Properties

Label 936.2.ed.c.739.12
Level $936$
Weight $2$
Character 936.739
Analytic conductor $7.474$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.ed (of order \(12\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.47399762919\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 739.12
Character \(\chi\) \(=\) 936.739
Dual form 936.2.ed.c.19.12

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39432 - 0.236374i) q^{2} +(1.88825 - 0.659163i) q^{4} +(-1.86647 + 1.86647i) q^{5} +(4.71214 - 1.26261i) q^{7} +(2.47702 - 1.36542i) q^{8} +(-2.16128 + 3.04365i) q^{10} +(1.99964 + 0.535801i) q^{11} +(-3.15234 + 1.75007i) q^{13} +(6.27177 - 2.87431i) q^{14} +(3.13101 - 2.48933i) q^{16} +(-3.84928 - 2.22238i) q^{17} +(2.62661 - 0.703799i) q^{19} +(-2.29407 + 4.75469i) q^{20} +(2.91478 + 0.274415i) q^{22} +(3.41537 + 5.91559i) q^{23} -1.96745i q^{25} +(-3.98170 + 3.18529i) q^{26} +(8.06544 - 5.49020i) q^{28} +(0.143621 - 0.0829197i) q^{29} +(3.77330 - 3.77330i) q^{31} +(3.77721 - 4.21102i) q^{32} +(-5.89244 - 2.18884i) q^{34} +(-6.43844 + 11.1517i) q^{35} +(-1.19716 + 4.46786i) q^{37} +(3.49598 - 1.60218i) q^{38} +(-2.07478 + 7.17181i) q^{40} +(2.06622 - 7.71126i) q^{41} +(-7.03012 - 4.05884i) q^{43} +(4.12900 - 0.306357i) q^{44} +(6.16041 + 7.44092i) q^{46} +(1.87036 + 1.87036i) q^{47} +(14.5479 - 8.39921i) q^{49} +(-0.465055 - 2.74326i) q^{50} +(-4.79885 + 5.38248i) q^{52} +8.22085i q^{53} +(-4.73233 + 2.73221i) q^{55} +(9.94806 - 9.56155i) q^{56} +(0.180654 - 0.149565i) q^{58} +(-0.352439 - 1.31532i) q^{59} +(0.601045 + 0.347013i) q^{61} +(4.36928 - 6.15310i) q^{62} +(4.27127 - 6.76434i) q^{64} +(2.61731 - 9.15022i) q^{65} +(1.26441 - 4.71883i) q^{67} +(-8.73333 - 1.65912i) q^{68} +(-6.34127 + 17.0709i) q^{70} +(-2.46409 - 9.19612i) q^{71} +(-11.2670 + 11.2670i) q^{73} +(-0.613136 + 6.51261i) q^{74} +(4.49579 - 3.06032i) q^{76} +10.0991 q^{77} +9.91660i q^{79} +(-1.19767 + 10.4902i) q^{80} +(1.05824 - 11.2404i) q^{82} +(-3.88441 - 3.88441i) q^{83} +(11.3326 - 3.03656i) q^{85} +(-10.7616 - 3.99758i) q^{86} +(5.68474 - 1.40315i) q^{88} +(-13.1559 - 3.52510i) q^{89} +(-12.6446 + 12.2267i) q^{91} +(10.3484 + 8.91886i) q^{92} +(3.04998 + 2.16577i) q^{94} +(-3.58888 + 6.21613i) q^{95} +(-1.52421 + 0.408410i) q^{97} +(18.2990 - 15.1499i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 2 q^{2} + 4 q^{8} - 6 q^{10} - 20 q^{11} + 28 q^{14} + 4 q^{16} - 12 q^{17} + 20 q^{19} - 4 q^{20} + 14 q^{22} + 12 q^{26} - 2 q^{28} + 18 q^{32} - 12 q^{35} + 52 q^{40} + 36 q^{41} + 12 q^{43} - 12 q^{44}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\) \(469\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39432 0.236374i 0.985933 0.167142i
\(3\) 0 0
\(4\) 1.88825 0.659163i 0.944127 0.329581i
\(5\) −1.86647 + 1.86647i −0.834713 + 0.834713i −0.988157 0.153445i \(-0.950963\pi\)
0.153445 + 0.988157i \(0.450963\pi\)
\(6\) 0 0
\(7\) 4.71214 1.26261i 1.78102 0.477223i 0.790251 0.612784i \(-0.209950\pi\)
0.990769 + 0.135561i \(0.0432836\pi\)
\(8\) 2.47702 1.36542i 0.875759 0.482748i
\(9\) 0 0
\(10\) −2.16128 + 3.04365i −0.683455 + 0.962486i
\(11\) 1.99964 + 0.535801i 0.602913 + 0.161550i 0.547348 0.836905i \(-0.315637\pi\)
0.0555651 + 0.998455i \(0.482304\pi\)
\(12\) 0 0
\(13\) −3.15234 + 1.75007i −0.874303 + 0.485381i
\(14\) 6.27177 2.87431i 1.67620 0.768193i
\(15\) 0 0
\(16\) 3.13101 2.48933i 0.782752 0.622333i
\(17\) −3.84928 2.22238i −0.933587 0.539007i −0.0456428 0.998958i \(-0.514534\pi\)
−0.887944 + 0.459951i \(0.847867\pi\)
\(18\) 0 0
\(19\) 2.62661 0.703799i 0.602586 0.161462i 0.0553871 0.998465i \(-0.482361\pi\)
0.547199 + 0.837002i \(0.315694\pi\)
\(20\) −2.29407 + 4.75469i −0.512969 + 1.06318i
\(21\) 0 0
\(22\) 2.91478 + 0.274415i 0.621434 + 0.0585055i
\(23\) 3.41537 + 5.91559i 0.712154 + 1.23349i 0.964047 + 0.265732i \(0.0856135\pi\)
−0.251893 + 0.967755i \(0.581053\pi\)
\(24\) 0 0
\(25\) 1.96745i 0.393490i
\(26\) −3.98170 + 3.18529i −0.780876 + 0.624686i
\(27\) 0 0
\(28\) 8.06544 5.49020i 1.52423 1.03755i
\(29\) 0.143621 0.0829197i 0.0266698 0.0153978i −0.486606 0.873622i \(-0.661765\pi\)
0.513276 + 0.858224i \(0.328432\pi\)
\(30\) 0 0
\(31\) 3.77330 3.77330i 0.677705 0.677705i −0.281775 0.959480i \(-0.590923\pi\)
0.959480 + 0.281775i \(0.0909233\pi\)
\(32\) 3.77721 4.21102i 0.667723 0.744410i
\(33\) 0 0
\(34\) −5.89244 2.18884i −1.01054 0.375383i
\(35\) −6.43844 + 11.1517i −1.08830 + 1.88498i
\(36\) 0 0
\(37\) −1.19716 + 4.46786i −0.196812 + 0.734512i 0.794978 + 0.606638i \(0.207482\pi\)
−0.991790 + 0.127874i \(0.959185\pi\)
\(38\) 3.49598 1.60218i 0.567122 0.259909i
\(39\) 0 0
\(40\) −2.07478 + 7.17181i −0.328051 + 1.13396i
\(41\) 2.06622 7.71126i 0.322690 1.20430i −0.593924 0.804521i \(-0.702422\pi\)
0.916614 0.399774i \(-0.130911\pi\)
\(42\) 0 0
\(43\) −7.03012 4.05884i −1.07208 0.618968i −0.143334 0.989674i \(-0.545782\pi\)
−0.928750 + 0.370707i \(0.879116\pi\)
\(44\) 4.12900 0.306357i 0.622471 0.0461851i
\(45\) 0 0
\(46\) 6.16041 + 7.44092i 0.908303 + 1.09710i
\(47\) 1.87036 + 1.87036i 0.272820 + 0.272820i 0.830234 0.557415i \(-0.188207\pi\)
−0.557415 + 0.830234i \(0.688207\pi\)
\(48\) 0 0
\(49\) 14.5479 8.39921i 2.07826 1.19989i
\(50\) −0.465055 2.74326i −0.0657687 0.387955i
\(51\) 0 0
\(52\) −4.79885 + 5.38248i −0.665480 + 0.746415i
\(53\) 8.22085i 1.12922i 0.825358 + 0.564610i \(0.190974\pi\)
−0.825358 + 0.564610i \(0.809026\pi\)
\(54\) 0 0
\(55\) −4.73233 + 2.73221i −0.638107 + 0.368411i
\(56\) 9.94806 9.56155i 1.32937 1.27772i
\(57\) 0 0
\(58\) 0.180654 0.149565i 0.0237210 0.0196388i
\(59\) −0.352439 1.31532i −0.0458837 0.171240i 0.939182 0.343420i \(-0.111586\pi\)
−0.985065 + 0.172180i \(0.944919\pi\)
\(60\) 0 0
\(61\) 0.601045 + 0.347013i 0.0769559 + 0.0444305i 0.537984 0.842955i \(-0.319186\pi\)
−0.461028 + 0.887385i \(0.652519\pi\)
\(62\) 4.36928 6.15310i 0.554899 0.781445i
\(63\) 0 0
\(64\) 4.27127 6.76434i 0.533908 0.845542i
\(65\) 2.61731 9.15022i 0.324638 1.13495i
\(66\) 0 0
\(67\) 1.26441 4.71883i 0.154472 0.576497i −0.844678 0.535275i \(-0.820208\pi\)
0.999150 0.0412224i \(-0.0131252\pi\)
\(68\) −8.73333 1.65912i −1.05907 0.201198i
\(69\) 0 0
\(70\) −6.34127 + 17.0709i −0.757927 + 2.04037i
\(71\) −2.46409 9.19612i −0.292434 1.09138i −0.943234 0.332129i \(-0.892233\pi\)
