Properties

Label 234.6.b.b.181.1
Level $234$
Weight $6$
Character 234.181
Analytic conductor $37.530$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [234,6,Mod(181,234)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(234, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("234.181");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 234.b (of order \(2\), degree \(1\), 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: \(37.5298138362\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 234.181
Dual form 234.6.b.b.181.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000i q^{2} -16.0000 q^{4} +51.0000i q^{5} -105.000i q^{7} +64.0000i q^{8} +O(q^{10})\) \(q-4.00000i q^{2} -16.0000 q^{4} +51.0000i q^{5} -105.000i q^{7} +64.0000i q^{8} +204.000 q^{10} +120.000i q^{11} +(-598.000 - 117.000i) q^{13} -420.000 q^{14} +256.000 q^{16} +1101.00 q^{17} +1170.00i q^{19} -816.000i q^{20} +480.000 q^{22} -1050.00 q^{23} +524.000 q^{25} +(-468.000 + 2392.00i) q^{26} +1680.00i q^{28} +4104.00 q^{29} -9624.00i q^{31} -1024.00i q^{32} -4404.00i q^{34} +5355.00 q^{35} -8709.00i q^{37} +4680.00 q^{38} -3264.00 q^{40} -9480.00i q^{41} +9995.00 q^{43} -1920.00i q^{44} +4200.00i q^{46} -2943.00i q^{47} +5782.00 q^{49} -2096.00i q^{50} +(9568.00 + 1872.00i) q^{52} +750.000 q^{53} -6120.00 q^{55} +6720.00 q^{56} -16416.0i q^{58} -40938.0i q^{59} -57920.0 q^{61} -38496.0 q^{62} -4096.00 q^{64} +(5967.00 - 30498.0i) q^{65} -22812.0i q^{67} -17616.0 q^{68} -21420.0i q^{70} +63741.0i q^{71} -58866.0i q^{73} -34836.0 q^{74} -18720.0i q^{76} +12600.0 q^{77} +63202.0 q^{79} +13056.0i q^{80} -37920.0 q^{82} +55458.0i q^{83} +56151.0i q^{85} -39980.0i q^{86} -7680.00 q^{88} -104778. i q^{89} +(-12285.0 + 62790.0i) q^{91} +16800.0 q^{92} -11772.0 q^{94} -59670.0 q^{95} -160452. i q^{97} -23128.0i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 32 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 32 q^{4} + 408 q^{10} - 1196 q^{13} - 840 q^{14} + 512 q^{16} + 2202 q^{17} + 960 q^{22} - 2100 q^{23} + 1048 q^{25} - 936 q^{26} + 8208 q^{29} + 10710 q^{35} + 9360 q^{38} - 6528 q^{40} + 19990 q^{43} + 11564 q^{49} + 19136 q^{52} + 1500 q^{53} - 12240 q^{55} + 13440 q^{56} - 115840 q^{61} - 76992 q^{62} - 8192 q^{64} + 11934 q^{65} - 35232 q^{68} - 69672 q^{74} + 25200 q^{77} + 126404 q^{79} - 75840 q^{82} - 15360 q^{88} - 24570 q^{91} + 33600 q^{92} - 23544 q^{94} - 119340 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/234\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 0 0
\(4\) −16.0000 −0.500000
\(5\) 51.0000i 0.912316i 0.889899 + 0.456158i \(0.150775\pi\)
−0.889899 + 0.456158i \(0.849225\pi\)
\(6\) 0 0
\(7\) 105.000i 0.809924i −0.914334 0.404962i \(-0.867285\pi\)
0.914334 0.404962i \(-0.132715\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 0 0
\(10\) 204.000 0.645105
\(11\) 120.000i 0.299020i 0.988760 + 0.149510i \(0.0477695\pi\)
−0.988760 + 0.149510i \(0.952230\pi\)
\(12\) 0 0
\(13\) −598.000 117.000i −0.981393 0.192012i
\(14\) −420.000 −0.572703
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) 1101.00 0.923985 0.461993 0.886884i \(-0.347135\pi\)
0.461993 + 0.886884i \(0.347135\pi\)
\(18\) 0 0
\(19\) 1170.00i 0.743536i 0.928326 + 0.371768i \(0.121248\pi\)
−0.928326 + 0.371768i \(0.878752\pi\)
\(20\) 816.000i 0.456158i
\(21\) 0 0
\(22\) 480.000 0.211439
\(23\) −1050.00 −0.413875 −0.206938 0.978354i \(-0.566350\pi\)
−0.206938 + 0.978354i \(0.566350\pi\)
\(24\) 0 0
\(25\) 524.000 0.167680
\(26\) −468.000 + 2392.00i −0.135773 + 0.693949i
\(27\) 0 0
\(28\) 1680.00i 0.404962i
\(29\) 4104.00 0.906176 0.453088 0.891466i \(-0.350322\pi\)
0.453088 + 0.891466i \(0.350322\pi\)
\(30\) 0 0
\(31\) 9624.00i 1.79867i −0.437261 0.899335i \(-0.644051\pi\)
0.437261 0.899335i \(-0.355949\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 0 0
\(34\) 4404.00i 0.653356i
