Properties

Label 210.6.i.b.121.1
Level $210$
Weight $6$
Character 210.121
Analytic conductor $33.681$
Analytic rank $0$
Dimension $4$
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] = [210,6,Mod(121,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.121");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 210.i (of order \(3\), degree \(2\), 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: \(33.6806021607\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{151})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 151x^{2} + 22801 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(-6.14410 + 10.6419i\) of defining polynomial
Character \(\chi\) \(=\) 210.121
Dual form 210.6.i.b.151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(12.5000 - 21.6506i) q^{5} -36.0000 q^{6} +(-127.009 + 25.9959i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(12.5000 - 21.6506i) q^{5} -36.0000 q^{6} +(-127.009 + 25.9959i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(50.0000 + 86.6025i) q^{10} +(188.085 + 325.773i) q^{11} +(72.0000 - 124.708i) q^{12} -444.087 q^{13} +(163.965 - 491.963i) q^{14} +225.000 q^{15} +(-128.000 + 221.703i) q^{16} +(435.207 + 753.801i) q^{17} +(-162.000 - 280.592i) q^{18} +(-131.701 + 228.113i) q^{19} -400.000 q^{20} +(-774.157 - 872.954i) q^{21} -1504.68 q^{22} +(2112.67 - 3659.26i) q^{23} +(288.000 + 498.831i) q^{24} +(-312.500 - 541.266i) q^{25} +(888.174 - 1538.36i) q^{26} -729.000 q^{27} +(1376.28 + 1551.92i) q^{28} -7291.74 q^{29} +(-450.000 + 779.423i) q^{30} +(-4352.32 - 7538.43i) q^{31} +(-512.000 - 886.810i) q^{32} +(-1692.77 + 2931.96i) q^{33} -3481.66 q^{34} +(-1024.78 + 3074.77i) q^{35} +1296.00 q^{36} +(1384.32 - 2397.71i) q^{37} +(-526.804 - 912.451i) q^{38} +(-1998.39 - 3461.32i) q^{39} +(800.000 - 1385.64i) q^{40} +10698.1 q^{41} +(4572.31 - 935.851i) q^{42} -15869.1 q^{43} +(3009.36 - 5212.37i) q^{44} +(1012.50 + 1753.70i) q^{45} +(8450.70 + 14637.0i) q^{46} +(-579.008 + 1002.87i) q^{47} -2304.00 q^{48} +(15455.4 - 6603.40i) q^{49} +2500.00 q^{50} +(-3916.86 + 6784.21i) q^{51} +(3552.70 + 6153.45i) q^{52} +(-16139.7 - 27954.8i) q^{53} +(1458.00 - 2525.33i) q^{54} +9404.26 q^{55} +(-8128.56 + 1663.74i) q^{56} -2370.62 q^{57} +(14583.5 - 25259.3i) q^{58} +(-18252.4 - 31614.1i) q^{59} +(-1800.00 - 3117.69i) q^{60} +(20727.4 - 35900.9i) q^{61} +34818.5 q^{62} +(3320.29 - 9962.25i) q^{63} +4096.00 q^{64} +(-5551.09 + 9614.77i) q^{65} +(-6771.06 - 11727.8i) q^{66} +(15020.1 + 26015.5i) q^{67} +(6963.32 - 12060.8i) q^{68} +38028.1 q^{69} +(-8601.74 - 9699.48i) q^{70} +37623.3 q^{71} +(-2592.00 + 4489.48i) q^{72} +(16199.3 + 28058.0i) q^{73} +(5537.27 + 9590.84i) q^{74} +(2812.50 - 4871.39i) q^{75} +4214.43 q^{76} +(-32357.2 - 36486.6i) q^{77} +15987.1 q^{78} +(32339.0 - 56012.9i) q^{79} +(3200.00 + 5542.56i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-21396.1 + 37059.1i) q^{82} -105250. q^{83} +(-5902.74 + 17710.7i) q^{84} +21760.4 q^{85} +(31738.2 - 54972.1i) q^{86} +(-32812.8 - 56833.5i) q^{87} +(12037.4 + 20849.5i) q^{88} +(11195.7 - 19391.5i) q^{89} -8100.00 q^{90} +(56402.9 - 11544.4i) q^{91} -67605.6 q^{92} +(39170.8 - 67845.9i) q^{93} +(-2316.03 - 4011.49i) q^{94} +(3292.53 + 5702.82i) q^{95} +(4608.00 - 7981.29i) q^{96} +37203.1 q^{97} +(-8036.00 + 66746.0i) q^{98} -30469.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 50 q^{5} - 144 q^{6} - 336 q^{7} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 50 q^{5} - 144 q^{6} - 336 q^{7} + 256 q^{8} - 162 q^{9} + 200 q^{10} + 482 q^{11} + 288 q^{12} - 56 q^{13} + 1344 q^{14} + 900 q^{15} - 512 q^{16} - 938 q^{17} - 648 q^{18} - 2198 q^{19} - 1600 q^{20} - 3856 q^{22} - 618 q^{23} + 1152 q^{24} - 1250 q^{25} + 112 q^{26} - 2916 q^{27} - 20172 q^{29} - 1800 q^{30} - 4138 q^{31} - 2048 q^{32} - 4338 q^{33} + 7504 q^{34} - 8400 q^{35} + 5184 q^{36} + 2072 q^{37} - 8792 q^{38} - 252 q^{39} + 3200 q^{40} + 5092 q^{41} + 12096 q^{42} - 53400 q^{43} + 7712 q^{44} + 4050 q^{45} - 2472 q^{46} + 3484 q^{47} - 9216 q^{48} + 4018 q^{49} + 10000 q^{50} + 8442 q^{51} + 448 q^{52} - 316 q^{53} + 5832 q^{54} + 24100 q^{55} - 21504 q^{56} - 39564 q^{57} + 40344 q^{58} - 66202 q^{59} - 7200 q^{60} + 44472 q^{61} + 33104 q^{62} + 27216 q^{63} + 16384 q^{64} - 700 q^{65} - 17352 q^{66} + 18964 q^{67} - 15008 q^{68} - 11124 q^{69} - 68876 q^{71} - 10368 q^{72} - 34516 q^{73} + 8288 q^{74} + 11250 q^{75} + 70336 q^{76} - 46508 q^{77} + 2016 q^{78} + 121590 q^{79} + 12800 q^{80} - 13122 q^{81} - 10184 q^{82} - 221588 q^{83} - 48384 q^{84} - 46900 q^{85} + 106800 q^{86} - 90774 q^{87} + 30848 q^{88} - 94246 q^{89} - 32400 q^{90} + 78694 q^{91} + 19776 q^{92} + 37242 q^{93} + 13936 q^{94} + 54950 q^{95} + 18432 q^{96} + 143504 q^{97} - 32144 q^{98} - 78084 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 + 3.46410i −0.353553 + 0.612372i
\(3\) 4.50000 + 7.79423i 0.288675 + 0.500000i
\(4\) −8.00000 13.8564i −0.250000 0.433013i
\(5\) 12.5000 21.6506i 0.223607 0.387298i
\(6\) −36.0000 −0.408248
\(7\) −127.009 + 25.9959i −0.979689 + 0.200521i
\(8\) 64.0000 0.353553
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 50.0000 + 86.6025i 0.158114 + 0.273861i
\(11\) 188.085 + 325.773i 0.468676 + 0.811771i 0.999359 0.0357997i \(-0.0113978\pi\)
−0.530683 + 0.847570i \(0.678065\pi\)
\(12\) 72.0000 124.708i 0.144338 0.250000i
\(13\) −444.087 −0.728803 −0.364401 0.931242i \(-0.618726\pi\)
−0.364401 + 0.931242i \(0.618726\pi\)
\(14\) 163.965 491.963i 0.223579 0.670830i
\(15\) 225.000 0.258199
\(16\) −128.000 + 221.703i −0.125000 + 0.216506i
\(17\) 435.207 + 753.801i 0.365236 + 0.632608i 0.988814 0.149154i \(-0.0476549\pi\)
−0.623578 + 0.781761i \(0.714322\pi\)
\(18\) −162.000 280.592i −0.117851 0.204124i
\(19\) −131.701 + 228.113i −0.0836961 + 0.144966i −0.904835 0.425763i \(-0.860006\pi\)
0.821139 + 0.570729i \(0.193339\pi\)
\(20\) −400.000 −0.223607
\(21\) −774.157 872.954i −0.383072 0.431959i
\(22\) −1504.68 −0.662808
\(23\) 2112.67 3659.26i 0.832747 1.44236i −0.0631053 0.998007i \(-0.520100\pi\)
0.895852 0.444353i \(-0.146566\pi\)
\(24\) 288.000 + 498.831i 0.102062 + 0.176777i
\(25\) −312.500 541.266i −0.100000 0.173205i
\(26\) 888.174 1538.36i 0.257671 0.446299i
\(27\) −729.000 −0.192450
\(28\) 1376.28 + 1551.92i 0.331750 + 0.374088i
\(29\) −7291.74 −1.61004 −0.805019 0.593249i \(-0.797845\pi\)
−0.805019 + 0.593249i \(0.797845\pi\)
\(30\) −450.000 + 779.423i −0.0912871 + 0.158114i
\(31\) −4352.32 7538.43i −0.813422 1.40889i −0.910455 0.413608i \(-0.864268\pi\)
0.0970327 0.995281i \(-0.469065\pi\)
\(32\) −512.000 886.810i −0.0883883 0.153093i
\(33\) −1692.77 + 2931.96i −0.270590 + 0.468676i
\(34\) −3481.66 −0.516522
\(35\) −1024.78 + 3074.77i −0.141404 + 0.424270i
\(36\) 1296.00 0.166667
\(37\) 1384.32 2397.71i 0.166239 0.287934i −0.770856 0.637010i \(-0.780171\pi\)
0.937094 + 0.349076i \(0.113504\pi\)
\(38\) −526.804 912.451i −0.0591821 0.102506i
\(39\) −1998.39 3461.32i −0.210387 0.364401i
\(40\) 800.000 1385.64i 0.0790569 0.136931i
\(41\) 10698.1 0.993906 0.496953 0.867778i \(-0.334452\pi\)
0.496953 + 0.867778i \(0.334452\pi\)
\(42\) 4572.31 935.851i 0.399957 0.0818622i
\(43\) −15869.1 −1.30882 −0.654411 0.756139i \(-0.727083\pi\)
−0.654411 + 0.756139i \(0.727083\pi\)
\(44\) 3009.36 5212.37i 0.234338 0.405885i
\(45\) 1012.50 + 1753.70i 0.0745356 + 0.129099i
\(46\) 8450.70 + 14637.0i 0.588841 + 1.01990i
\(47\) −579.008 + 1002.87i −0.0382332 + 0.0662218i −0.884509 0.466524i \(-0.845506\pi\)
0.846276 + 0.532745i \(0.178840\pi\)
\(48\) −2304.00 −0.144338
