Properties

Label 165.6.c.b.34.14
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 34.14
Character \(\chi\) \(=\) 165.34
Dual form 165.6.c.b.34.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.886559i q^{2} +9.00000i q^{3} +31.2140 q^{4} +(-37.4584 + 41.4954i) q^{5} -7.97903 q^{6} -224.774i q^{7} +56.0430i q^{8} -81.0000 q^{9} +O(q^{10})\) \(q+0.886559i q^{2} +9.00000i q^{3} +31.2140 q^{4} +(-37.4584 + 41.4954i) q^{5} -7.97903 q^{6} -224.774i q^{7} +56.0430i q^{8} -81.0000 q^{9} +(-36.7881 - 33.2091i) q^{10} +121.000 q^{11} +280.926i q^{12} +1065.64i q^{13} +199.275 q^{14} +(-373.459 - 337.125i) q^{15} +949.163 q^{16} +1347.75i q^{17} -71.8113i q^{18} -691.252 q^{19} +(-1169.23 + 1295.24i) q^{20} +2022.96 q^{21} +107.274i q^{22} +3396.13i q^{23} -504.387 q^{24} +(-318.739 - 3108.70i) q^{25} -944.749 q^{26} -729.000i q^{27} -7016.09i q^{28} -8603.02 q^{29} +(298.882 - 331.093i) q^{30} -320.509 q^{31} +2634.86i q^{32} +1089.00i q^{33} -1194.86 q^{34} +(9327.07 + 8419.65i) q^{35} -2528.34 q^{36} +1906.23i q^{37} -612.836i q^{38} -9590.72 q^{39} +(-2325.53 - 2099.28i) q^{40} +5821.85 q^{41} +1793.48i q^{42} +1421.42i q^{43} +3776.90 q^{44} +(3034.13 - 3361.13i) q^{45} -3010.87 q^{46} +6454.51i q^{47} +8542.47i q^{48} -33716.2 q^{49} +(2756.05 - 282.581i) q^{50} -12129.7 q^{51} +33262.8i q^{52} +9109.26i q^{53} +646.302 q^{54} +(-4532.46 + 5020.95i) q^{55} +12597.0 q^{56} -6221.27i q^{57} -7627.08i q^{58} -10213.6 q^{59} +(-11657.1 - 10523.0i) q^{60} -34276.3 q^{61} -284.150i q^{62} +18206.7i q^{63} +28037.3 q^{64} +(-44219.0 - 39917.0i) q^{65} -965.463 q^{66} +68436.0i q^{67} +42068.6i q^{68} -30565.2 q^{69} +(-7464.52 + 8269.00i) q^{70} +1883.92 q^{71} -4539.48i q^{72} -87733.7i q^{73} -1689.99 q^{74} +(27978.3 - 2868.66i) q^{75} -21576.8 q^{76} -27197.6i q^{77} -8502.74i q^{78} +52408.8 q^{79} +(-35554.1 + 39385.9i) q^{80} +6561.00 q^{81} +5161.42i q^{82} +58665.8i q^{83} +63144.8 q^{84} +(-55925.4 - 50484.5i) q^{85} -1260.17 q^{86} -77427.1i q^{87} +6781.20i q^{88} +113843. q^{89} +(2979.84 + 2689.94i) q^{90} +239527. q^{91} +106007. i q^{92} -2884.58i q^{93} -5722.30 q^{94} +(25893.2 - 28683.8i) q^{95} -23713.8 q^{96} +115329. i q^{97} -29891.4i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.886559i 0.156723i 0.996925 + 0.0783615i \(0.0249688\pi\)
−0.996925 + 0.0783615i \(0.975031\pi\)
\(3\) 9.00000i 0.577350i
\(4\) 31.2140 0.975438
\(5\) −37.4584 + 41.4954i −0.670076 + 0.742293i
\(6\) −7.97903 −0.0904841
\(7\) 224.774i 1.73380i −0.498478 0.866902i \(-0.666108\pi\)
0.498478 0.866902i \(-0.333892\pi\)
\(8\) 56.0430i 0.309597i
\(9\) −81.0000 −0.333333
\(10\) −36.7881 33.2091i −0.116334 0.105016i
\(11\) 121.000 0.301511
\(12\) 280.926i 0.563169i
\(13\) 1065.64i 1.74884i 0.485169 + 0.874420i \(0.338758\pi\)
−0.485169 + 0.874420i \(0.661242\pi\)
\(14\) 199.275 0.271727
\(15\) −373.459 337.125i −0.428563 0.386868i
\(16\) 949.163 0.926917
\(17\) 1347.75i 1.13106i 0.824727 + 0.565531i \(0.191329\pi\)
−0.824727 + 0.565531i \(0.808671\pi\)
\(18\) 71.8113i 0.0522410i
\(19\) −691.252 −0.439291 −0.219646 0.975580i \(-0.570490\pi\)
−0.219646 + 0.975580i \(0.570490\pi\)
\(20\) −1169.23 + 1295.24i −0.653617 + 0.724060i
\(21\) 2022.96 1.00101
\(22\) 107.274i 0.0472538i
\(23\) 3396.13i 1.33864i 0.742973 + 0.669321i \(0.233415\pi\)
−0.742973 + 0.669321i \(0.766585\pi\)
\(24\) −504.387 −0.178746
\(25\) −318.739 3108.70i −0.101997 0.994785i
\(26\) −944.749 −0.274084
\(27\) 729.000i 0.192450i
\(28\) 7016.09i 1.69122i
\(29\) −8603.02 −1.89957 −0.949786 0.312900i \(-0.898699\pi\)
−0.949786 + 0.312900i \(0.898699\pi\)
\(30\) 298.882 331.093i 0.0606312 0.0671657i
\(31\) −320.509 −0.0599013 −0.0299507 0.999551i \(-0.509535\pi\)
−0.0299507 + 0.999551i \(0.509535\pi\)
\(32\) 2634.86i 0.454866i
\(33\) 1089.00i 0.174078i
\(34\) −1194.86 −0.177263
\(35\) 9327.07 + 8419.65i 1.28699 + 1.16178i
\(36\) −2528.34 −0.325146
\(37\) 1906.23i 0.228913i 0.993428 + 0.114457i \(0.0365127\pi\)
−0.993428 + 0.114457i \(0.963487\pi\)
\(38\) 612.836i 0.0688471i
\(39\) −9590.72 −1.00969
\(40\) −2325.53 2099.28i −0.229811 0.207453i
\(41\) 5821.85 0.540881 0.270440 0.962737i \(-0.412831\pi\)
0.270440 + 0.962737i \(0.412831\pi\)
\(42\) 1793.48i 0.156882i
\(43\) 1421.42i 0.117234i 0.998281 + 0.0586168i \(0.0186690\pi\)
−0.998281 + 0.0586168i \(0.981331\pi\)
\(44\) 3776.90 0.294106
\(45\) 3034.13 3361.13i 0.223359 0.247431i
\(46\) −3010.87 −0.209796
\(47\) 6454.51i 0.426205i 0.977030 + 0.213102i \(0.0683568\pi\)
−0.977030 + 0.213102i \(0.931643\pi\)
\(48\) 8542.47i 0.535156i
\(49\) −33716.2 −2.00608
\(50\) 2756.05 282.581i 0.155906 0.0159852i
\(51\) −12129.7 −0.653019
\(52\) 33262.8i 1.70589i
\(53\) 9109.26i 0.445444i 0.974882 + 0.222722i \(0.0714943\pi\)
−0.974882 + 0.222722i \(0.928506\pi\)
\(54\) 646.302 0.0301614
\(55\) −4532.46 + 5020.95i −0.202035 + 0.223810i
\(56\) 12597.0 0.536780
\(57\) 6221.27i 0.253625i
\(58\) 7627.08i 0.297707i
\(59\) −10213.6 −0.381989 −0.190995 0.981591i \(-0.561171\pi\)
−0.190995 + 0.981591i \(0.561171\pi\)
\(60\) −11657.1 10523.0i −0.418036 0.377366i
\(61\) −34276.3 −1.17942 −0.589712 0.807614i \(-0.700759\pi\)
−0.589712 + 0.807614i \(0.700759\pi\)
\(62\) 284.150i 0.00938791i
\(63\) 18206.7i 0.577935i
\(64\) 28037.3 0.855629
\(65\) −44219.0 39917.0i −1.29815 1.17186i
\(66\) −965.463 −0.0272820
\(67\) 68436.0i 1.86251i 0.364374 + 0.931253i \(0.381283\pi\)
−0.364374 + 0.931253i \(0.618717\pi\)
\(68\) 42068.6i 1.10328i
\(69\) −30565.2 −0.772866
\(70\) −7464.52 + 8269.00i −0.182078 + 0.201701i
\(71\) 1883.92 0.0443524 0.0221762 0.999754i \(-0.492941\pi\)
0.0221762 + 0.999754i \(0.492941\pi\)
\(72\) 4539.48i 0.103199i
\(73\) 87733.7i 1.92690i −0.267885 0.963451i \(-0.586325\pi\)
0.267885 0.963451i \(-0.413675\pi\)
\(74\) −1689.99 −0.0358760
\(75\) 27978.3 2868.66i 0.574339 0.0588878i
\(76\) −21576.8 −0.428501
\(77\) 27197.6i 0.522762i
