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Properties

Label 27.7.f.a.2.16
Level $27$
Weight $7$
Character 27.2
Analytic conductor $6.211$
Analytic rank $0$
Dimension $102$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,7,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), 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: \(6.21146025774\)
Analytic rank: \(0\)
Dimension: \(102\)
Relative dimension: \(17\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 2.16
Character \(\chi\) \(=\) 27.2
Dual form 27.7.f.a.14.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.7878 + 2.43117i) q^{2} +(-26.9804 + 1.02752i) q^{3} +(124.053 + 45.1517i) q^{4} +(118.006 + 140.634i) q^{5} +(-374.500 - 51.4266i) q^{6} +(-10.3283 + 3.75918i) q^{7} +(824.665 + 476.120i) q^{8} +(726.888 - 55.4459i) q^{9} +O(q^{10})\) \(q+(13.7878 + 2.43117i) q^{2} +(-26.9804 + 1.02752i) q^{3} +(124.053 + 45.1517i) q^{4} +(118.006 + 140.634i) q^{5} +(-374.500 - 51.4266i) q^{6} +(-10.3283 + 3.75918i) q^{7} +(824.665 + 476.120i) q^{8} +(726.888 - 55.4459i) q^{9} +(1285.14 + 2225.93i) q^{10} +(-109.488 + 130.482i) q^{11} +(-3393.40 - 1090.74i) q^{12} +(-535.873 - 3039.09i) q^{13} +(-151.543 + 26.7212i) q^{14} +(-3328.35 - 3673.11i) q^{15} +(3740.54 + 3138.69i) q^{16} +(-6691.85 + 3863.54i) q^{17} +(10157.0 + 1002.71i) q^{18} +(5440.69 - 9423.54i) q^{19} +(8289.15 + 22774.2i) q^{20} +(274.798 - 112.037i) q^{21} +(-1826.82 + 1532.88i) q^{22} +(2838.25 - 7798.03i) q^{23} +(-22739.0 - 11998.6i) q^{24} +(-3139.26 + 17803.6i) q^{25} -43205.2i q^{26} +(-19554.8 + 2242.85i) q^{27} -1450.99 q^{28} +(33308.2 + 5873.13i) q^{29} +(-36960.8 - 58736.0i) q^{30} +(-13610.5 - 4953.82i) q^{31} +(4769.61 + 5684.20i) q^{32} +(2819.95 - 3632.97i) q^{33} +(-101659. + 37000.8i) q^{34} +(-1747.46 - 1008.90i) q^{35} +(92676.3 + 25942.0i) q^{36} +(33152.3 + 57421.5i) q^{37} +(97925.4 - 116703. i) q^{38} +(17580.8 + 81445.2i) q^{39} +(30356.6 + 172161. i) q^{40} +(9969.66 - 1757.92i) q^{41} +(4061.25 - 876.663i) q^{42} +(-71047.8 - 59616.2i) q^{43} +(-19473.8 + 11243.2i) q^{44} +(93574.6 + 95682.2i) q^{45} +(58091.6 - 100618. i) q^{46} +(2562.80 + 7041.24i) q^{47} +(-104147. - 80839.7i) q^{48} +(-90031.8 + 75545.7i) q^{49} +(-86567.1 + 237841. i) q^{50} +(176579. - 111116. i) q^{51} +(70743.1 - 401204. i) q^{52} +38708.4i q^{53} +(-275071. - 16616.9i) q^{54} -31270.4 q^{55} +(-10307.2 - 1817.43i) q^{56} +(-137109. + 259842. i) q^{57} +(444968. + 161955. i) q^{58} +(34050.8 + 40580.2i) q^{59} +(-247046. - 605942. i) q^{60} +(-142871. + 52000.8i) q^{61} +(-175616. - 101392. i) q^{62} +(-7299.06 + 3305.16i) q^{63} +(-104311. - 180671. i) q^{64} +(364162. - 433992. i) q^{65} +(47713.3 - 43234.9i) q^{66} +(48209.6 + 273410. i) q^{67} +(-1.00459e6 + 177136. i) q^{68} +(-68564.6 + 213311. i) q^{69} +(-21640.9 - 18158.9i) q^{70} +(292423. - 168831. i) q^{71} +(625838. + 300362. i) q^{72} +(-150680. + 260985. i) q^{73} +(317497. + 872317. i) q^{74} +(66405.0 - 483575. i) q^{75} +(1.10042e6 - 923365. i) q^{76} +(640.309 - 1759.24i) q^{77} +(44394.2 + 1.16569e6i) q^{78} +(72897.6 - 413423. i) q^{79} +896431. i q^{80} +(525292. - 80606.0i) q^{81} +141734. q^{82} +(-796135. - 140380. i) q^{83} +(39148.2 - 1490.92i) q^{84} +(-1.33302e6 - 485180. i) q^{85} +(-834658. - 994707. i) q^{86} +(-904703. - 124235. i) q^{87} +(-152416. + 55474.8i) q^{88} +(-290751. - 167865. i) q^{89} +(1.05757e6 + 1.54674e6i) q^{90} +(16959.1 + 29374.0i) q^{91} +(704188. - 839218. i) q^{92} +(372307. + 119671. i) q^{93} +(18217.0 + 103314. i) q^{94} +(1.96730e6 - 346888. i) q^{95} +(-134527. - 148461. i) q^{96} +(50419.6 + 42307.1i) q^{97} +(-1.42501e6 + 822728. i) q^{98} +(-72350.5 + 100917. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.7878 + 2.43117i 1.72348 + 0.303896i 0.945796 − 0.324762i \(-0.105284\pi\)
0.777682 + 0.628658i \(0.216395\pi\)
\(3\) −26.9804 + 1.02752i −0.999276 + 0.0380563i
\(4\) 124.053 + 45.1517i 1.93833 + 0.705495i
\(5\) 118.006 + 140.634i 0.944047 + 1.12507i 0.992002 + 0.126222i \(0.0402850\pi\)
−0.0479554 + 0.998849i \(0.515271\pi\)
\(6\) −374.500 − 51.4266i −1.73379 − 0.238086i
\(7\) −10.3283 + 3.75918i −0.0301115 + 0.0109597i −0.357032 − 0.934092i \(-0.616211\pi\)
0.326920 + 0.945052i \(0.393989\pi\)
\(8\) 824.665 + 476.120i 1.61067 + 0.929923i
\(9\) 726.888 − 55.4459i 0.997103 − 0.0760575i
\(10\) 1285.14 + 2225.93i 1.28514 + 2.22593i
\(11\) −109.488 + 130.482i −0.0822596 + 0.0980332i −0.805604 − 0.592454i \(-0.798159\pi\)
0.723345 + 0.690487i \(0.242604\pi\)
\(12\) −3393.40 − 1090.74i −1.96378 − 0.631218i
\(13\) −535.873 − 3039.09i −0.243911 − 1.38329i −0.823008 − 0.568030i \(-0.807706\pi\)
0.579097 − 0.815259i \(-0.303405\pi\)
\(14\) −151.543 + 26.7212i −0.0552272 + 0.00973804i
\(15\) −3328.35 − 3673.11i −0.986179 − 1.08833i
\(16\) 3740.54 + 3138.69i 0.913219 + 0.766281i
\(17\) −6691.85 + 3863.54i −1.36207 + 0.786391i −0.989899 − 0.141773i \(-0.954720\pi\)
−0.372171 + 0.928164i \(0.621386\pi\)
\(18\) 10157.0 + 1002.71i 1.74160 + 0.171932i
\(19\) 5440.69 − 9423.54i 0.793219 − 1.37389i −0.130746 − 0.991416i \(-0.541737\pi\)
0.923964 − 0.382479i \(-0.124930\pi\)
\(20\) 8289.15 + 22774.2i 1.03614 + 2.84678i
\(21\) 274.798 − 112.037i 0.0296726 − 0.0120977i
\(22\) −1826.82 + 1532.88i −0.171564 + 0.143960i
\(23\) 2838.25 − 7798.03i 0.233274 − 0.640916i −0.766725 − 0.641976i \(-0.778115\pi\)
0.999999 + 0.00105957i \(0.000337270\pi\)
\(24\) −22739.0 − 11998.6i −1.64490 − 0.867953i
\(25\) −3139.26 + 17803.6i −0.200912 + 1.13943i
\(26\) − 43205.2i − 2.45819i
\(27\) −19554.8 + 2242.85i −0.993487 + 0.113949i
\(28\) −1450.99 −0.0660981
\(29\) 33308.2 + 5873.13i 1.36570 + 0.240810i 0.807977 − 0.589214i \(-0.200563\pi\)
0.557727 + 0.830024i \(0.311674\pi\)
\(30\) −36960.8 − 58736.0i −1.36892 − 2.17541i
\(31\) −13610.5 − 4953.82i −0.456866 − 0.166286i 0.103327 − 0.994647i \(-0.467051\pi\)
−0.560194 + 0.828362i \(0.689273\pi\)
\(32\) 4769.61 + 5684.20i 0.145557 + 0.173468i
\(33\) 2819.95 − 3632.97i 0.0784692 − 0.101093i
\(34\) −101659. + 37000.8i −2.58648 + 0.941401i
\(35\) −1747.46 − 1008.90i −0.0407571 − 0.0235311i
\(36\) 92676.3 + 25942.0i 1.98637 + 0.556027i
\(37\) 33152.3 + 57421.5i 0.654499 + 1.13363i 0.982019 + 0.188781i \(0.0604537\pi\)
−0.327520 + 0.944844i \(0.606213\pi\)
\(38\) 97925.4 − 116703.i 1.78462 − 2.12682i
\(39\) 17580.8 + 81445.2i 0.296377 + 1.37300i
\(40\) 30356.6 + 172161.i 0.474322 + 2.69001i
\(41\) 9969.66 − 1757.92i 0.144653 − 0.0255063i −0.100852 − 0.994901i \(-0.532157\pi\)
0.245506 + 0.969395i \(0.421046\pi\)
