Properties

Label 49.6.c.f.18.1
Level $49$
Weight $6$
Character 49.18
Analytic conductor $7.859$
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] = [49,6,Mod(18,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.18");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 49.c (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: \(7.85880717084\)
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: \(\Z[a_1, \ldots, a_{4}]\)
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 18.1
Root \(1.77069 + 3.06693i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.6.c.f.30.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.54138 - 6.13385i) q^{2} +(-5.04138 + 8.73193i) q^{3} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +71.4138 q^{6} -97.9863 q^{8} +(70.6689 + 122.402i) q^{9} +O(q^{10})\) \(q+(-3.54138 - 6.13385i) q^{2} +(-5.04138 + 8.73193i) q^{3} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +71.4138 q^{6} -97.9863 q^{8} +(70.6689 + 122.402i) q^{9} +(-282.700 + 489.651i) q^{10} +(-175.952 + 304.757i) q^{11} +(-91.5793 - 158.620i) q^{12} +291.683 q^{13} +804.883 q^{15} +(637.655 + 1104.45i) q^{16} +(-185.038 + 320.495i) q^{17} +(500.531 - 866.946i) q^{18} +(752.463 + 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(212.855 + 368.676i) q^{23} +(493.986 - 855.609i) q^{24} +(-1623.72 + 2812.37i) q^{25} +(-1032.96 - 1789.14i) q^{26} -3875.19 q^{27} -7783.93 q^{29} +(-2850.40 - 4937.03i) q^{30} +(-1287.59 + 2230.17i) q^{31} +(2948.58 - 5107.09i) q^{32} +(-1774.08 - 3072.80i) q^{33} +2621.16 q^{34} -2567.48 q^{36} +(-369.809 - 640.528i) q^{37} +(5329.51 - 9230.99i) q^{38} +(-1470.48 + 2546.95i) q^{39} +(3911.01 + 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(-3196.26 - 5536.08i) q^{44} +(5641.33 - 9771.08i) q^{45} +(1507.60 - 2611.25i) q^{46} +(-766.342 - 1327.34i) q^{47} -12858.7 q^{48} +23000.9 q^{50} +(-1865.69 - 3231.47i) q^{51} +(-2649.28 + 4588.69i) q^{52} +(4768.73 - 8259.68i) q^{53} +(13723.5 + 23769.8i) q^{54} +28091.6 q^{55} -15173.8 q^{57} +(27565.9 + 47745.5i) q^{58} +(-14837.0 + 25698.5i) q^{59} +(-7310.56 + 12662.3i) q^{60} +(-23255.4 - 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(-11642.2 - 20164.8i) q^{65} +(-12565.4 + 21763.9i) q^{66} +(-13373.0 + 23162.8i) q^{67} +(-3361.31 - 5821.95i) q^{68} -4292.34 q^{69} -14388.8 q^{71} +(-6924.59 - 11993.7i) q^{72} +(-35047.6 + 60704.2i) q^{73} +(-2619.27 + 4536.71i) q^{74} +(-16371.6 - 28356.5i) q^{75} -27337.8 q^{76} +20830.2 q^{78} +(13542.9 + 23457.0i) q^{79} +(50902.5 - 88165.7i) q^{80} +(2363.74 - 4094.13i) q^{81} +(24895.3 + 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(-6499.26 - 11257.0i) q^{86} +(39241.8 - 67968.8i) q^{87} +(17240.9 - 29862.1i) q^{88} +(21788.7 + 37739.1i) q^{89} -79912.5 q^{90} -7733.26 q^{92} +(-12982.4 - 22486.2i) q^{93} +(-5427.82 + 9401.25i) q^{94} +(60067.3 - 104040. i) q^{95} +(29729.8 + 51493.6i) q^{96} -103374. q^{97} -49737.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9} - 778 q^{10} - 424 q^{11} - 196 q^{12} + 1848 q^{13} + 1784 q^{15} + 2064 q^{16} - 2346 q^{17} - 212 q^{18} - 360 q^{19} + 3416 q^{20} + 4252 q^{22} + 12 q^{23} + 1392 q^{24} - 1872 q^{25} + 1148 q^{26} - 5744 q^{27} - 14104 q^{29} - 5258 q^{30} + 3548 q^{31} + 8096 q^{32} - 3398 q^{33} - 14844 q^{34} - 2192 q^{36} - 11090 q^{37} + 20138 q^{38} - 1624 q^{39} + 15936 q^{40} - 7000 q^{41} - 25360 q^{43} - 5948 q^{44} + 1300 q^{45} + 5118 q^{46} - 22956 q^{47} - 22432 q^{48} + 59984 q^{50} + 384 q^{51} - 1400 q^{52} - 3042 q^{53} + 32546 q^{54} + 50152 q^{55} - 38116 q^{57} + 58852 q^{58} - 65808 q^{59} - 14084 q^{60} - 42486 q^{61} + 98724 q^{62} + 70912 q^{64} + 3164 q^{65} - 25894 q^{66} - 42312 q^{67} + 5460 q^{68} - 10308 q^{69} - 4416 q^{71} + 32448 q^{72} - 50506 q^{73} + 47370 q^{74} - 35608 q^{75} - 77672 q^{76} + 55048 q^{78} - 9004 q^{79} + 68816 q^{80} - 51178 q^{81} + 67732 q^{82} + 208656 q^{83} - 106212 q^{85} - 86776 q^{86} + 80008 q^{87} + 20496 q^{88} - 26666 q^{89} - 261304 q^{90} - 20568 q^{92} - 38718 q^{93} + 98034 q^{94} + 198140 q^{95} + 54880 q^{96} - 418264 q^{97} - 133888 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.54138 6.13385i −0.626034 1.08432i −0.988340 0.152263i \(-0.951344\pi\)
0.362306 0.932059i \(-0.381989\pi\)
\(3\) −5.04138 + 8.73193i −0.323405 + 0.560153i −0.981188 0.193054i \(-0.938161\pi\)
0.657783 + 0.753207i \(0.271494\pi\)
\(4\) −9.08276 + 15.7318i −0.283836 + 0.491619i
\(5\) −39.9138 69.1328i −0.714000 1.23668i −0.963344 0.268269i \(-0.913548\pi\)
0.249344 0.968415i \(-0.419785\pi\)
\(6\) 71.4138 0.809849
\(7\) 0 0
\(8\) −97.9863 −0.541303
\(9\) 70.6689 + 122.402i 0.290819 + 0.503713i
\(10\) −282.700 + 489.651i −0.893976 + 1.54841i
\(11\) −175.952 + 304.757i −0.438442 + 0.759403i −0.997570 0.0696781i \(-0.977803\pi\)
0.559128 + 0.829082i \(0.311136\pi\)
\(12\) −91.5793 158.620i −0.183588 0.317984i
\(13\) 291.683 0.478688 0.239344 0.970935i \(-0.423068\pi\)
0.239344 + 0.970935i \(0.423068\pi\)
\(14\) 0 0
\(15\) 804.883 0.923644
\(16\) 637.655 + 1104.45i 0.622710 + 1.07857i
\(17\) −185.038 + 320.495i −0.155288 + 0.268967i −0.933164 0.359451i \(-0.882964\pi\)
0.777876 + 0.628418i \(0.216297\pi\)
\(18\) 500.531 866.946i 0.364125 0.630682i
\(19\) 752.463 + 1303.30i 0.478190 + 0.828250i 0.999687 0.0250030i \(-0.00795952\pi\)
