Properties

Label 354.6.c.b.353.2
Level $354$
Weight $6$
Character 354.353
Analytic conductor $56.776$
Analytic rank $0$
Dimension $50$
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] = [354,6,Mod(353,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.353");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 354.c (of order \(2\), degree \(1\), 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: \(56.7758722138\)
Analytic rank: \(0\)
Dimension: \(50\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.2
Character \(\chi\) \(=\) 354.353
Dual form 354.6.c.b.353.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +(-15.5824 + 0.434789i) q^{3} +16.0000 q^{4} +38.7472i q^{5} +(-62.3296 + 1.73916i) q^{6} -41.9790 q^{7} +64.0000 q^{8} +(242.622 - 13.5501i) q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +(-15.5824 + 0.434789i) q^{3} +16.0000 q^{4} +38.7472i q^{5} +(-62.3296 + 1.73916i) q^{6} -41.9790 q^{7} +64.0000 q^{8} +(242.622 - 13.5501i) q^{9} +154.989i q^{10} +166.287 q^{11} +(-249.318 + 6.95663i) q^{12} -75.0672i q^{13} -167.916 q^{14} +(-16.8469 - 603.774i) q^{15} +256.000 q^{16} +428.041i q^{17} +(970.488 - 54.2005i) q^{18} -703.692 q^{19} +619.955i q^{20} +(654.133 - 18.2520i) q^{21} +665.149 q^{22} +2799.73 q^{23} +(-997.273 + 27.8265i) q^{24} +1623.66 q^{25} -300.269i q^{26} +(-3774.74 + 316.633i) q^{27} -671.663 q^{28} +647.558i q^{29} +(-67.3874 - 2415.10i) q^{30} -3883.69i q^{31} +1024.00 q^{32} +(-2591.15 + 72.2999i) q^{33} +1712.17i q^{34} -1626.57i q^{35} +(3881.95 - 216.802i) q^{36} -10063.6i q^{37} -2814.77 q^{38} +(32.6384 + 1169.73i) q^{39} +2479.82i q^{40} +18919.8i q^{41} +(2616.53 - 73.0080i) q^{42} +13342.8i q^{43} +2660.60 q^{44} +(525.029 + 9400.92i) q^{45} +11198.9 q^{46} -19122.3 q^{47} +(-3989.09 + 111.306i) q^{48} -15044.8 q^{49} +6494.62 q^{50} +(-186.108 - 6669.91i) q^{51} -1201.08i q^{52} +25973.9i q^{53} +(-15099.0 + 1266.53i) q^{54} +6443.16i q^{55} -2686.65 q^{56} +(10965.2 - 305.958i) q^{57} +2590.23i q^{58} +(5728.51 + 26117.2i) q^{59} +(-269.550 - 9660.38i) q^{60} +10016.2i q^{61} -15534.8i q^{62} +(-10185.0 + 568.820i) q^{63} +4096.00 q^{64} +2908.64 q^{65} +(-10364.6 + 289.200i) q^{66} +11220.5i q^{67} +6848.66i q^{68} +(-43626.5 + 1217.29i) q^{69} -6506.27i q^{70} -2995.96i q^{71} +(15527.8 - 867.207i) q^{72} +49102.6i q^{73} -40254.4i q^{74} +(-25300.4 + 705.948i) q^{75} -11259.1 q^{76} -6980.57 q^{77} +(130.554 + 4678.91i) q^{78} -38832.8 q^{79} +9919.28i q^{80} +(58681.8 - 6575.11i) q^{81} +75679.1i q^{82} +46082.8 q^{83} +(10466.1 - 292.032i) q^{84} -16585.4 q^{85} +53371.3i q^{86} +(-281.551 - 10090.5i) q^{87} +10642.4 q^{88} +85295.8 q^{89} +(2100.11 + 37603.7i) q^{90} +3151.24i q^{91} +44795.6 q^{92} +(1688.59 + 60517.2i) q^{93} -76489.1 q^{94} -27266.1i q^{95} +(-15956.4 + 445.224i) q^{96} +116154. i q^{97} -60179.1 q^{98} +(40344.9 - 2253.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 200 q^{2} - 13 q^{3} + 800 q^{4} - 52 q^{6} + 38 q^{7} + 3200 q^{8} + 51 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 200 q^{2} - 13 q^{3} + 800 q^{4} - 52 q^{6} + 38 q^{7} + 3200 q^{8} + 51 q^{9} + 652 q^{11} - 208 q^{12} + 152 q^{14} - 2107 q^{15} + 12800 q^{16} + 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} - 2456 q^{23} - 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} - 8428 q^{30} + 51200 q^{32} + 9744 q^{33} + 816 q^{36} - 3576 q^{38} - 1388 q^{39} - 15204 q^{42} + 10432 q^{44} + 33067 q^{45} - 9824 q^{46} + 27144 q^{47} - 3328 q^{48} + 85768 q^{49} - 95824 q^{50} + 3338 q^{51} + 39560 q^{54} + 2432 q^{56} - 63969 q^{57} + 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} + 9400 q^{65} + 38976 q^{66} + 115930 q^{69} + 3264 q^{72} + 24248 q^{75} - 14304 q^{76} + 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} + 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} - 104908 q^{89} + 132268 q^{90} - 39296 q^{92} + 91204 q^{93} + 108576 q^{94} - 13312 q^{96} + 343072 q^{98} + 111406 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) −15.5824 + 0.434789i −0.999611 + 0.0278917i
\(4\) 16.0000 0.500000
\(5\) 38.7472i 0.693131i 0.938026 + 0.346565i \(0.112652\pi\)
−0.938026 + 0.346565i \(0.887348\pi\)
\(6\) −62.3296 + 1.73916i −0.706832 + 0.0197224i
\(7\) −41.9790 −0.323807 −0.161904 0.986807i \(-0.551763\pi\)
−0.161904 + 0.986807i \(0.551763\pi\)
\(8\) 64.0000 0.353553
\(9\) 242.622 13.5501i 0.998444 0.0557618i
\(10\) 154.989i 0.490117i
\(11\) 166.287 0.414359 0.207180 0.978303i \(-0.433572\pi\)
0.207180 + 0.978303i \(0.433572\pi\)
\(12\) −249.318 + 6.95663i −0.499805 + 0.0139459i
\(13\) 75.0672i 0.123195i −0.998101 0.0615973i \(-0.980381\pi\)
0.998101 0.0615973i \(-0.0196195\pi\)
\(14\) −167.916 −0.228966
\(15\) −16.8469 603.774i −0.0193326 0.692861i
\(16\) 256.000 0.250000
\(17\) 428.041i 0.359222i 0.983738 + 0.179611i \(0.0574840\pi\)
−0.983738 + 0.179611i \(0.942516\pi\)
\(18\) 970.488 54.2005i 0.706007 0.0394295i
\(19\) −703.692 −0.447196 −0.223598 0.974681i \(-0.571780\pi\)
−0.223598 + 0.974681i \(0.571780\pi\)
\(20\) 619.955i 0.346565i
\(21\) 654.133 18.2520i 0.323681 0.00903155i
\(22\) 665.149 0.292996
\(23\) 2799.73 1.10356 0.551780 0.833990i \(-0.313949\pi\)
0.551780 + 0.833990i \(0.313949\pi\)
\(24\) −997.273 + 27.8265i −0.353416 + 0.00986122i
\(25\) 1623.66 0.519570
\(26\) 300.269i 0.0871118i
\(27\) −3774.74 + 316.633i −0.996500 + 0.0835884i
\(28\) −671.663 −0.161904
\(29\) 647.558i 0.142983i 0.997441 + 0.0714914i \(0.0227759\pi\)
−0.997441 + 0.0714914i \(0.977224\pi\)
\(30\) −67.3874 2415.10i −0.0136702 0.489927i
\(31\) 3883.69i 0.725839i −0.931820 0.362920i \(-0.881780\pi\)
0.931820 0.362920i \(-0.118220\pi\)
\(32\) 1024.00 0.176777
\(33\) −2591.15 + 72.2999i −0.414198 + 0.0115572i
\(34\) 1712.17i 0.254009i
\(35\) 1626.57i 0.224441i
\(36\) 3881.95 216.802i 0.499222 0.0278809i
\(37\) 10063.6i 1.20851i −0.796792 0.604254i \(-0.793471\pi\)
0.796792 0.604254i \(-0.206529\pi\)
\(38\) −2814.77 −0.316216
\(39\) 32.6384 + 1169.73i 0.00343611 + 0.123147i
\(40\) 2479.82i 0.245059i
\(41\) 18919.8i 1.75775i 0.477055 + 0.878874i \(0.341704\pi\)
−0.477055 + 0.878874i \(0.658296\pi\)
\(42\) 2616.53 73.0080i 0.228877 0.00638627i
\(43\) 13342.8i 1.10047i 0.835011 + 0.550233i \(0.185461\pi\)
−0.835011 + 0.550233i \(0.814539\pi\)
\(44\) 2660.60 0.207180
\(45\) 525.029 + 9400.92i 0.0386502 + 0.692052i
\(46\) 11198.9 0.780335
\(47\) −19122.3 −1.26268 −0.631342 0.775505i \(-0.717496\pi\)
−0.631342 + 0.775505i \(0.717496\pi\)
