Properties

Label 49.6.c.f.30.1
Level $49$
Weight $6$
Character 49.30
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 30.1
Root \(1.77069 - 3.06693i\) of defining polynomial
Character \(\chi\) \(=\) 49.30
Dual form 49.6.c.f.18.1

$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

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

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 0.362306 + 0.932059i \(0.381989\pi\)
−0.988340 + 0.152263i \(0.951344\pi\)
\(3\) −5.04138 8.73193i −0.323405 0.560153i 0.657783 0.753207i \(-0.271494\pi\)
−0.981188 + 0.193054i \(0.938161\pi\)
\(4\) −9.08276 15.7318i −0.283836 0.491619i
\(5\) −39.9138 + 69.1328i −0.714000 + 1.23668i 0.249344 + 0.968415i \(0.419785\pi\)
−0.963344 + 0.268269i \(0.913548\pi\)
\(6\) 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 0.559128 0.829082i \(-0.311136\pi\)
−0.997570 + 0.0696781i \(0.977803\pi\)
\(12\) −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 0.777876 0.628418i \(-0.216297\pi\)
−0.933164 + 0.359451i \(0.882964\pi\)
\(18\) 500.531 + 866.946i 0.364125 + 0.630682i
\(19\) 752.463 1303.30i 0.478190 0.828250i −0.521497 0.853253i \(-0.674626\pi\)
0.999687 + 0.0250030i \(0.00795952\pi\)
\(20\) 1450.11 0.810637
\(21\) 0 0
\(22\) 2492.45 1.09792
\(23\) 212.855 368.676i 0.0839006 0.145320i −0.821022 0.570897i \(-0.806596\pi\)
0.904922 + 0.425577i \(0.139929\pi\)
\(24\) 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 0.720255 0.693710i \(-0.244025\pi\)
−0.960898 + 0.276904i \(0.910692\pi\)
\(32\) 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 −0.887376 0.461047i \(-0.847474\pi\)
0.842966 + 0.537966i \(0.180807\pi\)
\(38\) 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 −0.890217 0.455536i \(-0.849448\pi\)
0.839614 + 0.543183i \(0.182781\pi\)
\(48\) −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 0.958746 0.284265i \(-0.0917497\pi\)
−0.725554 + 0.688165i \(0.758416\pi\)
\(54\) 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 −0.997911 0.0646022i \(-0.979422\pi\)
0.443008 0.896517i \(-0.353911\pi\)
\(60\) −7310.56 12662.3i −0.262164 0.454081i
\(61\) −23255.4 + 40279.5i −0.800201 + 1.38599i 0.119282 + 0.992860i \(0.461941\pi\)
−0.919483 + 0.393129i \(0.871393\pi\)
\(62\) 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 0.624656 0.780900i \(-0.285239\pi\)
−0.988607 + 0.150518i \(0.951906\pi\)
\(68\) −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 −0.937697 0.347453i \(-0.887047\pi\)
0.167946 0.985796i \(-0.446287\pi\)
\(74\) −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 −0.717748 0.696303i \(-0.754827\pi\)
0.961890 + 0.273436i \(0.0881601\pi\)
\(80\) 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 −0.682605 0.730788i \(-0.739153\pi\)
0.974183 + 0.225759i \(0.0724862\pi\)
\(90\) −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 0.927487 0.373855i \(-0.121964\pi\)
−0.787512 + 0.616300i \(0.788631\pi\)
\(102\) −13214.2 22887.7i −0.125760 0.217822i
\(103\) 14614.0 25312.1i 0.135730 0.235091i −0.790146 0.612918i \(-0.789995\pi\)
0.925876 + 0.377828i \(0.123329\pi\)
\(104\) −28580.9 −0.259115
\(105\) 0 0
\(106\) −67551.6 −0.583944
\(107\) −43929.2 + 76087.6i −0.370932 + 0.642472i −0.989709 0.143094i \(-0.954295\pi\)
0.618778 + 0.785566i \(0.287628\pi\)
\(108\) 35197.4 + 60963.7i 0.290370 + 0.502935i
\(109\) −110314. 191069.i −0.889333 1.54037i −0.840665 0.541555i \(-0.817836\pi\)
