Properties

Label 108.4.e.a.37.1
Level $108$
Weight $4$
Character 108.37
Analytic conductor $6.372$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,4,Mod(37,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.6831243.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 13x^{4} + 49x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{5} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(1.23396i\) of defining polynomial
Character \(\chi\) \(=\) 108.37
Dual form 108.4.e.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.92194 + 11.9892i) q^{5} +(-15.3540 - 26.5939i) q^{7} +O(q^{10})\) \(q+(-6.92194 + 11.9892i) q^{5} +(-15.3540 - 26.5939i) q^{7} +(-21.9523 - 38.0225i) q^{11} +(6.11853 - 10.5976i) q^{13} -76.0286 q^{17} -44.1789 q^{19} +(-39.3135 + 68.0930i) q^{23} +(-33.3265 - 57.7232i) q^{25} +(-46.3903 - 80.3504i) q^{29} +(71.5329 - 123.899i) q^{31} +425.118 q^{35} -32.4741 q^{37} +(-167.778 + 290.599i) q^{41} +(249.166 + 431.567i) q^{43} +(-140.882 - 244.016i) q^{47} +(-299.990 + 519.599i) q^{49} +628.565 q^{53} +607.810 q^{55} +(252.327 - 437.043i) q^{59} +(-185.951 - 322.076i) q^{61} +(84.7041 + 146.712i) q^{65} +(81.3304 - 140.868i) q^{67} -433.512 q^{71} -629.645 q^{73} +(-674.111 + 1167.59i) q^{77} +(-86.3649 - 149.588i) q^{79} +(-87.4288 - 151.431i) q^{83} +(526.265 - 911.518i) q^{85} -336.716 q^{89} -375.775 q^{91} +(305.804 - 529.668i) q^{95} +(-42.1594 - 73.0222i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{5} - 6 q^{7} - 51 q^{11} + 12 q^{13} + 222 q^{17} + 30 q^{19} - 210 q^{23} - 3 q^{25} - 456 q^{29} + 48 q^{31} + 1104 q^{35} - 96 q^{37} - 897 q^{41} + 129 q^{43} - 522 q^{47} - 225 q^{49} + 2208 q^{53} - 216 q^{55} - 453 q^{59} - 402 q^{61} - 1110 q^{65} - 213 q^{67} - 120 q^{71} + 750 q^{73} - 1128 q^{77} + 552 q^{79} + 612 q^{83} + 1188 q^{85} + 924 q^{89} - 264 q^{91} + 2184 q^{95} + 93 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −6.92194 + 11.9892i −0.619117 + 1.07234i 0.370530 + 0.928821i \(0.379176\pi\)
−0.989647 + 0.143522i \(0.954157\pi\)
\(6\) 0 0
\(7\) −15.3540 26.5939i −0.829038 1.43594i −0.898794 0.438372i \(-0.855555\pi\)
0.0697558 0.997564i \(-0.477778\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −21.9523 38.0225i −0.601715 1.04220i −0.992561 0.121745i \(-0.961151\pi\)
0.390846 0.920456i \(-0.372182\pi\)
\(12\) 0 0
\(13\) 6.11853 10.5976i 0.130536 0.226096i −0.793347 0.608770i \(-0.791663\pi\)
0.923883 + 0.382674i \(0.124997\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −76.0286 −1.08468 −0.542342 0.840158i \(-0.682462\pi\)
−0.542342 + 0.840158i \(0.682462\pi\)
\(18\) 0 0
\(19\) −44.1789 −0.533439 −0.266720 0.963774i \(-0.585940\pi\)
−0.266720 + 0.963774i \(0.585940\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −39.3135 + 68.0930i −0.356410 + 0.617321i −0.987358 0.158504i \(-0.949333\pi\)
0.630948 + 0.775825i \(0.282666\pi\)
\(24\) 0 0
\(25\) −33.3265 57.7232i −0.266612 0.461786i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −46.3903 80.3504i −0.297050 0.514506i 0.678409 0.734684i \(-0.262670\pi\)
−0.975460 + 0.220178i \(0.929336\pi\)
\(30\) 0 0
\(31\) 71.5329 123.899i 0.414442 0.717834i −0.580928 0.813955i \(-0.697310\pi\)
0.995370 + 0.0961208i \(0.0306435\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 425.118 2.05309
\(36\) 0 0
\(37\) −32.4741 −0.144289 −0.0721447 0.997394i \(-0.522984\pi\)
−0.0721447 + 0.997394i \(0.522984\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −167.778 + 290.599i −0.639084 + 1.10693i 0.346550 + 0.938031i \(0.387353\pi\)
−0.985634 + 0.168895i \(0.945980\pi\)
\(42\) 0 0
\(43\) 249.166 + 431.567i 0.883660 + 1.53054i 0.847242 + 0.531208i \(0.178262\pi\)
