Properties

Label 74.6.c.b.47.2
Level $74$
Weight $6$
Character 74.47
Analytic conductor $11.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,6,Mod(47,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.47");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), 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: \(11.8684026662\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 1317 x^{14} - 2712 x^{13} + 1206654 x^{12} - 2683704 x^{11} + 572597881 x^{10} - 1472178324 x^{9} + 197936317446 x^{8} + \cdots + 683643854869056 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 47.2
Root \(11.5099 + 19.9358i\) of defining polynomial
Character \(\chi\) \(=\) 74.47
Dual form 74.6.c.b.63.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{2} +(-12.0099 - 20.8018i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(51.5512 + 89.2893i) q^{5} -96.0793 q^{6} +(102.698 + 177.878i) q^{7} -64.0000 q^{8} +(-166.976 + 289.211i) q^{9} +O(q^{10})\) \(q+(2.00000 - 3.46410i) q^{2} +(-12.0099 - 20.8018i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(51.5512 + 89.2893i) q^{5} -96.0793 q^{6} +(102.698 + 177.878i) q^{7} -64.0000 q^{8} +(-166.976 + 289.211i) q^{9} +412.410 q^{10} -395.366 q^{11} +(-192.159 + 332.828i) q^{12} +(368.381 + 638.054i) q^{13} +821.585 q^{14} +(1238.25 - 2144.71i) q^{15} +(-128.000 + 221.703i) q^{16} +(-47.1240 + 81.6211i) q^{17} +(667.904 + 1156.84i) q^{18} +(-200.998 - 348.139i) q^{19} +(824.819 - 1428.63i) q^{20} +(2466.79 - 4272.61i) q^{21} +(-790.733 + 1369.59i) q^{22} +3297.11 q^{23} +(768.634 + 1331.31i) q^{24} +(-3752.56 + 6499.62i) q^{25} +2947.05 q^{26} +2184.65 q^{27} +(1643.17 - 2846.05i) q^{28} -3952.87 q^{29} +(-4953.01 - 8578.86i) q^{30} -4751.96 q^{31} +(512.000 + 886.810i) q^{32} +(4748.32 + 8224.32i) q^{33} +(188.496 + 326.484i) q^{34} +(-10588.4 + 18339.7i) q^{35} +5343.23 q^{36} +(8326.31 + 128.327i) q^{37} -1607.98 q^{38} +(8848.44 - 15325.9i) q^{39} +(-3299.28 - 5714.52i) q^{40} +(-1206.71 - 2090.08i) q^{41} +(-9867.16 - 17090.4i) q^{42} +14421.7 q^{43} +(3162.93 + 5478.36i) q^{44} -34431.3 q^{45} +(6594.22 - 11421.5i) q^{46} +18875.6 q^{47} +6149.08 q^{48} +(-12690.3 + 21980.2i) q^{49} +(15010.2 + 25998.5i) q^{50} +2263.82 q^{51} +(5894.09 - 10208.9i) q^{52} +(-17285.8 + 29939.8i) q^{53} +(4369.31 - 7567.87i) q^{54} +(-20381.6 - 35302.0i) q^{55} +(-6572.68 - 11384.2i) q^{56} +(-4827.94 + 8362.24i) q^{57} +(-7905.73 + 13693.1i) q^{58} +(18594.1 - 32205.9i) q^{59} -39624.0 q^{60} +(242.034 + 419.215i) q^{61} +(-9503.92 + 16461.3i) q^{62} -68592.5 q^{63} +4096.00 q^{64} +(-37980.9 + 65784.9i) q^{65} +37986.5 q^{66} +(-21219.9 - 36754.0i) q^{67} +1507.97 q^{68} +(-39598.0 - 68585.8i) q^{69} +(42353.7 + 73358.7i) q^{70} +(9423.11 + 16321.3i) q^{71} +(10686.5 - 18509.5i) q^{72} +18097.1 q^{73} +(17097.2 - 28586.5i) q^{74} +180271. q^{75} +(-3215.97 + 5570.22i) q^{76} +(-40603.4 - 70327.1i) q^{77} +(-35393.8 - 61303.8i) q^{78} +(2880.58 + 4989.31i) q^{79} -26394.2 q^{80} +(14337.7 + 24833.6i) q^{81} -9653.66 q^{82} +(-24374.9 + 42218.6i) q^{83} -78937.3 q^{84} -9717.19 q^{85} +(28843.5 - 49958.4i) q^{86} +(47473.6 + 82226.7i) q^{87} +25303.4 q^{88} +(63249.4 - 109551. i) q^{89} +(-68862.6 + 119273. i) q^{90} +(-75664.0 + 131054. i) q^{91} +(-26376.9 - 45686.1i) q^{92} +(57070.6 + 98849.2i) q^{93} +(37751.1 - 65386.9i) q^{94} +(20723.4 - 35894.0i) q^{95} +(12298.2 - 21301.0i) q^{96} -93103.5 q^{97} +(50761.1 + 87920.9i) q^{98} +(66016.7 - 114344. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9} + 560 q^{10} - 240 q^{11} - 128 q^{12} + 1614 q^{13} - 256 q^{14} + 728 q^{15} - 2048 q^{16} + 216 q^{17} + 2792 q^{18} - 950 q^{19} + 1120 q^{20} + 1718 q^{21} - 480 q^{22} + 1716 q^{23} + 512 q^{24} - 11760 q^{25} + 12912 q^{26} - 92 q^{27} - 512 q^{28} + 1112 q^{29} - 2912 q^{30} - 16816 q^{31} + 8192 q^{32} + 4744 q^{33} - 864 q^{34} - 5004 q^{35} + 22336 q^{36} + 3556 q^{37} - 7600 q^{38} + 17710 q^{39} - 4480 q^{40} - 8080 q^{41} - 6872 q^{42} - 19012 q^{43} + 1920 q^{44} - 58672 q^{45} + 3432 q^{46} + 29392 q^{47} + 4096 q^{48} + 474 q^{49} + 47040 q^{50} - 17856 q^{51} + 25824 q^{52} - 29250 q^{53} - 184 q^{54} + 15772 q^{55} + 2048 q^{56} + 16182 q^{57} + 2224 q^{58} + 61478 q^{59} - 23296 q^{60} - 132002 q^{61} - 33632 q^{62} - 103324 q^{63} + 65536 q^{64} - 37426 q^{65} + 37952 q^{66} - 45658 q^{67} - 6912 q^{68} - 23816 q^{69} + 20016 q^{70} + 13236 q^{71} + 44672 q^{72} + 270632 q^{73} - 81304 q^{74} + 419904 q^{75} - 15200 q^{76} - 184084 q^{77} - 70840 q^{78} + 123974 q^{79} - 35840 q^{80} + 96448 q^{81} - 64640 q^{82} - 16936 q^{83} - 54976 q^{84} - 251316 q^{85} - 38024 q^{86} + 168290 q^{87} + 15360 q^{88} + 52892 q^{89} - 117344 q^{90} - 432546 q^{91} - 13728 q^{92} + 220328 q^{93} + 58784 q^{94} + 47026 q^{95} + 8192 q^{96} - 546140 q^{97} - 1896 q^{98} - 9800 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 3.46410i 0.353553 0.612372i
\(3\) −12.0099 20.8018i −0.770436 1.33443i −0.937324 0.348459i \(-0.886705\pi\)
0.166888 0.985976i \(-0.446628\pi\)
\(4\) −8.00000 13.8564i −0.250000 0.433013i
\(5\) 51.5512 + 89.2893i 0.922176 + 1.59726i 0.796041 + 0.605243i \(0.206924\pi\)
0.126135 + 0.992013i \(0.459743\pi\)
\(6\) −96.0793 −1.08956
\(7\) 102.698 + 177.878i 0.792168 + 1.37207i 0.924622 + 0.380886i \(0.124381\pi\)
−0.132454 + 0.991189i \(0.542286\pi\)
\(8\) −64.0000 −0.353553
\(9\) −166.976 + 289.211i −0.687144 + 1.19017i
\(10\) 412.410 1.30415
\(11\) −395.366 −0.985185 −0.492593 0.870260i \(-0.663951\pi\)
−0.492593 + 0.870260i \(0.663951\pi\)
\(12\) −192.159 + 332.828i −0.385218 + 0.667217i
\(13\) 368.381 + 638.054i 0.604559 + 1.04713i 0.992121 + 0.125283i \(0.0399838\pi\)
−0.387562 + 0.921843i \(0.626683\pi\)
\(14\) 821.585 1.12029
\(15\) 1238.25 2144.71i 1.42096 2.46117i
\(16\) −128.000 + 221.703i −0.125000 + 0.216506i
\(17\) −47.1240 + 81.6211i −0.0395475 + 0.0684984i −0.885122 0.465360i \(-0.845925\pi\)
0.845574 + 0.533858i \(0.179258\pi\)
\(18\) 667.904 + 1156.84i 0.485884 + 0.841576i
\(19\) −200.998 348.139i −0.127734 0.221242i 0.795064 0.606525i \(-0.207437\pi\)
−0.922798 + 0.385283i \(0.874104\pi\)
\(20\) 824.819 1428.63i 0.461088 0.798628i
\(21\) 2466.79 4272.61i 1.22063 2.11419i
\(22\) −790.733 + 1369.59i −0.348316 + 0.603300i
\(23\) 3297.11 1.29961 0.649807 0.760100i \(-0.274850\pi\)
0.649807 + 0.760100i \(0.274850\pi\)
\(24\) 768.634 + 1331.31i 0.272390 + 0.471794i
\(25\) −3752.56 + 6499.62i −1.20082 + 2.07988i
\(26\) 2947.05 0.854975
\(27\) 2184.65 0.576731
\(28\) 1643.17 2846.05i 0.396084 0.686037i
\(29\) −3952.87 −0.872805 −0.436402 0.899752i \(-0.643748\pi\)
−0.436402 + 0.899752i \(0.643748\pi\)
\(30\) −4953.01 8578.86i −1.00477 1.74031i
\(31\) −4751.96 −0.888114 −0.444057 0.895999i \(-0.646461\pi\)
−0.444057 + 0.895999i \(0.646461\pi\)
\(32\) 512.000 + 886.810i 0.0883883 + 0.153093i
\(33\) 4748.32 + 8224.32i 0.759023 + 1.31467i
\(34\) 188.496 + 326.484i 0.0279643 + 0.0484357i
\(35\) −10588.4 + 18339.7i −1.46104 + 2.53059i
\(36\) 5343.23 0.687144
\(37\) 8326.31 + 128.327i 0.999881 + 0.0154104i
\(38\) −1607.98 −0.180644
\(39\) 8848.44 15325.9i 0.931548 1.61349i
\(40\) −3299.28 5714.52i −0.326038 0.564715i
\(41\) −1206.71 2090.08i −0.112110 0.194179i 0.804511 0.593938i \(-0.202427\pi\)
−0.916621 + 0.399758i \(0.869094\pi\)
\(42\) −9867.16 17090.4i −0.863116 1.49496i
\(43\) 14421.7 1.18945 0.594725 0.803929i \(-0.297261\pi\)
0.594725 + 0.803929i \(0.297261\pi\)
\(44\) 3162.93 + 5478.36i 0.246296 + 0.426598i
