Properties

Label 40.6.f.a.29.17
Level $40$
Weight $6$
Character 40.29
Analytic conductor $6.415$
Analytic rank $0$
Dimension $28$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,6,Mod(29,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.29");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 40.f (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: \(6.41535279252\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.17
Character \(\chi\) \(=\) 40.29
Dual form 40.6.f.a.29.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.42014 - 5.47569i) q^{2} -7.17847 q^{3} +(-27.9664 - 15.5525i) q^{4} +(-1.28331 - 55.8870i) q^{5} +(-10.1944 + 39.3071i) q^{6} +146.905i q^{7} +(-124.877 + 131.049i) q^{8} -191.470 q^{9} +(-307.842 - 72.3401i) q^{10} -42.4351i q^{11} +(200.756 + 111.643i) q^{12} -605.383 q^{13} +(804.405 + 208.625i) q^{14} +(9.21223 + 401.183i) q^{15} +(540.241 + 869.894i) q^{16} +409.138i q^{17} +(-271.913 + 1048.43i) q^{18} -2096.86i q^{19} +(-833.291 + 1582.92i) q^{20} -1054.55i q^{21} +(-232.362 - 60.2637i) q^{22} -3048.59i q^{23} +(896.424 - 940.730i) q^{24} +(-3121.71 + 143.441i) q^{25} +(-859.728 + 3314.89i) q^{26} +3118.83 q^{27} +(2284.73 - 4108.40i) q^{28} -4594.96i q^{29} +(2209.84 + 519.291i) q^{30} -5118.83 q^{31} +(5530.49 - 1722.83i) q^{32} +304.619i q^{33} +(2240.32 + 581.033i) q^{34} +(8210.06 - 188.525i) q^{35} +(5354.72 + 2977.82i) q^{36} -11248.5 q^{37} +(-11481.8 - 2977.83i) q^{38} +4345.73 q^{39} +(7484.18 + 6810.80i) q^{40} +11002.0 q^{41} +(-5774.40 - 1497.61i) q^{42} +8413.16 q^{43} +(-659.971 + 1186.76i) q^{44} +(245.715 + 10700.7i) q^{45} +(-16693.2 - 4329.42i) q^{46} +3975.72i q^{47} +(-3878.11 - 6244.51i) q^{48} -4774.02 q^{49} +(-3647.81 + 17297.2i) q^{50} -2936.99i q^{51} +(16930.4 + 9415.21i) q^{52} -38273.5 q^{53} +(4429.16 - 17077.7i) q^{54} +(-2371.57 + 54.4575i) q^{55} +(-19251.7 - 18345.0i) q^{56} +15052.2i q^{57} +(-25160.6 - 6525.47i) q^{58} +36611.0i q^{59} +(5981.75 - 11362.9i) q^{60} +3181.32i q^{61} +(-7269.44 + 28029.1i) q^{62} -28127.8i q^{63} +(-1579.62 - 32729.9i) q^{64} +(776.897 + 33833.0i) q^{65} +(1668.00 + 432.601i) q^{66} +41894.6 q^{67} +(6363.11 - 11442.1i) q^{68} +21884.2i q^{69} +(10627.1 - 45223.5i) q^{70} +72161.6 q^{71} +(23910.1 - 25091.9i) q^{72} -48275.5i q^{73} +(-15974.4 + 61593.2i) q^{74} +(22409.1 - 1029.69i) q^{75} +(-32611.3 + 58641.7i) q^{76} +6233.92 q^{77} +(6171.53 - 23795.9i) q^{78} -39428.9 q^{79} +(47922.4 - 31308.8i) q^{80} +24138.7 q^{81} +(15624.4 - 60243.7i) q^{82} -46504.5 q^{83} +(-16400.9 + 29492.0i) q^{84} +(22865.5 - 525.053i) q^{85} +(11947.8 - 46067.9i) q^{86} +32984.8i q^{87} +(5561.07 + 5299.16i) q^{88} -38217.3 q^{89} +(58942.4 + 13850.9i) q^{90} -88933.7i q^{91} +(-47413.2 + 85258.2i) q^{92} +36745.3 q^{93} +(21769.8 + 5646.07i) q^{94} +(-117187. + 2690.93i) q^{95} +(-39700.4 + 12367.3i) q^{96} -95979.0i q^{97} +(-6779.76 + 26141.1i) q^{98} +8125.03i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36}+ \cdots - 236176 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.42014 5.47569i 0.251047 0.967975i
\(3\) −7.17847 −0.460499 −0.230250 0.973132i \(-0.573954\pi\)
−0.230250 + 0.973132i \(0.573954\pi\)
\(4\) −27.9664 15.5525i −0.873951 0.486015i
\(5\) −1.28331 55.8870i −0.0229566 0.999736i
\(6\) −10.1944 + 39.3071i −0.115607 + 0.445751i
\(7\) 146.905i 1.13316i 0.824007 + 0.566580i \(0.191734\pi\)
−0.824007 + 0.566580i \(0.808266\pi\)
\(8\) −124.877 + 131.049i −0.689853 + 0.723950i
\(9\) −191.470 −0.787941
\(10\) −307.842 72.3401i −0.973483 0.228760i
\(11\) 42.4351i 0.105741i −0.998601 0.0528705i \(-0.983163\pi\)
0.998601 0.0528705i \(-0.0168371\pi\)
\(12\) 200.756 + 111.643i 0.402453 + 0.223809i
\(13\) −605.383 −0.993510 −0.496755 0.867891i \(-0.665475\pi\)
−0.496755 + 0.867891i \(0.665475\pi\)
\(14\) 804.405 + 208.625i 1.09687 + 0.284476i
\(15\) 9.21223 + 401.183i 0.0105715 + 0.460378i
\(16\) 540.241 + 869.894i 0.527579 + 0.849506i
\(17\) 409.138i 0.343359i 0.985153 + 0.171679i \(0.0549193\pi\)
−0.985153 + 0.171679i \(0.945081\pi\)
\(18\) −271.913 + 1048.43i −0.197810 + 0.762707i
\(19\) 2096.86i 1.33256i −0.745704 0.666278i \(-0.767886\pi\)
0.745704 0.666278i \(-0.232114\pi\)
\(20\) −833.291 + 1582.92i −0.465824 + 0.884878i
\(21\) 1054.55i 0.521819i
\(22\) −232.362 60.2637i −0.102355 0.0265460i
\(23\) 3048.59i 1.20166i −0.799379 0.600828i \(-0.794838\pi\)
0.799379 0.600828i \(-0.205162\pi\)
\(24\) 896.424 940.730i 0.317677 0.333378i
\(25\) −3121.71 + 143.441i −0.998946 + 0.0459011i
\(26\) −859.728 + 3314.89i −0.249418 + 0.961693i
\(27\) 3118.83 0.823345
\(28\) 2284.73 4108.40i 0.550732 0.990325i
\(29\) 4594.96i 1.01458i −0.861775 0.507290i \(-0.830647\pi\)
0.861775 0.507290i \(-0.169353\pi\)
\(30\) 2209.84 + 519.291i 0.448288 + 0.105344i
\(31\) −5118.83 −0.956679 −0.478339 0.878175i \(-0.658761\pi\)
−0.478339 + 0.878175i \(0.658761\pi\)
\(32\) 5530.49 1722.83i 0.954747 0.297418i
\(33\) 304.619i 0.0486937i
\(34\) 2240.32 + 581.033i 0.332363 + 0.0861992i
\(35\) 8210.06 188.525i 1.13286 0.0260135i
\(36\) 5354.72 + 2977.82i 0.688621 + 0.382951i
\(37\) −11248.5 −1.35080 −0.675398 0.737454i \(-0.736028\pi\)
−0.675398 + 0.737454i \(0.736028\pi\)
\(38\) −11481.8 2977.83i −1.28988 0.334534i
\(39\) 4345.73 0.457510
\(40\) 7484.18 + 6810.80i 0.739596 + 0.673052i
\(41\) 11002.0 1.02215 0.511073 0.859537i \(-0.329248\pi\)
0.511073 + 0.859537i \(0.329248\pi\)
\(42\) −5774.40 1497.61i −0.505107 0.131001i
\(43\) 8413.16 0.693886 0.346943 0.937886i \(-0.387220\pi\)
0.346943 + 0.937886i \(0.387220\pi\)
\(44\) −659.971 + 1186.76i −0.0513917 + 0.0924125i
\(45\) 245.715 + 10700.7i 0.0180884 + 0.787733i
\(46\) −16693.2 4329.42i −1.16317 0.301672i
\(47\) 3975.72i 0.262525i 0.991348 + 0.131263i \(0.0419031\pi\)
−0.991348 + 0.131263i \(0.958097\pi\)
\(48\) −3878.11 6244.51i −0.242950 0.391197i
\(49\) −4774.02 −0.284049
\(50\) −3647.81 + 17297.2i −0.206351 + 0.978478i
\(51\) 2936.99i 0.158116i
\(52\) 16930.4 + 9415.21i 0.868279 + 0.482860i
\(53\) −38273.5 −1.87158 −0.935790 0.352558i \(-0.885312\pi\)
−0.935790 + 0.352558i \(0.885312\pi\)
\(54\) 4429.16 17077.7i 0.206698 0.796977i
\(55\) −2371.57 + 54.4575i −0.105713 + 0.00242746i
\(56\) −19251.7 18345.0i −0.820350 0.781713i
\(57\) 15052.2i 0.613641i
\(58\) −25160.6 6525.47i −0.982088 0.254707i
\(59\) 36611.0i 1.36924i 0.728898 + 0.684622i \(0.240033\pi\)
−0.728898 + 0.684622i \(0.759967\pi\)
\(60\) 5981.75 11362.9i 0.214511 0.407485i
\(61\) 3181.32i 0.109467i 0.998501 + 0.0547335i \(0.0174309\pi\)
−0.998501 + 0.0547335i \(0.982569\pi\)
\(62\) −7269.44 + 28029.1i −0.240172 + 0.926041i
\(63\) 28127.8i 0.892862i
\(64\) −1579.62 32729.9i −0.0482062 0.998837i
\(65\) 776.897 + 33833.0i 0.0228076 + 0.993248i
\(66\) 1668.00 + 432.601i 0.0471342 + 0.0122244i
\(67\) 41894.6 1.14017 0.570087 0.821584i \(-0.306909\pi\)
0.570087 + 0.821584i \(0.306909\pi\)
\(68\) 6363.11 11442.1i 0.166877 0.300079i
\(69\) 21884.2i 0.553361i
\(70\) 10627.1 45223.5i 0.259221 1.10311i
\(71\) 72161.6 1.69887 0.849435 0.527693i \(-0.176943\pi\)
0.849435 + 0.527693i \(0.176943\pi\)
\(72\) 23910.1 25091.9i 0.543563 0.570429i
\(73\) 48275.5i 1.06028i −0.847911 0.530138i \(-0.822140\pi\)