0.0364186 + 0.999337i \(0.488405\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −140.882 244.016i −0.437230 0.757305i 0.560244 0.828327i \(-0.310707\pi\)
−0.997475 + 0.0710223i \(0.977374\pi\)
\(48\) 0 0
\(49\) −299.990 + 519.599i −0.874608 + 1.51487i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 628.565 1.62906 0.814529 0.580123i \(-0.196995\pi\)
0.814529 + 0.580123i \(0.196995\pi\)
\(54\) 0 0
\(55\) 607.810 1.49013
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 252.327 437.043i 0.556782 0.964375i −0.440980 0.897517i \(-0.645369\pi\)
0.997762 0.0668584i \(-0.0212976\pi\)
\(60\) 0 0
\(61\) −185.951 322.076i −0.390304 0.676026i 0.602186 0.798356i \(-0.294297\pi\)
−0.992489 + 0.122330i \(0.960963\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 84.7041 + 146.712i 0.161635 + 0.279960i
\(66\) 0 0
\(67\) 81.3304 140.868i 0.148300 0.256863i −0.782299 0.622903i \(-0.785953\pi\)
0.930599 + 0.366040i \(0.119287\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −433.512 −0.724626 −0.362313 0.932056i \(-0.618013\pi\)
−0.362313 + 0.932056i \(0.618013\pi\)
\(72\) 0 0
\(73\) −629.645 −1.00951 −0.504756 0.863262i \(-0.668418\pi\)
−0.504756 + 0.863262i \(0.668418\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −674.111 + 1167.59i −0.997689 + 1.72805i
\(78\) 0 0
\(79\) −86.3649 149.588i −0.122998 0.213038i 0.797951 0.602723i \(-0.205917\pi\)
−0.920948 + 0.389684i \(0.872584\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −87.4288 151.431i −0.115621 0.200262i 0.802407 0.596778i \(-0.203553\pi\)
−0.918028 + 0.396516i \(0.870219\pi\)
\(84\) 0 0
\(85\) 526.265 911.518i 0.671547 1.16315i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −336.716 −0.401032 −0.200516 0.979690i \(-0.564262\pi\)
−0.200516 + 0.979690i \(0.564262\pi\)
\(90\) 0 0
\(91\) −375.775 −0.432879
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 305.804 529.668i 0.330261 0.572029i
\(96\) 0 0
\(97\) −42.1594 73.0222i −0.0441303 0.0764358i 0.843117 0.537731i \(-0.180718\pi\)
−0.887247 + 0.461295i \(0.847385\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −874.902 1515.38i −0.861941 1.49293i −0.870053 0.492959i \(-0.835915\pi\)
0.00811161 0.999967i \(-0.497418\pi\)
\(102\) 0 0
\(103\) −55.6978 + 96.4714i −0.0532822 + 0.0922875i −0.891436 0.453146i \(-0.850302\pi\)
0.838154 + 0.545433i \(0.183635\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −895.520 −0.809095 −0.404548 0.914517i \(-0.632571\pi\)
−0.404548 + 0.914517i \(0.632571\pi\)
\(108\) 0 0
\(109\) −716.957 −0.630019 −0.315009 0.949089i \(-0.602008\pi\)
−0.315009 + 0.949089i \(0.602008\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 115.526 200.096i 0.0961746 0.166579i −0.813924 0.580972i \(-0.802673\pi\)
0.910098 + 0.414393i \(0.136006\pi\)
\(114\) 0 0
\(115\) −544.252 942.672i −0.441320 0.764388i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1167.34 + 2021.90i 0.899245 + 1.55754i
\(120\) 0 0
\(121\) −298.306 + 516.681i −0.224122 + 0.388190i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −807.748 −0.577978
\(126\) 0 0
\(127\) 1715.22 1.19843 0.599217 0.800586i \(-0.295478\pi\)
0.599217 + 0.800586i \(0.295478\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 666.435 1154.30i 0.444479 0.769859i −0.553537 0.832824i \(-0.686722\pi\)
0.998016 + 0.0629650i \(0.0200557\pi\)
\(132\) 0 0
\(133\) 678.323 + 1174.89i 0.442241 + 0.765984i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1259.49 + 2181.50i 0.785443 + 1.36043i 0.928734 + 0.370746i \(0.120898\pi\)
−0.143292 + 0.989680i \(0.545769\pi\)
\(138\) 0 0
\(139\) −311.442 + 539.433i −0.190044 + 0.329166i −0.945265 0.326305i \(-0.894196\pi\)
0.755220 + 0.655471i \(0.227530\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −537.263 −0.314183
\(144\) 0 0
