Properties

Label 36.6.h.a.23.8
Level $36$
Weight $6$
Character 36.23
Analytic conductor $5.774$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [36,6,Mod(11,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("36.11");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 36.h (of order \(6\), degree \(2\), 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: \(5.77381751327\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.8
Character \(\chi\) \(=\) 36.23
Dual form 36.6.h.a.11.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.91293 + 4.08522i) q^{2} +(-13.5204 + 7.75878i) q^{3} +(-1.37798 - 31.9703i) q^{4} +(-27.3241 - 15.7756i) q^{5} +(21.2081 - 85.5933i) q^{6} +(-2.81745 + 1.62665i) q^{7} +(135.998 + 119.468i) q^{8} +(122.603 - 209.804i) q^{9} +O(q^{10})\) \(q+(-3.91293 + 4.08522i) q^{2} +(-13.5204 + 7.75878i) q^{3} +(-1.37798 - 31.9703i) q^{4} +(-27.3241 - 15.7756i) q^{5} +(21.2081 - 85.5933i) q^{6} +(-2.81745 + 1.62665i) q^{7} +(135.998 + 119.468i) q^{8} +(122.603 - 209.804i) q^{9} +(171.364 - 49.8961i) q^{10} +(244.292 + 423.126i) q^{11} +(266.681 + 421.560i) q^{12} +(514.329 - 890.844i) q^{13} +(4.37923 - 17.8749i) q^{14} +(491.832 + 1.29066i) q^{15} +(-1020.20 + 88.1092i) q^{16} -544.497i q^{17} +(377.357 + 1321.81i) q^{18} -1086.90i q^{19} +(-466.698 + 895.298i) q^{20} +(25.4722 - 43.8530i) q^{21} +(-2684.46 - 657.677i) q^{22} +(969.831 - 1679.80i) q^{23} +(-2765.67 - 560.084i) q^{24} +(-1064.76 - 1844.22i) q^{25} +(1626.76 + 5586.95i) q^{26} +(-29.8209 + 3787.88i) q^{27} +(55.8870 + 87.8332i) q^{28} +(-271.322 + 156.648i) q^{29} +(-1929.78 + 2004.19i) q^{30} +(-4990.16 - 2881.07i) q^{31} +(3632.03 - 4512.51i) q^{32} +(-6585.87 - 3825.43i) q^{33} +(2224.39 + 2130.58i) q^{34} +102.646 q^{35} +(-6876.43 - 3630.54i) q^{36} +9789.25 q^{37} +(4440.21 + 4252.95i) q^{38} +(-42.0792 + 16035.1i) q^{39} +(-1831.33 - 5409.80i) q^{40} +(8802.77 + 5082.28i) q^{41} +(79.4780 + 275.653i) q^{42} +(16506.0 - 9529.76i) q^{43} +(13190.8 - 8393.16i) q^{44} +(-6659.78 + 3798.56i) q^{45} +(3067.45 + 10534.9i) q^{46} +(-11221.8 - 19436.8i) q^{47} +(13109.9 - 9106.79i) q^{48} +(-8398.21 + 14546.1i) q^{49} +(11700.4 + 2866.53i) q^{50} +(4224.63 + 7361.83i) q^{51} +(-29189.3 - 15215.7i) q^{52} -11691.5i q^{53} +(-15357.6 - 14943.5i) q^{54} -15415.4i q^{55} +(-577.499 - 115.374i) q^{56} +(8432.99 + 14695.3i) q^{57} +(421.723 - 1721.36i) q^{58} +(-19276.6 + 33388.1i) q^{59} +(-636.474 - 15725.8i) q^{60} +(3811.30 + 6601.36i) q^{61} +(31295.9 - 9112.46i) q^{62} +(-4.14910 + 790.543i) q^{63} +(4222.70 + 32494.8i) q^{64} +(-28107.2 + 16227.7i) q^{65} +(41397.7 - 11936.1i) q^{66} +(4430.73 + 2558.08i) q^{67} +(-17407.8 + 750.309i) q^{68} +(-79.3456 + 30236.2i) q^{69} +(-401.645 + 419.329i) q^{70} -65091.6 q^{71} +(41738.5 - 13885.7i) q^{72} +12156.6 q^{73} +(-38304.6 + 39991.2i) q^{74} +(28704.9 + 16673.4i) q^{75} +(-34748.4 + 1497.73i) q^{76} +(-1376.56 - 794.757i) q^{77} +(-65342.4 - 62916.3i) q^{78} +(64990.0 - 37522.0i) q^{79} +(29266.1 + 13686.8i) q^{80} +(-28986.1 - 51445.0i) q^{81} +(-55206.8 + 16074.6i) q^{82} +(-25579.5 - 44304.9i) q^{83} +(-1437.09 - 753.925i) q^{84} +(-8589.76 + 14877.9i) q^{85} +(-25655.8 + 104720. i) q^{86} +(2452.99 - 4223.07i) q^{87} +(-17327.0 + 86729.3i) q^{88} -126726. i q^{89} +(10541.3 - 42070.2i) q^{90} +3346.54i q^{91} +(-55040.0 - 28691.1i) q^{92} +(89822.5 + 235.711i) q^{93} +(123314. + 30211.1i) q^{94} +(-17146.4 + 29698.5i) q^{95} +(-14095.0 + 89191.1i) q^{96} +(-30959.8 - 53624.0i) q^{97} +(-26562.5 - 91226.4i) q^{98} +(118724. + 623.114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 3 q^{2} - q^{4} - 6 q^{5} - 27 q^{6} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 3 q^{2} - q^{4} - 6 q^{5} - 27 q^{6} + 18 q^{9} - 68 q^{10} - 486 q^{12} - 2 q^{13} - 1518 q^{14} - q^{16} + 1992 q^{18} - 1242 q^{20} + 330 q^{21} + 63 q^{22} + 2235 q^{24} + 12498 q^{25} - 2052 q^{28} - 11946 q^{29} - 6882 q^{30} - 7233 q^{32} + 17040 q^{33} + 6361 q^{34} + 6399 q^{36} - 8 q^{37} - 14877 q^{38} - 1526 q^{40} - 43536 q^{41} + 18564 q^{42} - 42 q^{45} - 26880 q^{46} - 5931 q^{48} + 38414 q^{49} + 38631 q^{50} + 24988 q^{52} + 37587 q^{54} + 21186 q^{56} - 90786 q^{57} - 3314 q^{58} + 60930 q^{60} - 2 q^{61} - 106342 q^{64} + 35970 q^{65} - 47838 q^{66} + 31413 q^{68} - 1854 q^{69} + 10524 q^{70} - 130941 q^{72} + 53620 q^{73} - 20406 q^{74} + 26193 q^{76} + 26178 q^{77} - 96684 q^{78} - 14790 q^{81} - 151286 q^{82} + 141630 q^{84} + 6248 q^{85} + 279237 q^{86} - 122541 q^{88} + 235278 q^{90} + 435804 q^{92} + 71838 q^{93} + 63480 q^{94} - 37476 q^{96} - 58148 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.91293 + 4.08522i −0.691715 + 0.722171i
\(3\) −13.5204 + 7.75878i −0.867335 + 0.497726i
\(4\) −1.37798 31.9703i −0.0430620 0.999072i
\(5\) −27.3241 15.7756i −0.488788 0.282202i 0.235283 0.971927i \(-0.424398\pi\)
−0.724072 + 0.689725i \(0.757732\pi\)
\(6\) 21.2081 85.5933i 0.240505 0.970648i
\(7\) −2.81745 + 1.62665i −0.0217325 + 0.0125473i −0.510827 0.859684i \(-0.670661\pi\)
0.489094 + 0.872231i \(0.337327\pi\)
\(8\) 135.998 + 119.468i 0.751288 + 0.659975i
\(9\) 122.603 209.804i 0.504538 0.863389i
\(10\) 171.364 49.8961i 0.541900 0.157785i
\(11\) 244.292 + 423.126i 0.608734 + 1.05436i 0.991449 + 0.130492i \(0.0416557\pi\)
−0.382715 + 0.923866i \(0.625011\pi\)
\(12\) 266.681 + 421.560i 0.534613 + 0.845097i
\(13\) 514.329 890.844i 0.844078 1.46199i −0.0423410 0.999103i \(-0.513482\pi\)
0.886419 0.462883i \(-0.153185\pi\)
\(14\) 4.37923 17.8749i 0.00597143 0.0243738i
\(15\) 491.832 + 1.29066i 0.564402 + 0.00148110i
\(16\) −1020.20 + 88.1092i −0.996291 + 0.0860441i
\(17\) 544.497i 0.456955i −0.973549 0.228478i \(-0.926625\pi\)
0.973549 0.228478i \(-0.0733748\pi\)
\(18\) 377.357 + 1321.81i 0.274518 + 0.961582i
\(19\) 1086.90i 0.690724i −0.938470 0.345362i \(-0.887756\pi\)
0.938470 0.345362i \(-0.112244\pi\)
\(20\) −466.698 + 895.298i −0.260892 + 0.500487i
\(21\) 25.4722 43.8530i 0.0126043 0.0216995i
\(22\) −2684.46 657.677i −1.18250 0.289705i
\(23\) 969.831 1679.80i 0.382275 0.662121i −0.609112 0.793084i \(-0.708474\pi\)
0.991387 + 0.130964i \(0.0418072\pi\)
\(24\) −2765.67 560.084i −0.980104 0.198484i
\(25\) −1064.76 1844.22i −0.340724 0.590151i
\(26\) 1626.76 + 5586.95i 0.471943 + 1.62085i
\(27\) −29.8209 + 3787.88i −0.00787247 + 0.999969i
\(28\) 55.8870 + 87.8332i 0.0134715 + 0.0211721i
\(29\) −271.322 + 156.648i −0.0599087 + 0.0345883i −0.529655 0.848213i \(-0.677679\pi\)
0.469746 + 0.882801i \(0.344345\pi\)
\(30\) −1929.78 + 2004.19i −0.391475 + 0.406570i
\(31\) −4990.16 2881.07i −0.932631 0.538455i −0.0449884 0.998988i \(-0.514325\pi\)
−0.887643 + 0.460533i \(0.847658\pi\)
\(32\) 3632.03 4512.51i 0.627011 0.779011i
\(33\) −6585.87 3825.43i −1.05276 0.611499i
\(34\) 2224.39 + 2130.58i 0.330000 + 0.316082i
\(35\) 102.646 0.0141635
\(36\) −6876.43 3630.54i −0.884315 0.466891i
\(37\) 9789.25 1.17556 0.587780 0.809021i \(-0.300002\pi\)
0.587780 + 0.809021i \(0.300002\pi\)
\(38\) 4440.21 + 4252.95i 0.498821 + 0.477784i
\(39\) −42.0792 + 16035.1i −0.00443003 + 1.68815i
\(40\) −1831.33 5409.80i −0.180974 0.534603i
\(41\) 8802.77 + 5082.28i 0.817823 + 0.472171i 0.849665 0.527322i \(-0.176804\pi\)
−0.0318420 + 0.999493i \(0.510137\pi\)
\(42\) 79.4780 + 275.653i 0.00695222 + 0.0241123i
\(43\) 16506.0 9529.76i 1.36136 0.785979i 0.371551 0.928413i \(-0.378826\pi\)
0.989804 + 0.142434i \(0.0454928\pi\)
\(44\) 13190.8 8393.16i 1.02717 0.653572i
\(45\) −6659.78 + 3798.56i −0.490263 + 0.279633i
\(46\) 3067.45 + 10534.9i 0.213739 + 0.734067i
\(47\) −11221.8 19436.8i −0.741000 1.28345i −0.952040 0.305973i \(-0.901018\pi\)
0.211040 0.977477i \(-0.432315\pi\)
\(48\) 13109.9 9106.79i 0.821291 0.570509i
\(49\) −8398.21 + 14546.1i −0.499685 + 0.865480i
\(50\) 11700.4 + 2866.53i 0.661874 + 0.162155i
\(51\) 4224.63 + 7361.83i 0.227438 + 0.396333i
\(52\) −29189.3 15215.7i −1.49698 0.780339i
\(53\) 11691.5i 0.571717i −0.958272 0.285858i \(-0.907721\pi\)
0.958272 0.285858i \(-0.0922787\pi\)
\(54\) −15357.6 14943.5i −0.716703 0.697378i
\(55\) 15415.4i 0.687144i
\(56\) −577.499 115.374i −0.0246083 0.00491631i
