Properties

Label 112.6.i.c.65.1
Level $112$
Weight $6$
Character 112.65
Analytic conductor $17.963$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [112,6,Mod(65,112)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(112, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("112.65");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 112.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.9629878191\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{37})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 65.1
Root \(1.77069 + 3.06693i\) of defining polynomial
Character \(\chi\) \(=\) 112.65
Dual form 112.6.i.c.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.04138 - 8.73193i) q^{3} +(39.9138 - 69.1328i) q^{5} +(-43.1587 - 122.247i) q^{7} +(70.6689 - 122.402i) q^{9} +O(q^{10})\) \(q+(-5.04138 - 8.73193i) q^{3} +(39.9138 - 69.1328i) q^{5} +(-43.1587 - 122.247i) q^{7} +(70.6689 - 122.402i) q^{9} +(175.952 + 304.757i) q^{11} -291.683 q^{13} -804.883 q^{15} +(185.038 + 320.495i) q^{17} +(752.463 - 1303.30i) q^{19} +(-849.873 + 993.152i) q^{21} +(-212.855 + 368.676i) q^{23} +(-1623.72 - 2812.37i) q^{25} -3875.19 q^{27} -7783.93 q^{29} +(-1287.59 - 2230.17i) q^{31} +(1774.08 - 3072.80i) q^{33} +(-10173.9 - 1895.67i) q^{35} +(-369.809 + 640.528i) q^{37} +(1470.48 + 2546.95i) q^{39} +7029.84 q^{41} -1835.23 q^{43} +(-5641.33 - 9771.08i) q^{45} +(-766.342 + 1327.34i) q^{47} +(-13081.7 + 10552.0i) q^{49} +(1865.69 - 3231.47i) q^{51} +(4768.73 + 8259.68i) q^{53} +28091.6 q^{55} -15173.8 q^{57} +(-14837.0 - 25698.5i) q^{59} +(23255.4 - 40279.5i) q^{61} +(-18013.3 - 3356.35i) q^{63} +(-11642.2 + 20164.8i) q^{65} +(13373.0 + 23162.8i) q^{67} +4292.34 q^{69} +14388.8 q^{71} +(35047.6 + 60704.2i) q^{73} +(-16371.6 + 28356.5i) q^{75} +(29661.8 - 34662.5i) q^{77} +(-13542.9 + 23457.0i) q^{79} +(2363.74 + 4094.13i) q^{81} +79755.4 q^{83} +29542.2 q^{85} +(39241.8 + 67968.8i) q^{87} +(-21788.7 + 37739.1i) q^{89} +(12588.6 + 35657.3i) q^{91} +(-12982.4 + 22486.2i) q^{93} +(-60067.3 - 104040. i) q^{95} +103374. q^{97} +49737.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{3} + 38 q^{5} + 168 q^{7} + 380 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{3} + 38 q^{5} + 168 q^{7} + 380 q^{9} + 424 q^{11} - 1848 q^{13} - 1784 q^{15} + 2346 q^{17} - 360 q^{19} - 1526 q^{21} - 12 q^{23} - 1872 q^{25} - 5744 q^{27} - 14104 q^{29} + 3548 q^{31} + 3398 q^{33} - 27496 q^{35} - 11090 q^{37} + 1624 q^{39} + 7000 q^{41} + 25360 q^{43} - 1300 q^{45} - 22956 q^{47} + 4900 q^{49} - 384 q^{51} - 3042 q^{53} + 50152 q^{55} - 38116 q^{57} - 65808 q^{59} + 42486 q^{61} + 4760 q^{63} + 3164 q^{65} + 42312 q^{67} + 10308 q^{69} + 4416 q^{71} + 50506 q^{73} - 35608 q^{75} + 65338 q^{77} + 9004 q^{79} - 51178 q^{81} + 208656 q^{83} - 106212 q^{85} + 80008 q^{87} + 26666 q^{89} - 135632 q^{91} - 38718 q^{93} - 198140 q^{95} + 418264 q^{97} + 133888 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −5.04138 8.73193i −0.323405 0.560153i 0.657783 0.753207i \(-0.271494\pi\)
−0.981188 + 0.193054i \(0.938161\pi\)
\(4\) 0 0
\(5\) 39.9138 69.1328i 0.714000 1.23668i −0.249344 0.968415i \(-0.580215\pi\)
0.963344 0.268269i \(-0.0864517\pi\)
\(6\) 0 0
\(7\) −43.1587 122.247i −0.332907 0.942960i
\(8\) 0 0
\(9\) 70.6689 122.402i 0.290819 0.503713i
\(10\) 0 0
\(11\) 175.952 + 304.757i 0.438442 + 0.759403i 0.997570 0.0696781i \(-0.0221972\pi\)
−0.559128 + 0.829082i \(0.688864\pi\)
\(12\) 0 0
\(13\) −291.683 −0.478688 −0.239344 0.970935i \(-0.576932\pi\)
−0.239344 + 0.970935i \(0.576932\pi\)
\(14\) 0 0
\(15\) −804.883 −0.923644
\(16\) 0 0
\(17\) 185.038 + 320.495i 0.155288 + 0.268967i 0.933164 0.359451i \(-0.117036\pi\)
−0.777876 + 0.628418i \(0.783703\pi\)
\(18\) 0 0
\(19\) 752.463 1303.30i 0.478190 0.828250i −0.521497 0.853253i \(-0.674626\pi\)
0.999687 + 0.0250030i \(0.00795952\pi\)
\(20\) 0 0
\(21\) −849.873 + 993.152i −0.420538 + 0.491437i
\(22\) 0 0
\(23\) −212.855 + 368.676i −0.0839006 + 0.145320i −0.904922 0.425577i \(-0.860071\pi\)
0.821022 + 0.570897i \(0.193404\pi\)
\(24\) 0 0
\(25\) −1623.72 2812.37i −0.519592 0.899960i
\(26\) 0 0
\(27\) −3875.19 −1.02302
\(28\) 0 0
\(29\) −7783.93 −1.71872 −0.859358 0.511374i \(-0.829137\pi\)
−0.859358 + 0.511374i \(0.829137\pi\)
\(30\) 0 0
