Properties

Label 14.6.c.a.9.1
Level $14$
Weight $6$
Character 14.9
Analytic conductor $2.245$
Analytic rank $0$
Dimension $4$
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] = [14,6,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
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("14.9");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 14.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: \(2.24537347738\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{79})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 79x^{2} + 6241 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.1
Root \(4.44410 + 7.69740i\) of defining polynomial
Character \(\chi\) \(=\) 14.9
Dual form 14.6.c.a.11.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 + 3.46410i) q^{2} +(-12.3882 - 21.4570i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(18.0528 - 31.2683i) q^{5} +99.1056 q^{6} +(-124.435 - 36.3731i) q^{7} +64.0000 q^{8} +(-185.435 + 321.182i) q^{9} +O(q^{10})\) \(q+(-2.00000 + 3.46410i) q^{2} +(-12.3882 - 21.4570i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(18.0528 - 31.2683i) q^{5} +99.1056 q^{6} +(-124.435 - 36.3731i) q^{7} +64.0000 q^{8} +(-185.435 + 321.182i) q^{9} +(72.2111 + 125.073i) q^{10} +(-77.7174 - 134.610i) q^{11} +(-198.211 + 343.312i) q^{12} +1158.87 q^{13} +(374.869 - 358.308i) q^{14} -894.565 q^{15} +(-128.000 + 221.703i) q^{16} +(-619.040 - 1072.21i) q^{17} +(-741.739 - 1284.73i) q^{18} +(140.140 - 242.729i) q^{19} -577.689 q^{20} +(761.065 + 3120.59i) q^{21} +621.739 q^{22} +(1741.20 - 3015.84i) q^{23} +(-792.844 - 1373.25i) q^{24} +(910.694 + 1577.37i) q^{25} +(-2317.74 + 4014.44i) q^{26} +3168.14 q^{27} +(491.478 + 2015.20i) q^{28} -5656.78 q^{29} +(1789.13 - 3098.87i) q^{30} +(1157.35 + 2004.59i) q^{31} +(-512.000 - 886.810i) q^{32} +(-1925.56 + 3335.16i) q^{33} +4952.32 q^{34} +(-3383.72 + 3234.23i) q^{35} +5933.91 q^{36} +(1166.59 - 2020.59i) q^{37} +(560.558 + 970.916i) q^{38} +(-14356.3 - 24865.8i) q^{39} +(1155.38 - 2001.17i) q^{40} +3812.61 q^{41} +(-12332.2 - 3604.77i) q^{42} +3925.73 q^{43} +(-1243.48 + 2153.77i) q^{44} +(6695.22 + 11596.5i) q^{45} +(6964.78 + 12063.4i) q^{46} +(5558.23 - 9627.13i) q^{47} +6342.76 q^{48} +(14161.0 + 9052.14i) q^{49} -7285.56 q^{50} +(-15337.6 + 26565.5i) q^{51} +(-9270.96 - 16057.8i) q^{52} +(5593.10 + 9687.54i) q^{53} +(-6336.29 + 10974.8i) q^{54} -5612.06 q^{55} +(-7963.82 - 2327.88i) q^{56} -6944.31 q^{57} +(11313.6 - 19595.7i) q^{58} +(3005.18 + 5205.12i) q^{59} +(7156.52 + 12395.5i) q^{60} +(7419.36 - 12850.7i) q^{61} -9258.81 q^{62} +(34756.9 - 33221.4i) q^{63} +4096.00 q^{64} +(20920.8 - 36235.9i) q^{65} +(-7702.22 - 13340.6i) q^{66} +(21491.9 + 37225.1i) q^{67} +(-9904.64 + 17155.3i) q^{68} -86281.1 q^{69} +(-4436.27 - 18190.0i) q^{70} -19962.4 q^{71} +(-11867.8 + 20555.7i) q^{72} +(-22775.3 - 39448.0i) q^{73} +(4666.35 + 8082.36i) q^{74} +(22563.7 - 39081.5i) q^{75} -4484.47 q^{76} +(4774.54 + 19577.0i) q^{77} +114850. q^{78} +(-54496.0 + 94389.9i) q^{79} +(4621.51 + 8004.69i) q^{80} +(5813.07 + 10068.5i) q^{81} +(-7625.22 + 13207.3i) q^{82} +55829.0 q^{83} +(37151.6 - 35510.4i) q^{84} -44701.6 q^{85} +(-7851.47 + 13599.1i) q^{86} +(70077.3 + 121377. i) q^{87} +(-4973.91 - 8615.07i) q^{88} +(47772.9 - 82745.1i) q^{89} -53561.8 q^{90} +(-144204. - 42151.6i) q^{91} -55718.2 q^{92} +(28675.0 - 49666.5i) q^{93} +(22232.9 + 38508.5i) q^{94} +(-5059.82 - 8763.86i) q^{95} +(-12685.5 + 21971.9i) q^{96} +15004.9 q^{97} +(-59679.5 + 30950.9i) q^{98} +57646.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} - 14 q^{3} - 32 q^{4} - 70 q^{5} + 112 q^{6} + 256 q^{8} - 244 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{2} - 14 q^{3} - 32 q^{4} - 70 q^{5} + 112 q^{6} + 256 q^{8} - 244 q^{9} - 280 q^{10} - 62 q^{11} - 224 q^{12} + 3640 q^{13} + 504 q^{14} - 4076 q^{15} - 512 q^{16} - 1694 q^{17} - 976 q^{18} - 826 q^{19} + 2240 q^{20} + 3542 q^{21} + 496 q^{22} + 2734 q^{23} - 896 q^{24} - 6312 q^{25} - 7280 q^{26} + 14308 q^{27} - 2016 q^{28} - 5704 q^{29} + 8152 q^{30} + 2674 q^{31} - 2048 q^{32} - 4858 q^{33} + 13552 q^{34} - 13286 q^{35} + 7808 q^{36} + 9146 q^{37} - 3304 q^{38} - 21588 q^{39} - 4480 q^{40} + 12264 q^{41} - 35392 q^{42} - 32080 q^{43} - 992 q^{44} + 26852 q^{45} + 10936 q^{46} + 25326 q^{47} + 7168 q^{48} + 56644 q^{49} + 50496 q^{50} - 25762 q^{51} - 29120 q^{52} - 14958 q^{53} - 28616 q^{54} - 31052 q^{55} - 37732 q^{57} + 11408 q^{58} + 1106 q^{59} + 32608 q^{60} + 28042 q^{61} - 21392 q^{62} + 77308 q^{63} + 16384 q^{64} - 28308 q^{65} - 19432 q^{66} + 102642 q^{67} - 27104 q^{68} - 188692 q^{69} - 88424 q^{70} - 22112 q^{71} - 15616 q^{72} - 35070 q^{73} + 36584 q^{74} + 132776 q^{75} + 26432 q^{76} + 27062 q^{77} + 172704 q^{78} - 101762 q^{79} - 17920 q^{80} + 23750 q^{81} - 24528 q^{82} - 89264 q^{83} + 84896 q^{84} + 7348 q^{85} + 64160 q^{86} + 170380 q^{87} - 3968 q^{88} + 75474 q^{89} - 214816 q^{90} - 123872 q^{91} - 87488 q^{92} + 53478 q^{93} + 101304 q^{94} - 127502 q^{95} - 14336 q^{96} - 16632 q^{97} - 113288 q^{98} + 139000 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −12.3882 21.4570i −0.794703 1.37647i −0.923028 0.384734i \(-0.874293\pi\)
0.128325 0.991732i \(-0.459040\pi\)
\(4\) −8.00000 13.8564i −0.250000 0.433013i
\(5\) 18.0528 31.2683i 0.322938 0.559345i −0.658155 0.752883i \(-0.728663\pi\)
0.981093 + 0.193538i \(0.0619962\pi\)
\(6\) 99.1056 1.12388
\(7\) −124.435 36.3731i −0.959835 0.280566i
\(8\) 64.0000 0.353553
\(9\) −185.435 + 321.182i −0.763106 + 1.32174i
\(10\) 72.2111 + 125.073i 0.228352 + 0.395517i
\(11\) −77.7174 134.610i −0.193658 0.335426i 0.752801 0.658248i \(-0.228702\pi\)
−0.946460 + 0.322821i \(0.895369\pi\)
\(12\) −198.211 + 343.312i −0.397352 + 0.688233i
\(13\) 1158.87 1.90185 0.950925 0.309422i \(-0.100136\pi\)
0.950925 + 0.309422i \(0.100136\pi\)
\(14\) 374.869 358.308i 0.511164 0.488581i
\(15\) −894.565 −1.02656
\(16\) −128.000 + 221.703i −0.125000 + 0.216506i
\(17\) −619.040 1072.21i −0.519513 0.899823i −0.999743 0.0226804i \(-0.992780\pi\)
0.480230 0.877143i \(-0.340553\pi\)
\(18\) −741.739 1284.73i −0.539597 0.934610i
\(19\) 140.140 242.729i 0.0890588 0.154254i −0.818055 0.575140i \(-0.804947\pi\)
0.907114 + 0.420886i \(0.138281\pi\)
\(20\) −577.689 −0.322938
\(21\) 761.065 + 3120.59i 0.376594 + 1.54415i
\(22\) 621.739 0.273874
\(23\) 1741.20 3015.84i 0.686322 1.18874i −0.286698 0.958021i \(-0.592557\pi\)
0.973019 0.230723i \(-0.0741092\pi\)
\(24\) −792.844 1373.25i −0.280970 0.486654i
\(25\) 910.694 + 1577.37i 0.291422 + 0.504758i
\(26\) −2317.74 + 4014.44i −0.672405 + 1.16464i
\(27\) 3168.14 0.836364
\(28\) 491.478 + 2015.20i 0.118470 + 0.485762i
\(29\) −5656.78 −1.24903 −0.624517 0.781011i \(-0.714704\pi\)
−0.624517 + 0.781011i \(0.714704\pi\)
\(30\) 1789.13 3098.87i 0.362943 0.628636i
\(31\) 1157.35 + 2004.59i 0.216302 + 0.374646i 0.953675 0.300840i \(-0.0972671\pi\)
−0.737372 + 0.675486i \(0.763934\pi\)
\(32\) −512.000 886.810i −0.0883883 0.153093i
\(33\) −1925.56 + 3335.16i −0.307802 + 0.533128i
\(34\) 4952.32 0.734703
\(35\) −3383.72 + 3234.23i −0.466900 + 0.446273i
\(36\) 5933.91 0.763106
\(37\) 1166.59 2020.59i 0.140092 0.242646i −0.787439 0.616392i \(-0.788594\pi\)
0.927531 + 0.373746i \(0.121927\pi\)
\(38\) 560.558 + 970.916i 0.0629741 + 0.109074i
\(39\) −14356.3 24865.8i −1.51141 2.61783i
\(40\) 1155.38 2001.17i 0.114176 0.197758i
\(41\) 3812.61 0.354211 0.177106 0.984192i \(-0.443327\pi\)
0.177106 + 0.984192i \(0.443327\pi\)
\(42\) −12332.2 3604.77i −1.07874 0.315322i
\(43\) 3925.73 0.323780 0.161890 0.986809i \(-0.448241\pi\)
0.161890 + 0.986809i \(0.448241\pi\)
\(44\) −1243.48 + 2153.77i −0.0968292 + 0.167713i
