Properties

Label 36.6.h.a.23.3
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 23.3
Character \(\chi\) \(=\) 36.23
Dual form 36.6.h.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.49437 + 1.34609i) q^{2} +(13.5204 - 7.75878i) q^{3} +(28.3761 - 14.7918i) q^{4} +(-27.3241 - 15.7756i) q^{5} +(-63.8421 + 60.8292i) q^{6} +(2.81745 - 1.62665i) q^{7} +(-135.998 + 119.468i) q^{8} +(122.603 - 209.804i) q^{9} +O(q^{10})\) \(q+(-5.49437 + 1.34609i) q^{2} +(13.5204 - 7.75878i) q^{3} +(28.3761 - 14.7918i) q^{4} +(-27.3241 - 15.7756i) q^{5} +(-63.8421 + 60.8292i) 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} +(268.890 - 420.155i) q^{12} +(514.329 - 890.844i) q^{13} +(-13.2905 + 12.7300i) q^{14} +(-491.832 - 1.29066i) q^{15} +(586.406 - 839.467i) q^{16} -544.497i q^{17} +(-391.211 + 1317.77i) q^{18} +1086.90i q^{19} +(-1008.70 - 43.4770i) q^{20} +(25.4722 - 43.8530i) q^{21} +(1911.79 + 1995.97i) q^{22} +(-969.831 + 1679.80i) q^{23} +(-911.816 + 2670.43i) 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} +(2704.04 - 654.957i) q^{30} +(4990.16 + 2881.07i) q^{31} +(-2091.93 + 5401.69i) q^{32} +(-6585.87 - 3825.43i) q^{33} +(732.941 + 2991.67i) q^{34} -102.646 q^{35} +(375.619 - 7766.92i) q^{36} +9789.25 q^{37} +(-1463.06 - 5971.81i) q^{38} +(42.0792 - 16035.1i) q^{39} +(5600.69 - 1118.92i) q^{40} +(8802.77 + 5082.28i) q^{41} +(-80.9236 + 275.232i) 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} +(1415.21 - 15899.7i) q^{48} +(-8398.21 + 14546.1i) q^{49} +(8332.68 + 8699.57i) q^{50} +(-4224.63 - 7361.83i) q^{51} +(1417.47 - 32886.5i) q^{52} -11691.5i q^{53} +(4934.97 + 20852.1i) q^{54} +15415.4i q^{55} +(-188.833 + 557.816i) q^{56} +(8432.99 + 14695.3i) q^{57} +(1279.88 - 1225.90i) q^{58} +(19276.6 - 33388.1i) q^{59} +(-13975.4 + 7238.45i) 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} +(41334.5 + 12153.2i) q^{66} +(-4430.73 - 2558.08i) q^{67} +(-8054.09 - 15450.7i) q^{68} +(-79.3456 + 30236.2i) q^{69} +(563.972 - 138.170i) q^{70} +65091.6 q^{71} +(8391.17 + 43179.9i) q^{72} +12156.6 q^{73} +(-53785.7 + 13177.2i) q^{74} +(-28704.9 - 16673.4i) q^{75} +(16077.2 + 30841.9i) q^{76} +(-1376.56 - 794.757i) q^{77} +(21353.5 + 88159.6i) 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} +(74.1376 - 1621.15i) q^{84} +(-8589.76 + 14877.9i) q^{85} +(77862.3 - 74578.5i) q^{86} +(-2452.99 + 4223.07i) q^{87} +(83773.3 + 28359.0i) q^{88} -126726. i q^{89} +(31478.1 - 29835.3i) q^{90} -3346.54i q^{91} +(-2672.82 + 62011.6i) q^{92} +(89822.5 + 235.711i) q^{93} +(-87820.3 - 91687.1i) q^{94} +(17146.4 - 29698.5i) q^{95} +(13626.7 + 89263.9i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.49437 + 1.34609i −0.971276 + 0.237957i
\(3\) 13.5204 7.75878i 0.867335 0.497726i
\(4\) 28.3761 14.7918i 0.886753 0.462243i
\(5\) −27.3241 15.7756i −0.488788 0.282202i 0.235283 0.971927i \(-0.424398\pi\)
−0.724072 + 0.689725i \(0.757732\pi\)
\(6\) −63.8421 + 60.8292i −0.723984 + 0.689817i
\(7\) 2.81745 1.62665i 0.0217325 0.0125473i −0.489094 0.872231i \(-0.662673\pi\)
0.510827 + 0.859684i \(0.329339\pi\)
\(8\) −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 \(-0.958344\pi\)
0.382715 0.923866i \(-0.374989\pi\)
\(12\) 268.890 420.155i 0.539041 0.842279i
\(13\) 514.329 890.844i 0.844078 1.46199i −0.0423410 0.999103i \(-0.513482\pi\)
0.886419 0.462883i \(-0.153185\pi\)
\(14\) −13.2905 + 12.7300i −0.0181226 + 0.0173583i
\(15\) −491.832 1.29066i −0.564402 0.00148110i
\(16\) 586.406 839.467i 0.572662 0.819792i
\(17\) 544.497i 0.456955i −0.973549 0.228478i \(-0.926625\pi\)
0.973549 0.228478i \(-0.0733748\pi\)
\(18\) −391.211 + 1317.77i −0.284596 + 0.958647i
\(19\) 1086.90i 0.690724i 0.938470 + 0.345362i \(0.112244\pi\)
−0.938470 + 0.345362i \(0.887756\pi\)
\(20\) −1008.70 43.4770i −0.563881 0.0243044i
\(21\) 25.4722 43.8530i 0.0126043 0.0216995i
\(22\) 1911.79 + 1995.97i 0.842140 + 0.879220i
\(23\) −969.831 + 1679.80i −0.382275 + 0.662121i −0.991387 0.130964i \(-0.958193\pi\)
0.609112 + 0.793084i \(0.291526\pi\)
\(24\) −911.816 + 2670.43i −0.323131 + 0.946354i
\(25\) −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 \(0.344345\pi\)
\(30\) 2704.04 654.957i 0.548543 0.132865i
\(31\) 4990.16 + 2881.07i 0.932631 + 0.538455i 0.887643 0.460533i \(-0.152342\pi\)
0.0449884 + 0.998988i \(0.485675\pi\)
\(32\) −2091.93 + 5401.69i −0.361138 + 0.932512i
\(33\) −6585.87 3825.43i −1.05276 0.611499i
\(34\) 732.941 + 2991.67i 0.108736 + 0.443829i
\(35\) −102.646 −0.0141635
\(36\) 375.619 7766.92i 0.0483049 0.998833i
\(37\) 9789.25 1.17556 0.587780 0.809021i \(-0.300002\pi\)
0.587780 + 0.809021i \(0.300002\pi\)
\(38\) −1463.06 5971.81i −0.164362 0.670883i
\(39\) 42.0792 16035.1i 0.00443003 1.68815i
\(40\) 5600.69 1118.92i 0.553467 0.110573i
\(41\) 8802.77 + 5082.28i 0.817823 + 0.472171i 0.849665 0.527322i \(-0.176804\pi\)
−0.0318420 + 0.999493i \(0.510137\pi\)
\(42\) −80.9236 + 275.232i −0.00707867 + 0.0240755i
\(43\) −16506.0 + 9529.76i −1.36136 + 0.785979i −0.989804 0.142434i \(-0.954507\pi\)
−0.371551 + 0.928413i \(0.621174\pi\)
\(44\) −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 \(0.0989817\pi\)
−0.211040 + 0.977477i \(0.567685\pi\)
\(48\) 1415.21 15899.7i 0.0886583 0.996062i
\(49\) −8398.21 + 14546.1i −0.499685 + 0.865480i
\(50\) 8332.68 + 8699.57i 0.471368 + 0.492122i
\(51\) −4224.63 7361.83i −0.227438 0.396333i
\(52\) 1417.47 32886.5i 0.0726954 1.68659i
\(53\) 11691.5i 0.571717i −0.958272 0.285858i \(-0.907721\pi\)
0.958272 0.285858i \(-0.0922787\pi\)
\(54\) 4934.97 + 20852.1i 0.230303 + 0.973119i
\(55\) 15415.4i 0.687144i
\(56\) −188.833 + 557.816i −0.00804650 + 0.0237696i
\(57\) 8432.99 + 14695.3i 0.343791 + 0.599089i
\(58\) 1279.88 1225.90i 0.0499573 0.0478505i
\(59\) 19276.6 33388.1i 0.720942 1.24871i −0.239680 0.970852i \(-0.577043\pi\)
0.960622 0.277857i \(-0.0896242\pi\)
\(60\) −13975.4 + 7238.45i −0.501170 + 0.259578i
\(61\) 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
\(66\) 41334.5 + 12153.2i 1.16803 + 0.343423i
\(67\) −4430.73 2558.08i −0.120584 0.0696189i 0.438495 0.898734i \(-0.355512\pi\)
−0.559079 + 0.829115i \(0.688845\pi\)
\(68\) −8054.09 15450.7i −0.211224 0.405206i
\(69\) −79.3456 + 30236.2i −0.00200632 + 0.764548i
\(70\) 563.972 138.170i 0.0137566 0.00337030i
\(71\) 65091.6 1.53242 0.766212 0.642588i \(-0.222139\pi\)
0.766212 + 0.642588i \(0.222139\pi\)
\(72\) 8391.17 + 43179.9i 0.190762 + 0.981636i