\(145\) 1284.44 0.735636
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1204.47 2086.21i 0.662243 1.14704i −0.317781 0.948164i \(-0.602938\pi\)
0.980025 0.198875i \(-0.0637289\pi\)
\(150\) 0 0
\(151\) −33.8218 58.5810i −0.0182277 0.0315712i 0.856768 0.515703i \(-0.172469\pi\)
−0.874995 + 0.484131i \(0.839136\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 990.293 + 1715.24i 0.513176 + 0.888847i
\(156\) 0 0
\(157\) 2.19676 3.80490i 0.00111669 0.00193417i −0.865467 0.500967i \(-0.832978\pi\)
0.866583 + 0.499033i \(0.166311\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2414.48 1.18191
\(162\) 0 0
\(163\) −2863.88 −1.37617 −0.688087 0.725628i \(-0.741549\pi\)
−0.688087 + 0.725628i \(0.741549\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 214.757 371.970i 0.0995114 0.172359i −0.811971 0.583698i \(-0.801605\pi\)
0.911483 + 0.411339i \(0.134939\pi\)
\(168\) 0 0
\(169\) 1023.63 + 1772.97i 0.465920 + 0.806998i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1287.14 2229.40i −0.565663 0.979756i −0.996988 0.0775599i \(-0.975287\pi\)
0.431325 0.902197i \(-0.358046\pi\)
\(174\) 0 0
\(175\) −1023.39 + 1772.56i −0.442063 + 0.765676i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −807.448 −0.337159 −0.168580 0.985688i \(-0.553918\pi\)
−0.168580 + 0.985688i \(0.553918\pi\)
\(180\) 0 0
\(181\) 4296.57 1.76443 0.882215 0.470847i \(-0.156052\pi\)
0.882215 + 0.470847i \(0.156052\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 224.784 389.337i 0.0893321 0.154728i
\(186\) 0 0
\(187\) 1669.00 + 2890.79i 0.652671 + 1.13046i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −153.147 265.259i −0.0580176 0.100489i 0.835558 0.549402i \(-0.185145\pi\)
−0.893575 + 0.448913i \(0.851811\pi\)
\(192\) 0 0
\(193\) 856.177 1482.94i 0.319321 0.553080i −0.661026 0.750363i \(-0.729879\pi\)
0.980347 + 0.197283i \(0.0632119\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 263.636 0.0953466 0.0476733 0.998863i \(-0.484819\pi\)
0.0476733 + 0.998863i \(0.484819\pi\)
\(198\) 0 0
\(199\) −3835.87 −1.36642 −0.683211 0.730221i \(-0.739417\pi\)
−0.683211 + 0.730221i \(0.739417\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1424.55 + 2467.40i −0.492532 + 0.853091i
\(204\) 0 0
\(205\) −2322.69 4023.02i −0.791336 1.37063i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 969.829 + 1679.79i 0.320978 + 0.555951i
\(210\) 0 0
\(211\) 2034.66 3524.14i 0.663848 1.14982i −0.315748 0.948843i \(-0.602255\pi\)
0.979596 0.200976i \(-0.0644112\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6898.84 −2.18836
\(216\) 0 0
\(217\) −4393.27 −1.37435
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −465.183 + 805.720i −0.141591 + 0.245243i
\(222\) 0 0
\(223\) −3078.07 5331.38i −0.924318 1.60097i −0.792654 0.609672i \(-0.791301\pi\)
−0.131664 0.991294i \(-0.542032\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.1307 + 21.0110i 0.00354689 + 0.00614339i 0.867793 0.496925i \(-0.165538\pi\)
−0.864247 + 0.503069i \(0.832204\pi\)
\(228\) 0 0
\(229\) 316.209 547.691i 0.0912476 0.158045i −0.816789 0.576937i \(-0.804248\pi\)
0.908036 + 0.418891i \(0.137581\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3163.59 0.889502 0.444751 0.895654i \(-0.353292\pi\)
0.444751 + 0.895654i \(0.353292\pi\)
\(234\) 0 0
\(235\) 3900.72 1.08279
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1110.57 1923.57i 0.300573 0.520608i −0.675693 0.737183i \(-0.736155\pi\)
0.976266 + 0.216575i \(0.0694887\pi\)
\(240\) 0 0
\(241\) 300.730 + 520.879i 0.0803805 + 0.139223i 0.903413 0.428771i \(-0.141053\pi\)
−0.823033 + 0.567994i \(0.807720\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4153.03 7193.26i −1.08297 1.87576i
\(246\) 0 0
