Properties

Label 192.7.e.f.65.1
Level $192$
Weight $7$
Character 192.65
Analytic conductor $44.170$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [192,7,Mod(65,192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(192, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("192.65");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\), degree \(1\), 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: \(44.1703840550\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.1
Root \(-1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 192.65
Dual form 192.7.e.f.65.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(21.0000 - 16.9706i) q^{3} -169.706i q^{5} -2.00000 q^{7} +(153.000 - 712.764i) q^{9} +O(q^{10})\) \(q+(21.0000 - 16.9706i) q^{3} -169.706i q^{5} -2.00000 q^{7} +(153.000 - 712.764i) q^{9} +33.9411i q^{11} +2950.00 q^{13} +(-2880.00 - 3563.82i) q^{15} -4480.23i q^{17} +5258.00 q^{19} +(-42.0000 + 33.9411i) q^{21} -10250.2i q^{23} -13175.0 q^{25} +(-8883.00 - 17564.5i) q^{27} +2206.17i q^{29} -22898.0 q^{31} +(576.000 + 712.764i) q^{33} +339.411i q^{35} -34058.0 q^{37} +(61950.0 - 50063.2i) q^{39} +16766.9i q^{41} -6406.00 q^{43} +(-120960. - 25965.0i) q^{45} +179888. i q^{47} -117645. q^{49} +(-76032.0 - 94084.8i) q^{51} -192548. i q^{53} +5760.00 q^{55} +(110418. - 89231.2i) q^{57} +326819. i q^{59} +62566.0 q^{61} +(-306.000 + 1425.53i) q^{63} -500632. i q^{65} +438698. q^{67} +(-173952. - 215255. i) q^{69} -68221.7i q^{71} -730510. q^{73} +(-276675. + 223587. i) q^{75} -67.8823i q^{77} -340562. q^{79} +(-484623. - 218106. i) q^{81} -496253. i q^{83} -760320. q^{85} +(37440.0 + 46329.6i) q^{87} +386725. i q^{89} -5900.00 q^{91} +(-480858. + 388592. i) q^{93} -892312. i q^{95} -281086. q^{97} +(24192.0 + 5192.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 42 q^{3} - 4 q^{7} + 306 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 42 q^{3} - 4 q^{7} + 306 q^{9} + 5900 q^{13} - 5760 q^{15} + 10516 q^{19} - 84 q^{21} - 26350 q^{25} - 17766 q^{27} - 45796 q^{31} + 1152 q^{33} - 68116 q^{37} + 123900 q^{39} - 12812 q^{43} - 241920 q^{45} - 235290 q^{49} - 152064 q^{51} + 11520 q^{55} + 220836 q^{57} + 125132 q^{61} - 612 q^{63} + 877396 q^{67} - 347904 q^{69} - 1461020 q^{73} - 553350 q^{75} - 681124 q^{79} - 969246 q^{81} - 1520640 q^{85} + 74880 q^{87} - 11800 q^{91} - 961716 q^{93} - 562172 q^{97} + 48384 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 21.0000 16.9706i 0.777778 0.628539i
\(4\) 0 0
\(5\) 169.706i 1.35765i −0.734302 0.678823i \(-0.762491\pi\)
0.734302 0.678823i \(-0.237509\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.00583090 −0.00291545 0.999996i \(-0.500928\pi\)
−0.00291545 + 0.999996i \(0.500928\pi\)
\(8\) 0 0
\(9\) 153.000 712.764i 0.209877 0.977728i
\(10\) 0 0
\(11\) 33.9411i 0.0255005i 0.999919 + 0.0127502i \(0.00405864\pi\)
−0.999919 + 0.0127502i \(0.995941\pi\)
\(12\) 0 0
\(13\) 2950.00 1.34274 0.671370 0.741122i \(-0.265706\pi\)
0.671370 + 0.741122i \(0.265706\pi\)
\(14\) 0 0
\(15\) −2880.00 3563.82i −0.853333 1.05595i
\(16\) 0 0
\(17\) 4480.23i 0.911913i −0.890002 0.455956i \(-0.849297\pi\)
0.890002 0.455956i \(-0.150703\pi\)
\(18\) 0 0
\(19\) 5258.00 0.766584 0.383292 0.923627i \(-0.374790\pi\)
0.383292 + 0.923627i \(0.374790\pi\)
\(20\) 0 0
\(21\) −42.0000 + 33.9411i −0.00453515 + 0.00366495i
\(22\) 0 0
\(23\) 10250.2i 0.842461i −0.906954 0.421230i \(-0.861598\pi\)
0.906954 0.421230i \(-0.138402\pi\)
\(24\) 0 0
\(25\) −13175.0 −0.843200
\(26\) 0 0
\(27\) −8883.00 17564.5i −0.451303 0.892371i
\(28\) 0 0
\(29\) 2206.17i 0.0904577i 0.998977 + 0.0452289i \(0.0144017\pi\)
−0.998977 + 0.0452289i \(0.985598\pi\)
\(30\) 0 0
\(31\) −22898.0 −0.768621 −0.384311 0.923204i \(-0.625561\pi\)
−0.384311 + 0.923204i \(0.625561\pi\)
\(32\) 0 0
\(33\) 576.000 + 712.764i 0.0160280 + 0.0198337i
\(34\) 0 0
\(35\) 339.411i 0.00791630i
\(36\) 0 0
