Properties

Label 26.6.b.a.25.1
Level $26$
Weight $6$
Character 26.25
Analytic conductor $4.170$
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] = [26,6,Mod(25,26)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(26, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("26.25");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 26.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: \(4.16997931514\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 25.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 26.25
Dual form 26.6.b.a.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000i q^{2} -13.0000 q^{3} -16.0000 q^{4} +51.0000i q^{5} +52.0000i q^{6} +105.000i q^{7} +64.0000i q^{8} -74.0000 q^{9} +O(q^{10})\) \(q-4.00000i q^{2} -13.0000 q^{3} -16.0000 q^{4} +51.0000i q^{5} +52.0000i q^{6} +105.000i q^{7} +64.0000i q^{8} -74.0000 q^{9} +204.000 q^{10} +120.000i q^{11} +208.000 q^{12} +(-598.000 + 117.000i) q^{13} +420.000 q^{14} -663.000i q^{15} +256.000 q^{16} -1101.00 q^{17} +296.000i q^{18} -1170.00i q^{19} -816.000i q^{20} -1365.00i q^{21} +480.000 q^{22} +1050.00 q^{23} -832.000i q^{24} +524.000 q^{25} +(468.000 + 2392.00i) q^{26} +4121.00 q^{27} -1680.00i q^{28} -4104.00 q^{29} -2652.00 q^{30} +9624.00i q^{31} -1024.00i q^{32} -1560.00i q^{33} +4404.00i q^{34} -5355.00 q^{35} +1184.00 q^{36} +8709.00i q^{37} -4680.00 q^{38} +(7774.00 - 1521.00i) q^{39} -3264.00 q^{40} -9480.00i q^{41} -5460.00 q^{42} +9995.00 q^{43} -1920.00i q^{44} -3774.00i q^{45} -4200.00i q^{46} -2943.00i q^{47} -3328.00 q^{48} +5782.00 q^{49} -2096.00i q^{50} +14313.0 q^{51} +(9568.00 - 1872.00i) q^{52} -750.000 q^{53} -16484.0i q^{54} -6120.00 q^{55} -6720.00 q^{56} +15210.0i q^{57} +16416.0i q^{58} -40938.0i q^{59} +10608.0i q^{60} -57920.0 q^{61} +38496.0 q^{62} -7770.00i q^{63} -4096.00 q^{64} +(-5967.00 - 30498.0i) q^{65} -6240.00 q^{66} +22812.0i q^{67} +17616.0 q^{68} -13650.0 q^{69} +21420.0i q^{70} +63741.0i q^{71} -4736.00i q^{72} +58866.0i q^{73} +34836.0 q^{74} -6812.00 q^{75} +18720.0i q^{76} -12600.0 q^{77} +(-6084.00 - 31096.0i) q^{78} +63202.0 q^{79} +13056.0i q^{80} -35591.0 q^{81} -37920.0 q^{82} +55458.0i q^{83} +21840.0i q^{84} -56151.0i q^{85} -39980.0i q^{86} +53352.0 q^{87} -7680.00 q^{88} -104778. i q^{89} -15096.0 q^{90} +(-12285.0 - 62790.0i) q^{91} -16800.0 q^{92} -125112. i q^{93} -11772.0 q^{94} +59670.0 q^{95} +13312.0i q^{96} +160452. i q^{97} -23128.0i q^{98} -8880.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 26 q^{3} - 32 q^{4} - 148 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 26 q^{3} - 32 q^{4} - 148 q^{9} + 408 q^{10} + 416 q^{12} - 1196 q^{13} + 840 q^{14} + 512 q^{16} - 2202 q^{17} + 960 q^{22} + 2100 q^{23} + 1048 q^{25} + 936 q^{26} + 8242 q^{27} - 8208 q^{29} - 5304 q^{30} - 10710 q^{35} + 2368 q^{36} - 9360 q^{38} + 15548 q^{39} - 6528 q^{40} - 10920 q^{42} + 19990 q^{43} - 6656 q^{48} + 11564 q^{49} + 28626 q^{51} + 19136 q^{52} - 1500 q^{53} - 12240 q^{55} - 13440 q^{56} - 115840 q^{61} + 76992 q^{62} - 8192 q^{64} - 11934 q^{65} - 12480 q^{66} + 35232 q^{68} - 27300 q^{69} + 69672 q^{74} - 13624 q^{75} - 25200 q^{77} - 12168 q^{78} + 126404 q^{79} - 71182 q^{81} - 75840 q^{82} + 106704 q^{87} - 15360 q^{88} - 30192 q^{90} - 24570 q^{91} - 33600 q^{92} - 23544 q^{94} + 119340 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).

\(n\) \(15\)
\(\chi(n)\) \(-1\)

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
\(3\) −13.0000 −0.833950 −0.416975 0.908918i \(-0.636910\pi\)
−0.416975 + 0.908918i \(0.636910\pi\)
\(4\) −16.0000 −0.500000
\(5\) 51.0000i 0.912316i 0.889899 + 0.456158i \(0.150775\pi\)
−0.889899 + 0.456158i \(0.849225\pi\)
\(6\) 52.0000i 0.589692i
\(7\) 105.000i 0.809924i 0.914334 + 0.404962i \(0.132715\pi\)
−0.914334 + 0.404962i \(0.867285\pi\)
\(8\) 64.0000i 0.353553i
\(9\) −74.0000 −0.304527
\(10\) 204.000 0.645105
\(11\) 120.000i 0.299020i 0.988760 + 0.149510i \(0.0477695\pi\)
−0.988760 + 0.149510i \(0.952230\pi\)
\(12\) 208.000 0.416975
\(13\) −598.000 + 117.000i −0.981393 + 0.192012i
\(14\) 420.000 0.572703
\(15\) 663.000i 0.760826i
\(16\) 256.000 0.250000
\(17\) −1101.00 −0.923985 −0.461993 0.886884i \(-0.652865\pi\)
−0.461993 + 0.886884i \(0.652865\pi\)
\(18\) 296.000i 0.215333i
\(19\) 1170.00i 0.743536i −0.928326 0.371768i \(-0.878752\pi\)
0.928326 0.371768i \(-0.121248\pi\)
\(20\) 816.000i 0.456158i
\(21\) 1365.00i 0.675436i
\(22\) 480.000 0.211439