\(247\) −270.310 + 468.191i −0.0696332 + 0.120608i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1350.71 −0.339665 −0.169833 0.985473i \(-0.554323\pi\)
−0.169833 + 0.985473i \(0.554323\pi\)
\(252\) 0 0
\(253\) 3452.09 0.857830
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3521.95 + 6100.20i −0.854838 + 1.48062i 0.0219564 + 0.999759i \(0.493010\pi\)
−0.876795 + 0.480865i \(0.840323\pi\)
\(258\) 0 0
\(259\) 498.607 + 863.613i 0.119621 + 0.207190i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1162.13 + 2012.87i 0.272472 + 0.471935i 0.969494 0.245114i \(-0.0788255\pi\)
−0.697022 + 0.717050i \(0.745492\pi\)
\(264\) 0 0
\(265\) −4350.89 + 7535.97i −1.00858 + 1.74691i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3675.87 0.833167 0.416584 0.909097i \(-0.363227\pi\)
0.416584 + 0.909097i \(0.363227\pi\)
\(270\) 0 0
\(271\) −1881.48 −0.421741 −0.210871 0.977514i \(-0.567630\pi\)
−0.210871 + 0.977514i \(0.567630\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1463.19 + 2534.31i −0.320849 + 0.555727i
\(276\) 0 0
\(277\) −732.008 1267.87i −0.158780 0.275015i 0.775649 0.631165i \(-0.217423\pi\)
−0.934429 + 0.356149i \(0.884089\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4116.28 7129.61i −0.873867 1.51358i −0.857965 0.513709i \(-0.828271\pi\)
−0.0159023 0.999874i \(-0.505062\pi\)
\(282\) 0 0
\(283\) −844.364 + 1462.48i −0.177358 + 0.307192i −0.940975 0.338477i \(-0.890088\pi\)
0.763617 + 0.645669i \(0.223422\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10304.2 2.11930
\(288\) 0 0
\(289\) 867.343 0.176540
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 255.866 443.173i 0.0510166 0.0883633i −0.839389 0.543531i \(-0.817087\pi\)
0.890406 + 0.455167i \(0.150421\pi\)
\(294\) 0 0
\(295\) 3493.18 + 6050.37i 0.689427 + 1.19412i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 481.082 + 833.258i 0.0930491 + 0.161166i
\(300\) 0 0
\(301\) 7651.37 13252.6i 1.46518 2.53776i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5148.55 0.966575
\(306\) 0 0
\(307\) −3171.98 −0.589690 −0.294845 0.955545i \(-0.595268\pi\)
−0.294845 + 0.955545i \(0.595268\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2530.39 4382.76i 0.461367 0.799112i −0.537662 0.843160i \(-0.680692\pi\)
0.999029 + 0.0440487i \(0.0140257\pi\)
\(312\) 0 0
\(313\) 4732.92 + 8197.66i 0.854698 + 1.48038i 0.876925 + 0.480628i \(0.159591\pi\)
−0.0222263 + 0.999753i \(0.507075\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3208.57 + 5557.40i 0.568489 + 0.984652i 0.996716 + 0.0809808i \(0.0258052\pi\)
−0.428226 + 0.903671i \(0.640861\pi\)
\(318\) 0 0
\(319\) −2036.75 + 3527.75i −0.357479 + 0.619172i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3358.86 0.578613
\(324\) 0 0
\(325\) −815.637 −0.139210
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4326.22 + 7493.23i −0.724961 + 1.25567i
\(330\) 0 0
\(331\) −3332.37 5771.83i −0.553364 0.958455i −0.998029 0.0627575i \(-0.980011\pi\)
0.444665 0.895697i \(-0.353323\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1125.93 + 1950.17i 0.183630 + 0.318056i
\(336\) 0 0
\(337\) −5244.05 + 9082.95i −0.847660 + 1.46819i 0.0356314 + 0.999365i \(0.488656\pi\)
−0.883291 + 0.468825i \(0.844678\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6281.25 −0.997503
\(342\) 0 0
\(343\) 7891.37 1.24226
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1074.48 1861.05i 0.166228 0.287915i −0.770863 0.637001i \(-0.780175\pi\)
0.937091 + 0.349086i \(0.113508\pi\)
\(348\) 0 0
\(349\) 1388.53 + 2405.00i 0.212969 + 0.368874i 0.952642 0.304093i \(-0.0983532\pi\)
−0.739673 + 0.672966i \(0.765020\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3898.72 + 6752.78i 0.587841 + 1.01817i 0.994515 + 0.104597i \(0.0333554\pi\)