\(37\) −34058.0 −0.672379 −0.336189 0.941794i \(-0.609138\pi\)
−0.336189 + 0.941794i \(0.609138\pi\)
\(38\) 0 0
\(39\) 61950.0 50063.2i 1.04435 0.843965i
\(40\) 0 0
\(41\) 16766.9i 0.243277i 0.992574 + 0.121639i \(0.0388149\pi\)
−0.992574 + 0.121639i \(0.961185\pi\)
\(42\) 0 0
\(43\) −6406.00 −0.0805715 −0.0402858 0.999188i \(-0.512827\pi\)
−0.0402858 + 0.999188i \(0.512827\pi\)
\(44\) 0 0
\(45\) −120960. 25965.0i −1.32741 0.284938i
\(46\) 0 0
\(47\) 179888.i 1.73264i 0.499489 + 0.866320i \(0.333521\pi\)
−0.499489 + 0.866320i \(0.666479\pi\)
\(48\) 0 0
\(49\) −117645. −0.999966
\(50\) 0 0
\(51\) −76032.0 94084.8i −0.573173 0.709266i
\(52\) 0 0
\(53\) 192548.i 1.29334i −0.762772 0.646668i \(-0.776162\pi\)
0.762772 0.646668i \(-0.223838\pi\)
\(54\) 0 0
\(55\) 5760.00 0.0346206
\(56\) 0 0
\(57\) 110418. 89231.2i 0.596232 0.481828i
\(58\) 0 0
\(59\) 326819.i 1.59130i 0.605758 + 0.795649i \(0.292870\pi\)
−0.605758 + 0.795649i \(0.707130\pi\)
\(60\) 0 0
\(61\) 62566.0 0.275644 0.137822 0.990457i \(-0.455990\pi\)
0.137822 + 0.990457i \(0.455990\pi\)
\(62\) 0 0
\(63\) −306.000 + 1425.53i −0.00122377 + 0.00570104i
\(64\) 0 0
\(65\) 500632.i 1.82296i
\(66\) 0 0
\(67\) 438698. 1.45862 0.729308 0.684185i \(-0.239842\pi\)
0.729308 + 0.684185i \(0.239842\pi\)
\(68\) 0 0
\(69\) −173952. 215255.i −0.529520 0.655247i
\(70\) 0 0
\(71\) 68221.7i 0.190611i −0.995448 0.0953053i \(-0.969617\pi\)
0.995448 0.0953053i \(-0.0303827\pi\)
\(72\) 0 0
\(73\) −730510. −1.87784 −0.938918 0.344141i \(-0.888170\pi\)
−0.938918 + 0.344141i \(0.888170\pi\)
\(74\) 0 0
\(75\) −276675. + 223587.i −0.655822 + 0.529984i
\(76\) 0 0
\(77\) 67.8823i 0.000148691i
\(78\) 0 0
\(79\) −340562. −0.690740 −0.345370 0.938467i \(-0.612247\pi\)
−0.345370 + 0.938467i \(0.612247\pi\)
\(80\) 0 0
\(81\) −484623. 218106.i −0.911904 0.410404i
\(82\) 0 0
\(83\) 496253.i 0.867899i −0.900937 0.433949i \(-0.857120\pi\)
0.900937 0.433949i \(-0.142880\pi\)
\(84\) 0 0
\(85\) −760320. −1.23805
\(86\) 0 0
\(87\) 37440.0 + 46329.6i 0.0568562 + 0.0703560i
\(88\) 0 0
\(89\) 386725.i 0.548570i 0.961648 + 0.274285i \(0.0884412\pi\)
−0.961648 + 0.274285i \(0.911559\pi\)
\(90\) 0 0
\(91\) −5900.00 −0.00782939
\(92\) 0 0
\(93\) −480858. + 388592.i −0.597817 + 0.483109i
\(94\) 0 0
\(95\) 892312.i 1.04075i
\(96\) 0 0
\(97\) −281086. −0.307981 −0.153991 0.988072i \(-0.549213\pi\)
−0.153991 + 0.988072i \(0.549213\pi\)
\(98\) 0 0
\(99\) 24192.0 + 5192.99i 0.0249325 + 0.00535195i
\(100\) 0 0
\(101\) 945362.i 0.917559i −0.888550 0.458780i \(-0.848287\pi\)
0.888550 0.458780i \(-0.151713\pi\)
\(102\) 0 0
\(103\) 865726. 0.792262 0.396131 0.918194i \(-0.370353\pi\)
0.396131 + 0.918194i \(0.370353\pi\)
\(104\) 0 0
\(105\) 5760.00 + 7127.64i 0.00497570 + 0.00615712i
\(106\) 0 0
\(107\) 1.47410e6i 1.20330i −0.798759 0.601651i \(-0.794510\pi\)
0.798759 0.601651i \(-0.205490\pi\)
\(108\) 0 0
\(109\) −650810. −0.502545 −0.251272 0.967916i \(-0.580849\pi\)
−0.251272 + 0.967916i \(0.580849\pi\)
\(110\) 0 0
\(111\) −715218. + 577983.i −0.522961 + 0.422616i
\(112\) 0 0
\(113\) 1.74417e6i 1.20879i −0.796683 0.604397i \(-0.793414\pi\)
0.796683 0.604397i \(-0.206586\pi\)
\(114\) 0 0
\(115\) −1.73952e6 −1.14376
\(116\) 0 0
\(117\) 451350. 2.10265e6i 0.281810 1.31283i
\(118\) 0 0
\(119\) 8960.46i 0.00531728i
\(120\) 0 0
\(121\) 1.77041e6 0.999350
\(122\) 0 0
\(123\) 284544. + 352105.i 0.152909 + 0.189216i
\(124\) 0 0
\(125\) 415779.i 0.212879i
\(126\) 0 0
\(127\) 2.28053e6 1.11333 0.556665 0.830737i \(-0.312081\pi\)
0.556665 + 0.830737i \(0.312081\pi\)
\(128\) 0 0
\(129\) −134526. + 108713.i −0.0626667 + 0.0506424i
\(130\) 0 0
\(131\) 1.07196e6i 0.476832i 0.971163 + 0.238416i \(0.0766282\pi\)
−0.971163 + 0.238416i \(0.923372\pi\)
\(132\) 0 0
\(133\) −10516.0 −0.00446988
\(134\) 0 0
\(135\) −2.98080e6 + 1.50750e6i −1.21152 + 0.612709i
\(136\) 0 0
\(137\) 2.78338e6i 1.08246i 0.840876 + 0.541228i \(0.182040\pi\)