\(48\) −3989.09 + 111.306i −0.249903 + 0.00697294i
\(49\) −15044.8 −0.895149
\(50\) 6494.62 0.367391
\(51\) −186.108 6669.91i −0.0100193 0.359083i
\(52\) 1201.08i 0.0615973i
\(53\) 25973.9i 1.27013i 0.772460 + 0.635063i \(0.219026\pi\)
−0.772460 + 0.635063i \(0.780974\pi\)
\(54\) −15099.0 + 1266.53i −0.704632 + 0.0591059i
\(55\) 6443.16i 0.287205i
\(56\) −2686.65 −0.114483
\(57\) 10965.2 305.958i 0.447022 0.0124731i
\(58\) 2590.23i 0.101104i
\(59\) 5728.51 + 26117.2i 0.214245 + 0.976780i
\(60\) −269.550 9660.38i −0.00966631 0.346430i
\(61\) 10016.2i 0.344650i 0.985040 + 0.172325i \(0.0551279\pi\)
−0.985040 + 0.172325i \(0.944872\pi\)
\(62\) 15534.8i 0.513246i
\(63\) −10185.0 + 568.820i −0.323303 + 0.0180561i
\(64\) 4096.00 0.125000
\(65\) 2908.64 0.0853900
\(66\) −10364.6 + 289.200i −0.292882 + 0.00817218i
\(67\) 11220.5i 0.305370i 0.988275 + 0.152685i \(0.0487920\pi\)
−0.988275 + 0.152685i \(0.951208\pi\)
\(68\) 6848.66i 0.179611i
\(69\) −43626.5 + 1217.29i −1.10313 + 0.0307802i
\(70\) 6506.27i 0.158704i
\(71\) 2995.96i 0.0705326i −0.999378 0.0352663i \(-0.988772\pi\)
0.999378 0.0352663i \(-0.0112279\pi\)
\(72\) 15527.8 867.207i 0.353003 0.0197148i
\(73\) 49102.6i 1.07844i 0.842164 + 0.539222i \(0.181282\pi\)
−0.842164 + 0.539222i \(0.818718\pi\)
\(74\) 40254.4i 0.854544i
\(75\) −25300.4 + 705.948i −0.519368 + 0.0144917i
\(76\) −11259.1 −0.223598
\(77\) −6980.57 −0.134173
\(78\) 130.554 + 4678.91i 0.00242970 + 0.0870779i
\(79\) −38832.8 −0.700054 −0.350027 0.936740i \(-0.613828\pi\)
−0.350027 + 0.936740i \(0.613828\pi\)
\(80\) 9919.28i 0.173283i
\(81\) 58681.8 6575.11i 0.993781 0.111350i
\(82\) 75679.1i 1.24291i
\(83\) 46082.8 0.734250 0.367125 0.930172i \(-0.380342\pi\)
0.367125 + 0.930172i \(0.380342\pi\)
\(84\) 10466.1 292.032i 0.161841 0.00451577i
\(85\) −16585.4 −0.248988
\(86\) 53371.3i 0.778147i
\(87\) −281.551 10090.5i −0.00398804 0.142927i
\(88\) 10642.4 0.146498
\(89\) 85295.8 1.14144 0.570720 0.821145i \(-0.306664\pi\)
0.570720 + 0.821145i \(0.306664\pi\)
\(90\) 2100.11 + 37603.7i 0.0273298 + 0.489355i
\(91\) 3151.24i 0.0398913i
\(92\) 44795.6 0.551780
\(93\) 1688.59 + 60517.2i 0.0202449 + 0.725557i
\(94\) −76489.1 −0.892852
\(95\) 27266.1i 0.309966i
\(96\) −15956.4 + 445.224i −0.176708 + 0.00493061i
\(97\) 116154.i 1.25345i 0.779242 + 0.626723i \(0.215604\pi\)
−0.779242 + 0.626723i \(0.784396\pi\)
\(98\) −60179.1 −0.632966
\(99\) 40344.9 2253.21i 0.413715 0.0231054i
\(100\) 25978.5 0.259785
\(101\) −97370.3 −0.949780 −0.474890 0.880045i \(-0.657512\pi\)
−0.474890 + 0.880045i \(0.657512\pi\)
\(102\) −744.431 26679.6i −0.00708474 0.253910i
\(103\) 180702.i 1.67830i 0.543897 + 0.839152i \(0.316948\pi\)
−0.543897 + 0.839152i \(0.683052\pi\)
\(104\) 4804.30i 0.0435559i
\(105\) 707.214 + 25345.8i 0.00626004 + 0.224353i
\(106\) 103895.i 0.898115i
\(107\) 64241.8i 0.542448i −0.962516 0.271224i \(-0.912572\pi\)
0.962516 0.271224i \(-0.0874284\pi\)
\(108\) −60395.8 + 5066.12i −0.498250 + 0.0417942i
\(109\) 191269.i 1.54198i 0.636848 + 0.770990i \(0.280238\pi\)
−0.636848 + 0.770990i \(0.719762\pi\)
\(110\) 25772.7i 0.203085i
\(111\) 4375.55 + 156815.i 0.0337074 + 1.20804i
\(112\) −10746.6 −0.0809518
\(113\) −9433.42 −0.0694981 −0.0347491 0.999396i \(-0.511063\pi\)
−0.0347491 + 0.999396i \(0.511063\pi\)
\(114\) 43860.8 1223.83i 0.316093 0.00881981i
\(115\) 108482.i 0.764912i
\(116\) 10360.9i 0.0714914i
\(117\) −1017.17 18213.0i −0.00686955 0.123003i
\(118\) 22914.0 + 104469.i 0.151494 + 0.690688i
\(119\) 17968.7i 0.116319i
\(120\) −1078.20 38641.5i −0.00683511 0.244963i
\(121\) −133400. −0.828306
\(122\) 40064.8i 0.243704i
\(123\) −8226.12 294815.i −0.0490266 1.75706i
\(124\) 62139.1i 0.362920i
\(125\) 183997.i 1.05326i
\(126\) −40740.1 + 2275.28i −0.228610 + 0.0127676i
\(127\) −79947.0 −0.439838 −0.219919 0.975518i \(-0.570579\pi\)
−0.219919 + 0.975518i \(0.570579\pi\)
\(128\) 16384.0 0.0883883
\(129\) −5801.32 207913.i −0.0306939 1.10004i
\(130\) 11634.6 0.0603798
\(131\) −144246. −0.734388 −0.367194 0.930144i \(-0.619682\pi\)
−0.367194 + 0.930144i \(0.619682\pi\)
\(132\) −41458.5 + 1156.80i −0.207099 + 0.00577860i
\(133\) 29540.2 0.144805
\(134\) 44882.2i 0.215929i
\(135\) −12268.6 146260.i −0.0579377 0.690705i
\(136\) 27394.6i 0.127004i
\(137\) 238777.i 1.08690i −0.839440 0.543452i \(-0.817117\pi\)
0.839440 0.543452i \(-0.182883\pi\)
\(138\) −174506. + 4869.17i −0.780032 + 0.0217649i
\(139\) 219083. 0.961770 0.480885 0.876784i \(-0.340315\pi\)
0.480885 + 0.876784i \(0.340315\pi\)
\(140\) 26025.1i 0.112220i
\(141\) 297971. 8314.15i 1.26219 0.0352185i
\(142\) 11983.8i 0.0498740i
\(143\) 12482.7i 0.0510469i
\(144\) 62111.2 3468.83i 0.249611 0.0139404i
\(145\) −25091.1 −0.0991058
\(146\) 196411.i 0.762575i
\(147\) 234433. 6541.30i 0.894801 0.0249673i
\(148\) 161018.i 0.604254i
\(149\) −100312. −0.370159 −0.185080 0.982724i \(-0.559254\pi\)
−0.185080 + 0.982724i \(0.559254\pi\)
\(150\) −101202. + 2823.79i −0.367248 + 0.0102472i
\(151\) 362945.i 1.29538i −0.761903 0.647691i \(-0.775735\pi\)
0.761903 0.647691i \(-0.224265\pi\)
\(152\) −45036.3 −0.158108
\(153\) 5800.01 + 103852.i 0.0200309 + 0.358663i
\(154\) −27922.3 −0.0948744
\(155\) 150482. 0.503102
\(156\) 522.215 + 18715.6i 0.00171806 + 0.0615734i
\(157\) 164128.i 0.531415i 0.964054 + 0.265708i \(0.0856056\pi\)
−0.964054 + 0.265708i \(0.914394\pi\)
\(158\) −155331. −0.495013
\(159\) −11293.2 404735.i −0.0354260 1.26963i
\(160\) 39677.1i 0.122529i
\(161\) −117530. −0.357341
\(162\) 234727. 26300.4i 0.702709 0.0787364i
\(163\) −443415. −1.30720 −0.653599 0.756841i \(-0.726742\pi\)
−0.653599 + 0.756841i \(0.726742\pi\)
\(164\) 302716.i 0.878874i
\(165\) −2801.42 100400.i −0.00801066 0.287094i
\(166\) 184331. 0.519193
\(167\) 664817.i 1.84464i −0.386430 0.922319i \(-0.626292\pi\)
0.386430 0.922319i \(-0.373708\pi\)
\(168\) 41864.5 1168.13i 0.114439 0.00319313i
\(169\) 365658. 0.984823
\(170\) −66341.6 −0.176061
\(171\) −170731. + 9535.10i −0.446501 + 0.0249365i
\(172\) 213485.i 0.550233i
\(173\) −183621. −0.466453 −0.233226 0.972422i \(-0.574928\pi\)
−0.233226 + 0.972422i \(0.574928\pi\)
\(174\) −1126.21 40362.0i −0.00281997 0.101065i
\(175\) −68159.4 −0.168241
\(176\) 42569.5 0.103590
\(177\) −100619. 404478.i −0.241406 0.970424i
\(178\) 341183. 0.807119
\(179\) 284365. 0.663351 0.331675 0.943394i \(-0.392386\pi\)
0.331675 + 0.943394i \(0.392386\pi\)
\(180\) 8400.46 + 150415.i 0.0193251 + 0.346026i
\(181\) −221445. −0.502424 −0.251212 0.967932i \(-0.580829\pi\)
−0.251212 + 0.967932i \(0.580829\pi\)