\(45\) −34431.3 −2.53467
\(46\) 6594.22 11421.5i 0.459483 0.795847i
\(47\) 18875.6 1.24639 0.623197 0.782065i \(-0.285834\pi\)
0.623197 + 0.782065i \(0.285834\pi\)
\(48\) 6149.08 0.385218
\(49\) −12690.3 + 21980.2i −0.755060 + 1.30780i
\(50\) 15010.2 + 25998.5i 0.849106 + 1.47070i
\(51\) 2263.82 0.121875
\(52\) 5894.09 10208.9i 0.302279 0.523563i
\(53\) −17285.8 + 29939.8i −0.845276 + 1.46406i 0.0401045 + 0.999195i \(0.487231\pi\)
−0.885381 + 0.464866i \(0.846102\pi\)
\(54\) 4369.31 7567.87i 0.203905 0.353174i
\(55\) −20381.6 35302.0i −0.908515 1.57359i
\(56\) −6572.68 11384.2i −0.280074 0.485102i
\(57\) −4827.94 + 8362.24i −0.196822 + 0.340906i
\(58\) −7905.73 + 13693.1i −0.308583 + 0.534482i
\(59\) 18594.1 32205.9i 0.695416 1.20450i −0.274625 0.961551i \(-0.588554\pi\)
0.970040 0.242944i \(-0.0781131\pi\)
\(60\) −39624.0 −1.42096
\(61\) 242.034 + 419.215i 0.00832821 + 0.0144249i 0.870159 0.492770i \(-0.164016\pi\)
−0.861831 + 0.507195i \(0.830682\pi\)
\(62\) −9503.92 + 16461.3i −0.313996 + 0.543856i
\(63\) −68592.5 −2.17733
\(64\) 4096.00 0.125000
\(65\) −37980.9 + 65784.9i −1.11502 + 1.93127i
\(66\) 37986.5 1.07342
\(67\) −21219.9 36754.0i −0.577507 1.00027i −0.995764 0.0919423i \(-0.970692\pi\)
0.418258 0.908328i \(-0.362641\pi\)
\(68\) 1507.97 0.0395475
\(69\) −39598.0 68585.8i −1.00127 1.73425i
\(70\) 42353.7 + 73358.7i 1.03311 + 1.78940i
\(71\) 9423.11 + 16321.3i 0.221844 + 0.384246i 0.955368 0.295418i \(-0.0954590\pi\)
−0.733524 + 0.679664i \(0.762126\pi\)
\(72\) 10686.5 18509.5i 0.242942 0.420788i
\(73\) 18097.1 0.397468 0.198734 0.980053i \(-0.436317\pi\)
0.198734 + 0.980053i \(0.436317\pi\)
\(74\) 17097.2 28586.5i 0.362948 0.606851i
\(75\) 180271. 3.70061
\(76\) −3215.97 + 5570.22i −0.0638672 + 0.110621i
\(77\) −40603.4 70327.1i −0.780432 1.35175i
\(78\) −35393.8 61303.8i −0.658704 1.14091i
\(79\) 2880.58 + 4989.31i 0.0519292 + 0.0899441i 0.890822 0.454353i \(-0.150130\pi\)
−0.838892 + 0.544297i \(0.816796\pi\)
\(80\) −26394.2 −0.461088
\(81\) 14337.7 + 24833.6i 0.242810 + 0.420559i
\(82\) −9653.66 −0.158547
\(83\) −24374.9 + 42218.6i −0.388372 + 0.672680i −0.992231 0.124412i \(-0.960296\pi\)
0.603859 + 0.797091i \(0.293629\pi\)
\(84\) −78937.3 −1.22063
\(85\) −9717.19 −0.145879
\(86\) 28843.5 49958.4i 0.420534 0.728387i
\(87\) 47473.6 + 82226.7i 0.672441 + 1.16470i
\(88\) 25303.4 0.348316
\(89\) 63249.4 109551.i 0.846412 1.46603i −0.0379777 0.999279i \(-0.512092\pi\)
0.884389 0.466750i \(-0.154575\pi\)
\(90\) −68862.6 + 119273.i −0.896142 + 1.55216i
\(91\) −75664.0 + 131054.i −0.957824 + 1.65900i
\(92\) −26376.9 45686.1i −0.324903 0.562749i
\(93\) 57070.6 + 98849.2i 0.684235 + 1.18513i
\(94\) 37751.1 65386.9i 0.440667 0.763257i
\(95\) 20723.4 35894.0i 0.235587 0.408049i
\(96\) 12298.2 21301.0i 0.136195 0.235897i
\(97\) −93103.5 −1.00470 −0.502350 0.864664i \(-0.667531\pi\)
−0.502350 + 0.864664i \(0.667531\pi\)
\(98\) 50761.1 + 87920.9i 0.533908 + 0.924755i
\(99\) 66016.7 114344.i 0.676965 1.17254i
\(100\) 120082. 1.20082
\(101\) 100789. 0.983127 0.491564 0.870842i \(-0.336426\pi\)
0.491564 + 0.870842i \(0.336426\pi\)
\(102\) 4527.64 7842.10i 0.0430895 0.0746332i
\(103\) 12605.5 0.117076 0.0585380 0.998285i \(-0.481356\pi\)
0.0585380 + 0.998285i \(0.481356\pi\)
\(104\) −23576.4 40835.5i −0.213744 0.370215i
\(105\) 508664. 4.50254
\(106\) 69143.0 + 119759.i 0.597701 + 1.03525i
\(107\) −65071.7 112708.i −0.549456 0.951686i −0.998312 0.0580815i \(-0.981502\pi\)
0.448856 0.893604i \(-0.351832\pi\)
\(108\) −17477.2 30271.5i −0.144183 0.249732i
\(109\) −50187.2 + 86926.8i −0.404601 + 0.700789i −0.994275 0.106852i \(-0.965923\pi\)
0.589674 + 0.807641i \(0.299256\pi\)
\(110\) −163053. −1.28483
\(111\) −97328.9 174743.i −0.749781 1.34615i
\(112\) −52581.4 −0.396084
\(113\) 70801.4 122632.i 0.521610 0.903455i −0.478074 0.878319i \(-0.658665\pi\)
0.999684 0.0251352i \(-0.00800163\pi\)
\(114\) 19311.8 + 33448.9i 0.139174 + 0.241057i
\(115\) 169970. + 294397.i 1.19847 + 2.07581i
\(116\) 31622.9 + 54772.5i 0.218201 + 0.377936i
\(117\) −246043. −1.66168
\(118\) −74376.3 128824.i −0.491733 0.851707i
\(119\) −19358.2 −0.125313
\(120\) −79248.1 + 137262.i −0.502384 + 0.870154i
\(121\) −4736.43 −0.0294095
\(122\) 1936.27 0.0117779
\(123\) −28984.9 + 50203.3i −0.172746 + 0.299206i
\(124\) 38015.7 + 65845.1i 0.222028 + 0.384564i
\(125\) −451600. −2.58511
\(126\) −137185. + 237611.i −0.769804 + 1.33334i
\(127\) −19181.4 + 33223.1i −0.105529 + 0.182781i −0.913954 0.405818i \(-0.866987\pi\)
0.808425 + 0.588599i \(0.200320\pi\)
\(128\) 8192.00 14189.0i 0.0441942 0.0765466i
\(129\) −173204. 299998.i −0.916396 1.58724i
\(130\) 151924. + 263140.i 0.788438 + 1.36561i
\(131\) −60785.5 + 105284.i −0.309472 + 0.536022i −0.978247 0.207443i \(-0.933486\pi\)
0.668775 + 0.743465i \(0.266819\pi\)
\(132\) 75973.1 131589.i 0.379511 0.657333i
\(133\) 41284.2 71506.4i 0.202374 0.350522i
\(134\) −169759. −0.816718
\(135\) 112622. + 195066.i 0.531848 + 0.921187i
\(136\) 3015.93 5223.75i 0.0139822 0.0242178i
\(137\) 265094. 1.20670 0.603348 0.797478i \(-0.293833\pi\)
0.603348 + 0.797478i \(0.293833\pi\)
\(138\) −316784. −1.41601
\(139\) 23589.5 40858.2i 0.103558 0.179367i −0.809590 0.586995i \(-0.800311\pi\)
0.913148 + 0.407628i \(0.133644\pi\)
\(140\) 338829. 1.46104
\(141\) −226694. 392645.i −0.960267 1.66323i
\(142\) 75384.9 0.313735
\(143\) −145645. 252265.i −0.595602 1.03161i
\(144\) −42745.9 74038.0i −0.171786 0.297542i
\(145\) −203775. 352949.i −0.804880 1.39409i
\(146\) 36194.2 62690.3i 0.140526 0.243399i
\(147\) 609637. 2.32690
\(148\) −64832.4 116399.i −0.243297 0.436814i
\(149\) −419756. −1.54893 −0.774464 0.632618i \(-0.781980\pi\)
−0.774464 + 0.632618i \(0.781980\pi\)
\(150\) 360543. 624479.i 1.30836 2.26615i
\(151\) 85369.2 + 147864.i 0.304691 + 0.527740i 0.977192 0.212356i \(-0.0681136\pi\)
−0.672502 + 0.740095i \(0.734780\pi\)
\(152\) 12863.9 + 22280.9i 0.0451609 + 0.0782210i
\(153\) −15737.1 27257.5i −0.0543497 0.0941365i
\(154\) −324827. −1.10370
\(155\) −244969. 424299.i −0.818997 1.41854i
\(156\) −283150. −0.931548
\(157\) 12609.3 21839.9i 0.0408265 0.0707135i −0.844890 0.534940i \(-0.820334\pi\)
0.885717 + 0.464226i \(0.153668\pi\)
\(158\) 23044.6 0.0734390
\(159\) 830402. 2.60493
\(160\) −52788.4 + 91432.3i −0.163019 + 0.282358i
\(161\) 338607. + 586485.i 1.02951 + 1.78317i
\(162\) 114701. 0.343385
\(163\) −265396. + 459680.i −0.782395 + 1.35515i 0.148148 + 0.988965i \(0.452669\pi\)
−0.930543 + 0.366183i \(0.880665\pi\)
\(164\) −19307.3 + 33441.3i −0.0560548 + 0.0970897i
\(165\) −489563. + 847948.i −1.39991 + 2.42471i
\(166\) 97499.6 + 168874.i 0.274620 + 0.475656i
\(167\) −101601. 175978.i −0.281907 0.488277i 0.689948 0.723859i \(-0.257634\pi\)
−0.971854 + 0.235583i \(0.924300\pi\)
\(168\) −157875. + 273447.i −0.431558 + 0.747480i
\(169\) −85762.1 + 148544.i −0.230982 + 0.400073i
\(170\) −19434.4 + 33661.3i −0.0515761 + 0.0893324i
\(171\) 134247. 0.351088
\(172\) −115374. 199833.i −0.297363 0.515047i
\(173\) 168746. 292276.i 0.428665 0.742469i −0.568090 0.822966i \(-0.692318\pi\)
0.996755 + 0.0804975i \(0.0256509\pi\)
\(174\) 379789. 0.950975
\(175\) −1.54152e6 −3.80500
\(176\) 50606.9 87653.7i 0.123148 0.213299i
\(177\) −893253. −2.14309
\(178\) −252998. 438205.i −0.598504 1.03664i
\(179\) 526576. 1.22837 0.614184 0.789163i \(-0.289485\pi\)
0.614184 + 0.789163i \(0.289485\pi\)
\(180\) 275450. + 477094.i 0.633668 + 1.09755i
\(181\) −12263.7 21241.4i −0.0278245 0.0481934i 0.851778 0.523903i \(-0.175525\pi\)