0.650800 0.759249i \(-0.274434\pi\)
\(72\) 0 0
\(73\) −11.2670 + 11.2670i −1.31870 + 1.31870i −0.403895 + 0.914805i \(0.632344\pi\)
−0.914805 + 0.403895i \(0.867656\pi\)
\(74\) −0.613136 + 6.51261i −0.0712756 + 0.757075i
\(75\) 0 0
\(76\) 4.49579 3.06032i 0.515703 0.351042i
\(77\) 10.0991 1.15090
\(78\) 0 0
\(79\) 9.91660i 1.11570i 0.829940 + 0.557852i \(0.188374\pi\)
−0.829940 + 0.557852i \(0.811626\pi\)
\(80\) −1.19767 + 10.4902i −0.133904 + 1.17284i
\(81\) 0 0
\(82\) 1.05824 11.2404i 0.116863 1.24129i
\(83\) −3.88441 3.88441i −0.426369 0.426369i 0.461020 0.887390i \(-0.347483\pi\)
−0.887390 + 0.461020i \(0.847483\pi\)
\(84\) 0 0
\(85\) 11.3326 3.03656i 1.22919 0.329361i
\(86\) −10.7616 3.99758i −1.16046 0.431071i
\(87\) 0 0
\(88\) 5.68474 1.40315i 0.605995 0.149576i
\(89\) −13.1559 3.52510i −1.39452 0.373660i −0.518145 0.855293i \(-0.673377\pi\)
−0.876373 + 0.481632i \(0.840044\pi\)
\(90\) 0 0
\(91\) −12.6446 + 12.2267i −1.32552 + 1.28171i
\(92\) 10.3484 + 8.91886i 1.07890 + 0.929856i
\(93\) 0 0
\(94\) 3.04998 + 2.16577i 0.314581 + 0.223382i
\(95\) −3.58888 + 6.21613i −0.368212 + 0.637761i
\(96\) 0 0
\(97\) −1.52421 + 0.408410i −0.154760 + 0.0414678i −0.335367 0.942088i \(-0.608860\pi\)
0.180607 + 0.983555i \(0.442194\pi\)
\(98\) 18.2990 15.1499i 1.84848 1.53037i
\(99\) 0 0
\(100\) −1.29687 3.71505i −0.129687 0.371505i
\(101\) 1.42809 + 2.47353i 0.142101 + 0.246126i 0.928287 0.371863i \(-0.121281\pi\)
−0.786187 + 0.617989i \(0.787948\pi\)
\(102\) 0 0
\(103\) −10.1257 −0.997716 −0.498858 0.866684i \(-0.666247\pi\)
−0.498858 + 0.866684i \(0.666247\pi\)
\(104\) −5.41885 + 8.63922i −0.531362 + 0.847145i
\(105\) 0 0
\(106\) 1.94320 + 11.4625i 0.188740 + 1.11334i
\(107\) −5.08478 8.80709i −0.491564 0.851414i 0.508389 0.861128i \(-0.330241\pi\)
−0.999953 + 0.00971375i \(0.996908\pi\)
\(108\) 0 0
\(109\) −5.06478 + 5.06478i −0.485118 + 0.485118i −0.906761 0.421644i \(-0.861453\pi\)
0.421644 + 0.906761i \(0.361453\pi\)
\(110\) −5.95256 + 4.92818i −0.567554 + 0.469883i
\(111\) 0 0
\(112\) 11.6107 15.6833i 1.09711 1.48194i
\(113\) 0.373640 0.647164i 0.0351491 0.0608801i −0.847916 0.530131i \(-0.822143\pi\)
0.883065 + 0.469251i \(0.155476\pi\)
\(114\) 0 0
\(115\) −17.4160 4.66660i −1.62405 0.435163i
\(116\) 0.216536 0.251243i 0.0201048 0.0233273i
\(117\) 0 0
\(118\) −0.802321 1.75067i −0.0738596 0.161162i
\(119\) −20.9443 5.61202i −1.91996 0.514453i
\(120\) 0 0
\(121\) −5.81481 3.35718i −0.528619 0.305198i
\(122\) 0.920073 + 0.341776i 0.0832995 + 0.0309429i
\(123\) 0 0
\(124\) 4.63773 9.61217i 0.416481 0.863199i
\(125\) −5.66017 5.66017i −0.506261 0.506261i
\(126\) 0 0
\(127\) −8.06962 13.9770i −0.716063 1.24026i −0.962548 0.271111i \(-0.912609\pi\)
0.246485 0.969147i \(-0.420724\pi\)
\(128\) 4.35660 10.4413i 0.385072 0.922886i
\(129\) 0 0
\(130\) 1.48649 13.3770i 0.130374 1.17324i
\(131\) −16.6579 −1.45540 −0.727702 0.685894i \(-0.759412\pi\)
−0.727702 + 0.685894i \(0.759412\pi\)
\(132\) 0 0
\(133\) 11.4883 6.63279i 0.996164 0.575136i
\(134\) 0.647577 6.87843i 0.0559421 0.594206i
\(135\) 0 0
\(136\) −12.5692 0.249012i −1.07780 0.0213526i
\(137\) 0.760062 + 2.83659i 0.0649365 + 0.242346i 0.990763 0.135601i \(-0.0432966\pi\)
−0.925827 + 0.377948i \(0.876630\pi\)
\(138\) 0 0
\(139\) 1.89159 3.27634i 0.160443 0.277895i −0.774585 0.632470i \(-0.782041\pi\)
0.935028 + 0.354575i \(0.115374\pi\)
\(140\) −4.80663 + 25.3013i −0.406234 + 2.13835i
\(141\) 0 0
\(142\) −5.60946 12.2399i −0.470735 1.02715i
\(143\) −7.24123 + 1.81047i −0.605542 + 0.151399i
\(144\) 0 0
\(145\) −0.113298 + 0.422832i −0.00940885 + 0.0351143i
\(146\) −13.0465 + 18.3730i −1.07974 + 1.52056i
\(147\) 0 0
\(148\) 0.684505 + 9.22558i 0.0562660 + 0.758338i
\(149\) −4.90868 18.3194i −0.402134 1.50079i −0.809280 0.587423i \(-0.800143\pi\)
0.407146 0.913363i \(-0.366524\pi\)
\(150\) 0 0
\(151\) 7.95676 + 7.95676i 0.647512 + 0.647512i 0.952391 0.304879i \(-0.0986160\pi\)
−0.304879 + 0.952391i \(0.598616\pi\)
\(152\) 5.54520 5.32975i 0.449775 0.432300i
\(153\) 0 0
\(154\) 14.0813 2.38716i 1.13471 0.192363i
\(155\) 14.0855i 1.13138i
\(156\) 0 0
\(157\) 9.73082i 0.776604i 0.921532 + 0.388302i \(0.126938\pi\)
−0.921532 + 0.388302i \(0.873062\pi\)
\(158\) 2.34403 + 13.8269i 0.186481 + 1.10001i
\(159\) 0 0
\(160\) 0.809682 + 14.9098i 0.0640110 + 1.17873i
\(161\) 23.5628 + 23.5628i 1.85701 + 1.85701i
\(162\) 0 0
\(163\) 6.44596 + 24.0567i 0.504887 + 1.88426i 0.465520 + 0.885038i \(0.345867\pi\)
0.0393670 + 0.999225i \(0.487466\pi\)
\(164\) −1.18141 15.9228i −0.0922529 1.24336i
\(165\) 0 0
\(166\) −6.33428 4.49793i −0.491635 0.349107i
\(167\) −2.58274 + 9.63891i −0.199858 + 0.745881i 0.791097 + 0.611690i \(0.209510\pi\)
−0.990956 + 0.134191i \(0.957157\pi\)
\(168\) 0 0
\(169\) 6.87453 11.0336i 0.528810 0.848740i
\(170\) 15.0835 6.91267i 1.15685 0.530178i
\(171\) 0 0
\(172\) −15.9501 3.03013i −1.21618 0.231046i
\(173\) −5.29984 + 9.17959i −0.402939 + 0.697911i −0.994079 0.108658i \(-0.965345\pi\)
0.591140 + 0.806569i \(0.298678\pi\)
\(174\) 0 0
\(175\) −2.48413 9.27090i −0.187783 0.700814i
\(176\) 7.59467 3.30017i 0.572470 0.248759i
\(177\) 0 0
\(178\) −19.1767 1.80541i −1.43736 0.135321i
\(179\) 13.8149 7.97602i 1.03257 0.596156i 0.114851 0.993383i \(-0.463361\pi\)
0.917720 + 0.397227i \(0.130027\pi\)
\(180\) 0 0
\(181\) −7.36580 −0.547496 −0.273748 0.961801i \(-0.588263\pi\)
−0.273748 + 0.961801i \(0.588263\pi\)
\(182\) −14.7405 + 20.0368i −1.09264 + 1.48523i
\(183\) 0 0
\(184\) 16.5372 + 9.98964i 1.21914 + 0.736446i
\(185\) −6.10468 10.5736i −0.448825 0.777388i
\(186\) 0 0
\(187\) −6.50641 6.50641i −0.475796 0.475796i
\(188\) 4.76458 + 2.29884i 0.347493 + 0.167660i
\(189\) 0 0
\(190\) −3.53472 + 9.51559i −0.256435 + 0.690333i
\(191\) −5.05273 2.91720i −0.365603 0.211081i 0.305933 0.952053i \(-0.401032\pi\)
−0.671536 + 0.740972i \(0.734365\pi\)
\(192\) 0 0
\(193\) 17.5387 + 4.69948i 1.26246 + 0.338276i 0.827139 0.561998i \(-0.189967\pi\)
0.435324 + 0.900274i \(0.356634\pi\)
\(194\) −2.02869 + 0.929738i −0.145652 + 0.0667513i
\(195\) 0 0
\(196\) 21.9336 25.4492i 1.56669 1.81780i
\(197\) 7.77095 + 2.08222i 0.553657 + 0.148352i 0.524791 0.851231i \(-0.324144\pi\)
0.0288665 + 0.999583i \(0.490810\pi\)
\(198\) 0 0
\(199\) −1.64080 + 2.84194i −0.116313 + 0.201460i −0.918304 0.395876i \(-0.870441\pi\)