\(57\) 8432.99 + 14695.3i 0.343791 + 0.599089i
\(58\) 421.723 1721.36i 0.0164610 0.0671895i
\(59\) −19276.6 + 33388.1i −0.720942 + 1.24871i 0.239680 + 0.970852i \(0.422957\pi\)
−0.960622 + 0.277857i \(0.910376\pi\)
\(60\) −636.474 15725.8i −0.0228246 0.563942i
\(61\) 3811.30 + 6601.36i 0.131144 + 0.227148i 0.924118 0.382108i \(-0.124802\pi\)
−0.792974 + 0.609256i \(0.791468\pi\)
\(62\) 31295.9 9112.46i 1.03397 0.301062i
\(63\) −4.14910 + 790.543i −0.000131705 + 0.0250942i
\(64\) 4222.70 + 32494.8i 0.128867 + 0.991662i
\(65\) −28107.2 + 16227.7i −0.825151 + 0.476401i
\(66\) 41397.7 11936.1i 1.16981 0.337288i
\(67\) 4430.73 + 2558.08i 0.120584 + 0.0696189i 0.559079 0.829115i \(-0.311155\pi\)
−0.438495 + 0.898734i \(0.644488\pi\)
\(68\) −17407.8 + 750.309i −0.456531 + 0.0196774i
\(69\) −79.3456 + 30236.2i −0.00200632 + 0.764548i
\(70\) −401.645 + 419.329i −0.00979709 + 0.0102285i
\(71\) −65091.6 −1.53242 −0.766212 0.642588i \(-0.777861\pi\)
−0.766212 + 0.642588i \(0.777861\pi\)
\(72\) 41738.5 13885.7i 0.948869 0.315671i
\(73\) 12156.6 0.266996 0.133498 0.991049i \(-0.457379\pi\)
0.133498 + 0.991049i \(0.457379\pi\)
\(74\) −38304.6 + 39991.2i −0.813152 + 0.848956i
\(75\) 28704.9 + 16673.4i 0.589255 + 0.342272i
\(76\) −34748.4 + 1497.73i −0.690083 + 0.0297440i
\(77\) −1376.56 794.757i −0.0264587 0.0152759i
\(78\) −65342.4 62916.3i −1.21607 1.17092i
\(79\) 64990.0 37522.0i 1.17160 0.676423i 0.217542 0.976051i \(-0.430196\pi\)
0.954056 + 0.299628i \(0.0968626\pi\)
\(80\) 29266.1 + 13686.8i 0.511257 + 0.239098i
\(81\) −28986.1 51445.0i −0.490882 0.871226i
\(82\) −55206.8 + 16074.6i −0.906688 + 0.264001i
\(83\) −25579.5 44304.9i −0.407564 0.705922i 0.587052 0.809549i \(-0.300289\pi\)
−0.994616 + 0.103627i \(0.966955\pi\)
\(84\) −1437.09 753.925i −0.0222222 0.0116582i
\(85\) −8589.76 + 14877.9i −0.128954 + 0.223354i
\(86\) −25655.8 + 104720.i −0.374058 + 1.52680i
\(87\) 2452.99 4223.07i 0.0347454 0.0598177i
\(88\) −17327.0 + 86729.3i −0.238515 + 1.19388i
\(89\) 126726.i 1.69587i −0.530104 0.847933i \(-0.677847\pi\)
0.530104 0.847933i \(-0.322153\pi\)
\(90\) 10541.3 42070.2i 0.137179 0.547480i
\(91\) 3346.54i 0.0423636i
\(92\) −55040.0 28691.1i −0.677968 0.353409i
\(93\) 89822.5 + 235.711i 1.07691 + 0.00282601i
\(94\) 123314. + 30211.1i 1.43943 + 0.352652i
\(95\) −17146.4 + 29698.5i −0.194924 + 0.337618i
\(96\) −14095.0 + 89191.1i −0.156094 + 0.987742i
\(97\) −30959.8 53624.0i −0.334094 0.578668i 0.649216 0.760604i \(-0.275097\pi\)
−0.983310 + 0.181936i \(0.941764\pi\)
\(98\) −26562.5 91226.4i −0.279385 0.959523i
\(99\) 118724. + 623.114i 1.21745 + 0.00638969i
\(100\) −57493.2 + 36582.1i −0.574932 + 0.365821i
\(101\) 75740.7 43728.9i 0.738798 0.426545i −0.0828340 0.996563i \(-0.526397\pi\)
0.821632 + 0.570018i \(0.193064\pi\)
\(102\) −46605.3 11547.8i −0.443543 0.109900i
\(103\) 92372.6 + 53331.3i 0.857926 + 0.495324i 0.863317 0.504661i \(-0.168383\pi\)
−0.00539101 + 0.999985i \(0.501716\pi\)
\(104\) 176375. 59706.7i 1.59902 0.541302i
\(105\) −1387.81 + 796.404i −0.0122845 + 0.00704953i
\(106\) 47762.3 + 45748.0i 0.412877 + 0.395465i
\(107\) 26946.6 0.227533 0.113767 0.993508i \(-0.463708\pi\)
0.113767 + 0.993508i \(0.463708\pi\)
\(108\) 121141. 4266.25i 0.999380 0.0351955i
\(109\) 71302.9 0.574832 0.287416 0.957806i \(-0.407204\pi\)
0.287416 + 0.957806i \(0.407204\pi\)
\(110\) 62975.2 + 60319.3i 0.496235 + 0.475307i
\(111\) −132355. + 75952.6i −1.01960 + 0.585107i
\(112\) 2731.04 1907.76i 0.0205723 0.0143707i
\(113\) 32800.9 + 18937.6i 0.241651 + 0.139517i 0.615935 0.787797i \(-0.288778\pi\)
−0.374284 + 0.927314i \(0.622112\pi\)
\(114\) −93031.1 23051.0i −0.670450 0.166122i
\(115\) −52999.5 + 30599.3i −0.373704 + 0.215758i
\(116\) 5381.96 + 8458.39i 0.0371360 + 0.0583637i
\(117\) −123844. 217128.i −0.836394 1.46640i
\(118\) −60969.5 209394.i −0.403095 1.38439i
\(119\) 885.709 + 1534.09i 0.00573355 + 0.00993080i
\(120\) 66733.8 + 58933.8i 0.423051 + 0.373604i
\(121\) −38831.7 + 67258.5i −0.241114 + 0.417622i
\(122\) −41881.3 10260.7i −0.254754 0.0624132i
\(123\) −158449. 415.801i −0.944338 0.00247812i
\(124\) −85232.3 + 163507.i −0.497794 + 0.954953i
\(125\) 165786.i 0.949016i
\(126\) −3213.30 3110.29i −0.0180312 0.0174532i
\(127\) 66387.5i 0.365239i −0.983184 0.182619i \(-0.941542\pi\)
0.983184 0.182619i \(-0.0584576\pi\)
\(128\) −149271. 109899.i −0.805288 0.592883i
\(129\) −149229. + 256913.i −0.789548 + 1.35929i
\(130\) 43687.7 178322.i 0.226726 0.925434i
\(131\) 28167.3 48787.1i 0.143406 0.248386i −0.785371 0.619025i \(-0.787528\pi\)
0.928777 + 0.370639i \(0.120861\pi\)
\(132\) −113225. + 215824.i −0.565598 + 1.07811i
\(133\) 1768.01 + 3062.27i 0.00866671 + 0.0150112i
\(134\) −27787.4 + 8090.89i −0.133686 + 0.0389255i
\(135\) 60570.8 103030.i 0.286041 0.486552i
\(136\) 65050.1 74050.4i 0.301579 0.343305i
\(137\) −364985. + 210724.i −1.66140 + 0.959207i −0.689346 + 0.724432i \(0.742102\pi\)
−0.972050 + 0.234775i \(0.924565\pi\)
\(138\) −123211. 118636.i −0.550747 0.530298i
\(139\) −332509. 191974.i −1.45971 0.842764i −0.460713 0.887549i \(-0.652406\pi\)
−0.998997 + 0.0447857i \(0.985739\pi\)
\(140\) −141.444 3281.61i −0.000609908 0.0141503i
\(141\) 302529. + 175725.i 1.28150 + 0.744366i
\(142\) 254699. 265913.i 1.06000 1.10667i
\(143\) 502586. 2.05528
\(144\) −106594. + 224845.i −0.428378 + 0.903600i
\(145\) 9884.83 0.0390435
\(146\) −47567.9 + 49662.3i −0.184685 + 0.192817i
\(147\) 687.090 261829.i 0.00262253 0.999367i
\(148\) −13489.4 312965.i −0.0506220 1.17447i
\(149\) 283272. + 163547.i 1.04529 + 0.603499i 0.921327 0.388788i \(-0.127106\pi\)
0.123964 + 0.992287i \(0.460439\pi\)
\(150\) −180435. + 52024.1i −0.654775 + 0.188789i
\(151\) −376668. + 217470.i −1.34436 + 0.776169i −0.987444 0.157967i \(-0.949506\pi\)
−0.356919 + 0.934135i \(0.616173\pi\)
\(152\) 129850. 147815.i 0.455860 0.518932i
\(153\) −114238. 66756.9i −0.394530 0.230551i
\(154\) 8633.13 2513.72i 0.0293337 0.00854111i
\(155\) 90901.0 + 157445.i 0.303906 + 0.526381i
\(156\) 512706. 20750.9i 1.68678 0.0682692i
\(157\) −6799.06 + 11776.3i −0.0220140 + 0.0381294i −0.876823 0.480814i \(-0.840341\pi\)
0.854809 + 0.518944i \(0.173675\pi\)
\(158\) −101016. + 412319.i −0.321919 + 1.31399i
\(159\) 90711.8 + 158074.i 0.284558 + 0.495870i
\(160\) −170429. + 66002.9i −0.526314 + 0.203828i
\(161\) 6310.32i 0.0191861i
\(162\) 323585. + 82886.2i 0.968724 + 0.248139i
\(163\) 473364.i 1.39549i 0.716347 + 0.697744i \(0.245813\pi\)
−0.716347 + 0.697744i \(0.754187\pi\)
\(164\) 150352. 288431.i 0.436515 0.837397i
\(165\) 119605. + 208422.i 0.342009 + 0.595984i
\(166\) 281086. + 68864.4i 0.791715 + 0.193966i
\(167\) 74868.1 129675.i 0.207733 0.359804i −0.743267 0.668995i \(-0.766725\pi\)
0.951000 + 0.309191i \(0.100058\pi\)
\(168\) 8703.19 2920.78i 0.0237906 0.00798410i
\(169\) −343422. 594825.i −0.924936 1.60204i
\(170\) −27168.3 93307.2i −0.0721009 0.247624i
\(171\) −228035. 133257.i −0.596364 0.348497i
\(172\) −327414. 514571.i −0.843872 1.32625i
\(173\) 147188. 84978.9i 0.373901 0.215872i −0.301260 0.953542i \(-0.597407\pi\)
0.675161 + 0.737670i \(0.264074\pi\)
\(174\) 7653.78 + 26545.5i 0.0191647 + 0.0664689i
\(175\) 5999.82 + 3464.00i 0.0148096 + 0.00855033i
\(176\) −286509. 410150.i −0.697198 0.998070i
\(177\) 1577.09 600983.i 0.00378377 1.44188i
\(178\) 517704. + 495870.i 1.22470 + 1.17305i
\(179\) 91825.1 0.214205 0.107102 0.994248i \(-0.465843\pi\)
0.107102 + 0.994248i \(0.465843\pi\)
\(180\) 130618. + 207681.i 0.300485 + 0.477766i
\(181\) 640763. 1.45379 0.726893 0.686750i \(-0.240963\pi\)
0.726893 + 0.686750i \(0.240963\pi\)
\(182\) −13671.3 13094.8i −0.0305938 0.0293035i
\(183\) −102749. 59682.1i −0.226803 0.131740i
\(184\) 332577. 112584.i 0.724182 0.245151i
\(185\) −267482. 154431.i −0.574600 0.331746i
\(186\) −352432. + 366022.i −0.746952 + 0.775756i
\(187\) 230391. 133016.i 0.481794 0.278164i
\(188\) −605936. + 385549.i −1.25035 + 0.795581i
\(189\) −6077.55 10720.7i −0.0123758 0.0218307i
\(190\) −54232.0 186255.i −0.108986 0.374303i
\(191\) 138848. + 240492.i 0.275395 + 0.476998i 0.970235 0.242167i \(-0.0778581\pi\)