\(73\) 12156.6 0.266996 0.133498 0.991049i \(-0.457379\pi\)
0.133498 + 0.991049i \(0.457379\pi\)
\(74\) −53785.7 + 13177.2i −1.14179 + 0.279733i
\(75\) −28704.9 16673.4i −0.589255 0.342272i
\(76\) 16077.2 + 30841.9i 0.319283 + 0.612501i
\(77\) −1376.56 794.757i −0.0264587 0.0152759i
\(78\) 21353.5 + 88159.6i 0.397404 + 1.64071i
\(79\) −64990.0 + 37522.0i −1.17160 + 0.676423i −0.954056 0.299628i \(-0.903137\pi\)
−0.217542 + 0.976051i \(0.569804\pi\)
\(80\) −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 0.994616 0.103627i \(-0.0330448\pi\)
−0.587052 + 0.809549i \(0.699711\pi\)
\(84\) 74.1376 1621.15i 0.00114641 0.0250684i
\(85\) −8589.76 + 14877.9i −0.128954 + 0.223354i
\(86\) 77862.3 74578.5i 1.13522 1.08735i
\(87\) −2452.99 + 4223.07i −0.0347454 + 0.0598177i
\(88\) 83773.3 + 28359.0i 1.15318 + 0.390377i
\(89\) 126726.i 1.69587i −0.530104 0.847933i \(-0.677847\pi\)
0.530104 0.847933i \(-0.322153\pi\)
\(90\) 31478.1 29835.3i 0.409640 0.388262i
\(91\) 3346.54i 0.0423636i
\(92\) −2672.82 + 62011.6i −0.0329231 + 0.763842i
\(93\) 89822.5 + 235.711i 1.07691 + 0.00282601i
\(94\) −87820.3 91687.1i −1.02512 1.07026i
\(95\) 17146.4 29698.5i 0.194924 0.337618i
\(96\) 13626.7 + 89263.9i 0.150908 + 0.988548i
\(97\) −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 \(0.193064\pi\)
\(102\) 33121.3 + 34761.8i 0.315215 + 0.330828i
\(103\) −92372.6 53331.3i −0.857926 0.495324i 0.00539101 0.999985i \(-0.498284\pi\)
−0.863317 + 0.504661i \(0.831617\pi\)
\(104\) 36480.0 + 182599.i 0.330728 + 1.65544i
\(105\) −1387.81 + 796.404i −0.0122845 + 0.00704953i
\(106\) 15737.8 + 64237.4i 0.136044 + 0.555295i
\(107\) −26946.6 −0.227533 −0.113767 0.993508i \(-0.536292\pi\)
−0.113767 + 0.993508i \(0.536292\pi\)
\(108\) −55183.3 107926.i −0.455248 0.890365i
\(109\) 71302.9 0.574832 0.287416 0.957806i \(-0.407204\pi\)
0.287416 + 0.957806i \(0.407204\pi\)
\(110\) −20750.5 84697.8i −0.163511 0.667406i
\(111\) 132355. 75952.6i 1.01960 0.585107i
\(112\) 286.646 3319.03i 0.00215924 0.0250015i
\(113\) 32800.9 + 18937.6i 0.241651 + 0.139517i 0.615935 0.787797i \(-0.288778\pi\)
−0.374284 + 0.927314i \(0.622112\pi\)
\(114\) −66115.1 69389.8i −0.476473 0.500073i
\(115\) 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
\(120\) 67042.2 58582.8i 0.425006 0.371378i
\(121\) −38831.7 + 67258.5i −0.241114 + 0.417622i
\(122\) −29826.7 31140.0i −0.181428 0.189417i
\(123\) 158449. + 415.801i 0.944338 + 0.00247812i
\(124\) 184217. + 7940.13i 1.07591 + 0.0463739i
\(125\) 165786.i 0.949016i
\(126\) 1041.34 + 4349.12i 0.00584342 + 0.0244048i
\(127\) 66387.5i 0.365239i 0.983184 + 0.182619i \(0.0584576\pi\)
−0.983184 + 0.182619i \(0.941542\pi\)
\(128\) 20539.7 + 184222.i 0.110808 + 0.993842i
\(129\) −149229. + 256913.i −0.789548 + 1.35929i
\(130\) 132587. 126995.i 0.688086 0.659067i
\(131\) −28167.3 + 48787.1i −0.143406 + 0.248386i −0.928777 0.370639i \(-0.879139\pi\)
0.785371 + 0.619025i \(0.212472\pi\)
\(132\) −243466. 11134.0i −1.21620 0.0556183i
\(133\) 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 \(0.924565\pi\)
\(138\) −40264.7 166236.i −0.179981 0.743065i
\(139\) 332509. + 191974.i 1.45971 + 0.842764i 0.998997 0.0447857i \(-0.0142605\pi\)
0.460713 + 0.887549i \(0.347594\pi\)
\(140\) −2912.68 + 1518.31i −0.0125595 + 0.00654698i
\(141\) 302529. + 175725.i 1.28150 + 0.744366i
\(142\) −357637. + 87618.9i −1.48841 + 0.364651i
\(143\) −502586. −2.05528
\(144\) −104228. 225951.i −0.418869 0.908047i
\(145\) 9884.83 0.0390435
\(146\) −66792.8 + 16363.8i −0.259327 + 0.0635336i
\(147\) −687.090 + 261829.i −0.00262253 + 0.999367i
\(148\) 277781. 144800.i 1.04243 0.543395i
\(149\) 283272. + 163547.i 1.04529 + 0.603499i 0.921327 0.388788i \(-0.127106\pi\)
0.123964 + 0.992287i \(0.460439\pi\)
\(150\) 180159. + 52970.4i 0.653775 + 0.192223i
\(151\) 376668. 217470.i 1.34436 0.776169i 0.356919 0.934135i \(-0.383827\pi\)
0.987444 + 0.157967i \(0.0504938\pi\)
\(152\) −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
\(156\) −235994. 455637.i −0.776408 1.49902i
\(157\) −6799.06 + 11776.3i −0.0220140 + 0.0381294i −0.876823 0.480814i \(-0.840341\pi\)
0.854809 + 0.518944i \(0.173675\pi\)
\(158\) 306571. 293642.i 0.976986 0.935783i
\(159\) −90711.8 158074.i −0.284558 0.495870i
\(160\) 142375. 114595.i 0.439677 0.353887i
\(161\) 6310.32i 0.0191861i
\(162\) 228510. + 243640.i 0.684096 + 0.729392i
\(163\) 473364.i 1.39549i −0.716347 0.697744i \(-0.754187\pi\)
0.716347 0.697744i \(-0.245813\pi\)
\(164\) 324964. + 14006.6i 0.943465 + 0.0406652i
\(165\) 119605. + 208422.i 0.342009 + 0.595984i
\(166\) −200181. 208995.i −0.563837 0.588663i
\(167\) −74868.1 + 129675.i −0.207733 + 0.359804i −0.951000 0.309191i \(-0.899942\pi\)
0.743267 + 0.668995i \(0.233275\pi\)
\(168\) 1774.88 + 9007.01i 0.00485171 + 0.0246211i
\(169\) −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 \(0.264074\pi\)
\(174\) 7792.99 26505.0i 0.0195133 0.0663674i
\(175\) −5999.82 3464.00i −0.0148096 0.00855033i
\(176\) −498455. 43048.7i −1.21295 0.104756i
\(177\) 1577.09 600983.i 0.00378377 1.44188i
\(178\) 170584. + 696280.i 0.403543 + 1.64715i
\(179\) −91825.1 −0.214205 −0.107102 0.994248i \(-0.534157\pi\)
−0.107102 + 0.994248i \(0.534157\pi\)
\(180\) −132791. + 206299.i −0.305483 + 0.474586i
\(181\) 640763. 1.45379 0.726893 0.686750i \(-0.240963\pi\)
0.726893 + 0.686750i \(0.240963\pi\)
\(182\) 4504.74 + 18387.1i 0.0100807 + 0.0411467i
\(183\) 102749. + 59682.1i 0.226803 + 0.131740i
\(184\) −68787.6 344312.i −0.149784 0.749735i
\(185\) −267482. 154431.i −0.574600 0.331746i
\(186\) −493835. + 119614.i −1.04665 + 0.253512i
\(187\) −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 0.694840 0.719165i \(-0.255475\pi\)
−0.970235 + 0.242167i \(0.922142\pi\)
\(192\) −195027. 472106.i −0.381805 0.924243i
\(193\) −432677. + 749418.i −0.836123 + 1.44821i 0.0569898 + 0.998375i \(0.481850\pi\)
−0.893113 + 0.449833i \(0.851484\pi\)
\(194\) 242287. + 252955.i 0.462196 + 0.482547i
\(195\) −254113. + 437482.i −0.478565 + 0.823898i
\(196\) −23145.2 + 536987.i −0.0430349 + 0.998443i
\(197\) 246048.i 0.451705i −0.974162 0.225852i \(-0.927483\pi\)
0.974162 0.225852i \(-0.0725167\pi\)
\(198\) 653153. 156390.i 1.18400 0.283495i
\(199\) 283324.i 0.507166i −0.967314 0.253583i \(-0.918391\pi\)
0.967314 0.253583i \(-0.0816091\pi\)
\(200\) 365131. + 123605.i 0.645467 + 0.218504i
\(201\) −79752.8 209.286i −0.139237 0.000365385i