−0.0486678 0.998815i \(-0.515498\pi\)
\(110\) −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 −0.996353 0.0853215i \(-0.972808\pi\)
0.572067 + 0.820207i \(0.306142\pi\)
\(132\) 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 0.832073 0.554666i \(-0.187154\pi\)
−0.896391 + 0.443264i \(0.853820\pi\)
\(138\) 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 −0.326030 0.945360i \(-0.605711\pi\)
0.981720 0.190330i \(-0.0609557\pi\)
\(150\) −115956. 200842.i −0.420791 0.728832i
\(151\) 179399. + 310727.i 0.640290 + 1.10901i 0.985368 + 0.170441i \(0.0545191\pi\)
−0.345078 + 0.938574i \(0.612148\pi\)
\(152\) −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 0.951155 + 0.308714i \(0.0998986\pi\)
−0.208223 + 0.978081i \(0.566768\pi\)
\(158\) 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 0.211618 + 0.977353i \(0.432127\pi\)
−0.952221 + 0.305410i \(0.901206\pi\)
\(164\) 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 −0.979749 0.200230i \(-0.935831\pi\)
0.663279 + 0.748373i \(0.269164\pi\)
\(174\) −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 0.773312 0.634026i \(-0.218599\pi\)
−0.935738 + 0.352695i \(0.885265\pi\)
\(180\) 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 −0.956502 0.291726i \(-0.905770\pi\)
0.730893 + 0.682492i \(0.239104\pi\)
\(192\) 4830.89 + 8367.34i 0.00945744 + 0.0163808i
\(193\) 336187. + 582293.i 0.649663 + 1.12525i 0.983203 + 0.182513i \(0.0584231\pi\)
−0.333541 + 0.942736i \(0.608244\pi\)
\(194\) 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 0.982546 0.186020i \(-0.0595591\pi\)
−0.652371 + 0.757900i \(0.726226\pi\)
\(200\) 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 −0.994729 0.102542i \(-0.967302\pi\)
0.408560 0.912731i \(-0.366031\pi\)
\(228\) 137820. + 238711.i 0.175580 + 0.304114i
\(229\) 260962. 452000.i 0.328843 0.569573i −0.653439 0.756979i \(-0.726675\pi\)
0.982283 + 0.187406i \(0.0600079\pi\)
\(230\) −240697. −0.300020
\(231\) 0 0
\(232\) 762719. 0.930346
\(233\) 521394. 903081.i 0.629182 1.08977i −0.358535 0.933516i \(-0.616723\pi\)
0.987716 0.156258i \(-0.0499432\pi\)
\(234\) 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 −0.997602 0.0692059i \(-0.977953\pi\)
0.438867 0.898552i \(-0.355380\pi\)
\(242\) 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 −0.963278 0.268505i \(-0.913470\pi\)
0.714171 + 0.699971i \(0.246804\pi\)
\(258\) 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 0.933763 0.357892i \(-0.116504\pi\)
−0.776825 + 0.629716i \(0.783171\pi\)
\(264\) 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 0.949182 0.314727i \(-0.101913\pi\)
−0.747153 + 0.664652i \(0.768580\pi\)
\(270\) 1.09552e6 + 1.89749e6i 0.914554 + 1.58405i
\(271\) −488805. + 846636.i −0.404308 + 0.700283i −0.994241 0.107170i \(-0.965821\pi\)
0.589932 + 0.807453i \(0.299154\pi\)
\(272\) −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 0.611670 0.791113i \(-0.290498\pi\)
−0.990959 + 0.134165i \(0.957165\pi\)
\(278\) 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 0.981223 + 0.192875i \(0.0617812\pi\)
−0.323577 + 0.946202i \(0.604885\pi\)
\(284\) 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 −0.963093 0.269169i \(-0.913251\pi\)
0.248439 0.968647i \(-0.420082\pi\)
\(312\) 144087. + 249566.i 0.0837990 + 0.145144i
\(313\) 1.21047e6 2.09659e6i 0.698381 1.20963i −0.270646 0.962679i \(-0.587237\pi\)
0.969028 0.246953i \(-0.0794293\pi\)
