Properties

Label 230.6.b.a.139.15
Level $230$
Weight $6$
Character 230.139
Analytic conductor $36.888$
Analytic rank $0$
Dimension $26$
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] = [230,6,Mod(139,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.139");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.b (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: \(36.8882785570\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.15
Character \(\chi\) \(=\) 230.139
Dual form 230.6.b.a.139.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000i q^{2} -19.5707i q^{3} -16.0000 q^{4} +(11.6274 - 54.6791i) q^{5} +78.2830 q^{6} +53.5462i q^{7} -64.0000i q^{8} -140.014 q^{9} +O(q^{10})\) \(q+4.00000i q^{2} -19.5707i q^{3} -16.0000 q^{4} +(11.6274 - 54.6791i) q^{5} +78.2830 q^{6} +53.5462i q^{7} -64.0000i q^{8} -140.014 q^{9} +(218.716 + 46.5095i) q^{10} -780.443 q^{11} +313.132i q^{12} +672.602i q^{13} -214.185 q^{14} +(-1070.11 - 227.556i) q^{15} +256.000 q^{16} +1468.88i q^{17} -560.055i q^{18} +644.576 q^{19} +(-186.038 + 874.866i) q^{20} +1047.94 q^{21} -3121.77i q^{22} +529.000i q^{23} -1252.53 q^{24} +(-2854.61 - 1271.55i) q^{25} -2690.41 q^{26} -2015.52i q^{27} -856.740i q^{28} +1678.02 q^{29} +(910.226 - 4280.44i) q^{30} +8393.89 q^{31} +1024.00i q^{32} +15273.8i q^{33} -5875.50 q^{34} +(2927.86 + 622.602i) q^{35} +2240.22 q^{36} -1726.62i q^{37} +2578.30i q^{38} +13163.3 q^{39} +(-3499.46 - 744.152i) q^{40} -3755.78 q^{41} +4191.76i q^{42} -5020.95i q^{43} +12487.1 q^{44} +(-1627.99 + 7655.83i) q^{45} -2116.00 q^{46} +22479.4i q^{47} -5010.11i q^{48} +13939.8 q^{49} +(5086.20 - 11418.4i) q^{50} +28747.0 q^{51} -10761.6i q^{52} +35954.8i q^{53} +8062.06 q^{54} +(-9074.51 + 42673.9i) q^{55} +3426.96 q^{56} -12614.8i q^{57} +6712.07i q^{58} +15530.7 q^{59} +(17121.8 + 3640.90i) q^{60} -44622.7 q^{61} +33575.5i q^{62} -7497.21i q^{63} -4096.00 q^{64} +(36777.3 + 7820.60i) q^{65} -61095.4 q^{66} -65599.9i q^{67} -23502.0i q^{68} +10352.9 q^{69} +(-2490.41 + 11711.4i) q^{70} +28123.0 q^{71} +8960.88i q^{72} +40306.9i q^{73} +6906.49 q^{74} +(-24885.2 + 55866.8i) q^{75} -10313.2 q^{76} -41789.8i q^{77} +52653.2i q^{78} -58608.1 q^{79} +(2976.61 - 13997.8i) q^{80} -73468.5 q^{81} -15023.1i q^{82} +102900. i q^{83} -16767.0 q^{84} +(80316.8 + 17079.2i) q^{85} +20083.8 q^{86} -32840.0i q^{87} +49948.4i q^{88} +126371. q^{89} +(-30623.3 - 6511.97i) q^{90} -36015.3 q^{91} -8464.00i q^{92} -164275. i q^{93} -89917.6 q^{94} +(7494.73 - 35244.8i) q^{95} +20040.4 q^{96} +38113.0i q^{97} +55759.2i q^{98} +109273. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 19.5707i 1.25546i −0.778430 0.627732i \(-0.783983\pi\)
0.778430 0.627732i \(-0.216017\pi\)
\(4\) −16.0000 −0.500000
\(5\) 11.6274 54.6791i 0.207997 0.978129i
\(6\) 78.2830 0.887747
\(7\) 53.5462i 0.413032i 0.978443 + 0.206516i \(0.0662126\pi\)
−0.978443 + 0.206516i \(0.933787\pi\)
\(8\) 64.0000i 0.353553i
\(9\) −140.014 −0.576188
\(10\) 218.716 + 46.5095i 0.691642 + 0.147076i
\(11\) −780.443 −1.94473 −0.972365 0.233464i \(-0.924994\pi\)
−0.972365 + 0.233464i \(0.924994\pi\)
\(12\) 313.132i 0.627732i
\(13\) 672.602i 1.10382i 0.833903 + 0.551912i \(0.186101\pi\)
−0.833903 + 0.551912i \(0.813899\pi\)
\(14\) −214.185 −0.292058
\(15\) −1070.11 227.556i −1.22801 0.261133i
\(16\) 256.000 0.250000
\(17\) 1468.88i 1.23271i 0.787467 + 0.616357i \(0.211392\pi\)
−0.787467 + 0.616357i \(0.788608\pi\)
\(18\) 560.055i 0.407427i
\(19\) 644.576 0.409628 0.204814 0.978801i \(-0.434341\pi\)
0.204814 + 0.978801i \(0.434341\pi\)
\(20\) −186.038 + 874.866i −0.103998 + 0.489065i
\(21\) 1047.94 0.518547
\(22\) 3121.77i 1.37513i
\(23\) 529.000i 0.208514i
\(24\) −1252.53 −0.443873
\(25\) −2854.61 1271.55i −0.913475 0.406896i
\(26\) −2690.41 −0.780521
\(27\) 2015.52i 0.532080i
\(28\) 856.740i 0.206516i
\(29\) 1678.02 0.370511 0.185256 0.982690i \(-0.440689\pi\)
0.185256 + 0.982690i \(0.440689\pi\)
\(30\) 910.226 4280.44i 0.184649 0.868331i
\(31\) 8393.89 1.56877 0.784384 0.620275i \(-0.212979\pi\)
0.784384 + 0.620275i \(0.212979\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 15273.8i 2.44154i
\(34\) −5875.50 −0.871661
\(35\) 2927.86 + 622.602i 0.403999 + 0.0859094i
\(36\) 2240.22 0.288094
\(37\) 1726.62i 0.207345i −0.994611 0.103672i \(-0.966941\pi\)
0.994611 0.103672i \(-0.0330593\pi\)
\(38\) 2578.30i 0.289651i
\(39\) 13163.3 1.38581
\(40\) −3499.46 744.152i −0.345821 0.0735380i
\(41\) −3755.78 −0.348932 −0.174466 0.984663i \(-0.555820\pi\)
−0.174466 + 0.984663i \(0.555820\pi\)
\(42\) 4191.76i 0.366668i
\(43\) 5020.95i 0.414109i −0.978329 0.207054i \(-0.933612\pi\)
0.978329 0.207054i \(-0.0663877\pi\)
\(44\) 12487.1 0.972365
\(45\) −1627.99 + 7655.83i −0.119845 + 0.563587i
\(46\) −2116.00 −0.147442
\(47\) 22479.4i 1.48436i 0.670199 + 0.742181i \(0.266209\pi\)
−0.670199 + 0.742181i \(0.733791\pi\)
\(48\) 5010.11i 0.313866i
\(49\) 13939.8 0.829405
\(50\) 5086.20 11418.4i 0.287719 0.645924i
\(51\) 28747.0 1.54763
\(52\) 10761.6i 0.551912i
\(53\) 35954.8i 1.75819i 0.476643 + 0.879097i \(0.341853\pi\)
−0.476643 + 0.879097i \(0.658147\pi\)
\(54\) 8062.06 0.376237
\(55\) −9074.51 + 42673.9i −0.404498 + 1.90220i
\(56\) 3426.96 0.146029
\(57\) 12614.8i 0.514273i
\(58\) 6712.07i 0.261991i
\(59\) 15530.7 0.580846 0.290423 0.956898i \(-0.406204\pi\)
0.290423 + 0.956898i \(0.406204\pi\)
\(60\) 17121.8 + 3640.90i 0.614003 + 0.130566i
\(61\) −44622.7 −1.53544 −0.767718 0.640788i \(-0.778608\pi\)
−0.767718 + 0.640788i \(0.778608\pi\)
\(62\) 33575.5i 1.10929i
\(63\) 7497.21i 0.237984i
\(64\) −4096.00 −0.125000
\(65\) 36777.3 + 7820.60i 1.07968 + 0.229592i
\(66\) −61095.4 −1.72643
\(67\) 65599.9i 1.78532i −0.450730 0.892660i \(-0.648836\pi\)
0.450730 0.892660i \(-0.351164\pi\)
\(68\) 23502.0i 0.616357i
\(69\) 10352.9 0.261782
\(70\) −2490.41 + 11711.4i −0.0607471 + 0.285670i
\(71\) 28123.0 0.662087 0.331044 0.943615i \(-0.392599\pi\)