\(49\) 15455.4 6603.40i 0.919583 0.392896i
\(50\) 2500.00 0.141421
\(51\) −3916.86 + 6784.21i −0.210869 + 0.365236i
\(52\) 3552.70 + 6153.45i 0.182201 + 0.315581i
\(53\) −16139.7 27954.8i −0.789233 1.36699i −0.926437 0.376449i \(-0.877145\pi\)
0.137204 0.990543i \(-0.456188\pi\)
\(54\) 1458.00 2525.33i 0.0680414 0.117851i
\(55\) 9404.26 0.419197
\(56\) −8128.56 + 1663.74i −0.346373 + 0.0708948i
\(57\) −2370.62 −0.0966439
\(58\) 14583.5 25259.3i 0.569235 0.985943i
\(59\) −18252.4 31614.1i −0.682638 1.18236i −0.974173 0.225803i \(-0.927499\pi\)
0.291535 0.956560i \(-0.405834\pi\)
\(60\) −1800.00 3117.69i −0.0645497 0.111803i
\(61\) 20727.4 35900.9i 0.713214 1.23532i −0.250431 0.968135i \(-0.580572\pi\)
0.963644 0.267188i \(-0.0860945\pi\)
\(62\) 34818.5 1.15035
\(63\) 3320.29 9962.25i 0.105396 0.316232i
\(64\) 4096.00 0.125000
\(65\) −5551.09 + 9614.77i −0.162965 + 0.282264i
\(66\) −6771.06 11727.8i −0.191336 0.331404i
\(67\) 15020.1 + 26015.5i 0.408776 + 0.708021i 0.994753 0.102307i \(-0.0326224\pi\)
−0.585977 + 0.810328i \(0.699289\pi\)
\(68\) 6963.32 12060.8i 0.182618 0.316304i
\(69\) 38028.1 0.961573
\(70\) −8601.74 9699.48i −0.209817 0.236594i
\(71\) 37623.3 0.885749 0.442874 0.896584i \(-0.353959\pi\)
0.442874 + 0.896584i \(0.353959\pi\)
\(72\) −2592.00 + 4489.48i −0.0589256 + 0.102062i
\(73\) 16199.3 + 28058.0i 0.355787 + 0.616241i 0.987252 0.159163i \(-0.0508797\pi\)
−0.631466 + 0.775404i \(0.717546\pi\)
\(74\) 5537.27 + 9590.84i 0.117548 + 0.203600i
\(75\) 2812.50 4871.39i 0.0577350 0.100000i
\(76\) 4214.43 0.0836961
\(77\) −32357.2 36486.6i −0.621934 0.701304i
\(78\) 15987.1 0.297532
\(79\) 32339.0 56012.9i 0.582988 1.00976i −0.412135 0.911123i \(-0.635217\pi\)
0.995123 0.0986416i \(-0.0314497\pi\)
\(80\) 3200.00 + 5542.56i 0.0559017 + 0.0968246i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) −21396.1 + 37059.1i −0.351399 + 0.608640i
\(83\) −105250. −1.67698 −0.838490 0.544917i \(-0.816561\pi\)
−0.838490 + 0.544917i \(0.816561\pi\)
\(84\) −5902.74 + 17710.7i −0.0912758 + 0.273865i
\(85\) 21760.4 0.326677
\(86\) 31738.2 54972.1i 0.462739 0.801487i
\(87\) −32812.8 56833.5i −0.464778 0.805019i
\(88\) 12037.4 + 20849.5i 0.165702 + 0.287004i
\(89\) 11195.7 19391.5i 0.149822 0.259499i −0.781340 0.624106i \(-0.785463\pi\)
0.931162 + 0.364607i \(0.118797\pi\)
\(90\) −8100.00 −0.105409
\(91\) 56402.9 11544.4i 0.714000 0.146140i
\(92\) −67605.6 −0.832747
\(93\) 39170.8 67845.9i 0.469630 0.813422i
\(94\) −2316.03 4011.49i −0.0270349 0.0468259i
\(95\) 3292.53 + 5702.82i 0.0374300 + 0.0648307i
\(96\) 4608.00 7981.29i 0.0510310 0.0883883i
\(97\) 37203.1 0.401467 0.200734 0.979646i \(-0.435667\pi\)
0.200734 + 0.979646i \(0.435667\pi\)
\(98\) −8036.00 + 66746.0i −0.0845230 + 0.702037i
\(99\) −30469.8 −0.312451
\(100\) −5000.00 + 8660.25i −0.0500000 + 0.0866025i
\(101\) −82301.6 142551.i −0.802795 1.39048i −0.917769 0.397114i \(-0.870012\pi\)
0.114974 0.993368i \(-0.463321\pi\)
\(102\) −15667.5 27136.8i −0.149107 0.258261i
\(103\) −42553.2 + 73704.3i −0.395220 + 0.684541i −0.993129 0.117023i \(-0.962665\pi\)
0.597909 + 0.801564i \(0.295998\pi\)
\(104\) −28421.6 −0.257671
\(105\) −28577.0 + 5849.07i −0.252955 + 0.0517742i
\(106\) 129117. 1.11614
\(107\) −25535.0 + 44227.9i −0.215614 + 0.373454i −0.953462 0.301512i \(-0.902509\pi\)
0.737849 + 0.674966i \(0.235842\pi\)
\(108\) 5832.00 + 10101.3i 0.0481125 + 0.0833333i
\(109\) −12926.5 22389.4i −0.104212 0.180500i 0.809204 0.587527i \(-0.199899\pi\)
−0.913416 + 0.407028i \(0.866565\pi\)
\(110\) −18808.5 + 32577.3i −0.148208 + 0.256704i
\(111\) 24917.7 0.191956
\(112\) 10493.8 31485.6i 0.0790472 0.237174i
\(113\) 38424.1 0.283079 0.141540 0.989933i \(-0.454795\pi\)
0.141540 + 0.989933i \(0.454795\pi\)
\(114\) 4741.24 8212.06i 0.0341688 0.0591821i
\(115\) −52816.8 91481.5i −0.372416 0.645043i
\(116\) 58333.9 + 101037.i 0.402510 + 0.697167i
\(117\) 17985.5 31151.9i 0.121467 0.210387i
\(118\) 146019. 0.965396
\(119\) −74870.8 84425.7i −0.484669 0.546522i
\(120\) 14400.0 0.0912871
\(121\) 9773.47 16928.1i 0.0606855 0.105110i
\(122\) 82909.5 + 143603.i 0.504318 + 0.873505i
\(123\) 48141.2 + 83383.1i 0.286916 + 0.496953i
\(124\) −69637.0 + 120615.i −0.406711 + 0.704444i
\(125\) −15625.0 −0.0894427
\(126\) 27869.7 + 31426.3i 0.156389 + 0.176347i
\(127\) −179221. −0.986004 −0.493002 0.870028i \(-0.664101\pi\)
−0.493002 + 0.870028i \(0.664101\pi\)
\(128\) −8192.00 + 14189.0i −0.0441942 + 0.0765466i
\(129\) −71410.9 123687.i −0.377824 0.654411i
\(130\) −22204.4 38459.1i −0.115234 0.199591i
\(131\) −117943. + 204283.i −0.600473 + 1.04005i 0.392277 + 0.919847i \(0.371688\pi\)
−0.992749 + 0.120202i \(0.961646\pi\)
\(132\) 54168.5 0.270590
\(133\) 10797.2 32396.0i 0.0529275 0.158804i
\(134\) −120161. −0.578097
\(135\) −9112.50 + 15783.3i −0.0430331 + 0.0745356i
\(136\) 27853.3 + 48243.3i 0.129130 + 0.223661i
\(137\) 60250.2 + 104356.i 0.274256 + 0.475026i 0.969947 0.243315i \(-0.0782349\pi\)
−0.695691 + 0.718341i \(0.744902\pi\)
\(138\) −76056.3 + 131733.i −0.339967 + 0.588841i
\(139\) 78689.4 0.345445 0.172723 0.984970i \(-0.444744\pi\)
0.172723 + 0.984970i \(0.444744\pi\)
\(140\) 50803.5 10398.3i 0.219065 0.0448378i
\(141\) −10422.1 −0.0441478
\(142\) −75246.5 + 130331.i −0.313159 + 0.542408i
\(143\) −83526.2 144672.i −0.341572 0.591621i
\(144\) −10368.0 17957.9i −0.0416667 0.0721688i
\(145\) −91146.8 + 157871.i −0.360016 + 0.623565i
\(146\) −129595. −0.503158
\(147\) 121018. + 90747.8i 0.461909 + 0.346372i
\(148\) −44298.2 −0.166239
\(149\) −129970. + 225116.i −0.479600 + 0.830691i −0.999726 0.0233979i \(-0.992552\pi\)
0.520126 + 0.854089i \(0.325885\pi\)
\(150\) 11250.0 + 19485.6i 0.0408248 + 0.0707107i
\(151\) 146790. + 254248.i 0.523907 + 0.907434i 0.999613 + 0.0278292i \(0.00885947\pi\)
−0.475706 + 0.879605i \(0.657807\pi\)
\(152\) −8428.86 + 14599.2i −0.0295910 + 0.0512532i
\(153\) −70503.6 −0.243491
\(154\) 191108. 39115.5i 0.649346 0.132907i
\(155\) −217616. −0.727547
\(156\) −31974.3 + 55381.1i −0.105194 + 0.182201i
\(157\) 194783. + 337374.i 0.630669 + 1.09235i 0.987415 + 0.158149i \(0.0505526\pi\)
−0.356747 + 0.934201i \(0.616114\pi\)
\(158\) 129356. + 224051.i 0.412235 + 0.714011i
\(159\) 145257. 251593.i 0.455664 0.789233i
\(160\) −25600.0 −0.0790569
\(161\) −173202. + 519679.i −0.526610 + 1.58005i
\(162\) 26244.0 0.0785674
\(163\) −116066. + 201033.i −0.342166 + 0.592649i −0.984835 0.173495i \(-0.944494\pi\)
0.642669 + 0.766144i \(0.277827\pi\)
\(164\) −85584.4 148237.i −0.248476 0.430374i
\(165\) 42319.2 + 73298.9i 0.121012 + 0.209598i
\(166\) 210501. 364598.i 0.592902 1.02694i
\(167\) −619069. −1.71770 −0.858851 0.512226i \(-0.828821\pi\)
−0.858851 + 0.512226i \(0.828821\pi\)
\(168\) −49546.0 55869.0i −0.135437 0.152721i
\(169\) −174080. −0.468847
\(170\) −43520.7 + 75380.1i −0.115498 + 0.200048i
\(171\) −10667.8 18477.1i −0.0278987 0.0483220i
\(172\) 126953. + 219888.i 0.327206 + 0.566737i
\(173\) −188434. + 326377.i −0.478678 + 0.829095i −0.999701 0.0244478i \(-0.992217\pi\)
0.521023 + 0.853543i \(0.325551\pi\)
\(174\) 262503. 0.657295
\(175\) 53760.9 + 60621.8i 0.132700 + 0.149635i
\(176\) −96299.6 −0.234338
\(177\) 164272. 284527.i 0.394121 0.682638i
\(178\) 44782.8 + 77566.0i 0.105940 + 0.183494i
\(179\) −334997. 580232.i −0.781463 1.35353i −0.931089 0.364792i \(-0.881140\pi\)
0.149626 0.988743i \(-0.452193\pi\)
\(180\) 16200.0 28059.2i 0.0372678 0.0645497i
\(181\) 260652. 0.591377 0.295689 0.955284i \(-0.404451\pi\)
0.295689 + 0.955284i \(0.404451\pi\)
\(182\) −72814.8 + 218474.i −0.162945 + 0.488902i
\(183\) 373093. 0.823548