\(23\) 1050.00 0.413875 0.206938 0.978354i \(-0.433650\pi\)
0.206938 + 0.978354i \(0.433650\pi\)
\(24\) 832.000i 0.294846i
\(25\) 524.000 0.167680
\(26\) 468.000 + 2392.00i 0.135773 + 0.693949i
\(27\) 4121.00 1.08791
\(28\) 1680.00i 0.404962i
\(29\) −4104.00 −0.906176 −0.453088 0.891466i \(-0.649678\pi\)
−0.453088 + 0.891466i \(0.649678\pi\)
\(30\) −2652.00 −0.537985
\(31\) 9624.00i 1.79867i 0.437261 + 0.899335i \(0.355949\pi\)
−0.437261 + 0.899335i \(0.644051\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 1560.00i 0.249367i
\(34\) 4404.00i 0.653356i
\(35\) −5355.00 −0.738906
\(36\) 1184.00 0.152263
\(37\) 8709.00i 1.04584i 0.852383 + 0.522918i \(0.175157\pi\)
−0.852383 + 0.522918i \(0.824843\pi\)
\(38\) −4680.00 −0.525759
\(39\) 7774.00 1521.00i 0.818433 0.160128i
\(40\) −3264.00 −0.322552
\(41\) 9480.00i 0.880742i −0.897816 0.440371i \(-0.854847\pi\)
0.897816 0.440371i \(-0.145153\pi\)
\(42\) −5460.00 −0.477606
\(43\) 9995.00 0.824350 0.412175 0.911105i \(-0.364769\pi\)
0.412175 + 0.911105i \(0.364769\pi\)
\(44\) 1920.00i 0.149510i
\(45\) 3774.00i 0.277825i
\(46\) 4200.00i 0.292654i
\(47\) 2943.00i 0.194333i −0.995268 0.0971663i \(-0.969022\pi\)
0.995268 0.0971663i \(-0.0309779\pi\)
\(48\) −3328.00 −0.208488
\(49\) 5782.00 0.344023
\(50\) 2096.00i 0.118568i
\(51\) 14313.0 0.770558
\(52\) 9568.00 1872.00i 0.490696 0.0960058i
\(53\) −750.000 −0.0366751 −0.0183376 0.999832i \(-0.505837\pi\)
−0.0183376 + 0.999832i \(0.505837\pi\)
\(54\) 16484.0i 0.769269i
\(55\) −6120.00 −0.272800
\(56\) −6720.00 −0.286351
\(57\) 15210.0i 0.620072i
\(58\) 16416.0i 0.640763i
\(59\) 40938.0i 1.53108i −0.643391 0.765538i \(-0.722473\pi\)
0.643391 0.765538i \(-0.277527\pi\)
\(60\) 10608.0i 0.380413i
\(61\) −57920.0 −1.99298 −0.996492 0.0836839i \(-0.973331\pi\)
−0.996492 + 0.0836839i \(0.973331\pi\)
\(62\) 38496.0 1.27185
\(63\) 7770.00i 0.246643i
\(64\) −4096.00 −0.125000
\(65\) −5967.00 30498.0i −0.175175 0.895340i
\(66\) −6240.00 −0.176329
\(67\) 22812.0i 0.620835i 0.950600 + 0.310418i \(0.100469\pi\)
−0.950600 + 0.310418i \(0.899531\pi\)
\(68\) 17616.0 0.461993
\(69\) −13650.0 −0.345152
\(70\) 21420.0i 0.522486i
\(71\) 63741.0i 1.50063i 0.661082 + 0.750314i \(0.270098\pi\)
−0.661082 + 0.750314i \(0.729902\pi\)
\(72\) 4736.00i 0.107666i
\(73\) 58866.0i 1.29288i 0.762966 + 0.646439i \(0.223742\pi\)
−0.762966 + 0.646439i \(0.776258\pi\)
\(74\) 34836.0 0.739518
\(75\) −6812.00 −0.139837
\(76\) 18720.0i 0.371768i
\(77\) −12600.0 −0.242183
\(78\) −6084.00 31096.0i −0.113228 0.578719i
\(79\) 63202.0 1.13937 0.569683 0.821865i \(-0.307066\pi\)
0.569683 + 0.821865i \(0.307066\pi\)
\(80\) 13056.0i 0.228079i
\(81\) −35591.0 −0.602737
\(82\) −37920.0 −0.622779
\(83\) 55458.0i 0.883627i 0.897107 + 0.441813i \(0.145665\pi\)
−0.897107 + 0.441813i \(0.854335\pi\)
\(84\) 21840.0i 0.337718i
\(85\) 56151.0i 0.842966i
\(86\) 39980.0i 0.582903i
\(87\) 53352.0 0.755705
\(88\) −7680.00 −0.105719
\(89\) 104778.i 1.40215i −0.713087 0.701076i \(-0.752703\pi\)
0.713087 0.701076i \(-0.247297\pi\)
\(90\) −15096.0 −0.196452
\(91\) −12285.0 62790.0i −0.155515 0.794853i
\(92\) −16800.0 −0.206938
\(93\) 125112.i 1.50000i
\(94\) −11772.0 −0.137414
\(95\) 59670.0 0.678339
\(96\) 13312.0i 0.147423i
\(97\) 160452.i 1.73147i 0.500500 + 0.865737i \(0.333150\pi\)
−0.500500 + 0.865737i \(0.666850\pi\)
\(98\) 23128.0i 0.243261i
\(99\) 8880.00i 0.0910594i
\(100\) −8384.00 −0.0838400
\(101\) −113124. −1.10345 −0.551723 0.834027i \(-0.686030\pi\)
−0.551723 + 0.834027i \(0.686030\pi\)
\(102\) 57252.0i 0.544867i
\(103\) 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
\(105\) 69615.0 0.616211
\(106\) 3000.00i 0.0259332i
\(107\) 24924.0 0.210455 0.105227 0.994448i \(-0.466443\pi\)
0.105227 + 0.994448i \(0.466443\pi\)
\(108\) −65936.0 −0.543955
\(109\) 144831.i 1.16760i 0.811896 + 0.583802i \(0.198435\pi\)
−0.811896 + 0.583802i \(0.801565\pi\)
\(110\) 24480.0i 0.192899i
\(111\) 113217.i 0.872176i
\(112\) 26880.0i 0.202481i
\(113\) 100266. 0.738682 0.369341 0.929294i \(-0.379583\pi\)
0.369341 + 0.929294i \(0.379583\pi\)
\(114\) 60840.0 0.438457
\(115\) 53550.0i 0.377585i
\(116\) 65664.0 0.453088
\(117\) 44252.0 8658.00i 0.298860 0.0584727i
\(118\) −163752. −1.08263
\(119\) 115605.i 0.748358i
\(120\) 42432.0 0.268993
\(121\) 146651. 0.910587
\(122\) 231680.i 1.40925i
\(123\) 123240.i 0.734495i
\(124\) 153984.i 0.899335i
\(125\) 186099.i 1.06529i
\(126\) −31080.0 −0.174403
\(127\) −202754. −1.11548 −0.557738 0.830017i \(-0.688331\pi\)