\(314\) −3.25035e6 −1.86040
\(315\) 0 0
\(316\) −492028. −0.277186
\(317\) −938057. + 1.62476e6i −0.524301 + 0.908116i 0.475298 + 0.879825i \(0.342340\pi\)
−0.999600 + 0.0282918i \(0.990993\pi\)
\(318\) 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 −0.697607 0.716480i \(-0.745752\pi\)
0.969294 + 0.245906i \(0.0790853\pi\)
\(332\) −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 0.995633 0.0933518i \(-0.0297581\pi\)
−0.578662 + 0.815568i \(0.696425\pi\)
\(348\) 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 0.797642 0.603132i \(-0.206081\pi\)
−0.921148 + 0.389212i \(0.872747\pi\)
\(354\) −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 −0.591092 0.806604i \(-0.701303\pi\)
0.994086 + 0.108598i \(0.0346362\pi\)
\(360\) −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 0.996074 0.0885223i \(-0.0282144\pi\)
−0.574700 + 0.818364i \(0.694881\pi\)
\(368\) −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 −0.965619 0.259963i \(-0.916290\pi\)
0.707944 + 0.706269i \(0.249623\pi\)
\(374\) −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 −0.425043 0.905173i \(-0.639741\pi\)
0.996424 0.0844886i \(-0.0269257\pi\)
\(384\) 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 0.999975 0.00703108i \(-0.00223808\pi\)
−0.506077 + 0.862488i \(0.668905\pi\)
\(390\) −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 −0.871487 0.490418i \(-0.836844\pi\)
0.860458 + 0.509521i \(0.170177\pi\)
\(398\) −2.61282e6 −0.826802
\(399\) 0 0
\(400\) −4.14151e6 −1.29422
\(401\) 1.67393e6 2.89933e6i 0.519848 0.900404i −0.479886 0.877331i \(-0.659322\pi\)
0.999734 0.0230725i \(-0.00734485\pi\)
\(402\) −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 0.996908 0.0785754i \(-0.0250371\pi\)
−0.566502 + 0.824060i \(0.691704\pi\)
\(410\) 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 −0.670592 0.741826i \(-0.733960\pi\)
−0.307144 0.951663i \(-0.599373\pi\)
\(432\) −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 −0.855430 0.517918i \(-0.826707\pi\)
0.876246 + 0.481865i \(0.160040\pi\)
\(440\) −2.75259e6 −0.677814
\(441\) 0 0
\(442\) 764546. 0.186143
\(443\) 1.42076e6 2.46082e6i 0.343962 0.595760i −0.641203 0.767372i \(-0.721564\pi\)
0.985165 + 0.171612i \(0.0548975\pi\)
\(444\) −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 −0.939953 0.341303i \(-0.889132\pi\)
0.765554 + 0.643372i \(0.222465\pi\)
\(458\) 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 −0.458800 0.888540i \(-0.651720\pi\)
0.998898 0.0469376i \(-0.0149462\pi\)
\(468\) −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 −0.900752 0.434334i \(-0.856984\pi\)
0.0742312 0.997241i \(-0.476350\pi\)
\(480\) 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 −0.902055 0.431621i \(-0.857942\pi\)
0.0772330 0.997013i \(-0.475391\pi\)
\(488\) 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 −0.946095 0.323890i \(-0.895009\pi\)
0.753544 + 0.657397i \(0.228343\pi\)
\(500\) −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 −0.0859643 + 0.996298i \(0.527397\pi\)
−0.819837 + 0.572596i \(0.805936\pi\)
\(510\) 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 0.622301 0.782778i \(-0.286198\pi\)
−0.989056 + 0.147540i \(0.952865\pi\)
\(522\) −3.89610e6 6.74825e6i −0.625827 1.08396i
\(523\) −2.63599e6 + 4.56566e6i −0.421394 + 0.729877i −0.996076 0.0885004i \(-0.971793\pi\)
0.574682 + 0.818377i \(0.305126\pi\)