\(42\) 4061.25 − 876.663i 0.0548166 − 0.0118327i
\(43\) −71047.8 − 59616.2i −0.893605 − 0.749823i 0.0753253 − 0.997159i \(-0.476000\pi\)
−0.968930 + 0.247336i \(0.920445\pi\)
\(44\) −19473.8 + 11243.2i −0.228608 + 0.131987i
\(45\) 93574.6 + 95682.2i 1.02688 + 1.05001i
\(46\) 58091.6 − 100618.i 0.596815 − 1.03371i
\(47\) 2562.80 + 7041.24i 0.0246843 + 0.0678196i 0.951423 − 0.307888i \(-0.0996221\pi\)
−0.926738 + 0.375707i \(0.877400\pi\)
\(48\) −104147. − 80839.7i −0.941719 − 0.730972i
\(49\) −90031.8 + 75545.7i −0.765258 + 0.642128i
\(50\) −86567.1 + 237841.i −0.692536 + 1.90273i
\(51\) 176579. − 111116.i 1.33116 − 0.837657i
\(52\) 70743.1 − 401204.i 0.503123 − 2.85335i
\(53\) 38708.4i 0.260002i 0.991514 + 0.130001i \(0.0414981\pi\)
−0.991514 + 0.130001i \(0.958502\pi\)
\(54\) −275071. − 16616.9i −1.74688 − 0.105528i
\(55\) −31270.4 −0.187951
\(56\) −10307.2 − 1817.43i −0.0586915 − 0.0103489i
\(57\) −137109. + 259842.i −0.740359 + 1.40309i
\(58\) 444968. + 161955.i 2.28058 + 0.830063i
\(59\) 34050.8 + 40580.2i 0.165795 + 0.197587i 0.842545 − 0.538626i \(-0.181056\pi\)
−0.676750 + 0.736213i \(0.736612\pi\)
\(60\) −247046. − 605942.i −1.14373 − 2.80529i
\(61\) −142871. + 52000.8i −0.629441 + 0.229098i −0.636988 − 0.770874i \(-0.719820\pi\)
0.00754706 + 0.999972i \(0.497598\pi\)
\(62\) −175616. − 101392.i −0.736865 − 0.425429i
\(63\) −7299.06 + 3305.16i −0.0291907 + 0.0132182i
\(64\) −104311. − 180671.i −0.397913 − 0.689206i
\(65\) 364162. − 433992.i 1.32603 − 1.58031i
\(66\) 47713.3 − 43234.9i 0.165962 − 0.150385i
\(67\) 48209.6 + 273410.i 0.160291 + 0.909055i 0.953788 + 0.300481i \(0.0971471\pi\)
−0.793497 + 0.608574i \(0.791742\pi\)
\(68\) −1.00459e6 + 177136.i −3.19494 + 0.563354i
\(69\) −68564.6 + 213311.i −0.208714 + 0.649329i
\(70\) −21640.9 − 18158.9i −0.0630930 − 0.0529413i
\(71\) 292423. − 168831.i 0.817027 − 0.471711i −0.0323630 − 0.999476i \(-0.510303\pi\)
0.849390 + 0.527765i \(0.176970\pi\)
\(72\) 625838. + 300362.i 1.67674 + 0.804725i
\(73\) −150680. + 260985.i −0.387335 + 0.670883i −0.992090 − 0.125528i \(-0.959938\pi\)
0.604755 + 0.796411i \(0.293271\pi\)
\(74\) 317497. + 872317.i 0.783511 + 2.15268i
\(75\) 66405.0 − 483575.i 0.157404 − 1.14625i
\(76\) 1.10042e6 − 923365.i 2.50680 − 2.10345i
\(77\) 640.309 − 1759.24i 0.00140255 − 0.00385347i
\(78\) 44394.2 + 1.16569e6i 0.0935498 + 2.45641i
\(79\) 72897.6 − 413423.i 0.147854 − 0.838520i −0.817178 − 0.576386i \(-0.804463\pi\)
0.965031 − 0.262134i \(-0.0844263\pi\)
\(80\) 896431.i 1.75084i
\(81\) 525292. − 80606.0i 0.988431 − 0.151674i
\(82\) 141734. 0.257058
\(83\) −796135. − 140380.i −1.39236 − 0.245511i −0.573361 − 0.819303i \(-0.694361\pi\)
−0.819001 + 0.573792i \(0.805472\pi\)
\(84\) 39148.2 − 1490.92i 0.0660502 − 0.00251545i
\(85\) −1.33302e6 − 485180.i −2.17060 − 0.790035i
\(86\) −834658. − 994707.i −1.31224 − 1.56387i
\(87\) −904703. − 124235.i −1.37388 − 0.188662i
\(88\) −152416. + 55474.8i −0.223657 + 0.0814044i
\(89\) −290751. − 167865.i −0.412430 − 0.238117i 0.279403 − 0.960174i \(-0.409863\pi\)
−0.691833 + 0.722057i \(0.743197\pi\)
\(90\) 1.05757e6 + 1.54674e6i 1.45072 + 2.12173i
\(91\) 16959.1 + 29374.0i 0.0225050 + 0.0389797i
\(92\) 704188. − 839218.i 0.904326 − 1.07773i
\(93\) 372307. + 119671.i 0.462863 + 0.148779i
\(94\) 18217.0 + 103314.i 0.0219328 + 0.124387i
\(95\) 1.96730e6 − 346888.i 2.29456 − 0.404594i
\(96\) −134527. − 148461.i −0.152053 − 0.167803i
\(97\) 50419.6 + 42307.1i 0.0552439 + 0.0463552i 0.669992 − 0.742369i \(-0.266298\pi\)
−0.614748 + 0.788724i \(0.710742\pi\)
\(98\) −1.42501e6 + 822728.i −1.51404 + 0.874134i
\(99\) −72350.5 + 100917.i −0.0745652 + 0.104006i
\(100\) −1.19330e6 + 2.06685e6i −1.19330 + 2.06685i
\(101\) 75167.7 + 206521.i 0.0729570 + 0.200448i 0.970811 − 0.239845i \(-0.0770968\pi\)
−0.897854 + 0.440293i \(0.854875\pi\)
\(102\) 2.70478e6 − 1.10276e6i 2.54878 − 1.03915i
\(103\) −82385.8 + 69129.9i −0.0753947 + 0.0632636i −0.679706 − 0.733485i \(-0.737893\pi\)
0.604311 + 0.796748i \(0.293448\pi\)
\(104\) 1.00506e6 − 2.76137e6i 0.893491 − 2.45485i
\(105\) 48183.9 + 25424.9i 0.0416231 + 0.0219630i
\(106\) −94106.5 + 533704.i −0.0790136 + 0.448108i
\(107\) 531592.i 0.433938i 0.976179 + 0.216969i \(0.0696170\pi\)
−0.976179 + 0.216969i \(0.930383\pi\)
\(108\) −2.52710e6 − 604699.i −2.00610 − 0.480030i
\(109\) −216737. −0.167361 −0.0836804 − 0.996493i \(-0.526667\pi\)
−0.0836804 + 0.996493i \(0.526667\pi\)
\(110\) −431150. − 76023.5i −0.323930 − 0.0571176i
\(111\) −953467. − 1.51519e6i −0.697167 − 1.10790i
\(112\) −50432.2 − 18355.8i −0.0358966 − 0.0130653i
\(113\) −97869.1 − 116636.i −0.0678282 − 0.0808345i 0.731063 − 0.682310i \(-0.239024\pi\)
−0.798892 + 0.601475i \(0.794580\pi\)
\(114\) −2.52216e6 + 3.24932e6i −1.70238 + 2.19320i
\(115\) 1.43160e6 − 521058.i 0.941298 − 0.342604i
\(116\) 3.86680e6 + 2.23250e6i 2.47730 + 1.43027i
\(117\) −558025. − 2.17936e6i −0.348414 − 1.36073i
\(118\) 370830. + 642296.i 0.225699 + 0.390921i
\(119\) 54591.4 − 65059.5i 0.0323954 − 0.0386073i
\(120\) −995933. − 4.61378e6i −0.576350 − 2.67001i
\(121\) 302590. + 1.71607e6i 0.170804 + 0.968679i
\(122\) −2.09630e6 + 369635.i −1.15445 + 0.203561i
\(123\) −267180. + 57673.5i −0.143578 + 0.0309928i
\(124\) −1.46475e6 − 1.22907e6i −0.768244 − 0.644634i
\(125\) −390041. + 225190.i −0.199701 + 0.115298i
\(126\) −108673. + 27825.8i −0.0543265 + 0.0139103i
\(127\) −104318. + 180684.i −0.0509269 + 0.0882080i −0.890365 − 0.455247i \(-0.849551\pi\)
0.839438 + 0.543455i \(0.182884\pi\)
\(128\) −1.16140e6 − 3.19091e6i −0.553797 − 1.52154i
\(129\) 1.97816e6 + 1.53547e6i 0.921493 + 0.715273i
\(130\) 6.07611e6 − 5.09846e6i 2.76564 − 2.32065i
\(131\) −1.38562e6 + 3.80695e6i −0.616353 + 1.69342i 0.0993864 + 0.995049i \(0.468312\pi\)
−0.715740 + 0.698367i \(0.753910\pi\)
\(132\) 513858. − 323356.i 0.223420 − 0.140591i
\(133\) −20768.0 + 117781.i −0.00882755 + 0.0500635i
\(134\) 3.88693e6i 1.61545i
\(135\) −2.62300e6 − 2.48540e6i −1.06610 − 1.01017i
\(136\) −7.35804e6 −2.92513
\(137\) 4.00787e6 + 706696.i 1.55866 + 0.274834i 0.885493 − 0.464654i \(-0.153821\pi\)
0.673170 + 0.739488i \(0.264932\pi\)
\(138\) −1.46395e6 + 2.77440e6i −0.557043 + 1.05568i
\(139\) −1.16110e6 − 422607.i −0.432341 − 0.157359i 0.116677 − 0.993170i \(-0.462776\pi\)
−0.549018 + 0.835811i \(0.684998\pi\)
\(140\) −171225. − 204058.i −0.0623997 − 0.0743651i
\(141\) −76380.5 − 187342.i −0.0272474 − 0.0668311i
\(142\) 4.44233e6 − 1.61688e6i 1.55148 − 0.564692i
\(143\) 455218. + 262820.i 0.155672 + 0.0898774i
\(144\) 2.89298e6 + 2.07408e6i 0.968855 + 0.694605i