\(202\) −357284. + 342216.i −0.616077 + 0.590095i
\(203\) −509.623 + 882.693i −0.000867979 + 0.00150338i
\(204\) −228773. 146410.i −0.384884 0.246318i
\(205\) −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
\(210\) 6553.11 6243.85i 0.0102541 0.00977021i
\(211\) −369932. 213580.i −0.572025 0.330259i 0.185932 0.982563i \(-0.440469\pi\)
−0.757958 + 0.652303i \(0.773803\pi\)
\(212\) −172938. 331759.i −0.264272 0.506972i
\(213\) 880064. 505031.i 1.32912 0.762727i
\(214\) 148055. 36272.5i 0.220997 0.0541431i
\(215\) 601350. 0.887219
\(216\) 448475. + 518705.i 0.654040 + 0.756460i
\(217\) 18746.0 0.0270246
\(218\) −391764. + 95979.9i −0.558320 + 0.136785i
\(219\) 164362. 94320.3i 0.231575 0.132891i
\(220\) 228021. + 437429.i 0.317628 + 0.609327i
\(221\) −485062. 280051.i −0.668062 0.385706i
\(222\) −624966. + 595472.i −0.851087 + 0.810922i
\(223\) −785917. + 453749.i −1.05831 + 0.611018i −0.924965 0.380051i \(-0.875906\pi\)
−0.133349 + 0.991069i \(0.542573\pi\)
\(224\) 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 0.964148 0.265364i \(-0.0854921\pi\)
−0.711886 + 0.702295i \(0.752159\pi\)
\(228\) 456665. + 292256.i 0.581782 + 0.372329i
\(229\) −240738. + 416970.i −0.303358 + 0.525432i −0.976894 0.213722i \(-0.931441\pi\)
0.673536 + 0.739154i \(0.264775\pi\)
\(230\) −250009. + 239466.i −0.311628 + 0.298486i
\(231\) −24778.0 65.0221i −0.0305517 8.01736e-5i
\(232\) 18184.7 53718.0i 0.0221813 0.0655240i
\(233\) 506837.i 0.611615i 0.952093 + 0.305808i \(0.0989265\pi\)
−0.952093 + 0.305808i \(0.901074\pi\)
\(234\) 972718. + 1.02628e6i 1.16131 + 1.22525i
\(235\) 708122.i 0.836447i
\(236\) 53125.7 1.23256e6i 0.0620905 1.44055i
\(237\) −587566. + 1.01156e6i −0.679495 + 1.16982i
\(238\) 6931.43 + 7236.62i 0.00793196 + 0.00828121i
\(239\) 150130. 260032.i 0.170009 0.294464i −0.768414 0.639953i \(-0.778954\pi\)
0.938423 + 0.345489i \(0.112287\pi\)
\(240\) −289497. + 412120.i −0.324426 + 0.461844i
\(241\) −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
\(246\) −871138. + 211002.i −0.917802 + 0.222305i
\(247\) 968256. + 559023.i 1.00983 + 0.583025i
\(248\) −1.02285e6 + 204347.i −1.05604 + 0.210978i
\(249\) 689597. + 400555.i 0.704850 + 0.409416i
\(250\) −223163. 910890.i −0.225825 0.921756i
\(251\) 1.40288e6 1.40551 0.702757 0.711430i \(-0.251952\pi\)
0.702757 + 0.711430i \(0.251952\pi\)
\(252\) −11575.8 22493.9i −0.0114829 0.0223133i
\(253\) 947688. 0.930816
\(254\) −89363.3 364757.i −0.0869111 0.354748i
\(255\) −702.761 + 267801.i −0.000676795 + 0.257906i
\(256\) −360832. 984536.i −0.344116 0.938927i
\(257\) −837694. 483643.i −0.791139 0.456764i 0.0492245 0.998788i \(-0.484325\pi\)
−0.840363 + 0.542024i \(0.817658\pi\)
\(258\) 474091. 1.61245e6i 0.443417 1.50812i
\(259\) 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 0.581427 0.813599i \(-0.302495\pi\)
−0.995311 + 0.0967310i \(0.969161\pi\)
\(264\) 1.35268e6 266552.i 1.19450 0.235382i
\(265\) −184440. + 319460.i −0.161340 + 0.279448i
\(266\) −13836.2 14445.4i −0.0119898 0.0125177i
\(267\) −983240. 1.71339e6i −0.844076 1.47088i
\(268\) −163565. 7049.99i −0.139109 0.00599586i
\(269\) 1.21595e6i 1.02455i 0.858820 + 0.512277i \(0.171198\pi\)
−0.858820 + 0.512277i \(0.828802\pi\)
\(270\) 194111. 647617.i 0.162047 0.540641i
\(271\) 2.02493e6i 1.67489i 0.546520 + 0.837446i \(0.315952\pi\)
−0.546520 + 0.837446i \(0.684048\pi\)
\(272\) −457087. 319297.i −0.374608 0.261681i
\(273\) −25965.1 45246.6i −0.0210854 0.0367434i
\(274\) 1.72171e6 1.64910e6i 1.38542 1.32700i
\(275\) −520226. + 901058.i −0.414821 + 0.718490i
\(276\) 444996. + 859160.i 0.351628 + 0.678893i
\(277\) 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 \(0.353150\pi\)
\(282\) −1.89875e6 558269.i −1.42182 0.418042i
\(283\) −441868. 255113.i −0.327964 0.189350i 0.326973 0.945034i \(-0.393971\pi\)
−0.654937 + 0.755684i \(0.727305\pi\)
\(284\) 1.84704e6 962821.i 1.35888 0.708353i
\(285\) 1402.81 534571.i 0.00102303 0.389846i
\(286\) 2.76139e6 676525.i 1.99624 0.489067i
\(287\) 33068.4 0.0236978
\(288\) 876817. + 1.10116e6i 0.622913 + 0.782291i
\(289\) 1.12338e6 0.791192
\(290\) −54310.9 + 13305.8i −0.0379221 + 0.00929068i
\(291\) −834646. 484808.i −0.577790 0.335612i
\(292\) 344957. 179818.i 0.236760 0.123417i
\(293\) 1.02752e6 + 593241.i 0.699234 + 0.403703i 0.807062 0.590467i \(-0.201056\pi\)
−0.107828 + 0.994170i \(0.534390\pi\)
\(294\) −348670. 1.43951e6i −0.235259 0.971285i
\(295\) −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
\(300\) −1.06116e6 48528.4i −0.680737 0.0311310i
\(301\) −31003.2 + 53699.2i −0.0197238 + 0.0341626i
\(302\) −1.77682e6 + 1.70189e6i −1.12105 + 1.07377i
\(303\) 684762. 1.17889e6i 0.428483 0.737676i
\(304\) 912414. + 637363.i 0.566250 + 0.395551i
\(305\) 240502.i 0.148036i
\(306\) 717523. + 213013.i 0.438059 + 0.130048i
\(307\) 1.41312e6i 0.855724i 0.903844 + 0.427862i \(0.140733\pi\)
−0.903844 + 0.427862i \(0.859267\pi\)
\(308\) −50817.3 2190.33i −0.0305235 0.00131562i
\(309\) −1.66270e6 4363.24i −0.990645 0.00259964i
\(310\) 711378. + 742701.i 0.420433 + 0.438944i
\(311\) 315266. 546057.i 0.184832 0.320138i −0.758688 0.651454i \(-0.774159\pi\)
0.943520 + 0.331316i \(0.107493\pi\)
\(312\) 1.90997e6 + 2.18577e6i 1.11081 + 1.27121i
\(313\) 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 \(0.318787\pi\)
\(318\) 711185. + 746410.i 0.394380 + 0.413914i
\(319\) 132564. + 76535.6i 0.0729369 + 0.0421101i
\(320\) −628005. + 821275.i −0.342838 + 0.448346i
\(321\) −364329. + 209073.i −0.197347 + 0.113249i
\(322\) −8494.24 34671.2i −0.00456546 0.0186350i
\(323\) 591813. 0.315630
\(324\) −1.58348e6 1.03105e6i −0.838010 0.545655i
\(325\) −2.19055e6 −1.15039
\(326\) 637189. + 2.60083e6i 0.332066 + 1.35540i
\(327\) 964044. 553223.i 0.498572 0.286109i
\(328\) −1.80433e6 + 360473.i −0.926041 + 0.185007i
\(329\) 63233.7 + 36508.0i 0.0322077 + 0.0185951i
\(330\) −937706. 984150.i −0.474004 0.497481i
\(331\) 696109. 401899.i 0.349227 0.201626i −0.315118 0.949053i \(-0.602044\pi\)
0.664345 + 0.747426i \(0.268711\pi\)
\(332\) 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
\(336\) −21876.0 47098.7i −0.0105711 0.0227594i
\(337\) 763890. 1.32310e6i 0.366400 0.634624i −0.622599 0.782541i \(-0.713923\pi\)
0.989000 + 0.147917i \(0.0472567\pi\)
\(338\) 2.68757e6 + 2.80591e6i 1.27958 + 1.33592i
\(339\) 590413. + 1549.36i 0.279034 + 0.000732238i
\(340\) −23673.1 + 549235.i −0.0111060 + 0.257668i
\(341\) 2.81529e6i 1.31110i
