Properties

Label 69.7.h.a.2.14
Level $69$
Weight $7$
Character 69.2
Analytic conductor $15.874$
Analytic rank $0$
Dimension $460$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,7,Mod(2,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 2]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.h (of order \(22\), degree \(10\), 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: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(460\)
Relative dimension: \(46\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 2.14
Character \(\chi\) \(=\) 69.2
Dual form 69.7.h.a.35.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.82614 + 5.95359i) q^{2} +(11.8375 + 24.2667i) q^{3} +(5.78070 + 12.6580i) q^{4} +(-31.2078 + 106.284i) q^{5} +(-189.766 - 22.3724i) q^{6} +(23.3861 - 26.9890i) q^{7} +(-545.799 - 78.4740i) q^{8} +(-448.748 + 574.514i) q^{9} +O(q^{10})\) \(q+(-3.82614 + 5.95359i) q^{2} +(11.8375 + 24.2667i) q^{3} +(5.78070 + 12.6580i) q^{4} +(-31.2078 + 106.284i) q^{5} +(-189.766 - 22.3724i) q^{6} +(23.3861 - 26.9890i) q^{7} +(-545.799 - 78.4740i) q^{8} +(-448.748 + 574.514i) q^{9} +(-513.366 - 592.456i) q^{10} +(-223.431 - 347.665i) q^{11} +(-238.738 + 290.117i) q^{12} +(1752.51 + 2022.51i) q^{13} +(71.2030 + 242.495i) q^{14} +(-2948.59 + 500.824i) q^{15} +(1972.29 - 2276.14i) q^{16} +(-4125.39 - 1884.00i) q^{17} +(-1703.44 - 4869.83i) q^{18} +(3513.30 + 7693.06i) q^{19} +(-1525.74 + 219.369i) q^{20} +(931.769 + 248.023i) q^{21} +2924.73 q^{22} +(7428.56 - 9636.00i) q^{23} +(-4556.57 - 14173.7i) q^{24} +(2822.20 + 1813.72i) q^{25} +(-18746.5 + 2695.35i) q^{26} +(-19253.6 - 4088.86i) q^{27} +(476.815 + 140.005i) q^{28} +(-9105.81 - 4158.48i) q^{29} +(8300.01 - 19470.9i) q^{30} +(7807.69 - 54303.7i) q^{31} +(-3937.46 - 13409.8i) q^{32} +(5791.83 - 9537.40i) q^{33} +(27000.9 - 17352.4i) q^{34} +(2138.68 + 3327.85i) q^{35} +(-9866.25 - 2359.15i) q^{36} +(-23544.2 + 6913.21i) q^{37} +(-59243.7 - 8517.95i) q^{38} +(-28334.3 + 66469.2i) q^{39} +(25373.7 - 55560.7i) q^{40} +(-11408.0 + 38852.1i) q^{41} +(-5041.70 + 4598.40i) q^{42} +(518.663 + 3607.38i) q^{43} +(3109.14 - 4837.92i) q^{44} +(-47057.2 - 65624.1i) q^{45} +(28946.1 + 81095.2i) q^{46} +3012.91i q^{47} +(78581.5 + 20917.2i) q^{48} +(16561.7 + 115189. i) q^{49} +(-21596.3 + 9862.68i) q^{50} +(-3115.63 - 122411. i) q^{51} +(-15470.1 + 33874.8i) q^{52} +(138532. + 120038. i) q^{53} +(98010.4 - 98983.5i) q^{54} +(43924.0 - 12897.3i) q^{55} +(-14882.1 + 12895.4i) q^{56} +(-145097. + 176323. i) q^{57} +(59598.0 - 38301.3i) q^{58} +(-21168.4 + 18342.5i) q^{59} +(-23384.3 - 34428.0i) q^{60} +(-28439.2 + 197799. i) q^{61} +(293428. + 254257. i) q^{62} +(5011.09 + 25546.9i) q^{63} +(279847. + 82170.5i) q^{64} +(-269653. + 123146. i) q^{65} +(34621.4 + 70973.6i) q^{66} +(-313888. - 201724. i) q^{67} -63109.9i q^{68} +(321769. + 66200.9i) q^{69} -27995.5 q^{70} +(-217872. + 339015. i) q^{71} +(290011. - 278354. i) q^{72} +(53852.9 + 117921. i) q^{73} +(48925.1 - 166624. i) q^{74} +(-10605.3 + 89955.4i) q^{75} +(-77069.1 + 88942.5i) q^{76} +(-14608.3 - 2100.36i) q^{77} +(-287319. - 423011. i) q^{78} +(-466337. - 538181. i) q^{79} +(180367. + 280657. i) q^{80} +(-128691. - 515624. i) q^{81} +(-187661. - 216572. i) q^{82} +(310247. + 1.05661e6i) q^{83} +(2246.81 + 13228.0i) q^{84} +(328984. - 379668. i) q^{85} +(-23461.3 - 10714.4i) q^{86} +(-6877.01 - 270194. i) q^{87} +(94665.4 + 207288. i) q^{88} +(-154604. + 22228.8i) q^{89} +(570746. - 29072.2i) q^{90} +95570.1 q^{91} +(164914. + 38327.6i) q^{92} +(1.41020e6 - 453351. i) q^{93} +(-17937.6 - 11527.8i) q^{94} +(-927292. + 133325. i) q^{95} +(278802. - 254287. i) q^{96} +(-137859. - 40479.1i) q^{97} +(-749156. - 342128. i) q^{98} +(300002. + 27650.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{11}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.82614 + 5.95359i −0.478267 + 0.744198i −0.993620 0.112780i \(-0.964025\pi\)
0.515353 + 0.856978i \(0.327661\pi\)
\(3\) 11.8375 + 24.2667i 0.438425 + 0.898768i
\(4\) 5.78070 + 12.6580i 0.0903234 + 0.197781i
\(5\) −31.2078 + 106.284i −0.249663 + 0.850273i 0.735335 + 0.677704i \(0.237025\pi\)
−0.984997 + 0.172569i \(0.944793\pi\)
\(6\) −189.766 22.3724i −0.878546 0.103576i
\(7\) 23.3861 26.9890i 0.0681812 0.0786853i −0.720634 0.693315i \(-0.756149\pi\)
0.788815 + 0.614630i \(0.210695\pi\)
\(8\) −545.799 78.4740i −1.06601 0.153269i
\(9\) −448.748 + 574.514i −0.615567 + 0.788085i
\(10\) −513.366 592.456i −0.513366 0.592456i
\(11\) −223.431 347.665i −0.167867 0.261206i 0.747120 0.664689i \(-0.231436\pi\)
−0.914987 + 0.403483i \(0.867799\pi\)
\(12\) −238.738 + 290.117i −0.138159 + 0.167892i
\(13\) 1752.51 + 2022.51i 0.797685 + 0.920578i 0.998252 0.0591024i \(-0.0188238\pi\)
−0.200567 + 0.979680i \(0.564278\pi\)
\(14\) 71.2030 + 242.495i 0.0259486 + 0.0883729i
\(15\) −2948.59 + 500.824i −0.873656 + 0.148392i
\(16\) 1972.29 2276.14i 0.481516 0.555699i
\(17\) −4125.39 1884.00i −0.839688 0.383473i −0.0513243 0.998682i \(-0.516344\pi\)
−0.788364 + 0.615209i \(0.789071\pi\)
\(18\) −1703.44 4869.83i −0.292086 0.835019i
\(19\) 3513.30 + 7693.06i 0.512218 + 1.12160i 0.972303 + 0.233725i \(0.0750917\pi\)
−0.460085 + 0.887875i \(0.652181\pi\)
\(20\) −1525.74 + 219.369i −0.190718 + 0.0274211i
\(21\) 931.769 + 248.023i 0.100612 + 0.0267814i
\(22\) 2924.73 0.274674
\(23\) 7428.56 9636.00i 0.610550 0.791978i
\(24\) −4556.57 14173.7i −0.329613 1.02530i
\(25\) 2822.20 + 1813.72i 0.180621 + 0.116078i
\(26\) −18746.5 + 2695.35i −1.06660 + 0.153354i
\(27\) −19253.6 4088.86i −0.978185 0.207736i
\(28\) 476.815 + 140.005i 0.0217208 + 0.00637780i
\(29\) −9105.81 4158.48i −0.373357 0.170507i 0.219894 0.975524i \(-0.429429\pi\)
−0.593252 + 0.805017i \(0.702156\pi\)
\(30\) 8300.01 19470.9i 0.307408 0.721145i
\(31\) 7807.69 54303.7i 0.262082 1.82282i −0.255064 0.966924i \(-0.582097\pi\)
0.517146 0.855897i \(-0.326994\pi\)
\(32\) −3937.46 13409.8i −0.120162 0.409234i
\(33\) 5791.83 9537.40i 0.161166 0.265392i
\(34\) 27000.9 17352.4i 0.686975 0.441492i
\(35\) 2138.68 + 3327.85i 0.0498817 + 0.0776174i
\(36\) −9866.25 2359.15i −0.211468 0.0505648i
\(37\) −23544.2 + 6913.21i −0.464814 + 0.136482i −0.505750 0.862680i \(-0.668784\pi\)
0.0409358 + 0.999162i \(0.486966\pi\)
\(38\) −59243.7 8517.95i −1.07967 0.155233i
\(39\) −28334.3 + 66469.2i −0.477660 + 1.12054i
\(40\) 25373.7 55560.7i 0.396465 0.868136i
\(41\) −11408.0 + 38852.1i −0.165523 + 0.563720i 0.834398 + 0.551162i \(0.185815\pi\)
−0.999921 + 0.0125574i \(0.996003\pi\)
\(42\) −5041.70 + 4598.40i −0.0680502 + 0.0620667i
\(43\) 518.663 + 3607.38i 0.00652349 + 0.0453719i 0.992823 0.119592i \(-0.0381585\pi\)
−0.986300 + 0.164963i \(0.947249\pi\)
\(44\) 3109.14 4837.92i 0.0364991 0.0567938i
\(45\) −47057.2 65624.1i −0.516403 0.720155i
\(46\) 28946.1 + 81095.2i 0.297383 + 0.833147i
\(47\) 3012.91i 0.0290196i 0.999895 + 0.0145098i \(0.00461878\pi\)
−0.999895 + 0.0145098i \(0.995381\pi\)
\(48\) 78581.5 + 20917.2i 0.710553 + 0.189139i
\(49\) 16561.7 + 115189.i 0.140772 + 0.979092i
\(50\) −21596.3 + 9862.68i −0.172770 + 0.0789014i
\(51\) −3115.63 122411.i −0.0234874 0.922809i
\(52\) −15470.1 + 33874.8i −0.110023 + 0.240916i
\(53\) 138532. + 120038.i 0.930512 + 0.806293i 0.981314 0.192416i \(-0.0616322\pi\)
−0.0508017 + 0.998709i \(0.516178\pi\)
\(54\) 98010.4 98983.5i 0.622430 0.628610i
\(55\) 43924.0 12897.3i 0.264006 0.0775192i
\(56\) −14882.1 + 12895.4i −0.0847420 + 0.0734294i
\(57\) −145097. + 176323.i −0.783489 + 0.952102i
\(58\) 59598.0 38301.3i 0.305455 0.196304i
\(59\) −21168.4 + 18342.5i −0.103070 + 0.0893106i −0.704871 0.709335i \(-0.748995\pi\)
0.601801 + 0.798646i \(0.294450\pi\)
\(60\) −23384.3 34428.0i −0.108261 0.159389i
\(61\) −28439.2 + 197799.i −0.125293 + 0.871434i 0.826115 + 0.563502i \(0.190546\pi\)
−0.951408 + 0.307933i \(0.900363\pi\)
\(62\) 293428. + 254257.i 1.23120 + 1.06684i
\(63\) 5011.09 + 25546.9i 0.0200406 + 0.102169i
\(64\) 279847. + 82170.5i 1.06753 + 0.313455i
\(65\) −269653. + 123146.i −0.981895 + 0.448416i
\(66\) 34621.4 + 70973.6i 0.120424 + 0.246868i
\(67\) −313888. 201724.i −1.04364 0.670707i −0.0977555 0.995210i \(-0.531166\pi\)
−0.945884 + 0.324504i \(0.894803\pi\)
\(68\) 63109.9i 0.200711i
\(69\) 321769. + 66200.9i 0.979485 + 0.201519i
\(70\) −27995.5 −0.0816195