0.801991 + 0.597336i \(0.203774\pi\)
\(200\) −2.68639 4.87342i −0.189957 0.344603i
\(201\) 0 0
\(202\) 2.57590 + 3.11133i 0.181240 + 0.218912i
\(203\) 0.572067 0.572067i 0.0401512 0.0401512i
\(204\) 0 0
\(205\) 10.5363 + 18.2494i 0.735887 + 1.27459i
\(206\) −14.1185 + 2.39346i −0.983681 + 0.166760i
\(207\) 0 0
\(208\) −5.51352 + 13.3267i −0.382294 + 0.924041i
\(209\) 5.62937 0.389392
\(210\) 0 0
\(211\) 6.16814 + 10.6835i 0.424632 + 0.735484i 0.996386 0.0849408i \(-0.0270701\pi\)
−0.571754 + 0.820425i \(0.693737\pi\)
\(212\) 5.41888 + 15.5231i 0.372170 + 1.06613i
\(213\) 0 0
\(214\) −9.17158 11.0780i −0.626956 0.757276i
\(215\) 20.6973 5.54582i 1.41154 0.378221i
\(216\) 0 0
\(217\) 13.0161 22.5445i 0.883590 1.53042i
\(218\) −5.86473 + 8.25910i −0.397210 + 0.559377i
\(219\) 0 0
\(220\) −7.13487 + 8.27849i −0.481033 + 0.558136i
\(221\) 16.0236 + 0.269216i 1.07786 + 0.0181094i
\(222\) 0 0
\(223\) −24.4285 6.54560i −1.63585 0.438326i −0.680250 0.732980i \(-0.738129\pi\)
−0.955604 + 0.294655i \(0.904795\pi\)
\(224\) 12.4819 24.6120i 0.833979 1.64446i
\(225\) 0 0
\(226\) 0.368001 0.990673i 0.0244791 0.0658986i
\(227\) 21.3233 5.71357i 1.41528 0.379223i 0.531473 0.847075i \(-0.321639\pi\)
0.883807 + 0.467852i \(0.154972\pi\)
\(228\) 0 0
\(229\) −11.7201 11.7201i −0.774485 0.774485i 0.204402 0.978887i \(-0.434475\pi\)
−0.978887 + 0.204402i \(0.934475\pi\)
\(230\) −25.3865 2.39004i −1.67394 0.157595i
\(231\) 0 0
\(232\) 0.242532 0.401497i 0.0159230 0.0263595i
\(233\) 4.91123i 0.321746i −0.986975 0.160873i \(-0.948569\pi\)
0.986975 0.160873i \(-0.0514309\pi\)
\(234\) 0 0
\(235\) −6.98195 −0.455452
\(236\) −1.53250 2.25135i −0.0997576 0.146550i
\(237\) 0 0
\(238\) −30.5296 2.87424i −1.97894 0.186310i
\(239\) −10.2089 + 10.2089i −0.660358 + 0.660358i −0.955465 0.295106i \(-0.904645\pi\)
0.295106 + 0.955465i \(0.404645\pi\)
\(240\) 0 0
\(241\) 0.695205 + 2.59454i 0.0447821 + 0.167129i 0.984695 0.174284i \(-0.0557611\pi\)
−0.939913 + 0.341413i \(0.889094\pi\)
\(242\) −8.90126 3.30651i −0.572195 0.212551i
\(243\) 0 0
\(244\) 1.36366 + 0.259063i 0.0872996 + 0.0165848i
\(245\) −11.4763 + 42.8301i −0.733193 + 2.73631i
\(246\) 0 0
\(247\) −7.04829 + 6.81536i −0.448472 + 0.433651i
\(248\) 4.19441 14.4987i 0.266346 0.920667i
\(249\) 0 0
\(250\) −9.23001 6.55417i −0.583757 0.414522i
\(251\) 2.76530 + 1.59655i 0.174544 + 0.100773i 0.584727 0.811230i \(-0.301202\pi\)
−0.410183 + 0.912003i \(0.634535\pi\)
\(252\) 0 0
\(253\) 3.65992 + 13.6590i 0.230097 + 0.858734i
\(254\) −14.5554 17.5809i −0.913289 1.10313i
\(255\) 0 0
\(256\) 3.60644 15.5883i 0.225402 0.974266i
\(257\) 11.7430 6.77983i 0.732509 0.422914i −0.0868303 0.996223i \(-0.527674\pi\)
0.819339 + 0.573309i \(0.194340\pi\)
\(258\) 0 0
\(259\) 22.5647i 1.40210i
\(260\) −1.08933 19.0032i −0.0675575 1.17853i
\(261\) 0 0
\(262\) −23.2264 + 3.93749i −1.43493 + 0.243259i
\(263\) 15.4394 8.91391i 0.952031 0.549655i 0.0583199 0.998298i \(-0.481426\pi\)
0.893711 + 0.448642i \(0.148092\pi\)
\(264\) 0 0
\(265\) −15.3440 15.3440i −0.942575 0.942575i
\(266\) 14.4506 11.9638i 0.886022 0.733546i
\(267\) 0 0
\(268\) −0.722955 9.74380i −0.0441615 0.595198i
\(269\) −15.1420 8.74224i −0.923225 0.533024i −0.0385623 0.999256i \(-0.512278\pi\)
−0.884662 + 0.466232i \(0.845611\pi\)
\(270\) 0 0
\(271\) −0.868914 + 3.24283i −0.0527828 + 0.196988i −0.987282 0.158976i \(-0.949181\pi\)
0.934500 + 0.355964i \(0.115847\pi\)
\(272\) −17.5844 + 2.62384i −1.06621 + 0.159094i
\(273\) 0 0
\(274\) 1.73027 + 3.77545i 0.104529 + 0.228083i
\(275\) 1.05416 3.93419i 0.0635684 0.237241i
\(276\) 0 0
\(277\) 12.8269 22.2168i 0.770694 1.33488i −0.166490 0.986043i \(-0.553243\pi\)
0.937183 0.348837i \(-0.113423\pi\)
\(278\) 1.86304 5.01538i 0.111738 0.300803i
\(279\) 0 0
\(280\) −0.721412 + 36.4142i −0.0431126 + 2.17616i
\(281\) −13.6396 + 13.6396i −0.813669 + 0.813669i −0.985182 0.171513i \(-0.945135\pi\)
0.171513 + 0.985182i \(0.445135\pi\)
\(282\) 0 0
\(283\) 4.91655 2.83857i 0.292258 0.168736i −0.346701 0.937976i \(-0.612698\pi\)
0.638960 + 0.769240i \(0.279365\pi\)
\(284\) −10.7146 15.7404i −0.635793 0.934020i
\(285\) 0 0
\(286\) −9.66864 + 4.23601i −0.571719 + 0.250481i
\(287\) 38.9453i 2.29887i
\(288\) 0 0
\(289\) 1.37796 + 2.38670i 0.0810565 + 0.140394i
\(290\) −0.0580264 + 0.616344i −0.00340743 + 0.0361930i
\(291\) 0 0
\(292\) −13.8482 + 28.7017i −0.810402 + 1.67964i
\(293\) −5.74107 + 1.53832i −0.335397 + 0.0898693i −0.422587 0.906322i \(-0.638878\pi\)
0.0871901 + 0.996192i \(0.472211\pi\)
\(294\) 0 0
\(295\) 3.11283 + 1.79719i 0.181236 + 0.104637i
\(296\) 3.13511 + 12.7016i 0.182225 + 0.738266i
\(297\) 0 0
\(298\) −11.1745 24.3828i −0.647322 1.41246i
\(299\) −21.1191 12.6709i −1.22135 0.732775i
\(300\) 0 0
\(301\) −38.2516 10.2495i −2.20479 0.590771i
\(302\) 12.9750 + 9.21350i 0.746630 + 0.530177i
\(303\) 0 0
\(304\) 6.47196 8.74211i 0.371192 0.501395i
\(305\) −1.76953 + 0.474143i −0.101323 + 0.0271493i
\(306\) 0 0
\(307\) −4.23600 + 4.23600i −0.241761 + 0.241761i −0.817578 0.575817i \(-0.804684\pi\)
0.575817 + 0.817578i \(0.304684\pi\)
\(308\) 19.0696 6.65693i 1.08659 0.379314i
\(309\) 0 0
\(310\) 3.32946 + 19.6397i 0.189101 + 1.11546i
\(311\) 23.2153 1.31642 0.658209 0.752836i \(-0.271315\pi\)
0.658209 + 0.752836i \(0.271315\pi\)
\(312\) 0 0
\(313\) 23.0016 1.30013 0.650064 0.759880i \(-0.274742\pi\)
0.650064 + 0.759880i \(0.274742\pi\)
\(314\) 2.30012 + 13.5679i 0.129803 + 0.765680i
\(315\) 0 0
\(316\) 6.53665 + 18.7251i 0.367715 + 1.05337i
\(317\) 13.3702 13.3702i 0.750944 0.750944i −0.223711 0.974655i \(-0.571817\pi\)
0.974655 + 0.223711i \(0.0718173\pi\)
\(318\) 0 0
\(319\) 0.331619 0.0888569i 0.0185671 0.00497503i
\(320\) 4.65325 + 20.5977i 0.260125 + 1.15144i
\(321\) 0 0
\(322\) 38.4237 + 27.2844i 2.14127 + 1.52050i
\(323\) −11.6747 3.12822i −0.649596 0.174059i
\(324\) 0 0
\(325\) 3.44317 + 6.20208i 0.190993 + 0.344030i
\(326\) 14.6741 + 32.0190i 0.812723 + 1.77337i
\(327\) 0 0
\(328\) −5.41101 21.9222i −0.298773 1.21045i
\(329\) 11.1749 + 6.45184i 0.616093 + 0.355701i
\(330\) 0 0
\(331\) 15.9030 4.26121i 0.874110 0.234217i 0.206246 0.978500i \(-0.433875\pi\)
0.667864 + 0.744283i \(0.267209\pi\)
\(332\) −9.89520 4.77429i −0.543070 0.262023i
\(333\) 0 0