\(45\) 6695.22 + 11596.5i 0.492872 + 0.853679i
\(46\) 6964.78 + 12063.4i 0.485303 + 0.840569i
\(47\) 5558.23 9627.13i 0.367022 0.635700i −0.622077 0.782956i \(-0.713711\pi\)
0.989098 + 0.147256i \(0.0470442\pi\)
\(48\) 6342.76 0.397352
\(49\) 14161.0 + 9052.14i 0.842566 + 0.538594i
\(50\) −7285.56 −0.412133
\(51\) −15337.6 + 26565.5i −0.825717 + 1.43018i
\(52\) −9270.96 16057.8i −0.475462 0.823525i
\(53\) 5593.10 + 9687.54i 0.273504 + 0.473722i 0.969757 0.244074i \(-0.0784841\pi\)
−0.696253 + 0.717797i \(0.745151\pi\)
\(54\) −6336.29 + 10974.8i −0.295699 + 0.512166i
\(55\) −5612.06 −0.250159
\(56\) −7963.82 2327.88i −0.339353 0.0991950i
\(57\) −6944.31 −0.283101
\(58\) 11313.6 19595.7i 0.441600 0.764874i
\(59\) 3005.18 + 5205.12i 0.112393 + 0.194671i 0.916735 0.399497i \(-0.130815\pi\)
−0.804342 + 0.594167i \(0.797482\pi\)
\(60\) 7156.52 + 12395.5i 0.256640 + 0.444513i
\(61\) 7419.36 12850.7i 0.255295 0.442183i −0.709681 0.704523i \(-0.751161\pi\)
0.964975 + 0.262340i \(0.0844942\pi\)
\(62\) −9258.81 −0.305897
\(63\) 34756.9 33221.4i 1.10329 1.05455i
\(64\) 4096.00 0.125000
\(65\) 20920.8 36235.9i 0.614179 1.06379i
\(66\) −7702.22 13340.6i −0.217649 0.376979i
\(67\) 21491.9 + 37225.1i 0.584909 + 1.01309i 0.994887 + 0.100997i \(0.0322032\pi\)
−0.409977 + 0.912096i \(0.634463\pi\)
\(68\) −9904.64 + 17155.3i −0.259757 + 0.449912i
\(69\) −86281.1 −2.18169
\(70\) −4436.27 18190.0i −0.108211 0.443698i
\(71\) −19962.4 −0.469967 −0.234984 0.971999i \(-0.575504\pi\)
−0.234984 + 0.971999i \(0.575504\pi\)
\(72\) −11867.8 + 20555.7i −0.269799 + 0.467305i
\(73\) −22775.3 39448.0i −0.500215 0.866398i −1.00000 0.000248463i \(-0.999921\pi\)
0.499785 0.866150i \(-0.333412\pi\)
\(74\) 4666.35 + 8082.36i 0.0990599 + 0.171577i
\(75\) 22563.7 39081.5i 0.463188 0.802266i
\(76\) −4484.47 −0.0890588
\(77\) 4774.54 + 19577.0i 0.0917709 + 0.376288i
\(78\) 114850. 2.13745
\(79\) −54496.0 + 94389.9i −0.982419 + 1.70160i −0.329534 + 0.944144i \(0.606892\pi\)
−0.652885 + 0.757457i \(0.726442\pi\)
\(80\) 4621.51 + 8004.69i 0.0807345 + 0.139836i
\(81\) 5813.07 + 10068.5i 0.0984448 + 0.170511i
\(82\) −7625.22 + 13207.3i −0.125233 + 0.216909i
\(83\) 55829.0 0.889538 0.444769 0.895645i \(-0.353286\pi\)
0.444769 + 0.895645i \(0.353286\pi\)
\(84\) 37151.6 35510.4i 0.574486 0.549107i
\(85\) −44701.6 −0.671082
\(86\) −7851.47 + 13599.1i −0.114473 + 0.198274i
\(87\) 70077.3 + 121377.i 0.992611 + 1.71925i
\(88\) −4973.91 8615.07i −0.0684686 0.118591i
\(89\) 47772.9 82745.1i 0.639303 1.10731i −0.346283 0.938130i \(-0.612556\pi\)
0.985586 0.169175i \(-0.0541103\pi\)
\(90\) −53561.8 −0.697026
\(91\) −144204. 42151.6i −1.82546 0.533594i
\(92\) −55718.2 −0.686322
\(93\) 28675.0 49666.5i 0.343792 0.595465i
\(94\) 22232.9 + 38508.5i 0.259523 + 0.449508i
\(95\) −5059.82 8763.86i −0.0575209 0.0996292i
\(96\) −12685.5 + 21971.9i −0.140485 + 0.243327i
\(97\) 15004.9 0.161922 0.0809609 0.996717i \(-0.474201\pi\)
0.0809609 + 0.996717i \(0.474201\pi\)
\(98\) −59679.5 + 30950.9i −0.627712 + 0.325542i
\(99\) 57646.0 0.591127
\(100\) 14571.1 25237.9i 0.145711 0.252379i
\(101\) −13438.1 23275.4i −0.131079 0.227036i 0.793014 0.609204i \(-0.208511\pi\)
−0.924093 + 0.382168i \(0.875178\pi\)
\(102\) −61350.3 106262.i −0.583870 1.01129i
\(103\) 25957.6 44959.9i 0.241086 0.417573i −0.719938 0.694038i \(-0.755830\pi\)
0.961024 + 0.276466i \(0.0891632\pi\)
\(104\) 74167.6 0.672405
\(105\) 111315. + 32538.1i 0.985327 + 0.288017i
\(106\) −44744.8 −0.386793
\(107\) 12487.4 21628.8i 0.105442 0.182630i −0.808477 0.588528i \(-0.799708\pi\)
0.913919 + 0.405898i \(0.133041\pi\)
\(108\) −25345.1 43899.1i −0.209091 0.362156i
\(109\) 1818.07 + 3148.99i 0.0146570 + 0.0253867i 0.873261 0.487253i \(-0.162001\pi\)
−0.858604 + 0.512640i \(0.828668\pi\)
\(110\) 11224.1 19440.7i 0.0884444 0.153190i
\(111\) −57807.7 −0.445326
\(112\) 23991.6 22931.7i 0.180724 0.172740i
\(113\) 62175.0 0.458057 0.229028 0.973420i \(-0.426445\pi\)
0.229028 + 0.973420i \(0.426445\pi\)
\(114\) 13888.6 24055.8i 0.100091 0.173363i
\(115\) −62866.8 108889.i −0.443279 0.767781i
\(116\) 45254.2 + 78382.7i 0.312259 + 0.540848i
\(117\) −214895. + 372208.i −1.45131 + 2.51375i
\(118\) −24041.4 −0.158948
\(119\) 38030.6 + 155936.i 0.246187 + 1.00944i
\(120\) −57252.2 −0.362943
\(121\) 68445.5 118551.i 0.424993 0.736109i
\(122\) 29677.4 + 51402.8i 0.180521 + 0.312671i
\(123\) −47231.3 81807.1i −0.281493 0.487560i
\(124\) 18517.6 32073.4i 0.108151 0.187323i
\(125\) 178592. 1.02232
\(126\) 45568.5 + 186844.i 0.255705 + 1.04846i
\(127\) 63550.3 0.349630 0.174815 0.984601i \(-0.444067\pi\)
0.174815 + 0.984601i \(0.444067\pi\)
\(128\) −8192.00 + 14189.0i −0.0441942 + 0.0765466i
\(129\) −48632.7 84234.4i −0.257309 0.445672i
\(130\) 83683.2 + 144944.i 0.434290 + 0.752213i
\(131\) −68148.5 + 118037.i −0.346959 + 0.600950i −0.985708 0.168465i \(-0.946119\pi\)
0.638749 + 0.769415i \(0.279452\pi\)
\(132\) 61617.8 0.307802
\(133\) −26267.0 + 25106.6i −0.128760 + 0.123072i
\(134\) −171935. −0.827187
\(135\) 57193.8 99062.5i 0.270094 0.467816i
\(136\) −39618.6 68621.4i −0.183676 0.318136i
\(137\) −167652. 290381.i −0.763144 1.32180i −0.941222 0.337788i \(-0.890321\pi\)
0.178078 0.984016i \(-0.443012\pi\)
\(138\) 172562. 298886.i 0.771343 1.33601i
\(139\) 58195.2 0.255476 0.127738 0.991808i \(-0.459228\pi\)
0.127738 + 0.991808i \(0.459228\pi\)
\(140\) 71884.6 + 21012.3i 0.309967 + 0.0906054i
\(141\) −275426. −1.16669
\(142\) 39924.9 69151.9i 0.166158 0.287795i
\(143\) −90064.3 155996.i −0.368309 0.637930i
\(144\) −47471.3 82222.7i −0.190776 0.330435i
\(145\) −102121. + 176878.i −0.403360 + 0.698641i
\(146\) 182202. 0.707411
\(147\) 18802.5 415992.i 0.0717665 1.58779i
\(148\) −37330.8 −0.140092
\(149\) −141529. + 245135.i −0.522251 + 0.904566i 0.477414 + 0.878679i \(0.341574\pi\)
−0.999665 + 0.0258870i \(0.991759\pi\)
\(150\) 90254.9 + 156326.i 0.327524 + 0.567287i
\(151\) 120779. + 209195.i 0.431071 + 0.746637i 0.996966 0.0778407i \(-0.0248026\pi\)
−0.565895 + 0.824477i \(0.691469\pi\)
\(152\) 8968.93 15534.6i 0.0314870 0.0545372i
\(153\) 459166. 1.58577
\(154\) −77365.9 22614.6i −0.262874 0.0768398i
\(155\) 83573.6 0.279409
\(156\) −229701. + 397853.i −0.755703 + 1.30892i
\(157\) 107014. + 185354.i 0.346492 + 0.600142i 0.985624 0.168956i \(-0.0540394\pi\)
−0.639132 + 0.769097i \(0.720706\pi\)
\(158\) −217984. 377559.i −0.694675 1.20321i
\(159\) 138577. 240022.i 0.434708 0.752937i
\(160\) −36972.1 −0.114176
\(161\) −326360. + 311942.i −0.992277 + 0.948440i
\(162\) −46504.5 −0.139222
\(163\) −32233.0 + 55829.2i −0.0950237 + 0.164586i −0.909619 0.415445i \(-0.863626\pi\)
0.814595 + 0.580030i \(0.196959\pi\)
\(164\) −30500.9 52829.1i −0.0885529 0.153378i
\(165\) 69523.3 + 120418.i 0.198802 + 0.344335i
\(166\) −111658. + 193397.i −0.314499 + 0.544729i
\(167\) −442694. −1.22832 −0.614162 0.789180i \(-0.710506\pi\)
−0.614162 + 0.789180i \(0.710506\pi\)
\(168\) 48708.2 + 199718.i 0.133146 + 0.545938i
\(169\) 971685. 2.61703
\(170\) 89403.2 154851.i 0.237263 0.410952i
\(171\) 51973.5 + 90020.7i 0.135923 + 0.235425i
\(172\) −31405.9 54396.6i −0.0809449 0.140201i
\(173\) 39299.5 68068.8i 0.0998325 0.172915i −0.811783 0.583960i \(-0.801503\pi\)
0.911615 + 0.411045i \(0.134836\pi\)
\(174\) −560618. −1.40376
\(175\) −55948.3 229404.i −0.138099 0.566247i
\(176\) 39791.3 0.0968292
\(177\) 74457.4 128964.i 0.178638 0.309411i
\(178\) 191092. + 330980.i 0.452055 + 0.782983i
\(179\) 255214. + 442043.i 0.595348 + 1.03117i 0.993498 + 0.113853i \(0.0363193\pi\)
−0.398149 + 0.917321i \(0.630347\pi\)
\(180\) 107124. 185543.i 0.246436 0.426839i
\(181\) −22051.8 −0.0500319 −0.0250160 0.999687i \(-0.507964\pi\)
−0.0250160 + 0.999687i \(0.507964\pi\)