\(35\) 5355.00 0.738906
\(36\) 0 0
\(37\) 8709.00i 1.04584i −0.852383 0.522918i \(-0.824843\pi\)
0.852383 0.522918i \(-0.175157\pi\)
\(38\) 4680.00 0.525759
\(39\) 0 0
\(40\) −3264.00 −0.322552
\(41\) 9480.00i 0.880742i −0.897816 0.440371i \(-0.854847\pi\)
0.897816 0.440371i \(-0.145153\pi\)
\(42\) 0 0
\(43\) 9995.00 0.824350 0.412175 0.911105i \(-0.364769\pi\)
0.412175 + 0.911105i \(0.364769\pi\)
\(44\) 1920.00i 0.149510i
\(45\) 0 0
\(46\) 4200.00i 0.292654i
\(47\) 2943.00i 0.194333i −0.995268 0.0971663i \(-0.969022\pi\)
0.995268 0.0971663i \(-0.0309779\pi\)
\(48\) 0 0
\(49\) 5782.00 0.344023
\(50\) 2096.00i 0.118568i
\(51\) 0 0
\(52\) 9568.00 + 1872.00i 0.490696 + 0.0960058i
\(53\) 750.000 0.0366751 0.0183376 0.999832i \(-0.494163\pi\)
0.0183376 + 0.999832i \(0.494163\pi\)
\(54\) 0 0
\(55\) −6120.00 −0.272800
\(56\) 6720.00 0.286351
\(57\) 0 0
\(58\) 16416.0i 0.640763i
\(59\) 40938.0i 1.53108i −0.643391 0.765538i \(-0.722473\pi\)
0.643391 0.765538i \(-0.277527\pi\)
\(60\) 0 0
\(61\) −57920.0 −1.99298 −0.996492 0.0836839i \(-0.973331\pi\)
−0.996492 + 0.0836839i \(0.973331\pi\)
\(62\) −38496.0 −1.27185
\(63\) 0 0
\(64\) −4096.00 −0.125000
\(65\) 5967.00 30498.0i 0.175175 0.895340i
\(66\) 0 0
\(67\) 22812.0i 0.620835i −0.950600 0.310418i \(-0.899531\pi\)
0.950600 0.310418i \(-0.100469\pi\)
\(68\) −17616.0 −0.461993
\(69\) 0 0
\(70\) 21420.0i 0.522486i
\(71\) 63741.0i 1.50063i 0.661082 + 0.750314i \(0.270098\pi\)
−0.661082 + 0.750314i \(0.729902\pi\)
\(72\) 0 0
\(73\) 58866.0i 1.29288i −0.762966 0.646439i \(-0.776258\pi\)
0.762966 0.646439i \(-0.223742\pi\)
\(74\) −34836.0 −0.739518
\(75\) 0 0
\(76\) 18720.0i 0.371768i
\(77\) 12600.0 0.242183
\(78\) 0 0
\(79\) 63202.0 1.13937 0.569683 0.821865i \(-0.307066\pi\)
0.569683 + 0.821865i \(0.307066\pi\)
\(80\) 13056.0i 0.228079i
\(81\) 0 0
\(82\) −37920.0 −0.622779
\(83\) 55458.0i 0.883627i 0.897107 + 0.441813i \(0.145665\pi\)
−0.897107 + 0.441813i \(0.854335\pi\)
\(84\) 0 0
\(85\) 56151.0i 0.842966i
\(86\) 39980.0i 0.582903i
\(87\) 0 0
\(88\) −7680.00 −0.105719
\(89\) 104778.i 1.40215i −0.713087 0.701076i \(-0.752703\pi\)
0.713087 0.701076i \(-0.247297\pi\)
\(90\) 0 0
\(91\) −12285.0 + 62790.0i −0.155515 + 0.794853i
\(92\) 16800.0 0.206938
\(93\) 0 0
\(94\) −11772.0 −0.137414
\(95\) −59670.0 −0.678339
\(96\) 0 0
\(97\) 160452.i 1.73147i −0.500500 0.865737i \(-0.666850\pi\)
0.500500 0.865737i \(-0.333150\pi\)
\(98\) 23128.0i 0.243261i
\(99\) 0 0
\(100\) −8384.00 −0.0838400
\(101\) 113124. 1.10345 0.551723 0.834027i \(-0.313970\pi\)
0.551723 + 0.834027i \(0.313970\pi\)
\(102\) 0 0
\(103\) 25046.0 0.232619 0.116310 0.993213i \(-0.462894\pi\)
0.116310 + 0.993213i \(0.462894\pi\)
\(104\) 7488.00 38272.0i 0.0678864 0.346975i
\(105\) 0 0
\(106\) 3000.00i 0.0259332i
\(107\) −24924.0 −0.210455 −0.105227 0.994448i \(-0.533557\pi\)
−0.105227 + 0.994448i \(0.533557\pi\)
\(108\) 0 0
\(109\) 144831.i 1.16760i −0.811896 0.583802i \(-0.801565\pi\)
0.811896 0.583802i \(-0.198435\pi\)
\(110\) 24480.0i 0.192899i
\(111\) 0 0
\(112\) 26880.0i 0.202481i
\(113\) −100266. −0.738682 −0.369341 0.929294i \(-0.620417\pi\)
−0.369341 + 0.929294i \(0.620417\pi\)
\(114\) 0 0
\(115\) 53550.0i 0.377585i
\(116\) −65664.0 −0.453088
\(117\) 0 0
\(118\) −163752. −1.08263
\(119\) 115605.i 0.748358i
\(120\) 0 0
\(121\) 146651. 0.910587
\(122\) 231680.i 1.40925i
\(123\) 0 0
\(124\) 153984.i 0.899335i
\(125\) 186099.i 1.06529i
\(126\) 0 0
\(127\) −202754. −1.11548 −0.557738 0.830017i \(-0.688331\pi\)
−0.557738 + 0.830017i \(0.688331\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) 0 0
\(130\) −121992. 23868.0i −0.633101 0.123868i
\(131\) 303855. 1.54699 0.773496 0.633801i \(-0.218506\pi\)
0.773496 + 0.633801i \(0.218506\pi\)
\(132\) 0 0
\(133\) 122850. 0.602207
\(134\) −91248.0 −0.438997
\(135\) 0 0
\(136\) 70464.0i 0.326678i
\(137\) 63738.0i 0.290133i −0.989422 0.145066i \(-0.953660\pi\)
