Properties

Label 43.6.g.a.24.17
Level $43$
Weight $6$
Character 43.24
Analytic conductor $6.897$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,6,Mod(9,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.9");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(17\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 24.17
Character \(\chi\) \(=\) 43.24
Dual form 43.6.g.a.9.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.32555 - 7.93199i) q^{2} +(2.21950 - 0.334535i) q^{3} +(-15.7832 - 69.1506i) q^{4} +(53.6893 - 36.6047i) q^{5} +(11.3860 - 19.7211i) q^{6} +(51.6195 + 89.4076i) q^{7} +(-355.837 - 171.362i) q^{8} +(-227.390 + 70.1405i) q^{9} +O(q^{10})\) \(q+(6.32555 - 7.93199i) q^{2} +(2.21950 - 0.334535i) q^{3} +(-15.7832 - 69.1506i) q^{4} +(53.6893 - 36.6047i) q^{5} +(11.3860 - 19.7211i) q^{6} +(51.6195 + 89.4076i) q^{7} +(-355.837 - 171.362i) q^{8} +(-227.390 + 70.1405i) q^{9} +(49.2659 - 657.407i) q^{10} +(20.3695 - 89.2448i) q^{11} +(-58.1640 - 148.200i) q^{12} +(17.7788 + 237.241i) q^{13} +(1035.70 + 156.107i) q^{14} +(106.918 - 99.2050i) q^{15} +(-1565.15 + 753.738i) q^{16} +(-325.466 - 221.899i) q^{17} +(-882.012 + 2247.33i) q^{18} +(1621.60 + 500.198i) q^{19} +(-3378.63 - 3134.91i) q^{20} +(144.479 + 181.171i) q^{21} +(-579.040 - 726.093i) q^{22} +(1673.07 + 1552.38i) q^{23} +(-847.106 - 261.298i) q^{24} +(400.941 - 1021.58i) q^{25} +(1994.26 + 1359.66i) q^{26} +(-972.642 + 468.400i) q^{27} +(5367.87 - 4980.65i) q^{28} +(8257.74 + 1244.65i) q^{29} +(-110.581 - 1475.59i) q^{30} +(-3376.13 - 8602.24i) q^{31} +(-1109.51 + 4861.07i) q^{32} +(15.3546 - 204.893i) q^{33} +(-3818.85 + 1177.96i) q^{34} +(6044.15 + 2910.71i) q^{35} +(8439.19 + 14617.1i) q^{36} +(-7700.94 + 13338.4i) q^{37} +(14225.1 - 9698.49i) q^{38} +(118.826 + 520.609i) q^{39} +(-25377.3 + 3825.01i) q^{40} +(-3536.56 + 4434.70i) q^{41} +2350.96 q^{42} +(-8795.47 - 8345.55i) q^{43} -6492.83 q^{44} +(-9640.93 + 12089.3i) q^{45} +(22896.5 - 3451.09i) q^{46} +(2559.75 + 11215.0i) q^{47} +(-3221.70 + 2196.52i) q^{48} +(3074.36 - 5324.94i) q^{49} +(-5567.00 - 9642.32i) q^{50} +(-796.603 - 383.624i) q^{51} +(16124.8 - 4973.84i) q^{52} +(767.090 - 10236.1i) q^{53} +(-2437.15 + 10677.9i) q^{54} +(-2173.16 - 5537.11i) q^{55} +(-3047.06 - 40660.2i) q^{56} +(3766.47 + 567.704i) q^{57} +(62107.3 - 57627.2i) q^{58} +(-24967.8 + 12023.8i) q^{59} +(-8547.59 - 5827.65i) q^{60} +(-7680.19 + 19568.8i) q^{61} +(-89588.7 - 27634.5i) q^{62} +(-18008.8 - 16709.8i) q^{63} +(-3120.12 - 3912.51i) q^{64} +(9638.68 + 12086.5i) q^{65} +(-1528.08 - 1417.85i) q^{66} +(-50242.1 - 15497.6i) q^{67} +(-10207.6 + 26008.4i) q^{68} +(4232.69 + 2885.80i) q^{69} +(61320.3 - 29530.3i) q^{70} +(-33932.4 + 31484.6i) q^{71} +(92933.2 + 14007.4i) q^{72} +(438.520 + 5851.64i) q^{73} +(57087.5 + 145457. i) q^{74} +(548.132 - 2401.52i) q^{75} +(8994.96 - 120029. i) q^{76} +(9030.63 - 2785.58i) q^{77} +(4881.10 + 2350.61i) q^{78} +(33115.0 + 57356.9i) q^{79} +(-56441.6 + 97759.7i) q^{80} +(45775.0 - 31208.8i) q^{81} +(12805.3 + 56103.8i) q^{82} +(15506.1 - 2337.18i) q^{83} +(10247.8 - 12850.3i) q^{84} -25596.6 q^{85} +(-121833. + 16975.3i) q^{86} +18744.4 q^{87} +(-22541.4 + 28266.1i) q^{88} +(-103789. + 15643.6i) q^{89} +(34908.3 + 152943. i) q^{90} +(-20293.4 + 13835.8i) q^{91} +(80941.6 - 140195. i) q^{92} +(-10371.1 - 17963.2i) q^{93} +(105149. + 50637.0i) q^{94} +(105372. - 32503.0i) q^{95} +(-836.349 + 11160.3i) q^{96} +(32132.4 - 140781. i) q^{97} +(-22790.4 - 58069.0i) q^{98} +(1627.85 + 21722.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9} + 303 q^{10} - 1340 q^{11} + 858 q^{12} + 814 q^{13} + 1202 q^{14} - 2083 q^{15} - 6248 q^{16} - 214 q^{17} - 174 q^{18} - 246 q^{19} - 17139 q^{20} + 3007 q^{21} + 2118 q^{22} + 3192 q^{23} + 15880 q^{24} + 3652 q^{25} - 1237 q^{26} + 108 q^{27} - 6780 q^{28} - 18827 q^{29} + 98080 q^{30} - 43196 q^{31} - 3930 q^{32} + 28181 q^{33} + 45155 q^{34} + 33275 q^{35} - 49399 q^{36} + 34607 q^{37} - 43374 q^{38} + 15155 q^{39} - 108727 q^{40} + 7156 q^{41} - 48066 q^{42} - 176452 q^{43} + 26068 q^{44} - 96386 q^{45} - 27185 q^{46} + 20402 q^{47} + 198899 q^{48} - 158742 q^{49} + 186243 q^{50} + 98589 q^{51} + 278918 q^{52} + 14102 q^{53} + 270894 q^{54} - 334770 q^{55} + 61999 q^{56} - 202490 q^{57} + 213658 q^{58} - 43753 q^{59} - 389005 q^{60} + 80516 q^{61} + 162349 q^{62} - 75177 q^{63} - 489850 q^{64} + 93726 q^{65} + 246095 q^{66} - 322922 q^{67} + 475089 q^{68} - 397079 q^{69} - 614985 q^{70} - 233345 q^{71} + 379655 q^{72} + 159391 q^{73} + 695938 q^{74} + 344081 q^{75} - 50808 q^{76} + 608177 q^{77} + 605548 q^{78} - 272109 q^{79} + 601054 q^{80} + 193536 q^{81} - 996896 q^{82} + 177813 q^{83} - 919009 q^{84} - 844524 q^{85} - 876752 q^{86} - 188214 q^{87} - 59998 q^{88} - 469041 q^{89} - 453431 q^{90} - 223189 q^{91} - 94922 q^{92} + 569174 q^{93} + 1175168 q^{94} + 435689 q^{95} + 1557688 q^{96} + 643751 q^{97} + 886196 q^{98} + 1422581 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.32555 7.93199i 1.11821 1.40219i 0.213090 0.977033i \(-0.431647\pi\)
0.905119 0.425158i \(-0.139781\pi\)
\(3\) 2.21950 0.334535i 0.142381 0.0214604i −0.0774651 0.996995i \(-0.524683\pi\)
0.219846 + 0.975535i \(0.429445\pi\)
\(4\) −15.7832 69.1506i −0.493224 2.16096i
\(5\) 53.6893 36.6047i 0.960423 0.654805i 0.0218044 0.999762i \(-0.493059\pi\)
0.938618 + 0.344957i \(0.112107\pi\)
\(6\) 11.3860 19.7211i 0.129120 0.223642i
\(7\) 51.6195 + 89.4076i 0.398170 + 0.689651i 0.993500 0.113830i \(-0.0363121\pi\)
−0.595330 + 0.803481i \(0.702979\pi\)
\(8\) −355.837 171.362i −1.96574 0.946651i
\(9\) −227.390 + 70.1405i −0.935761 + 0.288644i
\(10\) 49.2659 657.407i 0.155792 2.07890i
\(11\) 20.3695 89.2448i 0.0507574 0.222383i −0.943188 0.332260i \(-0.892189\pi\)
0.993945 + 0.109878i \(0.0350459\pi\)
\(12\) −58.1640 148.200i −0.116601 0.297094i
\(13\) 17.7788 + 237.241i 0.0291772 + 0.389343i 0.992606 + 0.121379i \(0.0387317\pi\)
−0.963429 + 0.267964i \(0.913649\pi\)
\(14\) 1035.70 + 156.107i 1.41226 + 0.212864i
\(15\) 106.918 99.2050i 0.122693 0.113843i
\(16\) −1565.15 + 753.738i −1.52847 + 0.736072i
\(17\) −325.466 221.899i −0.273139 0.186223i 0.419002 0.907985i \(-0.362380\pi\)
−0.692141 + 0.721762i \(0.743332\pi\)
\(18\) −882.012 + 2247.33i −0.641643 + 1.63488i
\(19\) 1621.60 + 500.198i 1.03053 + 0.317876i 0.763497 0.645812i \(-0.223481\pi\)
0.267032 + 0.963688i \(0.413957\pi\)
\(20\) −3378.63 3134.91i −1.88871 1.75247i
\(21\) 144.479 + 181.171i 0.0714920 + 0.0896481i
\(22\) −579.040 726.093i −0.255066 0.319842i
\(23\) 1673.07 + 1552.38i 0.659467 + 0.611896i 0.937213 0.348758i \(-0.113397\pi\)
−0.277745 + 0.960655i \(0.589587\pi\)
\(24\) −847.106 261.298i −0.300199 0.0925992i
\(25\) 400.941 1021.58i 0.128301 0.326906i
\(26\) 1994.26 + 1359.66i 0.578559 + 0.394455i
\(27\) −972.642 + 468.400i −0.256770 + 0.123654i
\(28\) 5367.87 4980.65i 1.29392 1.20058i
\(29\) 8257.74 + 1244.65i 1.82333 + 0.274823i 0.969387 0.245536i \(-0.0789640\pi\)
0.853947 + 0.520360i \(0.174202\pi\)
\(30\) −110.581 1475.59i −0.0224324 0.299339i
\(31\) −3376.13 8602.24i −0.630979 1.60771i −0.784898 0.619625i \(-0.787285\pi\)
0.153918 0.988084i \(-0.450811\pi\)
\(32\) −1109.51 + 4861.07i −0.191538 + 0.839184i
\(33\) 15.3546 204.893i 0.00245445 0.0327523i
\(34\) −3818.85 + 1177.96i −0.566546 + 0.174756i
\(35\) 6044.15 + 2910.71i 0.833998 + 0.401632i
\(36\) 8439.19 + 14617.1i 1.08529 + 1.87977i
\(37\) −7700.94 + 13338.4i −0.924782 + 1.60177i −0.132870 + 0.991133i \(0.542419\pi\)
−0.791912 + 0.610636i \(0.790914\pi\)
\(38\) 14225.1 9698.49i 1.59807 1.08955i
\(39\) 118.826 + 520.609i 0.0125097 + 0.0548088i
\(40\) −25377.3 + 3825.01i −2.50781 + 0.377992i
\(41\) −3536.56 + 4434.70i −0.328565 + 0.412007i −0.918486 0.395454i \(-0.870587\pi\)
0.589921 + 0.807461i \(0.299159\pi\)
\(42\) 2350.96 0.205647
\(43\) −8795.47 8345.55i −0.725417 0.688310i
\(44\) −6492.83 −0.505595
\(45\) −9640.93 + 12089.3i −0.709721 + 0.889962i
\(46\) 22896.5 3451.09i 1.59542 0.240471i
\(47\) 2559.75 + 11215.0i 0.169026 + 0.740549i 0.986389 + 0.164427i \(0.0525775\pi\)
−0.817364 + 0.576122i \(0.804565\pi\)
\(48\) −3221.70 + 2196.52i −0.201828 + 0.137604i
\(49\) 3074.36 5324.94i 0.182921 0.316829i
\(50\) −5567.00 9642.32i −0.314917 0.545452i