\(184\) 135211. 234193.i 0.294420 0.509951i
\(185\) −34608.0 59942.7i −0.0743441 0.128768i
\(186\) 156683. + 271384.i 0.332078 + 0.575177i
\(187\) −163712. + 283558.i −0.342355 + 0.592976i
\(188\) 18528.3 0.0382332
\(189\) 92589.4 18951.0i 0.188541 0.0385902i
\(190\) −26340.2 −0.0529340
\(191\) 120941. 209476.i 0.239878 0.415481i −0.720801 0.693142i \(-0.756226\pi\)
0.960679 + 0.277661i \(0.0895592\pi\)
\(192\) 18432.0 + 31925.2i 0.0360844 + 0.0625000i
\(193\) −432764. 749569.i −0.836292 1.44850i −0.892974 0.450107i \(-0.851386\pi\)
0.0566827 0.998392i \(-0.481948\pi\)
\(194\) −74406.3 + 128875.i −0.141940 + 0.245847i
\(195\) −99919.6 −0.188176
\(196\) −215143. 161329.i −0.400025 0.299967i
\(197\) 59334.4 0.108928 0.0544642 0.998516i \(-0.482655\pi\)
0.0544642 + 0.998516i \(0.482655\pi\)
\(198\) 60939.6 105550.i 0.110468 0.191336i
\(199\) −454112. 786545.i −0.812887 1.40796i −0.910835 0.412770i \(-0.864561\pi\)
0.0979483 0.995192i \(-0.468772\pi\)
\(200\) −20000.0 34641.0i −0.0353553 0.0612372i
\(201\) −135181. + 234140.i −0.236007 + 0.408776i
\(202\) 658413. 1.13532
\(203\) 926115. 189555.i 1.57734 0.322846i
\(204\) 125340. 0.210869
\(205\) 133726. 231620.i 0.222244 0.384938i
\(206\) −170213. 294817.i −0.279463 0.484044i
\(207\) 171127. + 296400.i 0.277582 + 0.480786i
\(208\) 56843.2 98455.2i 0.0911003 0.157790i
\(209\) −99084.0 −0.156905
\(210\) 36892.2 110692.i 0.0577279 0.173207i
\(211\) −389916. −0.602927 −0.301463 0.953478i \(-0.597475\pi\)
−0.301463 + 0.953478i \(0.597475\pi\)
\(212\) −258235. + 447276.i −0.394617 + 0.683496i
\(213\) 169305. + 293244.i 0.255694 + 0.442874i
\(214\) −102140. 176912.i −0.152462 0.264072i
\(215\) −198364. + 343576.i −0.292662 + 0.506905i
\(216\) −46656.0 −0.0680414
\(217\) 748750. + 844304.i 1.07941 + 1.21717i
\(218\) 103412. 0.147377
\(219\) −145794. + 252522.i −0.205414 + 0.355787i
\(220\) −75234.1 130309.i −0.104799 0.181517i
\(221\) −193270. 334753.i −0.266185 0.461046i
\(222\) −49835.5 + 86317.6i −0.0678666 + 0.117548i
\(223\) 432482. 0.582379 0.291189 0.956665i \(-0.405949\pi\)
0.291189 + 0.956665i \(0.405949\pi\)
\(224\) 88081.9 + 99322.7i 0.117291 + 0.132260i
\(225\) 50625.0 0.0666667
\(226\) −76848.3 + 133105.i −0.100084 + 0.173350i
\(227\) −382198. 661987.i −0.492294 0.852678i 0.507667 0.861553i \(-0.330508\pi\)
−0.999961 + 0.00887574i \(0.997175\pi\)
\(228\) 18964.9 + 32848.2i 0.0241610 + 0.0418480i
\(229\) 354080. 613284.i 0.446183 0.772811i −0.551951 0.833876i \(-0.686117\pi\)
0.998134 + 0.0610656i \(0.0194499\pi\)
\(230\) 422535. 0.526675
\(231\) 138777. 416389.i 0.171115 0.513416i
\(232\) −466671. −0.569235
\(233\) −635878. + 1.10137e6i −0.767333 + 1.32906i 0.171671 + 0.985154i \(0.445083\pi\)
−0.939004 + 0.343906i \(0.888250\pi\)
\(234\) 71942.1 + 124607.i 0.0858902 + 0.148766i
\(235\) 14475.2 + 25071.8i 0.0170984 + 0.0296153i
\(236\) −292039. + 505826.i −0.341319 + 0.591182i
\(237\) 582103. 0.673176
\(238\) 442201. 90508.7i 0.506031 0.103573i
\(239\) −300010. −0.339735 −0.169868 0.985467i \(-0.554334\pi\)
−0.169868 + 0.985467i \(0.554334\pi\)
\(240\) −28800.0 + 49883.1i −0.0322749 + 0.0559017i
\(241\) 28293.5 + 49005.9i 0.0313794 + 0.0543507i 0.881289 0.472578i \(-0.156677\pi\)
−0.849909 + 0.526929i \(0.823343\pi\)
\(242\) 39093.9 + 67712.6i 0.0429112 + 0.0743243i
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) −663276. −0.713214
\(245\) 50225.0 417162.i 0.0534570 0.444007i
\(246\) −385130. −0.405760
\(247\) 58486.7 101302.i 0.0609979 0.105651i
\(248\) −278548. 482460.i −0.287588 0.498117i
\(249\) −473626. 820345.i −0.484102 0.838490i
\(250\) 31250.0 54126.6i 0.0316228 0.0547723i
\(251\) 1.66302e6 1.66614 0.833071 0.553166i \(-0.186580\pi\)
0.833071 + 0.553166i \(0.186580\pi\)
\(252\) −164603. + 33690.6i −0.163282 + 0.0334201i
\(253\) 1.58945e6 1.56115
\(254\) 358441. 620839.i 0.348605 0.603802i
\(255\) 97921.6 + 169605.i 0.0943036 + 0.163339i
\(256\) −32768.0 56755.8i −0.0312500 0.0541266i
\(257\) 487587. 844525.i 0.460489 0.797590i −0.538496 0.842628i \(-0.681007\pi\)
0.998985 + 0.0450375i \(0.0143407\pi\)
\(258\) 571287. 0.534324
\(259\) −113490. + 340517.i −0.105126 + 0.315420i
\(260\) 177635. 0.162965
\(261\) 295316. 511502.i 0.268340 0.464778i
\(262\) −471771. 817132.i −0.424598 0.735426i
\(263\) 537984. + 931815.i 0.479601 + 0.830693i 0.999726 0.0233970i \(-0.00744819\pi\)
−0.520126 + 0.854090i \(0.674115\pi\)
\(264\) −108337. + 187645.i −0.0956681 + 0.165702i
\(265\) −806984. −0.705912
\(266\) 90628.7 + 102195.i 0.0785347 + 0.0885572i
\(267\) 201522. 0.173000
\(268\) 240321. 416249.i 0.204388 0.354010i
\(269\) −738079. 1.27839e6i −0.621902 1.07717i −0.989131 0.147036i \(-0.953027\pi\)
0.367229 0.930131i \(-0.380307\pi\)
\(270\) −36450.0 63133.3i −0.0304290 0.0527046i
\(271\) −663286. + 1.14884e6i −0.548627 + 0.950250i 0.449742 + 0.893159i \(0.351516\pi\)
−0.998369 + 0.0570916i \(0.981817\pi\)
\(272\) −222826. −0.182618
\(273\) 343793. + 387668.i 0.279184 + 0.314813i
\(274\) −482001. −0.387857
\(275\) 117553. 203608.i 0.0937352 0.162354i
\(276\) −304225. 526933.i −0.240393 0.416373i
\(277\) −745269. 1.29084e6i −0.583598 1.01082i −0.995049 0.0993891i \(-0.968311\pi\)
0.411451 0.911432i \(-0.365022\pi\)
\(278\) −157379. + 272588.i −0.122133 + 0.211541i
\(279\) 705075. 0.542282
\(280\) −65586.0 + 196785.i −0.0499938 + 0.150002i
\(281\) −1.00956e6 −0.762719 −0.381360 0.924427i \(-0.624544\pi\)
−0.381360 + 0.924427i \(0.624544\pi\)
\(282\) 20844.3 36103.4i 0.0156086 0.0270349i
\(283\) 497080. + 860968.i 0.368944 + 0.639030i 0.989401 0.145211i \(-0.0463861\pi\)
−0.620457 + 0.784241i \(0.713053\pi\)
\(284\) −300986. 521323.i −0.221437 0.383540i
\(285\) −29632.7 + 51325.4i −0.0216102 + 0.0374300i
\(286\) 668210. 0.483056
\(287\) −1.35875e6 + 278105.i −0.973719 + 0.199299i
\(288\) 82944.0 0.0589256
\(289\) 331118. 573513.i 0.233205 0.403923i
\(290\) −364587. 631483.i −0.254569 0.440927i
\(291\) 167414. + 289970.i 0.115894 + 0.200734i
\(292\) 259189. 448929.i 0.177893 0.308120i
\(293\) 1.69742e6 1.15510 0.577549 0.816356i \(-0.304009\pi\)
0.577549 + 0.816356i \(0.304009\pi\)
\(294\) −556395. + 237723.i −0.375418 + 0.160399i
\(295\) −912621. −0.610570
\(296\) 88596.4 153453.i 0.0587742 0.101800i
\(297\) −137114. 237489.i −0.0901967 0.156225i
\(298\) −519882. 900462.i −0.339128 0.587388i
\(299\) −938211. + 1.62503e6i −0.606908 + 1.05120i
\(300\) −90000.0 −0.0577350
\(301\) 2.01551e6 412531.i 1.28224 0.262446i
\(302\) −1.17432e6 −0.740917
\(303\) 740714. 1.28295e6i 0.463494 0.802795i
\(304\) −33715.5 58396.9i −0.0209240 0.0362415i
\(305\) −518184. 897522.i −0.318959 0.552453i
\(306\) 141007. 244232.i 0.0860870 0.149107i
\(307\) 2.95303e6 1.78822 0.894111 0.447846i \(-0.147809\pi\)
0.894111 + 0.447846i \(0.147809\pi\)
\(308\) −246715. + 740247.i −0.148190 + 0.444631i
\(309\) −765957. −0.456361
\(310\) 435232. 753843.i 0.257227 0.445530i
\(311\) 1.06071e6 + 1.83721e6i 0.621866 + 1.07710i 0.989138 + 0.146990i \(0.0469584\pi\)
−0.367272 + 0.930114i \(0.619708\pi\)
\(312\) −127897. 221524.i −0.0743831 0.128835i
\(313\) −192508. + 333434.i −0.111068 + 0.192375i −0.916201 0.400719i \(-0.868760\pi\)
0.805133 + 0.593094i \(0.202094\pi\)
\(314\) −1.55826e6 −0.891900
\(315\) −174185. 196415.i −0.0989089 0.111531i
\(316\) −1.03485e6 −0.582988
\(317\) −505089. + 874840.i −0.282306 + 0.488968i −0.971952 0.235178i \(-0.924433\pi\)
0.689646 + 0.724146i \(0.257766\pi\)
\(318\) 581029. + 1.00637e6i 0.322203 + 0.558072i
\(319\) −1.37147e6 2.37545e6i −0.754586 1.30698i
\(320\) 51200.0 88681.0i 0.0279508 0.0484123i
\(321\) −459630. −0.248969
