\(512\) −3.53972 −0.156435
\(513\) 0.133787 + 0.231727i 0.00590686 + 0.0102310i
\(514\) −7.54536 + 13.0690i −0.332812 + 0.576447i
\(515\) 4.22724 7.32179i 0.186274 0.322637i
\(516\) 22.5596 + 39.0744i 0.993132 + 1.72016i
\(517\) −0.541245 −0.0238039
\(518\) −25.0166 32.2841i −1.09917 1.41848i
\(519\) −28.8588 −1.26676
\(520\) 0 0
\(521\) −20.1176 + 34.8446i −0.881366 + 1.52657i −0.0315430 + 0.999502i \(0.510042\pi\)
−0.849823 + 0.527068i \(0.823291\pi\)
\(522\) 1.29844 2.24897i 0.0568313 0.0984348i
\(523\) 0.366073 + 0.634057i 0.0160073 + 0.0277254i 0.873918 0.486073i \(-0.161571\pi\)
−0.857911 + 0.513799i \(0.828238\pi\)
\(524\) −8.41189 −0.367475
\(525\) 16.5389 2.25724i 0.721818 0.0985142i
\(526\) −52.0286 −2.26856
\(527\) −8.14169 14.1018i −0.354658 0.614285i
\(528\) −0.346871 + 0.600798i −0.0150956 + 0.0261464i
\(529\) −19.0660 + 33.0234i −0.828959 + 1.43580i
\(530\) −2.64610 4.58319i −0.114939 0.199081i
\(531\) −1.36089 −0.0590577
\(532\) 0.156887 0.383898i 0.00680189 0.0166441i
\(533\) 0 0
\(534\) −29.7125 51.4636i −1.28579 2.22705i
\(535\) −4.17809 + 7.23667i −0.180635 + 0.312868i
\(536\) 3.06996 5.31733i 0.132602 0.229674i
\(537\) −2.13146 3.69179i −0.0919791 0.159312i
\(538\) 36.8553 1.58894
\(539\) −10.1389 + 2.82007i −0.436715 + 0.121469i
\(540\) 15.7989 0.679877
\(541\) −11.8268 20.4847i −0.508476 0.880705i −0.999952 0.00981448i \(-0.996876\pi\)
0.491476 0.870891i \(-0.336457\pi\)
\(542\) −10.0876 + 17.4722i −0.433298 + 0.750494i
\(543\) 1.00781 1.74558i 0.0432492 0.0749099i
\(544\) 5.47919 + 9.49024i 0.234918 + 0.406891i
\(545\) 9.83325 0.421210
\(546\) 0 0
\(547\) −12.9472 −0.553582 −0.276791 0.960930i \(-0.589271\pi\)
−0.276791 + 0.960930i \(0.589271\pi\)
\(548\) 3.08149 + 5.33730i 0.131635 + 0.227998i
\(549\) 1.87481 3.24727i 0.0800151 0.138590i
\(550\) −7.41388 + 12.8412i −0.316129 + 0.547552i
\(551\) 0.0322436 + 0.0558475i 0.00137362 + 0.00237918i
\(552\) 34.6267 1.47381
\(553\) 30.5636 4.17134i 1.29970 0.177384i
\(554\) −45.8771 −1.94913
\(555\) 4.18340 + 7.24585i 0.177575 + 0.307569i
\(556\) −25.7946 + 44.6775i −1.09393 + 1.89475i
\(557\) 3.20340 5.54845i 0.135732 0.235096i −0.790145 0.612921i \(-0.789995\pi\)
0.925877 + 0.377825i \(0.123328\pi\)
\(558\) 7.50685 + 13.0023i 0.317790 + 0.550429i
\(559\) 0 0
\(560\) −0.430045 0.554975i −0.0181727 0.0234520i
\(561\) 4.58827 0.193717
\(562\) −16.1498 27.9723i −0.681239 1.17994i
\(563\) −3.66042 + 6.34004i −0.154268 + 0.267201i −0.932792 0.360414i \(-0.882635\pi\)
0.778524 + 0.627615i \(0.215969\pi\)
\(564\) 0.876546 1.51822i 0.0369092 0.0639287i
\(565\) 1.47326 + 2.55176i 0.0619806 + 0.107354i
\(566\) 2.33226 0.0980324
\(567\) 9.43948 + 12.1817i 0.396421 + 0.511583i
\(568\) 42.7249 1.79270