0.989422 0.145066i \(-0.0463396\pi\)
\(138\) 0 0
\(139\) 13841.0 0.0607618 0.0303809 0.999538i \(-0.490328\pi\)
0.0303809 + 0.999538i \(0.490328\pi\)
\(140\) −85680.0 −0.369453
\(141\) 0 0
\(142\) 254964. 1.06110
\(143\) 14040.0 71760.0i 0.0574152 0.293456i
\(144\) 0 0
\(145\) 209304.i 0.826718i
\(146\) −235464. −0.914202
\(147\) 0 0
\(148\) 139344.i 0.522918i
\(149\) 276426.i 1.02003i −0.860165 0.510015i \(-0.829640\pi\)
0.860165 0.510015i \(-0.170360\pi\)
\(150\) 0 0
\(151\) 321333.i 1.14687i 0.819252 + 0.573433i \(0.194389\pi\)
−0.819252 + 0.573433i \(0.805611\pi\)
\(152\) −74880.0 −0.262880
\(153\) 0 0
\(154\) 50400.0i 0.171249i
\(155\) 490824. 1.64095
\(156\) 0 0
\(157\) 339506. 1.09925 0.549627 0.835410i \(-0.314770\pi\)
0.549627 + 0.835410i \(0.314770\pi\)
\(158\) 252808.i 0.805653i
\(159\) 0 0
\(160\) 52224.0 0.161276
\(161\) 110250.i 0.335208i
\(162\) 0 0
\(163\) 395718.i 1.16659i 0.812262 + 0.583293i \(0.198236\pi\)
−0.812262 + 0.583293i \(0.801764\pi\)
\(164\) 151680.i 0.440371i
\(165\) 0 0
\(166\) 221832. 0.624819
\(167\) 426708.i 1.18397i 0.805950 + 0.591984i \(0.201655\pi\)
−0.805950 + 0.591984i \(0.798345\pi\)
\(168\) 0 0
\(169\) 343915. + 139932.i 0.926263 + 0.376878i
\(170\) 224604. 0.596067
\(171\) 0 0
\(172\) −159920. −0.412175
\(173\) −16026.0 −0.0407108 −0.0203554 0.999793i \(-0.506480\pi\)
−0.0203554 + 0.999793i \(0.506480\pi\)
\(174\) 0 0
\(175\) 55020.0i 0.135808i
\(176\) 30720.0i 0.0747549i
\(177\) 0 0
\(178\) −419112. −0.991471
\(179\) 690045. 1.60970 0.804850 0.593479i \(-0.202246\pi\)
0.804850 + 0.593479i \(0.202246\pi\)
\(180\) 0 0
\(181\) −96478.0 −0.218893 −0.109446 0.993993i \(-0.534908\pi\)
−0.109446 + 0.993993i \(0.534908\pi\)
\(182\) 251160. + 49140.0i 0.562046 + 0.109966i
\(183\) 0 0
\(184\) 67200.0i 0.146327i
\(185\) 444159. 0.954134
\(186\) 0 0
\(187\) 132120.i 0.276290i
\(188\) 47088.0i 0.0971663i
\(189\) 0 0
\(190\) 238680.i 0.479658i
\(191\) −708180. −1.40462 −0.702312 0.711869i \(-0.747849\pi\)
−0.702312 + 0.711869i \(0.747849\pi\)
\(192\) 0 0
\(193\) 347862.i 0.672224i 0.941822 + 0.336112i \(0.109112\pi\)
−0.941822 + 0.336112i \(0.890888\pi\)
\(194\) −641808. −1.22434
\(195\) 0 0
\(196\) −92512.0 −0.172012
\(197\) 899589.i 1.65150i 0.564036 + 0.825750i \(0.309248\pi\)
−0.564036 + 0.825750i \(0.690752\pi\)
\(198\) 0 0
\(199\) 143116. 0.256186 0.128093 0.991762i \(-0.459114\pi\)
0.128093 + 0.991762i \(0.459114\pi\)
\(200\) 33536.0i 0.0592838i
\(201\) 0 0
\(202\) 452496.i 0.780255i
\(203\) 430920.i 0.733933i
\(204\) 0 0
\(205\) 483480. 0.803515
\(206\) 100184.i 0.164487i
\(207\) 0 0
\(208\) −153088. 29952.0i −0.245348 0.0480029i
\(209\) −140400. −0.222332
\(210\) 0 0
\(211\) −339731. −0.525326 −0.262663 0.964888i \(-0.584601\pi\)
−0.262663 + 0.964888i \(0.584601\pi\)
\(212\) −12000.0 −0.0183376
\(213\) 0 0
\(214\) 99696.0i 0.148814i
\(215\) 509745.i 0.752068i
\(216\) 0 0
\(217\) −1.01052e6 −1.45679
\(218\) −579324. −0.825620
\(219\) 0 0
\(220\) 97920.0 0.136400
\(221\) −658398. 128817.i −0.906792 0.177416i
\(222\) 0 0
\(223\) 623757.i 0.839950i −0.907536 0.419975i \(-0.862039\pi\)
0.907536 0.419975i \(-0.137961\pi\)
\(224\) −107520. −0.143176
\(225\) 0 0
\(226\) 401064.i 0.522327i
\(227\) 177612.i 0.228775i −0.993436 0.114387i \(-0.963510\pi\)
0.993436 0.114387i \(-0.0364905\pi\)
\(228\) 0 0
\(229\) 1.18705e6i 1.49582i 0.663799 + 0.747911i \(0.268943\pi\)
−0.663799 + 0.747911i \(0.731057\pi\)
\(230\) −214200. −0.266993
\(231\) 0 0
\(232\) 262656.i 0.320381i
\(233\) 112317. 0.135536 0.0677682 0.997701i \(-0.478412\pi\)
0.0677682 + 0.997701i \(0.478412\pi\)
\(234\) 0 0
\(235\) 150093. 0.177293
\(236\) 655008.i 0.765538i
\(237\) 0 0
\(238\) −462420. −0.529169
\(239\) 1.19805e6i 1.35669i −0.734743 0.678346i \(-0.762697\pi\)
0.734743 0.678346i \(-0.237303\pi\)
\(240\) 0 0
\(241\) 1.16629e6i 1.29349i −0.762707 0.646744i \(-0.776130\pi\)