\(51\) −796.603 383.624i −0.0428861 0.0206529i
\(52\) 16124.8 4973.84i 0.826962 0.255084i
\(53\) 767.090 10236.1i 0.0375108 0.500547i −0.946531 0.322612i \(-0.895439\pi\)
0.984042 0.177936i \(-0.0569418\pi\)
\(54\) −2437.15 + 10677.9i −0.113736 + 0.498310i
\(55\) −2173.16 5537.11i −0.0968689 0.246818i
\(56\) −3047.06 40660.2i −0.129841 1.73260i
\(57\) 3766.47 + 567.704i 0.153549 + 0.0231438i
\(58\) 62107.3 57627.2i 2.42422 2.24935i
\(59\) −24967.8 + 12023.8i −0.933791 + 0.449690i −0.837975 0.545709i \(-0.816260\pi\)
−0.0958163 + 0.995399i \(0.530546\pi\)
\(60\) −8547.59 5827.65i −0.306525 0.208985i
\(61\) −7680.19 + 19568.8i −0.264270 + 0.673348i −0.999992 0.00393486i \(-0.998747\pi\)
0.735723 + 0.677283i \(0.236843\pi\)
\(62\) −89588.7 27634.5i −2.95988 0.913002i
\(63\) −18008.8 16709.8i −0.571656 0.530419i
\(64\) −3120.12 3912.51i −0.0952186 0.119400i
\(65\) 9638.68 + 12086.5i 0.282966 + 0.354828i
\(66\) −1528.08 1417.85i −0.0431804 0.0400656i
\(67\) −50242.1 15497.6i −1.36735 0.421773i −0.477745 0.878498i \(-0.658546\pi\)
−0.889608 + 0.456726i \(0.849022\pi\)
\(68\) −10207.6 + 26008.4i −0.267701 + 0.682090i
\(69\) 4232.69 + 2885.80i 0.107027 + 0.0729698i
\(70\) 61320.3 29530.3i 1.49575 0.720315i
\(71\) −33932.4 + 31484.6i −0.798856 + 0.741230i −0.969761 0.244058i \(-0.921521\pi\)
0.170905 + 0.985288i \(0.445331\pi\)
\(72\) 92933.2 + 14007.4i 2.11271 + 0.318440i
\(73\) 438.520 + 5851.64i 0.00963124 + 0.128520i 0.999947 0.0103148i \(-0.00328337\pi\)
−0.990316 + 0.138835i \(0.955664\pi\)
\(74\) 57087.5 + 145457.i 1.21189 + 3.08783i
\(75\) 548.132 2401.52i 0.0112521 0.0492985i
\(76\) 8994.96 120029.i 0.178635 2.38371i
\(77\) 9030.63 2785.58i 0.173577 0.0535413i
\(78\) 4881.10 + 2350.61i 0.0908408 + 0.0437466i
\(79\) 33115.0 + 57356.9i 0.596976 + 1.03399i 0.993265 + 0.115867i \(0.0369647\pi\)
−0.396288 + 0.918126i \(0.629702\pi\)
\(80\) −56441.6 + 97759.7i −0.985994 + 1.70779i
\(81\) 45775.0 31208.8i 0.775203 0.528525i
\(82\) 12805.3 + 56103.8i 0.210308 + 0.921420i
\(83\) 15506.1 2337.18i 0.247064 0.0372388i −0.0243429 0.999704i \(-0.507749\pi\)
0.271406 + 0.962465i \(0.412511\pi\)
\(84\) 10247.8 12850.3i 0.158464 0.198708i
\(85\) −25596.6 −0.384268
\(86\) −121833. + 16975.3i −1.77631 + 0.247498i
\(87\) 18744.4 0.265506
\(88\) −22541.4 + 28266.1i −0.310295 + 0.389098i
\(89\) −103789. + 15643.6i −1.38891 + 0.209345i −0.800556 0.599257i \(-0.795463\pi\)
−0.588356 + 0.808602i \(0.700225\pi\)
\(90\) 34908.3 + 152943.i 0.454279 + 1.99033i
\(91\) −20293.4 + 13835.8i −0.256893 + 0.175147i
\(92\) 80941.6 140195.i 0.997016 1.72688i
\(93\) −10371.1 17963.2i −0.124341 0.215366i
\(94\) 105149. + 50637.0i 1.22740 + 0.591083i
\(95\) 105372. 32503.0i 1.19789 0.369500i
\(96\) −836.349 + 11160.3i −0.00926210 + 0.123594i
\(97\) 32132.4 140781.i 0.346748 1.51920i −0.437766 0.899089i \(-0.644230\pi\)
0.784514 0.620112i \(-0.212913\pi\)
\(98\) −22790.4 58069.0i −0.239710 0.610772i
\(99\) 1627.85 + 21722.1i 0.0166927 + 0.222748i
\(100\) −76971.1 11601.5i −0.769711 0.116015i
\(101\) −37253.3 + 34566.0i −0.363380 + 0.337167i −0.840640 0.541595i \(-0.817821\pi\)
0.477260 + 0.878762i \(0.341630\pi\)
\(102\) −8081.85 + 3892.01i −0.0769149 + 0.0370403i
\(103\) −26289.7 17924.0i −0.244170 0.166472i 0.435052 0.900405i \(-0.356730\pi\)
−0.679222 + 0.733933i \(0.737682\pi\)
\(104\) 34327.8 87465.9i 0.311217 0.792968i
\(105\) 14388.7 + 4438.33i 0.127365 + 0.0392868i
\(106\) −76340.4 70833.6i −0.659918 0.612314i
\(107\) −23881.6 29946.6i −0.201653 0.252865i 0.670714 0.741716i \(-0.265988\pi\)
−0.872367 + 0.488851i \(0.837416\pi\)
\(108\) 47741.5 + 59865.9i 0.393855 + 0.493879i
\(109\) 49554.3 + 45979.7i 0.399498 + 0.370680i 0.854183 0.519972i \(-0.174058\pi\)
−0.454685 + 0.890652i \(0.650248\pi\)
\(110\) −57666.7 17787.8i −0.454405 0.140165i
\(111\) −12630.0 + 32180.8i −0.0972965 + 0.247907i
\(112\) −148182. 101029.i −1.11622 0.761029i
\(113\) 229841. 110686.i 1.69329 0.815446i 0.698264 0.715840i \(-0.253956\pi\)
0.995027 0.0996062i \(-0.0317583\pi\)
\(114\) 28328.0 26284.6i 0.204152 0.189426i
\(115\) 146650. + 22103.9i 1.03404 + 0.155857i
\(116\) −44264.8 590673.i −0.305431 4.07570i
\(117\) −20682.9 52699.3i −0.139684 0.355910i
\(118\) −62561.9 + 274101.i −0.413623 + 1.81220i
\(119\) 3039.06 40553.4i 0.0196730 0.262519i
\(120\) −55045.2 + 16979.2i −0.348953 + 0.107638i
\(121\) 137552. + 66241.7i 0.854091 + 0.411309i
\(122\) 106638. + 184703.i 0.648653 + 1.12350i
\(123\) −6365.81 + 11025.9i −0.0379394 + 0.0657130i
\(124\) −541564. + 369232.i −3.16298 + 2.15648i
\(125\) 29317.4 + 128448.i 0.167823 + 0.735279i
\(126\) −246457. + 37147.5i −1.38298 + 0.208451i
\(127\) 32936.4 41301.0i 0.181204 0.227222i −0.682931 0.730483i \(-0.739295\pi\)
0.864135 + 0.503261i \(0.167866\pi\)
\(128\) −210325. −1.13466
\(129\) −22313.4 15580.5i −0.118057 0.0824343i
\(130\) 156840. 0.813952
\(131\) 115853. 145275.i 0.589832 0.739625i −0.393923 0.919143i \(-0.628882\pi\)
0.983755 + 0.179518i \(0.0574538\pi\)
\(132\) −14410.8 + 2172.08i −0.0719869 + 0.0108503i
\(133\) 38984.8 + 170803.i 0.191102 + 0.837274i
\(134\) −440736. + 300488.i −2.12039 + 1.44566i
\(135\) −35074.8 + 60751.3i −0.165638 + 0.286894i
\(136\) 77787.8 + 134732.i 0.360632 + 0.624633i
\(137\) −172309. 82979.4i −0.784342 0.377719i −0.00154696 0.999999i \(-0.500492\pi\)
−0.782795 + 0.622280i \(0.786207\pi\)
\(138\) 49664.2 15319.4i 0.221996 0.0684768i
\(139\) 14730.4 196563.i 0.0646661 0.862909i −0.866701 0.498828i \(-0.833764\pi\)
0.931367 0.364081i \(-0.118617\pi\)
\(140\) 105881. 463897.i 0.456562 2.00033i
\(141\) 9433.15 + 24035.3i 0.0399585 + 0.101813i
\(142\) 35094.9 + 468309.i 0.146057 + 1.94900i
\(143\) 21534.7 + 3245.84i 0.0880641 + 0.0132735i
\(144\) 303033. 281173.i 1.21782 1.12997i
\(145\) 488912. 235448.i 1.93113 0.929982i
\(146\) 49189.0 + 33536.5i 0.190979 + 0.130207i
\(147\) 5042.15 12847.2i 0.0192452 0.0490359i
\(148\) 1.04390e6 + 322002.i 3.91748 + 1.20838i
\(149\) −105128. 97544.6i −0.387930 0.359946i 0.461965 0.886898i \(-0.347144\pi\)
−0.849895 + 0.526952i \(0.823335\pi\)
\(150\) −15581.6 19538.7i −0.0565437 0.0709036i
\(151\) −121549. 152418.i −0.433821 0.543994i 0.516082 0.856539i \(-0.327390\pi\)
−0.949903 + 0.312545i \(0.898819\pi\)
\(152\) −491311. 455870.i −1.72483 1.60041i
\(153\) 89571.8 + 27629.2i 0.309345 + 0.0954202i
\(154\) 35028.5 89251.1i 0.119020 0.303258i
\(155\) −496145. 338266.i −1.65874 1.13091i
\(156\) 34125.0 16433.7i 0.112269 0.0540660i
\(157\) −300683. + 278993.i −0.973553 + 0.903325i −0.995339 0.0964378i \(-0.969255\pi\)
0.0217864 + 0.999763i \(0.493065\pi\)
\(158\) 664425. + 100146.i 2.11740 + 0.319147i
\(159\) −1721.79 22975.6i −0.00540115 0.0720733i
\(160\) 118370. + 301601.i 0.365544 + 0.931392i
\(161\) −52431.6 + 229718.i −0.159415 + 0.698441i
\(162\) 42003.6 560499.i 0.125747 1.67798i
\(163\) −544437. + 167937.i −1.60501 + 0.495081i −0.962520 0.271211i \(-0.912576\pi\)
−0.642493 + 0.766292i \(0.722100\pi\)
\(164\) 362480. + 174561.i 1.05239 + 0.506802i
\(165\) −6675.67 11562.6i −0.0190891 0.0330633i
\(166\) 79546.4 137778.i 0.224053 0.388071i
\(167\) −231757. + 158009.i −0.643044 + 0.438420i −0.840441 0.541904i \(-0.817704\pi\)
0.197396 + 0.980324i \(0.436751\pi\)
\(168\) −20365.2 89225.7i −0.0556692 0.243903i
\(169\) 311179. 46902.6i 0.838094 0.126322i
\(170\) −161912. + 203032.i −0.429692 + 0.538817i
\(171\) −403820. −1.05608
\(172\) −438279. + 739931.i −1.12961 + 1.90709i
\(173\) 447700. 1.13729 0.568646 0.822582i \(-0.307467\pi\)
0.568646 + 0.822582i \(0.307467\pi\)
\(174\) 118569. 148680.i 0.296891 0.372289i
\(175\) 112033. 16886.3i 0.276537 0.0416812i
\(176\) 35385.8 + 155035.i 0.0861087 + 0.377267i
\(177\) −51393.5 + 35039.5i −0.123303 + 0.0840668i
\(178\) −532435. + 922204.i −1.25955 + 2.18161i
\(179\) −164076. 284188.i −0.382747 0.662938i 0.608707 0.793395i \(-0.291689\pi\)
−0.991454 + 0.130458i \(0.958355\pi\)
\(180\) 988150. + 475868.i 2.27322 + 1.09472i
\(181\) 157920. 48711.9i 0.358296 0.110520i −0.110381 0.993889i \(-0.535207\pi\)
0.468677 + 0.883370i \(0.344731\pi\)
\(182\) −18621.5 + 248487.i −0.0416712 + 0.556063i
\(183\) −10499.7 + 46002.2i −0.0231766 + 0.101543i
\(184\) −329320. 839094.i −0.717090 1.82712i
\(185\) 74791.3 + 998021.i 0.160665 + 2.14393i
\(186\) −208087. 31364.0i −0.441024 0.0664736i
