Properties

Label 165.6.c.b.34.25
Level $165$
Weight $6$
Character 165.34
Analytic conductor $26.463$
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] = [165,6,Mod(34,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("165.34");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.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: \(26.4633302691\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.25
Character \(\chi\) \(=\) 165.34
Dual form 165.6.c.b.34.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.4306i q^{2} +9.00000i q^{3} -76.7973 q^{4} +(-52.2792 - 19.7960i) q^{5} -93.8753 q^{6} -21.9028i q^{7} -467.262i q^{8} -81.0000 q^{9} +O(q^{10})\) \(q+10.4306i q^{2} +9.00000i q^{3} -76.7973 q^{4} +(-52.2792 - 19.7960i) q^{5} -93.8753 q^{6} -21.9028i q^{7} -467.262i q^{8} -81.0000 q^{9} +(206.484 - 545.303i) q^{10} +121.000 q^{11} -691.175i q^{12} +460.797i q^{13} +228.459 q^{14} +(178.164 - 470.513i) q^{15} +2416.31 q^{16} -2318.63i q^{17} -844.878i q^{18} -800.141 q^{19} +(4014.90 + 1520.28i) q^{20} +197.125 q^{21} +1262.10i q^{22} +4781.90i q^{23} +4205.36 q^{24} +(2341.24 + 2069.84i) q^{25} -4806.39 q^{26} -729.000i q^{27} +1682.08i q^{28} -911.582 q^{29} +(4907.73 + 1858.35i) q^{30} -944.328 q^{31} +10251.1i q^{32} +1089.00i q^{33} +24184.7 q^{34} +(-433.588 + 1145.06i) q^{35} +6220.58 q^{36} -12825.4i q^{37} -8345.95i q^{38} -4147.17 q^{39} +(-9249.91 + 24428.1i) q^{40} +8712.22 q^{41} +2056.13i q^{42} -20504.8i q^{43} -9292.47 q^{44} +(4234.62 + 1603.47i) q^{45} -49878.1 q^{46} +9288.25i q^{47} +21746.8i q^{48} +16327.3 q^{49} +(-21589.6 + 24420.5i) q^{50} +20867.7 q^{51} -35388.0i q^{52} +23263.1i q^{53} +7603.90 q^{54} +(-6325.79 - 2395.31i) q^{55} -10234.4 q^{56} -7201.27i q^{57} -9508.34i q^{58} -20726.7 q^{59} +(-13682.5 + 36134.1i) q^{60} -6625.93 q^{61} -9849.90i q^{62} +1774.13i q^{63} -29603.6 q^{64} +(9121.93 - 24090.1i) q^{65} -11358.9 q^{66} -57904.9i q^{67} +178064. i q^{68} -43037.1 q^{69} +(-11943.7 - 4522.58i) q^{70} +38362.5 q^{71} +37848.2i q^{72} +8431.57i q^{73} +133777. q^{74} +(-18628.5 + 21071.1i) q^{75} +61448.7 q^{76} -2650.24i q^{77} -43257.5i q^{78} +1683.43 q^{79} +(-126323. - 47833.2i) q^{80} +6561.00 q^{81} +90873.6i q^{82} +7798.26i q^{83} -15138.7 q^{84} +(-45899.5 + 121216. i) q^{85} +213877. q^{86} -8204.23i q^{87} -56538.7i q^{88} +83079.0 q^{89} +(-16725.2 + 44169.6i) q^{90} +10092.8 q^{91} -367237. i q^{92} -8498.95i q^{93} -96882.0 q^{94} +(41830.8 + 15839.6i) q^{95} -92260.2 q^{96} -14678.5i q^{97} +170303. i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.4306i 1.84389i 0.387326 + 0.921943i \(0.373399\pi\)
−0.387326 + 0.921943i \(0.626601\pi\)
\(3\) 9.00000i 0.577350i
\(4\) −76.7973 −2.39991
\(5\) −52.2792 19.7960i −0.935199 0.354121i
\(6\) −93.8753 −1.06457
\(7\) 21.9028i 0.168949i −0.996426 0.0844744i \(-0.973079\pi\)
0.996426 0.0844744i \(-0.0269211\pi\)
\(8\) 467.262i 2.58128i
\(9\) −81.0000 −0.333333
\(10\) 206.484 545.303i 0.652959 1.72440i
\(11\) 121.000 0.301511
\(12\) 691.175i 1.38559i
\(13\) 460.797i 0.756225i 0.925760 + 0.378113i \(0.123427\pi\)
−0.925760 + 0.378113i \(0.876573\pi\)
\(14\) 228.459 0.311522
\(15\) 178.164 470.513i 0.204452 0.539938i
\(16\) 2416.31 2.35967
\(17\) 2318.63i 1.94585i −0.231127 0.972924i \(-0.574241\pi\)
0.231127 0.972924i \(-0.425759\pi\)
\(18\) 844.878i 0.614629i
\(19\) −800.141 −0.508490 −0.254245 0.967140i \(-0.581827\pi\)
−0.254245 + 0.967140i \(0.581827\pi\)
\(20\) 4014.90 + 1520.28i 2.24440 + 0.849861i
\(21\) 197.125 0.0975426
\(22\) 1262.10i 0.555952i
\(23\) 4781.90i 1.88487i 0.334391 + 0.942434i \(0.391469\pi\)
−0.334391 + 0.942434i \(0.608531\pi\)
\(24\) 4205.36 1.49030
\(25\) 2341.24 + 2069.84i 0.749196 + 0.662348i
\(26\) −4806.39 −1.39439
\(27\) 729.000i 0.192450i
\(28\) 1682.08i 0.405462i
\(29\) −911.582 −0.201280 −0.100640 0.994923i \(-0.532089\pi\)
−0.100640 + 0.994923i \(0.532089\pi\)
\(30\) 4907.73 + 1858.35i 0.995583 + 0.376986i
\(31\) −944.328 −0.176489 −0.0882447 0.996099i \(-0.528126\pi\)
−0.0882447 + 0.996099i \(0.528126\pi\)
\(32\) 10251.1i 1.76969i
\(33\) 1089.00i 0.174078i
\(34\) 24184.7 3.58792
\(35\) −433.588 + 1145.06i −0.0598283 + 0.158001i
\(36\) 6220.58 0.799971
\(37\) 12825.4i 1.54017i −0.637942 0.770084i \(-0.720214\pi\)
0.637942 0.770084i \(-0.279786\pi\)
\(38\) 8345.95i 0.937598i
\(39\) −4147.17 −0.436607
\(40\) −9249.91 + 24428.1i −0.914087 + 2.41401i
\(41\) 8712.22 0.809411 0.404706 0.914447i \(-0.367374\pi\)
0.404706 + 0.914447i \(0.367374\pi\)
\(42\) 2056.13i 0.179857i
\(43\) 20504.8i 1.69116i −0.533852 0.845578i \(-0.679256\pi\)
0.533852 0.845578i \(-0.320744\pi\)
\(44\) −9292.47 −0.723601
\(45\) 4234.62 + 1603.47i 0.311733 + 0.118040i
\(46\) −49878.1 −3.47548
\(47\) 9288.25i 0.613323i 0.951819 + 0.306662i \(0.0992120\pi\)
−0.951819 + 0.306662i \(0.900788\pi\)
\(48\) 21746.8i 1.36236i
\(49\) 16327.3 0.971456
\(50\) −21589.6 + 24420.5i −1.22129 + 1.38143i
\(51\) 20867.7 1.12344
\(52\) 35388.0i 1.81488i
\(53\) 23263.1i 1.13757i 0.822486 + 0.568785i \(0.192586\pi\)
−0.822486 + 0.568785i \(0.807414\pi\)
\(54\) 7603.90 0.354856
\(55\) −6325.79 2395.31i −0.281973 0.106772i
\(56\) −10234.4 −0.436104
\(57\) 7201.27i 0.293577i
\(58\) 9508.34i 0.371137i
\(59\) −20726.7 −0.775177 −0.387588 0.921833i \(-0.626692\pi\)
−0.387588 + 0.921833i \(0.626692\pi\)
\(60\) −13682.5 + 36134.1i −0.490667 + 1.29580i
\(61\) −6625.93 −0.227993 −0.113997 0.993481i \(-0.536365\pi\)
−0.113997 + 0.993481i \(0.536365\pi\)
\(62\) 9849.90i 0.325426i
\(63\) 1774.13i 0.0563162i
\(64\) −29603.6 −0.903429
\(65\) 9121.93 24090.1i 0.267796 0.707222i
\(66\) −11358.9 −0.320979
\(67\) 57904.9i 1.57590i −0.615739 0.787950i \(-0.711143\pi\)
0.615739 0.787950i \(-0.288857\pi\)
\(68\) 178064.i 4.66987i
\(69\) −43037.1 −1.08823
\(70\) −11943.7 4522.58i −0.291335 0.110317i
\(71\) 38362.5 0.903153 0.451577 0.892232i \(-0.350862\pi\)