0.762707 0.646744i \(-0.223870\pi\)
\(242\) 586604.i 0.643882i
\(243\) 0 0
\(244\) 926720. 0.996492
\(245\) 294882.i 0.313858i
\(246\) 0 0
\(247\) 136890. 699660.i 0.142767 0.729701i
\(248\) 615936. 0.635926
\(249\) 0 0
\(250\) 744396. 0.753276
\(251\) −648996. −0.650216 −0.325108 0.945677i \(-0.605401\pi\)
−0.325108 + 0.945677i \(0.605401\pi\)
\(252\) 0 0
\(253\) 126000.i 0.123757i
\(254\) 811016.i 0.788760i
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) 945885. 0.893317 0.446658 0.894705i \(-0.352614\pi\)
0.446658 + 0.894705i \(0.352614\pi\)
\(258\) 0 0
\(259\) −914445. −0.847048
\(260\) −95472.0 + 487968.i −0.0875876 + 0.447670i
\(261\) 0 0
\(262\) 1.21542e6i 1.09389i
\(263\) −1.01222e6 −0.902375 −0.451188 0.892429i \(-0.649000\pi\)
−0.451188 + 0.892429i \(0.649000\pi\)
\(264\) 0 0
\(265\) 38250.0i 0.0334593i
\(266\) 491400.i 0.425825i
\(267\) 0 0
\(268\) 364992.i 0.310418i
\(269\) 1.01772e6 0.857527 0.428763 0.903417i \(-0.358949\pi\)
0.428763 + 0.903417i \(0.358949\pi\)
\(270\) 0 0
\(271\) 463461.i 0.383345i −0.981459 0.191673i \(-0.938609\pi\)
0.981459 0.191673i \(-0.0613912\pi\)
\(272\) 281856. 0.230996
\(273\) 0 0
\(274\) −254952. −0.205155
\(275\) 62880.0i 0.0501396i
\(276\) 0 0
\(277\) 332528. 0.260393 0.130196 0.991488i \(-0.458439\pi\)
0.130196 + 0.991488i \(0.458439\pi\)
\(278\) 55364.0i 0.0429651i
\(279\) 0 0
\(280\) 342720.i 0.261243i
\(281\) 49122.0i 0.0371116i −0.999828 0.0185558i \(-0.994093\pi\)
0.999828 0.0185558i \(-0.00590684\pi\)
\(282\) 0 0
\(283\) −1.55848e6 −1.15674 −0.578371 0.815774i \(-0.696311\pi\)
−0.578371 + 0.815774i \(0.696311\pi\)
\(284\) 1.01986e6i 0.750314i
\(285\) 0 0
\(286\) −287040. 56160.0i −0.207504 0.0405987i
\(287\) −995400. −0.713334
\(288\) 0 0
\(289\) −207656. −0.146251
\(290\) 837216. 0.584578
\(291\) 0 0
\(292\) 941856.i 0.646439i
\(293\) 218463.i 0.148665i −0.997234 0.0743325i \(-0.976317\pi\)
0.997234 0.0743325i \(-0.0236826\pi\)
\(294\) 0 0
\(295\) 2.08784e6 1.39682
\(296\) 557376. 0.369759
\(297\) 0 0
\(298\) −1.10570e6 −0.721271
\(299\) 627900. + 122850.i 0.406174 + 0.0794689i
\(300\) 0 0
\(301\) 1.04948e6i 0.667661i
\(302\) 1.28533e6 0.810957
\(303\) 0 0
\(304\) 299520.i 0.185884i
\(305\) 2.95392e6i 1.81823i
\(306\) 0 0
\(307\) 321102.i 0.194445i −0.995263 0.0972226i \(-0.969004\pi\)
0.995263 0.0972226i \(-0.0309959\pi\)
\(308\) −201600. −0.121092
\(309\) 0 0
\(310\) 1.96330e6i 1.16033i
\(311\) −3.33725e6 −1.95654 −0.978269 0.207340i \(-0.933519\pi\)
−0.978269 + 0.207340i \(0.933519\pi\)
\(312\) 0 0
\(313\) 1.16568e6 0.672538 0.336269 0.941766i \(-0.390835\pi\)
0.336269 + 0.941766i \(0.390835\pi\)
\(314\) 1.35802e6i 0.777290i
\(315\) 0 0
\(316\) −1.01123e6 −0.569683
\(317\) 73518.0i 0.0410909i 0.999789 + 0.0205454i \(0.00654028\pi\)
−0.999789 + 0.0205454i \(0.993460\pi\)
\(318\) 0 0
\(319\) 492480.i 0.270964i
\(320\) 208896.i 0.114039i
\(321\) 0 0
\(322\) 441000. 0.237028
\(323\) 1.28817e6i 0.687016i
\(324\) 0 0
\(325\) −313352. 61308.0i −0.164560 0.0321965i
\(326\) 1.58287e6 0.824901
\(327\) 0 0
\(328\) 606720. 0.311389
\(329\) −309015. −0.157395
\(330\) 0 0
\(331\) 632682.i 0.317406i −0.987326 0.158703i \(-0.949269\pi\)
0.987326 0.158703i \(-0.0507313\pi\)
\(332\) 887328.i 0.441813i
\(333\) 0 0
\(334\) 1.70683e6 0.837191
\(335\) 1.16341e6 0.566398
\(336\) 0 0
\(337\) −326843. −0.156771 −0.0783853 0.996923i \(-0.524976\pi\)
−0.0783853 + 0.996923i \(0.524976\pi\)
\(338\) 559728. 1.37566e6i 0.266493 0.654967i
\(339\) 0 0
\(340\) 898416.i 0.421483i
\(341\) 1.15488e6 0.537837
\(342\) 0 0
\(343\) 2.37184e6i 1.08856i
\(344\) 639680.i 0.291452i
\(345\) 0 0
\(346\) 64104.0i 0.0287869i
\(347\) −2.96275e6 −1.32090 −0.660452 0.750868i \(-0.729635\pi\)
−0.660452 + 0.750868i \(0.729635\pi\)
\(348\) 0 0
\(349\) 866325.i 0.380730i −0.981713 0.190365i \(-0.939033\pi\)
0.981713 0.190365i \(-0.0609672\pi\)