−0.406673 + 0.913574i \(0.633311\pi\)
\(354\) 0 0
\(355\) 3000.75 5197.45i 0.448629 0.777047i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2309.31 −0.339500 −0.169750 0.985487i \(-0.554296\pi\)
−0.169750 + 0.985487i \(0.554296\pi\)
\(360\) 0 0
\(361\) −4907.22 −0.715443
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4358.36 7548.91i 0.625006 1.08254i
\(366\) 0 0
\(367\) 3105.66 + 5379.16i 0.441728 + 0.765095i 0.997818 0.0660271i \(-0.0210324\pi\)
−0.556090 + 0.831122i \(0.687699\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9650.99 16716.0i −1.35055 2.33922i
\(372\) 0 0
\(373\) −4349.61 + 7533.75i −0.603792 + 1.04580i 0.388450 + 0.921470i \(0.373011\pi\)
−0.992241 + 0.124328i \(0.960323\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1135.36 −0.155104
\(378\) 0 0
\(379\) 5954.77 0.807061 0.403531 0.914966i \(-0.367783\pi\)
0.403531 + 0.914966i \(0.367783\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2128.35 3686.41i 0.283952 0.491819i −0.688403 0.725329i \(-0.741688\pi\)
0.972354 + 0.233510i \(0.0750211\pi\)
\(384\) 0 0
\(385\) −9332.31 16164.0i −1.23537 2.13973i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 801.019 + 1387.41i 0.104404 + 0.180834i 0.913495 0.406851i \(-0.133373\pi\)
−0.809090 + 0.587684i \(0.800040\pi\)
\(390\) 0 0
\(391\) 2988.95 5177.02i 0.386593 0.669598i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2391.25 0.304600
\(396\) 0 0
\(397\) −7987.87 −1.00982 −0.504912 0.863171i \(-0.668475\pi\)
−0.504912 + 0.863171i \(0.668475\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3534.75 + 6122.36i −0.440191 + 0.762434i −0.997703 0.0677350i \(-0.978423\pi\)
0.557512 + 0.830169i \(0.311756\pi\)
\(402\) 0 0
\(403\) −875.352 1516.15i −0.108200 0.187407i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 712.881 + 1234.75i 0.0868211 + 0.150379i
\(408\) 0 0
\(409\) 5932.38 10275.2i 0.717207 1.24224i −0.244896 0.969549i \(-0.578754\pi\)
0.962102 0.272689i \(-0.0879129\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −15496.9 −1.84637
\(414\) 0 0
\(415\) 2420.71 0.286332
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6171.30 + 10689.0i −0.719541 + 1.24628i 0.241641 + 0.970366i \(0.422314\pi\)
−0.961182 + 0.275916i \(0.911019\pi\)
\(420\) 0 0
\(421\) −2732.93 4733.58i −0.316377 0.547982i 0.663352 0.748308i \(-0.269133\pi\)
−0.979729 + 0.200326i \(0.935800\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2533.77 + 4388.61i 0.289190 + 0.500892i
\(426\) 0 0
\(427\) −5710.17 + 9890.30i −0.647153 + 1.12090i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8997.67 −1.00557 −0.502787 0.864410i \(-0.667692\pi\)
−0.502787 + 0.864410i \(0.667692\pi\)
\(432\) 0 0
\(433\) −10967.4 −1.21723 −0.608615 0.793466i \(-0.708275\pi\)
−0.608615 + 0.793466i \(0.708275\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1736.83 3008.28i 0.190123 0.329303i
\(438\) 0 0
\(439\) −3563.51 6172.18i −0.387419 0.671029i 0.604683 0.796467i \(-0.293300\pi\)
−0.992102 + 0.125437i \(0.959967\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4434.28 + 7680.39i 0.475573 + 0.823716i 0.999608 0.0279799i \(-0.00890744\pi\)
−0.524036 + 0.851696i \(0.675574\pi\)
\(444\) 0 0
\(445\) 2330.73 4036.94i 0.248286 0.430043i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9835.05 −1.03373 −0.516865 0.856067i \(-0.672901\pi\)
−0.516865 + 0.856067i \(0.672901\pi\)
\(450\) 0 0
\(451\) 14732.4 1.53819
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2601.09 4505.23i 0.268003 0.464194i
\(456\) 0 0
\(457\) 4443.25 + 7695.93i 0.454806 + 0.787747i 0.998677 0.0514218i \(-0.0163753\pi\)
−0.543871 + 0.839169i \(0.683042\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 932.894 + 1615.82i 0.0942499 + 0.163246i 0.909295 0.416151i \(-0.136621\pi\)