−0.521497 + 0.853253i \(0.674626\pi\)
\(20\) 1450.11 0.810637
\(21\) 0 0
\(22\) 2492.45 1.09792
\(23\) 212.855 + 368.676i 0.0839006 + 0.145320i 0.904922 0.425577i \(-0.139929\pi\)
−0.821022 + 0.570897i \(0.806596\pi\)
\(24\) 493.986 855.609i 0.175060 0.303213i
\(25\) −1623.72 + 2812.37i −0.519592 + 0.899960i
\(26\) −1032.96 1789.14i −0.299675 0.519052i
\(27\) −3875.19 −1.02302
\(28\) 0 0
\(29\) −7783.93 −1.71872 −0.859358 0.511374i \(-0.829137\pi\)
−0.859358 + 0.511374i \(0.829137\pi\)
\(30\) −2850.40 4937.03i −0.578232 1.00153i
\(31\) −1287.59 + 2230.17i −0.240643 + 0.416805i −0.960898 0.276904i \(-0.910692\pi\)
0.720255 + 0.693710i \(0.244025\pi\)
\(32\) 2948.58 5107.09i 0.509024 0.881655i
\(33\) −1774.08 3072.80i −0.283588 0.491189i
\(34\) 2621.16 0.388862
\(35\) 0 0
\(36\) −2567.48 −0.330180
\(37\) −369.809 640.528i −0.0444092 0.0769190i 0.842966 0.537966i \(-0.180807\pi\)
−0.887376 + 0.461047i \(0.847474\pi\)
\(38\) 5329.51 9230.99i 0.598727 1.03703i
\(39\) −1470.48 + 2546.95i −0.154810 + 0.268139i
\(40\) 3911.01 + 6774.06i 0.386490 + 0.669421i
\(41\) −7029.84 −0.653109 −0.326554 0.945178i \(-0.605888\pi\)
−0.326554 + 0.945178i \(0.605888\pi\)
\(42\) 0 0
\(43\) 1835.23 0.151363 0.0756816 0.997132i \(-0.475887\pi\)
0.0756816 + 0.997132i \(0.475887\pi\)
\(44\) −3196.26 5536.08i −0.248891 0.431093i
\(45\) 5641.33 9771.08i 0.415289 0.719302i
\(46\) 1507.60 2611.25i 0.105049 0.181950i
\(47\) −766.342 1327.34i −0.0506032 0.0876473i 0.839614 0.543183i \(-0.182781\pi\)
−0.890217 + 0.455536i \(0.849448\pi\)
\(48\) −12858.7 −0.805550
\(49\) 0 0
\(50\) 23000.9 1.30113
\(51\) −1865.69 3231.47i −0.100442 0.173970i
\(52\) −2649.28 + 4588.69i −0.135869 + 0.235332i
\(53\) 4768.73 8259.68i 0.233192 0.403900i −0.725554 0.688165i \(-0.758416\pi\)
0.958746 + 0.284265i \(0.0917497\pi\)
\(54\) 13723.5 + 23769.8i 0.640444 + 1.10928i
\(55\) 28091.6 1.25219
\(56\) 0 0
\(57\) −15173.8 −0.618596
\(58\) 27565.9 + 47745.5i 1.07597 + 1.86364i
\(59\) −14837.0 + 25698.5i −0.554903 + 0.961120i 0.443008 + 0.896517i \(0.353911\pi\)
−0.997911 + 0.0646022i \(0.979422\pi\)
\(60\) −7310.56 + 12662.3i −0.262164 + 0.454081i
\(61\) −23255.4 40279.5i −0.800201 1.38599i −0.919483 0.393129i \(-0.871393\pi\)
0.119282 0.992860i \(-0.461941\pi\)
\(62\) 18239.4 0.602602
\(63\) 0 0
\(64\) −958.246 −0.0292434
\(65\) −11642.2 20164.8i −0.341783 0.591985i
\(66\) −12565.4 + 21763.9i −0.355072 + 0.615002i
\(67\) −13373.0 + 23162.8i −0.363951 + 0.630381i −0.988607 0.150518i \(-0.951906\pi\)
0.624656 + 0.780900i \(0.285239\pi\)
\(68\) −3361.31 5821.95i −0.0881527 0.152685i
\(69\) −4292.34 −0.108535
\(70\) 0 0
\(71\) −14388.8 −0.338748 −0.169374 0.985552i \(-0.554175\pi\)
−0.169374 + 0.985552i \(0.554175\pi\)
\(72\) −6924.59 11993.7i −0.157421 0.272661i
\(73\) −35047.6 + 60704.2i −0.769752 + 1.33325i 0.167946 + 0.985796i \(0.446287\pi\)
−0.937697 + 0.347453i \(0.887047\pi\)
\(74\) −2619.27 + 4536.71i −0.0556033 + 0.0963078i
\(75\) −16371.6 28356.5i −0.336077 0.582102i
\(76\) −27337.8 −0.542911
\(77\) 0 0
\(78\) 20830.2 0.387665
\(79\) 13542.9 + 23457.0i 0.244143 + 0.422868i 0.961890 0.273436i \(-0.0881601\pi\)
−0.717748 + 0.696303i \(0.754827\pi\)
\(80\) 50902.5 88165.7i 0.889230 1.54019i
\(81\) 2363.74 4094.13i 0.0400302 0.0693344i
\(82\) 24895.3 + 43120.0i 0.408868 + 0.708181i
\(83\) 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
\(86\) −6499.26 11257.0i −0.0947584 0.164126i
\(87\) 39241.8 67968.8i 0.555841 0.962745i
\(88\) 17240.9 29862.1i 0.237330 0.411067i
\(89\) 21788.7 + 37739.1i 0.291579 + 0.505029i 0.974183 0.225759i \(-0.0724862\pi\)
−0.682605 + 0.730788i \(0.739153\pi\)
\(90\) −79912.5 −1.03994
\(91\) 0 0
\(92\) −7733.26 −0.0952561
\(93\) −12982.4 22486.2i −0.155650 0.269594i
\(94\) −5427.82 + 9401.25i −0.0633586 + 0.109740i
\(95\) 60067.3 104040.i 0.682856 1.18274i
\(96\) 29729.8 + 51493.6i 0.329241 + 0.570263i
\(97\) −103374. −1.11553 −0.557765 0.829999i \(-0.688341\pi\)
−0.557765 + 0.829999i \(0.688341\pi\)
\(98\) 0 0
\(99\) −49737.3 −0.510028
\(100\) −29495.8 51088.3i −0.294958 0.510883i
\(101\) 14350.1 24855.1i 0.139975 0.242444i −0.787512 0.616300i \(-0.788631\pi\)
0.927487 + 0.373855i \(0.121964\pi\)
\(102\) −13214.2 + 22887.7i −0.125760 + 0.217822i
\(103\) 14614.0 + 25312.1i 0.135730 + 0.235091i 0.925876 0.377828i \(-0.123329\pi\)
−0.790146 + 0.612918i \(0.789995\pi\)
\(104\) −28580.9 −0.259115
\(105\) 0 0
\(106\) −67551.6 −0.583944
\(107\) −43929.2 76087.6i −0.370932 0.642472i 0.618778 0.785566i \(-0.287628\pi\)
−0.989709 + 0.143094i \(0.954295\pi\)
\(108\) 35197.4 60963.7i 0.290370 0.502935i
\(109\) −110314. + 191069.i −0.889333 + 1.54037i −0.0486678 + 0.998815i \(0.515498\pi\)
−0.840665 + 0.541555i \(0.817836\pi\)
\(110\) −99483.2 172310.i −0.783913 1.35778i
\(111\) 7457.39 0.0574486
\(112\) 0 0
\(113\) 39665.6 0.292225 0.146113 0.989268i \(-0.453324\pi\)
0.146113 + 0.989268i \(0.453324\pi\)
\(114\) 53736.2 + 93073.9i 0.387262 + 0.670758i
\(115\) 16991.7 29430.5i 0.119810 0.207517i
\(116\) 70699.6 122455.i 0.487834 0.844953i
\(117\) 20612.9 + 35702.6i 0.139211 + 0.241121i
\(118\) 210174. 1.38955
\(119\) 0 0
\(120\) −78867.5 −0.499971
\(121\) 18607.4 + 32229.0i 0.115538 + 0.200117i
\(122\) −164712. + 285290.i −1.00191 + 1.73535i