\(71\) −217872. + 339015.i −0.608731 + 0.947204i 0.390910 + 0.920429i \(0.372160\pi\)
−0.999641 + 0.0267754i \(0.991476\pi\)
\(72\) 290011. 278354.i 0.776992 0.745761i
\(73\) 53852.9 + 117921.i 0.138433 + 0.303126i 0.966133 0.258045i \(-0.0830782\pi\)
−0.827700 + 0.561171i \(0.810351\pi\)
\(74\) 48925.1 166624.i 0.120736 0.411189i
\(75\) −10605.3 + 89955.4i −0.0251384 + 0.213228i
\(76\) −77069.1 + 88942.5i −0.175566 + 0.202614i
\(77\) −14608.3 2100.36i −0.0319984 0.00460067i
\(78\) −287319. 423011.i −0.605453 0.891391i
\(79\) −466337. 538181.i −0.945841 1.09156i −0.995685 0.0928022i \(-0.970418\pi\)
0.0498431 0.998757i \(-0.484128\pi\)
\(80\) 180367. + 280657.i 0.352279 + 0.548157i
\(81\) −128691. 515624.i −0.242155 0.970238i
\(82\) −187661. 216572.i −0.340355 0.392791i
\(83\) 310247. + 1.05661e6i 0.542593 + 1.84790i 0.530029 + 0.847980i \(0.322181\pi\)
0.0125641 + 0.999921i \(0.496001\pi\)
\(84\) 2246.81 + 13228.0i 0.00379078 + 0.0223181i
\(85\) 328984. 379668.i 0.535695 0.618225i
\(86\) −23461.3 10714.4i −0.0368857 0.0168451i
\(87\) −6877.01 270194.i −0.0104434 0.410316i
\(88\) 94665.4 + 207288.i 0.138913 + 0.304177i
\(89\) −154604. + 22228.8i −0.219307 + 0.0315315i −0.251092 0.967963i \(-0.580790\pi\)
0.0317856 + 0.999495i \(0.489881\pi\)
\(90\) 570746. 29072.2i 0.782917 0.0398796i
\(91\) 95570.1 0.126823
\(92\) 164914. + 38327.6i 0.211785 + 0.0492208i
\(93\) 1.41020e6 453351.i 1.75320 0.563619i
\(94\) −17937.6 11527.8i −0.0215964 0.0138791i
\(95\) −927292. + 133325.i −1.08155 + 0.155503i
\(96\) 278802. 254287.i 0.315124 0.287416i
\(97\) −137859. 40479.1i −0.151050 0.0443523i 0.205333 0.978692i \(-0.434172\pi\)
−0.356383 + 0.934340i \(0.615990\pi\)
\(98\) −749156. 342128.i −0.795965 0.363505i
\(99\) 300002. + 27650.0i 0.309185 + 0.0284964i
\(100\) −6643.69 + 46207.9i −0.00664369 + 0.0462079i
\(101\) −271591. 924954.i −0.263604 0.897752i −0.979821 0.199875i \(-0.935946\pi\)
0.716218 0.697877i \(-0.245872\pi\)
\(102\) 740708. + 449814.i 0.697986 + 0.423870i
\(103\) −722919. + 464592.i −0.661573 + 0.425167i −0.827879 0.560907i \(-0.810453\pi\)
0.166306 + 0.986074i \(0.446816\pi\)
\(104\) −797805. 1.24141e6i −0.709246 1.10361i
\(105\) −55439.4 + 91292.0i −0.0478906 + 0.0788614i
\(106\) −1.24470e6 + 365477.i −1.04508 + 0.306862i
\(107\) 13078.2 + 1880.36i 0.0106757 + 0.00153494i 0.147651 0.989040i \(-0.452829\pi\)
−0.136975 + 0.990575i \(0.543738\pi\)
\(108\) −59542.7 267348.i −0.0472669 0.212229i
\(109\) −502347. + 1.09999e6i −0.387904 + 0.849391i 0.610451 + 0.792054i \(0.290988\pi\)
−0.998355 + 0.0573370i \(0.981739\pi\)
\(110\) −91274.4 + 310852.i −0.0685758 + 0.233548i
\(111\) −446466. 489507.i −0.326452 0.357923i
\(112\) −15306.7 106460.i −0.0108950 0.0757764i
\(113\) −738937. + 1.14981e6i −0.512120 + 0.796875i −0.996975 0.0777197i \(-0.975236\pi\)
0.484855 + 0.874595i \(0.338872\pi\)
\(114\) −494593. 1.53848e6i −0.333836 1.03843i
\(115\) 792324. + 1.09026e6i 0.520966 + 0.716861i
\(116\) 139300.i 0.0892436i
\(117\) −1.94840e6 + 99245.8i −1.21652 + 0.0619662i
\(118\) −28210.6 196209.i −0.0171698 0.119419i
\(119\) −147324. + 67280.8i −0.0874246 + 0.0399255i
\(120\) 1.64864e6 41961.3i 0.954073 0.0242831i
\(121\) 664983. 1.45611e6i 0.375366 0.821937i
\(122\) −1.06880e6 926122.i −0.588596 0.510022i
\(123\) −1.07786e6 + 183076.i −0.579222 + 0.0983821i
\(124\) 732508. 215084.i 0.384191 0.112809i
\(125\) −1.58889e6 + 1.37679e6i −0.813514 + 0.704914i
\(126\) −171269. 67912.2i −0.0856184 0.0339497i
\(127\) 742365. 477089.i 0.362415 0.232910i −0.346742 0.937961i \(-0.612712\pi\)
0.709157 + 0.705050i \(0.249076\pi\)
\(128\) −883956. + 765952.i −0.421503 + 0.365234i
\(129\) −81399.7 + 55288.6i −0.0379187 + 0.0257553i
\(130\) 298567. 2.07658e6i 0.135897 0.945187i
\(131\) 3.25428e6 + 2.81985e6i 1.44758 + 1.25433i 0.912217 + 0.409707i \(0.134369\pi\)
0.535358 + 0.844625i \(0.320177\pi\)
\(132\) 154205. + 18180.0i 0.0670465 + 0.00790444i
\(133\) 289791. + 85090.3i 0.123177 + 0.0361680i
\(134\) 2.40196e6 1.09694e6i 0.998278 0.455898i
\(135\) 1.03544e6 1.91875e6i 0.420848 0.779860i
\(136\) 2.10379e6 + 1.35202e6i 0.836344 + 0.537485i
\(137\) 1.63093e6i 0.634270i −0.948380 0.317135i \(-0.897279\pi\)
0.948380 0.317135i \(-0.102721\pi\)
\(138\) −1.62527e6 + 1.66239e6i −0.618426 + 0.632551i
\(139\) −1.52727e6 −0.568685 −0.284342 0.958723i \(-0.591775\pi\)
−0.284342 + 0.958723i \(0.591775\pi\)
\(140\) −29760.7 + 46308.6i −0.0108457 + 0.0168763i
\(141\) −73113.4 + 35665.2i −0.0260819 + 0.0127229i
\(142\) −1.18475e6 2.59423e6i −0.413772 0.906033i
\(143\) 311590. 1.06118e6i 0.106555 0.362894i
\(144\) 422614. + 2.15452e6i 0.141533 + 0.721545i
\(145\) 726153. 838026.i 0.238190 0.274886i
\(146\) −908103. 130566.i −0.291794 0.0419537i
\(147\) −2.59922e6 + 1.76545e6i −0.818258 + 0.555780i
\(148\) −223609. 258059.i −0.0689771 0.0796038i
\(149\) 1.04484e6 + 1.62580e6i 0.315856 + 0.491482i 0.962489 0.271319i \(-0.0874598\pi\)
−0.646633 + 0.762801i \(0.723823\pi\)
\(150\) −494980. 407321.i −0.146661 0.120688i
\(151\) 437826. + 505278.i 0.127166 + 0.146757i 0.815762 0.578388i \(-0.196318\pi\)
−0.688596 + 0.725145i \(0.741773\pi\)
\(152\) −1.31385e6 4.47456e6i −0.374124 1.27415i
\(153\) 2.93365e6 1.52465e6i 0.819093 0.425692i
\(154\) 68398.1 78935.6i 0.0187276 0.0216128i
\(155\) 5.52796e6 + 2.52453e6i 1.48446 + 0.677932i
\(156\) −1.00516e6 + 25583.3i −0.264765 + 0.00673881i
\(157\) 2.83881e6 + 6.21612e6i 0.733562 + 1.60628i 0.793863 + 0.608096i \(0.208066\pi\)
−0.0603016 + 0.998180i \(0.519206\pi\)
\(158\) 4.98838e6 717220.i 1.26470 0.181837i
\(159\) −1.27307e6 + 4.78267e6i −0.316711 + 1.18981i
\(160\) 1.54813e6 0.377960
\(161\) −86341.1 425838.i −0.0206890 0.102039i
\(162\) 3.56220e6 + 1.20668e6i 0.837864 + 0.283822i
\(163\) 3.43824e6 + 2.20962e6i 0.793914 + 0.510218i 0.873625 0.486600i \(-0.161763\pi\)
−0.0797104 + 0.996818i \(0.525400\pi\)
\(164\) −557735. + 80190.2i −0.126443 + 0.0181798i
\(165\) 832924. + 913221.i 0.185419 + 0.203294i
\(166\) −7.47764e6 2.19563e6i −1.63471 0.479994i
\(167\) 2.03525e6 + 929466.i 0.436986 + 0.199565i 0.621746 0.783219i \(-0.286424\pi\)
−0.184760 + 0.982784i \(0.559151\pi\)
\(168\) −489095. 208490.i −0.103149 0.0439701i
\(169\) −332311. + 2.31127e6i −0.0688469 + 0.478841i
\(170\) 1.00165e6 + 3.41129e6i 0.203877 + 0.694340i
\(171\) −5.99635e6 1.43381e6i −1.19922 0.286749i
\(172\) −42663.9 + 27418.4i −0.00838446 + 0.00538837i
\(173\) −783994. 1.21992e6i −0.151417 0.235609i 0.757256 0.653118i \(-0.226540\pi\)
−0.908673 + 0.417509i \(0.862903\pi\)
\(174\) 1.63494e6 + 992857.i 0.310351 + 0.188469i
\(175\) 114951. 33752.6i 0.0214486 0.00629787i
\(176\) −1.23200e6 177135.i −0.225982 0.0324913i
\(177\) −695694. 296559.i −0.125458 0.0534799i
\(178\) 459197. 1.00550e6i 0.0814215 0.178288i
\(179\) −546854. + 1.86241e6i −0.0953481 + 0.324726i −0.993330 0.115307i \(-0.963215\pi\)
0.897982 + 0.440033i \(0.145033\pi\)
\(180\) 558644. 975002.i 0.0957895 0.167181i
\(181\) −721166. 5.01582e6i −0.121618 0.845875i −0.955723 0.294268i \(-0.904924\pi\)
0.834105 0.551606i \(-0.185985\pi\)
\(182\) −365664. + 568985.i −0.0606553 + 0.0943815i
\(183\) −5.13658e6 + 1.65131e6i −0.838149 + 0.269449i
\(184\) −4.81067e6 + 4.67636e6i −0.772240 + 0.750680i
\(185\) 2.71813e6i 0.429294i
\(186\) −2.69654e6 + 1.01303e7i −0.419052 + 1.57429i
\(187\) 266737. + 1.85520e6i 0.0407904 + 0.283704i
\(188\) −38137.2 + 17416.7i −0.00573952 + 0.00262115i
\(189\) −560622. + 424014.i −0.0830395 + 0.0628051i
\(190\) 2.75419e6 6.03083e6i 0.401544 0.879258i
\(191\) −7.70184e6 6.67368e6i −1.10534 0.957779i −0.106006 0.994366i \(-0.533806\pi\)
−0.999330 + 0.0365864i \(0.988352\pi\)
\(192\) 1.31867e6 + 7.76366e6i 0.186309 + 1.09689i
\(193\) 1.58295e6 464796.i 0.220189 0.0646533i −0.169777 0.985482i \(-0.554305\pi\)
0.389966 + 0.920829i \(0.372487\pi\)
\(194\) 768464. 665878.i 0.105249 0.0911989i
\(195\) −6.18037e6 5.08585e6i −0.833509 0.685898i
\(196\) −1.36232e6 + 875511.i −0.180930 + 0.116277i
\(197\) 6.91099e6 5.98840e6i 0.903944 0.783272i −0.0728748 0.997341i \(-0.523217\pi\)
0.976818 + 0.214069i \(0.0686719\pi\)
\(198\) −1.31247e6 + 1.68030e6i −0.169080 + 0.216466i
\(199\) −1.10770e6 + 7.70423e6i −0.140560 + 0.977619i 0.790424 + 0.612560i \(0.209860\pi\)
−0.930984 + 0.365059i \(0.881049\pi\)
\(200\) −1.39802e6 1.21139e6i −0.174753 0.151424i