\(187\) −26432.9 + 24526.2i −0.0552766 + 0.0512892i
\(188\) 735122. 354016.i 1.51693 0.730514i
\(189\) −92085.7 62783.0i −0.187516 0.127846i
\(190\) 408723. 1.04141e6i 0.821383 2.09285i
\(191\) −357272. 110204.i −0.708624 0.218581i −0.0805671 0.996749i \(-0.525673\pi\)
−0.628056 + 0.778168i \(0.716149\pi\)
\(192\) −8233.97 7640.01i −0.0161197 0.0149569i
\(193\) −90081.9 112959.i −0.174078 0.218287i 0.687137 0.726528i \(-0.258867\pi\)
−0.861215 + 0.508241i \(0.830296\pi\)
\(194\) −913419. 1.14539e6i −1.74247 2.18499i
\(195\) 25436.4 + 23601.5i 0.0479037 + 0.0444481i
\(196\) −416746. 128549.i −0.774875 0.239017i
\(197\) 28298.2 72102.6i 0.0519509 0.132369i −0.902542 0.430601i \(-0.858302\pi\)
0.954493 + 0.298232i \(0.0963969\pi\)
\(198\) 182596. + 124492.i 0.331001 + 0.225673i
\(199\) 631823. 304270.i 1.13100 0.544661i 0.227726 0.973725i \(-0.426871\pi\)
0.903274 + 0.429064i \(0.141157\pi\)
\(200\) −317730. + 294810.i −0.561673 + 0.521156i
\(201\) −116697. 17589.2i −0.203736 0.0307083i
\(202\) 38529.6 + 514141.i 0.0664378 + 0.886551i
\(203\) 314979. + 802553.i 0.536465 + 1.36689i
\(204\) −13954.9 + 61140.4i −0.0234775 + 0.102862i
\(205\) −27544.1 + 367551.i −0.0457766 + 0.610847i
\(206\) −308469. + 95150.2i −0.506459 + 0.156222i
\(207\) −489323. 235645.i −0.793724 0.382237i
\(208\) −206644. 357919.i −0.331181 0.573622i
\(209\) 77671.4 134531.i 0.122997 0.213037i
\(210\) 126221. 86056.2i 0.197508 0.134658i
\(211\) −153653. 673200.i −0.237594 1.04097i −0.943164 0.332328i \(-0.892166\pi\)
0.705569 0.708641i \(-0.250691\pi\)
\(212\) −719940. + 108514.i −1.10016 + 0.165823i
\(213\) −64780.0 + 81231.6i −0.0978345 + 0.122681i
\(214\) −388601. −0.580055
\(215\) −777709. 126111.i −1.14742 0.186061i
\(216\) 426368. 0.621799
\(217\) 594831. 745895.i 0.857521 1.07530i
\(218\) 678168. 102217.i 0.966487 0.145675i
\(219\) 2930.87 + 12841.0i 0.00412940 + 0.0180921i
\(220\) −348595. + 237668.i −0.485585 + 0.331066i
\(221\) 46857.2 81159.1i 0.0645351 0.111778i
\(222\) 175366. + 303742.i 0.238815 + 0.413640i
\(223\) −262616. 126469.i −0.353637 0.170303i 0.248627 0.968599i \(-0.420021\pi\)
−0.602265 + 0.798296i \(0.705735\pi\)
\(224\) −491889. + 151728.i −0.655009 + 0.202043i
\(225\) −19515.7 + 260420.i −0.0256997 + 0.342939i
\(226\) 575914. 2.52324e6i 0.750044 3.28616i
\(227\) 307495. + 783485.i 0.396071 + 1.00917i 0.980288 + 0.197576i \(0.0633068\pi\)
−0.584216 + 0.811598i \(0.698598\pi\)
\(228\) −20189.8 269414.i −0.0257214 0.343228i
\(229\) 1.17208e6 + 176662.i 1.47696 + 0.222615i 0.837595 0.546292i \(-0.183961\pi\)
0.639361 + 0.768907i \(0.279199\pi\)
\(230\) 1.10297e6 1.02341e6i 1.37481 1.27564i
\(231\) 19111.6 9203.65i 0.0235649 0.0113483i
\(232\) −2.72512e6 1.85796e6i −3.32404 2.26629i
\(233\) −179092. + 456320.i −0.216116 + 0.550655i −0.997283 0.0736675i \(-0.976530\pi\)
0.781167 + 0.624322i \(0.214625\pi\)
\(234\) −548841. 169295.i −0.655250 0.202118i
\(235\) 547952. + 508425.i 0.647251 + 0.600561i
\(236\) 1.22553e6 + 1.53676e6i 1.43233 + 1.79608i
\(237\) 92686.5 + 116225.i 0.107188 + 0.134409i
\(238\) −302445. 280628.i −0.346102 0.321136i
\(239\) −1.07299e6 330974.i −1.21507 0.374799i −0.380022 0.924978i \(-0.624083\pi\)
−0.835047 + 0.550179i \(0.814560\pi\)
\(240\) −92567.8 + 235859.i −0.103737 + 0.264316i
\(241\) 1.26903e6 + 865211.i 1.40744 + 0.959576i 0.998903 + 0.0468342i \(0.0149133\pi\)
0.408537 + 0.912742i \(0.366039\pi\)
\(242\) 1.39552e6 672047.i 1.53179 0.737669i
\(243\) 283459. 263012.i 0.307946 0.285732i
\(244\) 1.47441e6 + 222232.i 1.58542 + 0.238964i
\(245\) −29858.1 398428.i −0.0317795 0.424068i
\(246\) 47190.1 + 120238.i 0.0497179 + 0.126679i
\(247\) −89837.5 + 393604.i −0.0936948 + 0.410504i
\(248\) −272746. + 3.63954e6i −0.281597 + 3.75766i
\(249\) 33634.0 10374.7i 0.0343779 0.0106042i
\(250\) 1.20430e6 + 579959.i 1.21866 + 0.586877i
\(251\) 697803. + 1.20863e6i 0.699115 + 1.21090i 0.968774 + 0.247947i \(0.0797559\pi\)
−0.269658 + 0.962956i \(0.586911\pi\)
\(252\) −871254. + 1.50906e6i −0.864258 + 1.49694i
\(253\) 172621. 117691.i 0.169548 0.115596i
\(254\) −119258. 522502.i −0.115985 0.508164i
\(255\) −56811.5 + 8562.96i −0.0547124 + 0.00824657i
\(256\) −1.23058e6 + 1.54310e6i −1.17357 + 1.47161i
\(257\) −688445. −0.650184 −0.325092 0.945682i \(-0.605395\pi\)
−0.325092 + 0.945682i \(0.605395\pi\)
\(258\) −264729. + 78434.1i −0.247601 + 0.0733594i
\(259\) −1.59007e6 −1.47288
\(260\) 683662. 857285.i 0.627203 0.786487i
\(261\) −1.96503e6 + 296180.i −1.78553 + 0.269126i
\(262\) −419485. 1.83788e6i −0.377540 1.65411i
\(263\) 814368. 555226.i 0.725991 0.494972i −0.143048 0.989716i \(-0.545690\pi\)
0.869039 + 0.494744i \(0.164738\pi\)
\(264\) −40574.6 + 70277.3i −0.0358298 + 0.0620591i
\(265\) −333505. 577648.i −0.291735 0.505300i
\(266\) 1.60141e6 + 771198.i 1.38771 + 0.668285i
\(267\) −225125. + 69441.9i −0.193262 + 0.0596134i
\(268\) −278691. + 3.71887e6i −0.237021 + 3.16282i
\(269\) −67466.2 + 295589.i −0.0568467 + 0.249062i −0.995365 0.0961673i \(-0.969342\pi\)
0.938518 + 0.345229i \(0.112199\pi\)
\(270\) 260011. + 662498.i 0.217062 + 0.553064i
\(271\) −115858. 1.54602e6i −0.0958305 1.27877i −0.813162 0.582038i \(-0.802256\pi\)
0.717331 0.696732i \(-0.245363\pi\)
\(272\) 676658. + 101990.i 0.554558 + 0.0835861i
\(273\) −40412.6 + 37497.5i −0.0328179 + 0.0304506i
\(274\) −1.74814e6 + 841859.i −1.40669 + 0.677428i
\(275\) −83003.8 56591.1i −0.0661861 0.0451249i
\(276\) 132749. 338240.i 0.104896 0.267271i
\(277\) 1.85353e6 + 571738.i 1.45144 + 0.447711i 0.917475 0.397794i \(-0.130224\pi\)
0.533968 + 0.845505i \(0.320700\pi\)
\(278\) −1.46596e6 1.36021e6i −1.13765 1.05559i
\(279\) 1.37106e6 + 1.71926e6i 1.05450 + 1.32230i
\(280\) −1.65195e6 2.07148e6i −1.25922 1.57901i
\(281\) 28348.0 + 26303.1i 0.0214169 + 0.0198720i 0.690809 0.723038i \(-0.257255\pi\)
−0.669392 + 0.742910i \(0.733445\pi\)
\(282\) 250317. + 77212.7i 0.187443 + 0.0578184i
\(283\) 950409. 2.42160e6i 0.705414 1.79737i 0.110026 0.993929i \(-0.464907\pi\)
0.595388 0.803438i \(-0.296998\pi\)
\(284\) 2.71274e6 + 1.84952e6i 1.99578 + 1.36070i
\(285\) 223000. 107391.i 0.162627 0.0783170i
\(286\) 161965. 150281.i 0.117086 0.108640i
\(287\) −579051. 87277.9i −0.414966 0.0625460i
\(288\) −88667.1 1.18318e6i −0.0629914 0.840562i
\(289\) −462043. 1.17727e6i −0.325415 0.829144i
\(290\) 1.22507e6 5.36738e6i 0.855394 3.74772i
\(291\) 24221.4 323213.i 0.0167675 0.223746i
\(292\) 397723. 122681.i 0.272976 0.0842018i
\(293\) −247590. 119233.i −0.168486 0.0811385i 0.347740 0.937591i \(-0.386949\pi\)
−0.516226 + 0.856452i \(0.672663\pi\)
\(294\) −70009.3 121260.i −0.0472376 0.0818178i
\(295\) −900372. + 1.55949e6i −0.602375 + 1.04334i
\(296\) 5.02598e6 3.42665e6i 3.33420 2.27322i
\(297\) 21990.0 + 96344.3i 0.0144655 + 0.0633775i
\(298\) −1.43872e6 + 216851.i −0.938500 + 0.141456i
\(299\) −338543. + 424520.i −0.218996 + 0.274612i
\(300\) −174718. −0.112082
\(301\) 292138. 1.21717e6i 0.185854 0.774349i
\(302\) −1.97785e6 −1.24789
\(303\) −71120.0 + 89181.6i −0.0445026 + 0.0558044i
\(304\) −2.91507e6 + 439377.i −1.80911 + 0.272680i
\(305\) 303967. + 1.33177e6i 0.187101 + 0.819744i
\(306\) 785745. 535712.i 0.479709 0.327060i
\(307\) 201901. 349703.i 0.122262 0.211765i −0.798397 0.602131i \(-0.794318\pi\)
0.920660 + 0.390367i \(0.127652\pi\)
\(308\) −335157. 580508.i −0.201313 0.348684i
\(309\) −64346.0 30987.4i −0.0383377 0.0184624i
\(310\) −5.82151e6 + 1.79570e6i −3.44058 + 1.06128i
\(311\) 33891.4 452249.i 0.0198696 0.265141i −0.978418 0.206637i \(-0.933748\pi\)
0.998287 0.0585036i \(-0.0186329\pi\)
\(312\) 46930.1 205614.i 0.0272938 0.119582i
\(313\) 322151. + 820827.i 0.185865 + 0.473577i 0.993187 0.116535i \(-0.0371788\pi\)
−0.807321 + 0.590112i \(0.799084\pi\)
\(314\) 310984. + 4.14979e6i 0.177998 + 2.37521i
\(315\) −1.57854e6 237926.i −0.896352 0.135103i
\(316\) 3.44360e6 3.19520e6i 1.93997 1.80003i
\(317\) −152158. + 73275.4i −0.0850446 + 0.0409553i −0.475923 0.879487i \(-0.657886\pi\)
0.390878 + 0.920443i \(0.372171\pi\)
\(318\) −193134. 131676.i −0.107100 0.0730196i
\(319\) 279285. 711608.i 0.153664 0.391529i
\(320\) −310733. 95848.6i −0.169634 0.0523252i
\(321\) −63023.4 58477.2i −0.0341381 0.0316755i
\(322\) 1.49046e6 + 1.86898e6i 0.801088 + 1.00453i