\(334\) −1.32277 + 14.0502i −0.0723788 + 0.768793i
\(335\) 6.44759 + 11.1676i 0.352270 + 0.610149i
\(336\) 0 0
\(337\) 27.5380i 1.50009i −0.661386 0.750046i \(-0.730031\pi\)
0.661386 0.750046i \(-0.269969\pi\)
\(338\) 6.97723 17.0094i 0.379511 0.925187i
\(339\) 0 0
\(340\) 19.3972 13.2038i 1.05196 0.716078i
\(341\) 9.56698 5.52350i 0.518081 0.299114i
\(342\) 0 0
\(343\) 33.7998 33.7998i 1.82502 1.82502i
\(344\) −22.9558 0.454783i −1.23769 0.0245203i
\(345\) 0 0
\(346\) −5.21985 + 14.0520i −0.280621 + 0.755442i
\(347\) −9.78651 + 16.9507i −0.525367 + 0.909963i 0.474196 + 0.880419i \(0.342739\pi\)
−0.999563 + 0.0295437i \(0.990595\pi\)
\(348\) 0 0
\(349\) 1.58449 5.91341i 0.0848160 0.316538i −0.910463 0.413590i \(-0.864275\pi\)
0.995279 + 0.0970522i \(0.0309414\pi\)
\(350\) −5.65507 12.3394i −0.302276 0.659569i
\(351\) 0 0
\(352\) 9.80933 6.39667i 0.522839 0.340944i
\(353\) −3.59259 + 13.4077i −0.191214 + 0.713621i 0.802000 + 0.597324i \(0.203769\pi\)
−0.993214 + 0.116297i \(0.962897\pi\)
\(354\) 0 0
\(355\) 21.7635 + 12.5652i 1.15509 + 0.666889i
\(356\) −27.1652 + 2.01556i −1.43975 + 0.106825i
\(357\) 0 0
\(358\) 17.3770 14.3866i 0.918404 0.760355i
\(359\) 12.7715 + 12.7715i 0.674055 + 0.674055i 0.958648 0.284593i \(-0.0918586\pi\)
−0.284593 + 0.958648i \(0.591859\pi\)
\(360\) 0 0
\(361\) −10.0507 + 5.80279i −0.528985 + 0.305410i
\(362\) −10.2703 + 1.74109i −0.539794 + 0.0915094i
\(363\) 0 0
\(364\) −15.8168 + 31.4221i −0.829027 + 1.64696i
\(365\) 42.0591i 2.20147i
\(366\) 0 0
\(367\) −1.71553 + 0.990463i −0.0895500 + 0.0517017i −0.544106 0.839016i \(-0.683131\pi\)
0.454556 + 0.890718i \(0.349798\pi\)
\(368\) 25.4194 + 10.0198i 1.32508 + 0.522318i
\(369\) 0 0
\(370\) −11.0112 13.3000i −0.572445 0.691435i
\(371\) 10.3798 + 38.7378i 0.538890 + 2.01116i
\(372\) 0 0
\(373\) 17.8013 + 10.2776i 0.921715 + 0.532152i 0.884182 0.467143i \(-0.154717\pi\)
0.0375332 + 0.999295i \(0.488050\pi\)
\(374\) −10.6100 7.53406i −0.548628 0.389577i
\(375\) 0 0
\(376\) 7.18673 + 2.07909i 0.370627 + 0.107221i
\(377\) −0.307628 + 0.512738i −0.0158436 + 0.0264073i
\(378\) 0 0
\(379\) −1.58993 + 5.93369i −0.0816691 + 0.304793i −0.994663 0.103181i \(-0.967098\pi\)
0.912993 + 0.407974i \(0.133765\pi\)
\(380\) −2.67928 + 14.1033i −0.137444 + 0.723483i
\(381\) 0 0
\(382\) −7.73468 2.87317i −0.395741 0.147004i
\(383\) 3.16308 + 11.8048i 0.161626 + 0.603196i 0.998446 + 0.0557191i \(0.0177451\pi\)
−0.836820 + 0.547477i \(0.815588\pi\)
\(384\) 0 0
\(385\) −18.8497 + 18.8497i −0.960668 + 0.960668i
\(386\) 25.5654 + 2.40688i 1.30124 + 0.122507i
\(387\) 0 0
\(388\) −2.60888 + 1.77588i −0.132446 + 0.0901568i
\(389\) −29.9634 −1.51920 −0.759601 0.650389i \(-0.774606\pi\)
−0.759601 + 0.650389i \(0.774606\pi\)
\(390\) 0 0
\(391\) 30.3610i 1.53542i
\(392\) 24.5669 40.6689i 1.24082 2.05409i
\(393\) 0 0
\(394\) 11.3274 + 1.06643i 0.570665 + 0.0537258i
\(395\) −18.5091 18.5091i −0.931293 0.931293i
\(396\) 0 0
\(397\) −11.2356 + 3.01057i −0.563899 + 0.151096i −0.529497 0.848312i \(-0.677619\pi\)
−0.0344019 + 0.999408i \(0.510953\pi\)
\(398\) −1.61603 + 4.35042i −0.0810044 + 0.218067i
\(399\) 0 0
\(400\) −4.89764 6.16011i −0.244882 0.308005i
\(401\) 24.4339 + 6.54704i 1.22017 + 0.326943i 0.810744 0.585400i \(-0.199063\pi\)
0.409425 + 0.912344i \(0.365729\pi\)
\(402\) 0 0
\(403\) −5.29121 + 18.4983i −0.263574 + 0.921465i
\(404\) 4.32706 + 3.72931i 0.215279 + 0.185540i
\(405\) 0 0
\(406\) 0.662422 0.932865i 0.0328754 0.0462973i
\(407\) −4.78777 + 8.29267i −0.237321 + 0.411052i
\(408\) 0 0
\(409\) 20.0336 5.36799i 0.990599 0.265430i 0.273097 0.961987i \(-0.411952\pi\)
0.717502 + 0.696556i \(0.245285\pi\)
\(410\) 19.0047 + 22.9550i 0.938574 + 1.13367i
\(411\) 0 0
\(412\) −19.1199 + 6.67449i −0.941971 + 0.328829i
\(413\) −3.32148 5.75297i −0.163439 0.283085i
\(414\) 0 0
\(415\) 14.5003 0.711791
\(416\) −4.53751 + 19.8849i −0.222470 + 0.974940i
\(417\) 0 0
\(418\) 7.84914 1.33064i 0.383914 0.0650836i
\(419\) 15.5683 + 26.9651i 0.760560 + 1.31733i 0.942562 + 0.334031i \(0.108409\pi\)
−0.182002 + 0.983298i \(0.558258\pi\)
\(420\) 0 0
\(421\) 0.590979 0.590979i 0.0288026 0.0288026i −0.692559 0.721361i \(-0.743517\pi\)
0.721361 + 0.692559i \(0.243517\pi\)
\(422\) 11.1257 + 13.4383i 0.541589 + 0.654164i
\(423\) 0 0
\(424\) 11.2249 + 20.3632i 0.545129 + 0.988926i
\(425\) −4.37243 + 7.57327i −0.212094 + 0.367357i
\(426\) 0 0
\(427\) 3.27035 + 0.876287i 0.158263 + 0.0424065i
\(428\) −15.4067 13.2783i −0.744709 0.641833i
\(429\) 0 0
\(430\) 27.5477 12.6249i 1.32847 0.608829i
\(431\) −8.41002 2.25346i −0.405096 0.108545i 0.0505166 0.998723i \(-0.483913\pi\)
−0.455613 + 0.890178i \(0.650580\pi\)
\(432\) 0 0
\(433\) −8.71099 5.02929i −0.418624 0.241692i 0.275865 0.961196i \(-0.411036\pi\)
−0.694488 + 0.719504i \(0.744369\pi\)
\(434\) 12.8196 34.5109i 0.615363 1.65658i
\(435\) 0 0
\(436\) −6.22507 + 12.9021i −0.298127 + 0.617898i
\(437\) 13.1342 + 13.1342i 0.628296 + 0.628296i
\(438\) 0 0
\(439\) 3.83901 + 6.64936i 0.183226 + 0.317357i 0.942977 0.332857i \(-0.108013\pi\)
−0.759751 + 0.650214i \(0.774679\pi\)
\(440\) −7.99147 + 13.2294i −0.380978 + 0.630685i
\(441\) 0 0
\(442\) 22.4056 3.41218i 1.06573 0.162301i
\(443\) 6.09878 0.289762 0.144881 0.989449i \(-0.453720\pi\)
0.144881 + 0.989449i \(0.453720\pi\)
\(444\) 0 0
\(445\) 31.1346 17.9756i 1.47592 0.852123i
\(446\) −35.6084 3.35239i −1.68610 0.158740i
\(447\) 0 0
\(448\) 11.5860 37.2674i 0.547389 1.76072i
\(449\) 6.24854 + 23.3199i 0.294887 + 1.10053i 0.941307 + 0.337551i \(0.109599\pi\)
−0.646421 + 0.762981i \(0.723735\pi\)
\(450\) 0 0
\(451\) 8.26340 14.3126i 0.389108 0.673955i
\(452\) 0.278942 1.46830i 0.0131203 0.0690630i
\(453\) 0 0
\(454\) 28.3810 13.0068i 1.33199 0.610441i
\(455\) 0.779944 46.4217i 0.0365643 2.17628i
\(456\) 0 0
\(457\) −5.14536 + 19.2027i −0.240690 + 0.898266i 0.734811 + 0.678272i \(0.237271\pi\)
−0.975501 + 0.219995i \(0.929396\pi\)
\(458\) −19.1119 13.5712i −0.893040 0.634142i
\(459\) 0 0
\(460\) −35.9619 + 2.66824i −1.67673 + 0.124407i
\(461\) 3.19035 + 11.9065i 0.148589 + 0.554543i 0.999569 + 0.0293448i \(0.00934209\pi\)
−0.850980 + 0.525198i \(0.823991\pi\)
\(462\) 0 0
\(463\) −5.89215 5.89215i −0.273832 0.273832i 0.556809 0.830641i \(-0.312026\pi\)
−0.830641 + 0.556809i \(0.812026\pi\)