\(182\) 12605.0i 0.0282074i
\(183\) −4354.94 156076.i −0.00961289 0.344516i
\(184\) 179183. 0.390168
\(185\) 389936. 0.837654
\(186\) 6754.35 + 242069.i 0.0143153 + 0.513046i
\(187\) 71177.8i 0.148847i
\(188\) −305956. −0.631342
\(189\) 158460. 13291.9i 0.322674 0.0270665i
\(190\) 109064.i 0.219179i
\(191\) 238946. 0.473932 0.236966 0.971518i \(-0.423847\pi\)
0.236966 + 0.971518i \(0.423847\pi\)
\(192\) −63825.5 + 1780.90i −0.124951 + 0.00348647i
\(193\) 550517. 1.06384 0.531921 0.846794i \(-0.321470\pi\)
0.531921 + 0.846794i \(0.321470\pi\)
\(194\) 464617.i 0.886321i
\(195\) −45323.6 + 1264.65i −0.0853568 + 0.00238168i
\(196\) −240716. −0.447574
\(197\) 15545.0i 0.0285381i 0.999898 + 0.0142691i \(0.00454214\pi\)
−0.999898 + 0.0142691i \(0.995458\pi\)
\(198\) 161380. 9012.85i 0.292541 0.0163380i
\(199\) −423063. −0.757308 −0.378654 0.925538i \(-0.623613\pi\)
−0.378654 + 0.925538i \(0.623613\pi\)
\(200\) 103914. 0.183696
\(201\) −4878.57 174843.i −0.00851731 0.305251i
\(202\) −389481. −0.671596
\(203\) 27183.8i 0.0462989i
\(204\) −2977.72 106719.i −0.00500967 0.179541i
\(205\) −733088. −1.21835
\(206\) 722809.i 1.18674i
\(207\) 679275. 37936.6i 1.10184 0.0615365i
\(208\) 19217.2i 0.0307987i
\(209\) −117015. −0.185300
\(210\) 2828.85 + 101383.i 0.00442652 + 0.158642i
\(211\) 456665.i 0.706141i 0.935597 + 0.353070i \(0.114862\pi\)
−0.935597 + 0.353070i \(0.885138\pi\)
\(212\) 415582.i 0.635063i
\(213\) 1302.61 + 46684.2i 0.00196728 + 0.0705051i
\(214\) 256967.i 0.383569i
\(215\) −516997. −0.762767
\(216\) −241583. + 20264.5i −0.352316 + 0.0295530i
\(217\) 163033.i 0.235032i
\(218\) 765076.i 1.09034i
\(219\) −21349.3 765137.i −0.0300797 1.07802i
\(220\) 103091.i 0.143603i
\(221\) 32131.9 0.0442543
\(222\) 17502.2 + 627260.i 0.0238347 + 0.854212i
\(223\) 450392. 0.606497 0.303248 0.952912i \(-0.401929\pi\)
0.303248 + 0.952912i \(0.401929\pi\)
\(224\) −42986.5 −0.0572416
\(225\) 393935. 22000.7i 0.518762 0.0289721i
\(226\) −37733.7 −0.0491426
\(227\) −212488. −0.273697 −0.136849 0.990592i \(-0.543697\pi\)
−0.136849 + 0.990592i \(0.543697\pi\)
\(228\) 175443. 4895.32i 0.223511 0.00623654i
\(229\) 27099.6i 0.0341487i −0.999854 0.0170744i \(-0.994565\pi\)
0.999854 0.0170744i \(-0.00543520\pi\)
\(230\) 433926.i 0.540874i
\(231\) 108774. 3035.08i 0.134120 0.00374231i
\(232\) 41443.7i 0.0505521i
\(233\) 180735. 0.218098 0.109049 0.994036i \(-0.465219\pi\)
0.109049 + 0.994036i \(0.465219\pi\)
\(234\) −4068.68 72851.8i −0.00485751 0.0869762i
\(235\) 740934.i 0.875205i
\(236\) 91656.1 + 417875.i 0.107123 + 0.488390i
\(237\) 605108. 16884.1i 0.699781 0.0195257i
\(238\) 71874.9i 0.0822498i
\(239\) 485691.i 0.550003i −0.961444 0.275002i \(-0.911322\pi\)
0.961444 0.275002i \(-0.0886784\pi\)
\(240\) −4312.80 154566.i −0.00483316 0.173215i
\(241\) 259306. 0.287588 0.143794 0.989608i \(-0.454070\pi\)
0.143794 + 0.989608i \(0.454070\pi\)
\(242\) −533598. −0.585701
\(243\) −911544. + 127970.i −0.990289 + 0.139025i
\(244\) 160259.i 0.172325i
\(245\) 582942.i 0.620455i
\(246\) −32904.5 1.17926e6i −0.0346671 1.24243i
\(247\) 52824.2i 0.0550922i
\(248\) 248556.i 0.256623i
\(249\) −718081. + 20036.3i −0.733964 + 0.0204795i
\(250\) 735988.i 0.744768i
\(251\) 700873.i 0.702190i −0.936340 0.351095i \(-0.885809\pi\)
0.936340 0.351095i \(-0.114191\pi\)
\(252\) −162960. + 9101.12i −0.161652 + 0.00902804i
\(253\) 465559. 0.457271
\(254\) −319788. −0.311013
\(255\) 258440. 7211.15i 0.248891 0.00694471i
\(256\) 65536.0 0.0625000
\(257\) 1.27937e6i 1.20826i 0.796884 + 0.604132i \(0.206480\pi\)
−0.796884 + 0.604132i \(0.793520\pi\)
\(258\) −23205.3 831653.i −0.0217039 0.777844i
\(259\) 422460.i 0.391324i
\(260\) 46538.3 0.0426950
\(261\) 8774.49 + 157112.i 0.00797298 + 0.142760i
\(262\) −576984. −0.519291
\(263\) 527749.i 0.470477i 0.971938 + 0.235238i \(0.0755871\pi\)
−0.971938 + 0.235238i \(0.924413\pi\)
\(264\) −165834. + 4627.19i −0.146441 + 0.00408609i
\(265\) −1.00641e6 −0.880363
\(266\) 118161. 0.102393
\(267\) −1.32911e6 + 37085.7i −1.14100 + 0.0318367i
\(268\) 179529.i 0.152685i
\(269\) 1.05984e6 0.893014 0.446507 0.894780i \(-0.352668\pi\)
0.446507 + 0.894780i \(0.352668\pi\)
\(270\) −49074.5 585042.i −0.0409681 0.488402i
\(271\) 1.41943e6 1.17406 0.587032 0.809564i \(-0.300296\pi\)
0.587032 + 0.809564i \(0.300296\pi\)
\(272\) 109579.i 0.0898056i
\(273\) −1370.13 49103.9i −0.00111264 0.0398758i
\(274\) 955108.i 0.768557i
\(275\) 269993. 0.215289
\(276\) −698023. + 19476.7i −0.551566 + 0.0153901i
\(277\) −111139. −0.0870299 −0.0435149 0.999053i \(-0.513856\pi\)
−0.0435149 + 0.999053i \(0.513856\pi\)
\(278\) 876331. 0.680074
\(279\) −52624.5 942269.i −0.0404741 0.724710i
\(280\) 104100.i 0.0793518i
\(281\) 536816.i 0.405565i −0.979224 0.202782i \(-0.935002\pi\)
0.979224 0.202782i \(-0.0649984\pi\)
\(282\) 1.19188e6 33256.6i 0.892505 0.0249032i
\(283\) 338215.i 0.251031i 0.992092 + 0.125515i \(0.0400584\pi\)
−0.992092 + 0.125515i \(0.959942\pi\)
\(284\) 47935.3i 0.0352663i
\(285\) 11855.0 + 424871.i 0.00864548 + 0.309845i
\(286\) 49930.9i 0.0360956i
\(287\) 794233.i 0.569171i
\(288\) 248445. 13875.3i 0.176502 0.00985738i
\(289\) 1.23664e6 0.870959
\(290\) −100364. −0.0700784
\(291\) −50502.6 1.80996e6i −0.0349608 1.25296i
\(292\) 785642.i 0.539222i
\(293\) 323406.i 0.220079i −0.993927 0.110040i \(-0.964902\pi\)
0.993927 0.110040i \(-0.0350978\pi\)
\(294\) 937734. 26165.2i 0.632720 0.0176545i
\(295\) −1.01197e6 + 221964.i −0.677036 + 0.148500i
\(296\) 644071.i 0.427272i
\(297\) −627691. + 52652.0i −0.412909 + 0.0346357i
\(298\) −401249. −0.261742
\(299\) 210168.i 0.135953i
\(300\) −404807. + 11295.2i −0.259684 + 0.00724586i
\(301\) 560118.i 0.356339i
\(302\) 1.45178e6i 0.915974i
\(303\) 1.51726e6 42335.6i 0.949411 0.0264910i
\(304\) −180145. −0.111799
\(305\) −388099. −0.238888
\(306\) 23200.0 + 415409.i 0.0141640 + 0.253613i
\(307\) −866266. −0.524573 −0.262286 0.964990i \(-0.584476\pi\)
−0.262286 + 0.964990i \(0.584476\pi\)
\(308\) −111689. −0.0670863
\(309\) −78567.4 2.81577e6i −0.0468108 1.67765i
\(310\) 601929. 0.355747
\(311\) 1.38735e6i 0.813367i −0.913569 0.406683i \(-0.866685\pi\)
0.913569 0.406683i \(-0.133315\pi\)
\(312\) 2088.86 + 74862.5i 0.00121485 + 0.0435389i
\(313\) 711564.i 0.410538i −0.978706 0.205269i \(-0.934193\pi\)
0.978706 0.205269i \(-0.0658069\pi\)
\(314\) 656513.i 0.375767i
\(315\) −22040.2 394641.i −0.0125152 0.224092i
\(316\) −621325. −0.350027
\(317\) 2.39954e6i 1.34116i 0.741839 + 0.670579i \(0.233954\pi\)
−0.741839 + 0.670579i \(0.766046\pi\)