0.331044 + 0.943615i \(0.392599\pi\)
\(72\) 8960.88i 0.203713i
\(73\) 40306.9i 0.885262i 0.896704 + 0.442631i \(0.145955\pi\)
−0.896704 + 0.442631i \(0.854045\pi\)
\(74\) 6906.49 0.146615
\(75\) −24885.2 + 55866.8i −0.510843 + 1.14683i
\(76\) −10313.2 −0.204814
\(77\) 41789.8i 0.803236i
\(78\) 52653.2i 0.979915i
\(79\) −58608.1 −1.05655 −0.528275 0.849073i \(-0.677161\pi\)
−0.528275 + 0.849073i \(0.677161\pi\)
\(80\) 2976.61 13997.8i 0.0519992 0.244532i
\(81\) −73468.5 −1.24420
\(82\) 15023.1i 0.246732i
\(83\) 102900.i 1.63954i 0.572696 + 0.819768i \(0.305898\pi\)
−0.572696 + 0.819768i \(0.694102\pi\)
\(84\) −16767.0 −0.259273
\(85\) 80316.8 + 17079.2i 1.20575 + 0.256401i
\(86\) 20083.8 0.292819
\(87\) 32840.0i 0.465163i
\(88\) 49948.4i 0.687566i
\(89\) 126371. 1.69111 0.845555 0.533888i \(-0.179270\pi\)
0.845555 + 0.533888i \(0.179270\pi\)
\(90\) −30623.3 6511.97i −0.398516 0.0847435i
\(91\) −36015.3 −0.455914
\(92\) 8464.00i 0.104257i
\(93\) 164275.i 1.96953i
\(94\) −89917.6 −1.04960
\(95\) 7494.73 35244.8i 0.0852014 0.400670i
\(96\) 20040.4 0.221937
\(97\) 38113.0i 0.411286i 0.978627 + 0.205643i \(0.0659286\pi\)
−0.978627 + 0.205643i \(0.934071\pi\)
\(98\) 55759.2i 0.586478i
\(99\) 109273. 1.12053
\(100\) 45673.7 + 20344.8i 0.456737 + 0.203448i
\(101\) −146414. −1.42817 −0.714085 0.700059i \(-0.753157\pi\)
−0.714085 + 0.700059i \(0.753157\pi\)
\(102\) 114988.i 1.09434i
\(103\) 209304.i 1.94395i 0.235090 + 0.971974i \(0.424461\pi\)
−0.235090 + 0.971974i \(0.575539\pi\)
\(104\) 43046.5 0.390260
\(105\) 12184.8 57300.4i 0.107856 0.507206i
\(106\) −143819. −1.24323
\(107\) 62158.7i 0.524859i 0.964951 + 0.262429i \(0.0845237\pi\)
−0.964951 + 0.262429i \(0.915476\pi\)
\(108\) 32248.3i 0.266040i
\(109\) −147391. −1.18824 −0.594120 0.804377i \(-0.702500\pi\)
−0.594120 + 0.804377i \(0.702500\pi\)
\(110\) −170696. 36298.0i −1.34506 0.286023i
\(111\) −33791.3 −0.260314
\(112\) 13707.8i 0.103258i
\(113\) 36497.6i 0.268886i 0.990921 + 0.134443i \(0.0429246\pi\)
−0.990921 + 0.134443i \(0.957075\pi\)
\(114\) 50459.3 0.363646
\(115\) 28925.2 + 6150.88i 0.203954 + 0.0433704i
\(116\) −26848.3 −0.185256
\(117\) 94173.5i 0.636010i
\(118\) 62122.8i 0.410720i
\(119\) −78652.7 −0.509151
\(120\) −14563.6 + 68487.1i −0.0923243 + 0.434166i
\(121\) 448040. 2.78198
\(122\) 178491.i 1.08572i
\(123\) 73503.5i 0.438071i
\(124\) −134302. −0.784384
\(125\) −102719. + 141303.i −0.587997 + 0.808863i
\(126\) 29988.8 0.168280
\(127\) 134203.i 0.738335i −0.929363 0.369167i \(-0.879643\pi\)
0.929363 0.369167i \(-0.120357\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −98263.6 −0.519898
\(130\) −31282.4 + 147109.i −0.162346 + 0.763450i
\(131\) 56217.3 0.286215 0.143107 0.989707i \(-0.454291\pi\)
0.143107 + 0.989707i \(0.454291\pi\)
\(132\) 244382.i 1.22077i
\(133\) 34514.6i 0.169190i
\(134\) 262400. 1.26241
\(135\) −110207. 23435.2i −0.520443 0.110671i
\(136\) 94008.0 0.435830
\(137\) 36226.1i 0.164900i 0.996595 + 0.0824500i \(0.0262745\pi\)
−0.996595 + 0.0824500i \(0.973726\pi\)
\(138\) 41411.7i 0.185108i
\(139\) −8168.50 −0.0358596 −0.0179298 0.999839i \(-0.505708\pi\)
−0.0179298 + 0.999839i \(0.505708\pi\)
\(140\) −46845.7 9961.64i −0.201999 0.0429547i
\(141\) 439938. 1.86356
\(142\) 112492.i 0.468166i
\(143\) 524927.i 2.14664i
\(144\) −35843.5 −0.144047
\(145\) 19510.9 91752.5i 0.0770652 0.362408i
\(146\) −161227. −0.625975
\(147\) 272812.i 1.04129i
\(148\) 27626.0i 0.103672i
\(149\) −194349. −0.717162 −0.358581 0.933499i \(-0.616739\pi\)
−0.358581 + 0.933499i \(0.616739\pi\)
\(150\) −223467. 99540.6i −0.810934 0.361220i
\(151\) 307204. 1.09644 0.548219 0.836335i \(-0.315306\pi\)
0.548219 + 0.836335i \(0.315306\pi\)
\(152\) 41252.9i 0.144825i
\(153\) 205663.i 0.710276i
\(154\) 167159. 0.567974
\(155\) 97598.9 458970.i 0.326299 1.53446i
\(156\) −210613. −0.692905
\(157\) 60613.2i 0.196254i −0.995174 0.0981269i \(-0.968715\pi\)
0.995174 0.0981269i \(-0.0312851\pi\)
\(158\) 234433.i 0.747094i
\(159\) 703661. 2.20735
\(160\) 55991.4 + 11906.4i 0.172910 + 0.0367690i
\(161\) −28326.0 −0.0861231
\(162\) 293874.i 0.879779i
\(163\) 295.269i 0.000870459i 1.00000 0.000435230i \(0.000138538\pi\)
−1.00000 0.000435230i \(0.999861\pi\)
\(164\) 60092.5 0.174466
\(165\) 835160. + 177595.i 2.38814 + 0.507832i
\(166\) −411601. −1.15933
\(167\) 437607.i 1.21421i −0.794623 0.607104i \(-0.792331\pi\)
0.794623 0.607104i \(-0.207669\pi\)
\(168\) 67068.1i 0.183334i
\(169\) −81099.9 −0.218426
\(170\) −68316.7 + 321267.i −0.181303 + 0.852597i
\(171\) −90249.5 −0.236023
\(172\) 80335.1i 0.207054i
\(173\) 427168.i 1.08513i 0.840012 + 0.542567i \(0.182548\pi\)
−0.840012 + 0.542567i \(0.817452\pi\)
\(174\) 131360. 0.328920
\(175\) 68086.7 152853.i 0.168061 0.377294i
\(176\) −199793. −0.486183
\(177\) 303947.i 0.729230i
\(178\) 505483.i 1.19580i
\(179\) −20401.9 −0.0475925 −0.0237962 0.999717i \(-0.507575\pi\)
−0.0237962 + 0.999717i \(0.507575\pi\)
\(180\) 26047.9 122493.i 0.0599227 0.281793i
\(181\) −271233. −0.615384 −0.307692 0.951486i \(-0.599557\pi\)
−0.307692 + 0.951486i \(0.599557\pi\)
\(182\) 144061.i 0.322380i
\(183\) 873300.i 1.92768i
\(184\) 33856.0 0.0737210
\(185\) −94410.2 20076.1i −0.202810 0.0431271i
\(186\) 657098. 1.39267
\(187\) 1.14637e6i 2.39730i
\(188\) 359670.i 0.742181i
\(189\) 107923. 0.219766
\(190\) 140979. + 29978.9i 0.283316 + 0.0602465i
\(191\) 730775. 1.44944 0.724720 0.689044i \(-0.241969\pi\)
0.724720 + 0.689044i \(0.241969\pi\)
\(192\) 80161.7i 0.156933i
\(193\) 114401.i 0.221074i 0.993872 + 0.110537i \(0.0352571\pi\)
−0.993872 + 0.110537i \(0.964743\pi\)
\(194\) −152452. −0.290823
\(195\) 153055. 719758.i 0.288244 1.35550i
\(196\) −223037. −0.414702
\(197\) 803909.i 1.47585i 0.674885 + 0.737923i \(0.264193\pi\)
−0.674885 + 0.737923i \(0.735807\pi\)
\(198\) 437091.i 0.792335i
\(199\) −752458. −1.34694 −0.673472 0.739213i \(-0.735198\pi\)
−0.673472 + 0.739213i \(0.735198\pi\)