\(342\) −1.43228e6 425206.i −0.662161 0.196578i
\(343\) 109322.i 0.0501734i
\(344\) 1.10628e6 3.26797e6i 0.504043 1.48896i
\(345\) 479162. 824926.i 0.216738 0.373136i
\(346\) −694314. + 665033.i −0.311793 + 0.298643i
\(347\) 423222. 733041.i 0.188688 0.326817i −0.756125 0.654427i \(-0.772910\pi\)
0.944813 + 0.327610i \(0.106243\pi\)
\(348\) −7139.50 + 156118.i −0.00316024 + 0.0691044i
\(349\) 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 \(0.225861\pi\)
\(354\) 800311. + 3.30414e6i 0.339430 + 1.40136i
\(355\) −1.77857e6 1.02686e6i −0.749031 0.432453i
\(356\) −1.87451e6 3.59599e6i −0.783902 1.50381i
\(357\) −23877.8 13869.5i −0.00991572 0.00575959i
\(358\) 504520. 123605.i 0.208052 0.0509714i
\(359\) −3.63496e6 −1.48855 −0.744275 0.667873i \(-0.767205\pi\)
−0.744275 + 0.667873i \(0.767205\pi\)
\(360\) 451907. 1.31223e6i 0.183778 0.533646i
\(361\) 1.29475e6 0.522901
\(362\) −3.52058e6 + 862522.i −1.41203 + 0.345938i
\(363\) −3176.97 + 1.21065e6i −0.00126545 + 0.482227i
\(364\) −49501.3 94961.8i −0.0195823 0.0375660i
\(365\) −332168. 191777.i −0.130505 0.0753469i
\(366\) −644877. 189606.i −0.251637 0.0739862i
\(367\) −366486. + 211591.i −0.142034 + 0.0820033i −0.569333 0.822107i \(-0.692798\pi\)
0.427299 + 0.904110i \(0.359465\pi\)
\(368\) 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
\(372\) 2.55230e6 1.32195e6i 0.956256 0.495287i
\(373\) 1.65892e6 2.87333e6i 0.617380 1.06933i −0.372582 0.927999i \(-0.621528\pi\)
0.989962 0.141334i \(-0.0451391\pi\)
\(374\) 1.08680e6 1.04097e6i 0.401764 0.384820i
\(375\) 1.28630e6 + 2.24150e6i 0.472350 + 0.823114i
\(376\) −3.84821e6 1.30270e6i −1.40375 0.475199i
\(377\) 322274.i 0.116781i
\(378\) 47823.2 + 50722.3i 0.0172151 + 0.0182587i
\(379\) 2.75509e6i 0.985230i −0.870247 0.492615i \(-0.836041\pi\)
0.870247 0.492615i \(-0.163959\pi\)
\(380\) 47255.0 1.09635e6i 0.0167876 0.389486i
\(381\) 515086. + 897586.i 0.181789 + 0.316784i
\(382\) 1.08660e6 + 1.13445e6i 0.380989 + 0.397764i
\(383\) −341107. + 590814.i −0.118821 + 0.205804i −0.919301 0.393556i \(-0.871245\pi\)
0.800480 + 0.599360i \(0.204578\pi\)
\(384\) 1.70705e6 + 2.33140e6i 0.590768 + 0.806841i
\(385\) 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 \(0.997430\pi\)
\(390\) 807303. 2.74574e6i 0.268766 0.914110i
\(391\) 914645. + 528070.i 0.302559 + 0.174683i
\(392\) −595663. 2.98156e6i −0.195788 0.980004i
\(393\) −2304.47 + 878166.i −0.000752645 + 0.286810i
\(394\) 331202. + 1.35188e6i 0.107486 + 0.438730i
\(395\) 2.36772e6 0.763551
\(396\) −3.37815e6 + 1.73846e6i −1.08253 + 0.557093i
\(397\) −4.32179e6 −1.37622 −0.688109 0.725607i \(-0.741559\pi\)
−0.688109 + 0.725607i \(0.741559\pi\)
\(398\) 381378. + 1.55668e6i 0.120684 + 0.492598i
\(399\) 47663.6 + 27685.6i 0.0149884 + 0.00870608i
\(400\) −2.17255e6 187631.i −0.678921 0.0586346i
\(401\) 2.13586e6 + 1.23314e6i 0.663302 + 0.382958i 0.793534 0.608526i \(-0.208239\pi\)
−0.130232 + 0.991484i \(0.541572\pi\)
\(402\) 438473. 106204.i 0.135325 0.0327776i
\(403\) 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
\(408\) 1.45404e6 + 496482.i 0.432441 + 0.147657i
\(409\) −1.88785e6 + 3.26985e6i −0.558031 + 0.966538i 0.439630 + 0.898179i \(0.355110\pi\)
−0.997661 + 0.0683591i \(0.978224\pi\)
\(410\) 1.25489e6 + 1.31014e6i 0.368677 + 0.384910i
\(411\) −3.29978e6 + 5.68091e6i −0.963564 + 1.65887i
\(412\) −3.41004e6 146979.i −0.989729 0.0426593i
\(413\) 125425.i 0.0361835i
\(414\) −1.83418e6 1.93517e6i −0.525946 0.554905i
\(415\) 1.61412e6i 0.460062i
\(416\) 3.73612e6 + 4.64183e6i 1.05849 + 1.31509i
\(417\) 5.98514e6 + 15706.1i 1.68552 + 0.00442313i
\(418\) −2.16942e6 + 2.07792e6i −0.607298 + 0.581686i
\(419\) 984571. 1.70533e6i 0.273976 0.474540i −0.695901 0.718138i \(-0.744995\pi\)
0.969876 + 0.243598i \(0.0783279\pi\)
\(420\) −27600.4 + 43127.0i −0.00763470 + 0.0119296i
\(421\) 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
\(426\) −4.15558e6 + 3.95947e6i −1.10945 + 1.05709i
\(427\) 21476.3 + 12399.3i 0.00570019 + 0.00329100i
\(428\) −764640. + 398589.i −0.201766 + 0.105176i
\(429\) −6.79517e6 + 3.89945e6i −1.78261 + 1.02296i
\(430\) −3.30403e6 + 809469.i −0.861734 + 0.211120i
\(431\) −1.70261e6 −0.441492 −0.220746 0.975331i \(-0.570849\pi\)
−0.220746 + 0.975331i \(0.570849\pi\)
\(432\) −3.16231e6 2.24627e6i −0.815258 0.579098i
\(433\) −1.19651e6 −0.306688 −0.153344 0.988173i \(-0.549004\pi\)
−0.153344 + 0.988173i \(0.549004\pi\)
\(434\) −102997. + 25233.8i −0.0262483 + 0.00643069i
\(435\) 133647. 76694.2i 0.0338638 0.0194330i
\(436\) 2.02330e6 1.05470e6i 0.509734 0.265712i
\(437\) −1.82577e6 1.05411e6i −0.457342 0.264047i
\(438\) −776103. + 739476.i −0.193301 + 0.184179i
\(439\) −2.13579e6 + 1.23310e6i −0.528929 + 0.305377i −0.740580 0.671968i \(-0.765449\pi\)
0.211651 + 0.977345i \(0.432116\pi\)
\(440\) −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 \(0.0361733\pi\)
−0.398570 + 0.917138i \(0.630493\pi\)
\(444\) 2.63223e6 4.11300e6i 0.633675 0.990150i
\(445\) −1.99918e6 + 3.46268e6i −0.478577 + 0.828919i
\(446\) 3.70733e6 3.55098e6i 0.882519 0.845300i
\(447\) 5.09887e6 + 13380.4i 1.20699 + 0.00316738i
\(448\) −40960.5 98421.2i −0.00964207 0.0231683i
\(449\) 95563.2i 0.0223705i 0.999937 + 0.0111852i \(0.00356044\pi\)
−0.999937 + 0.0111852i \(0.996440\pi\)
\(450\) 2.84681e6 681634.i 0.662716 0.158679i
\(451\) 4.96624e6i 1.14971i
\(452\) 1.21088e6 + 52191.4i 0.278776 + 0.0120158i
\(453\) 3.40541e6 5.86276e6i 0.779694 1.34232i
\(454\) −1.53267e6 1.60015e6i −0.348987 0.364353i
\(455\) −52793.6 + 91441.2i −0.0119551 + 0.0207068i
\(456\) −2.90249e6 991050.i −0.653669 0.223195i
\(457\) 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 \(0.354448\pi\)
\(462\) 136227. 32996.1i 0.0296932 0.00719213i
\(463\) −813063. 469422.i −0.176267 0.101768i 0.409270 0.912413i \(-0.365783\pi\)
−0.585538 + 0.810645i \(0.699117\pi\)
\(464\) −27604.2 + 319625.i −0.00595224 + 0.0689200i
\(465\) −2.45060e6 1.42344e6i −0.525582 0.305286i
\(466\) −682247. 2.78475e6i −0.145538 0.594047i
\(467\) −6.03297e6 −1.28009 −0.640043 0.768339i \(-0.721083\pi\)
−0.640043 + 0.768339i \(0.721083\pi\)
\(468\) −6.72593e6 4.32937e6i −1.41951 0.913714i
\(469\) −16644.4 −0.00349412
\(470\) 953194. + 3.89068e6i 0.199038 + 0.812421i
\(471\) −556.257 + 211973.i −0.000115538 + 0.0440279i
\(472\) 1.36724e6 + 6.84364e6i 0.282481 + 1.41394i
\(473\) 8.06458e6 + 4.65609e6i 1.65741 + 0.956904i