\(145\) 3.10460e6 + 5.37732e6i 1.01836 + 1.76385i
\(146\) −2.71204e6 + 3.23209e6i −0.871441 + 1.03854i
\(147\) 2.35147e6 − 2.13077e6i 0.740266 − 0.670785i
\(148\) 1.51998e6 + 8.62021e6i 0.468869 + 2.65909i
\(149\) −498120. + 87832.0i −0.150583 + 0.0265518i −0.248431 − 0.968650i \(-0.579915\pi\)
0.0978485 + 0.995201i \(0.468804\pi\)
\(150\) 2.09123e6 − 6.50601e6i 0.619624 − 1.92771i
\(151\) −115045. − 96534.3i −0.0334147 − 0.0280383i 0.625927 − 0.779881i \(-0.284721\pi\)
−0.659342 + 0.751843i \(0.729165\pi\)
\(152\) 8.97348e6 − 5.18084e6i 2.55523 − 1.47526i
\(153\) −4.65001e6 + 3.17940e6i −1.29831 + 0.887709i
\(154\) 13105.5 − 22699.3i 0.00358831 − 0.00621514i
\(155\) −909444. − 2.49868e6i −0.244220 − 0.670988i
\(156\) −1.49643e6 + 1.08973e7i −0.394170 + 2.87043i
\(157\) −1.66116e6 + 1.39388e6i −0.429253 + 0.360186i −0.831670 − 0.555271i \(-0.812615\pi\)
0.402417 + 0.915456i \(0.368170\pi\)
\(158\) 2.01020e6 − 5.52298e6i 0.509645 − 1.40024i
\(159\) −39773.7 − 1.04437e6i −0.00989474 − 0.259814i
\(160\) −236549. + 1.34154e6i −0.0577513 + 0.327524i
\(161\) 91209.5i 0.0218556i
\(162\) 7.43861e6 + 165691.i 1.74963 + 0.0389722i
\(163\) 954503. 0.220401 0.110201 − 0.993909i \(-0.464851\pi\)
0.110201 + 0.993909i \(0.464851\pi\)
\(164\) 1.31614e6 + 232071.i 0.298381 + 0.0526126i
\(165\) 843689. − 32131.0i 0.187815 − 0.00715273i
\(166\) −1.06357e7 − 3.87107e6i −2.32510 − 0.846266i
\(167\) 37010.3 + 44107.2i 0.00794646 + 0.00947022i 0.770003 − 0.638040i \(-0.220255\pi\)
−0.762057 + 0.647510i \(0.775810\pi\)
\(168\) 279959. + 38444.3i 0.0590428 + 0.00810782i
\(169\) −4.41316e6 + 1.60626e6i −0.914303 + 0.332779i
\(170\) −1.71999e7 − 9.93038e6i −3.50090 − 2.02125i
\(171\) 3.43227e6 − 7.15153e6i 0.686426 − 1.43025i
\(172\) −6.12194e6 − 1.06035e7i −1.20311 − 2.08384i
\(173\) 1.55910e6 − 1.85807e6i 0.301118 − 0.358858i −0.594175 − 0.804336i \(-0.702521\pi\)
0.895293 + 0.445477i \(0.146966\pi\)
\(174\) −1.21719e7 − 3.91241e6i −2.31052 − 0.742671i
\(175\) −34503.9 − 195681.i −0.00643804 − 0.0365120i
\(176\) −819086. + 144427.i −0.150242 + 0.0264917i
\(177\) −960404. − 1.05988e6i −0.173195 − 0.191134i
\(178\) −3.60071e6 − 3.02136e6i −0.638452 − 0.535725i
\(179\) −2.35358e6 + 1.35884e6i −0.410364 + 0.236924i −0.690946 − 0.722906i \(-0.742806\pi\)
0.280582 + 0.959830i \(0.409473\pi\)
\(180\) 7.28802e6 + 1.60947e7i 1.24966 + 2.75973i
\(181\) 3.95475e6 − 6.84983e6i 0.666935 − 1.15517i −0.311822 − 0.950141i \(-0.600939\pi\)
0.978757 − 0.205024i \(-0.0657274\pi\)
\(182\) 162416. + 446234.i 0.0269410 + 0.0740199i
\(183\) 3.80129e6 − 1.54981e6i 0.620266 − 0.252886i
\(184\) 6.05340e6 − 5.07941e6i 0.971731 − 0.815379i
\(185\) −4.16324e6 + 1.14384e7i −0.657532 + 1.80655i
\(186\) 4.84237e6 + 2.55515e6i 0.752522 + 0.397079i
\(187\) 228551. − 1.29618e6i 0.0349509 − 0.198216i
\(188\) 989203.i 0.148872i
\(189\) 193536. − 96674.7i 0.0286666 − 0.0143195i
\(190\) 2.79682e7 4.07759
\(191\) 9.91131e6 + 1.74763e6i 1.42243 + 0.250813i 0.831327 − 0.555784i \(-0.187582\pi\)
0.591103 + 0.806596i \(0.298693\pi\)
\(192\) 2.99999e6 + 4.76741e6i 0.423854 + 0.673563i
\(193\) 1.47427e6 + 536591.i 0.205071 + 0.0746399i 0.442514 − 0.896762i \(-0.354087\pi\)
−0.237442 + 0.971402i \(0.576309\pi\)
\(194\) 592321. + 705901.i 0.0811246 + 0.0966805i
\(195\) −9.37932e6 + 1.20835e7i −1.26493 + 1.62963i
\(196\) −1.45797e7 + 5.30659e6i −1.93634 + 0.704770i
\(197\) −6.79639e6 − 3.92389e6i −0.888954 − 0.513238i −0.0153538 − 0.999882i \(-0.504887\pi\)
−0.873600 + 0.486644i \(0.838221\pi\)
\(198\) −1.24290e6 + 1.21552e6i −0.160118 + 0.156591i
\(199\) −59392.2 − 102870.i −0.00753650 − 0.0130536i 0.862233 − 0.506513i \(-0.169066\pi\)
−0.869769 + 0.493459i \(0.835732\pi\)
\(200\) −1.10655e7 + 1.31873e7i −1.38319 + 1.64842i
\(201\) −1.58165e6 − 7.32719e6i −0.194770 − 0.902296i
\(202\) 534311. + 3.03023e6i 0.0648246 + 0.367639i
\(203\) −366093. + 64552.1i −0.0437626 + 0.00771653i
\(204\) 2.69223e7 − 5.81146e6i 3.17118 − 0.684533i
\(205\) 1.42370e6 + 1.19463e6i 0.165256 + 0.138666i
\(206\) −1.30399e6 + 752857.i −0.149167 + 0.0861214i
\(207\) 1.63072e6 − 5.82566e6i 0.183852 − 0.656802i
\(208\) 7.53429e6 − 1.30498e7i 0.837244 − 1.45015i
\(209\) 633917. + 1.74167e6i 0.0694374 + 0.190778i
\(210\) 602540. + 467698.i 0.0650620 + 0.0505019i
\(211\) −6.75739e6 + 5.67013e6i −0.719336 + 0.603595i −0.927202 − 0.374563i \(-0.877793\pi\)
0.207865 + 0.978157i \(0.433348\pi\)
\(212\) −1.74775e6 + 4.80190e6i −0.183430 + 0.503971i
\(213\) −7.71623e6 + 4.85559e6i −0.798484 + 0.502462i
\(214\) −1.29239e6 + 7.32950e6i −0.131872 + 0.747882i
\(215\) − 1.70268e7i − 1.71324i
\(216\) −1.71940e7 − 7.46084e6i −1.70615 − 0.740332i
\(217\) 159195. 0.0155794
\(218\) −2.98833e6 − 526924.i −0.288443 − 0.0508602i
\(219\) 3.79724e6 − 7.19632e6i 0.361523 − 0.685138i
\(220\) −3.87919e6 − 1.41191e6i −0.364312 − 0.132599i
\(221\) 1.53276e7 + 1.82667e7i 1.42003 + 1.69233i
\(222\) −9.46254e6 − 2.32093e7i −0.864866 − 2.12130i
\(223\) 1.07860e7 − 3.92579e6i 0.972629 − 0.354008i 0.193658 − 0.981069i \(-0.437965\pi\)
0.778970 + 0.627061i \(0.215742\pi\)
\(224\) −70629.6 − 40778.0i −0.00628410 − 0.00362812i
\(225\) −1.29475e6 + 1.31153e7i −0.113668 + 1.15141i
\(226\) −1.06584e6 − 1.84609e6i −0.0923352 − 0.159929i
\(227\) 3.57786e6 − 4.26393e6i 0.305877 − 0.364530i −0.591107 − 0.806593i \(-0.701309\pi\)
0.896984 + 0.442063i \(0.145753\pi\)
\(228\) −2.87411e7 + 2.60435e7i −2.42493 + 2.19733i
\(229\) 3.36581e6 + 1.90884e7i 0.280274 + 1.58951i 0.721694 + 0.692212i \(0.243364\pi\)
−0.441420 + 0.897300i \(0.645525\pi\)
\(230\) 2.10054e7 − 3.70382e6i 1.72642 − 0.304415i
\(231\) −15468.2 + 48122.9i −0.00125488 + 0.00390405i
\(232\) 2.46717e7 + 2.07021e7i 1.97577 + 1.65787i
\(233\) 1.08752e6 − 627880.i 0.0859745 − 0.0496374i −0.456396 − 0.889777i \(-0.650860\pi\)
0.542371 + 0.840139i \(0.317527\pi\)
\(234\) −2.39555e6 − 3.14053e7i −0.186964 − 2.45107i
\(235\) −687811. + 1.19132e6i −0.0529987 + 0.0917965i
\(236\) 2.39185e6 + 6.57156e6i 0.181969 + 0.499957i
\(237\) −1.54201e6 + 1.12292e7i −0.115836 + 0.843539i
\(238\) 910867. − 764308.i 0.0675653 − 0.0566940i
\(239\) 5.47625e6 − 1.50459e7i 0.401134 − 1.10211i −0.560591 − 0.828093i \(-0.689426\pi\)
0.961726 − 0.274014i \(-0.0883516\pi\)
\(240\) −921101. − 2.41861e7i −0.0666306 − 1.74957i
\(241\) 4.50499e6 − 2.55491e7i 0.321842 − 1.82526i −0.209154 − 0.977883i \(-0.567071\pi\)
0.530996 − 0.847374i \(-0.321818\pi\)
\(242\) 2.43966e7i 1.72140i
\(243\) −1.40898e7 + 2.71454e6i −0.981942 + 0.189181i
\(244\) −2.00715e7 −1.38169
\(245\) −2.12486e7 − 3.74669e6i −1.44488 − 0.254771i