0.451577 + 0.892232i \(0.350862\pi\)
\(72\) 37848.2i 0.860427i
\(73\) 8431.57i 0.185183i 0.995704 + 0.0925916i \(0.0295151\pi\)
−0.995704 + 0.0925916i \(0.970485\pi\)
\(74\) 133777. 2.83989
\(75\) −18628.5 + 21071.1i −0.382407 + 0.432549i
\(76\) 61448.7 1.22033
\(77\) 2650.24i 0.0509400i
\(78\) 43257.5i 0.805053i
\(79\) 1683.43 0.0303478 0.0151739 0.999885i \(-0.495170\pi\)
0.0151739 + 0.999885i \(0.495170\pi\)
\(80\) −126323. 47833.2i −2.20677 0.835611i
\(81\) 6561.00 0.111111
\(82\) 90873.6i 1.49246i
\(83\) 7798.26i 0.124252i 0.998068 + 0.0621259i \(0.0197880\pi\)
−0.998068 + 0.0621259i \(0.980212\pi\)
\(84\) −15138.7 −0.234094
\(85\) −45899.5 + 121216.i −0.689066 + 1.81976i
\(86\) 213877. 3.11830
\(87\) 8204.23i 0.116209i
\(88\) 56538.7i 0.778286i
\(89\) 83079.0 1.11177 0.555887 0.831258i \(-0.312379\pi\)
0.555887 + 0.831258i \(0.312379\pi\)
\(90\) −16725.2 + 44169.6i −0.217653 + 0.574800i
\(91\) 10092.8 0.127763
\(92\) 367237.i 4.52352i
\(93\) 8498.95i 0.101896i
\(94\) −96882.0 −1.13090
\(95\) 41830.8 + 15839.6i 0.475540 + 0.180067i
\(96\) −92260.2 −1.02173
\(97\) 14678.5i 0.158399i −0.996859 0.0791997i \(-0.974764\pi\)
0.996859 0.0791997i \(-0.0252365\pi\)
\(98\) 170303.i 1.79125i
\(99\) −9801.00 −0.100504
\(100\) −179801. 158958.i −1.79801 1.58958i
\(101\) −19178.1 −0.187069 −0.0935345 0.995616i \(-0.529817\pi\)
−0.0935345 + 0.995616i \(0.529817\pi\)
\(102\) 217662.i 2.07149i
\(103\) 127841.i 1.18735i −0.804705 0.593675i \(-0.797677\pi\)
0.804705 0.593675i \(-0.202323\pi\)
\(104\) 215313. 1.95203
\(105\) −10305.6 3902.29i −0.0912218 0.0345419i
\(106\) −242648. −2.09755
\(107\) 52736.6i 0.445300i −0.974898 0.222650i \(-0.928529\pi\)
0.974898 0.222650i \(-0.0714707\pi\)
\(108\) 55985.2i 0.461864i
\(109\) 233661. 1.88374 0.941869 0.335979i \(-0.109067\pi\)
0.941869 + 0.335979i \(0.109067\pi\)
\(110\) 24984.5 65981.7i 0.196875 0.519926i
\(111\) 115429. 0.889216
\(112\) 52923.9i 0.398664i
\(113\) 36635.5i 0.269902i −0.990852 0.134951i \(-0.956912\pi\)
0.990852 0.134951i \(-0.0430876\pi\)
\(114\) 75113.5 0.541323
\(115\) 94662.5 249994.i 0.667472 1.76273i
\(116\) 70007.0 0.483055
\(117\) 37324.6i 0.252075i
\(118\) 216192.i 1.42934i
\(119\) −50784.5 −0.328748
\(120\) −219853. 83249.2i −1.39373 0.527748i
\(121\) 14641.0 0.0909091
\(122\) 69112.4i 0.420394i
\(123\) 78410.0i 0.467314i
\(124\) 72521.8 0.423559
\(125\) −81423.7 154557.i −0.466096 0.884734i
\(126\) −18505.2 −0.103841
\(127\) 256889.i 1.41330i −0.707561 0.706652i \(-0.750205\pi\)
0.707561 0.706652i \(-0.249795\pi\)
\(128\) 19253.6i 0.103869i
\(129\) 184543. 0.976390
\(130\) 251274. + 95147.1i 1.30404 + 0.493784i
\(131\) −109508. −0.557531 −0.278765 0.960359i \(-0.589925\pi\)
−0.278765 + 0.960359i \(0.589925\pi\)
\(132\) 83632.2i 0.417771i
\(133\) 17525.4i 0.0859088i
\(134\) 603983. 2.90578
\(135\) −14431.3 + 38111.6i −0.0681507 + 0.179979i
\(136\) −1.08341e6 −5.02278
\(137\) 149903.i 0.682355i −0.939999 0.341177i \(-0.889174\pi\)
0.939999 0.341177i \(-0.110826\pi\)
\(138\) 448903.i 2.00657i
\(139\) 113251. 0.497168 0.248584 0.968610i \(-0.420035\pi\)
0.248584 + 0.968610i \(0.420035\pi\)
\(140\) 33298.4 87937.7i 0.143583 0.379188i
\(141\) −83594.3 −0.354102
\(142\) 400144.i 1.66531i
\(143\) 55756.4i 0.228011i
\(144\) −195721. −0.786558
\(145\) 47656.8 + 18045.7i 0.188237 + 0.0712775i
\(146\) −87946.3 −0.341456
\(147\) 146945.i 0.560871i
\(148\) 984959.i 3.69627i
\(149\) 61807.9 0.228075 0.114038 0.993476i \(-0.463622\pi\)
0.114038 + 0.993476i \(0.463622\pi\)
\(150\) −219785. 194307.i −0.797570 0.705115i
\(151\) −256778. −0.916465 −0.458233 0.888832i \(-0.651517\pi\)
−0.458233 + 0.888832i \(0.651517\pi\)
\(152\) 373876.i 1.31256i
\(153\) 187809.i 0.648616i
\(154\) 27643.6 0.0939275
\(155\) 49368.7 + 18693.9i 0.165053 + 0.0624987i
\(156\) 318492. 1.04782
\(157\) 116054.i 0.375761i 0.982192 + 0.187880i \(0.0601617\pi\)
−0.982192 + 0.187880i \(0.939838\pi\)
\(158\) 17559.2i 0.0559579i
\(159\) −209368. −0.656776
\(160\) 202931. 535921.i 0.626685 1.65501i
\(161\) 104737. 0.318446
\(162\) 68435.1i 0.204876i
\(163\) 322117.i 0.949609i −0.880091 0.474805i \(-0.842519\pi\)
0.880091 0.474805i \(-0.157481\pi\)
\(164\) −669075. −1.94252
\(165\) 21557.8 56932.1i 0.0616446 0.162797i
\(166\) −81340.5 −0.229106
\(167\) 435361.i 1.20797i 0.796994 + 0.603987i \(0.206422\pi\)
−0.796994 + 0.603987i \(0.793578\pi\)
\(168\) 92109.2i 0.251785i
\(169\) 158959. 0.428123
\(170\) −1.26436e6 478759.i −3.35542 1.27056i
\(171\) 64811.5 0.169497
\(172\) 1.57471e6i 4.05863i
\(173\) 700319.i 1.77902i −0.456916 0.889510i \(-0.651046\pi\)
0.456916 0.889510i \(-0.348954\pi\)
\(174\) 85575.0 0.214276
\(175\) 45335.3 51279.7i 0.111903 0.126576i
\(176\) 292373. 0.711469
\(177\) 186541.i 0.447548i
\(178\) 866563.i 2.04998i
\(179\) −228192. −0.532314 −0.266157 0.963930i \(-0.585754\pi\)
−0.266157 + 0.963930i \(0.585754\pi\)
\(180\) −325207. 123142.i −0.748133 0.283287i
\(181\) 511598. 1.16073 0.580366 0.814356i \(-0.302909\pi\)
0.580366 + 0.814356i \(0.302909\pi\)
\(182\) 105273.i 0.235581i
\(183\) 59633.4i 0.131632i
\(184\) 2.23440e6 4.86538
\(185\) −253892. + 670505.i −0.545406 + 1.44036i
\(186\) 88649.1 0.187885
\(187\) 280554.i 0.586695i
\(188\) 713312.i 1.47192i
\(189\) −15967.2 −0.0325142
\(190\) −165216. + 436320.i −0.332023 + 0.876841i
\(191\) −803150. −1.59299 −0.796496 0.604644i \(-0.793315\pi\)
−0.796496 + 0.604644i \(0.793315\pi\)
\(192\) 266432.i 0.521595i
\(193\) 578708.i 1.11832i −0.829059 0.559160i \(-0.811124\pi\)
0.829059 0.559160i \(-0.188876\pi\)
\(194\) 153106. 0.292070
\(195\) 216811. + 82097.4i 0.408315 + 0.154612i
\(196\) −1.25389e6 −2.33141
\(197\) 278554.i 0.511381i −0.966759 0.255690i \(-0.917697\pi\)
0.966759 0.255690i \(-0.0823027\pi\)
\(198\) 102230.i 0.185317i
\(199\) −843631. −1.51015 −0.755074 0.655639i \(-0.772399\pi\)
−0.755074 + 0.655639i \(0.772399\pi\)
\(200\) 967157. 1.09397e6i 1.70971 1.93389i
\(201\) 521144. 0.909846