\(78\) 8502.74i 0.158242i
\(79\) 52408.8 0.944793 0.472397 0.881386i \(-0.343389\pi\)
0.472397 + 0.881386i \(0.343389\pi\)
\(80\) −35554.1 + 39385.9i −0.621105 + 0.688044i
\(81\) 6561.00 0.111111
\(82\) 5161.42i 0.0847685i
\(83\) 58665.8i 0.934737i 0.884062 + 0.467369i \(0.154798\pi\)
−0.884062 + 0.467369i \(0.845202\pi\)
\(84\) 63144.8 0.976426
\(85\) −55925.4 50484.5i −0.839579 0.757898i
\(86\) −1260.17 −0.0183732
\(87\) 77427.1i 1.09672i
\(88\) 6781.20i 0.0933469i
\(89\) 113843. 1.52346 0.761728 0.647896i \(-0.224351\pi\)
0.761728 + 0.647896i \(0.224351\pi\)
\(90\) 2979.84 + 2689.94i 0.0387781 + 0.0350054i
\(91\) 239527. 3.03215
\(92\) 106007.i 1.30576i
\(93\) 2884.58i 0.0345840i
\(94\) −5722.30 −0.0667961
\(95\) 25893.2 28683.8i 0.294358 0.326083i
\(96\) −23713.8 −0.262617
\(97\) 115329.i 1.24454i 0.782802 + 0.622271i \(0.213790\pi\)
−0.782802 + 0.622271i \(0.786210\pi\)
\(98\) 29891.4i 0.314399i
\(99\) −9801.00 −0.100504
\(100\) −9949.14 97035.1i −0.0994914 0.970351i
\(101\) 39906.6 0.389261 0.194631 0.980877i \(-0.437649\pi\)
0.194631 + 0.980877i \(0.437649\pi\)
\(102\) 10753.7i 0.102343i
\(103\) 69320.0i 0.643822i 0.946770 + 0.321911i \(0.104325\pi\)
−0.946770 + 0.321911i \(0.895675\pi\)
\(104\) −59721.4 −0.541435
\(105\) −75776.9 + 83943.7i −0.670754 + 0.743044i
\(106\) −8075.90 −0.0698114
\(107\) 131149.i 1.10740i −0.832717 0.553700i \(-0.813216\pi\)
0.832717 0.553700i \(-0.186784\pi\)
\(108\) 22755.0i 0.187723i
\(109\) −146929. −1.18451 −0.592257 0.805749i \(-0.701763\pi\)
−0.592257 + 0.805749i \(0.701763\pi\)
\(110\) −4451.37 4018.30i −0.0350761 0.0316636i
\(111\) −17156.1 −0.132163
\(112\) 213347.i 1.60709i
\(113\) 57346.0i 0.422481i −0.977434 0.211240i \(-0.932250\pi\)
0.977434 0.211240i \(-0.0677503\pi\)
\(114\) 5515.52 0.0397489
\(115\) −140924. 127214.i −0.993664 0.896992i
\(116\) −268535. −1.85291
\(117\) 86316.5i 0.582947i
\(118\) 9055.00i 0.0598665i
\(119\) 302938. 1.96104
\(120\) 18893.5 20929.7i 0.119773 0.132682i
\(121\) 14641.0 0.0909091
\(122\) 30388.0i 0.184843i
\(123\) 52396.7i 0.312278i
\(124\) −10004.4 −0.0584300
\(125\) 140936. + 103221.i 0.806767 + 0.590870i
\(126\) −16141.3 −0.0905757
\(127\) 172649.i 0.949852i −0.880026 0.474926i \(-0.842475\pi\)
0.880026 0.474926i \(-0.157525\pi\)
\(128\) 109172.i 0.588963i
\(129\) −12792.8 −0.0676848
\(130\) 35388.8 39202.7i 0.183657 0.203450i
\(131\) 297723. 1.51577 0.757886 0.652387i \(-0.226233\pi\)
0.757886 + 0.652387i \(0.226233\pi\)
\(132\) 33992.1i 0.169802i
\(133\) 155375.i 0.761645i
\(134\) −60672.6 −0.291897
\(135\) 30250.2 + 27307.2i 0.142854 + 0.128956i
\(136\) −75531.8 −0.350173
\(137\) 45559.8i 0.207387i 0.994609 + 0.103693i \(0.0330661\pi\)
−0.994609 + 0.103693i \(0.966934\pi\)
\(138\) 27097.8i 0.121126i
\(139\) 124306. 0.545701 0.272850 0.962056i \(-0.412034\pi\)
0.272850 + 0.962056i \(0.412034\pi\)
\(140\) 291135. + 262811.i 1.25538 + 1.13324i
\(141\) −58090.6 −0.246070
\(142\) 1670.21i 0.00695104i
\(143\) 128942.i 0.527295i
\(144\) −76882.2 −0.308972
\(145\) 322255. 356986.i 1.27286 1.41004i
\(146\) 77781.2 0.301990
\(147\) 303445.i 1.15821i
\(148\) 59501.1i 0.223291i
\(149\) 107578. 0.396971 0.198485 0.980104i \(-0.436398\pi\)
0.198485 + 0.980104i \(0.436398\pi\)
\(150\) 2543.23 + 24804.4i 0.00922907 + 0.0900122i
\(151\) 147513. 0.526487 0.263244 0.964729i \(-0.415208\pi\)
0.263244 + 0.964729i \(0.415208\pi\)
\(152\) 38739.8i 0.136003i
\(153\) 109168.i 0.377021i
\(154\) 24112.3 0.0819288
\(155\) 12005.8 13299.7i 0.0401384 0.0444643i
\(156\) −299365. −0.984893
\(157\) 231901.i 0.750849i −0.926853 0.375425i \(-0.877497\pi\)
0.926853 0.375425i \(-0.122503\pi\)
\(158\) 46463.5i 0.148071i
\(159\) −81983.3 −0.257177
\(160\) −109335. 98697.8i −0.337644 0.304795i
\(161\) 763360. 2.32094
\(162\) 5816.72i 0.0174137i
\(163\) 6862.35i 0.0202304i −0.999949 0.0101152i \(-0.996780\pi\)
0.999949 0.0101152i \(-0.00321982\pi\)
\(164\) 181723. 0.527596
\(165\) −45188.5 40792.2i −0.129217 0.116645i
\(166\) −52010.7 −0.146495
\(167\) 10230.0i 0.0283847i 0.999899 + 0.0141923i \(0.00451771\pi\)
−0.999899 + 0.0141923i \(0.995482\pi\)
\(168\) 113373.i 0.309910i
\(169\) −764285. −2.05844
\(170\) 44757.5 49581.2i 0.118780 0.131581i
\(171\) 55991.4 0.146430
\(172\) 44368.3i 0.114354i
\(173\) 421259.i 1.07012i 0.844813 + 0.535062i \(0.179712\pi\)
−0.844813 + 0.535062i \(0.820288\pi\)
\(174\) 68643.8 0.171881
\(175\) −698754. + 71644.2i −1.72476 + 0.176842i
\(176\) 114849. 0.279476
\(177\) 91922.8i 0.220541i
\(178\) 100928.i 0.238761i
\(179\) −330517. −0.771012 −0.385506 0.922705i \(-0.625973\pi\)
−0.385506 + 0.922705i \(0.625973\pi\)
\(180\) 94707.3 104914.i 0.217872 0.241353i
\(181\) 668805. 1.51741 0.758705 0.651434i \(-0.225832\pi\)
0.758705 + 0.651434i \(0.225832\pi\)
\(182\) 212355.i 0.475207i
\(183\) 308487.i 0.680940i
\(184\) −190329. −0.414439
\(185\) −79099.8 71404.3i −0.169921 0.153389i
\(186\) 2557.35 0.00542012
\(187\) 163078.i 0.341028i
\(188\) 201471.i 0.415736i
\(189\) −163860. −0.333671
\(190\) 25429.9 + 22955.8i 0.0511047 + 0.0461327i
\(191\) −961866. −1.90779 −0.953896 0.300137i \(-0.902967\pi\)
−0.953896 + 0.300137i \(0.902967\pi\)
\(192\) 252335.i 0.493998i
\(193\) 87470.4i 0.169032i −0.996422 0.0845158i \(-0.973066\pi\)
0.996422 0.0845158i \(-0.0269343\pi\)
\(194\) −102246. −0.195048
\(195\) 359253. 397971.i 0.676571 0.749488i
\(196\) −1.05242e6 −1.95680
\(197\) 799656.i 1.46804i −0.679129 0.734019i \(-0.737642\pi\)
0.679129 0.734019i \(-0.262358\pi\)
\(198\) 8689.17i 0.0157513i
\(199\) 635515. 1.13761 0.568804 0.822473i \(-0.307406\pi\)
0.568804 + 0.822473i \(0.307406\pi\)
\(200\) 174221. 17863.1i 0.307982 0.0315778i
\(201\) −615924. −1.07532
\(202\) 35379.6i 0.0610062i
\(203\) 1.93373e6i 3.29349i
\(204\) −378618. −0.636980
\(205\) −218077. + 241580.i −0.362431 + 0.401492i
\(206\) −61456.3 −0.100902
\(207\) 275086.i 0.446214i