\(200\) −81379.2 + 182695.i −0.143859 + 0.322962i
\(201\) −1.28384e6 −2.24141
\(202\) 585657.i 1.00987i
\(203\) 89851.5i 0.153033i
\(204\) −459951. −0.773814
\(205\) −43669.9 + 205363.i −0.0725768 + 0.341301i
\(206\) −837216. −1.37458
\(207\) 74067.3i 0.120144i
\(208\) 172186.i 0.275956i
\(209\) −503055. −0.796617
\(210\) 229201. + 48739.2i 0.358649 + 0.0762658i
\(211\) −1.25423e6 −1.93942 −0.969710 0.244257i \(-0.921456\pi\)
−0.969710 + 0.244257i \(0.921456\pi\)
\(212\) 575276.i 0.879097i
\(213\) 550387.i 0.831226i
\(214\) −248635. −0.371131
\(215\) −274541. 58380.5i −0.405052 0.0861333i
\(216\) −128993. −0.188119
\(217\) 449461.i 0.647952i
\(218\) 589563.i 0.840212i
\(219\) 788835. 1.11141
\(220\) 145192. 682783.i 0.202249 0.951099i
\(221\) −987968. −1.36070
\(222\) 135165.i 0.184070i
\(223\) 90970.3i 0.122500i −0.998122 0.0612502i \(-0.980491\pi\)
0.998122 0.0612502i \(-0.0195087\pi\)
\(224\) −54831.3 −0.0730144
\(225\) 399684. + 178034.i 0.526333 + 0.234449i
\(226\) −145991. −0.190131
\(227\) 1.07836e6i 1.38899i 0.719495 + 0.694497i \(0.244373\pi\)
−0.719495 + 0.694497i \(0.755627\pi\)
\(228\) 201837.i 0.257137i
\(229\) −580885. −0.731984 −0.365992 0.930618i \(-0.619270\pi\)
−0.365992 + 0.930618i \(0.619270\pi\)
\(230\) −24603.5 + 115701.i −0.0306675 + 0.144217i
\(231\) −817857. −1.00843
\(232\) 107393.i 0.130996i
\(233\) 248758.i 0.300184i 0.988672 + 0.150092i \(0.0479570\pi\)
−0.988672 + 0.150092i \(0.952043\pi\)
\(234\) 376694. 0.449727
\(235\) 1.22915e6 + 261377.i 1.45190 + 0.308743i
\(236\) −248491. −0.290423
\(237\) 1.14700e6i 1.32646i
\(238\) 314611.i 0.360024i
\(239\) −1.04225e6 −1.18026 −0.590129 0.807309i \(-0.700923\pi\)
−0.590129 + 0.807309i \(0.700923\pi\)
\(240\) −273948. 58254.4i −0.307001 0.0652831i
\(241\) 214720. 0.238139 0.119069 0.992886i \(-0.462009\pi\)
0.119069 + 0.992886i \(0.462009\pi\)
\(242\) 1.79216e6i 1.96716i
\(243\) 948062.i 1.02996i
\(244\) 713964. 0.767718
\(245\) 162083. 762216.i 0.172514 0.811265i
\(246\) −294014. −0.309763
\(247\) 433543.i 0.452157i
\(248\) 537209.i 0.554643i
\(249\) 2.01383e6 2.05838
\(250\) −565210. 410875.i −0.571953 0.415776i
\(251\) 771736. 0.773187 0.386593 0.922250i \(-0.373652\pi\)
0.386593 + 0.922250i \(0.373652\pi\)
\(252\) 119955.i 0.118992i
\(253\) 412854.i 0.405504i
\(254\) 536813. 0.522082
\(255\) 334252. 1.57186e6i 0.321902 1.51378i
\(256\) 65536.0 0.0625000
\(257\) 1.40812e6i 1.32987i 0.746903 + 0.664933i \(0.231540\pi\)
−0.746903 + 0.664933i \(0.768460\pi\)
\(258\) 393054.i 0.367624i
\(259\) 92454.1 0.0856400
\(260\) −588436. 125130.i −0.539841 0.114796i
\(261\) −234946. −0.213484
\(262\) 224869.i 0.202384i
\(263\) 243557.i 0.217126i 0.994090 + 0.108563i \(0.0346249\pi\)
−0.994090 + 0.108563i \(0.965375\pi\)
\(264\) 977526. 0.863214
\(265\) 1.96597e6 + 418060.i 1.71974 + 0.365699i
\(266\) −138058. −0.119635
\(267\) 2.47317e6i 2.12313i
\(268\) 1.04960e6i 0.892660i
\(269\) −826330. −0.696263 −0.348131 0.937446i \(-0.613184\pi\)
−0.348131 + 0.937446i \(0.613184\pi\)
\(270\) 93740.7 440826.i 0.0782562 0.368009i
\(271\) −882227. −0.729721 −0.364861 0.931062i \(-0.618883\pi\)
−0.364861 + 0.931062i \(0.618883\pi\)
\(272\) 376032.i 0.308179i
\(273\) 704846.i 0.572384i
\(274\) −144904. −0.116602
\(275\) 2.22786e6 + 992372.i 1.77646 + 0.791303i
\(276\) −165647. −0.130891
\(277\) 190943.i 0.149522i 0.997201 + 0.0747610i \(0.0238194\pi\)
−0.997201 + 0.0747610i \(0.976181\pi\)
\(278\) 32674.0i 0.0253566i
\(279\) −1.17526e6 −0.903906
\(280\) 39846.6 187383.i 0.0303736 0.142835i
\(281\) −1.26870e6 −0.958500 −0.479250 0.877678i \(-0.659091\pi\)
−0.479250 + 0.877678i \(0.659091\pi\)
\(282\) 1.75975e6i 1.31774i
\(283\) 2.40747e6i 1.78688i −0.449183 0.893440i \(-0.648285\pi\)
0.449183 0.893440i \(-0.351715\pi\)
\(284\) −449967. −0.331044
\(285\) −689767. 146677.i −0.503026 0.106967i
\(286\) 2.09971e6 1.51790
\(287\) 201108.i 0.144120i
\(288\) 143374.i 0.101857i
\(289\) −737737. −0.519585
\(290\) 367010. + 78043.8i 0.256261 + 0.0544933i
\(291\) 745900. 0.516355
\(292\) 644910.i 0.442631i
\(293\) 125712.i 0.0855477i 0.999085 + 0.0427739i \(0.0136195\pi\)
−0.999085 + 0.0427739i \(0.986381\pi\)
\(294\) 1.09125e6 0.736301
\(295\) 180581. 849204.i 0.120814 0.568142i
\(296\) −110504. −0.0733075
\(297\) 1.57300e6i 1.03475i
\(298\) 777397.i 0.507110i
\(299\) −355806. −0.230163
\(300\) 398163. 893869.i 0.255421 0.573417i
\(301\) 268853. 0.171040
\(302\) 1.22881e6i 0.775298i
\(303\) 2.86543e6i 1.79301i
\(304\) 165011. 0.102407
\(305\) −518845. + 2.43993e6i −0.319366 + 1.50185i
\(306\) 822651. 0.502241
\(307\) 756024.i 0.457815i 0.973448 + 0.228907i \(0.0735153\pi\)
−0.973448 + 0.228907i \(0.926485\pi\)
\(308\) 668636.i 0.401618i
\(309\) 4.09623e6 2.44055
\(310\) 1.83588e6 + 390396.i 1.08503 + 0.230728i
\(311\) 307652. 0.180368 0.0901838 0.995925i \(-0.471255\pi\)
0.0901838 + 0.995925i \(0.471255\pi\)
\(312\) 842452.i 0.489958i
\(313\) 1.89986e6i 1.09613i −0.836437 0.548063i \(-0.815366\pi\)
0.836437 0.548063i \(-0.184634\pi\)
\(314\) 242453. 0.138772
\(315\) −409941. 87172.9i −0.232779 0.0495000i
\(316\) 937730. 0.528275
\(317\) 382866.i 0.213993i −0.994259 0.106996i \(-0.965877\pi\)
0.994259 0.106996i \(-0.0341233\pi\)
\(318\) 2.81465e6i 1.56083i
\(319\) −1.30960e6 −0.720545
\(320\) −47625.8 + 223966.i −0.0259996 + 0.122266i
\(321\) 1.21649e6 0.658941
\(322\) 113304.i 0.0608983i
\(323\) 946801.i 0.504955i
\(324\) 1.17550e6 0.622098
\(325\) 855246. 1.92001e6i 0.449141 1.00831i
\(326\) −1181.07 −0.000615508
\(327\) 2.88455e6i 1.49179i
\(328\) 240370.i 0.123366i
\(329\) −1.20369e6 −0.613089
\(330\) −710379. + 3.34064e6i −0.359092 + 1.68867i
\(331\) 102208. 0.0512761 0.0256381 0.999671i \(-0.491838\pi\)
0.0256381 + 0.999671i \(0.491838\pi\)
\(332\) 1.64640e6i 0.819768i
\(333\) 241751.i 0.119470i
\(334\) 1.75043e6 0.858574
\(335\) −3.58694e6 762755.i −1.74627 0.371341i
\(336\) 268272. 0.129637