−0.879602 + 0.475710i \(0.842191\pi\)
\(182\) 302656. + 524215.i 0.677284 + 1.17309i
\(183\) 5813.62 10069.5i 0.0128327 0.0222269i
\(184\) −211015. −0.459483
\(185\) 417773. + 750066.i 0.897452 + 1.61128i
\(186\) 456565. 0.967654
\(187\) 18631.2 32270.2i 0.0389617 0.0674836i
\(188\) −151004. 261547.i −0.311598 0.539704i
\(189\) 224360. + 388603.i 0.456868 + 0.791318i
\(190\) −82893.6 143576.i −0.166585 0.288534i
\(191\) −41380.7 −0.0820757 −0.0410379 0.999158i \(-0.513066\pi\)
−0.0410379 + 0.999158i \(0.513066\pi\)
\(192\) −49192.6 85204.1i −0.0963045 0.166804i
\(193\) 431522. 0.833891 0.416946 0.908931i \(-0.363101\pi\)
0.416946 + 0.908931i \(0.363101\pi\)
\(194\) −186207. + 322520.i −0.355215 + 0.615251i
\(195\) 1.82459e6 3.43620
\(196\) 406089. 0.755060
\(197\) 367477. 636488.i 0.674628 1.16849i −0.301950 0.953324i \(-0.597637\pi\)
0.976578 0.215166i \(-0.0690292\pi\)
\(198\) −264067. 457377.i −0.478686 0.829109i
\(199\) −14916.3 −0.0267011 −0.0133506 0.999911i \(-0.504250\pi\)
−0.0133506 + 0.999911i \(0.504250\pi\)
\(200\) 240164. 415975.i 0.424553 0.735348i
\(201\) −509699. + 882825.i −0.889864 + 1.54129i
\(202\) 201578. 349143.i 0.347588 0.602040i
\(203\) −405952. 703129.i −0.691408 1.19755i
\(204\) −18110.6 31368.4i −0.0304689 0.0527736i
\(205\) 124414. 215492.i 0.206769 0.358135i
\(206\) 25211.1 43666.8i 0.0413926 0.0716942i
\(207\) −550539. + 953561.i −0.893022 + 1.54676i
\(208\) −188611. −0.302279
\(209\) 79467.9 + 137642.i 0.125842 + 0.217965i
\(210\) 1.01733e6 1.76206e6i 1.59189 2.75723i
\(211\) 800984. 1.23856 0.619281 0.785169i \(-0.287424\pi\)
0.619281 + 0.785169i \(0.287424\pi\)
\(212\) 553144. 0.845276
\(213\) 226341. 392035.i 0.341834 0.592074i
\(214\) −520574. −0.777048
\(215\) 743458. + 1.28771e6i 1.09688 + 1.89986i
\(216\) −139818. −0.203905
\(217\) −488017. 845270.i −0.703535 1.21856i
\(218\) 200749. + 347707.i 0.286096 + 0.495533i
\(219\) −217345. 376452.i −0.306224 0.530395i
\(220\) −326106. + 564832.i −0.454257 + 0.786797i
\(221\) −69438.2 −0.0956352
\(222\) −799986. 12329.6i −1.08943 0.0167906i
\(223\) 374778. 0.504675 0.252338 0.967639i \(-0.418801\pi\)
0.252338 + 0.967639i \(0.418801\pi\)
\(224\) −105163. + 182147.i −0.140037 + 0.242551i
\(225\) −1.25317e6 2.17056e6i −1.65027 2.85835i
\(226\) −283206. 490526.i −0.368834 0.638839i
\(227\) −679305. 1.17659e6i −0.874984 1.51552i −0.856779 0.515683i \(-0.827538\pi\)
−0.0182048 0.999834i \(-0.505795\pi\)
\(228\) 154494. 0.196822
\(229\) 141201. + 244567.i 0.177929 + 0.308183i 0.941171 0.337930i \(-0.109727\pi\)
−0.763242 + 0.646113i \(0.776393\pi\)
\(230\) 1.35976e6 1.69490
\(231\) −975286. + 1.68924e6i −1.20255 + 2.08287i
\(232\) 252983. 0.308583
\(233\) 1.37724e6 1.66196 0.830979 0.556304i \(-0.187781\pi\)
0.830979 + 0.556304i \(0.187781\pi\)
\(234\) −492086. + 852318.i −0.587491 + 1.01756i
\(235\) 973058. + 1.68539e6i 1.14939 + 1.99081i
\(236\) −595010. −0.695416
\(237\) 69191.0 119842.i 0.0800163 0.138592i
\(238\) −38716.3 + 67058.6i −0.0443049 + 0.0767383i
\(239\) 785113. 1.35986e6i 0.889073 1.53992i 0.0481000 0.998843i \(-0.484683\pi\)
0.840973 0.541077i \(-0.181983\pi\)
\(240\) 316992. + 549047.i 0.355239 + 0.615292i
\(241\) 335694. + 581439.i 0.372307 + 0.644854i 0.989920 0.141628i \(-0.0452336\pi\)
−0.617613 + 0.786482i \(0.711900\pi\)
\(242\) −9472.87 + 16407.5i −0.0103978 + 0.0180096i
\(243\) 609824. 1.05625e6i 0.662504 1.14749i
\(244\) 3872.54 6707.44i 0.00416411 0.00721244i
\(245\) −2.61680e6 −2.78519
\(246\) 115940. + 200813.i 0.122150 + 0.211570i
\(247\) 148088. 256495.i 0.154446 0.267508i
\(248\) 304125. 0.313996
\(249\) 1.17096e6 1.19686
\(250\) −903200. + 1.56439e6i −0.913974 + 1.58305i
\(251\) −1.31724e6 −1.31972 −0.659859 0.751389i \(-0.729384\pi\)
−0.659859 + 0.751389i \(0.729384\pi\)
\(252\) 548740. + 950445.i 0.544334 + 0.942813i
\(253\) −1.30357e6 −1.28036
\(254\) 76725.5 + 132892.i 0.0746200 + 0.129246i
\(255\) 116703. + 202135.i 0.112391 + 0.194666i
\(256\) −32768.0 56755.8i −0.0312500 0.0541266i
\(257\) −441178. + 764143.i −0.416659 + 0.721675i −0.995601 0.0936938i \(-0.970133\pi\)
0.578942 + 0.815369i \(0.303466\pi\)
\(258\) −1.38563e6 −1.29598
\(259\) 832270. + 1.49425e6i 0.770930 + 1.38412i
\(260\) 1.21539e6 1.11502
\(261\) 660034. 1.14321e6i 0.599743 1.03879i
\(262\) 243142. + 421134.i 0.218830 + 0.379025i
\(263\) −575323. 996488.i −0.512888 0.888347i −0.999888 0.0149458i \(-0.995242\pi\)
0.487001 0.873402i \(-0.338091\pi\)
\(264\) −303892. 526357.i −0.268355 0.464805i
\(265\) −3.56441e6 −3.11797
\(266\) −165137. 286026.i −0.143100 0.247857i
\(267\) −3.03848e6 −2.60843
\(268\) −339519. + 588064.i −0.288753 + 0.500135i
\(269\) −296005. −0.249413 −0.124706 0.992194i \(-0.539799\pi\)
−0.124706 + 0.992194i \(0.539799\pi\)
\(270\) 900973. 0.752146
\(271\) −605333. + 1.04847e6i −0.500693 + 0.867225i 0.499307 + 0.866425i \(0.333588\pi\)
−1.00000 0.000800193i \(0.999745\pi\)
\(272\) −12063.7 20895.0i −0.00988689 0.0171246i
\(273\) 3.63487e6 2.95177
\(274\) 530188. 918312.i 0.426632 0.738948i
\(275\) 1.48363e6 2.56973e6i 1.18303 2.04906i
\(276\) −633568. + 1.09737e6i −0.500635 + 0.867125i
\(277\) −47249.7 81838.9i −0.0369998 0.0640856i 0.846932 0.531700i \(-0.178447\pi\)
−0.883932 + 0.467615i \(0.845113\pi\)
\(278\) −94358.0 163433.i −0.0732263 0.126832i
\(279\) 793463. 1.37432e6i 0.610262 1.05701i
\(280\) 677659. 1.17374e6i 0.516554 0.894698i
\(281\) 82232.5 142431.i 0.0621266 0.107606i −0.833289 0.552837i \(-0.813545\pi\)
0.895416 + 0.445231i \(0.146878\pi\)
\(282\) −1.81355e6 −1.35802
\(283\) 302440. + 523841.i 0.224477 + 0.388806i 0.956162 0.292837i \(-0.0945992\pi\)
−0.731685 + 0.681643i \(0.761266\pi\)
\(284\) 150770. 261141.i 0.110922 0.192123i
\(285\) −995544. −0.726020
\(286\) −1.16516e6 −0.842309
\(287\) 247853. 429294.i 0.177619 0.307645i
\(288\) −341967. −0.242942
\(289\) 705487. + 1.22194e6i 0.496872 + 0.860608i
\(290\) −1.63020e6 −1.13827
\(291\) 1.11817e6 + 1.93672e6i 0.774058 + 1.34071i
\(292\) −144777. 250761.i −0.0993670 0.172109i
\(293\) 329899. + 571401.i 0.224498 + 0.388841i 0.956169 0.292817i \(-0.0945926\pi\)
−0.731671 + 0.681658i \(0.761259\pi\)
\(294\) 1.21927e6 2.11184e6i 0.822684 1.42493i
\(295\) 3.83419e6 2.56518
\(296\) −532884. 8212.92i −0.353511 0.00544839i
\(297\) −863739. −0.568187
\(298\) −839512. + 1.45408e6i −0.547629 + 0.948521i
\(299\) 1.21459e6 + 2.10374e6i 0.785692 + 1.36086i
\(300\) −1.44217e6 2.49791e6i −0.925154 1.60241i
\(301\) 1.48108e6 + 2.56531e6i 0.942245 + 1.63202i
\(302\) 682954. 0.430898
\(303\) −1.21047e6 2.09659e6i −0.757437 1.31192i
\(304\) 102911. 0.0638672
\(305\) −24954.3 + 43222.1i −0.0153602 + 0.0266046i
\(306\) −125897. −0.0768621
\(307\) −1.85269e6 −1.12191 −0.560954 0.827847i \(-0.689566\pi\)
−0.560954 + 0.827847i \(0.689566\pi\)
\(308\) −649654. + 1.12523e6i −0.390216 + 0.675874i
\(309\) −151391. 262218.i −0.0901997 0.156230i
\(310\) −1.95975e6 −1.15824
\(311\) 695600. 1.20482e6i 0.407811 0.706349i −0.586833 0.809708i \(-0.699626\pi\)
0.994644 + 0.103359i \(0.0329589\pi\)
\(312\) −566300. + 980861.i −0.329352 + 0.570454i
\(313\) 343263. 594548.i 0.198046 0.343025i −0.749849 0.661609i \(-0.769874\pi\)
0.947895 + 0.318584i \(0.103207\pi\)
\(314\) −50437.2 87359.7i −0.0288687 0.0500020i
\(315\) −3.53603e6 6.12458e6i −2.00789 3.47776i
\(316\) 46089.2 79828.9i 0.0259646 0.0449720i
\(317\) 599318. 1.03805e6i 0.334973 0.580189i −0.648507 0.761209i \(-0.724606\pi\)
0.983480 + 0.181019i \(0.0579396\pi\)