\(202\) 200039.i 0.344934i
\(203\) 19966.2i 0.0340060i
\(204\) −1.60258e6 −2.69615
\(205\) −455468. 172467.i −0.756961 0.286630i
\(206\) 1.33346e6 2.18934
\(207\) 387334.i 0.628290i
\(208\) 1.11343e6i 1.78445i
\(209\) −96817.1 −0.153316
\(210\) 40703.2 107493.i 0.0636913 0.168203i
\(211\) 48614.4 0.0751724 0.0375862 0.999293i \(-0.488033\pi\)
0.0375862 + 0.999293i \(0.488033\pi\)
\(212\) 1.78654e6i 2.73007i
\(213\) 345263.i 0.521436i
\(214\) 550074. 0.821082
\(215\) −405912. + 1.07197e6i −0.598874 + 1.58157i
\(216\) −340634. −0.496768
\(217\) 20683.4i 0.0298177i
\(218\) 2.43723e6i 3.47340i
\(219\) −75884.1 −0.106916
\(220\) 485803. + 183954.i 0.676712 + 0.256243i
\(221\) 1.06842e6 1.47150
\(222\) 1.20399e6i 1.63961i
\(223\) 473625.i 0.637782i 0.947791 + 0.318891i \(0.103310\pi\)
−0.947791 + 0.318891i \(0.896690\pi\)
\(224\) 224529. 0.298987
\(225\) −189640. 167657.i −0.249732 0.220783i
\(226\) 382130. 0.497668
\(227\) 767793.i 0.988962i −0.869188 0.494481i \(-0.835358\pi\)
0.869188 0.494481i \(-0.164642\pi\)
\(228\) 553038.i 0.704560i
\(229\) −580162. −0.731073 −0.365536 0.930797i \(-0.619114\pi\)
−0.365536 + 0.930797i \(0.619114\pi\)
\(230\) 2.60759e6 + 987386.i 3.25027 + 1.23074i
\(231\) 23852.2 0.0294102
\(232\) 425947.i 0.519560i
\(233\) 298663.i 0.360406i 0.983629 + 0.180203i \(0.0576754\pi\)
−0.983629 + 0.180203i \(0.942325\pi\)
\(234\) 389317. 0.464798
\(235\) 183870. 485583.i 0.217191 0.573580i
\(236\) 1.59176e6 1.86036
\(237\) 15150.9i 0.0175213i
\(238\) 529712.i 0.606174i
\(239\) −324060. −0.366970 −0.183485 0.983023i \(-0.558738\pi\)
−0.183485 + 0.983023i \(0.558738\pi\)
\(240\) 430499. 1.13690e6i 0.482440 1.27408i
\(241\) −679917. −0.754073 −0.377036 0.926198i \(-0.623057\pi\)
−0.377036 + 0.926198i \(0.623057\pi\)
\(242\) 152714.i 0.167626i
\(243\) 59049.0i 0.0641500i
\(244\) 508853. 0.547165
\(245\) −853577. 323214.i −0.908505 0.344013i
\(246\) −817863. −0.861673
\(247\) 368703.i 0.384533i
\(248\) 441249.i 0.455569i
\(249\) −70184.4 −0.0717368
\(250\) 1.61212e6 849297.i 1.63135 0.859428i
\(251\) 1.78432e6 1.78767 0.893836 0.448393i \(-0.148004\pi\)
0.893836 + 0.448393i \(0.148004\pi\)
\(252\) 136248.i 0.135154i
\(253\) 578610.i 0.568309i
\(254\) 2.67950e6 2.60597
\(255\) −1.09094e6 413096.i −1.05064 0.397832i
\(256\) −1.14814e6 −1.09495
\(257\) 891074.i 0.841552i 0.907165 + 0.420776i \(0.138242\pi\)
−0.907165 + 0.420776i \(0.861758\pi\)
\(258\) 1.92489e6i 1.80035i
\(259\) −280913. −0.260209
\(260\) −700539. + 1.85006e6i −0.642686 + 1.69727i
\(261\) 73838.1 0.0670933
\(262\) 1.14224e6i 1.02802i
\(263\) 1.27856e6i 1.13980i −0.821713 0.569902i \(-0.806981\pi\)
0.821713 0.569902i \(-0.193019\pi\)
\(264\) 508848. 0.449344
\(265\) 460516. 1.21618e6i 0.402838 1.06385i
\(266\) −182800. −0.158406
\(267\) 747711.i 0.641883i
\(268\) 4.44694e6i 3.78203i
\(269\) −454281. −0.382775 −0.191388 0.981515i \(-0.561299\pi\)
−0.191388 + 0.981515i \(0.561299\pi\)
\(270\) −397526. 150527.i −0.331861 0.125662i
\(271\) −2.02780e6 −1.67726 −0.838632 0.544698i \(-0.816644\pi\)
−0.838632 + 0.544698i \(0.816644\pi\)
\(272\) 5.60252e6i 4.59157i
\(273\) 90834.8i 0.0737642i
\(274\) 1.56358e6 1.25818
\(275\) 283290. + 250450.i 0.225891 + 0.199705i
\(276\) 3.30513e6 2.61166
\(277\) 1.27638e6i 0.999496i −0.866171 0.499748i \(-0.833426\pi\)
0.866171 0.499748i \(-0.166574\pi\)
\(278\) 1.18127e6i 0.916722i
\(279\) 76490.6 0.0588298
\(280\) 535044. + 202599.i 0.407845 + 0.154434i
\(281\) −1.02183e6 −0.771994 −0.385997 0.922500i \(-0.626143\pi\)
−0.385997 + 0.922500i \(0.626143\pi\)
\(282\) 871938.i 0.652924i
\(283\) 75339.2i 0.0559184i −0.999609 0.0279592i \(-0.991099\pi\)
0.999609 0.0279592i \(-0.00890085\pi\)
\(284\) −2.94614e6 −2.16749
\(285\) −142556. + 376477.i −0.103962 + 0.274553i
\(286\) −581573. −0.420425
\(287\) 190822.i 0.136749i
\(288\) 830342.i 0.589896i
\(289\) −3.95618e6 −2.78632
\(290\) −188227. + 497089.i −0.131428 + 0.347087i
\(291\) 132107. 0.0914519
\(292\) 647522.i 0.444424i
\(293\) 661394.i 0.450082i 0.974349 + 0.225041i \(0.0722516\pi\)
−0.974349 + 0.225041i \(0.927748\pi\)
\(294\) −1.53273e6 −1.03418
\(295\) 1.08358e6 + 410306.i 0.724945 + 0.274507i
\(296\) −5.99284e6 −3.97561
\(297\) 88209.0i 0.0580259i
\(298\) 644693.i 0.420545i
\(299\) −2.20349e6 −1.42539
\(300\) 1.43062e6 1.61821e6i 0.917744 1.03808i
\(301\) −449112. −0.285719
\(302\) 2.67835e6i 1.68986i
\(303\) 172603.i 0.108004i
\(304\) −1.93339e6 −1.19987
\(305\) 346399. + 131167.i 0.213219 + 0.0807373i
\(306\) −1.95896e6 −1.19597
\(307\) 962329.i 0.582744i −0.956610 0.291372i \(-0.905888\pi\)
0.956610 0.291372i \(-0.0941117\pi\)
\(308\) 203531.i 0.122252i
\(309\) 1.15057e6 0.685517
\(310\) −194988. + 514945.i −0.115240 + 0.304338i
\(311\) 645247. 0.378290 0.189145 0.981949i \(-0.439428\pi\)
0.189145 + 0.981949i \(0.439428\pi\)
\(312\) 1.93782e6i 1.12701i
\(313\) 3.21424e6i 1.85446i −0.374495 0.927229i \(-0.622184\pi\)
0.374495 0.927229i \(-0.377816\pi\)
\(314\) −1.21051e6 −0.692860
\(315\) 35120.6 92750.1i 0.0199428 0.0526669i
\(316\) −129283. −0.0728321
\(317\) 1.59691e6i 0.892552i −0.894895 0.446276i \(-0.852750\pi\)
0.894895 0.446276i \(-0.147250\pi\)
\(318\) 2.18383e6i 1.21102i
\(319\) −110301. −0.0606882
\(320\) 1.54765e6 + 586031.i 0.844886 + 0.319923i
\(321\) 474629. 0.257094
\(322\) 1.09247e6i 0.587178i
\(323\) 1.85523e6i 0.989445i
\(324\) −503867. −0.266657
\(325\) −953775. + 1.07884e6i −0.500885 + 0.566561i
\(326\) 3.35987e6 1.75097
\(327\) 2.10295e6i 1.08758i
\(328\) 4.07089e6i 2.08932i
\(329\) 203439. 0.103620
\(330\) 593835. + 224861.i 0.300180 + 0.113666i
\(331\) 1.89235e6 0.949363 0.474682 0.880158i \(-0.342563\pi\)
0.474682 + 0.880158i \(0.342563\pi\)
\(332\) 598885.i 0.298194i
\(333\) 1.03886e6i 0.513389i
\(334\) −4.54107e6 −2.22737
\(335\) −1.14629e6 + 3.02723e6i −0.558060 + 1.47378i
\(336\) 476315. 0.230169
\(337\) 1.58818e6i 0.761772i −0.924622 0.380886i \(-0.875619\pi\)