−0.815045 + 0.579397i \(0.803288\pi\)
\(462\) 0 0
\(463\) 6811.70 11798.2i 0.683729 1.18425i −0.290105 0.956995i \(-0.593690\pi\)
0.973834 0.227259i \(-0.0729763\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9328.97 0.924397 0.462199 0.886776i \(-0.347061\pi\)
0.462199 + 0.886776i \(0.347061\pi\)
\(468\) 0 0
\(469\) −4994.99 −0.491785
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 10939.5 18947.8i 1.06342 1.84190i
\(474\) 0 0
\(475\) 1472.33 + 2550.15i 0.142221 + 0.246335i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1330.15 + 2303.89i 0.126881 + 0.219765i 0.922467 0.386077i \(-0.126170\pi\)
−0.795586 + 0.605841i \(0.792837\pi\)
\(480\) 0 0
\(481\) −198.694 + 344.147i −0.0188350 + 0.0326232i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1167.30 0.109287
\(486\) 0 0
\(487\) −20450.7 −1.90289 −0.951447 0.307813i \(-0.900403\pi\)
−0.951447 + 0.307813i \(0.900403\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10327.4 17887.7i 0.949228 1.64411i 0.202173 0.979350i \(-0.435200\pi\)
0.747055 0.664762i \(-0.231467\pi\)
\(492\) 0 0
\(493\) 3526.99 + 6108.92i 0.322206 + 0.558077i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6656.15 + 11528.8i 0.600743 + 1.04052i
\(498\) 0 0
\(499\) −8733.31 + 15126.5i −0.783480 + 1.35703i 0.146423 + 0.989222i \(0.453224\pi\)
−0.929903 + 0.367805i \(0.880109\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −19951.2 −1.76855 −0.884275 0.466966i \(-0.845347\pi\)
−0.884275 + 0.466966i \(0.845347\pi\)
\(504\) 0 0
\(505\) 24224.1 2.13457
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3638.88 + 6302.73i −0.316878 + 0.548848i −0.979835 0.199809i \(-0.935968\pi\)
0.662957 + 0.748657i \(0.269301\pi\)
\(510\) 0 0
\(511\) 9667.57 + 16744.7i 0.836924 + 1.44959i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −771.074 1335.54i −0.0659759 0.114274i
\(516\) 0 0
\(517\) −6185.39 + 10713.4i −0.526176 + 0.911364i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 11664.5 0.980866 0.490433 0.871479i \(-0.336839\pi\)
0.490433 + 0.871479i \(0.336839\pi\)
\(522\) 0 0
\(523\) −8925.51 −0.746243 −0.373122 0.927782i \(-0.621713\pi\)
−0.373122 + 0.927782i \(0.621713\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5438.55 + 9419.84i −0.449539 + 0.778624i
\(528\) 0 0
\(529\) 2992.39 + 5182.98i 0.245943 + 0.425986i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2053.10 + 3556.08i 0.166848 + 0.288988i
\(534\) 0 0
\(535\) 6198.74 10736.5i 0.500925 0.867627i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 26341.9 2.10506
\(540\) 0 0
\(541\) 12334.1 0.980193 0.490097 0.871668i \(-0.336962\pi\)
0.490097 + 0.871668i \(0.336962\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4962.74 8595.71i 0.390056 0.675596i
\(546\) 0 0
\(547\) −2284.81 3957.41i −0.178595 0.309336i 0.762804 0.646629i \(-0.223822\pi\)
−0.941400 + 0.337293i \(0.890489\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2049.47 + 3549.79i 0.158458 + 0.274458i
\(552\) 0 0
\(553\) −2652.09 + 4593.56i −0.203939 + 0.353233i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8154.40 0.620310 0.310155 0.950686i \(-0.399619\pi\)
0.310155 + 0.950686i \(0.399619\pi\)
\(558\) 0 0
\(559\) 6098.10 0.461399
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8086.82 + 14006.8i −0.605362 + 1.04852i 0.386632 + 0.922234i \(0.373638\pi\)
−0.991994 + 0.126284i \(0.959695\pi\)
\(564\) 0 0
\(565\) 1599.32 + 2770.11i 0.119087 + 0.206264i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4548.76 7878.69i −0.335139 0.580478i 0.648372 0.761323i \(-0.275450\pi\)
−0.983512 + 0.180845i \(0.942117\pi\)
\(570\) 0 0
\(571\) 1647.54 2853.63i 0.120749 0.209143i −0.799314 0.600913i \(-0.794804\pi\)