\(318\) 1.66080e6 2.87660e6i 0.920981 1.59519i
\(319\) 1.56283e6 0.859875
\(320\) 211154. + 365729.i 0.115272 + 0.199657i
\(321\) −1.56301e6 + 2.70722e6i −0.846642 + 1.46643i
\(322\) 2.70886e6 1.45595
\(323\) 37887.3 0.0202063
\(324\) 229403. 397337.i 0.121405 0.210279i
\(325\) −5.52947e6 −2.90386
\(326\) 1.06159e6 + 1.83872e6i 0.553237 + 0.958234i
\(327\) 2.41098e6 1.24688
\(328\) 77229.3 + 133765.i 0.0396367 + 0.0686528i
\(329\) 1.93848e6 + 3.35755e6i 0.987353 + 1.71015i
\(330\) 1.95825e6 + 3.39179e6i 0.989882 + 1.71453i
\(331\) 300320. 520169.i 0.150666 0.260960i −0.780807 0.624773i \(-0.785192\pi\)
0.931472 + 0.363812i \(0.118525\pi\)
\(332\) 779997. 0.388372
\(333\) −1.42741e6 + 2.38663e6i −0.705404 + 1.17944i
\(334\) −812805. −0.398676
\(335\) 2.18783e6 3.78943e6i 1.06513 1.84485i
\(336\) 631498. + 1.09379e6i 0.305157 + 0.528548i
\(337\) 773295. + 1.33939e6i 0.370912 + 0.642438i 0.989706 0.143115i \(-0.0457119\pi\)
−0.618794 + 0.785553i \(0.712379\pi\)
\(338\) 343048. + 594177.i 0.163329 + 0.282894i
\(339\) −3.40127e6 −1.60747
\(340\) 77737.5 + 134645.i 0.0364698 + 0.0631676i
\(341\) 1.87876e6 0.874957
\(342\) 268495. 465047.i 0.124128 0.214997i
\(343\) −1.76098e6 −0.808200
\(344\) −922991. −0.420534
\(345\) 4.08265e6 7.07136e6i 1.84669 3.19857i
\(346\) −674983. 1.16910e6i −0.303112 0.525005i
\(347\) 908469. 0.405029 0.202515 0.979279i \(-0.435089\pi\)
0.202515 + 0.979279i \(0.435089\pi\)
\(348\) 759577. 1.31563e6i 0.336220 0.582351i
\(349\) 1.60641e6 2.78238e6i 0.705981 1.22279i −0.260355 0.965513i \(-0.583840\pi\)
0.966336 0.257282i \(-0.0828269\pi\)
\(350\) −3.08304e6 + 5.33998e6i −1.34527 + 2.33007i
\(351\) 804784. + 1.39393e6i 0.348668 + 0.603910i
\(352\) −202428. 350615.i −0.0870789 0.150825i
\(353\) −1.42231e6 + 2.46351e6i −0.607515 + 1.05225i 0.384134 + 0.923277i \(0.374500\pi\)
−0.991649 + 0.128969i \(0.958833\pi\)
\(354\) −1.78651e6 + 3.09432e6i −0.757698 + 1.31237i
\(355\) −971545. + 1.68277e6i −0.409159 + 0.708684i
\(356\) −2.02398e6 −0.846412
\(357\) 232490. + 402684.i 0.0965458 + 0.167222i
\(358\) 1.05315e6 1.82411e6i 0.434294 0.752219i
\(359\) −480380. −0.196720 −0.0983600 0.995151i \(-0.531360\pi\)
−0.0983600 + 0.995151i \(0.531360\pi\)
\(360\) 2.20360e6 0.896142
\(361\) 1.15725e6 2.00441e6i 0.467368 0.809505i
\(362\) −98110.0 −0.0393497
\(363\) 56884.2 + 98526.3i 0.0226582 + 0.0392451i
\(364\) 2.42125e6 0.957824
\(365\) 932928. + 1.61588e6i 0.366536 + 0.634858i
\(366\) −23254.5 40277.9i −0.00907410 0.0157168i
\(367\) 1.72561e6 + 2.98885e6i 0.668772 + 1.15835i 0.978248 + 0.207440i \(0.0665131\pi\)
−0.309476 + 0.950907i \(0.600154\pi\)
\(368\) −422030. + 730978.i −0.162452 + 0.281374i
\(369\) 805965. 0.308142
\(370\) 3.43385e6 + 52923.2i 1.30400 + 0.0200975i
\(371\) −7.10086e6 −2.67840
\(372\) 913130. 1.58159e6i 0.342117 0.592565i
\(373\) −1.36199e6 2.35904e6i −0.506876 0.877936i −0.999968 0.00795847i \(-0.997467\pi\)
0.493092 0.869977i \(-0.335867\pi\)
\(374\) −74524.9 129081.i −0.0275501 0.0477181i
\(375\) 5.42368e6 + 9.39408e6i 1.99166 + 3.44966i
\(376\) −1.20804e6 −0.440667
\(377\) −1.45616e6 2.52214e6i −0.527662 0.913937i
\(378\) 1.79488e6 0.646109
\(379\) 1.18806e6 2.05778e6i 0.424855 0.735871i −0.571552 0.820566i \(-0.693658\pi\)
0.996407 + 0.0846953i \(0.0269917\pi\)
\(380\) −663148. −0.235587
\(381\) 921467. 0.325212
\(382\) −82761.5 + 143347.i −0.0290182 + 0.0502609i
\(383\) 1.89324e6 + 3.27918e6i 0.659489 + 1.14227i 0.980748 + 0.195277i \(0.0625607\pi\)
−0.321259 + 0.946991i \(0.604106\pi\)
\(384\) −393541. −0.136195
\(385\) 4.18631e6 7.25089e6i 1.43939 2.49310i
\(386\) 863044. 1.49484e6i 0.294825 0.510652i
\(387\) −2.40809e6 + 4.17093e6i −0.817324 + 1.41565i
\(388\) 744828. + 1.29008e6i 0.251175 + 0.435048i
\(389\) −431721. 747762.i −0.144654 0.250547i 0.784590 0.620015i \(-0.212873\pi\)
−0.929244 + 0.369468i \(0.879540\pi\)
\(390\) 3.64918e6 6.32057e6i 1.21488 2.10424i
\(391\) −155373. + 269114.i −0.0513965 + 0.0890214i
\(392\) 812178. 1.40673e6i 0.266954 0.462378i
\(393\) 2.92012e6 0.953715
\(394\) −1.46991e6 2.54595e6i −0.477034 0.826247i
\(395\) −296995. + 514410.i −0.0957758 + 0.165889i
\(396\) −2.11254e6 −0.676965
\(397\) −535341. −0.170472 −0.0852362 0.996361i \(-0.527164\pi\)
−0.0852362 + 0.996361i \(0.527164\pi\)
\(398\) −29832.7 + 51671.7i −0.00944027 + 0.0163510i
\(399\) −1.98328e6 −0.623666
\(400\) −960654. 1.66390e6i −0.300204 0.519969i
\(401\) 4.66669e6 1.44927 0.724633 0.689135i \(-0.242009\pi\)
0.724633 + 0.689135i \(0.242009\pi\)
\(402\) 2.03880e6 + 3.53130e6i 0.629229 + 1.08986i
\(403\) −1.75053e6 3.03201e6i −0.536917 0.929967i
\(404\) −806312. 1.39657e6i −0.245782 0.425707i
\(405\) −1.47825e6 + 2.56040e6i −0.447827 + 0.775658i
\(406\) −3.24761e6 −0.977798
\(407\) −3.29194e6 50736.1i −0.985069 0.0151821i
\(408\) −144884. −0.0430895
\(409\) −3.12109e6 + 5.40588e6i −0.922566 + 1.59793i −0.127136 + 0.991885i \(0.540578\pi\)
−0.795430 + 0.606046i \(0.792755\pi\)
\(410\) −497658. 861969.i −0.146208 0.253240i
\(411\) −3.18375e6 5.51442e6i −0.929683 1.61026i
\(412\) −100844. 174667.i −0.0292690 0.0506954i
\(413\) 7.63830e6 2.20354
\(414\) 2.20216e6 + 3.81424e6i 0.631462 + 1.09372i
\(415\) −5.02622e6 −1.43259
\(416\) −377222. + 653367.i −0.106872 + 0.185108i
\(417\) −1.13323e6 −0.319138
\(418\) 635743. 0.177968
\(419\) −106254. + 184038.i −0.0295672 + 0.0512120i −0.880430 0.474175i \(-0.842746\pi\)
0.850863 + 0.525387i \(0.176080\pi\)
\(420\) −4.06931e6 7.04826e6i −1.12564 1.94966i
\(421\) −1.51283e6 −0.415993 −0.207996 0.978130i \(-0.566694\pi\)
−0.207996 + 0.978130i \(0.566694\pi\)
\(422\) 1.60197e6 2.77469e6i 0.437898 0.758461i
\(423\) −3.15177e6 + 5.45902e6i −0.856452 + 1.48342i
\(424\) 1.10629e6 1.91615e6i 0.298850 0.517624i
\(425\) −353671. 612575.i −0.0949788 0.164508i
\(426\) −905366. 1.56814e6i −0.241713 0.418659i
\(427\) −49712.9 + 86105.2i −0.0131947 + 0.0228539i
\(428\) −1.04115e6 + 1.80332e6i −0.274728 + 0.475843i
\(429\) −3.49838e6 + 6.05936e6i −0.917747 + 1.58959i
\(430\) 5.94766e6 1.55123
\(431\) −2.42496e6 4.20015e6i −0.628798 1.08911i −0.987793 0.155771i \(-0.950214\pi\)
0.358995 0.933340i \(-0.383120\pi\)
\(432\) −279636. + 484343.i −0.0720914 + 0.124866i
\(433\) −1.39094e6 −0.356523 −0.178262 0.983983i \(-0.557047\pi\)
−0.178262 + 0.983983i \(0.557047\pi\)
\(434\) −3.90414e6 −0.994949
\(435\) −4.89464e6 + 8.47777e6i −1.24022 + 2.14812i
\(436\) 1.60599e6 0.404601
\(437\) −662713. 1.14785e6i −0.166005 0.287530i
\(438\) −1.73876e6 −0.433066
\(439\) 514433. + 891024.i 0.127399 + 0.220662i 0.922668 0.385595i \(-0.126004\pi\)
−0.795269 + 0.606257i \(0.792670\pi\)
\(440\) 1.30442e6 + 2.25933e6i 0.321208 + 0.556349i
\(441\) −4.23795e6 7.34034e6i −1.03767 1.79730i
\(442\) −138876. + 240541.i −0.0338122 + 0.0585644i
\(443\) −2.93007e6 −0.709363 −0.354682 0.934987i \(-0.615411\pi\)
−0.354682 + 0.934987i \(0.615411\pi\)
\(444\) −1.64268e6 + 2.74658e6i −0.395454 + 0.661202i
\(445\) 1.30423e7 3.12216
\(446\) 749556. 1.29827e6i 0.178430 0.309049i
\(447\) 5.04123e6 + 8.73167e6i 1.19335 + 2.06694i
\(448\) 420651. + 728589.i 0.0990210 + 0.171509i
\(449\) 223128. + 386469.i 0.0522322 + 0.0904688i 0.890959 0.454083i \(-0.150033\pi\)
−0.838727 + 0.544552i \(0.816700\pi\)
\(450\) −1.00254e7 −2.33383
\(451\) 477092. + 826347.i 0.110449 + 0.191303i
\(452\) −2.26564e6 −0.521610
\(453\) 2.05055e6 3.55166e6i 0.469489 0.813180i
\(454\) −5.43444e6 −1.23741
\(455\) −1.56023e7 −3.53313
\(456\) 308988. 535183.i 0.0695872 0.120529i