−0.694840 + 0.719165i \(0.744525\pi\)
\(192\) −309212. 406580.i −0.605346 0.795962i
\(193\) −432677. + 749418.i −0.836123 + 1.44821i 0.0569898 + 0.998375i \(0.481850\pi\)
−0.893113 + 0.449833i \(0.851484\pi\)
\(194\) 340209. + 83349.2i 0.648995 + 0.159000i
\(195\) 254113. 437482.i 0.478565 0.823898i
\(196\) 476617. + 248449.i 0.886195 + 0.461952i
\(197\) 246048.i 0.451705i −0.974162 0.225852i \(-0.927483\pi\)
0.974162 0.225852i \(-0.0725167\pi\)
\(198\) −467105. + 482576.i −0.846743 + 0.874788i
\(199\) 283324.i 0.507166i 0.967314 + 0.253583i \(0.0816091\pi\)
−0.967314 + 0.253583i \(0.918391\pi\)
\(200\) 75520.8 378015.i 0.133503 0.668243i
\(201\) −79752.8 209.286i −0.139237 0.000365385i
\(202\) −117726. + 480525.i −0.202999 + 0.828586i
\(203\) 509.623 882.693i 0.000867979 0.00150338i
\(204\) 229538. 145207.i 0.386171 0.244294i
\(205\) −160352. 277737.i −0.266495 0.461583i
\(206\) −579317. + 168680.i −0.951149 + 0.276947i
\(207\) −233523. 409422.i −0.378795 0.664118i
\(208\) −446228. + 954158.i −0.715152 + 1.52919i
\(209\) 459895. 265520.i 0.728270 0.420467i
\(210\) 2176.92 8785.78i 0.00340639 0.0137478i
\(211\) 369932. + 213580.i 0.572025 + 0.330259i 0.757958 0.652303i \(-0.226197\pi\)
−0.185932 + 0.982563i \(0.559531\pi\)
\(212\) −373781. + 16110.7i −0.571186 + 0.0246193i
\(213\) 880064. 505031.i 1.32912 0.762727i
\(214\) −105440. + 110083.i −0.157388 + 0.164318i
\(215\) −601350. −0.887219
\(216\) −456586. + 511580.i −0.665869 + 0.746069i
\(217\) 18746.0 0.0270246
\(218\) −279003. + 291288.i −0.397620 + 0.415127i
\(219\) −164362. + 94320.3i −0.231575 + 0.132891i
\(220\) −492835. + 21242.2i −0.686507 + 0.0295898i
\(221\) −485062. 280051.i −0.668062 0.385706i
\(222\) 207611. 837894.i 0.282728 1.14106i
\(223\) 785917. 453749.i 1.05831 0.611018i 0.133349 0.991069i \(-0.457427\pi\)
0.924965 + 0.380051i \(0.124094\pi\)
\(224\) −2892.77 + 18621.8i −0.00385206 + 0.0247972i
\(225\) −517467. 2715.88i −0.681439 0.00357647i
\(226\) −205711. + 59897.2i −0.267909 + 0.0780073i
\(227\) −195847. 339217.i −0.252262 0.436931i 0.711886 0.702295i \(-0.247841\pi\)
−0.964148 + 0.265364i \(0.914508\pi\)
\(228\) 458193. 289855.i 0.583729 0.369270i
\(229\) −240738. + 416970.i −0.303358 + 0.525432i −0.976894 0.213722i \(-0.931441\pi\)
0.673536 + 0.739154i \(0.264775\pi\)
\(230\) 82378.6 336247.i 0.102682 0.419121i
\(231\) 24778.0 + 65.0221i 0.0305517 + 8.01736e-5i
\(232\) −55613.5 11110.6i −0.0678361 0.0135525i
\(233\) 506837.i 0.611615i 0.952093 + 0.305808i \(0.0989265\pi\)
−0.952093 + 0.305808i \(0.901074\pi\)
\(234\) 1.37161e6 + 343677.i 1.63753 + 0.410308i
\(235\) 708122.i 0.836447i
\(236\) 1.09399e6 + 570271.i 1.27860 + 0.666502i
\(237\) −587566. + 1.01156e6i −0.679495 + 1.16982i
\(238\) −9732.81 2384.48i −0.0111377 0.00272867i
\(239\) −150130. + 260032.i −0.170009 + 0.294464i −0.938423 0.345489i \(-0.887713\pi\)
0.768414 + 0.639953i \(0.221046\pi\)
\(240\) −501882. + 42018.2i −0.562436 + 0.0470879i
\(241\) −266947. 462366.i −0.296062 0.512795i 0.679169 0.733982i \(-0.262340\pi\)
−0.975231 + 0.221187i \(0.929007\pi\)
\(242\) −122820. 421813.i −0.134812 0.463001i
\(243\) 791054. + 470661.i 0.859391 + 0.511320i
\(244\) 205796. 130945.i 0.221290 0.140804i
\(245\) 458947. 264973.i 0.488480 0.282024i
\(246\) 621699. 645672.i 0.655002 0.680259i
\(247\) −968256. 559023.i −1.00983 0.583025i
\(248\) −334453. 987983.i −0.345308 1.02005i
\(249\) 689597. + 400555.i 0.704850 + 0.409416i
\(250\) −677273. 648710.i −0.685352 0.656448i
\(251\) −1.40288e6 −1.40551 −0.702757 0.711430i \(-0.748048\pi\)
−0.702757 + 0.711430i \(0.748048\pi\)
\(252\) 25279.6 956.708i 0.0250766 0.000949025i
\(253\) 947688. 0.930816
\(254\) 271207. + 259769.i 0.263765 + 0.252641i
\(255\) 702.761 267801.i 0.000676795 0.257906i
\(256\) 1.03305e6 179778.i 0.985193 0.171450i
\(257\) −837694. 483643.i −0.791139 0.456764i 0.0492245 0.998788i \(-0.484325\pi\)
−0.840363 + 0.542024i \(0.817658\pi\)
\(258\) −465622. 1.61491e6i −0.435496 1.51043i
\(259\) −27580.7 + 15923.7i −0.0255479 + 0.0147501i
\(260\) 557535. + 876233.i 0.511492 + 0.803871i
\(261\) −399.560 + 76129.8i −0.000363062 + 0.0691756i
\(262\) 89089.5 + 305970.i 0.0801814 + 0.275376i
\(263\) 464267. + 804134.i 0.413884 + 0.716868i 0.995311 0.0967310i \(-0.0308387\pi\)
−0.581427 + 0.813599i \(0.697505\pi\)
\(264\) −438645. 1.30705e6i −0.387350 1.15420i
\(265\) −184440. + 319460.i −0.161340 + 0.279448i
\(266\) −19428.1 4759.78i −0.0168355 0.00412461i
\(267\) 983240. + 1.71339e6i 0.844076 + 1.47088i
\(268\) 75677.2 145177.i 0.0643618 0.123470i
\(269\) 1.21595e6i 1.02455i 0.858820 + 0.512277i \(0.171198\pi\)
−0.858820 + 0.512277i \(0.828802\pi\)
\(270\) 183890. + 650593.i 0.153514 + 0.543125i
\(271\) 2.02493e6i 1.67489i −0.546520 0.837446i \(-0.684048\pi\)
0.546520 0.837446i \(-0.315952\pi\)
\(272\) 47975.2 + 555498.i 0.0393183 + 0.455260i
\(273\) −25965.1 45246.6i −0.0210854 0.0367434i
\(274\) 567306. 2.31559e6i 0.456500 1.86331i
\(275\) 520226. 901058.i 0.414821 0.718490i
\(276\) 966771. 39128.3i 0.763926 0.0309185i
\(277\) 192874. + 334068.i 0.151034 + 0.261599i 0.931608 0.363465i \(-0.118406\pi\)
−0.780574 + 0.625064i \(0.785073\pi\)
\(278\) 2.08534e6 607190.i 1.61832 0.471208i
\(279\) −1.21627e6 + 693726.i −0.935444 + 0.533553i
\(280\) 13959.6 + 12262.9i 0.0106409 + 0.00934754i
\(281\) −142638. + 82351.9i −0.107763 + 0.0622168i −0.552913 0.833239i \(-0.686484\pi\)
0.445150 + 0.895456i \(0.353150\pi\)
\(282\) −1.90165e6 + 548296.i −1.42399 + 0.410575i
\(283\) 441868. + 255113.i 0.327964 + 0.189350i 0.654937 0.755684i \(-0.272695\pi\)
−0.326973 + 0.945034i \(0.606029\pi\)
\(284\) 89695.1 + 2.08100e6i 0.0659892 + 1.53100i
\(285\) 1402.81 534571.i 0.00102303 0.389846i
\(286\) −1.96658e6 + 2.05317e6i −1.42166 + 1.48426i
\(287\) −33068.4 −0.0236978
\(288\) −501444. 1.31526e6i −0.356239 0.934395i
\(289\) 1.12338e6 0.791192
\(290\) −38678.6 + 40381.7i −0.0270070 + 0.0281961i
\(291\) 834646. + 484808.i 0.577790 + 0.335612i
\(292\) −16751.6 388650.i −0.0114974 0.266749i
\(293\) 1.02752e6 + 593241.i 0.699234 + 0.403703i 0.807062 0.590467i \(-0.201056\pi\)
−0.107828 + 0.994170i \(0.534390\pi\)
\(294\) 1.06694e6 + 1.02733e6i 0.719900 + 0.693170i
\(295\) 1.05343e6 608199.i 0.704776 0.406903i
\(296\) 1.33131e6 + 1.16950e6i 0.883184 + 0.775840i
\(297\) −1.61004e6 + 912730.i −1.05912 + 0.600415i
\(298\) −1.77655e6 + 517278.i −1.15887 + 0.337430i
\(299\) −997625. 1.72794e6i −0.645341 1.11776i
\(300\) 493499. 940681.i 0.316580 0.603447i
\(301\) −31003.2 + 53699.2i −0.0197238 + 0.0341626i
\(302\) 585466. 2.38971e6i 0.369389 1.50775i
\(303\) −684762. + 1.17889e6i −0.428483 + 0.737676i
\(304\) 95765.6 + 1.10885e6i 0.0594327 + 0.688162i
\(305\) 240502.i 0.148036i
\(306\) 719720. 205470.i 0.439400 0.125443i
\(307\) 1.41312e6i 0.855724i −0.903844 0.427862i \(-0.859267\pi\)
0.903844 0.427862i \(-0.140733\pi\)
\(308\) −23511.8 + 45104.2i −0.0141224 + 0.0270920i
\(309\) −1.66270e6 4363.24i −0.990645 0.00259964i
\(310\) −998887. 244721.i −0.590353 0.144633i
\(311\) −315266. + 546057.i −0.184832 + 0.320138i −0.943520 0.331316i \(-0.892507\pi\)
0.758688 + 0.651454i \(0.225841\pi\)
\(312\) −1.92141e6 + 2.17571e6i −1.11747 + 1.26536i
\(313\) 197240. + 341630.i 0.113798 + 0.197104i 0.917299 0.398200i \(-0.130365\pi\)
−0.803501 + 0.595304i \(0.797032\pi\)
\(314\) −21504.6 73855.5i −0.0123085 0.0422726i
\(315\) 12584.6 21535.4i 0.00714602 0.0122286i
\(316\) −1.28915e6 2.02605e6i −0.726247 1.14138i
\(317\) 141567. 81733.6i 0.0791249 0.0456828i −0.459916 0.887963i \(-0.652120\pi\)
0.539040 + 0.842280i \(0.318787\pi\)
\(318\) −1.00072e6 247955.i −0.554936 0.137501i
\(319\) −132564. 76535.6i −0.0729369 0.0421101i
\(320\) 397242. 954506.i 0.216861 0.521079i
\(321\) −364329. + 209073.i −0.197347 + 0.113249i
\(322\) −25779.0 24691.8i −0.0138556 0.0132713i
\(323\) −591813. −0.315630
\(324\) −1.60477e6 + 997585.i −0.849279 + 0.527944i
\(325\) −2.19055e6 −1.15039
\(326\) −1.93379e6 1.85224e6i −1.00778 0.965279i
\(327\) −964044. + 553223.i −0.498572 + 0.286109i
\(328\) 589984. + 1.74283e6i 0.302800 + 0.894479i
\(329\) 63233.7 + 36508.0i 0.0322077 + 0.0185951i