\(31\) −1287.59 2230.17i −0.240643 0.416805i 0.720255 0.693710i \(-0.244025\pi\)
−0.960898 + 0.276904i \(0.910692\pi\)
\(32\) 0 0
\(33\) 1774.08 3072.80i 0.283588 0.491189i
\(34\) 0 0
\(35\) −10173.9 1895.67i −1.40384 0.261572i
\(36\) 0 0
\(37\) −369.809 + 640.528i −0.0444092 + 0.0769190i −0.887376 0.461047i \(-0.847474\pi\)
0.842966 + 0.537966i \(0.180807\pi\)
\(38\) 0 0
\(39\) 1470.48 + 2546.95i 0.154810 + 0.268139i
\(40\) 0 0
\(41\) 7029.84 0.653109 0.326554 0.945178i \(-0.394112\pi\)
0.326554 + 0.945178i \(0.394112\pi\)
\(42\) 0 0
\(43\) −1835.23 −0.151363 −0.0756816 0.997132i \(-0.524113\pi\)
−0.0756816 + 0.997132i \(0.524113\pi\)
\(44\) 0 0
\(45\) −5641.33 9771.08i −0.415289 0.719302i
\(46\) 0 0
\(47\) −766.342 + 1327.34i −0.0506032 + 0.0876473i −0.890217 0.455536i \(-0.849448\pi\)
0.839614 + 0.543183i \(0.182781\pi\)
\(48\) 0 0
\(49\) −13081.7 + 10552.0i −0.778346 + 0.627836i
\(50\) 0 0
\(51\) 1865.69 3231.47i 0.100442 0.173970i
\(52\) 0 0
\(53\) 4768.73 + 8259.68i 0.233192 + 0.403900i 0.958746 0.284265i \(-0.0917497\pi\)
−0.725554 + 0.688165i \(0.758416\pi\)
\(54\) 0 0
\(55\) 28091.6 1.25219
\(56\) 0 0
\(57\) −15173.8 −0.618596
\(58\) 0 0
\(59\) −14837.0 25698.5i −0.554903 0.961120i −0.997911 0.0646022i \(-0.979422\pi\)
0.443008 0.896517i \(-0.353911\pi\)
\(60\) 0 0
\(61\) 23255.4 40279.5i 0.800201 1.38599i −0.119282 0.992860i \(-0.538059\pi\)
0.919483 0.393129i \(-0.128607\pi\)
\(62\) 0 0
\(63\) −18013.3 3356.35i −0.571796 0.106541i
\(64\) 0 0
\(65\) −11642.2 + 20164.8i −0.341783 + 0.591985i
\(66\) 0 0
\(67\) 13373.0 + 23162.8i 0.363951 + 0.630381i 0.988607 0.150518i \(-0.0480943\pi\)
−0.624656 + 0.780900i \(0.714761\pi\)
\(68\) 0 0
\(69\) 4292.34 0.108535
\(70\) 0 0
\(71\) 14388.8 0.338748 0.169374 0.985552i \(-0.445825\pi\)
0.169374 + 0.985552i \(0.445825\pi\)
\(72\) 0 0
\(73\) 35047.6 + 60704.2i 0.769752 + 1.33325i 0.937697 + 0.347453i \(0.112953\pi\)
−0.167946 + 0.985796i \(0.553713\pi\)
\(74\) 0 0
\(75\) −16371.6 + 28356.5i −0.336077 + 0.582102i
\(76\) 0 0
\(77\) 29661.8 34662.5i 0.570126 0.666244i
\(78\) 0 0
\(79\) −13542.9 + 23457.0i −0.244143 + 0.422868i −0.961890 0.273436i \(-0.911840\pi\)
0.717748 + 0.696303i \(0.245173\pi\)
\(80\) 0 0
\(81\) 2363.74 + 4094.13i 0.0400302 + 0.0693344i
\(82\) 0 0
\(83\) 79755.4 1.27076 0.635382 0.772198i \(-0.280843\pi\)
0.635382 + 0.772198i \(0.280843\pi\)
\(84\) 0 0
\(85\) 29542.2 0.443502
\(86\) 0 0
\(87\) 39241.8 + 67968.8i 0.555841 + 0.962745i
\(88\) 0 0
\(89\) −21788.7 + 37739.1i −0.291579 + 0.505029i −0.974183 0.225759i \(-0.927514\pi\)
0.682605 + 0.730788i \(0.260847\pi\)
\(90\) 0 0
\(91\) 12588.6 + 35657.3i 0.159358 + 0.451383i
\(92\) 0 0
\(93\) −12982.4 + 22486.2i −0.155650 + 0.269594i
\(94\) 0 0
\(95\) −60067.3 104040.i −0.682856 1.18274i
\(96\) 0 0
\(97\) 103374. 1.11553 0.557765 0.829999i \(-0.311659\pi\)
0.557765 + 0.829999i \(0.311659\pi\)
\(98\) 0 0
\(99\) 49737.3 0.510028
\(100\) 0 0
\(101\) −14350.1 24855.1i −0.139975 0.242444i 0.787512 0.616300i \(-0.211369\pi\)
−0.927487 + 0.373855i \(0.878036\pi\)
\(102\) 0 0
\(103\) 14614.0 25312.1i 0.135730 0.235091i −0.790146 0.612918i \(-0.789995\pi\)
0.925876 + 0.377828i \(0.123329\pi\)
\(104\) 0 0
\(105\) 34737.7 + 98394.5i 0.307488 + 0.870959i
\(106\) 0 0
\(107\) 43929.2 76087.6i 0.370932 0.642472i −0.618778 0.785566i \(-0.712372\pi\)
0.989709 + 0.143094i \(0.0457051\pi\)
\(108\) 0 0
\(109\) −110314. 191069.i −0.889333 1.54037i −0.840665 0.541555i \(-0.817836\pi\)
−0.0486678 0.998815i \(-0.515498\pi\)
\(110\) 0 0
\(111\) 7457.39 0.0574486
\(112\) 0 0
\(113\) 39665.6 0.292225 0.146113 0.989268i \(-0.453324\pi\)
0.146113 + 0.989268i \(0.453324\pi\)
\(114\) 0 0
\(115\) 16991.7 + 29430.5i 0.119810 + 0.207517i
\(116\) 0 0
\(117\) −20612.9 + 35702.6i −0.139211 + 0.241121i
\(118\) 0 0
\(119\) 31193.5 36452.4i 0.201928 0.235971i
\(120\) 0 0
\(121\) 18607.4 32229.0i 0.115538 0.200117i
\(122\) 0 0
\(123\) −35440.1 61384.0i −0.211219 0.365841i
\(124\) 0 0
\(125\) −9774.87 −0.0559546
\(126\) 0 0
\(127\) −51740.3 −0.284655 −0.142328 0.989820i \(-0.545459\pi\)
−0.142328 + 0.989820i \(0.545459\pi\)
\(128\) 0 0
\(129\) 9252.11 + 16025.1i 0.0489515 + 0.0847866i
\(130\) 0 0
\(131\) −83336.9 + 144344.i −0.424286 + 0.734885i −0.996353 0.0853215i \(-0.972808\pi\)
0.572067 + 0.820207i \(0.306142\pi\)
\(132\) 0 0
\(133\) −191800. 35737.4i −0.940200 0.175184i