\(457\) 2.33406e6 + 4.04272e6i 0.522784 + 0.905488i 0.999649 + 0.0265113i \(0.00843979\pi\)
−0.476865 + 0.878977i \(0.658227\pi\)
\(458\) 1.12960e6 0.251630
\(459\) −102950. + 178314.i −0.0228083 + 0.0395051i
\(460\) 2.71952e6 4.71035e6i 0.599236 1.03791i
\(461\) 1.94278e6 3.36499e6i 0.425766 0.737448i −0.570726 0.821141i \(-0.693338\pi\)
0.996492 + 0.0836926i \(0.0266714\pi\)
\(462\) 3.90114e6 + 6.75698e6i 0.850329 + 1.47281i
\(463\) −3.49742e6 6.05770e6i −0.758219 1.31327i −0.943758 0.330637i \(-0.892736\pi\)
0.185539 0.982637i \(-0.440597\pi\)
\(464\) 505967. 876360.i 0.109101 0.188968i
\(465\) −5.88412e6 + 1.01916e7i −1.26197 + 2.18580i
\(466\) 2.75448e6 4.77090e6i 0.587591 1.01774i
\(467\) 510592. 0.108338 0.0541691 0.998532i \(-0.482749\pi\)
0.0541691 + 0.998532i \(0.482749\pi\)
\(468\) 1.96834e6 + 3.40927e6i 0.415419 + 0.719527i
\(469\) 4.35849e6 7.54913e6i 0.914964 1.58476i
\(470\) 7.78446e6 1.62549
\(471\) −605746. −0.125817
\(472\) −1.19002e6 + 2.06118e6i −0.245867 + 0.425853i
\(473\) −5.70187e6 −1.17183
\(474\) −276764. 479369.i −0.0565801 0.0979996i
\(475\) 3.01703e6 0.613543
\(476\) 154865. + 268235.i 0.0313283 + 0.0542622i
\(477\) −5.77262e6 9.99846e6i −1.16165 2.01204i
\(478\) −3.14045e6 5.43942e6i −0.628670 1.08889i
\(479\) 3.44049e6 5.95910e6i 0.685143 1.18670i −0.288249 0.957555i \(-0.593073\pi\)
0.973392 0.229147i \(-0.0735935\pi\)
\(480\) 2.53594e6 0.502384
\(481\) 2.98537e6 + 5.35991e6i 0.588350 + 1.05632i
\(482\) 2.68555e6 0.526521
\(483\) 8.13328e6 1.40873e7i 1.58635 2.74763i
\(484\) 37891.5 + 65630.0i 0.00735238 + 0.0127347i
\(485\) −4.79960e6 8.31315e6i −0.926511 1.60476i
\(486\) −2.43930e6 4.22498e6i −0.468461 0.811399i
\(487\) 2.84576e6 0.543722 0.271861 0.962337i \(-0.412361\pi\)
0.271861 + 0.962337i \(0.412361\pi\)
\(488\) −15490.2 26829.8i −0.00294447 0.00509997i
\(489\) 1.27496e7 2.41114
\(490\) −5.23360e6 + 9.06486e6i −0.984714 + 1.70557i
\(491\) −8.84738e6 −1.65619 −0.828097 0.560585i \(-0.810576\pi\)
−0.828097 + 0.560585i \(0.810576\pi\)
\(492\) 927517. 0.172746
\(493\) 186275. 322637.i 0.0345173 0.0597857i
\(494\) −592350. 1.02598e6i −0.109210 0.189157i
\(495\) 1.36130e7 2.49712
\(496\) 608251. 1.05352e6i 0.111014 0.192282i
\(497\) −1.93547e6 + 3.35233e6i −0.351476 + 0.608774i
\(498\) 2.34192e6 4.05633e6i 0.423155 0.732926i
\(499\) −591814. 1.02505e6i −0.106398 0.184287i 0.807910 0.589305i \(-0.200598\pi\)
−0.914309 + 0.405018i \(0.867265\pi\)
\(500\) 3.61280e6 + 6.25755e6i 0.646277 + 1.11939i
\(501\) −2.44043e6 + 4.22695e6i −0.434382 + 0.752372i
\(502\) −2.63448e6 + 4.56306e6i −0.466591 + 0.808159i
\(503\) −55908.5 + 96836.3i −0.00985275 + 0.0170655i −0.870910 0.491443i \(-0.836470\pi\)
0.861057 + 0.508508i \(0.169803\pi\)
\(504\) 4.38992e6 0.769804
\(505\) 5.19580e6 + 8.99938e6i 0.906616 + 1.57031i
\(506\) −2.60713e6 + 4.51569e6i −0.452676 + 0.784057i
\(507\) 4.11998e6 0.711829
\(508\) 613804. 0.105529
\(509\) −2.30496e6 + 3.99230e6i −0.394338 + 0.683013i −0.993016 0.117976i \(-0.962359\pi\)
0.598679 + 0.800989i \(0.295693\pi\)
\(510\) 933621. 0.158944
\(511\) 1.85854e6 + 3.21908e6i 0.314861 + 0.545356i
\(512\) −262144. −0.0441942
\(513\) −439111. 760563.i −0.0736684 0.127597i
\(514\) 1.76471e6 + 3.05657e6i 0.294623 + 0.510301i
\(515\) 649830. + 1.12554e6i 0.107965 + 0.187000i
\(516\) −2.77126e6 + 4.79997e6i −0.458198 + 0.793622i
\(517\) −7.46276e6 −1.22793
\(518\) 6.84077e6 + 105431.i 1.12016 + 0.0172642i
\(519\) −8.10649e6 −1.32103
\(520\) 2.43078e6 4.21023e6i 0.394219 0.682807i
\(521\) −3.44452e6 5.96608e6i −0.555948 0.962930i −0.997829 0.0658564i \(-0.979022\pi\)
0.441881 0.897074i \(-0.354311\pi\)
\(522\) −2.64014e6 4.57285e6i −0.424082 0.734532i
\(523\) −5.58785e6 9.67844e6i −0.893286 1.54722i −0.835911 0.548865i \(-0.815060\pi\)
−0.0573752 0.998353i \(-0.518273\pi\)
\(524\) 1.94514e6 0.309472
\(525\) 1.85135e7 + 3.20664e7i 2.93151 + 5.07752i
\(526\) −4.60258e6 −0.725333
\(527\) 223931. 387860.i 0.0351227 0.0608343i
\(528\) −2.43114e6 −0.379511
\(529\) 4.43460e6 0.688994
\(530\) −7.12881e6 + 1.23475e7i −1.10237 + 1.90936i
\(531\) 6.20953e6 + 1.07552e7i 0.955702 + 1.65532i
\(532\) −1.32110e6 −0.202374
\(533\) 889056. 1.53989e6i 0.135554 0.234786i
\(534\) −6.07696e6 + 1.05256e7i −0.922218 + 1.59733i
\(535\) 6.70905e6 1.16204e7i 1.01339 1.75524i
\(536\) 1.35808e6 + 2.35226e6i 0.204179 + 0.353649i
\(537\) −6.32414e6 1.09537e7i −0.946380 1.63918i
\(538\) −592011. + 1.02539e6i −0.0881808 + 0.152734i
\(539\) 5.01731e6 8.69024e6i 0.743874 1.28843i
\(540\) 1.80195e6 3.12106e6i 0.265924 0.460594i
\(541\) −1.53349e6 −0.225262 −0.112631 0.993637i \(-0.535928\pi\)
−0.112631 + 0.993637i \(0.535928\pi\)
\(542\) 2.42133e6 + 4.19387e6i 0.354043 + 0.613221i
\(543\) −294573. + 510216.i −0.0428740 + 0.0742599i
\(544\) −96509.9 −0.0139822
\(545\) −1.03488e7 −1.49245
\(546\) 7.26974e6 1.25916e7i 1.04361 1.80758i
\(547\) −1.21105e6 −0.173059 −0.0865296 0.996249i \(-0.527578\pi\)
−0.0865296 + 0.996249i \(0.527578\pi\)
\(548\) −2.12075e6 3.67325e6i −0.301674 0.522515i
\(549\) −161656. −0.0228907
\(550\) −5.93454e6 1.02789e7i −0.836527 1.44891i
\(551\) 794518. + 1.37615e6i 0.111487 + 0.193101i
\(552\) 2.53427e6 + 4.38949e6i 0.354002 + 0.613150i
\(553\) −591660. + 1.02478e6i −0.0822733 + 0.142502i
\(554\) −377998. −0.0523257
\(555\) 1.05853e7 1.76987e7i 1.45871 2.43898i
\(556\) −754864. −0.103558
\(557\) −3.47569e6 + 6.02008e6i −0.474683 + 0.822175i −0.999580 0.0289911i \(-0.990771\pi\)
0.524897 + 0.851166i \(0.324104\pi\)
\(558\) −3.17385e6 5.49728e6i −0.431521 0.747415i
\(559\) 5.31269e6 + 9.20185e6i 0.719093 + 1.24551i
\(560\) −2.71064e6 4.69496e6i −0.365259 0.632647i
\(561\) −895038. −0.120070
\(562\) −328930. 569723.i −0.0439301 0.0760892i
\(563\) 9.86649e6 1.31187 0.655936 0.754816i \(-0.272274\pi\)
0.655936 + 0.754816i \(0.272274\pi\)
\(564\) −3.62710e6 + 6.28232e6i −0.480133 + 0.831616i
\(565\) 1.45996e7 1.92406
\(566\) 2.41952e6 0.317459
\(567\) −2.94490e6 + 5.10072e6i −0.384692 + 0.666306i
\(568\) −603079. 1.04456e6i −0.0784338 0.135851i
\(569\) 9.95306e6 1.28877 0.644386 0.764701i \(-0.277113\pi\)
0.644386 + 0.764701i \(0.277113\pi\)
\(570\) −1.99109e6 + 3.44867e6i −0.256687 + 0.444595i
\(571\) 4.81461e6 8.33915e6i 0.617975 1.07036i −0.371880 0.928281i \(-0.621287\pi\)
0.989855 0.142083i \(-0.0453801\pi\)
\(572\) −2.33033e6 + 4.03624e6i −0.297801 + 0.515807i
\(573\) 496979. + 860793.i 0.0632341 + 0.109525i
\(574\) −991412. 1.71718e6i −0.125596 0.217538i
\(575\) −1.23726e7 + 2.14300e7i −1.56060 + 2.70304i
\(576\) −683934. + 1.18461e6i −0.0858930 + 0.148771i
\(577\) −3.02925e6 + 5.24682e6i −0.378788 + 0.656080i −0.990886 0.134702i \(-0.956992\pi\)
0.612098 + 0.790782i \(0.290326\pi\)
\(578\) 5.64390e6 0.702683
\(579\) −5.18254e6 8.97642e6i −0.642460 1.11277i
\(580\) −3.26040e6 + 5.64718e6i −0.402440 + 0.697046i
\(581\) −1.00130e7 −1.23062
\(582\) 8.94532e6 1.09468
\(583\) 6.83421e6 1.18372e7i 0.832754 1.44237i
\(584\) −1.15822e6 −0.140526
\(585\) −1.26838e7 2.19690e7i −1.53236 2.65412i
\(586\) 2.63919e6 0.317487
\(587\) −3.55915e6 6.16463e6i −0.426335 0.738434i 0.570209 0.821500i \(-0.306862\pi\)
−0.996544 + 0.0830659i \(0.973529\pi\)
\(588\) −4.87710e6 8.44738e6i −0.581725 1.00758i
\(589\) 955135. + 1.65434e6i 0.113443 + 0.196488i
\(590\) 7.66838e6 1.32820e7i 0.906929 1.57085i
\(591\) −1.76535e7 −2.07903
\(592\) −1.09422e6 + 1.82954e6i −0.128322 + 0.214554i
\(593\) 9.42260e6 1.10036 0.550179 0.835047i \(-0.314559\pi\)
0.550179 + 0.835047i \(0.314559\pi\)