\(182\) 434425. 415233.i 0.972156 0.929208i
\(183\) −367650. −0.811534
\(184\) 111436. 193014.i 0.242651 0.420285i
\(185\) −42120.3 72954.5i −0.0904820 0.156719i
\(186\) 114700. + 198666.i 0.243098 + 0.421057i
\(187\) −96220.4 + 166659.i −0.201216 + 0.348517i
\(188\) −177863. −0.367022
\(189\) −394227. 115235.i −0.802771 0.234655i
\(190\) 40478.5 0.0813469
\(191\) 279076. 483374.i 0.553528 0.958738i −0.444489 0.895784i \(-0.646615\pi\)
0.998016 0.0629535i \(-0.0200520\pi\)
\(192\) −50742.0 87887.8i −0.0993379 0.172058i
\(193\) 24658.1 + 42709.1i 0.0476504 + 0.0825330i 0.888867 0.458166i \(-0.151493\pi\)
−0.841216 + 0.540699i \(0.818160\pi\)
\(194\) −30009.9 + 51978.7i −0.0572480 + 0.0991564i
\(195\) −1.03668e6 −1.95236
\(196\) 12142.2 268638.i 0.0225765 0.499490i
\(197\) −941509. −1.72846 −0.864229 0.503099i \(-0.832193\pi\)
−0.864229 + 0.503099i \(0.832193\pi\)
\(198\) −115292. + 199692.i −0.208995 + 0.361990i
\(199\) −320006. 554267.i −0.572830 0.992170i −0.996274 0.0862477i \(-0.972512\pi\)
0.423444 0.905922i \(-0.360821\pi\)
\(200\) 58284.4 + 100952.i 0.103033 + 0.178459i
\(201\) 532493. 922304.i 0.929658 1.61022i
\(202\) 107505. 0.185374
\(203\) 703900. + 205754.i 1.19887 + 0.350436i
\(204\) 490803. 0.825717
\(205\) 68828.2 119214.i 0.114388 0.198126i
\(206\) 103830. + 179840.i 0.170473 + 0.295268i
\(207\) 645756. + 1.11848e6i 1.04747 + 1.81428i
\(208\) −148335. + 256924.i −0.237731 + 0.411762i
\(209\) −43565.1 −0.0689879
\(210\) −335345. + 320530.i −0.524740 + 0.501558i
\(211\) 921869. 1.42549 0.712743 0.701425i \(-0.247452\pi\)
0.712743 + 0.701425i \(0.247452\pi\)
\(212\) 89489.7 155001.i 0.136752 0.236861i
\(213\) 247298. + 428333.i 0.373484 + 0.646894i
\(214\) 49949.5 + 86515.1i 0.0745585 + 0.129139i
\(215\) 70870.4 122751.i 0.104561 0.181105i
\(216\) 202761. 0.295699
\(217\) −71101.5 291537.i −0.102501 0.420285i
\(218\) −14544.6 −0.0207281
\(219\) −564290. + 977378.i −0.795045 + 1.37706i
\(220\) 44896.5 + 77762.9i 0.0625396 + 0.108322i
\(221\) −717387. 1.24255e6i −0.988036 1.71133i
\(222\) 115615. 200252.i 0.157446 0.272705i
\(223\) −837700. −1.12805 −0.564023 0.825759i \(-0.690747\pi\)
−0.564023 + 0.825759i \(0.690747\pi\)
\(224\) 31454.6 + 128973.i 0.0418855 + 0.171743i
\(225\) −675497. −0.889544
\(226\) −124350. + 215380.i −0.161948 + 0.280501i
\(227\) 665344. + 1.15241e6i 0.857002 + 1.48437i 0.874775 + 0.484529i \(0.161009\pi\)
−0.0177731 + 0.999842i \(0.505658\pi\)
\(228\) 55554.4 + 96223.1i 0.0707753 + 0.122586i
\(229\) −505317. + 875234.i −0.636759 + 1.10290i 0.349381 + 0.936981i \(0.386392\pi\)
−0.986140 + 0.165918i \(0.946941\pi\)
\(230\) 502935. 0.626891
\(231\) 360916. 344971.i 0.445017 0.425357i
\(232\) −362034. −0.441600
\(233\) −743050. + 1.28700e6i −0.896661 + 1.55306i −0.0649249 + 0.997890i \(0.520681\pi\)
−0.831736 + 0.555172i \(0.812653\pi\)
\(234\) −859579. 1.48883e6i −1.02623 1.77749i
\(235\) −200683. 347593.i −0.237050 0.410583i
\(236\) 48082.8 83281.9i 0.0561966 0.0973353i
\(237\) 2.70043e6 3.12293
\(238\) −616241. 180131.i −0.705193 0.206132i
\(239\) 875637. 0.991584 0.495792 0.868441i \(-0.334878\pi\)
0.495792 + 0.868441i \(0.334878\pi\)
\(240\) 114504. 198327.i 0.128320 0.222257i
\(241\) −726472. 1.25829e6i −0.805706 1.39552i −0.915814 0.401604i \(-0.868453\pi\)
0.110108 0.993920i \(-0.464880\pi\)
\(242\) 273782. + 474204.i 0.300515 + 0.520508i
\(243\) 528956. 916179.i 0.574651 0.995324i
\(244\) −237419. −0.255295
\(245\) 538691. 279374.i 0.573356 0.297352i
\(246\) 377851. 0.398091
\(247\) 162403. 281291.i 0.169376 0.293369i
\(248\) 74070.4 + 128294.i 0.0764743 + 0.132457i
\(249\) −691621. 1.19792e6i −0.706919 1.22442i
\(250\) −357184. + 618661.i −0.361445 + 0.626041i
\(251\) −198384. −0.198757 −0.0993786 0.995050i \(-0.531685\pi\)
−0.0993786 + 0.995050i \(0.531685\pi\)
\(252\) −738385. 215835.i −0.732456 0.214101i
\(253\) −541284. −0.531648
\(254\) −127101. + 220145.i −0.123613 + 0.214104i
\(255\) 553772. + 959161.i 0.533311 + 0.923722i
\(256\) −32768.0 56755.8i −0.0312500 0.0541266i
\(257\) −239786. + 415321.i −0.226460 + 0.392240i −0.956756 0.290890i \(-0.906048\pi\)
0.730297 + 0.683130i \(0.239382\pi\)
\(258\) 389062. 0.363890
\(259\) −218659. + 208999.i −0.202543 + 0.193595i
\(260\) −669466. −0.614179
\(261\) 1.04896e6 1.81686e6i 0.953145 1.65090i
\(262\) −272594. 472147.i −0.245337 0.424936i
\(263\) −227471. 393992.i −0.202786 0.351235i 0.746639 0.665229i \(-0.231666\pi\)
−0.949425 + 0.313994i \(0.898333\pi\)
\(264\) −123236. + 213450.i −0.108824 + 0.188489i
\(265\) 403884. 0.353299
\(266\) −34437.7 141205.i −0.0298422 0.122362i
\(267\) −2.36728e6 −2.03222
\(268\) 343871. 595602.i 0.292455 0.506546i
\(269\) 430068. + 744900.i 0.362374 + 0.627650i 0.988351 0.152192i \(-0.0486331\pi\)
−0.625977 + 0.779841i \(0.715300\pi\)
\(270\) 228775. + 396250.i 0.190985 + 0.330796i
\(271\) −652790. + 1.13067e6i −0.539946 + 0.935214i 0.458960 + 0.888457i \(0.348222\pi\)
−0.998906 + 0.0467569i \(0.985111\pi\)
\(272\) 316949. 0.259757
\(273\) 881975. + 3.61636e6i 0.716226 + 2.93673i
\(274\) 1.34121e6 1.07925
\(275\) 141554. 245178.i 0.112873 0.195501i
\(276\) 690248. + 1.19555e6i 0.545422 + 0.944699i
\(277\) 271554. + 470346.i 0.212646 + 0.368314i 0.952542 0.304408i \(-0.0984586\pi\)
−0.739896 + 0.672721i \(0.765125\pi\)
\(278\) −116390. + 201594.i −0.0903245 + 0.156447i
\(279\) −858452. −0.660246
\(280\) −216558. + 206991.i −0.165074 + 0.157781i
\(281\) 998089. 0.754055 0.377028 0.926202i \(-0.376946\pi\)
0.377028 + 0.926202i \(0.376946\pi\)
\(282\) 550851. 954102.i 0.412488 0.714450i
\(283\) −888660. 1.53920e6i −0.659583 1.14243i −0.980724 0.195400i \(-0.937399\pi\)
0.321140 0.947032i \(-0.395934\pi\)
\(284\) 159699. + 276608.i 0.117492 + 0.203502i
\(285\) −125364. + 217137.i −0.0914241 + 0.158351i
\(286\) 720514. 0.520868
\(287\) −474421. 138676.i −0.339984 0.0993796i
\(288\) 379770. 0.269799
\(289\) −56493.2 + 97849.1i −0.0397880 + 0.0689148i
\(290\) −408482. 707512.i −0.285219 0.494014i
\(291\) −185884. 321961.i −0.128680 0.222880i
\(292\) −364405. + 631167.i −0.250108 + 0.433199i
\(293\) −1.63987e6 −1.11594 −0.557969 0.829862i \(-0.688419\pi\)
−0.557969 + 0.829862i \(0.688419\pi\)
\(294\) 1.40343e6 + 897118.i 0.946942 + 0.605315i
\(295\) 217007. 0.145184
\(296\) 74661.6 129318.i 0.0495300 0.0857884i
\(297\) −246220. 426465.i −0.161969 0.280538i
\(298\) −566116. 980541.i −0.369287 0.639625i
\(299\) 2.01782e6 3.49496e6i 1.30528 2.26081i
\(300\) −722039. −0.463188
\(301\) −488498. 142791.i −0.310775 0.0908415i
\(302\) −966231. −0.609626
\(303\) −332947. + 576681.i −0.208338 + 0.360852i
\(304\) 35875.7 + 62138.6i 0.0222647 + 0.0385636i
\(305\) −267880. 463982.i −0.164889 0.285595i
\(306\) −918332. + 1.59060e6i −0.560656 + 0.971084i
\(307\) 2.38130e6 1.44201 0.721006 0.692928i \(-0.243680\pi\)
0.721006 + 0.692928i \(0.243680\pi\)
\(308\) 233071. 222774.i 0.139995 0.133810i
\(309\) −1.28627e6 −0.766366
\(310\) −167147. + 289507.i −0.0987859 + 0.171102i
\(311\) 622564. + 1.07831e6i 0.364992 + 0.632184i 0.988775 0.149413i \(-0.0477385\pi\)
−0.623783 + 0.781597i \(0.714405\pi\)
\(312\) −918803. 1.59141e6i −0.534363 0.925543i
\(313\) −831495. + 1.44019e6i −0.479732 + 0.830921i −0.999730 0.0232470i \(-0.992600\pi\)
0.519997 + 0.854168i \(0.325933\pi\)
\(314\) −856115. −0.490014
\(315\) −411319. 1.68653e6i −0.233562 0.957673i
\(316\) 1.74387e6 0.982419
\(317\) 1.31243e6 2.27319e6i 0.733547 1.27054i −0.221812 0.975090i \(-0.571197\pi\)
0.955358 0.295450i \(-0.0954697\pi\)
\(318\) 554308. + 960089.i 0.307385 + 0.532407i
\(319\) 439630. + 761462.i 0.241886 + 0.418959i
\(320\) 73944.2 128075.i 0.0403672 0.0699181i
\(321\) −618784. −0.335179