\(350\) −220080. −0.0960308
\(351\) 0 0
\(352\) 122880. 0.0528597
\(353\) 1.66291e6i 0.710282i 0.934813 + 0.355141i \(0.115567\pi\)
−0.934813 + 0.355141i \(0.884433\pi\)
\(354\) 0 0
\(355\) −3.25079e6 −1.36905
\(356\) 1.67645e6i 0.701076i
\(357\) 0 0
\(358\) 2.76018e6i 1.13823i
\(359\) 625536.i 0.256163i 0.991764 + 0.128081i \(0.0408819\pi\)
−0.991764 + 0.128081i \(0.959118\pi\)
\(360\) 0 0
\(361\) 1.10720e6 0.447155
\(362\) 385912.i 0.154781i
\(363\) 0 0
\(364\) 196560. 1.00464e6i 0.0777574 0.397427i
\(365\) 3.00217e6 1.17951
\(366\) 0 0
\(367\) 1.08327e6 0.419829 0.209914 0.977720i \(-0.432681\pi\)
0.209914 + 0.977720i \(0.432681\pi\)
\(368\) −268800. −0.103469
\(369\) 0 0
\(370\) 1.77664e6i 0.674674i
\(371\) 78750.0i 0.0297041i
\(372\) 0 0
\(373\) −1.78896e6 −0.665775 −0.332888 0.942967i \(-0.608023\pi\)
−0.332888 + 0.942967i \(0.608023\pi\)
\(374\) 528480. 0.195366
\(375\) 0 0
\(376\) 188352. 0.0687069
\(377\) −2.45419e6 480168.i −0.889314 0.173996i
\(378\) 0 0
\(379\) 868614.i 0.310620i −0.987866 0.155310i \(-0.950362\pi\)
0.987866 0.155310i \(-0.0496376\pi\)
\(380\) 954720. 0.339170
\(381\) 0 0
\(382\) 2.83272e6i 0.993220i
\(383\) 1.07972e6i 0.376108i −0.982159 0.188054i \(-0.939782\pi\)
0.982159 0.188054i \(-0.0602179\pi\)
\(384\) 0 0
\(385\) 642600.i 0.220947i
\(386\) 1.39145e6 0.475334
\(387\) 0 0
\(388\) 2.56723e6i 0.865737i
\(389\) −1.28822e6 −0.431634 −0.215817 0.976434i \(-0.569241\pi\)
−0.215817 + 0.976434i \(0.569241\pi\)
\(390\) 0 0
\(391\) −1.15605e6 −0.382415
\(392\) 370048.i 0.121631i
\(393\) 0 0
\(394\) 3.59836e6 1.16779
\(395\) 3.22330e6i 1.03946i
\(396\) 0 0
\(397\) 5.46909e6i 1.74156i 0.491672 + 0.870781i \(0.336386\pi\)
−0.491672 + 0.870781i \(0.663614\pi\)
\(398\) 572464.i 0.181151i
\(399\) 0 0
\(400\) 134144. 0.0419200
\(401\) 1.58612e6i 0.492577i −0.969196 0.246289i \(-0.920789\pi\)
0.969196 0.246289i \(-0.0792112\pi\)
\(402\) 0 0
\(403\) −1.12601e6 + 5.75515e6i −0.345365 + 1.76520i
\(404\) −1.80998e6 −0.551723
\(405\) 0 0
\(406\) −1.72368e6 −0.518969
\(407\) 1.04508e6 0.312726
\(408\) 0 0
\(409\) 6.44192e6i 1.90418i −0.305825 0.952088i \(-0.598932\pi\)
0.305825 0.952088i \(-0.401068\pi\)
\(410\) 1.93392e6i 0.568171i
\(411\) 0 0
\(412\) −400736. −0.116310
\(413\) −4.29849e6 −1.24005
\(414\) 0 0
\(415\) −2.82836e6 −0.806147
\(416\) −119808. + 612352.i −0.0339432 + 0.173487i
\(417\) 0 0
\(418\) 561600.i 0.157212i
\(419\) 4.30545e6 1.19807 0.599037 0.800721i \(-0.295550\pi\)
0.599037 + 0.800721i \(0.295550\pi\)
\(420\) 0 0
\(421\) 1.51346e6i 0.416164i −0.978111 0.208082i \(-0.933278\pi\)
0.978111 0.208082i \(-0.0667221\pi\)
\(422\) 1.35892e6i 0.371462i
\(423\) 0 0
\(424\) 48000.0i 0.0129666i
\(425\) 576924. 0.154934
\(426\) 0 0
\(427\) 6.08160e6i 1.61417i
\(428\) 398784. 0.105227
\(429\) 0 0
\(430\) 2.03898e6 0.531792
\(431\) 1.43116e6i 0.371105i −0.982634 0.185552i \(-0.940593\pi\)
0.982634 0.185552i \(-0.0594074\pi\)
\(432\) 0 0
\(433\) 429613. 0.110118 0.0550589 0.998483i \(-0.482465\pi\)
0.0550589 + 0.998483i \(0.482465\pi\)
\(434\) 4.04208e6i 1.03010i
\(435\) 0 0
\(436\) 2.31730e6i 0.583802i
\(437\) 1.22850e6i 0.307731i
\(438\) 0 0
\(439\) 552038. 0.136712 0.0683562 0.997661i \(-0.478225\pi\)
0.0683562 + 0.997661i \(0.478225\pi\)
\(440\) 391680.i 0.0964494i
\(441\) 0 0
\(442\) −515268. + 2.63359e6i −0.125452 + 0.641199i
\(443\) −2.15255e6 −0.521128 −0.260564 0.965457i \(-0.583908\pi\)
−0.260564 + 0.965457i \(0.583908\pi\)
\(444\) 0 0
\(445\) 5.34368e6 1.27921
\(446\) −2.49503e6 −0.593934
\(447\) 0 0
\(448\) 430080.i 0.101240i
\(449\) 1.40429e6i 0.328731i 0.986400 + 0.164365i \(0.0525576\pi\)
−0.986400 + 0.164365i \(0.947442\pi\)
\(450\) 0 0
\(451\) 1.13760e6 0.263359
\(452\) 1.60426e6 0.369341
\(453\) 0 0
\(454\) −710448. −0.161768
\(455\) −3.20229e6 626535.i −0.725157 0.141879i
\(456\) 0 0
\(457\) 1.32818e6i 0.297485i 0.988876 + 0.148743i \(0.0475226\pi\)