\(208\) 1.01146e6i 1.62103i
\(209\) −83641.5 −0.132451
\(210\) −74421.0 67180.7i −0.116452 0.105123i
\(211\) −349594. −0.540578 −0.270289 0.962779i \(-0.587119\pi\)
−0.270289 + 0.962779i \(0.587119\pi\)
\(212\) 284337.i 0.434503i
\(213\) 16955.3i 0.0256069i
\(214\) 116271. 0.173555
\(215\) −58982.5 53244.2i −0.0870216 0.0785554i
\(216\) 40855.3 0.0595819
\(217\) 72042.0i 0.103857i
\(218\) 130261.i 0.185641i
\(219\) 789604. 1.11250
\(220\) −141476. + 156724.i −0.197073 + 0.218312i
\(221\) −1.43621e6 −1.97805
\(222\) 15209.9i 0.0207130i
\(223\) 309538.i 0.416824i −0.978041 0.208412i \(-0.933171\pi\)
0.978041 0.208412i \(-0.0668294\pi\)
\(224\) 592248. 0.788648
\(225\) 25817.9 + 251805.i 0.0339989 + 0.331595i
\(226\) 50840.6 0.0662124
\(227\) 509733.i 0.656566i 0.944579 + 0.328283i \(0.106470\pi\)
−0.944579 + 0.328283i \(0.893530\pi\)
\(228\) 194191.i 0.247395i
\(229\) 1.28351e6 1.61737 0.808684 0.588243i \(-0.200180\pi\)
0.808684 + 0.588243i \(0.200180\pi\)
\(230\) 112782. 124937.i 0.140579 0.155730i
\(231\) 244778. 0.301817
\(232\) 482139.i 0.588101i
\(233\) 312877.i 0.377558i 0.982020 + 0.188779i \(0.0604529\pi\)
−0.982020 + 0.188779i \(0.939547\pi\)
\(234\) 76524.7 0.0913612
\(235\) −267833. 241775.i −0.316369 0.285590i
\(236\) −318809. −0.372607
\(237\) 471679.i 0.545477i
\(238\) 268573.i 0.307340i
\(239\) 357254. 0.404559 0.202280 0.979328i \(-0.435165\pi\)
0.202280 + 0.979328i \(0.435165\pi\)
\(240\) −354473. 319987.i −0.397242 0.358595i
\(241\) −680168. −0.754351 −0.377176 0.926142i \(-0.623105\pi\)
−0.377176 + 0.926142i \(0.623105\pi\)
\(242\) 12980.1i 0.0142475i
\(243\) 59049.0i 0.0641500i
\(244\) −1.06990e6 −1.15045
\(245\) 1.26295e6 1.39907e6i 1.34422 1.48910i
\(246\) −46452.8 −0.0489411
\(247\) 736623.i 0.768250i
\(248\) 17962.3i 0.0185452i
\(249\) −527992. −0.539671
\(250\) −91511.3 + 124948.i −0.0926029 + 0.126439i
\(251\) 157817. 0.158114 0.0790568 0.996870i \(-0.474809\pi\)
0.0790568 + 0.996870i \(0.474809\pi\)
\(252\) 568303.i 0.563740i
\(253\) 410932.i 0.403616i
\(254\) 153064. 0.148864
\(255\) 454360. 503328.i 0.437572 0.484731i
\(256\) 800404. 0.763325
\(257\) 557296.i 0.526324i −0.964752 0.263162i \(-0.915235\pi\)
0.964752 0.263162i \(-0.0847654\pi\)
\(258\) 11341.6i 0.0106078i
\(259\) 428470. 0.396891
\(260\) −1.38025e6 1.24597e6i −1.26627 1.14307i
\(261\) 696844. 0.633191
\(262\) 263949.i 0.237556i
\(263\) 645647.i 0.575580i −0.957693 0.287790i \(-0.907079\pi\)
0.957693 0.287790i \(-0.0929206\pi\)
\(264\) −61030.8 −0.0538939
\(265\) −377993. 341218.i −0.330650 0.298482i
\(266\) −137749. −0.119367
\(267\) 1.02458e6i 0.879568i
\(268\) 2.13616e6i 1.81676i
\(269\) 219755. 0.185165 0.0925825 0.995705i \(-0.470488\pi\)
0.0925825 + 0.995705i \(0.470488\pi\)
\(270\) −24209.4 + 26818.6i −0.0202104 + 0.0223886i
\(271\) 1.54792e6 1.28034 0.640171 0.768233i \(-0.278864\pi\)
0.640171 + 0.768233i \(0.278864\pi\)
\(272\) 1.27923e6i 1.04840i
\(273\) 2.15574e6i 1.75061i
\(274\) −40391.5 −0.0325023
\(275\) −38567.5 376153.i −0.0307531 0.299939i
\(276\) −954061. −0.753882
\(277\) 980724.i 0.767976i 0.923338 + 0.383988i \(0.125450\pi\)
−0.923338 + 0.383988i \(0.874550\pi\)
\(278\) 110205.i 0.0855239i
\(279\) 25961.2 0.0199671
\(280\) −471862. + 522717.i −0.359683 + 0.398448i
\(281\) 2.46283e6 1.86067 0.930334 0.366713i \(-0.119517\pi\)
0.930334 + 0.366713i \(0.119517\pi\)
\(282\) 51500.7i 0.0385648i
\(283\) 838610.i 0.622435i −0.950339 0.311217i \(-0.899263\pi\)
0.950339 0.311217i \(-0.100737\pi\)
\(284\) 58804.8 0.0432630
\(285\) 258154. + 233039.i 0.188264 + 0.169948i
\(286\) −114315. −0.0826393
\(287\) 1.30860e6i 0.937782i
\(288\) 213424.i 0.151622i
\(289\) −396569. −0.279302
\(290\) 316489. + 285698.i 0.220985 + 0.199486i
\(291\) −1.03796e6 −0.718536
\(292\) 2.73852e6i 1.87957i
\(293\) 1.32689e6i 0.902955i 0.892282 + 0.451478i \(0.149103\pi\)
−0.892282 + 0.451478i \(0.850897\pi\)
\(294\) 269022. 0.181518
\(295\) 382587. 423820.i 0.255962 0.283548i
\(296\) −106831. −0.0708708
\(297\) 88209.0i 0.0580259i
\(298\) 95374.4i 0.0622144i
\(299\) −3.61904e6 −2.34107
\(300\) 873316. 89542.2i 0.560232 0.0574414i
\(301\) 319498. 0.203260
\(302\) 130779.i 0.0825126i
\(303\) 359159.i 0.224740i
\(304\) −656111. −0.407187
\(305\) 1.28394e6 1.42231e6i 0.790303 0.875477i
\(306\) 96783.6 0.0590878
\(307\) 1.04842e6i 0.634878i −0.948279 0.317439i \(-0.897177\pi\)
0.948279 0.317439i \(-0.102823\pi\)
\(308\) 848946.i 0.509922i
\(309\) −623880. −0.371711
\(310\) 11790.9 + 10643.8i 0.00696858 + 0.00629062i
\(311\) −1.53786e6 −0.901601 −0.450801 0.892625i \(-0.648861\pi\)
−0.450801 + 0.892625i \(0.648861\pi\)
\(312\) 537492.i 0.312598i
\(313\) 2.58473e6i 1.49126i −0.666359 0.745631i \(-0.732148\pi\)
0.666359 0.745631i \(-0.267852\pi\)
\(314\) 205594. 0.117675
\(315\) −755493. 681992.i −0.428997 0.387260i
\(316\) 1.63589e6 0.921587
\(317\) 1.29146e6i 0.721827i 0.932599 + 0.360914i \(0.117535\pi\)
−0.932599 + 0.360914i \(0.882465\pi\)
\(318\) 72683.1i 0.0403056i
\(319\) −1.04096e6 −0.572742
\(320\) −1.05023e6 + 1.16342e6i −0.573336 + 0.635127i
\(321\) 1.18034e6 0.639357
\(322\) 676764.i 0.363745i
\(323\) 931634.i 0.496866i
\(324\) 204795. 0.108382
\(325\) 3.31274e6 339660.i 1.73972 0.178376i
\(326\) 6083.88 0.00317057
\(327\) 1.32236e6i 0.683880i
\(328\) 326274.i 0.167455i
\(329\) 1.45080e6 0.738956
\(330\) 36164.7 40062.3i 0.0182810 0.0202512i
\(331\) 1.77716e6 0.891573 0.445787 0.895139i \(-0.352924\pi\)
0.445787 + 0.895139i \(0.352924\pi\)
\(332\) 1.83119e6i 0.911778i
\(333\) 154405.i 0.0763045i
\(334\) −9069.48 −0.00444853
\(335\) −2.83978e6 2.56350e6i −1.38252 1.24802i
\(336\) 1.92012e6 0.927856
\(337\) 1.99819e6i 0.958435i −0.877696 0.479217i \(-0.840921\pi\)
0.877696 0.479217i \(-0.159079\pi\)
\(338\) 677584.i 0.322605i
\(339\) 516114. 0.243919
\(340\) −1.74566e6 1.57582e6i −0.818957 0.739282i
\(341\) −38781.6 −0.0180609