−0.557738 + 0.830017i \(0.688331\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −129935. −0.687467
\(130\) −121992. + 23868.0i −0.633101 + 0.123868i
\(131\) −303855. −1.54699 −0.773496 0.633801i \(-0.781494\pi\)
−0.773496 + 0.633801i \(0.781494\pi\)
\(132\) 24960.0i 0.124684i
\(133\) 122850. 0.602207
\(134\) 91248.0 0.438997
\(135\) 210171.i 0.992518i
\(136\) 70464.0i 0.326678i
\(137\) 63738.0i 0.290133i −0.989422 0.145066i \(-0.953660\pi\)
0.989422 0.145066i \(-0.0463396\pi\)
\(138\) 54600.0i 0.244059i
\(139\) 13841.0 0.0607618 0.0303809 0.999538i \(-0.490328\pi\)
0.0303809 + 0.999538i \(0.490328\pi\)
\(140\) 85680.0 0.369453
\(141\) 38259.0i 0.162064i
\(142\) 254964. 1.06110
\(143\) −14040.0 71760.0i −0.0574152 0.293456i
\(144\) −18944.0 −0.0761317
\(145\) 209304.i 0.826718i
\(146\) 235464. 0.914202
\(147\) −75166.0 −0.286898
\(148\) 139344.i 0.522918i
\(149\) 276426.i 1.02003i −0.860165 0.510015i \(-0.829640\pi\)
0.860165 0.510015i \(-0.170360\pi\)
\(150\) 27248.0i 0.0988796i
\(151\) 321333.i 1.14687i −0.819252 0.573433i \(-0.805611\pi\)
0.819252 0.573433i \(-0.194389\pi\)
\(152\) 74880.0 0.262880
\(153\) 81474.0 0.281378
\(154\) 50400.0i 0.171249i
\(155\) −490824. −1.64095
\(156\) −124384. + 24336.0i −0.409216 + 0.0800641i
\(157\) 339506. 1.09925 0.549627 0.835410i \(-0.314770\pi\)
0.549627 + 0.835410i \(0.314770\pi\)
\(158\) 252808.i 0.805653i
\(159\) 9750.00 0.0305852
\(160\) 52224.0 0.161276
\(161\) 110250.i 0.335208i
\(162\) 142364.i 0.426199i
\(163\) 395718.i 1.16659i −0.812262 0.583293i \(-0.801764\pi\)
0.812262 0.583293i \(-0.198236\pi\)
\(164\) 151680.i 0.440371i
\(165\) 79560.0 0.227502
\(166\) 221832. 0.624819
\(167\) 426708.i 1.18397i 0.805950 + 0.591984i \(0.201655\pi\)
−0.805950 + 0.591984i \(0.798345\pi\)
\(168\) 87360.0 0.238803
\(169\) 343915. 139932.i 0.926263 0.376878i
\(170\) −224604. −0.596067
\(171\) 86580.0i 0.226427i
\(172\) −159920. −0.412175
\(173\) 16026.0 0.0407108 0.0203554 0.999793i \(-0.493520\pi\)
0.0203554 + 0.999793i \(0.493520\pi\)
\(174\) 213408.i 0.534364i
\(175\) 55020.0i 0.135808i
\(176\) 30720.0i 0.0747549i
\(177\) 532194.i 1.27684i
\(178\) −419112. −0.991471
\(179\) −690045. −1.60970 −0.804850 0.593479i \(-0.797754\pi\)
−0.804850 + 0.593479i \(0.797754\pi\)
\(180\) 60384.0i 0.138912i
\(181\) −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
\(183\) 752960. 1.66205
\(184\) 67200.0i 0.146327i
\(185\) −444159. −0.954134
\(186\) −500448. −1.06066
\(187\) 132120.i 0.276290i
\(188\) 47088.0i 0.0971663i
\(189\) 432705.i 0.881125i
\(190\) 238680.i 0.479658i
\(191\) 708180. 1.40462 0.702312 0.711869i \(-0.252151\pi\)
0.702312 + 0.711869i \(0.252151\pi\)
\(192\) 53248.0 0.104244
\(193\) 347862.i 0.672224i −0.941822 0.336112i \(-0.890888\pi\)
0.941822 0.336112i \(-0.109112\pi\)
\(194\) 641808. 1.22434
\(195\) 77571.0 + 396474.i 0.146087 + 0.746669i
\(196\) −92512.0 −0.172012
\(197\) 899589.i 1.65150i 0.564036 + 0.825750i \(0.309248\pi\)
−0.564036 + 0.825750i \(0.690752\pi\)
\(198\) −35520.0 −0.0643887
\(199\) 143116. 0.256186 0.128093 0.991762i \(-0.459114\pi\)
0.128093 + 0.991762i \(0.459114\pi\)
\(200\) 33536.0i 0.0592838i
\(201\) 296556.i 0.517746i
\(202\) 452496.i 0.780255i
\(203\) 430920.i 0.733933i
\(204\) −229008. −0.385279
\(205\) 483480. 0.803515
\(206\) 100184.i 0.164487i
\(207\) −77700.0 −0.126036
\(208\) −153088. + 29952.0i −0.245348 + 0.0480029i
\(209\) 140400. 0.222332
\(210\) 278460.i 0.435727i
\(211\) −339731. −0.525326 −0.262663 0.964888i \(-0.584601\pi\)
−0.262663 + 0.964888i \(0.584601\pi\)
\(212\) 12000.0 0.0183376
\(213\) 828633.i 1.25145i
\(214\) 99696.0i 0.148814i
\(215\) 509745.i 0.752068i
\(216\) 263744.i 0.384634i
\(217\) −1.01052e6 −1.45679
\(218\) 579324. 0.825620
\(219\) 765258.i 1.07820i
\(220\) 97920.0 0.136400
\(221\) 658398. 128817.i 0.906792 0.177416i
\(222\) −452868. −0.616722
\(223\) 623757.i 0.839950i 0.907536 + 0.419975i \(0.137961\pi\)
−0.907536 + 0.419975i \(0.862039\pi\)
\(224\) 107520. 0.143176
\(225\) −38776.0 −0.0510630
\(226\) 401064.i 0.522327i
\(227\) 177612.i 0.228775i −0.993436 0.114387i \(-0.963510\pi\)
0.993436 0.114387i \(-0.0364905\pi\)
\(228\) 243360.i 0.310036i
\(229\) 1.18705e6i 1.49582i −0.663799 0.747911i \(-0.731057\pi\)
0.663799 0.747911i \(-0.268943\pi\)
\(230\) 214200. 0.266993
\(231\) 163800. 0.201969
\(232\) 262656.i 0.320381i
\(233\) −112317. −0.135536 −0.0677682 0.997701i \(-0.521588\pi\)
−0.0677682 + 0.997701i \(0.521588\pi\)