\(337\) 934385.i 0.448178i 0.974569 + 0.224089i \(0.0719407\pi\)
−0.974569 + 0.224089i \(0.928059\pi\)
\(338\) 324400.i 0.154450i
\(339\) 714286. 0.337577
\(340\) −1.28507e6 273267.i −0.602877 0.128200i
\(341\) −6.55095e6 −3.05083
\(342\) 360998.i 0.166894i
\(343\) 1.64638e6i 0.755603i
\(344\) −321341. −0.146410
\(345\) 120377. 566088.i 0.0544499 0.256057i
\(346\) −1.70867e6 −0.767306
\(347\) 469939.i 0.209517i 0.994498 + 0.104758i \(0.0334069\pi\)
−0.994498 + 0.104758i \(0.966593\pi\)
\(348\) 525441.i 0.232582i
\(349\) −1.93259e6 −0.849328 −0.424664 0.905351i \(-0.639608\pi\)
−0.424664 + 0.905351i \(0.639608\pi\)
\(350\) 611414. + 272347.i 0.266787 + 0.118837i
\(351\) 1.35564e6 0.587322
\(352\) 799174.i 0.343783i
\(353\) 1.47738e6i 0.631040i −0.948919 0.315520i \(-0.897821\pi\)
0.948919 0.315520i \(-0.102179\pi\)
\(354\) 1.21579e6 0.515644
\(355\) 326996. 1.53774e6i 0.137712 0.647607i
\(356\) −2.02193e6 −0.845555
\(357\) 1.53929e6i 0.639220i
\(358\) 81607.7i 0.0336530i
\(359\) 2.81086e6 1.15107 0.575537 0.817776i \(-0.304793\pi\)
0.575537 + 0.817776i \(0.304793\pi\)
\(360\) 489973. + 104192.i 0.199258 + 0.0423718i
\(361\) −2.06062e6 −0.832205
\(362\) 1.08493e6i 0.435142i
\(363\) 8.76848e6i 3.49267i
\(364\) 576244. 0.227957
\(365\) 2.20394e6 + 468663.i 0.865901 + 0.184132i
\(366\) −3.49320e6 −1.36308
\(367\) 1.24139e6i 0.481107i 0.970636 + 0.240553i \(0.0773289\pi\)
−0.970636 + 0.240553i \(0.922671\pi\)
\(368\) 135424.i 0.0521286i
\(369\) 525861. 0.201051
\(370\) 80304.4 377641.i 0.0304954 0.143408i
\(371\) −1.92524e6 −0.726190
\(372\) 2.62839e6i 0.984766i
\(373\) 3.43064e6i 1.27674i −0.769729 0.638371i \(-0.779609\pi\)
0.769729 0.638371i \(-0.220391\pi\)
\(374\) 4.58549e6 1.69515
\(375\) 2.76540e6 + 2.01028e6i 1.01550 + 0.738208i
\(376\) 1.43868e6 0.524802
\(377\) 1.12864e6i 0.408979i
\(378\) 431693.i 0.155398i
\(379\) −1.99082e6 −0.711925 −0.355963 0.934500i \(-0.615847\pi\)
−0.355963 + 0.934500i \(0.615847\pi\)
\(380\) −119916. + 563917.i −0.0426007 + 0.200335i
\(381\) −2.62645e6 −0.926952
\(382\) 2.92310e6i 1.02491i
\(383\) 1.44737e6i 0.504177i 0.967704 + 0.252089i \(0.0811174\pi\)
−0.967704 + 0.252089i \(0.918883\pi\)
\(384\) −320647. −0.110968
\(385\) −2.28503e6 485906.i −0.785669 0.167071i
\(386\) −457605. −0.156323
\(387\) 703002.i 0.238605i
\(388\) 609809.i 0.205643i
\(389\) −555267. −0.186049 −0.0930246 0.995664i \(-0.529654\pi\)
−0.0930246 + 0.995664i \(0.529654\pi\)
\(390\) 2.87903e6 + 612219.i 0.958484 + 0.203819i
\(391\) −777035. −0.257039
\(392\) 892147.i 0.293239i
\(393\) 1.10021e6i 0.359332i
\(394\) −3.21563e6 −1.04358
\(395\) −681459. + 3.20464e6i −0.219759 + 1.03344i
\(396\) −1.74836e6 −0.560266
\(397\) 1.58334e6i 0.504195i 0.967702 + 0.252097i \(0.0811203\pi\)
−0.967702 + 0.252097i \(0.918880\pi\)
\(398\) 3.00983e6i 0.952433i
\(399\) 675476. 0.212411
\(400\) −730780. 325517.i −0.228369 0.101724i
\(401\) −4.49011e6 −1.39443 −0.697213 0.716864i \(-0.745577\pi\)
−0.697213 + 0.716864i \(0.745577\pi\)
\(402\) 5.13536e6i 1.58491i
\(403\) 5.64574e6i 1.73164i
\(404\) 2.34263e6 0.714085
\(405\) −854246. + 4.01719e6i −0.258789 + 1.21698i
\(406\) −359406. −0.108211
\(407\) 1.34753e6i 0.403230i
\(408\) 1.83981e6i 0.547169i
\(409\) 3.30151e6 0.975897 0.487949 0.872872i \(-0.337745\pi\)
0.487949 + 0.872872i \(0.337745\pi\)
\(410\) −821451. 174680.i −0.241336 0.0513195i
\(411\) 708972. 0.207026
\(412\) 3.34886e6i 0.971974i
\(413\) 831610.i 0.239908i
\(414\) 296269. 0.0849543
\(415\) 5.62649e6 + 1.19646e6i 1.60368 + 0.341018i
\(416\) −688744. −0.195130
\(417\) 159864.i 0.0450204i
\(418\) 2.01222e6i 0.563293i
\(419\) −1.20798e6 −0.336145 −0.168072 0.985775i \(-0.553754\pi\)
−0.168072 + 0.985775i \(0.553754\pi\)
\(420\) −194957. + 916806.i −0.0539281 + 0.253603i
\(421\) −3.15446e6 −0.867401 −0.433701 0.901057i \(-0.642792\pi\)
−0.433701 + 0.901057i \(0.642792\pi\)
\(422\) 5.01693e6i 1.37138i
\(423\) 3.14743e6i 0.855273i
\(424\) 2.30110e6 0.621615
\(425\) 1.86775e6 4.19306e6i 0.501586 1.12605i
\(426\) 2.20155e6 0.587766
\(427\) 2.38938e6i 0.634184i
\(428\) 994539.i 0.262429i
\(429\) −1.02732e7 −2.69503
\(430\) 233522. 1.09816e6i 0.0609055 0.286415i
\(431\) 3.27599e6 0.849473 0.424737 0.905317i \(-0.360367\pi\)
0.424737 + 0.905317i \(0.360367\pi\)
\(432\) 515972.i 0.133020i
\(433\) 1.75726e6i 0.450418i 0.974310 + 0.225209i \(0.0723065\pi\)
−0.974310 + 0.225209i \(0.927693\pi\)
\(434\) −1.79784e6 −0.458171
\(435\) −1.79566e6 381844.i −0.454990 0.0967525i
\(436\) 2.35825e6 0.594120
\(437\) 340981.i 0.0854134i
\(438\) 3.15534e6i 0.785889i
\(439\) 2.81340e6 0.696739 0.348369 0.937357i \(-0.386736\pi\)
0.348369 + 0.937357i \(0.386736\pi\)
\(440\) 2.73113e6 + 580769.i 0.672529 + 0.143012i
\(441\) −1.95176e6 −0.477893
\(442\) 3.95187e6i 0.962159i
\(443\) 1.90766e6i 0.461839i 0.972973 + 0.230919i \(0.0741734\pi\)
−0.972973 + 0.230919i \(0.925827\pi\)
\(444\) 540660. 0.130157
\(445\) 1.46936e6 6.90984e6i 0.351746 1.65412i
\(446\) 363881. 0.0866208
\(447\) 3.80356e6i 0.900371i
\(448\) 219325.i 0.0516290i
\(449\) 3.31733e6 0.776555 0.388278 0.921542i \(-0.373070\pi\)
0.388278 + 0.921542i \(0.373070\pi\)
\(450\) −712138. + 1.59874e6i −0.165780 + 0.372174i
\(451\) 2.93118e6 0.678579
\(452\) 583962.i 0.134443i
\(453\) 6.01220e6i 1.37654i
\(454\) −4.31345e6 −0.982167
\(455\) −418763. + 1.96928e6i −0.0948288 + 0.445943i
\(456\) −807349. −0.181823
\(457\) 5.76386e6i 1.29099i −0.763765 0.645495i \(-0.776651\pi\)
0.763765 0.645495i \(-0.223349\pi\)
\(458\) 2.32354e6i 0.517591i
\(459\) 2.96054e6 0.655903
\(460\) −462804. 98414.2i −0.101977 0.0216852i
\(461\) −727884. −0.159518 −0.0797591 0.996814i \(-0.525415\pi\)
−0.0797591 + 0.996814i \(0.525415\pi\)
\(462\) 3.27143e6i 0.713070i
\(463\) 7.57732e6i 1.64272i −0.570412 0.821359i \(-0.693216\pi\)
0.570412 0.821359i \(-0.306784\pi\)
\(464\) 429572. 0.0926278
\(465\) −8.98238e6 1.91008e6i −1.92646 0.409656i
\(466\) −995033. −0.212262