\(342\) 49639.7i 0.0229490i
\(343\) 3.80073e6i 1.74434i
\(344\) −79660.7 −0.0362951
\(345\) 1.14492e6 1.26831e6i 0.517879 0.573692i
\(346\) −373471. −0.167713
\(347\) 2.94954e6i 1.31501i −0.753449 0.657507i \(-0.771611\pi\)
0.753449 0.657507i \(-0.228389\pi\)
\(348\) 2.41681e6i 1.06978i
\(349\) 1.15473e6 0.507476 0.253738 0.967273i \(-0.418340\pi\)
0.253738 + 0.967273i \(0.418340\pi\)
\(350\) −63516.8 619487.i −0.0277152 0.270310i
\(351\) 776848. 0.336565
\(352\) 318819.i 0.137147i
\(353\) 829780.i 0.354427i −0.984172 0.177213i \(-0.943292\pi\)
0.984172 0.177213i \(-0.0567083\pi\)
\(354\) 81495.0 0.0345639
\(355\) −70568.7 + 78174.1i −0.0297195 + 0.0329224i
\(356\) 3.55349e6 1.48604
\(357\) 2.72644e6i 1.13221i
\(358\) 293023.i 0.120835i
\(359\) −3.60644e6 −1.47687 −0.738435 0.674325i \(-0.764435\pi\)
−0.738435 + 0.674325i \(0.764435\pi\)
\(360\) 188368. + 170042.i 0.0766038 + 0.0691511i
\(361\) −1.99827e6 −0.807023
\(362\) 592935.i 0.237813i
\(363\) 131769.i 0.0524864i
\(364\) 7.47659e6 2.95767
\(365\) 3.64055e6 + 3.28636e6i 1.43032 + 1.29117i
\(366\) 273492. 0.106719
\(367\) 403294.i 0.156299i 0.996942 + 0.0781496i \(0.0249012\pi\)
−0.996942 + 0.0781496i \(0.975099\pi\)
\(368\) 3.22348e6i 1.24081i
\(369\) −471570. −0.180294
\(370\) 63304.2 70126.7i 0.0240396 0.0266305i
\(371\) 2.04752e6 0.772313
\(372\) 90039.4i 0.0337346i
\(373\) 3.48177e6i 1.29577i 0.761739 + 0.647884i \(0.224346\pi\)
−0.761739 + 0.647884i \(0.775654\pi\)
\(374\) −144578. −0.0534470
\(375\) −928987. + 1.26843e6i −0.341139 + 0.465787i
\(376\) −361730. −0.131952
\(377\) 9.16768e6i 3.32205i
\(378\) 145272.i 0.0522939i
\(379\) 704863. 0.252062 0.126031 0.992026i \(-0.459776\pi\)
0.126031 + 0.992026i \(0.459776\pi\)
\(380\) 808230. 895336.i 0.287128 0.318073i
\(381\) 1.55384e6 0.548397
\(382\) 852751.i 0.298995i
\(383\) 2.16463e6i 0.754028i −0.926208 0.377014i \(-0.876951\pi\)
0.926208 0.377014i \(-0.123049\pi\)
\(384\) −982551. −0.340038
\(385\) 1.12858e6 + 1.01878e6i 0.388042 + 0.350290i
\(386\) 77547.7 0.0264911
\(387\) 115135.i 0.0390778i
\(388\) 3.59988e6i 1.21397i
\(389\) −2.50750e6 −0.840168 −0.420084 0.907485i \(-0.637999\pi\)
−0.420084 + 0.907485i \(0.637999\pi\)
\(390\) 352825. + 318499.i 0.117462 + 0.106034i
\(391\) −4.57713e6 −1.51409
\(392\) 1.88955e6i 0.621075i
\(393\) 2.67950e6i 0.875131i
\(394\) 708942. 0.230075
\(395\) −1.96315e6 + 2.17473e6i −0.633083 + 0.701313i
\(396\) −305929. −0.0980352
\(397\) 2.75852e6i 0.878417i 0.898385 + 0.439208i \(0.144741\pi\)
−0.898385 + 0.439208i \(0.855259\pi\)
\(398\) 563422.i 0.178289i
\(399\) −1.39838e6 −0.439736
\(400\) −302536. 2.95067e6i −0.0945424 0.922083i
\(401\) −6.11243e6 −1.89825 −0.949124 0.314901i \(-0.898029\pi\)
−0.949124 + 0.314901i \(0.898029\pi\)
\(402\) 546053.i 0.168527i
\(403\) 341546.i 0.104758i
\(404\) 1.24565e6 0.379700
\(405\) −245764. + 272251.i −0.0744529 + 0.0824770i
\(406\) −1.71437e6 −0.516165
\(407\) 230654.i 0.0690200i
\(408\) 679786.i 0.202172i
\(409\) −4.96574e6 −1.46783 −0.733915 0.679241i \(-0.762309\pi\)
−0.733915 + 0.679241i \(0.762309\pi\)
\(410\) −214175. 193338.i −0.0629230 0.0568013i
\(411\) −410039. −0.119735
\(412\) 2.16376e6i 0.628008i
\(413\) 2.29576e6i 0.662294i
\(414\) 243880. 0.0699320
\(415\) −2.43436e6 2.19753e6i −0.693849 0.626345i
\(416\) −2.80780e6 −0.795488
\(417\) 1.11875e6i 0.315061i
\(418\) 74153.2i 0.0207582i
\(419\) 3.30467e6 0.919589 0.459794 0.888025i \(-0.347923\pi\)
0.459794 + 0.888025i \(0.347923\pi\)
\(420\) −2.36530e6 + 2.62022e6i −0.654279 + 0.724793i
\(421\) 5.04577e6 1.38747 0.693733 0.720232i \(-0.255965\pi\)
0.693733 + 0.720232i \(0.255965\pi\)
\(422\) 309936.i 0.0847209i
\(423\) 522815.i 0.142068i
\(424\) −510510. −0.137908
\(425\) 4.18975e6 429581.i 1.12516 0.115365i
\(426\) −15031.9 −0.00401318
\(427\) 7.70441e6i 2.04489i
\(428\) 4.09367e6i 1.08020i
\(429\) −1.16048e6 −0.304434
\(430\) 47204.1 52291.5i 0.0123114 0.0136383i
\(431\) 889002. 0.230520 0.115260 0.993335i \(-0.463230\pi\)
0.115260 + 0.993335i \(0.463230\pi\)
\(432\) 691940.i 0.178385i
\(433\) 406627.i 0.104226i 0.998641 + 0.0521131i \(0.0165956\pi\)
−0.998641 + 0.0521131i \(0.983404\pi\)
\(434\) −63869.5 −0.0162768
\(435\) 3.21287e6 + 2.90030e6i 0.814086 + 0.734885i
\(436\) −4.58623e6 −1.15542
\(437\) 2.34758e6i 0.588054i
\(438\) 700031.i 0.174354i
\(439\) 5.04798e6 1.25013 0.625067 0.780571i \(-0.285072\pi\)
0.625067 + 0.780571i \(0.285072\pi\)
\(440\) −281389. 254013.i −0.0692907 0.0625495i
\(441\) 2.73101e6 0.668693
\(442\) 1.27328e6i 0.310006i
\(443\) 888258.i 0.215045i −0.994203 0.107523i \(-0.965708\pi\)
0.994203 0.107523i \(-0.0342918\pi\)
\(444\) −535510. −0.128917
\(445\) −4.26436e6 + 4.72395e6i −1.02083 + 1.13085i
\(446\) 274424. 0.0653259
\(447\) 968203.i 0.229191i
\(448\) 6.30203e6i 1.48349i
\(449\) −3.82230e6 −0.894765 −0.447383 0.894343i \(-0.647644\pi\)
−0.447383 + 0.894343i \(0.647644\pi\)
\(450\) −223240. + 22889.1i −0.0519686 + 0.00532841i
\(451\) 704444. 0.163082
\(452\) 1.79000e6i 0.412104i
\(453\) 1.32762e6i 0.303967i
\(454\) −451909. −0.102899
\(455\) −8.97228e6 + 9.93926e6i −2.03177 + 2.25074i
\(456\) 348658. 0.0785214
\(457\) 2.10600e6i 0.471703i −0.971789 0.235852i \(-0.924212\pi\)
0.971789 0.235852i \(-0.0757879\pi\)
\(458\) 1.13790e6i 0.253479i
\(459\) 982509. 0.217673
\(460\) −4.39880e6 3.97084e6i −0.969258 0.874960i
\(461\) −2.43217e6 −0.533017 −0.266508 0.963833i \(-0.585870\pi\)
−0.266508 + 0.963833i \(0.585870\pi\)
\(462\) 217011.i 0.0473016i
\(463\) 7.53506e6i 1.63356i 0.576951 + 0.816779i \(0.304242\pi\)
−0.576951 + 0.816779i \(0.695758\pi\)
\(464\) −8.16566e6 −1.76075
\(465\) 119697. + 108052.i 0.0256715 + 0.0231739i
\(466\) −277384. −0.0591720
\(467\) 3.17287e6i 0.673225i 0.941643 + 0.336612i \(0.109281\pi\)
−0.941643 + 0.336612i \(0.890719\pi\)
\(468\) 2.69428e6i 0.568628i
\(469\) 1.53826e7 3.22922
\(470\) 214348. 237449.i 0.0447585 0.0495823i