\(594\) −1.72748e6 + 2.99208e6i −0.200884 + 0.347942i
\(595\) −997937. 1.72848e6i −0.115561 0.200157i
\(596\) 3.35805e6 + 5.81631e6i 0.387232 + 0.670706i
\(597\) 179144. + 310286.i 0.0205715 + 0.0356309i
\(598\) 9.71674e6 1.11114
\(599\) 619395. + 1.07282e6i 0.0705343 + 0.122169i 0.899136 0.437670i \(-0.144196\pi\)
−0.828601 + 0.559839i \(0.810863\pi\)
\(600\) −1.15374e7 −1.30836
\(601\) 3.04422e6 5.27275e6i 0.343788 0.595458i −0.641345 0.767253i \(-0.721623\pi\)
0.985133 + 0.171795i \(0.0549566\pi\)
\(602\) 1.18487e7 1.33254
\(603\) 1.41729e7 1.58732
\(604\) 1.36591e6 2.36582e6i 0.152345 0.263870i
\(605\) −244169. 422913.i −0.0271208 0.0469746i
\(606\) −9.68374e6 −1.07118
\(607\) −2.18634e6 + 3.78685e6i −0.240849 + 0.417163i −0.960956 0.276699i \(-0.910759\pi\)
0.720107 + 0.693863i \(0.244093\pi\)
\(608\) 205822. 356494.i 0.0225805 0.0391105i
\(609\) −9.75089e6 + 1.68890e7i −1.06537 + 1.84528i
\(610\) 99817.2 + 172888.i 0.0108613 + 0.0188123i
\(611\) 6.95339e6 + 1.20436e7i 0.753518 + 1.30513i
\(612\) −251794. + 436121.i −0.0271749 + 0.0470683i
\(613\) −1.67511e6 + 2.90138e6i −0.180050 + 0.311855i −0.941897 0.335901i \(-0.890959\pi\)
0.761848 + 0.647756i \(0.224293\pi\)
\(614\) −3.70538e6 + 6.41791e6i −0.396654 + 0.687026i
\(615\) −5.97683e6 −0.637211
\(616\) 2.59862e6 + 4.50093e6i 0.275924 + 0.477915i
\(617\) −312937. + 542022.i −0.0330936 + 0.0573198i −0.882098 0.471066i \(-0.843869\pi\)
0.849004 + 0.528386i \(0.177203\pi\)
\(618\) −1.21113e6 −0.127562
\(619\) 4.23865e6 0.444632 0.222316 0.974975i \(-0.428638\pi\)
0.222316 + 0.974975i \(0.428638\pi\)
\(620\) −3.91951e6 + 6.78879e6i −0.409499 + 0.709272i
\(621\) 7.20305e6 0.749527
\(622\) −2.78240e6 4.81926e6i −0.288366 0.499464i
\(623\) 2.59824e7 2.68200
\(624\) 2.26520e6 + 3.92344e6i 0.232887 + 0.403372i
\(625\) −1.15538e7 2.00118e7i −1.18311 2.04920i
\(626\) −1.37305e6 2.37819e6i −0.140040 0.242556i
\(627\) 1.90880e6 3.30615e6i 0.193907 0.335856i
\(628\) −403497. −0.0408265
\(629\) −402843. + 673556.i −0.0405984 + 0.0678808i
\(630\) −2.82882e7 −2.83958
\(631\) −6.23079e6 + 1.07921e7i −0.622974 + 1.07902i 0.365955 + 0.930633i \(0.380742\pi\)
−0.988929 + 0.148390i \(0.952591\pi\)
\(632\) −184357. 319316.i −0.0183598 0.0318000i
\(633\) −9.61975e6 1.66619e7i −0.954233 1.65278i
\(634\) −2.39727e6 4.15220e6i −0.236861 0.410256i
\(635\) −3.95529e6 −0.389264
\(636\) −6.64321e6 1.15064e7i −0.651232 1.12797i
\(637\) −1.86994e7 −1.82591
\(638\) 3.12566e6 5.41380e6i 0.304012 0.526564i
\(639\) −6.29374e6 −0.609756
\(640\) 1.68923e6 0.163019
\(641\) −3.42273e6 + 5.92833e6i −0.329024 + 0.569885i −0.982318 0.187218i \(-0.940053\pi\)
0.653295 + 0.757104i \(0.273386\pi\)
\(642\) 6.25205e6 + 1.08289e7i 0.598666 + 1.03692i
\(643\) −5.22377e6 −0.498261 −0.249130 0.968470i \(-0.580145\pi\)
−0.249130 + 0.968470i \(0.580145\pi\)
\(644\) 5.41771e6 9.38375e6i 0.514756 0.891583i
\(645\) 1.78577e7 3.09305e7i 1.69016 2.92744i
\(646\) 75774.6 131245.i 0.00714402 0.0123738i
\(647\) 987639. + 1.71064e6i 0.0927550 + 0.160656i 0.908669 0.417516i \(-0.137099\pi\)
−0.815914 + 0.578173i \(0.803766\pi\)
\(648\) −917611. 1.58935e6i −0.0858462 0.148690i
\(649\) −7.35147e6 + 1.27331e7i −0.685113 + 1.18665i
\(650\) −1.10589e7 + 1.91547e7i −1.02667 + 1.77824i
\(651\) −1.17221e7 + 2.03032e7i −1.08406 + 1.87764i
\(652\) 8.49269e6 0.782395
\(653\) 1.11118e6 + 1.92462e6i 0.101977 + 0.176629i 0.912499 0.409079i \(-0.134150\pi\)
−0.810522 + 0.585708i \(0.800817\pi\)
\(654\) 4.82195e6 8.35187e6i 0.440838 0.763553i
\(655\) −1.25343e7 −1.14155
\(656\) 617834. 0.0560548
\(657\) −3.02179e6 + 5.23389e6i −0.273118 + 0.473054i
\(658\) 1.55079e7 1.39633
\(659\) −1.61293e6 2.79368e6i −0.144678 0.250589i 0.784575 0.620034i \(-0.212881\pi\)
−0.929253 + 0.369445i \(0.879548\pi\)
\(660\) 1.56660e7 1.39991
\(661\) 8.53576e6 + 1.47844e7i 0.759869 + 1.31613i 0.942917 + 0.333027i \(0.108070\pi\)
−0.183049 + 0.983104i \(0.558597\pi\)
\(662\) −1.20128e6 2.08068e6i −0.106537 0.184527i
\(663\) 833947. + 1.44444e6i 0.0736809 + 0.127619i
\(664\) 1.55999e6 2.70199e6i 0.137310 0.237828i
\(665\) 8.51301e6 0.746498
\(666\) 5.41273e6 + 9.71796e6i 0.472858 + 0.848964i
\(667\) −1.30330e7 −1.13431
\(668\) −1.62561e6 + 2.81564e6i −0.140953 + 0.244138i
\(669\) −4.50105e6 7.79605e6i −0.388820 0.673456i
\(670\) −8.75130e6 1.51577e7i −0.753157 1.30451i
\(671\) −95692.1 165744.i −0.00820483 0.0142112i
\(672\) 5.05199e6 0.431558
\(673\) 8.35440e6 + 1.44702e7i 0.711013 + 1.23151i 0.964477 + 0.264166i \(0.0850965\pi\)
−0.253465 + 0.967345i \(0.581570\pi\)
\(674\) 6.18636e6 0.524549
\(675\) −8.19804e6 + 1.41994e7i −0.692549 + 1.19953i
\(676\) 2.74439e6 0.230982
\(677\) 1.14872e7 0.963257 0.481629 0.876375i \(-0.340045\pi\)
0.481629 + 0.876375i \(0.340045\pi\)
\(678\) −6.80255e6 + 1.17824e7i −0.568326 + 0.984369i
\(679\) −9.56155e6 1.65611e7i −0.795892 1.37852i
\(680\) 621900. 0.0515761
\(681\) −1.63168e7 + 2.82615e7i −1.34824 + 2.33522i
\(682\) 3.75753e6 6.50823e6i 0.309344 0.535799i
\(683\) 3.25933e6 5.64532e6i 0.267347 0.463059i −0.700829 0.713330i \(-0.747186\pi\)
0.968176 + 0.250270i \(0.0805195\pi\)
\(684\) −1.07398e6 1.86019e6i −0.0877720 0.152026i
\(685\) 1.36659e7 + 2.36700e7i 1.11279 + 1.92740i
\(686\) −3.52196e6 + 6.10021e6i −0.285742 + 0.494919i
\(687\) 3.39161e6 5.87445e6i 0.274167 0.474871i
\(688\) −1.84598e6 + 3.19734e6i −0.148681 + 0.257524i
\(689\) −2.54710e7 −2.04408
\(690\) −1.63306e7 2.82854e7i −1.30581 2.26173i
\(691\) −1.03095e7 + 1.78566e7i −0.821380 + 1.42267i 0.0832746 + 0.996527i \(0.473462\pi\)
−0.904655 + 0.426145i \(0.859871\pi\)
\(692\) −5.39986e6 −0.428665
\(693\) 2.71192e7 2.14508
\(694\) 1.81694e6 3.14703e6i 0.143199 0.248029i
\(695\) 4.86427e6 0.381993
\(696\) −3.03831e6 5.26251e6i −0.237744 0.411784i
\(697\) 227459. 0.0177346
\(698\) −6.42564e6 1.11295e7i −0.499204 0.864647i
\(699\) −1.65405e7 2.86491e7i −1.28043 2.21777i
\(700\) 1.23322e7 + 2.13599e7i 0.951249 + 1.64761i
\(701\) 7.37806e6 1.27792e7i 0.567084 0.982218i −0.429769 0.902939i \(-0.641405\pi\)
0.996852 0.0792787i \(-0.0252617\pi\)
\(702\) 6.43828e6 0.493091
\(703\) −1.62890e6 2.92451e6i −0.124310 0.223185i
\(704\) −1.61942e6 −0.123148
\(705\) 2.33727e7 4.04827e7i 1.77107 3.06758i
\(706\) 5.68923e6 + 9.85404e6i 0.429578 + 0.744050i
\(707\) 1.03508e7 + 1.79282e7i 0.778802 + 1.34892i
\(708\) 7.14602e6 + 1.23773e7i 0.535774 + 0.927987i
\(709\) −2.84672e6 −0.212682 −0.106341 0.994330i \(-0.533913\pi\)
−0.106341 + 0.994330i \(0.533913\pi\)
\(710\) 3.88618e6 + 6.73106e6i 0.289319 + 0.501116i
\(711\) −1.92395e6 −0.142731
\(712\) −4.04796e6 + 7.01128e6i −0.299252 + 0.518319i
\(713\) −1.56677e7 −1.15420
\(714\) 1.85992e6 0.136536
\(715\) 1.50164e7 2.60091e7i 1.09850 1.90266i
\(716\) −4.21261e6 7.29645e6i −0.307092 0.531899i
\(717\) −3.77166e7 −2.73990
\(718\) −960760. + 1.66408e6i −0.0695511 + 0.120466i
\(719\) −6.14389e6 + 1.06415e7i −0.443222 + 0.767683i −0.997926 0.0643642i \(-0.979498\pi\)
0.554704 + 0.832048i \(0.312831\pi\)
\(720\) 4.40720e6 7.63350e6i 0.316834 0.548773i
\(721\) 1.29456e6 + 2.24225e6i 0.0927439 + 0.160637i
\(722\) −4.62900e6 8.01766e6i −0.330479 0.572406i
\(723\) 8.06331e6 1.39661e7i 0.573678 0.993639i
\(724\) −196220. + 339863.i −0.0139122 + 0.0240967i
\(725\) 1.48333e7 2.56921e7i 1.04808 1.81533i
\(726\) 455073. 0.0320435
\(727\) 1.07543e7 + 1.86270e7i 0.754653 + 1.30710i 0.945547 + 0.325486i \(0.105528\pi\)
−0.190894 + 0.981611i \(0.561139\pi\)
\(728\) 4.84249e6 8.38745e6i 0.338642 0.586545i