\(201\) 1.17953e6 1.00049e7i 0.145252 1.23204i
\(202\) 6.54594e6 + 1.92206e6i 0.794178 + 0.233192i
\(203\) −325183. + 148506.i −0.0388723 + 0.0177524i
\(204\) 1.53147e6 747061.i 0.180392 0.0879966i
\(205\) −3.77334e6 2.42498e6i −0.437991 0.281480i
\(206\) 6.08155e6i 0.695685i
\(207\) 2.20246e6 + 8.59194e6i 0.248312 + 0.968680i
\(208\) 8.05998e6 0.895662
\(209\) 1.88963e6 2.94031e6i 0.206984 0.322073i
\(210\) −331396. 679359.i −0.0357840 0.0733570i
\(211\) −2.19965e6 4.81657e6i −0.234157 0.512732i 0.755680 0.654941i \(-0.227307\pi\)
−0.989837 + 0.142209i \(0.954579\pi\)
\(212\) −718632. + 2.44744e6i −0.0754222 + 0.256864i
\(213\) −1.08058e7 1.27395e6i −1.11820 0.131830i
\(214\) −61234.0 + 70667.8i −0.00624814 + 0.00721074i
\(215\) −399594. 57452.9i −0.0402072 0.00578092i
\(216\) 1.01877e7 + 3.74260e6i 1.01092 + 0.371375i
\(217\) −1.28301e6 1.48068e6i −0.125560 0.144904i
\(218\) −4.62681e6 7.19946e6i −0.446594 0.694913i
\(219\) −2.22408e6 + 2.70272e6i −0.211748 + 0.257318i
\(220\) 417165. + 481434.i 0.0391777 + 0.0452135i
\(221\) −3.41939e6 1.16454e7i −0.316790 1.07889i
\(222\) 4.62256e6 785151.i 0.422497 0.0717619i
\(223\) 1.11890e7 1.29128e7i 1.00897 1.16441i 0.0226208 0.999744i \(-0.492799\pi\)
0.986349 0.164669i \(-0.0526556\pi\)
\(224\) −453999. 207334.i −0.0403934 0.0184471i
\(225\) −2.30846e6 + 807490.i −0.202663 + 0.0708907i
\(226\) −4.01821e6 8.79865e6i −0.348103 0.762238i
\(227\) 1.62238e7 2.33264e6i 1.38700 0.199420i 0.591955 0.805971i \(-0.298356\pi\)
0.795045 + 0.606551i \(0.207447\pi\)
\(228\) −3.07065e6 817360.i −0.259075 0.0689619i
\(229\) −9.90563e6 −0.824851 −0.412426 0.910991i \(-0.635318\pi\)
−0.412426 + 0.910991i \(0.635318\pi\)
\(230\) −9.52248e6 + 545700.i −0.782648 + 0.0448509i
\(231\) −121957. 379359.i −0.00989396 0.0307762i
\(232\) 4.64360e6 + 2.98426e6i 0.371870 + 0.238986i
\(233\) 5.01336e6 720813.i 0.396334 0.0569842i 0.0587335 0.998274i \(-0.481294\pi\)
0.337601 + 0.941289i \(0.390385\pi\)
\(234\) 6.86397e6 1.19797e7i 0.535707 0.934970i
\(235\) −320224. 94026.2i −0.0246746 0.00724512i
\(236\) −354547. 161916.i −0.0269736 0.0123184i
\(237\) 7.53965e6 1.76872e7i 0.566378 1.32866i
\(238\) 163121. 1.13453e6i 0.0120998 0.0841563i
\(239\) −6.58634e6 2.24310e7i −0.482448 1.64307i −0.736916 0.675985i \(-0.763719\pi\)
0.254468 0.967081i \(-0.418100\pi\)
\(240\) −4.67553e6 + 7.69918e6i −0.338218 + 0.556943i
\(241\) −3.06643e6 + 1.97067e6i −0.219069 + 0.140787i −0.645573 0.763698i \(-0.723381\pi\)
0.426504 + 0.904486i \(0.359745\pi\)
\(242\) 6.12476e6 + 9.53032e6i 0.432159 + 0.672452i
\(243\) 1.09891e7 9.22660e6i 0.765852 0.643017i
\(244\) −2.66813e6 + 783434.i −0.183670 + 0.0539303i
\(245\) −1.27596e7 1.83456e6i −0.867641 0.124748i
\(246\) 3.03407e6 7.11758e6i 0.203807 0.478109i
\(247\) −9.40217e6 + 2.05879e7i −0.623932 + 1.36622i
\(248\) −8.52285e6 + 2.90262e7i −0.558766 + 1.90298i
\(249\) −2.19678e7 + 2.00362e7i −1.42295 + 1.29783i
\(250\) −2.11748e6 1.47274e7i −0.135519 0.942553i
\(251\) −9.98909e6 + 1.55433e7i −0.631691 + 0.982930i 0.366921 + 0.930252i \(0.380412\pi\)
−0.998612 + 0.0526781i \(0.983224\pi\)
\(252\) −294405. + 211109.i −0.0183968 + 0.0131919i
\(253\) −5.00986e6 429671.i −0.309360 0.0265323i
\(254\) 6.24515e6i 0.381102i
\(255\) 1.31076e7 + 3.48906e6i 0.790503 + 0.210420i
\(256\) 1.47847e6 + 1.02830e7i 0.0881236 + 0.612913i
\(257\) 4.89518e6 2.23555e6i 0.288383 0.131700i −0.265971 0.963981i \(-0.585693\pi\)
0.554354 + 0.832281i \(0.312965\pi\)
\(258\) −17718.8 696162.i −0.00103175 0.0405370i
\(259\) −364028. + 797110.i −0.0209525 + 0.0458795i
\(260\) −3.11756e6 2.70138e6i −0.177376 0.153697i
\(261\) 6.47532e6 3.36530e6i 0.364200 0.189279i
\(262\) −2.92396e7 + 8.58551e6i −1.62580 + 0.477378i
\(263\) 2.02314e7 1.75306e7i 1.11214 0.963671i 0.112585 0.993642i \(-0.464087\pi\)
0.999551 + 0.0299708i \(0.00954144\pi\)
\(264\) −3.90961e6 + 4.75099e6i −0.212482 + 0.258210i
\(265\) −1.70815e7 + 1.09776e7i −0.917883 + 0.589888i
\(266\) −1.61537e6 + 1.39973e6i −0.0858277 + 0.0743701i
\(267\) −2.36954e6 3.48861e6i −0.124489 0.183282i
\(268\) 738918. 5.13929e6i 0.0383877 0.266992i
\(269\) 2.32883e7 + 2.01794e7i 1.19641 + 1.03670i 0.998403 + 0.0564957i \(0.0179927\pi\)
0.198008 + 0.980200i \(0.436553\pi\)
\(270\) 7.46169e6 + 1.35060e7i 0.379093 + 0.686176i
\(271\) 4.89434e6 + 1.43711e6i 0.245915 + 0.0722073i 0.402367 0.915478i \(-0.368187\pi\)
−0.156452 + 0.987686i \(0.550006\pi\)
\(272\) −1.24247e7 + 5.67418e6i −0.617419 + 0.281966i
\(273\) 1.13131e6 + 2.31917e6i 0.0556024 + 0.113984i
\(274\) 9.70989e6 + 6.24017e6i 0.472022 + 0.303350i
\(275\) 1.38642e6i 0.0666648i
\(276\) 1.02208e6 + 4.45563e6i 0.0486138 + 0.211925i
\(277\) 1.74868e7 0.822755 0.411378 0.911465i \(-0.365048\pi\)
0.411378 + 0.911465i \(0.365048\pi\)
\(278\) 5.84355e6 9.09273e6i 0.271983 0.423214i
\(279\) 2.76945e7 + 2.88543e7i 1.27521 + 1.32861i
\(280\) −906137. 1.98416e6i −0.0412781 0.0903865i
\(281\) −7.59880e6 + 2.58791e7i −0.342473 + 1.16635i 0.590689 + 0.806899i \(0.298856\pi\)
−0.933162 + 0.359456i \(0.882962\pi\)
\(282\) 67405.9 571747.i 0.00300574 0.0254951i
\(283\) 1.78631e7 2.06151e7i 0.788129 0.909550i −0.209539 0.977800i \(-0.567196\pi\)
0.997668 + 0.0682506i \(0.0217418\pi\)
\(284\) −5.55069e6 798068.i −0.242321 0.0348405i
\(285\) −1.42122e7 2.09241e7i −0.613939 0.903884i
\(286\) 5.12563e6 + 5.91529e6i 0.219103 + 0.252859i
\(287\) 781792. + 1.21649e6i 0.0330709 + 0.0514593i
\(288\) 9.47103e6 + 3.75549e6i 0.396479 + 0.157213i
\(289\) −2.33738e6 2.69748e6i −0.0968359 0.111755i
\(290\) 2.21090e6 + 7.52962e6i 0.0906513 + 0.308730i
\(291\) −649609. 3.82456e6i −0.0263617 0.155204i
\(292\) −1.18134e6 + 1.36334e6i −0.0474488 + 0.0547588i
\(293\) 1.95759e7 + 8.94001e6i 0.778249 + 0.355414i 0.764611 0.644493i \(-0.222931\pi\)
0.0136385 + 0.999907i \(0.495659\pi\)
\(294\) −565787. 2.22295e7i −0.0222644 0.874758i
\(295\) −1.28890e6 2.82230e6i −0.0502057 0.109935i
\(296\) 1.33929e7 1.92561e6i 0.516417 0.0742495i
\(297\) 2.88029e6 + 7.60738e6i 0.109943 + 0.290379i
\(298\) −1.36770e7 −0.516824
\(299\) 3.25075e7 1.86290e6i 1.21610 0.0696907i
\(300\) −1.19996e6 + 385764.i −0.0444429 + 0.0142876i
\(301\) 109489. + 70364.6i 0.00401488 + 0.00258021i
\(302\) −4.68340e6 + 673371.i −0.170036 + 0.0244475i
\(303\) 1.92307e7 1.75398e7i 0.691300 0.630515i
\(304\) 2.44397e7 + 7.17616e6i 0.869913 + 0.255430i
\(305\) −2.01354e7 9.19552e6i −0.709676 0.324098i
\(306\) −2.14740e6 + 2.32992e7i −0.0749460 + 0.813162i
\(307\) −867536. + 6.03385e6i −0.0299828 + 0.208535i −0.999306 0.0372555i \(-0.988138\pi\)
0.969323 + 0.245791i \(0.0790476\pi\)
\(308\) −57860.0 197053.i −0.00198028 0.00674421i
\(309\) −1.98317e7 1.20433e7i −0.672177 0.408197i
\(310\) −3.61807e7 + 2.32520e7i −1.21449 + 0.780503i
\(311\) 3.00328e7 + 4.67319e7i 0.998422 + 1.55358i 0.822179 + 0.569228i \(0.192758\pi\)
0.176243 + 0.984347i \(0.443606\pi\)
\(312\) 2.06809e7 3.40553e7i 0.680936 1.12130i
\(313\) 3.28303e7 9.63985e6i 1.07064 0.314367i 0.301510 0.953463i \(-0.402509\pi\)
0.769127 + 0.639096i \(0.220691\pi\)
\(314\) −4.78699e7 6.88265e6i −1.54623 0.222314i
\(315\) −2.87162e6 264666.i −0.0918746 0.00846772i
\(316\) 4.11653e6 9.01394e6i 0.130458 0.285663i
\(317\) −7.48627e6 + 2.54959e7i −0.235011 + 0.800373i 0.754548 + 0.656245i \(0.227856\pi\)
−0.989559 + 0.144129i \(0.953962\pi\)
\(318\) −2.36031e7 2.58785e7i −0.733985 0.804744i
\(319\) 588758. + 4.09490e6i 0.0181370 + 0.126145i
\(320\) −1.74668e7 + 2.71789e7i −0.533045 + 0.829435i
\(321\) 109183. + 339624.i 0.00330095 + 0.0102679i
\(322\) 2.86562e6 + 1.11528e6i 0.0858323 + 0.0334053i
\(323\) 3.83559e7i 1.13822i
\(324\) 5.78283e6 4.60963e6i 0.170022 0.135529i
\(325\) 1.27768e6 + 8.88649e6i 0.0372198 + 0.258869i
\(326\) −2.63104e7 + 1.20155e7i −0.759406 + 0.346809i
\(327\) −3.26396e7 + 830745.i −0.933472 + 0.0237588i
\(328\) 9.27536e6 2.03102e7i 0.262851 0.575563i
\(329\) 81315.4 + 70460.2i 0.00228342 + 0.00197859i
\(330\) −8.62382e6 + 1.46477e6i −0.239971 + 0.0407595i
\(331\) 4.75130e7 1.39511e7i 1.31017 0.384702i 0.449236 0.893413i \(-0.351696\pi\)
0.860937 + 0.508711i \(0.169878\pi\)
\(332\) −1.15810e7 + 1.00350e7i −0.316470 + 0.274223i
\(333\) 6.59370e6 1.66288e7i 0.178565 0.450327i
\(334\) −1.33208e7 + 8.56075e6i −0.357512 + 0.229759i
\(335\) 3.12358e7 2.70660e7i 0.830842 0.719928i