0.920063 + 0.391770i \(0.128137\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5240.73 0.380093
\(576\) 0 0
\(577\) 15544.7 1.12155 0.560775 0.827968i \(-0.310503\pi\)
0.560775 + 0.827968i \(0.310503\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2684.76 + 4650.14i −0.191709 + 0.332049i
\(582\) 0 0
\(583\) −13798.4 23899.6i −0.980229 1.69781i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2344.33 4060.50i −0.164840 0.285511i 0.771759 0.635916i \(-0.219377\pi\)
−0.936598 + 0.350405i \(0.886044\pi\)
\(588\) 0 0
\(589\) −3160.25 + 5473.71i −0.221079 + 0.382921i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16637.6 −1.15215 −0.576075 0.817397i \(-0.695416\pi\)
−0.576075 + 0.817397i \(0.695416\pi\)
\(594\) 0 0
\(595\) −32321.1 −2.22695
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2933.73 + 5081.37i −0.200115 + 0.346610i −0.948565 0.316581i \(-0.897465\pi\)
0.748450 + 0.663191i \(0.230798\pi\)
\(600\) 0 0
\(601\) −10337.9 17905.8i −0.701649 1.21529i −0.967887 0.251385i \(-0.919114\pi\)
0.266238 0.963907i \(-0.414219\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4129.71 7152.87i −0.277515 0.480671i
\(606\) 0 0
\(607\) −6303.86 + 10918.6i −0.421525 + 0.730103i −0.996089 0.0883567i \(-0.971838\pi\)
0.574564 + 0.818460i \(0.305172\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3447.97 −0.228298
\(612\) 0 0
\(613\) 12469.7 0.821608 0.410804 0.911724i \(-0.365248\pi\)
0.410804 + 0.911724i \(0.365248\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9293.48 16096.8i 0.606388 1.05030i −0.385442 0.922732i \(-0.625951\pi\)
0.991830 0.127563i \(-0.0407156\pi\)
\(618\) 0 0
\(619\) 5972.96 + 10345.5i 0.387841 + 0.671761i 0.992159 0.124983i \(-0.0398876\pi\)
−0.604318 + 0.796743i \(0.706554\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5169.94 + 8954.60i 0.332471 + 0.575856i
\(624\) 0 0
\(625\) 9757.00 16899.6i 0.624448 1.08158i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2468.96 0.156509
\(630\) 0 0
\(631\) 4285.35 0.270360 0.135180 0.990821i \(-0.456839\pi\)
0.135180 + 0.990821i \(0.456839\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −11872.7 + 20564.0i −0.741972 + 1.28513i
\(636\) 0 0
\(637\) 3671.00 + 6358.36i 0.228336 + 0.395490i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10879.1 18843.2i −0.670357 1.16109i −0.977803 0.209527i \(-0.932808\pi\)
0.307446 0.951566i \(-0.400526\pi\)
\(642\) 0 0
\(643\) 3671.54 6359.30i 0.225181 0.390025i −0.731193 0.682171i \(-0.761036\pi\)
0.956374 + 0.292146i \(0.0943692\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9483.24 −0.576236 −0.288118 0.957595i \(-0.593030\pi\)
−0.288118 + 0.957595i \(0.593030\pi\)
\(648\) 0 0
\(649\) −22156.6 −1.34010
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2392.09 4143.23i 0.143353 0.248295i −0.785404 0.618984i \(-0.787545\pi\)
0.928757 + 0.370688i \(0.120878\pi\)
\(654\) 0 0
\(655\) 9226.05 + 15980.0i 0.550369 + 0.953266i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16034.0 27771.6i −0.947791 1.64162i −0.750064 0.661365i \(-0.769977\pi\)
−0.197727 0.980257i \(-0.563356\pi\)
\(660\) 0 0
\(661\) 3762.64 6517.09i 0.221407 0.383488i −0.733829 0.679335i \(-0.762269\pi\)
0.955235 + 0.295847i \(0.0956019\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −18781.3 −1.09520
\(666\) 0 0
\(667\) 7295.07 0.423487
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8164.08 + 14140.6i −0.469703 + 0.813550i
\(672\) 0 0
\(673\) 3670.98 + 6358.32i 0.210261 + 0.364183i 0.951796 0.306731i \(-0.0992352\pi\)
−0.741535 + 0.670914i \(0.765902\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4760.52 + 8245.45i 0.270253 + 0.468092i 0.968927 0.247348i \(-0.0795592\pi\)
−0.698673 + 0.715441i \(0.746226\pi\)