−0.840876 + 0.541228i \(0.817960\pi\)
\(138\) 0 0
\(139\) 4.57395e6 1.70313 0.851563 0.524253i \(-0.175655\pi\)
0.851563 + 0.524253i \(0.175655\pi\)
\(140\) 0 0
\(141\) 3.05280e6 + 3.77765e6i 1.08903 + 1.34761i
\(142\) 0 0
\(143\) 100126.i 0.0342405i
\(144\) 0 0
\(145\) 374400. 0.122809
\(146\) 0 0
\(147\) −2.47054e6 + 1.99650e6i −0.777751 + 0.628518i
\(148\) 0 0
\(149\) 4.46010e6i 1.34830i 0.738595 + 0.674149i \(0.235489\pi\)
−0.738595 + 0.674149i \(0.764511\pi\)
\(150\) 0 0
\(151\) 2.20809e6 0.641338 0.320669 0.947191i \(-0.396092\pi\)
0.320669 + 0.947191i \(0.396092\pi\)
\(152\) 0 0
\(153\) −3.19334e6 685475.i −0.891603 0.191389i
\(154\) 0 0
\(155\) 3.88592e6i 1.04352i
\(156\) 0 0
\(157\) 1.28887e6 0.333051 0.166525 0.986037i \(-0.446745\pi\)
0.166525 + 0.986037i \(0.446745\pi\)
\(158\) 0 0
\(159\) −3.26765e6 4.04351e6i −0.812913 1.00593i
\(160\) 0 0
\(161\) 20500.4i 0.00491231i
\(162\) 0 0
\(163\) 879914. 0.203178 0.101589 0.994826i \(-0.467607\pi\)
0.101589 + 0.994826i \(0.467607\pi\)
\(164\) 0 0
\(165\) 120960. 97750.4i 0.0269271 0.0217604i
\(166\) 0 0
\(167\) 5.96760e6i 1.28130i 0.767834 + 0.640649i \(0.221335\pi\)
−0.767834 + 0.640649i \(0.778665\pi\)
\(168\) 0 0
\(169\) 3.87569e6 0.802951
\(170\) 0 0
\(171\) 804474. 3.74771e6i 0.160888 0.749511i
\(172\) 0 0
\(173\) 418867.i 0.0808981i 0.999182 + 0.0404490i \(0.0128788\pi\)
−0.999182 + 0.0404490i \(0.987121\pi\)
\(174\) 0 0
\(175\) 26350.0 0.00491662
\(176\) 0 0
\(177\) 5.54630e6 + 6.86320e6i 1.00019 + 1.23768i
\(178\) 0 0
\(179\) 302110.i 0.0526752i −0.999653 0.0263376i \(-0.991616\pi\)
0.999653 0.0263376i \(-0.00838448\pi\)
\(180\) 0 0
\(181\) 6.47618e6 1.09215 0.546076 0.837735i \(-0.316121\pi\)
0.546076 + 0.837735i \(0.316121\pi\)
\(182\) 0 0
\(183\) 1.31389e6 1.06178e6i 0.214390 0.173253i
\(184\) 0 0
\(185\) 5.77983e6i 0.912852i
\(186\) 0 0
\(187\) 152064. 0.0232542
\(188\) 0 0
\(189\) 17766.0 + 35129.1i 0.00263151 + 0.00520333i
\(190\) 0 0
\(191\) 5.02166e6i 0.720687i −0.932820 0.360344i \(-0.882659\pi\)
0.932820 0.360344i \(-0.117341\pi\)
\(192\) 0 0
\(193\) 3.50093e6 0.486980 0.243490 0.969903i \(-0.421708\pi\)
0.243490 + 0.969903i \(0.421708\pi\)
\(194\) 0 0
\(195\) −8.49600e6 1.05133e7i −1.14580 1.41786i
\(196\) 0 0
\(197\) 4.85423e6i 0.634923i 0.948271 + 0.317462i \(0.102830\pi\)
−0.948271 + 0.317462i \(0.897170\pi\)
\(198\) 0 0
\(199\) 9.50976e6 1.20673 0.603365 0.797465i \(-0.293826\pi\)
0.603365 + 0.797465i \(0.293826\pi\)
\(200\) 0 0
\(201\) 9.21266e6 7.44495e6i 1.13448 0.916798i
\(202\) 0 0
\(203\) 4412.35i 0.000527450i
\(204\) 0 0
\(205\) 2.84544e6 0.330284
\(206\) 0 0
\(207\) −7.30598e6 1.56828e6i −0.823697 0.176813i
\(208\) 0 0
\(209\) 178462.i 0.0195483i
\(210\) 0 0
\(211\) 7.06414e6 0.751990 0.375995 0.926622i \(-0.377301\pi\)
0.375995 + 0.926622i \(0.377301\pi\)
\(212\) 0 0
\(213\) −1.15776e6 1.43265e6i −0.119806 0.148253i
\(214\) 0 0
\(215\) 1.08713e6i 0.109388i
\(216\) 0 0
\(217\) 45796.0 0.00448176
\(218\) 0 0
\(219\) −1.53407e7 + 1.23972e7i −1.46054 + 1.18029i
\(220\) 0 0
\(221\) 1.32167e7i 1.22446i
\(222\) 0 0
\(223\) −4.66891e6 −0.421019 −0.210509 0.977592i \(-0.567512\pi\)
−0.210509 + 0.977592i \(0.567512\pi\)
\(224\) 0 0
\(225\) −2.01578e6 + 9.39066e6i −0.176968 + 0.824420i
\(226\) 0 0
\(227\) 1.96525e7i 1.68012i −0.542494 0.840059i \(-0.682520\pi\)
0.542494 0.840059i \(-0.317480\pi\)
\(228\) 0 0
\(229\) 4.48178e6 0.373202 0.186601 0.982436i \(-0.440253\pi\)
0.186601 + 0.982436i \(0.440253\pi\)
\(230\) 0 0
\(231\) −1152.00 1425.53i −9.34580e−5 0.000115648i
\(232\) 0 0
\(233\) 2.29286e6i 0.181263i −0.995884 0.0906316i \(-0.971111\pi\)
0.995884 0.0906316i \(-0.0288886\pi\)
\(234\) 0 0
\(235\) 3.05280e7 2.35231
\(236\) 0 0
\(237\) −7.15180e6 + 5.77953e6i −0.537243 + 0.434158i
\(238\) 0 0
\(239\) 2.64564e6i 0.193793i −0.995294 0.0968964i \(-0.969108\pi\)
0.995294 0.0968964i \(-0.0308915\pi\)
\(240\) 0 0