0.924622 0.380886i \(-0.124381\pi\)
\(338\) 1.65804e6i 0.789410i
\(339\) 329719. 0.155828
\(340\) 3.52496e6 9.30906e6i 1.65370 4.36726i
\(341\) −114264. −0.0532136
\(342\) 676022.i 0.312533i
\(343\) 725734.i 0.333075i
\(344\) −9.58110e6 −4.36535
\(345\) 2.24995e6 + 851962.i 1.01771 + 0.385365i
\(346\) 7.30474e6 3.28031
\(347\) 1.31246e6i 0.585141i 0.956244 + 0.292571i \(0.0945107\pi\)
−0.956244 + 0.292571i \(0.905489\pi\)
\(348\) 630063.i 0.278892i
\(349\) 3.90078e6 1.71430 0.857151 0.515065i \(-0.172232\pi\)
0.857151 + 0.515065i \(0.172232\pi\)
\(350\) 534878. + 472874.i 0.233391 + 0.206336i
\(351\) 335921. 0.145536
\(352\) 1.24039e6i 0.533581i
\(353\) 3.32103e6i 1.41852i 0.704946 + 0.709261i \(0.250971\pi\)
−0.704946 + 0.709261i \(0.749029\pi\)
\(354\) 1.94573e6 0.825228
\(355\) −2.00556e6 759424.i −0.844628 0.319826i
\(356\) −6.38024e6 −2.66816
\(357\) 457060.i 0.189803i
\(358\) 2.38018e6i 0.981527i
\(359\) −2.37759e6 −0.973647 −0.486823 0.873500i \(-0.661845\pi\)
−0.486823 + 0.873500i \(0.661845\pi\)
\(360\) 749243. 1.97868e6i 0.304696 0.804671i
\(361\) −1.83587e6 −0.741438
\(362\) 5.33627e6i 2.14026i
\(363\) 131769.i 0.0524864i
\(364\) −775096. −0.306621
\(365\) 166911. 440796.i 0.0655773 0.173183i
\(366\) 622011. 0.242714
\(367\) 3.52479e6i 1.36605i 0.730393 + 0.683027i \(0.239337\pi\)
−0.730393 + 0.683027i \(0.760663\pi\)
\(368\) 1.15545e7i 4.44768i
\(369\) −705690. −0.269804
\(370\) −6.99376e6 2.64825e6i −2.65587 1.00567i
\(371\) 509528. 0.192191
\(372\) 652696.i 0.244542i
\(373\) 3.82557e6i 1.42372i −0.702322 0.711859i \(-0.747853\pi\)
0.702322 0.711859i \(-0.252147\pi\)
\(374\) 2.92634e6 1.08180
\(375\) 1.39101e6 732813.i 0.510801 0.269101i
\(376\) 4.34005e6 1.58316
\(377\) 420054.i 0.152213i
\(378\) 166547.i 0.0599525i
\(379\) −3.70497e6 −1.32491 −0.662456 0.749101i \(-0.730486\pi\)
−0.662456 + 0.749101i \(0.730486\pi\)
\(380\) −3.21249e6 1.21644e6i −1.14126 0.432146i
\(381\) 2.31200e6 0.815972
\(382\) 8.37733e6i 2.93729i
\(383\) 789569.i 0.275038i −0.990499 0.137519i \(-0.956087\pi\)
0.990499 0.137519i \(-0.0439129\pi\)
\(384\) −173283. −0.0599691
\(385\) −52464.1 + 138553.i −0.0180389 + 0.0476390i
\(386\) 6.03627e6 2.06206
\(387\) 1.66089e6i 0.563719i
\(388\) 1.12727e6i 0.380145i
\(389\) 4.73042e6 1.58499 0.792494 0.609879i \(-0.208782\pi\)
0.792494 + 0.609879i \(0.208782\pi\)
\(390\) −856324. + 2.26147e6i −0.285087 + 0.752886i
\(391\) 1.10875e7 3.66767
\(392\) 7.62911e6i 2.50760i
\(393\) 985575.i 0.321891i
\(394\) 2.90549e6 0.942928
\(395\) −88008.4 33325.1i −0.0283812 0.0107468i
\(396\) 752690. 0.241200
\(397\) 2.42880e6i 0.773421i 0.922201 + 0.386711i \(0.126389\pi\)
−0.922201 + 0.386711i \(0.873611\pi\)
\(398\) 8.79957e6i 2.78454i
\(399\) −157728. −0.0495995
\(400\) 5.65715e6 + 5.00136e6i 1.76786 + 1.56293i
\(401\) 276251. 0.0857914 0.0428957 0.999080i \(-0.486342\pi\)
0.0428957 + 0.999080i \(0.486342\pi\)
\(402\) 5.43585e6i 1.67765i
\(403\) 435144.i 0.133466i
\(404\) 1.47282e6 0.448949
\(405\) −343004. 129881.i −0.103911 0.0393468i
\(406\) −208259. −0.0627032
\(407\) 1.55188e6i 0.464378i
\(408\) 9.75066e6i 2.89990i
\(409\) 563175. 0.166470 0.0832349 0.996530i \(-0.473475\pi\)
0.0832349 + 0.996530i \(0.473475\pi\)
\(410\) 1.79893e6 4.75081e6i 0.528513 1.39575i
\(411\) 1.34913e6 0.393958
\(412\) 9.81787e6i 2.84954i
\(413\) 453974.i 0.130965i
\(414\) 4.04012e6 1.15849
\(415\) 154374. 407687.i 0.0440002 0.116200i
\(416\) −4.72369e6 −1.33828
\(417\) 1.01926e6i 0.287040i
\(418\) 1.00986e6i 0.282696i
\(419\) −707010. −0.196739 −0.0983695 0.995150i \(-0.531363\pi\)
−0.0983695 + 0.995150i \(0.531363\pi\)
\(420\) 791439. + 299685.i 0.218924 + 0.0828976i
\(421\) 4.56766e6 1.25600 0.627999 0.778214i \(-0.283874\pi\)
0.627999 + 0.778214i \(0.283874\pi\)
\(422\) 507077.i 0.138609i
\(423\) 752349.i 0.204441i
\(424\) 1.08700e7 2.93639
\(425\) 4.79918e6 5.42846e6i 1.28883 1.45782i
\(426\) −3.60130e6 −0.961468
\(427\) 145127.i 0.0385192i
\(428\) 4.05003e6i 1.06868i
\(429\) −501808. −0.131642
\(430\) −1.11813e7 4.23390e6i −2.91623 1.10426i
\(431\) 6.16454e6 1.59848 0.799241 0.601011i \(-0.205235\pi\)
0.799241 + 0.601011i \(0.205235\pi\)
\(432\) 1.76149e6i 0.454120i
\(433\) 2.94520e6i 0.754910i −0.926028 0.377455i \(-0.876799\pi\)
0.926028 0.377455i \(-0.123201\pi\)
\(434\) −215741. −0.0549804
\(435\) −162411. + 428911.i −0.0411521 + 0.108679i
\(436\) −1.79446e7 −4.52081
\(437\) 3.82620e6i 0.958438i
\(438\) 791517.i 0.197140i
\(439\) 5.90123e6 1.46144 0.730720 0.682677i \(-0.239184\pi\)
0.730720 + 0.682677i \(0.239184\pi\)
\(440\) −1.11924e6 + 2.95580e6i −0.275608 + 0.727853i
\(441\) −1.32251e6 −0.323819
\(442\) 1.11442e7i 2.71328i
\(443\) 4.58354e6i 1.10966i 0.831963 + 0.554832i \(0.187217\pi\)
−0.831963 + 0.554832i \(0.812783\pi\)
\(444\) −8.86463e6 −2.13404
\(445\) −4.34331e6 1.64463e6i −1.03973 0.393703i
\(446\) −4.94019e6 −1.17600
\(447\) 556271.i 0.131679i
\(448\) 648401.i 0.152633i
\(449\) −6.61995e6 −1.54967 −0.774834 0.632164i \(-0.782167\pi\)
−0.774834 + 0.632164i \(0.782167\pi\)
\(450\) 1.74876e6 1.97806e6i 0.407098 0.460477i
\(451\) 1.05418e6 0.244047
\(452\) 2.81350e6i 0.647741i
\(453\) 2.31101e6i 0.529122i
\(454\) 8.00854e6 1.82353
\(455\) −527642. 199796.i −0.119484 0.0452437i
\(456\) −3.36488e6 −0.757805
\(457\) 6.37429e6i 1.42771i 0.700292 + 0.713857i \(0.253053\pi\)
−0.700292 + 0.713857i \(0.746947\pi\)
\(458\) 6.05143e6i 1.34801i
\(459\) −1.69028e6 −0.374478
\(460\) −7.26982e6 + 1.91989e7i −1.60188 + 4.23040i
\(461\) −5.36939e6 −1.17672 −0.588359 0.808600i \(-0.700226\pi\)
−0.588359 + 0.808600i \(0.700226\pi\)
\(462\) 248792.i 0.0542290i
\(463\) 7.13889e6i 1.54767i 0.633387 + 0.773835i \(0.281664\pi\)
−0.633387 + 0.773835i \(0.718336\pi\)
\(464\) −2.20266e6 −0.474955
\(465\) −168245. + 444319.i −0.0360836 + 0.0952933i
\(466\) −3.11523e6 −0.664547
\(467\) 5.11617e6i 1.08556i 0.839876 + 0.542779i \(0.182628\pi\)