0.847911 0.530138i \(-0.177860\pi\)
\(74\) −15974.4 + 61593.2i −0.339113 + 1.30754i
\(75\) 22409.1 1029.69i 0.460014 0.0211374i
\(76\) −32611.3 + 58641.7i −0.647642 + 1.16459i
\(77\) 6233.92 0.119821
\(78\) 6171.53 23795.9i 0.114857 0.442859i
\(79\) −39428.9 −0.710798 −0.355399 0.934715i \(-0.615655\pi\)
−0.355399 + 0.934715i \(0.615655\pi\)
\(80\) 47922.4 31308.8i 0.837170 0.546942i
\(81\) 24138.7 0.408791
\(82\) 15624.4 60243.7i 0.256607 0.989412i
\(83\) −46504.5 −0.740968 −0.370484 0.928839i \(-0.620808\pi\)
−0.370484 + 0.928839i \(0.620808\pi\)
\(84\) −16400.9 + 29492.0i −0.253612 + 0.456044i
\(85\) 22865.5 525.053i 0.343268 0.00788235i
\(86\) 11947.8 46067.9i 0.174198 0.671664i
\(87\) 32984.8i 0.467213i
\(88\) 5561.07 + 5299.16i 0.0765512 + 0.0729458i
\(89\) −38217.3 −0.511428 −0.255714 0.966752i \(-0.582311\pi\)
−0.255714 + 0.966752i \(0.582311\pi\)
\(90\) 58942.4 + 13850.9i 0.767047 + 0.180249i
\(91\) 88933.7i 1.12580i
\(92\) −47413.2 + 85258.2i −0.584022 + 1.05019i
\(93\) 36745.3 0.440550
\(94\) 21769.8 + 5646.07i 0.254118 + 0.0659062i
\(95\) −117187. + 2690.93i −1.33220 + 0.0305910i
\(96\) −39700.4 + 12367.3i −0.439660 + 0.136961i
\(97\) 95979.0i 1.03573i −0.855462 0.517865i \(-0.826727\pi\)
0.855462 0.517865i \(-0.173273\pi\)
\(98\) −6779.76 + 26141.1i −0.0713098 + 0.274953i
\(99\) 8125.03i 0.0833177i
\(100\) 89533.8 + 44538.7i 0.895338 + 0.445387i
\(101\) 83900.0i 0.818386i −0.912448 0.409193i \(-0.865810\pi\)
0.912448 0.409193i \(-0.134190\pi\)
\(102\) −16082.0 4170.93i −0.153053 0.0396947i
\(103\) 10693.4i 0.0993165i 0.998766 + 0.0496583i \(0.0158132\pi\)
−0.998766 + 0.0496583i \(0.984187\pi\)
\(104\) 75598.3 79334.8i 0.685376 0.719251i
\(105\) −58935.7 + 1353.32i −0.521681 + 0.0119792i
\(106\) −54353.6 + 209574.i −0.469855 + 1.81164i
\(107\) −109794. −0.927081 −0.463540 0.886076i \(-0.653421\pi\)
−0.463540 + 0.886076i \(0.653421\pi\)
\(108\) −87222.4 48505.5i −0.719563 0.400158i
\(109\) 135615.i 1.09330i −0.837361 0.546651i \(-0.815903\pi\)
0.837361 0.546651i \(-0.184097\pi\)
\(110\) −3069.76 + 13063.3i −0.0241893 + 0.102937i
\(111\) 80746.9 0.622040
\(112\) −127792. + 79364.0i −0.962625 + 0.597831i
\(113\) 195440.i 1.43985i 0.694050 + 0.719927i \(0.255825\pi\)
−0.694050 + 0.719927i \(0.744175\pi\)
\(114\) 82421.5 + 21376.3i 0.593989 + 0.154053i
\(115\) −170377. + 3912.30i −1.20134 + 0.0275859i
\(116\) −71462.9 + 128504.i −0.493101 + 0.886693i
\(117\) 115913. 0.782827
\(118\) 200470. + 51992.6i 1.32539 + 0.343745i
\(119\) −60104.4 −0.389080
\(120\) −53725.0 48891.1i −0.340583 0.309940i
\(121\) 159250. 0.988819
\(122\) 17420.0 + 4517.92i 0.105961 + 0.0274814i
\(123\) −78977.7 −0.470697
\(124\) 143155. + 79610.4i 0.836090 + 0.464960i
\(125\) 12022.6 + 174279.i 0.0688214 + 0.997629i
\(126\) −154019. 39945.3i −0.864268 0.224150i
\(127\) 171245.i 0.942126i 0.882100 + 0.471063i \(0.156130\pi\)
−0.882100 + 0.471063i \(0.843870\pi\)
\(128\) −181462. 37831.4i −0.978952 0.204093i
\(129\) −60393.6 −0.319534
\(130\) 186363. + 43793.5i 0.967165 + 0.227275i
\(131\) 111420.i 0.567265i −0.958933 0.283632i \(-0.908460\pi\)
0.958933 0.283632i \(-0.0915395\pi\)
\(132\) 4737.58 8519.11i 0.0236658 0.0425559i
\(133\) 308039. 1.51000
\(134\) 59496.1 229402.i 0.286238 1.10366i
\(135\) −4002.43 174302.i −0.0189012 0.823128i
\(136\) −53617.1 51091.9i −0.248574 0.236867i
\(137\) 282243.i 1.28476i −0.766387 0.642379i \(-0.777948\pi\)
0.766387 0.642379i \(-0.222052\pi\)
\(138\) 119831. + 31078.6i 0.535640 + 0.138920i
\(139\) 44060.1i 0.193423i 0.995312 + 0.0967117i \(0.0308325\pi\)
−0.995312 + 0.0967117i \(0.969168\pi\)
\(140\) −232538. 122414.i −1.00271 0.527852i
\(141\) 28539.6i 0.120893i
\(142\) 102479. 395135.i 0.426496 1.64446i
\(143\) 25689.5i 0.105055i
\(144\) −103440. 166558.i −0.415701 0.669360i
\(145\) −256798. + 5896.77i −1.01431 + 0.0232913i
\(146\) −264342. 68557.8i −1.02632 0.266180i
\(147\) 34270.1 0.130804
\(148\) 314580. + 174942.i 1.18053 + 0.656506i
\(149\) 251552.i 0.928244i 0.885771 + 0.464122i \(0.153630\pi\)
−0.885771 + 0.464122i \(0.846370\pi\)
\(150\) 26185.7 124167.i 0.0950246 0.450588i
\(151\) 95790.0 0.341883 0.170942 0.985281i \(-0.445319\pi\)
0.170942 + 0.985281i \(0.445319\pi\)
\(152\) 274791. + 261849.i 0.964703 + 0.919267i
\(153\) 78337.6i 0.270546i
\(154\) 8853.02 34135.0i 0.0300808 0.115984i
\(155\) 6569.06 + 286076.i 0.0219621 + 0.956427i
\(156\) −121534. 67586.8i −0.399841 0.222357i
\(157\) −178462. −0.577824 −0.288912 0.957356i \(-0.593294\pi\)
−0.288912 + 0.957356i \(0.593294\pi\)
\(158\) −55994.4 + 215900.i −0.178444 + 0.688035i
\(159\) 274745. 0.861861
\(160\) −103381. 306871.i −0.319257 0.947668i
\(161\) 447853. 1.36167
\(162\) 34280.3 132176.i 0.102626 0.395699i
\(163\) 147330. 0.434332 0.217166 0.976135i \(-0.430319\pi\)
0.217166 + 0.976135i \(0.430319\pi\)
\(164\) −307687. 171109.i −0.893305 0.496778i
\(165\) 17024.2 390.922i 0.0486808 0.00111784i
\(166\) −66042.7 + 254644.i −0.186018 + 0.717239i
\(167\) 310989.i 0.862888i 0.902140 + 0.431444i \(0.141996\pi\)
−0.902140 + 0.431444i \(0.858004\pi\)
\(168\) 138198. + 131689.i 0.377770 + 0.359978i
\(169\) −4803.84 −0.0129381
\(170\) 29597.1 125950.i 0.0785466 0.334254i
\(171\) 401485.i 1.04997i
\(172\) −235286. 130845.i −0.606422 0.337239i
\(173\) −120278. −0.305542 −0.152771 0.988262i \(-0.548820\pi\)
−0.152771 + 0.988262i \(0.548820\pi\)
\(174\) 180614. + 46842.9i 0.452251 + 0.117293i
\(175\) −21072.2 458594.i −0.0520133 1.13196i
\(176\) 36914.0 22925.2i 0.0898276 0.0557868i
\(177\) 262811.i 0.630536i
\(178\) −54273.8 + 209266.i −0.128393 + 0.495050i
\(179\) 180544.i 0.421162i −0.977576 0.210581i \(-0.932464\pi\)
0.977576 0.210581i \(-0.0675356\pi\)
\(180\) 159550. 303080.i 0.367041 0.697231i
\(181\) 149699.i 0.339643i −0.985475 0.169821i \(-0.945681\pi\)
0.985475 0.169821i \(-0.0543191\pi\)
\(182\) −486974. 126298.i −1.08975 0.282630i
\(183\) 22837.0i 0.0504095i
\(184\) 399515. + 380698.i 0.869938 + 0.828965i
\(185\) 14435.3 + 628643.i 0.0310097 + 1.35044i
\(186\) 52183.4 201206.i 0.110599 0.426441i
\(187\) 17361.8 0.0363071
\(188\) 61832.2 111187.i 0.127591 0.229434i
\(189\) 458171.i 0.932981i
\(190\) −151687. + 645502.i −0.304835 + 1.29722i
\(191\) 213909. 0.424273 0.212136 0.977240i \(-0.431958\pi\)
0.212136 + 0.977240i \(0.431958\pi\)
\(192\) 11339.3 + 234951.i 0.0221989 + 0.459964i
\(193\) 729587.i 1.40988i 0.709265 + 0.704942i \(0.249027\pi\)
−0.709265 + 0.704942i \(0.750973\pi\)
\(194\) −525551. 136303.i −1.00256 0.260017i
\(195\) −5576.93 242869.i −0.0105029 0.457390i
\(196\) 133512. + 74247.8i 0.248245 + 0.138052i
\(197\) −922110. −1.69285 −0.846423 0.532512i \(-0.821248\pi\)
−0.846423 + 0.532512i \(0.821248\pi\)
\(198\) 44490.2 + 11538.7i 0.0806494 + 0.0209167i
\(199\) −985328. −1.76379 −0.881897 0.471442i \(-0.843734\pi\)
−0.881897 + 0.471442i \(0.843734\pi\)
\(200\) 371031. 427009.i 0.655896 0.754852i
\(201\) −300739. −0.525049
\(202\) −459410. 119149.i −0.792177 0.205454i
\(203\) 675021. 1.14968
\(204\) −45677.4 + 82137.0i −0.0768469 + 0.138186i
\(205\) −14119.0 614870.i −0.0234650 1.02188i
\(206\) 58553.6 + 15186.0i 0.0961359 + 0.0249331i
\(207\) 583713.i 0.946833i
\(208\) −327053. 526619.i −0.524155 0.843992i