\(322\) −1.45381e6 1.63935e6i −0.781393 0.881113i
\(323\) −229269. −0.122275
\(324\) −52488.0 + 90911.9i −0.0277778 + 0.0481125i
\(325\) 138777. + 240369.i 0.0728803 + 0.126232i
\(326\) −464265. 804131.i −0.241948 0.419066i
\(327\) 116339. 201505.i 0.0601666 0.104212i
\(328\) 684675. 0.351399
\(329\) 47468.6 142425.i 0.0241778 0.0725433i
\(330\) −338553. −0.171136
\(331\) −1.78311e6 + 3.08844e6i −0.894558 + 1.54942i −0.0602084 + 0.998186i \(0.519177\pi\)
−0.834350 + 0.551235i \(0.814157\pi\)
\(332\) 842002. + 1.45839e6i 0.419245 + 0.726154i
\(333\) 112130. + 194215.i 0.0554128 + 0.0959779i
\(334\) 1.23814e6 2.14452e6i 0.607299 1.05187i
\(335\) 751004. 0.365620
\(336\) 292628. 59894.5i 0.141406 0.0289427i
\(337\) −1.16658e6 −0.559551 −0.279776 0.960065i \(-0.590260\pi\)
−0.279776 + 0.960065i \(0.590260\pi\)
\(338\) 348159. 603029.i 0.165762 0.287109i
\(339\) 172909. + 299487.i 0.0817180 + 0.141540i
\(340\) −174083. 301520.i −0.0816693 0.141455i
\(341\) 1.63721e6 2.83573e6i 0.762463 1.32063i
\(342\) 85342.3 0.0394547
\(343\) −1.79131e6 + 1.24047e6i −0.822122 + 0.569311i
\(344\) −1.01562e6 −0.462739
\(345\) 475352. 823333.i 0.215014 0.372416i
\(346\) −753735. 1.30551e6i −0.338477 0.586259i
\(347\) −1.09312e6 1.89333e6i −0.487351 0.844117i 0.512543 0.858662i \(-0.328704\pi\)
−0.999894 + 0.0145443i \(0.995370\pi\)
\(348\) −525005. + 909336.i −0.232389 + 0.402510i
\(349\) 488943. 0.214880 0.107440 0.994212i \(-0.465735\pi\)
0.107440 + 0.994212i \(0.465735\pi\)
\(350\) −317522. + 64989.7i −0.138549 + 0.0283579i
\(351\) 323740. 0.140258
\(352\) 192599. 333592.i 0.0828510 0.143502i
\(353\) −462447. 800981.i −0.197526 0.342125i 0.750200 0.661212i \(-0.229957\pi\)
−0.947726 + 0.319086i \(0.896624\pi\)
\(354\) 657087. + 1.13811e6i 0.278686 + 0.482698i
\(355\) 470291. 814568.i 0.198059 0.343049i
\(356\) −358262. −0.149822
\(357\) 321115. 963476.i 0.133349 0.400102i
\(358\) 2.67998e6 1.10516
\(359\) −157198. + 272274.i −0.0643739 + 0.111499i −0.896416 0.443214i \(-0.853838\pi\)
0.832042 + 0.554712i \(0.187172\pi\)
\(360\) 64800.0 + 112237.i 0.0263523 + 0.0456435i
\(361\) 1.20336e6 + 2.08428e6i 0.485990 + 0.841759i
\(362\) −521304. + 902925.i −0.209083 + 0.362143i
\(363\) 175922. 0.0700736
\(364\) −611188. 689187.i −0.241781 0.272636i
\(365\) 809966. 0.318225
\(366\) −746186. + 1.29243e6i −0.291168 + 0.504318i
\(367\) 1.48827e6 + 2.57775e6i 0.576787 + 0.999024i 0.995845 + 0.0910644i \(0.0290269\pi\)
−0.419058 + 0.907959i \(0.637640\pi\)
\(368\) 540845. + 936770.i 0.208187 + 0.360590i
\(369\) −433271. + 750448.i −0.165651 + 0.286916i
\(370\) 276864. 0.105138
\(371\) 2.77659e6 + 3.13093e6i 1.04731 + 1.18097i
\(372\) −1.25347e6 −0.469630
\(373\) −1.77167e6 + 3.06862e6i −0.659341 + 1.14201i 0.321445 + 0.946928i \(0.395831\pi\)
−0.980787 + 0.195084i \(0.937502\pi\)
\(374\) −654848. 1.13423e6i −0.242081 0.419297i
\(375\) −70312.5 121785.i −0.0258199 0.0447214i
\(376\) −37056.5 + 64183.8i −0.0135175 + 0.0234129i
\(377\) 3.23817e6 1.17340
\(378\) −119531. + 358641.i −0.0430278 + 0.129101i
\(379\) −2.68890e6 −0.961559 −0.480780 0.876842i \(-0.659646\pi\)
−0.480780 + 0.876842i \(0.659646\pi\)
\(380\) 52680.4 91245.1i 0.0187150 0.0324154i
\(381\) −806493. 1.39689e6i −0.284635 0.493002i
\(382\) 483764. + 837905.i 0.169619 + 0.293789i
\(383\) −2.30505e6 + 3.99246e6i −0.802940 + 1.39073i 0.114734 + 0.993396i \(0.463399\pi\)
−0.917673 + 0.397336i \(0.869935\pi\)
\(384\) −147456. −0.0510310
\(385\) −1.19442e6 + 244472.i −0.410682 + 0.0840576i
\(386\) 3.46211e6 1.18270
\(387\) 642698. 1.11319e6i 0.218137 0.377824i
\(388\) −297625. 515502.i −0.100367 0.173840i
\(389\) −1.41964e6 2.45889e6i −0.475669 0.823883i 0.523942 0.851754i \(-0.324461\pi\)
−0.999612 + 0.0278705i \(0.991127\pi\)
\(390\) 199839. 346132.i 0.0665303 0.115234i
\(391\) 3.67780e6 1.21660
\(392\) 989148. 422618.i 0.325122 0.138910i
\(393\) −2.12297e6 −0.693366
\(394\) −118669. + 205540.i −0.0385120 + 0.0667047i
\(395\) −808476. 1.40032e6i −0.260720 0.451580i
\(396\) 243758. + 422202.i 0.0781127 + 0.135295i
\(397\) −148862. + 257837.i −0.0474033 + 0.0821049i −0.888753 0.458385i \(-0.848428\pi\)
0.841350 + 0.540490i \(0.181761\pi\)
\(398\) 3.63290e6 1.14960
\(399\) 301089. 61626.3i 0.0946810 0.0193791i
\(400\) 160000. 0.0500000
\(401\) 2.28859e6 3.96396e6i 0.710734 1.23103i −0.253847 0.967244i \(-0.581696\pi\)
0.964582 0.263784i \(-0.0849705\pi\)
\(402\) −540723. 936560.i −0.166882 0.289048i
\(403\) 1.93281e6 + 3.34772e6i 0.592824 + 1.02680i
\(404\) −1.31683e6 + 2.28081e6i −0.401398 + 0.695241i
\(405\) −164025. −0.0496904
\(406\) −1.19559e6 + 3.58727e6i −0.359971 + 1.08006i
\(407\) 1.04148e6 0.311648
\(408\) −250679. + 434189.i −0.0745535 + 0.129130i
\(409\) 1.84079e6 + 3.18833e6i 0.544120 + 0.942444i 0.998662 + 0.0517185i \(0.0164699\pi\)
−0.454541 + 0.890726i \(0.650197\pi\)
\(410\) 534903. + 926479.i 0.157150 + 0.272192i
\(411\) −542252. + 939207.i −0.158342 + 0.274256i
\(412\) 1.36170e6 0.395220
\(413\) 3.14005e6 + 3.54078e6i 0.905861 + 1.02147i
\(414\) −1.36901e6 −0.392561
\(415\) −1.31563e6 + 2.27873e6i −0.374984 + 0.649492i
\(416\) 227373. + 393821.i 0.0644177 + 0.111575i
\(417\) 354103. + 613324.i 0.0997215 + 0.172723i
\(418\) 198168. 343237.i 0.0554744 0.0960845i
\(419\) −1.50062e6 −0.417576 −0.208788 0.977961i \(-0.566952\pi\)
−0.208788 + 0.977961i \(0.566952\pi\)
\(420\) 309663. + 349181.i 0.0856576 + 0.0965891i
\(421\) −2.98818e6 −0.821679 −0.410839 0.911708i \(-0.634764\pi\)
−0.410839 + 0.911708i \(0.634764\pi\)
\(422\) 779832. 1.35071e6i 0.213167 0.369216i
\(423\) −46899.7 81232.6i −0.0127444 0.0220739i
\(424\) −1.03294e6 1.78910e6i −0.279036 0.483305i
\(425\) 272005. 471126.i 0.0730472 0.126522i
\(426\) −1.35444e6 −0.361605
\(427\) −1.69928e6 + 5.09855e6i −0.451020 + 1.35325i
\(428\) 817120. 0.215614
\(429\) 751736. 1.30204e6i 0.197207 0.341572i
\(430\) −793454. 1.37430e6i −0.206943 0.358436i
\(431\) −1.51519e6 2.62438e6i −0.392892 0.680509i 0.599938 0.800047i \(-0.295192\pi\)
−0.992830 + 0.119538i \(0.961859\pi\)
\(432\) 93312.0 161621.i 0.0240563 0.0416667i
\(433\) 1.41809e6 0.363483 0.181742 0.983346i \(-0.441827\pi\)
0.181742 + 0.983346i \(0.441827\pi\)
\(434\) −4.42226e6 + 905138.i −1.12699 + 0.230670i
\(435\) −1.64064e6 −0.415710
\(436\) −206825. + 358231.i −0.0521058 + 0.0902499i
\(437\) 556483. + 963856.i 0.139395 + 0.241440i
\(438\) −583176. 1.01009e6i −0.145249 0.251579i
\(439\) −1.86019e6 + 3.22194e6i −0.460676 + 0.797914i −0.998995 0.0448275i \(-0.985726\pi\)
0.538319 + 0.842741i \(0.319060\pi\)
\(440\) 601872. 0.148208
\(441\) −162729. + 1.35161e6i −0.0398445 + 0.330943i
\(442\) 1.54616e6 0.376443
\(443\) 400436. 693575.i 0.0969446 0.167913i −0.813474 0.581601i \(-0.802426\pi\)
0.910419 + 0.413688i \(0.135760\pi\)
\(444\) −199342. 345270.i −0.0479889 0.0831193i
\(445\) −279892. 484788.i −0.0670025 0.116052i
\(446\) −864964. + 1.49816e6i −0.205902 + 0.356633i
\(447\) −2.33947e6 −0.553794
\(448\) −520228. + 106479.i −0.122461 + 0.0250651i
\(449\) 3.89383e6 0.911510 0.455755 0.890105i \(-0.349369\pi\)
0.455755 + 0.890105i \(0.349369\pi\)
\(450\) −101250. + 175370.i −0.0235702 + 0.0408248i
\(451\) 2.01214e6 + 3.48514e6i 0.465820 + 0.806823i
\(452\) −307393. 532421.i −0.0707698 0.122577i
\(453\) −1.32111e6 + 2.28823e6i −0.302478 + 0.523907i
\(454\) 3.05759e6 0.696208
\(455\) 455093. 1.36547e6i 0.103056 0.309209i
\(456\) −151720. −0.0341688
\(457\) 1.61339e6 2.79447e6i 0.361367 0.625906i −0.626819 0.779165i \(-0.715644\pi\)
0.988186 + 0.153259i \(0.0489768\pi\)
\(458\) 1.41632e6 + 2.45314e6i 0.315499 + 0.546460i