\(474\) 1.86666e6 6.34877e6i 0.381610 1.29791i
\(475\) 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 0.679698 0.733492i \(-0.262111\pi\)
−0.975072 + 0.221890i \(0.928777\pi\)
\(480\) 1.03585e6 2.65402e6i 0.205208 0.525777i
\(481\) 5.03489e6 8.72069e6i 0.992265 1.71865i
\(482\) 2.08909e6 + 2.18107e6i 0.409581 + 0.427615i
\(483\) 48960.3 + 85318.0i 0.00954941 + 0.0166408i
\(484\) −107019. + 2.48292e6i −0.0207657 + 0.481781i
\(485\) 1.95364e6i 0.377128i
\(486\) 4.97989e6 + 1.52116e6i 0.956377 + 0.292135i
\(487\) 7.19915e6i 1.37549i 0.725950 + 0.687747i \(0.241400\pi\)
−0.725950 + 0.687747i \(0.758600\pi\)
\(488\) −1.30698e6 442441.i −0.248439 0.0841019i
\(489\) −3.67272e6 6.40007e6i −0.694570 1.21035i
\(490\) −2.16494e6 + 2.07364e6i −0.407340 + 0.390161i
\(491\) −1.94528e6 + 3.36932e6i −0.364148 + 0.630723i −0.988639 0.150309i \(-0.951973\pi\)
0.624491 + 0.781032i \(0.285306\pi\)
\(492\) 4.50232e6 2.33195e6i 0.838540 0.434316i
\(493\) 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
\(498\) −4.32808e6 1.27254e6i −0.782027 0.229931i
\(499\) 3.16514e6 + 1.82739e6i 0.569038 + 0.328534i 0.756765 0.653687i \(-0.226779\pi\)
−0.187727 + 0.982221i \(0.560112\pi\)
\(500\) 2.45228e6 + 4.70437e6i 0.438676 + 0.841543i
\(501\) −6125.24 + 2.33415e6i −0.00109026 + 0.415464i
\(502\) −7.70792e6 + 1.88839e6i −1.36514 + 0.334452i
\(503\) −6.99423e6 −1.23259 −0.616297 0.787514i \(-0.711368\pi\)
−0.616297 + 0.787514i \(0.711368\pi\)
\(504\) 93880.4 + 108008.i 0.0164626 + 0.0189399i
\(505\) −2.75939e6 −0.481488
\(506\) −5.20694e6 + 1.27567e6i −0.904079 + 0.221494i
\(507\) −9.25832e6 5.37774e6i −1.59960 0.929137i
\(508\) 981990. + 1.88382e6i 0.168829 + 0.323877i
\(509\) −6.20968e6 3.58516e6i −1.06237 0.613358i −0.136281 0.990670i \(-0.543515\pi\)
−0.926086 + 0.377312i \(0.876848\pi\)
\(510\) −356623. 1.47234e6i −0.0607132 0.250659i
\(511\) 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
\(516\) −434336. + 9.49755e6i −0.0718127 + 1.57032i
\(517\) 5.48280e6 9.49649e6i 0.902144 1.56256i
\(518\) −130104. + 124617.i −0.0213042 + 0.0204057i
\(519\) 1.33071e6 2.29095e6i 0.216852 0.373333i
\(520\) 1.88382e6 5.56484e6i 0.305513 0.902493i
\(521\) 6.81856e6i 1.10052i −0.834993 0.550261i \(-0.814528\pi\)
0.834993 0.550261i \(-0.185472\pi\)
\(522\) −100282. 418823.i −0.0161082 0.0672750i
\(523\) 5.81403e6i 0.929444i −0.885457 0.464722i \(-0.846154\pi\)
0.885457 0.464722i \(-0.153846\pi\)
\(524\) −77628.1 + 1.80103e6i −0.0123507 + 0.286545i
\(525\) −107996. 283.403i −0.0171006 4.48752e-5i
\(526\) 3.63329e6 + 3.79326e6i 0.572579 + 0.597790i
\(527\) 1.56873e6 2.71713e6i 0.246050 0.426171i
\(528\) −7.07331e6 + 3.28536e6i −1.10418 + 0.512859i
\(529\) 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
\(534\) 7.70865e6 + 8.09046e6i 1.16984 + 1.22778i
\(535\) 736292. + 425098.i 0.111216 + 0.0642103i
\(536\) 908178. 181438.i 0.136540 0.0272782i
\(537\) −1.24151e6 + 712450.i −0.185787 + 0.106615i
\(538\) −1.63678e6 6.68088e6i −0.243800 0.995125i
\(539\) 8.20646e6 1.21670
\(540\) −194766. + 3.81954e6i −0.0287428 + 0.563672i
\(541\) −6.49473e6 −0.954043 −0.477021 0.878892i \(-0.658284\pi\)
−0.477021 + 0.878892i \(0.658284\pi\)
\(542\) −2.72573e6 1.11257e7i −0.398552 1.62678i
\(543\) 8.66337e6 4.97153e6i 1.26092 0.723587i
\(544\) 2.94121e6 + 1.13905e6i 0.426116 + 0.165024i
\(545\) −1.94829e6 1.12484e6i −0.280971 0.162219i
\(546\) 203567. + 213650.i 0.0292231 + 0.0306705i
\(547\) 3.41406e6 1.97111e6i 0.487868 0.281671i −0.235822 0.971796i \(-0.575778\pi\)
0.723690 + 0.690126i \(0.242445\pi\)
\(548\) −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
\(552\) −3.60148e6 4.12153e6i −0.503075 0.575720i
\(553\) −122071. + 211432.i −0.0169745 + 0.0294008i
\(554\) −1.50941e6 1.57587e6i −0.208945 0.218145i
\(555\) −4.81466e6 12634.6i −0.663489 0.00174112i
\(556\) 1.22749e7 + 529075.i 1.68396 + 0.0725822i
\(557\) 9.50351e6i 1.29791i 0.760825 + 0.648957i \(0.224795\pi\)
−0.760825 + 0.648957i \(0.775205\pi\)
\(558\) −5.74879e6 + 5.44878e6i −0.781612 + 0.740822i
\(559\) 1.96057e7i 2.65371i
\(560\) −60192.0 + 86167.5i −0.00811089 + 0.0116111i
\(561\) −2.08294e6 + 3.58599e6i −0.279428 + 0.481063i
\(562\) 672850. 644474.i 0.0898623 0.0860725i
\(563\) −1.12664e6 + 1.95140e6i −0.149801 + 0.259463i −0.931154 0.364627i \(-0.881197\pi\)
0.781353 + 0.624089i \(0.214530\pi\)
\(564\) 1.11839e7 + 511454.i 1.48045 + 0.0677031i
\(565\) −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 \(0.612295\pi\)
\(570\) 711871. + 2.93902e6i 0.0917729 + 0.378891i
\(571\) −5.96127e6 3.44174e6i −0.765154 0.441762i 0.0659893 0.997820i \(-0.478980\pi\)
−0.831143 + 0.556059i \(0.812313\pi\)
\(572\) −1.42614e7 + 7.43415e6i −1.82252 + 0.950038i
\(573\) −3.74320e6 2.17425e6i −0.476274 0.276646i
\(574\) −181690. + 44513.0i −0.0230171 + 0.00563906i
\(575\) 4.13056e6 0.521002
\(576\) −6.29981e6 4.86989e6i −0.791172 0.611593i
\(577\) 7.44098e6 0.930444 0.465222 0.885194i \(-0.345974\pi\)
0.465222 + 0.885194i \(0.345974\pi\)
\(578\) −6.17226e6 + 1.51217e6i −0.768466 + 0.188270i
\(579\) −35398.9 + 1.34895e7i −0.00438827 + 1.67224i
\(580\) 280493. 146214.i 0.0346220 0.0180476i
\(581\) 144138. + 83217.9i 0.0177148 + 0.0102277i
\(582\) 5.23844e6 + 1.54021e6i 0.641054 + 0.188483i
\(583\) −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 0.752159 0.658982i \(-0.229013\pi\)
−0.946774 + 0.321898i \(0.895679\pi\)
\(588\) 3.85343e6 + 7.43986e6i 0.459625 + 0.887404i
\(589\) −3.13142e6 + 5.42379e6i −0.371924 + 0.644191i
\(590\) 4.96925e6 4.75968e6i 0.587707 0.562921i
\(591\) −1.90903e6 3.32667e6i −0.224825 0.391779i
\(592\) 5.74047e6 8.21774e6i 0.673199 0.963714i
\(593\) 944104.i 0.110251i −0.998479 0.0551256i \(-0.982444\pi\)
0.998479 0.0551256i \(-0.0175559\pi\)
\(594\) 7.61751e6 7.18212e6i 0.885823 0.835193i
\(595\) 55890.3i 0.00647208i
\(596\) 1.04573e7 + 450730.i 1.20588 + 0.0519758i
\(597\) −2.19824e6 3.83065e6i −0.252429 0.439882i
\(598\) −7.80727e6 8.15102e6i −0.892783 0.932093i
\(599\) 97761.8 169328.i 0.0111327 0.0192825i −0.860405 0.509610i \(-0.829790\pi\)
0.871538 + 0.490328i \(0.163123\pi\)
\(600\) 5.89574e6 1.16179e6i 0.668591 0.131749i
\(601\) 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
\(606\) −2.17545e6 + 7.39899e6i −0.240640 + 0.818447i
\(607\) 682314. + 393934.i 0.0751644 + 0.0433962i 0.537111 0.843511i \(-0.319516\pi\)
−0.461947 + 0.886908i \(0.652849\pi\)
\(608\) −5.87108e6 2.27372e6i −0.644109 0.249446i
