Properties

Label 112.6.i.c.81.1
Level $112$
Weight $6$
Character 112.81
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 81.1
Root \(1.77069 - 3.06693i\) of defining polynomial
Character \(\chi\) \(=\) 112.81
Dual form 112.6.i.c.65.1

$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.981188 0.193054i \(-0.938161\pi\)
0.657783 + 0.753207i \(0.271494\pi\)
\(4\) 0 0
\(5\) 39.9138 + 69.1328i 0.714000 + 1.23668i 0.963344 + 0.268269i \(0.0864517\pi\)
−0.249344 + 0.968415i \(0.580215\pi\)
\(6\) 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 −0.559128 0.829082i \(-0.688864\pi\)
0.997570 + 0.0696781i \(0.0221972\pi\)
\(12\) 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 −0.777876 0.628418i \(-0.783703\pi\)
0.933164 + 0.359451i \(0.117036\pi\)
\(18\) 0 0
\(19\) 752.463 + 1303.30i 0.478190 + 0.828250i 0.999687 0.0250030i \(-0.00795952\pi\)
−0.521497 + 0.853253i \(0.674626\pi\)
\(20\) 0 0
\(21\) −849.873 993.152i −0.420538 0.491437i
\(22\) 0 0
\(23\) −212.855 368.676i −0.0839006 0.145320i 0.821022 0.570897i \(-0.193404\pi\)
−0.904922 + 0.425577i \(0.860071\pi\)
\(24\) 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 −0.960898 0.276904i \(-0.910692\pi\)
0.720255 + 0.693710i \(0.244025\pi\)
\(32\) 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 0.842966 0.537966i \(-0.180807\pi\)
−0.887376 + 0.461047i \(0.847474\pi\)
\(38\) 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 0.839614 0.543183i \(-0.182781\pi\)
−0.890217 + 0.455536i \(0.849448\pi\)
\(48\) 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 −0.725554 0.688165i \(-0.758416\pi\)
0.958746 + 0.284265i \(0.0917497\pi\)
\(54\) 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 0.443008 + 0.896517i \(0.353911\pi\)
−0.997911 + 0.0646022i \(0.979422\pi\)
\(60\) 0 0
\(61\) 23255.4 + 40279.5i 0.800201 + 1.38599i 0.919483 + 0.393129i \(0.128607\pi\)
−0.119282 + 0.992860i \(0.538059\pi\)
\(62\) 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 −0.624656 0.780900i \(-0.714761\pi\)
0.988607 + 0.150518i \(0.0480943\pi\)
\(68\) 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 −0.167946 0.985796i \(-0.553713\pi\)
0.937697 0.347453i \(-0.112953\pi\)
\(74\) 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 0.717748 0.696303i \(-0.245173\pi\)
−0.961890 + 0.273436i \(0.911840\pi\)
\(80\) 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 0.682605 0.730788i \(-0.260847\pi\)
−0.974183 + 0.225759i \(0.927514\pi\)
\(90\) 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 −0.927487 0.373855i \(-0.878036\pi\)
0.787512 + 0.616300i \(0.211369\pi\)
\(102\) 0 0
\(103\) 14614.0 + 25312.1i 0.135730 + 0.235091i 0.925876 0.377828i \(-0.123329\pi\)
−0.790146 + 0.612918i \(0.789995\pi\)
\(104\) 0 0
\(105\) 34737.7 98394.5i 0.307488 0.870959i
\(106\) 0 0
\(107\) 43929.2 + 76087.6i 0.370932 + 0.642472i 0.989709 0.143094i \(-0.0457051\pi\)
−0.618778 + 0.785566i \(0.712372\pi\)
\(108\) 0 0
\(109\) −110314. + 191069.i −0.889333 + 1.54037i −0.0486678 + 0.998815i \(0.515498\pi\)
−0.840665 + 0.541555i \(0.817836\pi\)
\(110\) 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 0.572067 0.820207i \(-0.306142\pi\)
−0.996353 + 0.0853215i \(0.972808\pi\)
\(132\) 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 −0.896391 0.443264i \(-0.853820\pi\)
0.832073 + 0.554666i \(0.187154\pi\)
\(138\) 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 0.981720 + 0.190330i \(0.0609557\pi\)
−0.326030 + 0.945360i \(0.605711\pi\)
\(150\) 0 0
\(151\) −179399. + 310727.i −0.640290 + 1.10901i 0.345078 + 0.938574i \(0.387852\pi\)
−0.985368 + 0.170441i \(0.945481\pi\)
\(152\) 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 0.208223 + 0.978081i \(0.433232\pi\)
−0.951155 + 0.308714i \(0.900101\pi\)
\(158\) 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 0.952221 + 0.305410i \(0.0987935\pi\)
−0.211618 + 0.977353i \(0.567873\pi\)
\(164\) 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 0.979749 0.200230i \(-0.0641689\pi\)
−0.663279 + 0.748373i \(0.730836\pi\)
\(174\) 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 −0.773312 0.634026i \(-0.781401\pi\)
0.935738 + 0.352695i \(0.114735\pi\)
\(180\) 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 0.956502 0.291726i \(-0.0942295\pi\)
−0.730893 + 0.682492i \(0.760896\pi\)
\(192\) 0 0
\(193\) 336187. 582293.i 0.649663 1.12525i −0.333541 0.942736i \(-0.608244\pi\)