\(318\) −45172.6 1.61894e6i −0.0250500 0.897765i
\(319\) 107681.i 0.0592463i
\(320\) 158708.i 0.0866413i
\(321\) 27931.6 + 1.00104e6i 0.0151298 + 0.542237i
\(322\) −470119. −0.252678
\(323\) 301209.i 0.160643i
\(324\) 938909. 105202.i 0.496891 0.0556750i
\(325\) 121883.i 0.0640082i
\(326\) −1.77366e6 −0.924329
\(327\) −83161.7 2.98043e6i −0.0430085 1.54138i
\(328\) 1.21087e6i 0.621457i
\(329\) 802733. 0.408866
\(330\) −11205.7 401600.i −0.00566439 0.203006i
\(331\) 3.15985e6 1.58525 0.792623 0.609712i \(-0.208715\pi\)
0.792623 + 0.609712i \(0.208715\pi\)
\(332\) 737325. 0.367125
\(333\) −136363. 2.44165e6i −0.0673885 1.20663i
\(334\) 2.65927e6i 1.30436i
\(335\) −434764. −0.211661
\(336\) 167458. 4672.51i 0.0809203 0.00225789i
\(337\) 3.00078e6i 1.43933i 0.694323 + 0.719664i \(0.255704\pi\)
−0.694323 + 0.719664i \(0.744296\pi\)
\(338\) 1.46263e6 0.696375
\(339\) 146995. 4101.55i 0.0694711 0.00193842i
\(340\) −265366. −0.124494
\(341\) 645809.i 0.300758i
\(342\) −682924. + 38140.4i −0.315724 + 0.0176327i
\(343\) 1.33710e6 0.613663
\(344\) 853941.i 0.389074i
\(345\) −47166.6 1.69040e6i −0.0213347 0.764614i
\(346\) −734485. −0.329832
\(347\) 4.17314e6 1.86054 0.930271 0.366874i \(-0.119572\pi\)
0.930271 + 0.366874i \(0.119572\pi\)
\(348\) −4504.82 161448.i −0.00199402 0.0714636i
\(349\) 2.65064e6i 1.16490i −0.812868 0.582448i \(-0.802095\pi\)
0.812868 0.582448i \(-0.197905\pi\)
\(350\) −272638. −0.118964
\(351\) 23768.7 + 283359.i 0.0102976 + 0.122764i
\(352\) 170278. 0.0732491
\(353\) −1.44753e6 −0.618290 −0.309145 0.951015i \(-0.600043\pi\)
−0.309145 + 0.951015i \(0.600043\pi\)
\(354\) −402477. 1.61791e6i −0.170700 0.686194i
\(355\) 116085. 0.0488883
\(356\) 1.36473e6 0.570720
\(357\) 7812.61 + 279996.i 0.00324433 + 0.116274i
\(358\) 1.13746e6 0.469060
\(359\) 787279.i 0.322398i −0.986922 0.161199i \(-0.948464\pi\)
0.986922 0.161199i \(-0.0515361\pi\)
\(360\) 33601.8 + 601659.i 0.0136649 + 0.244677i
\(361\) −1.98092e6 −0.800015
\(362\) −885781. −0.355267
\(363\) 2.07868e6 58000.7i 0.827984 0.0231029i
\(364\) 50419.9i 0.0199457i
\(365\) −1.90259e6 −0.747503
\(366\) −17419.7 624305.i −0.00679734 0.243610i
\(367\) 3.84735e6i 1.49107i 0.666469 + 0.745533i \(0.267805\pi\)
−0.666469 + 0.745533i \(0.732195\pi\)
\(368\) 716730. 0.275890
\(369\) 256365. + 4.59035e6i 0.0980151 + 1.75501i
\(370\) 1.55975e6 0.592311
\(371\) 1.09036e6i 0.411276i
\(372\) 27017.4 + 968276.i 0.0101225 + 0.362779i
\(373\) −3.04456e6 −1.13306 −0.566529 0.824042i \(-0.691714\pi\)
−0.566529 + 0.824042i \(0.691714\pi\)
\(374\) 284711.i 0.105251i
\(375\) −79999.9 2.86711e6i −0.0293773 1.05285i
\(376\) −1.22382e6 −0.446426
\(377\) 48610.4 0.0176147
\(378\) 633838. 53167.6i 0.228165 0.0191389i
\(379\) −3.35683e6 −1.20042 −0.600208 0.799844i \(-0.704915\pi\)
−0.600208 + 0.799844i \(0.704915\pi\)
\(380\) 436257.i 0.154983i
\(381\) 1.24577e6 34760.1i 0.439667 0.0122679i
\(382\) 955784. 0.335121
\(383\) 4.56073e6i 1.58868i −0.607471 0.794342i \(-0.707816\pi\)
0.607471 0.794342i \(-0.292184\pi\)
\(384\) −255302. + 7123.59i −0.0883540 + 0.00246531i
\(385\) 270477.i 0.0929992i
\(386\) 2.20207e6 0.752250
\(387\) 180797. + 3.23726e6i 0.0613640 + 1.09875i
\(388\) 1.85847e6i 0.626723i
\(389\) 3.04699e6i 1.02093i −0.859898 0.510466i \(-0.829473\pi\)
0.859898 0.510466i \(-0.170527\pi\)
\(390\) −181294. + 5058.59i −0.0603564 + 0.00168410i
\(391\) 1.19840e6i 0.396424i
\(392\) −962865. −0.316483
\(393\) 2.24770e6 62716.7i 0.734103 0.0204834i
\(394\) 62180.1i 0.0201795i
\(395\) 1.50466e6i 0.485229i
\(396\) 645519. 36051.4i 0.206857 0.0115527i
\(397\) 4.90310e6i 1.56133i 0.624950 + 0.780665i \(0.285119\pi\)
−0.624950 + 0.780665i \(0.714881\pi\)
\(398\) −1.69225e6 −0.535497
\(399\) −460308. + 12843.8i −0.144749 + 0.00403888i
\(400\) 415656. 0.129892
\(401\) 1.05620e6 0.328009 0.164005 0.986460i \(-0.447559\pi\)
0.164005 + 0.986460i \(0.447559\pi\)
\(402\) −19514.3 699371.i −0.00602265 0.215845i
\(403\) −291538. −0.0894196
\(404\) −1.55792e6 −0.474890
\(405\) 254767. + 2.27375e6i 0.0771801 + 0.688820i
\(406\) 108735.i 0.0327383i
\(407\) 1.67345e6i 0.500757i
\(408\) −11910.9 426874.i −0.00354237 0.126955i
\(409\) 3.92820e6i 1.16114i 0.814209 + 0.580572i \(0.197171\pi\)
−0.814209 + 0.580572i \(0.802829\pi\)
\(410\) −2.93235e6 −0.861502
\(411\) 103818. + 3.72072e6i 0.0303157 + 1.08648i
\(412\) 2.89124e6i 0.839152i
\(413\) −240477. 1.09637e6i −0.0693742 0.316288i
\(414\) 2.71710e6 151747.i 0.779121 0.0435129i
\(415\) 1.78558e6i 0.508931i
\(416\) 76868.8i 0.0217779i
\(417\) −3.41383e6 + 95254.8i −0.961396 + 0.0268254i
\(418\) −468060. −0.131027
\(419\) −4.02300e6 −1.11948 −0.559738 0.828669i \(-0.689098\pi\)
−0.559738 + 0.828669i \(0.689098\pi\)
\(420\) 11315.4 + 405533.i 0.00313002 + 0.112177i
\(421\) 510067.i 0.140256i −0.997538 0.0701281i \(-0.977659\pi\)
0.997538 0.0701281i \(-0.0223408\pi\)
\(422\) 1.82666e6i 0.499317i
\(423\) −4.63948e6 + 259109.i −1.26072 + 0.0704095i
\(424\) 1.66233e6i 0.449057i
\(425\) 694992.i 0.186641i
\(426\) 5210.44 + 186737.i 0.00139107 + 0.0498546i
\(427\) 420470.i 0.111600i
\(428\) 1.02787e6i 0.271224i
\(429\) 5427.35 + 194511.i 0.00142379 + 0.0510270i
\(430\) −2.06799e6 −0.539358
\(431\) 809863. 0.210000 0.105000 0.994472i \(-0.466516\pi\)
0.105000 + 0.994472i \(0.466516\pi\)
\(432\) −966333. + 81057.9i −0.249125 + 0.0208971i
\(433\) −2.58437e6 −0.662423 −0.331211 0.943557i \(-0.607457\pi\)
−0.331211 + 0.943557i \(0.607457\pi\)
\(434\) 652134.i 0.166193i
\(435\) 390979. 10909.3i 0.0990672 0.00276423i
\(436\) 3.06031e6i 0.770990i
\(437\) −1.97014e6 −0.493508
\(438\) −85397.2 3.06055e6i −0.0212696 0.762279i
\(439\) 1.71289e6 0.424199 0.212099 0.977248i \(-0.431970\pi\)
0.212099 + 0.977248i \(0.431970\pi\)
\(440\) 412362.i 0.101542i
\(441\) −3.65019e6 + 203858.i −0.893756 + 0.0499151i
\(442\) 128527. 0.0312925
\(443\) 428626. 0.103769 0.0518847 0.998653i \(-0.483477\pi\)
0.0518847 + 0.998653i \(0.483477\pi\)
\(444\) 70008.8 + 2.50904e6i 0.0168537 + 0.604019i
\(445\) 3.30497e6i 0.791167i
\(446\) 1.80157e6 0.428858
\(447\) 1.56310e6 43614.7i 0.370015 0.0103244i
\(448\) −171946. −0.0404759
\(449\) 3.89386e6i 0.911516i 0.890104 + 0.455758i \(0.150632\pi\)
−0.890104 + 0.455758i \(0.849368\pi\)
\(450\) 1.57574e6 88002.9i 0.366820 0.0204864i
\(451\) 3.14612e6i 0.728339i
\(452\) −150935. −0.0347491
\(453\) 157804. + 5.65555e6i 0.0361305 + 1.29488i
\(454\) −849954. −0.193533
\(455\) −122102. −0.0276499
\(456\) 701773. 19581.3i 0.158046 0.00440990i