\(459\) −317266. 549521.i −0.0702897 0.121745i
\(460\) −845070. + 1.46370e6i −0.186208 + 0.322521i
\(461\) 4.10832e6 0.900351 0.450176 0.892940i \(-0.351361\pi\)
0.450176 + 0.892940i \(0.351361\pi\)
\(462\) 1.16486e6 + 1.31352e6i 0.253903 + 0.286306i
\(463\) −1.48281e6 −0.321465 −0.160733 0.986998i \(-0.551386\pi\)
−0.160733 + 0.986998i \(0.551386\pi\)
\(464\) 933343. 1.61660e6i 0.201255 0.348584i
\(465\) −979271. 1.69615e6i −0.210025 0.363774i
\(466\) −2.54351e6 4.40549e6i −0.542587 0.939787i
\(467\) 1.14431e6 1.98201e6i 0.242803 0.420546i −0.718709 0.695311i \(-0.755267\pi\)
0.961511 + 0.274765i \(0.0886000\pi\)
\(468\) −575537. −0.121467
\(469\) −2.58398e6 2.91374e6i −0.542446 0.611672i
\(470\) −115802. −0.0241808
\(471\) −1.75304e6 + 3.03636e6i −0.364117 + 0.630669i
\(472\) −1.16815e6 2.02330e6i −0.241349 0.418029i
\(473\) −2.98474e6 5.16972e6i −0.613414 1.06246i
\(474\) −1.16421e6 + 2.01646e6i −0.238004 + 0.412235i
\(475\) 164626. 0.0334784
\(476\) −570870. + 1.71285e6i −0.115484 + 0.346498i
\(477\) 2.61463e6 0.526156
\(478\) 600020. 1.03926e6i 0.120115 0.208045i
\(479\) −252312. 437018.i −0.0502458 0.0870283i 0.839809 0.542883i \(-0.182667\pi\)
−0.890054 + 0.455854i \(0.849334\pi\)
\(480\) −115200. 199532.i −0.0228218 0.0395285i
\(481\) −614758. + 1.06479e6i −0.121155 + 0.209847i
\(482\) −226348. −0.0443772
\(483\) −4.82990e6 + 988574.i −0.942043 + 0.192815i
\(484\) −312751. −0.0606855
\(485\) 465039. 805471.i 0.0897708 0.155488i
\(486\) 118098. + 204552.i 0.0226805 + 0.0392837i
\(487\) 739529. + 1.28090e6i 0.141297 + 0.244733i 0.927985 0.372617i \(-0.121539\pi\)
−0.786688 + 0.617350i \(0.788206\pi\)
\(488\) 1.32655e6 2.29766e6i 0.252159 0.436752i
\(489\) −2.08919e6 −0.395100
\(490\) 1.34464e6 + 1.00831e6i 0.252998 + 0.189716i
\(491\) 7.51661e6 1.40708 0.703539 0.710657i \(-0.251602\pi\)
0.703539 + 0.710657i \(0.251602\pi\)
\(492\) 770260. 1.33413e6i 0.143458 0.248476i
\(493\) −3.17342e6 5.49652e6i −0.588044 1.01852i
\(494\) 233947. + 405208.i 0.0431320 + 0.0747069i
\(495\) −380872. + 659690.i −0.0698661 + 0.121012i
\(496\) 2.22839e6 0.406711
\(497\) −4.77848e6 + 978049.i −0.867759 + 0.177611i
\(498\) 3.78901e6 0.684624
\(499\) −1.21517e6 + 2.10474e6i −0.218468 + 0.378397i −0.954340 0.298723i \(-0.903439\pi\)
0.735872 + 0.677121i \(0.236773\pi\)
\(500\) 125000. + 216506.i 0.0223607 + 0.0387298i
\(501\) −2.78581e6 4.82516e6i −0.495858 0.858851i
\(502\) −3.32603e6 + 5.76086e6i −0.589070 + 1.02030i
\(503\) −5.24665e6 −0.924617 −0.462309 0.886719i \(-0.652979\pi\)
−0.462309 + 0.886719i \(0.652979\pi\)
\(504\) 212499. 637584.i 0.0372632 0.111805i
\(505\) −4.11508e6 −0.718042
\(506\) −3.17890e6 + 5.50602e6i −0.551951 + 0.956007i
\(507\) −783358. 1.35682e6i −0.135344 0.234423i
\(508\) 1.43377e6 + 2.48335e6i 0.246501 + 0.426952i
\(509\) −2.54111e6 + 4.40134e6i −0.434740 + 0.752992i −0.997274 0.0737822i \(-0.976493\pi\)
0.562534 + 0.826774i \(0.309826\pi\)
\(510\) −783373. −0.133365
\(511\) −2.78685e6 3.14250e6i −0.472129 0.532382i
\(512\) 262144. 0.0441942
\(513\) 96010.0 166294.i 0.0161073 0.0278987i
\(514\) 1.95035e6 + 3.37810e6i 0.325615 + 0.563982i
\(515\) 1.06383e6 + 1.84261e6i 0.176748 + 0.306136i
\(516\) −1.14257e6 + 1.97900e6i −0.188912 + 0.327206i
\(517\) −435611. −0.0716759
\(518\) −952604. 1.07417e6i −0.155987 0.175894i
\(519\) −3.39181e6 −0.552730
\(520\) −355270. + 615345.i −0.0576169 + 0.0997954i
\(521\) −1.16985e6 2.02623e6i −0.188814 0.327036i 0.756041 0.654524i \(-0.227131\pi\)
−0.944855 + 0.327488i \(0.893798\pi\)
\(522\) 1.18126e6 + 2.04601e6i 0.189745 + 0.328648i
\(523\) −3.29946e6 + 5.71483e6i −0.527459 + 0.913586i 0.472029 + 0.881583i \(0.343522\pi\)
−0.999488 + 0.0320025i \(0.989812\pi\)
\(524\) 3.77417e6 0.600473
\(525\) −230576. + 691823.i −0.0365103 + 0.109546i
\(526\) −4.30387e6 −0.678258
\(527\) 3.78832e6 6.56156e6i 0.594183 1.02915i
\(528\) −433348. 750581.i −0.0676476 0.117169i
\(529\) −5.70861e6 9.88760e6i −0.886934 1.53621i
\(530\) 1.61397e6 2.79548e6i 0.249577 0.432281i
\(531\) 2.95689e6 0.455092
\(532\) −535270. + 109558.i −0.0819962 + 0.0167828i
\(533\) −4.75087e6 −0.724361
\(534\) −403045. + 698094.i −0.0611646 + 0.105940i
\(535\) 638375. + 1.10570e6i 0.0964254 + 0.167014i
\(536\) 961285. + 1.66500e6i 0.144524 + 0.250323i
\(537\) 3.01498e6 5.22209e6i 0.451178 0.781463i
\(538\) 5.90463e6 0.879502
\(539\) 5.05815e6 + 3.79296e6i 0.749928 + 0.562350i
\(540\) 291600. 0.0430331
\(541\) 4.18341e6 7.24587e6i 0.614521 1.06438i −0.375947 0.926641i \(-0.622683\pi\)
0.990468 0.137741i \(-0.0439841\pi\)
\(542\) −2.65314e6 4.59538e6i −0.387938 0.671928i
\(543\) 1.17293e6 + 2.03158e6i 0.170716 + 0.295689i
\(544\) 445652. 771892.i 0.0645652 0.111830i
\(545\) −646327. −0.0932097
\(546\) −2.03051e6 + 415600.i −0.291489 + 0.0596614i
\(547\) −1.01705e6 −0.145337 −0.0726684 0.997356i \(-0.523151\pi\)
−0.0726684 + 0.997356i \(0.523151\pi\)
\(548\) 964003. 1.66970e6i 0.137128 0.237513i
\(549\) 1.67892e6 + 2.90797e6i 0.237738 + 0.411774i
\(550\) 470213. + 814433.i 0.0662808 + 0.114802i
\(551\) 960330. 1.66334e6i 0.134754 0.233401i
\(552\) 2.43380e6 0.339967
\(553\) −2.65124e6 + 7.95480e6i −0.368668 + 1.10616i
\(554\) 5.96215e6 0.825332
\(555\) 311472. 539485.i 0.0429226 0.0743441i
\(556\) −629516. 1.09035e6i −0.0863614 0.149582i
\(557\) −4.56175e6 7.90117e6i −0.623007 1.07908i −0.988923 0.148432i \(-0.952577\pi\)
0.365915 0.930648i \(-0.380756\pi\)
\(558\) −1.41015e6 + 2.44245e6i −0.191726 + 0.332078i
\(559\) 7.04726e6 0.953873
\(560\) −550512. 620767.i −0.0741816 0.0836486i
\(561\) −2.94682e6 −0.395317
\(562\) 2.01911e6 3.49721e6i 0.269662 0.467068i
\(563\) 3.19124e6 + 5.52739e6i 0.424315 + 0.734935i 0.996356 0.0852900i \(-0.0271817\pi\)
−0.572041 + 0.820225i \(0.693848\pi\)
\(564\) 83377.2 + 144414.i 0.0110370 + 0.0191166i
\(565\) 480302. 831907.i 0.0632985 0.109636i
\(566\) −3.97664e6 −0.521765
\(567\) 564360. + 636383.i 0.0737223 + 0.0831306i
\(568\) 2.40789e6 0.313159
\(569\) 4.51774e6 7.82496e6i 0.584980 1.01321i −0.409898 0.912131i \(-0.634436\pi\)
0.994878 0.101083i \(-0.0322309\pi\)
\(570\) −118531. 205302.i −0.0152807 0.0264670i
\(571\) −7.13771e6 1.23629e7i −0.916154 1.58682i −0.805203 0.592999i \(-0.797944\pi\)
−0.110950 0.993826i \(-0.535389\pi\)
\(572\) −1.33642e6 + 2.31475e6i −0.170786 + 0.295810i
\(573\) 2.17694e6 0.276987
\(574\) 1.75411e6 5.26304e6i 0.222217 0.666741i
\(575\) −2.64084e6 −0.333099
\(576\) −165888. + 287326.i −0.0208333 + 0.0360844i
\(577\) 3.94911e6 + 6.84005e6i 0.493809 + 0.855303i 0.999975 0.00713385i \(-0.00227079\pi\)
−0.506165 + 0.862436i \(0.668937\pi\)
\(578\) 1.32447e6 + 2.29405e6i 0.164901 + 0.285617i
\(579\) 3.89488e6 6.74612e6i 0.482833 0.836292i
\(580\) 2.91670e6 0.360016
\(581\) 1.33677e7 2.73607e6i 1.64292 0.336269i
\(582\) −1.33931e6 −0.163898
\(583\) 6.07127e6 1.05157e7i 0.739789 1.28135i
\(584\) 1.03676e6 + 1.79571e6i 0.125790 + 0.217874i
\(585\) −449638. 778796.i −0.0543217 0.0940880i
\(586\) −3.39483e6 + 5.88002e6i −0.408389 + 0.707351i
\(587\) −480037. −0.0575016 −0.0287508 0.999587i \(-0.509153\pi\)
−0.0287508 + 0.999587i \(0.509153\pi\)
\(588\) 289296. 2.40286e6i 0.0345064 0.286605i
\(589\) 2.29282e6 0.272321
\(590\) 1.82524e6 3.16141e6i 0.215869 0.373896i
\(591\) 267005. + 462466.i 0.0314449 + 0.0544642i
\(592\) 354386. + 613814.i 0.0415596 + 0.0719834i
\(593\) 5.03687e6 8.72412e6i 0.588199 1.01879i −0.406269 0.913753i \(-0.633170\pi\)
0.994468 0.105037i \(-0.0334962\pi\)
\(594\) 1.09691e6 0.127557
\(595\) −2.76376e6 + 565679.i −0.320042 + 0.0655055i
\(596\) 4.15906e6 0.479600