\(467\) 6.84806e6i 1.45303i −0.687149 0.726517i \(-0.741138\pi\)
0.687149 0.726517i \(-0.258862\pi\)
\(468\) 1.50678e6i 0.318005i
\(469\) 3.51263e6 0.737395
\(470\) −1.04551e6 + 4.91661e6i −0.218314 + 1.02665i
\(471\) −1.18624e6 −0.246389
\(472\) 993964.i 0.205360i
\(473\) 3.91856e6i 0.805330i
\(474\) −4.58802e6 −0.937949
\(475\) −1.84001e6 819610.i −0.374185 0.166676i
\(476\) 1.25844e6 0.254575
\(477\) 5.03416e6i 1.01305i
\(478\) 4.16900e6i 0.834569i
\(479\) 9.44682e6 1.88125 0.940626 0.339446i \(-0.110239\pi\)
0.940626 + 0.339446i \(0.110239\pi\)
\(480\) 233018. 1.09579e6i 0.0461621 0.217083i
\(481\) 1.16133e6 0.228872
\(482\) 858880.i 0.168390i
\(483\) 554360.i 0.108124i
\(484\) −7.16865e6 −1.39099
\(485\) 2.08399e6 + 443155.i 0.402291 + 0.0855463i
\(486\) −3.79225e6 −0.728293
\(487\) 9.32525e6i 1.78171i 0.454284 + 0.890857i \(0.349895\pi\)
−0.454284 + 0.890857i \(0.650105\pi\)
\(488\) 2.85585e6i 0.542858i
\(489\) 5778.63 0.00109283
\(490\) 3.04886e6 + 648334.i 0.573651 + 0.121986i
\(491\) 1.36714e6 0.255923 0.127961 0.991779i \(-0.459157\pi\)
0.127961 + 0.991779i \(0.459157\pi\)
\(492\) 1.17606e6i 0.219036i
\(493\) 2.46480e6i 0.456735i
\(494\) −1.73417e6 −0.319723
\(495\) 1.27056e6 5.97494e6i 0.233067 1.09602i
\(496\) 2.14883e6 0.392192
\(497\) 1.50588e6i 0.273463i
\(498\) 8.05533e6i 1.45549i
\(499\) −1.48585e6 −0.267130 −0.133565 0.991040i \(-0.542643\pi\)
−0.133565 + 0.991040i \(0.542643\pi\)
\(500\) 1.64350e6 2.26084e6i 0.293998 0.404432i
\(501\) −8.56429e6 −1.52439
\(502\) 3.08694e6i 0.546725i
\(503\) 4.47115e6i 0.787950i 0.919121 + 0.393975i \(0.128900\pi\)
−0.919121 + 0.393975i \(0.871100\pi\)
\(504\) −479821. −0.0841401
\(505\) −1.70241e6 + 8.00579e6i −0.297055 + 1.39693i
\(506\) 1.65142e6 0.286735
\(507\) 1.58719e6i 0.274225i
\(508\) 2.14725e6i 0.369167i
\(509\) −2.69478e6 −0.461029 −0.230515 0.973069i \(-0.574041\pi\)
−0.230515 + 0.973069i \(0.574041\pi\)
\(510\) 6.28743e6 + 1.33701e6i 1.07040 + 0.227619i
\(511\) −2.15828e6 −0.365642
\(512\) 262144.i 0.0441942i
\(513\) 1.29915e6i 0.217955i
\(514\) −5.63249e6 −0.940357
\(515\) 1.14446e7 + 2.43366e6i 1.90143 + 0.404335i
\(516\) 1.57222e6 0.259949
\(517\) 1.75439e7i 2.88669i
\(518\) 369816.i 0.0605567i
\(519\) 8.36000e6 1.36235
\(520\) 500518. 2.35374e6i 0.0811730 0.381725i
\(521\) 7.16127e6 1.15583 0.577917 0.816095i \(-0.303866\pi\)
0.577917 + 0.816095i \(0.303866\pi\)
\(522\) 939782.i 0.150956i
\(523\) 6.27593e6i 1.00328i −0.865075 0.501642i \(-0.832729\pi\)
0.865075 0.501642i \(-0.167271\pi\)
\(524\) −899477. −0.143107
\(525\) −2.99146e6 1.33251e6i −0.473679 0.210994i
\(526\) −974228. −0.153531
\(527\) 1.23296e7i 1.93384i
\(528\) 3.91010e6i 0.610385i
\(529\) −279841. −0.0434783
\(530\) −1.67224e6 + 7.86390e6i −0.258588 + 1.21604i
\(531\) −2.17451e6 −0.334677
\(532\) 552234.i 0.0845948i
\(533\) 2.52615e6i 0.385159i
\(534\) 9.89268e6 1.50128
\(535\) 3.39878e6 + 722743.i 0.513380 + 0.109169i
\(536\) −4.19839e6 −0.631206
\(537\) 399281.i 0.0597506i
\(538\) 3.30532e6i 0.492332i
\(539\) −1.08792e7 −1.61297
\(540\) 1.76331e6 + 374963.i 0.260222 + 0.0553355i
\(541\) 4.63215e6 0.680440 0.340220 0.940346i \(-0.389499\pi\)
0.340220 + 0.940346i \(0.389499\pi\)
\(542\) 3.52891e6i 0.515991i
\(543\) 5.30823e6i 0.772592i
\(544\) −1.50413e6 −0.217915
\(545\) −1.71377e6 + 8.05920e6i −0.247150 + 1.16225i
\(546\) −2.81938e6 −0.404736
\(547\) 1.21288e7i 1.73321i −0.498996 0.866604i \(-0.666298\pi\)
0.498996 0.866604i \(-0.333702\pi\)
\(548\) 579618.i 0.0824500i
\(549\) 6.24780e6 0.884700
\(550\) −3.96949e6 + 8.91144e6i −0.559536 + 1.25615i
\(551\) 1.08161e6 0.151772
\(552\) 662587.i 0.0925540i
\(553\) 3.13824e6i 0.436389i
\(554\) −763773. −0.105728
\(555\) −392904. + 1.84768e6i −0.0541445 + 0.254621i
\(556\) 130696. 0.0179298
\(557\) 3.23067e6i 0.441220i −0.975362 0.220610i \(-0.929195\pi\)
0.975362 0.220610i \(-0.0708048\pi\)
\(558\) 4.70104e6i 0.639158i
\(559\) 3.37710e6 0.457103
\(560\) 749532. + 159386.i 0.101000 + 0.0214773i
\(561\) −2.24354e7 −3.00972
\(562\) 5.07479e6i 0.677762i
\(563\) 1.05981e7i 1.40914i 0.709632 + 0.704572i \(0.248861\pi\)
−0.709632 + 0.704572i \(0.751139\pi\)
\(564\) −7.03902e6 −0.931782
\(565\) 1.99566e6 + 424372.i 0.263006 + 0.0559275i
\(566\) 9.62989e6 1.26351
\(567\) 3.93396e6i 0.513893i
\(568\) 1.79987e6i 0.234083i
\(569\) 861625. 0.111567 0.0557837 0.998443i \(-0.482234\pi\)
0.0557837 + 0.998443i \(0.482234\pi\)
\(570\) 586709. 2.75907e6i 0.0756373 0.355693i
\(571\) 2.42311e6 0.311016 0.155508 0.987835i \(-0.450299\pi\)
0.155508 + 0.987835i \(0.450299\pi\)
\(572\) 8.39884e6i 1.07332i
\(573\) 1.43018e7i 1.81972i
\(574\) 804432. 0.101908
\(575\) 672650. 1.51009e6i 0.0848436 0.190473i
\(576\) 573496. 0.0720236
\(577\) 1.06364e7i 1.33001i 0.746838 + 0.665006i \(0.231571\pi\)
−0.746838 + 0.665006i \(0.768429\pi\)
\(578\) 2.95095e6i 0.367402i
\(579\) 2.23892e6 0.277550
\(580\) −312175. + 1.46804e6i −0.0385326 + 0.181204i
\(581\) −5.50992e6 −0.677181
\(582\) 2.98360e6i 0.365118i
\(583\) 2.80606e7i 3.41921i
\(584\) 2.57964e6 0.312987
\(585\) −5.14932e6 1.09499e6i −0.622100 0.132288i
\(586\) −502849. −0.0604914
\(587\) 1.21123e7i 1.45088i −0.688287 0.725439i \(-0.741637\pi\)
0.688287 0.725439i \(-0.258363\pi\)
\(588\) 4.36500e6i 0.520644i
\(589\) 5.41050e6 0.642612
\(590\) 3.39682e6 + 722325.i 0.401737 + 0.0854285i
\(591\) 1.57331e7 1.85287
\(592\) 442015.i 0.0518362i
\(593\) 588269.i 0.0686972i −0.999410 0.0343486i \(-0.989064\pi\)
0.999410 0.0343486i \(-0.0109357\pi\)
\(594\) −6.29198e6 −0.731680
\(595\) −914525. + 4.30066e6i −0.105902 + 0.498015i
\(596\) 3.10959e6 0.358581
\(597\) 1.47262e7i 1.69104i
\(598\) 1.42322e6i 0.162750i
\(599\) 2.11966e6 0.241379 0.120690 0.992690i \(-0.461489\pi\)
0.120690 + 0.992690i \(0.461489\pi\)
\(600\) 3.57547e6 + 1.59265e6i 0.405467 + 0.180610i
\(601\) 1.05488e7 1.19129 0.595645 0.803248i \(-0.296897\pi\)
0.595645 + 0.803248i \(0.296897\pi\)