\(241\) −6.99581e6 −0.499789 −0.249894 0.968273i \(-0.580396\pi\)
−0.249894 + 0.968273i \(0.580396\pi\)
\(242\) 0 0
\(243\) −1.38785e7 + 3.64411e6i −0.967214 + 0.253964i
\(244\) 0 0
\(245\) 1.99650e7i 1.35760i
\(246\) 0 0
\(247\) 1.55111e7 1.02932
\(248\) 0 0
\(249\) −8.42170e6 1.04213e7i −0.545508 0.675032i
\(250\) 0 0
\(251\) 2.84990e7i 1.80223i 0.433585 + 0.901113i \(0.357248\pi\)
−0.433585 + 0.901113i \(0.642752\pi\)
\(252\) 0 0
\(253\) 347904. 0.0214831
\(254\) 0 0
\(255\) −1.59667e7 + 1.29031e7i −0.962931 + 0.778166i
\(256\) 0 0
\(257\) 186812.i 0.0110054i 0.999985 + 0.00550269i \(0.00175157\pi\)
−0.999985 + 0.00550269i \(0.998248\pi\)
\(258\) 0 0
\(259\) 68116.0 0.00392058
\(260\) 0 0
\(261\) 1.57248e6 + 337544.i 0.0884430 + 0.0189850i
\(262\) 0 0
\(263\) 8.61541e6i 0.473597i −0.971559 0.236798i \(-0.923902\pi\)
0.971559 0.236798i \(-0.0760981\pi\)
\(264\) 0 0
\(265\) −3.26765e7 −1.75589
\(266\) 0 0
\(267\) 6.56294e6 + 8.12123e6i 0.344798 + 0.426666i
\(268\) 0 0
\(269\) 7.55132e6i 0.387941i −0.981007 0.193971i \(-0.937863\pi\)
0.981007 0.193971i \(-0.0621367\pi\)
\(270\) 0 0
\(271\) −1.39445e7 −0.700642 −0.350321 0.936630i \(-0.613927\pi\)
−0.350321 + 0.936630i \(0.613927\pi\)
\(272\) 0 0
\(273\) −123900. + 100126.i −0.00608952 + 0.00492108i
\(274\) 0 0
\(275\) 447174.i 0.0215020i
\(276\) 0 0
\(277\) −2.81293e7 −1.32349 −0.661744 0.749730i \(-0.730183\pi\)
−0.661744 + 0.749730i \(0.730183\pi\)
\(278\) 0 0
\(279\) −3.50339e6 + 1.63209e7i −0.161316 + 0.751503i
\(280\) 0 0
\(281\) 2.23430e7i 1.00698i −0.864000 0.503491i \(-0.832049\pi\)
0.864000 0.503491i \(-0.167951\pi\)
\(282\) 0 0
\(283\) 1.01418e7 0.447464 0.223732 0.974651i \(-0.428176\pi\)
0.223732 + 0.974651i \(0.428176\pi\)
\(284\) 0 0
\(285\) −1.51430e7 1.87386e7i −0.654152 0.809471i
\(286\) 0 0
\(287\) 33533.8i 0.00141853i
\(288\) 0 0
\(289\) 4.06512e6 0.168415
\(290\) 0 0
\(291\) −5.90281e6 + 4.77019e6i −0.239541 + 0.193578i
\(292\) 0 0
\(293\) 2.78468e7i 1.10706i −0.832828 0.553532i \(-0.813280\pi\)
0.832828 0.553532i \(-0.186720\pi\)
\(294\) 0 0
\(295\) 5.54630e7 2.16042
\(296\) 0 0
\(297\) 596160. 301499.i 0.0227559 0.0115084i
\(298\) 0 0
\(299\) 3.02381e7i 1.13121i
\(300\) 0 0
\(301\) 12812.0 0.000469805
\(302\) 0 0
\(303\) −1.60433e7 1.98526e7i −0.576722 0.713657i
\(304\) 0 0
\(305\) 1.06178e7i 0.374227i
\(306\) 0 0
\(307\) −3.63254e7 −1.25544 −0.627718 0.778440i \(-0.716011\pi\)
−0.627718 + 0.778440i \(0.716011\pi\)
\(308\) 0 0
\(309\) 1.81802e7 1.46919e7i 0.616204 0.497968i
\(310\) 0 0
\(311\) 3.59921e7i 1.19654i 0.801296 + 0.598268i \(0.204144\pi\)
−0.801296 + 0.598268i \(0.795856\pi\)
\(312\) 0 0
\(313\) 4.01099e7 1.30803 0.654016 0.756480i \(-0.273083\pi\)
0.654016 + 0.756480i \(0.273083\pi\)
\(314\) 0 0
\(315\) 241920. + 51929.9i 0.00773998 + 0.00166145i
\(316\) 0 0
\(317\) 3.94377e7i 1.23804i −0.785377 0.619018i \(-0.787531\pi\)
0.785377 0.619018i \(-0.212469\pi\)
\(318\) 0 0
\(319\) −74880.0 −0.00230671
\(320\) 0 0
\(321\) −2.50163e7 3.09560e7i −0.756323 0.935902i
\(322\) 0 0
\(323\) 2.35570e7i 0.699058i
\(324\) 0 0
\(325\) −3.88662e7 −1.13220
\(326\) 0 0
\(327\) −1.36670e7 + 1.10446e7i −0.390868 + 0.315869i
\(328\) 0 0
\(329\) 359776.i 0.0101029i
\(330\) 0 0
\(331\) 2.78363e7 0.767586 0.383793 0.923419i \(-0.374618\pi\)
0.383793 + 0.923419i \(0.374618\pi\)
\(332\) 0 0
\(333\) −5.21087e6 + 2.42753e7i −0.141117 + 0.657403i
\(334\) 0 0
\(335\) 7.44495e7i 1.98028i
\(336\) 0 0
\(337\) −2.37897e7 −0.621582 −0.310791 0.950478i \(-0.600594\pi\)
−0.310791 + 0.950478i \(0.600594\pi\)
\(338\) 0 0
\(339\) −2.95995e7 3.66275e7i −0.759775 0.940174i
\(340\) 0 0
\(341\) 777184.i 0.0196002i
\(342\) 0 0
\(343\) 470588. 0.0116616
\(344\) 0 0
\(345\) −3.65299e7 + 2.95206e7i −0.889593 + 0.718900i
\(346\) 0 0
\(347\) 5.34078e7i 1.27825i 0.769103 + 0.639125i \(0.220703\pi\)
−0.769103 + 0.639125i \(0.779297\pi\)
\(348\) 0 0