\(209\) −88980.5 −0.140906
\(210\) −76286.4 + 324636.i −0.119371 + 0.507982i
\(211\) 932526.i 1.44197i −0.692953 0.720983i \(-0.743691\pi\)
0.692953 0.720983i \(-0.256309\pi\)
\(212\) 1.07037e6 + 595247.i 1.63567 + 0.909615i
\(213\) −518010. −0.782328
\(214\) −155922. + 601196.i −0.232741 + 0.897391i
\(215\) −10796.7 470186.i −0.0159293 0.693703i
\(216\) −389469. + 408719.i −0.567987 + 0.596060i
\(217\) 751980.i 1.08407i
\(218\) −742584. 192591.i −1.05829 0.274470i
\(219\) 346544.i 0.488257i
\(220\) 67171.3 + 35360.8i 0.0935679 + 0.0492567i
\(221\) 247686.i 0.341130i
\(222\) 114672. 442145.i 0.156161 0.602119i
\(223\) 748564.i 1.00801i −0.863699 0.504007i \(-0.831858\pi\)
0.863699 0.504007i \(-0.168142\pi\)
\(224\) 253092. + 812455.i 0.337022 + 1.08188i
\(225\) 597712. 27464.6i 0.787110 0.0361674i
\(226\) 1.07017e6 + 277552.i 1.39374 + 0.361471i
\(227\) 1.47117e6 1.89495 0.947475 0.319829i \(-0.103626\pi\)
0.947475 + 0.319829i \(0.103626\pi\)
\(228\) 234100. 420957.i 0.298238 0.536292i
\(229\) 835029.i 1.05223i −0.850412 0.526117i \(-0.823647\pi\)
0.850412 0.526117i \(-0.176353\pi\)
\(230\) −220536. + 938486.i −0.274890 + 1.16979i
\(231\) −44750.0 −0.0551777
\(232\) 602164. + 573803.i 0.734505 + 0.699911i
\(233\) 284718.i 0.343577i −0.985134 0.171789i \(-0.945045\pi\)
0.985134 0.171789i \(-0.0549546\pi\)
\(234\) 164612. 634701.i 0.196526 0.757757i
\(235\) 222191. 5102.09i 0.262456 0.00602669i
\(236\) 569391. 1.02388e6i 0.665473 1.19665i
\(237\) 283039. 0.327322
\(238\) −85356.5 + 329113.i −0.0976774 + 0.376620i
\(239\) 800635. 0.906650 0.453325 0.891345i \(-0.350238\pi\)
0.453325 + 0.891345i \(0.350238\pi\)
\(240\) −344010. + 224749.i −0.385516 + 0.251866i
\(241\) −1.50596e6 −1.67021 −0.835107 0.550088i \(-0.814594\pi\)
−0.835107 + 0.550088i \(0.814594\pi\)
\(242\) 226157. 872005.i 0.248240 0.957152i
\(243\) −931154. −1.01159
\(244\) 49477.4 88970.2i 0.0532026 0.0956688i
\(245\) 6126.56 + 266805.i 0.00652081 + 0.283975i
\(246\) −112159. + 432458.i −0.118167 + 0.455623i
\(247\) 1.26940e6i 1.32391i
\(248\) 639222. 670817.i 0.659968 0.692587i
\(249\) 333831. 0.341215
\(250\) 971370. + 181667.i 0.982957 + 0.183835i
\(251\) 1.10255e6i 1.10463i 0.833637 + 0.552313i \(0.186255\pi\)
−0.833637 + 0.552313i \(0.813745\pi\)
\(252\) −437457. + 786634.i −0.433944 + 0.780317i
\(253\) −129367. −0.127064
\(254\) 937686. + 243192.i 0.911955 + 0.236518i
\(255\) −164139. + 3769.08i −0.158075 + 0.00362981i
\(256\) −464854. + 939905.i −0.443320 + 0.896364i
\(257\) 1.41038e6i 1.33200i −0.745953 0.665999i \(-0.768006\pi\)
0.745953 0.665999i \(-0.231994\pi\)
\(258\) −85767.2 + 330697.i −0.0802181 + 0.309301i
\(259\) 1.65246e6i 1.53067i
\(260\) 504460. 958272.i 0.462800 0.879135i
\(261\) 879794.i 0.799429i
\(262\) −610103. 158232.i −0.549098 0.142410i
\(263\) 1.68879e6i 1.50552i −0.658298 0.752758i \(-0.728723\pi\)
0.658298 0.752758i \(-0.271277\pi\)
\(264\) −39920.0 38039.8i −0.0352518 0.0335915i
\(265\) 49116.9 + 2.13899e6i 0.0429651 + 1.87109i
\(266\) 437457. 1.68673e6i 0.379081 1.46164i
\(267\) 274342. 0.235512
\(268\) −1.17164e6 651565.i −0.996456 0.554141i
\(269\) 305848.i 0.257706i 0.991664 + 0.128853i \(0.0411295\pi\)
−0.991664 + 0.128853i \(0.958870\pi\)
\(270\) −960107. 225616.i −0.801512 0.188348i
\(271\) −1.25325e6 −1.03661 −0.518306 0.855195i \(-0.673437\pi\)
−0.518306 + 0.855195i \(0.673437\pi\)
\(272\) −355907. + 221034.i −0.291685 + 0.181149i
\(273\) 638408.i 0.518432i
\(274\) −1.54547e6 400823.i −1.24361 0.322535i
\(275\) 6086.93 + 132470.i 0.00485363 + 0.105630i
\(276\) 340354. 612024.i 0.268942 0.483610i
\(277\) 483396. 0.378533 0.189267 0.981926i \(-0.439389\pi\)
0.189267 + 0.981926i \(0.439389\pi\)
\(278\) 241260. + 62571.4i 0.187229 + 0.0485584i
\(279\) 980100. 0.753806
\(280\) −1.00054e6 + 1.09946e6i −0.762674 + 0.838079i
\(281\) 88721.8 0.0670293 0.0335147 0.999438i \(-0.489330\pi\)
0.0335147 + 0.999438i \(0.489330\pi\)
\(282\) −156274. 40530.1i −0.117021 0.0303497i
\(283\) −1.76445e6 −1.30961 −0.654807 0.755796i \(-0.727250\pi\)
−0.654807 + 0.755796i \(0.727250\pi\)
\(284\) −2.01810e6 1.12229e6i −1.48473 0.825676i
\(285\) 841224. 19316.7i 0.613479 0.0140871i
\(286\) 140668. + 36482.6i 0.101690 + 0.0263737i
\(287\) 1.61625e6i 1.15825i
\(288\) −1.05892e6 + 329869.i −0.752284 + 0.234347i
\(289\) 1.25246e6 0.882105
\(290\) −332400. + 1.41452e6i −0.232095 + 0.987677i
\(291\) 688982.i 0.476953i
\(292\) −750803. + 1.35009e6i −0.515310 + 0.926630i
\(293\) −9124.96 −0.00620957 −0.00310479 0.999995i \(-0.500988\pi\)
−0.00310479 + 0.999995i \(0.500988\pi\)
\(294\) 48668.3 187653.i 0.0328381 0.126615i
\(295\) 2.04608e6 46983.3i 1.36888 0.0314332i
\(296\) 1.40467e6 1.47410e6i 0.931850 0.977908i
\(297\) 132348.i 0.0870614i
\(298\) 1.37742e6 + 357238.i 0.898517 + 0.233033i
\(299\) 1.84557e6i 1.19386i
\(300\) −642716. 319720.i −0.412302 0.205100i
\(301\) 1.23593e6i 0.786283i
\(302\) 136035. 524516.i 0.0858288 0.330934i
\(303\) 602273.i 0.376866i
\(304\) 1.82405e6 1.13281e6i 1.13201 0.703029i
\(305\) 177795. 4082.64i 0.109438 0.00251299i
\(306\) −428952. 111250.i −0.261882 0.0679199i
\(307\) −2.64214e6 −1.59996 −0.799980 0.600026i \(-0.795157\pi\)
−0.799980 + 0.600026i \(0.795157\pi\)
\(308\) −174340. 96952.9i −0.104718 0.0582350i
\(309\) 76762.0i 0.0457352i
\(310\) 1.57579e6 + 370297.i 0.931311 + 0.218849i
\(311\) −1.40253e6 −0.822262 −0.411131 0.911576i \(-0.634866\pi\)
−0.411131 + 0.911576i \(0.634866\pi\)
\(312\) −542680. + 569503.i −0.315615 + 0.331214i
\(313\) 1.35907e6i 0.784115i −0.919941 0.392058i \(-0.871763\pi\)
0.919941 0.392058i \(-0.128237\pi\)
\(314\) −253440. + 977201.i −0.145061 + 0.559319i
\(315\) −1.57198e6 + 36096.8i −0.892627 + 0.0204971i
\(316\) 1.10268e6 + 613216.i 0.621203 + 0.345458i
\(317\) 300344. 0.167869 0.0839344 0.996471i \(-0.473251\pi\)
0.0839344 + 0.996471i \(0.473251\pi\)
\(318\) 390176. 1.50442e6i 0.216368 0.834259i
\(319\) −194987. −0.107283
\(320\) −1.82715e6 + 130283.i −0.997468 + 0.0711234i
\(321\) 788150. 0.426920
\(322\) 636013. 2.45231e6i 0.341842 1.31806i
\(323\) 857906. 0.457545
\(324\) −675073. 375416.i −0.357263 0.198678i
\(325\) 1.88983e6 86836.8i 0.992463 0.0456032i
\(326\) 209228. 806732.i 0.109038 0.420422i
\(327\) 973505.i 0.503464i
\(328\) −1.37390e6 + 1.44180e6i −0.705130 + 0.739982i
\(329\) −584052. −0.297483
\(330\) 22036.2 93774.7i 0.0111391 0.0474024i
\(331\) 2.37543e6i 1.19172i 0.803090 + 0.595858i \(0.203188\pi\)
−0.803090 + 0.595858i \(0.796812\pi\)
\(332\) 1.30056e6 + 723259.i 0.647570 + 0.360121i
\(333\) 2.15374e6 1.06435
\(334\) 1.70288e6 + 441647.i 0.835253 + 0.216625i
\(335\) −53763.9 2.34136e6i −0.0261745 1.13987i
\(336\) 917348. 569712.i 0.443288 0.275301i
\(337\) 3.69929e6i 1.77437i −0.461416 0.887184i \(-0.652659\pi\)
0.461416 0.887184i \(-0.347341\pi\)
\(338\) −6822.11 + 26304.4i −0.00324808 + 0.0125238i
\(339\) 1.40296e6i 0.663051i
\(340\) −647632. 340931.i −0.303830 0.159945i
\(341\) 217218.i 0.101160i
\(342\) 2.19841e6 + 570164.i 1.01635 + 0.263593i
\(343\) 1.76770e6i 0.811286i
\(344\) −1.05061e6 + 1.10254e6i −0.478679 + 0.502339i
\(345\) 1.22304e6 28084.3i 0.553215 0.0127033i
\(346\) −170811. + 658605.i −0.0767054 + 0.295757i
