Properties

Label 37.6.c.a.10.1
Level $37$
Weight $6$
Character 37.10
Analytic conductor $5.934$
Analytic rank $0$
Dimension $30$
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] = [37,6,Mod(10,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.10");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 37.c (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: \(5.93420133308\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 10.1
Character \(\chi\) \(=\) 37.10
Dual form 37.6.c.a.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.29373 + 9.16901i) q^{2} +(-7.75625 - 13.4342i) q^{3} +(-40.0472 - 69.3637i) q^{4} +(14.2918 + 24.7542i) q^{5} +164.238 q^{6} +(10.7449 + 18.6107i) q^{7} +509.197 q^{8} +(1.18106 - 2.04566i) q^{9} +O(q^{10})\) \(q+(-5.29373 + 9.16901i) q^{2} +(-7.75625 - 13.4342i) q^{3} +(-40.0472 - 69.3637i) q^{4} +(14.2918 + 24.7542i) q^{5} +164.238 q^{6} +(10.7449 + 18.6107i) q^{7} +509.197 q^{8} +(1.18106 - 2.04566i) q^{9} -302.628 q^{10} -76.4480 q^{11} +(-621.232 + 1076.01i) q^{12} +(377.201 + 653.332i) q^{13} -227.522 q^{14} +(221.702 - 383.999i) q^{15} +(-1414.04 + 2449.19i) q^{16} +(1162.24 - 2013.06i) q^{17} +(12.5045 + 21.6584i) q^{18} +(974.165 + 1687.30i) q^{19} +(1144.69 - 1982.67i) q^{20} +(166.680 - 288.698i) q^{21} +(404.695 - 700.952i) q^{22} +3500.15 q^{23} +(-3949.46 - 6840.67i) q^{24} +(1153.99 - 1998.76i) q^{25} -7987.21 q^{26} -3806.18 q^{27} +(860.603 - 1490.61i) q^{28} +5347.24 q^{29} +(2347.26 + 4065.58i) q^{30} -547.123 q^{31} +(-6823.97 - 11819.5i) q^{32} +(592.950 + 1027.02i) q^{33} +(12305.2 + 21313.2i) q^{34} +(-307.127 + 531.960i) q^{35} -189.193 q^{36} +(-8095.55 - 1950.92i) q^{37} -20627.9 q^{38} +(5851.34 - 10134.8i) q^{39} +(7277.35 + 12604.7i) q^{40} +(-3364.04 - 5826.70i) q^{41} +(1764.72 + 3056.58i) q^{42} +4181.80 q^{43} +(3061.53 + 5302.72i) q^{44} +67.5182 q^{45} +(-18528.8 + 32092.9i) q^{46} -2603.06 q^{47} +43870.7 q^{48} +(8172.60 - 14155.4i) q^{49} +(12217.8 + 21161.8i) q^{50} -36058.6 q^{51} +(30211.7 - 52328.2i) q^{52} +(10068.1 - 17438.5i) q^{53} +(20148.9 - 34898.9i) q^{54} +(-1092.58 - 1892.41i) q^{55} +(5471.25 + 9476.49i) q^{56} +(15111.7 - 26174.3i) q^{57} +(-28306.8 + 49028.9i) q^{58} +(-22085.0 + 38252.3i) q^{59} -35514.2 q^{60} +(12156.5 + 21055.7i) q^{61} +(2896.32 - 5016.58i) q^{62} +50.7615 q^{63} +53998.2 q^{64} +(-10781.8 + 18674.6i) q^{65} -12555.7 q^{66} +(16756.9 + 29023.8i) q^{67} -186178. q^{68} +(-27148.0 - 47021.8i) q^{69} +(-3251.70 - 5632.11i) q^{70} +(19911.2 + 34487.2i) q^{71} +(601.394 - 1041.64i) q^{72} -10784.0 q^{73} +(60743.6 - 63900.5i) q^{74} -35802.5 q^{75} +(78025.1 - 135143. i) q^{76} +(-821.423 - 1422.75i) q^{77} +(61950.8 + 107302. i) q^{78} +(8215.11 + 14229.0i) q^{79} -80837.0 q^{80} +(29234.7 + 50636.0i) q^{81} +71233.4 q^{82} +(56127.2 - 97215.2i) q^{83} -26700.2 q^{84} +66442.2 q^{85} +(-22137.3 + 38343.0i) q^{86} +(-41474.5 - 71836.0i) q^{87} -38927.1 q^{88} +(-581.269 + 1006.79i) q^{89} +(-357.423 + 619.075i) q^{90} +(-8105.96 + 14039.9i) q^{91} +(-140171. - 242783. i) q^{92} +(4243.62 + 7350.17i) q^{93} +(13779.9 - 23867.5i) q^{94} +(-27845.2 + 48229.3i) q^{95} +(-105857. + 183349. i) q^{96} -15860.3 q^{97} +(86527.0 + 149869. i) q^{98} +(-90.2899 + 156.387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9} - 44 q^{10} - 1556 q^{11} + 708 q^{12} - 888 q^{13} + 1888 q^{14} + 1020 q^{15} - 4566 q^{16} - 437 q^{17} - 7302 q^{18} + 4358 q^{19} - 1204 q^{20} + 2354 q^{21} + 7958 q^{22} + 2824 q^{23} + 13824 q^{24} - 620 q^{25} - 17604 q^{26} - 32 q^{27} + 11414 q^{28} + 16954 q^{29} + 15994 q^{30} - 4548 q^{31} - 9148 q^{32} - 680 q^{33} - 4576 q^{34} + 11606 q^{35} + 5828 q^{36} + 12449 q^{37} - 84560 q^{38} + 13468 q^{39} - 23018 q^{40} + 32319 q^{41} + 26750 q^{42} - 49916 q^{43} + 12034 q^{44} + 81730 q^{45} + 5300 q^{46} - 57476 q^{47} - 14944 q^{48} - 52069 q^{49} - 19224 q^{50} - 78336 q^{51} + 1316 q^{52} + 65784 q^{53} + 72114 q^{54} - 24742 q^{55} - 81130 q^{56} - 3762 q^{57} - 73868 q^{58} - 49372 q^{59} - 288608 q^{60} + 137725 q^{61} + 118854 q^{62} - 81596 q^{63} + 427612 q^{64} + 35600 q^{65} + 289576 q^{66} + 64042 q^{67} - 60500 q^{68} - 141544 q^{69} + 5200 q^{70} + 136206 q^{71} - 294660 q^{72} - 270556 q^{73} + 133162 q^{74} - 240592 q^{75} + 209502 q^{76} + 152148 q^{77} + 152814 q^{78} - 61886 q^{79} + 264936 q^{80} - 104975 q^{81} - 28160 q^{82} + 202892 q^{83} - 197912 q^{84} + 576930 q^{85} + 154822 q^{86} - 312 q^{87} - 884284 q^{88} - 12065 q^{89} - 312764 q^{90} + 206252 q^{91} - 291924 q^{92} - 60752 q^{93} - 116814 q^{94} + 506 q^{95} + 81968 q^{96} + 132062 q^{97} + 249798 q^{98} + 289874 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.29373 + 9.16901i −0.935808 + 1.62087i −0.162622 + 0.986688i \(0.551995\pi\)
−0.773186 + 0.634179i \(0.781338\pi\)
\(3\) −7.75625 13.4342i −0.497564 0.861806i 0.502432 0.864617i \(-0.332439\pi\)
−0.999996 + 0.00281069i \(0.999105\pi\)
\(4\) −40.0472 69.3637i −1.25147 2.16762i
\(5\) 14.2918 + 24.7542i 0.255660 + 0.442816i 0.965075 0.261975i \(-0.0843739\pi\)
−0.709415 + 0.704791i \(0.751041\pi\)
\(6\) 164.238 1.86250
\(7\) 10.7449 + 18.6107i 0.0828812 + 0.143554i 0.904486 0.426503i \(-0.140254\pi\)
−0.821605 + 0.570057i \(0.806921\pi\)
\(8\) 509.197 2.81294
\(9\) 1.18106 2.04566i 0.00486034 0.00841836i
\(10\) −302.628 −0.956995
\(11\) −76.4480 −0.190495 −0.0952477 0.995454i \(-0.530364\pi\)