\(569\) 2.15872 + 3.73901i 0.0904981 + 0.156747i 0.907721 0.419575i \(-0.137821\pi\)
−0.817223 + 0.576322i \(0.804487\pi\)
\(570\) −0.0681842 + 0.118098i −0.00285592 + 0.00494660i
\(571\) −17.0847 + 29.5916i −0.714974 + 1.23837i 0.247996 + 0.968761i \(0.420228\pi\)
−0.962970 + 0.269610i \(0.913105\pi\)
\(572\) 0 0
\(573\) 2.22956 0.0931413
\(574\) 60.4903 8.25576i 2.52482 0.344589i
\(575\) 33.4804 1.39623
\(576\) −5.31166 9.20007i −0.221319 0.383336i
\(577\) −3.17828 + 5.50494i −0.132314 + 0.229174i −0.924568 0.381017i \(-0.875574\pi\)
0.792254 + 0.610191i \(0.208907\pi\)
\(578\) 14.6364 25.3511i 0.608796 1.05447i
\(579\) 5.12283 + 8.87301i 0.212898 + 0.368750i
\(580\) 3.80763 0.158103
\(581\) −11.5464 + 28.2537i −0.479025 + 1.17216i
\(582\) −1.44643 −0.0599563
\(583\) 2.03847 + 3.53074i 0.0844249 + 0.146228i
\(584\) −10.1620 + 17.6011i −0.420507 + 0.728339i
\(585\) 0 0
\(586\) −0.229446 0.397412i −0.00947832 0.0164169i
\(587\) −31.4120 −1.29651 −0.648256 0.761422i \(-0.724501\pi\)
−0.648256 + 0.761422i \(0.724501\pi\)
\(588\) 8.50954 33.0073i 0.350927 1.36120i
\(589\) −0.372827 −0.0153621
\(590\) −1.60143 2.77376i −0.0659298 0.114194i
\(591\) 11.4018 19.7484i 0.469006 0.812342i
\(592\) −1.04954 + 1.81786i −0.0431359 + 0.0747136i
\(593\) 0.236506 + 0.409641i 0.00971215 + 0.0168219i 0.870841 0.491565i \(-0.163575\pi\)
−0.861128 + 0.508387i \(0.830242\pi\)
\(594\) −19.5361 −0.801575
\(595\) −1.75663 + 4.29842i −0.0720146 + 0.176218i
\(596\) −21.0320 −0.861505
\(597\) 4.87335 + 8.44089i 0.199453 + 0.345463i
\(598\) 0 0
\(599\) 4.81348 8.33719i 0.196673 0.340648i −0.750774 0.660559i \(-0.770320\pi\)
0.947448 + 0.319910i \(0.103653\pi\)
\(600\) −9.48206 16.4234i −0.387103 0.670483i
\(601\) −41.0799 −1.67568 −0.837842 0.545914i \(-0.816183\pi\)
−0.837842 + 0.545914i \(0.816183\pi\)
\(602\) 55.9451 7.63543i 2.28015 0.311197i
\(603\) 1.69379 0.0689765
\(604\) −1.09743 1.90080i −0.0446537 0.0773424i
\(605\) 3.70257 6.41304i 0.150531 0.260727i
\(606\) 16.4077 28.4190i 0.666518 1.15444i
\(607\) −9.54289 16.5288i −0.387334 0.670882i 0.604756 0.796411i \(-0.293271\pi\)
−0.992090 + 0.125529i \(0.959937\pi\)
\(608\) 0.250905 0.0101755
\(609\) 3.24655 + 4.18969i 0.131557 + 0.169775i
\(610\) 8.82474 0.357303
\(611\) 0 0
\(612\) 2.83840 4.91626i 0.114736 0.198728i
\(613\) 19.0024 32.9131i 0.767500 1.32935i −0.171415 0.985199i \(-0.554834\pi\)
0.938915 0.344149i \(-0.111833\pi\)
\(614\) −31.3249 54.2563i −1.26417 2.18961i
\(615\) −12.5067 −0.504318
\(616\) 7.32335 + 9.45082i 0.295066 + 0.380784i
\(617\) 8.31519 0.334757 0.167378 0.985893i \(-0.446470\pi\)
0.167378 + 0.985893i \(0.446470\pi\)
\(618\) −16.9308 29.3250i −0.681056 1.17962i
\(619\) 22.2364 38.5146i 0.893756 1.54803i 0.0584199 0.998292i \(-0.481394\pi\)