−0.839876 + 0.542779i \(0.817372\pi\)
\(468\) 2.86642e6i 0.604959i
\(469\) −1.26828e6 −0.266246
\(470\) 5.06492e6 + 1.91787e6i 1.05762 + 0.400475i
\(471\) −1.04449e6 −0.216946
\(472\) 9.68481e6i 2.00095i
\(473\) 2.48108e6i 0.509903i
\(474\) −158033. −0.0323073
\(475\) −1.87332e6 1.65616e6i −0.380959 0.336798i
\(476\) 3.90011e6 0.788968
\(477\) 1.88431e6i 0.379190i
\(478\) 3.38013e6i 0.676650i
\(479\) 715144. 0.142415 0.0712074 0.997462i \(-0.477315\pi\)
0.0712074 + 0.997462i \(0.477315\pi\)
\(480\) 4.82329e6 + 1.82638e6i 0.955522 + 0.361816i
\(481\) 5.90993e6 1.16471
\(482\) 7.09194e6i 1.39042i
\(483\) 942634.i 0.183855i
\(484\) −1.12439e6 −0.218174
\(485\) −290576. + 767383.i −0.0560926 + 0.148135i
\(486\) −615916. −0.118285
\(487\) 9.41305e6i 1.79849i −0.437445 0.899245i \(-0.644117\pi\)
0.437445 0.899245i \(-0.355883\pi\)
\(488\) 3.09605e6i 0.588515i
\(489\) 2.89906e6 0.548257
\(490\) 3.37132e6 8.90332e6i 0.634321 1.67518i
\(491\) −2.03825e6 −0.381551 −0.190776 0.981634i \(-0.561100\pi\)
−0.190776 + 0.981634i \(0.561100\pi\)
\(492\) 6.02167e6i 1.12151i
\(493\) 2.11362e6i 0.391660i
\(494\) 3.84579e6 0.709036
\(495\) 512389. + 194020.i 0.0939911 + 0.0355905i
\(496\) −2.28179e6 −0.416458
\(497\) 840248.i 0.152587i
\(498\) 732065.i 0.132274i
\(499\) 2.29272e6 0.412192 0.206096 0.978532i \(-0.433924\pi\)
0.206096 + 0.978532i \(0.433924\pi\)
\(500\) 6.25311e6 + 1.18695e7i 1.11859 + 2.12329i
\(501\) −3.91825e6 −0.697425
\(502\) 1.86115e7i 3.29626i
\(503\) 6.36926e6i 1.12246i 0.827661 + 0.561228i \(0.189671\pi\)
−0.827661 + 0.561228i \(0.810329\pi\)
\(504\) 828983. 0.145368
\(505\) 1.00262e6 + 379649.i 0.174947 + 0.0662451i
\(506\) −6.03525e6 −1.04790
\(507\) 1.43063e6i 0.247177i
\(508\) 1.97284e7i 3.39181i
\(509\) 5.66660e6 0.969456 0.484728 0.874665i \(-0.338919\pi\)
0.484728 + 0.874665i \(0.338919\pi\)
\(510\) 4.30883e6 1.13792e7i 0.733558 1.93725i
\(511\) 184675. 0.0312864
\(512\) 1.13597e7i 1.91510i
\(513\) 583303.i 0.0978590i
\(514\) −9.29442e6 −1.55172
\(515\) −2.53075e6 + 6.68345e6i −0.420466 + 1.11041i
\(516\) −1.41724e7 −2.34325
\(517\) 1.12388e6i 0.184924i
\(518\) 2.93009e6i 0.479796i
\(519\) 6.30287e6 1.02712
\(520\) −1.12564e7 4.26233e6i −1.82554 0.691256i
\(521\) 6.07157e6 0.979956 0.489978 0.871735i \(-0.337005\pi\)
0.489978 + 0.871735i \(0.337005\pi\)
\(522\) 770175.i 0.123712i
\(523\) 2.50083e6i 0.399789i −0.979817 0.199894i \(-0.935940\pi\)
0.979817 0.199894i \(-0.0640599\pi\)
\(524\) 8.40994e6 1.33803
\(525\) 461517. + 408018.i 0.0730785 + 0.0646072i
\(526\) 1.33361e7 2.10167
\(527\) 2.18954e6i 0.343421i
\(528\) 2.63136e6i 0.410767i
\(529\) −1.64302e7 −2.55273
\(530\) 1.26855e7 + 4.80346e6i 1.96163 + 0.742787i
\(531\) 1.67886e6 0.258392
\(532\) 1.34590e6i 0.206174i
\(533\) 4.01457e6i 0.612098i
\(534\) −7.79907e6 −1.18356
\(535\) −1.04397e6 + 2.75703e6i −0.157690 + 0.416444i
\(536\) −2.70568e7 −4.06784
\(537\) 2.05373e6i 0.307332i
\(538\) 4.73842e6i 0.705794i
\(539\) 1.97560e6 0.292905
\(540\) 1.10828e6 2.92686e6i 0.163556 0.431935i
\(541\) 2.70948e6 0.398009 0.199004 0.979999i \(-0.436229\pi\)
0.199004 + 0.979999i \(0.436229\pi\)
\(542\) 2.11511e7i 3.09268i
\(543\) 4.60438e6i 0.670149i
\(544\) 2.37686e7 3.44354
\(545\) −1.22156e7 4.62556e6i −1.76167 0.667072i
\(546\) −947461. −0.136013
\(547\) 9.99302e6i 1.42800i −0.700145 0.714000i \(-0.746881\pi\)
0.700145 0.714000i \(-0.253119\pi\)
\(548\) 1.15122e7i 1.63759i
\(549\) 536700. 0.0759978
\(550\) −2.61235e6 + 2.95488e6i −0.368234 + 0.416517i
\(551\) 729394. 0.102349
\(552\) 2.01096e7i 2.80903i
\(553\) 36871.9i 0.00512722i
\(554\) 1.33134e7 1.84296
\(555\) −6.03454e6 2.28503e6i −0.831595 0.314891i
\(556\) −8.69734e6 −1.19316
\(557\) 2.85519e6i 0.389940i 0.980809 + 0.194970i \(0.0624609\pi\)
−0.980809 + 0.194970i \(0.937539\pi\)
\(558\) 797842.i 0.108475i
\(559\) 9.44854e6 1.27890
\(560\) −1.04768e6 + 2.76682e6i −0.141175 + 0.372830i
\(561\) 2.52499e6 0.338729
\(562\) 1.06583e7i 1.42347i
\(563\) 8.74359e6i 1.16257i −0.813700 0.581285i \(-0.802550\pi\)
0.813700 0.581285i \(-0.197450\pi\)
\(564\) 6.41981e6 0.849815
\(565\) −725235. + 1.91527e6i −0.0955779 + 0.252412i
\(566\) 785832. 0.103107
\(567\) 143704.i 0.0187721i
\(568\) 1.79254e7i 2.33129i
\(569\) −4.89251e6 −0.633507 −0.316753 0.948508i \(-0.602593\pi\)
−0.316753 + 0.948508i \(0.602593\pi\)
\(570\) −3.92688e6 1.48695e6i −0.506245 0.191694i
\(571\) 1.65650e6 0.212619 0.106310 0.994333i \(-0.466097\pi\)
0.106310 + 0.994333i \(0.466097\pi\)
\(572\) 4.28194e6i 0.547206i
\(573\) 7.22835e6i 0.919714i
\(574\) 1.99039e6 0.252150
\(575\) −9.89776e6 + 1.11956e7i −1.24844 + 1.41214i
\(576\) 2.39789e6 0.301143
\(577\) 1.33417e7i 1.66829i −0.551547 0.834144i \(-0.685962\pi\)
0.551547 0.834144i \(-0.314038\pi\)
\(578\) 4.12653e7i 5.13766i
\(579\) 5.20837e6 0.645663
\(580\) −3.65991e6 1.38586e6i −0.451753 0.171060i
\(581\) 170804. 0.0209922
\(582\) 1.37795e6i 0.168627i
\(583\) 2.81484e6i 0.342990i
\(584\) 3.93975e6 0.478010
\(585\) −738876. + 1.95130e6i −0.0892652 + 0.235741i
\(586\) −6.89874e6 −0.829900
\(587\) 3.82733e6i 0.458460i −0.973372 0.229230i \(-0.926379\pi\)
0.973372 0.229230i \(-0.0736207\pi\)
\(588\) 1.12850e7i 1.34604i
\(589\) 755596. 0.0897432
\(590\) −4.27973e6 + 1.13024e7i −0.506159 + 1.33672i
\(591\) 2.50699e6 0.295246
\(592\) 3.09902e7i 3.63430i
\(593\) 3.31931e6i 0.387625i 0.981039 + 0.193812i \(0.0620853\pi\)
−0.981039 + 0.193812i \(0.937915\pi\)
\(594\) 920072. 0.106993
\(595\) 2.65497e6 + 1.00533e6i 0.307445 + 0.116417i
\(596\) −4.74668e6 −0.547362
\(597\) 7.59268e6i 0.871885i
\(598\) 2.29837e7i 2.62825i
\(599\) 7.82165e6 0.890699 0.445350 0.895357i \(-0.353079\pi\)
0.445350 + 0.895357i \(0.353079\pi\)
\(600\) 9.84574e6 + 8.70441e6i 1.11653 + 0.987100i
\(601\) 1.52108e7 1.71778 0.858889 0.512162i \(-0.171155\pi\)
0.858889 + 0.512162i \(0.171155\pi\)
\(602\) 4.68451e6i 0.526833i
\(603\) 4.69030e6i 0.525300i
\(604\) 1.97199e7 2.19944