\(234\) −34632.0 177008.i −0.0413464 0.211326i
\(235\) 150093. 0.177293
\(236\) 655008.i 0.765538i
\(237\) −821626. −0.950174
\(238\) −462420. −0.529169
\(239\) 1.19805e6i 1.35669i −0.734743 0.678346i \(-0.762697\pi\)
0.734743 0.678346i \(-0.237303\pi\)
\(240\) 169728.i 0.190207i
\(241\) 1.16629e6i 1.29349i 0.762707 + 0.646744i \(0.223870\pi\)
−0.762707 + 0.646744i \(0.776130\pi\)
\(242\) 586604.i 0.643882i
\(243\) −538720. −0.585258
\(244\) 926720. 0.996492
\(245\) 294882.i 0.313858i
\(246\) 492960. 0.519366
\(247\) 136890. + 699660.i 0.142767 + 0.729701i
\(248\) −615936. −0.635926
\(249\) 720954.i 0.736901i
\(250\) 744396. 0.753276
\(251\) 648996. 0.650216 0.325108 0.945677i \(-0.394599\pi\)
0.325108 + 0.945677i \(0.394599\pi\)
\(252\) 124320.i 0.123322i
\(253\) 126000.i 0.123757i
\(254\) 811016.i 0.788760i
\(255\) 729963.i 0.702992i
\(256\) 65536.0 0.0625000
\(257\) −945885. −0.893317 −0.446658 0.894705i \(-0.647386\pi\)
−0.446658 + 0.894705i \(0.647386\pi\)
\(258\) 519740.i 0.486113i
\(259\) −914445. −0.847048
\(260\) 95472.0 + 487968.i 0.0875876 + 0.447670i
\(261\) 303696. 0.275955
\(262\) 1.21542e6i 1.09389i
\(263\) 1.01222e6 0.902375 0.451188 0.892429i \(-0.351000\pi\)
0.451188 + 0.892429i \(0.351000\pi\)
\(264\) 99840.0 0.0881647
\(265\) 38250.0i 0.0334593i
\(266\) 491400.i 0.425825i
\(267\) 1.36211e6i 1.16933i
\(268\) 364992.i 0.310418i
\(269\) −1.01772e6 −0.857527 −0.428763 0.903417i \(-0.641051\pi\)
−0.428763 + 0.903417i \(0.641051\pi\)
\(270\) 840684. 0.701816
\(271\) 463461.i 0.383345i 0.981459 + 0.191673i \(0.0613912\pi\)
−0.981459 + 0.191673i \(0.938609\pi\)
\(272\) −281856. −0.230996
\(273\) 159705. + 816270.i 0.129692 + 0.662868i
\(274\) −254952. −0.205155
\(275\) 62880.0i 0.0501396i
\(276\) 218400. 0.172576
\(277\) 332528. 0.260393 0.130196 0.991488i \(-0.458439\pi\)
0.130196 + 0.991488i \(0.458439\pi\)
\(278\) 55364.0i 0.0429651i
\(279\) 712176.i 0.547743i
\(280\) 342720.i 0.261243i
\(281\) 49122.0i 0.0371116i −0.999828 0.0185558i \(-0.994093\pi\)
0.999828 0.0185558i \(-0.00590684\pi\)
\(282\) 153036. 0.114596
\(283\) −1.55848e6 −1.15674 −0.578371 0.815774i \(-0.696311\pi\)
−0.578371 + 0.815774i \(0.696311\pi\)
\(284\) 1.01986e6i 0.750314i
\(285\) −775710. −0.565701
\(286\) −287040. + 56160.0i −0.207504 + 0.0405987i
\(287\) 995400. 0.713334
\(288\) 75776.0i 0.0538332i
\(289\) −207656. −0.146251
\(290\) −837216. −0.584578
\(291\) 2.08588e6i 1.44396i
\(292\) 941856.i 0.646439i
\(293\) 218463.i 0.148665i −0.997234 0.0743325i \(-0.976317\pi\)
0.997234 0.0743325i \(-0.0236826\pi\)
\(294\) 300664.i 0.202868i
\(295\) 2.08784e6 1.39682
\(296\) −557376. −0.369759
\(297\) 494520.i 0.325306i
\(298\) −1.10570e6 −0.721271
\(299\) −627900. + 122850.i −0.406174 + 0.0794689i
\(300\) 108992. 0.0699184
\(301\) 1.04948e6i 0.667661i
\(302\) −1.28533e6 −0.810957
\(303\) 1.47061e6 0.920220
\(304\) 299520.i 0.185884i
\(305\) 2.95392e6i 1.81823i
\(306\) 325896.i 0.198964i
\(307\) 321102.i 0.194445i 0.995263 + 0.0972226i \(0.0309959\pi\)
−0.995263 + 0.0972226i \(0.969004\pi\)
\(308\) 201600. 0.121092
\(309\) −325598. −0.193993
\(310\) 1.96330e6i 1.16033i
\(311\) 3.33725e6 1.95654 0.978269 0.207340i \(-0.0664805\pi\)
0.978269 + 0.207340i \(0.0664805\pi\)
\(312\) 97344.0 + 497536.i 0.0566139 + 0.289360i
\(313\) 1.16568e6 0.672538 0.336269 0.941766i \(-0.390835\pi\)
0.336269 + 0.941766i \(0.390835\pi\)
\(314\) 1.35802e6i 0.777290i
\(315\) 396270. 0.225017
\(316\) −1.01123e6 −0.569683
\(317\) 73518.0i 0.0410909i 0.999789 + 0.0205454i \(0.00654028\pi\)
−0.999789 + 0.0205454i \(0.993460\pi\)
\(318\) 39000.0i 0.0216270i
\(319\) 492480.i 0.270964i
\(320\) 208896.i 0.114039i
\(321\) −324012. −0.175509
\(322\) 441000. 0.237028
\(323\) 1.28817e6i 0.687016i
\(324\) 569456. 0.301368
\(325\) −313352. + 61308.0i −0.164560 + 0.0321965i
\(326\) −1.58287e6 −0.824901
\(327\) 1.88280e6i 0.973723i
\(328\) 606720. 0.311389
\(329\) 309015. 0.157395
\(330\) 318240.i 0.160868i
\(331\) 632682.i 0.317406i 0.987326 + 0.158703i \(0.0507313\pi\)
−0.987326 + 0.158703i \(0.949269\pi\)
\(332\) 887328.i 0.441813i
\(333\) 644466.i 0.318485i
\(334\) 1.70683e6 0.837191
\(335\) −1.16341e6 −0.566398
\(336\) 349440.i 0.168859i
\(337\) −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
\(339\) −1.30346e6 −0.616024
\(340\) 898416.i 0.421483i
\(341\) −1.15488e6 −0.537837
\(342\) 346320. 0.160108
\(343\) 2.37184e6i 1.08856i
\(344\) 639680.i 0.291452i
\(345\) 696150.i 0.314887i
\(346\) 64104.0i 0.0287869i