\(322\) −427879. 1.75443e6i −0.229976 0.942967i
\(323\) −347008. −0.185069
\(324\) 93009.0 161096.i 0.0492224 0.0852557i
\(325\) 1.05538e6 + 1.82796e6i 0.554241 + 0.959974i
\(326\) −128932. 223317.i −0.0671919 0.116380i
\(327\) 45045.3 78020.7i 0.0232959 0.0403497i
\(328\) 244007. 0.125233
\(329\) −1.04180e6 + 995780.i −0.530636 + 0.507193i
\(330\) −556186. −0.281148
\(331\) −869428. + 1.50589e6i −0.436178 + 0.755482i −0.997391 0.0721894i \(-0.977001\pi\)
0.561213 + 0.827671i \(0.310335\pi\)
\(332\) −446632. 773589.i −0.222385 0.385181i
\(333\) 432652. + 749375.i 0.213810 + 0.370330i
\(334\) 885389. 1.53354e6i 0.434278 0.752191i
\(335\) 1.55196e6 0.755558
\(336\) −789259. 230705.i −0.381392 0.111483i
\(337\) 853564. 0.409413 0.204706 0.978823i \(-0.434376\pi\)
0.204706 + 0.978823i \(0.434376\pi\)
\(338\) −1.94337e6 + 3.36602e6i −0.925260 + 1.60260i
\(339\) −770236. 1.33409e6i −0.364019 0.630500i
\(340\) 357613. + 619403.i 0.167771 + 0.290587i
\(341\) 179892. 311583.i 0.0837774 0.145107i
\(342\) −415788. −0.192224
\(343\) −1.43287e6 1.64148e6i −0.657613 0.753356i
\(344\) 251247. 0.114473
\(345\) −1.55761e6 + 2.69786e6i −0.704550 + 1.22032i
\(346\) 157198. + 272275.i 0.0705922 + 0.122269i
\(347\) 1.49250e6 + 2.58508e6i 0.665411 + 1.15253i 0.979174 + 0.203024i \(0.0650770\pi\)
−0.313763 + 0.949501i \(0.601590\pi\)
\(348\) 1.12124e6 1.94204e6i 0.496306 0.859627i
\(349\) 2.87467e6 1.26335 0.631676 0.775233i \(-0.282367\pi\)
0.631676 + 0.775233i \(0.282367\pi\)
\(350\) 906576. + 264998.i 0.395580 + 0.115631i
\(351\) 3.67146e6 1.59064
\(352\) −79582.6 + 137841.i −0.0342343 + 0.0592955i
\(353\) −735546. 1.27400e6i −0.314176 0.544169i 0.665086 0.746767i \(-0.268395\pi\)
−0.979262 + 0.202598i \(0.935062\pi\)
\(354\) 297830. + 515856.i 0.126316 + 0.218786i
\(355\) −360377. + 624192.i −0.151770 + 0.262874i
\(356\) −1.52873e6 −0.639303
\(357\) 2.87480e6 2.74779e6i 1.19381 1.14107i
\(358\) −2.04171e6 −0.841950
\(359\) −1.53900e6 + 2.66562e6i −0.630233 + 1.09160i 0.357270 + 0.934001i \(0.383707\pi\)
−0.987504 + 0.157595i \(0.949626\pi\)
\(360\) 428494. + 742174.i 0.174256 + 0.301821i
\(361\) 1.19877e6 + 2.07633e6i 0.484137 + 0.838550i
\(362\) 44103.6 76389.6i 0.0176890 0.0306382i
\(363\) −3.39167e6 −1.35097
\(364\) 569559. + 2.33536e6i 0.225312 + 0.923846i
\(365\) −1.64463e6 −0.646154
\(366\) 735299. 1.27358e6i 0.286920 0.496961i
\(367\) −808349. 1.40010e6i −0.313281 0.542618i 0.665790 0.746139i \(-0.268095\pi\)
−0.979071 + 0.203521i \(0.934761\pi\)
\(368\) 445746. + 772055.i 0.171580 + 0.297186i
\(369\) −706990. + 1.22454e6i −0.270301 + 0.468175i
\(370\) 336962. 0.127961
\(371\) −343611. 1.40890e6i −0.129608 0.531431i
\(372\) −917599. −0.343792
\(373\) 2.38059e6 4.12331e6i 0.885958 1.53452i 0.0413462 0.999145i \(-0.486835\pi\)
0.844612 0.535379i \(-0.179831\pi\)
\(374\) −384881. 666634.i −0.142281 0.246439i
\(375\) −2.21243e6 3.83205e6i −0.812442 1.40719i
\(376\) 355727. 616136.i 0.129762 0.224754i
\(377\) −6.55547e6 −2.37548
\(378\) 1.18764e6 1.13517e6i 0.427519 0.408632i
\(379\) 1.00193e6 0.358294 0.179147 0.983822i \(-0.442666\pi\)
0.179147 + 0.983822i \(0.442666\pi\)
\(380\) −80957.1 + 140222.i −0.0287605 + 0.0498146i
\(381\) −787273. 1.36360e6i −0.277852 0.481253i
\(382\) 1.11630e6 + 1.93350e6i 0.391403 + 0.677930i
\(383\) 1.41076e6 2.44351e6i 0.491424 0.851172i −0.508527 0.861046i \(-0.669810\pi\)
0.999951 + 0.00987425i \(0.00314312\pi\)
\(384\) 405936. 0.140485
\(385\) 698335. + 204128.i 0.240111 + 0.0701859i
\(386\) −197265. −0.0673879
\(387\) −727967. + 1.26088e6i −0.247078 + 0.427952i
\(388\) −120040. 207915.i −0.0404804 0.0701142i
\(389\) 621198. + 1.07595e6i 0.208140 + 0.360510i 0.951129 0.308795i \(-0.0999256\pi\)
−0.742988 + 0.669304i \(0.766592\pi\)
\(390\) 2.07337e6 3.59118e6i 0.690264 1.19557i
\(391\) −4.31148e6 −1.42621
\(392\) 906304. + 579337.i 0.297892 + 0.190422i
\(393\) 3.37695e6 1.10292
\(394\) 1.88302e6 3.26148e6i 0.611102 1.05846i
\(395\) 1.96761e6 + 3.40800e6i 0.634521 + 1.09902i
\(396\) −461168. 798766.i −0.147782 0.255966i
\(397\) −1.37281e6 + 2.37778e6i −0.437154 + 0.757173i −0.997469 0.0711068i \(-0.977347\pi\)
0.560315 + 0.828280i \(0.310680\pi\)
\(398\) 2.56005e6 0.810103
\(399\) 864113. + 252586.i 0.271730 + 0.0794285i
\(400\) −466276. −0.145711
\(401\) 1.85668e6 3.21586e6i 0.576601 0.998702i −0.419265 0.907864i \(-0.637712\pi\)
0.995866 0.0908378i \(-0.0289545\pi\)
\(402\) 2.12997e6 + 3.68922e6i 0.657368 + 1.13859i
\(403\) 1.34122e6 + 2.32306e6i 0.411374 + 0.712521i
\(404\) −215009. + 372407.i −0.0655396 + 0.113518i
\(405\) 419768. 0.127166
\(406\) −2.12055e6 + 2.02687e6i −0.638461 + 0.610255i
\(407\) −362656. −0.108520
\(408\) −981605. + 1.70019e6i −0.291935 + 0.505647i
\(409\) −1.87970e6 3.25574e6i −0.555623 0.962367i −0.997855 0.0654664i \(-0.979146\pi\)
0.442232 0.896901i \(-0.354187\pi\)
\(410\) 275313. + 476856.i 0.0808847 + 0.140096i
\(411\) −4.15380e6 + 7.19460e6i −1.21295 + 2.10088i
\(412\) −830643. −0.241086
\(413\) −184622. 757005.i −0.0532609 0.218385i
\(414\) −5.16605e6 −1.48135
\(415\) 1.00787e6 1.74568e6i 0.287266 0.497559i
\(416\) −593341. 1.02770e6i −0.168101 0.291160i
\(417\) −720934. 1.24869e6i −0.203028 0.351654i
\(418\) 87130.2 150914.i 0.0243909 0.0422463i
\(419\) 4.60027e6 1.28011 0.640056 0.768328i \(-0.278911\pi\)
0.640056 + 0.768328i \(0.278911\pi\)
\(420\) −439659. 1.80273e6i −0.121617 0.498663i
\(421\) −404864. −0.111328 −0.0556639 0.998450i \(-0.517728\pi\)
−0.0556639 + 0.998450i \(0.517728\pi\)
\(422\) −1.84374e6 + 3.19345e6i −0.503986 + 0.872929i
\(423\) 2.06138e6 + 3.57041e6i 0.560153 + 0.970213i
\(424\) 357959. + 620003.i 0.0966982 + 0.167486i
\(425\) 1.12751e6 1.95291e6i 0.302795 0.524457i
\(426\) −1.97839e6 −0.528187
\(427\) −1.39065e6 + 1.32921e6i −0.369102 + 0.352796i
\(428\) −399596. −0.105442
\(429\) −2.23147e6 + 3.86502e6i −0.585393 + 1.01393i
\(430\) 283482. + 491004.i 0.0739356 + 0.128060i
\(431\) −47379.2 82063.2i −0.0122856 0.0212792i 0.859817 0.510602i \(-0.170577\pi\)
−0.872103 + 0.489323i \(0.837244\pi\)
\(432\) −405522. + 702385.i −0.104546 + 0.181078i
\(433\) 4.31727e6 1.10660 0.553298 0.832983i \(-0.313369\pi\)
0.553298 + 0.832983i \(0.313369\pi\)
\(434\) 1.15212e6 + 336771.i 0.293611 + 0.0858244i
\(435\) 5.06036e6 1.28221
\(436\) 29089.2 50383.9i 0.00732850 0.0126933i
\(437\) −488021. 845277.i −0.122246 0.211736i
\(438\) −2.25716e6 3.90951e6i −0.562182 0.973727i
\(439\) 1.11184e6 1.92576e6i 0.275346 0.476914i −0.694876 0.719130i \(-0.744541\pi\)
0.970222 + 0.242216i \(0.0778741\pi\)
\(440\) −359172. −0.0884444
\(441\) −5.53333e6 + 2.86968e6i −1.35485 + 0.702647i
\(442\) 5.73909e6 1.39729
\(443\) 2.34213e6 4.05668e6i 0.567024 0.982114i −0.429835 0.902908i \(-0.641428\pi\)
0.996858 0.0792062i \(-0.0252386\pi\)
\(444\) 462461. + 801006.i 0.111331 + 0.192832i
\(445\) −1.72487e6 2.98756e6i −0.412910 0.715182i
\(446\) 1.67540e6 2.90188e6i 0.398824 0.690784i
\(447\) 7.01315e6 1.66014
\(448\) −509685. 148984.i −0.119979 0.0350707i
\(449\) 897932. 0.210198 0.105099 0.994462i \(-0.466484\pi\)
0.105099 + 0.994462i \(0.466484\pi\)
\(450\) 1.35099e6 2.33999e6i 0.314501 0.544732i
\(451\) −296306. 513217.i −0.0685960 0.118812i
\(452\) −497400. 861522.i −0.114514 0.198344i
\(453\) 2.99246e6 5.18310e6i 0.685147 1.18671i
\(454\) −5.32276e6 −1.21198
\(455\) −3.92129e6 + 3.74805e6i −0.887974 + 0.848745i
\(456\) −444436. −0.100091
\(457\) −2.99091e6 + 5.18040e6i −0.669903 + 1.16031i 0.308027 + 0.951377i \(0.400331\pi\)
−0.977931 + 0.208929i \(0.933002\pi\)
\(458\) −2.02127e6 3.50094e6i −0.450256 0.779867i
\(459\) −1.96121e6 3.39691e6i −0.434502 0.752580i
\(460\) −1.00587e6 + 1.74222e6i −0.221639 + 0.383891i
\(461\) 1.62507e6 0.356138 0.178069 0.984018i \(-0.443015\pi\)