\(464\) 0.243264 0.617143i 0.0112933 0.0286501i
\(465\) 0 0
\(466\) −1.16089 6.84783i −0.0537771 0.317220i
\(467\) 23.5141i 1.08810i −0.839051 0.544052i \(-0.816889\pi\)
0.839051 0.544052i \(-0.183111\pi\)
\(468\) 0 0
\(469\) 23.8322i 1.10047i
\(470\) −9.73506 + 1.65035i −0.449045 + 0.0761251i
\(471\) 0 0
\(472\) −2.66896 2.77685i −0.122849 0.127815i
\(473\) −11.8830 11.8830i −0.546379 0.546379i
\(474\) 0 0
\(475\) −1.38469 5.16773i −0.0635339 0.237112i
\(476\) −43.2474 + 3.20880i −1.98224 + 0.147075i
\(477\) 0 0
\(478\) −11.8213 + 16.6476i −0.540696 + 0.761443i
\(479\) 0.824761 3.07805i 0.0376843 0.140640i −0.944521 0.328452i \(-0.893473\pi\)
0.982205 + 0.187812i \(0.0601397\pi\)
\(480\) 0 0
\(481\) −4.04520 16.1793i −0.184445 0.737715i
\(482\) 1.58262 + 3.45329i 0.0720864 + 0.157293i
\(483\) 0 0
\(484\) −13.1928 2.50631i −0.599672 0.113923i
\(485\) 2.08261 3.60718i 0.0945663 0.163794i
\(486\) 0 0
\(487\) 4.40943 + 16.4562i 0.199810 + 0.745702i 0.990969 + 0.134091i \(0.0428115\pi\)
−0.791159 + 0.611611i \(0.790522\pi\)
\(488\) 1.96262 + 0.0388820i 0.0888435 + 0.00176010i
\(489\) 0 0
\(490\) −5.87768 + 62.4315i −0.265527 + 2.82037i
\(491\) −10.5370 + 6.08352i −0.475527 + 0.274546i −0.718551 0.695475i \(-0.755194\pi\)
0.243024 + 0.970020i \(0.421861\pi\)
\(492\) 0 0
\(493\) −0.737117 −0.0331981
\(494\) −8.21659 + 11.1688i −0.369682 + 0.502509i
\(495\) 0 0
\(496\) 2.42124 21.2073i 0.108717 0.952234i
\(497\) −23.2223 40.2222i −1.04166 1.80421i
\(498\) 0 0
\(499\) −28.9374 28.9374i −1.29542 1.29542i −0.931389 0.364027i \(-0.881402\pi\)
−0.364027 0.931389i \(-0.618598\pi\)
\(500\) −14.4188 6.95687i −0.644829 0.311121i
\(501\) 0 0
\(502\) 4.23309 + 1.57245i 0.188932 + 0.0701818i
\(503\) 21.8800 + 12.6324i 0.975580 + 0.563252i 0.900933 0.433958i \(-0.142884\pi\)
0.0746475 + 0.997210i \(0.476217\pi\)
\(504\) 0 0
\(505\) −7.28228 1.95128i −0.324057 0.0868309i
\(506\) 8.33174 + 18.1799i 0.370391 + 0.808196i
\(507\) 0 0
\(508\) −24.4506 21.0729i −1.08482 0.934960i
\(509\) 18.9678 + 5.08241i 0.840734 + 0.225274i 0.653391 0.757021i \(-0.273346\pi\)
0.187343 + 0.982295i \(0.440012\pi\)
\(510\) 0 0
\(511\) −38.8657 + 67.3174i −1.71932 + 2.97795i
\(512\) 1.34387 22.5875i 0.0593911 0.998235i
\(513\) 0 0
\(514\) 14.7709 12.2290i 0.651518 0.539398i
\(515\) 18.8994 18.8994i 0.832806 0.832806i
\(516\) 0 0
\(517\) 2.73790 + 4.74218i 0.120413 + 0.208561i
\(518\) 5.33372 + 31.4624i 0.234350 + 1.38238i
\(519\) 0 0
\(520\) −6.01074 26.2390i −0.263588 1.15066i
\(521\) 8.50132 0.372450 0.186225 0.982507i \(-0.440375\pi\)
0.186225 + 0.982507i \(0.440375\pi\)
\(522\) 0 0
\(523\) −22.1486 38.3625i −0.968490 1.67747i −0.699932 0.714209i \(-0.746786\pi\)
−0.268558 0.963264i \(-0.586547\pi\)
\(524\) −31.4543 + 10.9802i −1.37409 + 0.479674i
\(525\) 0 0
\(526\) 19.4204 16.0783i 0.846768 0.701048i
\(527\) −22.9102 + 6.13877i −0.997984 + 0.267409i
\(528\) 0 0
\(529\) −11.8295 + 20.4893i −0.514326 + 0.890839i
\(530\) −25.0214 17.7675i −1.08686 0.771772i
\(531\) 0 0
\(532\) 17.3208 20.0971i 0.750952 0.871319i
\(533\) 6.98176 + 27.9246i 0.302414 + 1.20955i
\(534\) 0 0
\(535\) 25.9288 + 6.94761i 1.12100 + 0.300371i
\(536\) −3.31121 13.4151i −0.143023 0.579444i
\(537\) 0 0
\(538\) −23.1792 8.61030i −0.999328 0.371216i
\(539\) 33.5907 9.00061i 1.44686 0.387684i
\(540\) 0 0
\(541\) 12.5837 + 12.5837i 0.541018 + 0.541018i 0.923827 0.382810i \(-0.125044\pi\)
−0.382810 + 0.923827i \(0.625044\pi\)
\(542\) −0.445022 + 4.72693i −0.0191153 + 0.203039i
\(543\) 0 0
\(544\) −23.8980 + 7.81496i −1.02462 + 0.335064i
\(545\) 18.9065i 0.809867i
\(546\) 0 0
\(547\) −2.39098 −0.102231 −0.0511154 0.998693i \(-0.516278\pi\)
−0.0511154 + 0.998693i \(0.516278\pi\)
\(548\) 3.30496 + 4.85520i 0.141181 + 0.207404i
\(549\) 0 0
\(550\) 0.539899 5.73470i 0.0230214 0.244528i
\(551\) 0.318878 0.318878i 0.0135847 0.0135847i
\(552\) 0 0
\(553\) 12.5208 + 46.7284i 0.532440 + 1.98709i
\(554\) 12.6333 34.0093i 0.536738 1.44492i
\(555\) 0 0
\(556\) 1.41217 7.43342i 0.0598894 0.315247i
\(557\) 3.10542 11.5896i 0.131581 0.491067i −0.868408 0.495851i \(-0.834856\pi\)
0.999989 + 0.00478427i \(0.00152289\pi\)
\(558\) 0 0
\(559\) 29.2646 + 0.491682i 1.23776 + 0.0207959i
\(560\) 7.60150 + 50.9436i 0.321222 + 2.15276i
\(561\) 0 0
\(562\) −15.7939 + 22.2420i −0.666225 + 0.938222i
\(563\) 20.5535 + 11.8665i 0.866225 + 0.500115i 0.866092 0.499885i \(-0.166624\pi\)
0.000133111 1.00000i \(0.499958\pi\)
\(564\) 0 0
\(565\) 0.510525 + 1.90531i 0.0214779 + 0.0801568i
\(566\) 6.18428 5.12002i 0.259944 0.215211i
\(567\) 0 0
\(568\) −18.6602 19.4145i −0.782963 0.814613i
\(569\) 26.9109 15.5370i 1.12816 0.651346i 0.184692 0.982796i \(-0.440871\pi\)
0.943473 + 0.331450i \(0.107538\pi\)
\(570\) 0 0
\(571\) 10.8606i 0.454500i −0.973836 0.227250i \(-0.927027\pi\)
0.973836 0.227250i \(-0.0729735\pi\)
\(572\) −12.4799 + 8.19178i −0.521811 + 0.342515i
\(573\) 0 0
\(574\) −9.20567 54.3022i −0.384237 2.26653i
\(575\) 11.6386 6.71958i 0.485365 0.280226i
\(576\) 0 0
\(577\) 24.2438 + 24.2438i 1.00928 + 1.00928i 0.999956 + 0.00932743i \(0.00296906\pi\)
0.00932743 + 0.999956i \(0.497031\pi\)
\(578\) 2.48547 + 3.00211i 0.103382 + 0.124871i
\(579\) 0 0
\(580\) 0.0647806 + 0.873097i 0.00268987 + 0.0362534i
\(581\) −23.2084 13.3993i −0.962845 0.555899i
\(582\) 0 0
\(583\) −4.40474 + 16.4387i −0.182426 + 0.680822i
\(584\) −12.5244 + 43.2927i −0.518264 + 1.79146i
\(585\) 0 0
\(586\) −7.64127 + 3.50194i −0.315658 + 0.144664i
\(587\) −0.397645 + 1.48403i −0.0164125 + 0.0612525i −0.973646 0.228063i \(-0.926761\pi\)
0.957234 + 0.289315i \(0.0934276\pi\)
\(588\) 0 0
\(589\) 7.25536 12.5666i 0.298952 0.517800i
\(590\) 4.76509 + 1.77007i 0.196176 + 0.0728726i
\(591\) 0 0
\(592\) 7.37368 + 16.9690i 0.303056 + 0.697424i
\(593\) −4.86193 + 4.86193i −0.199656 + 0.199656i −0.799852 0.600197i \(-0.795089\pi\)
0.600197 + 0.799852i \(0.295089\pi\)
\(594\) 0 0
\(595\) 49.5667 28.6174i 2.03204 1.17320i
\(596\) −21.3443 31.3561i −0.874297 1.28440i
\(597\) 0 0
\(598\) −32.4418 12.6752i −1.32665 0.518328i
\(599\) 4.73413i 0.193431i 0.995312 + 0.0967156i \(0.0308337\pi\)
−0.995312 + 0.0967156i \(0.969166\pi\)
\(600\) 0 0
\(601\) −5.84939 10.1314i −0.238602 0.413270i 0.721712 0.692194i \(-0.243356\pi\)
−0.960313 + 0.278924i \(0.910022\pi\)