\(605\) −765420. 289833.i −0.0850181 0.0321928i
\(606\) 1.80035e6 0.199148
\(607\) 1.34079e7i 1.47703i 0.674236 + 0.738516i \(0.264473\pi\)
−0.674236 + 0.738516i \(0.735527\pi\)
\(608\) 8.20235e6i 0.899870i
\(609\) −179696. −0.0196334
\(610\) −1.36815e6 + 3.61314e6i −0.148870 + 0.393152i
\(611\) −4.28000e6 −0.463811
\(612\) 1.44232e7i 1.55662i
\(613\) 1.15459e7i 1.24102i 0.784199 + 0.620509i \(0.213074\pi\)
−0.784199 + 0.620509i \(0.786926\pi\)
\(614\) 1.00377e7 1.07451
\(615\) 1.55220e6 4.09922e6i 0.165486 0.437032i
\(616\) −1.23836e6 −0.131490
\(617\) 1.07188e7i 1.13353i 0.823881 + 0.566763i \(0.191805\pi\)
−0.823881 + 0.566763i \(0.808195\pi\)
\(618\) 1.20012e7i 1.26401i
\(619\) −8.11579e6 −0.851342 −0.425671 0.904878i \(-0.639962\pi\)
−0.425671 + 0.904878i \(0.639962\pi\)
\(620\) −3.79138e6 1.43564e6i −0.396113 0.149991i
\(621\) 3.48601e6 0.362743
\(622\) 6.73031e6i 0.697524i
\(623\) 1.81966e6i 0.187833i
\(624\) −1.00208e7 −1.03025
\(625\) 1.19717e6 + 9.69197e6i 0.122590 + 0.992457i
\(626\) 3.35264e7 3.41941
\(627\) 871354.i 0.0885168i
\(628\) 8.91264e6i 0.901793i
\(629\) −2.97374e7 −2.99693
\(630\) 967438. + 366329.i 0.0971118 + 0.0367722i
\(631\) 1.00476e7 1.00459 0.502295 0.864696i \(-0.332489\pi\)
0.502295 + 0.864696i \(0.332489\pi\)
\(632\) 786603.i 0.0783362i
\(633\) 437529.i 0.0434008i
\(634\) 1.66568e7 1.64576
\(635\) −5.08537e6 + 1.34299e7i −0.500481 + 1.32172i
\(636\) 1.60789e7 1.57621
\(637\) 7.52356e6i 0.734640i
\(638\) 1.15051e6i 0.111902i
\(639\) −3.10737e6 −0.301051
\(640\) 381145. 1.00657e6i 0.0367824 0.0971387i
\(641\) −1.25041e6 −0.120200 −0.0601002 0.998192i \(-0.519142\pi\)
−0.0601002 + 0.998192i \(0.519142\pi\)
\(642\) 4.95067e6i 0.474052i
\(643\) 1.68108e7i 1.60347i 0.597681 + 0.801734i \(0.296089\pi\)
−0.597681 + 0.801734i \(0.703911\pi\)
\(644\) −8.04353e6 −0.764244
\(645\) −9.64776e6 3.65321e6i −0.913119 0.345760i
\(646\) −1.93511e7 −1.82442
\(647\) 1.96602e6i 0.184640i −0.995729 0.0923202i \(-0.970572\pi\)
0.995729 0.0923202i \(-0.0294283\pi\)
\(648\) 3.06571e6i 0.286809i
\(649\) −2.50793e6 −0.233725
\(650\) −1.12529e7 9.94844e6i −1.04467 0.923574i
\(651\) −186151. −0.0172152
\(652\) 2.47377e7i 2.27898i
\(653\) 2.26355e6i 0.207734i −0.994591 0.103867i \(-0.966878\pi\)
0.994591 0.103867i \(-0.0331216\pi\)
\(654\) −2.19350e7 −2.00537
\(655\) 5.72501e6 + 2.16782e6i 0.521402 + 0.197434i
\(656\) 2.10514e7 1.90995
\(657\) 682957.i 0.0617277i
\(658\) 2.12199e6i 0.191064i
\(659\) 4.02181e6 0.360752 0.180376 0.983598i \(-0.442269\pi\)
0.180376 + 0.983598i \(0.442269\pi\)
\(660\) −1.65558e6 + 4.37223e6i −0.147942 + 0.390700i
\(661\) −1.60875e7 −1.43214 −0.716071 0.698027i \(-0.754061\pi\)
−0.716071 + 0.698027i \(0.754061\pi\)
\(662\) 1.97384e7i 1.75052i
\(663\) 9.61575e6i 0.849570i
\(664\) 3.64383e6 0.320729
\(665\) 346932. 916212.i 0.0304221 0.0803419i
\(666\) −1.08359e7 −0.946631
\(667\) 4.35909e6i 0.379386i
\(668\) 3.34345e7i 2.89904i
\(669\) −4.26262e6 −0.368224
\(670\) −3.15758e7 1.19564e7i −2.71748 1.02900i
\(671\) −801738. −0.0687426
\(672\) 2.02076e6i 0.172620i
\(673\) 5.69741e6i 0.484886i 0.970166 + 0.242443i \(0.0779487\pi\)
−0.970166 + 0.242443i \(0.922051\pi\)
\(674\) 1.65657e7 1.40462
\(675\) 1.50891e6 1.70676e6i 0.127469 0.144183i
\(676\) −1.22076e7 −1.02746
\(677\) 2.57893e6i 0.216256i 0.994137 + 0.108128i \(0.0344856\pi\)
−0.994137 + 0.108128i \(0.965514\pi\)
\(678\) 3.43917e6i 0.287329i
\(679\) −321501. −0.0267614
\(680\) 5.66397e7 + 2.14471e7i 4.69730 + 1.77867i
\(681\) 6.91014e6 0.570978
\(682\) 1.19184e6i 0.0981197i
\(683\) 1.28680e7i 1.05550i −0.849400 0.527750i \(-0.823036\pi\)
0.849400 0.527750i \(-0.176964\pi\)
\(684\) −4.97734e6 −0.406778
\(685\) −2.96749e6 + 7.83684e6i −0.241636 + 0.638138i
\(686\) 7.56983e6 0.614152
\(687\) 5.22146e6i 0.422085i
\(688\) 4.95458e7i 3.99058i
\(689\) −1.07196e7 −0.860259
\(690\) −8.88647e6 + 2.34683e7i −0.710570 + 1.87654i
\(691\) −3.61306e6 −0.287859 −0.143930 0.989588i \(-0.545974\pi\)
−0.143930 + 0.989588i \(0.545974\pi\)
\(692\) 5.37826e7i 4.26949i
\(693\) 214670.i 0.0169800i
\(694\) −1.36897e7 −1.07893
\(695\) −5.92066e6 2.24191e6i −0.464952 0.176058i
\(696\) −3.83353e6 −0.299968
\(697\) 2.02004e7i 1.57499i
\(698\) 4.06874e7i 3.16098i
\(699\) −2.68797e6 −0.208080
\(700\) −3.48163e6 + 3.93814e6i −0.268557 + 0.303771i
\(701\) 1.60588e7 1.23429 0.617147 0.786848i \(-0.288288\pi\)
0.617147 + 0.786848i \(0.288288\pi\)
\(702\) 3.50386e6i 0.268351i
\(703\) 1.02622e7i 0.783161i
\(704\) −3.58203e6 −0.272394
\(705\) 4.37025e6 + 1.65483e6i 0.331156 + 0.125395i
\(706\) −3.46403e7 −2.61559
\(707\) 420054.i 0.0316051i
\(708\) 1.43258e7i 1.07408i
\(709\) 6.79151e6 0.507400 0.253700 0.967283i \(-0.418352\pi\)
0.253700 + 0.967283i \(0.418352\pi\)
\(710\) 7.92124e6 2.09192e7i 0.589722 1.55740i
\(711\) −136358. −0.0101159
\(712\) 3.88197e7i 2.86980i
\(713\) 4.51568e6i 0.332659i
\(714\) 4.76741e6 0.349975
\(715\) 1.10375e6 2.91490e6i 0.0807434 0.213235i
\(716\) 1.75245e7 1.27751
\(717\) 2.91654e6i 0.211870i
\(718\) 2.47997e7i 1.79529i
\(719\) −9.17382e6 −0.661802 −0.330901 0.943666i \(-0.607353\pi\)
−0.330901 + 0.943666i \(0.607353\pi\)
\(720\) 1.02321e7 + 3.87449e6i 0.735589 + 0.278537i
\(721\) −2.80009e6 −0.200601
\(722\) 1.91492e7i 1.36713i
\(723\) 6.11925e6i 0.435364i
\(724\) −3.92893e7 −2.78566
\(725\) −2.13423e6 1.88683e6i −0.150798 0.133317i
\(726\) −1.37443e6 −0.0967789
\(727\) 1.19986e7i 0.841966i 0.907069 + 0.420983i \(0.138315\pi\)
−0.907069 + 0.420983i \(0.861685\pi\)
\(728\) 4.71596e6i 0.329793i
\(729\) −531441. −0.0370370
\(730\) 4.59776e6 + 1.74098e6i 0.319330 + 0.120917i
\(731\) −4.75429e7 −3.29073
\(732\) 4.57968e6i 0.315906i
\(733\) 3.87027e6i 0.266061i −0.991112 0.133031i \(-0.957529\pi\)
0.991112 0.133031i \(-0.0424709\pi\)
\(734\) −3.67657e7 −2.51885
\(735\) 2.90893e6 7.68219e6i 0.198616 0.524526i
\(736\) −4.90199e7 −3.33563
\(737\) 7.00650e6i 0.475152i