\(347\) 2.96275e6 1.32090 0.660452 0.750868i \(-0.270365\pi\)
0.660452 + 0.750868i \(0.270365\pi\)
\(348\) −853632. −0.377853
\(349\) 866325.i 0.380730i 0.981713 + 0.190365i \(0.0609672\pi\)
−0.981713 + 0.190365i \(0.939033\pi\)
\(350\) 220080. 0.0960308
\(351\) −2.46436e6 + 482157.i −1.06767 + 0.208891i
\(352\) 122880. 0.0528597
\(353\) 1.66291e6i 0.710282i 0.934813 + 0.355141i \(0.115567\pi\)
−0.934813 + 0.355141i \(0.884433\pi\)
\(354\) 2.12878e6 0.902863
\(355\) −3.25079e6 −1.36905
\(356\) 1.67645e6i 0.701076i
\(357\) 1.50286e6i 0.624093i
\(358\) 2.76018e6i 1.13823i
\(359\) 625536.i 0.256163i 0.991764 + 0.128081i \(0.0408819\pi\)
−0.991764 + 0.128081i \(0.959118\pi\)
\(360\) 241536. 0.0982258
\(361\) 1.10720e6 0.447155
\(362\) 385912.i 0.154781i
\(363\) −1.90646e6 −0.759385
\(364\) 196560. + 1.00464e6i 0.0777574 + 0.397427i
\(365\) −3.00217e6 −1.17951
\(366\) 3.01184e6i 1.17525i
\(367\) 1.08327e6 0.419829 0.209914 0.977720i \(-0.432681\pi\)
0.209914 + 0.977720i \(0.432681\pi\)
\(368\) 268800. 0.103469
\(369\) 701520.i 0.268209i
\(370\) 1.77664e6i 0.674674i
\(371\) 78750.0i 0.0297041i
\(372\) 2.00179e6i 0.750001i
\(373\) −1.78896e6 −0.665775 −0.332888 0.942967i \(-0.608023\pi\)
−0.332888 + 0.942967i \(0.608023\pi\)
\(374\) −528480. −0.195366
\(375\) 2.41929e6i 0.888401i
\(376\) 188352. 0.0687069
\(377\) 2.45419e6 480168.i 0.889314 0.173996i
\(378\) 1.73082e6 0.623049
\(379\) 868614.i 0.310620i 0.987866 + 0.155310i \(0.0496376\pi\)
−0.987866 + 0.155310i \(0.950362\pi\)
\(380\) −954720. −0.339170
\(381\) 2.63580e6 0.930251
\(382\) 2.83272e6i 0.993220i
\(383\) 1.07972e6i 0.376108i −0.982159 0.188054i \(-0.939782\pi\)
0.982159 0.188054i \(-0.0602179\pi\)
\(384\) 212992.i 0.0737115i
\(385\) 642600.i 0.220947i
\(386\) −1.39145e6 −0.475334
\(387\) −739630. −0.251037
\(388\) 2.56723e6i 0.865737i
\(389\) 1.28822e6 0.431634 0.215817 0.976434i \(-0.430759\pi\)
0.215817 + 0.976434i \(0.430759\pi\)
\(390\) 1.58590e6 310284.i 0.527975 0.103299i
\(391\) −1.15605e6 −0.382415
\(392\) 370048.i 0.121631i
\(393\) 3.95012e6 1.29011
\(394\) 3.59836e6 1.16779
\(395\) 3.22330e6i 1.03946i
\(396\) 142080.i 0.0455297i
\(397\) 5.46909e6i 1.74156i −0.491672 0.870781i \(-0.663614\pi\)
0.491672 0.870781i \(-0.336386\pi\)
\(398\) 572464.i 0.181151i
\(399\) −1.59705e6 −0.502211
\(400\) 134144. 0.0419200
\(401\) 1.58612e6i 0.492577i −0.969196 0.246289i \(-0.920789\pi\)
0.969196 0.246289i \(-0.0792112\pi\)
\(402\) −1.18622e6 −0.366102
\(403\) −1.12601e6 5.75515e6i −0.345365 1.76520i
\(404\) 1.80998e6 0.551723
\(405\) 1.81514e6i 0.549886i
\(406\) −1.72368e6 −0.518969
\(407\) −1.04508e6 −0.312726
\(408\) 916032.i 0.272433i
\(409\) 6.44192e6i 1.90418i 0.305825 + 0.952088i \(0.401068\pi\)
−0.305825 + 0.952088i \(0.598932\pi\)
\(410\) 1.93392e6i 0.568171i
\(411\) 828594.i 0.241956i
\(412\) −400736. −0.116310
\(413\) 4.29849e6 1.24005
\(414\) 310800.i 0.0891210i
\(415\) −2.82836e6 −0.806147
\(416\) 119808. + 612352.i 0.0339432 + 0.173487i
\(417\) −179933. −0.0506723
\(418\) 561600.i 0.157212i
\(419\) −4.30545e6 −1.19807 −0.599037 0.800721i \(-0.704450\pi\)
−0.599037 + 0.800721i \(0.704450\pi\)
\(420\) −1.11384e6 −0.308106
\(421\) 1.51346e6i 0.416164i 0.978111 + 0.208082i \(0.0667221\pi\)
−0.978111 + 0.208082i \(0.933278\pi\)
\(422\) 1.35892e6i 0.371462i
\(423\) 217782.i 0.0591795i
\(424\) 48000.0i 0.0129666i
\(425\) −576924. −0.154934
\(426\) −3.31453e6 −0.884908
\(427\) 6.08160e6i 1.61417i
\(428\) −398784. −0.105227
\(429\) 182520. + 932880.i 0.0478814 + 0.244727i
\(430\) 2.03898e6 0.531792
\(431\) 1.43116e6i 0.371105i −0.982634 0.185552i \(-0.940593\pi\)
0.982634 0.185552i \(-0.0594074\pi\)
\(432\) 1.05498e6 0.271978
\(433\) 429613. 0.110118 0.0550589 0.998483i \(-0.482465\pi\)
0.0550589 + 0.998483i \(0.482465\pi\)
\(434\) 4.04208e6i 1.03010i
\(435\) 2.72095e6i 0.689442i
\(436\) 2.31730e6i 0.583802i
\(437\) 1.22850e6i 0.307731i
\(438\) −3.06103e6 −0.762399
\(439\) 552038. 0.136712 0.0683562 0.997661i \(-0.478225\pi\)
0.0683562 + 0.997661i \(0.478225\pi\)
\(440\) 391680.i 0.0964494i
\(441\) −427868. −0.104764
\(442\) −515268. 2.63359e6i −0.125452 0.641199i
\(443\) 2.15255e6 0.521128 0.260564 0.965457i \(-0.416092\pi\)
0.260564 + 0.965457i \(0.416092\pi\)
\(444\) 1.81147e6i 0.436088i
\(445\) 5.34368e6 1.27921
\(446\) 2.49503e6 0.593934
\(447\) 3.59354e6i 0.850655i
\(448\) 430080.i 0.101240i
\(449\) 1.40429e6i 0.328731i 0.986400 + 0.164365i \(0.0525576\pi\)
−0.986400 + 0.164365i \(0.947442\pi\)