\(134\) 0 0
\(135\) −154674. + 267902.i −0.730435 + 1.26515i
\(136\) 0 0
\(137\) −14129.7 24473.4i −0.0643178 0.111402i 0.832073 0.554666i \(-0.187154\pi\)
−0.896391 + 0.443264i \(0.853820\pi\)
\(138\) 0 0
\(139\) −336393. −1.47676 −0.738380 0.674384i \(-0.764409\pi\)
−0.738380 + 0.674384i \(0.764409\pi\)
\(140\) 0 0
\(141\) 15453.7 0.0654612
\(142\) 0 0
\(143\) −51322.1 88892.4i −0.209877 0.363517i
\(144\) 0 0
\(145\) −310686. + 538125.i −1.22716 + 2.12551i
\(146\) 0 0
\(147\) 158089. + 61031.3i 0.603405 + 0.232948i
\(148\) 0 0
\(149\) 177691. 307769.i 0.655691 1.13569i −0.326030 0.945360i \(-0.605711\pi\)
0.981720 0.190330i \(-0.0609557\pi\)
\(150\) 0 0
\(151\) −179399. 310727.i −0.640290 1.10901i −0.985368 0.170441i \(-0.945481\pi\)
0.345078 0.938574i \(-0.387852\pi\)
\(152\) 0 0
\(153\) 52305.7 0.180643
\(154\) 0 0
\(155\) −205570. −0.687275
\(156\) 0 0
\(157\) −229455. 397428.i −0.742932 1.28680i −0.951155 0.308714i \(-0.900101\pi\)
0.208223 0.978081i \(-0.433232\pi\)
\(158\) 0 0
\(159\) 48082.0 83280.4i 0.150831 0.261246i
\(160\) 0 0
\(161\) 54256.1 + 10109.3i 0.164962 + 0.0307368i
\(162\) 0 0
\(163\) 251220. 435126.i 0.740603 1.28276i −0.211618 0.977353i \(-0.567873\pi\)
0.952221 0.305410i \(-0.0987935\pi\)
\(164\) 0 0
\(165\) −141621. 245294.i −0.404964 0.701418i
\(166\) 0 0
\(167\) 676652. 1.87748 0.938738 0.344632i \(-0.111996\pi\)
0.938738 + 0.344632i \(0.111996\pi\)
\(168\) 0 0
\(169\) −286214. −0.770858
\(170\) 0 0
\(171\) −106351. 184206.i −0.278133 0.481741i
\(172\) 0 0
\(173\) 124580. 215779.i 0.316470 0.548143i −0.663279 0.748373i \(-0.730836\pi\)
0.979749 + 0.200230i \(0.0641689\pi\)
\(174\) 0 0
\(175\) −273726. + 319874.i −0.675650 + 0.789557i
\(176\) 0 0
\(177\) −149598. + 259112.i −0.358916 + 0.621661i
\(178\) 0 0
\(179\) 69628.9 + 120601.i 0.162427 + 0.281331i 0.935738 0.352695i \(-0.114735\pi\)
−0.773312 + 0.634026i \(0.781401\pi\)
\(180\) 0 0
\(181\) 306246. 0.694823 0.347412 0.937713i \(-0.387061\pi\)
0.347412 + 0.937713i \(0.387061\pi\)
\(182\) 0 0
\(183\) −468957. −1.03516
\(184\) 0 0
\(185\) 29521.0 + 51131.8i 0.0634163 + 0.109840i
\(186\) 0 0
\(187\) −65115.4 + 112783.i −0.136169 + 0.235852i
\(188\) 0 0
\(189\) 167248. + 473730.i 0.340570 + 0.964665i
\(190\) 0 0
\(191\) 113747. 197015.i 0.225609 0.390766i −0.730893 0.682492i \(-0.760896\pi\)
0.956502 + 0.291726i \(0.0942295\pi\)
\(192\) 0 0
\(193\) 336187. + 582293.i 0.649663 + 1.12525i 0.983203 + 0.182513i \(0.0584231\pi\)
−0.333541 + 0.942736i \(0.608244\pi\)
\(194\) 0 0
\(195\) 234770. 0.442137
\(196\) 0 0
\(197\) −1282.76 −0.00235493 −0.00117747 0.999999i \(-0.500375\pi\)
−0.00117747 + 0.999999i \(0.500375\pi\)
\(198\) 0 0
\(199\) 184449. + 319475.i 0.330175 + 0.571879i 0.982546 0.186020i \(-0.0595591\pi\)
−0.652371 + 0.757900i \(0.726226\pi\)
\(200\) 0 0
\(201\) 134837. 233545.i 0.235407 0.407737i
\(202\) 0 0
\(203\) 335944. + 951563.i 0.572173 + 1.62068i
\(204\) 0 0
\(205\) 280588. 485992.i 0.466320 0.807690i
\(206\) 0 0
\(207\) 30084.5 + 52107.9i 0.0487997 + 0.0845236i
\(208\) 0 0
\(209\) 529589. 0.838635
\(210\) 0 0
\(211\) −502168. −0.776503 −0.388251 0.921553i \(-0.626921\pi\)
−0.388251 + 0.921553i \(0.626921\pi\)
\(212\) 0 0
\(213\) −72539.2 125642.i −0.109553 0.189751i
\(214\) 0 0
\(215\) −73251.1 + 126875.i −0.108073 + 0.187188i
\(216\) 0 0
\(217\) −217061. + 253655.i −0.312919 + 0.365674i
\(218\) 0 0
\(219\) 353376. 612066.i 0.497883 0.862358i
\(220\) 0 0
\(221\) −53972.3 93482.7i −0.0743344 0.128751i
\(222\) 0 0
\(223\) 1.17328e6 1.57993 0.789967 0.613149i \(-0.210098\pi\)
0.789967 + 0.613149i \(0.210098\pi\)
\(224\) 0 0
\(225\) −458988. −0.604428
\(226\) 0 0
\(227\) −455079. 788220.i −0.586168 1.01527i −0.994729 0.102542i \(-0.967302\pi\)
0.408560 0.912731i \(-0.366031\pi\)
\(228\) 0 0
\(229\) −260962. + 452000.i −0.328843 + 0.569573i −0.982283 0.187406i \(-0.939992\pi\)
0.653439 + 0.756979i \(0.273325\pi\)
\(230\) 0 0
\(231\) −452207. 84258.1i −0.557580 0.103892i
\(232\) 0 0
\(233\) 521394. 903081.i 0.629182 1.08977i −0.358535 0.933516i \(-0.616723\pi\)
0.987716 0.156258i \(-0.0499432\pi\)
\(234\) 0 0
\(235\) 61175.2 + 105959.i 0.0722613 + 0.125160i
\(236\) 0 0
\(237\) 273100. 0.315828
\(238\) 0 0
\(239\) 1.53447e6 1.73766 0.868830 0.495110i \(-0.164872\pi\)
0.868830 + 0.495110i \(0.164872\pi\)