−0.988876 + 0.148743i \(0.952477\pi\)
\(458\) 4.74820e6 1.05771
\(459\) 0 0
\(460\) 856800.i 0.188793i
\(461\) 5.89070e6i 1.29096i 0.763775 + 0.645482i \(0.223344\pi\)
−0.763775 + 0.645482i \(0.776656\pi\)
\(462\) 0 0
\(463\) 2.37139e6i 0.514104i −0.966398 0.257052i \(-0.917249\pi\)
0.966398 0.257052i \(-0.0827511\pi\)
\(464\) 1.05062e6 0.226544
\(465\) 0 0
\(466\) 449268.i 0.0958387i
\(467\) −7.17827e6 −1.52310 −0.761548 0.648108i \(-0.775560\pi\)
−0.761548 + 0.648108i \(0.775560\pi\)
\(468\) 0 0
\(469\) −2.39526e6 −0.502829
\(470\) 600372.i 0.125365i
\(471\) 0 0
\(472\) 2.62003e6 0.541317
\(473\) 1.19940e6i 0.246497i
\(474\) 0 0
\(475\) 613080.i 0.124676i
\(476\) 1.84968e6i 0.374179i
\(477\) 0 0
\(478\) −4.79221e6 −0.959326
\(479\) 7.25193e6i 1.44416i 0.691810 + 0.722079i \(0.256814\pi\)
−0.691810 + 0.722079i \(0.743186\pi\)
\(480\) 0 0
\(481\) −1.01895e6 + 5.20798e6i −0.200813 + 1.02638i
\(482\) −4.66514e6 −0.914634
\(483\) 0 0
\(484\) −2.34642e6 −0.455294
\(485\) 8.18305e6 1.57965
\(486\) 0 0
\(487\) 2.53364e6i 0.484087i 0.970265 + 0.242043i \(0.0778176\pi\)
−0.970265 + 0.242043i \(0.922182\pi\)
\(488\) 3.70688e6i 0.704626i
\(489\) 0 0
\(490\) 1.17953e6 0.221931
\(491\) −8.46186e6 −1.58403 −0.792013 0.610504i \(-0.790967\pi\)
−0.792013 + 0.610504i \(0.790967\pi\)
\(492\) 0 0
\(493\) 4.51850e6 0.837293
\(494\) −2.79864e6 547560.i −0.515976 0.100952i
\(495\) 0 0
\(496\) 2.46374e6i 0.449667i
\(497\) 6.69280e6 1.21539
\(498\) 0 0
\(499\) 1.95383e6i 0.351265i 0.984456 + 0.175633i \(0.0561971\pi\)
−0.984456 + 0.175633i \(0.943803\pi\)
\(500\) 2.97758e6i 0.532646i
\(501\) 0 0
\(502\) 2.59598e6i 0.459772i
\(503\) −119778. −0.0211085 −0.0105542 0.999944i \(-0.503360\pi\)
−0.0105542 + 0.999944i \(0.503360\pi\)
\(504\) 0 0
\(505\) 5.76932e6i 1.00669i
\(506\) −504000. −0.0875093
\(507\) 0 0
\(508\) 3.24406e6 0.557738
\(509\) 1.03653e7i 1.77332i −0.462420 0.886661i \(-0.653019\pi\)
0.462420 0.886661i \(-0.346981\pi\)
\(510\) 0 0
\(511\) −6.18093e6 −1.04713
\(512\) 262144.i 0.0441942i
\(513\) 0 0
\(514\) 3.78354e6i 0.631670i
\(515\) 1.27735e6i 0.212222i
\(516\) 0 0
\(517\) 353160. 0.0581092
\(518\) 3.65778e6i 0.598954i
\(519\) 0 0
\(520\) 1.95187e6 + 381888.i 0.316550 + 0.0619338i
\(521\) 1.04899e7 1.69307 0.846537 0.532330i \(-0.178684\pi\)
0.846537 + 0.532330i \(0.178684\pi\)
\(522\) 0 0
\(523\) 4.42662e6 0.707649 0.353824 0.935312i \(-0.384881\pi\)
0.353824 + 0.935312i \(0.384881\pi\)
\(524\) −4.86168e6 −0.773496
\(525\) 0 0
\(526\) 4.04890e6i 0.638076i
\(527\) 1.05960e7i 1.66194i
\(528\) 0 0
\(529\) −5.33384e6 −0.828707
\(530\) 153000. 0.0236593
\(531\) 0 0
\(532\) −1.96560e6 −0.301104
\(533\) −1.10916e6 + 5.66904e6i −0.169113 + 0.864354i
\(534\) 0 0
\(535\) 1.27112e6i 0.192001i
\(536\) 1.45997e6 0.219498
\(537\) 0 0
\(538\) 4.07088e6i 0.606363i
\(539\) 693840.i 0.102870i
\(540\) 0 0
\(541\) 2.26377e6i 0.332536i −0.986081 0.166268i \(-0.946828\pi\)
0.986081 0.166268i \(-0.0531717\pi\)
\(542\) −1.85384e6 −0.271066
\(543\) 0 0
\(544\) 1.12742e6i 0.163339i
\(545\) 7.38638e6 1.06522
\(546\) 0 0
\(547\) 7.21090e6 1.03044 0.515218 0.857059i \(-0.327711\pi\)
0.515218 + 0.857059i \(0.327711\pi\)
\(548\) 1.01981e6i 0.145066i
\(549\) 0 0
\(550\) 251520. 0.0354540
\(551\) 4.80168e6i 0.673774i
\(552\) 0 0
\(553\) 6.63621e6i 0.922799i
\(554\) 1.33011e6i 0.184125i
\(555\) 0 0
\(556\) −221456. −0.0303809
\(557\) 273507.i 0.0373534i 0.999826 + 0.0186767i \(0.00594533\pi\)
−0.999826 + 0.0186767i \(0.994055\pi\)
\(558\) 0 0
\(559\) −5.97701e6 1.16942e6i −0.809011 0.158285i
\(560\) 1.37088e6 0.184727
\(561\) 0 0
\(562\) −196488. −0.0262419
\(563\) 959349. 0.127557 0.0637787 0.997964i \(-0.479685\pi\)
0.0637787 + 0.997964i \(0.479685\pi\)
\(564\) 0 0
\(565\) 5.11357e6i 0.673911i
\(566\) 6.23394e6i 0.817940i
\(567\) 0 0
\(568\) −4.07942e6 −0.530552
\(569\) 1.19403e7 1.54609 0.773044 0.634352i \(-0.218733\pi\)