\(597\) 4.08701e6 7.07890e6i 0.469321 0.812887i
\(598\) −3.75285e6 6.50012e6i −0.429149 0.743307i
\(599\) 1.47865e6 + 2.56110e6i 0.168383 + 0.291649i 0.937852 0.347036i \(-0.112812\pi\)
−0.769468 + 0.638685i \(0.779479\pi\)
\(600\) 180000. 311769.i 0.0204124 0.0353553i
\(601\) −1.95113e6 −0.220344 −0.110172 0.993913i \(-0.535140\pi\)
−0.110172 + 0.993913i \(0.535140\pi\)
\(602\) −2.60198e6 + 7.80700e6i −0.292625 + 0.877997i
\(603\) −2.43325e6 −0.272517
\(604\) 2.34864e6 4.06797e6i 0.261954 0.453717i
\(605\) −244337. 423204.i −0.0271394 0.0470068i
\(606\) 2.96286e6 + 5.13182e6i 0.327740 + 0.567662i
\(607\) 1.00418e6 1.73930e6i 0.110622 0.191603i −0.805399 0.592733i \(-0.798049\pi\)
0.916021 + 0.401130i \(0.131382\pi\)
\(608\) 269724. 0.0295910
\(609\) 5.64495e6 + 6.36535e6i 0.616761 + 0.695471i
\(610\) 4.14548e6 0.451076
\(611\) 257130. 445363.i 0.0278644 0.0482626i
\(612\) 564029. + 976926.i 0.0608727 + 0.105435i
\(613\) −6.88619e6 1.19272e7i −0.740164 1.28200i −0.952420 0.304787i \(-0.901415\pi\)
0.212257 0.977214i \(-0.431919\pi\)
\(614\) −5.90605e6 + 1.02296e7i −0.632232 + 1.09506i
\(615\) 2.40706e6 0.256625
\(616\) −2.07086e6 2.33514e6i −0.219887 0.247948i
\(617\) 5.75202e6 0.608286 0.304143 0.952626i \(-0.401630\pi\)
0.304143 + 0.952626i \(0.401630\pi\)
\(618\) 1.53191e6 2.65335e6i 0.161348 0.279463i
\(619\) −1.63386e6 2.82994e6i −0.171392 0.296859i 0.767515 0.641031i \(-0.221493\pi\)
−0.938907 + 0.344172i \(0.888160\pi\)
\(620\) 1.74093e6 + 3.01537e6i 0.181887 + 0.315037i
\(621\) −1.54014e6 + 2.66760e6i −0.160262 + 0.277582i
\(622\) −8.48570e6 −0.879451
\(623\) −917851. + 2.75393e6i −0.0947441 + 0.284271i
\(624\) 1.02318e6 0.105194
\(625\) −195312. + 338291.i −0.0200000 + 0.0346410i
\(626\) −770032. 1.33374e6i −0.0785368 0.136030i
\(627\) −445878. 772283.i −0.0452947 0.0784527i
\(628\) 3.11652e6 5.39798e6i 0.315334 0.546175i
\(629\) 2.40986e6 0.242865
\(630\) 1.02877e6 210567.i 0.103268 0.0211367i
\(631\) −4.01563e6 −0.401495 −0.200748 0.979643i \(-0.564337\pi\)
−0.200748 + 0.979643i \(0.564337\pi\)
\(632\) 2.06970e6 3.58482e6i 0.206117 0.357006i
\(633\) −1.75462e6 3.03909e6i −0.174050 0.301463i
\(634\) −2.02036e6 3.49936e6i −0.199620 0.345753i
\(635\) −2.24026e6 + 3.88024e6i −0.220477 + 0.381878i
\(636\) −4.64823e6 −0.455664
\(637\) −6.86356e6 + 2.93249e6i −0.670194 + 0.286344i
\(638\) 1.09717e7 1.06715
\(639\) −1.52374e6 + 2.63920e6i −0.147625 + 0.255694i
\(640\) 204800. + 354724.i 0.0197642 + 0.0342327i
\(641\) 1.62418e6 + 2.81316e6i 0.156131 + 0.270427i 0.933470 0.358655i \(-0.116764\pi\)
−0.777339 + 0.629082i \(0.783431\pi\)
\(642\) 919260. 1.59220e6i 0.0880239 0.152462i
\(643\) −4.88701e6 −0.466140 −0.233070 0.972460i \(-0.574877\pi\)
−0.233070 + 0.972460i \(0.574877\pi\)
\(644\) 8.58650e6 1.75747e6i 0.815833 0.166983i
\(645\) −3.57054e6 −0.337936
\(646\) 458538. 794211.i 0.0432309 0.0748780i
\(647\) −504818. 874370.i −0.0474104 0.0821173i 0.841346 0.540496i \(-0.181764\pi\)
−0.888757 + 0.458379i \(0.848430\pi\)
\(648\) −209952. 363648.i −0.0196419 0.0340207i
\(649\) 6.86602e6 1.18923e7i 0.639872 1.10829i
\(650\) −1.11022e6 −0.103068
\(651\) −3.21133e6 + 9.63530e6i −0.296983 + 0.891072i
\(652\) 3.71412e6 0.342166
\(653\) 2.59693e6 4.49802e6i 0.238330 0.412799i −0.721906 0.691992i \(-0.756733\pi\)
0.960235 + 0.279193i \(0.0900668\pi\)
\(654\) 465356. + 806019.i 0.0425442 + 0.0736887i
\(655\) 2.94857e6 + 5.10707e6i 0.268540 + 0.465124i
\(656\) −1.36935e6 + 2.37179e6i −0.124238 + 0.215187i
\(657\) −2.62429e6 −0.237191
\(658\) 398438. + 449287.i 0.0358754 + 0.0404537i
\(659\) −2.06522e7 −1.85248 −0.926240 0.376934i \(-0.876978\pi\)
−0.926240 + 0.376934i \(0.876978\pi\)
\(660\) 677106. 1.17278e6i 0.0605058 0.104799i
\(661\) −219603. 380364.i −0.0195495 0.0338607i 0.856085 0.516835i \(-0.172890\pi\)
−0.875635 + 0.482974i \(0.839557\pi\)
\(662\) −7.13245e6 1.23538e7i −0.632548 1.09561i
\(663\) 1.73943e6 3.01278e6i 0.153682 0.266185i
\(664\) −6.73602e6 −0.592902
\(665\) −566429. 638716.i −0.0496697 0.0560085i
\(666\) −897038. −0.0783656
\(667\) −1.54051e7 + 2.66824e7i −1.34075 + 2.32225i
\(668\) 4.95255e6 + 8.57807e6i 0.429425 + 0.743787i
\(669\) 1.94617e6 + 3.37086e6i 0.168118 + 0.291189i
\(670\) −1.50201e6 + 2.60155e6i −0.129266 + 0.223896i
\(671\) 1.55940e7 1.33706
\(672\) −377776. + 1.13348e6i −0.0322709 + 0.0968259i
\(673\) 5.73639e6 0.488204 0.244102 0.969750i \(-0.421507\pi\)
0.244102 + 0.969750i \(0.421507\pi\)
\(674\) 2.33316e6 4.04115e6i 0.197831 0.342654i
\(675\) 227812. + 394583.i 0.0192450 + 0.0333333i
\(676\) 1.39264e6 + 2.41212e6i 0.117212 + 0.203017i
\(677\) −223788. + 387612.i −0.0187657 + 0.0325031i −0.875256 0.483660i \(-0.839307\pi\)
0.856490 + 0.516164i \(0.172640\pi\)
\(678\) −1.38327e6 −0.115567
\(679\) −4.72512e6 + 967127.i −0.393313 + 0.0805025i
\(680\) 1.39266e6 0.115498
\(681\) 3.43979e6 5.95788e6i 0.284226 0.492294i
\(682\) 6.54885e6 + 1.13429e7i 0.539143 + 0.933823i
\(683\) −8.57813e6 1.48578e7i −0.703624 1.21871i −0.967186 0.254071i \(-0.918230\pi\)
0.263561 0.964643i \(-0.415103\pi\)
\(684\) −170685. + 295634.i −0.0139493 + 0.0241610i
\(685\) 3.01251e6 0.245302
\(686\) −714478. 8.68623e6i −0.0579667 0.704727i
\(687\) 6.37344e6 0.515207
\(688\) 2.03124e6 3.51822e6i 0.163603 0.283368i
\(689\) 7.16743e6 + 1.24143e7i 0.575195 + 0.996267i
\(690\) 1.90141e6 + 3.29333e6i 0.152038 + 0.263338i
\(691\) 9.83358e6 1.70323e7i 0.783460 1.35699i −0.146455 0.989217i \(-0.546786\pi\)
0.929915 0.367775i \(-0.119880\pi\)
\(692\) 6.02988e6 0.478678
\(693\) 3.86993e6 792089.i 0.306105 0.0626528i
\(694\) 8.74492e6 0.689219
\(695\) 983618. 1.70368e6i 0.0772440 0.133790i
\(696\) −2.10002e6 3.63734e6i −0.164324 0.284617i
\(697\) 4.65587e6 + 8.06420e6i 0.363010 + 0.628752i
\(698\) −977887. + 1.69375e6i −0.0759714 + 0.131586i
\(699\) −1.14458e7 −0.886040
\(700\) 409913. 1.22991e6i 0.0316189 0.0948696i
\(701\) −1.37912e7 −1.06000 −0.530001 0.847997i \(-0.677809\pi\)
−0.530001 + 0.847997i \(0.677809\pi\)
\(702\) −647479. + 1.12147e6i −0.0495887 + 0.0858902i
\(703\) 364632. + 631562.i 0.0278270 + 0.0481978i
\(704\) 770397. + 1.33437e6i 0.0585845 + 0.101471i
\(705\) −130277. + 225646.i −0.00987176 + 0.0170984i
\(706\) 3.69957e6 0.279344
\(707\) 1.41587e7 + 1.59657e7i 1.06531 + 1.20126i
\(708\) −5.25670e6 −0.394121
\(709\) 1.17884e7 2.04181e7i 0.880722 1.52546i 0.0301832 0.999544i \(-0.490391\pi\)
0.850539 0.525912i \(-0.176276\pi\)
\(710\) 1.88116e6 + 3.25827e6i 0.140049 + 0.242572i
\(711\) 2.61946e6 + 4.53704e6i 0.194329 + 0.336588i
\(712\) 716524. 1.24106e6i 0.0529701 0.0917469i
\(713\) −3.67801e7 −2.70950
\(714\) 2.69535e6 + 3.03933e6i 0.197865 + 0.223117i
\(715\) −4.17631e6 −0.305512
\(716\) −5.35996e6 + 9.28372e6i −0.390732 + 0.676767i
\(717\) −1.35004e6 2.33835e6i −0.0980732 0.169868i
\(718\) −628790. 1.08910e6i −0.0455192 0.0788415i
\(719\) −8.38687e6 + 1.45265e7i −0.605031 + 1.04794i 0.387015 + 0.922073i \(0.373506\pi\)
−0.992047 + 0.125872i \(0.959827\pi\)
\(720\) −518400. −0.0372678
\(721\) 3.48862e6 1.04673e7i 0.249928 0.749888i
\(722\) −9.62687e6 −0.687294
\(723\) −254642. + 441053.i −0.0181169 + 0.0313794i
\(724\) −2.08522e6 3.61170e6i −0.147844 0.256074i
\(725\) 2.27867e6 + 3.94677e6i 0.161004 + 0.278867i
\(726\) −351845. + 609413.i −0.0247748 + 0.0429112i
\(727\) 58043.8 0.00407305 0.00203653 0.999998i \(-0.499352\pi\)
0.00203653 + 0.999998i \(0.499352\pi\)
\(728\) 3.60979e6 738844.i 0.252437 0.0516683i
\(729\) 531441. 0.0370370
\(730\) −1.61993e6 + 2.80580e6i −0.112510 + 0.194872i
\(731\) −6.90634e6 1.19621e7i −0.478029 0.827971i
\(732\) −2.98474e6 5.16973e6i −0.205887 0.356607i