\(323\) −416783. 522629.i −0.222281 0.278732i
\(324\) −2.88059e6 2.67279e6i −1.52447 1.41450i
\(325\) 249490. + 76957.3i 0.131022 + 0.0404149i
\(326\) −2.11179e6 + 5.38076e6i −1.10054 + 2.80414i
\(327\) 125367. + 85474.0i 0.0648358 + 0.0442043i
\(328\) 2.01838e6 971999.i 1.03590 0.498863i
\(329\) −870571. + 807772.i −0.443419 + 0.411433i
\(330\) −133942. 20188.5i −0.0677066 0.0102051i
\(331\) −18902.1 252230.i −0.00948285 0.126540i 0.990453 0.137849i \(-0.0440190\pi\)
−0.999936 + 0.0113096i \(0.996400\pi\)
\(332\) −406353. 1.03537e6i −0.202329 0.515526i
\(333\) 815553. 3.57317e6i 0.403034 1.76581i
\(334\) −212662. + 2.83778e6i −0.104310 + 1.39192i
\(335\) −3.26475e6 + 1.00704e6i −1.58942 + 0.490270i
\(336\) −362688. 174661.i −0.175261 0.0844012i
\(337\) 227602. + 394219.i 0.109170 + 0.189087i 0.915434 0.402468i \(-0.131847\pi\)
−0.806264 + 0.591555i \(0.798514\pi\)
\(338\) 1.59634e6 2.76495e6i 0.760037 1.31642i
\(339\) 473103. 322556.i 0.223592 0.152443i
\(340\) 403995. + 1.77002e6i 0.189530 + 0.830387i
\(341\) −836476. + 126078.i −0.389554 + 0.0587158i
\(342\) −2.55438e6 + 3.20309e6i −1.18092 + 1.48083i
\(343\) 2.36992e6 1.08768
\(344\) 1.69964e6 + 4.47687e6i 0.774393 + 2.03975i
\(345\) 332884. 0.150572
\(346\) 2.83195e6 3.55115e6i 1.27173 1.59470i
\(347\) −688897. + 103835.i −0.307136 + 0.0462933i −0.300802 0.953687i \(-0.597254\pi\)
−0.00633413 + 0.999980i \(0.502016\pi\)
\(348\) −295846. 1.29619e6i −0.130954 0.573746i
\(349\) 1.84323e6 1.25670e6i 0.810059 0.552289i −0.0859630 0.996298i \(-0.527397\pi\)
0.896022 + 0.444009i \(0.146444\pi\)
\(350\) 574731. 995463.i 0.250781 0.434365i
\(351\) −128416. 222423.i −0.0556355 0.0963635i
\(352\) 411225. + 198036.i 0.176898 + 0.0851897i
\(353\) −3.24161e6 + 999905.i −1.38460 + 0.427093i −0.895472 0.445119i \(-0.853161\pi\)
−0.489129 + 0.872211i \(0.662685\pi\)
\(354\) −47159.2 + 629296.i −0.0200013 + 0.266899i
\(355\) −669318. + 2.93247e6i −0.281878 + 1.23499i
\(356\) 2.71988e6 + 6.93014e6i 1.13743 + 2.89813i
\(357\) −6821.37 91024.8i −0.00283270 0.0377998i
\(358\) −3.29204e6 496196.i −1.35756 0.204619i
\(359\) 2.72186e6 2.52552e6i 1.11463 1.03422i 0.115464 0.993312i \(-0.463164\pi\)
0.999163 0.0409113i \(-0.0130261\pi\)
\(360\) 5.50225e6 2.64975e6i 2.23761 1.07758i
\(361\) 333544. + 227407.i 0.134706 + 0.0918407i
\(362\) 612550. 1.56075e6i 0.245680 0.625982i
\(363\) 327457. + 101007.i 0.130433 + 0.0402333i
\(364\) 1.27705e6 + 1.18493e6i 0.505190 + 0.468748i
\(365\) 237741. + 298118.i 0.0934056 + 0.117127i
\(366\) 298472. + 374272.i 0.116467 + 0.146044i
\(367\) −1.01122e6 938277.i −0.391905 0.363635i 0.459469 0.888194i \(-0.348040\pi\)
−0.851374 + 0.524559i \(0.824230\pi\)
\(368\) −3.78869e6 1.16866e6i −1.45838 0.449850i
\(369\) 493125. 1.25646e6i 0.188535 0.480378i
\(370\) 8.38938e6 + 5.71978e6i 3.18585 + 2.17208i
\(371\) 954783. 459799.i 0.360139 0.173434i
\(372\) −1.07848e6 + 1.00068e6i −0.404068 + 0.374920i
\(373\) −405564. 61129.0i −0.150934 0.0227497i 0.0731405 0.997322i \(-0.476698\pi\)
−0.224075 + 0.974572i \(0.571936\pi\)
\(374\) 27338.5 + 364807.i 0.0101064 + 0.134860i
\(375\) 108040. + 275282.i 0.0396741 + 0.101088i
\(376\) 1.01097e6 4.42935e6i 0.368781 1.61574i
\(377\) −148471. + 1.98121e6i −0.0538007 + 0.717921i
\(378\) −1.08049e6 + 333286.i −0.388946 + 0.119974i
\(379\) −2.60603e6 1.25500e6i −0.931925 0.448791i −0.0946112 0.995514i \(-0.530161\pi\)
−0.837314 + 0.546723i \(0.815875\pi\)
\(380\) −3.91071e6 6.77355e6i −1.38930 2.40634i
\(381\) 59285.6 102686.i 0.0209236 0.0362408i
\(382\) −3.13408e6 + 2.13678e6i −1.09888 + 0.749205i
\(383\) −461621. 2.02249e6i −0.160801 0.704515i −0.989465 0.144769i \(-0.953756\pi\)
0.828665 0.559746i \(-0.189101\pi\)
\(384\) −466816. + 70361.2i −0.161554 + 0.0243503i
\(385\) 382882. 480119.i 0.131648 0.165081i
\(386\) −1.46581e6 −0.500736
\(387\) 2.58536e6 + 1.28078e6i 0.877494 + 0.434706i
\(388\) −1.02423e7 −3.45395
\(389\) 1.80809e6 2.26727e6i 0.605822 0.759677i −0.380450 0.924801i \(-0.624231\pi\)
0.986273 + 0.165124i \(0.0528025\pi\)
\(390\) 348106. 52468.6i 0.115891 0.0174678i
\(391\) −200055. 876497.i −0.0661770 0.289940i
\(392\) −2.00646e6 + 1.36798e6i −0.659502 + 0.449641i
\(393\) 208535. 361194.i 0.0681080 0.117966i
\(394\) −392915. 680549.i −0.127514 0.220861i
\(395\) 3.87745e6 + 1.86728e6i 1.25041 + 0.602168i
\(396\) 1.47640e6 455410.i 0.473116 0.145937i
\(397\) −241719. + 3.22552e6i −0.0769724 + 1.02712i 0.816306 + 0.577620i \(0.196019\pi\)
−0.893278 + 0.449505i \(0.851601\pi\)
\(398\) 1.58316e6 6.93628e6i 0.500977 2.19492i
\(399\) 143666. + 366056.i 0.0451775 + 0.115111i
\(400\) 142470. + 1.90114e6i 0.0445220 + 0.594105i
\(401\) 2.96258e6 + 446537.i 0.920046 + 0.138675i 0.591954 0.805971i \(-0.298357\pi\)
0.328091 + 0.944646i \(0.393595\pi\)
\(402\) −877687. + 814375.i −0.270879 + 0.251339i
\(403\) 1.98078e6 953895.i 0.607540 0.292576i
\(404\) 2.97823e6 + 2.03053e6i 0.907832 + 0.618949i
\(405\) 1.31523e6 3.35116e6i 0.398442 1.01521i
\(406\) 8.35825e6 + 2.57818e6i 2.51652 + 0.776244i
\(407\) 1.03352e6 + 958966.i 0.309266 + 0.286957i
\(408\) 217722. + 273015.i 0.0647519 + 0.0811964i
\(409\) 1.21318e6 + 1.52128e6i 0.358606 + 0.449677i 0.928107 0.372313i \(-0.121435\pi\)
−0.569502 + 0.821990i \(0.692864\pi\)
\(410\) 2.74117e6 + 2.54344e6i 0.805336 + 0.747242i
\(411\) −410198. 126529.i −0.119781 0.0369476i
\(412\) −824521. + 2.10084e6i −0.239309 + 0.609749i
\(413\) −2.36385e6 1.61164e6i −0.681937 0.464937i
\(414\) −4.96437e6 + 2.39072e6i −1.42352 + 0.685531i
\(415\) 746962. 693079.i 0.212901 0.197543i
\(416\) −1.17297e6 176797.i −0.332319 0.0500890i
\(417\) −33063.3 441199.i −0.00931120 0.124249i
\(418\) −575782. 1.46707e6i −0.161182 0.410686i
\(419\) −851662. + 3.73137e6i −0.236991 + 1.03833i 0.706704 + 0.707510i \(0.250181\pi\)
−0.943695 + 0.330817i \(0.892676\pi\)
\(420\) 79813.6 1.06504e6i 0.0220777 0.294606i
\(421\) 2.05105e6 632667.i 0.563991 0.173968i 0.000367308 1.00000i \(-0.499883\pi\)
0.563624 + 0.826032i \(0.309407\pi\)
\(422\) −6.31175e6 3.03958e6i −1.72532 0.830869i
\(423\) −1.36868e6 2.37063e6i −0.371923 0.644189i
\(424\) −2.02704e6 + 3.51094e6i −0.547580 + 0.948437i
\(425\) −357180. + 243521.i −0.0959213 + 0.0653981i
\(426\) 234559. + 1.02767e6i 0.0626221 + 0.274365i
\(427\) −2.14605e6 + 323464.i −0.569599 + 0.0858533i
\(428\) −1.69390e6 + 2.12408e6i −0.446970 + 0.560482i
\(429\) 48882.1 0.0128235
\(430\) −5.91974e6 + 5.37105e6i −1.54394 + 1.40084i
\(431\) 3.19023e6 0.827235 0.413618 0.910451i \(-0.364265\pi\)
0.413618 + 0.910451i \(0.364265\pi\)
\(432\) 1.16928e6 1.46623e6i 0.301447 0.378002i
\(433\) −2.61410e6 + 394012.i −0.670042 + 0.100993i −0.475248 0.879852i \(-0.657642\pi\)
−0.194794 + 0.980844i \(0.562404\pi\)
\(434\) −2.15379e6 9.43639e6i −0.548883 2.40481i
\(435\) 1.00637e6 686134.i 0.254998 0.173854i
\(436\) 2.39740e6 4.15241e6i 0.603982 1.04613i
\(437\) 1.93655e6 + 3.35420e6i 0.485093 + 0.840206i
\(438\) 120394. + 57978.7i 0.0299861 + 0.0144405i
\(439\) −1.12289e6 + 346367.i −0.278085 + 0.0857778i −0.430661 0.902514i \(-0.641719\pi\)
0.152576 + 0.988292i \(0.451243\pi\)
\(440\) −175562. + 2.34271e6i −0.0432312 + 0.576881i
\(441\) −325584. + 1.42648e6i −0.0797198 + 0.349275i
\(442\) −347355. 885046.i −0.0845703 0.215482i
\(443\) 6860.19 + 91542.9i 0.00166084 + 0.0221623i 0.997973 0.0636443i \(-0.0202723\pi\)
−0.996312 + 0.0858066i \(0.972653\pi\)
\(444\) 2.42466e6 + 365459.i 0.583706 + 0.0879795i
\(445\) −4.99971e6 + 4.63905e6i −1.19686 + 1.11053i
\(446\) −2.66434e6 + 1.28308e6i −0.634238 + 0.305433i
\(447\) −265964. 181331.i −0.0629584 0.0429243i
\(448\) 188749. 480924.i 0.0444313 0.113209i
\(449\) 924643. + 285215.i 0.216450 + 0.0667661i 0.401084 0.916041i \(-0.368634\pi\)
−0.184633 + 0.982807i \(0.559110\pi\)
\(450\) 1.94220e6 + 1.80209e6i 0.452128 + 0.419514i
\(451\) 323736. + 405952.i 0.0749462 + 0.0939796i
\(452\) −1.12816e7 1.41467e7i −2.59732 3.25693i
\(453\) −320768. 297629.i −0.0734421 0.0681443i
\(454\) 8.15967e6 + 2.51692e6i 1.85794 + 0.573100i
\(455\) −583083. + 1.48567e6i −0.132039 + 0.336430i
\(456\) −1.24297e6 847441.i −0.279929 0.190852i
\(457\) −3.95586e6 + 1.90504e6i −0.886033 + 0.426691i −0.820824 0.571181i \(-0.806486\pi\)
−0.0652088 + 0.997872i \(0.520771\pi\)
\(458\) 8.81531e6 8.17941e6i 1.96369 1.82204i