−0.0952477 + 0.995454i \(0.530364\pi\)
\(12\) −621.232 + 1076.01i −1.24538 + 2.15706i
\(13\) 377.201 + 653.332i 0.619035 + 1.07220i 0.989662 + 0.143418i \(0.0458092\pi\)
−0.370628 + 0.928782i \(0.620857\pi\)
\(14\) −227.522 −0.310244
\(15\) 221.702 383.999i 0.254414 0.440659i
\(16\) −1414.04 + 2449.19i −1.38090 + 2.39179i
\(17\) 1162.24 2013.06i 0.975381 1.68941i 0.296709 0.954968i \(-0.404111\pi\)
0.678672 0.734442i \(-0.262556\pi\)
\(18\) 12.5045 + 21.6584i 0.00909670 + 0.0157559i
\(19\) 974.165 + 1687.30i 0.619082 + 1.07228i 0.989654 + 0.143478i \(0.0458286\pi\)
−0.370571 + 0.928804i \(0.620838\pi\)
\(20\) 1144.69 1982.67i 0.639904 1.10835i
\(21\) 166.680 288.698i 0.0824774 0.142855i
\(22\) 404.695 700.952i 0.178267 0.308768i
\(23\) 3500.15 1.37964 0.689822 0.723979i \(-0.257689\pi\)
0.689822 + 0.723979i \(0.257689\pi\)
\(24\) −3949.46 6840.67i −1.39962 2.42421i
\(25\) 1153.99 1998.76i 0.369276 0.639605i
\(26\) −7987.21 −2.31719
\(27\) −3806.18 −1.00480
\(28\) 860.603 1490.61i 0.207447 0.359309i
\(29\) 5347.24 1.18069 0.590343 0.807152i \(-0.298992\pi\)
0.590343 + 0.807152i \(0.298992\pi\)
\(30\) 2347.26 + 4065.58i 0.476166 + 0.824744i
\(31\) −547.123 −0.102254 −0.0511270 0.998692i \(-0.516281\pi\)
−0.0511270 + 0.998692i \(0.516281\pi\)
\(32\) −6823.97 11819.5i −1.17805 2.04043i
\(33\) 592.950 + 1027.02i 0.0947836 + 0.164170i
\(34\) 12305.2 + 21313.2i 1.82554 + 3.16193i
\(35\) −307.127 + 531.960i −0.0423788 + 0.0734022i
\(36\) −189.193 −0.0243304
\(37\) −8095.55 1950.92i −0.972169 0.234280i
\(38\) −20627.9 −2.31737
\(39\) 5851.34 10134.8i 0.616018 1.06698i
\(40\) 7277.35 + 12604.7i 0.719157 + 1.24562i
\(41\) −3364.04 5826.70i −0.312537 0.541331i 0.666374 0.745618i \(-0.267846\pi\)
−0.978911 + 0.204287i \(0.934512\pi\)
\(42\) 1764.72 + 3056.58i 0.154366 + 0.267370i
\(43\) 4181.80 0.344899 0.172450 0.985018i \(-0.444832\pi\)
0.172450 + 0.985018i \(0.444832\pi\)
\(44\) 3061.53 + 5302.72i 0.238400 + 0.412921i
\(45\) 67.5182 0.00497038
\(46\) −18528.8 + 32092.9i −1.29108 + 2.23622i
\(47\) −2603.06 −0.171885 −0.0859427 0.996300i \(-0.527390\pi\)
−0.0859427 + 0.996300i \(0.527390\pi\)
\(48\) 43870.7 2.74835
\(49\) 8172.60 14155.4i 0.486261 0.842229i
\(50\) 12217.8 + 21161.8i 0.691143 + 1.19709i
\(51\) −36058.6 −1.94126
\(52\) 30211.7 52328.2i 1.54941 2.68366i
\(53\) 10068.1 17438.5i 0.492334 0.852747i −0.507627 0.861577i \(-0.669477\pi\)
0.999961 + 0.00882980i \(0.00281065\pi\)
\(54\) 20148.9 34898.9i 0.940301 1.62865i
\(55\) −1092.58 1892.41i −0.0487020 0.0843544i
\(56\) 5471.25 + 9476.49i 0.233140 + 0.403810i
\(57\) 15111.7 26174.3i 0.616066 1.06706i
\(58\) −28306.8 + 49028.9i −1.10490 + 1.91374i