0.178069 + 0.984018i \(0.443015\pi\)
\(462\) 473184. + 1.94019e6i 0.103139 + 0.422902i
\(463\) −8.46295e6 −1.83472 −0.917359 0.398060i \(-0.869683\pi\)
−0.917359 + 0.398060i \(0.869683\pi\)
\(464\) 724068. 1.25412e6i 0.156129 0.270424i
\(465\) −1.03533e6 1.79324e6i −0.222047 0.384596i
\(466\) −2.97220e6 5.14800e6i −0.634035 1.09818i
\(467\) −3.83297e6 + 6.63890e6i −0.813286 + 1.40865i 0.0972658 + 0.995258i \(0.468990\pi\)
−0.910552 + 0.413395i \(0.864343\pi\)
\(468\) 6.87663e6 1.45131
\(469\) −1.32035e6 5.41383e6i −0.277177 1.13651i
\(470\) 1.60546e6 0.335240
\(471\) 2.65143e6 4.59241e6i 0.550717 0.953869i
\(472\) 192331. + 333127.i 0.0397370 + 0.0688265i
\(473\) −305098. 528445.i −0.0627027 0.108604i
\(474\) −5.40086e6 + 9.35456e6i −1.10412 + 1.91239i
\(475\) 510497. 0.103815
\(476\) 1.85647e6 1.77446e6i 0.375553 0.358962i
\(477\) −4.14862e6 −0.834849
\(478\) −1.75127e6 + 3.03330e6i −0.350578 + 0.607219i
\(479\) 1.20146e6 + 2.08099e6i 0.239261 + 0.414412i 0.960502 0.278272i \(-0.0897616\pi\)
−0.721242 + 0.692683i \(0.756428\pi\)
\(480\) 458017. + 793309.i 0.0907358 + 0.157159i
\(481\) 1.35192e6 2.34160e6i 0.266434 0.461477i
\(482\) 5.81178e6 1.13944
\(483\) 1.07364e7 + 3.13831e6i 2.09406 + 0.612107i
\(484\) −2.19026e6 −0.424993
\(485\) 270881. 469180.i 0.0522907 0.0905701i
\(486\) 2.11582e6 + 3.66472e6i 0.406339 + 0.703801i
\(487\) 85150.8 + 147486.i 0.0162692 + 0.0281791i 0.874045 0.485844i \(-0.161488\pi\)
−0.857776 + 0.514023i \(0.828154\pi\)
\(488\) 474839. 822445.i 0.0902603 0.156335i
\(489\) 1.59724e6 0.302063
\(490\) −109600. + 2.42483e6i −0.0206215 + 0.456237i
\(491\) −5.77628e6 −1.08130 −0.540648 0.841249i \(-0.681821\pi\)
−0.540648 + 0.841249i \(0.681821\pi\)
\(492\) −755701. + 1.30891e6i −0.140746 + 0.243780i
\(493\) 3.50177e6 + 6.06525e6i 0.648890 + 1.12391i
\(494\) 649614. + 1.12516e6i 0.119767 + 0.207443i
\(495\) 1.04067e6 1.80249e6i 0.190897 0.330644i
\(496\) −592564. −0.108151
\(497\) 2.48402e6 + 726095.i 0.451091 + 0.131857i
\(498\) 5.53296e6 0.999734
\(499\) −271801. + 470773.i −0.0488652 + 0.0846369i −0.889423 0.457084i \(-0.848894\pi\)
0.840558 + 0.541721i \(0.182227\pi\)
\(500\) −1.42874e6 2.47464e6i −0.255580 0.442678i
\(501\) 5.48418e6 + 9.49888e6i 0.976152 + 1.69075i
\(502\) 396769. 687223.i 0.0702713 0.121713i
\(503\) −5.40086e6 −0.951794 −0.475897 0.879501i \(-0.657876\pi\)
−0.475897 + 0.879501i \(0.657876\pi\)
\(504\) 2.22444e6 2.12617e6i 0.390072 0.372839i
\(505\) −970378. −0.169322
\(506\) 1.08257e6 1.87506e6i 0.187966 0.325567i
\(507\) −1.20374e7 2.08494e7i −2.07976 3.60225i
\(508\) −508402. 880579.i −0.0874074 0.151394i
\(509\) −4.17209e6 + 7.22628e6i −0.713772 + 1.23629i 0.249659 + 0.968334i \(0.419681\pi\)
−0.963431 + 0.267955i \(0.913652\pi\)
\(510\) −4.43018e6 −0.754216
\(511\) 1.39919e6 + 5.73710e6i 0.237042 + 0.971942i
\(512\) 262144. 0.0441942
\(513\) 443982. 769000.i 0.0744856 0.129013i
\(514\) −959144. 1.66129e6i −0.160131 0.277355i
\(515\) −937213. 1.62330e6i −0.155711 0.269700i
\(516\) −778124. + 1.34775e6i −0.128654 + 0.222836i
\(517\) −1.72788e6 −0.284307
\(518\) −286676. 1.17546e6i −0.0469426 0.192478i
\(519\) −1.94740e6 −0.317349
\(520\) 1.33893e6 2.31910e6i 0.217145 0.376106i
\(521\) 5.73919e6 + 9.94057e6i 0.926310 + 1.60442i 0.789441 + 0.613827i \(0.210371\pi\)
0.136870 + 0.990589i \(0.456296\pi\)
\(522\) 4.19585e6 + 7.26743e6i 0.673976 + 1.16736i
\(523\) 2.19367e6 3.79955e6i 0.350685 0.607404i −0.635685 0.771949i \(-0.719282\pi\)
0.986370 + 0.164545i \(0.0526155\pi\)
\(524\) 2.18075e6 0.346959
\(525\) −4.22922e6 + 4.04238e6i −0.669673 + 0.640088i
\(526\) 1.81977e6 0.286782
\(527\) 1.43289e6 2.48184e6i 0.224744 0.389267i
\(528\) −492942. 853801.i −0.0769505 0.133282i
\(529\) −2.84535e6 4.92829e6i −0.442075 0.765697i
\(530\) −807769. + 1.39910e6i −0.124910 + 0.216350i
\(531\) −2.22906e6 −0.343071
\(532\) 558023. + 163114.i 0.0854817 + 0.0249869i
\(533\) 4.41832e6 0.673657
\(534\) 4.73456e6 8.20050e6i 0.718500 1.24448i
\(535\) −450864. 780919.i −0.0681022 0.117956i
\(536\) 1.37548e6 + 2.38241e6i 0.206797 + 0.358182i
\(537\) 6.32327e6 1.09522e7i 0.946250 1.63895i
\(538\) −3.44055e6 −0.512474
\(539\) 117957. 2.60973e6i 0.0174885 0.386922i
\(540\) −1.83020e6 −0.270094
\(541\) −3.61153e6 + 6.25535e6i −0.530515 + 0.918879i 0.468851 + 0.883277i \(0.344668\pi\)
−0.999366 + 0.0356020i \(0.988665\pi\)
\(542\) −2.61116e6 4.52266e6i −0.381799 0.661296i
\(543\) 273182. + 473165.i 0.0397605 + 0.0688673i
\(544\) −633897. + 1.09794e6i −0.0918378 + 0.159068i
\(545\) 131285. 0.0189332
\(546\) −1.42914e7 4.17746e6i −2.05160 0.599696i
\(547\) 3.54529e6 0.506622 0.253311 0.967385i \(-0.418480\pi\)
0.253311 + 0.967385i \(0.418480\pi\)
\(548\) −2.68243e6 + 4.64610e6i −0.381572 + 0.660902i
\(549\) 2.75161e6 + 4.76593e6i 0.389634 + 0.674865i
\(550\) 566214. + 980712.i 0.0798131 + 0.138240i
\(551\) −792739. + 1.37306e6i −0.111237 + 0.192669i
\(552\) −5.52199e6 −0.771343
\(553\) 1.02144e7 9.76319e6i 1.42037 1.35762i
\(554\) −2.17243e6 −0.300727
\(555\) −1.04359e6 + 1.80755e6i −0.143813 + 0.249091i
\(556\) −465562. 806377.i −0.0638691 0.110624i
\(557\) −5.18314e6 8.97747e6i −0.707873 1.22607i −0.965645 0.259866i \(-0.916322\pi\)
0.257772 0.966206i \(-0.417012\pi\)
\(558\) 1.71690e6 2.97377e6i 0.233432 0.404316i
\(559\) 4.54941e6 0.615780
\(560\) −283921. 1.16416e6i −0.0382585 0.156871i
\(561\) 4.76799e6 0.639628
\(562\) −1.99618e6 + 3.45748e6i −0.266599 + 0.461763i
\(563\) 2.24141e6 + 3.88223e6i 0.298023 + 0.516191i 0.975684 0.219184i \(-0.0703394\pi\)
−0.677660 + 0.735375i \(0.737006\pi\)
\(564\) 2.20340e6 + 3.81641e6i 0.291673 + 0.505193i
\(565\) 1.12243e6 1.94411e6i 0.147924 0.256212i
\(566\) 7.10928e6 0.932792
\(567\) −357124. 1.46431e6i −0.0466511 0.191283i
\(568\) −1.27760e6 −0.166158
\(569\) −3.24668e6 + 5.62341e6i −0.420396 + 0.728147i −0.995978 0.0895969i \(-0.971442\pi\)
0.575582 + 0.817744i \(0.304775\pi\)
\(570\) −501456. 868547.i −0.0646466 0.111971i
\(571\) 248754. + 430854.i 0.0319286 + 0.0553019i 0.881548 0.472094i \(-0.156502\pi\)
−0.849620 + 0.527396i \(0.823168\pi\)
\(572\) −1.44103e6 + 2.49593e6i −0.184155 + 0.318965i
\(573\) −1.38290e7 −1.75956
\(574\) 1.42923e6 1.36609e6i 0.181060 0.173061i
\(575\) 6.34279e6 0.800038
\(576\) −759541. + 1.31556e6i −0.0953882 + 0.165217i
\(577\) 3.27561e6 + 5.67353e6i 0.409594 + 0.709437i 0.994844 0.101416i \(-0.0323372\pi\)
−0.585250 + 0.810853i \(0.699004\pi\)
\(578\) −225973. 391397.i −0.0281343 0.0487301i
\(579\) 610939. 1.05818e6i 0.0757359 0.131178i
\(580\) 3.26786e6 0.403360
\(581\) −6.94707e6 2.03067e6i −0.853810 0.249574i
\(582\) 1.48707e6 0.181981
\(583\) 869363. 1.50578e6i 0.105933 0.183481i
\(584\) −1.45762e6 2.52467e6i −0.176853 0.306318i
\(585\) 7.75889e6 + 1.34388e7i 0.937368 + 1.62357i
\(586\) 3.27974e6 5.68067e6i 0.394543 0.683369i
\(587\) −30793.5 −0.00368862 −0.00184431 0.999998i \(-0.500587\pi\)
−0.00184431 + 0.999998i \(0.500587\pi\)
\(588\) −5.91457e6 + 3.06740e6i −0.705473 + 0.365870i
\(589\) 648763. 0.0770544
\(590\) −434014. + 751735.i −0.0513303 + 0.0889067i
\(591\) 1.16636e7 + 2.02019e7i 1.37361 + 2.37916i
\(592\) 298646. + 517271.i 0.0350230 + 0.0606616i
\(593\) −285468. + 494446.i −0.0333366 + 0.0577407i −0.882212 0.470852i \(-0.843947\pi\)
0.848876 + 0.528592i \(0.177280\pi\)
\(594\) 1.96976e6 0.229059
\(595\) 5.56243e6 + 1.62593e6i 0.644128 + 0.188283i
\(596\) 4.52893e6 0.522251
\(597\) −7.92859e6 + 1.37327e7i −0.910459 + 1.57696i
\(598\) 8.07127e6 + 1.39799e7i 0.922973 + 1.59864i
\(599\) −4.53555e6 7.85581e6i −0.516492 0.894590i −0.999817 0.0191488i \(-0.993904\pi\)
0.483325 0.875441i \(-0.339429\pi\)
\(600\) 1.44408e6 2.50122e6i 0.163762 0.283644i