\(246\) −3.82404e6 + 145634.i −0.256872 + 0.00978270i
\(247\) −3.15545e7 − 1.14849e7i −2.09397 − 0.762142i
\(248\) −8.86549e6 − 1.05655e7i −0.581229 − 0.692682i
\(249\) 2.16243e7 + 2.96947e6i 1.40070 + 0.192345i
\(250\) −5.92530e6 + 2.15663e6i −0.379219 + 0.138024i
\(251\) 1.09683e7 + 6.33253e6i 0.693612 + 0.400457i 0.804964 − 0.593324i \(-0.202185\pi\)
−0.111352 + 0.993781i \(0.535518\pi\)
\(252\) −1.05470e6 + 80451.3i −0.0659067 + 0.00502726i
\(253\) 706750. + 1.22413e6i 0.0436420 + 0.0755901i
\(254\) −1.87759e6 + 2.23762e6i −0.114577 + 0.136548i
\(255\) 3.64641e7 + 1.17207e7i 2.19910 + 0.706858i
\(256\) −5.93699e6 − 3.36704e7i −0.353872 − 2.00691i
\(257\) −2.79596e7 + 4.93002e6i −1.64714 + 0.290435i −0.918784 − 0.394762i \(-0.870827\pi\)
−0.728358 + 0.685197i \(0.759716\pi\)
\(258\) 2.35415e7 + 2.59800e7i 1.37080 + 1.51279i
\(259\) −558263. − 468439.i −0.0321322 − 0.0269621i
\(260\) 6.47709e7 − 3.73955e7i 3.68519 − 2.12765i
\(261\) 2.45370e7 + 2.42231e6i 1.38006 + 0.136241i
\(262\) −2.83600e7 + 4.91209e7i −1.57689 + 2.73126i
\(263\) −1.01571e7 − 2.79065e7i −0.558347 − 1.53404i −0.822035 − 0.569437i \(-0.807161\pi\)
0.263689 − 0.964608i \(-0.415061\pi\)
\(264\) 4.05524e6 − 1.65334e6i 0.220397 − 0.0898569i
\(265\) −5.44371e6 + 4.56781e6i −0.292521 + 0.245454i
\(266\) −572691. + 1.57346e6i −0.0304282 + 0.0836007i
\(267\) 8.01706e6 + 4.23032e6i 0.421193 + 0.222249i
\(268\) −6.36437e6 + 3.60941e7i −0.330637 + 1.87513i
\(269\) − 5.30803e6i − 0.272695i −0.990661 − 0.136347i \(-0.956464\pi\)
0.990661 − 0.136347i \(-0.0435363\pi\)
\(270\) −3.01231e7 − 4.06452e7i −1.53041 − 2.06499i
\(271\) −2.74775e7 −1.38060 −0.690302 − 0.723521i \(-0.742523\pi\)
−0.690302 + 0.723521i \(0.742523\pi\)
\(272\) −3.71576e7 − 6.55189e6i −1.84646 − 0.325582i
\(273\) −487746. − 775098.i −0.0239721 − 0.0380950i
\(274\) 5.35417e7 + 1.94876e7i 2.60280 + 0.947342i
\(275\) −1.97934e6 − 2.35889e6i −0.0951751 − 0.113425i
\(276\) −1.81370e7 + 2.33660e7i −0.862656 + 1.11137i
\(277\) −3.50031e6 + 1.27401e6i −0.164690 + 0.0599422i −0.423049 − 0.906107i \(-0.639040\pi\)
0.258360 + 0.966049i \(0.416818\pi\)
\(278\) −1.49817e7 − 8.64966e6i −0.697309 − 0.402592i
\(279\) −1.01680e7 − 2.84623e6i −0.468190 − 0.131056i
\(280\) −960713. − 1.66400e6i −0.0437643 − 0.0758019i
\(281\) 2.47988e7 − 2.95541e7i 1.11767 − 1.33198i 0.180309 − 0.983610i \(-0.442290\pi\)
0.937356 − 0.348372i \(-0.113265\pi\)
\(282\) −597661. − 2.76874e6i −0.0266506 − 0.123462i
\(283\) −5.62913e6 − 3.19244e7i −0.248360 − 1.40852i −0.812557 − 0.582881i \(-0.801925\pi\)
0.564197 − 0.825640i \(-0.309186\pi\)
\(284\) 4.38990e7 − 7.74058e6i 1.91646 − 0.337923i
\(285\) −5.27222e7 + 1.13806e7i −2.27750 + 0.491623i
\(286\) 5.63750e6 + 4.73043e6i 0.240984 + 0.202210i
\(287\) −96360.9 + 55634.0i −0.00407620 + 0.00235339i
\(288\) 3.78214e6 + 3.86732e6i 0.158329 + 0.161895i
\(289\) 1.77851e7 − 3.08047e7i 0.736823 − 1.27621i
\(290\) 2.97325e7 + 8.16893e7i 1.21909 + 3.34943i
\(291\) −1.40382e6 − 1.08966e6i −0.0569680 − 0.0442192i
\(292\) −3.04762e7 + 2.55726e7i −1.22409 + 1.02713i
\(293\) 4.37693e6 − 1.20255e7i 0.174007 − 0.478080i −0.821777 − 0.569809i \(-0.807017\pi\)
0.995784 + 0.0917290i \(0.0292394\pi\)
\(294\) 3.76019e7 − 2.36618e7i 1.47968 − 0.931120i
\(295\) −1.68875e6 + 9.57740e6i −0.0657810 + 0.373063i
\(296\) 6.31380e7i 2.43453i
\(297\) 1.84835e6 − 2.79712e6i 0.0705531 − 0.106768i
\(298\) −7.08153e6 −0.267595
\(299\) −2.52198e7 − 4.44693e6i −0.943470 − 0.166359i
\(300\) 3.00720e7 − 5.69907e7i 1.11378 − 2.11077i
\(301\) 957908. + 348650.i 0.0351256 + 0.0127847i
\(302\) −1.35153e6 − 1.61069e6i −0.0490688 − 0.0584779i
\(303\) −2.24026e6 − 5.49480e6i −0.0805325 − 0.197526i
\(304\) 4.99287e7 − 1.81726e7i 1.77717 − 0.646838i
\(305\) −2.41727e7 − 1.39561e7i −0.851973 − 0.491887i
\(306\) −7.18432e7 + 3.25321e7i −2.50739 + 1.13540i
\(307\) 2.30176e7 + 3.98676e7i 0.795507 + 1.37786i 0.922516 + 0.385958i \(0.126129\pi\)
−0.127009 + 0.991902i \(0.540538\pi\)
\(308\) 158865. − 189328.i 0.00543720 − 0.00647981i
\(309\) 2.15177e6 − 1.94981e6i 0.0729325 − 0.0660871i
\(310\) −6.46456e6 − 3.66623e7i −0.216997 − 1.23065i
\(311\) 2.58471e7 − 4.55754e6i 0.859271 − 0.151513i 0.273384 − 0.961905i \(-0.411857\pi\)
0.585888 + 0.810392i \(0.300746\pi\)
\(312\) −2.42795e7 + 7.55356e7i −0.799421 + 2.48707i
\(313\) 2.77182e7 + 2.32583e7i 0.903923 + 0.758481i 0.970953 − 0.239269i \(-0.0769079\pi\)
−0.0670302 + 0.997751i \(0.521352\pi\)
\(314\) −2.62926e7 + 1.51800e7i −0.849266 + 0.490324i
\(315\) −1.32615e6 − 636466.i −0.0424288 − 0.0203631i
\(316\) 2.77099e7 − 4.79950e7i 0.878161 − 1.52102i
\(317\) 5.51762e6 + 1.51595e7i 0.173210 + 0.475892i 0.995673 − 0.0929276i \(-0.0296225\pi\)
−0.822462 + 0.568819i \(0.807400\pi\)
\(318\) 1.99064e6 − 1.44963e7i 0.0619030 − 0.450791i
\(319\) −4.41317e6 + 3.70309e6i −0.135950 + 0.114075i
\(320\) 1.30992e7 − 3.59898e7i 0.399757 − 1.09832i
\(321\) −546222. − 1.43426e7i −0.0165141 − 0.433623i
\(322\) −221745. + 1.25758e6i −0.00664181 + 0.0376676i
\(323\) 8.40813e7i 2.49512i
\(324\) 6.88037e7 + 1.37184e7i 2.02291 + 0.403337i
\(325\) 5.57889e7 1.62517
\(326\) 1.31605e7 + 2.32055e6i 0.379857 + 0.0669791i
\(327\) 5.84766e6 − 222702.i 0.167240 − 0.00636914i
\(328\) 9.05861e6 + 3.29706e6i 0.256708 + 0.0934342i
\(329\) −52938.5 − 63089.6i −0.00148656 − 0.00177162i
\(330\) 1.17107e7 + 1.60813e6i 0.325869 + 0.0447486i
\(331\) 4.56674e6 − 1.66216e6i 0.125928 − 0.0458340i −0.278288 − 0.960498i \(-0.589767\pi\)
0.404215 + 0.914664i \(0.367545\pi\)
\(332\) −9.24247e7 − 5.33614e7i −2.52565 − 1.45819i
\(333\) 2.72818e7 + 3.99009e7i 0.738824 + 1.08056i
\(334\) 403060. + 698121.i 0.0108176 + 0.0187366i
\(335\) −3.27617e7 + 3.90439e7i −0.871429 + 1.03853i
\(336\) 1.37954e6 + 443428.i 0.0363678 + 0.0116897i
\(337\) −4.66900e6 − 2.64792e7i −0.121993 − 0.691855i −0.983049 − 0.183345i \(-0.941308\pi\)
0.861056 − 0.508510i \(-0.169804\pi\)
\(338\) −6.47530e7 + 1.14177e7i −1.67691 + 0.295685i
\(339\) 2.76040e6 + 3.04633e6i 0.0708553 + 0.0781947i
\(340\) −1.43459e8 − 1.20376e8i −3.64998 − 3.06270i
\(341\) 2.13656e6 − 1.23355e6i 0.0538831 − 0.0311094i
\(342\) 6.47101e7 − 9.02596e7i 1.61769 − 2.25639i
\(343\) 1.29243e6 − 2.23855e6i 0.0320276 − 0.0554734i
\(344\) −3.02061e7 − 8.29907e7i −0.742027 − 2.03870i
\(345\) −3.80897e7 + 1.55294e7i −0.927578 + 0.378179i
\(346\) 2.60139e7 − 2.18283e7i 0.628026 − 0.526976i
\(347\) −2.52915e7 + 6.94879e7i −0.605322 + 1.66311i 0.134991 + 0.990847i \(0.456899\pi\)
−0.740313 + 0.672262i \(0.765323\pi\)
\(348\) −1.06622e8 − 5.62606e7i −2.52993 − 1.33495i