0.835336 0.549739i \(-0.185273\pi\)
\(620\) −11.0068 + 19.0643i −0.442042 + 0.765640i
\(621\) 22.0558 + 38.2018i 0.885069 + 1.53298i
\(622\) 62.4206 2.50284
\(623\) −45.9048 + 6.26512i −1.83914 + 0.251007i
\(624\) 0 0
\(625\) −7.37342 12.7711i −0.294937 0.510845i
\(626\) 25.4263 44.0397i 1.01624 1.76018i
\(627\) 0.0525269 0.0909792i 0.00209772 0.00363336i
\(628\) 27.3921 + 47.4445i 1.09306 + 1.89324i
\(629\) 13.8829 0.553549
\(630\) 1.61966 3.96326i 0.0645286 0.157900i
\(631\) 11.7524 0.467858 0.233929 0.972254i \(-0.424842\pi\)
0.233929 + 0.972254i \(0.424842\pi\)
\(632\) −17.5227 30.3501i −0.697014 1.20726i
\(633\) −5.96290 + 10.3280i −0.237004 + 0.410503i
\(634\) 8.14001 14.0989i 0.323281 0.559939i
\(635\) 6.65117 + 11.5202i 0.263944 + 0.457164i
\(636\) −13.2052 −0.523620
\(637\) 0 0
\(638\) −4.70831 −0.186404
\(639\) 5.89315 + 10.2072i 0.233129 + 0.403792i
\(640\) 8.01854 13.8885i 0.316961 0.548992i
\(641\) −5.24342 + 9.08186i −0.207102 + 0.358712i −0.950801 0.309804i \(-0.899737\pi\)
0.743698 + 0.668516i \(0.233070\pi\)
\(642\) 16.7339 + 28.9840i 0.660436 + 1.14391i
\(643\) 31.2822 1.23365 0.616825 0.787101i \(-0.288419\pi\)
0.616825 + 0.787101i \(0.288419\pi\)
\(644\) 25.8638 63.2882i 1.01918 2.49390i
\(645\) −11.5669 −0.455448
\(646\) 0.113137 + 0.195959i 0.00445133 + 0.00770992i
\(647\) 13.4337 23.2679i 0.528135 0.914757i −0.471327 0.881959i \(-0.656225\pi\)
0.999462 0.0327983i \(-0.0104419\pi\)
\(648\) 8.75422 15.1627i 0.343898 0.595649i
\(649\) 1.23369 + 2.13681i 0.0484265 + 0.0838772i
\(650\) 0 0
\(651\) −30.3621 + 4.14384i −1.18998 + 0.162410i
\(652\) 29.9148 1.17155
\(653\) 2.07081 + 3.58674i 0.0810369 + 0.140360i 0.903696 0.428176i \(-0.140844\pi\)
−0.822659 + 0.568536i \(0.807510\pi\)
\(654\) 19.6919 34.1073i 0.770014 1.33370i
\(655\) 1.07825 1.86759i 0.0421308 0.0729726i
\(656\) −1.56886 2.71734i −0.0612536 0.106094i
\(657\) −5.60668 −0.218738
\(658\) −1.34379 1.73417i −0.0523863 0.0676048i
\(659\) 21.4551 0.835773 0.417887 0.908499i \(-0.362771\pi\)
0.417887 + 0.908499i \(0.362771\pi\)
\(660\) −3.10144 5.37185i −0.120723 0.209099i
\(661\) −21.1936 + 36.7084i −0.824335 + 1.42779i 0.0780909 + 0.996946i \(0.475118\pi\)
−0.902426 + 0.430844i \(0.858216\pi\)
\(662\) 7.58763 13.1422i 0.294902 0.510785i
\(663\) 0 0
\(664\) 34.6762 1.34570
\(665\) 0.0651220 + 0.0840403i 0.00252532 + 0.00325894i
\(666\) −12.8004 −0.496006
\(667\) 5.31558 + 9.20685i 0.205820 + 0.356491i
\(668\) 4.39175 7.60673i 0.169922 0.294313i
\(669\) −11.8297 + 20.4896i −0.457361 + 0.792173i
\(670\) 1.99317 + 3.45226i 0.0770027 + 0.133373i
\(671\) −6.79830 −0.262445
\(672\) 20.4330 2.78872i 0.788222 0.107577i
\(673\) −29.5856 −1.14044 −0.570220 0.821492i \(-0.693142\pi\)