\(336\) 2.40225e6 1.63167e6i 0.0633288 0.0430144i
\(337\) 7.89220e6 5.48914e7i 0.206209 1.43422i −0.579172 0.815205i \(-0.696624\pi\)
0.785382 0.619012i \(-0.212467\pi\)
\(338\) −1.24889e7 1.08217e7i −0.323425 0.280250i
\(339\) −3.66492e7 4.32075e6i −0.940732 0.110907i
\(340\) 6.70758e6 + 1.96952e6i 0.170659 + 0.0501100i
\(341\) −2.06239e7 + 9.41864e6i −0.520126 + 0.237534i
\(342\) 3.14792e7 3.02139e7i 0.786946 0.755315i
\(343\) 7.03063e6 + 4.51831e6i 0.174226 + 0.111968i
\(344\) 2.00961e6i 0.0493669i
\(345\) −1.70778e7 + 3.21330e7i −0.415887 + 0.782517i
\(346\) 1.02626e7 0.247758
\(347\) −1.60399e7 + 2.49586e7i −0.383896 + 0.597354i −0.978396 0.206742i \(-0.933714\pi\)
0.594499 + 0.804096i \(0.297350\pi\)
\(348\) 3.38035e6 1.64896e6i 0.0802093 0.0391266i
\(349\) 1.19846e7 + 2.62425e7i 0.281933 + 0.617347i 0.996625 0.0820926i \(-0.0261603\pi\)
−0.714692 + 0.699439i \(0.753433\pi\)
\(350\) −238869. + 813512.i −0.00557128 + 0.0189740i
\(351\) −2.54725e7 4.61064e7i −0.589047 1.06620i
\(352\) −3.78235e6 + 4.36507e6i −0.0867230 + 0.100084i
\(353\) −6.34620e7 9.12446e6i −1.44275 0.207435i −0.623924 0.781485i \(-0.714463\pi\)
−0.818821 + 0.574049i \(0.805372\pi\)
\(354\) 4.42741e6 3.00720e6i 0.0998021 0.0677879i
\(355\) −2.92326e7 3.37362e7i −0.653405 0.754069i
\(356\) −1.17509e6 1.82848e6i −0.0260448 0.0405266i
\(357\) −3.37663e6 2.77864e6i −0.0742128 0.0610701i
\(358\) −8.99570e6 1.03816e7i −0.196059 0.226264i
\(359\) −1.18946e6 4.05094e6i −0.0257080 0.0875534i 0.945640 0.325216i \(-0.105437\pi\)
−0.971348 + 0.237662i \(0.923619\pi\)
\(360\) 2.05340e7 + 3.95103e7i 0.440114 + 0.846844i
\(361\) −1.60313e7 + 1.85011e7i −0.340760 + 0.393258i
\(362\) 3.26214e7 + 1.48977e7i 0.687665 + 0.314046i
\(363\) 4.32068e7 1.09970e6i 0.903300 0.0229909i
\(364\) 552462. + 1.20972e6i 0.0114551 + 0.0250831i
\(365\) −1.42138e7 + 2.04364e6i −0.292302 + 0.0420267i
\(366\) 9.82203e6 3.68993e7i 0.200336 0.752618i
\(367\) 6.08576e6 0.123117 0.0615583 0.998103i \(-0.480393\pi\)
0.0615583 + 0.998103i \(0.480393\pi\)
\(368\) −7.28164e6 3.59134e7i −0.146112 0.720632i
\(369\) −1.72017e7 2.39889e7i −0.342368 0.477453i
\(370\) 1.61826e7 + 1.03999e7i 0.319480 + 0.205317i
\(371\) 6.47945e6 931604.i 0.126887 0.0182436i
\(372\) 1.38904e7 + 1.52295e7i 0.269828 + 0.295840i
\(373\) −1.63980e7 4.81488e6i −0.315983 0.0927810i 0.119895 0.992787i \(-0.461744\pi\)
−0.435878 + 0.900006i \(0.643562\pi\)
\(374\) −1.20656e7 5.51019e6i −0.230640 0.105330i
\(375\) −5.22186e7 2.22596e7i −0.990219 0.422108i
\(376\) 236435. 1.64444e6i 0.00444782 0.0309353i
\(377\) −7.54749e6 2.57044e7i −0.140857 0.479715i
\(378\) −379386. 4.96005e6i −0.00702435 0.0918355i
\(379\) −2.02173e7 + 1.29928e7i −0.371368 + 0.238664i −0.712991 0.701173i \(-0.752660\pi\)
0.341623 + 0.939837i \(0.389024\pi\)
\(380\) −7.04801e6 1.09669e7i −0.128445 0.199864i
\(381\) 2.03651e7 + 1.23672e7i 0.368224 + 0.223614i
\(382\) 6.92006e7 2.03191e7i 1.24142 0.364515i
\(383\) 2.36519e7 + 3.40063e6i 0.420988 + 0.0605290i 0.349554 0.936916i \(-0.386333\pi\)
0.0714345 + 0.997445i \(0.477242\pi\)
\(384\) −2.90510e7 1.23838e7i −0.513058 0.218705i
\(385\) 679129. 1.48708e6i 0.0119006 0.0260587i
\(386\) −3.28938e6 + 1.12026e7i −0.0571943 + 0.194786i
\(387\) −2.30524e6 1.32083e6i −0.0397725 0.0227884i
\(388\) −284539. 1.97901e6i −0.00487132 0.0338808i
\(389\) −2.43886e7 + 3.79494e7i −0.414322 + 0.644697i −0.984206 0.177028i \(-0.943352\pi\)
0.569884 + 0.821725i \(0.306988\pi\)
\(390\) 5.39260e7 1.73362e7i 0.909084 0.292254i
\(391\) −4.87999e7 + 2.57568e7i −0.816373 + 0.430885i
\(392\) 6.41697e7i 1.06530i
\(393\) −2.99061e7 + 1.12351e8i −0.492699 + 1.85096i
\(394\) 9.21009e6 + 6.40576e7i 0.150583 + 1.04733i
\(395\) 7.17535e7 3.27687e7i 1.16426 0.531702i
\(396\) 1.38423e6 + 3.95725e6i 0.0222906 + 0.0637248i
\(397\) −4.90779e7 + 1.07466e8i −0.784358 + 1.71750i −0.0922214 + 0.995739i \(0.529397\pi\)
−0.692137 + 0.721766i \(0.743331\pi\)
\(398\) −4.16296e7 3.60722e7i −0.660317 0.572168i
\(399\) 1.36553e6 + 8.03953e6i 0.0214972 + 0.126565i
\(400\) 9.69448e6 2.84655e6i 0.151476 0.0444774i
\(401\) −7.50292e7 + 6.50132e7i −1.16358 + 1.00825i −0.163819 + 0.986490i \(0.552381\pi\)
−0.999763 + 0.0217596i \(0.993073\pi\)
\(402\) 5.50522e7 + 4.53027e7i 0.847416 + 0.697342i
\(403\) 1.23513e8 7.93768e7i 1.88711 1.21277i
\(404\) 1.01381e7 8.78467e6i 0.153748 0.133224i
\(405\) 5.88188e7 + 2.41371e6i 0.885424 + 0.0363345i
\(406\) 360051. 2.50421e6i 0.00538005 0.0374191i
\(407\) 7.66398e6 + 6.64088e6i 0.113677 + 0.0985014i
\(408\) −7.90561e6 + 6.70565e7i −0.116401 + 0.987326i
\(409\) −1.13851e8 3.34296e7i −1.66405 0.488608i −0.691707 0.722178i \(-0.743141\pi\)
−0.972340 + 0.233570i \(0.924959\pi\)
\(410\) 2.88747e7 1.31866e7i 0.418953 0.191329i
\(411\) 3.95774e7 1.93061e7i 0.570061 0.278080i
\(412\) −1.00598e7 6.46502e6i −0.143845 0.0924438i
\(413\) 1.00028e6i 0.0141994i
\(414\) −5.95798e7 1.97614e7i −0.839649 0.278495i
\(415\) −1.21983e8 −1.70669
\(416\) 2.02209e7 3.14644e7i 0.280880 0.437058i
\(417\) −1.80790e7 3.70618e7i −0.249326 0.511115i
\(418\) 1.02755e7 + 2.25001e7i 0.140693 + 0.308074i
\(419\) −1.26524e7 + 4.30902e7i −0.172001 + 0.585783i 0.827696 + 0.561177i \(0.189651\pi\)
−0.999697 + 0.0246059i \(0.992167\pi\)
\(420\) −1.47605e6 174018.i −0.0199229 0.00234881i
\(421\) 1.37166e7 1.58298e7i 0.183823 0.212143i −0.656357 0.754450i \(-0.727904\pi\)
0.840180 + 0.542307i \(0.182449\pi\)
\(422\) 3.70920e7 + 5.33303e6i 0.493564 + 0.0709638i
\(423\) −1.73096e6 1.35204e6i −0.0228699 0.0178635i
\(424\) −6.61906e7 7.63880e7i −0.868357 1.00214i
\(425\) −8.22562e6 1.27993e7i −0.107152 0.166732i
\(426\) 4.89292e7 5.94591e7i 0.632906 0.769112i
\(427\) 4.67332e6 + 5.39330e6i 0.0600264 + 0.0692741i
\(428\) 51799.7 + 176413.i 0.000660687 + 0.00225009i
\(429\) 2.94397e7 5.00040e6i 0.372874 0.0633334i
\(430\) 1.87095e6 2.15919e6i 0.0235319 0.0271573i
\(431\) 9.62459e7 + 4.39540e7i 1.20213 + 0.548993i 0.912867 0.408258i \(-0.133864\pi\)
0.289260 + 0.957251i \(0.406591\pi\)
\(432\) −4.72805e7 + 3.57596e7i −0.586450 + 0.443548i
\(433\) −4.54372e7 9.94936e7i −0.559691 1.22555i −0.952107 0.305764i \(-0.901088\pi\)
0.392417 0.919787i \(-0.371639\pi\)
\(434\) 1.37243e7 1.97326e6i 0.167889 0.0241387i
\(435\) 2.89320e7 + 7.70126e6i 0.351488 + 0.0935608i
\(436\) −1.68275e7 −0.203030
\(437\) 1.00229e8 + 2.32942e7i 1.20102 + 0.279127i
\(438\) −7.58125e6 2.35823e7i −0.0902233 0.280649i
\(439\) 3.45840e7 + 2.22258e7i 0.408772 + 0.262702i 0.728828 0.684697i \(-0.240065\pi\)
−0.320056 + 0.947399i \(0.603702\pi\)
\(440\) −2.49858e7 + 3.59241e6i −0.293315 + 0.0421724i
\(441\) −7.36098e7 4.21760e7i −0.858262 0.491756i
\(442\) 8.24148e7 + 2.41992e7i 0.954417 + 0.280242i
\(443\) 5.81489e7 + 2.65557e7i 0.668852 + 0.305455i 0.720747 0.693198i \(-0.243799\pi\)
−0.0518949 + 0.998653i \(0.516526\pi\)
\(444\) 3.61528e6 8.48104e6i 0.0413040 0.0968947i
\(445\) 2.46230e6 1.71257e7i 0.0279423 0.194343i
\(446\) 3.40669e7 + 1.16021e8i 0.383997 + 1.30777i
\(447\) −2.70846e7 + 4.46001e7i −0.303249 + 0.499360i
\(448\) 8.76224e6 5.63115e6i 0.0974498 0.0626272i
\(449\) −4.66102e6 7.25269e6i −0.0514923 0.0801236i 0.814553 0.580089i \(-0.196982\pi\)
−0.866045 + 0.499966i \(0.833346\pi\)
\(450\) 4.02504e6 1.68332e7i 0.0441705 0.184726i
\(451\) 1.60564e7 4.71459e6i 0.175033 0.0513942i
\(452\) −1.88258e7 2.70674e6i −0.203863 0.0293111i
\(453\) −7.07869e6 + 1.66058e7i −0.0761480 + 0.178635i
\(454\) −4.81871e7 + 1.05515e8i −0.514948 + 1.12758i
\(455\) −2.98254e6 + 1.01576e7i −0.0316630 + 0.107834i
\(456\) 9.30303e7 8.48504e7i 0.981138 0.894868i
\(457\) −1.05493e7 7.33723e7i −0.110529 0.768748i −0.967407 0.253228i \(-0.918508\pi\)
0.856878 0.515520i \(-0.172401\pi\)
\(458\) 3.79003e7 5.89740e7i 0.394499 0.613853i
\(459\) 7.17252e7 + 5.31420e7i 0.741709 + 0.549540i
\(460\) −9.22024e6 + 1.63317e7i −0.0947259 + 0.167786i
\(461\) 9.93795e7i 1.01436i −0.861839 0.507182i \(-0.830687\pi\)
0.861839 0.507182i \(-0.169313\pi\)
\(462\) 2.72517e6 + 725400.i 0.0276355 + 0.00735616i
\(463\) 1.88274e7 + 1.30948e8i 0.189692 + 1.31933i 0.832807 + 0.553564i \(0.186733\pi\)
−0.643115 + 0.765770i \(0.722358\pi\)
\(464\) −2.74246e7 + 1.25244e7i −0.274528 + 0.125373i
\(465\) 4.17489e6 + 1.64030e8i 0.0415228 + 1.63141i
\(466\) −1.48904e7 + 3.26054e7i −0.147146 + 0.322205i