\(602\) −55.7577 5.24937i −2.27252 0.213948i
\(603\) 0 0
\(604\) 20.2692 + 9.77959i 0.824742 + 0.397926i
\(605\) 17.1193 4.58710i 0.695998 0.186492i
\(606\) 0 0
\(607\) 5.29055 + 3.05450i 0.214737 + 0.123978i 0.603511 0.797355i \(-0.293768\pi\)
−0.388774 + 0.921333i \(0.627101\pi\)
\(608\) 6.95757 13.7191i 0.282167 0.556383i
\(609\) 0 0
\(610\) −2.35521 + 1.07938i −0.0953596 + 0.0437027i
\(611\) −9.16926 2.62276i −0.370948 0.106105i
\(612\) 0 0
\(613\) 34.2679 + 9.18205i 1.38407 + 0.370860i 0.872597 0.488442i \(-0.162434\pi\)
0.511470 + 0.859301i \(0.329101\pi\)
\(614\) −4.90505 + 6.90762i −0.197952 + 0.278769i
\(615\) 0 0
\(616\) 25.0156 13.7895i 1.00791 0.555593i
\(617\) −24.2158 + 6.48861i −0.974892 + 0.261221i −0.710892 0.703301i \(-0.751709\pi\)
−0.264000 + 0.964523i \(0.585042\pi\)
\(618\) 0 0
\(619\) −10.1532 + 10.1532i −0.408091 + 0.408091i −0.881072 0.472982i \(-0.843178\pi\)
0.472982 + 0.881072i \(0.343178\pi\)
\(620\) 9.28466 + 26.5971i 0.372881 + 1.06816i
\(621\) 0 0
\(622\) 32.3695 5.48749i 1.29790 0.220028i
\(623\) −66.4430 −2.66198
\(624\) 0 0
\(625\) 30.9664 1.23866
\(626\) 32.0716 5.43699i 1.28184 0.217306i
\(627\) 0 0
\(628\) 6.41420 + 18.3743i 0.255954 + 0.733213i
\(629\) 14.5375 14.5375i 0.579648 0.579648i
\(630\) 0 0
\(631\) −13.5488 + 3.63038i −0.539368 + 0.144523i −0.518211 0.855253i \(-0.673402\pi\)
−0.0211573 + 0.999776i \(0.506735\pi\)
\(632\) 13.5403 + 24.5636i 0.538604 + 0.977088i
\(633\) 0 0
\(634\) 15.4819 21.8027i 0.614866 0.865895i
\(635\) 41.1494 + 11.0260i 1.63297 + 0.437552i
\(636\) 0 0
\(637\) −31.1606 + 51.9369i −1.23463 + 2.05781i
\(638\) 0.441379 0.202281i 0.0174744 0.00800838i
\(639\) 0 0
\(640\) 11.3569 + 27.6198i 0.448920 + 1.09177i
\(641\) 16.2594 + 9.38735i 0.642206 + 0.370778i 0.785464 0.618908i \(-0.212424\pi\)
−0.143258 + 0.989685i \(0.545758\pi\)
\(642\) 0 0
\(643\) 37.3113 9.99754i 1.47142 0.394265i 0.567999 0.823029i \(-0.307718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(644\) 60.0243 + 28.9608i 2.36529 + 1.14122i
\(645\) 0 0
\(646\) −17.0177 1.60214i −0.669551 0.0630355i
\(647\) 22.8502 + 39.5777i 0.898333 + 1.55596i 0.829624 + 0.558322i \(0.188555\pi\)
0.0687090 + 0.997637i \(0.478112\pi\)
\(648\) 0 0
\(649\) 2.81900i 0.110655i
\(650\) 6.26689 + 7.83381i 0.245808 + 0.307267i
\(651\) 0 0
\(652\) 28.0289 + 41.1761i 1.09769 + 1.61258i
\(653\) 17.6262 10.1765i 0.689767 0.398237i −0.113758 0.993509i \(-0.536289\pi\)
0.803525 + 0.595271i \(0.202955\pi\)
\(654\) 0 0
\(655\) 31.0915 31.0915i 1.21484 1.21484i
\(656\) −12.7265 29.2875i −0.496887 1.14349i
\(657\) 0 0
\(658\) 17.1064 + 6.35446i 0.666879 + 0.247723i
\(659\) 2.92527 5.06672i 0.113952 0.197371i −0.803408 0.595429i \(-0.796982\pi\)
0.917361 + 0.398057i \(0.130316\pi\)
\(660\) 0 0
\(661\) 9.08145 33.8924i 0.353227 1.31826i −0.529473 0.848327i \(-0.677610\pi\)
0.882701 0.469936i \(-0.155723\pi\)
\(662\) 21.1667 9.70056i 0.822667 0.377023i
\(663\) 0 0
\(664\) −14.9256 4.31792i −0.579225 0.167568i
\(665\) −9.06274 + 33.8226i −0.351438 + 1.31158i
\(666\) 0 0
\(667\) 0.981038 + 0.566403i 0.0379860 + 0.0219312i
\(668\) 1.47674 + 19.9032i 0.0571369 + 0.770076i
\(669\) 0 0
\(670\) 11.6297 + 14.0471i 0.449296 + 0.542687i
\(671\) 1.01594 + 1.01594i 0.0392200 + 0.0392200i
\(672\) 0 0
\(673\) −36.8546 + 21.2780i −1.42064 + 0.820207i −0.996353 0.0853213i \(-0.972808\pi\)
−0.424286 + 0.905528i \(0.639475\pi\)
\(674\) −6.50928 38.3968i −0.250728 1.47899i
\(675\) 0 0
\(676\) 5.70792 25.3657i 0.219535 0.975605i
\(677\) 28.9422i 1.11234i −0.831069 0.556169i \(-0.812271\pi\)
0.831069 0.556169i \(-0.187729\pi\)
\(678\) 0 0
\(679\) −6.66661 + 3.84897i −0.255841 + 0.147710i
\(680\) 23.9249 22.9954i 0.917478 0.881832i
\(681\) 0 0
\(682\) 12.0338 9.96291i 0.460798 0.381499i
\(683\) −8.32432 31.0668i −0.318521 1.18874i −0.920666 0.390351i \(-0.872354\pi\)
0.602145 0.798387i \(-0.294313\pi\)
\(684\) 0 0
\(685\) −6.71306 3.87578i −0.256493 0.148086i
\(686\) 39.1384 55.1172i 1.49431 2.10438i
\(687\) 0 0
\(688\) −32.1152 + 4.79204i −1.22438 + 0.182695i
\(689\) −14.3870 25.9149i −0.548103 0.987281i
\(690\) 0 0
\(691\) −0.974151 + 3.63558i −0.0370584 + 0.138304i −0.981977 0.189003i \(-0.939474\pi\)
0.944918 + 0.327307i \(0.106141\pi\)
\(692\) −3.95660 + 20.8269i −0.150407 + 0.791718i
\(693\) 0 0
\(694\) −9.63880 + 25.9480i −0.365884 + 0.984973i
\(695\) 2.58459 + 9.64581i 0.0980389 + 0.365886i
\(696\) 0 0
\(697\) −25.0908 + 25.0908i −0.950383 + 0.950383i
\(698\) 0.811513 8.61972i 0.0307162 0.326261i
\(699\) 0 0
\(700\) −10.8017 15.8684i −0.408266 0.599768i
\(701\) 26.5127 1.00137 0.500685 0.865630i \(-0.333082\pi\)
0.500685 + 0.865630i \(0.333082\pi\)
\(702\) 0 0
\(703\) 12.5779i 0.474385i
\(704\) 12.1653 11.2377i 0.458498 0.423536i
\(705\) 0 0
\(706\) −1.83998 + 19.5438i −0.0692484 + 0.735542i
\(707\) 9.85248 + 9.85248i 0.370541 + 0.370541i
\(708\) 0 0
\(709\) −5.29377 + 1.41846i −0.198812 + 0.0532715i −0.356851 0.934161i \(-0.616150\pi\)
0.158039 + 0.987433i \(0.449483\pi\)
\(710\) 33.3153 + 12.3755i 1.25030 + 0.464445i
\(711\) 0 0
\(712\) −37.4006 + 9.23150i −1.40165 + 0.345965i
\(713\) 35.2085 + 9.43410i 1.31857 + 0.353310i
\(714\) 0 0
\(715\) 10.1364 16.8948i 0.379079 0.631828i
\(716\) 20.8285 24.1670i 0.778397 0.903163i
\(717\) 0 0
\(718\) 20.8264 + 14.7887i 0.777236 + 0.551910i
\(719\) 10.1805 17.6332i 0.379670 0.657608i −0.611344 0.791365i \(-0.709371\pi\)
0.991014 + 0.133757i \(0.0427041\pi\)
\(720\) 0 0
\(721\) −47.7137 + 12.7849i −1.77695 + 0.476133i
\(722\) −12.6423 + 10.4667i −0.470497 + 0.389529i
\(723\) 0 0
\(724\) −13.9085 + 4.85526i −0.516906 + 0.180444i
\(725\) −0.163140 0.282568i −0.00605888 0.0104943i
\(726\) 0 0
\(727\) 16.4107 0.608639 0.304320 0.952570i \(-0.401571\pi\)
0.304320 + 0.952570i \(0.401571\pi\)
\(728\) −14.6264 + 47.5511i −0.542089 + 1.76236i
\(729\) 0 0
\(730\) −9.94168 58.6438i −0.367958 2.17050i
\(731\) 18.0406 + 31.2472i 0.667256 + 1.15572i
\(732\) 0 0
\(733\) −26.6302 + 26.6302i −0.983610 + 0.983610i −0.999868 0.0162577i \(-0.994825\pi\)
0.0162577 + 0.999868i \(0.494825\pi\)
\(734\) −2.15788 + 1.78653i −0.0796488 + 0.0659420i
\(735\) 0 0
\(736\) 37.8112 + 7.96228i 1.39374 + 0.293494i
\(737\) 5.05671 8.75848i 0.186266 0.322623i
\(738\) 0 0
\(739\) −16.2372 4.35076i −0.597296 0.160045i −0.0525107 0.998620i \(-0.516722\pi\)