0.773044 + 0.634352i \(0.218733\pi\)
\(570\) 0 0
\(571\) 7.20205e6 0.924413 0.462206 0.886772i \(-0.347058\pi\)
0.462206 + 0.886772i \(0.347058\pi\)
\(572\) −224640. + 1.14816e6i −0.0287076 + 0.146728i
\(573\) 0 0
\(574\) 3.98160e6i 0.504403i
\(575\) −550200. −0.0693986
\(576\) 0 0
\(577\) 1.66990e6i 0.208810i 0.994535 + 0.104405i \(0.0332938\pi\)
−0.994535 + 0.104405i \(0.966706\pi\)
\(578\) 830624.i 0.103415i
\(579\) 0 0
\(580\) 3.34886e6i 0.413359i
\(581\) 5.82309e6 0.715671
\(582\) 0 0
\(583\) 90000.0i 0.0109666i
\(584\) 3.76742e6 0.457101
\(585\) 0 0
\(586\) −873852. −0.105122
\(587\) 8.29913e6i 0.994117i 0.867717 + 0.497059i \(0.165587\pi\)
−0.867717 + 0.497059i \(0.834413\pi\)
\(588\) 0 0
\(589\) 1.12601e7 1.33738
\(590\) 8.35135e6i 0.987704i
\(591\) 0 0
\(592\) 2.22950e6i 0.261459i
\(593\) 4.48969e6i 0.524300i −0.965027 0.262150i \(-0.915568\pi\)
0.965027 0.262150i \(-0.0844315\pi\)
\(594\) 0 0
\(595\) 5.89586e6 0.682738
\(596\) 4.42282e6i 0.510015i
\(597\) 0 0
\(598\) 491400. 2.51160e6i 0.0561930 0.287209i
\(599\) −1.38261e6 −0.157446 −0.0787232 0.996897i \(-0.525084\pi\)
−0.0787232 + 0.996897i \(0.525084\pi\)
\(600\) 0 0
\(601\) 1.04021e7 1.17472 0.587359 0.809327i \(-0.300168\pi\)
0.587359 + 0.809327i \(0.300168\pi\)
\(602\) −4.19790e6 −0.472107
\(603\) 0 0
\(604\) 5.14133e6i 0.573433i
\(605\) 7.47920e6i 0.830743i
\(606\) 0 0
\(607\) −4.78668e6 −0.527306 −0.263653 0.964618i \(-0.584927\pi\)
−0.263653 + 0.964618i \(0.584927\pi\)
\(608\) 1.19808e6 0.131440
\(609\) 0 0
\(610\) −1.18157e7 −1.28568
\(611\) −344331. + 1.75991e6i −0.0373141 + 0.190717i
\(612\) 0 0
\(613\) 1.04783e7i 1.12627i −0.826366 0.563134i \(-0.809596\pi\)
0.826366 0.563134i \(-0.190404\pi\)
\(614\) −1.28441e6 −0.137493
\(615\) 0 0
\(616\) 806400.i 0.0856246i
\(617\) 1.79106e7i 1.89407i −0.321128 0.947036i \(-0.604062\pi\)
0.321128 0.947036i \(-0.395938\pi\)
\(618\) 0 0
\(619\) 4.43222e6i 0.464938i 0.972604 + 0.232469i \(0.0746804\pi\)
−0.972604 + 0.232469i \(0.925320\pi\)
\(620\) −7.85318e6 −0.820477
\(621\) 0 0
\(622\) 1.33490e7i 1.38348i
\(623\) −1.10017e7 −1.13564
\(624\) 0 0
\(625\) −7.85355e6 −0.804203
\(626\) 4.66270e6i 0.475556i
\(627\) 0 0
\(628\) −5.43210e6 −0.549627
\(629\) 9.58861e6i 0.966338i
\(630\) 0 0
\(631\) 1.43291e7i 1.43267i −0.697756 0.716335i \(-0.745818\pi\)
0.697756 0.716335i \(-0.254182\pi\)
\(632\) 4.04493e6i 0.402827i
\(633\) 0 0
\(634\) 294072. 0.0290556
\(635\) 1.03405e7i 1.01767i
\(636\) 0 0
\(637\) −3.45764e6 676494.i −0.337622 0.0660565i
\(638\) 1.96992e6 0.191601
\(639\) 0 0
\(640\) −835584. −0.0806381
\(641\) −6.65869e6 −0.640094 −0.320047 0.947402i \(-0.603699\pi\)
−0.320047 + 0.947402i \(0.603699\pi\)
\(642\) 0 0
\(643\) 1.55224e7i 1.48058i −0.672286 0.740291i \(-0.734688\pi\)
0.672286 0.740291i \(-0.265312\pi\)
\(644\) 1.76400e6i 0.167604i
\(645\) 0 0
\(646\) 5.15268e6 0.485794
\(647\) 2.44454e6 0.229581 0.114791 0.993390i \(-0.463380\pi\)
0.114791 + 0.993390i \(0.463380\pi\)
\(648\) 0 0
\(649\) 4.91256e6 0.457821
\(650\) −245232. + 1.25341e6i −0.0227664 + 0.116361i
\(651\) 0 0
\(652\) 6.33149e6i 0.583293i
\(653\) −1.16500e7 −1.06916 −0.534580 0.845118i \(-0.679530\pi\)
−0.534580 + 0.845118i \(0.679530\pi\)
\(654\) 0 0
\(655\) 1.54966e7i 1.41135i
\(656\) 2.42688e6i 0.220185i
\(657\) 0 0
\(658\) 1.23606e6i 0.111295i
\(659\) −1.33185e7 −1.19465 −0.597326 0.801999i \(-0.703770\pi\)
−0.597326 + 0.801999i \(0.703770\pi\)
\(660\) 0 0
\(661\) 1.35722e7i 1.20822i 0.796900 + 0.604112i \(0.206472\pi\)
−0.796900 + 0.604112i \(0.793528\pi\)
\(662\) −2.53073e6 −0.224440
\(663\) 0 0
\(664\) −3.54931e6 −0.312409
\(665\) 6.26535e6i 0.549403i
\(666\) 0 0
\(667\) −4.30920e6 −0.375044
\(668\) 6.82733e6i 0.591984i
\(669\) 0 0
\(670\) 4.65365e6i 0.400504i
\(671\) 6.95040e6i 0.595941i
\(672\) 0 0
\(673\) −1.58674e7 −1.35042 −0.675209 0.737626i \(-0.735947\pi\)