\(349\) −4.71677e7 −1.10961 −0.554803 0.831982i \(-0.687206\pi\)
−0.554803 + 0.831982i \(0.687206\pi\)
\(350\) 0 0
\(351\) −2.62048e7 5.18154e7i −0.605983 1.19822i
\(352\) 0 0
\(353\) 1.75443e7i 0.398852i 0.979913 + 0.199426i \(0.0639078\pi\)
−0.979913 + 0.199426i \(0.936092\pi\)
\(354\) 0 0
\(355\) −1.15776e7 −0.258782
\(356\) 0 0
\(357\) 152064. + 188170.i 0.00334212 + 0.00413566i
\(358\) 0 0
\(359\) 6.18249e7i 1.33623i 0.744059 + 0.668113i \(0.232898\pi\)
−0.744059 + 0.668113i \(0.767102\pi\)
\(360\) 0 0
\(361\) −1.93993e7 −0.412349
\(362\) 0 0
\(363\) 3.71786e7 3.00448e7i 0.777272 0.628131i
\(364\) 0 0
\(365\) 1.23972e8i 2.54943i
\(366\) 0 0
\(367\) 3.40461e7 0.688761 0.344381 0.938830i \(-0.388089\pi\)
0.344381 + 0.938830i \(0.388089\pi\)
\(368\) 0 0
\(369\) 1.19508e7 + 2.56534e6i 0.237859 + 0.0510582i
\(370\) 0 0
\(371\) 385096.i 0.00754132i
\(372\) 0 0
\(373\) 5.15781e7 0.993892 0.496946 0.867782i \(-0.334455\pi\)
0.496946 + 0.867782i \(0.334455\pi\)
\(374\) 0 0
\(375\) −7.05600e6 8.73135e6i −0.133803 0.165572i
\(376\) 0 0
\(377\) 6.50821e6i 0.121461i
\(378\) 0 0
\(379\) 4.28828e7 0.787709 0.393855 0.919173i \(-0.371141\pi\)
0.393855 + 0.919173i \(0.371141\pi\)
\(380\) 0 0
\(381\) 4.78910e7 3.87018e7i 0.865923 0.699772i
\(382\) 0 0
\(383\) 1.51307e7i 0.269316i 0.990892 + 0.134658i \(0.0429936\pi\)
−0.990892 + 0.134658i \(0.957006\pi\)
\(384\) 0 0
\(385\) −11520.0 −0.000201869
\(386\) 0 0
\(387\) −980118. + 4.56596e6i −0.0169101 + 0.0787770i
\(388\) 0 0
\(389\) 6.15319e7i 1.04533i −0.852540 0.522663i \(-0.824939\pi\)
0.852540 0.522663i \(-0.175061\pi\)
\(390\) 0 0
\(391\) −4.59233e7 −0.768251
\(392\) 0 0
\(393\) 1.81918e7 + 2.25112e7i 0.299708 + 0.370870i
\(394\) 0 0
\(395\) 5.77953e7i 0.937780i
\(396\) 0 0
\(397\) 8.55816e7 1.36776 0.683878 0.729596i \(-0.260292\pi\)
0.683878 + 0.729596i \(0.260292\pi\)
\(398\) 0 0
\(399\) −220836. + 178462.i −0.00347657 + 0.00280949i
\(400\) 0 0
\(401\) 4.09739e7i 0.635439i −0.948185 0.317719i \(-0.897083\pi\)
0.948185 0.317719i \(-0.102917\pi\)
\(402\) 0 0
\(403\) −6.75491e7 −1.03206
\(404\) 0 0
\(405\) −3.70138e7 + 8.22433e7i −0.557183 + 1.23804i
\(406\) 0 0
\(407\) 1.15597e6i 0.0171460i
\(408\) 0 0
\(409\) 6.10556e7 0.892391 0.446196 0.894935i \(-0.352779\pi\)
0.446196 + 0.894935i \(0.352779\pi\)
\(410\) 0 0
\(411\) 4.72355e7 + 5.84509e7i 0.680366 + 0.841910i
\(412\) 0 0
\(413\) 653638.i 0.00927870i
\(414\) 0 0
\(415\) −8.42170e7 −1.17830
\(416\) 0 0
\(417\) 9.60529e7 7.76224e7i 1.32465 1.07048i
\(418\) 0 0
\(419\) 3.38860e7i 0.460657i 0.973113 + 0.230329i \(0.0739801\pi\)
−0.973113 + 0.230329i \(0.926020\pi\)
\(420\) 0 0
\(421\) 1.96156e7 0.262879 0.131439 0.991324i \(-0.458040\pi\)
0.131439 + 0.991324i \(0.458040\pi\)
\(422\) 0 0
\(423\) 1.28218e8 + 2.75229e7i 1.69405 + 0.363641i
\(424\) 0 0
\(425\) 5.90270e7i 0.768925i
\(426\) 0 0
\(427\) −125132. −0.00160725
\(428\) 0 0
\(429\) 1.69920e6 + 2.10265e6i 0.0215215 + 0.0266315i
\(430\) 0 0
\(431\) 4.01587e7i 0.501589i 0.968040 + 0.250795i \(0.0806919\pi\)
−0.968040 + 0.250795i \(0.919308\pi\)
\(432\) 0 0
\(433\) −845854. −0.0104191 −0.00520957 0.999986i \(-0.501658\pi\)
−0.00520957 + 0.999986i \(0.501658\pi\)
\(434\) 0 0
\(435\) 7.86240e6 6.35378e6i 0.0955185 0.0771906i
\(436\) 0 0
\(437\) 5.38957e7i 0.645817i
\(438\) 0 0
\(439\) 7.48204e7 0.884354 0.442177 0.896928i \(-0.354206\pi\)
0.442177 + 0.896928i \(0.354206\pi\)
\(440\) 0 0
\(441\) −1.79997e7 + 8.38531e7i −0.209869 + 0.977695i
\(442\) 0 0
\(443\) 1.25246e8i 1.44063i −0.693649 0.720313i \(-0.743998\pi\)
0.693649 0.720313i \(-0.256002\pi\)
\(444\) 0 0
\(445\) 6.56294e7 0.744764
\(446\) 0 0
\(447\) 7.56904e7 + 9.36621e7i 0.847458 + 1.04868i
\(448\) 0 0
\(449\) 1.12812e8i 1.24628i 0.782109 + 0.623142i \(0.214144\pi\)
−0.782109 + 0.623142i \(0.785856\pi\)
\(450\) 0 0
\(451\) −569088. −0.00620369
\(452\) 0 0
\(453\) 4.63700e7 3.74726e7i 0.498818 0.403106i
\(454\) 0 0