\(123\) 35440.1 61384.0i 0.211219 0.365841i
\(124\) −23389.7 40512.2i −0.136606 0.236609i
\(125\) 9774.87 0.0559546
\(126\) 0 0
\(127\) 51740.3 0.284655 0.142328 0.989820i \(-0.454541\pi\)
0.142328 + 0.989820i \(0.454541\pi\)
\(128\) −90961.0 157549.i −0.490716 0.849946i
\(129\) −9252.11 + 16025.1i −0.0489515 + 0.0847866i
\(130\) −82458.7 + 142823.i −0.427935 + 0.741206i
\(131\) −83336.9 144344.i −0.424286 0.734885i 0.572067 0.820207i \(-0.306142\pi\)
−0.996353 + 0.0853215i \(0.972808\pi\)
\(132\) 64454.2 0.321971
\(133\) 0 0
\(134\) 189436. 0.911382
\(135\) 154674. + 267902.i 0.730435 + 1.26515i
\(136\) 18131.2 31404.1i 0.0840578 0.145592i
\(137\) −14129.7 + 24473.4i −0.0643178 + 0.111402i −0.896391 0.443264i \(-0.853820\pi\)
0.832073 + 0.554666i \(0.187154\pi\)
\(138\) 15200.8 + 26328.6i 0.0679468 + 0.117687i
\(139\) −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
\(142\) 50956.1 + 88258.5i 0.212068 + 0.367312i
\(143\) −51322.1 + 88892.4i −0.209877 + 0.363517i
\(144\) −90124.9 + 156101.i −0.362192 + 0.627334i
\(145\) 310686. + 538125.i 1.22716 + 2.12551i
\(146\) 496467. 1.92756
\(147\) 0 0
\(148\) 13435.5 0.0504198
\(149\) 177691. + 307769.i 0.655691 + 1.13569i 0.981720 + 0.190330i \(0.0609557\pi\)
−0.326030 + 0.945360i \(0.605711\pi\)
\(150\) −115956. + 200842.i −0.420791 + 0.728832i
\(151\) 179399. 310727.i 0.640290 1.10901i −0.345078 0.938574i \(-0.612148\pi\)
0.985368 0.170441i \(-0.0545191\pi\)
\(152\) −73731.0 127706.i −0.258846 0.448334i
\(153\) −52305.7 −0.180643
\(154\) 0 0
\(155\) 205570. 0.687275
\(156\) −26712.1 46266.7i −0.0878813 0.152215i
\(157\) 229455. 397428.i 0.742932 1.28680i −0.208223 0.978081i \(-0.566768\pi\)
0.951155 0.308714i \(-0.0998986\pi\)
\(158\) 95921.1 166140.i 0.305683 0.529459i
\(159\) 48082.0 + 83280.4i 0.150831 + 0.261246i
\(160\) −470756. −1.45377
\(161\) 0 0
\(162\) −33483.7 −0.100241
\(163\) −251220. 435126.i −0.740603 1.28276i −0.952221 0.305410i \(-0.901206\pi\)
0.211618 0.977353i \(-0.432127\pi\)
\(164\) 63850.3 110592.i 0.185376 0.321081i
\(165\) −141621. + 245294.i −0.404964 + 0.701418i
\(166\) −282444. 489208.i −0.795541 1.37792i
\(167\) 676652. 1.87748 0.938738 0.344632i \(-0.111996\pi\)
0.938738 + 0.344632i \(0.111996\pi\)
\(168\) 0 0
\(169\) −286214. −0.770858
\(170\) −104620. 181208.i −0.277647 0.480900i
\(171\) −106351. + 184206.i −0.278133 + 0.481741i
\(172\) −16669.0 + 28871.5i −0.0429623 + 0.0744130i
\(173\) −124580. 215779.i −0.316470 0.548143i 0.663279 0.748373i \(-0.269164\pi\)
−0.979749 + 0.200230i \(0.935831\pi\)
\(174\) −555880. −1.39190
\(175\) 0 0
\(176\) −448786. −1.09209
\(177\) −149598. 259112.i −0.358916 0.621661i
\(178\) 154324. 267297.i 0.365076 0.632330i
\(179\) −69628.9 + 120601.i −0.162427 + 0.281331i −0.935738 0.352695i \(-0.885265\pi\)
0.773312 + 0.634026i \(0.218599\pi\)
\(180\) 102478. + 177497.i 0.235748 + 0.408328i
\(181\) −306246. −0.694823 −0.347412 0.937713i \(-0.612939\pi\)
−0.347412 + 0.937713i \(0.612939\pi\)
\(182\) 0 0
\(183\) 468957. 1.03516
\(184\) −20856.9 36125.2i −0.0454156 0.0786622i
\(185\) −29521.0 + 51131.8i −0.0634163 + 0.109840i
\(186\) −91951.5 + 159265.i −0.194884 + 0.337549i
\(187\) −65115.4 112783.i −0.136169 0.235852i
\(188\) 27842.0 0.0574521
\(189\) 0 0
\(190\) −850885. −1.70996
\(191\) −113747. 197015.i −0.225609 0.390766i 0.730893 0.682492i \(-0.239104\pi\)
−0.956502 + 0.291726i \(0.905770\pi\)
\(192\) 4830.89 8367.34i 0.00945744 0.0163808i
\(193\) 336187. 582293.i 0.649663 1.12525i −0.333541 0.942736i \(-0.608244\pi\)
0.983203 0.182513i \(-0.0584231\pi\)
\(194\) 366086. + 634079.i 0.698359 + 1.20959i
\(195\) 234770. 0.442137
\(196\) 0 0
\(197\) −1282.76 −0.00235493 −0.00117747 0.999999i \(-0.500375\pi\)
−0.00117747 + 0.999999i \(0.500375\pi\)
\(198\) 176139. + 305081.i 0.319295 + 0.553035i
\(199\) 184449. 319475.i 0.330175 0.571879i −0.652371 0.757900i \(-0.726226\pi\)
0.982546 + 0.186020i \(0.0595591\pi\)
\(200\) 159103. 275574.i 0.281257 0.487151i
\(201\) −134837. 233545.i −0.235407 0.407737i
\(202\) −203277. −0.350517
\(203\) 0 0
\(204\) 67782.5 0.114036
\(205\) 280588. + 485992.i 0.466320 + 0.807690i
\(206\) 103507. 179280.i 0.169943 0.294349i
\(207\) −30084.5 + 52107.9i −0.0487997 + 0.0845236i
\(208\) 185993. + 322149.i 0.298084 + 0.516296i
\(209\) −529589. −0.838635
\(210\) 0 0
\(211\) 502168. 0.776503 0.388251 0.921553i \(-0.373079\pi\)
0.388251 + 0.921553i \(0.373079\pi\)
\(212\) 86626.5 + 150042.i 0.132377 + 0.229283i
\(213\) 72539.2 125642.i 0.109553 0.189751i
\(214\) −311140. + 538910.i −0.464431 + 0.804419i
\(215\) −73251.1 126875.i −0.108073 0.187188i
\(216\) 379715. 0.553763
\(217\) 0 0
\(218\) 1.56266e6 2.22701
\(219\) −353376. 612066.i −0.497883 0.862358i
\(220\) −255150. + 441932.i −0.355417 + 0.615600i
\(221\) −53972.3 + 93482.7i −0.0743344 + 0.128751i
\(222\) −26409.5 45742.5i −0.0359647 0.0622928i
\(223\) 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
\(226\) −140471. 243303.i −0.182943 0.316867i
\(227\) −455079. + 788220.i −0.586168 + 1.01527i 0.408560 + 0.912731i \(0.366031\pi\)
−0.994729 + 0.102542i \(0.967302\pi\)
\(228\) 137820. 238711.i 0.175580 0.304114i
\(229\) 260962. + 452000.i 0.328843 + 0.569573i 0.982283 0.187406i \(-0.0600079\pi\)
−0.653439 + 0.756979i \(0.726675\pi\)
\(230\) −240697. −0.300020