\(729\) −2.23276e7 −1.55605
\(730\) 7.46343e6 0.518360
\(731\) −679610. + 1.17712e6i −0.0470399 + 0.0814754i
\(732\) −186036. −0.0128327
\(733\) 4.59209e6 + 7.95373e6i 0.315682 + 0.546778i 0.979582 0.201043i \(-0.0644332\pi\)
−0.663900 + 0.747821i \(0.731100\pi\)
\(734\) 1.38049e7 0.945786
\(735\) 3.14275e7 + 5.44341e7i 2.14581 + 3.71666i
\(736\) 1.68812e6 + 2.92391e6i 0.114871 + 0.198962i
\(737\) 8.38965e6 + 1.45313e7i 0.568951 + 0.985452i
\(738\) 1.61193e6 2.79195e6i 0.108945 0.188697i
\(739\) −5.02845e6 −0.338706 −0.169353 0.985555i \(-0.554168\pi\)
−0.169353 + 0.985555i \(0.554168\pi\)
\(740\) 7.05104e6 1.17894e7i 0.473340 0.791428i
\(741\) −7.11408e6 −0.475963
\(742\) −1.42017e7 + 2.45981e7i −0.946958 + 1.64018i
\(743\) −4.42667e6 7.66721e6i −0.294174 0.509525i 0.680618 0.732638i \(-0.261711\pi\)
−0.974792 + 0.223113i \(0.928378\pi\)
\(744\) −3.65252e6 6.32635e6i −0.241914 0.419007i
\(745\) −2.16389e7 3.74797e7i −1.42838 2.47404i
\(746\) −1.08959e7 −0.716831
\(747\) −8.14005e6 1.40990e7i −0.533735 0.924456i
\(748\) −596199. −0.0389617
\(749\) 1.33655e7 2.31497e7i 0.870523 1.50779i
\(750\) 4.33894e7 2.81664
\(751\) 5.56144e6 0.359822 0.179911 0.983683i \(-0.442419\pi\)
0.179911 + 0.983683i \(0.442419\pi\)
\(752\) −2.41607e6 + 4.18476e6i −0.155799 + 0.269852i
\(753\) 1.58200e7 + 2.74010e7i 1.01676 + 1.76108i
\(754\) −1.16493e7 −0.746226
\(755\) −8.80178e6 + 1.52451e7i −0.561957 + 0.973338i
\(756\) 3.58976e6 6.21764e6i 0.228434 0.395659i
\(757\) 1.14793e7 1.98827e7i 0.728072 1.26106i −0.229625 0.973279i \(-0.573750\pi\)
0.957697 0.287778i \(-0.0929166\pi\)
\(758\) −4.75225e6 8.23113e6i −0.300418 0.520339i
\(759\) 1.56557e7 + 2.71165e7i 0.986436 + 1.70856i
\(760\) −1.32630e6 + 2.29721e6i −0.0832927 + 0.144267i
\(761\) −6.27405e6 + 1.08670e7i −0.392723 + 0.680216i −0.992808 0.119720i \(-0.961800\pi\)
0.600085 + 0.799937i \(0.295134\pi\)
\(762\) 1.84293e6 3.19205e6i 0.114980 0.199151i
\(763\) −2.06165e7 −1.28205
\(764\) 331046. + 573388.i 0.0205189 + 0.0355398i
\(765\) 1.62254e6 2.81032e6i 0.100240 0.173621i
\(766\) 1.51459e7 0.932659
\(767\) 2.73988e7 1.68168
\(768\) −787082. + 1.36327e6i −0.0481523 + 0.0834022i
\(769\) −1.96795e7 −1.20004 −0.600022 0.799984i \(-0.704842\pi\)
−0.600022 + 0.799984i \(0.704842\pi\)
\(770\) −1.67452e7 2.90036e7i −1.01780 1.76289i
\(771\) 2.11940e7 1.28404
\(772\) −3.45218e6 5.97934e6i −0.208473 0.361086i
\(773\) −5.16058e6 8.93839e6i −0.310635 0.538035i 0.667865 0.744282i \(-0.267208\pi\)
−0.978500 + 0.206247i \(0.933875\pi\)
\(774\) 9.63234e6 + 1.66837e7i 0.577936 + 1.00101i
\(775\) 1.78320e7 3.08859e7i 1.06646 1.84717i
\(776\) 5.95863e6 0.355215
\(777\) 2.10876e7 3.52585e7i 1.25307 2.09513i
\(778\) −3.45377e6 −0.204571
\(779\) −485092. + 840204.i −0.0286405 + 0.0496068i
\(780\) −1.45967e7 2.52823e7i −0.859051 1.48792i
\(781\) −3.72558e6 6.45290e6i −0.218558 0.378553i
\(782\) 621492. + 1.07646e6i 0.0363428 + 0.0629476i
\(783\) −8.63565e6 −0.503374
\(784\) −3.24871e6 5.62694e6i −0.188765 0.326950i
\(785\) 2.60010e6 0.150597
\(786\) 5.84023e6 1.01156e7i 0.337189 0.584029i
\(787\) 2.79254e6 0.160717 0.0803587 0.996766i \(-0.474393\pi\)
0.0803587 + 0.996766i \(0.474393\pi\)
\(788\) −1.17593e7 −0.674628
\(789\) −1.38192e7 + 2.39355e7i −0.790294 + 1.36883i
\(790\) 1.18798e6 + 2.05764e6i 0.0677237 + 0.117301i
\(791\) 2.90847e7 1.65281
\(792\) −4.22507e6 + 7.31804e6i −0.239343 + 0.414554i
\(793\) −178321. + 308862.i −0.0100698 + 0.0174414i
\(794\) −1.07068e6 + 1.85447e6i −0.0602711 + 0.104393i
\(795\) 4.28082e7 + 7.41460e7i 2.40220 + 4.16073i
\(796\) 119331. + 206687.i 0.00667528 + 0.0115619i
\(797\) 9.30020e6 1.61084e7i 0.518616 0.898270i −0.481150 0.876639i \(-0.659781\pi\)
0.999766 0.0216316i \(-0.00688608\pi\)
\(798\) −3.96656e6 + 6.87028e6i −0.220499 + 0.381916i
\(799\) −889491. + 1.54064e6i −0.0492918 + 0.0853759i
\(800\) −7.68523e6 −0.424553
\(801\) 2.11223e7 + 3.65849e7i 1.16321 + 2.01475i
\(802\) 9.33339e6 1.61659e7i 0.512393 0.887491i
\(803\) −7.15499e6 −0.391580
\(804\) 1.63104e7 0.889864
\(805\) −3.49112e7 + 6.04680e7i −1.89878 + 3.28879i
\(806\) −1.40042e7 −0.759315
\(807\) 3.55500e6 + 6.15744e6i 0.192157 + 0.332825i
\(808\) −6.45050e6 −0.347588
\(809\) −1.56542e6 2.71140e6i −0.0840932 0.145654i 0.820911 0.571056i \(-0.193466\pi\)
−0.905004 + 0.425402i \(0.860133\pi\)
\(810\) 5.91299e6 + 1.02416e7i 0.316661 + 0.548473i
\(811\) 2.14826e6 + 3.72089e6i 0.114692 + 0.198653i 0.917657 0.397374i \(-0.130079\pi\)
−0.802964 + 0.596027i \(0.796745\pi\)
\(812\) −6.49523e6 + 1.12501e7i −0.345704 + 0.598777i
\(813\) 2.90800e7 1.54301
\(814\) −6.75964e6 + 1.13022e7i −0.357571 + 0.597861i
\(815\) −5.47260e7 −2.88602
\(816\) −289769. + 501894.i −0.0152344 + 0.0263868i
\(817\) −2.89874e6 5.02077e6i −0.151934 0.263157i
\(818\) 1.24843e7 + 2.16235e7i 0.652353 + 1.12991i
\(819\) −2.52681e7 4.37657e7i −1.31633 2.27994i
\(820\) −3.98126e6 −0.206769
\(821\) 1.20562e7 + 2.08819e7i 0.624239 + 1.08121i 0.988688 + 0.149990i \(0.0479242\pi\)
−0.364449 + 0.931224i \(0.618743\pi\)
\(822\) −2.54700e7 −1.31477
\(823\) −1.01013e7 + 1.74960e7i −0.519849 + 0.900406i 0.479884 + 0.877332i \(0.340679\pi\)
−0.999734 + 0.0230738i \(0.992655\pi\)
\(824\) −806754. −0.0413926
\(825\) −7.12733e7 −3.64579
\(826\) 1.52766e7 2.64599e7i 0.779070 1.34939i
\(827\) 1.43337e6 + 2.48267e6i 0.0728777 + 0.126228i 0.900161 0.435557i \(-0.143448\pi\)
−0.827284 + 0.561784i \(0.810115\pi\)
\(828\) 1.76172e7 0.893022
\(829\) 477710. 827419.i 0.0241423 0.0418157i −0.853702 0.520762i \(-0.825648\pi\)
0.877844 + 0.478946i \(0.158981\pi\)
\(830\) −1.00524e7 + 1.74113e7i −0.506497 + 0.877278i
\(831\) −1.13493e6 + 1.96576e6i −0.0570120 + 0.0987477i
\(832\) 1.50889e6 + 2.61347e6i 0.0755698 + 0.130891i
\(833\) −1.19603e6 2.07159e6i −0.0597215 0.103441i
\(834\) −2.26646e6 + 3.92563e6i −0.112832 + 0.195431i
\(835\) 1.04753e7 1.81437e7i 0.519935 0.900554i
\(836\) 1.27149e6 2.20228e6i 0.0629210 0.108982i
\(837\) −1.03814e7 −0.512203
\(838\) 425017. + 736150.i 0.0209072 + 0.0362123i
\(839\) 1.85410e7 3.21140e7i 0.909344 1.57503i 0.0943674 0.995537i \(-0.469917\pi\)
0.814977 0.579493i \(-0.196750\pi\)
\(840\) −3.25545e7 −1.59189
\(841\) −4.88600e6 −0.238212
\(842\) −3.02567e6 + 5.24061e6i −0.147076 + 0.254743i
\(843\) −3.95042e6 −0.191458
\(844\) −6.40787e6 1.10988e7i −0.309641 0.536313i
\(845\) −1.76846e7 −0.852026
\(846\) 1.26071e7 + 2.18361e7i 0.605603 + 1.04894i
\(847\) −486423. 842509.i −0.0232973 0.0403521i
\(848\) −4.42515e6 7.66459e6i −0.211319 0.366015i
\(849\) 7.26455e6 1.25826e7i 0.345891 0.599101i
\(850\) −2.82936e6 −0.134320
\(851\) 2.74528e7 + 423108.i 1.29946 + 0.0200275i
\(852\) −7.24293e6 −0.341834
\(853\) −6.60414e6 + 1.14387e7i −0.310773 + 0.538275i −0.978530 0.206105i \(-0.933921\pi\)
0.667757 + 0.744380i \(0.267255\pi\)
\(854\) 198851. + 344421.i 0.00933005 + 0.0161601i
\(855\) 6.92062e6 + 1.19869e7i 0.323765 + 0.560777i
\(856\) 4.16459e6 + 7.21328e6i 0.194262 + 0.336472i
\(857\) 2.61370e7 1.21564 0.607818 0.794076i \(-0.292045\pi\)
0.607818 + 0.794076i \(0.292045\pi\)
\(858\) 1.39935e7 + 2.42375e7i 0.648945 + 1.12401i
\(859\) −2.51655e7 −1.16365 −0.581825 0.813314i \(-0.697661\pi\)
−0.581825 + 0.813314i \(0.697661\pi\)
\(860\) 1.18953e7 2.06033e7i 0.548442 0.949929i
\(861\) −1.19068e7 −0.547377
\(862\) −1.93997e7 −0.889255
\(863\) −5.74881e6 + 9.95722e6i −0.262755 + 0.455105i −0.966973 0.254879i \(-0.917964\pi\)
0.704218 + 0.709984i \(0.251298\pi\)
\(864\) 1.11854e6 + 1.93737e6i 0.0509763 + 0.0882936i