\(240\) 0 0
\(241\) 503789. + 872588.i 0.558735 + 0.967758i 0.997602 + 0.0692059i \(0.0220465\pi\)
−0.438867 + 0.898552i \(0.644620\pi\)
\(242\) 0 0
\(243\) −447002. + 774231.i −0.485617 + 0.841114i
\(244\) 0 0
\(245\) 207353. + 1.32554e6i 0.220696 + 1.41084i
\(246\) 0 0
\(247\) −219480. + 380151.i −0.228904 + 0.396473i
\(248\) 0 0
\(249\) −402077. 696419.i −0.410971 0.711823i
\(250\) 0 0
\(251\) −8511.89 −0.00852789 −0.00426394 0.999991i \(-0.501357\pi\)
−0.00426394 + 0.999991i \(0.501357\pi\)
\(252\) 0 0
\(253\) −149809. −0.147142
\(254\) 0 0
\(255\) −148934. 257961.i −0.143431 0.248429i
\(256\) 0 0
\(257\) 263766. 456856.i 0.249107 0.431466i −0.714171 0.699971i \(-0.753196\pi\)
0.963278 + 0.268505i \(0.0865295\pi\)
\(258\) 0 0
\(259\) 94263.0 + 17563.7i 0.0873156 + 0.0162692i
\(260\) 0 0
\(261\) −550082. + 952771.i −0.499835 + 0.865739i
\(262\) 0 0
\(263\) −176042. 304914.i −0.156938 0.271824i 0.776825 0.629716i \(-0.216829\pi\)
−0.933763 + 0.357892i \(0.883496\pi\)
\(264\) 0 0
\(265\) 761353. 0.665996
\(266\) 0 0
\(267\) 439380. 0.377192
\(268\) 0 0
\(269\) −239770. 415294.i −0.202029 0.349925i 0.747153 0.664652i \(-0.231420\pi\)
−0.949182 + 0.314727i \(0.898087\pi\)
\(270\) 0 0
\(271\) −488805. + 846636.i −0.404308 + 0.700283i −0.994241 0.107170i \(-0.965821\pi\)
0.589932 + 0.807453i \(0.299154\pi\)
\(272\) 0 0
\(273\) 247893. 289685.i 0.201307 0.235245i
\(274\) 0 0
\(275\) 571395. 989684.i 0.455622 0.789160i
\(276\) 0 0
\(277\) −484362. 838939.i −0.379289 0.656948i 0.611670 0.791113i \(-0.290498\pi\)
−0.990959 + 0.134165i \(0.957165\pi\)
\(278\) 0 0
\(279\) −363970. −0.279934
\(280\) 0 0
\(281\) −318333. −0.240501 −0.120250 0.992744i \(-0.538370\pi\)
−0.120250 + 0.992744i \(0.538370\pi\)
\(282\) 0 0
\(283\) 886051. + 1.53468e6i 0.657646 + 1.13908i 0.981223 + 0.192875i \(0.0617812\pi\)
−0.323577 + 0.946202i \(0.604885\pi\)
\(284\) 0 0
\(285\) −605644. + 1.04901e6i −0.441678 + 0.765008i
\(286\) 0 0
\(287\) −303398. 859377.i −0.217425 0.615855i
\(288\) 0 0
\(289\) 641451. 1.11103e6i 0.451771 0.782491i
\(290\) 0 0
\(291\) −521147. 902652.i −0.360768 0.624868i
\(292\) 0 0
\(293\) 1.64148e6 1.11703 0.558516 0.829494i \(-0.311371\pi\)
0.558516 + 0.829494i \(0.311371\pi\)
\(294\) 0 0
\(295\) −2.36881e6 −1.58480
\(296\) 0 0
\(297\) −681846. 1.18099e6i −0.448534 0.776883i
\(298\) 0 0
\(299\) 62086.2 107536.i 0.0401622 0.0695629i
\(300\) 0 0
\(301\) 79206.2 + 224352.i 0.0503898 + 0.142729i
\(302\) 0 0
\(303\) −144689. + 250608.i −0.0905374 + 0.156815i
\(304\) 0 0
\(305\) −1.85642e6 3.21542e6i −1.14269 1.97919i
\(306\) 0 0
\(307\) 466930. 0.282752 0.141376 0.989956i \(-0.454847\pi\)
0.141376 + 0.989956i \(0.454847\pi\)
\(308\) 0 0
\(309\) −294698. −0.175582
\(310\) 0 0
\(311\) −1.21898e6 2.11134e6i −0.714654 1.23782i −0.963093 0.269169i \(-0.913251\pi\)
0.248439 0.968647i \(-0.420082\pi\)
\(312\) 0 0
\(313\) −1.21047e6 + 2.09659e6i −0.698381 + 1.20963i 0.270646 + 0.962679i \(0.412763\pi\)
−0.969028 + 0.246953i \(0.920571\pi\)
\(314\) 0 0
\(315\) −951012. + 1.11134e6i −0.540020 + 0.631062i
\(316\) 0 0
\(317\) −938057. + 1.62476e6i −0.524301 + 0.908116i 0.475298 + 0.879825i \(0.342340\pi\)
−0.999600 + 0.0282918i \(0.990993\pi\)
\(318\) 0 0
\(319\) −1.36960e6 2.37221e6i −0.753557 1.30520i
\(320\) 0 0
\(321\) −885855. −0.479844
\(322\) 0 0
\(323\) 556936. 0.297029
\(324\) 0 0
\(325\) 473612. + 820321.i 0.248722 + 0.430800i
\(326\) 0 0
\(327\) −1.11227e6 + 1.92651e6i −0.575229 + 0.996326i
\(328\) 0 0
\(329\) 195338. + 36396.6i 0.0994940 + 0.0185384i
\(330\) 0 0
\(331\) −541549. + 937990.i −0.271686 + 0.470575i −0.969294 0.245906i \(-0.920915\pi\)
0.697607 + 0.716480i \(0.254248\pi\)
\(332\) 0 0
\(333\) 52268.0 + 90530.8i 0.0258301 + 0.0447390i
\(334\) 0 0
\(335\) 2.13507e6 1.03944
\(336\) 0 0
\(337\) −2.59465e6 −1.24453 −0.622263 0.782809i \(-0.713786\pi\)
−0.622263 + 0.782809i \(0.713786\pi\)
\(338\) 0 0
\(339\) −199969. 346357.i −0.0945071 0.163691i
\(340\) 0 0
\(341\) 453107. 784804.i 0.211016 0.365490i
\(342\) 0 0
\(343\) 1.85454e6 + 1.14378e6i 0.851141 + 0.524938i
\(344\) 0 0
\(345\) 171324. 296741.i 0.0774943 0.134224i
\(346\) 0 0
\(347\) −935255. 1.61991e6i −0.416972 0.722216i 0.578662 0.815568i \(-0.303575\pi\)
−0.995633 + 0.0933518i \(0.970242\pi\)
\(348\) 0 0
\(349\) −1.61685e6 −0.710568 −0.355284 0.934758i \(-0.615616\pi\)