\(231\) 0 0
\(232\) 762719. 0.930346
\(233\) 521394. + 903081.i 0.629182 + 1.08977i 0.987716 + 0.156258i \(0.0499432\pi\)
−0.358535 + 0.933516i \(0.616723\pi\)
\(234\) 145996. 252873.i 0.174302 0.301900i
\(235\) −61175.2 + 105959.i −0.0722613 + 0.125160i
\(236\) −269522. 466826.i −0.315003 0.545601i
\(237\) −273100. −0.315828
\(238\) 0 0
\(239\) −1.53447e6 −1.73766 −0.868830 0.495110i \(-0.835128\pi\)
−0.868830 + 0.495110i \(0.835128\pi\)
\(240\) 513238. + 888954.i 0.575163 + 0.996211i
\(241\) −503789. + 872588.i −0.558735 + 0.967758i 0.438867 + 0.898552i \(0.355380\pi\)
−0.997602 + 0.0692059i \(0.977953\pi\)
\(242\) 131792. 228271.i 0.144661 0.250560i
\(243\) −447002. 774231.i −0.485617 0.841114i
\(244\) 844893. 0.908505
\(245\) 0 0
\(246\) −502028. −0.528920
\(247\) 219480. + 380151.i 0.228904 + 0.396473i
\(248\) 126166. 218526.i 0.130261 0.225618i
\(249\) −402077. + 696419.i −0.410971 + 0.711823i
\(250\) −34616.6 59957.6i −0.0350295 0.0606729i
\(251\) −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
\(254\) −183232. 317367.i −0.178204 0.308658i
\(255\) −148934. + 257961.i −0.143431 + 0.248429i
\(256\) −659587. + 1.14244e6i −0.629032 + 1.08951i
\(257\) −263766. 456856.i −0.249107 0.431466i 0.714171 0.699971i \(-0.246804\pi\)
−0.963278 + 0.268505i \(0.913470\pi\)
\(258\) 131061. 0.122581
\(259\) 0 0
\(260\) 422972. 0.388042
\(261\) −550082. 952771.i −0.499835 0.865739i
\(262\) −590255. + 1.02235e6i −0.531235 + 0.920126i
\(263\) 176042. 304914.i 0.156938 0.271824i −0.776825 0.629716i \(-0.783171\pi\)
0.933763 + 0.357892i \(0.116504\pi\)
\(264\) 173836. + 301092.i 0.153507 + 0.265882i
\(265\) −761353. −0.665996
\(266\) 0 0
\(267\) −439380. −0.377192
\(268\) −242928. 420764.i −0.206605 0.357850i
\(269\) 239770. 415294.i 0.202029 0.349925i −0.747153 0.664652i \(-0.768580\pi\)
0.949182 + 0.314727i \(0.101913\pi\)
\(270\) 1.09552e6 1.89749e6i 0.914554 1.58405i
\(271\) −488805. 846636.i −0.404308 0.700283i 0.589932 0.807453i \(-0.299154\pi\)
−0.994241 + 0.107170i \(0.965821\pi\)
\(272\) −471961. −0.386798
\(273\) 0 0
\(274\) 200155. 0.161061
\(275\) −571395. 989684.i −0.455622 0.789160i
\(276\) 38986.3 67526.2i 0.0308063 0.0533580i
\(277\) −484362. + 838939.i −0.379289 + 0.656948i −0.990959 0.134165i \(-0.957165\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(278\) 1.19130e6 + 2.06339e6i 0.924502 + 1.60128i
\(279\) −363970. −0.279934
\(280\) 0 0
\(281\) −318333. −0.240501 −0.120250 0.992744i \(-0.538370\pi\)
−0.120250 + 0.992744i \(0.538370\pi\)
\(282\) −54727.4 94790.6i −0.0409809 0.0709811i
\(283\) 886051. 1.53468e6i 0.657646 1.13908i −0.323577 0.946202i \(-0.604885\pi\)
0.981223 0.192875i \(-0.0617812\pi\)
\(284\) 130690. 226361.i 0.0961491 0.166535i
\(285\) 605644. + 1.04901e6i 0.441678 + 0.765008i
\(286\) 727004. 0.525559
\(287\) 0 0
\(288\) 833492. 0.592134
\(289\) 641451. + 1.11103e6i 0.451771 + 0.782491i
\(290\) 2.20052e6 3.81141e6i 1.53649 2.66128i
\(291\) 521147. 902652.i 0.360768 0.624868i
\(292\) −636657. 1.10272e6i −0.436967 0.756849i
\(293\) −1.64148e6 −1.11703 −0.558516 0.829494i \(-0.688629\pi\)
−0.558516 + 0.829494i \(0.688629\pi\)
\(294\) 0 0
\(295\) 2.36881e6 1.58480
\(296\) 36236.2 + 62762.9i 0.0240388 + 0.0416365i
\(297\) 681846. 1.18099e6i 0.448534 0.776883i
\(298\) 1.25854e6 2.17986e6i 0.820969 1.42196i
\(299\) 62086.2 + 107536.i 0.0401622 + 0.0695629i
\(300\) 594799. 0.381563
\(301\) 0 0
\(302\) −2.54128e6 −1.60337
\(303\) 144689. + 250608.i 0.0905374 + 0.156815i
\(304\) −959623. + 1.66212e6i −0.595548 + 1.03152i
\(305\) −1.85642e6 + 3.21542e6i −1.14269 + 1.97919i
\(306\) 185234. + 320835.i 0.113088 + 0.195875i
\(307\) 466930. 0.282752 0.141376 0.989956i \(-0.454847\pi\)
0.141376 + 0.989956i \(0.454847\pi\)
\(308\) 0 0
\(309\) −294698. −0.175582
\(310\) −728002. 1.26094e6i −0.430257 0.745228i
\(311\) −1.21898e6 + 2.11134e6i −0.714654 + 1.23782i 0.248439 + 0.968647i \(0.420082\pi\)
−0.963093 + 0.269169i \(0.913251\pi\)
\(312\) 144087. 249566.i 0.0837990 0.145144i
\(313\) 1.21047e6 + 2.09659e6i 0.698381 + 1.20963i 0.969028 + 0.246953i \(0.0794293\pi\)
−0.270646 + 0.962679i \(0.587237\pi\)
\(314\) −3.25035e6 −1.86040
\(315\) 0 0
\(316\) −492028. −0.277186
\(317\) −938057. 1.62476e6i −0.524301 0.908116i −0.999600 0.0282918i \(-0.990993\pi\)
0.475298 0.879825i \(-0.342340\pi\)
\(318\) 340553. 589856.i 0.188850 0.327098i
\(319\) 1.36960e6 2.37221e6i 0.753557 1.30520i
\(320\) 38247.3 + 66246.2i 0.0208798 + 0.0361648i
\(321\) 885855. 0.479844
\(322\) 0 0
\(323\) −556936. −0.297029
\(324\) 42938.7 + 74371.9i 0.0227241 + 0.0393592i
\(325\) −473612. + 820321.i −0.248722 + 0.430800i
\(326\) −1.77933e6 + 3.08190e6i −0.927285 + 1.60611i
\(327\) −1.11227e6 1.92651e6i −0.575229 0.996326i
\(328\) 688828. 0.353530
\(329\) 0 0
\(330\) 2.00613e6 1.01408
\(331\) 541549. + 937990.i 0.271686 + 0.470575i 0.969294 0.245906i \(-0.0790853\pi\)
−0.697607 + 0.716480i \(0.745752\pi\)
\(332\) −724399. + 1.25470e6i −0.360689 + 0.624732i
\(333\) 52268.0 90530.8i 0.0258301 0.0447390i
\(334\) −2.39628e6 4.15048e6i −1.17536 2.03579i
\(335\) 2.13507e6 1.03944
\(336\) 0 0
\(337\) −2.59465e6 −1.24453 −0.622263 0.782809i \(-0.713786\pi\)
−0.622263 + 0.782809i \(0.713786\pi\)
\(338\) 1.01359e6 + 1.75560e6i 0.482583 + 0.835859i
\(339\) −199969. + 346357.i −0.0945071 + 0.163691i