\(602\) 1.07541e6i 0.120944i
\(603\) 9.18489e6i 1.02868i
\(604\) −4.91526e6 −0.548219
\(605\) 5.20954e6 2.44984e7i 0.578643 2.72113i
\(606\) −1.14617e7 −1.26785
\(607\) 5.38842e6i 0.593595i 0.954940 + 0.296797i \(0.0959186\pi\)
−0.954940 + 0.296797i \(0.904081\pi\)
\(608\) 660046.i 0.0724127i
\(609\) 1.75846e6 0.192127
\(610\) −9.75972e6 2.07538e6i −1.06197 0.225826i
\(611\) −1.51197e7 −1.63847
\(612\) 3.29060e6i 0.355138i
\(613\) 1.09383e7i 1.17571i 0.808968 + 0.587853i \(0.200027\pi\)
−0.808968 + 0.587853i \(0.799973\pi\)
\(614\) −3.02410e6 −0.323724
\(615\) 4.01910e6 + 854653.i 0.428491 + 0.0911175i
\(616\) −2.67455e6 −0.283987
\(617\) 1.36733e6i 0.144597i −0.997383 0.0722984i \(-0.976967\pi\)
0.997383 0.0722984i \(-0.0230334\pi\)
\(618\) 1.63849e7i 1.72573i
\(619\) 1.32601e7 1.39097 0.695487 0.718539i \(-0.255189\pi\)
0.695487 + 0.718539i \(0.255189\pi\)
\(620\) −1.56158e6 + 7.34352e6i −0.163150 + 0.767229i
\(621\) 1.06621e6 0.110946
\(622\) 1.23061e6i 0.127539i
\(623\) 6.76668e6i 0.698483i
\(624\) 3.36981e6 0.346452
\(625\) 6.53195e6 + 7.25955e6i 0.668872 + 0.743378i
\(626\) 7.59943e6 0.775077
\(627\) 9.84515e6i 1.00012i
\(628\) 969811.i 0.0981269i
\(629\) 2.53619e6 0.255597
\(630\) 348692. 1.63976e6i 0.0350018 0.164600i
\(631\) −1.18972e7 −1.18952 −0.594759 0.803904i \(-0.702752\pi\)
−0.594759 + 0.803904i \(0.702752\pi\)
\(632\) 3.75092e6i 0.373547i
\(633\) 2.45463e7i 2.43487i
\(634\) 1.53147e6 0.151316
\(635\) −7.33811e6 1.56043e6i −0.722187 0.153571i
\(636\) −1.12586e7 −1.10367
\(637\) 9.37593e6i 0.915516i
\(638\) 5.23839e6i 0.509502i
\(639\) −3.93760e6 −0.381487
\(640\) −895862. 190503.i −0.0864552 0.0183845i
\(641\) 5.59030e6 0.537390 0.268695 0.963225i \(-0.413408\pi\)
0.268695 + 0.963225i \(0.413408\pi\)
\(642\) 4.86597e6i 0.465942i
\(643\) 6.57079e6i 0.626744i −0.949631 0.313372i \(-0.898541\pi\)
0.949631 0.313372i \(-0.101459\pi\)
\(644\) 453215. 0.0430616
\(645\) −1.14255e6 + 5.37297e6i −0.108137 + 0.508528i
\(646\) −3.78721e6 −0.357057
\(647\) 1.89036e6i 0.177535i 0.996052 + 0.0887675i \(0.0282928\pi\)
−0.996052 + 0.0887675i \(0.971707\pi\)
\(648\) 4.70198e6i 0.439889i
\(649\) −1.21208e7 −1.12959
\(650\) 7.68006e6 + 3.42098e6i 0.712986 + 0.317591i
\(651\) 8.79628e6 0.813480
\(652\) 4724.30i 0.000435230i
\(653\) 5.78907e6i 0.531283i −0.964072 0.265642i \(-0.914416\pi\)
0.964072 0.265642i \(-0.0855838\pi\)
\(654\) −1.15382e7 −1.05486
\(655\) 653660. 3.07391e6i 0.0595318 0.279955i
\(656\) −961481. −0.0872330
\(657\) 5.64352e6i 0.510078i
\(658\) 4.81475e6i 0.433520i
\(659\) 9.61079e6 0.862076 0.431038 0.902334i \(-0.358148\pi\)
0.431038 + 0.902334i \(0.358148\pi\)
\(660\) −1.33626e7 2.84152e6i −1.19407 0.253916i
\(661\) 2.38311e6 0.212149 0.106074 0.994358i \(-0.466172\pi\)
0.106074 + 0.994358i \(0.466172\pi\)
\(662\) 408832.i 0.0362577i
\(663\) 1.93353e7i 1.70831i
\(664\) 6.58561e6 0.579663
\(665\) 1.88723e6 + 401314.i 0.165489 + 0.0351909i
\(666\) −967004. −0.0844778
\(667\) 887671.i 0.0772569i
\(668\) 7.00171e6i 0.607104i
\(669\) −1.78036e6 −0.153795
\(670\) 3.05102e6 1.43478e7i 0.262578 1.23480i
\(671\) 3.48255e7 2.98601
\(672\) 1.07309e6i 0.0916670i
\(673\) 2.50943e6i 0.213568i 0.994282 + 0.106784i \(0.0340554\pi\)
−0.994282 + 0.106784i \(0.965945\pi\)
\(674\) −3.73754e6 −0.316910
\(675\) −2.56283e6 + 5.75351e6i −0.216501 + 0.486041i
\(676\) 1.29760e6 0.109213
\(677\) 1.40322e7i 1.17667i 0.808618 + 0.588334i \(0.200216\pi\)
−0.808618 + 0.588334i \(0.799784\pi\)
\(678\) 2.85714e6i 0.238703i
\(679\) −2.04081e6 −0.169874
\(680\) 1.09307e6 5.14027e6i 0.0906514 0.426299i
\(681\) 2.11044e7 1.74383
\(682\) 2.62038e7i 2.15726i
\(683\) 8.92764e6i 0.732293i −0.930557 0.366147i \(-0.880677\pi\)
0.930557 0.366147i \(-0.119323\pi\)
\(684\) 1.44399e6 0.118012
\(685\) 1.98081e6 + 421215.i 0.161293 + 0.0342987i
\(686\) −6.58550e6 −0.534292
\(687\) 1.13683e7i 0.918979i
\(688\) 1.28536e6i 0.103527i
\(689\) −2.41832e7 −1.94074
\(690\) 2.26435e6 + 481509.i 0.181060 + 0.0385019i
\(691\) −2.95681e6 −0.235574 −0.117787 0.993039i \(-0.537580\pi\)
−0.117787 + 0.993039i \(0.537580\pi\)
\(692\) 6.83469e6i 0.542567i
\(693\) 5.85114e6i 0.462815i
\(694\) −1.87976e6 −0.148151
\(695\) −94978.3 + 446646.i −0.00745868 + 0.0350753i
\(696\) −2.10176e6 −0.164460
\(697\) 5.51678e6i 0.430134i
\(698\) 7.73035e6i 0.600565i
\(699\) 4.86838e6 0.376870
\(700\) −1.08939e6 + 2.44566e6i −0.0840305 + 0.188647i
\(701\) −1.61483e7 −1.24117 −0.620586 0.784138i \(-0.713105\pi\)
−0.620586 + 0.784138i \(0.713105\pi\)
\(702\) 5.42256e6i 0.415300i
\(703\) 1.11294e6i 0.0849343i
\(704\) 3.19669e6 0.243091
\(705\) 5.11533e6 2.40554e7i 0.387615 1.82281i
\(706\) 5.90954e6 0.446213
\(707\) 7.83993e6i 0.589880i
\(708\) 4.86315e6i 0.364615i
\(709\) 2.50051e7 1.86815 0.934077 0.357071i \(-0.116224\pi\)
0.934077 + 0.357071i \(0.116224\pi\)
\(710\) 6.15095e6 + 1.30799e6i 0.457927 + 0.0973771i
\(711\) 8.20595e6 0.608772
\(712\) 8.08773e6i 0.597898i
\(713\) 4.44037e6i 0.327111i
\(714\) −6.15717e6 −0.451997
\(715\) −2.87025e7 6.10353e6i −2.09969 0.446494i
\(716\) 326431. 0.0237962
\(717\) 2.03976e7i 1.48177i
\(718\) 1.12434e7i 0.813932i
\(719\) 8.14571e6 0.587634 0.293817 0.955862i \(-0.405074\pi\)
0.293817 + 0.955862i \(0.405074\pi\)
\(720\) −416766. + 1.95989e6i −0.0299614 + 0.140897i
\(721\) −1.12074e7 −0.802912
\(722\) 8.24248e6i 0.588458i
\(723\) 4.20223e6i 0.298975i
\(724\) 4.33973e6 0.307692
\(725\) −4.79008e6 2.13368e6i −0.338453 0.150759i
\(726\) 3.50739e7 2.46969
\(727\) 1.19636e7i 0.839513i 0.907637 + 0.419757i \(0.137885\pi\)
−0.907637 + 0.419757i \(0.862115\pi\)
\(728\) 2.30498e6i 0.161190i
\(729\) 701432. 0.0488840
\(730\) −1.87465e6 + 8.81577e6i −0.130201 + 0.612284i
\(731\) 7.37514e6 0.510478
\(732\) 1.39728e7i 0.963841i
\(733\) 2.10035e7i 1.44388i 0.691953 + 0.721942i \(0.256750\pi\)
−0.691953 + 0.721942i \(0.743250\pi\)
\(734\) −4.96554e6 −0.340194
\(735\) −1.49171e7 3.17209e6i −1.01851 0.216585i