\(459\) 420499. + 63380.0i 0.0931608 + 0.0140417i
\(460\) −786103. 1.04898e7i −0.173215 2.31139i
\(461\) 1.09655e6 + 2.79395e6i 0.240312 + 0.612304i 0.999244 0.0388649i \(-0.0123742\pi\)
−0.758933 + 0.651169i \(0.774279\pi\)
\(462\) 47888.0 209811.i 0.0104381 0.0457323i
\(463\) −319415. + 4.26230e6i −0.0692473 + 0.924041i 0.849092 + 0.528246i \(0.177150\pi\)
−0.918339 + 0.395795i \(0.870469\pi\)
\(464\) −1.38628e7 + 4.27610e6i −2.98920 + 0.922047i
\(465\) −1.21435e6 584802.i −0.260443 0.125423i
\(466\) 2.48667e6 + 4.30703e6i 0.530460 + 0.918783i
\(467\) 2.77011e6 4.79797e6i 0.587766 1.01804i −0.406759 0.913536i \(-0.633341\pi\)
0.994524 0.104505i \(-0.0333257\pi\)
\(468\) −3.31775e6 + 2.26200e6i −0.700210 + 0.477395i
\(469\) −1.20786e6 5.29200e6i −0.253563 1.11093i
\(470\) 7.49892e6 1.13028e6i 1.56586 0.236016i
\(471\) −574031. + 719813.i −0.119229 + 0.149509i
\(472\) 1.09449e7 2.26129
\(473\) −923957. + 614955.i −0.189889 + 0.126383i
\(474\) 1.50819e6 0.308326
\(475\) 1.16116e6 1.45605e6i 0.236134 0.296102i
\(476\) −2.85226e6 + 429909.i −0.576994 + 0.0869679i
\(477\) 543537. + 2.38139e6i 0.109379 + 0.479220i
\(478\) −9.41252e6 + 6.41735e6i −1.88424 + 1.28465i
\(479\) −537588. + 931131.i −0.107056 + 0.185426i −0.914576 0.404413i \(-0.867476\pi\)
0.807520 + 0.589840i \(0.200809\pi\)
\(480\) 363617. + 629803.i 0.0720346 + 0.124768i
\(481\) −3.30134e6 1.58984e6i −0.650620 0.313322i
\(482\) 1.48902e7 4.59301e6i 2.91932 0.900491i
\(483\) −39523.0 + 527398.i −0.00770872 + 0.102866i
\(484\) 2.40964e6 1.05573e7i 0.467562 2.04852i
\(485\) −3.42809e6 8.73463e6i −0.661756 1.68613i
\(486\) −293170. 3.91209e6i −0.0563027 0.751307i
\(487\) 4.18642e6 + 631001.i 0.799872 + 0.120561i 0.536244 0.844063i \(-0.319843\pi\)
0.263628 + 0.964624i \(0.415081\pi\)
\(488\) 6.08625e6 5.64721e6i 1.15691 1.07346i
\(489\) −1.15219e6 + 554868.i −0.217898 + 0.104934i
\(490\) −3.34920e6 2.28344e6i −0.630160 0.429636i
\(491\) −2.16952e6 + 5.52785e6i −0.406125 + 1.03479i 0.570777 + 0.821105i \(0.306642\pi\)
−0.976903 + 0.213685i \(0.931453\pi\)
\(492\) 862921. + 266176.i 0.160716 + 0.0495742i
\(493\) −2.41143e6 2.23748e6i −0.446845 0.414611i
\(494\) 2.55379e6 + 3.20235e6i 0.470834 + 0.590407i
\(495\) 882530. + 1.10666e6i 0.161889 + 0.203002i
\(496\) 1.17680e7 + 1.09191e7i 2.14782 + 1.99289i
\(497\) −4.56654e6 1.40859e6i −0.829270 0.255796i
\(498\) 130461. 332410.i 0.0235726 0.0600621i
\(499\) −4.19751e6 2.86181e6i −0.754641 0.514505i 0.123829 0.992304i \(-0.460483\pi\)
−0.878470 + 0.477798i \(0.841435\pi\)
\(500\) 8.41954e6 4.05464e6i 1.50613 0.725315i
\(501\) −461523. + 428231.i −0.0821484 + 0.0762226i
\(502\) 1.40008e7 + 2.11029e6i 2.47967 + 0.373751i
\(503\) 638076. + 8.51454e6i 0.112448 + 1.50052i 0.713131 + 0.701030i \(0.247276\pi\)
−0.600683 + 0.799487i \(0.705105\pi\)
\(504\) 3.54479e6 + 9.03199e6i 0.621605 + 1.58382i
\(505\) −734823. + 3.21947e6i −0.128219 + 0.561766i
\(506\) 158399. 2.11369e6i 0.0275028 0.366999i
\(507\) 674969. 208200.i 0.116618 0.0359718i
\(508\) −3.37583e6 1.62571e6i −0.580391 0.279502i
\(509\) −4.14350e6 7.17676e6i −0.708881 1.22782i −0.965273 0.261245i \(-0.915867\pi\)
0.256392 0.966573i \(-0.417466\pi\)
\(510\) −291443. + 504793.i −0.0496167 + 0.0859386i
\(511\) −500545. + 341266.i −0.0847990 + 0.0578150i
\(512\) 2.95808e6 + 1.29602e7i 0.498695 + 2.18492i
\(513\) −1.81153e6 + 273044.i −0.303915 + 0.0458078i
\(514\) −4.35479e6 + 5.46073e6i −0.727042 + 0.911682i
\(515\) −2.06758e6 −0.343513
\(516\) −725227. + 1.78889e6i −0.119908 + 0.295774i
\(517\) 1.05302e6 0.173265
\(518\) −1.00581e7 + 1.26124e7i −1.64699 + 2.06526i
\(519\) 993669. 149772.i 0.161929 0.0244068i
\(520\) −1.35863e6 5.95254e6i −0.220340 0.965370i
\(521\) −7.85448e6 + 5.35509e6i −1.26772 + 0.864316i −0.995203 0.0978352i \(-0.968808\pi\)
−0.272516 + 0.962151i \(0.587856\pi\)
\(522\) −1.00806e7 + 1.74601e7i −1.61923 + 2.80459i
\(523\) 2.40579e6 + 4.16694e6i 0.384594 + 0.666137i 0.991713 0.128475i \(-0.0410081\pi\)
−0.607119 + 0.794611i \(0.707675\pi\)
\(524\) −1.18744e7 5.71839e6i −1.88922 0.909799i
\(525\) 243009. 74958.3i 0.0384790 0.0118692i
\(526\) 747273. 9.97166e6i 0.117765 1.57146i
\(527\) −810012. + 3.54890e6i −0.127047 + 0.556630i
\(528\) 130403. + 332262.i 0.0203565 + 0.0518676i
\(529\) −91717.6 1.22389e6i −0.0142499 0.190152i
\(530\) −6.69150e6 1.00858e6i −1.03475 0.155963i
\(531\) 4.83406e6 4.48535e6i 0.744005 0.690336i
\(532\) 1.11959e7 5.39164e6i 1.71506 0.825927i
\(533\) −1.11497e6 760174.i −0.169999 0.115903i
\(534\) −873228. + 2.22495e6i −0.132518 + 0.337650i
\(535\) −2.37838e6 733632.i −0.359249 0.110814i
\(536\) 1.52223e7 + 1.41242e7i 2.28859 + 2.12350i
\(537\) −459237. 575864.i −0.0687228 0.0861756i
\(538\) 1.91784e6 + 2.40490e6i 0.285665 + 0.358213i
\(539\) −412600. 382837.i −0.0611727 0.0567600i
\(540\) 4.75458e6 + 1.46659e6i 0.701662 + 0.216434i
\(541\) 116501. 296839.i 0.0171134 0.0436042i −0.922062 0.387043i \(-0.873497\pi\)
0.939175 + 0.343439i \(0.111592\pi\)
\(542\) −1.29959e7 8.86045e6i −1.90024 1.29556i
\(543\) 334208. 160946.i 0.0486426 0.0234250i
\(544\) 1.43977e6 1.33591e6i 0.208592 0.193545i
\(545\) 4.34361e6 + 654693.i 0.626411 + 0.0944162i
\(546\) 41797.2 + 557744.i 0.00600019 + 0.0800670i
\(547\) −1.07221e6 2.73195e6i −0.153219 0.390395i 0.833569 0.552416i \(-0.186294\pi\)
−0.986787 + 0.162021i \(0.948199\pi\)
\(548\) −3.01850e6 + 1.32249e7i −0.429378 + 1.88123i
\(549\) 373832. 4.98844e6i 0.0529353 0.706373i
\(550\) −973924. + 300416.i −0.137284 + 0.0423464i
\(551\) 1.27682e7 + 6.14884e6i 1.79164 + 0.862808i
\(552\) −1.01163e6 1.75220e6i −0.141310 0.244757i
\(553\) −3.41876e6 + 5.92146e6i −0.475396 + 0.823410i
\(554\) 1.62596e7 1.10856e7i 2.25079 1.53456i
\(555\) 499872. + 2.19008e6i 0.0688853 + 0.301806i
\(556\) −1.38249e7 + 2.08377e6i −1.89660 + 0.285867i
\(557\) −3.73031e6 + 4.67766e6i −0.509456 + 0.638837i −0.968333 0.249662i \(-0.919680\pi\)
0.458877 + 0.888500i \(0.348252\pi\)
\(558\) 2.23099e7 3.03327
\(559\) 1.82354e6 2.23502e6i 0.246823 0.302519i
\(560\) −1.16539e7 −1.57037
\(561\) −50462.9 + 63278.5i −0.00676963 + 0.00848885i
\(562\) 387952. 58474.4i 0.0518128 0.00780953i
\(563\) 1.43975e6 + 6.30795e6i 0.191433 + 0.838721i 0.975842 + 0.218477i \(0.0701090\pi\)
−0.784410 + 0.620243i \(0.787034\pi\)
\(564\) 1.51317e6 1.03166e6i 0.200304 0.136565i
\(565\) 8.28839e6 1.43559e7i 1.09232 1.89195i
\(566\) −1.31963e7 2.28566e7i −1.73145 2.99896i
\(567\) 5.15319e6 + 2.48164e6i 0.673160 + 0.324177i
\(568\) 1.74697e7 5.38868e6i 2.27203 0.700828i
\(569\) 253906. 3.38814e6i 0.0328770 0.438713i −0.956340 0.292256i \(-0.905594\pi\)
0.989217 0.146457i \(-0.0467870\pi\)
\(570\) 558772. 2.44814e6i 0.0720356 0.315609i
\(571\) −3.42699e6 8.73183e6i −0.439868 1.12077i −0.963235 0.268659i \(-0.913420\pi\)
0.523367 0.852107i \(-0.324676\pi\)
\(572\) −115435. 1.54037e6i −0.0147518 0.196850i
\(573\) −829831. 125077.i −0.105585 0.0159144i
\(574\) −4.35510e6 + 4.04094e6i −0.551720 + 0.511921i
\(575\) 2.25668e6 1.08676e6i 0.284643 0.137077i
\(576\) 983910. + 670818.i 0.123566 + 0.0842459i
\(577\) −4.45862e6 + 1.13604e7i −0.557521 + 1.42054i 0.322939 + 0.946420i \(0.395329\pi\)
−0.880460 + 0.474121i \(0.842766\pi\)
\(578\) −1.22607e7 3.78194e6i −1.52650 0.470863i
\(579\) −237725. 220577.i −0.0294699 0.0273441i
\(580\) −2.39980e7 3.00925e7i −2.96213 3.71439i
\(581\) 1.00938e6 + 1.26572e6i 0.124055 + 0.155560i
\(582\) −2.41050e6 2.23662e6i −0.294985 0.273706i
\(583\) −897895. 276964.i −0.109409 0.0337483i
\(584\) 846708. 2.15738e6i 0.102731 0.261754i
\(585\) −3.03950e6 2.07229e6i −0.367208 0.250358i
\(586\) −2.51189e6 + 1.20966e6i −0.302174 + 0.145519i
\(587\) −5.80254e6 + 5.38397e6i −0.695061 + 0.644922i −0.946408 0.322975i \(-0.895317\pi\)
0.251347 + 0.967897i \(0.419127\pi\)
\(588\) −967971. 145898.i −0.115457 0.0174023i
\(589\) −1.17192e6 1.56381e7i −0.139190 1.85736i
\(590\) 6.67451e6 + 1.70064e7i 0.789385 + 2.01132i
\(591\) 38686.9 169498.i 0.00455612 0.0199617i
\(592\) 1.99948e6 2.66812e7i 0.234483 3.12896i
\(593\) 308353. 95114.3i 0.0360090 0.0111073i −0.276698 0.960957i \(-0.589240\pi\)
0.312707 + 0.949850i \(0.398764\pi\)
\(594\) 903300. + 435007.i 0.105043 + 0.0505859i
\(595\) −1.32128e6 2.28853e6i −0.153004 0.265011i
\(596\) −5.08602e6 + 8.80924e6i −0.586492 + 1.01583i