\(347\) 1.98355e6 0.884339 0.442170 0.896931i \(-0.354209\pi\)
0.442170 + 0.896931i \(0.354209\pi\)
\(348\) 512994. 922466.i 0.227072 0.408321i
\(349\) 1.51829e6i 0.667256i −0.942705 0.333628i \(-0.891727\pi\)
0.942705 0.333628i \(-0.108273\pi\)
\(350\) −2.54104e6 535881.i −1.10877 0.233829i
\(351\) −1.88809e6 −0.818001
\(352\) −73108.4 234687.i −0.0314493 0.100956i
\(353\) 2.06194e6i 0.880724i 0.897820 + 0.440362i \(0.145150\pi\)
−0.897820 + 0.440362i \(0.854850\pi\)
\(354\) −1.43907e6 373227.i −0.610343 0.158294i
\(355\) −92605.9 4.03289e6i −0.0390003 1.69842i
\(356\) 1.06880e6 + 594373.i 0.446963 + 0.248562i
\(357\) 431458. 0.179171
\(358\) −988602. 256397.i −0.407675 0.105732i
\(359\) 1.33255e6 0.545691 0.272846 0.962058i \(-0.412035\pi\)
0.272846 + 0.962058i \(0.412035\pi\)
\(360\) −1.43299e6 1.30406e6i −0.582757 0.530325i
\(361\) −1.92072e6 −0.775705
\(362\) −819705. 212593.i −0.328766 0.0852663i
\(363\) −1.14317e6 −0.455350
\(364\) −1.38314e6 + 2.48716e6i −0.547158 + 0.983898i
\(365\) −2.69797e6 + 61952.6i −1.06000 + 0.0243404i
\(366\) −125049. 32431.7i −0.0487951 0.0126552i
\(367\) 313330.i 0.121433i −0.998155 0.0607166i \(-0.980661\pi\)
0.998155 0.0607166i \(-0.0193386\pi\)
\(368\) 2.65195e6 1.64698e6i 1.02081 0.633969i
\(369\) −2.10655e6 −0.805390
\(370\) 3.46276e6 + 813716.i 1.31498 + 0.309007i
\(371\) 5.62256e6i 2.12080i
\(372\) −1.02764e6 571481.i −0.385019 0.214114i
\(373\) 2.93069e6 1.09068 0.545341 0.838215i \(-0.316400\pi\)
0.545341 + 0.838215i \(0.316400\pi\)
\(374\) 24656.2 95068.1i 0.00911480 0.0351444i
\(375\) −86303.9 1.25105e6i −0.0316922 0.459407i
\(376\) −521014. 496475.i −0.190055 0.181104i
\(377\) 2.78171e6i 1.00800i
\(378\) 2.50880e6 + 650665.i 0.903102 + 0.234222i
\(379\) 4.10811e6i 1.46907i 0.678569 + 0.734537i \(0.262601\pi\)
−0.678569 + 0.734537i \(0.737399\pi\)
\(380\) 3.31916e6 + 1.74729e6i 1.17915 + 0.620736i
\(381\) 1.22928e6i 0.433848i
\(382\) 303780. 1.17130e6i 0.106512 0.410685i
\(383\) 958991.i 0.334055i −0.985952 0.167027i \(-0.946583\pi\)
0.985952 0.167027i \(-0.0534168\pi\)
\(384\) 1.30262e6 + 271572.i 0.450806 + 0.0939846i
\(385\) −8000.07 348395.i −0.00275069 0.119790i
\(386\) 3.99499e6 + 1.03611e6i 1.36473 + 0.353948i
\(387\) −1.61086e6 −0.546741
\(388\) −1.49271e6 + 2.68419e6i −0.503380 + 0.905178i
\(389\) 647634.i 0.216998i −0.994097 0.108499i \(-0.965396\pi\)
0.994097 0.108499i \(-0.0346044\pi\)
\(390\) −1.33780e6 314370.i −0.445379 0.104660i
\(391\) 1.24730e6 0.412599
\(392\) 596164. 625630.i 0.195952 0.205637i
\(393\) 799827.i 0.261225i
\(394\) −1.30952e6 + 5.04919e6i −0.424984 + 1.63863i
\(395\) 50599.6 + 2.20356e6i 0.0163175 + 0.710611i
\(396\) 126364. 227228.i 0.0404936 0.0728155i
\(397\) −2.06284e6 −0.656885 −0.328443 0.944524i \(-0.606524\pi\)
−0.328443 + 0.944524i \(0.606524\pi\)
\(398\) −1.39930e6 + 5.39535e6i −0.442796 + 1.70731i
\(399\) −2.21125e6 −0.695352
\(400\) −1.81125e6 2.63806e6i −0.566017 0.824394i
\(401\) −1.92225e6 −0.596964 −0.298482 0.954415i \(-0.596480\pi\)
−0.298482 + 0.954415i \(0.596480\pi\)
\(402\) −427091. + 1.64676e6i −0.131812 + 0.508234i
\(403\) 3.09885e6 0.950470
\(404\) −1.30485e6 + 2.34638e6i −0.397748 + 0.715229i
\(405\) −30977.5 1.34904e6i −0.00938446 0.408683i
\(406\) 958623. 3.69621e6i 0.288624 1.11286i
\(407\) 477330.i 0.142834i
\(408\) 384889. + 366761.i 0.114468 + 0.109077i
\(409\) 1.40471e6 0.415221 0.207610 0.978212i \(-0.433431\pi\)
0.207610 + 0.978212i \(0.433431\pi\)
\(410\) −3.38689e6 795888.i −0.995042 0.233826i
\(411\) 2.02607e6i 0.591630i
\(412\) 166308. 299055.i 0.0482693 0.0867977i
\(413\) −5.37833e6 −1.55157
\(414\) 3.19623e6 + 828952.i 0.916511 + 0.237700i
\(415\) 59679.8 + 2.59899e6i 0.0170101 + 0.740773i
\(416\) −3.34807e6 + 1.04297e6i −0.948551 + 0.295487i
\(417\) 316284.i 0.0890712i
\(418\) −126364. + 487230.i −0.0353740 + 0.136393i
\(419\) 4.03594e6i 1.12308i −0.827451 0.561538i \(-0.810210\pi\)
0.827451 0.561538i \(-0.189790\pi\)
\(420\) 1.66927e6 + 878748.i 0.461746 + 0.243075i
\(421\) 594910.i 0.163586i −0.996649 0.0817929i \(-0.973935\pi\)
0.996649 0.0817929i \(-0.0260646\pi\)
\(422\) −5.10623e6 1.32432e6i −1.39579 0.362001i
\(423\) 761229.i 0.206854i
\(424\) 4.77947e6 5.01570e6i 1.29111 1.35493i
\(425\) −58687.2 1.27721e6i −0.0157605 0.342997i
\(426\) −735645. + 2.83646e6i −0.196401 + 0.757274i
\(427\) −467352. −0.124044
\(428\) 3.07053e6 + 1.70756e6i 0.810223 + 0.450575i
\(429\) 184411.i 0.0483776i
\(430\) −2.58993e6 608609.i −0.675486 0.158733i
\(431\) 4.15801e6 1.07818 0.539091 0.842247i \(-0.318768\pi\)
0.539091 + 0.842247i \(0.318768\pi\)
\(432\) 1.68492e6 + 2.71305e6i 0.434380 + 0.699436i
\(433\) 2.27636e6i 0.583474i 0.956499 + 0.291737i \(0.0942333\pi\)
−0.956499 + 0.291737i \(0.905767\pi\)
\(434\) −4.11761e6 1.06792e6i −1.04935 0.272153i
\(435\) 1.84342e6 42329.8i 0.467090 0.0107256i
\(436\) −2.10914e6 + 3.79265e6i −0.531361 + 0.955492i
\(437\) −6.39247e6 −1.60127
\(438\) 1.89757e6 + 492140.i 0.472620 + 0.122575i
\(439\) −1.28126e6 −0.317305 −0.158653 0.987334i \(-0.550715\pi\)
−0.158653 + 0.987334i \(0.550715\pi\)
\(440\) 289017. 317592.i 0.0711692 0.0782056i
\(441\) 914079. 0.223814
\(442\) −1.35625e6 351748.i −0.330205 0.0856398i
\(443\) 6.01266e6 1.45565 0.727825 0.685763i \(-0.240531\pi\)
0.727825 + 0.685763i \(0.240531\pi\)
\(444\) −2.25820e6 1.25581e6i −0.543632 0.302320i
\(445\) 49044.7 + 2.13585e6i 0.0117407 + 0.511294i
\(446\) −4.09891e6 1.06306e6i −0.975733 0.253059i
\(447\) 1.80576e6i 0.427455i
\(448\) 4.80818e6 232054.i 1.13184 0.0546253i
\(449\) 2.11543e6 0.495202 0.247601 0.968862i \(-0.420358\pi\)
0.247601 + 0.968862i \(0.420358\pi\)
\(450\) 698445. 3.31189e6i 0.162593 0.770983i
\(451\) 466872.i 0.108083i
\(452\) 3.03958e6 5.46577e6i 0.699790 1.25836i
\(453\) −687625. −0.157437
\(454\) 2.08926e6 8.05567e6i 0.475722 1.83426i
\(455\) −4.97024e6 + 114130.i −1.12551 + 0.0258447i
\(456\) −1.97258e6 1.87967e6i −0.444245 0.423322i
\(457\) 1.35964e6i 0.304533i −0.988339 0.152267i \(-0.951343\pi\)
0.988339 0.152267i \(-0.0486573\pi\)
\(458\) −4.57236e6 1.18586e6i −1.01854 0.264161i
\(459\) 1.27603e6i 0.282703i
\(460\) 4.82567e6 + 2.54036e6i 1.06332 + 0.559759i
\(461\) 2.06438e6i 0.452415i 0.974079 + 0.226208i \(0.0726328\pi\)
−0.974079 + 0.226208i \(0.927367\pi\)
\(462\) −63551.2 + 245037.i −0.0138522 + 0.0534106i
\(463\) 1.48917e6i 0.322843i 0.986886 + 0.161421i \(0.0516078\pi\)
−0.986886 + 0.161421i \(0.948392\pi\)
\(464\) 3.99712e6 2.48239e6i 0.861892 0.535272i
\(465\) −47155.8 2.05359e6i −0.0101135 0.440434i
\(466\) −1.55903e6 404338.i −0.332574 0.0862541i
\(467\) 7.05856e6 1.49770 0.748849 0.662741i \(-0.230607\pi\)
0.748849 + 0.662741i \(0.230607\pi\)
\(468\) −3.24166e6 1.80273e6i −0.684152 0.380465i
\(469\) 6.15452e6i 1.29200i
\(470\) 287604. 1.22389e6i 0.0600552 0.255564i
\(471\) 1.28108e6 0.266087
\(472\) −4.79783e6 4.57186e6i −0.991264 0.944577i
\(473\) 357014.i 0.0733722i
\(474\) 401954. 1.54983e6i 0.0821732 0.316839i
\(475\) 300776. + 6.54578e6i 0.0611658 + 1.33115i
\(476\) 1.68090e6 + 934772.i 0.340037 + 0.189099i
\(477\) 7.32821e6 1.47469
\(478\) 1.13701e6 4.38403e6i 0.227612 0.877614i
\(479\) 1.47482e6 0.293697 0.146849 0.989159i \(-0.453087\pi\)