\(457\) 5.94641e6i 1.33188i 0.746006 + 0.665939i \(0.231969\pi\)
−0.746006 + 0.665939i \(0.768031\pi\)
\(458\) 108398.i 0.0241468i
\(459\) −135532. 1.61574e6i −0.0300268 0.357965i
\(460\) 1.73570e6i 0.382456i
\(461\) 5.30111e6i 1.16175i 0.813991 + 0.580877i \(0.197290\pi\)
−0.813991 + 0.580877i \(0.802710\pi\)
\(462\) 435096. 12140.3i 0.0948375 0.00264621i
\(463\) 4.37774e6i 0.949068i 0.880237 + 0.474534i \(0.157383\pi\)
−0.880237 + 0.474534i \(0.842617\pi\)
\(464\) 165775.i 0.0357457i
\(465\) −2.34487e6 + 65428.0i −0.502906 + 0.0140324i
\(466\) 722940. 0.154219
\(467\) 3.59111e6 0.761967 0.380984 0.924582i \(-0.375585\pi\)
0.380984 + 0.924582i \(0.375585\pi\)
\(468\) −16274.7 291407.i −0.00343478 0.0615015i
\(469\) 471027.i 0.0988811i
\(470\) 2.96374e6i 0.618863i
\(471\) −71361.2 2.55751e6i −0.0148221 0.531209i
\(472\) 366624. + 1.67150e6i 0.0757472 + 0.345344i
\(473\) 2.21874e6i 0.455989i
\(474\) 2.42043e6 67536.4i 0.494820 0.0138068i
\(475\) −1.14255e6 −0.232350
\(476\) 287500.i 0.0581594i
\(477\) 351949. + 6.30183e6i 0.0708245 + 1.26815i
\(478\) 1.94276e6i 0.388911i
\(479\) 4.40542e6i 0.877301i −0.898658 0.438651i \(-0.855457\pi\)
0.898658 0.438651i \(-0.144543\pi\)
\(480\) −17251.2 618264.i −0.00341756 0.122482i
\(481\) −755447. −0.148882
\(482\) 1.03722e6 0.203355
\(483\) 1.83139e6 51100.6i 0.357202 0.00996686i
\(484\) −2.13439e6 −0.414153
\(485\) −4.50065e6 −0.868802
\(486\) −3.64618e6 + 511881.i −0.700240 + 0.0983055i
\(487\) 3.38142e6 0.646066 0.323033 0.946388i \(-0.395298\pi\)
0.323033 + 0.946388i \(0.395298\pi\)
\(488\) 641037.i 0.121852i
\(489\) 6.90947e6 192792.i 1.30669 0.0364600i
\(490\) 2.33177e6i 0.438728i
\(491\) 2.64422e6i 0.494987i 0.968890 + 0.247494i \(0.0796069\pi\)
−0.968890 + 0.247494i \(0.920393\pi\)
\(492\) −131618. 4.71705e6i −0.0245133 0.878532i
\(493\) −277182. −0.0513626
\(494\) 211297.i 0.0389561i
\(495\) 87305.6 + 1.56325e6i 0.0160151 + 0.286758i
\(496\) 994225.i 0.181460i
\(497\) 125767.i 0.0228390i
\(498\) −2.87232e6 + 80145.2i −0.518991 + 0.0144812i
\(499\) 3.53350e6 0.635264 0.317632 0.948214i \(-0.397112\pi\)
0.317632 + 0.948214i \(0.397112\pi\)
\(500\) 2.94395e6i 0.526630i
\(501\) 289055. + 1.03594e7i 0.0514502 + 1.84392i
\(502\) 2.80349e6i 0.496524i
\(503\) 2.10626e6 0.371187 0.185593 0.982627i \(-0.440579\pi\)
0.185593 + 0.982627i \(0.440579\pi\)
\(504\) −651841. + 36404.5i −0.114305 + 0.00638379i
\(505\) 3.77282e6i 0.658322i
\(506\) 1.86224e6 0.323339
\(507\) −5.69783e6 + 158984.i −0.984440 + 0.0274684i
\(508\) −1.27915e6 −0.219919
\(509\) 6.61209e6 1.13121 0.565606 0.824675i \(-0.308642\pi\)
0.565606 + 0.824675i \(0.308642\pi\)
\(510\) 1.03376e6 28844.6i 0.175993 0.00491065i
\(511\) 2.06128e6i 0.349208i
\(512\) 262144. 0.0441942
\(513\) 2.65625e6 222812.i 0.445631 0.0373805i
\(514\) 5.11746e6i 0.854372i
\(515\) −7.00170e6 −1.16328
\(516\) −92821.1 3.32661e6i −0.0153470 0.550019i
\(517\) −3.17979e6 −0.523205
\(518\) 1.68984e6i 0.276708i
\(519\) 2.86126e6 79836.6i 0.466271 0.0130102i
\(520\) 186153. 0.0301899
\(521\) 1.07711e6i 0.173846i 0.996215 + 0.0869230i \(0.0277034\pi\)
−0.996215 + 0.0869230i \(0.972297\pi\)
\(522\) 35098.0 + 628447.i 0.00563775 + 0.100947i
\(523\) −5.91391e6 −0.945411 −0.472706 0.881220i \(-0.656723\pi\)
−0.472706 + 0.881220i \(0.656723\pi\)
\(524\) −2.30794e6 −0.367194
\(525\) 1.06209e6 29635.0i 0.168175 0.00469252i
\(526\) 2.11100e6i 0.332677i
\(527\) 1.66238e6 0.260738
\(528\) −663335. + 18508.8i −0.103550 + 0.00288930i
\(529\) 1.40213e6 0.217846
\(530\) −4.02566e6 −0.622511
\(531\) 1.74375e6 + 6.25898e6i 0.268379 + 0.963313i
\(532\) 472644. 0.0724027
\(533\) 1.42025e6 0.216545
\(534\) −5.31645e6 + 148343.i −0.806805 + 0.0225120i
\(535\) 2.48919e6 0.375987
\(536\) 718114.i 0.107965i
\(537\) −4.43109e6 + 123639.i −0.663093 + 0.0185020i
\(538\) 4.23935e6 0.631457
\(539\) −2.50175e6 −0.370913
\(540\) −196298. 2.34017e6i −0.0289689 0.345352i
\(541\) 3.30916e6i 0.486099i −0.970014 0.243050i \(-0.921852\pi\)
0.970014 0.243050i \(-0.0781478\pi\)
\(542\) 5.67774e6 0.830189
\(543\) 3.45065e6 96282.1i 0.502228 0.0140135i
\(544\) 438314.i 0.0635021i
\(545\) −7.41114e6 −1.06879
\(546\) −5480.51 196416.i −0.000786754 0.0281965i
\(547\) 1.11368e6 0.159144 0.0795720 0.996829i \(-0.474645\pi\)
0.0795720 + 0.996829i \(0.474645\pi\)
\(548\) 3.82043e6i 0.543452i
\(549\) 135721. + 2.43015e6i 0.0192183 + 0.344114i
\(550\) 1.07997e6 0.152232
\(551\) 455681.i 0.0639414i
\(552\) −2.79209e6 + 77906.7i −0.390016 + 0.0108825i
\(553\) 1.63016e6 0.226682
\(554\) −444557. −0.0615394
\(555\) −6.07614e6 + 169540.i −0.837328 + 0.0233636i
\(556\) 3.50532e6 0.480885
\(557\) 1.62594e6i 0.222058i −0.993817 0.111029i \(-0.964585\pi\)
0.993817 0.111029i \(-0.0354146\pi\)
\(558\) −210498. 3.76908e6i −0.0286195 0.512447i
\(559\) 1.00161e6 0.135572
\(560\) 416401.i 0.0561102i
\(561\) −30947.3 1.10912e6i −0.00415161 0.148789i
\(562\) 2.14727e6i 0.286777i
\(563\) 1.34602e7 1.78970 0.894851 0.446365i \(-0.147282\pi\)
0.894851 + 0.446365i \(0.147282\pi\)
\(564\) 4.76753e6 133026.i 0.631096 0.0176092i
\(565\) 365518.i 0.0481713i
\(566\) 1.35286e6i 0.177505i
\(567\) −2.46340e6 + 276016.i −0.321794 + 0.0360560i
\(568\) 191741.i 0.0249370i
\(569\) 9.26475e6 1.19965 0.599823 0.800133i \(-0.295238\pi\)
0.599823 + 0.800133i \(0.295238\pi\)
\(570\) 47420.0 + 1.69948e6i 0.00611328 + 0.219093i
\(571\) 1.08390e7i 1.39123i −0.718414 0.695616i \(-0.755131\pi\)
0.718414 0.695616i \(-0.244869\pi\)
\(572\) 199724.i 0.0255234i
\(573\) −3.72335e6 + 103891.i −0.473748 + 0.0132188i
\(574\) 3.17693e6i 0.402465i
\(575\) 4.54579e6 0.573377
\(576\) 993779. 55501.3i 0.124806 0.00697022i
\(577\) −6.04404e6 −0.755767 −0.377884 0.925853i \(-0.623348\pi\)
−0.377884 + 0.925853i \(0.623348\pi\)
\(578\) 4.94655e6 0.615861
\(579\) −8.57837e6 + 239359.i −1.06343 + 0.0296724i
\(580\) −401457. −0.0495529
\(581\) −1.93451e6 −0.237755
\(582\) −202010. 7.23985e6i −0.0247210 0.885976i
\(583\) 4.31912e6i 0.526289i
\(584\) 3.14257e6i 0.381288i
\(585\) 705700. 39412.4i 0.0852571 0.00476150i
\(586\) 1.29362e6i 0.155620i
\(587\) −1.08758e7 −1.30277 −0.651383 0.758749i \(-0.725811\pi\)
−0.651383 + 0.758749i \(0.725811\pi\)
\(588\) 3.75094e6 104661.i 0.447400 0.0124836i
\(589\) 2.73292e6i 0.324593i
\(590\) −4.04787e6 + 887854.i −0.478737 + 0.105005i
\(591\) −6758.81 242229.i −0.000795979 0.0285270i
\(592\) 2.57628e6i 0.302127i
\(593\) 1.80779e6i 0.211111i −0.994413 0.105555i \(-0.966338\pi\)
0.994413 0.105555i \(-0.0336620\pi\)
\(594\) −2.51076e6 + 210608.i −0.291971 + 0.0244911i