\(330\) −1.31945e6 326931.i −0.666975 0.165261i
\(331\) −696109. + 401899.i −0.349227 + 0.201626i −0.664345 0.747426i \(-0.731289\pi\)
0.315118 + 0.949053i \(0.397956\pi\)
\(332\) −1.38119e6 + 878835.i −0.687717 + 0.437585i
\(333\) 1.20019e6 2.05382e6i 0.593115 1.01497i
\(334\) 236798. + 813262.i 0.116148 + 0.398900i
\(335\) −80710.4 139795.i −0.0392932 0.0680578i
\(336\) −22122.9 + 46983.2i −0.0106904 + 0.0227036i
\(337\) 763890. 1.32310e6i 0.366400 0.634624i −0.622599 0.782541i \(-0.713923\pi\)
0.989000 + 0.147917i \(0.0472567\pi\)
\(338\) 3.77378e6 + 924553.i 1.79674 + 0.440190i
\(339\) −590413. 1549.36i −0.279034 0.000732238i
\(340\) 487488. + 254116.i 0.228700 + 0.119216i
\(341\) 2.81529e6i 1.31110i
\(342\) 1.43667e6 410148.i 0.664188 0.189616i
\(343\) 109322.i 0.0501734i
\(344\) 3.38328e6 + 675921.i 1.54150 + 0.307964i
\(345\) 479162. 824926.i 0.216738 0.373136i
\(346\) −228778. + 933810.i −0.102736 + 0.419342i
\(347\) −423222. + 733041.i −0.188688 + 0.326817i −0.944813 0.327610i \(-0.893757\pi\)
0.756125 + 0.654427i \(0.227090\pi\)
\(348\) −138393. 72603.5i −0.0612584 0.0321373i
\(349\) 194050. + 336105.i 0.0852807 + 0.147711i 0.905511 0.424323i \(-0.139488\pi\)
−0.820230 + 0.572034i \(0.806155\pi\)
\(350\) −37628.1 + 10956.2i −0.0164188 + 0.00478068i
\(351\) 3.35907e6 + 1.97478e6i 1.45530 + 0.855562i
\(352\) 2.79664e6 + 434438.i 1.20304 + 0.186884i
\(353\) 1.34326e6 775534.i 0.573753 0.331256i −0.184894 0.982758i \(-0.559194\pi\)
0.758647 + 0.651502i \(0.225861\pi\)
\(354\) 2.44898e6 + 2.35805e6i 1.03867 + 1.00010i
\(355\) 1.77857e6 + 1.02686e6i 0.749031 + 0.432453i
\(356\) −4.05148e6 + 174627.i −1.69429 + 0.0730274i
\(357\) −23877.8 13869.5i −0.00991572 0.00575959i
\(358\) −359305. + 375125.i −0.148168 + 0.154692i
\(359\) 3.63496e6 1.48855 0.744275 0.667873i \(-0.232795\pi\)
0.744275 + 0.667873i \(0.232795\pi\)
\(360\) −1.35952e6 279037.i −0.552879 0.113476i
\(361\) 1.29475e6 0.522901
\(362\) −2.50726e6 + 2.61765e6i −1.00561 + 1.04988i
\(363\) 3176.97 1.21065e6i 0.00126545 0.482227i
\(364\) 106990. 4611.48i 0.0423243 0.00182426i
\(365\) −332168. 191777.i −0.130505 0.0753469i
\(366\) 645863. 186219.i 0.252022 0.0726645i
\(367\) 366486. 211591.i 0.142034 0.0820033i −0.427299 0.904110i \(-0.640535\pi\)
0.569333 + 0.822107i \(0.307202\pi\)
\(368\) −841418. + 1.79918e6i −0.323886 + 0.692558i
\(369\) 2.14552e6 1.22375e6i 0.820290 0.467872i
\(370\) 1.67752e6 488446.i 0.637036 0.185486i
\(371\) 19018.0 + 32940.2i 0.00717350 + 0.0124249i
\(372\) −116238. 2.87198e6i −0.0435504 1.07603i
\(373\) 1.65892e6 2.87333e6i 0.617380 1.06933i −0.372582 0.927999i \(-0.621528\pi\)
0.989962 0.141334i \(-0.0451391\pi\)
\(374\) −358103. + 1.46168e6i −0.132382 + 0.540348i
\(375\) −1.28630e6 2.24150e6i −0.472350 0.823114i
\(376\) 795934. 3.98400e6i 0.290340 1.45328i
\(377\) 322274.i 0.116781i
\(378\) 67577.2 + 17121.1i 0.0243260 + 0.00616312i
\(379\) 2.75509e6i 0.985230i 0.870247 + 0.492615i \(0.163959\pi\)
−0.870247 + 0.492615i \(0.836041\pi\)
\(380\) 973097. + 507253.i 0.345698 + 0.180204i
\(381\) 515086. + 897586.i 0.181789 + 0.316784i
\(382\) −1.52576e6 373803.i −0.534969 0.131064i
\(383\) 341107. 590814.i 0.118821 0.205804i −0.800480 0.599360i \(-0.795422\pi\)
0.919301 + 0.393556i \(0.128755\pi\)
\(384\) 2.87089e6 + 327718.i 0.993548 + 0.113415i
\(385\) 25075.5 + 43432.0i 0.00862180 + 0.0149334i
\(386\) −1.36850e6 4.70000e6i −0.467495 1.60557i
\(387\) 24307.5 4.63140e6i 0.00825017 1.57194i
\(388\) −1.67171e6 + 1.06369e6i −0.563745 + 0.358703i
\(389\) −4.49750e6 + 2.59663e6i −1.50694 + 0.870034i −0.506976 + 0.861960i \(0.669237\pi\)
−0.999967 + 0.00807397i \(0.997430\pi\)
\(390\) 792881. + 2.74994e6i 0.263965 + 0.915508i
\(391\) −914645. 528070.i −0.302559 0.174683i
\(392\) −2.87994e6 + 974919.i −0.946602 + 0.320445i
\(393\) −2304.47 + 878166.i −0.000752645 + 0.286810i
\(394\) 1.00516e6 + 962769.i 0.326208 + 0.312451i
\(395\) −2.36772e6 −0.763551
\(396\) −143679. 3.79651e6i −0.0460421 1.21660i
\(397\) −4.32179e6 −1.37622 −0.688109 0.725607i \(-0.741559\pi\)
−0.688109 + 0.725607i \(0.741559\pi\)
\(398\) −1.15744e6 1.10862e6i −0.366261 0.350814i
\(399\) −47663.6 27685.6i −0.0149884 0.00870608i
\(400\) 1.24877e6 + 1.78767e6i 0.390239 + 0.558645i
\(401\) 2.13586e6 + 1.23314e6i 0.663302 + 0.382958i 0.793534 0.608526i \(-0.208239\pi\)
−0.130232 + 0.991484i \(0.541572\pi\)
\(402\) 312922. 324989.i 0.0965764 0.100300i
\(403\) −5.13317e6 + 2.96363e6i −1.57443 + 0.908996i
\(404\) −1.50240e6 2.36120e6i −0.457964 0.719745i
\(405\) −19555.7 + 1.86296e6i −0.00592429 + 0.564373i
\(406\) 1611.87 + 5535.84i 0.000485306 + 0.00166674i
\(407\) 2.39143e6 + 4.14209e6i 0.715604 + 1.23946i
\(408\) −304964. + 1.50590e6i −0.0906981 + 0.447864i
\(409\) −1.88785e6 + 3.26985e6i −0.558031 + 0.966538i 0.439630 + 0.898179i \(0.355110\pi\)
−0.997661 + 0.0683591i \(0.978224\pi\)
\(410\) 1.76206e6 + 431695.i 0.517680 + 0.126829i
\(411\) 3.29978e6 5.68091e6i 0.963564 1.65887i
\(412\) 1.57773e6 3.02667e6i 0.457920 0.878460i
\(413\) 125425.i 0.0361835i
\(414\) 2.58634e6 + 648045.i 0.741625 + 0.185825i
\(415\) 1.61412e6i 0.460062i
\(416\) −2.15188e6 5.55649e6i −0.609657 1.57423i
\(417\) 5.98514e6 + 15706.1i 1.68552 + 0.00442313i
\(418\) −714827. + 2.91773e6i −0.200106 + 0.816779i
\(419\) −984571. + 1.70533e6i −0.273976 + 0.474540i −0.969876 0.243598i \(-0.921672\pi\)
0.695901 + 0.718138i \(0.255005\pi\)
\(420\) 27373.7 + 43271.3i 0.00757199 + 0.0119695i
\(421\) 437124. + 757121.i 0.120199 + 0.208190i 0.919846 0.392280i \(-0.128314\pi\)
−0.799647 + 0.600470i \(0.794980\pi\)
\(422\) −2.32004e6 + 675527.i −0.634182 + 0.184655i
\(423\) −5.45373e6 28623.4i −1.48198 0.00777805i
\(424\) 1.39676e6 1.59002e6i 0.377319 0.429524i
\(425\) −1.00417e6 + 579760.i −0.269673 + 0.155696i
\(426\) −1.38047e6 + 5.57140e6i −0.368555 + 1.48744i
\(427\) −21476.3 12399.3i −0.00570019 0.00329100i
\(428\) −37132.0 861492.i −0.00979803 0.227322i
\(429\) −6.79517e6 + 3.89945e6i −1.78261 + 1.02296i
\(430\) 2.35304e6 2.45664e6i 0.613702 0.640724i
\(431\) 1.70261e6 0.441492 0.220746 0.975331i \(-0.429151\pi\)
0.220746 + 0.975331i \(0.429151\pi\)
\(432\) −303324. 3.86703e6i −0.0781982 0.996938i
\(433\) −1.19651e6 −0.306688 −0.153344 0.988173i \(-0.549004\pi\)
−0.153344 + 0.988173i \(0.549004\pi\)
\(434\) −73351.8 + 76581.5i −0.0186933 + 0.0195164i
\(435\) −133647. + 76694.2i −0.0338638 + 0.0194330i
\(436\) −98254.3 2.27958e6i −0.0247534 0.574299i
\(437\) −1.82577e6 1.05411e6i −0.457342 0.264047i
\(438\) 257819. 1.04052e6i 0.0642139 0.259159i
\(439\) 2.13579e6 1.23310e6i 0.528929 0.305377i −0.211651 0.977345i \(-0.567884\pi\)
0.740580 + 0.671968i \(0.234551\pi\)
\(440\) 1.84165e6 2.09646e6i 0.453498 0.516243i
\(441\) 2.02219e6 + 3.54537e6i 0.495136 + 0.868091i
\(442\) 3.04208e6 885766.i 0.740654 0.215657i
\(443\) −2.45760e6 4.25669e6i −0.594980 1.03054i −0.993550 0.113397i \(-0.963827\pi\)
0.398570 0.917138i \(-0.369507\pi\)
\(444\) 2.61061e6 + 4.12676e6i 0.628470 + 0.993462i
\(445\) −1.99918e6 + 3.46268e6i −0.478577 + 0.828919i
\(446\) −1.22157e6 + 4.98613e6i −0.290792 + 1.18693i
\(447\) −5.09887e6 13380.4i −1.20699 0.00316738i
\(448\) −64755.0 84683.4i −0.0152433 0.0199344i
\(449\) 95563.2i 0.0223705i 0.999937 + 0.0111852i \(0.00356044\pi\)
−0.999937 + 0.0111852i \(0.996440\pi\)
\(450\) 2.03591e6 2.10334e6i 0.473944 0.489641i
\(451\) 4.96624e6i 1.14971i
\(452\) 560241. 1.07475e6i 0.128982 0.247435i
\(453\) 3.40541e6 5.86276e6i 0.779694 1.34232i
\(454\) 2.15211e6 + 527254.i 0.490032 + 0.120055i
\(455\) 52793.6 91441.2i 0.0119551 0.0207068i
\(456\) −608753. + 3.00600e6i −0.137097 + 0.676981i
\(457\) 1.65475e6 + 2.86612e6i 0.370632 + 0.641953i 0.989663 0.143414i \(-0.0458079\pi\)
−0.619031 + 0.785366i \(0.712475\pi\)
\(458\) −761424. 2.61504e6i −0.169614 0.582526i
\(459\) 2.06249e6 + 16237.4i 0.456941 + 0.00359736i
\(460\) 1.05130e6 + 1.65225e6i 0.231650 + 0.364066i
\(461\) −523886. + 302466.i −0.114811 + 0.0662863i −0.556306 0.830978i \(-0.687782\pi\)
0.441495 + 0.897264i \(0.354448\pi\)
\(462\) −97220.1 + 100969.i −0.0211910 + 0.0220081i