−0.570220 + 0.821492i \(0.693142\pi\)
\(674\) −4.86323 8.42336i −0.187324 0.324456i
\(675\) 12.0794 20.9221i 0.464935 0.805292i
\(676\) 0 0
\(677\) −16.0830 27.8565i −0.618118 1.07061i −0.989829 0.142263i \(-0.954562\pi\)
0.371711 0.928349i \(-0.378771\pi\)
\(678\) 11.8013 0.453227
\(679\) −0.426604 + 1.04389i −0.0163716 + 0.0400609i
\(680\) 5.27551 0.202306
\(681\) 0.954596 + 1.65341i 0.0365802 + 0.0633587i
\(682\) 13.6104 23.5738i 0.521168 0.902689i
\(683\) 4.30118 7.44986i 0.164580 0.285061i −0.771926 0.635712i \(-0.780706\pi\)
0.936506 + 0.350651i \(0.114040\pi\)
\(684\) −0.0649885 0.112563i −0.00248490 0.00430397i
\(685\) −1.57997 −0.0603674
\(686\) −34.2082 25.4838i −1.30608 0.972978i
\(687\) 30.6717 1.17020
\(688\) −1.45097 2.51316i −0.0553179 0.0958134i
\(689\) 0 0
\(690\) −11.2406 + 19.4694i −0.427924 + 0.741186i
\(691\) −10.2210 17.7033i −0.388826 0.673466i 0.603466 0.797388i \(-0.293786\pi\)
−0.992292 + 0.123923i \(0.960452\pi\)
\(692\) 64.7359 2.46089
\(693\) −1.24773 + 3.05316i −0.0473973 + 0.115980i
\(694\) −20.9477 −0.795164
\(695\) −6.61279 11.4537i −0.250837 0.434463i
\(696\) 3.01087 5.21498i 0.114127 0.197673i
\(697\) −10.3761 + 17.9719i −0.393023 + 0.680736i
\(698\) −10.6187 18.3921i −0.401922 0.696150i
\(699\) 19.6020 0.741415
\(700\) −37.1000 + 5.06344i −1.40225 + 0.191380i
\(701\) 25.1373 0.949422 0.474711 0.880142i \(-0.342553\pi\)
0.474711 + 0.880142i \(0.342553\pi\)
\(702\) 0 0
\(703\) 0.158933 0.275280i 0.00599427 0.0103824i
\(704\) −9.63036 + 16.6803i −0.362958 + 0.628661i
\(705\) 0.224715 + 0.389217i 0.00846324 + 0.0146588i
\(706\) 4.96236 0.186761
\(707\) −15.6709 20.2233i −0.589363 0.760576i
\(708\) −7.99182 −0.300351
\(709\) 14.7464 + 25.5416i 0.553814 + 0.959234i 0.997995 + 0.0632970i \(0.0201615\pi\)
−0.444181 + 0.895937i \(0.646505\pi\)
\(710\) −13.8695 + 24.0227i −0.520514 + 0.901556i
\(711\) 4.83389 8.37254i 0.181285 0.313995i
\(712\) 26.3180 + 45.5841i 0.986309 + 1.70834i
\(713\) −61.4632 −2.30182
\(714\) 11.3916 + 14.7009i 0.426320 + 0.550169i
\(715\) 0 0
\(716\) 4.78127 + 8.28140i 0.178684 + 0.309491i
\(717\) 9.84591 17.0536i 0.367702 0.636879i
\(718\) −9.85518 + 17.0697i −0.367792 + 0.637034i
\(719\) 4.16576 + 7.21531i 0.155357 + 0.269086i 0.933189 0.359386i \(-0.117014\pi\)
−0.777832 + 0.628472i \(0.783681\pi\)
\(720\) −0.220044 −0.00820055
\(721\) −26.1574 + 3.56999i −0.974154 + 0.132953i
\(722\) −43.7569 −1.62846
\(723\) −0.614504 1.06435i −0.0228537 0.0395837i
\(724\) −2.26071 + 3.91567i −0.0840188 + 0.145525i
\(725\) 2.91120 5.04235i 0.108119 0.187268i
\(726\) −14.8294 25.6853i −0.550371 0.953271i
\(727\) −9.66141 −0.358322 −0.179161 0.983820i \(-0.557338\pi\)
−0.179161 + 0.983820i \(0.557338\pi\)