\(349\) 8.08345e6 − 4.58435e7i 0.190160 − 1.07845i −0.728983 − 0.684531i \(-0.760007\pi\)
0.919144 − 0.393922i \(-0.128882\pi\)
\(350\) − 2.78190e6i − 0.0648840i
\(351\) 1.72951e7 + 5.82268e7i 0.399946 + 1.34649i
\(352\) −1.26390e6 −0.0289791
\(353\) −1.26989e7 − 2.23916e6i −0.288696 − 0.0509050i 0.0274245 − 0.999624i \(-0.491269\pi\)
−0.316121 + 0.948719i \(0.602381\pi\)
\(354\) −1.06651e7 − 1.69484e7i −0.240412 − 0.382049i
\(355\) 5.82509e7 + 2.12016e7i 1.30202 + 0.473897i
\(356\) −2.84892e7 − 3.39521e7i −0.631436 − 0.752517i
\(357\) −1.40605e6 + 1.81143e6i −0.0309027 + 0.0398122i
\(358\) −3.57543e7 + 1.30135e7i −0.779254 + 0.283625i
\(359\) 5.14659e7 + 2.97139e7i 1.11234 + 0.642208i 0.939434 − 0.342730i \(-0.111352\pi\)
0.172904 + 0.984939i \(0.444685\pi\)
\(360\) 3.16115e7 + 1.23459e8i 0.677544 + 2.64614i
\(361\) −3.56792e7 − 6.17982e7i −0.758391 − 1.31357i
\(362\) 7.11805e7 − 8.48296e7i 1.50050 − 1.78822i
\(363\) −9.92732e6 − 4.59895e7i −0.207545 − 0.961478i
\(364\) 777544. + 4.40967e6i 0.0161221 + 0.0914328i
\(365\) −5.44844e7 + 9.60708e6i −1.12045 + 0.197566i
\(366\) 5.61794e7 − 1.21269e7i 1.14587 − 0.247347i
\(367\) 5.54540e7 + 4.65314e7i 1.12185 + 0.941343i 0.998696 − 0.0510444i \(-0.0162550\pi\)
0.123153 + 0.992388i \(0.460699\pi\)
\(368\) 3.50922e7 − 2.02605e7i 0.704152 − 0.406543i
\(369\) 7.14936e6 − 1.83059e6i 0.142295 − 0.0364344i
\(370\) −8.52108e7 + 1.47589e8i −1.68224 + 2.91373i
\(371\) −145512. − 399790.i −0.00284955 − 0.00782907i
\(372\) 4.07826e7 + 3.16559e7i 0.792220 + 0.614930i
\(373\) −5.34123e7 + 4.48182e7i −1.02924 + 0.863631i −0.990760 − 0.135628i \(-0.956695\pi\)
−0.0384758 + 0.999260i \(0.512250\pi\)
\(374\) 6.30244e6 − 1.73158e7i 0.120474 − 0.331000i
\(375\) 1.02921e7 − 6.47651e6i 0.195169 − 0.122814i
\(376\) −1.23903e6 + 7.02686e6i −0.0233086 + 0.132190i
\(377\) − 1.04374e8i − 1.94790i
\(378\) 2.90347e6 − 862416.i 0.0537578 − 0.0159677i
\(379\) −2.72904e7 −0.501294 −0.250647 − 0.968079i \(-0.580643\pi\)
−0.250647 + 0.968079i \(0.580643\pi\)
\(380\) 2.59713e8 + 4.57944e7i 4.73306 + 0.834567i
\(381\) 2.62889e6 − 4.98212e6i 0.0475332 − 0.0900822i
\(382\) 1.32407e8 + 4.81921e7i 2.37531 + 0.864540i
\(383\) −1.86469e6 − 2.22225e6i −0.0331902 − 0.0395545i 0.749194 − 0.662351i \(-0.230441\pi\)
−0.782384 + 0.622796i \(0.785997\pi\)
\(384\) 3.46137e7 + 8.48988e7i 0.611300 + 1.49937i
\(385\) 322968. − 117551.i 0.00565950 − 0.00205989i
\(386\) 1.90224e7 + 1.09826e7i 0.330753 + 0.190961i
\(387\) −5.49493e7 − 3.93950e7i −0.948046 − 0.679686i
\(388\) 4.34448e6 + 7.52486e6i 0.0743777 + 0.128826i
\(389\) −2.81746e7 + 3.35772e7i −0.478641 + 0.570422i −0.950291 − 0.311364i \(-0.899214\pi\)
0.471650 + 0.881786i \(0.343659\pi\)
\(390\) −1.58697e8 + 1.43802e8i −2.67532 + 2.42422i
\(391\) 1.11349e7 + 6.31489e7i 0.186275 + 1.05642i
\(392\) −1.10215e8 + 1.94339e7i −1.82971 + 0.322627i
\(393\) 3.34729e7 − 1.04137e8i 0.551461 − 1.71565i
\(394\) −8.41677e7 − 7.06251e7i −1.37612 − 1.15470i
\(395\) 6.67436e7 − 3.85345e7i 1.08298 − 0.625256i
\(396\) −1.35319e7 + 9.25228e6i −0.217907 + 0.148992i
\(397\) 2.82960e7 − 4.90100e7i 0.452223 − 0.783274i −0.546301 − 0.837589i \(-0.683964\pi\)
0.998524 + 0.0543156i \(0.0172977\pi\)
\(398\) −568794. − 1.56275e6i −0.00902206 − 0.0247879i
\(399\) 439307. − 3.19913e6i 0.00691592 − 0.0503632i
\(400\) −6.76225e7 + 5.67420e7i −1.05660 + 0.886594i
\(401\) −1.69896e7 + 4.66785e7i −0.263481 + 0.723909i 0.735445 + 0.677584i \(0.236973\pi\)
−0.998926 + 0.0463249i \(0.985249\pi\)
\(402\) −3.99391e6 − 1.04871e8i −0.0614780 − 1.61428i
\(403\) −7.76158e6 + 4.40181e7i −0.118586 + 0.672537i
\(404\) 2.90136e7i 0.440005i
\(405\) 7.33235e7 + 6.43619e7i 1.10377 + 0.968867i
\(406\) −5.20456e6 −0.0777690
\(407\) −1.11223e7 − 1.96115e6i −0.164972 − 0.0290890i
\(408\) 1.98523e8 − 7.56054e6i 2.92301 − 0.111320i
\(409\) 9.01805e7 + 3.28230e7i 1.31808 + 0.479743i 0.902843 − 0.429970i \(-0.141476\pi\)
0.415239 + 0.909712i \(0.363698\pi\)
\(410\) 1.67254e7 + 1.99326e7i 0.242675 + 0.289209i
\(411\) −1.08860e8 − 1.49488e7i −1.56799 − 0.215318i
\(412\) −1.33416e7 + 4.85593e6i −0.190772 + 0.0694353i
\(413\) −504234. − 291120.i −0.00715784 − 0.00413258i
\(414\) 3.66473e7 − 7.63587e7i 0.516464 − 1.07611i
\(415\) −7.42064e7 − 1.28529e8i −1.03824 − 1.79828i
\(416\) 1.47189e7 − 1.75413e7i 0.204453 − 0.243658i
\(417\) 3.17613e7 + 1.02091e7i 0.438016 + 0.140792i
\(418\) 4.50604e6 + 2.55550e7i 0.0616973 + 0.349903i
\(419\) 6.07694e7 − 1.07153e7i 0.826119 − 0.145667i 0.255424 − 0.966829i \(-0.417785\pi\)
0.570695 + 0.821162i \(0.306674\pi\)
\(420\) 4.82939e6 + 5.32963e6i 0.0651846 + 0.0719365i
\(421\) 3.46383e7 + 2.90650e7i 0.464205 + 0.389514i 0.844675 − 0.535279i \(-0.179793\pi\)
−0.380470 + 0.924793i \(0.624238\pi\)
\(422\) −1.06955e8 + 6.17504e7i −1.42319 + 0.821679i
\(423\) 2.25328e6 + 4.97610e6i 0.0297710 + 0.0657457i
\(424\) −1.84298e7 + 3.19214e7i −0.241782 + 0.418779i
\(425\) −4.77776e7 − 1.31268e8i −0.622382 − 1.70998i
\(426\) −1.18195e8 + 4.81886e7i −1.52887 + 0.623327i
\(427\) 1.28013e6 − 1.07416e6i 0.0164426 − 0.0137970i
\(428\) −2.40023e7 + 6.59457e7i −0.306141 + 0.841115i
\(429\) −1.25520e7 − 6.62326e6i −0.158980 − 0.0838880i
\(430\) 4.13949e7 − 2.34762e8i 0.520645 − 2.95273i
\(431\) 2.27577e7i 0.284247i 0.989849 + 0.142124i \(0.0453930\pi\)
−0.989849 + 0.142124i \(0.954607\pi\)
\(432\) −8.01852e7 − 5.29869e7i −0.994587 − 0.657230i
\(433\) −5.44260e7 −0.670414 −0.335207 − 0.942145i \(-0.608806\pi\)
−0.335207 + 0.942145i \(0.608806\pi\)
\(434\) 2.19495e6 + 387029.i 0.0268507 + 0.00473451i
\(435\) −8.92887e7 − 1.41892e8i −1.08475 − 1.72382i
\(436\) −2.68869e7 − 9.78604e6i −0.324401 − 0.118072i
\(437\) −5.80430e7 − 6.91730e7i −0.695514 − 0.828881i
\(438\) 6.98511e7 − 8.99899e7i 0.831287 − 1.07096i
\(439\) −6.84233e7 + 2.49041e7i −0.808743 + 0.294358i −0.713105 − 0.701058i \(-0.752712\pi\)
−0.0956386 + 0.995416i \(0.530489\pi\)
\(440\) −2.57876e7 − 1.48885e7i −0.302728 − 0.174780i
\(441\) −6.12544e7 + 5.99052e7i −0.714203 + 0.698471i
\(442\) 1.66925e8 + 2.89122e8i 1.93310 + 3.34823i
\(443\) −4.48161e7 + 5.34098e7i −0.515493 + 0.614341i −0.959509 − 0.281678i \(-0.909109\pi\)
0.444016 + 0.896019i \(0.353553\pi\)
\(444\) −4.98671e7 − 2.31015e8i −0.569724 − 2.63932i
\(445\) −1.07028e7 − 6.06984e7i −0.121455 − 0.688807i
\(446\) 1.58260e8 − 2.79055e7i 1.78389 − 0.314547i
\(447\) 1.33493e7 − 2.88158e6i 0.149463 − 0.0322632i
\(448\) 1.75652e6 + 1.47390e6i 0.0195353 + 0.0163920i
\(449\) 6.37671e7 − 3.68160e7i 0.704462 − 0.406721i −0.104545 − 0.994520i \(-0.533339\pi\)