\(463\) 813063. + 469422.i 0.176267 + 0.101768i 0.585538 0.810645i \(-0.300883\pi\)
−0.409270 + 0.912413i \(0.634217\pi\)
\(464\) 263001. 183718.i 0.0567104 0.0396148i
\(465\) −2.45060e6 1.42344e6i −0.525582 0.305286i
\(466\) −2.07054e6 1.98322e6i −0.441691 0.423063i
\(467\) 6.03297e6 1.28009 0.640043 0.768339i \(-0.278917\pi\)
0.640043 + 0.768339i \(0.278917\pi\)
\(468\) −6.77100e6 + 4.25853e6i −1.42902 + 0.898764i
\(469\) −16644.4 −0.00349412
\(470\) −2.89283e6 2.77083e6i −0.604058 0.578583i
\(471\) 556.257 211973.i 0.000115538 0.0440279i
\(472\) −6.61038e6 + 2.23776e6i −1.36575 + 0.462336i
\(473\) 8.06458e6 + 4.65609e6i 1.65741 + 0.956904i
\(474\) −1.83332e6 6.35848e6i −0.374793 1.29989i
\(475\) −2.00448e6 + 1.15729e6i −0.407632 + 0.235346i
\(476\) 47824.9 30430.3i 0.00967469 0.00615587i
\(477\) −2.45292e6 1.43341e6i −0.493614 0.288453i
\(478\) −474842. 1.63080e6i −0.0950559 0.326461i
\(479\) 1.48324e6 + 2.56904e6i 0.295374 + 0.511602i 0.975072 0.221890i \(-0.0712226\pi\)
−0.679698 + 0.733492i \(0.737889\pi\)
\(480\) 1.79217e6 2.21471e6i 0.355040 0.438747i
\(481\) 5.03489e6 8.72069e6i 0.992265 1.71865i
\(482\) 2.93341e6 + 718669.i 0.575116 + 0.140900i
\(483\) −48960.3 85318.0i −0.00954941 0.0166408i
\(484\) 2.20378e6 + 1.14878e6i 0.427618 + 0.222907i
\(485\) 1.95364e6i 0.377128i
\(486\) −5.01809e6 + 1.38997e6i −0.963713 + 0.266940i
\(487\) 7.19915e6i 1.37549i −0.725950 0.687747i \(-0.758600\pi\)
0.725950 0.687747i \(-0.241400\pi\)
\(488\) −270325. + 1.35310e6i −0.0513851 + 0.257205i
\(489\) −3.67272e6 6.40007e6i −0.694570 1.21035i
\(490\) −713354. + 2.91172e6i −0.134219 + 0.547847i
\(491\) 1.94528e6 3.36932e6i 0.364148 0.630723i −0.624491 0.781032i \(-0.714694\pi\)
0.988639 + 0.150309i \(0.0480269\pi\)
\(492\) 205047. + 5.06625e6i 0.0381893 + 0.943569i
\(493\) 85294.3 + 147734.i 0.0158053 + 0.0273756i
\(494\) 6.07245e6 1.76812e6i 1.11956 0.325982i
\(495\) −3.23420e6 1.88997e6i −0.593273 0.346690i
\(496\) 5.34482e6 + 2.49959e6i 0.975503 + 0.456210i
\(497\) 183392. 105881.i 0.0333035 0.0192278i
\(498\) −4.33470e6 + 1.24981e6i −0.783223 + 0.225824i
\(499\) −3.16514e6 1.82739e6i −0.569038 0.328534i 0.187727 0.982221i \(-0.439888\pi\)
−0.756765 + 0.653687i \(0.773221\pi\)
\(500\) 5.30024e6 228451.i 0.948136 0.0408665i
\(501\) −6125.24 + 2.33415e6i −0.00109026 + 0.415464i
\(502\) 5.48935e6 5.73105e6i 0.972214 1.01502i
\(503\) 6.99423e6 1.23259 0.616297 0.787514i \(-0.288632\pi\)
0.616297 + 0.787514i \(0.288632\pi\)
\(504\) −95009.0 + 107016.i −0.0166605 + 0.0187661i
\(505\) −2.75939e6 −0.481488
\(506\) −3.70823e6 + 3.87151e6i −0.643859 + 0.672209i
\(507\) 9.25832e6 + 5.37774e6i 1.59960 + 0.929137i
\(508\) −2.12243e6 + 91480.9i −0.364900 + 0.0157279i
\(509\) −6.20968e6 3.58516e6i −1.06237 0.613358i −0.136281 0.990670i \(-0.543515\pi\)
−0.926086 + 0.377312i \(0.876848\pi\)
\(510\) 1.09128e6 + 1.05076e6i 0.185784 + 0.178886i
\(511\) −34250.6 + 19774.6i −0.00580251 + 0.00335008i
\(512\) −3.30782e6 + 4.92369e6i −0.557656 + 0.830072i
\(513\) 4.11703e6 + 32412.2i 0.690702 + 0.00543770i
\(514\) 5.25362e6 1.52970e6i 0.877104 0.255387i
\(515\) −1.68266e6 2.91446e6i −0.279563 0.484217i
\(516\) 8.41922e6 + 4.41687e6i 1.39203 + 0.730282i
\(517\) 5.48280e6 9.49649e6i 0.902144 1.56256i
\(518\) 42869.4 174981.i 0.00701977 0.0286528i
\(519\) −1.33071e6 + 2.29095e6i −0.216852 + 0.373333i
\(520\) −5.76120e6 1.15099e6i −0.934339 0.186665i
\(521\) 6.81856e6i 1.10052i −0.834993 0.550261i \(-0.814528\pi\)
0.834993 0.550261i \(-0.185472\pi\)
\(522\) −309443. 299523.i −0.0497055 0.0481120i
\(523\) 5.81403e6i 0.929444i 0.885457 + 0.464722i \(0.153846\pi\)
−0.885457 + 0.464722i \(0.846154\pi\)
\(524\) −1.59855e6 833289.i −0.254331 0.132577i
\(525\) −107996. 283.403i −0.0171006 4.48752e-5i
\(526\) −5.10170e6 1.24989e6i −0.803991 0.196973i
\(527\) −1.56873e6 + 2.71713e6i −0.246050 + 0.426171i
\(528\) 7.05597e6 + 3.32244e6i 1.10147 + 0.518647i
\(529\) 1.33703e6 + 2.31580e6i 0.207731 + 0.359800i
\(530\) −583361. 2.00350e6i −0.0902086 0.309813i
\(531\) 4.64157e6 + 8.13777e6i 0.714379 + 1.25248i
\(532\) 95465.6 60743.4i 0.0146241 0.00930509i
\(533\) 9.05504e6 5.22793e6i 1.38061 0.797098i
\(534\) −1.08469e7 2.68762e6i −1.64609 0.407864i
\(535\) −736292. 425098.i −0.111216 0.0642103i
\(536\) 296959. + 877224.i 0.0446462 + 0.131886i
\(537\) −1.24151e6 + 712450.i −0.185787 + 0.106615i
\(538\) −4.96742e6 4.75793e6i −0.739904 0.708699i
\(539\) −8.20646e6 −1.21670
\(540\) −3.37736e6 1.79449e6i −0.498418 0.264824i
\(541\) −6.49473e6 −0.954043 −0.477021 0.878892i \(-0.658284\pi\)
−0.477021 + 0.878892i \(0.658284\pi\)
\(542\) 8.27228e6 + 7.92341e6i 1.20956 + 1.15855i
\(543\) −8.66337e6 + 4.97153e6i −1.26092 + 0.723587i
\(544\) −2.45705e6 1.97763e6i −0.355973 0.286516i
\(545\) −1.94829e6 1.12484e6i −0.280971 0.162219i
\(546\) 286442. + 70973.8i 0.0411201 + 0.0101886i
\(547\) −3.41406e6 + 1.97111e6i −0.487868 + 0.281671i −0.723690 0.690126i \(-0.757555\pi\)
0.235822 + 0.971796i \(0.424222\pi\)
\(548\) 7.23985e6 + 1.13783e7i 1.02986 + 1.61855i
\(549\) 1.85227e6 + 9721.46i 0.262284 + 0.00137658i
\(550\) 1.64541e6 + 5.65101e6i 0.231935 + 0.796562i
\(551\) 170260. + 294899.i 0.0238910 + 0.0413804i
\(552\) −3.62306e6 + 4.10258e6i −0.506090 + 0.573072i
\(553\) −122071. + 211432.i −0.0169745 + 0.0294008i
\(554\) −2.11945e6 519252.i −0.293392 0.0718792i
\(555\) 4.81466e6 + 12634.6i 0.663489 + 0.00174112i
\(556\) −5.67928e6 + 1.08950e7i −0.779124 + 1.49465i
\(557\) 9.50351e6i 1.29791i 0.760825 + 0.648957i \(0.224795\pi\)
−0.760825 + 0.648957i \(0.775205\pi\)
\(558\) 1.92514e6 7.68321e6i 0.261744 1.04462i
\(559\) 1.96057e7i 2.65371i
\(560\) −104719. + 9044.02i −0.0141110 + 0.00121868i
\(561\) −2.08294e6 + 3.58599e6i −0.279428 + 0.481063i
\(562\) 221706. 904943.i 0.0296098 0.120859i
\(563\) 1.12664e6 1.95140e6i 0.149801 0.259463i −0.781353 0.624089i \(-0.785470\pi\)
0.931154 + 0.364627i \(0.118803\pi\)
\(564\) 5.20111e6 9.91409e6i 0.688491 1.31237i
\(565\) −597502. 1.03490e6i −0.0787442 0.136389i
\(566\) −2.77119e6 + 806889.i −0.363601 + 0.105870i
\(567\) 165350. + 97793.3i 0.0215996 + 0.0127747i
\(568\) −8.85230e6 7.77637e6i −1.15129 1.01136i
\(569\) −1.02789e7 + 5.93451e6i −1.33096 + 0.768430i −0.985447 0.169984i \(-0.945628\pi\)
−0.345513 + 0.938414i \(0.612295\pi\)
\(570\) 2.17835e6 + 2.09747e6i 0.280828 + 0.270401i
\(571\) 5.96127e6 + 3.44174e6i 0.765154 + 0.441762i 0.831143 0.556059i \(-0.187687\pi\)
−0.0659893 + 0.997820i \(0.521020\pi\)
\(572\) −692556. 1.60678e7i −0.0885043 2.05337i
\(573\) −3.74320e6 2.17425e6i −0.476274 0.276646i
\(574\) 129394. 135092.i 0.0163921 0.0171139i
\(575\) −4.13056e6 −0.521002
\(576\) 7.33524e6 + 3.09801e6i 0.921208 + 0.389069i
\(577\) 7.44098e6 0.930444 0.465222 0.885194i \(-0.345974\pi\)
0.465222 + 0.885194i \(0.345974\pi\)
\(578\) −4.39570e6 + 4.58925e6i −0.547279 + 0.571376i
\(579\) 35398.9 1.34895e7i 0.00438827 1.67224i
\(580\) −13621.1 316021.i −0.00168129 0.0390073i
\(581\) 144138. + 83217.9i 0.0177148 + 0.0102277i
\(582\) −5.24645e6 + 1.51269e6i −0.642035 + 0.185115i
\(583\) 4.94698e6 2.85614e6i 0.602794 0.348023i
\(584\) 1.65327e6 + 1.45233e6i 0.200591 + 0.176211i
\(585\) −41391.8 + 7.88654e6i −0.00500063 + 0.952789i
\(586\) −6.44414e6 + 1.87635e6i −0.775213 + 0.225719i
\(587\) 1.62470e6 + 2.81406e6i 0.194615 + 0.337084i 0.946774 0.321898i \(-0.104321\pi\)
−0.752159 + 0.658982i \(0.770987\pi\)
\(588\) −8.37171e6 + 338830.i −0.998553 + 0.0404146i
\(589\) −3.13142e6 + 5.42379e6i −0.371924 + 0.644191i
\(590\) −1.63738e6 + 6.68334e6i −0.193651 + 0.790430i
\(591\) 1.90903e6 + 3.32667e6i 0.224825 + 0.391779i
\(592\) −9.98701e6 + 862522.i −1.17120 + 0.101150i
\(593\) 944104.i 0.110251i −0.998479 0.0551256i \(-0.982444\pi\)
0.998479 0.0551256i \(-0.0175559\pi\)
\(594\) 2.57125e6 1.01488e7i 0.299005 1.18018i
\(595\) 55890.3i 0.00647208i
\(596\) 4.83830e6 9.28165e6i 0.557927 1.07031i
\(597\) −2.19824e6 3.83065e6i −0.252429 0.439882i
\(598\) 1.09626e7 + 2.68578e6i 1.25361 + 0.307127i
\(599\) −97761.8 + 169328.i −0.0111327 + 0.0192825i −0.871538 0.490328i \(-0.836877\pi\)
0.860405 + 0.509610i \(0.170210\pi\)
\(600\) 1.91186e6 + 5.69687e6i 0.216810 + 0.646038i