\(467\) −4.00858e7 3.47345e7i −0.393586 0.341044i 0.435476 0.900200i \(-0.356580\pi\)
−0.829063 + 0.559156i \(0.811125\pi\)
\(468\) −1.25193e7 2.40890e7i −0.122136 0.235007i
\(469\) −1.27850e7 + 3.75400e6i −0.123931 + 0.0363895i
\(470\) 1.78501e6 1.54672e6i 0.0171929 0.0148977i
\(471\) −1.17241e8 + 1.42472e8i −1.12206 + 1.36353i
\(472\) 1.29931e7 8.35016e6i 0.123563 0.0794088i
\(473\) 1.13827e6 986321.i 0.0107563 0.00932040i
\(474\) 7.64544e7 + 1.12562e8i 0.717906 + 1.05695i
\(475\) −4.03779e6 + 2.80835e7i −0.0376759 + 0.262042i
\(476\) −1.70327e6 1.47590e6i −0.0157930 0.0136847i
\(477\) −1.31130e8 + 2.57213e7i −1.20822 + 0.236995i
\(478\) 1.58745e8 + 4.66118e7i 1.45351 + 0.426788i
\(479\) 1.85560e8 8.47426e7i 1.68841 0.771072i 0.689508 0.724278i \(-0.257827\pi\)
0.998905 0.0467940i \(-0.0149004\pi\)
\(480\) 1.83259e7 + 3.75679e7i 0.165707 + 0.339699i
\(481\) −5.52437e7 3.55029e7i −0.496418 0.319028i
\(482\) 2.57963e7i 0.230365i
\(483\) 9.31165e6 7.13607e6i 0.0826390 0.0633312i
\(484\) 2.22755e7 0.196467
\(485\) 8.60457e6 1.33890e7i 0.0754231 0.117361i
\(486\) 1.28854e7 + 1.00727e8i 0.112251 + 0.877480i
\(487\) −2.32604e6 5.09331e6i −0.0201386 0.0440974i 0.899295 0.437342i \(-0.144080\pi\)
−0.919434 + 0.393244i \(0.871353\pi\)
\(488\) 3.10442e7 1.05727e8i 0.267129 0.909756i
\(489\) −1.29202e7 + 1.09591e8i −0.110495 + 0.937237i
\(490\) 5.97423e7 6.89463e7i 0.507801 0.586034i
\(491\) 1.76784e8 + 2.54177e7i 1.49348 + 0.214729i 0.840153 0.542350i \(-0.182465\pi\)
0.653323 + 0.757079i \(0.273374\pi\)
\(492\) −8.54813e6 1.25852e7i −0.0717754 0.105673i
\(493\) 2.97304e7 + 3.43107e7i 0.248119 + 0.286345i
\(494\) −8.65977e7 1.34749e8i −0.718333 1.11775i
\(495\) −1.23012e7 + 3.10226e7i −0.101422 + 0.255777i
\(496\) −1.08204e8 1.24874e8i −0.886743 1.02336i
\(497\) 4.05451e6 + 1.38084e7i 0.0330270 + 0.112480i
\(498\) −3.52356e7 2.07449e8i −0.285294 1.67967i
\(499\) −1.24011e8 + 1.43116e8i −0.998065 + 1.15183i −0.00966516 + 0.999953i \(0.503077\pi\)
−0.988400 + 0.151875i \(0.951469\pi\)
\(500\) −2.66122e7 1.21534e7i −0.212898 0.0972271i
\(501\) 1.53709e6 + 6.03913e7i 0.0122232 + 0.480243i
\(502\) −5.43189e7 1.18942e8i −0.429378 0.940207i
\(503\) −9.56083e7 + 1.37464e7i −0.751262 + 0.108015i −0.507300 0.861769i \(-0.669356\pi\)
−0.243962 + 0.969785i \(0.578447\pi\)
\(504\) −730272. 1.43367e7i −0.00570418 0.111985i
\(505\) 1.06784e8 0.829146
\(506\) 2.17265e7 2.81827e7i 0.167702 0.217536i
\(507\) −6.00207e7 + 1.92955e7i −0.460551 + 0.148058i
\(508\) 1.03304e7 + 6.63893e6i 0.0787997 + 0.0506415i
\(509\) −1.88805e8 + 2.71461e7i −1.43173 + 0.205852i −0.814149 0.580656i \(-0.802796\pi\)
−0.617581 + 0.786508i \(0.711887\pi\)
\(510\) −7.09240e7 + 6.46878e7i −0.534666 + 0.487654i
\(511\) 4.44199e6 + 1.30429e6i 0.0332901 + 0.00977486i
\(512\) −1.34970e8 6.16386e7i −1.00560 0.459244i
\(513\) −3.61879e7 1.62485e8i −0.268047 1.20354i
\(514\) −5.42007e6 + 3.76974e7i −0.0399131 + 0.277602i
\(515\) −2.68180e7 9.13337e7i −0.196338 0.668666i
\(516\) −1.17039e6 710748.i −0.00851885 0.00517329i
\(517\) 1.04748e6 673175.i 0.00758009 0.00487143i
\(518\) −3.35284e6 5.21712e6i −0.0241226 0.0375355i
\(519\) 2.03229e7 3.34657e7i 0.145373 0.239386i
\(520\) 1.56840e8 4.60523e7i 1.11544 0.327523i
\(521\) 1.54054e8 + 2.21496e7i 1.08933 + 0.156622i 0.663496 0.748179i \(-0.269072\pi\)
0.425834 + 0.904801i \(0.359981\pi\)
\(522\) −4.73987e6 + 5.14275e7i −0.0333239 + 0.361563i
\(523\) −2.06631e7 + 4.52458e7i −0.144441 + 0.316281i −0.968000 0.250949i \(-0.919257\pi\)
0.823560 + 0.567230i \(0.191985\pi\)
\(524\) −1.68816e7 + 5.74933e7i −0.117333 + 0.399598i
\(525\) 2.17979e6 + 2.38994e6i 0.0150639 + 0.0165161i
\(526\) 2.69618e7 + 1.87524e8i 0.185264 + 1.28854i
\(527\) −1.34518e8 + 2.09314e8i −0.919069 + 1.43010i
\(528\) −1.02853e7 3.19936e7i −0.0698741 0.217351i
\(529\) −3.76690e7 1.43163e8i −0.254458 0.967084i
\(530\) 1.43698e8i 0.965211i
\(531\) −1.03875e6 2.03927e7i −0.00693787 0.136205i
\(532\) 598124. + 4.16004e6i 0.00397243 + 0.0276289i
\(533\) −9.85715e7 + 4.50161e7i −0.650983 + 0.297294i
\(534\) 2.98359e7 759387.i 0.195937 0.00498700i
\(535\) −607996. + 1.33132e6i −0.00397044 + 0.00869406i
\(536\) 1.55490e8 + 1.34733e8i 1.00973 + 0.874940i
\(537\) −5.16680e7 + 8.77592e6i −0.333656 + 0.0566721i
\(538\) −2.09244e8 + 6.14396e7i −1.34371 + 0.394549i
\(539\) 3.63468e7 3.14947e7i 0.232113 0.201127i
\(540\) 3.02731e7 + 2.01491e6i 0.192254 + 0.0127960i
\(541\) 1.90434e8 1.22384e8i 1.20269 0.772919i 0.223267 0.974757i \(-0.428328\pi\)
0.979419 + 0.201838i \(0.0646915\pi\)
\(542\) −2.72823e7 + 2.36403e7i −0.171350 + 0.148475i
\(543\) 1.13181e8 7.68750e7i 0.706924 0.480159i
\(544\) −9.02046e6 + 6.27387e7i −0.0560315 + 0.389708i
\(545\) −1.01234e8 8.77197e7i −0.625369 0.541885i
\(546\) −1.81360e7 2.13813e6i −0.111420 0.0131358i
\(547\) 1.53842e8 + 4.51721e7i 0.939969 + 0.276000i 0.715605 0.698506i \(-0.246151\pi\)
0.224364 + 0.974505i \(0.427969\pi\)
\(548\) 2.06443e7 9.42792e6i 0.125446 0.0572894i
\(549\) −1.00876e8 1.05101e8i −0.609637 0.635168i
\(550\) 8.25417e6 + 5.30463e6i 0.0496118 + 0.0318836i
\(551\) 8.46615e7i 0.506094i
\(552\) −1.70426e8 6.13829e7i −1.01326 0.364947i
\(553\) −2.54308e7 −0.150378
\(554\) −6.69068e7 + 1.04109e8i −0.393497 + 0.612293i
\(555\) 6.59600e7 3.21758e7i 0.385835 0.188213i
\(556\) −8.82869e6 1.93321e7i −0.0513655 0.112475i
\(557\) 5.31420e7 1.80985e8i 0.307519 1.04731i −0.650237 0.759732i \(-0.725330\pi\)
0.957756 0.287582i \(-0.0928515\pi\)
\(558\) −2.77750e8 + 5.44811e7i −1.59864 + 0.313577i
\(559\) −6.38700e6 + 7.37099e6i −0.0365647 + 0.0421979i
\(560\) 1.17927e7 + 1.69554e6i 0.0671507 + 0.00965482i
\(561\) −4.18620e7 + 2.84337e7i −0.237100 + 0.161044i
\(562\) −1.25000e8 1.44257e8i −0.704206 0.812697i
\(563\) −8.24883e7 1.28354e8i −0.462240 0.719259i 0.529389 0.848379i \(-0.322421\pi\)
−0.991629 + 0.129120i \(0.958785\pi\)
\(564\) −874095. 719296.i −0.00487216 0.00400932i
\(565\) −9.91458e7 1.14420e8i −0.549704 0.634392i
\(566\) 5.43872e7 + 1.85226e8i 0.299949 + 1.02153i
\(567\) −1.69258e7 8.58521e6i −0.0928538 0.0470979i
\(568\) 1.45518e8 1.67937e8i 0.794093 0.916432i
\(569\) −2.68316e8 1.22536e8i −1.45650 0.665160i −0.479331 0.877634i \(-0.659121\pi\)
−0.977167 + 0.212474i \(0.931848\pi\)
\(570\) 1.78951e8 4.55468e6i 0.966296 0.0245943i
\(571\) −9.40934e7 2.06036e8i −0.505418 1.10671i −0.974670 0.223647i \(-0.928204\pi\)
0.469252 0.883064i \(-0.344524\pi\)
\(572\) 1.52336e7 2.19025e6i 0.0813979 0.0117032i
\(573\) 7.07781e7 2.65898e8i 0.376214 1.41335i
\(574\) −1.02337e7 −0.0541126
\(575\) 3.84418e7 1.37214e7i 0.202209 0.0721764i
\(576\) −1.72789e8 + 1.23902e8i −0.904166 + 0.648352i
\(577\) 2.56779e8 + 1.65022e8i 1.33669 + 0.859040i 0.996683 0.0813813i \(-0.0259332\pi\)
0.340010 + 0.940422i \(0.389570\pi\)
\(578\) 2.50029e7 3.59487e6i 0.129481 0.0186166i
\(579\) 3.00172e7 + 3.29110e7i 0.154645 + 0.169553i
\(580\) 1.48054e7 + 4.34725e6i 0.0758814 + 0.0222808i
\(581\) 3.57723e7 + 1.63366e7i 0.182397 + 0.0832980i
\(582\) 2.52554e7 + 1.07658e7i 0.128110 + 0.0546106i
\(583\) 1.07809e7 7.49829e7i 0.0544064 0.378405i
\(584\) −2.01391e7 6.85873e7i −0.101112 0.344354i
\(585\) 5.02570e7 2.10181e8i 0.251032 1.04985i
\(586\) −1.28125e8 + 8.23410e7i −0.636710 + 0.409189i
\(587\) 1.29889e8 + 2.02111e8i 0.642182 + 0.999255i 0.997907 + 0.0646640i \(0.0205976\pi\)
−0.355725 + 0.934591i \(0.615766\pi\)
\(588\) −3.73722e7 2.26953e7i −0.183830 0.111636i
\(589\) 4.45192e8 1.30720e8i 2.17872 0.639730i
\(590\) 2.17343e7 + 3.12492e6i 0.105825 + 0.0152154i
\(591\) 2.27128e8 + 9.68194e7i 1.10029 + 0.469030i
\(592\) −3.07006e7 + 6.72249e7i −0.147973 + 0.324015i
\(593\) 7.62907e7 2.59822e8i 0.365854 1.24598i −0.546805 0.837260i \(-0.684156\pi\)
0.912658 0.408723i \(-0.134026\pi\)
\(594\) −5.63116e7 1.19588e7i −0.268682 0.0570596i
\(595\) −2.55320e6 1.77579e7i −0.0121209 0.0843027i
\(596\) −1.45394e7 + 2.26238e7i −0.0686765 + 0.106863i
\(597\) −2.00069e8 + 6.43183e7i −0.940278 + 0.302282i
\(598\) −1.13287e8 + 2.00664e8i −0.529759 + 0.938353i
\(599\) 2.15493e8i 1.00266i 0.865257 + 0.501329i \(0.167155\pi\)
−0.865257 + 0.501329i \(0.832845\pi\)
\(600\) 1.28475e7 4.82653e7i 0.0594792 0.223450i
\(601\) 4.08544e7 + 2.84148e8i 0.188198 + 1.30895i 0.836670 + 0.547708i \(0.184499\pi\)
−0.648472 + 0.761239i \(0.724591\pi\)