\(733\) 2.00069e6 3.46530e6i 0.137537 0.238222i −0.789026 0.614359i \(-0.789415\pi\)
0.926564 + 0.376137i \(0.122748\pi\)
\(734\) −1.19061e7 −0.815699
\(735\) 3.47747e6 1.48577e6i 0.237435 0.101445i
\(736\) −4.32676e6 −0.294420
\(737\) −5.65011e6 + 9.78628e6i −0.383167 + 0.663665i
\(738\) −1.73308e6 3.00179e6i −0.117133 0.202880i
\(739\) 5.24156e6 + 9.07865e6i 0.353061 + 0.611519i 0.986784 0.162041i \(-0.0518076\pi\)
−0.633723 + 0.773560i \(0.718474\pi\)
\(740\) −553727. + 959084.i −0.0371721 + 0.0643839i
\(741\) 1.05276e6 0.0704343
\(742\) −1.63990e7 + 3.35652e6i −1.09347 + 0.223810i
\(743\) −1.19520e7 −0.794269 −0.397134 0.917761i \(-0.629995\pi\)
−0.397134 + 0.917761i \(0.629995\pi\)
\(744\) 2.50693e6 4.34214e6i 0.166039 0.287588i
\(745\) 3.24926e6 + 5.62789e6i 0.214484 + 0.371497i
\(746\) −7.08667e6 1.22745e7i −0.466225 0.807525i
\(747\) 4.26264e6 7.38310e6i 0.279497 0.484102i
\(748\) 5.23878e6 0.342355
\(749\) 2.09342e6 6.28114e6i 0.136349 0.409104i
\(750\) 562500. 0.0365148
\(751\) −1.38281e7 + 2.39510e7i −0.894669 + 1.54961i −0.0604551 + 0.998171i \(0.519255\pi\)
−0.834214 + 0.551441i \(0.814078\pi\)
\(752\) −148226. 256735.i −0.00955829 0.0165554i
\(753\) 7.48357e6 + 1.29619e7i 0.480974 + 0.833071i
\(754\) −6.47634e6 + 1.12173e7i −0.414860 + 0.718558i
\(755\) 7.33950e6 0.468597
\(756\) −1.00331e6 1.13135e6i −0.0638454 0.0719932i
\(757\) −1.38554e7 −0.878780 −0.439390 0.898296i \(-0.644805\pi\)
−0.439390 + 0.898296i \(0.644805\pi\)
\(758\) 5.37779e6 9.31461e6i 0.339962 0.588832i
\(759\) 7.15253e6 + 1.23885e7i 0.450666 + 0.780577i
\(760\) 210722. + 364981.i 0.0132335 + 0.0229211i
\(761\) −6.29999e6 + 1.09119e7i −0.394347 + 0.683029i −0.993018 0.117967i \(-0.962362\pi\)
0.598671 + 0.800995i \(0.295696\pi\)
\(762\) 6.45195e6 0.402535
\(763\) 2.22382e6 + 2.50762e6i 0.138289 + 0.155937i
\(764\) −3.87012e6 −0.239878
\(765\) −881295. + 1.52645e6i −0.0544462 + 0.0943036i
\(766\) −9.22019e6 1.59698e7i −0.567764 0.983396i
\(767\) 8.10566e6 + 1.40394e7i 0.497508 + 0.861709i
\(768\) 294912. 510803.i 0.0180422 0.0312500i
\(769\) 2.90665e7 1.77246 0.886230 0.463245i \(-0.153315\pi\)
0.886230 + 0.463245i \(0.153315\pi\)
\(770\) 1.54197e6 4.62654e6i 0.0937236 0.281209i
\(771\) 8.77657e6 0.531727
\(772\) −6.92422e6 + 1.19931e7i −0.418146 + 0.724250i
\(773\) −8.03098e6 1.39101e7i −0.483415 0.837299i 0.516404 0.856345i \(-0.327270\pi\)
−0.999819 + 0.0190465i \(0.993937\pi\)
\(774\) 2.57079e6 + 4.45274e6i 0.154246 + 0.267162i
\(775\) −2.72020e6 + 4.71152e6i −0.162684 + 0.281778i
\(776\) 2.38100e6 0.141940
\(777\) −3.16477e6 + 647758.i −0.188057 + 0.0384911i
\(778\) 1.13571e7 0.672698
\(779\) −1.40894e6 + 2.44036e6i −0.0831860 + 0.144082i
\(780\) 799357. + 1.38453e6i 0.0470440 + 0.0814826i
\(781\) 7.07638e6 + 1.22566e7i 0.415129 + 0.719025i
\(782\) −7.35561e6 + 1.27403e7i −0.430132 + 0.745010i
\(783\) 5.31568e6 0.309852
\(784\) −514304. + 4.27174e6i −0.0298834 + 0.248208i
\(785\) 9.73913e6 0.564087
\(786\) 4.24594e6 7.35419e6i 0.245142 0.424598i
\(787\) 1.83559e6 + 3.17933e6i 0.105642 + 0.182978i 0.914000 0.405713i \(-0.132977\pi\)
−0.808358 + 0.588691i \(0.799643\pi\)
\(788\) −474675. 822161.i −0.0272321 0.0471674i
\(789\) −4.84185e6 + 8.38634e6i −0.276898 + 0.479601i
\(790\) 6.46781e6 0.368714
\(791\) −4.88020e6 + 998869.i −0.277330 + 0.0567633i
\(792\) −1.95007e6 −0.110468
\(793\) −9.20476e6 + 1.59431e7i −0.519792 + 0.900306i
\(794\) −595449. 1.03135e6i −0.0335192 0.0580569i
\(795\) −3.63143e6 6.28982e6i −0.203779 0.352956i
\(796\) −7.26579e6 + 1.25847e7i −0.406443 + 0.703981i
\(797\) −2.53970e7 −1.41624 −0.708121 0.706092i \(-0.750457\pi\)
−0.708121 + 0.706092i \(0.750457\pi\)
\(798\) −388699. + 1.16626e6i −0.0216076 + 0.0648316i
\(799\) −1.00795e6 −0.0558565
\(800\) −320000. + 554256.i −0.0176777 + 0.0306186i
\(801\) 906851. + 1.57071e6i 0.0499407 + 0.0864998i
\(802\) 9.15437e6 + 1.58558e7i 0.502565 + 0.870468i
\(803\) −6.09370e6 + 1.05546e7i −0.333497 + 0.577634i
\(804\) 4.32578e6 0.236007
\(805\) 9.08634e6 + 1.02459e7i 0.494196 + 0.557265i
\(806\) −1.54625e7 −0.838380
\(807\) 6.64271e6 1.15055e7i 0.359055 0.621902i
\(808\) −5.26730e6 9.12323e6i −0.283831 0.491610i
\(809\) 4.93977e6 + 8.55593e6i 0.265360 + 0.459617i 0.967658 0.252266i \(-0.0811758\pi\)
−0.702298 + 0.711883i \(0.747843\pi\)
\(810\) 328050. 568199.i 0.0175682 0.0304290i
\(811\) 1.11209e7 0.593726 0.296863 0.954920i \(-0.404059\pi\)
0.296863 + 0.954920i \(0.404059\pi\)
\(812\) −1.00355e7 1.13162e7i −0.534131 0.602296i
\(813\) −1.19391e7 −0.633500
\(814\) −2.08296e6 + 3.60779e6i −0.110184 + 0.190845i
\(815\) 2.90166e6 + 5.02582e6i 0.153021 + 0.265041i
\(816\) −1.00272e6 1.73676e6i −0.0527173 0.0913090i
\(817\) 2.08997e6 3.61994e6i 0.109543 0.189735i
\(818\) −1.47263e7 −0.769502
\(819\) −1.47450e6 + 4.42411e6i −0.0768130 + 0.230471i
\(820\) −4.27922e6 −0.222244
\(821\) −1.29397e7 + 2.24122e7i −0.669986 + 1.16045i 0.307922 + 0.951412i \(0.400366\pi\)
−0.977908 + 0.209038i \(0.932967\pi\)
\(822\) −2.16901e6 3.75683e6i −0.111965 0.193929i
\(823\) −1.47239e7 2.55026e7i −0.757747 1.31246i −0.943997 0.329953i \(-0.892967\pi\)
0.186251 0.982502i \(-0.440366\pi\)
\(824\) −2.72340e6 + 4.71707e6i −0.139731 + 0.242022i
\(825\) 2.11596e6 0.108236
\(826\) −1.85457e7 + 3.79590e6i −0.945788 + 0.193582i
\(827\) −2.61824e7 −1.33121 −0.665605 0.746304i \(-0.731826\pi\)
−0.665605 + 0.746304i \(0.731826\pi\)
\(828\) 2.73803e6 4.74240e6i 0.138791 0.240393i
\(829\) 1.79483e7 + 3.10874e7i 0.907063 + 1.57108i 0.818123 + 0.575043i \(0.195015\pi\)
0.0889398 + 0.996037i \(0.471652\pi\)
\(830\) −5.26251e6 9.11494e6i −0.265154 0.459260i
\(831\) 6.70742e6 1.16176e7i 0.336940 0.583598i
\(832\) −1.81898e6 −0.0911003
\(833\) 1.17040e7 + 8.77647e6i 0.584414 + 0.438235i
\(834\) −2.83282e6 −0.141028
\(835\) −7.73836e6 + 1.34032e7i −0.384090 + 0.665263i
\(836\) 792672. + 1.37295e6i 0.0392263 + 0.0679420i
\(837\) 3.17284e6 + 5.49552e6i 0.156543 + 0.271141i
\(838\) 3.00124e6 5.19829e6i 0.147635 0.255712i
\(839\) 1.26587e7 0.620845 0.310422 0.950599i \(-0.399530\pi\)
0.310422 + 0.950599i \(0.399530\pi\)
\(840\) −1.82893e6 + 374340.i −0.0894330 + 0.0183050i
\(841\) 3.26583e7 1.59222
\(842\) 5.97637e6 1.03514e7i 0.290507 0.503173i
\(843\) −4.54300e6 7.86871e6i −0.220178 0.381360i
\(844\) 3.11933e6 + 5.40283e6i 0.150732 + 0.261075i
\(845\) −2.17599e6 + 3.76893e6i −0.104837 + 0.181584i
\(846\) 375197. 0.0180233
\(847\) −801254. + 2.40409e6i −0.0383762 + 0.115144i
\(848\) 8.26352e6 0.394617
\(849\) −4.47372e6 + 7.74871e6i −0.213010 + 0.368944i
\(850\) 1.08802e6 + 1.88450e6i 0.0516522 + 0.0894642i
\(851\) −5.84923e6 1.01312e7i −0.276869 0.479551i
\(852\) 2.70887e6 4.69191e6i 0.127847 0.221437i
\(853\) 1.53972e6 0.0724552 0.0362276 0.999344i \(-0.488466\pi\)
0.0362276 + 0.999344i \(0.488466\pi\)
\(854\) −1.42633e7 1.60836e7i −0.669231 0.754637i
\(855\) −533389. −0.0249533
\(856\) −1.63424e6 + 2.83059e6i −0.0762310 + 0.132036i
\(857\) 6.19178e6 + 1.07245e7i 0.287981 + 0.498798i 0.973328 0.229419i \(-0.0736827\pi\)
−0.685347 + 0.728217i \(0.740349\pi\)
\(858\) 3.00694e6 + 5.20818e6i 0.139446 + 0.241528i
\(859\) 1.67108e7 2.89439e7i 0.772705 1.33836i −0.163370 0.986565i \(-0.552237\pi\)
0.936075 0.351799i \(-0.114430\pi\)
\(860\) 6.34763e6 0.292662
\(861\) −8.28197e6 9.33890e6i −0.380738 0.429327i
\(862\) 1.21215e7 0.555633
\(863\) −1.73246e7 + 3.00071e7i −0.791838 + 1.37150i 0.132990 + 0.991117i \(0.457542\pi\)
−0.924828 + 0.380386i \(0.875791\pi\)
\(864\) 373248. + 646484.i 0.0170103 + 0.0294628i
\(865\) 4.71085e6 + 8.15942e6i 0.214071 + 0.370783i