\(597\) 1.30054e6 886693.i 0.149344 0.101821i
\(598\) 1.22581e6 + 5.37064e6i 0.140175 + 0.614148i
\(599\) 283304. 42701.2i 0.0322616 0.00486265i −0.132892 0.991131i \(-0.542426\pi\)
0.165153 + 0.986268i \(0.447188\pi\)
\(600\) −606576. + 760622.i −0.0687871 + 0.0862563i
\(601\) −1.03167e6 −0.116508 −0.0582538 0.998302i \(-0.518553\pi\)
−0.0582538 + 0.998302i \(0.518553\pi\)
\(602\) −7.80668e6 1.00165e7i −0.877961 1.12649i
\(603\) 1.25116e7 1.40126
\(604\) −8.62137e6 + 1.08109e7i −0.961577 + 1.20578i
\(605\) 9.80984e6 1.47859e6i 1.08962 0.164233i
\(606\) 257515. + 1.12824e6i 0.0284853 + 0.124802i
\(607\) −1.03224e7 + 7.03767e6i −1.13712 + 0.775277i −0.977298 0.211868i \(-0.932045\pi\)
−0.159824 + 0.987145i \(0.551093\pi\)
\(608\) −4.23068e6 + 7.32775e6i −0.464142 + 0.803918i
\(609\) 967577. + 1.67589e6i 0.105716 + 0.183106i
\(610\) 1.24863e7 + 6.01309e6i 1.35866 + 0.654294i
\(611\) −2.61515e6 + 806666.i −0.283396 + 0.0874160i
\(612\) 496851. 6.63002e6i 0.0536226 0.715544i
\(613\) 1.58402e6 6.94005e6i 0.170259 0.745953i −0.815633 0.578569i \(-0.803611\pi\)
0.985892 0.167383i \(-0.0535317\pi\)
\(614\) −1.49670e6 3.81354e6i −0.160219 0.408232i
\(615\) 61824.6 + 824991.i 0.00659133 + 0.0879552i
\(616\) −3.69078e6 556295.i −0.391891 0.0590681i
\(617\) 320850. 297705.i 0.0339304 0.0314828i −0.663025 0.748597i \(-0.730728\pi\)
0.696956 + 0.717114i \(0.254537\pi\)
\(618\) −652816. + 314379.i −0.0687574 + 0.0331118i
\(619\) 5.67299e6 + 3.86778e6i 0.595093 + 0.405728i 0.823071 0.567939i \(-0.192259\pi\)
−0.227977 + 0.973666i \(0.573211\pi\)
\(620\) −1.55605e7 + 3.96476e7i −1.62572 + 4.14227i
\(621\) −2.35443e6 726244.i −0.244994 0.0755708i
\(622\) −3.37285e6 3.12955e6i −0.349559 0.324344i
\(623\) −6.75617e6 8.47197e6i −0.697398 0.874509i
\(624\) −578383. 725269.i −0.0594640 0.0745655i
\(625\) 8.78984e6 + 8.15578e6i 0.900080 + 0.835152i
\(626\) 8.54856e6 + 2.63688e6i 0.871881 + 0.268940i
\(627\) 127386. 324574.i 0.0129406 0.0329720i
\(628\) 2.40383e7 + 1.63890e7i 2.43223 + 1.65826i
\(629\) 5.46617e6 2.63237e6i 0.550880 0.265290i
\(630\) −1.18723e7 + 1.10159e7i −1.19175 + 1.10578i
\(631\) 9.53006e6 + 1.43643e6i 0.952845 + 0.143618i 0.607025 0.794683i \(-0.292363\pi\)
0.345820 + 0.938301i \(0.387601\pi\)
\(632\) −1.95475e6 2.60844e7i −0.194670 2.59769i
\(633\) −566242. 1.44276e6i −0.0561685 0.143115i
\(634\) −381263. + 1.67042e6i −0.0376705 + 0.165045i
\(635\) 256522. 3.42305e6i 0.0252459 0.336883i
\(636\) −1.56160e6 + 481691.i −0.153083 + 0.0472200i
\(637\) 1.31796e6 + 634694.i 0.128692 + 0.0619749i
\(638\) −3.87783e6 6.71660e6i −0.377170 0.653277i
\(639\) 5.50753e6 9.53932e6i 0.533586 0.924199i
\(640\) −1.12922e7 + 7.69889e6i −1.08975 + 0.742982i
\(641\) 418314. + 1.83275e6i 0.0402121 + 0.176181i 0.991046 0.133520i \(-0.0426281\pi\)
−0.950834 + 0.309701i \(0.899771\pi\)
\(642\) −862498. + 130001.i −0.0825887 + 0.0124482i
\(643\) 1.10384e7 1.38417e7i 1.05288 1.32027i 0.107534 0.994201i \(-0.465704\pi\)
0.945346 0.326069i \(-0.105724\pi\)
\(644\) 1.67127e7 1.58793
\(645\) −1.76831e6 19731.5i −0.167363 0.00186750i
\(646\) −6.78186e6 −0.639393
\(647\) −1.78691e6 + 2.24072e6i −0.167820 + 0.210439i −0.858629 0.512598i \(-0.828683\pi\)
0.690809 + 0.723037i \(0.257255\pi\)
\(648\) −2.16364e7 + 3.26117e6i −2.02418 + 0.305096i
\(649\) 564484. + 2.47316e6i 0.0526065 + 0.230484i
\(650\) 2.18858e6 1.49215e6i 0.203179 0.138525i
\(651\) 1.07070e6 1.85450e6i 0.0990181 0.171504i
\(652\) 2.02059e7 + 3.49976e7i 1.86148 + 3.22418i
\(653\) 1.35163e7 + 6.50913e6i 1.24044 + 0.597365i 0.934933 0.354824i \(-0.115459\pi\)
0.305508 + 0.952189i \(0.401174\pi\)
\(654\) 1.47100e6 453742.i 0.134483 0.0414825i
\(655\) 902307. 1.20404e7i 0.0821771 1.09658i
\(656\) 2.19265e6 9.60663e6i 0.198934 0.871588i
\(657\) −510152. 1.29985e6i −0.0461090 0.117484i
\(658\) 900397. + 1.20150e7i 0.0810717 + 1.08183i
\(659\) −9.51352e6 1.43393e6i −0.853351 0.128622i −0.292222 0.956350i \(-0.594395\pi\)
−0.561129 + 0.827728i \(0.689633\pi\)
\(660\) −694198. + 644121.i −0.0620331 + 0.0575583i
\(661\) −1.89007e7 + 9.10209e6i −1.68257 + 0.810284i −0.685996 + 0.727605i \(0.740633\pi\)
−0.996576 + 0.0826785i \(0.973653\pi\)
\(662\) −2.12025e6 1.44556e6i −0.188037 0.128201i
\(663\) 76848.8 195808.i 0.00678975 0.0173000i
\(664\) −5.91816e6 1.82551e6i −0.520915 0.160681i
\(665\) 8.34527e6 + 7.74328e6i 0.731790 + 0.679002i
\(666\) −2.31835e7 2.90712e7i −2.02532 2.53967i
\(667\) 1.18836e7 + 1.49015e7i 1.03427 + 1.29693i
\(668\) 1.45843e7 + 1.35322e7i 1.26457 + 1.17335i
\(669\) −625183. 192843.i −0.0540059 0.0166586i
\(670\) −1.26635e7 + 3.22660e7i −1.08985 + 2.77689i
\(671\) 1.58997e6 + 1.08402e6i 0.136327 + 0.0929465i
\(672\) −1.04099e6 + 501313.i −0.0889247 + 0.0428239i
\(673\) 8.43740e6 7.82877e6i 0.718077 0.666278i −0.233965 0.972245i \(-0.575170\pi\)
0.952042 + 0.305967i \(0.0989796\pi\)
\(674\) 4.56665e6 + 688311.i 0.387211 + 0.0583627i
\(675\) 88536.2 + 1.18143e6i 0.00747931 + 0.0998044i
\(676\) −8.15473e6 2.07779e7i −0.686346 1.74878i
\(677\) −3.34032e6 + 1.46349e7i −0.280102 + 1.22721i 0.617559 + 0.786524i \(0.288122\pi\)
−0.897662 + 0.440685i \(0.854736\pi\)
\(678\) 434125. 5.79299e6i 0.0362694 0.483982i
\(679\) 1.42456e7 4.39417e6i 1.18578 0.365765i
\(680\) 9.10821e6 + 4.38628e6i 0.755372 + 0.363768i
\(681\) 944588. + 1.63607e6i 0.0780503 + 0.135187i
\(682\) −4.29112e6 + 7.43243e6i −0.353272 + 0.611885i
\(683\) 1.31434e7 8.96102e6i 1.07809 0.735031i 0.112125 0.993694i \(-0.464234\pi\)
0.965968 + 0.258663i \(0.0832820\pi\)
\(684\) 6.37356e6 + 2.79244e7i 0.520885 + 2.28215i
\(685\) −1.22886e7 + 1.85220e6i −1.00063 + 0.150821i
\(686\) 1.49911e7 1.87982e7i 1.21625 1.52513i
\(687\) 2.66052e6 0.215068
\(688\) 2.00566e7 + 6.43259e6i 1.61542 + 0.518101i
\(689\) 2.44207e6 0.195979
\(690\) 2.10567e6 2.64043e6i 0.168371 0.211131i
\(691\) −2.23263e7 + 3.36515e6i −1.77878 + 0.268108i −0.954529 0.298118i \(-0.903641\pi\)
−0.824250 + 0.566226i \(0.808403\pi\)
\(692\) −7.06613e6 3.09588e7i −0.560940 2.45764i
\(693\) −1.85809e6 + 1.26683e6i −0.146972 + 0.100204i
\(694\) −3.53404e6 + 6.12114e6i −0.278530 + 0.482429i
\(695\) −6.40427e6 1.10925e7i −0.502930 0.871101i
\(696\) −6.66996e6 3.21208e6i −0.521915 0.251341i
\(697\) 2.13508e6 658586.i 0.166469 0.0513488i
\(698\) 1.69137e6 2.25698e7i 0.131402 1.75343i
\(699\) −244840. + 1.07271e6i −0.0189535 + 0.0830406i
\(700\) −2.93594e6 7.48066e6i −0.226466 0.577025i
\(701\) −1.80965e6 2.41481e7i −0.139091 1.85604i −0.434500 0.900672i \(-0.643075\pi\)
0.295409 0.955371i \(-0.404544\pi\)
\(702\) −2.57656e6 388354.i −0.197332 0.0297430i
\(703\) −1.91597e7 + 1.77776e7i −1.46218 + 1.35670i
\(704\) −412727. + 198759.i −0.0313856 + 0.0151145i
\(705\) 1.38626e6 + 945139.i 0.105044 + 0.0716181i
\(706\) −1.25737e7 + 3.20374e7i −0.949408 + 2.41905i
\(707\) −5.01345e6 1.54645e6i −0.377215 0.116355i
\(708\) 3.23415e6 + 3.00086e6i 0.242481 + 0.224989i
\(709\) 7.01541e6 + 8.79705e6i 0.524128 + 0.657236i 0.971480 0.237122i \(-0.0762041\pi\)
−0.447351 + 0.894358i \(0.647633\pi\)
\(710\) 1.90265e7 + 2.38585e7i 1.41649 + 1.77622i
\(711\) −1.15531e7 1.07197e7i −0.857083 0.795257i
\(712\) 3.96126e7 + 1.22189e7i 2.92842 + 0.903297i
\(713\) 7.70544e6 1.96331e7i 0.567641 1.44633i
\(714\) −765157. 521675.i −0.0561700 0.0382961i
\(715\) 1.27500e6 614006.i 0.0932704 0.0449166i
\(716\) −1.70621e7 + 1.58313e7i −1.24380 + 1.15408i
\(717\) −2.49222e6 375642.i −0.181046 0.0272883i
\(718\) −2.81511e6 3.75650e7i −0.203791 2.71940i
\(719\) −5.67471e6 1.44589e7i −0.409375 1.04307i −0.975743 0.218919i \(-0.929747\pi\)
0.566368 0.824153i \(-0.308348\pi\)
\(720\) 5.97733e6 2.61884e7i 0.429711 1.88269i
\(721\) 245481. 3.27572e6i 0.0175865 0.234676i
\(722\) 3.91364e6 1.20720e6i 0.279407 0.0861857i
\(723\) 3.10605e6 + 1.49580e6i 0.220985 + 0.106421i
\(724\) −5.86094e6 1.01515e7i −0.415548 0.719750i
\(725\) 4.58238e6 7.93692e6i 0.323777 0.560799i
\(726\) 2.87253e6 1.95846e6i 0.202266 0.137903i
\(727\) −750726. 3.28915e6i −0.0526800 0.230806i 0.941734 0.336360i \(-0.109196\pi\)
−0.994414 + 0.105553i \(0.966339\pi\)
\(728\) 9.59210e6 1.44578e6i 0.670788 0.101105i
\(729\) −7.85264e6 + 9.84690e6i −0.547264 + 0.686247i
\(730\) 3.86852e6 0.268681
\(731\) 1.01076e6 + 4.66790e6i 0.0699605 + 0.323093i
\(732\) 3.34680e6 0.230862