\(865\) 3.47962e7 1.58122
\(866\) −2.78188e6 + 4.81835e6i −0.126050 + 0.218325i
\(867\) 1.69457e7 2.93508e7i 0.765616 1.32609i
\(868\) −7.80827e6 + 1.35243e7i −0.351767 + 0.609279i
\(869\) −1.13888e6 1.97260e6i −0.0511599 0.0886116i
\(870\) 1.95786e7 + 3.39111e7i 0.876966 + 1.51895i
\(871\) 1.56340e7 2.70789e7i 0.698273 1.20944i
\(872\) 3.21198e6 5.56332e6i 0.143048 0.247766i
\(873\) 1.55461e7 2.69266e7i 0.690375 1.19576i
\(874\) −5.30170e6 −0.234767
\(875\) −4.63784e7 8.03298e7i −2.04784 3.54696i
\(876\) −3.47752e6 + 6.02324e6i −0.153112 + 0.265198i
\(877\) −4.63660e6 −0.203564 −0.101782 0.994807i \(-0.532454\pi\)
−0.101782 + 0.994807i \(0.532454\pi\)
\(878\) 4.11546e6 0.180170
\(879\) 7.92411e6 1.37250e7i 0.345922 0.599155i
\(880\) 1.04354e7 0.454257
\(881\) 1.51867e7 + 2.63042e7i 0.659210 + 1.14179i 0.980820 + 0.194914i \(0.0624426\pi\)
−0.321610 + 0.946872i \(0.604224\pi\)
\(882\) −3.39036e7 −1.46749
\(883\) −497335. 861410.i −0.0214658 0.0371799i 0.855093 0.518475i \(-0.173500\pi\)
−0.876559 + 0.481295i \(0.840167\pi\)
\(884\) 555506. + 962164.i 0.0239088 + 0.0414113i
\(885\) −4.60483e7 7.97579e7i −1.97631 3.42307i
\(886\) −5.86014e6 + 1.01501e7i −0.250798 + 0.434395i
\(887\) −1.42289e7 −0.607241 −0.303621 0.952793i \(-0.598196\pi\)
−0.303621 + 0.952793i \(0.598196\pi\)
\(888\) 6.22905e6 + 1.11836e7i 0.265088 + 0.475936i
\(889\) −7.87956e6 −0.334386
\(890\) 2.60847e7 4.51800e7i 1.10385 1.91193i
\(891\) −5.66863e6 9.81836e6i −0.239213 0.414328i
\(892\) −2.99822e6 5.19308e6i −0.126169 0.218531i
\(893\) −3.79395e6 6.57132e6i −0.159207 0.275755i
\(894\) 4.03299e7 1.68765
\(895\) 2.71456e7 + 4.70176e7i 1.13277 + 1.96202i
\(896\) 3.36521e6 0.140037
\(897\) 2.91743e7 5.05314e7i 1.21065 2.09691i
\(898\) 1.78502e6 0.0738675
\(899\) 1.87839e7 0.775150
\(900\) −2.00508e7 + 3.47290e7i −0.825135 + 1.42918i
\(901\) −1.62915e6 2.82177e6i −0.0668572 0.115800i
\(902\) 3.81673e6 0.156198
\(903\) 3.55754e7 6.16184e7i 1.45188 2.51473i
\(904\) −4.53129e6 + 7.84842e6i −0.184417 + 0.319419i
\(905\) 1.26442e6 2.19004e6i 0.0513181 0.0888856i
\(906\) −8.20222e6 1.42067e7i −0.331979 0.575005i
\(907\) −2.19475e7 3.80142e7i −0.885863 1.53436i −0.844721 0.535206i \(-0.820234\pi\)
−0.0411417 0.999153i \(-0.513099\pi\)
\(908\) −1.08689e7 + 1.88255e7i −0.437492 + 0.757759i
\(909\) −1.68294e7 + 2.91493e7i −0.675550 + 1.17009i
\(910\) −3.12046e7 + 5.40479e7i −1.24915 + 2.16359i
\(911\) −2.73730e7 −1.09276 −0.546382 0.837536i \(-0.683995\pi\)
−0.546382 + 0.837536i \(0.683995\pi\)
\(912\) −1.23595e6 2.14073e6i −0.0492056 0.0852266i
\(913\) 9.63702e6 1.66918e7i 0.382618 0.662714i
\(914\) 1.86725e7 0.739328
\(915\) 1.19880e6 0.0473361
\(916\) 2.25921e6 3.91307e6i 0.0889647 0.154091i
\(917\) −2.49702e7 −0.980616
\(918\) 411798. + 713256.i 0.0161279 + 0.0279343i
\(919\) 9.32028e6 0.364033 0.182016 0.983296i \(-0.441738\pi\)
0.182016 + 0.983296i \(0.441738\pi\)
\(920\) −1.08781e7 1.88414e7i −0.423724 0.733911i
\(921\) 2.22507e7 + 3.85393e7i 0.864359 + 1.49711i
\(922\) −7.77111e6 1.34600e7i −0.301062 0.521455i
\(923\) −6.94258e6 + 1.20249e7i −0.268236 + 0.464598i
\(924\) 3.12091e7 1.20255
\(925\) −3.20790e7 + 5.36363e7i −1.23273 + 2.06113i
\(926\) −2.79793e7 −1.07228
\(927\) −2.10482e6 + 3.64566e6i −0.0804482 + 0.139340i
\(928\) −2.02387e6 3.50544e6i −0.0771458 0.133620i
\(929\) 2.35370e6 + 4.07673e6i 0.0894770 + 0.154979i 0.907290 0.420505i \(-0.138147\pi\)
−0.817813 + 0.575484i \(0.804814\pi\)
\(930\) 2.35365e7 + 4.07664e7i 0.892348 + 1.54559i
\(931\) 1.02029e7 0.385788
\(932\) −1.10179e7 1.90836e7i −0.415490 0.719649i
\(933\) −3.34164e7 −1.25677
\(934\) 1.02118e6 1.76874e6i 0.0383033 0.0663433i
\(935\) 3.84185e6 0.143718
\(936\) 1.57468e7 0.587491
\(937\) −1.88772e7 + 3.26963e7i −0.702406 + 1.21660i 0.265213 + 0.964190i \(0.414558\pi\)
−0.967619 + 0.252414i \(0.918776\pi\)
\(938\) −1.74340e7 3.01965e7i −0.646977 1.12060i
\(939\) −1.64902e7 −0.610327
\(940\) 1.55689e7 2.69662e7i 0.574697 0.995405i
\(941\) −1.38473e7 + 2.39842e7i −0.509790 + 0.882982i 0.490146 + 0.871641i \(0.336944\pi\)
−0.999936 + 0.0113418i \(0.996390\pi\)
\(942\) −1.21149e6 + 2.09837e6i −0.0444829 + 0.0770467i
\(943\) −3.97865e6 6.89122e6i −0.145699 0.252358i
\(944\) 4.76008e6 + 8.24470e6i 0.173854 + 0.301124i
\(945\) −2.31320e7 + 4.00659e7i −0.842625 + 1.45947i
\(946\) −1.14037e7 + 1.97519e7i −0.414304 + 0.717596i
\(947\) −1.13434e7 + 1.96474e7i −0.411026 + 0.711918i −0.995002 0.0998530i \(-0.968163\pi\)
0.583976 + 0.811771i \(0.301496\pi\)
\(948\) −2.21411e6 −0.0800163
\(949\) 6.66663e6 + 1.15469e7i 0.240293 + 0.416199i
\(950\) 6.03405e6 1.04513e7i 0.216920 0.375717i
\(951\) −2.87910e7 −1.03230
\(952\) 1.23892e6 0.0443049
\(953\) −2.26437e6 + 3.92200e6i −0.0807635 + 0.139887i −0.903578 0.428423i \(-0.859069\pi\)
0.822815 + 0.568310i \(0.192403\pi\)
\(954\) −4.61809e7 −1.64283
\(955\) −2.13323e6 3.69486e6i −0.0756883 0.131096i
\(956\) −2.51236e7 −0.889073
\(957\) −1.87695e7 3.25097e7i −0.662479 1.14745i
\(958\) −1.37619e7 2.38364e7i −0.484469 0.839125i
\(959\) 2.72246e7 + 4.71544e7i 0.955906 + 1.65568i
\(960\) 5.07188e6 8.78475e6i 0.177620 0.307646i
\(961\) −6.04803e6 −0.211254
\(962\) 2.45380e7 + 378185.i 0.854874 + 0.0131755i
\(963\) 4.34617e7 1.51022
\(964\) 5.37111e6 9.30303e6i 0.186153 0.322427i
\(965\) 2.22455e7 + 3.85303e7i 0.768995 + 1.33194i
\(966\) −3.25331e7 5.63490e7i −1.12172 1.94287i
\(967\) 8.87152e6 + 1.53659e7i 0.305093 + 0.528436i 0.977282 0.211943i \(-0.0679792\pi\)
−0.672189 + 0.740379i \(0.734646\pi\)
\(968\) 303132. 0.0103978
\(969\) −455023. 788123.i −0.0155677 0.0269640i
\(970\) −3.83968e7 −1.31028
\(971\) −8.98454e6 + 1.55617e7i −0.305807 + 0.529674i −0.977441 0.211210i \(-0.932260\pi\)
0.671633 + 0.740884i \(0.265593\pi\)
\(972\) −1.95144e7 −0.662504
\(973\) 9.69039e6 0.328140
\(974\) 5.69153e6 9.85802e6i 0.192235 0.332960i
\(975\) 6.64085e7 + 1.15023e8i 2.23724 + 3.87501i
\(976\) −123921. −0.00416411
\(977\) 1.04737e7 1.81410e7i 0.351046 0.608030i −0.635387 0.772194i \(-0.719159\pi\)
0.986433 + 0.164164i \(0.0524926\pi\)
\(978\) 2.54991e7 4.41657e7i 0.852468 1.47652i
\(979\) −2.50067e7 + 4.33129e7i −0.833873 + 1.44431i
\(980\) 2.09344e7 + 3.62594e7i 0.696298 + 1.20602i
\(981\) −1.67601e7 2.90294e7i −0.556038 0.963087i
\(982\) −1.76948e7 + 3.06482e7i −0.585553 + 1.01421i
\(983\) −2.72947e7 + 4.72759e7i −0.900939 + 1.56047i −0.0746606 + 0.997209i \(0.523787\pi\)
−0.826278 + 0.563262i \(0.809546\pi\)
\(984\) 1.85503e6 3.21301e6i 0.0610751 0.105785i
\(985\) 7.57755e7 2.48850
\(986\) −745099. 1.29055e6i −0.0244074 0.0422749i
\(987\) 4.65620e7 8.06478e7i 1.52139 2.63512i
\(988\) −4.73880e6 −0.154446
\(989\) 4.75501e7 1.54583
\(990\) 2.72259e7 4.71567e7i 0.882866 1.52917i
\(991\) 5.06058e7 1.63688 0.818438 0.574594i \(-0.194840\pi\)
0.818438 + 0.574594i \(0.194840\pi\)
\(992\) −2.43300e6 4.21409e6i −0.0784989 0.135964i
\(993\) −1.44273e7 −0.464313
\(994\) 7.74188e6 + 1.34093e7i 0.248531 + 0.430468i
\(995\) −768955. 1.33187e6i −0.0246231 0.0426485i
\(996\) −9.36770e6 1.62253e7i −0.299216 0.518257i
\(997\) 8.99550e6 1.55807e7i 0.286607 0.496418i −0.686390 0.727233i \(-0.740806\pi\)
0.972998 + 0.230815i \(0.0741392\pi\)
\(998\) −4.73451e6 −0.150470
\(999\) 1.81901e7 + 280350.i 0.576663 + 0.00888764i
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 74.6.c.b.47.2 16
37.26 even 3 inner 74.6.c.b.63.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.6.c.b.47.2 16 1.1 even 1 trivial
74.6.c.b.63.2 yes 16 37.26 even 3 inner