\(736\) −541696. −0.0368605
\(737\) 5.11970e7i 3.47197i
\(738\) 2.10345e6i 0.142164i
\(739\) −1.94336e6 −0.130901 −0.0654504 0.997856i \(-0.520848\pi\)
−0.0654504 + 0.997856i \(0.520848\pi\)
\(740\) 1.51056e6 + 321218.i 0.101405 + 0.0215635i
\(741\) 8.48475e6 0.567667
\(742\) 7.70097e6i 0.513494i
\(743\) 2.01868e7i 1.34152i −0.741676 0.670759i \(-0.765969\pi\)
0.741676 0.670759i \(-0.234031\pi\)
\(744\) −1.05136e7 −0.696335
\(745\) −2.25977e6 + 1.06268e7i −0.149168 + 0.701477i
\(746\) 1.37226e7 0.902793
\(747\) 1.44074e7i 0.944682i
\(748\) 1.83420e7i 1.19865i
\(749\) −3.32836e6 −0.216784
\(750\) −8.04113e6 + 1.10616e7i −0.521992 + 0.718066i
\(751\) 9.14175e6 0.591465 0.295733 0.955271i \(-0.404436\pi\)
0.295733 + 0.955271i \(0.404436\pi\)
\(752\) 5.75473e6i 0.371091i
\(753\) 1.51034e7i 0.970707i
\(754\) −4.51455e6 −0.289192
\(755\) 3.57197e6 1.67976e7i 0.228056 1.07246i
\(756\) −1.72677e6 −0.109883
\(757\) 5.63495e6i 0.357397i −0.983904 0.178698i \(-0.942811\pi\)
0.983904 0.178698i \(-0.0571886\pi\)
\(758\) 7.96329e6i 0.503407i
\(759\) −8.07986e6 −0.509096
\(760\) −2.25567e6 479663.i −0.141658 0.0301233i
\(761\) 1.12069e7 0.701493 0.350746 0.936471i \(-0.385928\pi\)
0.350746 + 0.936471i \(0.385928\pi\)
\(762\) 1.05058e7i 0.655454i
\(763\) 7.89222e6i 0.490781i
\(764\) −1.16924e7 −0.724720
\(765\) −1.12455e7 2.39132e6i −0.694742 0.147735i
\(766\) −5.78949e6 −0.356507
\(767\) 1.04460e7i 0.641151i
\(768\) 1.28259e6i 0.0784665i
\(769\) −2.71072e7 −1.65298 −0.826491 0.562949i \(-0.809667\pi\)
−0.826491 + 0.562949i \(0.809667\pi\)
\(770\) 1.94362e6 9.14011e6i 0.118137 0.555552i
\(771\) 2.75580e7 1.66960
\(772\) 1.83042e6i 0.110537i
\(773\) 2.01774e7i 1.21455i 0.794492 + 0.607275i \(0.207737\pi\)
−0.794492 + 0.607275i \(0.792263\pi\)
\(774\) −2.81201e6 −0.168719
\(775\) −2.39613e7 1.06732e7i −1.43303 0.638325i
\(776\) 2.43923e6 0.145412
\(777\) 1.80940e6i 0.107518i
\(778\) 2.22107e6i 0.131557i
\(779\) −2.42089e6 −0.142932
\(780\) −2.44888e6 + 1.15161e7i −0.144122 + 0.677751i
\(781\) −2.19484e7 −1.28758
\(782\) 3.10814e6i 0.181754i
\(783\) 3.38207e6i 0.197142i
\(784\) 3.56859e6 0.207351
\(785\) −3.31427e6 704773.i −0.191962 0.0408202i
\(786\) 4.40086e6 0.254086
\(787\) 6.49867e6i 0.374014i 0.982359 + 0.187007i \(0.0598787\pi\)
−0.982359 + 0.187007i \(0.940121\pi\)
\(788\) 1.28625e7i 0.737923i
\(789\) 4.76659e6 0.272594
\(790\) −1.28186e7 2.72584e6i −0.730754 0.155393i
\(791\) −1.95431e6 −0.111059
\(792\) 6.99346e6i 0.396168i
\(793\) 3.00133e7i 1.69485i
\(794\) −6.33337e6 −0.356520
\(795\) 8.18174e6 3.84756e7i 0.459122 2.15907i
\(796\) 1.20393e7 0.673472
\(797\) 1.37055e6i 0.0764272i 0.999270 + 0.0382136i \(0.0121667\pi\)
−0.999270 + 0.0382136i \(0.987833\pi\)
\(798\) 2.70190e6i 0.150198i
\(799\) −3.30194e7 −1.82980
\(800\) 1.30207e6 2.92312e6i 0.0719297 0.161481i
\(801\) −1.76937e7 −0.974398
\(802\) 1.79604e7i 0.986009i
\(803\) 3.14572e7i 1.72160i
\(804\) 2.05414e7 1.12070
\(805\) −329357. + 1.54884e6i −0.0179133 + 0.0842396i
\(806\) −2.25830e7 −1.22446
\(807\) 1.61719e7i 0.874132i
\(808\) 9.37051e6i 0.504934i
\(809\) −5.75863e6 −0.309348 −0.154674 0.987966i \(-0.549433\pi\)
−0.154674 + 0.987966i \(0.549433\pi\)
\(810\) −1.60688e7 3.41698e6i −0.860538 0.182991i
\(811\) 2.12716e7 1.13566 0.567829 0.823147i \(-0.307784\pi\)
0.567829 + 0.823147i \(0.307784\pi\)
\(812\) 1.43762e6i 0.0765165i
\(813\) 1.72658e7i 0.916138i
\(814\) −5.39012e6 −0.285127
\(815\) 16145.0 + 3433.20i 0.000851422 + 0.000181053i
\(816\) 7.35922e6 0.386907
\(817\) 3.23638e6i 0.169631i
\(818\) 1.32060e7i 0.690063i
\(819\) 5.04264e6 0.262693
\(820\) 698719. 3.28581e6i 0.0362884 0.170650i
\(821\) −2.14080e6 −0.110846 −0.0554229 0.998463i \(-0.517651\pi\)
−0.0554229 + 0.998463i \(0.517651\pi\)
\(822\) 2.83589e6i 0.146389i
\(823\) 2.73634e7i 1.40822i −0.710092 0.704109i \(-0.751347\pi\)
0.710092 0.704109i \(-0.248653\pi\)
\(824\) 1.33955e7 0.687289
\(825\) 1.94215e7 4.36008e7i 0.993452 2.23028i
\(826\) −3.32644e6 −0.169640
\(827\) 1.03201e7i 0.524709i −0.964972 0.262354i \(-0.915501\pi\)
0.964972 0.262354i \(-0.0844990\pi\)
\(828\) 1.18508e6i 0.0600718i
\(829\) 1.77400e7 0.896534 0.448267 0.893900i \(-0.352041\pi\)
0.448267 + 0.893900i \(0.352041\pi\)
\(830\) −4.78584e6 + 2.25060e7i −0.241136 + 1.13397i
\(831\) 3.73690e6 0.187719
\(832\) 2.75498e6i 0.137978i
\(833\) 2.04758e7i 1.02242i
\(834\) −639454. −0.0318342
\(835\) −2.39279e7 5.08822e6i −1.18765 0.252551i
\(836\) 8.04888e6 0.398308
\(837\) 1.69180e7i 0.834710i
\(838\) 4.83194e6i 0.237690i
\(839\) −1.66701e7 −0.817587 −0.408793 0.912627i \(-0.634050\pi\)
−0.408793 + 0.912627i \(0.634050\pi\)
\(840\) −3.66722e6 779826.i −0.179324 0.0381329i
\(841\) −1.76954e7 −0.862721
\(842\) 1.26178e7i 0.613345i
\(843\) 2.48293e7i 1.20336i
\(844\) 2.00677e7 0.969710
\(845\) −942980. + 4.43447e6i −0.0454319 + 0.213649i
\(846\) 1.25897e7 0.604769
\(847\) 2.39909e7i 1.14905i
\(848\) 9.20442e6i 0.439548i
\(849\) −4.71160e7 −2.24336
\(850\) 1.67722e7 + 7.47099e6i 0.796240 + 0.354675i
\(851\) 913383. 0.0432344
\(852\) 8.80619e6i 0.415613i
\(853\) 1.87430e7i 0.881995i 0.897508 + 0.440998i \(0.145375\pi\)
−0.897508 + 0.440998i \(0.854625\pi\)
\(854\) 9.55751e6 0.448436
\(855\) −1.04937e6 + 4.93476e6i −0.0490921 + 0.230861i
\(856\) 3.97816e6 0.185566
\(857\) 2.38821e7i 1.11076i −0.831597 0.555380i \(-0.812573\pi\)
0.831597 0.555380i \(-0.187427\pi\)
\(858\) 4.10929e7i 1.90567i
\(859\) 1.33765e7 0.618529 0.309265 0.950976i \(-0.399917\pi\)
0.309265 + 0.950976i \(0.399917\pi\)
\(860\) 4.39265e6 + 934087.i 0.202526 + 0.0430667i
\(861\) −3.93583e6 −0.180938
\(862\) 1.31040e7i 0.600668i
\(863\) 1.81344e6i 0.0828850i 0.999141 + 0.0414425i \(0.0131953\pi\)
−0.999141 + 0.0414425i \(0.986805\pi\)
\(864\) 2.06389e6 0.0940593
\(865\) 2.33572e7 + 4.96685e6i 1.06140 + 0.225705i
\(866\) −7.02903e6 −0.318494
\(867\) 1.44381e7i 0.652320i
\(868\) 7.19137e6i 0.323976i
\(869\) 4.57403e7 2.05471