−0.544786 + 0.838575i \(0.683389\pi\)
\(740\) −18.4969 15.9417i −0.679960 0.586029i
\(741\) 0 0
\(742\) 23.6293 + 51.5593i 0.867459 + 1.89280i
\(743\) −13.7938 3.69604i −0.506046 0.135594i −0.00324119 0.999995i \(-0.501032\pi\)
−0.502804 + 0.864400i \(0.667698\pi\)
\(744\) 0 0
\(745\) 43.3546 + 25.0308i 1.58839 + 0.917058i
\(746\) 27.2500 + 10.1225i 0.997694 + 0.370609i
\(747\) 0 0
\(748\) −16.5745 7.99697i −0.606025 0.292398i
\(749\) −35.0801 35.0801i −1.28180 1.28180i
\(750\) 0 0
\(751\) −20.9053 36.2090i −0.762844 1.32129i −0.941379 0.337351i \(-0.890469\pi\)
0.178534 0.983934i \(-0.442864\pi\)
\(752\) 10.5120 + 1.20016i 0.383335 + 0.0437654i
\(753\) 0 0
\(754\) −0.307734 + 0.787636i −0.0112070 + 0.0286840i
\(755\) −29.7022 −1.08097
\(756\) 0 0
\(757\) −33.0464 + 19.0794i −1.20109 + 0.693451i −0.960798 0.277249i \(-0.910577\pi\)
−0.240294 + 0.970700i \(0.577244\pi\)
\(758\) −0.814296 + 8.64928i −0.0295766 + 0.314156i
\(759\) 0 0
\(760\) −0.402125 + 20.2978i −0.0145866 + 0.736279i
\(761\) 0.805403 + 3.00580i 0.0291958 + 0.108960i 0.978986 0.203927i \(-0.0653705\pi\)
−0.949790 + 0.312887i \(0.898704\pi\)
\(762\) 0 0
\(763\) −17.4711 + 30.2608i −0.632495 + 1.09551i
\(764\) −11.4638 2.17784i −0.414744 0.0787914i
\(765\) 0 0
\(766\) 7.20070 + 15.7120i 0.260172 + 0.567697i
\(767\) 3.41291 + 3.52955i 0.123233 + 0.127445i
\(768\) 0 0
\(769\) 2.20764 8.23902i 0.0796094 0.297106i −0.914629 0.404293i \(-0.867518\pi\)
0.994239 + 0.107187i \(0.0341842\pi\)
\(770\) −21.8269 + 30.7380i −0.786586 + 1.10772i
\(771\) 0 0
\(772\) 36.2152 2.68704i 1.30341 0.0967086i
\(773\) 7.00923 + 26.1588i 0.252105 + 0.940867i 0.969678 + 0.244385i \(0.0785860\pi\)
−0.717574 + 0.696483i \(0.754747\pi\)
\(774\) 0 0
\(775\) −7.42379 7.42379i −0.266670 0.266670i
\(776\) −3.21784 + 3.09282i −0.115514 + 0.111026i
\(777\) 0 0
\(778\) −41.7785 + 7.08257i −1.49783 + 0.253922i
\(779\) 21.7087i 0.777794i
\(780\) 0 0
\(781\) 19.7092i 0.705250i
\(782\) −7.17657 42.3330i −0.256633 1.51382i
\(783\) 0 0
\(784\) 24.6410 62.5124i 0.880037 2.23259i
\(785\) −18.1623 18.1623i −0.648241 0.648241i
\(786\) 0 0
\(787\) −2.25972 8.43338i −0.0805502 0.300617i 0.913884 0.405975i \(-0.133068\pi\)
−0.994434 + 0.105357i \(0.966401\pi\)
\(788\) 16.0461 1.19056i 0.571617 0.0424119i
\(789\) 0 0
\(790\) −30.1826 21.4325i −1.07385 0.762534i
\(791\) 0.943526 3.52129i 0.0335479 0.125203i
\(792\) 0 0
\(793\) −2.50199 0.0420367i −0.0888484 0.00149277i
\(794\) −14.9544 + 6.85351i −0.530712 + 0.243222i
\(795\) 0 0
\(796\) −1.22494 + 6.44786i −0.0434168 + 0.228538i
\(797\) −15.5889 + 27.0008i −0.552188 + 0.956418i 0.445928 + 0.895069i \(0.352874\pi\)
−0.998116 + 0.0613490i \(0.980460\pi\)
\(798\) 0 0
\(799\) −3.04288 11.3562i −0.107649 0.401752i
\(800\) −8.28497 7.43148i −0.292918 0.262743i
\(801\) 0 0
\(802\) 35.6162 + 3.35312i 1.25765 + 0.118403i
\(803\) −28.5667 + 16.4930i −1.00810 + 0.582026i
\(804\) 0 0
\(805\) −87.9587 −3.10014
\(806\) −3.00512 + 27.0432i −0.105851 + 0.952556i
\(807\) 0 0
\(808\) 6.91482 + 4.17704i 0.243263 + 0.146948i
\(809\) −3.86999 6.70302i −0.136062 0.235666i 0.789941 0.613183i \(-0.210111\pi\)
−0.926003 + 0.377517i \(0.876778\pi\)
\(810\) 0 0
\(811\) 7.65096 + 7.65096i 0.268661 + 0.268661i 0.828561 0.559899i \(-0.189160\pi\)
−0.559899 + 0.828561i \(0.689160\pi\)
\(812\) 0.703122 1.45729i 0.0246748 0.0511409i
\(813\) 0 0
\(814\) −4.71551 + 12.6943i −0.165279 + 0.444936i
\(815\) −56.9323 32.8699i −1.99425 1.15138i
\(816\) 0 0
\(817\) −21.3220 5.71322i −0.745963 0.199880i
\(818\) 26.6644 12.2201i 0.932300 0.427267i
\(819\) 0 0
\(820\) 31.9246 + 27.5144i 1.11485 + 0.960844i
\(821\) 2.11509 + 0.566738i 0.0738173 + 0.0197793i 0.295539 0.955331i \(-0.404501\pi\)
−0.221721 + 0.975110i \(0.571168\pi\)
\(822\) 0 0
\(823\) 22.8632 39.6002i 0.796960 1.38037i −0.124627 0.992204i \(-0.539774\pi\)
0.921587 0.388171i \(-0.126893\pi\)
\(824\) −25.0816 + 13.8258i −0.873759 + 0.481646i
\(825\) 0 0
\(826\) −5.99106 7.23637i −0.208456 0.251786i
\(827\) −1.50831 + 1.50831i −0.0524490 + 0.0524490i −0.732845 0.680396i \(-0.761808\pi\)
0.680396 + 0.732845i \(0.261808\pi\)
\(828\) 0 0
\(829\) −2.20284 3.81543i −0.0765077 0.132515i 0.825233 0.564792i \(-0.191044\pi\)
−0.901741 + 0.432277i \(0.857710\pi\)
\(830\) 20.2180 3.42750i 0.701778 0.118970i
\(831\) 0 0
\(832\) −1.62645 + 28.7985i −0.0563871 + 0.998409i
\(833\) −74.6650 −2.58699
\(834\) 0 0
\(835\) −13.1702 22.8114i −0.455772 0.789420i
\(836\) 10.6297 3.71067i 0.367635 0.128336i
\(837\) 0 0
\(838\) 28.0810 + 33.9180i 0.970042 + 1.17168i
\(839\) 9.23752 2.47519i 0.318915 0.0854529i −0.0958107 0.995400i \(-0.530544\pi\)
0.414725 + 0.909947i \(0.363878\pi\)
\(840\) 0 0
\(841\) −14.4862 + 25.0909i −0.499526 + 0.865204i
\(842\) 0.684322 0.963707i 0.0235833 0.0332115i
\(843\) 0 0
\(844\) 18.6892 + 16.1074i 0.643309 + 0.554440i
\(845\) 7.76283 + 33.4251i 0.267050 + 1.14986i
\(846\) 0 0
\(847\) −31.6390 8.47765i −1.08713 0.291295i
\(848\) 20.4644 + 25.7396i 0.702752 + 0.883900i
\(849\) 0 0
\(850\) −4.30644 + 11.5931i −0.147710 + 0.397640i
\(851\) −30.5188 + 8.17749i −1.04617 + 0.280321i
\(852\) 0 0
\(853\) −28.6500 28.6500i −0.980956 0.980956i 0.0188661 0.999822i \(-0.493994\pi\)
−0.999822 + 0.0188661i \(0.993994\pi\)
\(854\) 4.76704 + 0.448798i 0.163125 + 0.0153575i
\(855\) 0 0
\(856\) −24.6205 14.8725i −0.841510 0.508332i
\(857\) 11.6602i 0.398306i 0.979968 + 0.199153i \(0.0638191\pi\)
−0.979968 + 0.199153i \(0.936181\pi\)
\(858\) 0 0
\(859\) 29.0257 0.990343 0.495172 0.868795i \(-0.335105\pi\)
0.495172 + 0.868795i \(0.335105\pi\)
\(860\) 35.4261 24.1148i 1.20802 0.822307i
\(861\) 0 0
\(862\) −12.2589 1.15413i −0.417540 0.0393098i
\(863\) −8.05746 + 8.05746i −0.274279 + 0.274279i −0.830820 0.556541i \(-0.812128\pi\)
0.556541 + 0.830820i \(0.312128\pi\)
\(864\) 0 0
\(865\) −7.24145 27.0255i −0.246217 0.918894i
\(866\) −13.3347 4.95339i −0.453132 0.168323i
\(867\) 0 0
\(868\) 9.71718 51.1495i 0.329823 1.73613i
\(869\) −5.31333 + 19.8296i −0.180242 + 0.672673i
\(870\) 0 0
\(871\) 4.27243 + 17.0882i 0.144766 + 0.579011i
\(872\) −5.63002 + 19.4611i −0.190657 + 0.659036i
\(873\) 0 0
\(874\) 21.4179 + 15.2087i 0.724472 + 0.514443i
\(875\) −33.8181 19.5249i −1.14326 0.660062i
\(876\) 0 0