0.983203 0.182513i \(-0.0584231\pi\)
\(194\) 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 −0.652371 0.757900i \(-0.726226\pi\)
0.982546 + 0.186020i \(0.0595591\pi\)
\(200\) 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 0.408560 + 0.912731i \(0.366031\pi\)
−0.994729 + 0.102542i \(0.967302\pi\)
\(228\) 0 0
\(229\) −260962. 452000.i −0.328843 0.569573i 0.653439 0.756979i \(-0.273325\pi\)
−0.982283 + 0.187406i \(0.939992\pi\)
\(230\) 0 0
\(231\) −452207. + 84258.1i −0.557580 + 0.103892i
\(232\) 0 0
\(233\) 521394. + 903081.i 0.629182 + 1.08977i 0.987716 + 0.156258i \(0.0499432\pi\)
−0.358535 + 0.933516i \(0.616723\pi\)
\(234\) 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 −0.438867 0.898552i \(-0.644620\pi\)
0.997602 0.0692059i \(-0.0220465\pi\)
\(242\) 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 0.963278 0.268505i \(-0.0865295\pi\)
−0.714171 + 0.699971i \(0.753196\pi\)
\(258\) 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 −0.933763 0.357892i \(-0.883496\pi\)
0.776825 + 0.629716i \(0.216829\pi\)
\(264\) 0 0
\(265\) 761353. 0.665996
\(266\) 0 0
\(267\) 439380. 0.377192
\(268\) 0 0
\(269\) −239770. + 415294.i −0.202029 + 0.349925i −0.949182 0.314727i \(-0.898087\pi\)
0.747153 + 0.664652i \(0.231420\pi\)
\(270\) 0 0
\(271\) −488805. 846636.i −0.404308 0.700283i 0.589932 0.807453i \(-0.299154\pi\)
−0.994241 + 0.107170i \(0.965821\pi\)
\(272\) 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 −0.990959 0.134165i \(-0.957165\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(278\) 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 −0.323577 0.946202i \(-0.604885\pi\)
0.981223 0.192875i \(-0.0617812\pi\)
\(284\) 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 0.248439 + 0.968647i \(0.420082\pi\)
−0.963093 + 0.269169i \(0.913251\pi\)
\(312\) 0 0
\(313\) −1.21047e6 2.09659e6i −0.698381 1.20963i −0.969028 0.246953i \(-0.920571\pi\)
0.270646 0.962679i \(-0.412763\pi\)
\(314\) 0 0
\(315\) −951012. 1.11134e6i −0.540020 0.631062i
\(316\) 0 0
\(317\) −938057. 1.62476e6i −0.524301 0.908116i −0.999600 0.0282918i \(-0.990993\pi\)
0.475298 0.879825i \(-0.342340\pi\)
\(318\) 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 0.697607 0.716480i \(-0.254248\pi\)
−0.969294 + 0.245906i \(0.920915\pi\)
\(332\) 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 −0.995633 0.0933518i \(-0.970242\pi\)
0.578662 + 0.815568i \(0.303575\pi\)
\(348\) 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 −0.797642 0.603132i \(-0.793919\pi\)
0.921148 + 0.389212i \(0.127253\pi\)
\(354\) 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 0.591092 0.806604i \(-0.298697\pi\)
−0.994086 + 0.108598i \(0.965364\pi\)
\(360\) 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 −0.574700 0.818364i \(-0.694881\pi\)
0.996074 + 0.0885223i \(0.0282144\pi\)
\(368\) 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 0.707944 0.706269i \(-0.249623\pi\)
−0.965619 + 0.259963i \(0.916290\pi\)
\(374\) 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 0.996424 + 0.0844886i \(0.0269257\pi\)
−0.425043 + 0.905173i \(0.639741\pi\)
\(384\) 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 −0.506077 0.862488i \(-0.668905\pi\)
0.999975 + 0.00703108i \(0.00223808\pi\)
\(390\) 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 0.871487 0.490418i \(-0.163156\pi\)
−0.860458 + 0.509521i \(0.829823\pi\)
\(398\) 0 0
\(399\) 654881. 1.85495e6i 0.205935 0.583311i
\(400\) 0 0
\(401\) 1.67393e6 + 2.89933e6i 0.519848 + 0.900404i 0.999734 + 0.0230725i \(0.00734485\pi\)
−0.479886 + 0.877331i \(0.659322\pi\)
\(402\) 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 −0.996908 0.0785754i \(-0.974963\pi\)
0.566502 + 0.824060i \(0.308296\pi\)
\(410\) 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 0.307144 0.951663i \(-0.400627\pi\)
0.670592 0.741826i \(-0.266040\pi\)
\(432\) 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 0.876246 0.481865i \(-0.160040\pi\)
−0.855430 + 0.517918i \(0.826707\pi\)
\(440\) 0 0
\(441\) 367126. 2.34693e6i 0.0898914 0.574649i
\(442\) 0 0
\(443\) −1.42076e6 2.46082e6i −0.343962 0.595760i 0.641203 0.767372i \(-0.278436\pi\)
−0.985165 + 0.171612i \(0.945102\pi\)
\(444\) 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 0.765554 0.643372i \(-0.222465\pi\)
−0.939953 + 0.341303i \(0.889132\pi\)
\(458\) 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 0.998898 + 0.0469376i \(0.0149462\pi\)