0.146849 + 0.989159i \(0.453087\pi\)
\(480\) 742117. + 2.20287e6i 0.147018 + 0.436400i
\(481\) 6.80964e6 1.34203
\(482\) −2.13867e6 + 8.24619e6i −0.419302 + 1.61672i
\(483\) −3.21490e6 −0.627046
\(484\) −4.45366e6 2.47673e6i −0.864179 0.480580i
\(485\) −5.36397e6 + 123171.i −1.03546 + 0.0237769i
\(486\) −1.32237e6 + 5.09871e6i −0.253958 + 0.979196i
\(487\) 9.13416e6i 1.74520i −0.488433 0.872602i \(-0.662431\pi\)
0.488433 0.872602i \(-0.337569\pi\)
\(488\) −416909. 397273.i −0.0792486 0.0755161i
\(489\) −1.05760e6 −0.200009
\(490\) 1.46964e6 + 345353.i 0.276517 + 0.0649790i
\(491\) 4.74188e6i 0.887660i 0.896111 + 0.443830i \(0.146381\pi\)
−0.896111 + 0.443830i \(0.853619\pi\)
\(492\) 2.20872e6 + 1.22830e6i 0.411366 + 0.228766i
\(493\) 1.87997e6 0.348365
\(494\) 6.95087e6 + 1.80273e6i 1.28151 + 0.332363i
\(495\) 454083. 10427.0i 0.0832957 0.00191269i
\(496\) −2.76540e6 4.45284e6i −0.504724 0.812704i
\(497\) 1.06009e7i 1.92509i
\(498\) 474086. 1.82796e6i 0.0856611 0.330288i
\(499\) 539009.i 0.0969046i −0.998825 0.0484523i \(-0.984571\pi\)
0.998825 0.0484523i \(-0.0154289\pi\)
\(500\) 2.37423e6 5.06093e6i 0.424716 0.905327i
\(501\) 2.23243e6i 0.397359i
\(502\) 6.03724e6 + 1.56578e6i 1.06925 + 0.277313i
\(503\) 2.21657e6i 0.390627i 0.980741 + 0.195313i \(0.0625724\pi\)
−0.980741 + 0.195313i \(0.937428\pi\)
\(504\) 3.68612e6 + 3.51251e6i 0.646387 + 0.615943i
\(505\) −4.68891e6 + 107670.i −0.818171 + 0.0187874i
\(506\) −183719. + 708376.i −0.0318991 + 0.122995i
\(507\) 34484.2 0.00595800
\(508\) 2.66329e6 4.78912e6i 0.457887 0.823372i
\(509\) 3.35132e6i 0.573352i −0.958028 0.286676i \(-0.907450\pi\)
0.958028 0.286676i \(-0.0925503\pi\)
\(510\) −212462. + 904129.i −0.0361706 + 0.153924i
\(511\) 7.09190e6 1.20146
\(512\) 4.48648e6 + 3.88019e6i 0.756363 + 0.654152i
\(513\) 6.53974e6i 1.09715i
\(514\) −7.72281e6 2.00293e6i −1.28934 0.334394i
\(515\) 597620. 13722.9i 0.0992903 0.00227997i
\(516\) 1.68899e6 + 939270.i 0.279257 + 0.155298i
\(517\) 168710. 0.0277597
\(518\) −9.04834e6 2.34671e6i −1.48165 0.384269i
\(519\) 863411. 0.140702
\(520\) −4.53080e6 4.12315e6i −0.734795 0.668683i
\(521\) 5.01924e6 0.810109 0.405054 0.914293i \(-0.367253\pi\)
0.405054 + 0.914293i \(0.367253\pi\)
\(522\) 4.81748e6 + 1.24943e6i 0.773827 + 0.200694i
\(523\) −3.44581e6 −0.550855 −0.275428 0.961322i \(-0.588819\pi\)
−0.275428 + 0.961322i \(0.588819\pi\)
\(524\) −1.73286e6 + 3.11602e6i −0.275699 + 0.495761i
\(525\) 151266. + 3.29200e6i 0.0239521 + 0.521269i
\(526\) −9.24727e6 2.39831e6i −1.45730 0.377955i
\(527\) 2.09431e6i 0.328484i
\(528\) −264986. + 164568.i −0.0413655 + 0.0256898i
\(529\) −2.85758e6 −0.443975
\(530\) 1.17822e7 + 2.76871e6i 1.82195 + 0.428142i
\(531\) 7.00988e6i 1.07888i
\(532\) −8.61474e6 4.79076e6i −1.31966 0.733881i
\(533\) −6.66044e6 −1.01551
\(534\) 389603. 1.50221e6i 0.0591247 0.227970i
\(535\) 140900. + 6.13603e6i 0.0212826 + 0.926836i
\(536\) −5.23166e6 + 5.49024e6i −0.786552 + 0.825429i
\(537\) 1.29603e6i 0.193945i
\(538\) 1.67473e6 + 434346.i 0.249453 + 0.0646963i
\(539\) 202586.i 0.0300357i
\(540\) −2.59889e6 + 4.93684e6i −0.383534 + 0.728559i
\(541\) 3.97667e6i 0.584153i −0.956395 0.292076i \(-0.905654\pi\)
0.956395 0.292076i \(-0.0943461\pi\)
\(542\) −1.77979e6 + 6.86244e6i −0.260238 + 1.00341i
\(543\) 1.07461e6i 0.156405i
\(544\) 704875. + 2.26274e6i 0.102121 + 0.327821i
\(545\) −7.57908e6 + 174036.i −1.09301 + 0.0250985i
\(546\) 3.49573e6 + 906627.i 0.501829 + 0.130151i
\(547\) −9.20664e6 −1.31563 −0.657814 0.753181i \(-0.728519\pi\)
−0.657814 + 0.753181i \(0.728519\pi\)
\(548\) −4.38957e6 + 7.89332e6i −0.624411 + 1.12281i
\(549\) 609127.i 0.0862535i
\(550\) 734009. + 154795.i 0.103465 + 0.0218198i
\(551\) −9.63498e6 −1.35198
\(552\) −2.86790e6 2.73283e6i −0.400606 0.381738i
\(553\) 5.79229e6i 0.805448i
\(554\) 686489. 2.64693e6i 0.0950296 0.366410i
\(555\) −103624. 4.51270e6i −0.0142799 0.621876i
\(556\) 685244. 1.23220e6i 0.0940066 0.169042i
\(557\) 6.00805e6 0.820531 0.410266 0.911966i \(-0.365436\pi\)
0.410266 + 0.911966i \(0.365436\pi\)
\(558\) 1.39188e6 5.36672e6i 0.189241 0.729665i
\(559\) −5.09319e6 −0.689383
\(560\) 4.59941e6 + 7.04003e6i 0.619773 + 0.948647i
\(561\) −124631. −0.0167194
\(562\) 125997. 485814.i 0.0168275 0.0648827i
\(563\) −3.22469e6 −0.428763 −0.214381 0.976750i \(-0.568774\pi\)
−0.214381 + 0.976750i \(0.568774\pi\)
\(564\) −443861. + 798150.i −0.0587556 + 0.105654i
\(565\) 1.09226e7 250811.i 1.43947 0.0330542i
\(566\) −2.50576e6 + 9.66158e6i −0.328775 + 1.26767i
\(567\) 3.54609e6i 0.463225i
\(568\) −9.01130e6 + 9.45669e6i −1.17197 + 1.22990i
\(569\) −3.74802e6 −0.485312 −0.242656 0.970112i \(-0.578019\pi\)
−0.242656 + 0.970112i \(0.578019\pi\)
\(570\) 1.08888e6 4.63372e6i 0.140376 0.597369i
\(571\) 4.37966e6i 0.562148i −0.959686 0.281074i \(-0.909309\pi\)
0.959686 0.281074i \(-0.0906906\pi\)
\(572\) 399535. 718444.i 0.0510582 0.0918127i
\(573\) −1.53554e6 −0.195377
\(574\) 8.85009e6 + 2.29530e6i 1.12116 + 0.290776i
\(575\) 437293. + 9.51681e6i 0.0551573 + 1.20039i
\(576\) 302449. + 6.26678e6i 0.0379836 + 0.787025i
\(577\) 1.03145e7i 1.28976i 0.764284 + 0.644880i \(0.223093\pi\)
−0.764284 + 0.644880i \(0.776907\pi\)
\(578\) 1.77867e6 6.85810e6i 0.221450 0.853855i
\(579\) 5.23732e6i 0.649251i
\(580\) 7.27344e6 + 3.82893e6i 0.897779 + 0.472615i
\(581\) 6.83173e6i 0.839635i
\(582\) 3.77266e6 + 978449.i 0.461679 + 0.119738i
\(583\) 1.62414e6i 0.197903i
\(584\) 6.32645e6 + 6.02848e6i 0.767587 + 0.731435i
\(585\) −148752. 6.47800e6i −0.0179710 0.782620i
\(586\) −12958.7 + 49965.5i −0.00155890 + 0.00601071i
\(587\) −5.88489e6 −0.704925 −0.352463 0.935826i \(-0.614656\pi\)
−0.352463 + 0.935826i \(0.614656\pi\)
\(588\) −958413. 532985.i −0.114317 0.0635729i
\(589\) 1.07335e7i 1.27483i
\(590\) 2.64844e6 1.12704e7i 0.313228 1.33294i
\(591\) 6.61934e6 0.779554
\(592\) −6.07689e6 9.78498e6i −0.712652 1.14751i
\(593\) 1.07458e7i 1.25488i −0.778664 0.627442i \(-0.784102\pi\)
0.778664 0.627442i \(-0.215898\pi\)
\(594\) −724696. 187952.i −0.0842732 0.0218565i
\(595\) 77132.8 + 3.35905e6i 0.00893196 + 0.388977i
\(596\) 3.91226e6 7.03501e6i 0.451140 0.811239i
\(597\) 7.07314e6 0.812226
\(598\) 1.01058e7 + 2.62096e6i 1.15562 + 0.299714i
\(599\) 1.01249e6 0.115299 0.0576493 0.998337i \(-0.481639\pi\)
0.0576493 + 0.998337i \(0.481639\pi\)
\(600\) −2.66343e6 + 3.06527e6i −0.302039 + 0.347608i
\(601\) 7.16049e6 0.808643 0.404321 0.914617i \(-0.367508\pi\)
0.404321 + 0.914617i \(0.367508\pi\)
\(602\) 6.76759e6 + 1.75520e6i 0.761102 + 0.197394i
\(603\) −8.02154e6 −0.898390
\(604\) −2.67890e6 1.48977e6i −0.298789 0.166160i
\(605\) −204368. 8.90001e6i −0.0226999 0.988558i
\(606\) 3.29786e6 + 855311.i 0.364797 + 0.0946112i
\(607\) 1.22036e7i 1.34437i −0.740385 0.672183i \(-0.765357\pi\)
0.740385 0.672183i \(-0.234643\pi\)
\(608\) −3.61253e6 1.15967e7i −0.396326 1.27225i
\(609\) −4.84562e6 −0.529427
\(610\) 230137. 979346.i 0.0250416 0.106564i
\(611\) 2.40683e6i 0.260821i
\(612\) −1.21834e6 + 2.19082e6i −0.131489 + 0.236444i
\(613\) 1.15888e7 1.24563 0.622815 0.782369i \(-0.285989\pi\)
0.622815 + 0.782369i \(0.285989\pi\)
\(614\) −3.75220e6 + 1.44675e7i −0.401666 + 1.54872i