\(455\) 1.00126e6i 0.0106295i
\(456\) 0 0
\(457\) 1.57358e8 1.64870 0.824350 0.566081i \(-0.191541\pi\)
0.824350 + 0.566081i \(0.191541\pi\)
\(458\) 0 0
\(459\) −7.86931e7 + 3.97979e7i −0.813764 + 0.411549i
\(460\) 0 0
\(461\) 1.83107e8i 1.86897i 0.356002 + 0.934485i \(0.384140\pi\)
−0.356002 + 0.934485i \(0.615860\pi\)
\(462\) 0 0
\(463\) −1.77978e8 −1.79318 −0.896588 0.442866i \(-0.853962\pi\)
−0.896588 + 0.442866i \(0.853962\pi\)
\(464\) 0 0
\(465\) 6.59462e7 + 8.16043e7i 0.655890 + 0.811623i
\(466\) 0 0
\(467\) 9.35797e7i 0.918821i −0.888224 0.459410i \(-0.848061\pi\)
0.888224 0.459410i \(-0.151939\pi\)
\(468\) 0 0
\(469\) −877396. −0.00850505
\(470\) 0 0
\(471\) 2.70663e7 2.18728e7i 0.259039 0.209335i
\(472\) 0 0
\(473\) 217427.i 0.00205461i
\(474\) 0 0
\(475\) −6.92742e7 −0.646384
\(476\) 0 0
\(477\) −1.37241e8 2.94598e7i −1.26453 0.271441i
\(478\) 0 0
\(479\) 1.07662e8i 0.979617i −0.871830 0.489808i \(-0.837067\pi\)
0.871830 0.489808i \(-0.162933\pi\)
\(480\) 0 0
\(481\) −1.00471e8 −0.902830
\(482\) 0 0
\(483\) 347904. + 430509.i 0.00308758 + 0.00382068i
\(484\) 0 0
\(485\) 4.77019e7i 0.418129i
\(486\) 0 0
\(487\) 4.14432e6 0.0358811 0.0179406 0.999839i \(-0.494289\pi\)
0.0179406 + 0.999839i \(0.494289\pi\)
\(488\) 0 0
\(489\) 1.84782e7 1.49326e7i 0.158028 0.127706i
\(490\) 0 0
\(491\) 1.19347e8i 1.00824i 0.863633 + 0.504122i \(0.168184\pi\)
−0.863633 + 0.504122i \(0.831816\pi\)
\(492\) 0 0
\(493\) 9.88416e6 0.0824896
\(494\) 0 0
\(495\) 881280. 4.10552e6i 0.00726605 0.0338495i
\(496\) 0 0
\(497\) 136443.i 0.00111143i
\(498\) 0 0
\(499\) 1.17436e8 0.945144 0.472572 0.881292i \(-0.343326\pi\)
0.472572 + 0.881292i \(0.343326\pi\)
\(500\) 0 0
\(501\) 1.01273e8 + 1.25320e8i 0.805346 + 0.996565i
\(502\) 0 0
\(503\) 1.99753e8i 1.56960i −0.619747 0.784802i \(-0.712765\pi\)
0.619747 0.784802i \(-0.287235\pi\)
\(504\) 0 0
\(505\) −1.60433e8 −1.24572
\(506\) 0 0
\(507\) 8.13895e7 6.57727e7i 0.624517 0.504686i
\(508\) 0 0
\(509\) 1.12725e8i 0.854804i −0.904062 0.427402i \(-0.859429\pi\)
0.904062 0.427402i \(-0.140571\pi\)
\(510\) 0 0
\(511\) 1.46102e6 0.0109495
\(512\) 0 0
\(513\) −4.67068e7 9.23543e7i −0.345962 0.684077i
\(514\) 0 0
\(515\) 1.46919e8i 1.07561i
\(516\) 0 0
\(517\) −6.10560e6 −0.0441832
\(518\) 0 0
\(519\) 7.10842e6 + 8.79622e6i 0.0508476 + 0.0629207i
\(520\) 0 0
\(521\) 1.14581e8i 0.810215i −0.914269 0.405108i \(-0.867234\pi\)
0.914269 0.405108i \(-0.132766\pi\)
\(522\) 0 0
\(523\) −1.49806e8 −1.04719 −0.523594 0.851968i \(-0.675409\pi\)
−0.523594 + 0.851968i \(0.675409\pi\)
\(524\) 0 0
\(525\) 553350. 447174.i 0.00382404 0.00309029i
\(526\) 0 0
\(527\) 1.02588e8i 0.700916i
\(528\) 0 0
\(529\) 4.29689e7 0.290260
\(530\) 0 0
\(531\) 2.32945e8 + 5.00033e7i 1.55586 + 0.333976i
\(532\) 0 0
\(533\) 4.94624e7i 0.326658i
\(534\) 0 0
\(535\) −2.50163e8 −1.63366
\(536\) 0 0
\(537\) −5.12698e6 6.34431e6i −0.0331084 0.0409696i
\(538\) 0 0
\(539\) 3.99300e6i 0.0254996i
\(540\) 0 0
\(541\) 1.57017e8 0.991644 0.495822 0.868424i \(-0.334867\pi\)
0.495822 + 0.868424i \(0.334867\pi\)
\(542\) 0 0
\(543\) 1.36000e8 1.09904e8i 0.849452 0.686461i
\(544\) 0 0
\(545\) 1.10446e8i 0.682277i
\(546\) 0 0
\(547\) −2.79469e8 −1.70754 −0.853770 0.520650i \(-0.825690\pi\)
−0.853770 + 0.520650i \(0.825690\pi\)
\(548\) 0 0
\(549\) 9.57260e6 4.45948e7i 0.0578513 0.269505i
\(550\) 0 0
\(551\) 1.16001e7i 0.0693434i
\(552\) 0 0
\(553\) 681124. 0.00402764
\(554\) 0 0
\(555\) 9.80870e7 + 1.21377e8i 0.573763 + 0.709996i
\(556\) 0 0
\(557\) 1.50294e8i 0.869712i −0.900500 0.434856i \(-0.856799\pi\)
0.900500 0.434856i \(-0.143201\pi\)
\(558\) 0 0
\(559\) −1.88977e7 −0.108187
\(560\) 0 0
\(561\) 3.19334e6 2.58061e6i 0.0180866 0.0146162i
\(562\) 0 0
\(563\) 8.27836e7i 0.463894i 0.972728 + 0.231947i \(0.0745097\pi\)
−0.972728 + 0.231947i \(0.925490\pi\)
\(564\) 0 0
\(565\) −2.95995e8 −1.64111
\(566\) 0 0
\(567\) 969246. + 436211.i 0.00531722 + 0.00239303i