−0.458800 + 0.888540i \(0.651720\pi\)
\(468\) 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 0.0742312 + 0.997241i \(0.476350\pi\)
−0.900752 + 0.434334i \(0.856984\pi\)
\(480\) 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 −0.0772330 0.997013i \(-0.524609\pi\)
0.902055 0.431621i \(-0.142058\pi\)
\(488\) 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 0.946095 0.323890i \(-0.104991\pi\)
−0.753544 + 0.657397i \(0.771657\pi\)
\(500\) 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 0.819837 + 0.572596i \(0.194064\pi\)
0.0859643 + 0.996298i \(0.472603\pi\)
\(510\) 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 −0.622301 0.782778i \(-0.713802\pi\)
0.989056 + 0.147540i \(0.0471354\pi\)
\(522\) 0 0
\(523\) −2.63599e6 4.56566e6i −0.421394 0.729877i 0.574682 0.818377i \(-0.305126\pi\)
−0.996076 + 0.0885004i \(0.971793\pi\)
\(524\) 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 0.561496 0.827480i \(-0.310226\pi\)
−0.997366 + 0.0725298i \(0.976893\pi\)
\(542\) 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 −0.822833 0.568283i \(-0.807608\pi\)
0.903564 + 0.428453i \(0.140941\pi\)
\(558\) 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 −0.698065 0.716034i \(-0.745955\pi\)
0.969136 + 0.246525i \(0.0792888\pi\)
\(564\) 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 −0.999414 0.0342216i \(-0.989105\pi\)
0.470070 0.882629i \(-0.344229\pi\)
\(570\) 0 0
\(571\) 1.65307e6 2.86321e6i 0.212179 0.367504i −0.740217 0.672368i \(-0.765277\pi\)
0.952396 + 0.304863i \(0.0986108\pi\)
\(572\) 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 −0.551165 0.834396i \(-0.685816\pi\)
0.998191 + 0.0601245i \(0.0191498\pi\)
\(578\) 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 0.604456 0.796639i \(-0.293391\pi\)
−0.992137 + 0.125154i \(0.960057\pi\)
\(594\) 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 −0.943438 0.331550i \(-0.892428\pi\)
0.758849 + 0.651266i \(0.225762\pi\)
\(600\) 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 0.872443 0.488716i \(-0.162535\pi\)
−0.859462 + 0.511200i \(0.829201\pi\)
\(608\) 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 −0.886445 0.462834i \(-0.846833\pi\)
0.844049 + 0.536267i \(0.180166\pi\)
\(614\) 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 −0.565691 0.824617i \(-0.691390\pi\)
0.996985 + 0.0775941i \(0.0247238\pi\)
\(620\) 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 −0.486743 0.873545i \(-0.661815\pi\)
0.999884 0.0152411i \(-0.00485157\pi\)
\(642\) 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 −0.958314 0.285719i \(-0.907768\pi\)
0.726596 + 0.687065i \(0.241101\pi\)
\(648\) 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 0.704351 0.709852i \(-0.251238\pi\)
−0.966925 + 0.255059i \(0.917905\pi\)
\(654\) 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 −0.0291249 0.999576i \(-0.509272\pi\)
0.880220 0.474565i \(-0.157395\pi\)
\(662\) 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 0.509790 0.860299i \(-0.329723\pi\)
−0.999936 + 0.0113419i \(0.996390\pi\)
\(678\) 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 −0.192920 0.981214i \(-0.561796\pi\)
0.946217 0.323534i \(-0.104871\pi\)
\(684\) 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 0.768125 + 0.640300i \(0.221190\pi\)
0.170454 + 0.985366i \(0.445477\pi\)
\(692\) 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 0.965171 0.261619i \(-0.0842564\pi\)
−0.709154 + 0.705053i \(0.750923\pi\)
\(710\) 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 0.726172 + 0.687513i \(0.241298\pi\)
0.232318 + 0.972640i \(0.425369\pi\)
\(720\) 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 0.992772 + 0.120018i \(0.0382951\pi\)
−0.392447 + 0.919774i \(0.628372\pi\)
\(734\) 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 −0.998939 0.0460536i \(-0.985335\pi\)
0.539353 + 0.842080i \(0.318669\pi\)
\(740\) 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 −0.905723 0.423871i \(-0.860671\pi\)
0.0857783 0.996314i \(-0.472662\pi\)
\(752\) 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 0.856809 0.515634i \(-0.172443\pi\)
−0.874956 + 0.484202i \(0.839110\pi\)
\(762\) 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 −0.408001 0.912982i \(-0.633774\pi\)
0.994666 0.103152i \(-0.0328927\pi\)
\(774\) 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