\(870\) 1.52737e6 7.18265e6i 0.0684144 0.321726i
\(871\) 4.41226e7 1.97068
\(872\) 9.43301e6i 0.420106i
\(873\) 5.33635e6i 0.236978i
\(874\) −1.36392e6 −0.0603964
\(875\) −7.56622e6 5.50020e6i −0.334086 0.242861i
\(876\) −1.26214e7 −0.555707
\(877\) 9.61599e6i 0.422177i −0.977467 0.211089i \(-0.932299\pi\)
0.977467 0.211089i \(-0.0677009\pi\)
\(878\) 1.12536e7i 0.492669i
\(879\) 2.46028e6 0.107402
\(880\) −2.32307e6 + 1.09245e7i −0.101125 + 0.475550i
\(881\) −3.25972e7 −1.41495 −0.707473 0.706740i \(-0.750165\pi\)
−0.707473 + 0.706740i \(0.750165\pi\)
\(882\) 7.80706e6i 0.337922i
\(883\) 3.13913e7i 1.35490i −0.735569 0.677450i \(-0.763085\pi\)
0.735569 0.677450i \(-0.236915\pi\)
\(884\) 1.58075e7 0.680349
\(885\) −1.66196e7 3.53411e6i −0.713282 0.151678i
\(886\) −7.63062e6 −0.326569
\(887\) 2.47183e7i 1.05490i 0.849588 + 0.527448i \(0.176851\pi\)
−0.849588 + 0.527448i \(0.823149\pi\)
\(888\) 2.16264e6i 0.0920348i
\(889\) 7.18607e6 0.304956
\(890\) 2.76394e7 + 5.87745e6i 1.16964 + 0.248722i
\(891\) 5.73380e7 2.41963
\(892\) 1.45552e6i 0.0612502i
\(893\) 1.44897e7i 0.608037i
\(894\) −1.52142e7 −0.636658
\(895\) −237221. + 1.11556e6i −0.00989909 + 0.0465516i
\(896\) 877301. 0.0365072
\(897\) 6.96339e6i 0.288961i
\(898\) 1.32693e7i 0.549107i
\(899\) 1.40851e7 0.581246
\(900\) −6.39495e6 2.84855e6i −0.263167 0.117224i
\(901\) −5.28131e7 −2.16735
\(902\) 1.17247e7i 0.479828i
\(903\) 5.26165e6i 0.214735i
\(904\) 2.33585e6 0.0950657
\(905\) −3.15373e6 + 1.48308e7i −0.127998 + 0.601925i
\(906\) 2.40488e7 0.973359
\(907\) 4.82951e7i 1.94933i −0.223673 0.974664i \(-0.571805\pi\)
0.223673 0.974664i \(-0.428195\pi\)
\(908\) 1.72538e7i 0.694497i
\(909\) 2.05000e7 0.822895
\(910\) −7.87713e6 1.67505e6i −0.315330 0.0670541i
\(911\) −1.21362e7 −0.484492 −0.242246 0.970215i \(-0.577884\pi\)
−0.242246 + 0.970215i \(0.577884\pi\)
\(912\) 3.22939e6i 0.128568i
\(913\) 8.03077e7i 3.18846i
\(914\) 2.30554e7 0.912867
\(915\) 4.77512e7 + 1.01542e7i 1.88552 + 0.400952i
\(916\) 9.29416e6 0.365992
\(917\) 3.01023e6i 0.118216i
\(918\) 1.18422e7i 0.463793i
\(919\) 2.48523e7 0.970684 0.485342 0.874324i \(-0.338695\pi\)
0.485342 + 0.874324i \(0.338695\pi\)
\(920\) 393657. 1.85122e6i 0.0153337 0.0721087i
\(921\) 1.47960e7 0.574770
\(922\) 2.91154e6i 0.112796i
\(923\) 1.89155e7i 0.730827i
\(924\) 1.30857e7 0.504217
\(925\) −2.19549e6 + 4.92883e6i −0.0843677 + 0.189404i
\(926\) 3.03093e7 1.16158
\(927\) 2.93054e7i 1.12008i
\(928\) 1.71829e6i 0.0654978i
\(929\) −2.82241e7 −1.07295 −0.536477 0.843915i \(-0.680245\pi\)
−0.536477 + 0.843915i \(0.680245\pi\)
\(930\) 7.64033e6 3.59295e7i 0.289671 1.36221i
\(931\) 8.98526e6 0.339748
\(932\) 3.98013e6i 0.150092i
\(933\) 6.02097e6i 0.226445i
\(934\) 2.73923e7 1.02745
\(935\) −6.26827e7 1.33293e7i −2.34487 0.498631i
\(936\) −6.02710e6 −0.224864
\(937\) 1.78987e7i 0.665999i −0.942927 0.333000i \(-0.891939\pi\)
0.942927 0.333000i \(-0.108061\pi\)
\(938\) 1.40505e7i 0.521417i
\(939\) −3.71816e7 −1.37614
\(940\) −1.96665e7 4.18202e6i −0.725950 0.154371i
\(941\) −1.57831e7 −0.581057 −0.290528 0.956866i \(-0.593831\pi\)
−0.290528 + 0.956866i \(0.593831\pi\)
\(942\) 4.74498e6i 0.174224i
\(943\) 1.98681e6i 0.0727574i
\(944\) 3.97586e6 0.145211
\(945\) 1.25487e6 5.90115e6i 0.0457107 0.214960i
\(946\) −1.56743e7 −0.569454
\(947\) 2.94240e7i 1.06617i 0.846062 + 0.533085i \(0.178967\pi\)
−0.846062 + 0.533085i \(0.821033\pi\)
\(948\) 1.83521e7i 0.663230i
\(949\) −2.71105e7 −0.977173
\(950\) 3.27844e6 7.36004e6i 0.117858 0.264589i
\(951\) −7.49298e6 −0.268660
\(952\) 5.03377e6i 0.180012i
\(953\) 3.16123e7i 1.12752i 0.825939 + 0.563760i \(0.190646\pi\)
−0.825939 + 0.563760i \(0.809354\pi\)
\(954\) 2.01367e7 0.716335
\(955\) 8.49700e6 3.99581e7i 0.301479 1.41774i
\(956\) 1.66760e7 0.590129
\(957\) 2.56298e7i 0.904617i
\(958\) 3.77873e7i 1.33025i
\(959\) −1.93977e6 −0.0681089
\(960\) 4.38317e6 + 932071.i 0.153501 + 0.0326416i
\(961\) 4.18282e7 1.46103
\(962\) 4.64532e6i 0.161837i
\(963\) 8.70308e6i 0.302418i
\(964\) −3.43552e6 −0.119069
\(965\) 6.25536e6 + 1.33019e6i 0.216239 + 0.0459827i
\(966\) −2.21744e6 −0.0764555
\(967\) 4.06367e7i 1.39750i −0.715366 0.698750i \(-0.753740\pi\)
0.715366 0.698750i \(-0.246260\pi\)
\(968\) 2.86746e7i 0.983578i
\(969\) 1.85296e7 0.633952
\(970\) −1.77262e6 + 8.33595e6i −0.0604904 + 0.284463i
\(971\) −5.45379e7 −1.85631 −0.928154 0.372197i \(-0.878605\pi\)
−0.928154 + 0.372197i \(0.878605\pi\)
\(972\) 1.51690e7i 0.514981i
\(973\) 437392.i 0.0148112i
\(974\) −3.73010e7 −1.25986
\(975\) −3.75761e7 1.67378e7i −1.26590 0.563880i
\(976\) −1.14234e7 −0.383859
\(977\) 1.04362e7i 0.349788i 0.984587 + 0.174894i \(0.0559583\pi\)
−0.984587 + 0.174894i \(0.944042\pi\)
\(978\) 23114.5i 0.000772747i
\(979\) −9.86253e7 −3.28875
\(980\) −2.59333e6 + 1.21955e7i −0.0862568 + 0.405633i
\(981\) 2.06367e7 0.684650
\(982\) 5.46855e6i 0.180965i
\(983\) 2.08178e6i 0.0687150i −0.999410 0.0343575i \(-0.989062\pi\)
0.999410 0.0343575i \(-0.0109385\pi\)
\(984\) 4.70422e6 0.154882
\(985\) 4.39570e7 + 9.34735e6i 1.44357 + 0.306972i
\(986\) −9.85919e6 −0.322960
\(987\) 2.35570e7i 0.769711i
\(988\) 6.93668e6i 0.226079i
\(989\) 2.65608e6 0.0863476
\(990\) 2.38998e7 + 5.08223e6i 0.775007 + 0.164803i
\(991\) −4.04409e7 −1.30809 −0.654044 0.756457i \(-0.726929\pi\)
−0.654044 + 0.756457i \(0.726929\pi\)
\(992\) 8.59534e6i 0.277322i
\(993\) 2.00029e6i 0.0643753i
\(994\) −6.02351e6 −0.193368
\(995\) −8.74912e6 + 4.11437e7i −0.280160 + 1.31749i
\(996\) −3.22213e7 −1.02919
\(997\) 6.40147e6i 0.203959i 0.994787 + 0.101979i \(0.0325175\pi\)
−0.994787 + 0.101979i \(0.967482\pi\)
\(998\) 5.94340e6i 0.188890i
\(999\) −3.48004e6 −0.110324
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 230.6.b.a.139.15 yes 26
5.4 even 2 inner 230.6.b.a.139.12 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.6.b.a.139.12 26 5.4 even 2 inner
230.6.b.a.139.15 yes 26 1.1 even 1 trivial