\(568\) 0 0
\(569\) 2.57230e8i 1.39632i −0.715942 0.698160i \(-0.754003\pi\)
0.715942 0.698160i \(-0.245997\pi\)
\(570\) 0 0
\(571\) 2.84039e7 0.152570 0.0762852 0.997086i \(-0.475694\pi\)
0.0762852 + 0.997086i \(0.475694\pi\)
\(572\) 0 0
\(573\) −8.52204e7 1.05455e8i −0.452980 0.560535i
\(574\) 0 0
\(575\) 1.35047e8i 0.710363i
\(576\) 0 0
\(577\) 6.52476e7 0.339654 0.169827 0.985474i \(-0.445679\pi\)
0.169827 + 0.985474i \(0.445679\pi\)
\(578\) 0 0
\(579\) 7.35195e7 5.94128e7i 0.378763 0.306086i
\(580\) 0 0
\(581\) 992506.i 0.00506063i
\(582\) 0 0
\(583\) 6.53530e6 0.0329807
\(584\) 0 0
\(585\) −3.56832e8 7.65966e7i −1.78236 0.382597i
\(586\) 0 0
\(587\) 6.66740e7i 0.329642i 0.986324 + 0.164821i \(0.0527046\pi\)
−0.986324 + 0.164821i \(0.947295\pi\)
\(588\) 0 0
\(589\) −1.20398e8 −0.589213
\(590\) 0 0
\(591\) 8.23789e7 + 1.01939e8i 0.399074 + 0.493829i
\(592\) 0 0
\(593\) 1.53324e8i 0.735271i −0.929970 0.367635i \(-0.880167\pi\)
0.929970 0.367635i \(-0.119833\pi\)
\(594\) 0 0
\(595\) 1.52064e6 0.00721897
\(596\) 0 0
\(597\) 1.99705e8 1.61386e8i 0.938568 0.758478i
\(598\) 0 0
\(599\) 2.18294e8i 1.01569i 0.861448 + 0.507846i \(0.169558\pi\)
−0.861448 + 0.507846i \(0.830442\pi\)
\(600\) 0 0
\(601\) 1.08478e8 0.499709 0.249854 0.968283i \(-0.419617\pi\)
0.249854 + 0.968283i \(0.419617\pi\)
\(602\) 0 0
\(603\) 6.71208e7 3.12688e8i 0.306129 1.42613i
\(604\) 0 0
\(605\) 3.00448e8i 1.35676i
\(606\) 0 0
\(607\) 3.43321e8 1.53509 0.767547 0.640993i \(-0.221477\pi\)
0.767547 + 0.640993i \(0.221477\pi\)
\(608\) 0 0
\(609\) −74880.0 92659.3i −0.000331523 0.000410239i
\(610\) 0 0
\(611\) 5.30669e8i 2.32649i
\(612\) 0 0
\(613\) −2.96325e8 −1.28643 −0.643216 0.765685i \(-0.722400\pi\)
−0.643216 + 0.765685i \(0.722400\pi\)
\(614\) 0 0
\(615\) 5.97542e7 4.82887e7i 0.256888 0.207597i
\(616\) 0 0
\(617\) 1.32676e8i 0.564853i 0.959289 + 0.282426i \(0.0911393\pi\)
−0.959289 + 0.282426i \(0.908861\pi\)
\(618\) 0 0
\(619\) −4.14773e8 −1.74879 −0.874397 0.485211i \(-0.838743\pi\)
−0.874397 + 0.485211i \(0.838743\pi\)
\(620\) 0 0
\(621\) −1.80040e8 + 9.10527e7i −0.751787 + 0.380205i
\(622\) 0 0
\(623\) 773450.i 0.00319866i
\(624\) 0 0
\(625\) −2.76419e8 −1.13221
\(626\) 0 0
\(627\) 3.02861e6 + 3.74771e6i 0.0122868 + 0.0152042i
\(628\) 0 0
\(629\) 1.52588e8i 0.613151i
\(630\) 0 0
\(631\) −3.03858e8 −1.20944 −0.604718 0.796440i \(-0.706714\pi\)
−0.604718 + 0.796440i \(0.706714\pi\)
\(632\) 0 0
\(633\) 1.48347e8 1.19882e8i 0.584881 0.472655i
\(634\) 0 0
\(635\) 3.87018e8i 1.51151i
\(636\) 0 0
\(637\) −3.47053e8 −1.34269
\(638\) 0 0
\(639\) −4.86259e7 1.04379e7i −0.186365 0.0400047i
\(640\) 0 0
\(641\) 1.81629e8i 0.689622i 0.938672 + 0.344811i \(0.112057\pi\)
−0.938672 + 0.344811i \(0.887943\pi\)
\(642\) 0 0
\(643\) 1.73811e8 0.653798 0.326899 0.945059i \(-0.393996\pi\)
0.326899 + 0.945059i \(0.393996\pi\)
\(644\) 0 0
\(645\) 1.84493e7 + 2.28298e7i 0.0687544 + 0.0850792i
\(646\) 0 0
\(647\) 2.43137e8i 0.897713i 0.893604 + 0.448856i \(0.148168\pi\)
−0.893604 + 0.448856i \(0.851832\pi\)
\(648\) 0 0
\(649\) −1.10926e7 −0.0405788
\(650\) 0 0
\(651\) 961716. 777184.i 0.00348581 0.00281696i
\(652\) 0 0
\(653\) 4.47562e7i 0.160736i −0.996765 0.0803681i \(-0.974390\pi\)
0.996765 0.0803681i \(-0.0256096\pi\)
\(654\) 0 0
\(655\) 1.81918e8 0.647369
\(656\) 0 0
\(657\) −1.11768e8 + 5.20681e8i −0.394114 + 1.83601i
\(658\) 0 0
\(659\) 1.13574e8i 0.396845i 0.980117 + 0.198423i \(0.0635819\pi\)
−0.980117 + 0.198423i \(0.936418\pi\)
\(660\) 0 0
\(661\) 9.93464e7 0.343992 0.171996 0.985098i \(-0.444978\pi\)
0.171996 + 0.985098i \(0.444978\pi\)
\(662\) 0 0
\(663\) −2.24294e8 2.77550e8i −0.769623 0.952359i
\(664\) 0 0
\(665\) 1.78462e6i 0.00606851i
\(666\) 0 0
\(667\) 2.26138e7 0.0762071
\(668\) 0 0
\(669\) −9.80472e7 + 7.92341e7i −0.327459 + 0.264627i
\(670\) 0 0
\(671\) 2.12356e6i 0.00702906i
\(672\) 0 0