\(450\) 155104.i 0.0361070i
\(451\) 1.13760e6 0.263359
\(452\) −1.60426e6 −0.369341
\(453\) 4.17733e6i 0.956430i
\(454\) −710448. −0.161768
\(455\) 3.20229e6 626535.i 0.725157 0.141879i
\(456\) −973440. −0.219229
\(457\) 1.32818e6i 0.297485i −0.988876 0.148743i \(-0.952477\pi\)
0.988876 0.148743i \(-0.0475226\pi\)
\(458\) −4.74820e6 −1.05771
\(459\) −4.53722e6 −1.00521
\(460\) 856800.i 0.188793i
\(461\) 5.89070e6i 1.29096i 0.763775 + 0.645482i \(0.223344\pi\)
−0.763775 + 0.645482i \(0.776656\pi\)
\(462\) 655200.i 0.142813i
\(463\) 2.37139e6i 0.514104i 0.966398 + 0.257052i \(0.0827511\pi\)
−0.966398 + 0.257052i \(0.917249\pi\)
\(464\) −1.05062e6 −0.226544
\(465\) 6.38071e6 1.36847
\(466\) 449268.i 0.0958387i
\(467\) 7.17827e6 1.52310 0.761548 0.648108i \(-0.224440\pi\)
0.761548 + 0.648108i \(0.224440\pi\)
\(468\) −708032. + 138528.i −0.149430 + 0.0292363i
\(469\) −2.39526e6 −0.502829
\(470\) 600372.i 0.125365i
\(471\) −4.41358e6 −0.916724
\(472\) 2.62003e6 0.541317
\(473\) 1.19940e6i 0.246497i
\(474\) 3.28650e6i 0.671875i
\(475\) 613080.i 0.124676i
\(476\) 1.84968e6i 0.374179i
\(477\) 55500.0 0.0111686
\(478\) −4.79221e6 −0.959326
\(479\) 7.25193e6i 1.44416i 0.691810 + 0.722079i \(0.256814\pi\)
−0.691810 + 0.722079i \(0.743186\pi\)
\(480\) −678912. −0.134496
\(481\) −1.01895e6 5.20798e6i −0.200813 1.02638i
\(482\) 4.66514e6 0.914634
\(483\) 1.43325e6i 0.279547i
\(484\) −2.34642e6 −0.455294
\(485\) −8.18305e6 −1.57965
\(486\) 2.15488e6i 0.413840i
\(487\) 2.53364e6i 0.484087i −0.970265 0.242043i \(-0.922182\pi\)
0.970265 0.242043i \(-0.0778176\pi\)
\(488\) 3.70688e6i 0.704626i
\(489\) 5.14433e6i 0.972875i
\(490\) 1.17953e6 0.221931
\(491\) 8.46186e6 1.58403 0.792013 0.610504i \(-0.209033\pi\)
0.792013 + 0.610504i \(0.209033\pi\)
\(492\) 1.97184e6i 0.367248i
\(493\) 4.51850e6 0.837293
\(494\) 2.79864e6 547560.i 0.515976 0.100952i
\(495\) 452880. 0.0830750
\(496\) 2.46374e6i 0.449667i
\(497\) −6.69280e6 −1.21539
\(498\) −2.88382e6 −0.521068
\(499\) 1.95383e6i 0.351265i −0.984456 0.175633i \(-0.943803\pi\)
0.984456 0.175633i \(-0.0561971\pi\)
\(500\) 2.97758e6i 0.532646i
\(501\) 5.54720e6i 0.987370i
\(502\) 2.59598e6i 0.459772i
\(503\) 119778. 0.0211085 0.0105542 0.999944i \(-0.496640\pi\)
0.0105542 + 0.999944i \(0.496640\pi\)
\(504\) 497280. 0.0872016
\(505\) 5.76932e6i 1.00669i
\(506\) 504000. 0.0875093
\(507\) −4.47090e6 + 1.81912e6i −0.772457 + 0.314297i
\(508\) 3.24406e6 0.557738
\(509\) 1.03653e7i 1.77332i −0.462420 0.886661i \(-0.653019\pi\)
0.462420 0.886661i \(-0.346981\pi\)
\(510\) 2.91985e6 0.497090
\(511\) −6.18093e6 −1.04713
\(512\) 262144.i 0.0441942i
\(513\) 4.82157e6i 0.808900i
\(514\) 3.78354e6i 0.631670i
\(515\) 1.27735e6i 0.212222i
\(516\) 2.07896e6 0.343734
\(517\) 353160. 0.0581092
\(518\) 3.65778e6i 0.598954i
\(519\) −208338. −0.0339508
\(520\) 1.95187e6 381888.i 0.316550 0.0619338i
\(521\) −1.04899e7 −1.69307 −0.846537 0.532330i \(-0.821316\pi\)
−0.846537 + 0.532330i \(0.821316\pi\)
\(522\) 1.21478e6i 0.195129i
\(523\) 4.42662e6 0.707649 0.353824 0.935312i \(-0.384881\pi\)
0.353824 + 0.935312i \(0.384881\pi\)
\(524\) 4.86168e6 0.773496
\(525\) 715260.i 0.113257i
\(526\) 4.04890e6i 0.638076i
\(527\) 1.05960e7i 1.66194i
\(528\) 399360.i 0.0623419i
\(529\) −5.33384e6 −0.828707
\(530\) −153000. −0.0236593
\(531\) 3.02941e6i 0.466253i
\(532\) −1.96560e6 −0.301104
\(533\) 1.10916e6 + 5.66904e6i 0.169113 + 0.864354i
\(534\) 5.44846e6 0.826838
\(535\) 1.27112e6i 0.192001i
\(536\) −1.45997e6 −0.219498
\(537\) 8.97058e6 1.34241
\(538\) 4.07088e6i 0.606363i
\(539\) 693840.i 0.102870i
\(540\) 3.36274e6i 0.496259i
\(541\) 2.26377e6i 0.332536i 0.986081 + 0.166268i \(0.0531717\pi\)
−0.986081 + 0.166268i \(0.946828\pi\)
\(542\) 1.85384e6 0.271066
\(543\) 1.25421e6 0.182546
\(544\) 1.12742e6i 0.163339i
\(545\) −7.38638e6 −1.06522
\(546\) 3.26508e6 638820.i 0.468719 0.0917058i
\(547\) 7.21090e6 1.03044 0.515218 0.857059i \(-0.327711\pi\)
0.515218 + 0.857059i \(0.327711\pi\)
\(548\) 1.01981e6i 0.145066i
\(549\) 4.28608e6 0.606917
\(550\) 251520. 0.0354540
\(551\) 4.80168e6i 0.673774i
\(552\) 873600.i 0.122030i
\(553\) 6.63621e6i 0.922799i
\(554\) 1.33011e6i 0.184125i
\(555\) 5.77407e6 0.795700
\(556\) −221456. −0.0303809
\(557\) 273507.i 0.0373534i 0.999826 + 0.0186767i \(0.00594533\pi\)
−0.999826 + 0.0186767i \(0.994055\pi\)
\(558\) −2.84870e6 −0.387313
\(559\) −5.97701e6 + 1.16942e6i −0.809011 + 0.158285i
\(560\) −1.37088e6 −0.184727