\(601\) 3.73826e6 + 6.47485e6i 0.422166 + 0.731213i 0.996151 0.0876529i \(-0.0279366\pi\)
−0.573985 + 0.818866i \(0.694603\pi\)
\(602\) −98059.3 336776.i −0.0110280 0.0378748i
\(603\) 1.07991e6 615954.i 0.120947 0.0689851i
\(604\) 7.47161e6 + 1.17425e7i 0.833340 + 1.30969i
\(605\) 2.12208e6 1.22518e6i 0.235708 0.136086i
\(606\) −2.13659e6 7.41030e6i −0.236341 0.819699i
\(607\) −682314. 393934.i −0.0751644 0.0433962i 0.461947 0.886908i \(-0.347151\pi\)
−0.537111 + 0.843511i \(0.680484\pi\)
\(608\) −4.90464e6 3.94765e6i −0.538081 0.433091i
\(609\) −41.6942 + 15888.4i −4.55547e−6 + 0.00173595i
\(610\) 982502. + 941066.i 0.106908 + 0.102399i
\(611\) −2.30868e7 −2.50185
\(612\) −1.97682e6 + 3.74420e6i −0.213348 + 0.404092i
\(613\) −261841. −0.0281441 −0.0140720 0.999901i \(-0.504479\pi\)
−0.0140720 + 0.999901i \(0.504479\pi\)
\(614\) 5.77291e6 + 5.52944e6i 0.617979 + 0.591917i
\(615\) 4.32292e6 + 2.51099e6i 0.460882 + 0.267705i
\(616\) −92260.6 272540.i −0.00979636 0.0289387i
\(617\) −3.01771e6 1.74228e6i −0.319128 0.184249i 0.331876 0.943323i \(-0.392318\pi\)
−0.651004 + 0.759074i \(0.725652\pi\)
\(618\) 6.52385e6 6.77542e6i 0.687121 0.713617i
\(619\) 1.28016e7 7.39099e6i 1.34288 0.775311i 0.355649 0.934620i \(-0.384260\pi\)
0.987229 + 0.159309i \(0.0509266\pi\)
\(620\) 4.90831e6 3.12309e6i 0.512806 0.326291i
\(621\) 6.33394e6 + 3.72369e6i 0.659091 + 0.387476i
\(622\) −997147. 3.42461e6i −0.103344 0.354924i
\(623\) 206140. + 357044.i 0.0212785 + 0.0368555i
\(624\) −1.36991e6 1.63628e7i −0.140842 1.68227i
\(625\) −712009. + 1.23324e6i −0.0729097 + 0.126283i
\(626\) −2.16742e6 531005.i −0.221058 0.0541580i
\(627\) −4.15785e6 + 7.15816e6i −0.422377 + 0.727165i
\(628\) 385862. + 201141.i 0.0390420 + 0.0203517i
\(629\) 5.33022e6i 0.537178i
\(630\) 38734.0 + 135677.i 0.00388814 + 0.0136194i
\(631\) 5.75639e6i 0.575541i 0.957699 + 0.287771i \(0.0929141\pi\)
−0.957699 + 0.287771i \(0.907086\pi\)
\(632\) 1.33212e7 + 2.66134e6i 1.32663 + 0.265037i
\(633\) −6.65875e6 17473.8i −0.660516 0.00173332i
\(634\) −220041. + 898149.i −0.0217411 + 0.0887412i
\(635\) −1.04730e6 + 1.81398e6i −0.103071 + 0.178524i
\(636\) 4.92868e6 3.11791e6i 0.483156 0.305647i
\(637\) 8.63889e6 + 1.49630e7i 0.843547 + 1.46107i
\(638\) 831376. 242072.i 0.0808622 0.0235447i
\(639\) −7.98041e6 + 1.36564e7i −0.773166 + 1.32308i
\(640\) 2.34498e6 + 5.35773e6i 0.226303 + 0.517048i
\(641\) 1.33983e7 7.73550e6i 1.28796 0.743607i 0.309674 0.950843i \(-0.399780\pi\)
0.978291 + 0.207236i \(0.0664468\pi\)
\(642\) 571487. 2.30645e6i 0.0547228 0.220855i
\(643\) 1.40298e7 + 8.10012e6i 1.33821 + 0.772617i 0.986542 0.163507i \(-0.0522808\pi\)
0.351669 + 0.936124i \(0.385614\pi\)
\(644\) 201743. 8695.52i 0.0191683 0.000826191i
\(645\) 8.13049e6 4.66574e6i 0.769516 0.441592i
\(646\) 2.31572e6 2.41768e6i 0.218326 0.227939i
\(647\) −5.07623e6 −0.476739 −0.238369 0.971175i \(-0.576613\pi\)
−0.238369 + 0.971175i \(0.576613\pi\)
\(648\) 2.20400e6 1.04593e7i 0.206193 0.978511i
\(649\) −1.88365e7 −1.75545
\(650\) 8.57148e6 8.94888e6i 0.795742 0.830779i
\(651\) −253454. + 145446.i −0.0234394 + 0.0134508i
\(652\) 1.51336e7 652288.i 1.39419 0.0600925i
\(653\) 1.12780e6 + 651134.i 0.103502 + 0.0597569i 0.550857 0.834599i \(-0.314301\pi\)
−0.447356 + 0.894356i \(0.647634\pi\)
\(654\) 1.51220e6 6.10305e6i 0.138250 0.557960i
\(655\) −1.53929e6 + 888710.i −0.140190 + 0.0809388i
\(656\) −9.42840e6 4.40935e6i −0.855418 0.400050i
\(657\) 1.49043e6 2.55050e6i 0.134710 0.230522i
\(658\) −396572. + 115470.i −0.0357073 + 0.0103969i
\(659\) −8.68751e6 1.50472e7i −0.779259 1.34972i −0.932369 0.361508i \(-0.882262\pi\)
0.153110 0.988209i \(-0.451071\pi\)
\(660\) 6.49851e6 4.11100e6i 0.580703 0.367356i
\(661\) −3.21752e6 + 5.57291e6i −0.286430 + 0.496111i −0.972955 0.230995i \(-0.925802\pi\)
0.686525 + 0.727106i \(0.259135\pi\)
\(662\) 1.08198e6 4.41636e6i 0.0959566 0.391669i
\(663\) 8.73109e6 + 22912.0i 0.771409 + 0.00202432i
\(664\) 1.81428e6 9.08130e6i 0.159693 0.799333i
\(665\) 111565.i 0.00978306i
\(666\) 3.69404e6 + 1.29395e7i 0.322713 + 1.13040i
\(667\) 607687.i 0.0528890i
\(668\) −4.24893e6 2.21487e6i −0.368416 0.192046i
\(669\) −7.10538e6 + 1.22326e7i −0.613793 + 1.05671i
\(670\) 886905. + 217286.i 0.0763291 + 0.0187002i
\(671\) −1.86214e6 + 3.22532e6i −0.159664 + 0.276546i
\(672\) −105371. 274219.i −0.00900116 0.0234247i
\(673\) −3.26993e6 5.66368e6i −0.278292 0.482016i 0.692668 0.721256i \(-0.256435\pi\)
−0.970960 + 0.239240i \(0.923102\pi\)
\(674\) 2.41609e6 + 8.29783e6i 0.204863 + 0.703582i
\(675\) 7.01744e6 3.97819e6i 0.592815 0.336068i
\(676\) −1.85435e7 + 1.17990e7i −1.56072 + 0.993065i
\(677\) 3.46325e6 1.99951e6i 0.290411 0.167669i −0.347716 0.937600i \(-0.613043\pi\)
0.638127 + 0.769931i \(0.279709\pi\)
\(678\) 2.31657e6 2.40590e6i 0.193541 0.201004i
\(679\) 174455. + 100722.i 0.0145214 + 0.00838396i
\(680\) −2.94562e6 + 997156.i −0.244290 + 0.0826972i
\(681\) 5.27984e6 + 3.06682e6i 0.436268 + 0.253408i
\(682\) 1.15011e7 + 1.10160e7i 0.946841 + 0.906909i
\(683\) 189908. 0.0155773 0.00778864 0.999970i \(-0.497521\pi\)
0.00778864 + 0.999970i \(0.497521\pi\)
\(684\) −3.94603e6 + 7.47397e6i −0.322493 + 0.610817i
\(685\) 1.32972e7 1.08276
\(686\) 446605. + 427770.i 0.0362337 + 0.0347056i
\(687\) 19695.7 7.50544e6i 0.00159213 0.606715i
\(688\) −1.59998e7 + 1.11766e7i −1.28868 + 0.900200i
\(689\) −1.04153e7 6.01328e6i −0.835842 0.482574i
\(690\) 1.49507e6 + 5.18536e6i 0.119547 + 0.414625i
\(691\) −1.27744e7 + 7.37528e6i −1.01776 + 0.587602i −0.913454 0.406943i \(-0.866595\pi\)
−0.104304 + 0.994545i \(0.533261\pi\)
\(692\) −2.91963e6 4.58854e6i −0.231772 0.364258i
\(693\) −335513. + 191368.i −0.0265385 + 0.0151369i
\(694\) −1.33860e6 4.59729e6i −0.105500 0.362329i
\(695\) 6.05700e6 + 1.04910e7i 0.475659 + 0.823866i
\(696\) 838123. 281273.i 0.0655820 0.0220092i
\(697\) 2.76729e6 4.79308e6i 0.215761 0.373709i
\(698\) −2.13237e6 522418.i −0.165662 0.0405863i
\(699\) −3.93243e6 6.85264e6i −0.304417 0.530475i
\(700\) 102478. 196590.i 0.00790466 0.0151641i
\(701\) 1.07971e7i 0.829870i 0.909851 + 0.414935i \(0.136196\pi\)
−0.909851 + 0.414935i \(0.863804\pi\)
\(702\) −2.12112e7 + 5.99535e6i −1.62451 + 0.459168i
\(703\) 1.06399e7i 0.811988i
\(704\) −1.27178e7 + 9.72495e6i −0.967122 + 0.739530i
\(705\) −5.49416e6 9.57410e6i −0.416321 0.725480i
\(706\) −2.08787e6 + 8.52214e6i −0.157649 + 0.643483i
\(707\) −142264. + 246408.i −0.0107040 + 0.0185398i
\(708\) −1.92158e7 + 777725.i −1.44071 + 0.0583100i
\(709\) −8.22095e6 1.42391e7i −0.614195 1.06382i −0.990525 0.137332i \(-0.956147\pi\)
0.376330 0.926486i \(-0.377186\pi\)
\(710\) −1.11543e7 + 3.24782e6i −0.830420 + 0.241794i
\(711\) 95707.1 1.82354e7i 0.00710019 1.35283i
\(712\) 1.51397e7 1.72345e7i 1.11923 1.27408i
\(713\) −9.67922e6 + 5.58830e6i −0.713044 + 0.411676i
\(714\) 150092. 43275.5i 0.0110183 0.00317685i
\(715\) −1.37327e7 7.92858e6i −1.00460 0.580003i
\(716\) −126533. 2.93568e6i −0.00922408 0.214006i
\(717\) 12282.7 4.68057e6i 0.000892269 0.340017i
\(718\) −1.42233e7 + 1.48496e7i −1.02965 + 1.07499i
\(719\) 2.43648e7 1.75769 0.878843 0.477111i \(-0.158316\pi\)
0.878843 + 0.477111i \(0.158316\pi\)
\(720\) 6.45964e6 4.46209e6i 0.464384 0.320780i
\(721\) −347006. −0.0248599
\(722\) −5.06628e6 + 5.28935e6i −0.361698 + 0.377624i
\(723\) 7.19663e6 + 4.18020e6i 0.512016 + 0.297407i
\(724\) −882961. 2.04854e7i −0.0626030 1.45244i
\(725\) 577787. + 333585.i 0.0408247 + 0.0235701i
\(726\) 4.93333e6 + 4.75016e6i 0.347375 + 0.334477i
\(727\) 8.20393e6 4.73654e6i 0.575686 0.332372i −0.183731 0.982977i \(-0.558818\pi\)
0.759417 + 0.650604i \(0.225484\pi\)
\(728\) −399805. + 455122.i −0.0279589 + 0.0318272i
\(729\) −1.43471e7 225916.i −0.999876 0.0157444i
\(730\) 2.08320e6 606568.i 0.144685 0.0421281i
\(731\) −5.18893e6 8.98749e6i −0.359157 0.622078i
\(732\) −1.76647e6 + 3.36715e6i −0.121851 + 0.232266i
\(733\) 2.49849e6 4.32752e6i 0.171758 0.297494i −0.767276 0.641317i \(-0.778388\pi\)
0.939035 + 0.343822i \(0.111722\pi\)
\(734\) −569639. + 2.32511e6i −0.0390265 + 0.159296i
\(735\) −4.14928e6 + 7.14341e6i −0.283305 + 0.487739i