\(595\) 696238. 0.0806241
\(596\) −1.60500e6 −0.185080
\(597\) 6.59233e6 183943.i 0.757013 0.0211226i
\(598\) 840671.i 0.0961331i
\(599\) 6.76335e6i 0.770185i 0.922878 + 0.385093i \(0.125830\pi\)
−0.922878 + 0.385093i \(0.874170\pi\)
\(600\) −1.61923e6 + 45180.7i −0.183624 + 0.00512359i
\(601\) 1.28566e7i 1.45191i −0.687743 0.725954i \(-0.741398\pi\)
0.687743 0.725954i \(-0.258602\pi\)
\(602\) 2.24047e6i 0.251970i
\(603\) 152040. + 2.72235e6i 0.0170280 + 0.304895i
\(604\) 5.80712e6i 0.647691i
\(605\) 5.16886e6i 0.574124i
\(606\) 6.06905e6 169342.i 0.671335 0.0187320i
\(607\) 8.27006e6 0.911039 0.455520 0.890226i \(-0.349454\pi\)
0.455520 + 0.890226i \(0.349454\pi\)
\(608\) −720580. −0.0790539
\(609\) 11819.2 + 423589.i 0.00129136 + 0.0462809i
\(610\) −1.55240e6 −0.168919
\(611\) 1.43546e6i 0.155556i
\(612\) 92800.1 + 1.66164e6i 0.0100154 + 0.179332i
\(613\) 6.57376e6i 0.706582i −0.935513 0.353291i \(-0.885063\pi\)
0.935513 0.353291i \(-0.114937\pi\)
\(614\) −3.46507e6 −0.370929
\(615\) 1.14233e7 318739.i 1.21787 0.0339819i
\(616\) −446756. −0.0474372
\(617\) 958721.i 0.101386i −0.998714 0.0506931i \(-0.983857\pi\)
0.998714 0.0506931i \(-0.0161430\pi\)
\(618\) −314270. 1.12631e7i −0.0331002 1.18628i
\(619\) −1.12144e7 −1.17638 −0.588190 0.808723i \(-0.700159\pi\)
−0.588190 + 0.808723i \(0.700159\pi\)
\(620\) 2.40771e6 0.251551
\(621\) −1.05682e7 + 886485.i −1.09970 + 0.0922449i
\(622\) 5.54942e6i 0.575137i
\(623\) −3.58063e6 −0.369606
\(624\) 8355.43 + 299450.i 0.000859028 + 0.0307867i
\(625\) −2.05544e6 −0.210477
\(626\) 2.84626e6i 0.290294i
\(627\) 1.82337e6 50876.8i 0.185228 0.00516834i
\(628\) 2.62605e6i 0.265708i
\(629\) 4.30764e6 0.434123
\(630\) −88160.6 1.57856e6i −0.00884959 0.158457i
\(631\) 4.27214e6 0.427142 0.213571 0.976928i \(-0.431491\pi\)
0.213571 + 0.976928i \(0.431491\pi\)
\(632\) −2.48530e6 −0.247506
\(633\) −198553. 7.11593e6i −0.0196955 0.705866i
\(634\) 9.59816e6i 0.948341i
\(635\) 3.09772e6i 0.304865i
\(636\) −180690. 6.47576e6i −0.0177130 0.634816i
\(637\) 1.12937e6i 0.110278i
\(638\) 430723.i 0.0418935i
\(639\) −40595.5 726885.i −0.00393302 0.0704228i
\(640\) 634834.i 0.0612647i
\(641\) 7.46254e6i 0.717367i −0.933459 0.358684i \(-0.883226\pi\)
0.933459 0.358684i \(-0.116774\pi\)
\(642\) 111727. + 4.00416e6i 0.0106984 + 0.383419i
\(643\) 1.82096e6 0.173690 0.0868448 0.996222i \(-0.472322\pi\)
0.0868448 + 0.996222i \(0.472322\pi\)
\(644\) −1.88047e6 −0.178670
\(645\) 8.05605e6 224785.i 0.762470 0.0212749i
\(646\) 1.20484e6i 0.113592i
\(647\) 3.46423e6i 0.325347i −0.986680 0.162673i \(-0.947988\pi\)
0.986680 0.162673i \(-0.0520117\pi\)
\(648\) 3.75563e6 420807.i 0.351355 0.0393682i
\(649\) 952578. + 4.34296e6i 0.0887746 + 0.404738i
\(650\) 487533.i 0.0452607i
\(651\) −70885.2 2.54045e6i −0.00655546 0.234941i
\(652\) −7.09464e6 −0.653599
\(653\) 7.27715e6i 0.667849i 0.942600 + 0.333924i \(0.108373\pi\)
−0.942600 + 0.333924i \(0.891627\pi\)
\(654\) −332647. 1.19217e7i −0.0304116 1.08992i
\(655\) 5.58913e6i 0.509027i
\(656\) 4.84346e6i 0.439437i
\(657\) 665346. + 1.19134e7i 0.0601360 + 1.07677i
\(658\) 3.21093e6 0.289112
\(659\) −1.99900e7 −1.79308 −0.896540 0.442962i \(-0.853927\pi\)
−0.896540 + 0.442962i \(0.853927\pi\)
\(660\) −44822.7 1.60640e6i −0.00400533 0.143547i
\(661\) 696282. 0.0619842 0.0309921 0.999520i \(-0.490133\pi\)
0.0309921 + 0.999520i \(0.490133\pi\)
\(662\) 1.26394e7 1.12094
\(663\) −500691. + 13970.6i −0.0442371 + 0.00123433i
\(664\) 2.94930e6 0.259596
\(665\) 1.14460e6i 0.100369i
\(666\) −545452. 9.76661e6i −0.0476509 0.853214i
\(667\) 1.81299e6i 0.157790i
\(668\) 1.06371e7i 0.922319i
\(669\) −7.01819e6 + 195826.i −0.606261 + 0.0169163i
\(670\) −1.73906e6 −0.149667
\(671\) 1.66557e6i 0.142809i
\(672\) 669832. 18690.0i 0.0572193 0.00159657i
\(673\) 1.67712e7i 1.42734i −0.700484 0.713668i \(-0.747032\pi\)
0.700484 0.713668i \(-0.252968\pi\)
\(674\) 1.20031e7i 1.01776i
\(675\) −6.12888e6 + 514102.i −0.517752 + 0.0434300i
\(676\) 5.85053e6 0.492412
\(677\) 1.86809e7i 1.56648i 0.621718 + 0.783241i \(0.286435\pi\)
−0.621718 + 0.783241i \(0.713565\pi\)
\(678\) 587981. 16406.2i 0.0491235 0.00137067i
\(679\) 4.87604e6i 0.405875i
\(680\) −1.06147e6 −0.0880306
\(681\) 3.31108e6 92387.7i 0.273591 0.00763390i
\(682\) 2.58323e6i 0.212668i
\(683\) 1.53915e7 1.26249 0.631246 0.775583i \(-0.282544\pi\)
0.631246 + 0.775583i \(0.282544\pi\)
\(684\) −2.73170e6 + 152562.i −0.223250 + 0.0124682i
\(685\) 9.25194e6 0.753367
\(686\) 5.34842e6 0.433925
\(687\) 11782.6 + 422277.i 0.000952467 + 0.0341354i
\(688\) 3.41576e6i 0.275117i
\(689\) 1.94979e6 0.156473
\(690\) −188666. 6.76161e6i −0.0150859 0.540664i
\(691\) 1.22261e7i 0.974074i −0.873381 0.487037i \(-0.838078\pi\)
0.873381 0.487037i \(-0.161922\pi\)
\(692\) −2.93794e6 −0.233226
\(693\) −1.69364e6 + 94587.5i −0.133964 + 0.00748170i
\(694\) 1.66926e7 1.31560
\(695\) 8.48884e6i 0.666632i
\(696\) −18019.3 645793.i −0.00140999 0.0505324i
\(697\) −8.09845e6 −0.631422
\(698\) 1.06026e7i 0.823706i
\(699\) −2.81628e6 + 78581.6i −0.218013 + 0.00608314i
\(700\) −1.09055e6 −0.0841203
\(701\) −424402. −0.0326198 −0.0163099 0.999867i \(-0.505192\pi\)
−0.0163099 + 0.999867i \(0.505192\pi\)
\(702\) 95074.9 + 1.13344e6i 0.00728154 + 0.0868069i
\(703\) 7.08168e6i 0.540440i
\(704\) 681113. 0.0517949
\(705\) 322150. + 1.15455e7i 0.0244110 + 0.874864i
\(706\) −5.79014e6 −0.437197
\(707\) 4.08750e6 0.307546
\(708\) −1.60991e6 6.47165e6i −0.120703 0.485212i
\(709\) −4.54949e6 −0.339897 −0.169948 0.985453i \(-0.554360\pi\)
−0.169948 + 0.985453i \(0.554360\pi\)
\(710\) 464339. 0.0345692
\(711\) −9.42169e6 + 526189.i −0.698964 + 0.0390362i
\(712\) 5.45893e6 0.403560
\(713\) 1.08733e7i 0.801008i
\(714\) 31250.4 + 1.11998e6i 0.00229409 + 0.0822178i
\(715\) 483670. 0.0353822
\(716\) 4.54984e6 0.331675
\(717\) 211173. + 7.56823e6i 0.0153406 + 0.549790i
\(718\) 3.14912e6i 0.227970i
\(719\) 3.37342e6 0.243359 0.121680 0.992569i \(-0.461172\pi\)
0.121680 + 0.992569i \(0.461172\pi\)
\(720\) 134407. + 2.40663e6i 0.00966255 + 0.173013i
\(721\) 7.58569e6i 0.543447i
\(722\) −7.92367e6 −0.565696
\(723\) −4.04061e6 + 112744.i −0.287476 + 0.00802132i
\(724\) −3.54313e6 −0.251212
\(725\) 1.05141e6i 0.0742896i
\(726\) 8.31474e6 232003.i 0.585473 0.0163362i
\(727\) −1.29643e7 −0.909734 −0.454867 0.890560i \(-0.650313\pi\)
−0.454867 + 0.890560i \(0.650313\pi\)
\(728\) 201680.i 0.0141037i
\(729\) 1.41484e7 2.39041e6i 0.986026 0.166592i
\(730\) −7.61035e6 −0.528564
\(731\) −5.71128e6 −0.395312