\(561\) 1.71756e6i 0.230412i
\(562\) −196488. −0.0262419
\(563\) −959349. −0.127557 −0.0637787 0.997964i \(-0.520315\pi\)
−0.0637787 + 0.997964i \(0.520315\pi\)
\(564\) 612144.i 0.0810319i
\(565\) 5.11357e6i 0.673911i
\(566\) 6.23394e6i 0.817940i
\(567\) 3.73706e6i 0.488171i
\(568\) −4.07942e6 −0.530552
\(569\) −1.19403e7 −1.54609 −0.773044 0.634352i \(-0.781267\pi\)
−0.773044 + 0.634352i \(0.781267\pi\)
\(570\) 3.10284e6i 0.400011i
\(571\) 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
\(573\) −9.20634e6 −1.17139
\(574\) 3.98160e6i 0.504403i
\(575\) 550200. 0.0693986
\(576\) 303104. 0.0380658
\(577\) 1.66990e6i 0.208810i −0.994535 0.104405i \(-0.966706\pi\)
0.994535 0.104405i \(-0.0332938\pi\)
\(578\) 830624.i 0.103415i
\(579\) 4.52221e6i 0.560601i
\(580\) 3.34886e6i 0.413359i
\(581\) −5.82309e6 −0.715671
\(582\) −8.34350e6 −1.02104
\(583\) 90000.0i 0.0109666i
\(584\) −3.76742e6 −0.457101
\(585\) 441558. + 2.25685e6i 0.0533455 + 0.272655i
\(586\) −873852. −0.105122
\(587\) 8.29913e6i 0.994117i 0.867717 + 0.497059i \(0.165587\pi\)
−0.867717 + 0.497059i \(0.834413\pi\)
\(588\) 1.20266e6 0.143449
\(589\) 1.12601e7 1.33738
\(590\) 8.35135e6i 0.987704i
\(591\) 1.16947e7i 1.37727i
\(592\) 2.22950e6i 0.261459i
\(593\) 4.48969e6i 0.524300i −0.965027 0.262150i \(-0.915568\pi\)
0.965027 0.262150i \(-0.0844315\pi\)
\(594\) 1.97808e6 0.230026
\(595\) 5.89586e6 0.682738
\(596\) 4.42282e6i 0.510015i
\(597\) −1.86051e6 −0.213646
\(598\) 491400. + 2.51160e6i 0.0561930 + 0.287209i
\(599\) 1.38261e6 0.157446 0.0787232 0.996897i \(-0.474916\pi\)
0.0787232 + 0.996897i \(0.474916\pi\)
\(600\) 435968.i 0.0494398i
\(601\) 1.04021e7 1.17472 0.587359 0.809327i \(-0.300168\pi\)
0.587359 + 0.809327i \(0.300168\pi\)
\(602\) 4.19790e6 0.472107
\(603\) 1.68809e6i 0.189061i
\(604\) 5.14133e6i 0.573433i
\(605\) 7.47920e6i 0.830743i
\(606\) 5.88245e6i 0.650694i
\(607\) −4.78668e6 −0.527306 −0.263653 0.964618i \(-0.584927\pi\)
−0.263653 + 0.964618i \(0.584927\pi\)
\(608\) −1.19808e6 −0.131440
\(609\) 5.60196e6i 0.612064i
\(610\) −1.18157e7 −1.28568
\(611\) 344331. + 1.75991e6i 0.0373141 + 0.190717i
\(612\) −1.30358e6 −0.140689
\(613\) 1.04783e7i 1.12627i 0.826366 + 0.563134i \(0.190404\pi\)
−0.826366 + 0.563134i \(0.809596\pi\)
\(614\) 1.28441e6 0.137493
\(615\) −6.28524e6 −0.670091
\(616\) 806400.i 0.0856246i
\(617\) 1.79106e7i 1.89407i −0.321128 0.947036i \(-0.604062\pi\)
0.321128 0.947036i \(-0.395938\pi\)
\(618\) 1.30239e6i 0.137174i
\(619\) 4.43222e6i 0.464938i −0.972604 0.232469i \(-0.925320\pi\)
0.972604 0.232469i \(-0.0746804\pi\)
\(620\) 7.85318e6 0.820477
\(621\) 4.32705e6 0.450260
\(622\) 1.33490e7i 1.38348i
\(623\) 1.10017e7 1.13564
\(624\) 1.99014e6 389376.i 0.204608 0.0400320i
\(625\) −7.85355e6 −0.804203
\(626\) 4.66270e6i 0.475556i
\(627\) −1.82520e6 −0.185414
\(628\) −5.43210e6 −0.549627
\(629\) 9.58861e6i 0.966338i
\(630\) 1.58508e6i 0.159111i
\(631\) 1.43291e7i 1.43267i 0.697756 + 0.716335i \(0.254182\pi\)
−0.697756 + 0.716335i \(0.745818\pi\)
\(632\) 4.04493e6i 0.402827i
\(633\) 4.41650e6 0.438096
\(634\) 294072. 0.0290556
\(635\) 1.03405e7i 1.01767i
\(636\) −156000. −0.0152926
\(637\) −3.45764e6 + 676494.i −0.337622 + 0.0660565i
\(638\) −1.96992e6 −0.191601
\(639\) 4.71683e6i 0.456981i
\(640\) −835584. −0.0806381
\(641\) 6.65869e6 0.640094 0.320047 0.947402i \(-0.396301\pi\)
0.320047 + 0.947402i \(0.396301\pi\)
\(642\) 1.29605e6i 0.124103i
\(643\) 1.55224e7i 1.48058i 0.672286 + 0.740291i \(0.265312\pi\)
−0.672286 + 0.740291i \(0.734688\pi\)
\(644\) 1.76400e6i 0.167604i
\(645\) 6.62668e6i 0.627187i
\(646\) 5.15268e6 0.485794
\(647\) −2.44454e6 −0.229581 −0.114791 0.993390i \(-0.536620\pi\)
−0.114791 + 0.993390i \(0.536620\pi\)
\(648\) 2.27782e6i 0.213100i
\(649\) 4.91256e6 0.457821
\(650\) 245232. + 1.25341e6i 0.0227664 + 0.116361i
\(651\) 1.31368e7 1.21489
\(652\) 6.33149e6i 0.583293i
\(653\) 1.16500e7 1.06916 0.534580 0.845118i \(-0.320470\pi\)
0.534580 + 0.845118i \(0.320470\pi\)
\(654\) −7.53121e6 −0.688526
\(655\) 1.54966e7i 1.41135i
\(656\) 2.42688e6i 0.220185i
\(657\) 4.35608e6i 0.393716i
\(658\) 1.23606e6i 0.111295i
\(659\) 1.33185e7 1.19465 0.597326 0.801999i \(-0.296230\pi\)
0.597326 + 0.801999i \(0.296230\pi\)
\(660\) −1.27296e6 −0.113751
\(661\) 1.35722e7i 1.20822i −0.796900 0.604112i \(-0.793528\pi\)
0.796900 0.604112i \(-0.206472\pi\)
\(662\) 2.53073e6 0.224440
\(663\) −8.55917e6 + 1.67462e6i −0.756220 + 0.147956i
\(664\) −3.54931e6 −0.312409