\(615\) 101353. + 4.41382e6i 0.0108056 + 0.470573i
\(616\) −778471. + 816948.i −0.0826591 + 0.0867447i
\(617\) 1.47499e6i 0.155983i 0.996954 + 0.0779915i \(0.0248507\pi\)
−0.996954 + 0.0779915i \(0.975149\pi\)
\(618\) −420325. 109013.i −0.0442705 0.0114817i
\(619\) 6.94510e6i 0.728537i 0.931294 + 0.364269i \(0.118681\pi\)
−0.931294 + 0.364269i \(0.881319\pi\)
\(620\) 4.26547e6 8.10268e6i 0.445644 0.846544i
\(621\) 9.50803e6i 0.989377i
\(622\) −1.99178e6 + 7.67981e6i −0.206427 + 0.795929i
\(623\) 5.61430e6i 0.579530i
\(624\) 2.34774e6 + 3.78032e6i 0.241373 + 0.388658i
\(625\) 9.72447e6 895561.i 0.995786 0.0917055i
\(626\) −7.44183e6 1.93006e6i −0.759004 0.196850i
\(627\) 638744. 0.0648870
\(628\) 4.99093e6 + 2.77552e6i 0.504990 + 0.280831i
\(629\) 4.60218e6i 0.463807i
\(630\) −2.03477e6 + 8.65893e6i −0.204251 + 0.869186i
\(631\) 3.38551e6 0.338494 0.169247 0.985574i \(-0.445867\pi\)
0.169247 + 0.985574i \(0.445867\pi\)
\(632\) 4.92374e6 5.16711e6i 0.490346 0.514582i
\(633\) 6.69411e6i 0.664024i
\(634\) 426529. 1.64459e6i 0.0421430 0.162493i
\(635\) 9.57037e6 219761.i 0.941878 0.0216280i
\(636\) −7.68364e6 4.27296e6i −0.753224 0.418877i
\(637\) 2.89011e6 0.282206
\(638\) −276909. + 1.06769e6i −0.0269330 + 0.103847i
\(639\) −1.38167e7 −1.33861
\(640\) −1.88141e6 + 1.01899e7i −0.181566 + 0.983379i
\(641\) −6.43478e6 −0.618570 −0.309285 0.950969i \(-0.600090\pi\)
−0.309285 + 0.950969i \(0.600090\pi\)
\(642\) 1.11928e6 4.31567e6i 0.107177 0.413248i
\(643\) 819506. 0.0781672 0.0390836 0.999236i \(-0.487556\pi\)
0.0390836 + 0.999236i \(0.487556\pi\)
\(644\) −1.25248e7 6.96522e6i −1.19003 0.661790i
\(645\) 77504.0 + 3.37522e6i 0.00733541 + 0.319450i
\(646\) 1.21834e6 4.69763e6i 0.114865 0.442892i
\(647\) 1.00673e7i 0.945482i −0.881201 0.472741i \(-0.843265\pi\)
0.881201 0.472741i \(-0.156735\pi\)
\(648\) −3.01436e6 + 3.16335e6i −0.282006 + 0.295944i
\(649\) 1.55359e6 0.144785
\(650\) 2.20833e6 1.04714e7i 0.205012 0.972127i
\(651\) 5.39807e6i 0.499213i
\(652\) −4.12029e6 2.29134e6i −0.379584 0.211092i
\(653\) 3.73524e6 0.342796 0.171398 0.985202i \(-0.445172\pi\)
0.171398 + 0.985202i \(0.445172\pi\)
\(654\) 5.33061e6 + 1.38251e6i 0.487341 + 0.126393i
\(655\) −6.22694e6 + 142987.i −0.567115 + 0.0130225i
\(656\) 5.94375e6 + 9.57059e6i 0.539263 + 0.868319i
\(657\) 9.24328e6i 0.835435i
\(658\) −829434. + 3.19809e6i −0.0746822 + 0.287956i
\(659\) 2.11585e6i 0.189789i −0.995487 0.0948947i \(-0.969749\pi\)
0.995487 0.0948947i \(-0.0302514\pi\)
\(660\) −482187. 253836.i −0.0430879 0.0226827i
\(661\) 1.89096e7i 1.68337i 0.539970 + 0.841684i \(0.318435\pi\)
−0.539970 + 0.841684i \(0.681565\pi\)
\(662\) 1.30071e7 + 3.37344e6i 1.15355 + 0.299177i
\(663\) 1.77800e6i 0.157090i
\(664\) 5.80733e6 6.09436e6i 0.511159 0.536424i
\(665\) −395310. 1.72154e7i −0.0346644 1.50960i
\(666\) 3.05861e6 1.17932e7i 0.267201 1.03026i
\(667\) −1.40082e7 −1.21918
\(668\) 4.83665e6 8.69726e6i 0.419376 0.754121i
\(669\) 5.37355e6i 0.464190i
\(670\) −1.28969e7 3.03066e6i −1.10994 0.260826i
\(671\) 135000. 0.0115752
\(672\) −1.81681e6 5.83218e6i −0.155198 0.498205i
\(673\) 2.10683e6i 0.179304i −0.995973 0.0896522i \(-0.971424\pi\)
0.995973 0.0896522i \(-0.0285755\pi\)
\(674\) −2.02562e7 5.25350e6i −1.71754 0.445450i
\(675\) −9.73606e6 + 447368.i −0.822477 + 0.0377925i
\(676\) 134346. + 74711.6i 0.0113073 + 0.00628813i
\(677\) −5.17934e6 −0.434313 −0.217156 0.976137i \(-0.569678\pi\)
−0.217156 + 0.976137i \(0.569678\pi\)
\(678\) −7.68220e6 1.99240e6i −0.641817 0.166457i
\(679\) 1.40998e7 1.17365
\(680\) −2.78656e6 + 3.06207e6i −0.231098 + 0.253947i
\(681\) −1.05607e7 −0.872623
\(682\) 1.18942e6 + 308479.i 0.0979206 + 0.0253960i
\(683\) 8.80956e6 0.722608 0.361304 0.932448i \(-0.382332\pi\)
0.361304 + 0.932448i \(0.382332\pi\)
\(684\) 6.24408e6 1.12281e7i 0.510303 0.917626i
\(685\) −1.57737e7 + 362206.i −1.28442 + 0.0294937i
\(686\) 9.67940e6 + 2.51038e6i 0.785304 + 0.203671i
\(687\) 5.99423e6i 0.484553i
\(688\) 4.54514e6 + 7.31856e6i 0.366080 + 0.589460i
\(689\) 2.31701e7 1.85943
\(690\) 1.58311e6 6.73689e6i 0.126587 0.538688i
\(691\) 5.78539e6i 0.460933i 0.973080 + 0.230466i \(0.0740252\pi\)
−0.973080 + 0.230466i \(0.925975\pi\)
\(692\) 3.36374e6 + 1.87062e6i 0.267028 + 0.148498i
\(693\) −1.19361e6 −0.0944122
\(694\) 2.81691e6 1.08613e7i 0.222011 0.856018i
\(695\) 2.46239e6 56543.0i 0.193372 0.00444034i
\(696\) −4.32262e6 4.11903e6i −0.338239 0.322308i
\(697\) 4.50135e6i 0.350963i
\(698\) −8.31371e6 2.15619e6i −0.645887 0.167513i
\(699\) 2.04384e6i 0.158217i
\(700\) −6.54295e6 + 1.31529e7i −0.504694 + 1.01456i
\(701\) 2.01716e7i 1.55041i 0.631711 + 0.775204i \(0.282353\pi\)
−0.631711 + 0.775204i \(0.717647\pi\)
\(702\) −2.68134e6 + 1.03386e7i −0.205357 + 0.791805i
\(703\) 2.35865e7i 1.80001i
\(704\) −1.38890e6 + 67031.4i −0.105618 + 0.00509738i
\(705\) −1.59499e6 + 36625.2i −0.120861 + 0.00277528i
\(706\) 1.12906e7 + 2.92824e6i 0.852519 + 0.221103i
\(707\) 1.23253e7 0.927362
\(708\) −4.08735e6 + 7.34987e6i −0.306450 + 0.551057i
\(709\) 1.71661e7i 1.28250i −0.767334 0.641248i \(-0.778417\pi\)
0.767334 0.641248i \(-0.221583\pi\)
\(710\) −2.22144e7 5.22018e6i −1.65382 0.388633i
\(711\) 7.54943e6 0.560067
\(712\) 4.77245e6 5.00833e6i 0.352810 0.370248i
\(713\) 1.56052e7i 1.14960i
\(714\) 612729. 2.36253e6i 0.0449804 0.173433i
\(715\) 1.43571e6 32967.7i 0.105027 0.00241170i
\(716\) −2.80790e6 + 5.04916e6i −0.204691 + 0.368075i
\(717\) −5.74733e6 −0.417511
\(718\) 1.89240e6 7.29663e6i 0.136994 0.528215i
\(719\) 1.37927e7 0.995009 0.497505 0.867461i \(-0.334250\pi\)
0.497505 + 0.867461i \(0.334250\pi\)
\(720\) −9.17569e6 + 5.99468e6i −0.659641 + 0.430958i
\(721\) −1.57091e6 −0.112541
\(722\) −2.72769e6 + 1.05173e7i −0.194739 + 0.750863i
\(723\) 1.08105e7 0.769132
\(724\) −2.32819e6 + 4.18654e6i −0.165071 + 0.296831i
\(725\) 659105. + 1.43441e7i 0.0465704 + 1.01351i
\(726\) −1.62346e6 + 6.25966e6i −0.114314 + 0.440767i
\(727\) 9.10175e6i 0.638688i −0.947639 0.319344i \(-0.896537\pi\)
0.947639 0.319344i \(-0.103463\pi\)
\(728\) 1.16547e7 + 1.11058e7i 0.815026 + 0.776640i
\(729\) 818554. 0.0570465
\(730\) −3.49225e6 + 1.48612e7i −0.242549 + 1.03216i
\(731\) 3.44215e6i 0.238252i
\(732\) −355172. + 638670.i −0.0244997 + 0.0440554i
\(733\) −1.79637e7 −1.23491 −0.617456 0.786605i \(-0.711837\pi\)
−0.617456 + 0.786605i \(0.711837\pi\)
\(734\) −1.71570e6 444972.i −0.117544 0.0304855i
\(735\) −43979.3 1.91525e6i −0.00300283 0.130770i
\(736\) −5.25220e6 1.68602e7i −0.357394 1.14728i
\(737\) 1.77780e6i 0.120563i
\(738\) −2.99159e6 + 1.15348e7i −0.202191 + 0.779598i
\(739\) 1.38839e7i 0.935192i 0.883942 + 0.467596i \(0.154880\pi\)
−0.883942 + 0.467596i \(0.845120\pi\)
\(740\) 9.37325e6 1.78054e7i 0.629232 1.19529i
\(741\) 9.11238e6i 0.609658i
\(742\) −3.07874e7 7.98480e6i −2.05288 0.532420i
\(743\) 2.37521e6i 0.157845i 0.996881 + 0.0789225i \(0.0251480\pi\)
−0.996881 + 0.0789225i \(0.974852\pi\)
\(744\) −4.58864e6 + 4.81544e6i −0.303914 + 0.318936i
\(745\) 1.40585e7 322820.i 0.927999 0.0213093i
\(746\) 4.16198e6 1.60476e7i 0.273812 1.05575i
\(747\) 8.90419e6 0.583839
\(748\) −485548. 270019.i −0.0317306 0.0176458i
\(749\) 1.61292e7i 1.05053i