\(340\) −268325. + 464753.i −0.125882 + 0.218034i
\(341\) −453107. 784804.i −0.211016 0.365490i
\(342\) 1.50652e6 0.696484
\(343\) 0 0
\(344\) −179828. −0.0819333
\(345\) 171324. + 296741.i 0.0774943 + 0.134224i
\(346\) −882371. + 1.52831e6i −0.396242 + 0.686312i
\(347\) 935255. 1.61991e6i 0.416972 0.722216i −0.578662 0.815568i \(-0.696425\pi\)
0.995633 + 0.0933518i \(0.0297581\pi\)
\(348\) 712847. + 1.23469e6i 0.315536 + 0.546524i
\(349\) 1.61685e6 0.710568 0.355284 0.934758i \(-0.384384\pi\)
0.355284 + 0.934758i \(0.384384\pi\)
\(350\) 0 0
\(351\) −1.13033e6 −0.489706
\(352\) 1.03762e6 + 1.79720e6i 0.446354 + 0.773109i
\(353\) −289153. + 500827.i −0.123507 + 0.213920i −0.921148 0.389212i \(-0.872747\pi\)
0.797642 + 0.603132i \(0.206081\pi\)
\(354\) −1.05957e6 + 1.83523e6i −0.449387 + 0.778362i
\(355\) 574310. + 994734.i 0.241866 + 0.418925i
\(356\) −791605. −0.331042
\(357\) 0 0
\(358\) 986330. 0.406738
\(359\) 984090. + 1.70449e6i 0.402994 + 0.698006i 0.994086 0.108598i \(-0.0346362\pi\)
−0.591092 + 0.806604i \(0.701303\pi\)
\(360\) −552773. + 957432.i −0.224797 + 0.389360i
\(361\) 105650. 182990.i 0.0426677 0.0739027i
\(362\) 1.08453e6 + 1.87847e6i 0.434983 + 0.753412i
\(363\) −375229. −0.149462
\(364\) 0 0
\(365\) 5.59553e6 2.19841
\(366\) −1.66076e6 2.87651e6i −0.648042 1.12244i
\(367\) 1.08726e6 1.88319e6i 0.421375 0.729842i −0.574700 0.818364i \(-0.694881\pi\)
0.996074 + 0.0885223i \(0.0282144\pi\)
\(368\) −271457. + 470177.i −0.104491 + 0.180985i
\(369\) −496791. 860468.i −0.189936 0.328979i
\(370\) 418180. 0.158803
\(371\) 0 0
\(372\) 471666. 0.176716
\(373\) −692379. 1.19924e6i −0.257675 0.446306i 0.707944 0.706269i \(-0.249623\pi\)
−0.965619 + 0.259963i \(0.916290\pi\)
\(374\) −461197. + 798817.i −0.170493 + 0.295303i
\(375\) −49278.9 + 85353.5i −0.0180960 + 0.0313432i
\(376\) 75091.0 + 130061.i 0.0273916 + 0.0474437i
\(377\) −2.27044e6 −0.822728
\(378\) 0 0
\(379\) 3.37190e6 1.20580 0.602902 0.797815i \(-0.294011\pi\)
0.602902 + 0.797815i \(0.294011\pi\)
\(380\) 1.09115e6 + 1.88993e6i 0.387639 + 0.671410i
\(381\) −260842. + 451792.i −0.0920589 + 0.159451i
\(382\) −805642. + 1.39541e6i −0.282478 + 0.489265i
\(383\) 1.64030e6 + 2.84108e6i 0.571382 + 0.989662i 0.996424 + 0.0844886i \(0.0269257\pi\)
−0.425043 + 0.905173i \(0.639741\pi\)
\(384\) 1.83428e6 0.634800
\(385\) 0 0
\(386\) −4.76227e6 −1.62684
\(387\) 129694. + 224637.i 0.0440192 + 0.0762435i
\(388\) 938919. 1.62626e6i 0.316628 0.548415i
\(389\) 1.47405e6 2.55313e6i 0.493899 0.855457i −0.506077 0.862488i \(-0.668905\pi\)
0.999975 + 0.00703108i \(0.00223808\pi\)
\(390\) −831412. 1.44005e6i −0.276793 0.479419i
\(391\) −157545. −0.0521150
\(392\) 0 0
\(393\) 1.68053e6 0.548865
\(394\) 4542.73 + 7868.24i 0.00147427 + 0.00255351i
\(395\) 1.08110e6 1.87251e6i 0.348636 0.603855i
\(396\) 451752. 782458.i 0.144765 0.250740i
\(397\) −34635.1 59989.7i −0.0110291 0.0191030i 0.860458 0.509521i \(-0.170177\pi\)
−0.871487 + 0.490418i \(0.836844\pi\)
\(398\) −2.61282e6 −0.826802
\(399\) 0 0
\(400\) −4.14151e6 −1.29422
\(401\) 1.67393e6 + 2.89933e6i 0.519848 + 0.900404i 0.999734 + 0.0230725i \(0.00734485\pi\)
−0.479886 + 0.877331i \(0.659322\pi\)
\(402\) −955019. + 1.65414e6i −0.294745 + 0.510514i
\(403\) −375567. + 650501.i −0.115193 + 0.199520i
\(404\) 260677. + 451506.i 0.0794602 + 0.137629i
\(405\) −377384. −0.114326
\(406\) 0 0
\(407\) 260274. 0.0778834
\(408\) 182812. + 316640.i 0.0543694 + 0.0941706i
\(409\) 1.45608e6 2.52201e6i 0.430406 0.745485i −0.566502 0.824060i \(-0.691704\pi\)
0.996908 + 0.0785754i \(0.0250371\pi\)
\(410\) 1.98734e6 3.44217e6i 0.583864 1.01128i
\(411\) −142466. 246759.i −0.0416014 0.0720557i
\(412\) −530940. −0.154100
\(413\) 0 0
\(414\) 426163. 0.122201
\(415\) −3.18334e6 5.51371e6i −0.907326 1.57153i
\(416\) 860050. 1.48965e6i 0.243663 0.422037i
\(417\) 1.69589e6 2.93736e6i 0.477592 0.827213i
\(418\) 1.87547e6 + 3.24842e6i 0.525014 + 0.909350i
\(419\) 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 \(0.617787\pi\)
\(422\) −1.77837e6 3.08023e6i −0.486117 0.841979i
\(423\) 108313. 187604.i 0.0294327 0.0509789i
\(424\) −467270. + 809336.i −0.126227 + 0.218632i
\(425\) −600901. 1.04079e6i −0.161373 0.279506i
\(426\) −1.02756e6 −0.274335
\(427\) 0 0
\(428\) 1.59599e6 0.421135
\(429\) −517468. 896281.i −0.135750 0.235126i
\(430\) −518820. + 898623.i −0.135315 + 0.234372i
\(431\) −3.77064e6 + 6.53094e6i −0.977736 + 1.69349i −0.307144 + 0.951663i \(0.599373\pi\)
−0.670592 + 0.741826i \(0.733960\pi\)
\(432\) −2.47103e6 4.27996e6i −0.637044 1.10339i
\(433\) −5.83558e6 −1.49577 −0.747883 0.663830i \(-0.768930\pi\)
−0.747883 + 0.663830i \(0.768930\pi\)
\(434\) 0 0
\(435\) −6.26516e6 −1.58748
\(436\) −2.00391e6 3.47088e6i −0.504850 0.874426i
\(437\) −320331. + 554830.i −0.0802409 + 0.138981i
\(438\) −2.50288e6 + 4.33512e6i −0.623383 + 1.07973i
\(439\) 84051.9 + 145582.i 0.0208155 + 0.0360535i 0.876246 0.481865i \(-0.160040\pi\)
−0.855430 + 0.517918i \(0.826707\pi\)
\(440\) −2.75259e6 −0.677814
\(441\) 0 0
\(442\) 764546. 0.186143
\(443\) 1.42076e6 + 2.46082e6i 0.343962 + 0.595760i 0.985165 0.171612i \(-0.0548975\pi\)
−0.641203 + 0.767372i \(0.721564\pi\)
\(444\) −67733.7 + 117318.i −0.0163060 + 0.0282428i
\(445\) 1.73934e6 3.01262e6i 0.416374 0.721181i