\(601\) −1.36309e7 −1.53936 −0.769679 0.638431i \(-0.779584\pi\)
−0.769679 + 0.638431i \(0.779584\pi\)
\(602\) 1.47164e6 1.40662e6i 0.165504 0.158193i
\(603\) −1.59414e7 −1.78539
\(604\) 1.93246e6 3.34712e6i 0.215535 0.373318i
\(605\) −2.47126e6 4.28035e6i −0.274493 0.475435i
\(606\) −1.33179e6 2.30672e6i −0.147317 0.255161i
\(607\) 1.97825e6 3.42644e6i 0.217927 0.377460i −0.736247 0.676713i \(-0.763404\pi\)
0.954174 + 0.299253i \(0.0967373\pi\)
\(608\) −287006. −0.0314870
\(609\) −4.30518e6 1.76525e7i −0.470379 1.92869i
\(610\) 2.14304e6 0.233188
\(611\) 6.44126e6 1.11566e7i 0.698020 1.20901i
\(612\) −3.67333e6 6.36239e6i −0.396444 0.686660i
\(613\) −661552. 1.14584e6i −0.0711070 0.123161i 0.828280 0.560315i \(-0.189320\pi\)
−0.899387 + 0.437154i \(0.855987\pi\)
\(614\) −4.76261e6 + 8.24908e6i −0.509828 + 0.883049i
\(615\) −3.41063e6 −0.363619
\(616\) 305571. + 1.25293e6i 0.0324459 + 0.133038i
\(617\) 9.26370e6 0.979651 0.489826 0.871820i \(-0.337060\pi\)
0.489826 + 0.871820i \(0.337060\pi\)
\(618\) 2.57254e6 4.45577e6i 0.270951 0.469301i
\(619\) −334693. 579705.i −0.0351091 0.0608107i 0.847937 0.530097i \(-0.177845\pi\)
−0.883046 + 0.469286i \(0.844511\pi\)
\(620\) −668589. 1.15803e6i −0.0698521 0.120987i
\(621\) 5.51636e6 9.55461e6i 0.574015 0.994223i
\(622\) −4.98051e6 −0.516176
\(623\) −8.95430e6 + 8.55872e6i −0.924297 + 0.883463i
\(624\) 7.35043e6 0.755703
\(625\) 378164. 654999.i 0.0387240 0.0670719i
\(626\) −3.32598e6 5.76077e6i −0.339222 0.587550i
\(627\) 539693. + 934776.i 0.0548249 + 0.0949595i
\(628\) 1.71223e6 2.96567e6i 0.173246 0.300071i
\(629\) −2.88866e6 −0.291118
\(630\) 6.66495e6 + 1.94821e6i 0.669030 + 0.195562i
\(631\) −666246. −0.0666133 −0.0333067 0.999445i \(-0.510604\pi\)
−0.0333067 + 0.999445i \(0.510604\pi\)
\(632\) −3.48774e6 + 6.04095e6i −0.347338 + 0.601607i
\(633\) −1.14203e7 1.97805e7i −1.13284 1.96213i
\(634\) 5.24972e6 + 9.09277e6i 0.518696 + 0.898407i
\(635\) 1.14726e6 1.98711e6i 0.112909 0.195564i
\(636\) −4.43446e6 −0.434708
\(637\) 1.64108e7 + 1.04903e7i 1.60243 + 1.02432i
\(638\) −3.51704e6 −0.342078
\(639\) 3.70173e6 6.41158e6i 0.358635 0.621173i
\(640\) 295777. + 512300.i 0.0285439 + 0.0494396i
\(641\) 1.05439e6 + 1.82625e6i 0.101357 + 0.175556i 0.912244 0.409647i \(-0.134348\pi\)
−0.810887 + 0.585203i \(0.801015\pi\)
\(642\) 1.23757e6 2.14353e6i 0.118504 0.205254i
\(643\) 1.25977e7 1.20161 0.600806 0.799395i \(-0.294846\pi\)
0.600806 + 0.799395i \(0.294846\pi\)
\(644\) 6.93328e6 + 2.02664e6i 0.658756 + 0.192558i
\(645\) −3.51182e6 −0.332379
\(646\) 694016. 1.20207e6i 0.0654317 0.113331i
\(647\) −8.56496e6 1.48349e7i −0.804386 1.39324i −0.916705 0.399565i \(-0.869161\pi\)
0.112319 0.993672i \(-0.464172\pi\)
\(648\) 372036. + 644386.i 0.0348055 + 0.0602849i
\(649\) 467109. 809056.i 0.0435318 0.0753992i
\(650\) −8.44301e6 −0.783815
\(651\) −5.37469e6 + 5.13724e6i −0.497051 + 0.475092i
\(652\) 1.03146e6 0.0950237
\(653\) 4.12762e6 7.14925e6i 0.378806 0.656112i −0.612083 0.790794i \(-0.709668\pi\)
0.990889 + 0.134682i \(0.0430013\pi\)
\(654\) 180181. + 312083.i 0.0164727 + 0.0285316i
\(655\) 2.46054e6 + 4.26178e6i 0.224092 + 0.388139i
\(656\) −488014. + 845265.i −0.0442764 + 0.0766890i
\(657\) 1.68933e7 1.52687
\(658\) −1.36587e6 5.60048e6i −0.122983 0.504267i
\(659\) −1.05417e7 −0.945581 −0.472790 0.881175i \(-0.656753\pi\)
−0.472790 + 0.881175i \(0.656753\pi\)
\(660\) 1.11237e6 1.92668e6i 0.0994009 0.172167i
\(661\) −2.23820e6 3.87668e6i −0.199249 0.345109i 0.749036 0.662529i \(-0.230517\pi\)
−0.948285 + 0.317420i \(0.897184\pi\)
\(662\) −3.47771e6 6.02357e6i −0.308424 0.534206i
\(663\) −1.77743e7 + 3.07859e7i −1.57039 + 2.72000i
\(664\) 3.57306e6 0.314499
\(665\) 310848. + 1.27457e6i 0.0272580 + 0.111766i
\(666\) −3.46121e6 −0.302373
\(667\) −9.84956e6 + 1.70599e7i −0.857240 + 1.48478i
\(668\) 3.54155e6 + 6.13415e6i 0.307081 + 0.531880i
\(669\) 1.03776e7 + 1.79745e7i 0.896461 + 1.55272i
\(670\) −3.10391e6 + 5.37614e6i −0.267130 + 0.462683i
\(671\) −2.30645e6 −0.197760
\(672\) 2.37771e6 2.27266e6i 0.203112 0.194139i
\(673\) −1.87165e7 −1.59289 −0.796447 0.604708i \(-0.793290\pi\)
−0.796447 + 0.604708i \(0.793290\pi\)
\(674\) −1.70713e6 + 2.95683e6i −0.144749 + 0.250713i
\(675\) 2.88521e6 + 4.99733e6i 0.243735 + 0.422162i
\(676\) −7.77348e6 1.34641e7i −0.654258 1.13321i
\(677\) −2.08116e6 + 3.60467e6i −0.174515 + 0.302270i −0.939993 0.341192i \(-0.889169\pi\)
0.765478 + 0.643462i \(0.222503\pi\)
\(678\) 6.16188e6 0.514801
\(679\) −1.86714e6 545776.i −0.155418 0.0454297i
\(680\) −2.86090e6 −0.237263
\(681\) 1.64848e7 2.85526e7i 1.36212 2.35927i
\(682\) 719570. + 1.24633e6i 0.0592396 + 0.102606i
\(683\) 6.43455e6 + 1.11450e7i 0.527796 + 0.914170i 0.999475 + 0.0323992i \(0.0103148\pi\)
−0.471679 + 0.881770i \(0.656352\pi\)
\(684\) 831576. 1.44033e6i 0.0679613 0.117712i
\(685\) −1.21063e7 −0.985793
\(686\) 8.55199e6 1.68063e6i 0.693836 0.136352i
\(687\) 2.50398e7 2.02414
\(688\) −502494. + 870345.i −0.0404725 + 0.0701004i
\(689\) 6.48168e6 + 1.12266e7i 0.520163 + 0.900949i
\(690\) −6.23045e6 1.07915e7i −0.498192 0.862894i
\(691\) 4.64518e6 8.04569e6i 0.370090 0.641015i −0.619489 0.785006i \(-0.712660\pi\)
0.989579 + 0.143990i \(0.0459934\pi\)
\(692\) −1.25758e6 −0.0998325
\(693\) −7.17316e6 2.09676e6i −0.567385 0.165850i
\(694\) −1.19400e7 −0.941033
\(695\) 1.05059e6 1.81967e6i 0.0825029 0.142899i
\(696\) 4.48495e6 + 7.76816e6i 0.350941 + 0.607848i
\(697\) −2.36016e6 4.08791e6i −0.184018 0.318728i
\(698\) −5.74934e6 + 9.95815e6i −0.446662 + 0.773642i
\(699\) 3.68202e7 2.85032
\(700\) −2.73113e6 + 2.61048e6i −0.210668 + 0.201361i
\(701\) 2.50809e7 1.92774 0.963870 0.266375i \(-0.0858258\pi\)
0.963870 + 0.266375i \(0.0858258\pi\)
\(702\) −7.34293e6 + 1.27183e7i −0.562376 + 0.974063i
\(703\) −326970. 566329.i −0.0249528 0.0432196i
\(704\) −318330. 551364.i −0.0242073 0.0419283i
\(705\) −4.97220e6 + 8.61210e6i −0.376769 + 0.652584i
\(706\) 5.88437e6 0.444312
\(707\) 825564. + 3.38505e6i 0.0621158 + 0.254693i
\(708\) −2.38264e6 −0.178638
\(709\) −4.96890e6 + 8.60639e6i −0.371231 + 0.642991i −0.989755 0.142774i \(-0.954398\pi\)
0.618524 + 0.785766i \(0.287731\pi\)
\(710\) −1.44151e6 2.49677e6i −0.107318 0.185880i
\(711\) −2.02109e7 3.50063e7i −1.49938 2.59700i
\(712\) 3.05747e6 5.29569e6i 0.226028 0.391491i
\(713\) 8.06069e6 0.593811
\(714\) 3.76904e6 + 1.54542e7i 0.276685 + 1.13449i
\(715\) −6.50364e6 −0.475764
\(716\) 4.08342e6 7.07269e6i 0.297674 0.515587i
\(717\) −1.08476e7 1.87885e7i −0.788015 1.36488i
\(718\) −6.15598e6 1.06625e7i −0.445642 0.771875i
\(719\) 7.00047e6 1.21252e7i 0.505016 0.874713i −0.494968 0.868911i \(-0.664820\pi\)
0.999983 0.00580117i \(-0.00184658\pi\)
\(720\) −3.42795e6 −0.246436
\(721\) −4.86536e6 + 4.65041e6i −0.348559 + 0.333160i
\(722\) −9.59017e6 −0.684673
\(723\) −1.79994e7 + 3.11758e7i −1.28059 + 2.21805i
\(724\) 176414. + 305559.i 0.0125080 + 0.0216645i
\(725\) −5.15160e6 8.92283e6i −0.363996 0.630460i
\(726\) 6.78333e6 1.17491e7i 0.477641 0.827298i
\(727\) 8.27315e6 0.580544 0.290272 0.956944i \(-0.406254\pi\)
0.290272 + 0.956944i \(0.406254\pi\)
\(728\) −9.22903e6 2.69770e6i −0.645398 0.188654i
\(729\) −2.33861e7 −1.62982
\(730\) 3.28926e6 5.69716e6i 0.228450 0.395687i
\(731\) −2.43019e6 4.20921e6i −0.168208 0.291345i
\(732\) 2.94120e6 + 5.09430e6i 0.202883 + 0.351404i
\(733\) 1.64295e6 2.84568e6i 0.112945 0.195626i −0.804012 0.594614i \(-0.797305\pi\)
0.916956 + 0.398988i \(0.130638\pi\)
\(734\) 6.46679e6 0.443046
\(735\) −1.26679e7 8.09773e6i −0.864943 0.552898i
\(736\) −3.56597e6 −0.242651
\(737\) 3.34059e6 5.78608e6i 0.226545 0.392388i
\(738\) −2.82796e6 4.89817e6i −0.191132 0.331050i
\(739\) −5.04564e6 8.73930e6i −0.339864 0.588662i 0.644543 0.764568i \(-0.277048\pi\)