\(665\) 6.26535e6i 0.549403i
\(666\) −2.57786e6 −0.225203
\(667\) −4.30920e6 −0.375044
\(668\) 6.82733e6i 0.591984i
\(669\) 8.10884e6i 0.700476i
\(670\) 4.65365e6i 0.400504i
\(671\) 6.95040e6i 0.595941i
\(672\) −1.39776e6 −0.119401
\(673\) −1.58674e7 −1.35042 −0.675209 0.737626i \(-0.735947\pi\)
−0.675209 + 0.737626i \(0.735947\pi\)
\(674\) 1.30737e6i 0.110854i
\(675\) 2.15940e6 0.182421
\(676\) −5.50264e6 + 2.23891e6i −0.463132 + 0.188439i
\(677\) −2.24264e7 −1.88056 −0.940281 0.340398i \(-0.889438\pi\)
−0.940281 + 0.340398i \(0.889438\pi\)
\(678\) 5.21383e6i 0.435595i
\(679\) −1.68475e7 −1.40236
\(680\) 3.59366e6 0.298034
\(681\) 2.30896e6i 0.190787i
\(682\) 4.61952e6i 0.380308i
\(683\) 8.11034e6i 0.665254i 0.943059 + 0.332627i \(0.107935\pi\)
−0.943059 + 0.332627i \(0.892065\pi\)
\(684\) 1.38528e6i 0.113213i
\(685\) 3.25064e6 0.264693
\(686\) 9.48738e6 0.769726
\(687\) 1.54316e7i 1.24744i
\(688\) 2.55872e6 0.206088
\(689\) 448500. 87750.0i 0.0359927 0.00704205i
\(690\) −2.78460e6 −0.222659
\(691\) 2.00020e7i 1.59359i 0.604246 + 0.796797i \(0.293474\pi\)
−0.604246 + 0.796797i \(0.706526\pi\)
\(692\) −256416. −0.0203554
\(693\) 932400. 0.0737512
\(694\) 1.18510e7i 0.934020i
\(695\) 705891.i 0.0554339i
\(696\) 3.41453e6i 0.267182i
\(697\) 1.04375e7i 0.813793i
\(698\) 3.46530e6 0.269217
\(699\) 1.46012e6 0.113031
\(700\) 880320.i 0.0679040i
\(701\) −2.22272e6 −0.170840 −0.0854200 0.996345i \(-0.527223\pi\)
−0.0854200 + 0.996345i \(0.527223\pi\)
\(702\) 1.92863e6 + 9.85743e6i 0.147709 + 0.754955i
\(703\) 1.01895e7 0.777617
\(704\) 491520.i 0.0373774i
\(705\) −1.95121e6 −0.147853
\(706\) 6.65162e6 0.502245
\(707\) 1.18780e7i 0.893708i
\(708\) 8.51510e6i 0.638420i
\(709\) 2.03634e7i 1.52137i 0.649122 + 0.760684i \(0.275136\pi\)
−0.649122 + 0.760684i \(0.724864\pi\)
\(710\) 1.30032e7i 0.968062i
\(711\) −4.67695e6 −0.346967
\(712\) 6.70579e6 0.495736
\(713\) 1.01052e7i 0.744425i
\(714\) 6.01146e6 0.441301
\(715\) 3.65976e6 716040.i 0.267724 0.0523808i
\(716\) 1.10407e7 0.804850
\(717\) 1.55747e7i 1.13141i
\(718\) 2.50214e6 0.181135
\(719\) −1.98255e7 −1.43022 −0.715108 0.699014i \(-0.753623\pi\)
−0.715108 + 0.699014i \(0.753623\pi\)
\(720\) 966144.i 0.0694561i
\(721\) 2.62983e6i 0.188404i
\(722\) 4.42880e6i 0.316186i
\(723\) 1.51617e7i 1.07870i
\(724\) 1.54365e6 0.109446
\(725\) −2.15050e6 −0.151948
\(726\) 7.62585e6i 0.536966i
\(727\) −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
\(729\) 1.56520e7 1.09081
\(730\) 1.20087e7i 0.834041i
\(731\) −1.10045e7 −0.761687
\(732\) −1.20474e7 −0.831025
\(733\) 1.48114e7i 1.01821i −0.860704 0.509105i \(-0.829976\pi\)
0.860704 0.509105i \(-0.170024\pi\)
\(734\) 4.33309e6i 0.296864i
\(735\) 3.83347e6i 0.261742i
\(736\) 1.07520e6i 0.0731635i
\(737\) −2.73744e6 −0.185642
\(738\) 2.80608e6 0.189653
\(739\) 5.67210e6i 0.382061i −0.981584 0.191031i \(-0.938817\pi\)
0.981584 0.191031i \(-0.0611830\pi\)
\(740\) 7.10654e6 0.477067
\(741\) −1.77957e6 9.09558e6i −0.119061 0.608534i
\(742\) −315000. −0.0210039
\(743\) 2.75704e7i 1.83219i −0.400960 0.916095i \(-0.631323\pi\)
0.400960 0.916095i \(-0.368677\pi\)
\(744\) 8.00717e6 0.530330
\(745\) 1.40977e7 0.930590
\(746\) 7.15582e6i 0.470774i
\(747\) 4.10389e6i 0.269088i
\(748\) 2.11392e6i 0.138145i
\(749\) 2.61702e6i 0.170452i
\(750\) −9.67715e6 −0.628195
\(751\) −4.09636e6 −0.265032 −0.132516 0.991181i \(-0.542306\pi\)
−0.132516 + 0.991181i \(0.542306\pi\)
\(752\) 753408.i 0.0485831i
\(753\) −8.43695e6 −0.542248
\(754\) −1.92067e6 9.81677e6i −0.123034 0.628840i
\(755\) 1.63880e7 1.04630
\(756\) 6.92328e6i 0.440562i
\(757\) 1.09396e7 0.693844 0.346922 0.937894i \(-0.387227\pi\)
0.346922 + 0.937894i \(0.387227\pi\)
\(758\) 3.47446e6 0.219641
\(759\) 1.63800e6i 0.103207i
\(760\) 3.81888e6i 0.239829i
\(761\) 1.36940e6i 0.0857172i 0.999081 + 0.0428586i \(0.0136465\pi\)
−0.999081 + 0.0428586i \(0.986354\pi\)
\(762\) 1.05432e7i 0.657787i
\(763\) −1.52073e7 −0.945670
\(764\) −1.13309e7 −0.702312
\(765\) 4.15517e6i 0.256706i
\(766\) −4.31886e6 −0.265948
\(767\) 4.78975e6 + 2.44809e7i 0.293984 + 1.50259i
\(768\) −851968. −0.0521219
\(769\) 1.08375e7i 0.660867i −0.943829 0.330433i \(-0.892805\pi\)
0.943829 0.330433i \(-0.107195\pi\)
\(770\) −2.57040e6 −0.156233
\(771\) 1.22965e7 0.744982
\(772\) 5.56579e6i 0.336112i
\(773\) 2.05445e7i 1.23665i −0.785922 0.618325i \(-0.787812\pi\)
0.785922 0.618325i \(-0.212188\pi\)
\(774\) 2.95852e6i 0.177510i
\(775\) 5.04298e6i 0.301601i
\(776