0.809007 + 0.587799i \(0.200005\pi\)
\(450\) −4.97373e7 + 1.77684e8i −0.545814 + 1.94989i
\(451\) −862176. + 1.49333e6i −0.00939867 + 0.0162790i
\(452\) −6.87467e6 − 1.88880e7i −0.0744452 − 0.204537i
\(453\) 3.20316e6 + 2.48633e6i 0.0344575 + 0.0267463i
\(454\) 5.96973e7 − 5.00920e7i 0.637951 − 0.535304i
\(455\) −2.12971e6 + 5.85133e6i −0.0226092 + 0.0621184i
\(456\) −2.36785e8 + 1.49002e8i −2.49724 + 1.57144i
\(457\) −5.17782e6 + 2.93649e7i −0.0542499 + 0.307666i −0.999844 − 0.0176834i \(-0.994371\pi\)
0.945594 + 0.325350i \(0.105482\pi\)
\(458\) 2.71371e8i 2.82466i
\(459\) 1.22192e8 − 9.05596e7i 1.26359 − 0.936475i
\(460\) 2.01121e8 2.06625
\(461\) 3.17852e7 + 5.60459e6i 0.324431 + 0.0572059i 0.333492 − 0.942753i \(-0.391773\pi\)
−0.00906092 + 0.999959i \(0.502884\pi\)
\(462\) −330267. + 625904.i −0.00334919 + 0.00634720i
\(463\) −1.72582e8 − 6.28148e7i −1.73882 − 0.632877i −0.739622 − 0.673023i \(-0.764995\pi\)
−0.999194 + 0.0401460i \(0.987218\pi\)
\(464\) 1.06157e8 + 1.26513e8i 1.06266 + 1.26643i
\(465\) 2.71046e7 + 6.64809e7i 0.269578 + 0.661208i
\(466\) 1.65210e7 − 6.01316e6i 0.163260 − 0.0594217i
\(467\) 9.07267e7 + 5.23811e7i 0.890808 + 0.514308i 0.874207 − 0.485554i \(-0.161382\pi\)
0.0166016 + 0.999862i \(0.494715\pi\)
\(468\) 2.91772e7 − 2.95553e8i 0.284646 − 2.88335i
\(469\) −1.52572e6 − 2.64262e6i −0.0147896 − 0.0256163i
\(470\) −1.23797e7 + 1.47536e7i −0.119239 + 0.142103i
\(471\) 4.33866e7 − 3.93144e7i 0.415234 − 0.376261i
\(472\) 8.75946e6 + 4.96774e7i 0.0833012 + 0.472425i
\(473\) 1.55577e7 − 2.74324e6i 0.147015 − 0.0259227i
\(474\) −4.85611e7 + 1.51078e8i −0.455988 + 1.41862i
\(475\) 1.50693e8 + 1.26447e8i 1.40609 + 1.17985i
\(476\) 9.70978e6 − 5.60594e6i 0.0900303 − 0.0519790i
\(477\) 2.14622e6 + 2.81367e7i 0.0197751 + 0.259249i
\(478\) 1.12085e8 − 1.94136e8i 1.02627 − 1.77755i
\(479\) 5.00039e7 + 1.37385e8i 0.454985 + 1.25006i 0.929175 + 0.369639i \(0.120519\pi\)
−0.474190 + 0.880422i \(0.657259\pi\)
\(480\) 5.00374e6 − 3.64383e7i 0.0452451 − 0.329484i
\(481\) 1.56744e8 − 1.31523e8i 1.40849 − 1.18187i
\(482\) 1.24228e8 − 3.41314e8i 1.10938 − 3.04798i
\(483\) −93719.6 − 2.46087e6i −0.000831743 − 0.0218397i
\(484\) −3.99464e7 + 2.26547e8i −0.352323 + 1.99812i
\(485\) 1.20832e7i 0.105915i
\(486\) −2.00867e8 + 3.17290e6i −1.74985 + 0.0276406i
\(487\) −1.45722e8 −1.26165 −0.630825 − 0.775925i \(-0.717283\pi\)
−0.630825 + 0.775925i \(0.717283\pi\)
\(488\) −1.42579e8 − 2.51406e7i −1.22687 − 0.216330i
\(489\) −2.57529e7 + 980772.i −0.220242 + 0.00838767i
\(490\) −2.83863e8 − 1.03318e8i −2.41279 − 0.878184i
\(491\) −5.50941e7 − 6.56585e7i −0.465436 − 0.554685i 0.481358 − 0.876524i \(-0.340144\pi\)
−0.946795 + 0.321839i \(0.895699\pi\)
\(492\) −3.57485e7 − 4.90902e6i −0.300167 − 0.0412192i
\(493\) −2.45584e8 + 8.93853e7i −2.04956 + 0.745977i
\(494\) −4.07146e8 − 2.35066e8i −3.37730 − 1.94988i
\(495\) −2.27301e7 + 1.73382e6i −0.187407 + 0.0142951i
\(496\) −3.53622e7 − 6.12491e7i −0.289797 − 0.501943i
\(497\) −2.38556e6 + 2.84299e6i −0.0194321 + 0.0231583i
\(498\) 2.90933e8 + 9.35148e7i 2.35562 + 0.757168i
\(499\) 1.68446e7 + 9.55304e7i 0.135568 + 0.768847i 0.974462 + 0.224552i \(0.0720917\pi\)
−0.838894 + 0.544295i \(0.816797\pi\)
\(500\) −5.85536e7 + 1.03246e7i −0.468429 + 0.0825966i
\(501\) −1.04388e6 − 1.15200e6i −0.00830111 − 0.00916095i
\(502\) 1.35833e8 + 1.13977e8i 1.07373 + 0.900965i
\(503\) 9.55121e7 − 5.51439e7i 0.750506 − 0.433305i −0.0753704 − 0.997156i \(-0.524014\pi\)
0.825877 + 0.563851i \(0.190681\pi\)
\(504\) −7.59293e6 − 749579.i −0.0593086 − 0.00585499i
\(505\) −2.01737e7 + 3.49419e7i −0.156643 + 0.271314i
\(506\) 6.76849e6 + 1.85963e7i 0.0522445 + 0.143541i
\(507\) 1.17419e8 − 4.78722e7i 0.900976 − 0.367333i
\(508\) −2.10991e7 + 1.77043e7i −0.160944 + 0.135048i
\(509\) 3.65990e7 − 1.00555e8i 0.277534 − 0.762518i −0.720107 − 0.693863i \(-0.755907\pi\)
0.997641 − 0.0686543i \(-0.0218706\pi\)
\(510\) 4.74265e8 + 2.50253e8i 3.57528 + 1.88655i
\(511\) 575170. − 3.26195e6i 0.00431056 − 0.0244464i
\(512\) − 2.61350e8i − 1.94721i
\(513\) −8.52559e7 + 1.96478e8i −0.631499 + 1.45533i
\(514\) −3.97487e8 −2.92707
\(515\) −1.94440e7 − 3.42850e6i −0.142352 − 0.0251005i
\(516\) 1.76068e8 + 2.79797e8i 1.28154 + 2.03654i
\(517\) −1.19935e6 − 436528.i −0.00867909 − 0.00315893i
\(518\) −6.55839e6 − 7.81598e6i −0.0471854 − 0.0562334i
\(519\) −4.01561e7 + 5.17335e7i −0.287243 + 0.370058i
\(520\) 5.06944e8 − 1.84513e8i 3.60537 − 1.31225i
\(521\) 1.89936e8 + 1.09660e8i 1.34306 + 0.775415i 0.987255 − 0.159146i \(-0.0508741\pi\)
0.355803 + 0.934561i \(0.384207\pi\)
\(522\) 3.32422e8 + 9.30517e7i 2.33711 + 0.654203i
\(523\) −2.73298e7 − 4.73367e7i −0.191043 − 0.330897i 0.754553 − 0.656239i \(-0.227854\pi\)
−0.945596 + 0.325342i \(0.894520\pi\)
\(524\) −3.43781e8 + 4.09702e8i −2.38939 + 2.84757i
\(525\) 1.13200e6 + 5.24411e6i 0.00782289 + 0.0362405i
\(526\) −7.21995e7 − 4.09463e8i −0.496109 − 2.81357i
\(527\) 1.10219e8 − 1.94345e7i 0.753049 − 0.132783i
\(528\) 2.19509e7 − 4.73833e6i 0.149125 − 0.0321902i
\(529\) 6.06485e7 + 5.08902e7i 0.409688 + 0.343769i
\(530\) −8.61620e7 + 4.97457e7i −0.578746 + 0.334139i
\(531\) 2.70012e7 + 2.76093e7i 0.180343 + 0.184405i
\(532\) −7.89436e6 + 1.36734e7i −0.0524303 + 0.0908119i
\(533\) −1.06849e7 − 2.93566e7i −0.0705652 − 0.193876i
\(534\) 1.00253e8 + 7.78177e7i 0.658377 + 0.511040i
\(535\) −7.47599e7 + 6.27310e7i −0.488211 + 0.409657i
\(536\) −9.04194e7 + 2.48425e8i −0.587174 + 1.61325i
\(537\) 6.21043e7 − 3.90804e7i 0.401051 − 0.252369i
\(538\) 1.29047e7 − 7.31862e7i 0.0828707 − 0.469983i
\(539\) − 2.00189e7i − 0.127842i
\(540\) −2.13172e8 − 4.26754e8i −1.35378 − 2.71017i
\(541\) 2.47803e8 1.56500 0.782501 − 0.622649i \(-0.213944\pi\)
0.782501 + 0.622649i \(0.213944\pi\)
\(542\) −3.78855e8 − 6.68024e7i −2.37944 − 0.419560i
\(543\) −9.96626e7 + 1.88875e8i −0.622490 + 1.17971i
\(544\) −5.38786e7 − 1.96102e7i −0.334672 − 0.121811i
\(545\) −2.55762e7 − 3.04806e7i −0.157996 − 0.188293i
\(546\) −4.84057e6 − 1.18727e7i −0.0297384 − 0.0729410i
\(547\) −9.89671e7 + 3.60211e7i −0.604684 + 0.220087i −0.626176 − 0.779682i \(-0.715381\pi\)
0.0214914 + 0.999769i \(0.493159\pi\)
\(548\) 4.65281e8 + 2.68630e8i 2.82731 + 1.63235i
\(549\) −1.00968e8 + 4.57204e7i −0.610193 + 0.276308i
\(550\) −2.15560e7 − 3.73361e7i −0.129563 − 0.224409i
\(551\) 2.36565e8 − 2.81927e8i 1.41415 − 1.68532i
\(552\) −1.58104e8 + 1.43265e8i −0.939997 + 0.851769i
\(553\) 801225. + 4.54397e6i 0.00473783 + 0.0268695i
\(554\) −5.13589e7 + 9.05597e6i −0.302055 + 0.0532605i