\(733\) −3.98214e6 + 4.99344e6i −0.273751 + 0.343273i −0.899635 0.436643i \(-0.856167\pi\)
0.625883 + 0.779917i \(0.284739\pi\)
\(734\) −1.38389e7 + 2.08588e6i −0.948118 + 0.142906i
\(735\) −199558. 874322.i −0.0136255 0.0596971i
\(736\) −9.40250e6 + 6.41052e6i −0.639807 + 0.436213i
\(737\) −2.40649e6 + 4.16817e6i −0.163198 + 0.282668i
\(738\) −6.84695e6 1.18593e7i −0.462761 0.801525i
\(739\) 2.47560e6 + 1.19218e6i 0.166751 + 0.0803031i 0.515397 0.856951i \(-0.327644\pi\)
−0.348646 + 0.937254i \(0.613359\pi\)
\(740\) 6.78333e7 2.09238e7i 4.55369 1.40463i
\(741\) −67719.7 + 903656.i −0.00453074 + 0.0604585i
\(742\) 2.39240e6 1.04818e7i 0.159523 0.698918i
\(743\) 7.91587e6 + 2.01693e7i 0.526050 + 1.34035i 0.909082 + 0.416618i \(0.136785\pi\)
−0.383032 + 0.923735i \(0.625120\pi\)
\(744\) 612196. + 8.16918e6i 0.0405469 + 0.541061i
\(745\) −9.21485e6 1.38891e6i −0.608271 0.0916822i
\(746\) −3.05029e6 + 2.83026e6i −0.200675 + 0.186200i
\(747\) −3.36201e6 + 1.61906e6i −0.220444 + 0.106160i
\(748\) 2.11319e6 + 1.44075e6i 0.138097 + 0.0941532i
\(749\) 1.44470e6 3.68103e6i 0.0940962 0.239753i
\(750\) 2.86695e6 + 884337.i 0.186109 + 0.0574069i
\(751\) −2.84077e6 2.63585e6i −0.183796 0.170538i 0.582909 0.812538i \(-0.301914\pi\)
−0.766705 + 0.642000i \(0.778105\pi\)
\(752\) −1.24596e7 1.56238e7i −0.803448 1.00749i
\(753\) 1.95310e6 + 2.44911e6i 0.125527 + 0.157406i
\(754\) 1.47757e7 + 1.37099e7i 0.946501 + 0.878224i
\(755\) −1.21051e7 3.73394e6i −0.772862 0.238396i
\(756\) −2.88808e6 + 7.35870e6i −0.183783 + 0.468270i
\(757\) −2.01813e7 1.37594e7i −1.28000 0.872689i −0.283723 0.958906i \(-0.591570\pi\)
−0.996276 + 0.0862179i \(0.972522\pi\)
\(758\) −2.64392e7 + 1.27324e7i −1.67138 + 0.804893i
\(759\) 343760. 318963.i 0.0216597 0.0200972i
\(760\) −4.30651e7 6.49102e6i −2.70453 0.407642i
\(761\) 2.13865e6 + 2.85383e7i 0.133868 + 1.78635i 0.510390 + 0.859943i \(0.329501\pi\)
−0.376522 + 0.926408i \(0.622880\pi\)
\(762\) −439488. 1.11980e6i −0.0274195 0.0698637i
\(763\) −1.55296e6 + 6.80397e6i −0.0965717 + 0.423108i
\(764\) −1.98177e6 + 2.64449e7i −0.122835 + 1.63911i
\(765\) 5.82040e6 1.79536e6i 0.359583 0.110917i
\(766\) −1.89624e7 9.13181e6i −1.16767 0.562322i
\(767\) −3.29645e6 5.70962e6i −0.202329 0.350444i
\(768\) −2.21504e6 + 3.83657e6i −0.135512 + 0.234714i
\(769\) −1.60600e7 + 1.09495e7i −0.979332 + 0.667697i −0.943400 0.331657i \(-0.892392\pi\)
−0.0359316 + 0.999354i \(0.511440\pi\)
\(770\) −1.38636e6 6.07404e6i −0.0842653 0.369191i
\(771\) −1.52800e6 + 230309.i −0.0925737 + 0.0139532i
\(772\) −6.38941e6 + 8.01207e6i −0.385849 + 0.483840i
\(773\) 4.10525e6 0.247111 0.123555 0.992338i \(-0.460570\pi\)
0.123555 + 0.992338i \(0.460570\pi\)
\(774\) 2.65129e7 1.24054e7i 1.59076 0.744321i
\(775\) −1.01415e7 −0.606525
\(776\) −3.55584e7 + 4.45889e7i −2.11977 + 2.65811i
\(777\) −3.52916e6 + 531936.i −0.209710 + 0.0316087i
\(778\) −6.54681e6 2.86834e7i −0.387776 1.69896i
\(779\) −7.95311e6 + 5.42234e6i −0.469563 + 0.320142i
\(780\) 1.23059e6 2.13145e6i 0.0724232 0.125441i
\(781\) 2.11865e6 + 3.66962e6i 0.124289 + 0.215275i
\(782\) −8.21782e6 3.95749e6i −0.480551 0.231421i
\(783\) −8.61482e6 + 2.65732e6i −0.502160 + 0.154896i
\(784\) −798228. + 1.06516e7i −0.0463807 + 0.618907i
\(785\) −5.93098e6 + 2.59853e7i −0.343520 + 1.50506i
\(786\) −1.54588e6 3.93884e6i −0.0892525 0.227412i
\(787\) 1.65759e6 + 2.21190e7i 0.0953980 + 1.27300i 0.815347 + 0.578972i \(0.196546\pi\)
−0.719949 + 0.694027i \(0.755835\pi\)
\(788\) −5.43258e6 818829.i −0.311667 0.0469762i
\(789\) 1.62174e6 1.50476e6i 0.0927448 0.0860546i
\(790\) 3.93383e7 1.89443e7i 2.24258 1.07997i
\(791\) 2.17604e7 + 1.48360e7i 1.23659 + 0.843093i
\(792\) 3.14310e6 8.00848e6i 0.178051 0.453667i
\(793\) −4.77907e6 1.47415e6i −0.269874 0.0832451i
\(794\) 2.40558e7 + 2.23205e7i 1.35415 + 1.25647i
\(795\) −933458. 1.17052e6i −0.0523814 0.0656842i
\(796\) −3.10126e7 3.88886e7i −1.73483 2.17540i
\(797\) 3.57221e6 + 3.31453e6i 0.199201 + 0.184832i 0.773466 0.633838i \(-0.218521\pi\)
−0.574265 + 0.818670i \(0.694712\pi\)
\(798\) 3.81232e6 + 1.17594e6i 0.211925 + 0.0653701i
\(799\) 1.65548e6 4.21810e6i 0.0917397 0.233749i
\(800\) 4.52113e6 + 3.08246e6i 0.249760 + 0.170283i
\(801\) 2.25032e7 1.08370e7i 1.23926 0.596798i
\(802\) 2.22819e7 2.06746e7i 1.22325 1.13501i
\(803\) 531161. + 80059.6i 0.0290695 + 0.00438152i
\(804\) 625540. + 8.34726e6i 0.0341283 + 0.455411i
\(805\) 5.59374e6 + 1.42526e7i 0.304237 + 0.775184i
\(806\) 4.96326e6 2.17455e7i 0.269110 1.17905i
\(807\) −50856.1 + 678628.i −0.00274890 + 0.0366816i
\(808\) 1.91794e7 5.91606e6i 1.03349 0.318790i
\(809\) −1.93400e7 9.31366e6i −1.03893 0.500321i −0.164958 0.986301i \(-0.552749\pi\)
−0.873970 + 0.485979i \(0.838463\pi\)
\(810\) −1.82618e7 3.16303e7i −0.977981 1.69391i
\(811\) 1.43470e7 2.48497e7i 0.765963 1.32669i −0.173773 0.984786i \(-0.555596\pi\)
0.939736 0.341901i \(-0.111071\pi\)
\(812\) 5.05257e7 3.44478e7i 2.68919 1.83346i
\(813\) −774346. 3.39263e6i −0.0410874 0.180016i
\(814\) 1.41441e7 2.13188e6i 0.748193 0.112772i
\(815\) −2.30831e7 + 2.89453e7i −1.21731 + 1.52646i
\(816\) 1.53596e6 0.0807522
\(817\) −1.00883e7 1.79326e7i −0.528766 0.939916i
\(818\) 1.97408e7 1.03153
\(819\) 3.64407e6 4.56952e6i 0.189835 0.238046i
\(820\) 2.58511e7 3.89642e6i 1.34259 0.202363i
\(821\) −5.89685e6 2.58358e7i −0.305325 1.33772i −0.861967 0.506964i \(-0.830768\pi\)
0.556643 0.830752i \(-0.312089\pi\)
\(822\) −3.59835e6 + 2.45332e6i −0.185748 + 0.126641i
\(823\) 9.41317e6 1.63041e7i 0.484436 0.839068i −0.515404 0.856947i \(-0.672358\pi\)
0.999840 + 0.0178796i \(0.00569156\pi\)
\(824\) 6.28335e6 + 1.08831e7i 0.322384 + 0.558385i
\(825\) −203158. 97835.9i −0.0103920 0.00500453i
\(826\) −2.77361e7 + 8.55547e6i −1.41448 + 0.436308i
\(827\) 872398. 1.16413e7i 0.0443558 0.591888i −0.930100 0.367307i \(-0.880280\pi\)
0.974456 0.224580i \(-0.0721012\pi\)
\(828\) −8.57196e6 + 3.75562e7i −0.434514 + 1.90373i
\(829\) −188674. 480733.i −0.00953510 0.0242950i 0.926027 0.377457i \(-0.123202\pi\)
−0.935562 + 0.353162i \(0.885106\pi\)
\(830\) −772553. 1.03090e7i −0.0389254 0.519423i
\(831\) 4.30517e6 + 648900.i 0.216266 + 0.0325968i
\(832\) 872737. 809782.i 0.0437094 0.0405564i
\(833\) −2.18220e6 + 1.05089e6i −0.108964 + 0.0524741i
\(834\) −3.70872e6 2.52857e6i −0.184633 0.125881i
\(835\) −6.65897e6 + 1.69668e7i −0.330515 + 0.842137i
\(836\) −1.05288e7 3.24770e6i −0.521030 0.160716i
\(837\) 7.31305e6 + 6.78552e6i 0.360815 + 0.334788i
\(838\) 2.42100e7 + 3.03584e7i 1.19093 + 1.49337i
\(839\) −1.11695e7 1.40061e7i −0.547808 0.686929i 0.428444 0.903568i \(-0.359062\pi\)
−0.976252 + 0.216639i \(0.930490\pi\)
\(840\) −4.35947e6 4.04500e6i −0.213175 0.197797i
\(841\) 4.70413e7 + 1.45103e7i 2.29345 + 0.707435i
\(842\) 7.95574e6 2.02709e7i 0.386723 0.985355i
\(843\) 71717.5 + 48896.2i 0.00347581 + 0.00236977i
\(844\) −4.41270e7 + 2.12505e7i −2.13230 + 1.02686i
\(845\) 1.49901e7 1.39088e7i 0.722208 0.670111i
\(846\) −2.74615e7 4.13915e6i −1.31916 0.198832i
\(847\) 1.17787e6 + 1.57176e7i 0.0564142 + 0.752795i
\(848\) 6.51473e6 + 1.65993e7i 0.311105 + 0.792683i
\(849\) 1.29932e6 5.69268e6i 0.0618652 0.271049i
\(850\) −327753. + 4.37356e6i −0.0155596 + 0.207629i
\(851\) −3.35904e7 + 1.03613e7i −1.58998 + 0.490444i
\(852\) 6.63965e6 + 3.19749e6i 0.313362 + 0.150907i
\(853\) −1.55031e7 2.68521e7i −0.729533 1.26359i −0.957081 0.289821i \(-0.906404\pi\)
0.227548 0.973767i \(-0.426929\pi\)
\(854\) −1.10092e7 + 1.90685e7i −0.516549 + 0.894688i
\(855\) −2.16808e7 + 1.47817e7i −1.01429 + 0.691528i
\(856\) 3.36626e6 + 1.47485e7i 0.157023 + 0.687962i
\(857\) −6.70495e6 + 1.01061e6i −0.311848 + 0.0470036i −0.303102 0.952958i \(-0.598022\pi\)
−0.00874645 + 0.999962i \(0.502784\pi\)
\(858\) 309206. 387732.i 0.0143393 0.0179810i
\(859\) 2.71278e7 1.25439 0.627193 0.778864i \(-0.284204\pi\)
0.627193 + 0.778864i \(0.284204\pi\)
\(860\) 3.55407e6 + 5.57695e7i 0.163863 + 2.57129i
\(861\) −1.31440e6 −0.0604254
\(862\) 2.01800e7 2.53049e7i 0.925022 1.15994i
\(863\) 2.66645e7 4.01903e6i 1.21873 0.183694i 0.491985 0.870604i \(-0.336271\pi\)
0.726742 + 0.686910i \(0.241033\pi\)
\(864\) −1.19777e6 5.24778e6i −0.0545870 0.239161i
\(865\) 2.40367e7 1.63879e7i 1.09228 0.744705i
\(866\) −1.34103e7 + 2.32273e7i −0.607637 + 1.05246i