\(446\) −4.15503e6 7.19672e6i −0.989092 1.71316i
\(447\) −3.58323e6 −0.848214
\(448\) 0 0
\(449\) −1.41567e6 −0.331396 −0.165698 0.986177i \(-0.552988\pi\)
−0.165698 + 0.986177i \(0.552988\pi\)
\(450\) 1.62545e6 + 2.81536e6i 0.378392 + 0.655395i
\(451\) 1.23691e6 2.14240e6i 0.286350 0.495973i
\(452\) −360273. + 624012.i −0.0829442 + 0.143664i
\(453\) 1.80883e6 + 3.13299e6i 0.414146 + 0.717321i
\(454\) 6.44644e6 1.46784
\(455\) 0 0
\(456\) 1.48682e6 0.334848
\(457\) −778637. 1.34864e6i −0.174399 0.302068i 0.765554 0.643372i \(-0.222465\pi\)
−0.939953 + 0.341303i \(0.889132\pi\)
\(458\) 1.84833e6 3.20141e6i 0.411734 0.713144i
\(459\) 717056. 1.24198e6i 0.158862 0.275158i
\(460\) 308664. + 534621.i 0.0680129 + 0.117802i
\(461\) 4.45345e6 0.975987 0.487994 0.872847i \(-0.337729\pi\)
0.487994 + 0.872847i \(0.337729\pi\)
\(462\) 0 0
\(463\) 4.92263e6 1.06720 0.533599 0.845738i \(-0.320839\pi\)
0.533599 + 0.845738i \(0.320839\pi\)
\(464\) −4.96347e6 8.59698e6i −1.07026 1.85375i
\(465\) −1.03636e6 + 1.79502e6i −0.222268 + 0.384980i
\(466\) 3.69291e6 6.39631e6i 0.787778 1.36447i
\(467\) 2.54545e6 + 4.40885e6i 0.540098 + 0.935477i 0.998898 + 0.0469376i \(0.0149462\pi\)
−0.458800 + 0.888540i \(0.651720\pi\)
\(468\) −748889. −0.158053
\(469\) 0 0
\(470\) 866579. 0.180952
\(471\) 2.31354e6 + 4.00717e6i 0.480535 + 0.832312i
\(472\) 1.45383e6 2.51810e6i 0.300370 0.520257i
\(473\) −322912. + 559301.i −0.0663639 + 0.114946i
\(474\) 967150. + 1.67515e6i 0.197719 + 0.342459i
\(475\) −4.88717e6 −0.993856
\(476\) 0 0
\(477\) 1.34800e6 0.271266
\(478\) 5.43416e6 + 9.41224e6i 1.08783 + 1.88418i
\(479\) −4.15042e6 + 7.18874e6i −0.826521 + 1.43158i 0.0742312 + 0.997241i \(0.476350\pi\)
−0.900752 + 0.434334i \(0.856984\pi\)
\(480\) 2.37326e6 4.11061e6i 0.470157 0.814335i
\(481\) −107867. 186831.i −0.0212581 0.0368202i
\(482\) 7.13644e6 1.39915
\(483\) 0 0
\(484\) −676028. −0.131175
\(485\) 4.12604e6 + 7.14651e6i 0.796488 + 1.37956i
\(486\) −3.16601e6 + 5.48369e6i −0.608025 + 1.05313i
\(487\) −4.31701e6 + 7.47727e6i −0.824822 + 1.42863i 0.0772330 + 0.997013i \(0.475391\pi\)
−0.902055 + 0.431621i \(0.857942\pi\)
\(488\) 2.27871e6 + 3.94684e6i 0.433151 + 0.750240i
\(489\) 5.06599e6 0.958059
\(490\) 0 0
\(491\) 95039.5 0.0177910 0.00889550 0.999960i \(-0.497168\pi\)
0.00889550 + 0.999960i \(0.497168\pi\)
\(492\) 643788. + 1.11507e6i 0.119903 + 0.207678i
\(493\) 1.44032e6 2.49471e6i 0.266896 0.462277i
\(494\) 1.55453e6 2.69252e6i 0.286603 0.496411i
\(495\) 1.98521e6 + 3.43848e6i 0.364160 + 0.630744i
\(496\) −3.28415e6 −0.599402
\(497\) 0 0
\(498\) 5.69564e6 1.02913
\(499\) −1.07102e6 1.85506e6i −0.192551 0.333507i 0.753544 0.657397i \(-0.228343\pi\)
−0.946095 + 0.323890i \(0.895009\pi\)
\(500\) −88782.9 + 153776.i −0.0158820 + 0.0275084i
\(501\) −3.41126e6 + 5.90848e6i −0.607185 + 1.05167i
\(502\) 30143.8 + 52210.7i 0.00533875 + 0.00924698i
\(503\) −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
\(506\) 530531. + 918907.i 0.0921159 + 0.159549i
\(507\) 1.44292e6 2.49920e6i 0.249299 0.431799i
\(508\) −469945. + 813968.i −0.0807956 + 0.139942i
\(509\) −5.29453e6 9.17040e6i −0.905802 1.56889i −0.819837 0.572596i \(-0.805936\pi\)
−0.0859643 0.996298i \(-0.527397\pi\)
\(510\) 2.10972e6 0.359170
\(511\) 0 0
\(512\) 3.52190e6 0.593747
\(513\) −2.91593e6 5.05055e6i −0.489198 0.847315i
\(514\) −1.86819e6 + 3.23580e6i −0.311899 + 0.540225i
\(515\) 1.16660e6 2.02061e6i 0.193822 0.335709i
\(516\) −168069. 291105.i −0.0277885 0.0481310i
\(517\) 539357. 0.0887462
\(518\) 0 0
\(519\) 2.51222e6 0.409392
\(520\) 1.14077e6 + 1.97588e6i 0.185008 + 0.320443i
\(521\) −2.27232e6 + 3.93578e6i −0.366755 + 0.635238i −0.989056 0.147540i \(-0.952865\pi\)
0.622301 + 0.782778i \(0.286198\pi\)
\(522\) −3.89610e6 + 6.74825e6i −0.625827 + 1.08396i
\(523\) −2.63599e6 4.56566e6i −0.421394 0.729877i 0.574682 0.818377i \(-0.305126\pi\)
−0.996076 + 0.0885004i \(0.971793\pi\)
\(524\) 3.02772e6 0.481711
\(525\) 0 0
\(526\) −2.49373e6 −0.392993
\(527\) −476504. 825330.i −0.0747378 0.129450i
\(528\) 2.26250e6 3.91877e6i 0.353187 0.611737i
\(529\) 3.12756e6 5.41709e6i 0.485921 0.841641i
\(530\) 2.69624e6 + 4.67003e6i 0.416936 + 0.722154i
\(531\) −4.19407e6 −0.645504
\(532\) 0 0
\(533\) −2.05048e6 −0.312635
\(534\) 1.55601e6 + 2.69509e6i 0.236135 + 0.408997i
\(535\) −3.50676e6 + 6.07389e6i −0.529690 + 0.917451i
\(536\) 1.31037e6 2.26963e6i 0.197008 0.341227i
\(537\) −702052. 1.21599e6i −0.105059 0.181968i
\(538\) −3.39647e6 −0.505908
\(539\) 0 0
\(540\) −5.61945e6 −0.829296
\(541\) −2.96723e6 5.13939e6i −0.435871 0.754950i 0.561496 0.827480i \(-0.310226\pi\)
−0.997366 + 0.0725298i \(0.976893\pi\)
\(542\) −3.46209e6 + 5.99652e6i −0.506221 + 0.876801i
\(543\) 1.54390e6 2.67412e6i 0.224709 0.389208i
\(544\) 1.09120e6 + 1.89001e6i 0.158091 + 0.273821i
\(545\) 1.76122e7 2.53994
\(546\) 0 0
\(547\) −8.82017e6 −1.26040 −0.630200 0.776433i \(-0.717027\pi\)
−0.630200 + 0.776433i \(0.717027\pi\)
\(548\) −256673. 444571.i −0.0365115 0.0632397i
\(549\) 3.28687e6 5.69302e6i 0.465427 0.806143i
\(550\) −4.04705e6 + 7.00970e6i −0.570469 + 0.988081i
\(551\) −5.85712e6 1.01448e7i −0.821874 1.42353i
\(552\) 420590. 0.0587505
\(553\) 0 0
\(554\) 6.86124e6 0.949791
\(555\) −297653. 515550.i −0.0410183 0.0710458i