\(609\) −41.6942 + 15888.4i −4.55547e−6 + 0.00173595i
\(610\) 323736. + 1.32140e6i 0.0352263 + 0.143784i
\(611\) 2.30868e7 2.50185
\(612\) −4.22907e6 204523.i −0.456422 0.0220732i
\(613\) −261841. −0.0281441 −0.0140720 0.999901i \(-0.504479\pi\)
−0.0140720 + 0.999901i \(0.504479\pi\)
\(614\) −1.90218e6 7.76421e6i −0.203625 0.831144i
\(615\) −4.32292e6 2.51099e6i −0.460882 0.267705i
\(616\) 282157. 56370.0i 0.0299598 0.00598545i
\(617\) −3.01771e6 1.74228e6i −0.319128 0.184249i 0.331876 0.943323i \(-0.392318\pi\)
−0.651004 + 0.759074i \(0.725652\pi\)
\(618\) 9.14136e6 2.21417e6i 0.962808 0.233206i
\(619\) −1.28016e7 + 7.39099e6i −1.34288 + 0.775311i −0.987229 0.159309i \(-0.949073\pi\)
−0.355649 + 0.934620i \(0.615740\pi\)
\(620\) −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
\(624\) −1.34363e7 9.43842e6i −1.38139 0.970372i
\(625\) −712009. + 1.23324e6i −0.0729097 + 0.126283i
\(626\) −1.54357e6 1.61154e6i −0.157431 0.164363i
\(627\) 4.15785e6 7.15816e6i 0.422377 0.727165i
\(628\) −18738.0 + 434736.i −0.00189594 + 0.0439872i
\(629\) 5.33022e6i 0.537178i
\(630\) 40156.0 135263.i 0.00403088 0.0135778i
\(631\) 5.75639e6i 0.575541i −0.957699 0.287771i \(-0.907086\pi\)
0.957699 0.287771i \(-0.0929141\pi\)
\(632\) 4.35580e6 1.28671e7i 0.433786 1.28141i
\(633\) −6.65875e6 17473.8i −0.660516 0.00173332i
\(634\) −667799. + 639636.i −0.0659816 + 0.0631989i
\(635\) 1.04730e6 1.81398e6i 0.103071 0.178524i
\(636\) −4.91224e6 3.14373e6i −0.481545 0.308179i
\(637\) 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 \(0.0664468\pi\)
\(642\) 1.72033e6 1.63914e6i 0.164730 0.156956i
\(643\) −1.40298e7 8.10012e6i −1.33821 0.772617i −0.351669 0.936124i \(-0.614386\pi\)
−0.986542 + 0.163507i \(0.947719\pi\)
\(644\) 93340.9 + 179062.i 0.00886864 + 0.0170133i
\(645\) 8.13049e6 4.66574e6i 0.769516 0.441592i
\(646\) −3.25164e6 + 796632.i −0.306564 + 0.0751063i
\(647\) 5.07623e6 0.476739 0.238369 0.971175i \(-0.423387\pi\)
0.238369 + 0.971175i \(0.423387\pi\)
\(648\) 1.00881e7 + 3.53348e6i 0.943781 + 0.330572i
\(649\) −1.88365e7 −1.75545
\(650\) 1.20357e7 2.94868e6i 1.11735 0.273743i
\(651\) 253454. 145446.i 0.0234394 0.0134508i
\(652\) −7.00190e6 1.34322e7i −0.645055 1.23745i
\(653\) 1.12780e6 + 651134.i 0.103502 + 0.0597569i 0.550857 0.834599i \(-0.314301\pi\)
−0.447356 + 0.894356i \(0.647634\pi\)
\(654\) −4.55213e6 + 4.33730e6i −0.416169 + 0.396529i
\(655\) 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 \(0.117738\pi\)
−0.153110 + 0.988209i \(0.548929\pi\)
\(660\) 6.47685e6 + 4.14505e6i 0.578767 + 0.370399i
\(661\) −3.21752e6 + 5.57291e6i −0.286430 + 0.496111i −0.972955 0.230995i \(-0.925802\pi\)
0.686525 + 0.727106i \(0.259135\pi\)
\(662\) −3.28369e6 + 3.14520e6i −0.291217 + 0.278935i
\(663\) −8.73109e6 22912.0i −0.771409 0.00202432i
\(664\) −8.77178e6 2.96943e6i −0.772089 0.261369i
\(665\) 111565.i 0.00978306i
\(666\) −3.82966e6 + 1.29000e7i −0.334560 + 1.12695i
\(667\) 607687.i 0.0528890i
\(668\) −206334. + 4.78711e6i −0.0178908 + 0.415081i
\(669\) −7.10538e6 + 1.22326e7i −0.613793 + 1.05671i
\(670\) −631628. 659439.i −0.0543594 0.0567528i
\(671\) 1.86214e6 3.22532e6i 0.159664 0.276546i
\(672\) 183594. + 229330.i 0.0156832 + 0.0195902i
\(673\) −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 \(0.279709\pi\)
\(678\) −3.24603e6 + 786235.i −0.271193 + 0.0656868i
\(679\) −174455. 100722.i −0.0145214 0.00838396i
\(680\) −609249. 3.04956e6i −0.0505269 0.252910i
\(681\) 5.27984e6 + 3.06682e6i 0.436268 + 0.253408i
\(682\) 3.78962e6 + 1.54682e7i 0.311986 + 1.27344i
\(683\) −189908. −0.0155773 −0.00778864 0.999970i \(-0.502479\pi\)
−0.00778864 + 0.999970i \(0.502479\pi\)
\(684\) 8.44185e6 + 408259.i 0.689918 + 0.0333653i
\(685\) 1.32972e7 1.08276
\(686\) −147157. 600656.i −0.0119391 0.0487322i
\(687\) −19695.7 + 7.50544e6i −0.00159213 + 0.606715i
\(688\) −1.67932e6 + 1.94446e7i −0.135258 + 1.56613i
\(689\) −1.04153e7 6.01328e6i −0.835842 0.482574i
\(690\) −1.52227e6 + 5.17744e6i −0.121722 + 0.413992i
\(691\) 1.27744e7 7.37528e6i 1.01776 0.587602i 0.104304 0.994545i \(-0.466739\pi\)
0.913454 + 0.406943i \(0.133405\pi\)
\(692\) 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
\(696\) −170922. 867381.i −0.0133744 0.0678714i
\(697\) 2.76729e6 4.79308e6i 0.215761 0.373709i
\(698\) −1.51861e6 1.58548e6i −0.117980 0.123175i
\(699\) 3.93243e6 + 6.85264e6i 0.304417 + 0.530475i
\(700\) −221490. 9546.67i −0.0170848 0.000736388i
\(701\) 1.07971e7i 0.829870i 0.909851 + 0.414935i \(0.136196\pi\)
−0.909851 + 0.414935i \(0.863804\pi\)
\(702\) 2.11142e7 + 6.32857e6i 1.61708 + 0.484688i
\(703\) 1.06399e7i 0.811988i
\(704\) −1.47810e7 + 6.15148e6i −1.12401 + 0.467787i
\(705\) −5.49416e6 9.57410e6i −0.416321 0.725480i
\(706\) −6.33645e6 + 6.06922e6i −0.478448 + 0.458270i
\(707\) 142264. 246408.i 0.0107040 0.0185398i
\(708\) −8.84486e6 1.70769e7i −0.663144 1.28034i
\(709\) −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
\(714\) 149863. + 44062.7i 0.0110014 + 0.00323464i
\(715\) 1.37327e7 + 7.92858e6i 1.00460 + 0.580003i
\(716\) −2.60564e6 + 1.35826e6i −0.189947 + 0.0990146i
\(717\) 12282.7 4.68057e6i 0.000892269 0.340017i
\(718\) 1.99718e7 4.89297e6i 1.44579 0.354211i
\(719\) −2.43648e7 −1.75769 −0.878843 0.477111i \(-0.841684\pi\)
−0.878843 + 0.477111i \(0.841684\pi\)
\(720\) −716569. + 7.81817e6i −0.0515142 + 0.562048i
\(721\) −347006. −0.0248599
\(722\) −7.11385e6 + 1.74285e6i −0.507881 + 0.124428i
\(723\) −7.19663e6 4.18020e6i −0.512016 0.297407i
\(724\) 1.81823e7 9.47802e6i 1.28915 0.672003i
\(725\) 577787. + 333585.i 0.0408247 + 0.0235701i
\(726\) −1.61218e6 6.65602e6i −0.113520 0.468676i
\(727\) −8.20393e6 + 4.73654e6i −0.575686 + 0.332372i −0.759417 0.650604i \(-0.774516\pi\)
0.183731 + 0.982977i \(0.441182\pi\)
\(728\) 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
\(732\) 3.79842e6 + 173707.i 0.262014 + 0.0119823i
\(733\) 2.49849e6 4.32752e6i 0.171758 0.297494i −0.767276 0.641317i \(-0.778388\pi\)
0.939035 + 0.343822i \(0.111722\pi\)
\(734\) 1.72879e6 1.65588e6i 0.118441 0.113446i
\(735\) 4.14928e6 7.14341e6i 0.283305 0.487739i
\(736\) −7.04492e6 8.75275e6i −0.479382 0.595593i
\(737\) 2.49968e6i 0.169518i
\(738\) −1.01410e7 + 9.61179e6i −0.685395 + 0.649626i
\(739\) 1.74764e7i 1.17718i −0.808433 0.588588i \(-0.799684\pi\)
0.808433 0.588588i \(-0.200316\pi\)
\(740\) −9.87441e6 425607.i −0.662876 0.0285713i
\(741\) 1.74285e7 + 45735.8i 1.16605 + 0.00305992i