\(750\) −6.97295e6 1.30409e6i −0.452651 0.0846556i
\(751\) −1.99260e7 −1.28920 −0.644600 0.764520i \(-0.722976\pi\)
−0.644600 + 0.764520i \(0.722976\pi\)
\(752\) −3.45845e6 + 2.14785e6i −0.223017 + 0.138503i
\(753\) 7.91465e6i 0.508679i
\(754\) 1.52318e7 + 3.95041e6i 0.975714 + 0.253054i
\(755\) −122929. 5.35341e6i −0.00784848 0.341793i
\(756\) 7.12568e6 1.28134e7i 0.453442 0.815379i
\(757\) −1.30771e7 −0.829413 −0.414707 0.909955i \(-0.636116\pi\)
−0.414707 + 0.909955i \(0.636116\pi\)
\(758\) 2.24947e7 + 5.83407e6i 1.42203 + 0.368807i
\(759\) 928660. 0.0585130
\(760\) 1.42813e7 1.56933e7i 0.896879 0.985552i
\(761\) −1.75251e7 −1.09698 −0.548492 0.836156i \(-0.684798\pi\)
−0.548492 + 0.836156i \(0.684798\pi\)
\(762\) −6.73115e6 1.74574e6i −0.419954 0.108916i
\(763\) 1.99224e7 1.23888
\(764\) −5.98226e6 3.32681e6i −0.370794 0.206203i
\(765\) −4.37805e6 + 100532.i −0.270475 + 0.00621082i
\(766\) −5.25114e6 1.36190e6i −0.323356 0.0838634i
\(767\) 2.21637e7i 1.36036i
\(768\) 3.33694e6 6.74708e6i 0.204148 0.412775i
\(769\) −3.13820e7 −1.91366 −0.956830 0.290647i \(-0.906129\pi\)
−0.956830 + 0.290647i \(0.906129\pi\)
\(770\) −1.91906e6 450963.i −0.116644 0.0274103i
\(771\) 1.01244e7i 0.613384i
\(772\) 1.13469e7 2.04039e7i 0.685225 1.23217i
\(773\) 103265. 0.00621590 0.00310795 0.999995i \(-0.499011\pi\)
0.00310795 + 0.999995i \(0.499011\pi\)
\(774\) −2.28765e6 + 8.82060e6i −0.137258 + 0.529232i
\(775\) 1.59795e7 734250.i 0.955671 0.0439126i
\(776\) 1.25779e7 + 1.19855e7i 0.749817 + 0.714502i
\(777\) 1.18621e7i 0.704870i
\(778\) −3.54625e6 919729.i −0.210049 0.0544767i
\(779\) 2.30697e7i 1.36207i
\(780\) −3.62125e6 + 6.87893e6i −0.213119 + 0.404841i
\(781\) 3.06218e6i 0.179640i
\(782\) 1.77133e6 6.82981e6i 0.103582 0.399385i
\(783\) 1.43309e7i 0.835350i
\(784\) −2.57912e6 4.15289e6i −0.149859 0.241302i
\(785\) 229022. + 9.97368e6i 0.0132649 + 0.577672i
\(786\) 4.37960e6 + 1.13586e6i 0.252859 + 0.0655798i
\(787\) 5.01823e6 0.288811 0.144405 0.989519i \(-0.453873\pi\)
0.144405 + 0.989519i \(0.453873\pi\)
\(788\) 2.57881e7 + 1.43411e7i 1.47946 + 0.822748i
\(789\) 1.21229e7i 0.693288i
\(790\) 1.21379e7 + 2.85229e6i 0.691950 + 0.162602i
\(791\) −2.87111e7 −1.63158
\(792\) −1.06478e6 1.01463e6i −0.0603178 0.0574769i
\(793\) 1.92592e6i 0.108757i
\(794\) −2.92952e6 + 1.12955e7i −0.164909 + 0.635849i
\(795\) −352584. 1.53547e7i −0.0197854 0.861634i
\(796\) 2.75561e7 + 1.53243e7i 1.54147 + 0.857230i
\(797\) 9.61578e6 0.536215 0.268107 0.963389i \(-0.413602\pi\)
0.268107 + 0.963389i \(0.413602\pi\)
\(798\) −3.14027e6 + 1.21081e7i −0.174566 + 0.673084i
\(799\) −1.62662e6 −0.0901403
\(800\) −1.70174e7 + 6.17146e6i −0.940089 + 0.340928i
\(801\) 7.31745e6 0.402975
\(802\) −2.72985e6 + 1.05256e7i −0.149866 + 0.577846i
\(803\) −2.04857e6 −0.112115
\(804\) 8.41060e6 + 4.67724e6i 0.458867 + 0.255182i
\(805\) −574736. 2.50291e7i −0.0312592 1.36131i
\(806\) 4.40080e6 1.69684e7i 0.238613 0.920031i
\(807\) 2.19552e6i 0.118673i
\(808\) 1.09950e7 + 1.04771e7i 0.592470 + 0.564566i
\(809\) 2.06325e7 1.10836 0.554181 0.832396i \(-0.313032\pi\)
0.554181 + 0.832396i \(0.313032\pi\)
\(810\) −7.43092e6 1.74620e6i −0.397951 0.0935149i
\(811\) 3.18795e7i 1.70200i −0.525164 0.851001i \(-0.675996\pi\)
0.525164 0.851001i \(-0.324004\pi\)
\(812\) −1.88779e7 1.04982e7i −1.00476 0.558762i
\(813\) 8.99645e6 0.477359
\(814\) 2.61371e6 + 677875.i 0.138260 + 0.0358582i
\(815\) −189070. 8.23381e6i −0.00997078 0.434217i
\(816\) 2.55487e6 1.58668e6i 0.134321 0.0834189i
\(817\) 1.76412e7i 0.924642i
\(818\) 1.99488e6 7.69177e6i 0.104240 0.401923i
\(819\) 1.70281e7i 0.887067i
\(820\) −9.16788e6 + 1.74153e7i −0.476140 + 0.904474i
\(821\) 7.88522e6i 0.408278i 0.978942 + 0.204139i \(0.0654394\pi\)
−0.978942 + 0.204139i \(0.934561\pi\)
\(822\) 1.10941e7 + 2.87730e6i 0.572683 + 0.148527i
\(823\) 51764.9i 0.00266401i 0.999999 + 0.00133200i \(0.000423990\pi\)
−0.999999 + 0.00133200i \(0.999576\pi\)
\(824\) −1.40135e6 1.33535e6i −0.0719002 0.0685138i
\(825\) −43694.9 950932.i −0.00223509 0.0486423i
\(826\) −7.63796e6 + 2.94501e7i −0.389518 + 1.50188i
\(827\) 5.24793e6 0.266824 0.133412 0.991061i \(-0.457407\pi\)
0.133412 + 0.991061i \(0.457407\pi\)
\(828\) 9.07818e6 1.63244e7i 0.460175 0.827485i
\(829\) 6.76109e6i 0.341689i −0.985298 0.170844i \(-0.945350\pi\)
0.985298 0.170844i \(-0.0546495\pi\)
\(830\) 1.43160e7 + 3.36414e6i 0.721320 + 0.169504i
\(831\) −3.47004e6 −0.174314
\(832\) 956277. + 1.98141e7i 0.0478934 + 0.992355i
\(833\) 1.95323e6i 0.0975308i
\(834\) −1.73188e6 449167.i −0.0862187 0.0223611i
\(835\) 1.73802e7 399097.i 0.862660 0.0198090i
\(836\) 2.48847e6 + 1.38387e6i 0.123145 + 0.0684823i
\(837\) −1.59647e7 −0.787677
\(838\) −2.20995e7 5.73158e6i −1.08711 0.281945i
\(839\) −5.32681e6 −0.261254 −0.130627 0.991432i \(-0.541699\pi\)
−0.130627 + 0.991432i \(0.541699\pi\)
\(840\) 7.18234e6 7.89245e6i 0.351211 0.385935i
\(841\) −602476. −0.0293731
\(842\) −3.25754e6 844853.i −0.158347 0.0410678i
\(843\) −636887. −0.0308669
\(844\) −1.45031e7 + 2.60794e7i −0.700816 + 1.26021i
\(845\) 6164.83 + 268472.i 0.000297016 + 0.0129347i
\(846\) −4.16826e6 1.08105e6i −0.200230 0.0519302i
\(847\) 2.33946e7i 1.12049i
\(848\) −2.06769e7 3.32939e7i −0.987407 1.58992i
\(849\) 1.26660e7 0.603076
\(850\) −7.07695e6 1.49246e6i −0.335969 0.0708525i
\(851\) 3.42920e7i 1.62319i
\(852\) 1.44869e7 + 8.05633e6i 0.683716 + 0.380223i
\(853\) −8.20548e6 −0.386128 −0.193064 0.981186i \(-0.561843\pi\)
−0.193064 + 0.981186i \(0.561843\pi\)
\(854\) −663704. + 2.55907e6i −0.0311408 + 0.120071i
\(855\) 2.24378e7 515231.i 1.04970 0.0241039i
\(856\) 1.37107e7 1.43883e7i 0.639549 0.671160i
\(857\) 5.45868e6i 0.253884i −0.991910 0.126942i \(-0.959484\pi\)
0.991910 0.126942i \(-0.0405162\pi\)
\(858\) −1.00978e6 261889.i −0.0468283 0.0121451i
\(859\) 3.18230e7i 1.47149i −0.677257 0.735747i \(-0.736831\pi\)
0.677257 0.735747i \(-0.263169\pi\)
\(860\) −7.01061e6 + 1.33173e7i −0.323229 + 0.614004i
\(861\) 1.16022e7i 0.533375i
\(862\) 5.90494e6 2.27680e7i 0.270675 1.04365i
\(863\) 9.28914e6i 0.424569i 0.977208 + 0.212285i \(0.0680904\pi\)
−0.977208 + 0.212285i \(0.931910\pi\)
\(864\) 1.72486e7 5.37320e6i 0.786086 0.244877i
\(865\) 154354. + 6.72196e6i 0.00701420 + 0.305461i
\(866\) 1.24647e7 + 3.23275e6i 0.564789 + 0.146480i
\(867\) −8.99077e6 −0.406208
\(868\) −1.16951e7 + 2.10302e7i −0.526874 + 0.947423i
\(869\) 1.67317e6i 0.0751606i
\(870\) 2.38612e6 1.01541e7i 0.106880 0.454824i
\(871\) −2.53623e7 −1.13277
\(872\) 1.77721e7 + 1.69351e7i 0.791495 + 0.754217i
\(873\) 1.83771e7i 0.816094i
\(874\) −9.07819e6 + 3.50032e7i −0.401995 + 1.54999i
\(875\) −2.56024e7 + 1.76618e6i −1.13047 + 0.0779856i
\(876\) 5.38961e6 9.69159e6i 0.237300 0.426712i
\(877\) 1.60806e7 0.705997 0.352999 0.935624i \(-0.385162\pi\)
0.352999 + 0.935624i \(0.385162\pi\)
\(878\) −1.81957e6 + 7.01580e6i −0.0796585 + 0.307143i
\(879\) 65503.2 0.00285950
\(880\) −1.32859e6 2.03359e6i −0.0578342 0.0885233i
\(881\) −1.74471e7 −0.757327 −0.378663 0.925535i \(-0.623616\pi\)
−0.378663 + 0.925535i \(0.623616\pi\)
\(882\) 1.29812e6 5.00522e6i 0.0561879 0.216646i
\(883\) −2.18862e7 −0.944645 −0.472323 0.881426i \(-0.656584\pi\)
−0.472323 + 0.881426i \(0.656584\pi\)