\(602\) −837843. + 382630.i −0.00384037 + 0.00175384i
\(603\) 2.56750e8 8.98099e7i 1.17100 0.409612i
\(604\) −3.86485e6 + 8.46285e6i −0.0175397 + 0.0384066i
\(605\) 1.34009e8 + 1.16119e8i 0.605156 + 0.524370i
\(606\) 3.08453e7 + 1.81601e8i 0.138602 + 0.816019i
\(607\) 1.88310e8 5.52927e7i 0.841989 0.247230i 0.167829 0.985816i \(-0.446324\pi\)
0.674160 + 0.738586i \(0.264506\pi\)
\(608\) 8.93286e7 7.74037e7i 0.397448 0.344390i
\(609\) −7.45311e6 6.13320e6i −0.0329978 0.0271541i
\(610\) 1.31787e8 8.46944e7i 0.580608 0.373134i
\(611\) −6.09363e6 + 5.28016e6i −0.0267148 + 0.0231485i
\(612\) 3.62575e7 + 2.83204e7i 0.158177 + 0.123551i
\(613\) 1.59260e7 1.10768e8i 0.0691393 0.480874i −0.925606 0.378489i \(-0.876444\pi\)
0.994745 0.102385i \(-0.0326473\pi\)
\(614\) −3.26037e7 2.82513e7i −0.140852 0.122049i
\(615\) 1.41795e7 1.20272e8i 0.0609586 0.517060i
\(616\) 7.80837e6 + 2.29275e6i 0.0334055 + 0.00980875i
\(617\) −2.40810e8 + 1.09974e8i −1.02522 + 0.468204i −0.855782 0.517336i \(-0.826924\pi\)
−0.169441 + 0.985540i \(0.554196\pi\)
\(618\) 1.47579e8 7.19902e7i 0.625259 0.305006i
\(619\) 3.13611e7 + 2.01546e7i 0.132227 + 0.0849770i 0.605082 0.796163i \(-0.293140\pi\)
−0.472855 + 0.881140i \(0.656777\pi\)
\(620\) 8.45662e7i 0.354831i
\(621\) −1.82427e8 + 1.55153e8i −0.761753 + 0.647868i
\(622\) −3.93132e8 −1.63368
\(623\) −3.01567e6 + 4.69247e6i −0.0124715 + 0.0194061i
\(624\) 9.54099e7 + 1.95589e8i 0.392681 + 0.804992i
\(625\) −7.49692e7 1.64160e8i −0.307074 0.672398i
\(626\) −6.82216e7 + 2.32342e8i −0.278099 + 0.947118i
\(627\) 9.37202e7 + 1.10491e7i 0.380216 + 0.0448255i
\(628\) −6.22731e7 + 7.18670e7i −0.251433 + 0.290169i
\(629\) 1.10154e8 + 1.58377e7i 0.442636 + 0.0636415i
\(630\) 1.25629e7 1.60838e7i 0.0502423 0.0643231i
\(631\) 2.49524e8 + 2.87966e8i 0.993173 + 1.14618i 0.989257 + 0.146190i \(0.0467011\pi\)
0.00391620 + 0.999992i \(0.498753\pi\)
\(632\) 2.12293e8 + 3.30334e8i 0.840976 + 1.30858i
\(633\) 9.08440e7 1.10394e8i 0.358167 0.435247i
\(634\) −1.23149e8 1.42121e8i −0.483239 0.557687i
\(635\) 2.75394e7 + 9.37906e7i 0.107556 + 0.366301i
\(636\) −6.78981e7 + 1.15326e7i −0.263928 + 0.0448288i
\(637\) −2.03947e8 + 2.35367e8i −0.789038 + 0.910599i
\(638\) −2.66320e7 1.21624e7i −0.102551 0.0468337i
\(639\) −9.69991e7 2.77302e8i −0.371762 1.06280i
\(640\) −5.38222e7 1.17854e8i −0.205315 0.449578i
\(641\) −1.76181e8 + 2.53310e7i −0.668937 + 0.0961786i −0.468412 0.883510i \(-0.655174\pi\)
−0.200525 + 0.979689i \(0.564265\pi\)
\(642\) −2.43973e6 649420.i −0.00922013 0.00245426i
\(643\) −3.52224e8 −1.32491 −0.662454 0.749103i \(-0.730485\pi\)
−0.662454 + 0.749103i \(0.730485\pi\)
\(644\) 4.89114e6 3.55455e6i 0.0183127 0.0133084i
\(645\) −3.33599e6 1.03769e7i −0.0124321 0.0386714i
\(646\) 2.28355e8 + 1.46755e8i 0.847058 + 0.544371i
\(647\) −2.39223e8 + 3.43951e7i −0.883264 + 0.126994i −0.568996 0.822340i \(-0.692668\pi\)
−0.314268 + 0.949334i \(0.601759\pi\)
\(648\) 2.97763e7 + 2.91526e8i 0.109432 + 1.07140i
\(649\) 1.11067e7 + 3.26123e6i 0.0406305 + 0.0119302i
\(650\) −5.77951e7 2.63941e7i −0.210451 0.0961097i
\(651\) 2.07435e7 4.86620e7i 0.0751864 0.176379i
\(652\) −8.09390e6 + 5.62943e7i −0.0292022 + 0.203106i
\(653\) 3.14965e7 + 1.07267e8i 0.113116 + 0.385237i 0.996518 0.0833789i \(-0.0265712\pi\)
−0.883402 + 0.468615i \(0.844753\pi\)
\(654\) 1.19938e8 1.97501e8i 0.428768 0.706051i
\(655\) −4.01265e8 + 2.57877e8i −1.42793 + 0.917675i
\(656\) 6.59331e7 + 1.02594e8i 0.233556 + 0.363421i
\(657\) −9.19138e7 2.19778e7i −0.324104 0.0774975i
\(658\) −730615. + 214528.i −0.00256455 + 0.000753019i
\(659\) 2.31461e8 + 3.32790e7i 0.808762 + 0.116282i 0.534278 0.845309i \(-0.320584\pi\)
0.274485 + 0.961591i \(0.411493\pi\)
\(660\) −6.74464e6 + 1.58222e7i −0.0234599 + 0.0550344i
\(661\) −1.97681e8 + 4.32860e8i −0.684478 + 1.49880i 0.173349 + 0.984860i \(0.444541\pi\)
−0.857828 + 0.513938i \(0.828186\pi\)
\(662\) −9.87324e7 + 3.36252e8i −0.340319 + 1.15902i
\(663\) 2.42118e8 2.20829e8i 0.830781 0.757733i
\(664\) −8.64165e7 6.01040e8i −0.295184 2.05305i
\(665\) −1.80875e7 + 2.81447e7i −0.0615054 + 0.0957043i
\(666\) 7.37725e7 + 1.02880e8i 0.249731 + 0.348264i
\(667\) −1.07714e8 + 5.68520e7i −0.362991 + 0.191588i
\(668\) 3.11350e7i 0.104453i
\(669\) 4.45802e8 + 1.18666e8i 1.48889 + 0.396322i
\(670\) 4.16272e7 + 2.89523e8i 0.138405 + 0.962629i
\(671\) 7.51219e7 3.43070e7i 0.248656 0.113557i
\(672\) −342875. 1.34714e7i −0.00112987 0.0443920i
\(673\) 5.93783e6 1.30020e7i 0.0194797 0.0426546i −0.899642 0.436628i \(-0.856173\pi\)
0.919122 + 0.393974i \(0.128900\pi\)
\(674\) 2.96604e8 + 2.57009e8i 0.968719 + 0.839400i
\(675\) −4.69215e7 4.64602e7i −0.152567 0.151067i
\(676\) −3.11770e7 + 9.15439e6i −0.100924 + 0.0296339i
\(677\) 3.00648e8 2.60513e8i 0.968929 0.839582i −0.0181468 0.999835i \(-0.505777\pi\)
0.987076 + 0.160254i \(0.0512312\pi\)
\(678\) 1.65949e8 2.01663e8i 0.532458 0.647048i
\(679\) −4.31649e6 + 2.77404e6i −0.0137886 + 0.00886141i
\(680\) −2.09353e8 + 1.81405e8i −0.665813 + 0.576930i
\(681\) 2.48655e8 + 3.66087e8i 0.787328 + 1.15916i
\(682\) 2.28354e7 1.58823e8i 0.0719871 0.500681i
\(683\) −4.08036e8 3.53565e8i −1.28067 1.10970i −0.988158 0.153442i \(-0.950964\pi\)
−0.292510 0.956262i \(-0.594491\pi\)
\(684\) −1.65140e7 8.41900e7i −0.0516042 0.263083i
\(685\) 1.73342e8 + 5.08978e7i 0.539302 + 0.158353i
\(686\) −5.38003e7 + 2.45698e7i −0.166653 + 0.0761078i
\(687\) −1.17258e8 2.40377e8i −0.361635 0.741350i
\(688\) 9.23388e6 + 5.93425e6i 0.0283543 + 0.0182222i
\(689\) 4.90551e8i 1.49978i
\(690\) −1.25964e8 2.24620e8i −0.383443 0.683755i
\(691\) −3.18445e8 −0.965162 −0.482581 0.875851i \(-0.660301\pi\)
−0.482581 + 0.875851i \(0.660301\pi\)
\(692\) 1.09097e7 1.69758e7i 0.0329225 0.0512284i
\(693\) 7.76214e6 7.45015e6i 0.0233229 0.0223854i
\(694\) −8.72223e7 1.90990e8i −0.260945 0.571390i
\(695\) 4.76628e7 1.62325e8i 0.141979 0.483537i
\(696\) −1.74498e7 + 1.48011e8i −0.0517561 + 0.439003i
\(697\) 1.20260e8 1.38787e8i 0.355159 0.409875i
\(698\) −2.02092e8 2.90564e7i −0.594268 0.0854428i
\(699\) 7.68373e7 + 1.13125e8i 0.224978 + 0.331229i
\(700\) 1.09174e6 + 1.25993e6i 0.00318290 + 0.00367327i
\(701\) −1.48987e8 2.31828e8i −0.432508 0.672995i 0.554769 0.832004i \(-0.312806\pi\)
−0.987277 + 0.159009i \(0.949170\pi\)
\(702\) 3.71960e8 + 2.47569e7i 1.07519 + 0.0715623i
\(703\) −1.35902e8 1.56839e8i −0.391164 0.451428i
\(704\) −3.39586e7 1.15652e8i −0.0973266 0.331464i
\(705\) −1.50893e6 8.88382e6i −0.00430629 0.0253532i
\(706\) 2.97138e8 3.42915e8i 0.844391 0.974479i
\(707\) −3.13151e7 1.43011e7i −0.0886126 0.0404680i
\(708\) −267766. 1.05204e7i −0.000754493 0.0296437i
\(709\) 3.27695e7 + 7.17552e7i 0.0919457 + 0.201333i 0.950017 0.312197i \(-0.101065\pi\)
−0.858072 + 0.513530i \(0.828338\pi\)
\(710\) 3.12699e8 4.49594e7i 0.873679 0.125616i
\(711\) 5.18460e8 2.64089e7i 1.44247 0.0734753i
\(712\) 8.61272e7 0.238616
\(713\) −4.65270e8 4.78633e8i −1.28362 1.32049i
\(714\) 2.94624e7 9.47159e6i 0.0809418 0.0260213i
\(715\) 1.03062e8 + 6.62341e7i 0.281956 + 0.181202i
\(716\) −2.67356e7 + 3.84399e6i −0.0728367 + 0.0104723i
\(717\) 4.66361e8 4.25355e8i 1.26522 1.15397i
\(718\) 2.86687e7 + 8.41789e6i 0.0774524 + 0.0227421i
\(719\) 3.44406e8 + 1.57285e8i 0.926583 + 0.423156i 0.820789 0.571232i \(-0.193534\pi\)
0.105794 + 0.994388i \(0.466262\pi\)
\(720\) −2.42180e8 2.23208e7i −0.648846 0.0598016i
\(721\) −4.36739e6 + 3.03759e7i −0.0116524 + 0.0810445i
\(722\) −4.88101e7 1.66232e8i −0.129687 0.441675i
\(723\) −8.41206e7 5.10844e7i −0.222581 0.135168i
\(724\) 5.93212e7 3.81234e7i 0.156313 0.100456i
\(725\) −1.81561e7 2.82514e7i −0.0476440 0.0741356i
\(726\) −1.58768e8 + 2.61443e8i −0.414909 + 0.683230i
\(727\) −1.91086e7 + 5.61080e6i −0.0497309 + 0.0146023i −0.306503 0.951870i \(-0.599159\pi\)
0.256773 + 0.966472i \(0.417341\pi\)
\(728\) −5.21620e7 7.49977e6i −0.135195 0.0194381i
\(729\) 3.53983e8 + 1.57451e8i 0.913692 + 0.406408i
\(730\) 4.22170e7 9.24423e7i 0.108522 0.237630i
\(731\) 4.65663e6 1.58590e7i 0.0119212 0.0405998i
\(732\) −5.05953e7 5.54729e7i −0.128996 0.141432i
\(733\) −1.06240e7 7.38914e7i −0.0269759 0.187621i 0.971878 0.235485i \(-0.0756678\pi\)
−0.998854 + 0.0478636i \(0.984759\pi\)
\(734\) −2.32850e7 + 3.62321e7i −0.0588827 + 0.0916232i
\(735\) −1.06523e8 3.31351e8i −0.268276 0.834500i