−0.355284 + 0.934758i \(0.615616\pi\)
\(350\) 0 0
\(351\) 1.13033e6 0.489706
\(352\) 0 0
\(353\) 289153. + 500827.i 0.123507 + 0.213920i 0.921148 0.389212i \(-0.127253\pi\)
−0.797642 + 0.603132i \(0.793919\pi\)
\(354\) 0 0
\(355\) 574310. 994734.i 0.241866 0.418925i
\(356\) 0 0
\(357\) −475558. 88609.1i −0.197485 0.0367966i
\(358\) 0 0
\(359\) −984090. + 1.70449e6i −0.402994 + 0.698006i −0.994086 0.108598i \(-0.965364\pi\)
0.591092 + 0.806604i \(0.298697\pi\)
\(360\) 0 0
\(361\) 105650. + 182990.i 0.0426677 + 0.0739027i
\(362\) 0 0
\(363\) −375229. −0.149462
\(364\) 0 0
\(365\) 5.59553e6 2.19841
\(366\) 0 0
\(367\) 1.08726e6 + 1.88319e6i 0.421375 + 0.729842i 0.996074 0.0885223i \(-0.0282144\pi\)
−0.574700 + 0.818364i \(0.694881\pi\)
\(368\) 0 0
\(369\) 496791. 860468.i 0.189936 0.328979i
\(370\) 0 0
\(371\) 803910. 939440.i 0.303230 0.354352i
\(372\) 0 0
\(373\) −692379. + 1.19924e6i −0.257675 + 0.446306i −0.965619 0.259963i \(-0.916290\pi\)
0.707944 + 0.706269i \(0.249623\pi\)
\(374\) 0 0
\(375\) 49278.9 + 85353.5i 0.0180960 + 0.0313432i
\(376\) 0 0
\(377\) 2.27044e6 0.822728
\(378\) 0 0
\(379\) −3.37190e6 −1.20580 −0.602902 0.797815i \(-0.705989\pi\)
−0.602902 + 0.797815i \(0.705989\pi\)
\(380\) 0 0
\(381\) 260842. + 451792.i 0.0920589 + 0.159451i
\(382\) 0 0
\(383\) 1.64030e6 2.84108e6i 0.571382 0.989662i −0.425043 0.905173i \(-0.639741\pi\)
0.996424 0.0844886i \(-0.0269257\pi\)
\(384\) 0 0
\(385\) −1.21240e6 3.43412e6i −0.416863 1.18076i
\(386\) 0 0
\(387\) −129694. + 224637.i −0.0440192 + 0.0762435i
\(388\) 0 0
\(389\) 1.47405e6 + 2.55313e6i 0.493899 + 0.855457i 0.999975 0.00703108i \(-0.00223808\pi\)
−0.506077 + 0.862488i \(0.668905\pi\)
\(390\) 0 0
\(391\) −157545. −0.0521150
\(392\) 0 0
\(393\) 1.68053e6 0.548865
\(394\) 0 0
\(395\) 1.08110e6 + 1.87251e6i 0.348636 + 0.603855i
\(396\) 0 0
\(397\) 34635.1 59989.7i 0.0110291 0.0191030i −0.860458 0.509521i \(-0.829823\pi\)
0.871487 + 0.490418i \(0.163156\pi\)
\(398\) 0 0
\(399\) 654881. + 1.85495e6i 0.205935 + 0.583311i
\(400\) 0 0
\(401\) 1.67393e6 2.89933e6i 0.519848 0.900404i −0.479886 0.877331i \(-0.659322\pi\)
0.999734 0.0230725i \(-0.00734485\pi\)
\(402\) 0 0
\(403\) 375567. + 650501.i 0.115193 + 0.199520i
\(404\) 0 0
\(405\) 377384. 0.114326
\(406\) 0 0
\(407\) −260274. −0.0778834
\(408\) 0 0
\(409\) −1.45608e6 2.52201e6i −0.430406 0.745485i 0.566502 0.824060i \(-0.308296\pi\)
−0.996908 + 0.0785754i \(0.974963\pi\)
\(410\) 0 0
\(411\) −142466. + 246759.i −0.0416014 + 0.0720557i
\(412\) 0 0
\(413\) −2.50122e6 + 2.92289e6i −0.721566 + 0.843214i
\(414\) 0 0
\(415\) 3.18334e6 5.51371e6i 0.907326 1.57153i
\(416\) 0 0
\(417\) 1.69589e6 + 2.93736e6i 0.477592 + 0.827213i
\(418\) 0 0
\(419\) 4.62361e6 1.28661 0.643304 0.765611i \(-0.277563\pi\)
0.643304 + 0.765611i \(0.277563\pi\)
\(420\) 0 0
\(421\) −2.63042e6 −0.723303 −0.361652 0.932313i \(-0.617787\pi\)
−0.361652 + 0.932313i \(0.617787\pi\)
\(422\) 0 0
\(423\) 108313. + 187604.i 0.0294327 + 0.0509789i
\(424\) 0 0
\(425\) 600901. 1.04079e6i 0.161373 0.279506i
\(426\) 0 0
\(427\) −5.92772e6 1.10449e6i −1.57332 0.293152i
\(428\) 0 0
\(429\) −517468. + 896281.i −0.135750 + 0.235126i
\(430\) 0 0
\(431\) 3.77064e6 + 6.53094e6i 0.977736 + 1.69349i 0.670592 + 0.741826i \(0.266040\pi\)
0.307144 + 0.951663i \(0.400627\pi\)
\(432\) 0 0
\(433\) 5.83558e6 1.49577 0.747883 0.663830i \(-0.231070\pi\)
0.747883 + 0.663830i \(0.231070\pi\)
\(434\) 0 0
\(435\) 6.26516e6 1.58748
\(436\) 0 0
\(437\) 320331. + 554830.i 0.0802409 + 0.138981i
\(438\) 0 0
\(439\) 84051.9 145582.i 0.0208155 0.0360535i −0.855430 0.517918i \(-0.826707\pi\)
0.876246 + 0.481865i \(0.160040\pi\)
\(440\) 0 0
\(441\) 367126. + 2.34693e6i 0.0898914 + 0.574649i
\(442\) 0 0
\(443\) −1.42076e6 + 2.46082e6i −0.343962 + 0.595760i −0.985165 0.171612i \(-0.945102\pi\)
0.641203 + 0.767372i \(0.278436\pi\)
\(444\) 0 0
\(445\) 1.73934e6 + 3.01262e6i 0.416374 + 0.721181i
\(446\) 0 0
\(447\) −3.58323e6 −0.848214
\(448\) 0 0
\(449\) −1.41567e6 −0.331396 −0.165698 0.986177i \(-0.552988\pi\)
−0.165698 + 0.986177i \(0.552988\pi\)
\(450\) 0 0
\(451\) 1.23691e6 + 2.14240e6i 0.286350 + 0.495973i
\(452\) 0 0
\(453\) −1.80883e6 + 3.13299e6i −0.414146 + 0.717321i
\(454\) 0 0
\(455\) 2.96755e6 + 552933.i 0.672000 + 0.125211i
\(456\) 0 0