\(738\) 7.36077e6i 0.497487i
\(739\) 1.26699e7 0.853416 0.426708 0.904390i \(-0.359673\pi\)
0.426708 + 0.904390i \(0.359673\pi\)
\(740\) 1.94982e7 5.14929e7i 1.30893 3.45675i
\(741\) 3.31832e6 0.222010
\(742\) 5.31468e6i 0.354378i
\(743\) 1.07430e7i 0.713929i 0.934118 + 0.356965i \(0.116188\pi\)
−0.934118 + 0.356965i \(0.883812\pi\)
\(744\) −3.97124e6 −0.263023
\(745\) −3.23127e6 1.22355e6i −0.213296 0.0807664i
\(746\) 3.99030e7 2.62517
\(747\) 631659.i 0.0414173i
\(748\) 2.15458e7i 1.40802i
\(749\) −1.15508e6 −0.0752329
\(750\) 7.64367e6 + 1.45091e7i 0.496191 + 0.941859i
\(751\) −1.60278e7 −1.03699 −0.518493 0.855082i \(-0.673507\pi\)
−0.518493 + 0.855082i \(0.673507\pi\)
\(752\) 2.24433e7i 1.44724i
\(753\) 1.60589e7i 1.03211i
\(754\) 4.38141e6 0.280663
\(755\) 1.34242e7 + 5.08318e6i 0.857078 + 0.324540i
\(756\) 1.22623e6 0.0780313
\(757\) 2.27246e7i 1.44131i −0.693294 0.720654i \(-0.743841\pi\)
0.693294 0.720654i \(-0.256159\pi\)
\(758\) 3.86451e7i 2.44299i
\(759\) −5.20749e6 −0.328114
\(760\) 7.40124e6 1.95459e7i 0.464804 1.22750i
\(761\) 1.62869e7 1.01948 0.509738 0.860330i \(-0.329742\pi\)
0.509738 + 0.860330i \(0.329742\pi\)
\(762\) 2.41155e7i 1.50456i
\(763\) 5.11784e6i 0.318255i
\(764\) 6.16797e7 3.82304
\(765\) 3.71786e6 9.81850e6i 0.229689 0.606585i
\(766\) 8.23568e6 0.507139
\(767\) 9.55081e6i 0.586208i
\(768\) 1.03333e7i 0.632171i
\(769\) −8.82491e6 −0.538139 −0.269069 0.963121i \(-0.586716\pi\)
−0.269069 + 0.963121i \(0.586716\pi\)
\(770\) −1.44519e6 547232.i −0.0878409 0.0332617i
\(771\) −8.01966e6 −0.485870
\(772\) 4.44432e7i 2.68387i
\(773\) 2.36592e7i 1.42413i −0.702111 0.712067i \(-0.747759\pi\)
0.702111 0.712067i \(-0.252241\pi\)
\(774\) −1.73240e7 −1.03943
\(775\) −2.21090e6 1.95461e6i −0.132225 0.116897i
\(776\) −6.85872e6 −0.408873
\(777\) 2.52822e6i 0.150232i
\(778\) 4.93411e7i 2.92254i
\(779\) −6.97101e6 −0.411578
\(780\) −1.66505e7 6.30485e6i −0.979920 0.371055i
\(781\) 4.64187e6 0.272311
\(782\) 1.15649e8i 6.76276i
\(783\) 664543.i 0.0387363i
\(784\) 3.94517e7 2.29232
\(785\) 2.29740e6 6.06722e6i 0.133065 0.351411i
\(786\) 1.02801e7 0.593529
\(787\) 1.96332e7i 1.12994i 0.825112 + 0.564969i \(0.191112\pi\)
−0.825112 + 0.564969i \(0.808888\pi\)
\(788\) 2.13922e7i 1.22727i
\(789\) 1.15070e7 0.658066
\(790\) 347601. 917980.i 0.0198159 0.0523318i
\(791\) −802420. −0.0455995
\(792\) 4.57963e6i 0.259429i
\(793\) 3.05321e6i 0.172414i
\(794\) −2.53339e7 −1.42610
\(795\) 1.09456e7 + 4.14464e6i 0.614217 + 0.232578i
\(796\) 6.47885e7 3.62423
\(797\) 2.52639e7i 1.40882i −0.709795 0.704408i \(-0.751212\pi\)
0.709795 0.704408i \(-0.248788\pi\)
\(798\) 1.64520e6i 0.0914557i
\(799\) 2.15360e7 1.19343
\(800\) −2.12182e7 + 2.40003e7i −1.17215 + 1.32584i
\(801\) −6.72940e6 −0.370591
\(802\) 2.88147e6i 0.158189i
\(803\) 1.02022e6i 0.0558348i
\(804\) −4.00225e7 −2.18355
\(805\) −5.47558e6 2.07337e6i −0.297811 0.112769i
\(806\) 4.53880e6 0.246096
\(807\) 4.08853e6i 0.220995i
\(808\) 8.96119e6i 0.482878i
\(809\) 1.60088e6 0.0859978 0.0429989 0.999075i \(-0.486309\pi\)
0.0429989 + 0.999075i \(0.486309\pi\)
\(810\) 1.35474e6 3.57774e6i 0.0725510 0.191600i
\(811\) −1.70463e7 −0.910079 −0.455040 0.890471i \(-0.650375\pi\)
−0.455040 + 0.890471i \(0.650375\pi\)
\(812\) 1.53335e6i 0.0816115i
\(813\) 1.82502e7i 0.968369i
\(814\) 1.61870e7 0.856260
\(815\) −6.37663e6 + 1.68400e7i −0.336277 + 0.888074i
\(816\) 5.04227e7 2.65094
\(817\) 1.64067e7i 0.859937i
\(818\) 5.87425e6i 0.306951i
\(819\) −817513. −0.0425878
\(820\) 3.49787e7 + 1.32450e7i 1.81664 + 0.687887i
\(821\) 1.11036e7 0.574919 0.287459 0.957793i \(-0.407189\pi\)
0.287459 + 0.957793i \(0.407189\pi\)
\(822\) 1.40722e7i 0.726413i
\(823\) 1.15634e7i 0.595097i −0.954707 0.297548i \(-0.903831\pi\)
0.954707 0.297548i \(-0.0961690\pi\)
\(824\) −5.97355e7 −3.06488
\(825\) −2.25405e6 + 2.54961e6i −0.115300 + 0.130418i
\(826\) −4.73522e6 −0.241485
\(827\) 3.02353e7i 1.53727i −0.639686 0.768636i \(-0.720936\pi\)
0.639686 0.768636i \(-0.279064\pi\)
\(828\) 2.97462e7i 1.50784i
\(829\) 1.68978e7 0.853974 0.426987 0.904258i \(-0.359575\pi\)
0.426987 + 0.904258i \(0.359575\pi\)
\(830\) 4.25242e6 + 1.61022e6i 0.214260 + 0.0811314i
\(831\) 1.14874e7 0.577060
\(832\) 1.36412e7i 0.683196i
\(833\) 3.78569e7i 1.89031i
\(834\) −1.06314e7 −0.529270
\(835\) 8.61839e6 2.27603e7i 0.427770 1.12970i
\(836\) 7.43529e6 0.367944
\(837\) 688415.i 0.0339654i
\(838\) 7.37454e6i 0.362764i
\(839\) 6.03413e6 0.295944 0.147972 0.988992i \(-0.452725\pi\)
0.147972 + 0.988992i \(0.452725\pi\)
\(840\) −1.82339e6 + 4.81540e6i −0.0891624 + 0.235469i
\(841\) −1.96802e7 −0.959486
\(842\) 4.76434e7i 2.31592i
\(843\) 9.19650e6i 0.445711i
\(844\) −3.73345e6 −0.180407
\(845\) −8.31026e6 3.14675e6i −0.400380 0.151607i
\(846\) 7.84744e6 0.376966
\(847\) 320679.i 0.0153590i
\(848\) 5.62108e7i 2.68429i
\(849\) 678053. 0.0322845
\(850\) 5.66221e7 + 5.00583e7i 2.68806 + 2.37645i
\(851\) 6.13300e7 2.90301
\(852\) 2.65152e7i 1.25140i
\(853\) 2.44547e7i 1.15077i 0.817882 + 0.575386i \(0.195148\pi\)
−0.817882 + 0.575386i \(0.804852\pi\)
\(854\) −1.51376e6 −0.0710250
\(855\) −3.38829e6 1.28301e6i −0.158513 0.0600224i
\(856\) −2.46418e7 −1.14945
\(857\) 9.19253e6i 0.427546i 0.976883 + 0.213773i \(0.0685753\pi\)
−0.976883 + 0.213773i \(0.931425\pi\)
\(858\) 5.23415e6i 0.242733i
\(859\) 1.84087e7 0.851219 0.425610 0.904907i \(-0.360060\pi\)
0.425610 + 0.904907i \(0.360060\pi\)
\(860\) 3.11729e7 8.23246e7i 1.43725 3.79563i
\(861\) 1.71740e6 0.0789521
\(862\) 6.42999e7i 2.94742i
\(863\) 8.55693e6i 0.391103i 0.980693 + 0.195551i \(0.0626497\pi\)
−0.980693 + 0.195551i \(0.937350\pi\)
\(864\) 7.47308e6 0.340577
\(865\) −1.38635e7 + 3.66121e7i −0.629989 + 1.66374i
\(866\) 3.07202e7 1.39197
\(867\) 3.56056e7i 1.60868i
\(868\) 1.58843e6i 0.0715598i
\(869\) 203695. 0.00915021
\(870\) −4.47380e6 1.69404e6i −0.200391 0.0758798i
\(871\) 2.66824e7 1.19174
\(872\) 1.09181e8i 4.86246i