−0.675209 + 0.737626i \(0.735947\pi\)
\(674\) 1.30737e6i 0.110854i
\(675\) 0 0
\(676\) −5.50264e6 2.23891e6i −0.463132 0.188439i
\(677\) 2.24264e7 1.88056 0.940281 0.340398i \(-0.110562\pi\)
0.940281 + 0.340398i \(0.110562\pi\)
\(678\) 0 0
\(679\) −1.68475e7 −1.40236
\(680\) −3.59366e6 −0.298034
\(681\) 0 0
\(682\) 4.61952e6i 0.380308i
\(683\) 8.11034e6i 0.665254i 0.943059 + 0.332627i \(0.107935\pi\)
−0.943059 + 0.332627i \(0.892065\pi\)
\(684\) 0 0
\(685\) 3.25064e6 0.264693
\(686\) −9.48738e6 −0.769726
\(687\) 0 0
\(688\) 2.55872e6 0.206088
\(689\) −448500. 87750.0i −0.0359927 0.00704205i
\(690\) 0 0
\(691\) 2.00020e7i 1.59359i −0.604246 0.796797i \(-0.706526\pi\)
0.604246 0.796797i \(-0.293474\pi\)
\(692\) 256416. 0.0203554
\(693\) 0 0
\(694\) 1.18510e7i 0.934020i
\(695\) 705891.i 0.0554339i
\(696\) 0 0
\(697\) 1.04375e7i 0.813793i
\(698\) −3.46530e6 −0.269217
\(699\) 0 0
\(700\) 880320.i 0.0679040i
\(701\) 2.22272e6 0.170840 0.0854200 0.996345i \(-0.472777\pi\)
0.0854200 + 0.996345i \(0.472777\pi\)
\(702\) 0 0
\(703\) 1.01895e7 0.777617
\(704\) 491520.i 0.0373774i
\(705\) 0 0
\(706\) 6.65162e6 0.502245
\(707\) 1.18780e7i 0.893708i
\(708\) 0 0
\(709\) 2.03634e7i 1.52137i −0.649122 0.760684i \(-0.724864\pi\)
0.649122 0.760684i \(-0.275136\pi\)
\(710\) 1.30032e7i 0.968062i
\(711\) 0 0
\(712\) 6.70579e6 0.495736
\(713\) 1.01052e7i 0.744425i
\(714\) 0 0
\(715\) 3.65976e6 + 716040.i 0.267724 + 0.0523808i
\(716\) −1.10407e7 −0.804850
\(717\) 0 0
\(718\) 2.50214e6 0.181135
\(719\) 1.98255e7 1.43022 0.715108 0.699014i \(-0.246377\pi\)
0.715108 + 0.699014i \(0.246377\pi\)
\(720\) 0 0
\(721\) 2.62983e6i 0.188404i
\(722\) 4.42880e6i 0.316186i
\(723\) 0 0
\(724\) 1.54365e6 0.109446
\(725\) 2.15050e6 0.151948
\(726\) 0 0
\(727\) −9.24667e6 −0.648857 −0.324429 0.945910i \(-0.605172\pi\)
−0.324429 + 0.945910i \(0.605172\pi\)
\(728\) −4.01856e6 786240.i −0.281023 0.0549828i
\(729\) 0 0
\(730\) 1.20087e7i 0.834041i
\(731\) 1.10045e7 0.761687
\(732\) 0 0
\(733\) 1.48114e7i 1.01821i 0.860704 + 0.509105i \(0.170024\pi\)
−0.860704 + 0.509105i \(0.829976\pi\)
\(734\) 4.33309e6i 0.296864i
\(735\) 0 0
\(736\) 1.07520e6i 0.0731635i
\(737\) 2.73744e6 0.185642
\(738\) 0 0
\(739\) 5.67210e6i 0.382061i 0.981584 + 0.191031i \(0.0611830\pi\)
−0.981584 + 0.191031i \(0.938817\pi\)
\(740\) −7.10654e6 −0.477067
\(741\) 0 0
\(742\) −315000. −0.0210039
\(743\) 2.75704e7i 1.83219i −0.400960 0.916095i \(-0.631323\pi\)
0.400960 0.916095i \(-0.368677\pi\)
\(744\) 0 0
\(745\) 1.40977e7 0.930590
\(746\) 7.15582e6i 0.470774i
\(747\) 0 0
\(748\) 2.11392e6i 0.138145i
\(749\) 2.61702e6i 0.170452i
\(750\) 0 0
\(751\) −4.09636e6 −0.265032 −0.132516 0.991181i \(-0.542306\pi\)
−0.132516 + 0.991181i \(0.542306\pi\)
\(752\) 753408.i 0.0485831i
\(753\) 0 0
\(754\) −1.92067e6 + 9.81677e6i −0.123034 + 0.628840i
\(755\) −1.63880e7 −1.04630
\(756\) 0 0
\(757\) 1.09396e7 0.693844 0.346922 0.937894i \(-0.387227\pi\)
0.346922 + 0.937894i \(0.387227\pi\)
\(758\) −3.47446e6 −0.219641
\(759\) 0 0
\(760\) 3.81888e6i 0.239829i
\(761\) 1.36940e6i 0.0857172i 0.999081 + 0.0428586i \(0.0136465\pi\)
−0.999081 + 0.0428586i \(0.986354\pi\)
\(762\) 0 0
\(763\) −1.52073e7 −0.945670
\(764\) 1.13309e7 0.702312
\(765\) 0 0
\(766\) −4.31886e6 −0.265948
\(767\) −4.78975e6 + 2.44809e7i −0.293984 + 1.50259i
\(768\) 0 0
\(769\) 1.08375e7i 0.660867i 0.943829 + 0.330433i \(0.107195\pi\)
−0.943829 + 0.330433i \(0.892805\pi\)
\(770\) 2.57040e6 0.156233
\(771\) 0 0
\(772\) 5.56579e6i 0.336112i
\(773\) 2.05445e7i 1.23665i −0.785922 0.618325i \(-0.787812\pi\)
0.785922 0.618325i \(-0.212188\pi\)
\(774\) 0 0
\(775\) 5.04298e6i 0.301601i
\(776\) 1.02689e7 0.612168
\(777\) 0 0
\(778\) 5.15287e6i 0.305211i
\(779\) 1.10916e7 0.654863
\(780\) 0 0
\(781\) −7.64892e6 −0.448717
\(782\) 4.62420e6i 0.270408i
\(783\) 0 0
\(784\) 1.48019e6 0.0860058
\(785\) 1.73148e7i 1.00287i