\(736\) −4.05764e6 1.04775e7i −0.276108 0.712953i
\(737\) 2.49968e6i 0.169518i
\(738\) −3.39600e6 + 1.35534e7i −0.229523 + 0.916024i
\(739\) 1.74764e7i 1.17718i 0.808433 + 0.588588i \(0.200316\pi\)
−0.808433 + 0.588588i \(0.799684\pi\)
\(740\) −4.56862e6 + 8.76430e6i −0.306694 + 0.588353i
\(741\) 1.74285e7 + 45735.8i 1.16605 + 0.00305992i
\(742\) −208984. 51199.9i −0.0139349 0.00341397i
\(743\) 1.71665e6 2.97332e6i 0.114080 0.197592i −0.803332 0.595532i \(-0.796941\pi\)
0.917412 + 0.397940i \(0.130275\pi\)
\(744\) 1.21875e7 + 1.07630e7i 0.807201 + 0.712854i
\(745\) −5.16009e6 8.93754e6i −0.340617 0.589967i
\(746\) 5.24694e6 + 1.80202e7i 0.345191 + 1.18553i
\(747\) −1.24315e7 65245.4i −0.815118 0.00427808i
\(748\) −4.57005e6 7.18238e6i −0.298653 0.469369i
\(749\) −75920.6 + 43832.8i −0.00494487 + 0.00285492i
\(750\) 1.41902e7 + 3.51601e6i 0.921161 + 0.228243i
\(751\) −4.54796e6 2.62576e6i −0.294250 0.169885i 0.345607 0.938379i \(-0.387673\pi\)
−0.639857 + 0.768494i \(0.721006\pi\)
\(752\) 1.31611e7 + 1.88407e7i 0.848686 + 1.21493i
\(753\) 1.89675e7 1.08846e7i 1.21905 0.699560i
\(754\) −1.31656e6 1.26103e6i −0.0843358 0.0807790i
\(755\) 1.37228e7 0.876146
\(756\) −334368. + 209074.i −0.0212775 + 0.0133044i
\(757\) 2.98204e7 1.89136 0.945679 0.325102i \(-0.105399\pi\)
0.945679 + 0.325102i \(0.105399\pi\)
\(758\) −1.12551e7 1.07805e7i −0.711505 0.681498i
\(759\) −1.28131e7 + 7.35290e6i −0.807329 + 0.463291i
\(760\) −5.87990e6 + 1.99047e6i −0.369263 + 0.125003i
\(761\) 3.94493e6 + 2.27761e6i 0.246932 + 0.142566i 0.618359 0.785896i \(-0.287798\pi\)
−0.371427 + 0.928462i \(0.621131\pi\)
\(762\) −5.68232e6 1.40795e6i −0.354518 0.0878417i
\(763\) −200892. + 115985.i −0.0124926 + 0.00721259i
\(764\) 7.49726e6 4.77040e6i 0.464696 0.295680i
\(765\) 2.06831e6 + 3.62623e6i 0.127780 + 0.224028i
\(766\) 1.07888e6 + 3.70531e6i 0.0664355 + 0.228167i
\(767\) 1.98290e7 + 3.43449e7i 1.21706 + 2.10802i
\(768\) −1.25724e7 + 1.04459e7i −0.769157 + 0.639060i
\(769\) −9.29907e6 + 1.61065e7i −0.567053 + 0.982164i 0.429803 + 0.902923i \(0.358583\pi\)
−0.996855 + 0.0792415i \(0.974750\pi\)
\(770\) −275548. 67507.6i −0.0167483 0.00410323i
\(771\) 1.50784e7 + 39568.7i 0.913525 + 0.00239726i
\(772\) 2.45554e7 + 1.28001e7i 1.48287 + 0.772985i
\(773\) 1.48809e7i 0.895736i −0.894100 0.447868i \(-0.852184\pi\)
0.894100 0.447868i \(-0.147816\pi\)
\(774\) 1.88252e7 + 1.82216e7i 1.12950 + 1.09329i
\(775\) 1.22706e7i 0.733858i
\(776\) 2.19590e6 1.09914e7i 0.130906 0.655240i
\(777\) 249353. 429287.i 0.0148171 0.0255091i
\(778\) 6.99058e6 2.85337e7i 0.414061 1.69009i
\(779\) 5.52391e6 9.56770e6i 0.326139 0.564890i
\(780\) −1.43366e7 7.52124e6i −0.843742 0.442642i
\(781\) −1.59013e7 2.75419e7i −0.932838 1.61572i
\(782\) 5.73622e6 1.67022e6i 0.335436 0.0976690i
\(783\) −585271. 1.03241e6i −0.0341156 0.0601791i
\(784\) 7.28622e6 1.55799e7i 0.423362 0.905265i
\(785\) 371556. 214518.i 0.0215204 0.0124248i
\(786\) −3.57848e6 3.44561e6i −0.206606 0.198935i
\(787\) −2.29308e7 1.32391e7i −1.31972 0.761943i −0.336040 0.941848i \(-0.609088\pi\)
−0.983684 + 0.179904i \(0.942421\pi\)
\(788\) −7.86624e6 + 339051.i −0.451286 + 0.0194513i
\(789\) −1.25162e7 7.27008e6i −0.715779 0.415764i
\(790\) 9.26473e6 9.67266e6i 0.528160 0.551415i
\(791\) −123220. −0.00700226
\(792\) 1.60718e7 + 1.42685e7i 0.910439 + 0.808288i
\(793\) 7.84105e6 0.442783
\(794\) 1.69108e7 1.76554e7i 0.951950 0.993865i
\(795\) 15089.8 5.75026e6i 0.000846768 0.322678i
\(796\) 9.05794e6 390415.i 0.506695 0.0218396i
\(797\) −70624.5 40775.1i −0.00393831 0.00227378i 0.498030 0.867160i \(-0.334057\pi\)
−0.501968 + 0.864886i \(0.667390\pi\)
\(798\) 299606. 86384.4i 0.0166550 0.00480206i
\(799\) −1.05833e7 + 6.11025e6i −0.586479 + 0.338604i
\(800\) −1.21893e7 1.89353e6i −0.673372 0.104603i
\(801\) −2.65876e7 1.55370e7i −1.46419 0.855629i
\(802\) −1.33951e7 + 3.90026e6i −0.735377 + 0.214120i
\(803\) 2.96976e6 + 5.14378e6i 0.162530 + 0.281510i
\(804\) 103207. + 2.55001e6i 0.00563079 + 0.139124i
\(805\) 99548.9 172424.i 0.00541435 0.00937793i
\(806\) 7.97862e6 3.25666e7i 0.432604 1.76577i
\(807\) −9.43429e6 1.64401e7i −0.509947 0.888632i
\(808\) 1.55248e7 + 3.10158e6i 0.836559 + 0.167130i
\(809\) 2.33658e7i 1.25519i 0.778540 + 0.627595i \(0.215960\pi\)
−0.778540 + 0.627595i \(0.784040\pi\)
\(810\) −7.53408e6 7.36952e6i −0.403476 0.394663i
\(811\) 2.11526e7i 1.12930i 0.825329 + 0.564652i \(0.190990\pi\)
−0.825329 + 0.564652i \(0.809010\pi\)
\(812\) −28922.2 15076.5i −0.00153937 0.000802435i
\(813\) 1.57110e7 + 2.73779e7i 0.833637 + 1.45269i
\(814\) −2.62788e7 6.43816e6i −1.39010 0.340566i
\(815\) 7.46759e6 1.29342e7i 0.393810 0.682098i
\(816\) −4.95863e6 7.13832e6i −0.260697 0.375293i
\(817\) −1.03579e7 1.79404e7i −0.542894 0.940320i
\(818\) −5.97102e6 2.05069e7i −0.312008 1.07156i
\(819\) 702116. + 410295.i 0.0365763 + 0.0213740i
\(820\) −8.65839e6 + 5.50921e6i −0.449679 + 0.286124i
\(821\) 1.27326e7 7.35120e6i 0.659266 0.380627i −0.132731 0.991152i \(-0.542375\pi\)
0.791997 + 0.610525i \(0.209041\pi\)
\(822\) 1.02959e7 + 3.57093e7i 0.531479 + 1.84332i
\(823\) −7.60185e6 4.38893e6i −0.391219 0.225870i 0.291469 0.956580i \(-0.405856\pi\)
−0.682688 + 0.730710i \(0.739189\pi\)
\(824\) 6.19105e6 + 1.82885e7i 0.317648 + 0.938341i
\(825\) −42561.7 + 1.62190e7i −0.00217713 + 0.829638i
\(826\) 512390. + 490781.i 0.0261307 + 0.0250287i
\(827\) 1.32716e7 0.674774 0.337387 0.941366i \(-0.390457\pi\)
0.337387 + 0.941366i \(0.390457\pi\)
\(828\) −1.27676e7 + 8.02999e6i −0.647190 + 0.407042i
\(829\) 2.90903e6 0.147015 0.0735075 0.997295i \(-0.476581\pi\)
0.0735075 + 0.997295i \(0.476581\pi\)
\(830\) −6.59404e6 6.31595e6i −0.332244 0.318232i
\(831\) −5.19970e6 3.02027e6i −0.261202 0.151720i
\(832\) 3.11196e7 + 1.29512e7i 1.55857 + 0.648639i
\(833\) 7.92033e6 + 4.57280e6i 0.395486 + 0.228334i
\(834\) −2.34836e7 + 2.43891e7i −1.16909 + 1.21418i
\(835\) −4.09140e6 + 2.36217e6i −0.203075 + 0.117245i
\(836\) −9.12250e6 1.43371e7i −0.451438 0.709489i
\(837\) 1.10619e7 1.88162e7i 0.545780 0.928363i
\(838\) −3.11407e6 1.06950e7i −0.153186 0.526103i
\(839\) −7.37154e6 1.27679e7i −0.361537 0.626201i 0.626677 0.779279i \(-0.284415\pi\)
−0.988214 + 0.153078i \(0.951081\pi\)
\(840\) −283884. 57490.1i −0.0138817 0.00281122i
\(841\) −1.02065e7 + 1.76782e7i −0.497607 + 0.861881i
\(842\) −4.80344e6 1.17681e6i −0.233492 0.0572042i
\(843\) 1.28957e6 2.22012e6i 0.0624994 0.107599i
\(844\) 6.31846e6 1.21211e7i 0.305320 0.585716i
\(845\) 2.16707e7i 1.04408i
\(846\) 2.14570e7 2.21677e7i 1.03072 1.06486i
\(847\) 252663.i 0.0121013i
\(848\) 1.03013e6 + 1.19277e7i 0.0491929 + 0.569596i
\(849\) −7.95359e6 20871.7i −0.378699 0.000993778i
\(850\) 1.56082e6 6.37083e6i 0.0740977 0.302447i
\(851\) 9.49391e6 1.64439e7i 0.449388 0.778363i
\(852\) −1.73587e7 2.74400e7i −0.819254 1.29505i
\(853\) 2.06240e7 + 3.57217e7i 0.970508 + 1.68097i 0.694024 + 0.719951i \(0.255836\pi\)
0.276484 + 0.961019i \(0.410831\pi\)
\(854\) 134689. 39217.5i 0.00631957 0.00184007i
\(855\) 4.12865e6 + 7.23850e6i 0.193149 + 0.338636i
\(856\) 3.66467e6 + 3.21926e6i 0.170943 + 0.150166i
\(857\) −2.34826e7 + 1.35577e7i −1.09218 + 0.630571i −0.934156 0.356864i \(-0.883846\pi\)
−0.158025 + 0.987435i \(0.550513\pi\)
\(858\) 1.06589e7 4.30180e7i 0.494304 1.99495i
\(859\) 2.06184e7 + 1.19041e7i 0.953395 + 0.550443i 0.894134 0.447800i \(-0.147792\pi\)
0.0592610 + 0.998243i \(0.481126\pi\)
\(860\) 828650. + 1.92253e7i 0.0382054 + 0.886396i
\(861\) 447099. 256571.i 0.0205540 0.0117950i
\(862\) −6.66220e6 + 6.95554e6i −0.305386 + 0.318832i
\(863\) 1.77520e6 0.0811371 0.0405685 0.999177i \(-0.487083\pi\)
0.0405685 + 0.999177i \(0.487083\pi\)
\(864\) 1.69845e7 + 1.38923e7i 0.774050 + 0.633124i
\(865\) −5.36236e6 −0.243678
\(866\) 4.68186e6 4.88800e6i 0.212140 0.221481i
\(867\) −1.51885e7 + 8.71605e6i −0.686228 + 0.393797i
\(868\) −25831.7 599316.i −0.00116373 0.0269995i
\(869\) 3.17531e7 + 1.83326e7i 1.42638 + 0.823523i
\(870\) 209639. 846076.i 0.00939016 0.0378975i
\(871\) 4.55770e6 2.63139e6i 0.203564 0.117528i
\(872\) 9.69703e6 + 8.51843e6i 0.431864 + 0.379375i
\(873\) −1.50463e7 78969.0i −0.668180 0.00350688i