\(471\) 2.08711e6 0.433503
\(472\) 572403.i 0.118262i
\(473\) 171992.i 0.0353472i
\(474\) −418172. −0.0854887
\(475\) 220329. + 2.14890e6i 0.0448062 + 0.437000i
\(476\) 9.45592e6 1.91287
\(477\) 737850.i 0.148481i
\(478\) 316727.i 0.0634038i
\(479\) −3.20281e6 −0.637811 −0.318905 0.947787i \(-0.603315\pi\)
−0.318905 + 0.947787i \(0.603315\pi\)
\(480\) 888280. 984013.i 0.175973 0.194939i
\(481\) −2.03135e6 −0.400333
\(482\) 603009.i 0.118224i
\(483\) 6.87024e6i 1.34000i
\(484\) 457004. 0.0886762
\(485\) −4.78563e6 4.32004e6i −0.923814 0.833937i
\(486\) −52350.4 −0.0100538
\(487\) 4.45541e6i 0.851266i 0.904896 + 0.425633i \(0.139949\pi\)
−0.904896 + 0.425633i \(0.860051\pi\)
\(488\) 1.92095e6i 0.365145i
\(489\) 61761.2 0.0116800
\(490\) 1.24036e6 + 1.11968e6i 0.233376 + 0.210671i
\(491\) 150957. 0.0282586 0.0141293 0.999900i \(-0.495502\pi\)
0.0141293 + 0.999900i \(0.495502\pi\)
\(492\) 1.63551e6i 0.304608i
\(493\) 1.15947e7i 2.14853i
\(494\) 653060. 0.120403
\(495\) 367130. 406697.i 0.0673452 0.0746032i
\(496\) −304216. −0.0555235
\(497\) 423456.i 0.0768984i
\(498\) 468096.i 0.0845789i
\(499\) 4.56196e6 0.820163 0.410081 0.912049i \(-0.365500\pi\)
0.410081 + 0.912049i \(0.365500\pi\)
\(500\) 4.39919e6 + 3.22193e6i 0.786951 + 0.576357i
\(501\) −92069.8 −0.0163879
\(502\) 139914.i 0.0247800i
\(503\) 5.18773e6i 0.914234i −0.889407 0.457117i \(-0.848882\pi\)
0.889407 0.457117i \(-0.151118\pi\)
\(504\) −1.02036e6 −0.178927
\(505\) −1.49484e6 + 1.65594e6i −0.260835 + 0.288946i
\(506\) −364315. −0.0632559
\(507\) 6.87857e6i 1.18844i
\(508\) 5.38908e6i 0.926521i
\(509\) −6.85927e6 −1.17350 −0.586750 0.809768i \(-0.699593\pi\)
−0.586750 + 0.809768i \(0.699593\pi\)
\(510\) 446230. + 402817.i 0.0759685 + 0.0685777i
\(511\) −1.97202e7 −3.34087
\(512\) 4.20312e6i 0.708593i
\(513\) 503923.i 0.0845416i
\(514\) 494076. 0.0824871
\(515\) −2.87646e6 2.59662e6i −0.477904 0.431409i
\(516\) −399314. −0.0660223
\(517\) 780995.i 0.128506i
\(518\) 379864.i 0.0622020i
\(519\) −3.79133e6 −0.617836
\(520\) 2.23707e6 2.47816e6i 0.362803 0.401903i
\(521\) −3.91860e6 −0.632466 −0.316233 0.948682i \(-0.602418\pi\)
−0.316233 + 0.948682i \(0.602418\pi\)
\(522\) 617794.i 0.0992356i
\(523\) 3.64804e6i 0.583183i −0.956543 0.291592i \(-0.905815\pi\)
0.956543 0.291592i \(-0.0941848\pi\)
\(524\) 9.29312e6 1.47854
\(525\) −644798. 6.28879e6i −0.102100 0.995792i
\(526\) 572405. 0.0902067
\(527\) 431966.i 0.0677521i
\(528\) 1.03364e6i 0.161356i
\(529\) −5.09735e6 −0.791964
\(530\) 302510. 335113.i 0.0467789 0.0518205i
\(531\) 827305. 0.127330
\(532\) 4.84988e6i 0.742938i
\(533\) 6.20397e6i 0.945914i
\(534\) −908355. −0.137849
\(535\) 5.44207e6 + 4.91261e6i 0.822014 + 0.742041i
\(536\) −3.83536e6 −0.576625
\(537\) 2.97465e6i 0.445144i
\(538\) 194826.i 0.0290196i
\(539\) −4.07966e6 −0.604855
\(540\) 944229. + 852366.i 0.139345 + 0.125789i
\(541\) −4.23861e6 −0.622630 −0.311315 0.950307i \(-0.600769\pi\)
−0.311315 + 0.950307i \(0.600769\pi\)
\(542\) 1.37232e6i 0.200659i
\(543\) 6.01924e6i 0.876077i
\(544\) −3.55113e6 −0.514482
\(545\) 5.50371e6 6.09687e6i 0.793715 0.879256i
\(546\) −1.91119e6 −0.274361
\(547\) 513913.i 0.0734380i 0.999326 + 0.0367190i \(0.0116907\pi\)
−0.999326 + 0.0367190i \(0.988309\pi\)
\(548\) 1.42211e6i 0.202293i
\(549\) 2.77638e6 0.393141
\(550\) 333482. 34192.4i 0.0470073 0.00481973i
\(551\) 5.94685e6 0.834465
\(552\) 1.71296e6i 0.239277i
\(553\) 1.17801e7i 1.63809i
\(554\) −869470. −0.120359
\(555\) 642639. 711899.i 0.0885594 0.0981038i
\(556\) 3.88009e6 0.532297
\(557\) 1.04431e7i 1.42624i 0.701041 + 0.713121i \(0.252719\pi\)
−0.701041 + 0.713121i \(0.747281\pi\)
\(558\) 23016.2i 0.00312930i
\(559\) −1.51472e6 −0.205023
\(560\) 8.85291e6 + 7.99162e6i 1.19293 + 1.07687i
\(561\) −1.46770e6 −0.196893
\(562\) 2.18345e6i 0.291610i
\(563\) 5.42113e6i 0.720806i 0.932797 + 0.360403i \(0.117361\pi\)
−0.932797 + 0.360403i \(0.882639\pi\)
\(564\) −1.81324e6 −0.240026
\(565\) 2.37959e6 + 2.14809e6i 0.313604 + 0.283094i
\(566\) 743477. 0.0975499
\(567\) 1.47474e6i 0.192645i
\(568\) 105581.i 0.0137313i
\(569\) 4.65152e6 0.602301 0.301151 0.953577i \(-0.402629\pi\)
0.301151 + 0.953577i \(0.402629\pi\)
\(570\) −206603. + 228869.i −0.0266348 + 0.0295053i
\(571\) 836920. 0.107422 0.0537111 0.998557i \(-0.482895\pi\)
0.0537111 + 0.998557i \(0.482895\pi\)
\(572\) 4.02479e6i 0.514344i
\(573\) 8.65679e6i 1.10146i
\(574\) 1.16015e6 0.146972
\(575\) 1.05576e7 1.08248e6i 1.33166 0.136537i
\(576\) −2.27102e6 −0.285210
\(577\) 1.22020e7i 1.52578i 0.646526 + 0.762892i \(0.276221\pi\)
−0.646526 + 0.762892i \(0.723779\pi\)
\(578\) 351582.i 0.0437730i
\(579\) 787233. 0.0975904
\(580\) 1.00589e7 1.11430e7i 1.24159 1.37540i
\(581\) 1.31865e7 1.62065
\(582\) 920214.i 0.112611i
\(583\) 1.10222e6i 0.134307i
\(584\) 4.91686e6 0.596562
\(585\) 3.58174e6 + 3.23327e6i 0.432717 + 0.390619i
\(586\) −1.17637e6 −0.141514
\(587\) 4.64629e6i 0.556559i 0.960500 + 0.278279i \(0.0897641\pi\)
−0.960500 + 0.278279i \(0.910236\pi\)
\(588\) 9.47175e6i 1.12976i
\(589\) 221553. 0.0263141
\(590\) 375741. + 339186.i 0.0444384 + 0.0401151i
\(591\) 7.19690e6 0.847572
\(592\) 1.80932e6i 0.212184i
\(593\) 3.76104e6i 0.439209i −0.975589 0.219605i \(-0.929523\pi\)
0.975589 0.219605i \(-0.0704767\pi\)
\(594\) 78202.5 0.00909399
\(595\) −1.13476e7 + 1.25705e7i −1.31405 + 1.45567i
\(596\) 3.35794e6 0.387220
\(597\) 5.71963e6i 0.656799i
\(598\) 3.20849e6i 0.366900i
\(599\) 2.65769e6 0.302648 0.151324 0.988484i \(-0.451646\pi\)
0.151324 + 0.988484i \(0.451646\pi\)
\(600\) 160768. + 1.56799e6i 0.0182315 + 0.177813i
\(601\) 5.84003e6 0.659521 0.329761 0.944065i \(-0.393032\pi\)
0.329761 + 0.944065i \(0.393032\pi\)
\(602\) 283254.i 0.0318555i
\(603\) 5.54331e6i 0.620835i
\(604\) 4.60447e6 0.513555
\(605\) −548428. + 607534.i −0.0609160 + 0.0674811i
\(606\) −318416. −0.0352220