\(742\) 148832. + 155386.i 0.00992402 + 0.0103610i
\(743\) −1.71665e6 + 2.97332e6i −0.114080 + 0.197592i −0.917412 0.397940i \(-0.869725\pi\)
0.803332 + 0.595532i \(0.203059\pi\)
\(744\) −1.22438e7 + 1.06989e7i −0.810931 + 0.708608i
\(745\) −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
\(750\) −1.00846e7 1.05841e7i −0.654648 0.687072i
\(751\) 4.54796e6 + 2.62576e6i 0.294250 + 0.169885i 0.639857 0.768494i \(-0.278994\pi\)
−0.345607 + 0.938379i \(0.612327\pi\)
\(752\) 2.28970e7 + 1.97749e6i 1.47650 + 0.127517i
\(753\) 1.89675e7 1.08846e7i 1.21905 0.699560i
\(754\) −433809. 1.77069e6i −0.0277888 0.113426i
\(755\) −1.37228e7 −0.876146
\(756\) −331035. 214312.i −0.0210654 0.0136378i
\(757\) 2.98204e7 1.89136 0.945679 0.325102i \(-0.105399\pi\)
0.945679 + 0.325102i \(0.105399\pi\)
\(758\) 3.70859e6 + 1.51375e7i 0.234442 + 0.956930i
\(759\) 1.28131e7 7.35290e6i 0.807329 0.463291i
\(760\) 1.21615e6 + 6.08738e6i 0.0763754 + 0.382293i
\(761\) 3.94493e6 + 2.27761e6i 0.246932 + 0.142566i 0.618359 0.785896i \(-0.287798\pi\)
−0.371427 + 0.928462i \(0.621131\pi\)
\(762\) −4.03830e6 4.23831e6i −0.251948 0.264427i
\(763\) 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
\(768\) −1.25174e7 1.05117e7i −0.765792 0.643088i
\(769\) −9.29907e6 + 1.61065e7i −0.567053 + 0.982164i 0.429803 + 0.902923i \(0.358583\pi\)
−0.996855 + 0.0792415i \(0.974750\pi\)
\(770\) −196237. 204878.i −0.0119276 0.0124528i
\(771\) −1.50784e7 39568.7i −0.913525 0.00239726i
\(772\) −1.19244e6 + 2.76656e7i −0.0720103 + 1.67069i
\(773\) 1.48809e7i 0.895736i −0.894100 0.447868i \(-0.852184\pi\)
0.894100 0.447868i \(-0.147816\pi\)
\(774\) −6.10071e6 2.54793e7i −0.366040 1.52875i
\(775\) 1.22706e7i 0.733858i
\(776\) 1.06168e7 + 3.59402e6i 0.632908 + 0.214253i
\(777\) 249353. 429287.i 0.0148171 0.0255091i
\(778\) 2.12156e7 2.03209e7i 1.25663 1.20363i
\(779\) −5.52391e6 + 9.56770e6i −0.326139 + 0.564890i
\(780\) −739605. + 1.61728e7i −0.0435274 + 0.951808i
\(781\) −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
\(786\) −1.16943e6 4.82806e6i −0.0675175 0.278751i
\(787\) 2.29308e7 + 1.32391e7i 1.31972 + 0.761943i 0.983684 0.179904i \(-0.0575788\pi\)
0.336040 + 0.941848i \(0.390912\pi\)
\(788\) −3.63949e6 6.98189e6i −0.208798 0.400551i
\(789\) −1.25162e7 7.27008e6i −0.715779 0.415764i
\(790\) −1.30091e7 + 3.18716e6i −0.741619 + 0.181692i
\(791\) 123220. 0.00700226
\(792\) 1.62207e7 1.40990e7i 0.918873 0.798687i
\(793\) 7.84105e6 0.442783
\(794\) 2.37455e7 5.81750e6i 1.33669 0.327480i
\(795\) −15089.8 + 5.75026e6i −0.000846768 + 0.322678i
\(796\) −4.19086e6 8.03962e6i −0.234434 0.449731i
\(797\) −70624.5 40775.1i −0.00393831 0.00227378i 0.498030 0.867160i \(-0.334057\pi\)
−0.501968 + 0.864886i \(0.667390\pi\)
\(798\) −299149. 87955.6i −0.0166295 0.00488941i
\(799\) 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
\(804\) −2.26617e6 + 1.17375e6i −0.123638 + 0.0640375i
\(805\) 99548.9 172424.i 0.00541435 0.00937793i
\(806\) −2.42142e7 + 2.31930e7i −1.31290 + 1.25753i
\(807\) 9.43429e6 + 1.64401e7i 0.509947 + 0.888632i
\(808\) −5.07634e6 + 1.49956e7i −0.273541 + 0.808046i
\(809\) 2.33658e7i 1.25519i 0.778540 + 0.627595i \(0.215960\pi\)
−0.778540 + 0.627595i \(0.784040\pi\)
\(810\) −2.40026e6 1.02621e7i −0.128542 0.549572i
\(811\) 2.11526e7i 1.12930i −0.825329 0.564652i \(-0.809010\pi\)
0.825329 0.564652i \(-0.190990\pi\)
\(812\) −1404.51 + 32585.6i −7.47538e−5 + 0.00173435i
\(813\) 1.57110e7 + 2.73779e7i 0.833637 + 1.45269i
\(814\) 1.87150e7 + 1.95391e7i 0.989987 + 1.03358i
\(815\) −7.46759e6 + 1.29342e7i −0.393810 + 0.682098i
\(816\) −8.65736e6 770581.i −0.455156 0.0405129i
\(817\) −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 \(0.209041\pi\)
\(822\) 1.04832e7 3.56548e7i 0.541146 1.84051i
\(823\) 7.60185e6 + 4.38893e6i 0.391219 + 0.225870i 0.682688 0.730710i \(-0.260811\pi\)
−0.291469 + 0.956580i \(0.594144\pi\)
\(824\) 1.89338e7 3.78265e6i 0.971451 0.194079i
\(825\) −42561.7 + 1.62190e7i −0.00217713 + 0.829638i
\(826\) 168834. + 689133.i 0.00861011 + 0.0351442i
\(827\) −1.32716e7 −0.674774 −0.337387 0.941366i \(-0.609543\pi\)
−0.337387 + 0.941366i \(0.609543\pi\)
\(828\) 1.26826e7 + 8.16357e6i 0.642882 + 0.413813i
\(829\) 2.90903e6 0.147015 0.0735075 0.997295i \(-0.476581\pi\)
0.0735075 + 0.997295i \(0.476581\pi\)
\(830\) 2.17275e6 + 8.86858e6i 0.109475 + 0.446847i
\(831\) 5.19970e6 + 3.02027e6i 0.261202 + 0.151720i
\(832\) −2.67759e7 2.04748e7i −1.34102 1.02544i
\(833\) 7.92033e6 + 4.57280e6i 0.395486 + 0.228334i
\(834\) −3.29057e7 + 7.97023e6i −1.63816 + 0.396785i
\(835\) 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 0.988214 0.153078i \(-0.0489187\pi\)
−0.626677 + 0.779279i \(0.715585\pi\)
\(840\) 93593.9 274108.i 0.00457667 0.0134037i
\(841\) −1.02065e7 + 1.76782e7i −0.497607 + 0.861881i
\(842\) −3.42087e6 3.57149e6i −0.166286 0.173608i
\(843\) −1.28957e6 + 2.22012e6i −0.0624994 + 0.107599i
\(844\) −1.36564e7 588620.i −0.659905 0.0284432i
\(845\) 2.16707e7i 1.04408i
\(846\) −3.00033e7 + 7.18392e6i −1.44126 + 0.345093i
\(847\) 252663.i 0.0121013i
\(848\) −9.81463e6 6.85597e6i −0.468689 0.327400i
\(849\) −7.95359e6 20871.7i −0.378699 0.000993778i
\(850\) 4.73689e6 4.53712e6i 0.224878 0.215394i
\(851\) −9.49391e6 + 1.64439e7i −0.449388 + 0.778363i
\(852\) 1.75025e7 2.73485e7i 0.826039 1.29073i
\(853\) 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 \(0.550513\pi\)
\(858\) 3.20861e7 3.05719e7i 1.48799 1.41776i
\(859\) −2.06184e7 1.19041e7i −0.953395 0.550443i −0.0592610 0.998243i \(-0.518874\pi\)
−0.894134 + 0.447800i \(0.852208\pi\)
\(860\) 1.70640e7 8.89504e6i 0.786744 0.410111i
\(861\) 447099. 256571.i 0.0205540 0.0117950i
\(862\) 9.35477e6 2.29186e6i 0.428810 0.105056i
\(863\) −1.77520e6 −0.0811371 −0.0405685 0.999177i \(-0.512917\pi\)
−0.0405685 + 0.999177i \(0.512917\pi\)
\(864\) 2.03986e7 + 8.08507e6i 0.929641 + 0.368468i
\(865\) −5.36236e6 −0.243678
\(866\) 6.57406e6 1.61061e6i 0.297878 0.0729785i
\(867\) 1.51885e7 8.71605e6i 0.686228 0.393797i
\(868\) 531938. 277287.i 0.0239641 0.0124919i
\(869\) 3.17531e7 + 1.83326e7i 1.42638 + 0.823523i
\(870\) −631068. + 601286.i −0.0282669 + 0.0269329i
\(871\) −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
\(876\) 3.26879e6 5.10765e6i 0.143922 0.224885i
\(877\) −1.80935e7 + 3.13389e7i −0.794373 + 1.37589i 0.128864 + 0.991662i \(0.458867\pi\)
−0.923237 + 0.384231i \(0.874467\pi\)