\(555\) 1.00573e8 − 3.12891e8i 0.588304 − 1.83027i
\(556\) −1.24957e8 − 1.04851e8i −0.727004 − 0.610029i
\(557\) −9.75993e7 + 5.63490e7i −0.564783 + 0.326077i −0.755063 − 0.655652i \(-0.772394\pi\)
0.190280 + 0.981730i \(0.439060\pi\)
\(558\) −1.33275e8 − 6.39633e7i −0.767088 − 0.368153i
\(559\) −1.43106e8 + 2.47867e8i −0.819262 + 1.41900i
\(560\) −3.36984e6 − 9.25856e6i −0.0191887 − 0.0527205i
\(561\) −4.83455e6 + 3.52063e7i −0.0273822 + 0.199403i
\(562\) 4.13773e8 − 3.47196e8i 2.33106 − 1.95599i
\(563\) −5.35400e7 + 1.47100e8i −0.300022 + 0.824303i 0.694473 + 0.719519i \(0.255638\pi\)
−0.994495 + 0.104785i \(0.966585\pi\)
\(564\) −1.01643e6 − 2.66891e7i −0.00566551 − 0.148764i
\(565\) 4.85383e6 − 2.75274e7i 0.0269116 − 0.152623i
\(566\) − 4.53853e8i − 2.50303i
\(567\) −5.12234e6 + 2.80719e6i −0.0281008 + 0.0154000i
\(568\) 3.21535e8 1.75462
\(569\) −2.45663e8 − 4.33170e7i −1.33353 − 0.235137i −0.538971 − 0.842324i \(-0.681187\pi\)
−0.794559 + 0.607187i \(0.792298\pi\)
\(570\) −7.54593e8 + 2.87379e7i −4.07463 + 0.155178i
\(571\) −2.11133e8 − 7.68463e7i −1.13409 − 0.412776i −0.294316 − 0.955708i \(-0.595092\pi\)
−0.839777 + 0.542932i \(0.817314\pi\)
\(572\) 4.46045e7 + 5.31575e7i 0.238336 + 0.284038i
\(573\) −2.69207e8 − 3.69678e7i −1.43094 − 0.196499i
\(574\) −1.46386e6 + 532802.i −0.00774042 + 0.00281728i
\(575\) 1.29923e8 + 7.50111e7i 0.683412 + 0.394568i
\(576\) −8.58396e7 − 1.25544e8i −0.449180 − 0.656945i
\(577\) −1.23658e8 − 2.14182e8i −0.643716 − 1.11495i −0.984597 − 0.174842i \(-0.944059\pi\)
0.340881 − 0.940106i \(-0.389275\pi\)
\(578\) 3.20109e8 − 3.81491e8i 1.65773 − 1.97561i
\(579\) −4.03278e7 − 1.29626e7i −0.207763 − 0.0667816i
\(580\) 1.42340e8 + 8.07251e8i 0.729531 + 4.13737i
\(581\) 8.75039e6 − 1.54293e6i 0.0446169 − 0.00786716i
\(582\) −1.67064e7 − 1.84369e7i −0.0847451 − 0.0935231i
\(583\) −5.05075e6 − 4.23808e6i −0.0254889 − 0.0213877i
\(584\) −2.48521e8 + 1.43483e8i −1.24774 + 0.720383i
\(585\) 2.40642e8 − 3.35655e8i 1.20200 − 1.67658i
\(586\) 8.95843e7 − 1.55165e8i 0.445184 − 0.771081i
\(587\) 1.69663e7 + 4.66144e7i 0.0838826 + 0.230465i 0.974542 − 0.224206i \(-0.0719789\pi\)
−0.890659 + 0.454672i \(0.849757\pi\)
\(588\) 3.87915e8 − 1.58155e8i 1.90812 − 0.777950i
\(589\) −1.20733e8 + 1.01307e8i −0.590854 + 0.495785i
\(590\) −4.65685e7 + 1.27946e8i −0.226744 + 0.622975i
\(591\) 1.87401e8 + 9.88850e7i 0.907842 + 0.479036i
\(592\) −5.62205e7 + 3.18843e8i −0.270975 + 1.53678i
\(593\) 3.61551e7i 0.173382i 0.996235 + 0.0866912i \(0.0276293\pi\)
−0.996235 + 0.0866912i \(0.972371\pi\)
\(594\) 3.22850e7 − 3.40725e7i 0.154043 − 0.162572i
\(595\) 1.55917e7 0.0740187
\(596\) −6.57592e7 − 1.15951e7i −0.310612 − 0.0547692i
\(597\) 1.70813e6 + 2.71446e6i 0.00802782 + 0.0127573i
\(598\) −3.36915e8 − 1.22627e8i −1.57549 − 0.573433i
\(599\) 1.04478e8 + 1.24512e8i 0.486120 + 0.579336i 0.952226 − 0.305393i \(-0.0987879\pi\)
−0.466106 + 0.884729i \(0.654343\pi\)
\(600\) 2.85002e8 − 3.67170e8i 1.31945 − 1.69986i
\(601\) 3.69936e8 − 1.34646e8i 1.70413 − 0.620254i 0.707847 − 0.706365i \(-0.249666\pi\)
0.996285 + 0.0861118i \(0.0274442\pi\)
\(602\) 1.23598e7 + 7.13595e6i 0.0566530 + 0.0327086i
\(603\) 5.02024e7 + 1.96066e8i 0.228967 + 0.894230i
\(604\) −9.91303e6 − 1.71699e7i −0.0449879 − 0.0779213i
\(605\) −2.05631e8 + 2.45061e8i −0.928586 + 1.10665i
\(606\) −1.75296e7 − 8.12078e7i −0.0787686 − 0.364905i
\(607\) 5.62367e7 + 3.18934e8i 0.251451 + 1.42605i 0.805020 + 0.593248i \(0.202155\pi\)
−0.553568 + 0.832804i \(0.686734\pi\)
\(608\) 7.95152e7 − 1.40207e7i 0.353785 − 0.0623819i
\(609\) 9.81103e6 − 2.11781e6i 0.0434373 − 0.00937639i
\(610\) −2.99359e8 − 2.51192e8i −1.31887 − 1.10667i
\(611\) 2.00256e7 − 1.15618e7i 0.0877933 − 0.0506875i
\(612\) −7.20404e8 + 1.84459e8i −3.14284 + 0.804721i
\(613\) 1.66473e7 − 2.88340e7i 0.0722709 − 0.125177i −0.827625 − 0.561281i \(-0.810309\pi\)
0.899896 + 0.436104i \(0.143642\pi\)
\(614\) 2.20437e8 + 6.05647e8i 0.952314 + 2.61646i
\(615\) −3.96396e7 − 3.07687e7i −0.170413 − 0.132277i
\(616\) 1.36565e6 − 1.14592e6i 0.00584247 − 0.00490242i
\(617\) 3.43405e6 − 9.43498e6i 0.0146201 − 0.0401685i −0.932168 − 0.362026i \(-0.882085\pi\)
0.946788 + 0.321858i \(0.104307\pi\)
\(618\) 3.44086e7 − 2.16523e7i 0.145781 − 0.0917357i
\(619\) 7.41247e7 − 4.20382e8i 0.312529 − 1.77244i −0.273222 − 0.961951i \(-0.588089\pi\)
0.585751 − 0.810491i \(-0.300800\pi\)
\(620\) − 3.51032e8i − 1.47289i
\(621\) −3.80116e7 + 1.58855e8i −0.158724 + 0.663323i
\(622\) 3.67455e8 1.52698
\(623\) 3.63398e6 + 640769.i 0.0150286 + 0.00264995i
\(624\) −1.89869e8 + 3.59830e8i −0.781450 + 1.48096i
\(625\) 1.87741e8 + 6.83322e7i 0.768988 + 0.279889i
\(626\) 3.25628e8 + 3.88069e8i 1.32739 + 1.58192i
\(627\) −1.88930e7 − 4.63397e7i −0.0766474 − 0.187997i
\(628\) −2.69009e8 + 9.79111e7i −1.08614 + 0.395324i
\(629\) −4.43701e8 − 2.56171e8i −1.78295 − 1.02938i
\(630\) −1.67374e7 − 1.19996e7i −0.0669368 − 0.0479893i
\(631\) 1.25332e7 + 2.17081e7i 0.0498854 + 0.0864041i 0.889890 − 0.456175i \(-0.150781\pi\)
−0.840004 + 0.542580i \(0.817448\pi\)
\(632\) 2.56955e8 − 3.06227e8i 1.01790 − 1.21309i
\(633\) 1.76491e8 − 1.59926e8i 0.695844 − 0.630533i
\(634\) 3.92206e7 + 2.22431e8i 0.153903 + 0.872827i
\(635\) −3.77204e7 + 6.65112e6i −0.147318 + 0.0259761i
\(636\) 4.22210e7 − 1.31353e8i 0.164118 − 0.510586i
\(637\) 2.77835e8 + 2.33132e8i 1.07490 + 0.901951i
\(638\) −6.98508e7 + 4.03284e7i −0.268973 + 0.155292i
\(639\) 2.03198e8 − 1.38935e8i 0.778784 − 0.532486i
\(640\) 3.11699e8 − 5.39878e8i 1.18904 − 2.05947i
\(641\) −7.01808e6 − 1.92820e7i −0.0266468 − 0.0732113i 0.925656 − 0.378366i \(-0.123514\pi\)
−0.952303 + 0.305155i \(0.901292\pi\)
\(642\) 2.73380e7 − 1.99081e8i 0.103315 − 0.752359i
\(643\) 6.08260e7 − 5.10390e7i 0.228800 − 0.191986i −0.521179 − 0.853447i \(-0.674508\pi\)
0.749979 + 0.661461i \(0.230063\pi\)
\(644\) −4.11826e6 + 1.13148e7i −0.0154190 + 0.0423633i
\(645\) 1.74954e7 + 4.59390e8i 0.0651995 + 1.71200i
\(646\) −2.04415e8 + 1.15930e9i −0.758256 + 4.30029i
\(647\) − 1.03899e8i − 0.383616i −0.981432 − 0.191808i \(-0.938565\pi\)
0.981432 − 0.191808i \(-0.0614351\pi\)
\(648\) 4.71568e8 + 1.83630e8i 1.73308 + 0.674866i
\(649\) −9.02314e6 −0.0330083
\(650\) 7.69208e8 + 1.35632e8i 2.80094 + 0.493881i
\(651\) −4.29515e6 + 163576.i −0.0155681 + 0.000592894i
\(652\) 1.18409e8 + 4.30974e7i 0.427211 + 0.155492i
\(653\) 1.57422e8 + 1.87609e8i 0.565362 + 0.673773i 0.970672 − 0.240407i \(-0.0772808\pi\)
−0.405310 + 0.914179i \(0.632836\pi\)
\(654\) 8.11679e7 + 1.11461e7i 0.290169 + 0.0398463i