\(59\) −22085.0 + 38252.3i −0.825976 + 1.43063i 0.0751957 + 0.997169i \(0.476042\pi\)
−0.901171 + 0.433463i \(0.857291\pi\)
\(60\) −35514.2 −1.27357
\(61\) 12156.5 + 21055.7i 0.418296 + 0.724510i 0.995768 0.0919005i \(-0.0292942\pi\)
−0.577472 + 0.816410i \(0.695961\pi\)
\(62\) 2896.32 5016.58i 0.0956902 0.165740i
\(63\) 50.7615 0.00161132
\(64\) 53998.2 1.64790
\(65\) −10781.8 + 18674.6i −0.316525 + 0.548237i
\(66\) −12555.7 −0.354797
\(67\) 16756.9 + 29023.8i 0.456045 + 0.789893i 0.998748 0.0500322i \(-0.0159324\pi\)
−0.542703 + 0.839925i \(0.682599\pi\)
\(68\) −186178. −4.88266
\(69\) −27148.0 47021.8i −0.686461 1.18898i
\(70\) −3251.70 5632.11i −0.0793168 0.137381i
\(71\) 19911.2 + 34487.2i 0.468761 + 0.811917i 0.999362 0.0357040i \(-0.0113674\pi\)
−0.530602 + 0.847621i \(0.678034\pi\)
\(72\) 601.394 1041.64i 0.0136719 0.0236804i
\(73\) −10784.0 −0.236850 −0.118425 0.992963i \(-0.537785\pi\)
−0.118425 + 0.992963i \(0.537785\pi\)
\(74\) 60743.6 63900.5i 1.28950 1.35652i
\(75\) −35802.5 −0.734954
\(76\) 78025.1 135143.i 1.54953 2.68387i
\(77\) −821.423 1422.75i −0.0157885 0.0273464i
\(78\) 61950.8 + 107302.i 1.15295 + 1.99697i
\(79\) 8215.11 + 14229.0i 0.148097 + 0.256511i 0.930524 0.366231i \(-0.119352\pi\)
−0.782427 + 0.622742i \(0.786019\pi\)
\(80\) −80837.0 −1.41216
\(81\) 29234.7 + 50636.0i 0.495092 + 0.857525i
\(82\) 71233.4 1.16990
\(83\) 56127.2 97215.2i 0.894289 1.54895i 0.0596080 0.998222i \(-0.481015\pi\)
0.834681 0.550733i \(-0.185652\pi\)
\(84\) −26700.2 −0.412873
\(85\) 66442.2 0.997463
\(86\) −22137.3 + 38343.0i −0.322760 + 0.559036i
\(87\) −41474.5 71836.0i −0.587467 1.01752i
\(88\) −38927.1 −0.535852
\(89\) −581.269 + 1006.79i −0.00777862 + 0.0134730i −0.869889 0.493248i \(-0.835809\pi\)
0.862110 + 0.506721i \(0.169143\pi\)
\(90\) −357.423 + 619.075i −0.00465132 + 0.00805633i
\(91\) −8105.96 + 14039.9i −0.102613 + 0.177730i
\(92\) −140171. 242783.i −1.72659 2.99054i
\(93\) 4243.62 + 7350.17i 0.0508779 + 0.0881232i
\(94\) 13779.9 23867.5i 0.160852 0.278603i
\(95\) −27845.2 + 48229.3i −0.316549 + 0.548279i
\(96\) −105857. + 183349.i −1.17231 + 2.03049i
\(97\) −15860.3 −0.171152 −0.0855758 0.996332i \(-0.527273\pi\)
−0.0855758 + 0.996332i \(0.527273\pi\)
\(98\) 86527.0 + 149869.i 0.910095 + 1.57633i
\(99\) −90.2899 + 156.387i −0.000925873 + 0.00160366i
\(100\) −184856. −1.84856
\(101\) 172602. 1.68362 0.841809 0.539776i \(-0.181491\pi\)
0.841809 + 0.539776i \(0.181491\pi\)
\(102\) 190884. 330621.i 1.81664 3.14652i
\(103\) −34437.4 −0.319843 −0.159922 0.987130i \(-0.551124\pi\)
−0.159922 + 0.987130i \(0.551124\pi\)
\(104\) 192070. + 332675.i 1.74131 + 3.01603i
\(105\) 9528.63 0.0843446
\(106\) 106596. + 184630.i 0.921460 + 1.59602i