\(878\) 1.00750e7 9.65006e6i 0.441069 0.422468i
\(879\) 1.84954e7 + 48535.3i 0.807403 + 0.00211878i
\(880\) 1.29407e7 + 9.03968e6i 0.563315 + 0.393501i
\(881\) 4.28630e7i 1.86056i −0.366855 0.930278i \(-0.619566\pi\)
0.366855 0.930278i \(-0.380434\pi\)
\(882\) −1.58830e7 1.67575e7i −0.687482 0.725334i
\(883\) 1.61400e7i 0.696628i 0.937378 + 0.348314i \(0.113246\pi\)
−0.937378 + 0.348314i \(0.886754\pi\)
\(884\) −1.79066e7 771811.i −0.770696 0.0332185i
\(885\) −9.52395e6 + 1.63964e7i −0.408751 + 0.703706i
\(886\) −1.92328e7 2.00797e7i −0.823112 0.859354i
\(887\) 1.19750e7 2.07414e7i 0.511055 0.885173i −0.488863 0.872361i \(-0.662588\pi\)
0.999918 0.0128126i \(-0.00407849\pi\)
\(888\) −8.92599e6 + 2.61415e7i −0.379860 + 1.11250i
\(889\) 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
\(894\) −2.80331e7 + 6.79001e6i −1.17308 + 0.284136i
\(895\) 2.50904e6 + 1.44859e6i 0.104701 + 0.0604489i
\(896\) 357535. + 485625.i 0.0148782 + 0.0202084i
\(897\) 2.68950e7 + 1.56221e7i 1.11607 + 0.648272i
\(898\) −128636. 525059.i −0.00532320 0.0217279i
\(899\) −1.80525e6 −0.0744969
\(900\) −1.47239e7 + 7.57720e6i −0.605921 + 0.311819i
\(901\) −6.36600e6 −0.261249
\(902\) 6.68499e6 + 2.72863e7i 0.273580 + 1.11668i
\(903\) −2536.49 + 966582.i −0.000103518 + 0.0394475i
\(904\) −6.72328e6 + 1.34319e6i −0.273628 + 0.0546660i
\(905\) −1.75083e7 1.01084e7i −0.710594 0.410262i
\(906\) −1.08188e7 + 3.67961e7i −0.437883 + 1.48930i
\(907\) 2.47076e7 1.42649e7i 0.997268 0.575773i 0.0898289 0.995957i \(-0.471368\pi\)
0.907439 + 0.420185i \(0.138035\pi\)
\(908\) 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 \(0.258792\pi\)
0.285396 + 0.958410i \(0.407875\pi\)
\(912\) 1.72814e7 + 1.53819e6i 0.688004 + 0.0612384i
\(913\) 1.24977e7 2.16467e7i 0.496197 0.859438i
\(914\) −1.29499e7 1.35200e7i −0.512743 0.535319i
\(915\) −1.86600e6 3.25168e6i −0.0736815 0.128397i
\(916\) −663466. + 1.53929e7i −0.0261264 + 0.606154i
\(917\) 183274.i 0.00719741i
\(918\) 1.13539e7 2.68708e6i 0.444672 0.105238i
\(919\) 6.66802e6i 0.260440i −0.991485 0.130220i \(-0.958432\pi\)
0.991485 0.130220i \(-0.0415684\pi\)
\(920\) −3.55217e6 + 1.04932e7i −0.138364 + 0.408731i
\(921\) 1.09641e7 + 1.91060e7i 0.425916 + 0.742199i
\(922\) 2.47128e6 2.36705e6i 0.0957401 0.0917024i
\(923\) 3.34785e7 5.79864e7i 1.29349 2.24038i
\(924\) −704064. + 364666.i −0.0271289 + 0.0140513i
\(925\) −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 \(0.403748\pi\)
\(930\) 1.53806e7 + 4.52219e6i 0.583130 + 0.171452i
\(931\) −1.58101e7 9.12799e6i −0.597808 0.345144i
\(932\) 7.49702e6 + 1.43821e7i 0.282715 + 0.542352i
\(933\) 25793.1 9.82899e6i 0.000970063 0.369662i
\(934\) 3.31473e7 8.12090e6i 1.24332 0.304605i
\(935\) 8.39364e6 0.313994
\(936\) 4.27824e7 + 1.47335e7i 1.59616 + 0.549687i
\(937\) 129328. 0.00481219 0.00240609 0.999997i \(-0.499234\pi\)
0.00240609 + 0.999997i \(0.499234\pi\)
\(938\) 91450.7 22404.9i 0.00339375 0.000831449i
\(939\) 5.31739e6 + 3.08863e6i 0.196804 + 0.114315i
\(940\) −1.04744e7 2.00937e7i −0.386642 0.741722i
\(941\) −1.98367e7 1.14527e7i −0.730291 0.421633i 0.0882379 0.996099i \(-0.471876\pi\)
−0.818528 + 0.574466i \(0.805210\pi\)
\(942\) −282278. 1.16541e6i −0.0103645 0.0427908i
\(943\) −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 \(-0.909469\pi\)
0.236914 0.971531i \(-0.423864\pi\)
\(948\) −1.71013e6 + 3.73952e7i −0.0618029 + 1.35143i
\(949\) 6.25249e6 1.08296e7i 0.225366 0.390345i
\(950\) −9.45554e6 + 9.05676e6i −0.339920 + 0.325585i
\(951\) 1.27989e6 2.20346e6i 0.0458903 0.0790048i
\(952\) 303730. + 102819.i 0.0108616 + 0.00367689i
\(953\) 3.01554e7i 1.07556i −0.843086 0.537778i \(-0.819264\pi\)
0.843086 0.537778i \(-0.180736\pi\)
\(954\) 1.54067e7 + 4.57384e6i 0.548075 + 0.162709i
\(955\) 8.76162e6i 0.310868i
\(956\) 413753. 9.59940e6i 0.0146419 0.339703i
\(957\) 2.38614e6 + 6261.67i 0.0842200 + 0.000221009i
\(958\) 1.16076e7 + 1.21187e7i 0.408628 + 0.426621i
\(959\) −685550. + 1.18741e6i −0.0240709 + 0.0416920i
\(960\) −2.11880e6 + 1.59765e7i −0.0742013 + 0.559505i
\(961\) 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
\(966\) −383851. 402864.i −0.0132349 0.0138904i
\(967\) −4.48583e6 2.58989e6i −0.154268 0.0890668i 0.420879 0.907117i \(-0.361722\pi\)
−0.575147 + 0.818050i \(0.695055\pi\)
\(968\) −2.75423e6 1.37861e7i −0.0944739 0.472884i
\(969\) 8.00155e6 4.59174e6i 0.273757 0.157097i
\(970\) −2.62976e6 1.07340e7i −0.0897403 0.366296i
\(971\) 1.12452e7 0.382754 0.191377 0.981517i \(-0.438705\pi\)
0.191377 + 0.981517i \(0.438705\pi\)
\(972\) −2.94090e7 1.65441e6i −0.998421 0.0561667i
\(973\) 1.24910e6 0.0422976
\(974\) −9.69069e6 3.95548e7i −0.327308 1.33598i
\(975\) −2.96172e7 + 1.69960e7i −0.997774 + 0.572579i
\(976\) 7.77659e6 + 671621.i 0.261315 + 0.0225683i
\(977\) 4.56993e7 + 2.63845e7i 1.53170 + 0.884327i 0.999284 + 0.0378433i \(0.0120488\pi\)
0.532415 + 0.846483i \(0.321285\pi\)
\(978\) 2.87943e7 + 3.02205e7i 0.962631 + 1.01031i
\(979\) −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 \(0.0161078\pi\)
−0.455554 + 0.890208i \(0.650559\pi\)
\(984\) −2.15984e7 + 1.88731e7i −0.711105 + 0.621377i
\(985\) −3.88155e6 + 6.72304e6i −0.127472 + 0.220788i
\(986\) −667501. 696891.i −0.0218655 0.0228283i
\(987\) 1.13820e6 + 2986.86i 0.0371901 + 9.75938e-5i
\(988\) 3.57443e7 + 1.54065e6i 1.16497 + 0.0502125i
\(989\) 3.69690e7i 1.20184i
\(990\) −2.03140e7 6.03066e6i −0.658729 0.195559i
\(991\) 3.03835e7i 0.982775i −0.870941 0.491388i \(-0.836490\pi\)
0.870941 0.491388i \(-0.163510\pi\)
\(992\) −2.60017e7 + 2.09283e7i −0.838924 + 0.675234i
\(993\) 6.29344e6 1.08348e7i 0.202542 0.348696i
\(994\) −865097. + 828613.i −0.0277715 + 0.0266002i
\(995\) −4.46959e6 + 7.74156e6i −0.143123 + 0.247897i
\(996\) 2.54930e7 + 1.16583e6i 0.814278 + 0.0372380i
\(997\) −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.23.3 yes 56
3.2 odd 2 108.6.h.a.71.26 56
4.3 odd 2 inner 36.6.h.a.23.8 yes 56
9.2 odd 6 inner 36.6.h.a.11.8 yes 56
9.7 even 3 108.6.h.a.35.21 56
12.11 even 2 108.6.h.a.71.21 56
36.7 odd 6 108.6.h.a.35.26 56
36.11 even 6 inner 36.6.h.a.11.3 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.h.a.11.3 56 36.11 even 6 inner
36.6.h.a.11.8 yes 56 9.2 odd 6 inner
36.6.h.a.23.3 yes 56 1.1 even 1 trivial
36.6.h.a.23.8 yes 56 4.3 odd 2 inner
108.6.h.a.35.21 56 9.7 even 3
108.6.h.a.35.26 56 36.7 odd 6
108.6.h.a.71.21 56 12.11 even 2
108.6.h.a.71.26 56 3.2 odd 2