\(556\) 3.05538e6 5.29207e6i 0.419158 0.726004i
\(557\) 591120. 1.02385e6i 0.0807304 0.139829i −0.822833 0.568283i \(-0.807608\pi\)
0.903564 + 0.428453i \(0.140941\pi\)
\(558\) 1.28896e6 + 2.23254e6i 0.175248 + 0.303538i
\(559\) 535306. 0.0724556
\(560\) 0 0
\(561\) 1.31309e6 0.176151
\(562\) 1.12734e6 + 1.95261e6i 0.150561 + 0.260780i
\(563\) 2.03870e6 3.53114e6i 0.271071 0.469509i −0.698065 0.716034i \(-0.745955\pi\)
0.969136 + 0.246525i \(0.0792888\pi\)
\(564\) −140362. + 243114.i −0.0185803 + 0.0321820i
\(565\) −1.58321e6 2.74219e6i −0.208649 0.361391i
\(566\) −1.25514e7 −1.64684
\(567\) 0 0
\(568\) 1.40990e6 0.183366
\(569\) −4.08807e6 7.08075e6i −0.529344 0.916851i −0.999414 0.0342216i \(-0.989105\pi\)
0.470070 0.882629i \(-0.344229\pi\)
\(570\) 4.28964e6 7.42987e6i 0.553010 0.957842i
\(571\) −1.65307e6 + 2.86321e6i −0.212179 + 0.367504i −0.952396 0.304863i \(-0.901389\pi\)
0.740217 + 0.672368i \(0.234723\pi\)
\(572\) −932292. 1.61478e6i −0.119141 0.206359i
\(573\) 2.29377e6 0.291852
\(574\) 0 0
\(575\) −1.38247e6 −0.174376
\(576\) −67718.3 117291.i −0.00850452 0.0147303i
\(577\) −3.57497e6 + 6.19203e6i −0.447026 + 0.774272i −0.998191 0.0601245i \(-0.980850\pi\)
0.551165 + 0.834396i \(0.314184\pi\)
\(578\) 4.54324e6 7.86913e6i 0.565648 0.979731i
\(579\) 3.38970e6 + 5.87112e6i 0.420208 + 0.727821i
\(580\) −1.12876e7 −1.39325
\(581\) 0 0
\(582\) −7.38232e6 −0.903411
\(583\) 1.67813e6 + 2.90661e6i 0.204482 + 0.354173i
\(584\) 3.43418e6 5.94818e6i 0.416669 0.721692i
\(585\) 1.64548e6 2.85005e6i 0.198794 0.344321i
\(586\) 5.81309e6 + 1.00686e7i 0.699300 + 1.21122i
\(587\) −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
\(590\) −8.38886e6 1.45299e7i −0.992139 1.71844i
\(591\) 6466.87 11200.9i 0.000761597 0.00131912i
\(592\) 471621. 816872.i 0.0553081 0.0957965i
\(593\) 3.31980e6 + 5.75006e6i 0.387682 + 0.671484i 0.992137 0.125154i \(-0.0399426\pi\)
−0.604456 + 0.796639i \(0.706609\pi\)
\(594\) −9.65871e6 −1.12319
\(595\) 0 0
\(596\) −6.45569e6 −0.744435
\(597\) 1.85976e6 + 3.22119e6i 0.213560 + 0.369897i
\(598\) 439742. 761655.i 0.0502857 0.0870974i
\(599\) 1.62096e6 2.80758e6i 0.184588 0.319716i −0.758849 0.651266i \(-0.774238\pi\)
0.943438 + 0.331550i \(0.107572\pi\)
\(600\) 1.60420e6 + 2.77855e6i 0.181919 + 0.315094i
\(601\) 5.65076e6 0.638147 0.319074 0.947730i \(-0.396628\pi\)
0.319074 + 0.947730i \(0.396628\pi\)
\(602\) 0 0
\(603\) −3.78023e6 −0.423375
\(604\) 3.25887e6 + 5.64453e6i 0.363475 + 0.629557i
\(605\) 1.48539e6 2.57277e6i 0.164988 0.285767i
\(606\) 1.02480e6 1.77500e6i 0.113359 0.196343i
\(607\) 117837. + 204100.i 0.0129811 + 0.0224839i 0.872443 0.488716i \(-0.162535\pi\)
−0.859462 + 0.511200i \(0.829201\pi\)
\(608\) 8.87478e6 0.973641
\(609\) 0 0
\(610\) 2.62972e7 2.86144
\(611\) −223529. 387163.i −0.0242231 0.0419557i
\(612\) 475080. 822863.i 0.0512729 0.0888073i
\(613\) −394438. + 683187.i −0.0423963 + 0.0734325i −0.886445 0.462834i \(-0.846833\pi\)
0.844049 + 0.536267i \(0.180166\pi\)
\(614\) −1.65358e6 2.86408e6i −0.177012 0.306595i
\(615\) −5.65820e6 −0.603240
\(616\) 0 0
\(617\) 1.67739e7 1.77387 0.886935 0.461894i \(-0.152830\pi\)
0.886935 + 0.461894i \(0.152830\pi\)
\(618\) 1.04364e6 + 1.80763e6i 0.109921 + 0.190388i
\(619\) 4.11150e6 7.12132e6i 0.431294 0.747023i −0.565691 0.824617i \(-0.691390\pi\)
0.996985 + 0.0775941i \(0.0247238\pi\)
\(620\) −1.86714e6 + 3.23399e6i −0.195074 + 0.337878i
\(621\) −824854. 1.42869e6i −0.0858318 0.148665i
\(622\) 1.72675e7 1.78959
\(623\) 0 0
\(624\) −3.75065e6 −0.385607
\(625\) 4.68399e6 + 8.11290e6i 0.479640 + 0.830761i
\(626\) 8.57346e6 1.48497e7i 0.874420 1.51454i
\(627\) 2.66986e6 4.62433e6i 0.271218 0.469764i
\(628\) 4.16818e6 + 7.21949e6i 0.421742 + 0.730479i
\(629\) 273714. 0.0275849
\(630\) 0 0
\(631\) −5.94507e6 −0.594406 −0.297203 0.954814i \(-0.596054\pi\)
−0.297203 + 0.954814i \(0.596054\pi\)
\(632\) −1.32702e6 2.29846e6i −0.132155 0.228899i
\(633\) −2.53162e6 + 4.38490e6i −0.251125 + 0.434961i
\(634\) −6.64403e6 + 1.15078e7i −0.656460 + 1.13702i
\(635\) −2.06515e6 3.57695e6i −0.203244 0.352029i
\(636\) −1.74687e6 −0.171245
\(637\) 0 0
\(638\) −1.94011e7 −1.88701
\(639\) −1.01684e6 1.76122e6i −0.0985144 0.170632i
\(640\) −7.26120e6 + 1.25768e7i −0.700743 + 1.21372i
\(641\) 5.33804e6 9.24576e6i 0.513141 0.888786i −0.486743 0.873545i \(-0.661815\pi\)
0.999884 0.0152411i \(-0.00485157\pi\)
\(642\) −3.13715e6 5.43371e6i −0.300399 0.520306i
\(643\) 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
\(646\) 1.97232e6 + 3.41616e6i 0.185950 + 0.322075i
\(647\) −2.46728e6 + 4.27346e6i −0.231717 + 0.401346i −0.958314 0.285719i \(-0.907768\pi\)
0.726596 + 0.687065i \(0.241101\pi\)
\(648\) −231615. + 401168.i −0.0216685 + 0.0375309i
\(649\) −5.22120e6 9.04339e6i −0.486585 0.842790i
\(650\) 6.70897e6 0.622834
\(651\) 0 0
\(652\) 9.12710e6 0.840841
\(653\) −2.86112e6 4.95561e6i −0.262575 0.454793i 0.704351 0.709852i \(-0.251238\pi\)
−0.966925 + 0.255059i \(0.917905\pi\)
\(654\) −7.87794e6 + 1.36450e7i −0.720226 + 1.24747i
\(655\) −6.65258e6 + 1.15226e7i −0.605881 + 1.04942i
\(656\) −4.48261e6 7.76411e6i −0.406698 0.704421i
\(657\) −9.90710e6 −0.895433
\(658\) 0 0
\(659\) 362477. 0.0325137 0.0162569 0.999868i \(-0.494825\pi\)
0.0162569 + 0.999868i \(0.494825\pi\)
\(660\) −2.57261e6 4.45590e6i −0.229887 0.398176i