\(884\) −3.85212e6 + 6.92688e6i −0.165794 + 0.298131i
\(885\) −1.46877e7 + 337268.i −0.630370 + 0.0144750i
\(886\) 8.53880e6 3.29235e7i 0.365437 1.40903i
\(887\) 4.00556e7i 1.70944i 0.519088 + 0.854721i \(0.326272\pi\)
−0.519088 + 0.854721i \(0.673728\pi\)
\(888\) −1.00834e7 + 1.05818e7i −0.429116 + 0.450326i
\(889\) −2.51567e7 −1.06758
\(890\) 1.17649e7 + 2.76464e6i 0.497867 + 0.116994i
\(891\) 1.02433e6i 0.0432260i
\(892\) −1.16420e7 + 2.09347e7i −0.489910 + 0.880955i
\(893\) 8.33653e6 0.349830
\(894\) −9.88778e6 2.56442e6i −0.413766 0.107311i
\(895\) −1.00900e7 + 231694.i −0.421051 + 0.00966846i
\(896\) 5.55762e6 2.66577e7i 0.231270 1.10931i
\(897\) 1.32484e7i 0.549770i
\(898\) 3.00420e6 1.15834e7i 0.124319 0.479343i
\(899\) 2.35208e7i 0.970628i
\(900\) −1.71430e7 8.52781e6i −0.705473 0.350939i
\(901\) 1.56592e7i 0.642623i
\(902\) −2.55645e6 663022.i −0.104621 0.0271339i
\(903\) 8.87211e6i 0.362083i
\(904\) −2.56123e7 2.44060e7i −1.04238 0.993287i
\(905\) −8.36622e6 + 192111.i −0.339553 + 0.00779704i
\(906\) −976522. + 3.76523e6i −0.0395241 + 0.152395i
\(907\) 1.61797e7 0.653060 0.326530 0.945187i \(-0.394121\pi\)
0.326530 + 0.945187i \(0.394121\pi\)
\(908\) −4.11433e7 2.28803e7i −1.65609 0.920974i
\(909\) 1.60643e7i 0.644840i
\(910\) −6.43348e6 + 2.73776e7i −0.257539 + 1.09595i
\(911\) 3.81429e7 1.52271 0.761356 0.648334i \(-0.224534\pi\)
0.761356 + 0.648334i \(0.224534\pi\)
\(912\) −1.30939e7 + 8.13185e6i −0.521291 + 0.323744i
\(913\) 1.97342e6i 0.0783508i
\(914\) −7.44500e6 1.93088e6i −0.294781 0.0764523i
\(915\) −1.27629e6 + 29307.1i −0.0503962 + 0.00115723i
\(916\) −1.29868e7 + 2.33528e7i −0.511402 + 0.919601i
\(917\) 1.63682e7 0.642801
\(918\) 6.98716e6 + 1.81214e6i 0.273649 + 0.0709717i
\(919\) −5.75041e6 −0.224600 −0.112300 0.993674i \(-0.535822\pi\)
−0.112300 + 0.993674i \(0.535822\pi\)
\(920\) 2.07634e7 2.28162e7i 0.808776 0.888739i
\(921\) 1.89665e7 0.736780
\(922\) 1.13039e7 + 2.93170e6i 0.437927 + 0.113578i
\(923\) −4.36854e7 −1.68784
\(924\) 1.25150e6 + 695973.i 0.0482225 + 0.0268171i
\(925\) 3.51144e7 1.61349e6i 1.34937 0.0620030i
\(926\) 8.15422e6 + 2.11482e6i 0.312504 + 0.0810487i
\(927\) 2.04745e6i 0.0782555i
\(928\) −7.91632e6 2.54124e7i −0.301754 0.968668i
\(929\) 1.58033e7 0.600771 0.300386 0.953818i \(-0.402885\pi\)
0.300386 + 0.953818i \(0.402885\pi\)
\(930\) −1.13118e7 2.65816e6i −0.428868 0.100780i
\(931\) 1.00104e7i 0.378512i
\(932\) −4.42806e6 + 7.96254e6i −0.166984 + 0.300270i
\(933\) 1.00680e7 0.378651
\(934\) 1.00241e7 3.86505e7i 0.375993 1.44973i
\(935\) −22280.7 970300.i −0.000833488 0.0362975i
\(936\) −1.44748e7 + 1.51902e7i −0.540035 + 0.566727i
\(937\) 1.61564e7i 0.601167i −0.953756 0.300583i \(-0.902819\pi\)
0.953756 0.300583i \(-0.0971814\pi\)
\(938\) 3.37003e7 + 8.74026e6i 1.25062 + 0.324353i
\(939\) 9.75602e6i 0.361084i
\(940\) −6.29323e6 3.31293e6i −0.232303 0.122290i
\(941\) 4.39614e7i 1.61844i 0.587504 + 0.809221i \(0.300111\pi\)
−0.587504 + 0.809221i \(0.699889\pi\)
\(942\) 1.81931e6 7.01481e6i 0.0668005 0.257566i
\(943\) 3.35407e7i 1.22827i
\(944\) −3.18476e7 + 1.97788e7i −1.16318 + 0.722385i
\(945\) 2.56058e7 587976.i 0.932735 0.0214181i
\(946\) −1.95490e6 507008.i −0.0710225 0.0184199i
\(947\) −4.52665e7 −1.64022 −0.820111 0.572205i \(-0.806088\pi\)
−0.820111 + 0.572205i \(0.806088\pi\)
\(948\) −7.91558e6 4.40195e6i −0.286063 0.159083i
\(949\) 2.92252e7i 1.05340i
\(950\) 3.62698e7 + 7.64895e6i 1.30388 + 0.274975i
\(951\) −2.15601e6 −0.0773035
\(952\) 7.50564e6 7.87661e6i 0.268408 0.281674i
\(953\) 3.21216e6i 0.114569i −0.998358 0.0572843i \(-0.981756\pi\)
0.998358 0.0572843i \(-0.0182441\pi\)
\(954\) 1.04071e7 4.01270e7i 0.370218 1.42747i
\(955\) −274512. 1.19547e7i −0.00973986 0.424161i
\(956\) −2.23909e7 1.24518e7i −0.792367 0.440645i
\(957\) 1.39971e6 0.0494036
\(958\) 2.09444e6 8.07565e6i 0.0737318 0.284292i
\(959\) 4.14628e7 1.45583
\(960\) 1.31161e7 935232.i 0.459333 0.0327523i
\(961\) −2.42676e6 −0.0847654
\(962\) 9.67063e6 3.72875e7i 0.336912 1.29905i
\(963\) 2.10221e7 0.730485
\(964\) 4.21164e7 + 2.34215e7i 1.45968 + 0.811748i
\(965\) 4.07744e7 936288.i 1.40951 0.0323662i
\(966\) −4.56560e6 + 1.76038e7i −0.157418 + 0.606965i
\(967\) 4.06241e6i 0.139707i 0.997557 + 0.0698533i \(0.0222531\pi\)
−0.997557 + 0.0698533i \(0.977747\pi\)
\(968\) −1.98866e7 + 2.08696e7i −0.682139 + 0.715855i
\(969\) −6.15845e6 −0.210699
\(970\) −6.94313e6 + 2.95464e7i −0.236933 + 1.00827i
\(971\) 2.41409e7i 0.821685i −0.911706 0.410842i \(-0.865235\pi\)
0.911706 0.410842i \(-0.134765\pi\)
\(972\) 2.60410e7 + 1.44817e7i 0.884082 + 0.491649i
\(973\) −6.47264e6 −0.219179
\(974\) −5.00158e7 1.29718e7i −1.68931 0.438128i
\(975\) −1.35661e7 + 623355.i −0.457028 + 0.0210002i
\(976\) −2.76741e6 + 1.71868e6i −0.0929928 + 0.0577526i
\(977\) 1.48416e7i 0.497443i −0.968575 0.248722i \(-0.919990\pi\)
0.968575 0.248722i \(-0.0800104\pi\)
\(978\) −1.50194e6 + 5.79110e6i −0.0502118 + 0.193604i
\(979\) 1.62175e6i 0.0540790i
\(980\) 3.97814e6 7.55687e6i 0.132317 0.251349i
\(981\) 2.59661e7i 0.861457i
\(982\) 2.59651e7 + 6.73412e6i 0.859233 + 0.222845i
\(983\) 3.34107e7i 1.10281i −0.834237 0.551406i \(-0.814092\pi\)
0.834237 0.551406i \(-0.185908\pi\)
\(984\) 9.86247e6 1.03499e7i 0.324712 0.340761i
\(985\) 1.18336e6 + 5.15339e7i 0.0388620 + 1.69240i
\(986\) 2.66982e6 1.02942e7i 0.0874560 0.337208i
\(987\) 4.19260e6 0.136991
\(988\) 1.97424e7 3.55007e7i 0.643438 1.15703i
\(989\) 2.56483e7i 0.833812i
\(990\) 587766. 2.50123e6i 0.0190597 0.0811083i
\(991\) 5.15057e7 1.66599 0.832993 0.553284i \(-0.186626\pi\)
0.832993 + 0.553284i \(0.186626\pi\)
\(992\) −2.83096e7 + 8.81886e6i −0.913387 + 0.284533i
\(993\) 1.70520e7i 0.548784i
\(994\) 5.80472e7 + 1.50547e7i 1.86344 + 0.483288i
\(995\) 1.26448e6 + 5.50670e7i 0.0404907 + 1.76333i
\(996\) −9.33606e6 5.19190e6i −0.298205 0.165836i
\(997\) −1.18985e7 −0.379102 −0.189551 0.981871i \(-0.560703\pi\)
−0.189551 + 0.981871i \(0.560703\pi\)
\(998\) −2.95144e6 765466.i −0.0938012 0.0243276i
\(999\) −3.50821e7 −1.11217
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 40.6.f.a.29.17 yes 28
4.3 odd 2 160.6.f.a.49.17 28
5.2 odd 4 200.6.d.e.101.26 28
5.3 odd 4 200.6.d.e.101.3 28
5.4 even 2 inner 40.6.f.a.29.12 yes 28
8.3 odd 2 160.6.f.a.49.11 28
8.5 even 2 inner 40.6.f.a.29.11 28
20.3 even 4 800.6.d.e.401.8 28
20.7 even 4 800.6.d.e.401.21 28
20.19 odd 2 160.6.f.a.49.12 28
40.3 even 4 800.6.d.e.401.7 28
40.13 odd 4 200.6.d.e.101.4 28
40.19 odd 2 160.6.f.a.49.18 28
40.27 even 4 800.6.d.e.401.22 28
40.29 even 2 inner 40.6.f.a.29.18 yes 28
40.37 odd 4 200.6.d.e.101.25 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.f.a.29.11 28 8.5 even 2 inner
40.6.f.a.29.12 yes 28 5.4 even 2 inner
40.6.f.a.29.17 yes 28 1.1 even 1 trivial
40.6.f.a.29.18 yes 28 40.29 even 2 inner
160.6.f.a.49.11 28 8.3 odd 2
160.6.f.a.49.12 28 20.19 odd 2
160.6.f.a.49.17 28 4.3 odd 2
160.6.f.a.49.18 28 40.19 odd 2
200.6.d.e.101.3 28 5.3 odd 4
200.6.d.e.101.4 28 40.13 odd 4
200.6.d.e.101.25 28 40.37 odd 4
200.6.d.e.101.26 28 5.2 odd 4
800.6.d.e.401.7 28 40.3 even 4
800.6.d.e.401.8 28 20.3 even 4
800.6.d.e.401.21 28 20.7 even 4
800.6.d.e.401.22 28 40.27 even 4