\(728\) 0 0
\(729\) 29.7672 1.10249
\(730\) −6.59766 11.4275i −0.244190 0.422950i
\(731\) −9.59645 + 16.6215i −0.354938 + 0.614770i
\(732\) 11.0098 19.0696i 0.406935 0.704832i
\(733\) 7.00894 + 12.1398i 0.258881 + 0.448395i 0.965942 0.258757i \(-0.0833129\pi\)
−0.707061 + 0.707152i \(0.749980\pi\)
\(734\) 5.29344 0.195384
\(735\) 6.23743 + 6.12021i 0.230071 + 0.225747i
\(736\) 41.3635 1.52468
\(737\) −1.53547 2.65951i −0.0565598 0.0979644i
\(738\) 9.56704 16.5706i 0.352168 0.609972i
\(739\) 19.4073 33.6145i 0.713910 1.23653i −0.249468 0.968383i \(-0.580256\pi\)
0.963378 0.268146i \(-0.0864108\pi\)
\(740\) −9.38417 16.2539i −0.344969 0.597504i
\(741\) 0 0
\(742\) −6.25153 + 15.2973i −0.229501 + 0.561583i
\(743\) −34.3942 −1.26180 −0.630901 0.775863i \(-0.717315\pi\)
−0.630901 + 0.775863i \(0.717315\pi\)
\(744\) 17.4071 + 30.1500i 0.638175 + 1.10535i
\(745\) 2.69592 4.66948i 0.0987710 0.171076i
\(746\) −13.5528 + 23.4742i −0.496205 + 0.859452i
\(747\) 4.78297 + 8.28434i 0.175000 + 0.303108i
\(748\) −10.2924 −0.376327
\(749\) 25.8533 3.52848i 0.944660 0.128928i
\(750\) 26.6890 0.974545
\(751\) −24.0735 41.6965i −0.878454 1.52153i −0.853037 0.521850i \(-0.825242\pi\)
−0.0254165 0.999677i \(-0.508091\pi\)
\(752\) −0.0563770 + 0.0976479i −0.00205586 + 0.00356085i
\(753\) 20.0908 34.7983i 0.732150 1.26812i
\(754\) 0 0
\(755\) 0.562681 0.0204781
\(756\) −30.2177 38.9961i −1.09901 1.41828i
\(757\) −6.90638 −0.251016 −0.125508 0.992093i \(-0.540056\pi\)
−0.125508 + 0.992093i \(0.540056\pi\)
\(758\) −9.20262 15.9394i −0.334254 0.578945i
\(759\) 8.65942 14.9986i 0.314317 0.544413i
\(760\) 0.0603945 0.104606i 0.00219074 0.00379447i
\(761\) 15.9865 + 27.6895i 0.579511 + 1.00374i 0.995535 + 0.0943888i \(0.0300897\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(762\) 53.2781 1.93006
\(763\) −18.8075 24.2712i −0.680878 0.878676i
\(764\) −5.00135 −0.180942
\(765\) 0.727663 + 1.26035i 0.0263087 + 0.0455680i
\(766\) −32.5274 + 56.3391i −1.17526 + 2.03562i
\(767\) 0 0
\(768\) −13.2397 22.9319i −0.477748 0.827483i
\(769\) −14.3950 −0.519099 −0.259549 0.965730i \(-0.583574\pi\)
−0.259549 + 0.965730i \(0.583574\pi\)
\(770\) −7.69119 + 1.04970i −0.277171 + 0.0378285i
\(771\) −9.65328 −0.347654
\(772\) −11.4915 19.9039i −0.413589 0.716357i
\(773\) −18.6385 + 32.2829i −0.670382 + 1.16114i 0.307414 + 0.951576i \(0.400536\pi\)
−0.977796 + 0.209560i \(0.932797\pi\)
\(774\) 8.84818 15.3255i 0.318041 0.550864i
\(775\) 16.8309 + 29.1520i 0.604583 + 1.04717i
\(776\) 1.28118 0.0459917
\(777\) 9.88344 24.1845i 0.354566 0.867616i
\(778\) 17.6911 0.634255
\(779\) 0.237573 + 0.411489i 0.00851194 + 0.0147431i
\(780\) 0 0
\(781\) 10.6846 18.5063i 0.382326 0.662208i
\(782\) 18.6515 + 32.3053i