\(673\) −2.79412e8 −0.916642 −0.458321 0.888787i \(-0.651549\pi\)
−0.458321 + 0.888787i \(0.651549\pi\)
\(674\) 0 0
\(675\) 1.17034e8 + 2.31413e8i 0.380539 + 0.752447i
\(676\) 0 0
\(677\) 4.09293e7i 0.131907i 0.997823 + 0.0659536i \(0.0210089\pi\)
−0.997823 + 0.0659536i \(0.978991\pi\)
\(678\) 0 0
\(679\) 562172. 0.00179581
\(680\) 0 0
\(681\) −3.33514e8 4.12702e8i −1.05602 1.30676i
\(682\) 0 0
\(683\) 3.74260e8i 1.17466i −0.809348 0.587329i \(-0.800180\pi\)
0.809348 0.587329i \(-0.199820\pi\)
\(684\) 0 0
\(685\) 4.72355e8 1.46959
\(686\) 0 0
\(687\) 9.41174e7 7.60584e7i 0.290268 0.234572i
\(688\) 0 0
\(689\) 5.68017e8i 1.73661i
\(690\) 0 0
\(691\) 1.15164e8 0.349047 0.174524 0.984653i \(-0.444161\pi\)
0.174524 + 0.984653i \(0.444161\pi\)
\(692\) 0 0
\(693\) −48384.0 10386.0i −0.000145379 3.12067e-5i
\(694\) 0 0
\(695\) 7.76224e8i 2.31224i
\(696\) 0 0
\(697\) 7.51196e7 0.221848
\(698\) 0 0
\(699\) −3.89111e7 4.81500e7i −0.113931 0.140982i
\(700\) 0 0
\(701\) 5.65717e7i 0.164227i 0.996623 + 0.0821137i \(0.0261671\pi\)
−0.996623 + 0.0821137i \(0.973833\pi\)
\(702\) 0 0
\(703\) −1.79077e8 −0.515435
\(704\) 0 0
\(705\) 6.41088e8 5.18077e8i 1.82958 1.47852i
\(706\) 0 0
\(707\) 1.89072e6i 0.00535020i
\(708\) 0 0
\(709\) 1.28652e8 0.360975 0.180488 0.983577i \(-0.442232\pi\)
0.180488 + 0.983577i \(0.442232\pi\)
\(710\) 0 0
\(711\) −5.21060e7 + 2.42740e8i −0.144970 + 0.675356i
\(712\) 0 0
\(713\) 2.34710e8i 0.647533i
\(714\) 0 0
\(715\) 1.69920e7 0.0464864
\(716\) 0 0
\(717\) −4.48980e7 5.55585e7i −0.121806 0.150728i
\(718\) 0 0
\(719\) 2.01053e8i 0.540908i −0.962733 0.270454i \(-0.912826\pi\)
0.962733 0.270454i \(-0.0871738\pi\)
\(720\) 0 0
\(721\) −1.73145e6 −0.00461960
\(722\) 0 0
\(723\) −1.46912e8 + 1.18723e8i −0.388725 + 0.314137i
\(724\) 0 0
\(725\) 2.90663e7i 0.0762739i
\(726\) 0 0
\(727\) −5.23208e8 −1.36167 −0.680833 0.732438i \(-0.738382\pi\)
−0.680833 + 0.732438i \(0.738382\pi\)
\(728\) 0 0
\(729\) −2.29605e8 + 3.12051e8i −0.592651 + 0.805459i
\(730\) 0 0
\(731\) 2.87003e7i 0.0734742i
\(732\) 0 0
\(733\) 6.57372e8 1.66917 0.834583 0.550882i \(-0.185709\pi\)
0.834583 + 0.550882i \(0.185709\pi\)
\(734\) 0 0
\(735\) 3.38818e8 + 4.19265e8i 0.853304 + 1.05591i
\(736\) 0 0
\(737\) 1.48899e7i 0.0371954i
\(738\) 0 0
\(739\) 3.50495e8 0.868458 0.434229 0.900803i \(-0.357021\pi\)
0.434229 + 0.900803i \(0.357021\pi\)
\(740\) 0 0
\(741\) 3.25733e8 2.63232e8i 0.800585 0.646970i
\(742\) 0 0
\(743\) 4.66667e8i 1.13773i −0.822429 0.568867i \(-0.807382\pi\)
0.822429 0.568867i \(-0.192618\pi\)
\(744\) 0 0
\(745\) 7.56904e8 1.83051
\(746\) 0 0
\(747\) −3.53711e8 7.59267e7i −0.848569 0.182152i
\(748\) 0 0
\(749\) 2.94819e6i 0.00701634i
\(750\) 0 0
\(751\) 3.36993e7 0.0795612 0.0397806 0.999208i \(-0.487334\pi\)
0.0397806 + 0.999208i \(0.487334\pi\)
\(752\) 0 0
\(753\) 4.83645e8 + 5.98480e8i 1.13277 + 1.40173i
\(754\) 0 0
\(755\) 3.74726e8i 0.870709i
\(756\) 0 0
\(757\) −2.98552e8 −0.688227 −0.344113 0.938928i \(-0.611820\pi\)
−0.344113 + 0.938928i \(0.611820\pi\)
\(758\) 0 0
\(759\) 7.30598e6 5.90413e6i 0.0167091 0.0135030i
\(760\) 0 0
\(761\) 3.98702e8i 0.904679i 0.891846 + 0.452340i \(0.149410\pi\)
−0.891846 + 0.452340i \(0.850590\pi\)
\(762\) 0 0
\(763\) 1.30162e6 0.00293029
\(764\) 0 0
\(765\) −1.16329e8 + 5.41928e8i −0.259839 + 1.21048i
\(766\) 0 0
\(767\) 9.64116e8i 2.13670i
\(768\) 0 0
\(769\) −5.17372e8 −1.13769 −0.568845 0.822444i \(-0.692610\pi\)
−0.568845 + 0.822444i \(0.692610\pi\)
\(770\) 0 0
\(771\) 3.17030e6 + 3.92305e6i 0.00691732 + 0.00855974i
\(772\) 0 0
\(773\) 1.83241e8i 0.396719i 0.980129 + 0.198360i \(0.0635614\pi\)
−0.980129 + 0.198360i \(0.936439\pi\)
\(774\) 0 0
\(775\) 3.01681e8 0.648102
\(776\) 0 0
\(777\) 1.43044e6 1.15597e6i 0.00304934 0.00246424i
\(778\) 0 0
\(779\) 8.81604e7i 0.186493i
\(780\) 0 0
\(781\) 2.31552e6 0.00486066
\(782\) 0 0
\(783\) 3.87504e7 1.95974e7i 0.0807218 0.0408239i
\(784\) 0 0
\(785\) &m