\(607\) 7.10119e6i 0.782274i 0.920332 + 0.391137i \(0.127918\pi\)
−0.920332 + 0.391137i \(0.872082\pi\)
\(608\) 1.82136e6i 0.199819i
\(609\) −1.74036e7 −1.90150
\(610\) 1.26096e6 + 1.13828e6i 0.137207 + 0.123859i
\(611\) −6.87815e6 −0.745364
\(612\) 3.40756e6i 0.367760i
\(613\) 1.10978e7i 1.19285i −0.802670 0.596423i \(-0.796588\pi\)
0.802670 0.596423i \(-0.203412\pi\)
\(614\) 929488. 0.0995000
\(615\) −2.17422e6 1.96270e6i −0.231801 0.209250i
\(616\) 1.52423e6 0.161845
\(617\) 1.34866e7i 1.42623i −0.701049 0.713114i \(-0.747284\pi\)
0.701049 0.713114i \(-0.252716\pi\)
\(618\) 553107.i 0.0582556i
\(619\) 1.19228e7 1.25069 0.625346 0.780347i \(-0.284958\pi\)
0.625346 + 0.780347i \(0.284958\pi\)
\(620\) 374748. 415136.i 0.0391525 0.0433722i
\(621\) 2.47578e6 0.257622
\(622\) 1.36340e6i 0.141302i
\(623\) 2.55888e7i 2.64138i
\(624\) −9.10315e6 −0.935902
\(625\) −9.56244e6 + 1.98173e6i −0.979193 + 0.202929i
\(626\) 2.29151e6 0.233715
\(627\) 752774.i 0.0764708i
\(628\) 7.23855e6i 0.732407i
\(629\) −2.56912e6 −0.258915
\(630\) 604626. 669789.i 0.0606926 0.0672337i
\(631\) −5.56411e6 −0.556317 −0.278159 0.960535i \(-0.589724\pi\)
−0.278159 + 0.960535i \(0.589724\pi\)
\(632\) 2.93715e6i 0.292505i
\(633\) 3.14635e6i 0.312103i
\(634\) −1.14496e6 −0.113127
\(635\) 7.16416e6 + 6.46717e6i 0.705068 + 0.636473i
\(636\) −2.55903e6 −0.250861
\(637\) 3.59291e7i 3.50831i
\(638\) 922877.i 0.0897619i
\(639\) −152598. −0.0147841
\(640\) −4.53015e6 4.08942e6i −0.437183 0.394650i
\(641\) 7.43898e6 0.715103 0.357551 0.933894i \(-0.383612\pi\)
0.357551 + 0.933894i \(0.383612\pi\)
\(642\) 1.04644e6i 0.100202i
\(643\) 8.56732e6i 0.817180i 0.912718 + 0.408590i \(0.133979\pi\)
−0.912718 + 0.408590i \(0.866021\pi\)
\(644\) 2.38275e7 2.26394
\(645\) 479197. 530842.i 0.0453540 0.0502419i
\(646\) 825949. 0.0778703
\(647\) 1.65852e7i 1.55762i 0.627263 + 0.778808i \(0.284175\pi\)
−0.627263 + 0.778808i \(0.715825\pi\)
\(648\) 367698.i 0.0343996i
\(649\) −1.23585e6 −0.115174
\(650\) 301129. + 2.93694e6i 0.0279556 + 0.272654i
\(651\) −648378. −0.0599620
\(652\) 214202.i 0.0197335i
\(653\) 7.12943e6i 0.654292i −0.944974 0.327146i \(-0.893913\pi\)
0.944974 0.327146i \(-0.106087\pi\)
\(654\) 1.17235e6 0.107180
\(655\) −1.11522e7 + 1.23541e7i −1.01568 + 1.12515i
\(656\) 5.52589e6 0.501352
\(657\) 7.10643e6i 0.642301i
\(658\) 1.28622e6i 0.115811i
\(659\) −1.00795e7 −0.904116 −0.452058 0.891988i \(-0.649310\pi\)
−0.452058 + 0.891988i \(0.649310\pi\)
\(660\) −1.41051e6 1.27329e6i −0.126043 0.113780i
\(661\) 1.12712e7 1.00338 0.501689 0.865048i \(-0.332712\pi\)
0.501689 + 0.865048i \(0.332712\pi\)
\(662\) 1.57556e6i 0.139730i
\(663\) 1.29259e7i 1.14203i
\(664\) −3.28780e6 −0.289392
\(665\) −6.44736e6 5.82010e6i −0.565364 0.510360i
\(666\) 136889. 0.0119587
\(667\) 2.92170e7i 2.54285i
\(668\) 319319.i 0.0276875i
\(669\) 2.78585e6 0.240653
\(670\) 2.27270e6 2.51763e6i 0.195593 0.216673i
\(671\) −4.14743e6 −0.355609
\(672\) 5.33023e6i 0.455326i
\(673\) 2.71329e6i 0.230918i −0.993312 0.115459i \(-0.963166\pi\)
0.993312 0.115459i \(-0.0368340\pi\)
\(674\) 1.77152e6 0.150209
\(675\) −2.26624e6 + 232361.i −0.191446 + 0.0196293i
\(676\) −2.38564e7 −2.00788
\(677\) 1.70935e6i 0.143337i 0.997429 + 0.0716686i \(0.0228324\pi\)
−0.997429 + 0.0716686i \(0.977168\pi\)
\(678\) 457565.i 0.0382278i
\(679\) 2.59229e7 2.15779
\(680\) 2.82930e6 3.13422e6i 0.234642 0.259931i
\(681\) −4.58760e6 −0.379069
\(682\) 34382.2i 0.00283056i
\(683\) 2.06905e7i 1.69715i 0.529079 + 0.848573i \(0.322538\pi\)
−0.529079 + 0.848573i \(0.677462\pi\)
\(684\) 1.74772e6 0.142834
\(685\) −1.89052e6 1.70660e6i −0.153942 0.138965i
\(686\) −3.36957e6 −0.273379
\(687\) 1.15516e7i 0.933788i
\(688\) 1.34916e6i 0.108666i
\(689\) −9.70715e6 −0.779011
\(690\) 1.12444e6 + 1.01504e6i 0.0899108 + 0.0811635i
\(691\) 3.42722e6 0.273053 0.136526 0.990636i \(-0.456406\pi\)
0.136526 + 0.990636i \(0.456406\pi\)
\(692\) 1.31492e7i 1.04384i
\(693\) 2.20301e6i 0.174254i
\(694\) 2.61494e6 0.206093
\(695\) −4.65630e6 + 5.15812e6i −0.365661 + 0.405070i
\(696\) 4.33925e6 0.339540
\(697\) 7.84639e6i 0.611770i
\(698\) 1.02373e6i 0.0795331i
\(699\) −2.81589e6 −0.217983
\(700\) −2.18109e7 + 2.23630e6i −1.68240 + 0.172499i
\(701\) 1.05204e7 0.808608 0.404304 0.914625i \(-0.367514\pi\)
0.404304 + 0.914625i \(0.367514\pi\)
\(702\) 688722.i 0.0527474i
\(703\) 1.31769e6i 0.100560i
\(704\) 3.39251e6 0.257982
\(705\) 2.17598e6 2.41049e6i 0.164885 0.182656i
\(706\) 735650. 0.0555468
\(707\) 8.96995e6i 0.674903i
\(708\) 2.86928e6i 0.215124i
\(709\) 5.27905e6 0.394403 0.197202 0.980363i \(-0.436815\pi\)
0.197202 + 0.980363i \(0.436815\pi\)
\(710\) −69306.0 62563.3i −0.00515971 0.00465772i
\(711\) −4.24512e6 −0.314931
\(712\) 6.38008e6i 0.471657i
\(713\) 1.08849e6i 0.0801864i
\(714\) −2.41715e6 −0.177443
\(715\) −5.35050e6 4.82995e6i −0.391407 0.353328i
\(716\) −1.03168e7 −0.752074
\(717\) 3.21529e6i 0.233572i
\(718\) 3.19732e6i 0.231459i
\(719\) 5.38506e6 0.388480 0.194240 0.980954i \(-0.437776\pi\)
0.194240 + 0.980954i \(0.437776\pi\)
\(720\) 2.87988e6 3.19026e6i 0.207035 0.229348i
\(721\) 1.55813e7 1.11626
\(722\) 1.77158e6i 0.126479i
\(723\) 6.12151e6i 0.435525i
\(724\) 2.08761e7 1.48014
\(725\) 2.74212e6 + 2.67442e7i 0.193750 + 1.88967i
\(726\) −116821. −0.00822583
\(727\) 1.05731e6i 0.0741934i 0.999312 + 0.0370967i \(0.0118110\pi\)
−0.999312 + 0.0370967i \(0.988189\pi\)
\(728\) 1.34238e7i 0.938743i
\(729\) −531441. −0.0370370
\(730\) −2.91356e6 + 3.22756e6i −0.202356 + 0.224165i
\(731\) −1.91572e6 −0.132598
\(732\) 9.62911e6i 0.664215i
\(733\) 1.02639e6i 0.0705589i 0.999377 + 0.0352794i \(0.0112321\pi\)
−0.999377 + 0.0352794i \(0.988768\pi\)
\(734\) −357544. −0.0244957
\(735\) 1.25916e7 + 1.13666e7i 0.859731 + 0.776088i
\(736\) −8.94834e6 −0.608903
\(737\) 8.28075e6i 0.561566i
\(738\) 418075.i 0.0282562i
\(739\) 3.33815e6 0.224851 0.112426 0.993660i \(-0.464138\pi\)