\(877\) 1.68176 + 6.27643i 0.0567891 + 0.211940i 0.988490 0.151287i \(-0.0483417\pi\)
−0.931701 + 0.363227i \(0.881675\pi\)
\(878\) 6.92454 + 8.36389i 0.233692 + 0.282268i
\(879\) 0 0
\(880\) −8.01559 + 20.3349i −0.270205 + 0.685490i
\(881\) −16.3109 + 9.41711i −0.549528 + 0.317270i −0.748932 0.662647i \(-0.769433\pi\)
0.199403 + 0.979917i \(0.436100\pi\)
\(882\) 0 0
\(883\) 7.15931i 0.240930i 0.992718 + 0.120465i \(0.0384385\pi\)
−0.992718 + 0.120465i \(0.961561\pi\)
\(884\) 30.4340 10.0538i 1.02361 0.338145i
\(885\) 0 0
\(886\) 8.50365 1.44160i 0.285686 0.0484314i
\(887\) 5.21027 3.00815i 0.174944 0.101004i −0.409971 0.912098i \(-0.634461\pi\)
0.584915 + 0.811095i \(0.301128\pi\)
\(888\) 0 0
\(889\) −55.6727 55.6727i −1.86720 1.86720i
\(890\) 39.1626 32.4231i 1.31273 1.08682i
\(891\) 0 0
\(892\) −50.4418 + 3.74260i −1.68892 + 0.125312i
\(893\) 6.22906 + 3.59635i 0.208447 + 0.120347i
\(894\) 0 0
\(895\) −10.8981 + 40.6721i −0.364282 + 1.35952i
\(896\) 7.34559 54.7014i 0.245399 1.82744i
\(897\) 0 0
\(898\) 14.2247 + 31.0383i 0.474684 + 1.03576i
\(899\) 0.229045 0.854807i 0.00763907 0.0285094i
\(900\) 0 0
\(901\) 18.2699 31.6443i 0.608658 1.05423i
\(902\) 8.13868 21.9096i 0.270989 0.729511i
\(903\) 0 0
\(904\) 0.0418655 2.11321i 0.00139242 0.0702845i
\(905\) 13.7481 13.7481i 0.457002 0.457002i
\(906\) 0 0
\(907\) 7.90224 4.56236i 0.262390 0.151491i −0.363035 0.931776i \(-0.618259\pi\)
0.625424 + 0.780285i \(0.284926\pi\)
\(908\) 36.4977 24.8442i 1.21122 0.824485i
\(909\) 0 0
\(910\) −9.88541 64.9111i −0.327698 2.15178i
\(911\) 33.8691i 1.12213i 0.827770 + 0.561067i \(0.189609\pi\)
−0.827770 + 0.561067i \(0.810391\pi\)
\(912\) 0 0
\(913\) −5.68614 9.84868i −0.188184 0.325944i
\(914\) −2.63524 + 27.9910i −0.0871660 + 0.925860i
\(915\) 0 0
\(916\) −29.8560 14.4051i −0.986469 0.475957i
\(917\) −78.4941 + 21.0324i −2.59210 + 0.694552i
\(918\) 0 0
\(919\) 15.7907 + 9.11677i 0.520887 + 0.300734i 0.737298 0.675568i \(-0.236102\pi\)
−0.216410 + 0.976302i \(0.569435\pi\)
\(920\) −49.5117 + 12.2209i −1.63235 + 0.402910i
\(921\) 0 0
\(922\) 7.26276 + 15.8474i 0.239186 + 0.521907i
\(923\) 23.8615 + 24.6770i 0.785411 + 0.812253i
\(924\) 0 0
\(925\) 8.79030 + 2.35535i 0.289023 + 0.0774436i
\(926\) −9.60830 6.82279i −0.315748 0.224211i
\(927\) 0 0
\(928\) 0.193311 0.917996i 0.00634576 0.0301347i
\(929\) −41.6902 + 11.1709i −1.36781 + 0.366504i −0.866679 0.498866i \(-0.833750\pi\)
−0.501133 + 0.865370i \(0.667083\pi\)
\(930\) 0 0
\(931\) 32.3002 32.3002i 1.05860 1.05860i
\(932\) −3.23730 9.27366i −0.106041 0.303769i
\(933\) 0 0
\(934\) −5.55814 32.7862i −0.181868 1.07280i
\(935\) 24.2881 0.794305
\(936\) 0 0
\(937\) 12.5702 0.410650 0.205325 0.978694i \(-0.434175\pi\)
0.205325 + 0.978694i \(0.434175\pi\)
\(938\) −5.63333 33.2297i −0.183935 1.08499i
\(939\) 0 0
\(940\) −13.1837 + 4.60224i −0.430005 + 0.150108i
\(941\) −19.4028 + 19.4028i −0.632512 + 0.632512i −0.948697 0.316185i \(-0.897598\pi\)
0.316185 + 0.948697i \(0.397598\pi\)
\(942\) 0 0
\(943\) 52.6736 14.1138i 1.71529 0.459610i
\(944\) −4.37776 3.24094i −0.142484 0.105484i
\(945\) 0 0
\(946\) −19.3775 13.7598i −0.630016 0.447370i
\(947\) 23.2132 + 6.21995i 0.754327 + 0.202121i 0.615437 0.788186i \(-0.288980\pi\)
0.138890 + 0.990308i \(0.455646\pi\)
\(948\) 0 0
\(949\) 15.7994 55.2354i 0.512871 1.79302i
\(950\) −3.15222 6.87817i −0.102271 0.223157i
\(951\) 0 0
\(952\) −59.5423 + 14.6967i −1.92978 + 0.476322i
\(953\) 7.54135 + 4.35400i 0.244288 + 0.141040i 0.617146 0.786849i \(-0.288289\pi\)
−0.372858 + 0.927889i \(0.621622\pi\)
\(954\) 0 0
\(955\) 14.8757 3.98592i 0.481365 0.128981i
\(956\) −12.5477 + 26.0063i −0.405821 + 0.841104i
\(957\) 0 0
\(958\) 0.422409 4.48674i 0.0136474 0.144960i
\(959\) 7.16303 + 12.4067i 0.231306 + 0.400634i
\(960\) 0 0
\(961\) 2.52438i 0.0814317i
\(962\) −9.46468 21.6030i −0.305154 0.696509i
\(963\) 0 0
\(964\) 3.02295 + 4.44090i 0.0973626 + 0.143032i
\(965\) −41.5070 + 23.9641i −1.33616 + 0.771430i
\(966\) 0 0
\(967\) −32.8150 + 32.8150i −1.05526 + 1.05526i −0.0568771 + 0.998381i \(0.518114\pi\)
−0.998381 + 0.0568771i \(0.981886\pi\)
\(968\) −18.9874 0.376164i −0.610277 0.0120904i
\(969\) 0 0
\(970\) 2.05118 5.52184i 0.0658593 0.177296i
\(971\) −0.777271 + 1.34627i −0.0249438 + 0.0432040i −0.878228 0.478242i \(-0.841274\pi\)
0.853284 + 0.521446i \(0.174607\pi\)
\(972\) 0 0
\(973\) 4.77670 17.8269i 0.153134 0.571504i
\(974\) 10.0380 + 21.9029i 0.321638 + 0.701816i
\(975\) 0 0
\(976\) 2.74571 0.409699i 0.0878880 0.0131141i
\(977\) −10.8059 + 40.3282i −0.345712 + 1.29021i 0.546067 + 0.837742i \(0.316125\pi\)
−0.891778 + 0.452472i \(0.850542\pi\)
\(978\) 0 0
\(979\) −24.4182 14.0979i −0.780409 0.450569i
\(980\) 6.56184 + 88.4388i 0.209610 + 2.82508i
\(981\) 0 0
\(982\) −13.2539 + 10.9730i −0.422950 + 0.350164i
\(983\) 18.5465 + 18.5465i 0.591540 + 0.591540i 0.938047 0.346507i \(-0.112632\pi\)
−0.346507 + 0.938047i \(0.612632\pi\)
\(984\) 0 0
\(985\) −18.3907 + 10.6179i −0.585976 + 0.338313i
\(986\) −1.02778 + 0.174235i −0.0327311 + 0.00554879i
\(987\) 0 0
\(988\) −8.81653 + 17.5151i −0.280491 + 0.557230i
\(989\) 55.4498i 1.76320i
\(990\) 0 0
\(991\) −38.3423 + 22.1369i −1.21798 + 0.703203i −0.964486 0.264133i \(-0.914914\pi\)
−0.253497 + 0.967336i \(0.581581\pi\)
\(992\) −1.63687 30.1420i −0.0519707 0.957010i
\(993\) 0 0
\(994\) −41.8868 50.5934i −1.32857 1.60473i
\(995\) −2.24191 8.36691i −0.0710733 0.265249i
\(996\) 0 0
\(997\) 11.1621 + 6.44442i 0.353506 + 0.204097i 0.666228 0.745748i \(-0.267908\pi\)
−0.312722 + 0.949845i \(0.601241\pi\)
\(998\) −47.1880 33.5079i −1.49371 1.06067i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 936.2.ed.c.739.12 48
3.2 odd 2 312.2.bt.c.115.1 yes 48
8.3 odd 2 inner 936.2.ed.c.739.3 48
13.6 odd 12 inner 936.2.ed.c.19.3 48
24.11 even 2 312.2.bt.c.115.10 yes 48
39.32 even 12 312.2.bt.c.19.10 yes 48
104.19 even 12 inner 936.2.ed.c.19.12 48
312.227 odd 12 312.2.bt.c.19.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
312.2.bt.c.19.1 48 312.227 odd 12
312.2.bt.c.19.10 yes 48 39.32 even 12
312.2.bt.c.115.1 yes 48 3.2 odd 2
312.2.bt.c.115.10 yes 48 24.11 even 2
936.2.ed.c.19.3 48 13.6 odd 12 inner
936.2.ed.c.19.12 48 104.19 even 12 inner
936.2.ed.c.739.3 48 8.3 odd 2 inner
936.2.ed.c.739.12 48 1.1 even 1 trivial