−0.984407 + 0.175907i \(0.943714\pi\)
\(740\) −673925. + 1.16727e6i −0.0452410 + 0.0783597i
\(741\) −8.04754e6 −0.538416
\(742\) 5.56781e6 + 1.62751e6i 0.371257 + 0.108521i
\(743\) 1.73443e7 1.15261 0.576307 0.817233i \(-0.304493\pi\)
0.576307 + 0.817233i \(0.304493\pi\)
\(744\) 1.83520e6 3.17866e6i 0.121549 0.210529i
\(745\) 5.10998e6 + 8.85074e6i 0.337309 + 0.584237i
\(746\) 9.52237e6 + 1.64932e7i 0.626467 + 1.08507i
\(747\) −1.03526e7 + 1.79313e7i −0.678812 + 1.17574i
\(748\) 3.07905e6 0.201216
\(749\) −2.34057e6 + 2.23717e6i −0.152446 + 0.145711i
\(750\) 1.76995e7 1.14897
\(751\) 8.79857e6 1.52396e7i 0.569262 0.985990i −0.427377 0.904073i \(-0.640562\pi\)
0.996639 0.0819170i \(-0.0261042\pi\)
\(752\) 1.42291e6 + 2.46455e6i 0.0917554 + 0.158925i
\(753\) 2.45762e6 + 4.25673e6i 0.157953 + 0.273583i
\(754\) 1.31109e7 2.27088e7i 0.839857 1.45468i
\(755\) 8.72158e6 0.556836
\(756\) 1.55707e6 + 6.38445e6i 0.0990841 + 0.406274i
\(757\) −4.66480e6 −0.295865 −0.147932 0.988997i \(-0.547262\pi\)
−0.147932 + 0.988997i \(0.547262\pi\)
\(758\) −2.00386e6 + 3.47079e6i −0.126676 + 0.219409i
\(759\) 6.70554e6 + 1.16143e7i 0.422502 + 0.731795i
\(760\) −323828. 560887.i −0.0203367 0.0352242i
\(761\) −9.13585e6 + 1.58238e7i −0.571857 + 0.990485i 0.424518 + 0.905419i \(0.360443\pi\)
−0.996375 + 0.0850658i \(0.972890\pi\)
\(762\) 6.29819e6 0.392942
\(763\) −111693. 457973.i −0.00694566 0.0284792i
\(764\) −8.93044e6 −0.553528
\(765\) 8.28923e6 1.43574e7i 0.512107 0.886995i
\(766\) 5.64305e6 + 9.77404e6i 0.347489 + 0.601869i
\(767\) 3.48261e6 + 6.03205e6i 0.213755 + 0.370234i
\(768\) −811873. + 1.40620e6i −0.0496689 + 0.0860291i
\(769\) −2.31895e7 −1.41409 −0.707043 0.707171i \(-0.749971\pi\)
−0.707043 + 0.707171i \(0.749971\pi\)
\(770\) −2.10379e6 + 2.01085e6i −0.127872 + 0.122223i
\(771\) 1.18821e7 0.719873
\(772\) 394530. 683346.i 0.0238252 0.0412665i
\(773\) −1.01074e6 1.75066e6i −0.0608405 0.105379i 0.834001 0.551763i \(-0.186045\pi\)
−0.894841 + 0.446384i \(0.852711\pi\)
\(774\) −2.91187e6 5.04351e6i −0.174711 0.302608i
\(775\) −2.10799e6 + 3.65114e6i −0.126070 + 0.218360i
\(776\) 960317. 0.0572480
\(777\) 7.19328e6 + 2.10264e6i 0.427439 + 0.124943i
\(778\) −4.96959e6 −0.294355
\(779\) 534297. 925430.i 0.0315456 0.0546387i
\(780\) 8.29347e6 + 1.43647e7i 0.488090 + 0.845397i
\(781\) 1.55143e6 + 2.68715e6i 0.0910131 + 0.157639i
\(782\) 8.62296e6 1.49354e7i 0.504243 0.873374i
\(783\) −1.79215e7 −1.04465
\(784\) −3.81949e6 + 1.98085e6i −0.221930 + 0.115097i
\(785\) 7.72763e6 0.447582
\(786\) −6.75389e6 + 1.16981e7i −0.389940 + 0.675396i
\(787\) −7.88722e6 1.36611e7i −0.453928 0.786227i 0.544698 0.838632i \(-0.316644\pi\)
−0.998626 + 0.0524059i \(0.983311\pi\)
\(788\) 7.53207e6 + 1.30459e7i 0.432114 + 0.748444i
\(789\) −5.63592e6 + 9.76170e6i −0.322309 + 0.558255i
\(790\) −1.57409e7 −0.897348
\(791\) −7.73672e6 2.26149e6i −0.439659 0.128515i
\(792\) 3.68934e6 0.208995
\(793\) 8.59807e6 1.48923e7i 0.485532 0.840966i
\(794\) −5.49124e6 9.51111e6i −0.309115 0.535402i
\(795\) −5.00340e6 8.66614e6i −0.280768 0.486304i
\(796\) −5.12010e6 + 8.86827e6i −0.286415 + 0.496085i
\(797\) 1.22436e6 0.0682750 0.0341375 0.999417i \(-0.489132\pi\)
0.0341375 + 0.999417i \(0.489132\pi\)
\(798\) −2.60321e6 + 2.48820e6i −0.144711 + 0.138318i
\(799\) −1.37631e7 −0.762690
\(800\) 932551. 1.61523e6i 0.0515167 0.0892295i
\(801\) 1.77175e7 + 3.06876e7i 0.975712 + 1.68998i
\(802\) 7.42670e6 + 1.28634e7i 0.407718 + 0.706189i
\(803\) −3.54007e6 + 6.13158e6i −0.193742 + 0.335571i
\(804\) −1.70398e7 −0.929658
\(805\) 3.86221e6 + 1.58362e7i 0.210061 + 0.861312i
\(806\) −1.07297e7 −0.581771
\(807\) 1.06555e7 1.84559e7i 0.575959 0.997590i
\(808\) −860037. 1.48963e6i −0.0463435 0.0802692i
\(809\) 1.38662e7 + 2.40170e7i 0.744882 + 1.29017i 0.950250 + 0.311489i \(0.100828\pi\)
−0.205368 + 0.978685i \(0.565839\pi\)
\(810\) −839536. + 1.45412e6i −0.0449600 + 0.0778731i
\(811\) −1.19246e7 −0.636636 −0.318318 0.947984i \(-0.603118\pi\)
−0.318318 + 0.947984i \(0.603118\pi\)
\(812\) −2.78018e6 1.13996e7i −0.147973 0.606734i
\(813\) 3.23476e7 1.71639
\(814\) 725313. 1.25628e6i 0.0383676 0.0664546i
\(815\) 1.16379e6 + 2.01575e6i 0.0613735 + 0.106302i
\(816\) −3.92642e6 6.80076e6i −0.206429 0.357546i
\(817\) 550151. 952889.i 0.0288354 0.0499444i
\(818\) 1.50376e7 0.785770
\(819\) 4.02787e7 3.84993e7i 2.09829 2.00559i
\(820\) −2.20250e6 −0.114388
\(821\) −8.02312e6 + 1.38965e7i −0.415418 + 0.719525i −0.995472 0.0950526i \(-0.969698\pi\)
0.580054 + 0.814578i \(0.303031\pi\)
\(822\) −1.66152e7 2.87784e7i −0.857682 1.48555i
\(823\) 5.61533e6 + 9.72603e6i 0.288985 + 0.500537i 0.973568 0.228398i \(-0.0733489\pi\)
−0.684583 + 0.728935i \(0.740016\pi\)
\(824\) 1.66129e6 2.87743e6i 0.0852367 0.147634i
\(825\) −7.01437e6 −0.358801
\(826\) 2.99159e6 + 874460.i 0.152564 + 0.0445954i
\(827\) −2.68427e7 −1.36478 −0.682389 0.730989i \(-0.739059\pi\)
−0.682389 + 0.730989i \(0.739059\pi\)
\(828\) 1.03321e7 1.78957e7i 0.523736 0.907138i
\(829\) −1.40210e7 2.42850e7i −0.708584 1.22730i −0.965382 0.260839i \(-0.916001\pi\)
0.256798 0.966465i \(-0.417332\pi\)
\(830\) 4.03147e6 + 6.98272e6i 0.203127 + 0.351827i
\(831\) 6.72813e6 1.16535e7i 0.337981 0.585400i
\(832\) 4.74673e6 0.237731
\(833\) 939564. 2.07872e7i 0.0469152 1.03797i
\(834\) 5.76747e6 0.287125
\(835\) −7.99186e6 + 1.38423e7i −0.396672 + 0.687056i
\(836\) 348521. + 603656.i 0.0172470 + 0.0298727i
\(837\) 3.66665e6 + 6.35083e6i 0.180907 + 0.313341i
\(838\) −9.20054e6 + 1.59358e7i −0.452588 + 0.783905i
\(839\) −3.30603e7 −1.62145 −0.810723 0.585430i \(-0.800926\pi\)
−0.810723 + 0.585430i \(0.800926\pi\)
\(840\) 7.12416e6 + 2.08244e6i 0.348366 + 0.101830i
\(841\) 1.14880e7 0.560086
\(842\) 809728. 1.40249e6i 0.0393604 0.0681741i
\(843\) −1.23645e7 2.14160e7i −0.599250 1.03793i
\(844\) −7.37495e6 1.27738e7i −0.356372 0.617254i
\(845\) 1.75416e7 3.03830e7i 0.845139 1.46382i
\(846\) −1.64910e7 −0.792176
\(847\) −1.28291e7 + 1.22623e7i −0.614450 + 0.587305i
\(848\) −2.86367e6 −0.136752
\(849\) −2.20178e7 + 3.81359e7i −1.04835 + 1.81579i
\(850\) 4.51005e6 + 7.81164e6i 0.214109 + 0.370847i
\(851\) −4.06251e6 7.03648e6i −0.192296 0.333067i
\(852\) 3.95677e6 6.85334e6i 0.186742 0.323447i
\(853\) 2.73897e7 1.28889 0.644444 0.764652i \(-0.277089\pi\)
0.644444 + 0.764652i \(0.277089\pi\)
\(854\) −1.82322e6 7.47575e6i −0.0855452 0.350760i
\(855\) 3.75306e6 0.175578
\(856\) 799192. 1.38424e6i 0.0372792 0.0645695i
\(857\) 1.48360e6 + 2.56968e6i 0.0690027 + 0.119516i 0.898463 0.439050i \(-0.144685\pi\)
−0.829460 + 0.558566i \(0.811352\pi\)
\(858\) −8.92587e6 1.54601e7i −0.413935 0.716957i
\(859\) 1.98980e7 3.44643e7i 0.920081 1.59363i 0.120794 0.992678i \(-0.461456\pi\)
0.799287 0.600949i \(-0.205211\pi\)
\(860\) −2.26785e6 −0.104561
\(861\) 2.90164e6 + 1.18976e7i 0.133394 + 0.546954i
\(862\) 379034. 0.0173744
\(863\) −3.59799e6 + 6.23190e6i −0.164450 + 0.284835i −0.936460 0.350775i \(-0.885918\pi\)
0.772010 + 0.635610i \(0.219251\pi\)
\(864\) −1.62209e6 2.80954e6i −0.0739248 0.128042i
\(865\) −1.41893e6 2.45766e6i −0.0644794 0.111682i
\(866\) −8.63453e6 + 1.49554e7i −0.391241 + 0.677649i
\(867\) 2.79940e6 0.126478
\(868\) −3.47084e6 + 3.31751e6i −0.156364 + 0.149456i
\(869\) 1.69411e7 0.761015
\(870\) −1.01207e7 + 1.75296e7i −0.453329 + 0.785188i
\(871\) 2.49063e7 + 4.31391e7i 1.11241 + 1.92675i
\(872\) 116357. + 201536.i 0.00518203 + 0.00897554i
\(873\) −2.78244e6 + 4.81932e6i −0.123563 + 0.214018i
\(874\) 3.90417e6 0.172882
\(875\) −2.22231e7 6.49594e6i −0.981259 0.286828i
\(876\) 1.80573e7 0.795045
\(877\) −1.25621e7 + 2.17582e7i −0.551523 + 0.955266i 0.446642 + 0.894713i \(0.352620\pi\)