\(678\) 0 0
\(679\) −1294.63 + 2242.36i −0.0731713 + 0.126736i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1475.06 0.0826377 0.0413188 0.999146i \(-0.486844\pi\)
0.0413188 + 0.999146i \(0.486844\pi\)
\(684\) 0 0
\(685\) −34872.5 −1.94512
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3845.89 6661.28i 0.212651 0.368323i
\(690\) 0 0
\(691\) −17080.4 29584.0i −0.940329 1.62870i −0.764844 0.644215i \(-0.777184\pi\)
−0.175484 0.984482i \(-0.556149\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4311.56 7467.84i −0.235319 0.407585i
\(696\) 0 0
\(697\) 12755.9 22093.8i 0.693205 1.20067i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29427.2 1.58552 0.792759 0.609535i \(-0.208644\pi\)
0.792759 + 0.609535i \(0.208644\pi\)
\(702\) 0 0
\(703\) 1434.67 0.0769696
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −26866.5 + 46534.1i −1.42916 + 2.47538i
\(708\) 0 0
\(709\) −9846.43 17054.5i −0.521566 0.903379i −0.999685 0.0250840i \(-0.992015\pi\)
0.478119 0.878295i \(-0.341319\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5624.42 + 9741.79i 0.295423 + 0.511687i
\(714\) 0 0
\(715\) 3718.90 6441.32i 0.194516 0.336912i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 33746.9 1.75041 0.875206 0.483751i \(-0.160726\pi\)
0.875206 + 0.483751i \(0.160726\pi\)
\(720\) 0 0
\(721\) 3420.74 0.176692
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3092.05 + 5355.60i −0.158395 + 0.274347i
\(726\) 0 0
\(727\) −10380.4 17979.4i −0.529558 0.917221i −0.999406 0.0344737i \(-0.989025\pi\)
0.469848 0.882748i \(-0.344309\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −18943.7 32811.4i −0.958492 1.66016i
\(732\) 0 0
\(733\) −7122.02 + 12335.7i −0.358878 + 0.621596i −0.987774 0.155894i \(-0.950174\pi\)
0.628895 + 0.777490i \(0.283507\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7141.55 −0.356937
\(738\) 0 0
\(739\) 27490.2 1.36839 0.684196 0.729298i \(-0.260153\pi\)
0.684196 + 0.729298i \(0.260153\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18234.0 31582.3i 0.900326 1.55941i 0.0732537 0.997313i \(-0.476662\pi\)
0.827072 0.562096i \(-0.190005\pi\)
\(744\) 0 0
\(745\) 16674.6 + 28881.2i 0.820013 + 1.42030i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 13749.8 + 23815.4i 0.670771 + 1.16181i
\(750\) 0 0
\(751\) −19341.5 + 33500.5i −0.939791 + 1.62777i −0.173931 + 0.984758i \(0.555647\pi\)
−0.765860 + 0.643007i \(0.777686\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 936.449 0.0451402
\(756\) 0 0
\(757\) 37768.4 1.81337 0.906683 0.421813i \(-0.138606\pi\)
0.906683 + 0.421813i \(0.138606\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10406.6 + 18024.7i −0.495714 + 0.858603i −0.999988 0.00494154i \(-0.998427\pi\)
0.504273 + 0.863544i \(0.331760\pi\)
\(762\) 0 0
\(763\) 11008.2 + 19066.7i 0.522310 + 0.904667i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3087.74 5348.12i −0.145361 0.251772i
\(768\) 0 0
\(769\) −3060.85 + 5301.55i −0.143533 + 0.248607i −0.928825 0.370519i \(-0.879180\pi\)
0.785291 + 0.619126i \(0.212513\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34251.2 1.59370 0.796850 0.604177i \(-0.206498\pi\)
0.796850 + 0.604177i \(0.206498\pi\)
\(774\) 0 0
\(775\) −9535.78 −0.441981
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7412.23 12838.4i 0.340912 0.590478i
\(780\) 0 0
\(781\) 9516.59 + 16483.2i 0.436018 + 0.755206i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 30.4117 + 52.6746i 0.00138273 + 0.00239495i
\(786\) 0 0
\(787\) 4561.34 7900.47i 0.206600 0.357842i −0.744041 0.668134i \(-0.767093\pi\)
0.950641 + 0.310292i \(0.100427\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7095.12 −0.318930
\(792\) 0 0
\(793\) −4550.97 −0.203795
\(794\) 0 0