\(457\) −778637. + 1.34864e6i −0.174399 + 0.302068i −0.939953 0.341303i \(-0.889132\pi\)
0.765554 + 0.643372i \(0.222465\pi\)
\(458\) 0 0
\(459\) −717056. 1.24198e6i −0.158862 0.275158i
\(460\) 0 0
\(461\) −4.45345e6 −0.975987 −0.487994 0.872847i \(-0.662271\pi\)
−0.487994 + 0.872847i \(0.662271\pi\)
\(462\) 0 0
\(463\) −4.92263e6 −1.06720 −0.533599 0.845738i \(-0.679161\pi\)
−0.533599 + 0.845738i \(0.679161\pi\)
\(464\) 0 0
\(465\) 1.03636e6 + 1.79502e6i 0.222268 + 0.384980i
\(466\) 0 0
\(467\) 2.54545e6 4.40885e6i 0.540098 0.935477i −0.458800 0.888540i \(-0.651720\pi\)
0.998898 0.0469376i \(-0.0149462\pi\)
\(468\) 0 0
\(469\) 2.25442e6 2.63449e6i 0.473262 0.553049i
\(470\) 0 0
\(471\) −2.31354e6 + 4.00717e6i −0.480535 + 0.832312i
\(472\) 0 0
\(473\) −322912. 559301.i −0.0663639 0.114946i
\(474\) 0 0
\(475\) −4.88717e6 −0.993856
\(476\) 0 0
\(477\) 1.34800e6 0.271266
\(478\) 0 0
\(479\) −4.15042e6 7.18874e6i −0.826521 1.43158i −0.900752 0.434334i \(-0.856984\pi\)
0.0742312 0.997241i \(-0.476350\pi\)
\(480\) 0 0
\(481\) 107867. 186831.i 0.0212581 0.0368202i
\(482\) 0 0
\(483\) −185252. 524726.i −0.0361322 0.102344i
\(484\) 0 0
\(485\) 4.12604e6 7.14651e6i 0.796488 1.37956i
\(486\) 0 0
\(487\) 4.31701e6 + 7.47727e6i 0.824822 + 1.42863i 0.902055 + 0.431621i \(0.142058\pi\)
−0.0772330 + 0.997013i \(0.524609\pi\)
\(488\) 0 0
\(489\) −5.06599e6 −0.958059
\(490\) 0 0
\(491\) −95039.5 −0.0177910 −0.00889550 0.999960i \(-0.502832\pi\)
−0.00889550 + 0.999960i \(0.502832\pi\)
\(492\) 0 0
\(493\) −1.44032e6 2.49471e6i −0.266896 0.462277i
\(494\) 0 0
\(495\) 1.98521e6 3.43848e6i 0.364160 0.630744i
\(496\) 0 0
\(497\) −621000. 1.75898e6i −0.112772 0.319426i
\(498\) 0 0
\(499\) 1.07102e6 1.85506e6i 0.192551 0.333507i −0.753544 0.657397i \(-0.771657\pi\)
0.946095 + 0.323890i \(0.104991\pi\)
\(500\) 0 0
\(501\) −3.41126e6 5.90848e6i −0.607185 1.05167i
\(502\) 0 0
\(503\) −5.24794e6 −0.924844 −0.462422 0.886660i \(-0.653019\pi\)
−0.462422 + 0.886660i \(0.653019\pi\)
\(504\) 0 0
\(505\) −2.29107e6 −0.399769
\(506\) 0 0
\(507\) 1.44292e6 + 2.49920e6i 0.249299 + 0.431799i
\(508\) 0 0
\(509\) 5.29453e6 9.17040e6i 0.905802 1.56889i 0.0859643 0.996298i \(-0.472603\pi\)
0.819837 0.572596i \(-0.194064\pi\)
\(510\) 0 0
\(511\) 5.90829e6 6.90437e6i 1.00094 1.16969i
\(512\) 0 0
\(513\) −2.91593e6 + 5.05055e6i −0.489198 + 0.847315i
\(514\) 0 0
\(515\) −1.16660e6 2.02061e6i −0.193822 0.335709i
\(516\) 0 0
\(517\) −539357. −0.0887462
\(518\) 0 0
\(519\) −2.51222e6 −0.409392
\(520\) 0 0
\(521\) 2.27232e6 + 3.93578e6i 0.366755 + 0.635238i 0.989056 0.147540i \(-0.0471354\pi\)
−0.622301 + 0.782778i \(0.713802\pi\)
\(522\) 0 0
\(523\) −2.63599e6 + 4.56566e6i −0.421394 + 0.729877i −0.996076 0.0885004i \(-0.971793\pi\)
0.574682 + 0.818377i \(0.305126\pi\)
\(524\) 0 0
\(525\) 4.17307e6 + 777554.i 0.660782 + 0.123121i
\(526\) 0 0
\(527\) 476504. 825330.i 0.0747378 0.129450i
\(528\) 0 0
\(529\) 3.12756e6 + 5.41709e6i 0.485921 + 0.841641i
\(530\) 0 0
\(531\) −4.19407e6 −0.645504
\(532\) 0 0
\(533\) −2.05048e6 −0.312635
\(534\) 0 0
\(535\) −3.50676e6 6.07389e6i −0.529690 0.917451i
\(536\) 0 0
\(537\) 702052. 1.21599e6i 0.105059 0.181968i
\(538\) 0 0
\(539\) −5.51755e6 2.13008e6i −0.818040 0.315809i
\(540\) 0 0
\(541\) −2.96723e6 + 5.13939e6i −0.435871 + 0.754950i −0.997366 0.0725298i \(-0.976893\pi\)
0.561496 + 0.827480i \(0.310226\pi\)
\(542\) 0 0
\(543\) −1.54390e6 2.67412e6i −0.224709 0.389208i
\(544\) 0 0
\(545\) −1.76122e7 −2.53994
\(546\) 0 0
\(547\) 8.82017e6 1.26040 0.630200 0.776433i \(-0.282973\pi\)
0.630200 + 0.776433i \(0.282973\pi\)
\(548\) 0 0
\(549\) −3.28687e6 5.69302e6i −0.465427 0.806143i
\(550\) 0 0
\(551\) −5.85712e6 + 1.01448e7i −0.821874 + 1.42353i
\(552\) 0 0
\(553\) 3.45204e6 + 643206.i 0.480024 + 0.0894411i
\(554\) 0 0
\(555\) 297653. 515550.i 0.0410183 0.0710458i
\(556\) 0 0
\(557\) 591120. + 1.02385e6i 0.0807304 + 0.139829i 0.903564 0.428453i \(-0.140941\pi\)
−0.822833 + 0.568283i \(0.807608\pi\)
\(558\) 0 0
\(559\) 535306. 0.0724556
\(560\) 0 0
\(561\) 1.31309e6 0.176151
\(562\) 0 0
\(563\) 2.03870e6 + 3.53114e6i 0.271071 + 0.469509i 0.969136 0.246525i \(-0.0792888\pi\)
−0.698065 + 0.716034i \(0.745955\pi\)
\(564\) 0 0
\(565\) 1.58321e6 2.74219e6i 0.208649 0.361391i
\(566\) 0 0
\(567\) 398478. 465658.i 0.0520532 0.0608288i