\(736\) −1.58466e8 6.16739e7i −0.397469 0.154692i
\(737\) 1.54199e8i 0.385194i
\(738\) 2.08636e8 1.06273e7i 0.519063 0.0264396i
\(739\) 6.52860e6 + 4.54074e7i 0.0161766 + 0.112511i 0.996310 0.0858295i \(-0.0273540\pi\)
−0.980133 + 0.198340i \(0.936445\pi\)
\(740\) 3.44059e7 1.57127e7i 0.0849060 0.0387753i
\(741\) −6.10898e8 + 1.55486e7i −1.50146 + 0.0382153i
\(742\) −1.92449e7 + 4.21404e7i −0.0471090 + 0.103154i
\(743\) 2.67084e8 + 2.31430e8i 0.651151 + 0.564226i 0.916554 0.399912i \(-0.130959\pi\)
−0.265402 + 0.964138i \(0.585505\pi\)
\(744\) −8.05259e8 + 1.36775e8i −1.95532 + 0.332114i
\(745\) −2.05404e8 + 6.03120e7i −0.496752 + 0.145859i
\(746\) 9.14067e7 7.92044e7i 0.220172 0.190780i
\(747\) −7.46257e8 2.95909e8i −1.79030 0.709898i
\(748\) −2.19411e7 + 1.41007e7i −0.0524268 + 0.0336926i
\(749\) 356598. 308994.i 0.000848660 0.000735368i
\(750\) 3.32320e8 2.25719e8i 0.787722 0.535039i
\(751\) 8.16650e7 5.67993e8i 0.192804 1.34098i −0.631738 0.775182i \(-0.717658\pi\)
0.824543 0.565800i \(-0.191433\pi\)
\(752\) 6.85780e6 + 5.94232e6i 0.0161262 + 0.0139734i
\(753\) −4.95431e8 5.84088e7i −1.16038 0.136802i
\(754\) 1.81911e8 + 5.34139e7i 0.424370 + 0.124606i
\(755\) −6.73667e7 + 3.07653e7i −0.156532 + 0.0714859i
\(756\) −8.60794e6 4.64524e6i −0.0199220 0.0107508i
\(757\) 5.19385e8 + 3.33788e8i 1.19730 + 0.769456i 0.978486 0.206312i \(-0.0661461\pi\)
0.218810 + 0.975767i \(0.429782\pi\)
\(758\) 1.70078e8i 0.390517i
\(759\) −4.88774e7 1.26659e8i −0.111785 0.289675i
\(760\) 5.16577e8 1.17678
\(761\) −3.00280e8 + 4.67244e8i −0.681353 + 1.06021i 0.312545 + 0.949903i \(0.398818\pi\)
−0.993898 + 0.110303i \(0.964818\pi\)
\(762\) −1.51549e8 + 7.39268e7i −0.342522 + 0.167085i
\(763\) 1.79396e7 + 3.92823e7i 0.0403868 + 0.0884348i
\(764\) 3.99532e7 1.36068e8i 0.0895925 0.305124i
\(765\) 7.04933e7 + 3.59381e8i 0.157458 + 0.802732i
\(766\) −1.10741e8 + 1.27802e8i −0.246390 + 0.284350i
\(767\) −7.41959e7 1.06678e7i −0.164435 0.0236422i
\(768\) −2.32033e8 + 1.57602e8i −0.512231 + 0.347919i
\(769\) −5.01831e8 5.79144e8i −1.10352 1.27352i −0.958809 0.284050i \(-0.908322\pi\)
−0.144706 0.989475i \(-0.546224\pi\)
\(770\) 6.25505e6 + 9.73304e6i 0.0137012 + 0.0213195i
\(771\) 1.12196e8 + 9.23267e7i 0.244802 + 0.201449i
\(772\) 1.50339e7 + 1.73501e7i 0.0326754 + 0.0377094i
\(773\) −2.19701e8 7.48231e8i −0.475656 1.61993i −0.752201 0.658934i \(-0.771008\pi\)
0.276545 0.961001i \(-0.410810\pi\)
\(774\) 1.66838e7 8.67078e6i 0.0359810 0.0186997i
\(775\) 1.20526e8 1.39095e8i 0.258927 0.298817i
\(776\) 7.20668e7 + 3.29118e7i 0.154223 + 0.0704314i
\(777\) −2.36524e7 + 602004.i −0.0504211 + 0.00128332i
\(778\) −1.32621e8 2.90399e8i −0.281626 0.616675i
\(779\) −3.38971e8 + 4.87367e7i −0.717052 + 0.103097i
\(780\) 2.86497e7 1.07631e8i 0.0603720 0.226805i
\(781\) 1.66543e8 0.349601
\(782\) 3.33698e7 3.89084e8i 0.0697804 0.813622i
\(783\) 1.58316e8 + 1.17298e8i 0.329792 + 0.244347i
\(784\) 2.94851e8 + 1.89490e8i 0.611864 + 0.393221i
\(785\) −7.49268e8 + 1.07728e8i −1.54892 + 0.222701i
\(786\) −5.54465e8 6.07918e8i −1.14184 1.25192i
\(787\) 6.98903e8 + 2.05216e8i 1.43381 + 0.421006i 0.904155 0.427205i \(-0.140502\pi\)
0.529659 + 0.848211i \(0.322320\pi\)
\(788\) 1.15751e8 + 5.28619e7i 0.236563 + 0.108035i
\(789\) 6.64898e8 + 2.83431e8i 1.35370 + 0.577054i
\(790\) −7.94473e7 + 5.52568e8i −0.161138 + 1.12074i
\(791\) 1.37513e7 + 4.68328e7i 0.0277853 + 0.0946282i
\(792\) −1.61571e8 3.86337e7i −0.325228 0.0777662i
\(793\) −4.49890e8 + 2.89127e8i −0.902168 + 0.579788i
\(794\) −4.52027e8 7.03368e8i −0.903031 1.40514i
\(795\) −4.68592e8 2.84564e8i −0.932595 0.566342i
\(796\) −1.03923e8 + 3.05146e7i −0.206050 + 0.0605018i
\(797\) 3.27877e8 + 4.71416e7i 0.647643 + 0.0931170i 0.458305 0.888795i \(-0.348457\pi\)
0.189338 + 0.981912i \(0.439366\pi\)
\(798\) −5.30887e7 2.26305e7i −0.104471 0.0445335i
\(799\) 5.67632e6 1.24294e7i 0.0111282 0.0243674i
\(800\) 1.32092e7 4.49865e7i 0.0257993 0.0878643i
\(801\) 5.66077e7 9.87974e7i 0.110148 0.192242i
\(802\) −9.99895e7 6.95442e8i −0.193835 1.34815i
\(803\) 2.89647e7 4.50700e7i 0.0559400 0.0870444i
\(804\) 1.33461e8 4.29051e7i 0.256794 0.0825545i
\(805\) 4.79544e7 + 4.11281e6i 0.0919265 + 0.00788408i
\(806\) 1.03905e9i 1.98441i
\(807\) −2.14014e8 + 8.04003e8i −0.407212 + 1.52981i
\(808\) 7.56492e7 + 5.26152e8i 0.143407 + 0.997417i
\(809\) 9.86852e7 4.50680e7i 0.186383 0.0851183i −0.320038 0.947405i \(-0.603696\pi\)
0.506421 + 0.862287i \(0.330968\pi\)
\(810\) −2.39419e8 + 3.40948e8i −0.450509 + 0.641553i
\(811\) −2.57026e8 + 5.62809e8i −0.481854 + 1.05511i 0.500096 + 0.865970i \(0.333298\pi\)
−0.981950 + 0.189143i \(0.939429\pi\)
\(812\) −3.75957e6 3.25769e6i −0.00702215 0.00608473i
\(813\) 2.30627e7 + 1.35781e8i 0.0429179 + 0.252678i
\(814\) −6.88605e7 + 2.02193e7i −0.127672 + 0.0374880i
\(815\) −3.42148e8 + 2.96473e8i −0.632035 + 0.547662i
\(816\) −2.84771e8 2.34339e8i −0.524113 0.431295i
\(817\) −2.59296e7 + 1.66639e7i −0.0475477 + 0.0305570i
\(818\) 6.34634e8 5.49914e8i 1.15948 1.00470i
\(819\) −4.28869e7 + 5.49063e7i −0.0780680 + 0.0999473i
\(820\) 8.88276e6 6.17809e7i 0.0161104 0.112050i
\(821\) −1.38539e8 1.20044e8i −0.250346 0.216926i 0.520643 0.853775i \(-0.325692\pi\)
−0.770989 + 0.636848i \(0.780238\pi\)
\(822\) −3.64879e7 + 3.09495e8i −0.0656951 + 0.557235i
\(823\) 1.02448e9 + 3.00814e8i 1.83782 + 0.539633i 0.999980 0.00628052i \(-0.00199916\pi\)
0.837841 + 0.545914i \(0.183817\pi\)
\(824\) 4.31026e8 1.96843e8i 0.770411 0.351835i
\(825\) 3.36439e7 1.64117e7i 0.0599162 0.0292275i
\(826\) −5.95523e6 3.82719e6i −0.0105672 0.00679110i
\(827\) 1.46322e8i 0.258697i −0.991599 0.129349i \(-0.958711\pi\)
0.991599 0.129349i \(-0.0412887\pi\)
\(828\) −9.60248e7 + 7.75461e7i −0.169158 + 0.136606i
\(829\) 8.80562e7 0.154560 0.0772799 0.997009i \(-0.475377\pi\)
0.0772799 + 0.997009i \(0.475377\pi\)
\(830\) 4.66722e8 7.26234e8i 0.816252 1.27011i
\(831\) 2.06999e8 + 4.24347e8i 0.360716 + 0.739466i
\(832\) 3.24245e8 + 7.09998e8i 0.562994 + 1.23278i
\(833\) 1.48693e8 5.06402e8i 0.257250 0.876114i
\(834\) 2.89824e8 + 3.41687e7i 0.499615 + 0.0589020i
\(835\) −1.62303e8 + 1.87308e8i −0.278784 + 0.321734i
\(836\) 4.81417e7 + 6.92174e6i 0.0823954 + 0.0118467i
\(837\) −3.72366e8 + 1.01362e9i −0.635030 + 1.72861i
\(838\) −2.08131e8 2.40196e8i −0.353676 0.408164i
\(839\) 2.21516e8 + 3.44685e8i 0.375075 + 0.583628i 0.976557 0.215258i \(-0.0690592\pi\)
−0.601482 + 0.798886i \(0.705423\pi\)
\(840\) 3.74228e7 4.54765e7i 0.0631391 0.0767271i
\(841\) −3.23904e8 3.73805e8i −0.544538 0.628430i
\(842\) 4.17625e7 + 1.42230e8i 0.0699601 + 0.238262i
\(843\) −7.17952e8 + 1.21946e8i −1.19843 + 0.203556i
\(844\) 4.82524e7 5.56863e7i 0.0802586 0.0926234i
\(845\) −2.35281e8 1.07449e8i −0.389957 0.178087i
\(846\) 1.46723e7 5.13232e6i 0.0242319 0.00847622i
\(847\) −2.37476e7 5.20001e7i −0.0390814 0.0855764i
\(848\) 5.46450e8 7.85676e7i 0.896112 0.128842i
\(849\) 7.11715e8 + 1.89448e8i 1.16301 + 0.309576i
\(850\) 1.07674e8 0.175329
\(851\) −1.08284e8 + 2.78227e8i −0.175702 + 0.451452i
\(852\) −4.63396e7 1.44144e8i −0.0749262 0.233066i
\(853\) −1.48777e8 9.56134e7i −0.239712 0.154054i 0.415270 0.909698i \(-0.363687\pi\)
−0.654982 + 0.755645i \(0.727324\pi\)
\(854\) −4.99903e7 + 7.18752e6i −0.0802624 + 0.0115400i
\(855\) 3.39524e8 5.92571e8i 0.543216 0.948074i
\(856\) −6.99051e6 2.05260e6i −0.0111452 0.00327252i
\(857\) 7.60822e8 + 3.47456e8i 1.20876 + 0.552023i 0.914844 0.403808i \(-0.132314\pi\)
0.293918 + 0.955831i \(0.405041\pi\)
\(858\) −8.28702e7 + 1.94404e8i −0.131201 + 0.307783i
\(859\) 1.15216e8 8.01344e8i 0.181774 1.26427i −0.670790 0.741647i \(-0.734045\pi\)
0.852565 0.522622i \(-0.175046\pi\)
\(860\) −1.58270e6 5.39016e6i −0.00248830 0.00847436i
\(861\) −2.02658e7 + 3.33717e7i −0.0317508 + 0.0522841i
\(862\) −6.29934e8 + 4.04834e8i −0.983497 + 0.632055i
\(863\) −4.04979e8 6.30160e8i −0.630086 0.980433i −0.998706 0.0508532i \(-0.983806\pi\)
0.368620 0.929580i \(-0.379830\pi\)
\(864\) 2.09797e7 + 2.74286e8i 0.0325281 + 0.425268i
\(865\) 1.54125e8 4.52551e7i 0.238135 0.0699229i
\(866\) 7.66193e8 + 1.10162e8i 1.17973 + 0.169620i
\(867\) 3.77904e7 8.86521e7i 0.0579861 0.136029i
\(868\) 1.13256e7 2.47997e7i 0.0173182 0.0379216i
\(869\) −8.29128e7 + 2.82375e8i −0.126346 + 0.430296i
\(870\) −1.56548e8 + 1.42783e8i −0.237733 + 0.216830i