\(655\) −6.98898e8 + 2.54378e8i −2.48708 + 0.905223i
\(656\) 4.28095e7 + 2.47161e7i 0.151645 + 0.0875524i
\(657\) −9.50568e7 + 1.98062e8i −0.335187 + 0.698400i
\(658\) −576525. − 998571.i −0.00202367 − 0.00350511i
\(659\) 6.44700e7 − 7.68323e7i 0.225269 − 0.268465i −0.641558 − 0.767075i \(-0.721711\pi\)
0.866827 + 0.498610i \(0.166156\pi\)
\(660\) 1.06113e8 + 3.41080e7i 0.369094 + 0.118638i
\(661\) −4.87815e7 − 2.76654e8i −0.168908 − 0.957926i −0.944943 − 0.327236i \(-0.893883\pi\)
0.776035 − 0.630690i \(-0.217228\pi\)
\(662\) 6.70063e7 − 1.18150e7i 0.230963 − 0.0407250i
\(663\) −4.32315e8 − 4.77095e8i −1.48341 − 1.63706i
\(664\) −5.89706e8 − 4.94822e8i −2.01433 − 1.69023i
\(665\) −1.90148e7 + 1.09782e7i −0.0646586 + 0.0373307i
\(666\) 2.79152e8 + 6.16473e8i 0.944969 + 2.08685i
\(667\) 1.40336e8 − 2.43068e8i 0.472923 − 0.819127i
\(668\) 2.59974e6 + 7.14272e6i 0.00872168 + 0.0239626i
\(669\) −2.86978e8 + 1.17003e8i −0.958452 + 0.390766i
\(670\) −5.46635e8 + 4.58681e8i −1.81749 + 1.52506i
\(671\) 8.85742e6 − 2.43356e7i 0.0293184 − 0.0805516i
\(672\) 1.94752e6 + 1.02764e6i 0.00641762 + 0.00338635i
\(673\) 7.24372e7 − 4.10812e8i 0.237638 − 1.34771i −0.599348 − 0.800489i \(-0.704573\pi\)
0.836986 − 0.547224i \(-0.184316\pi\)
\(674\) − 3.76442e8i − 1.22947i
\(675\) 2.14567e7 − 3.55187e8i 0.0697673 − 1.15490i
\(676\) −6.19993e8 −2.00700
\(677\) 8.01234e7 + 1.41279e7i 0.258222 + 0.0455315i 0.301260 − 0.953542i \(-0.402593\pi\)
−0.0430383 + 0.999073i \(0.513704\pi\)
\(678\) 3.06538e7 + 4.87132e7i 0.0983546 + 0.156299i
\(679\) −679787. − 247422.i −0.00217152 − 0.000790368i
\(680\) −8.68292e8 − 1.03479e9i −2.76146 − 3.29098i
\(681\) −9.21511e7 + 1.18719e8i −0.291782 + 0.375906i
\(682\) 3.24575e7 − 1.18136e7i 0.102320 − 0.0372416i
\(683\) −2.90598e8 − 1.67777e8i −0.912075 − 0.526587i −0.0309766 − 0.999520i \(-0.509862\pi\)
−0.881098 + 0.472934i \(0.843195\pi\)
\(684\) 7.48688e8 − 7.32197e8i 2.33955 − 2.28802i
\(685\) 3.73567e8 + 6.47037e8i 1.16224 + 2.01306i
\(686\) 2.32621e7 − 2.77226e7i 0.0720569 − 0.0858741i
\(687\) −1.10425e8 − 5.11556e8i −0.340562 − 1.57769i
\(688\) −7.86408e7 − 4.45994e8i −0.241481 − 1.36950i
\(689\) 1.17638e8 − 2.07428e7i 0.359658 − 0.0634175i
\(690\) −5.62929e8 + 1.21514e8i −1.71359 + 0.369896i
\(691\) −1.77948e7 − 1.49316e7i −0.0539335 − 0.0452556i 0.615422 − 0.788197i \(-0.288985\pi\)
−0.669356 + 0.742942i \(0.733430\pi\)
\(692\) 2.77307e8 − 1.60103e8i 0.836839 − 0.483149i
\(693\) 367891. − 1.31427e6i 0.00110540 − 0.00394898i
\(694\) −5.17652e8 + 8.96599e8i −1.54867 + 2.68238i
\(695\) −7.75841e7 − 2.13160e8i −0.231110 − 0.634969i
\(696\) −6.86926e8 − 5.33200e8i −2.03743 − 1.58147i
\(697\) −5.99237e7 + 5.02819e7i −0.176970 + 0.148496i
\(698\) 2.22906e8 − 6.12430e8i 0.655475 − 1.80090i
\(699\) −2.86966e7 + 1.80579e7i −0.0840232 + 0.0528733i
\(700\) 4.55502e6 − 2.58328e7i 0.0132799 − 0.0753143i
\(701\) 4.03516e8i 1.17140i 0.810527 + 0.585702i \(0.199181\pi\)
−0.810527 + 0.585702i \(0.800819\pi\)
\(702\) 9.69027e7 + 8.44868e8i 0.280107 + 2.44218i
\(703\) 7.21486e8 2.07664
\(704\) 3.49951e7 + 6.17057e6i 0.100297 + 0.0176851i
\(705\) 1.73333e7 − 3.28492e7i 0.0494669 − 0.0937469i
\(706\) −1.69646e8 − 6.17462e7i −0.482092 − 0.175467i
\(707\) −1.55270e6 − 1.85044e6i −0.00439369 − 0.00523620i
\(708\) −7.12856e7 − 1.74846e8i −0.200864 − 0.492669i
\(709\) 3.72357e8 − 1.35527e8i 1.04477 − 0.380266i 0.238084 − 0.971245i \(-0.423481\pi\)
0.806687 + 0.590979i \(0.201258\pi\)
\(710\) 7.51609e8 + 4.33942e8i 2.09999 + 1.21243i
\(711\) 3.00658e7 − 3.04554e8i 0.0836497 − 0.847337i
\(712\) −1.59848e8 − 2.76865e8i −0.442860 − 0.767057i
\(713\) −7.72600e7 + 9.20749e7i −0.213150 + 0.254023i
\(714\) −2.37902e7 + 2.15573e7i −0.0653588 + 0.0592243i
\(715\) 1.67569e7 + 9.50334e7i 0.0458434 + 0.259991i
\(716\) −3.53323e8 + 6.23003e7i −0.962571 + 0.169727i
\(717\) −1.32292e8 + 4.11571e8i −0.358901 + 1.11657i
\(718\) 6.37364e8 + 5.34812e8i 1.72192 + 1.44487i
\(719\) −3.93488e8 + 2.27181e8i −1.05863 + 0.611202i −0.925054 − 0.379836i \(-0.875980\pi\)
−0.133579 + 0.991038i \(0.542647\pi\)
\(720\) 4.97034e7 + 6.51605e8i 0.133165 + 1.74577i
\(721\) 591030. − 1.02369e6i 0.00157690 − 0.00273127i
\(722\) −3.41697e8 − 9.38804e8i −0.907882 − 2.49438i
\(723\) −9.52944e7 + 6.93954e8i −0.252146 + 1.83618i
\(724\) 7.99881e8 − 6.71180e8i 2.10770 − 1.76857i
\(725\) −2.09126e8 + 5.74568e8i −0.548774 + 1.50774i
\(726\) −2.50680e7 − 6.58231e8i −0.0655103 − 1.72016i
\(727\) 8.69501e7 − 4.93119e8i 0.226291 − 1.28336i −0.633911 − 0.773406i \(-0.718552\pi\)
0.860202 − 0.509953i \(-0.170337\pi\)
\(728\) 3.22983e7i 0.0837115i
\(729\) 3.77360e8 − 8.77169e7i 0.974031 − 0.226413i
\(730\) −7.74578e8 −1.99112
\(731\) 7.05771e8 + 1.24446e8i 1.80681 + 0.318589i
\(732\) 5.41539e8 − 2.06239e7i 1.38069 − 0.0525821i
\(733\) −1.45029e8 − 5.27863e7i −0.368250 − 0.134032i 0.151265 − 0.988493i \(-0.451665\pi\)
−0.519515 + 0.854461i \(0.673888\pi\)
\(734\) 6.51464e8 + 7.76385e8i 1.64741 + 1.96331i
\(735\) 5.77145e8 + 7.92541e7i 1.45353 + 0.199600i
\(736\) 5.78629e7 − 2.10604e7i 0.145133 − 0.0528241i
\(737\) −4.09535e7 − 2.36445e7i −0.102303 − 0.0590647i
\(738\) 1.03025e8 − 7.85856e6i 0.256314 − 0.0195512i
\(739\) −9.39930e7 − 1.62801e8i −0.232896 − 0.403388i 0.725763 − 0.687945i \(-0.241487\pi\)
−0.958659 + 0.284557i \(0.908154\pi\)
\(740\) −1.03293e9 + 1.23099e9i −2.54903 + 3.03781i
\(741\) 8.63155e8 + 2.77444e8i 2.12146 + 0.681901i
\(742\) −1.03433e6 − 5.86600e6i −0.00253191 − 0.0143592i
\(743\) −6.36604e8 + 1.12250e8i −1.55204 + 0.273667i −0.882933 − 0.469499i \(-0.844435\pi\)
−0.669107 + 0.743166i \(0.733323\pi\)
\(744\) 2.50051e8 + 2.75952e8i 0.607169 + 0.670061i
\(745\) −7.11333e7 − 5.96879e7i −0.172030 − 0.144350i
\(746\) −8.45400e8 + 4.88092e8i −2.03632 + 1.17567i
\(747\) −5.86485e8 − 5.78982e7i −1.40700 − 0.138900i
\(748\) 8.68770e7 − 1.50475e8i 0.207587 − 0.359551i
\(749\) −1.99835e6 − 5.49042e6i −0.00475583 − 0.0130665i
\(750\) 1.57651e8 − 6.42752e7i 0.373692 − 0.152356i
\(751\) 2.43473e8 − 2.04298e8i 0.574820 − 0.482331i −0.308422 − 0.951250i \(-0.599801\pi\)
0.883241 + 0.468919i \(0.155356\pi\)
\(752\) −1.25140e7 + 3.43819e7i −0.0294267 + 0.0808493i
\(753\) −3.02435e8 − 1.59584e8i −0.708350 − 0.373771i
\(754\) 2.53749e8 − 1.43908e9i 0.591958 − 3.35716i
\(755\) − 2.75709e7i − 0.0640633i
\(756\) 2.83737e7 − 3.25434e6i 0.0656676 − 0.00753178i
\(757\) −3.61614e8 −0.833599 −0.416800 − 0.908998i \(-0.636848\pi\)
−0.416800 + 0.908998i \(0.636848\pi\)
\(758\) −3.76276e8 − 6.63475e7i −0.863970 − 0.152341i
\(759\) −2.03263e7 − 3.23013e7i