0.112426 + 0.993660i \(0.464138\pi\)
\(740\) −2.46902e6 2.22882e6i −0.165747 0.149622i
\(741\) 6.62960e6 0.443550
\(742\) 1.81525e6i 0.121039i
\(743\) 2.15478e7i 1.43196i −0.698120 0.715981i \(-0.745980\pi\)
0.698120 0.715981i \(-0.254020\pi\)
\(744\) 161661. 0.0107071
\(745\) −4.02970e6 + 4.46400e6i −0.266000 + 0.294668i
\(746\) −3.08679e6 −0.203077
\(747\) 4.75193e6i 0.311579i
\(748\) 5.09030e6i 0.332652i
\(749\) −2.94787e7 −1.92001
\(750\) −1.12454e6 823602.i −0.0729996 0.0534643i
\(751\) −2.02621e7 −1.31095 −0.655474 0.755218i \(-0.727531\pi\)
−0.655474 + 0.755218i \(0.727531\pi\)
\(752\) 6.12638e6i 0.395057i
\(753\) 1.42035e6i 0.0912869i
\(754\) 8.12769e6 0.520641
\(755\) −5.52560e6 + 6.12111e6i −0.352786 + 0.390807i
\(756\) −5.11473e6 −0.325475
\(757\) 1.23455e7i 0.783012i −0.920176 0.391506i \(-0.871954\pi\)
0.920176 0.391506i \(-0.128046\pi\)
\(758\) 624903.i 0.0395039i
\(759\) −3.69838e6 −0.233028
\(760\) 1.60753e6 + 1.45113e6i 0.100954 + 0.0911324i
\(761\) 9.77671e6 0.611971 0.305986 0.952036i \(-0.401014\pi\)
0.305986 + 0.952036i \(0.401014\pi\)
\(762\) 1.37758e6i 0.0859465i
\(763\) 3.30257e7i 2.05372i
\(764\) −3.00237e7 −1.86093
\(765\) 4.52996e6 + 4.08924e6i 0.279860 + 0.252633i
\(766\) 1.91908e6 0.118174
\(767\) 1.08840e7i 0.668038i
\(768\) 7.20364e6i 0.440706i
\(769\) 4.31458e6 0.263101 0.131551 0.991309i \(-0.458004\pi\)
0.131551 + 0.991309i \(0.458004\pi\)
\(770\) −903207. + 1.00055e6i −0.0548985 + 0.0608151i
\(771\) 5.01567e6 0.303873
\(772\) 2.73030e6i 0.164880i
\(773\) 3.28419e7i 1.97688i 0.151620 + 0.988439i \(0.451551\pi\)
−0.151620 + 0.988439i \(0.548449\pi\)
\(774\) 102074. 0.00612440
\(775\) 102159. + 996368.i 0.00610973 + 0.0595889i
\(776\) −6.46338e6 −0.385306
\(777\) 3.85623e6i 0.229145i
\(778\) 2.22304e6i 0.131674i
\(779\) −4.02437e6 −0.237604
\(780\) 1.12137e7 1.24223e7i 0.659953 0.731079i
\(781\) 227955. 0.0133727
\(782\) 4.05790e6i 0.237292i
\(783\) 6.27160e6i 0.365573i
\(784\) −3.20021e7 −1.85947
\(785\) 9.62281e6 + 8.68662e6i 0.557350 + 0.503126i
\(786\) −2.37554e6 −0.137153
\(787\) 1.45886e7i 0.839608i −0.907615 0.419804i \(-0.862099\pi\)
0.907615 0.419804i \(-0.137901\pi\)
\(788\) 2.49605e7i 1.43198i
\(789\) 5.81083e6 0.332312
\(790\) −1.92802e6 1.74045e6i −0.109912 0.0992187i
\(791\) −1.28899e7 −0.732499
\(792\) 549277.i 0.0311156i
\(793\) 3.65261e7i 2.06262i
\(794\) −2.44560e6 −0.137668
\(795\) 3.07096e6 3.40193e6i 0.172328 0.190901i
\(796\) 1.98370e7 1.10967
\(797\) 4.63451e6i 0.258439i −0.991616 0.129220i \(-0.958753\pi\)
0.991616 0.129220i \(-0.0412472\pi\)
\(798\) 1.23974e6i 0.0689168i
\(799\) −8.69905e6 −0.482064
\(800\) 8.19101e6 839835.i 0.452494 0.0463948i
\(801\) −9.22126e6 −0.507819
\(802\) 5.41903e6i 0.297499i
\(803\) 1.06158e7i 0.580983i
\(804\) −1.92255e7 −1.04891
\(805\) −2.85942e7 + 3.16759e7i −1.55521 + 1.72282i
\(806\) 302801. 0.0164180
\(807\) 1.97780e6i 0.106905i
\(808\) 2.23648e6i 0.120514i
\(809\) −1.28933e6 −0.0692618 −0.0346309 0.999400i \(-0.511026\pi\)
−0.0346309 + 0.999400i \(0.511026\pi\)
\(810\) −241367. 217885.i −0.0129260 0.0116685i
\(811\) 6.47343e6 0.345607 0.172803 0.984956i \(-0.444718\pi\)
0.172803 + 0.984956i \(0.444718\pi\)
\(812\) 6.03595e7i 3.21259i
\(813\) 1.39313e7i 0.739205i
\(814\) −204488. −0.0108170
\(815\) 284756. + 257053.i 0.0150169 + 0.0135559i
\(816\) −1.15131e7 −0.605294
\(817\) 982561.i 0.0514997i
\(818\) 4.40242e6i 0.230043i
\(819\) −1.94017e7 −1.01072
\(820\) −6.80707e6 + 7.54069e6i −0.353529 + 0.391630i
\(821\) 2.48796e7 1.28820 0.644102 0.764939i \(-0.277231\pi\)
0.644102 + 0.764939i \(0.277231\pi\)
\(822\) 363524.i 0.0187652i
\(823\) 2.73317e7i 1.40659i 0.710898 + 0.703295i \(0.248289\pi\)
−0.710898 + 0.703295i \(0.751711\pi\)
\(824\) −3.88490e6 −0.199325
\(825\) 3.38538e6 347107.i 0.173170 0.0177553i
\(826\) −2.03533e6 −0.103797
\(827\) 3.20369e7i 1.62887i −0.580252 0.814437i \(-0.697046\pi\)
0.580252 0.814437i \(-0.302954\pi\)
\(828\) 8.58655e6i 0.435254i
\(829\) 2.54756e7 1.28747 0.643736 0.765247i \(-0.277383\pi\)
0.643736 + 0.765247i \(0.277383\pi\)
\(830\) 1.94824e6 2.15821e6i 0.0981627 0.108742i
\(831\) −8.82652e6 −0.443391
\(832\) 2.98775e7i 1.49636i
\(833\) 4.54409e7i 2.26900i
\(834\) −991841. −0.0493772
\(835\) −424497. 383199.i −0.0210697 0.0190199i
\(836\) −2.61079e6 −0.129198
\(837\) 233651.i 0.0115280i
\(838\) 2.92979e6i 0.144121i
\(839\) 2.56179e7 1.25643 0.628216 0.778039i \(-0.283785\pi\)
0.628216 + 0.778039i \(0.283785\pi\)
\(840\) −4.70445e6 4.24676e6i −0.230044 0.207663i
\(841\) 5.35007e7 2.60837
\(842\) 4.47338e6i 0.217448i
\(843\) 2.21655e7i 1.07426i
\(844\) −1.09122e7 −0.527300
\(845\) 2.86289e7 3.17143e7i 1.37931 1.52797i
\(846\) 463507. 0.0222654
\(847\) 3.29091e6i 0.157619i
\(848\) 8.64617e6i 0.412890i
\(849\) 7.54749e6 0.359363
\(850\) 380849. + 3.71446e6i 0.0180803 + 0.176339i
\(851\) −6.47381e6 −0.306433
\(852\) 529243.i 0.0249779i
\(853\) 8.49389e6i 0.399700i 0.979827 + 0.199850i \(0.0640454\pi\)
−0.979827 + 0.199850i \(0.935955\pi\)
\(854\) −6.83042e6 −0.320481
\(855\) −2.09735e6 + 2.32339e6i −0.0981195 + 0.108694i
\(856\) 7.34996e6 0.342847
\(857\) 2.29100e7i 1.06555i −0.846258 0.532773i \(-0.821150\pi\)
0.846258 0.532773i \(-0.178850\pi\)
\(858\) 1.02883e6i 0.0477118i
\(859\) −1.05172e7 −0.486315 −0.243158 0.969987i \(-0.578183\pi\)
−0.243158 + 0.969987i \(0.578183\pi\)
\(860\) −1.84108e6 1.66196e6i −0.0848841 0.0766259i
\(861\) 1.17774e7 0.541429
\(862\) 788153.i 0.0361279i
\(863\) 2.93900e7i 1.34330i 0.740870 + 0.671649i \(0.234413\pi\)
−0.740870 + 0.671649i \(0.765587\pi\)
\(864\) 1.92082e6 0.0875390
\(865\) −1.74803e7 1.57797e7i −0.794344 0.717064i
\(866\) −360499. −0.0163346
\(867\) 3.56912e6i 0.161255i
\(868\) 2.24872e6i 0.101306i
\(869\) 6.34147e6 0.284866
\(870\) −2.57128e6 + 2.84840e6i −0.115173 + 0.127586i
\(871\) −7.29278e7 −3.25722
\(872\) 8.23432e6i 0.366722i