\(732\) −69679.0 2.49722e6i −0.00480645 0.172258i
\(733\) 6.01595e6 0.413565 0.206783 0.978387i \(-0.433701\pi\)
0.206783 + 0.978387i \(0.433701\pi\)
\(734\) 1.53894e7i 1.05434i
\(735\) 253457. + 9.08364e6i 0.0173056 + 0.620214i
\(736\) 2.86692e6 0.195084
\(737\) 1.86583e6i 0.126533i
\(738\) 1.02546e6 + 1.83614e7i 0.0693071 + 1.24098i
\(739\) 1.23591e7i 0.832481i 0.909255 + 0.416240i \(0.136652\pi\)
−0.909255 + 0.416240i \(0.863348\pi\)
\(740\) 6.23898e6 0.418827
\(741\) −22967.4 823127.i −0.00153662 0.0550708i
\(742\) 4.36142e6i 0.290816i
\(743\) 1.15052e7i 0.764578i −0.924043 0.382289i \(-0.875136\pi\)
0.924043 0.382289i \(-0.124864\pi\)
\(744\) 108070. + 3.87310e6i 0.00715766 + 0.256523i
\(745\) 3.88682e6i 0.256569i
\(746\) −1.21782e7 −0.801193
\(747\) 1.11807e7 624427.i 0.733107 0.0409431i
\(748\) 1.13885e6i 0.0744236i
\(749\) 2.69680e6i 0.175649i
\(750\) −320000. 1.14685e7i −0.0207729 0.744478i
\(751\) 1.68066e7i 1.08738i −0.839287 0.543688i \(-0.817027\pi\)
0.839287 0.543688i \(-0.182973\pi\)
\(752\) −4.89530e6 −0.315671
\(753\) 304732. + 1.09213e7i 0.0195853 + 0.701917i
\(754\) 194442. 0.0124555
\(755\) 1.40631e7 0.897869
\(756\) 2.53535e6 212671.i 0.161337 0.0135333i
\(757\) 1.97078e7 1.24997 0.624984 0.780638i \(-0.285105\pi\)
0.624984 + 0.780638i \(0.285105\pi\)
\(758\) −1.34273e7 −0.848822
\(759\) −7.25452e6 + 202420.i −0.457093 + 0.0127541i
\(760\) 1.74503e6i 0.109589i
\(761\) 3.81411e6i 0.238744i −0.992850 0.119372i \(-0.961912\pi\)
0.992850 0.119372i \(-0.0380881\pi\)
\(762\) 4.98306e6 139040.i 0.310892 0.00867468i
\(763\) 8.02928e6i 0.499304i
\(764\) 3.82314e6 0.236966
\(765\) −4.02398e6 + 224734.i −0.248601 + 0.0138840i
\(766\) 1.82429e7i 1.12337i
\(767\) 1.96055e6 430023.i 0.120334 0.0263939i
\(768\) −1.02121e6 + 28494.3i −0.0624757 + 0.00174323i
\(769\) 6.75823e6i 0.412114i −0.978540 0.206057i \(-0.933937\pi\)
0.978540 0.206057i \(-0.0660632\pi\)
\(770\) 1.08191e6i 0.0657603i
\(771\) −556254. 1.99356e7i −0.0337006 1.20779i
\(772\) 8.80827e6 0.531921
\(773\) −2.44929e7 −1.47432 −0.737161 0.675717i \(-0.763834\pi\)
−0.737161 + 0.675717i \(0.763834\pi\)
\(774\) 723187. + 1.29490e7i 0.0433909 + 0.776936i
\(775\) 6.30578e6i 0.377124i
\(776\) 7.43387e6i 0.443160i
\(777\) −183681. 6.58294e6i −0.0109147 0.391171i
\(778\) 1.21879e7i 0.721907i
\(779\) 1.33137e7i 0.786058i
\(780\) −725178. + 20234.3i −0.0426784 + 0.00119084i
\(781\) 498189.i 0.0292258i
\(782\) 4.79360e6i 0.280314i
\(783\) −205038. 2.44436e6i −0.0119517 0.142482i
\(784\) −3.85146e6 −0.223787
\(785\) −6.35951e6 −0.368340
\(786\) 8.99080e6 250867.i 0.519089 0.0144839i
\(787\) 1.52116e7 0.875461 0.437730 0.899106i \(-0.355782\pi\)
0.437730 + 0.899106i \(0.355782\pi\)
\(788\) 248720.i 0.0142691i
\(789\) −229460. 8.22360e6i −0.0131224 0.470294i
\(790\) 6.01865e6i 0.343108i
\(791\) 396005. 0.0225040
\(792\) 2.58208e6 144206.i 0.146270 0.00816900i
\(793\) 751888. 0.0424591
\(794\) 1.96124e7i 1.10403i
\(795\) 1.56823e7 437578.i 0.880021 0.0245549i
\(796\) −6.76901e6 −0.378654
\(797\) 2.28925e6 0.127658 0.0638289 0.997961i \(-0.479669\pi\)
0.0638289 + 0.997961i \(0.479669\pi\)
\(798\) −1.84123e6 + 51375.1i −0.102353 + 0.00285592i
\(799\) 8.18512e6i 0.453584i
\(800\) 1.66262e6 0.0918479
\(801\) 2.06946e7 1.15577e6i 1.13966 0.0636487i
\(802\) 4.22481e6 0.231937
\(803\) 8.16514e6i 0.446864i
\(804\) −78057.1 2.79749e6i −0.00425865 0.152626i
\(805\) 4.55394e6i 0.247684i
\(806\) −1.16615e6 −0.0632292
\(807\) −1.65148e7 + 460806.i −0.892667 + 0.0249077i
\(808\) −6.23170e6 −0.335798
\(809\) −6.82774e6 −0.366780 −0.183390 0.983040i \(-0.558707\pi\)
−0.183390 + 0.983040i \(0.558707\pi\)
\(810\) 1.01907e6 + 9.09502e6i 0.0545746 + 0.487069i
\(811\) 1.53148e7i 0.817634i −0.912616 0.408817i \(-0.865941\pi\)
0.912616 0.408817i \(-0.134059\pi\)
\(812\) 434941.i 0.0231494i
\(813\) −2.21182e7 + 617155.i −1.17361 + 0.0327467i
\(814\) 6.69380e6i 0.354088i
\(815\) 1.71811e7i 0.906059i
\(816\) −47643.6 1.70750e6i −0.00250483 0.0897706i
\(817\) 9.38924e6i 0.492125i
\(818\) 1.57128e7i 0.821052i
\(819\) 42699.7 + 764561.i 0.00222441 + 0.0398293i
\(820\) −1.17294e7 −0.609174
\(821\) 2.50169e7 1.29532 0.647658 0.761931i \(-0.275749\pi\)
0.647658 + 0.761931i \(0.275749\pi\)
\(822\) 415271. + 1.48829e7i 0.0214364 + 0.768258i
\(823\) 4.64963e6i 0.239287i −0.992817 0.119643i \(-0.961825\pi\)
0.992817 0.119643i \(-0.0381751\pi\)
\(824\) 1.15649e7i 0.593370i
\(825\) −4.20714e6 + 117390.i −0.215205 + 0.00600478i
\(826\) −961907. 4.38549e6i −0.0490550 0.223650i
\(827\) 1.65370e7i 0.840800i −0.907339 0.420400i \(-0.861890\pi\)
0.907339 0.420400i \(-0.138110\pi\)
\(828\) 1.08684e7 606986.i 0.550922 0.0307683i
\(829\) −2.15245e6 −0.108779 −0.0543897 0.998520i \(-0.517321\pi\)
−0.0543897 + 0.998520i \(0.517321\pi\)
\(830\) 7.14232e6i 0.359869i
\(831\) 1.73182e6 48322.2i 0.0869960 0.00242741i
\(832\) 307475.i 0.0153993i
\(833\) 6.43978e6i 0.321557i
\(834\) −1.36553e7 + 381019.i −0.679809 + 0.0189684i
\(835\) 2.57598e7 1.27857
\(836\) −1.87224e6 −0.0926501
\(837\) 1.22970e6 + 1.46599e7i 0.0606718 + 0.723299i
\(838\) −1.60920e7 −0.791589
\(839\) 1.85802e7 0.911267 0.455633 0.890168i \(-0.349413\pi\)
0.455633 + 0.890168i \(0.349413\pi\)
\(840\) 45261.7 + 1.62213e6i 0.00221326 + 0.0793209i
\(841\) 2.00918e7 0.979556
\(842\) 2.04027e6i 0.0991762i
\(843\) 233402. + 8.36488e6i 0.0113119 + 0.405407i
\(844\) 7.30664e6i 0.353070i
\(845\) 1.41682e7i 0.682611i
\(846\) −1.85579e7 + 1.03644e6i −0.891463 + 0.0497870i
\(847\) 5.59997e6 0.268212
\(848\) 6.64931e6i 0.317532i
\(849\) −147052. 5.27020e6i −0.00700168 0.250933i
\(850\) 2.77997e6i 0.131975i
\(851\) 2.81754e7i 1.33366i
\(852\) 20841.8 + 746947.i 0.000983638 + 0.0352526i
\(853\) 2.43055e7 1.14375 0.571876 0.820340i \(-0.306216\pi\)
0.571876 + 0.820340i \(0.306216\pi\)
\(854\) 1.68188e6i 0.0789133i
\(855\) −369458. 6.61535e6i −0.0172842 0.309483i
\(856\) 4.11147e6i 0.191784i
\(857\) −3.42121e7 −1.59121 −0.795606 0.605815i \(-0.792847\pi\)
−0.795606 + 0.605815i \(0.792847\pi\)
\(858\) 21709.4 + 778043.i 0.00100677 + 0.0360816i
\(859\) 2.36643e7i 1.09423i 0.837056 + 0.547117i \(0.184275\pi\)
−0.837056 + 0.547117i \(0.815725\pi\)
\(860\) −8.27195e6 −0.381383
\(861\) 345324. + 1.23760e7i 0.0158752 + 0.568950i
\(862\) 3.23945e6 0.148492
\(863\) −4.21822e7 −1.92798 −0.963989 0.265942i \(-0.914317\pi\)
−0.963989 + 0.265942i \(0.914317\pi\)
\(864\) −3.86533e6 + 324232.i −0.176158 + 0.0147765i
\(865\) 7.11481e6i 0.323313i
\(866\) −1.03375e7 −0.468404
\(867\) −1.92698e7 + 537677.i −0.870620 + 0.0242926i