\(524\) 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 −0.997366 0.0725298i \(-0.976893\pi\)
0.561496 + 0.827480i \(0.310226\pi\)
\(542\) −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 0.903564 0.428453i \(-0.140941\pi\)
−0.822833 + 0.568283i \(0.807608\pi\)
\(558\) 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 0.969136 0.246525i \(-0.0792888\pi\)
−0.698065 + 0.716034i \(0.745955\pi\)
\(564\) −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 0.470070 + 0.882629i \(0.344229\pi\)
−0.999414 + 0.0342216i \(0.989105\pi\)
\(570\) 4.28964e6 + 7.42987e6i 0.553010 + 0.957842i
\(571\) −1.65307e6 2.86321e6i −0.212179 0.367504i 0.740217 0.672368i \(-0.234723\pi\)
−0.952396 + 0.304863i \(0.901389\pi\)
\(572\) −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 0.551165 0.834396i \(-0.314184\pi\)
−0.998191 + 0.0601245i \(0.980850\pi\)
\(578\) 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 −0.604456 0.796639i \(-0.706609\pi\)
0.992137 + 0.125154i \(0.0399426\pi\)
\(594\) −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 0.943438 0.331550i \(-0.107572\pi\)
−0.758849 + 0.651266i \(0.774238\pi\)
\(600\) 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 −0.859462 0.511200i \(-0.829201\pi\)
0.872443 + 0.488716i \(0.162535\pi\)
\(608\) 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 0.844049 0.536267i \(-0.180166\pi\)
−0.886445 + 0.462834i \(0.846833\pi\)
\(614\) −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 0.996985 0.0775941i \(-0.0247238\pi\)
−0.565691 + 0.824617i \(0.691390\pi\)
\(620\) −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 0.999884 + 0.0152411i \(0.00485157\pi\)
−0.486743 + 0.873545i \(0.661815\pi\)
\(642\) −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 0.726596 0.687065i \(-0.241101\pi\)
−0.958314 + 0.285719i \(0.907768\pi\)
\(648\) −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 −0.966925 0.255059i \(-0.917905\pi\)
0.704351 + 0.709852i \(0.251238\pi\)
\(654\) −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 −0.880220 0.474565i \(-0.842605\pi\)
0.0291249 0.999576i \(-0.490728\pi\)
\(662\) 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 −0.509790 0.860299i \(-0.670277\pi\)
0.999936 + 0.0113419i \(0.00361030\pi\)
\(678\) 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 −0.946217 0.323534i \(-0.895129\pi\)
0.192920 0.981214i \(-0.438204\pi\)
\(684\) −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 0.170454 0.985366i \(-0.445477\pi\)
0.768125 0.640300i \(-0.221190\pi\)
\(692\) 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 −0.709154 0.705053i \(-0.750923\pi\)
0.965171 + 0.261619i \(0.0842564\pi\)
\(710\) 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 0.232318 0.972640i \(-0.425369\pi\)
0.726172 0.687513i \(-0.241298\pi\)
\(720\) 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 0.392447 + 0.919774i \(0.371628\pi\)
−0.992772 + 0.120018i \(0.961705\pi\)
\(734\) −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 0.998939 0.0460536i \(-0.0146645\pi\)
−0.539353 + 0.842080i \(0.681331\pi\)
\(740\) −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 −0.0857783 0.996314i \(-0.527338\pi\)
0.905723 0.423871i \(-0.139329\pi\)
\(752\) 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 −0.856809 0.515634i \(-0.827557\pi\)
0.874956 + 0.484202i \(0.160890\pi\)
\(762\) 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
\(769\)