\(568\) 0 0
\(569\) −4.08807e6 + 7.08075e6i −0.529344 + 0.916851i 0.470070 + 0.882629i \(0.344229\pi\)
−0.999414 + 0.0342216i \(0.989105\pi\)
\(570\) 0 0
\(571\) 1.65307e6 + 2.86321e6i 0.212179 + 0.367504i 0.952396 0.304863i \(-0.0986108\pi\)
−0.740217 + 0.672368i \(0.765277\pi\)
\(572\) 0 0
\(573\) −2.29377e6 −0.291852
\(574\) 0 0
\(575\) 1.38247e6 0.174376
\(576\) 0 0
\(577\) 3.57497e6 + 6.19203e6i 0.447026 + 0.774272i 0.998191 0.0601245i \(-0.0191498\pi\)
−0.551165 + 0.834396i \(0.685816\pi\)
\(578\) 0 0
\(579\) 3.38970e6 5.87112e6i 0.420208 0.727821i
\(580\) 0 0
\(581\) −3.44214e6 9.74986e6i −0.423046 1.19828i
\(582\) 0 0
\(583\) −1.67813e6 + 2.90661e6i −0.204482 + 0.354173i
\(584\) 0 0
\(585\) 1.64548e6 + 2.85005e6i 0.198794 + 0.344321i
\(586\) 0 0
\(587\) −9.69191e6 −1.16095 −0.580476 0.814277i \(-0.697133\pi\)
−0.580476 + 0.814277i \(0.697133\pi\)
\(588\) 0 0
\(589\) −3.87545e6 −0.460292
\(590\) 0 0
\(591\) 6466.87 + 11200.9i 0.000761597 + 0.00131912i
\(592\) 0 0
\(593\) −3.31980e6 + 5.75006e6i −0.387682 + 0.671484i −0.992137 0.125154i \(-0.960057\pi\)
0.604456 + 0.796639i \(0.293391\pi\)
\(594\) 0 0
\(595\) −1.27500e6 3.61145e6i −0.147645 0.418205i
\(596\) 0 0
\(597\) 1.85976e6 3.22119e6i 0.213560 0.369897i
\(598\) 0 0
\(599\) −1.62096e6 2.80758e6i −0.184588 0.319716i 0.758849 0.651266i \(-0.225762\pi\)
−0.943438 + 0.331550i \(0.892428\pi\)
\(600\) 0 0
\(601\) −5.65076e6 −0.638147 −0.319074 0.947730i \(-0.603372\pi\)
−0.319074 + 0.947730i \(0.603372\pi\)
\(602\) 0 0
\(603\) 3.78023e6 0.423375
\(604\) 0 0
\(605\) −1.48539e6 2.57277e6i −0.164988 0.285767i
\(606\) 0 0
\(607\) 117837. 204100.i 0.0129811 0.0224839i −0.859462 0.511200i \(-0.829201\pi\)
0.872443 + 0.488716i \(0.162535\pi\)
\(608\) 0 0
\(609\) 6.61535e6 7.73063e6i 0.722786 0.844640i
\(610\) 0 0
\(611\) 223529. 387163.i 0.0242231 0.0419557i
\(612\) 0 0
\(613\) −394438. 683187.i −0.0423963 0.0734325i 0.844049 0.536267i \(-0.180166\pi\)
−0.886445 + 0.462834i \(0.846833\pi\)
\(614\) 0 0
\(615\) −5.65820e6 −0.603240
\(616\) 0 0
\(617\) 1.67739e7 1.77387 0.886935 0.461894i \(-0.152830\pi\)
0.886935 + 0.461894i \(0.152830\pi\)
\(618\) 0 0
\(619\) 4.11150e6 + 7.12132e6i 0.431294 + 0.747023i 0.996985 0.0775941i \(-0.0247238\pi\)
−0.565691 + 0.824617i \(0.691390\pi\)
\(620\) 0 0
\(621\) 824854. 1.42869e6i 0.0858318 0.148665i
\(622\) 0 0
\(623\) 5.55386e6 + 1.03483e6i 0.573290 + 0.106819i
\(624\) 0 0
\(625\) 4.68399e6 8.11290e6i 0.479640 0.830761i
\(626\) 0 0
\(627\) −2.66986e6 4.62433e6i −0.271218 0.469764i
\(628\) 0 0
\(629\) −273714. −0.0275849
\(630\) 0 0
\(631\) 5.94507e6 0.594406 0.297203 0.954814i \(-0.403946\pi\)
0.297203 + 0.954814i \(0.403946\pi\)
\(632\) 0 0
\(633\) 2.53162e6 + 4.38490e6i 0.251125 + 0.434961i
\(634\) 0 0
\(635\) −2.06515e6 + 3.57695e6i −0.203244 + 0.352029i
\(636\) 0 0
\(637\) 3.81569e6 3.07785e6i 0.372585 0.300537i
\(638\) 0 0
\(639\) 1.01684e6 1.76122e6i 0.0985144 0.170632i
\(640\) 0 0
\(641\) 5.33804e6 + 9.24576e6i 0.513141 + 0.888786i 0.999884 + 0.0152411i \(0.00485157\pi\)
−0.486743 + 0.873545i \(0.661815\pi\)
\(642\) 0 0
\(643\) 3.13159e6 0.298701 0.149351 0.988784i \(-0.452282\pi\)
0.149351 + 0.988784i \(0.452282\pi\)
\(644\) 0 0
\(645\) 1.47715e6 0.139806
\(646\) 0 0
\(647\) −2.46728e6 4.27346e6i −0.231717 0.401346i 0.726596 0.687065i \(-0.241101\pi\)
−0.958314 + 0.285719i \(0.907768\pi\)
\(648\) 0 0
\(649\) 5.22120e6 9.04339e6i 0.486585 0.842790i
\(650\) 0 0
\(651\) 3.30918e6 + 616588.i 0.306033 + 0.0570220i
\(652\) 0 0
\(653\) −2.86112e6 + 4.95561e6i −0.262575 + 0.454793i −0.966925 0.255059i \(-0.917905\pi\)
0.704351 + 0.709852i \(0.251238\pi\)
\(654\) 0 0
\(655\) 6.65258e6 + 1.15226e7i 0.605881 + 1.04942i
\(656\) 0 0
\(657\) 9.90710e6 0.895433
\(658\) 0 0
\(659\) −362477. −0.0325137 −0.0162569 0.999868i \(-0.505175\pi\)
−0.0162569 + 0.999868i \(0.505175\pi\)
\(660\) 0 0
\(661\) 9.56053e6 + 1.65593e7i 0.851096 + 1.47414i 0.880220 + 0.474565i \(0.157395\pi\)
−0.0291249 + 0.999576i \(0.509272\pi\)
\(662\) 0 0
\(663\) −544190. + 942564.i −0.0480802 + 0.0832774i
\(664\) 0 0
\(665\) −1.01261e7 + 1.18333e7i −0.887950 + 1.03765i
\(666\) 0 0
\(667\) 1.65685e6 2.86975e6i 0.144201 0.249764i
\(668\) 0 0
\(669\) −5.91495e6 1.02450e7i −0.510958 0.885006i
\(670\) 0 0
\(671\) 1.63673e7 1.40337
\(672\) 0 0