\(866\) −2.83618e6 + 4.91241e6i −0.128511 + 0.222587i
\(867\) 5.96012e6 0.269282
\(868\) 5.70902e6 1.71294e7i 0.257195 0.771691i
\(869\) 2.43300e7 1.09293
\(870\) 3.28128e6 5.68335e6i 0.146976 0.254569i
\(871\) −6.67023e6 1.15532e7i −0.297917 0.516007i
\(872\) −827299. 1.43292e6i −0.0368444 0.0638163i
\(873\) −1.50673e6 + 2.60973e6i −0.0669112 + 0.115894i
\(874\) −4.45186e6 −0.197135
\(875\) 1.98451e6 406185.i 0.0876261 0.0179351i
\(876\) 4.66540e6 0.205414
\(877\) 1.83963e7 3.18634e7i 0.807666 1.39892i −0.106810 0.994279i \(-0.534064\pi\)
0.914476 0.404640i \(-0.132603\pi\)
\(878\) −7.44075e6 1.28878e7i −0.325747 0.564210i
\(879\) 7.63837e6 + 1.32300e7i 0.333448 + 0.577549i
\(880\) −1.20374e6 + 2.08495e6i −0.0523996 + 0.0907587i
\(881\) −1.37404e7 −0.596432 −0.298216 0.954498i \(-0.596392\pi\)
−0.298216 + 0.954498i \(0.596392\pi\)
\(882\) −4.35664e6 3.26692e6i −0.188573 0.141406i
\(883\) −6.26276e6 −0.270311 −0.135156 0.990824i \(-0.543153\pi\)
−0.135156 + 0.990824i \(0.543153\pi\)
\(884\) −3.09232e6 + 5.35605e6i −0.133093 + 0.230523i
\(885\) −4.10679e6 7.11318e6i −0.176256 0.305285i
\(886\) 1.60174e6 + 2.77430e6i 0.0685502 + 0.118732i
\(887\) 2.22623e7 3.85594e7i 0.950082 1.64559i 0.204841 0.978795i \(-0.434332\pi\)
0.745241 0.666795i \(-0.232334\pi\)
\(888\) 1.59473e6 0.0678666
\(889\) 2.27626e7 4.65900e6i 0.965978 0.197714i
\(890\) 2.23914e6 0.0947558
\(891\) 1.23403e6 2.13740e6i 0.0520751 0.0901967i
\(892\) −3.45985e6 5.99264e6i −0.145595 0.252178i
\(893\) −152512. 264158.i −0.00639993 0.0110850i
\(894\) 4.67894e6 8.10416e6i 0.195796 0.339128i
\(895\) −1.67499e7 −0.698962
\(896\) 671601. 2.01508e6i 0.0279474 0.0838537i
\(897\) −1.68878e7 −0.700797
\(898\) −7.78767e6 + 1.34886e7i −0.322268 + 0.558184i
\(899\) 3.17360e7 + 5.49683e7i 1.30964 + 2.26837i
\(900\) −405000. 701481.i −0.0166667 0.0288675i
\(901\) 1.40482e7 2.43322e7i 0.576513 0.998550i
\(902\) −1.60972e7 −0.658769
\(903\) 1.22852e7 + 1.38530e7i 0.501374 + 0.565358i
\(904\) 2.45915e6 0.100084
\(905\) 3.25815e6 5.64328e6i 0.132236 0.229039i
\(906\) −5.28444e6 9.15292e6i −0.213884 0.370458i
\(907\) 1.39004e7 + 2.40762e7i 0.561060 + 0.971784i 0.997404 + 0.0720046i \(0.0229396\pi\)
−0.436344 + 0.899780i \(0.643727\pi\)
\(908\) −6.11518e6 + 1.05918e7i −0.246147 + 0.426339i
\(909\) 1.33329e7 0.535197
\(910\) 3.81992e6 + 4.30742e6i 0.152915 + 0.172430i
\(911\) 1.67045e7 0.666864 0.333432 0.942774i \(-0.391793\pi\)
0.333432 + 0.942774i \(0.391793\pi\)
\(912\) 303439. 525572.i 0.0120805 0.0209240i
\(913\) −1.97960e7 3.42877e7i −0.785960 1.36132i
\(914\) 6.45355e6 + 1.11779e7i 0.255525 + 0.442582i
\(915\) 4.66366e6 8.07770e6i 0.184151 0.318959i
\(916\) −1.13306e7 −0.446183
\(917\) 9.66925e6 2.90117e7i 0.379725 1.13933i
\(918\) 2.53813e6 0.0994047
\(919\) 1.08291e7 1.87565e7i 0.422963 0.732593i −0.573265 0.819370i \(-0.694323\pi\)
0.996228 + 0.0867770i \(0.0276568\pi\)
\(920\) −3.38028e6 5.85481e6i −0.131669 0.228057i
\(921\) 1.32886e7 + 2.30166e7i 0.516215 + 0.894111i
\(922\) −8.21664e6 + 1.42316e7i −0.318322 + 0.551350i
\(923\) −1.67080e7 −0.645536
\(924\) −6.87987e6 + 1.40816e6i −0.265094 + 0.0542589i
\(925\) −1.73040e6 −0.0664954
\(926\) 2.96563e6 5.13662e6i 0.113655 0.196856i
\(927\) −3.44681e6 5.97005e6i −0.131740 0.228180i
\(928\) 3.73337e6 + 6.46639e6i 0.142309 + 0.246486i
\(929\) −1.15385e7 + 1.99853e7i −0.438642 + 0.759750i −0.997585 0.0694559i \(-0.977874\pi\)
0.558943 + 0.829206i \(0.311207\pi\)
\(930\) 7.83417e6 0.297020
\(931\) −529175. + 4.39526e6i −0.0200090 + 0.166192i
\(932\) 2.03481e7 0.767333
\(933\) −9.54641e6 + 1.65349e7i −0.359034 + 0.621866i
\(934\) 4.57726e6 + 7.92804e6i 0.171687 + 0.297371i
\(935\) 4.09280e6 + 7.08894e6i 0.153106 + 0.265187i
\(936\) 1.15107e6 1.99372e6i 0.0429451 0.0743831i
\(937\) 2.57761e7 0.959110 0.479555 0.877512i \(-0.340798\pi\)
0.479555 + 0.877512i \(0.340798\pi\)
\(938\) 1.52615e7 3.12368e6i 0.566355 0.115920i
\(939\) −3.46515e6 −0.128250
\(940\) 231603. 401149.i 0.00854919 0.0148076i
\(941\) −1.53396e7 2.65690e7i −0.564729 0.978139i −0.997075 0.0764314i \(-0.975647\pi\)
0.432346 0.901708i \(-0.357686\pi\)
\(942\) −7.01218e6 1.21454e7i −0.257469 0.445950i
\(943\) 2.26015e7 3.91469e7i 0.827672 1.43357i
\(944\) 9.34524e6 0.341319
\(945\) 747066. 2.24151e6i 0.0272132 0.0816508i
\(946\) 2.38779e7 0.867498
\(947\) 1.42412e7 2.46666e7i 0.516028 0.893786i −0.483799 0.875179i \(-0.660743\pi\)
0.999827 0.0186072i \(-0.00592319\pi\)
\(948\) −4.65682e6 8.06585e6i −0.168294 0.291494i
\(949\) −7.19391e6 1.24602e7i −0.259298 0.449118i
\(950\) −329253. + 570282.i −0.0118364 + 0.0205013i
\(951\) −9.09161e6 −0.325979
\(952\) −4.79173e6 5.40325e6i −0.171356 0.193225i
\(953\) −2.00240e7 −0.714199 −0.357100 0.934066i \(-0.616234\pi\)
−0.357100 + 0.934066i \(0.616234\pi\)
\(954\) −5.22926e6 + 9.05734e6i −0.186024 + 0.322203i
\(955\) −3.02353e6 5.23690e6i −0.107277 0.185809i
\(956\) 2.40008e6 + 4.15706e6i 0.0849339 + 0.147110i
\(957\) 1.23432e7 2.13791e7i 0.435661 0.754586i
\(958\) 2.01850e6 0.0710583
\(959\) −1.03651e7 1.16879e7i −0.363939 0.410384i
\(960\) 921600. 0.0322749
\(961\) −2.35707e7 + 4.08257e7i −0.823312 + 1.42602i
\(962\) −2.45903e6 4.25917e6i −0.0856696 0.148384i
\(963\) −2.06833e6 3.58246e6i −0.0718712 0.124485i
\(964\) 452697. 784094.i 0.0156897 0.0271754i
\(965\) −2.16382e7 −0.748002
\(966\) 6.23529e6 1.87084e7i 0.214988 0.645052i
\(967\) 1.74233e7 0.599189 0.299595 0.954067i \(-0.403149\pi\)
0.299595 + 0.954067i \(0.403149\pi\)
\(968\) 625502. 1.08340e6i 0.0214556 0.0371622i
\(969\) −1.03171e6 1.78697e6i −0.0352978 0.0611377i
\(970\) 1.86016e6 + 3.22189e6i 0.0634775 + 0.109946i
\(971\) 5.62603e6 9.74456e6i 0.191493 0.331676i −0.754252 0.656585i \(-0.772000\pi\)
0.945745 + 0.324909i \(0.105334\pi\)
\(972\) −944784. −0.0320750
\(973\) −9.99425e6 + 2.04560e6i −0.338429 + 0.0692690i
\(974\) −5.91623e6 −0.199824
\(975\) −1.24900e6 + 2.16332e6i −0.0420774 + 0.0728803i
\(976\) 5.30621e6 + 9.19062e6i 0.178303 + 0.308831i
\(977\) −2.22637e7 3.85618e7i −0.746208 1.29247i −0.949628 0.313379i \(-0.898539\pi\)
0.203420 0.979092i \(-0.434794\pi\)
\(978\) 4.17839e6 7.23718e6i 0.139689 0.241948i
\(979\) 8.42297e6 0.280872
\(980\) −6.18217e6 + 2.64136e6i −0.205625 + 0.0878542i
\(981\) 2.09410e6 0.0694744
\(982\) −1.50332e7 + 2.60383e7i −0.497477 + 0.861656i
\(983\) 9.94307e6 + 1.72219e7i 0.328199 + 0.568457i 0.982154 0.188076i \(-0.0602251\pi\)
−0.653956 + 0.756533i \(0.726892\pi\)
\(984\) 3.08104e6 + 5.33652e6i 0.101440 + 0.175699i
\(985\) 741680. 1.28463e6i 0.0243571 0.0421878i
\(986\) 2.53873e7 0.831620
\(987\) 1.32370e6 270933.i 0.0432512 0.00885256i
\(988\) −1.87158e6 −0.0609979
\(989\) −3.35262e7 + 5.80691e7i −1.08992 + 1.88779i
\(990\) −1.52349e6 2.63876e6i −0.0494028 0.0855681i
\(991\) −2.46286e6 4.26580e6i −0.0796628 0.137980i 0.823442 0.567401i \(-0.192051\pi\)
−0.903104 + 0.429421i \(0.858718\pi\)
\(992\) −4.45677e6 + 7.71935e6i −0.143794 + 0.249059i
\(993\) −3.20960e7 −1.03295
\(994\) 6.16890e6 1.85092e7i 0.198035 0.594187i
\(995\) −2.27056e7 −0.727068
\(996\) −7.57802e6 + 1.31255e7i −0.242051 + 0.419245i
\(997\) 5.96238e6 + 1.03271e7i 0.189968 + 0.329035i 0.945239 0.326378i \(-0.105828\pi\)
−0.755271 + 0.655413i \(0.772495\pi\)
\(998\) −4.86070e6 8.41898e6i −0.154480 0.267567i
\(999\) −1.00917e6 + 1.74793e6i −0.0319926 + 0.0554128i
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 210.6.i.b.121.1 4
7.4 even 3 inner 210.6.i.b.151.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.6.i.b.121.1 4 1.1 even 1 trivial
210.6.i.b.151.1 yes 4 7.4 even 3 inner