\(873\) 1.18896e6i 0.0527998i
\(874\) 3.99095e7 1.76725
\(875\) −3.38523e6 + 1.78341e6i −0.149475 + 0.0787464i
\(876\) 5.82769e6 0.256588
\(877\) 3.62307e7i 1.59066i −0.606177 0.795330i \(-0.707298\pi\)
0.606177 0.795330i \(-0.292702\pi\)
\(878\) 6.15533e7i 2.69473i
\(879\) −5.95255e6 −0.259855
\(880\) −1.52850e7 5.78781e6i −0.665365 0.251946i
\(881\) −2.54635e7 −1.10530 −0.552649 0.833414i \(-0.686383\pi\)
−0.552649 + 0.833414i \(0.686383\pi\)
\(882\) 1.37945e7i 0.597085i
\(883\) 1.25573e6i 0.0541995i −0.999633 0.0270998i \(-0.991373\pi\)
0.999633 0.0270998i \(-0.00862718\pi\)
\(884\) −8.20515e7 −3.53147
\(885\) −3.69275e6 + 9.75220e6i −0.158486 + 0.418547i
\(886\) −4.78090e7 −2.04609
\(887\) 2.38712e7i 1.01874i 0.860547 + 0.509371i \(0.170122\pi\)
−0.860547 + 0.509371i \(0.829878\pi\)
\(888\) 5.39356e7i 2.29532i
\(889\) −5.62659e6 −0.238776
\(890\) 1.71545e7 4.53033e7i 0.725943 1.91714i
\(891\) 793881. 0.0335013
\(892\) 3.63731e7i 1.53062i
\(893\) 7.43192e6i 0.311869i
\(894\) −5.80224e6 −0.242802
\(895\) 1.19297e7 + 4.51729e6i 0.497820 + 0.188504i
\(896\) 421709. 0.0175486
\(897\) 1.98314e7i 0.822947i
\(898\) 6.90500e7i 2.85741i
\(899\) 860832. 0.0355238
\(900\) 1.45639e7 + 1.28756e7i 0.599336 + 0.529860i
\(901\) 5.39385e7 2.21354
\(902\) 1.09957e7i 0.449994i
\(903\) 4.04201e6i 0.164960i
\(904\) −1.71184e7 −0.696692
\(905\) −2.67459e7 1.01276e7i −1.08552 0.411040i
\(906\) 2.41052e7 0.975640
\(907\) 1.51874e7i 0.613007i 0.951870 + 0.306504i \(0.0991591\pi\)
−0.951870 + 0.306504i \(0.900841\pi\)
\(908\) 5.89644e7i 2.37342i
\(909\) 1.55342e6 0.0623563
\(910\) 2.08399e6 5.50361e6i 0.0834242 0.220315i
\(911\) 2.87742e6 0.114870 0.0574352 0.998349i \(-0.481708\pi\)
0.0574352 + 0.998349i \(0.481708\pi\)
\(912\) 1.74005e7i 0.692746i
\(913\) 943590.i 0.0374633i
\(914\) −6.64876e7 −2.63254
\(915\) −1.18050e6 + 3.11759e6i −0.0466137 + 0.123102i
\(916\) 4.45549e7 1.75451
\(917\) 2.39854e6i 0.0941941i
\(918\) 1.76306e7i 0.690495i
\(919\) −3.83454e7 −1.49770 −0.748849 0.662741i \(-0.769393\pi\)
−0.748849 + 0.662741i \(0.769393\pi\)
\(920\) −1.16813e8 4.42322e7i −4.55010 1.72293i
\(921\) 8.66096e6 0.336447
\(922\) 5.60059e7i 2.16973i
\(923\) 1.76773e7i 0.682987i
\(924\) −1.83178e6 −0.0705820
\(925\) 2.65466e7 3.00274e7i 1.02013 1.15389i
\(926\) −7.44629e7 −2.85373
\(927\) 1.03552e7i 0.395783i
\(928\) 9.34474e6i 0.356203i
\(929\) −3.31484e7 −1.26015 −0.630077 0.776533i \(-0.716977\pi\)
−0.630077 + 0.776533i \(0.716977\pi\)
\(930\) −4.63451e6 1.75490e6i −0.175710 0.0665341i
\(931\) −1.30641e7 −0.493976
\(932\) 2.29365e7i 0.864943i
\(933\) 5.80722e6i 0.218406i
\(934\) −5.33647e7 −2.00164
\(935\) −5.55384e6 + 1.46671e7i −0.207761 + 0.548677i
\(936\) −1.74403e7 −0.650677
\(937\) 2.93312e7i 1.09139i −0.837984 0.545695i \(-0.816266\pi\)
0.837984 0.545695i \(-0.183734\pi\)
\(938\) 1.32289e7i 0.490928i
\(939\) 2.89281e7 1.07067
\(940\) −1.41207e7 + 3.72914e7i −0.521239 + 1.37654i
\(941\) −9.43943e6 −0.347513 −0.173757 0.984789i \(-0.555591\pi\)
−0.173757 + 0.984789i \(0.555591\pi\)
\(942\) 1.08946e7i 0.400023i
\(943\) 4.16610e7i 1.52563i
\(944\) −5.00821e7 −1.82917
\(945\) 834751. + 316086.i 0.0304073 + 0.0115140i
\(946\) 2.58791e7 0.940202
\(947\) 2.37783e7i 0.861601i −0.902447 0.430801i \(-0.858231\pi\)
0.902447 0.430801i \(-0.141769\pi\)
\(948\) 1.16355e6i 0.0420496i
\(949\) −3.88524e6 −0.140040
\(950\) 1.72748e7 1.95399e7i 0.621016 0.702445i
\(951\) 1.43722e7 0.515315
\(952\) 2.37297e7i 0.848592i
\(953\) 2.31442e7i 0.825488i −0.910847 0.412744i \(-0.864571\pi\)
0.910847 0.412744i \(-0.135429\pi\)
\(954\) 1.96545e7 0.699183
\(955\) 4.19881e7 + 1.58991e7i 1.48976 + 0.564112i
\(956\) 2.48869e7 0.880696
\(957\) 992712.i 0.0350383i
\(958\) 7.45938e6i 0.262597i
\(959\) −3.28331e6 −0.115283
\(960\) −5.27428e6 + 1.39289e7i −0.184708 + 0.487795i
\(961\) −2.77374e7 −0.968851
\(962\) 6.16440e7i 2.14760i
\(963\) 4.27167e6i 0.148433i
\(964\) 5.22158e7 1.80971
\(965\) −1.14561e7 + 3.02544e7i −0.396021 + 1.04585i
\(966\) −9.83223e6 −0.339008
\(967\) 7.71333e6i 0.265262i −0.991165 0.132631i \(-0.957657\pi\)
0.991165 0.132631i \(-0.0423426\pi\)
\(968\) 6.84118e6i 0.234662i
\(969\) −1.66971e7 −0.571256
\(970\) −8.00426e6 3.03088e6i −0.273144 0.103428i
\(971\) −4.66559e7 −1.58803 −0.794014 0.607899i \(-0.792012\pi\)
−0.794014 + 0.607899i \(0.792012\pi\)
\(972\) 4.53480e6i 0.153955i
\(973\) 2.48051e6i 0.0839960i
\(974\) 9.81837e7 3.31621
\(975\) −9.70952e6 8.58398e6i −0.327104 0.289186i
\(976\) −1.60103e7 −0.537990
\(977\) 1.28308e7i 0.430050i −0.976609 0.215025i \(-0.931017\pi\)
0.976609 0.215025i \(-0.0689833\pi\)
\(978\) 3.02389e7i 1.01092i
\(979\) 1.00526e7 0.335212
\(980\) 6.55524e7 + 2.48220e7i 2.18034 + 0.825603i
\(981\) −1.89266e7 −0.627913
\(982\) 2.12601e7i 0.703537i
\(983\) 7.06277e6i 0.233126i 0.993183 + 0.116563i \(0.0371878\pi\)
−0.993183 + 0.116563i \(0.962812\pi\)
\(984\) 3.66380e7 1.20627
\(985\) −5.51426e6 + 1.45626e7i −0.181091 + 0.478243i
\(986\) −2.20463e7 −0.722176
\(987\) 1.83095e6i 0.0598251i
\(988\) 2.83154e7i 0.922847i
\(989\) 9.80518e7 3.18761
\(990\) −2.02375e6 + 5.34452e6i −0.0656249 + 0.173309i
\(991\) 1.51956e7 0.491512 0.245756 0.969332i \(-0.420964\pi\)
0.245756 + 0.969332i \(0.420964\pi\)
\(992\) 9.68043e6i 0.312331i
\(993\) 1.70312e7i 0.548115i
\(994\) 8.76428e6 0.281352
\(995\) 4.41044e7 + 1.67005e7i 1.41229 + 0.534776i
\(996\) 5.38997e6 0.172162
\(997\) 3.19469e7i 1.01787i −0.860806 0.508934i \(-0.830040\pi\)
0.860806 0.508934i \(-0.169960\pi\)
\(998\) 2.39144e7i 0.760035i
\(999\) −9.34975e6 −0.296405
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 165.6.c.b.34.25 yes 26
5.2 odd 4 825.6.a.y.1.1 13
5.3 odd 4 825.6.a.v.1.13 13
5.4 even 2 inner 165.6.c.b.34.2 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.c.b.34.2 26 5.4 even 2 inner
165.6.c.b.34.25 yes 26 1.1 even 1 trivial
825.6.a.v.1.13 13 5.3 odd 4
825.6.a.y.1.1 13 5.2 odd 4