\(661\) −9.56053e6 + 1.65593e7i −0.851096 + 1.47414i 0.0291249 + 0.999576i \(0.490728\pi\)
−0.880220 + 0.474565i \(0.842605\pi\)
\(662\) 3.83566e6 6.64356e6i 0.340170 0.589191i
\(663\) −544190. 942564.i −0.0480802 0.0832774i
\(664\) −7.81494e6 −0.687868
\(665\) 0 0
\(666\) −740404. −0.0646819
\(667\) −1.65685e6 2.86975e6i −0.144201 0.249764i
\(668\) −6.14587e6 + 1.06450e7i −0.532896 + 0.923003i
\(669\) −5.91495e6 + 1.02450e7i −0.510958 + 0.885006i
\(670\) −7.56111e6 1.30962e7i −0.650727 1.12709i
\(671\) 1.63673e7 1.40337
\(672\) 0 0
\(673\) −573374. −0.0487978 −0.0243989 0.999702i \(-0.507767\pi\)
−0.0243989 + 0.999702i \(0.507767\pi\)
\(674\) 9.18864e6 + 1.59152e7i 0.779115 + 1.34947i
\(675\) 6.29224e6 1.08985e7i 0.531552 0.920675i
\(676\) 2.59962e6 4.50267e6i 0.218798 0.378968i
\(677\) 5.84516e6 + 1.01241e7i 0.490146 + 0.848957i 0.999936 0.0113419i \(-0.00361030\pi\)
−0.509790 + 0.860299i \(0.670277\pi\)
\(678\) 2.83267e6 0.236659
\(679\) 0 0
\(680\) −2.89473e6 −0.240069
\(681\) −4.58846e6 7.94744e6i −0.379139 0.656689i
\(682\) −3.20925e6 + 5.55858e6i −0.264206 + 0.457618i
\(683\) −9.18370e6 + 1.59066e7i −0.753297 + 1.30475i 0.192920 + 0.981214i \(0.438204\pi\)
−0.946217 + 0.323534i \(0.895129\pi\)
\(684\) −1.93193e6 3.34620e6i −0.157889 0.273471i
\(685\) 2.25588e6 0.183692
\(686\) 0 0
\(687\) −5.26244e6 −0.425398
\(688\) 1.17025e6 + 2.02693e6i 0.0942554 + 0.163255i
\(689\) 1.39096e6 2.40921e6i 0.111626 0.193342i
\(690\) 1.21344e6 2.10175e6i 0.0970280 0.168057i
\(691\) 1.17806e7 + 2.04045e7i 0.938579 + 1.62567i 0.768125 + 0.640300i \(0.221190\pi\)
0.170454 + 0.985366i \(0.445477\pi\)
\(692\) 4.52612e6 0.359303
\(693\) 0 0
\(694\) −1.32484e7 −1.04415
\(695\) 1.34267e7 + 2.32558e7i 1.05441 + 1.82629i
\(696\) −3.84516e6 + 6.66001e6i −0.300878 + 0.521137i
\(697\) 1.30078e6 2.25303e6i 0.101420 0.175665i
\(698\) −5.72587e6 9.91750e6i −0.444839 0.770484i
\(699\) −1.05142e7 −0.813921
\(700\) 0 0
\(701\) 1.32980e7 1.02210 0.511048 0.859552i \(-0.329257\pi\)
0.511048 + 0.859552i \(0.329257\pi\)
\(702\) 4.00291e6 + 6.93325e6i 0.306573 + 0.530999i
\(703\) 556535. 963946.i 0.0424721 0.0735639i
\(704\) 168605. 292033.i 0.0128215 0.0222075i
\(705\) −616815. 1.06836e6i −0.0467393 0.0809549i
\(706\) 4.09600e6 0.309277
\(707\) 0 0
\(708\) 5.43506e6 0.407494
\(709\) 3.42677e6 + 5.93533e6i 0.256017 + 0.443434i 0.965171 0.261619i \(-0.0842564\pi\)
−0.709154 + 0.705053i \(0.750923\pi\)
\(710\) 4.06770e6 7.04547e6i 0.302833 0.524522i
\(711\) −1.91412e6 + 3.31536e6i −0.142003 + 0.245956i
\(712\) −2.13499e6 3.69791e6i −0.157832 0.273374i
\(713\) −1.09628e6 −0.0807602
\(714\) 0 0
\(715\) 8.19384e6 0.599408
\(716\) −1.26485e6 2.19078e6i −0.0922051 0.159704i
\(717\) 7.73587e6 1.33989e7i 0.561968 0.973357i
\(718\) 6.97008e6 1.20725e7i 0.504576 0.873951i
\(719\) 1.32865e7 + 2.30128e7i 0.958490 + 1.66015i 0.726172 + 0.687513i \(0.241298\pi\)
0.232318 + 0.972640i \(0.425369\pi\)
\(720\) 1.43889e7 1.03442
\(721\) 0 0
\(722\) −1.49658e6 −0.106846
\(723\) −5.07958e6 8.79810e6i −0.361395 0.625955i
\(724\) 2.78156e6 4.81781e6i 0.197216 0.341588i
\(725\) 1.26390e7 2.18913e7i 0.893031 1.54678i
\(726\) 1.32883e6 + 2.30160e6i 0.0935680 + 0.162065i
\(727\) −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
\(730\) −1.98159e7 3.43221e7i −1.37628 2.38379i
\(731\) −339587. + 588182.i −0.0235049 + 0.0407116i
\(732\) −4.25943e6 + 7.37755e6i −0.293815 + 0.508902i
\(733\) −8.73265e6 1.51254e7i −0.600324 1.03979i −0.992772 0.120018i \(-0.961705\pi\)
0.392447 0.919774i \(-0.371628\pi\)
\(734\) −1.54016e7 −1.05518
\(735\) 0 0
\(736\) 2.51048e6 0.170829
\(737\) −4.70602e6 8.15106e6i −0.319143 0.552771i
\(738\) −3.51865e6 + 6.09449e6i −0.237813 + 0.411904i
\(739\) 6.82304e6 1.18178e7i 0.459586 0.796026i −0.539353 0.842080i \(-0.681331\pi\)
0.998939 + 0.0460536i \(0.0146645\pi\)
\(740\) −536264. 928836.i −0.0359997 0.0623533i
\(741\) −4.42594e6 −0.296114
\(742\) 0 0
\(743\) 1.48965e7 0.989944 0.494972 0.868909i \(-0.335178\pi\)
0.494972 + 0.868909i \(0.335178\pi\)
\(744\) 1.27210e6 + 2.20334e6i 0.0842538 + 0.145932i
\(745\) 1.41846e7 2.45685e7i 0.936326 1.62176i
\(746\) −4.90396e6 + 8.49390e6i −0.322626 + 0.558805i
\(747\) 5.63623e6 + 9.76224e6i 0.369562 + 0.640100i
\(748\) 2.36571e6 0.154599
\(749\) 0 0
\(750\) 698061. 0.0453148
\(751\) 1.26731e7 + 2.19505e7i 0.819944 + 1.42019i 0.905723 + 0.423871i \(0.139329\pi\)
−0.0857783 + 0.996314i \(0.527338\pi\)
\(752\) 977324. 1.69277e6i 0.0630222 0.109158i
\(753\) 42911.7 74325.2i 0.00275796 0.00477693i
\(754\) 8.04049e6 + 1.39265e7i 0.515056 + 0.892102i
\(755\) −2.86419e7 −1.82867
\(756\) 0 0
\(757\) −2.66725e7 −1.69170 −0.845852 0.533417i \(-0.820908\pi\)
−0.845852 + 0.533417i \(0.820908\pi\)
\(758\) −1.19412e7 2.06828e7i −0.754875 1.30748i
\(759\) 755245. 1.30812e6i 0.0475864 0.0824221i
\(760\) −5.88577e6 + 1.01945e7i −0.369632 + 0.640221i
\(761\) 289914. + 502146.i 0.0181471 + 0.0314318i 0.874956 0.484202i \(-0.160890\pi\)
−0.856809 + 0.515634i \(0.827557\pi\)
\(762\) 3.69497e6 0.230528
\(763\) 0 0
\(764\) 4.13255e6 0.256144
\(765\) 2.08772e6 + 3.61604e6i 0.128979 + 0.223398i
\(766\) 1.16179e7 2.01227e7i 0.715408 1.23912i
\(767\) −4.32770e6 + 7.49580e6i −0.265625 + 0.460076i
\(768\) −6.65046e6 1.15189e7i −0.406864 0.704708i
\(769\)