\(867\) −1.41934e6 2.45837e6i −0.0641267 0.111071i
\(868\) −6.09674e7 2.93604e7i −2.74662 1.32270i
\(869\) 5.79334e6 1.78701e6i 0.260243 0.0802745i
\(870\) 923460. 1.23227e7i 0.0413638 0.551961i
\(871\) 2.78344e6 1.21950e7i 0.124319 0.544675i
\(872\) −9.75408e6 2.48530e7i −0.434405 1.10685i
\(873\) 2.56788e6 + 3.42660e7i 0.114035 + 1.52170i
\(874\) 3.88552e7 + 5.85648e6i 1.72056 + 0.259333i
\(875\) −9.97087e6 + 9.25162e6i −0.440264 + 0.408505i
\(876\) 841704. 405343.i 0.0370595 0.0178469i
\(877\) 1.33101e7 + 9.07467e6i 0.584362 + 0.398412i 0.819103 0.573647i \(-0.194472\pi\)
−0.234741 + 0.972058i \(0.575424\pi\)
\(878\) −4.35554e6 + 1.10977e7i −0.190680 + 0.485845i
\(879\) −589412. 181810.i −0.0257304 0.00793678i
\(880\) 7.57486e6 + 7.02844e6i 0.329737 + 0.305951i
\(881\) 2.75075e7 + 3.44933e7i 1.19402 + 1.49725i 0.822440 + 0.568852i \(0.192612\pi\)
0.371579 + 0.928401i \(0.378816\pi\)
\(882\) 9.25529e6 + 1.16058e7i 0.400607 + 0.502345i
\(883\) 1.52283e7 + 1.41298e7i 0.657280 + 0.609867i 0.936629 0.350323i \(-0.113928\pi\)
−0.279349 + 0.960190i \(0.590119\pi\)
\(884\) −6.35175e6 1.95926e6i −0.273378 0.0843258i
\(885\) −1.47667e6 + 3.76249e6i −0.0633760 + 0.161479i
\(886\) 769512. + 524644.i 0.0329330 + 0.0224533i
\(887\) −2.43185e7 + 1.17112e7i −1.03783 + 0.499794i −0.873609 0.486629i \(-0.838227\pi\)
−0.164225 + 0.986423i \(0.552512\pi\)
\(888\) 1.00088e7 9.28681e6i 0.425941 0.395216i
\(889\) 5.39278e6 + 812831.i 0.228854 + 0.0344942i
\(890\) 5.17099e6 + 6.90021e7i 0.218826 + 2.92003i
\(891\) −1.85281e6 4.72089e6i −0.0781875 0.199218i
\(892\) −4.60050e6 + 2.01561e7i −0.193594 + 0.848193i
\(893\) −1.45882e6 + 1.94666e7i −0.0612172 + 0.816886i
\(894\) −3.12068e6 + 962602.i −0.130589 + 0.0402813i
\(895\) −1.92117e7 9.25188e6i −0.801694 0.386076i
\(896\) −1.08569e7 1.88047e7i −0.451788 0.782520i
\(897\) −609379. + 1.05547e6i −0.0252875 + 0.0437993i
\(898\) 8.11119e6 5.53012e6i 0.335656 0.228846i
\(899\) −1.71724e7 7.52372e7i −0.708650 3.10480i
\(900\) 1.83162e7 2.76072e6i 0.753753 0.113610i
\(901\) −2.52104e6 + 3.16129e6i −0.103459 + 0.129733i
\(902\) 5.26781e6 0.215583
\(903\) 241211. 2.79924e6i 0.00984415 0.114241i
\(904\) −1.00753e8 −4.10051
\(905\) 6.69554e6 8.39594e6i 0.271746 0.340759i
\(906\) −4.38982e6 + 661659.i −0.177675 + 0.0267802i
\(907\) 4.07831e6 + 1.78682e7i 0.164612 + 0.721212i 0.988092 + 0.153866i \(0.0491726\pi\)
−0.823480 + 0.567346i \(0.807970\pi\)
\(908\) 4.93252e7 3.36294e7i 1.98543 1.35364i
\(909\) 6.04654e6 1.04729e7i 0.242715 0.420396i
\(910\) 8.09601e6 + 1.40227e7i 0.324091 + 0.561343i
\(911\) 1.12956e6 + 543967.i 0.0450934 + 0.0217158i 0.456295 0.889829i \(-0.349176\pi\)
−0.411201 + 0.911545i \(0.634891\pi\)
\(912\) −6.32301e6 + 1.95039e6i −0.251731 + 0.0776487i
\(913\) 107272. 1.43145e6i 0.00425903 0.0568328i
\(914\) −9.91221e6 + 4.34282e7i −0.392469 + 1.71952i
\(915\) 1.12018e6 + 2.85416e6i 0.0442317 + 0.112701i
\(916\) −6.28280e6 8.38381e7i −0.247408 3.30144i
\(917\) 1.89689e7 + 2.85910e6i 0.744936 + 0.112281i
\(918\) 3.16262e6 2.93448e6i 0.123862 0.114928i
\(919\) −3.95382e6 + 1.90406e6i −0.154429 + 0.0743689i −0.509502 0.860470i \(-0.670170\pi\)
0.355073 + 0.934839i \(0.384456\pi\)
\(920\) −4.83957e7 3.29957e7i −1.88511 1.28525i
\(921\) 331131. 843708.i 0.0128632 0.0327750i
\(922\) 2.90979e7 + 8.97550e6i 1.12729 + 0.347721i
\(923\) −8.07273e6 7.49040e6i −0.311901 0.289402i
\(924\) −938079. 1.17631e6i −0.0361459 0.0453256i
\(925\) 1.05387e7 + 1.32151e7i 0.404977 + 0.507826i
\(926\) 3.17880e7 + 2.94950e7i 1.21825 + 1.13037i
\(927\) 7.23520e6 + 2.23177e6i 0.276536 + 0.0853000i
\(928\) −1.52124e7 + 3.87605e7i −0.579866 + 1.47747i
\(929\) 3.59865e7 + 2.45352e7i 1.36805 + 0.932717i 0.999996 + 0.00291101i \(0.000926605\pi\)
0.368049 + 0.929806i \(0.380026\pi\)
\(930\) −1.23201e7 + 5.93304e6i −0.467096 + 0.224942i
\(931\) 7.64891e6 7.09715e6i 0.289218 0.268355i
\(932\) 3.43814e7 + 5.18217e6i 1.29654 + 0.195421i
\(933\) −76071.4 1.01510e6i −0.00286100 0.0381774i
\(934\) −2.05350e7 5.23222e7i −0.770241 1.96254i
\(935\) −521391. + 2.28436e6i −0.0195045 + 0.0854547i
\(936\) −1.67090e6 + 2.22966e7i −0.0623392 + 0.831859i
\(937\) −1.24430e6 + 383814.i −0.0462993 + 0.0142814i −0.317818 0.948152i \(-0.602950\pi\)
0.271519 + 0.962433i \(0.412474\pi\)
\(938\) −4.96165e7 2.38940e7i −1.84128 0.886712i
\(939\) 989608. + 1.71405e6i 0.0366268 + 0.0634395i
\(940\) 2.65095e7 4.59158e7i 0.978547 1.69489i
\(941\) 1.03293e7 7.04239e6i 0.380274 0.259266i −0.358064 0.933697i \(-0.616563\pi\)
0.738338 + 0.674431i \(0.235611\pi\)
\(942\) 2.07848e6 + 9.10642e6i 0.0763165 + 0.334365i
\(943\) −1.28012e7 + 1.92947e6i −0.468783 + 0.0706577i
\(944\) 3.00156e7 3.76383e7i 1.09627 1.37468i
\(945\) −7.24217e6 −0.263809
\(946\) −966720. + 1.12187e7i −0.0351215 + 0.407583i
\(947\) −1.49230e7 −0.540732 −0.270366 0.962758i \(-0.587145\pi\)
−0.270366 + 0.962758i \(0.587145\pi\)
\(948\) 6.57416e6 8.24373e6i 0.237585 0.297922i
\(949\) −1.38045e6 + 208070.i −0.0497573 + 0.00749970i
\(950\) −4.20438e6 1.84206e7i −0.151145 0.662208i
\(951\) −313201. + 213537.i −0.0112298 + 0.00765634i
\(952\) −8.03073e6 + 1.39096e7i −0.287186 + 0.497420i
\(953\) −9.94119e6 1.72186e7i −0.354573 0.614139i 0.632472 0.774584i \(-0.282041\pi\)
−0.987045 + 0.160445i \(0.948707\pi\)
\(954\) 2.23273e7 + 1.07523e7i 0.794266 + 0.382498i
\(955\) −2.32157e7 + 7.16108e6i −0.823707 + 0.254080i
\(956\) −5.95183e6 + 7.94217e7i −0.210623 + 2.81057i
\(957\) 381815. 1.67284e6i 0.0134764 0.0590439i
\(958\) 3.98517e6 + 1.01541e7i 0.140292 + 0.357459i
\(959\) −1.47549e6 1.96890e7i −0.0518072 0.691318i
\(960\) −721736. 108784.i −0.0252755 0.00380968i
\(961\) −4.16137e7 + 3.86118e7i −1.45354 + 1.34869i
\(962\) −3.34934e7 + 1.61296e7i −1.16687 + 0.561933i
\(963\) 7.53092e6 + 5.13449e6i 0.261687 + 0.178415i
\(964\) 3.98005e7 1.01410e8i 1.37942 3.51470i
\(965\) −8.97127e6 2.76727e6i −0.310124 0.0956606i
\(966\) 3.93331e6 + 3.64958e6i 0.135617 + 0.125834i
\(967\) −2.85606e7 3.58139e7i −0.982203 1.23164i −0.972790 0.231688i \(-0.925575\pi\)
−0.00941244 0.999956i \(-0.502996\pi\)
\(968\) −3.75949e7 4.71425e7i −1.28956 1.61705i
\(969\) −1.09989e6 1.02054e6i −0.0376303 0.0349158i
\(970\) −9.09675e7 2.80598e7i −3.10425 0.957535i
\(971\) 6.20520e6 1.58106e7i 0.211207 0.538146i −0.785534 0.618819i \(-0.787612\pi\)
0.996741 + 0.0806726i \(0.0257068\pi\)
\(972\) −2.26613e7 1.54502e7i −0.769341 0.524528i
\(973\) 1.83346e7 8.82947e6i 0.620854 0.298987i
\(974\) 3.14865e7 2.92152e7i 1.06347 0.986759i
\(975\) 579486. + 87343.5i 0.0195223 + 0.00294252i
\(976\) −2.72908e6 3.64170e7i −0.0917047 1.22371i
\(977\) 542960. + 1.38344e6i 0.0181983 + 0.0463685i 0.939684 0.342043i \(-0.111119\pi\)
−0.921486 + 0.388412i \(0.873024\pi\)
\(978\) −2.88706e6 + 1.26490e7i −0.0965181 + 0.422873i
\(979\) −718016. + 9.58125e6i −0.0239429 + 0.319496i
\(980\) −2.70803e7 + 8.35317e6i −0.900717 + 0.277835i
\(981\) −1.44932e7 6.97955e6i −0.480830 0.231555i
\(982\) 3.01234e7 + 5.21753e7i 0.996840 + 1.72658i
\(983\) −1.80440e7 + 3.12531e7i −0.595592 + 1.03160i 0.397871 + 0.917441i \(0.369749\pi\)
−0.993463 + 0.114154i \(0.963584\pi\)
\(984\) 4.15461e6 2.83257e6i 0.136786 0.0932594i
\(985\) −1.11999e6 4.90698e6i −0.0367809 0.161148i
\(986\) −3.30012e7 + 4.97413e6i −1.08103 + 0.162939i
\(987\) −1.66200e6 + 2.08408e6i −0.0543048 + 0.0680961i
\(988\) 2.86359e7 0.933293
\(989\) −1.75995e6 2.76165e7i −0.0572148 0.897798i
\(990\) 1.43605e7 0.465673
\(991\) 2.77059e7 3.47422e7i 0.896167 1.12376i −0.0955643 0.995423i \(-0.530466\pi\)
0.991731 0.128334i \(-0.0409630\pi\)
\(992\) 4.55620e7 6.86736e6i 1.47002 0.221570i
\(993\) −126333. 553501.i −0.00406578 0.0178133i
\(994\) −4.00588e7 + 2.73116e7i −1.28597 + 0.876761i
\(995\) 2.27844e7 3.94637e7i 0.729591 1.26369i
\(996\) −1.24827e6 2.16206e6i −0.0398712 0.0690590i
\(997\) 2.45273e7 + 1.18117e7i 0.781470 + 0.376336i 0.781693 0.623664i \(-0.214357\pi\)
−0.000222389 1.00000i \(0.500071\pi\)
\(998\) −4.92514e7 + 1.51920e7i −1.56528 + 0.482825i
\(999\) 1.24255e6 1.65806e7i 0.0393911 0.525638i
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 43.6.g.a.24.17 yes 204
43.9 even 21 inner 43.6.g.a.9.17 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.g.a.9.17 204 43.9 even 21 inner
43.6.g.a.24.17 yes 204 1.1 even 1 trivial