−0.998165 + 0.0605532i \(0.980714\pi\)
\(878\) 4.44734e6 + 7.70303e6i 0.194699 + 0.337229i
\(879\) 2.03150e7 + 3.51866e7i 0.886839 + 1.53605i
\(880\) 718343. 1.24421e6i 0.0312698 0.0541609i
\(881\) 120262. 0.00522022 0.00261011 0.999997i \(-0.499169\pi\)
0.00261011 + 0.999997i \(0.499169\pi\)
\(882\) 1.12579e6 2.49074e7i 0.0487289 1.07809i
\(883\) 2.43497e7 1.05097 0.525487 0.850802i \(-0.323883\pi\)
0.525487 + 0.850802i \(0.323883\pi\)
\(884\) −1.14782e7 + 1.98808e7i −0.494018 + 0.855664i
\(885\) −2.68833e6 4.65632e6i −0.115378 0.199841i
\(886\) 9.36851e6 + 1.62267e7i 0.400946 + 0.694459i
\(887\) 1.41383e7 2.44883e7i 0.603377 1.04508i −0.388929 0.921268i \(-0.627155\pi\)
0.992306 0.123812i \(-0.0395120\pi\)
\(888\) −3.69969e6 −0.157446
\(889\) −7.90786e6 2.31152e6i −0.335587 0.0980941i
\(890\) 1.37989e7 0.583943
\(891\) 903552. 1.56500e6i 0.0381293 0.0660419i
\(892\) 6.70160e6 + 1.16075e7i 0.282011 + 0.488458i
\(893\) −1.55786e6 2.69828e6i −0.0653730 0.113229i
\(894\) −1.40263e7 + 2.42943e7i −0.586948 + 1.01662i
\(895\) 1.84293e7 0.769042
\(896\) 1.53547e6 1.46763e6i 0.0638955 0.0610727i
\(897\) −9.99885e7 −4.14924
\(898\) −1.79586e6 + 3.11053e6i −0.0743161 + 0.128719i
\(899\) −6.54688e6 1.13395e7i −0.270169 0.467946i
\(900\) 5.40398e6 + 9.35997e6i 0.222386 + 0.385184i
\(901\) 6.92471e6 1.19940e7i 0.284178 0.492210i
\(902\) 2.37045e6 0.0970094
\(903\) 2.98774e6 + 1.22506e7i 0.121934 + 0.499963i
\(904\) 3.97920e6 0.161948
\(905\) −398096. + 689523.i −0.0161572 + 0.0279851i
\(906\) 1.19699e7 + 2.07324e7i 0.484472 + 0.839130i
\(907\) 1.21584e7 + 2.10590e7i 0.490748 + 0.850000i 0.999943 0.0106507i \(-0.00339029\pi\)
−0.509195 + 0.860651i \(0.670057\pi\)
\(908\) 1.06455e7 1.84386e7i 0.428501 0.742186i
\(909\) 9.96754e6 0.400109
\(910\) −5.14106e6 2.10798e7i −0.205802 0.843847i
\(911\) −3.36224e7 −1.34225 −0.671123 0.741346i \(-0.734188\pi\)
−0.671123 + 0.741346i \(0.734188\pi\)
\(912\) 888871. 1.53957e6i 0.0353876 0.0612932i
\(913\) −4.33888e6 7.51517e6i −0.172267 0.298374i
\(914\) −1.19636e7 2.07216e7i −0.473693 0.820461i
\(915\) −6.63710e6 + 1.14958e7i −0.262075 + 0.453927i
\(916\) 1.61701e7 0.636759
\(917\) 1.27734e7 1.22091e7i 0.501629 0.479468i
\(918\) 1.56897e7 0.614479
\(919\) 4.06874e6 7.04727e6i 0.158917 0.275253i −0.775561 0.631272i \(-0.782533\pi\)
0.934479 + 0.356019i \(0.115866\pi\)
\(920\) −4.02348e6 6.96887e6i −0.156723 0.271452i
\(921\) −2.95001e7 5.10956e7i −1.14597 1.98488i
\(922\) −3.25013e6 + 5.62939e6i −0.125914 + 0.218089i
\(923\) −2.31338e7 −0.893807
\(924\) −7.66739e6 2.24123e6i −0.295439 0.0863587i
\(925\) 4.24962e6 0.163304
\(926\) 1.69259e7 2.93165e7i 0.648671 1.12353i
\(927\) 9.62688e6 + 1.66742e7i 0.367948 + 0.637304i
\(928\) 2.89627e6 + 5.01649e6i 0.110400 + 0.191219i
\(929\) −1.79027e7 + 3.10084e7i −0.680580 + 1.17880i 0.294224 + 0.955736i \(0.404939\pi\)
−0.974804 + 0.223063i \(0.928395\pi\)
\(930\) 8.28261e6 0.314022
\(931\) 4.18173e6 2.16872e6i 0.158118 0.0820029i
\(932\) 2.37776e7 0.896661
\(933\) 1.54249e7 2.67167e7i 0.580120 1.00480i
\(934\) −1.53319e7 2.65556e7i −0.575080 0.996068i
\(935\) 3.47409e6 + 6.01730e6i 0.129961 + 0.225098i
\(936\) −1.37533e7 + 2.38213e7i −0.513116 + 0.888744i
\(937\) 4.65849e7 1.73339 0.866694 0.498840i \(-0.166241\pi\)
0.866694 + 0.498840i \(0.166241\pi\)
\(938\) 2.13947e7 + 6.25382e6i 0.793963 + 0.232080i
\(939\) 4.12029e7 1.52498
\(940\) −3.21093e6 + 5.56149e6i −0.118525 + 0.205292i
\(941\) 1.03362e6 + 1.79029e6i 0.0380529 + 0.0659096i 0.884425 0.466683i \(-0.154551\pi\)
−0.846372 + 0.532593i \(0.821218\pi\)
\(942\) 1.06057e7 + 1.83697e7i 0.389415 + 0.674487i
\(943\) 6.63850e6 1.14982e7i 0.243103 0.421067i
\(944\) −1.53865e6 −0.0561966
\(945\) −1.07201e7 + 1.02465e7i −0.390498 + 0.373247i
\(946\) 2.44078e6 0.0886750
\(947\) −1.18386e7 + 2.05051e7i −0.428970 + 0.742998i −0.996782 0.0801602i \(-0.974457\pi\)
0.567812 + 0.823158i \(0.307790\pi\)
\(948\) −2.16034e7 3.74182e7i −0.780732 1.35227i
\(949\) −2.63936e7 4.57150e7i −0.951334 1.64776i
\(950\) −1.02099e6 + 1.76841e6i −0.0367041 + 0.0635734i
\(951\) −6.50345e7 −2.33181
\(952\) 2.43396e6 + 9.97993e6i 0.0870403 + 0.356891i
\(953\) −3.40521e6 −0.121454 −0.0607270 0.998154i \(-0.519342\pi\)
−0.0607270 + 0.998154i \(0.519342\pi\)
\(954\) 8.29725e6 1.43713e7i 0.295164 0.511239i
\(955\) −1.00762e7 1.74525e7i −0.357510 0.619226i
\(956\) −7.00510e6 1.21332e7i −0.247896 0.429368i
\(957\) 1.08924e7 1.88663e7i 0.384455 0.665896i
\(958\) −9.61170e6 −0.338366
\(959\) 1.02996e7 + 4.22315e7i 0.361639 + 1.48283i
\(960\) −3.66414e6 −0.128320
\(961\) 1.16357e7 2.01535e7i 0.406427 0.703952i
\(962\) 5.40769e6 + 9.36639e6i 0.188397 + 0.326313i
\(963\) 4.63119e6 + 8.02145e6i 0.160926 + 0.278732i
\(964\) −1.16236e7 + 2.01326e7i −0.402853 + 0.697762i
\(965\) 1.78059e6 0.0615525
\(966\) −3.23441e7 + 3.09152e7i −1.11520 + 1.06593i
\(967\) 1.44238e6 0.0496036 0.0248018 0.999692i \(-0.492105\pi\)
0.0248018 + 0.999692i \(0.492105\pi\)
\(968\) 4.38051e6 7.58727e6i 0.150258 0.260254i
\(969\) 4.29880e6 + 7.44575e6i 0.147075 + 0.254741i
\(970\) 1.08352e6 + 1.87672e6i 0.0369751 + 0.0640427i
\(971\) 2.57977e6 4.46830e6i 0.0878078 0.152088i −0.818776 0.574113i \(-0.805347\pi\)
0.906584 + 0.422025i \(0.138681\pi\)
\(972\) −1.69266e7 −0.574651
\(973\) −7.24151e6 2.11674e6i −0.245215 0.0716779i
\(974\) −681206. −0.0230081
\(975\) 2.61484e7 4.52904e7i 0.880914 1.52579i
\(976\) 1.89936e6 + 3.28978e6i 0.0638237 + 0.110546i
\(977\) 3.48825e6 + 6.04183e6i 0.116915 + 0.202503i 0.918544 0.395319i \(-0.129366\pi\)
−0.801628 + 0.597823i \(0.796033\pi\)
\(978\) −3.19447e6 + 5.53299e6i −0.106795 + 0.184975i
\(979\) −1.48511e7 −0.495225
\(980\) −8.18065e6 5.22932e6i −0.272096 0.173932i
\(981\) −1.34853e6 −0.0447394
\(982\) 1.15526e7 2.00096e7i 0.382296 0.662156i
\(983\) 1.40784e7 + 2.43845e7i 0.464696 + 0.804878i 0.999188 0.0402961i \(-0.0128301\pi\)
−0.534491 + 0.845174i \(0.679497\pi\)
\(984\) −3.02281e6 5.23565e6i −0.0995228 0.172378i
\(985\) −1.69968e7 + 2.94394e7i −0.558184 + 0.966804i
\(986\) −2.80142e7 −0.917669
\(987\) 3.42725e7 + 1.00181e7i 1.11983 + 0.327334i
\(988\) −5.19691e6 −0.169376
\(989\) 6.83547e6 1.18394e7i 0.222217 0.384891i
\(990\) 4.16268e6 + 7.20997e6i 0.134985 + 0.233801i
\(991\) 1.17022e7 + 2.02687e7i 0.378514 + 0.655606i 0.990846 0.134995i \(-0.0431018\pi\)
−0.612332 + 0.790601i \(0.709768\pi\)
\(992\) 1.18513e6 2.05270e6i 0.0382372 0.0662287i
\(993\) 4.30825e7 1.38653
\(994\) −7.48330e6 + 7.15271e6i −0.240230 + 0.229617i
\(995\) −2.31080e7 −0.739954
\(996\) −1.10659e7 + 1.91668e7i −0.353459 + 0.612210i
\(997\) 2.15142e7 + 3.72637e7i 0.685468 + 1.18727i 0.973290 + 0.229581i \(0.0737356\pi\)
−0.287822 + 0.957684i \(0.592931\pi\)
\(998\) −1.08720e6 1.88309e6i −0.0345529 0.0598474i
\(999\) 3.69592e6 6.40151e6i 0.117168 0.202941i
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 14.6.c.a.9.1 4
3.2 odd 2 126.6.g.j.37.1 4
4.3 odd 2 112.6.i.d.65.2 4
7.2 even 3 98.6.a.h.1.2 2
7.3 odd 6 98.6.c.e.67.2 4
7.4 even 3 inner 14.6.c.a.11.1 yes 4
7.5 odd 6 98.6.a.g.1.1 2
7.6 odd 2 98.6.c.e.79.2 4
21.2 odd 6 882.6.a.ba.1.2 2
21.5 even 6 882.6.a.bi.1.1 2
21.11 odd 6 126.6.g.j.109.1 4
28.11 odd 6 112.6.i.d.81.2 4
28.19 even 6 784.6.a.bb.1.2 2
28.23 odd 6 784.6.a.s.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.c.a.9.1 4 1.1 even 1 trivial
14.6.c.a.11.1 yes 4 7.4 even 3 inner
98.6.a.g.1.1 2 7.5 odd 6
98.6.a.h.1.2 2 7.2 even 3
98.6.c.e.67.2 4 7.3 odd 6
98.6.c.e.79.2 4 7.6 odd 2
112.6.i.d.65.2 4 4.3 odd 2
112.6.i.d.81.2 4 28.11 odd 6
126.6.g.j.37.1 4 3.2 odd 2
126.6.g.j.109.1 4 21.11 odd 6
784.6.a.s.1.1 2 28.23 odd 6
784.6.a.bb.1.2 2 28.19 even 6
882.6.a.ba.1.2 2 21.2 odd 6
882.6.a.bi.1.1 2 21.5 even 6