\(868\) 2.60853e6i 0.117516i
\(869\) −6.45740e6 −0.290074
\(870\) 1.56391e6 43637.3i 0.0700511 0.00195461i
\(871\) 842295. 0.0376200
\(872\) 1.22412e7i 0.545172i
\(873\) 1.57390e6 + 2.81816e7i 0.0698944 + 1.25150i
\(874\) −7.88058e6 −0.348963
\(875\) 7.72400e6i 0.341053i
\(876\) −341589. 1.22422e7i −0.0150398 0.539012i
\(877\) −3.26201e7 −1.43214 −0.716071 0.698028i \(-0.754061\pi\)
−0.716071 + 0.698028i \(0.754061\pi\)
\(878\) 6.85158e6 0.299954
\(879\) 140613. + 5.03944e6i 0.00613839 + 0.219994i
\(880\) 1.64945e6i 0.0718013i
\(881\) 1.54894e7 0.672348 0.336174 0.941800i \(-0.390867\pi\)
0.336174 + 0.941800i \(0.390867\pi\)
\(882\) −1.46008e7 + 815433.i −0.631981 + 0.0352953i
\(883\) −2.50379e7 −1.08068 −0.540339 0.841448i \(-0.681704\pi\)
−0.540339 + 0.841448i \(0.681704\pi\)
\(884\) 514110. 0.0221271
\(885\) 1.56724e7 3.89872e6i 0.672631 0.167326i
\(886\) 1.71450e6 0.0733760
\(887\) 2.45180e7 1.04635 0.523174 0.852226i \(-0.324748\pi\)
0.523174 + 0.852226i \(0.324748\pi\)
\(888\) 280035. + 1.00362e7i 0.0119174 + 0.427106i
\(889\) 3.35609e6 0.142423
\(890\) 1.32199e7i 0.559439i
\(891\) 9.75803e6 1.09336e6i 0.411783 0.0461389i
\(892\) 7.20627e6 0.303248
\(893\) 1.34562e7 0.564668
\(894\) 6.25242e6 174459.i 0.261640 0.00730044i
\(895\) 1.10183e7i 0.459789i
\(896\) −687783. −0.0286208
\(897\) 91378.7 + 3.27492e6i 0.00379196 + 0.135900i
\(898\) 1.55754e7i 0.644539i
\(899\) 2.51492e6 0.103783
\(900\) 6.30295e6 352012.i 0.259381 0.0144861i
\(901\) −1.11179e7 −0.456258
\(902\) 1.25845e7i 0.515014i
\(903\) 243533. + 8.72798e6i 0.00993891 + 0.356200i
\(904\) −603739. −0.0245713
\(905\) 8.58038e6i 0.348245i
\(906\) 631218. + 2.26222e7i 0.0255481 + 0.915618i
\(907\) −3.85574e7 −1.55629 −0.778144 0.628086i \(-0.783839\pi\)
−0.778144 + 0.628086i \(0.783839\pi\)
\(908\) −3.39981e6 −0.136849
\(909\) −2.36242e7 + 1.31938e6i −0.948302 + 0.0529614i
\(910\) −488407. −0.0195514
\(911\) 1.61965e7i 0.646585i −0.946299 0.323293i \(-0.895210\pi\)
0.946299 0.323293i \(-0.104790\pi\)
\(912\) 2.80709e6 78325.1i 0.111756 0.00311827i
\(913\) 7.66299e6 0.304243
\(914\) 2.37856e7i 0.941780i
\(915\) 6.04752e6 168741.i 0.238795 0.00666299i
\(916\) 433594.i 0.0170744i
\(917\) 6.05530e6 0.237800
\(918\) −542127. 6.46298e6i −0.0212322 0.253120i
\(919\) 3.55693e7i 1.38927i −0.719362 0.694636i \(-0.755566\pi\)
0.719362 0.694636i \(-0.244434\pi\)
\(920\) 6.94282e6i 0.270437i
\(921\) 1.34985e7 376643.i 0.524368 0.0146312i
\(922\) 2.12044e7i 0.821484i
\(923\) −224898. −0.00868923
\(924\) 1.74038e6 48561.2i 0.0670602 0.00187115i
\(925\) 1.63398e7i 0.627904i
\(926\) 1.75110e7i 0.671093i
\(927\) 2.44854e6 + 4.38423e7i 0.0935852 + 1.67569i
\(928\) 663100.i 0.0252760i
\(929\) 1.60484e7 0.610089 0.305045 0.952338i \(-0.401329\pi\)
0.305045 + 0.952338i \(0.401329\pi\)
\(930\) −9.37949e6 + 261712.i −0.355608 + 0.00992239i
\(931\) 1.05869e7 0.400307
\(932\) 2.89176e6 0.109049
\(933\) 603207. + 2.16183e7i 0.0226862 + 0.813050i
\(934\) 1.43644e7 0.538792
\(935\) −2.75794e6 −0.103171
\(936\) −65098.8 1.16563e6i −0.00242875 0.0434881i
\(937\) 1.78410e7i 0.663849i 0.943306 + 0.331924i \(0.107698\pi\)
−0.943306 + 0.331924i \(0.892302\pi\)
\(938\) 1.88411e6i 0.0699195i
\(939\) 309380. + 1.10879e7i 0.0114506 + 0.410378i
\(940\) 1.18549e7i 0.437602i
\(941\) −2.23757e7 −0.823764 −0.411882 0.911237i \(-0.635128\pi\)
−0.411882 + 0.911237i \(0.635128\pi\)
\(942\) −285445. 1.02300e7i −0.0104808 0.375621i
\(943\) 5.29702e7i 1.93978i
\(944\) 1.46650e6 + 6.68600e6i 0.0535613 + 0.244195i
\(945\) 515024. + 6.13986e6i 0.0187606 + 0.223655i
\(946\) 8.87497e6i 0.322433i
\(947\) 7.50347e6i 0.271886i −0.990717 0.135943i \(-0.956594\pi\)
0.990717 0.135943i \(-0.0434064\pi\)
\(948\) 9.68173e6 270146.i 0.349891 0.00976286i
\(949\) 3.68600e6 0.132859
\(950\) −4.57021e6 −0.164296
\(951\) −1.04329e6 3.73906e7i −0.0374072 1.34064i
\(952\) 1.15000e6i 0.0411249i
\(953\) 3.51975e7i 1.25539i −0.778458 0.627696i \(-0.783998\pi\)
0.778458 0.627696i \(-0.216002\pi\)
\(954\) 1.40780e6 + 2.52073e7i 0.0500805 + 0.896717i
\(955\) 9.25848e6i 0.328497i
\(956\) 7.77106e6i 0.275002i
\(957\) −46818.4 1.67792e6i −0.00165248 0.0592232i
\(958\) 1.76217e7i 0.620346i
\(959\) 1.00236e7i 0.351947i
\(960\) −69004.7 2.47306e6i −0.00241658 0.0866076i
\(961\) 1.35461e7 0.473157
\(962\) −3.02179e6 −0.105275
\(963\) −870483. 1.55865e7i −0.0302479 0.541604i
\(964\) 4.14890e6 0.143794
\(965\) 2.13310e7i 0.737382i
\(966\) 7.32557e6 204403.i 0.252580 0.00704764i
\(967\) 1.59141e7i 0.547287i −0.961831 0.273643i \(-0.911771\pi\)
0.961831 0.273643i \(-0.0882288\pi\)
\(968\) −8.53757e6 −0.292850
\(969\) 130962. + 4.69356e6i 0.00448061 + 0.160580i
\(970\) −1.80026e7 −0.614336
\(971\) 2.92552e7i 0.995761i −0.867246 0.497881i \(-0.834112\pi\)
0.867246 0.497881i \(-0.165888\pi\)
\(972\) −1.45847e7 + 2.04752e6i −0.495144 + 0.0695125i
\(973\) −9.19687e6 −0.311428
\(974\) 1.35257e7 0.456837
\(975\) 52993.6 + 1.89923e6i 0.00178530 + 0.0639833i
\(976\) 2.56415e6i 0.0861625i
\(977\) 4.12285e7 1.38185 0.690926 0.722926i \(-0.257203\pi\)
0.690926 + 0.722926i \(0.257203\pi\)
\(978\) 2.76379e7 771169.i 0.923969 0.0257811i
\(979\) 1.41836e7 0.472966
\(980\) 9.32708e6i 0.310228i
\(981\) 2.59172e6 + 4.64061e7i 0.0859835 + 1.53958i
\(982\) 1.05769e7i 0.350009i
\(983\) 3.62217e7 1.19560 0.597799 0.801646i \(-0.296042\pi\)
0.597799 + 0.801646i \(0.296042\pi\)
\(984\) −526471. 1.88682e7i −0.0173335 0.621216i
\(985\) −602326. −0.0197807
\(986\) −1.10873e6 −0.0363189
\(987\) −1.25085e7 + 349020.i −0.408707 + 0.0114040i
\(988\) 845187.i 0.0275461i
\(989\) 3.73563e7i 1.21443i
\(990\) 349222. + 6.25301e6i 0.0113244 + 0.202769i
\(991\) 3.46914e7i 1.12212i −0.827776 0.561058i \(-0.810394\pi\)
0.827776 0.561058i \(-0.189606\pi\)
\(992\) 3.97690e6i 0.128312i
\(993\) −4.92380e7 + 1.37387e6i −1.58463 + 0.0442153i
\(994\) 503069.i 0.0161496i
\(995\) 1.63925e7i 0.524913i
\(996\) −1.14893e7 + 320581.i −0.366982 + 0.0102398i
\(997\) −5.97624e6 −0.190410 −0.0952051 0.995458i \(-0.530351\pi\)
−0.0952051 + 0.995458i \(0.530351\pi\)
\(998\) 1.41340e7 0.449200
\(999\) 3.18647e6 + 3.79875e7i 0.101017 + 1.20428i
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 354.6.c.b.353.2 yes 50
3.2 odd 2 354.6.c.a.353.1 50
59.58 odd 2 354.6.c.a.353.2 yes 50
177.176 even 2 inner 354.6.c.b.353.1 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.6.c.a.353.1 50 3.2 odd 2
354.6.c.a.353.2 yes 50 59.58 odd 2
354.6.c.b.353.1 yes 50 177.176 even 2 inner
354.6.c.b.353.2 yes 50 1.1 even 1 trivial