\(673\) −573374. −0.0487978 −0.0243989 0.999702i \(-0.507767\pi\)
−0.0243989 + 0.999702i \(0.507767\pi\)
\(674\) 0 0
\(675\) 6.29224e6 + 1.08985e7i 0.531552 + 0.920675i
\(676\) 0 0
\(677\) −5.84516e6 + 1.01241e7i −0.490146 + 0.848957i −0.999936 0.0113419i \(-0.996390\pi\)
0.509790 + 0.860299i \(0.329723\pi\)
\(678\) 0 0
\(679\) −4.46148e6 1.26371e7i −0.371368 1.05190i
\(680\) 0 0
\(681\) −4.58846e6 + 7.94744e6i −0.379139 + 0.656689i
\(682\) 0 0
\(683\) 9.18370e6 + 1.59066e7i 0.753297 + 1.30475i 0.946217 + 0.323534i \(0.104871\pi\)
−0.192920 + 0.981214i \(0.561796\pi\)
\(684\) 0 0
\(685\) −2.25588e6 −0.183692
\(686\) 0 0
\(687\) 5.26244e6 0.425398
\(688\) 0 0
\(689\) −1.39096e6 2.40921e6i −0.111626 0.193342i
\(690\) 0 0
\(691\) 1.17806e7 2.04045e7i 0.938579 1.62567i 0.170454 0.985366i \(-0.445477\pi\)
0.768125 0.640300i \(-0.221190\pi\)
\(692\) 0 0
\(693\) −2.14660e6 6.08024e6i −0.169792 0.480936i
\(694\) 0 0
\(695\) −1.34267e7 + 2.32558e7i −1.05441 + 1.82629i
\(696\) 0 0
\(697\) 1.30078e6 + 2.25303e6i 0.101420 + 0.175665i
\(698\) 0 0
\(699\) −1.05142e7 −0.813921
\(700\) 0 0
\(701\) 1.32980e7 1.02210 0.511048 0.859552i \(-0.329257\pi\)
0.511048 + 0.859552i \(0.329257\pi\)
\(702\) 0 0
\(703\) 556535. + 963946.i 0.0424721 + 0.0735639i
\(704\) 0 0
\(705\) 616815. 1.06836e6i 0.0467393 0.0809549i
\(706\) 0 0
\(707\) −2.41913e6 + 2.82697e6i −0.182016 + 0.212703i
\(708\) 0 0
\(709\) 3.42677e6 5.93533e6i 0.256017 0.443434i −0.709154 0.705053i \(-0.750923\pi\)
0.965171 + 0.261619i \(0.0842564\pi\)
\(710\) 0 0
\(711\) 1.91412e6 + 3.31536e6i 0.142003 + 0.245956i
\(712\) 0 0
\(713\) 1.09628e6 0.0807602
\(714\) 0 0
\(715\) −8.19384e6 −0.599408
\(716\) 0 0
\(717\) −7.73587e6 1.33989e7i −0.561968 0.973357i
\(718\) 0 0
\(719\) 1.32865e7 2.30128e7i 0.958490 1.66015i 0.232318 0.972640i \(-0.425369\pi\)
0.726172 0.687513i \(-0.241298\pi\)
\(720\) 0 0
\(721\) −3.72505e6 694075.i −0.266866 0.0497242i
\(722\) 0 0
\(723\) 5.07958e6 8.79810e6i 0.361395 0.625955i
\(724\) 0 0
\(725\) 1.26390e7 + 2.18913e7i 0.893031 + 1.54678i
\(726\) 0 0
\(727\) −2.16991e6 −0.152267 −0.0761335 0.997098i \(-0.524258\pi\)
−0.0761335 + 0.997098i \(0.524258\pi\)
\(728\) 0 0
\(729\) 1.01628e7 0.708264
\(730\) 0 0
\(731\) −339587. 588182.i −0.0235049 0.0407116i
\(732\) 0 0
\(733\) 8.73265e6 1.51254e7i 0.600324 1.03979i −0.392447 0.919774i \(-0.628372\pi\)
0.992772 0.120018i \(-0.0382951\pi\)
\(734\) 0 0
\(735\) 1.05292e7 8.49316e6i 0.718914 0.579897i
\(736\) 0 0
\(737\) −4.70602e6 + 8.15106e6i −0.319143 + 0.552771i
\(738\) 0 0
\(739\) −6.82304e6 1.18178e7i −0.459586 0.796026i 0.539353 0.842080i \(-0.318669\pi\)
−0.998939 + 0.0460536i \(0.985335\pi\)
\(740\) 0 0
\(741\) 4.42594e6 0.296114
\(742\) 0 0
\(743\) −1.48965e7 −0.989944 −0.494972 0.868909i \(-0.664822\pi\)
−0.494972 + 0.868909i \(0.664822\pi\)
\(744\) 0 0
\(745\) −1.41846e7 2.45685e7i −0.936326 1.62176i
\(746\) 0 0
\(747\) 5.63623e6 9.76224e6i 0.369562 0.640100i
\(748\) 0 0
\(749\) −1.11974e7 2.08637e6i −0.729311 0.135890i
\(750\) 0 0
\(751\) −1.26731e7 + 2.19505e7i −0.819944 + 1.42019i 0.0857783 + 0.996314i \(0.472662\pi\)
−0.905723 + 0.423871i \(0.860671\pi\)
\(752\) 0 0
\(753\) 42911.7 + 74325.2i 0.00275796 + 0.00477693i
\(754\) 0 0
\(755\) −2.86419e7 −1.82867
\(756\) 0 0
\(757\) −2.66725e7 −1.69170 −0.845852 0.533417i \(-0.820908\pi\)
−0.845852 + 0.533417i \(0.820908\pi\)
\(758\) 0 0
\(759\) 755245. + 1.30812e6i 0.0475864 + 0.0824221i
\(760\) 0 0
\(761\) −289914. + 502146.i −0.0181471 + 0.0314318i −0.874956 0.484202i \(-0.839110\pi\)
0.856809 + 0.515634i \(0.172443\pi\)
\(762\) 0 0
\(763\) −1.85967e7 + 2.17319e7i −1.15644 + 1.35141i
\(764\) 0 0
\(765\) 2.08772e6 3.61604e6i 0.128979 0.223398i
\(766\) 0 0
\(767\) 4.32770e6 + 7.49580e6i 0.265625 + 0.460076i
\(768\) 0 0
\(769\) 1.52438e7 0.929562 0.464781 0.885426i \(-0.346133\pi\)
0.464781 + 0.885426i \(0.346133\pi\)
\(770\) 0 0
\(771\) −5.31898e6 −0.322250
\(772\) 0 0
\(773\) 9.74628e6 + 1.68810e7i 0.586665 + 1.01613i 0.994666 + 0.103152i \(0.0328927\pi\)
−0.408001 + 0.912982i \(0.633774\pi\)
\(774\) 0 0
\(775\) −4.18138e6 + 7.24236e6i −0.250072 + 0.433137i
\(776\) 0 0
\(777\) −321851. 911643.i −0.0191250 0.0541717i
\(778\) 0 0
\(779\) 5.28969e6 9.16201e6i 0.312311 0.540938i
\(780\) 0 0
\(781\) 2.53173e6 + 4.38508e6i 0.148521 + 0.257247i
\(782\) 0 0