\(871\) −1.42106e8 9.88366e8i −0.215058 1.49576i
\(872\) 3.60500e8 5.60950e8i 0.543696 0.846008i
\(873\) 8.51199e7 6.10371e7i 0.127935 0.0917383i
\(874\) −5.22174e8 + 5.07596e8i −0.782133 + 0.760297i
\(875\) 7.50804e7i 0.112073i
\(876\) −4.70677e7 1.25287e7i −0.0700182 0.0186378i
\(877\) 2.95262e7 + 2.05360e8i 0.0437733 + 0.304450i 0.999933 + 0.0116033i \(0.00369351\pi\)
−0.956159 + 0.292847i \(0.905397\pi\)
\(878\) −2.64646e8 + 1.20860e8i −0.391005 + 0.178566i
\(879\) 1.47844e7 + 5.80870e8i 0.0217689 + 0.855288i
\(880\) 5.72749e7 1.25414e8i 0.0840458 0.184035i
\(881\) 6.09435e8 + 5.28078e8i 0.891250 + 0.772273i 0.974531 0.224253i \(-0.0719943\pi\)
−0.0832805 + 0.996526i \(0.526540\pi\)
\(882\) 5.32740e8 2.76871e8i 0.776443 0.403526i
\(883\) 5.12407e8 1.50456e8i 0.744274 0.218538i 0.112457 0.993657i \(-0.464128\pi\)
0.631816 + 0.775118i \(0.282310\pi\)
\(884\) 1.27640e8 1.10601e8i 0.184770 0.160104i
\(885\) 5.32306e7 6.46862e7i 0.0767947 0.0933216i
\(886\) −3.80587e8 + 2.44589e8i −0.547209 + 0.351670i
\(887\) 5.21517e8 4.51897e8i 0.747304 0.647543i −0.195571 0.980690i \(-0.562656\pi\)
0.942875 + 0.333147i \(0.108111\pi\)
\(888\) 2.05267e8 + 3.02208e8i 0.293143 + 0.431586i
\(889\) 4.48488e6 3.11930e7i 0.00638330 0.0443968i
\(890\) 9.25382e7 + 8.01848e7i 0.131266 + 0.113742i
\(891\) −1.50511e8 + 1.59947e8i −0.212782 + 0.226123i
\(892\) 2.28131e8 + 6.69852e7i 0.321432 + 0.0943809i
\(893\) −2.31784e7 + 1.05852e7i −0.0325484 + 0.0148644i
\(894\) −1.61901e8 3.31897e8i −0.226589 0.464505i
\(895\) −1.80879e8 1.16244e8i −0.252301 0.162144i
\(896\) 4.17698e7i 0.0580682i
\(897\) 4.30014e8 + 7.66800e8i 0.595806 + 1.06244i
\(898\) 6.10132e7 0.0842549
\(899\) −2.96916e8 + 4.62011e8i −0.408653 + 0.635877i
\(900\) −2.35657e7 2.45526e7i −0.0323261 0.0336798i
\(901\) −3.45345e8 7.56199e8i −0.472148 1.03386i
\(902\) −3.33653e7 + 1.13632e8i −0.0454649 + 0.154839i
\(903\) −411440. + 3.48989e6i −0.000558782 + 0.00473967i
\(904\) 4.93541e8 5.69576e8i 0.668064 0.770986i
\(905\) 5.55608e8 + 7.98843e7i 0.749588 + 0.107774i
\(906\) −7.17802e7 1.05680e8i −0.0965206 0.142104i
\(907\) 1.66263e8 + 1.91878e8i 0.222830 + 0.257160i 0.856146 0.516733i \(-0.172852\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(908\) 1.23312e8 + 1.91877e8i 0.164720 + 0.256309i
\(909\) 6.53275e8 + 2.59039e8i 0.869770 + 0.344884i
\(910\) −4.90625e7 5.66211e7i −0.0651066 0.0751371i
\(911\) 2.33374e8 + 7.94798e8i 0.308672 + 1.05124i 0.957050 + 0.289922i \(0.0936293\pi\)
−0.648378 + 0.761318i \(0.724553\pi\)
\(912\) 1.15163e8 + 6.78020e8i 0.151820 + 0.893837i
\(913\) 2.98026e8 3.43940e8i 0.391599 0.451929i
\(914\) 4.77192e8 + 2.17926e8i 0.624963 + 0.285411i
\(915\) −1.52069e7 5.97471e8i −0.0198508 0.779927i
\(916\) −5.72614e7 1.25385e8i −0.0745034 0.163140i
\(917\) 1.52210e8 2.18845e7i 0.197395 0.0283811i
\(918\) −5.90816e8 + 2.23694e8i −0.763702 + 0.289152i
\(919\) −1.22108e9 −1.57325 −0.786627 0.617428i \(-0.788175\pi\)
−0.786627 + 0.617428i \(0.788175\pi\)
\(920\) −3.46893e8 6.57237e8i −0.445484 0.844031i
\(921\) −1.56691e8 + 5.03733e7i −0.200570 + 0.0644794i
\(922\) 5.91664e8 + 3.80240e8i 0.754888 + 0.485137i
\(923\) −1.06748e9 + 1.53481e8i −1.35755 + 0.195186i
\(924\) 4.09692e6 3.73668e6i 0.00519327 0.00473664i
\(925\) −7.89852e7 2.31921e7i −0.0997977 0.0293032i
\(926\) −8.51644e8 3.88933e8i −1.07257 0.489826i
\(927\) 5.74943e7 6.23812e8i 0.0721748 0.783095i
\(928\) −1.99105e7 + 1.38481e8i −0.0249137 + 0.173279i
\(929\) −1.78242e8 6.07037e8i −0.222312 0.757126i −0.992812 0.119685i \(-0.961811\pi\)
0.770500 0.637440i \(-0.220007\pi\)
\(930\) −9.92538e8 6.02744e8i −1.23395 0.749349i
\(931\) −8.27971e8 + 5.32104e8i −1.02604 + 0.659398i
\(932\) 3.81048e7 + 5.92922e7i 0.0470686 + 0.0732402i
\(933\) −7.78518e8 + 1.28198e9i −0.958570 + 1.57848i
\(934\) 3.60169e8 1.05755e8i 0.442044 0.129796i
\(935\) −2.05502e8 2.95467e7i −0.251409 0.0361472i
\(936\) 1.07122e9 + 9.87302e7i 1.30633 + 0.120399i
\(937\) −2.27330e7 + 4.97783e7i −0.0276336 + 0.0605092i −0.922946 0.384931i \(-0.874225\pi\)
0.895312 + 0.445440i \(0.146953\pi\)
\(938\) 2.65673e7 9.04797e7i 0.0321913 0.109633i
\(939\) 6.22556e8 + 6.82573e8i 0.751937 + 0.824427i
\(940\) −660937. 4.59692e6i −0.000795750 0.00553456i
\(941\) −1.42435e8 + 2.21634e8i −0.170942 + 0.265991i −0.916145 0.400847i \(-0.868716\pi\)
0.745203 + 0.666837i \(0.232352\pi\)
\(942\) −3.99639e8 1.24312e9i −0.478096 1.48717i
\(943\) 2.89634e8 + 3.98543e8i 0.345394 + 0.475269i
\(944\) 8.43591e7i 0.100280i
\(945\) −2.75702e7 7.28178e7i −0.0326696 0.0862864i
\(946\) 1.51695e6 + 1.05506e7i 0.00179183 + 0.0124625i
\(947\) −8.01198e8 + 3.65895e8i −0.943387 + 0.430830i −0.826892 0.562361i \(-0.809893\pi\)
−0.116495 + 0.993191i \(0.537166\pi\)
\(948\) 2.67468e8 6.80762e6i 0.313940 0.00799043i
\(949\) −1.44119e8 + 3.15577e8i −0.168625 + 0.369238i
\(950\) −1.51748e8 1.31491e8i −0.176992 0.153364i
\(951\) −7.07321e8 + 1.20140e8i −0.822384 + 0.139684i
\(952\) 8.56892e7 2.51606e7i 0.0993151 0.0291615i
\(953\) 8.81851e8 7.64128e8i 1.01886 0.882851i 0.0257115 0.999669i \(-0.491815\pi\)
0.993153 + 0.116818i \(0.0372694\pi\)
\(954\) 3.48586e8 8.79105e8i 0.401481 1.01250i
\(955\) 9.49664e8 6.10312e8i 1.09033 0.700716i
\(956\) 2.45857e8 2.13036e8i 0.281390 0.243826i
\(957\) −9.24004e7 + 6.27605e7i −0.105424 + 0.0716062i
\(958\) −2.05457e8 + 1.42899e9i −0.233682 + 1.62529i
\(959\) −4.40173e7 3.81412e7i −0.0499077 0.0432452i
\(960\) −8.66307e8 1.02133e8i −0.979170 0.115439i
\(961\) −2.03637e9 5.97933e8i −2.29450 0.673725i
\(962\) 4.22740e8 1.93059e8i 0.474841 0.216852i
\(963\) −6.94912e6 + 6.66980e6i −0.00778128 + 0.00746852i
\(964\) −4.26708e7 2.74229e7i −0.0476321 0.0306113i
\(965\) 1.82748e8i 0.203362i
\(966\) 6.85756e6 + 8.27413e7i 0.00760743 + 0.0917890i
\(967\) −1.89304e8 −0.209353 −0.104677 0.994506i \(-0.533381\pi\)
−0.104677 + 0.994506i \(0.533381\pi\)
\(968\) −4.77214e8 + 7.42559e8i −0.526123 + 0.818663i
\(969\) 9.30772e8 4.54037e8i 1.02299 0.499022i
\(970\) 4.67902e7 + 1.02456e8i 0.0512672 + 0.112259i
\(971\) 4.17869e8 1.42313e9i 0.456439 1.55449i −0.334380 0.942438i \(-0.608527\pi\)
0.790819 0.612050i \(-0.209655\pi\)
\(972\) 1.80315e8 + 8.57639e7i 0.196351 + 0.0933911i
\(973\) −3.57170e7 + 4.12196e7i −0.0387736 + 0.0447471i
\(974\) 3.92232e7 + 5.63945e6i 0.0424489 + 0.00610323i
\(975\) −2.00522e8 + 1.36199e8i −0.216345 + 0.146947i
\(976\) 3.94129e8 + 4.54849e8i 0.423924 + 0.489235i
\(977\) 4.09344e8 + 6.36951e8i 0.438939 + 0.683003i 0.988290 0.152589i \(-0.0487611\pi\)
−0.549350 + 0.835592i \(0.685125\pi\)
\(978\) −6.03026e8 4.96233e8i −0.644644 0.530480i
\(979\) 4.22715e7 + 4.87839e7i 0.0450505 + 0.0519910i
\(980\) −5.05378e7 1.72116e8i −0.0536955 0.182870i
\(981\) −4.06530e8 7.82222e8i −0.430611 0.828558i
\(982\) −8.27726e8 + 9.55246e8i −0.874082 + 1.00874i
\(983\) 3.53299e8 + 1.61346e8i 0.371948 + 0.169863i 0.592614 0.805486i \(-0.298096\pi\)
−0.220666 + 0.975349i \(0.570823\pi\)
\(984\) 6.02659e8 1.53389e7i 0.632537 0.0160994i
\(985\) 4.20795e8 + 9.21413e8i 0.440314 + 0.964153i
\(986\) −3.18024e8 + 4.57250e7i −0.331764 + 0.0477005i
\(987\) −747270. + 2.80733e6i −0.000777188 + 0.00291973i
\(988\) −3.14952e8 −0.326568
\(989\) 3.86137e7 + 2.17998e7i 0.0399165 + 0.0225353i
\(990\) −1.37630e8 1.91933e8i −0.141842 0.197808i
\(991\) 3.38530e8 + 2.17560e8i 0.347838 + 0.223542i 0.702880 0.711309i \(-0.251897\pi\)
−0.355042 + 0.934850i \(0.615534\pi\)
\(992\) −7.58942e8 + 1.09119e8i −0.777452 + 0.111781i
\(993\) 9.00982e8 + 9.87840e8i 0.920170 + 1.00888i
\(994\) −9.77226e7 2.86939e7i −0.0995029 0.0292167i
\(995\) −7.84268e8 3.58163e8i −0.796151 0.363590i
\(996\) −3.80607e8 1.62244e8i −0.385211 0.164207i
\(997\) −3.04842e7 + 2.12022e8i −0.0307602 + 0.213942i −0.999404 0.0345104i \(-0.989013\pi\)
0.968644 + 0.248452i \(0.0799219\pi\)
\(998\) −3.77572e8 1.28589e9i −0.379847 1.29364i
\(999\) 4.81579e8 3.68352e7i 0.483027 0.0369459i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.7.h.a.2.14 460
3.2 odd 2 inner 69.7.h.a.2.33 yes 460
23.12 even 11 inner 69.7.h.a.35.33 yes 460
69.35 odd 22 inner 69.7.h.a.35.14 yes 460
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.7.h.a.2.14 460 1.1 even 1 trivial
69.7.h.a.2.33 yes 460 3.2 odd 2 inner
69.7.h.a.35.14 yes 460 69.35 odd 22 inner
69.7.h.a.35.33 yes 460 23.12 even 11 inner