\(873\) 9.34165e6i 0.414847i
\(874\) 2.08127e6 0.0921616
\(875\) 2.32013e7 3.16788e7i 1.02445 1.39878i
\(876\) 2.46467e7 1.08517
\(877\) 3.81404e7i 1.67451i 0.546816 + 0.837253i \(0.315840\pi\)
−0.546816 + 0.837253i \(0.684160\pi\)
\(878\) 4.47533e6i 0.195925i
\(879\) −1.19420e7 −0.521321
\(880\) −4.30205e6 + 4.76570e6i −0.187270 + 0.207453i
\(881\) 2.39208e7 1.03833 0.519165 0.854674i \(-0.326243\pi\)
0.519165 + 0.854674i \(0.326243\pi\)
\(882\) 2.42120e6i 0.104800i
\(883\) 1.95650e6i 0.0844457i −0.999108 0.0422229i \(-0.986556\pi\)
0.999108 0.0422229i \(-0.0134440\pi\)
\(884\) −4.48298e7 −1.92946
\(885\) 3.81438e6 + 3.44328e6i 0.163706 + 0.147780i
\(886\) 787493. 0.0337025
\(887\) 2.80192e7i 1.19577i 0.801583 + 0.597884i \(0.203992\pi\)
−0.801583 + 0.597884i \(0.796008\pi\)
\(888\) 961478.i 0.0409173i
\(889\) −3.88070e7 −1.64686
\(890\) −4.18806e6 3.78061e6i −0.177230 0.159988i
\(891\) 793881. 0.0335013
\(892\) 9.66194e6i 0.406586i
\(893\) 4.46169e6i 0.187228i
\(894\) −858369. −0.0359195
\(895\) 1.23806e7 1.37149e7i 0.516637 0.572317i
\(896\) 2.45391e7 1.02115
\(897\) 3.25713e7i 1.35162i
\(898\) 3.38870e6i 0.140230i
\(899\) 2.75735e6 0.113787
\(900\) 805880. + 7.85984e6i 0.0331638 + 0.323450i
\(901\) −1.22770e7 −0.503825
\(902\) 624532.i 0.0255587i
\(903\) 2.87548e6i 0.117352i
\(904\) 3.21384e6 0.130799
\(905\) −2.50523e7 + 2.77523e7i −1.01678 + 1.12636i
\(906\) −1.17701e6 −0.0476387
\(907\) 5.99454e6i 0.241957i 0.992655 + 0.120978i \(0.0386032\pi\)
−0.992655 + 0.120978i \(0.961397\pi\)
\(908\) 1.59108e7i 0.640439i
\(909\) −3.23243e6 −0.129754
\(910\) −8.81174e6 7.95446e6i −0.352743 0.318425i
\(911\) −3.83047e7 −1.52917 −0.764585 0.644523i \(-0.777056\pi\)
−0.764585 + 0.644523i \(0.777056\pi\)
\(912\) 5.90500e6i 0.235089i
\(913\) 7.09856e6i 0.281834i
\(914\) 1.86710e6 0.0739267
\(915\) 1.28008e7 + 1.15554e7i 0.505457 + 0.456282i
\(916\) 4.00634e7 1.57764
\(917\) 6.69202e7i 2.62805i
\(918\) 871052.i 0.0341144i
\(919\) 4.41558e7 1.72464 0.862321 0.506362i \(-0.169010\pi\)
0.862321 + 0.506362i \(0.169010\pi\)
\(920\) 7.12942e6 7.89779e6i 0.277706 0.307635i
\(921\) 9.43580e6 0.366547
\(922\) 2.15626e6i 0.0835360i
\(923\) 2.00757e6i 0.0775652i
\(924\) 7.64052e6 0.294403
\(925\) 5.92590e6 607591.i 0.227720 0.0233484i
\(926\) −6.68028e6 −0.256016
\(927\) 5.61492e6i 0.214607i
\(928\) 2.26678e7i 0.864050i
\(929\) −1.00353e7 −0.381499 −0.190749 0.981639i \(-0.561092\pi\)
−0.190749 + 0.981639i \(0.561092\pi\)
\(930\) −95794.3 + 106118.i −0.00363189 + 0.00402331i
\(931\) 2.33064e7 0.881253
\(932\) 9.76613e6i 0.368284i
\(933\) 1.38407e7i 0.520540i
\(934\) −2.81294e6 −0.105510
\(935\) −6.76697e6 6.10862e6i −0.253143 0.228515i
\(936\) 4.83743e6 0.180478
\(937\) 3.04913e7i 1.13456i −0.823526 0.567279i \(-0.807996\pi\)
0.823526 0.567279i \(-0.192004\pi\)
\(938\) 1.36376e7i 0.506093i
\(939\) 2.32626e7 0.860981
\(940\) −8.36013e6 7.54678e6i −0.308598 0.278575i
\(941\) −4.13865e7 −1.52365 −0.761824 0.647785i \(-0.775696\pi\)
−0.761824 + 0.647785i \(0.775696\pi\)
\(942\) 1.85034e6i 0.0679399i
\(943\) 1.97718e7i 0.724046i
\(944\) −9.69442e6 −0.354072
\(945\) 6.13793e6 6.79944e6i 0.223585 0.247681i
\(946\) −152481. −0.00553973
\(947\) 9.38834e6i 0.340184i 0.985428 + 0.170092i \(0.0544065\pi\)
−0.985428 + 0.170092i \(0.945594\pi\)
\(948\) 1.47230e7i 0.532079i
\(949\) 9.34922e7 3.36984
\(950\) −1.90512e6 + 195335.i −0.0684880 + 0.00702217i
\(951\) −1.16232e7 −0.416747
\(952\) 1.69776e7i 0.607132i
\(953\) 3.35369e7i 1.19616i 0.801435 + 0.598081i \(0.204070\pi\)
−0.801435 + 0.598081i \(0.795930\pi\)
\(954\) 654148. 0.0232705
\(955\) 3.60299e7 3.99130e7i 1.27837 1.41614i
\(956\) 1.11513e7 0.394623
\(957\) 9.36868e6i 0.330673i
\(958\) 2.83948e6i 0.0999597i
\(959\) 1.02406e7 0.359568
\(960\) −1.04708e7 9.45207e6i −0.366691 0.331016i
\(961\) −2.85264e7 −0.996412
\(962\) 1.80091e6i 0.0627414i
\(963\) 1.06230e7i 0.369133i
\(964\) −2.12308e7 −0.735823
\(965\) 3.62962e6 + 3.27650e6i 0.125471 + 0.113264i
\(966\) −6.09088e6 −0.210009
\(967\) 5.35398e7i 1.84124i 0.390459 + 0.920620i \(0.372316\pi\)
−0.390459 + 0.920620i \(0.627684\pi\)
\(968\) 820525.i 0.0281451i
\(969\) 8.38471e6 0.286866
\(970\) 3.82997e6 4.24274e6i 0.130697 0.144783i
\(971\) −3.17286e7 −1.07995 −0.539974 0.841682i \(-0.681566\pi\)
−0.539974 + 0.841682i \(0.681566\pi\)
\(972\) 1.84316e6i 0.0625744i
\(973\) 2.79407e7i 0.946139i
\(974\) −3.94999e6 −0.133413
\(975\) 3.05694e6 + 2.98147e7i 0.102985 + 1.00443i
\(976\) −3.25338e7 −1.09323
\(977\) 5.28990e6i 0.177301i −0.996063 0.0886505i \(-0.971745\pi\)
0.996063 0.0886505i \(-0.0282554\pi\)
\(978\) 54754.9i 0.00183053i
\(979\) 1.37750e7 0.459340
\(980\) 3.94218e7 4.36705e7i 1.31121 1.45252i
\(981\) 1.19012e7 0.394838
\(982\) 133832.i 0.00442877i
\(983\) 2.55796e7i 0.844327i −0.906520 0.422164i \(-0.861271\pi\)
0.906520 0.422164i \(-0.138729\pi\)
\(984\) −2.93647e6 −0.0966801
\(985\) 3.31820e7 + 2.99538e7i 1.08971 + 0.983697i
\(986\) 1.02794e7 0.336725
\(987\) 1.30572e7i 0.426637i
\(988\) 2.29930e7i 0.749380i
\(989\) −4.82733e6 −0.156934
\(990\) 360561. + 325482.i 0.0116920 + 0.0105545i
\(991\) 4.14167e7 1.33965 0.669825 0.742519i \(-0.266369\pi\)
0.669825 + 0.742519i \(0.266369\pi\)
\(992\) 844498.i 0.0272471i
\(993\) 1.59945e7i 0.514750i
\(994\) 375419. 0.0120517
\(995\) −2.38054e7 + 2.63710e7i −0.762284 + 0.844439i
\(996\) −1.64808e7 −0.526415
\(997\) 3.02210e7i 0.962877i −0.876480 0.481438i \(-0.840115\pi\)
0.876480 0.481438i \(-0.159885\pi\)
\(998\) 4.04445e6i 0.128538i
\(999\) 1.38964e6 0.0440544
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.34.14 yes 26
5.2 odd 4 825.6.a.y.1.6 13
5.3 odd 4 825.6.a.v.1.8 13
5.4 even 2 inner 165.6.c.b.34.13 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.c.b.34.13 26 5.4 even 2 inner
165.6.c.b.34.14 yes 26 1.1 even 1 trivial
825.6.a.v.1.8 13 5.3 odd 4
825.6.a.y.1.6 13 5.2 odd 4