\(874\) 1.14503e7 3.33401e6i 0.507037 0.147634i
\(875\) −269677. 467094.i −0.0119076 0.0206245i
\(876\) 3.24194e6 + 5.12474e6i 0.142740 + 0.225638i
\(877\) −1.80935e7 + 3.13389e7i −0.794373 + 1.37589i 0.128864 + 0.991662i \(0.458867\pi\)
−0.923237 + 0.384231i \(0.874467\pi\)
\(878\) −3.31972e6 + 1.35502e7i −0.145333 + 0.593211i
\(879\) −1.84954e7 48535.3i −0.807403 0.00211878i
\(880\) 1.35824e6 + 1.57268e7i 0.0591247 + 0.684596i
\(881\) 4.28630e7i 1.86056i −0.366855 0.930278i \(-0.619566\pi\)
0.366855 0.930278i \(-0.380434\pi\)
\(882\) −2.23963e7 5.61171e6i −0.969403 0.242898i
\(883\) 1.61400e7i 0.696628i −0.937378 0.348314i \(-0.886754\pi\)
0.937378 0.348314i \(-0.113246\pi\)
\(884\) −8.28491e6 + 1.58935e7i −0.356580 + 0.684052i
\(885\) −9.52395e6 + 1.63964e7i −0.408751 + 0.703706i
\(886\) 2.70059e7 + 6.61629e6i 1.15578 + 0.283159i
\(887\) −1.19750e7 + 2.07414e7i −0.511055 + 0.885173i 0.488863 + 0.872361i \(0.337412\pi\)
−0.999918 + 0.0128126i \(0.995922\pi\)
\(888\) −2.70738e7 5.48280e6i −1.15217 0.233330i
\(889\) 107989. + 187043.i 0.00458276 + 0.00793757i
\(890\) −6.32315e6 2.17163e7i −0.267583 0.918989i
\(891\) 1.46867e7 2.48324e7i 0.619768 1.04791i
\(892\) −1.55895e7 2.45008e7i −0.656024 1.03102i
\(893\) −2.11258e7 + 1.21970e7i −0.886510 + 0.511827i
\(894\) 2.00062e7 2.07776e7i 0.837183 0.869465i
\(895\) −2.50904e6 1.44859e6i −0.104701 0.0604489i
\(896\) 599332. + 66822.1i 0.0249400 + 0.00278067i
\(897\) 2.68950e7 + 1.56221e7i 1.11607 + 0.648272i
\(898\) −390396. 373932.i −0.0161553 0.0154740i
\(899\) 1.80525e6 0.0744969
\(900\) 626234. + 1.65473e7i 0.0257710 + 0.680961i
\(901\) −6.36600e6 −0.261249
\(902\) −2.02882e7 1.94325e7i −0.830284 0.795268i
\(903\) 2536.49 966582.i 0.000103518 0.0394475i
\(904\) 2.19840e6 + 6.49412e6i 0.0894716 + 0.264301i
\(905\) −1.75083e7 1.01084e7i −0.710594 0.410262i
\(906\) 1.06255e7 + 3.68524e7i 0.430061 + 1.49158i
\(907\) −2.47076e7 + 1.42649e7i −0.997268 + 0.575773i −0.907439 0.420185i \(-0.861965\pi\)
−0.0898289 + 0.995957i \(0.528632\pi\)
\(908\) −1.05750e7 + 6.72873e6i −0.425663 + 0.270843i
\(909\) 111539. 2.12520e7i 0.00447731 0.853079i
\(910\) 166980. + 573476.i 0.00668436 + 0.0229568i
\(911\) −2.43656e7 4.22025e7i −0.972705 1.68477i −0.687309 0.726365i \(-0.741208\pi\)
−0.285396 0.958410i \(-0.592125\pi\)
\(912\) −9.89815e6 1.42491e7i −0.394064 0.567286i
\(913\) 1.24977e7 2.16467e7i 0.496197 0.859438i
\(914\) −1.81836e7 4.45488e6i −0.719971 0.176389i
\(915\) 1.86600e6 + 3.25168e6i 0.0736815 + 0.128397i
\(916\) 1.36624e7 + 7.12189e6i 0.538008 + 0.280451i
\(917\) 183274.i 0.00719741i
\(918\) −8.13671e6 + 8.36218e6i −0.318671 + 0.327501i
\(919\) 6.66802e6i 0.260440i 0.991485 + 0.130220i \(0.0415684\pi\)
−0.991485 + 0.130220i \(0.958432\pi\)
\(920\) −1.08634e7 2.17033e6i −0.423154 0.0845387i
\(921\) 1.09641e7 + 1.91060e7i 0.425916 + 0.742199i
\(922\) 814291. 3.32371e6i 0.0315466 0.128765i
\(923\) −3.34785e7 + 5.79864e7i −1.29349 + 2.24038i
\(924\) −32064.9 792250.i −0.00123552 0.0305269i
\(925\) −1.04232e7 1.80536e7i −0.400542 0.693758i
\(926\) −5.09915e6 + 1.48472e6i −0.195421 + 0.0569008i
\(927\) 2.25142e7 1.28415e7i 0.860514 0.490814i
\(928\) −278575. + 1.79329e6i −0.0106187 + 0.0683567i
\(929\) −9.99691e6 + 5.77172e6i −0.380038 + 0.219415i −0.677835 0.735214i \(-0.737081\pi\)
0.297797 + 0.954629i \(0.403748\pi\)
\(930\) 1.54041e7 4.44141e6i 0.584021 0.168389i
\(931\) 1.58101e7 + 9.12799e6i 0.597808 + 0.345144i
\(932\) 1.62037e7 698413.i 0.611048 0.0263374i
\(933\) 25793.1 9.82899e6i 0.000970063 0.369662i
\(934\) −2.36066e7 + 2.46460e7i −0.885454 + 0.924441i
\(935\) −8.39364e6 −0.313994
\(936\) 9.09740e6 4.43243e7i 0.339412 1.65368i
\(937\) 129328. 0.00481219 0.00240609 0.999997i \(-0.499234\pi\)
0.00240609 + 0.999997i \(0.499234\pi\)
\(938\) 65128.5 67996.2i 0.00241693 0.00252335i
\(939\) −5.31739e6 3.08863e6i −0.196804 0.114315i
\(940\) 2.26389e7 975781.i 0.835671 0.0360191i
\(941\) −1.98367e7 1.14527e7i −0.730291 0.421633i 0.0882379 0.996099i \(-0.471876\pi\)
−0.818528 + 0.574466i \(0.805210\pi\)
\(942\) 863779. + 831708.i 0.0317158 + 0.0305382i
\(943\) 1.70744e7 9.85790e6i 0.625268 0.360998i
\(944\) 1.67242e7 3.57610e7i 0.610825 1.30611i
\(945\) −3060.98 + 388809.i −0.000111502 + 0.0141630i
\(946\) −5.05773e7 + 1.47266e7i −1.83750 + 0.535026i
\(947\) 1.99508e7 + 3.45559e7i 0.722914 + 1.25212i 0.959827 + 0.280592i \(0.0905308\pi\)
−0.236914 + 0.971531i \(0.576136\pi\)
\(948\) 3.31494e7 + 1.73908e7i 1.19799 + 0.628490i
\(949\) 6.25249e6 1.08296e7i 0.225366 0.390345i
\(950\) 3.11562e6 1.27171e7i 0.112004 0.457172i
\(951\) −1.27989e6 + 2.20346e6i −0.0458903 + 0.0790048i
\(952\) −62821.0 + 314447.i −0.00224653 + 0.0112449i
\(953\) 3.01554e7i 1.07556i −0.843086 0.537778i \(-0.819264\pi\)
0.843086 0.537778i \(-0.180736\pi\)
\(954\) 1.54539e7 4.41187e6i 0.549752 0.156947i
\(955\) 8.76162e6i 0.310868i
\(956\) 8.52020e6 + 4.44138e6i 0.301512 + 0.157171i
\(957\) 2.38614e6 + 6261.67i 0.0842200 + 0.000221009i
\(958\) −1.62989e7 3.99313e6i −0.573778 0.140572i
\(959\) 685550. 1.18741e6i 0.0240709 0.0416920i
\(960\) 2.03492e6 + 1.59874e7i 0.0712638 + 0.559887i
\(961\) 2.28653e6 + 3.96039e6i 0.0798673 + 0.138334i
\(962\) 1.59247e7 + 5.46921e7i 0.554798 + 1.90540i
\(963\) 3.30373e6 5.65350e6i 0.114799 0.196450i
\(964\) −1.44141e7 + 9.17152e6i −0.499570 + 0.317869i
\(965\) 2.36450e7 1.36514e7i 0.817374 0.471911i
\(966\) 540121. + 133830.i 0.0186229 + 0.00461435i
\(967\) 4.48583e6 + 2.58989e6i 0.154268 + 0.0890668i 0.575147 0.818050i \(-0.304945\pi\)
−0.420879 + 0.907117i \(0.638278\pi\)
\(968\) −1.33163e7 + 4.50784e6i −0.456766 + 0.154625i
\(969\) 8.00155e6 4.59174e6i 0.273757 0.157097i
\(970\) −7.98103e6 7.64444e6i −0.272351 0.260865i
\(971\) −1.12452e7 −0.382754 −0.191377 0.981517i \(-0.561295\pi\)
−0.191377 + 0.981517i \(0.561295\pi\)
\(972\) 1.39571e7 2.59388e7i 0.473838 0.880612i
\(973\) 1.24910e6 0.0422976
\(974\) 2.94101e7 + 2.81698e7i 0.993343 + 0.951450i
\(975\) 2.96172e7 1.69960e7i 0.997774 0.572579i
\(976\) −4.46994e6 6.39892e6i −0.150202 0.215022i
\(977\) 4.56993e7 + 2.63845e7i 1.53170 + 0.884327i 0.999284 + 0.0378433i \(0.0120488\pi\)
0.532415 + 0.846483i \(0.321285\pi\)
\(978\) 4.05168e7 + 1.00392e7i 1.35453 + 0.335622i
\(979\) 5.36212e7 3.09582e7i 1.78805 1.03233i
\(980\) −9.10370e6 1.43075e7i −0.302798 0.475883i
\(981\) 8.74194e6 1.49596e7i 0.290025 0.496304i
\(982\) 6.15267e6 + 2.11308e7i 0.203603 + 0.699257i
\(983\) −1.64557e7 2.85021e7i −0.543166 0.940790i −0.998720 0.0505824i \(-0.983892\pi\)
0.455554 0.890208i \(-0.349441\pi\)
\(984\) −2.14990e7 1.89862e7i −0.707834 0.625101i
\(985\) −3.88155e6 + 6.72304e6i −0.127472 + 0.220788i
\(986\) −937276. 229627.i −0.0307026 0.00752196i
\(987\) −1.13820e6 2986.86i −0.0371901 9.75938e-5i
\(988\) −1.65379e7 + 3.17258e7i −0.538999 + 1.03400i
\(989\) 3.69690e7i 1.20184i
\(990\) 2.03761e7 5.81711e6i 0.660745 0.188634i
\(991\) 3.03835e7i 0.982775i 0.870941 + 0.491388i \(0.163510\pi\)
−0.870941 + 0.491388i \(0.836490\pi\)
\(992\) −3.11253e7 + 1.20540e7i −1.00423 + 0.388913i
\(993\) 6.29344e6 1.08348e7i 0.202542 0.348696i
\(994\) −285051. + 1.16350e6i −0.00915076 + 0.0373509i
\(995\) 4.46959e6 7.74156e6i 0.143123 0.247897i
\(996\) 1.18556e7 2.25986e7i 0.378683 0.721827i
\(997\) −2.34281e7 4.05786e7i −0.746447 1.29288i −0.949516 0.313719i \(-0.898425\pi\)
0.203069 0.979164i \(-0.434908\pi\)
\(998\) 1.98503e7 5.77982e6i 0.630870 0.183691i
\(999\) −291924. + 3.70805e7i −0.00925456 + 1.17552i
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 36.6.h.a.23.8 yes 56
3.2 odd 2 108.6.h.a.71.21 56
4.3 odd 2 inner 36.6.h.a.23.3 yes 56
9.2 odd 6 inner 36.6.h.a.11.3 56
9.7 even 3 108.6.h.a.35.26 56
12.11 even 2 108.6.h.a.71.26 56
36.7 odd 6 108.6.h.a.35.21 56
36.11 even 6 inner 36.6.h.a.11.8 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.h.a.11.3 56 9.2 odd 6 inner
36.6.h.a.11.8 yes 56 36.11 even 6 inner
36.6.h.a.23.3 yes 56 4.3 odd 2 inner
36.6.h.a.23.8 yes 56 1.1 even 1 trivial
108.6.h.a.35.21 56 36.7 odd 6
108.6.h.a.35.26 56 9.7 even 3
108.6.h.a.71.21 56 3.2 odd 2
108.6.h.a.71.26 56 12.11 even 2