\(107\) −88604.9 153468.i −0.748167 1.29586i −0.948701 0.316176i \(-0.897601\pi\)
0.200534 0.979687i \(-0.435732\pi\)
\(108\) 152427. + 264011.i 1.25748 + 2.17802i
\(109\) −53253.4 + 92237.6i −0.429320 + 0.743604i −0.996813 0.0797741i \(-0.974580\pi\)
0.567493 + 0.823378i \(0.307913\pi\)
\(110\) 23135.3 0.182303
\(111\) 36582.0 + 123889.i 0.281813 + 0.954390i
\(112\) −60774.8 −0.457803
\(113\) −16286.5 + 28209.0i −0.119986 + 0.207822i −0.919762 0.392477i \(-0.871618\pi\)
0.799776 + 0.600299i \(0.204952\pi\)
\(114\) 159995. + 277119.i 1.15304 + 1.99712i
\(115\) 50023.5 + 86643.2i 0.352719 + 0.610928i
\(116\) −214142. 370904.i −1.47760 2.55928i
\(117\) 1782.00 0.0120349
\(118\) −233824. 404995.i −1.54591 2.67759i
\(119\) 49952.5 0.323363
\(120\) 112890. 195531.i 0.715653 1.23955i
\(121\) −155207. −0.963712
\(122\) −257413. −1.56578
\(123\) −52184.8 + 90386.7i −0.311015 + 0.538693i
\(124\) 21910.7 + 37950.5i 0.127968 + 0.221648i
\(125\) 155294. 0.888956
\(126\) −268.718 + 465.433i −0.00150789 + 0.00261174i
\(127\) −104434. + 180885.i −0.574558 + 0.995163i 0.421532 + 0.906814i \(0.361493\pi\)
−0.996090 + 0.0883495i \(0.971841\pi\)
\(128\) −67485.3 + 116888.i −0.364069 + 0.630587i
\(129\) −32435.1 56179.3i −0.171609 0.297236i
\(130\) −114152. 197717.i −0.592413 1.02609i
\(131\) −87591.1 + 151712.i −0.445946 + 0.772400i −0.998118 0.0613298i \(-0.980466\pi\)
0.552172 + 0.833730i \(0.313799\pi\)
\(132\) 47491.9 82258.5i 0.237238 0.410909i
\(133\) −20934.5 + 36259.7i −0.102621 + 0.177744i
\(134\) −354827. −1.70708
\(135\) −54397.3 94218.9i −0.256887 0.444942i
\(136\) 591810. 1.02505e6i 2.74369 4.75221i
\(137\) −53015.1 −0.241323 −0.120661 0.992694i \(-0.538502\pi\)
−0.120661 + 0.992694i \(0.538502\pi\)
\(138\) 574857. 2.56958
\(139\) 104217. 180509.i 0.457510 0.792431i −0.541319 0.840818i \(-0.682075\pi\)
0.998829 + 0.0483868i \(0.0154080\pi\)
\(140\) 49198.3 0.212144
\(141\) 20190.0 + 34970.1i 0.0855240 + 0.148132i
\(142\) −421618. −1.75468
\(143\) −28836.3 49945.9i −0.117923 0.204249i
\(144\) 3340.15 + 5785.31i 0.0134233 + 0.0232498i
\(145\) 76421.8 + 132366.i 0.301854 + 0.522827i
\(146\) 57087.7 98878.7i 0.221646 0.383902i
\(147\) −253555. −0.967785
\(148\) 188881. + 639666.i 0.708816 + 2.40049i
\(149\) 265717. 0.980515 0.490257 0.871578i \(-0.336903\pi\)
0.490257 + 0.871578i \(0.336903\pi\)
\(150\) 189529. 328273.i 0.687776 1.19126i
\(151\) −152436. 264027.i −0.544058 0.942336i −0.998666 0.0516441i \(-0.983554\pi\)
0.454608 0.890692i \(-0.349779\pi\)
\(152\) 496042. + 859169.i 1.74144 + 3.01627i
\(153\) −2745.36 4755.11i −0.00948137 0.0164222i
\(154\) 17393.6 0.0590999
\(155\) −7819.38 13543.6i −0.0261423 0.0452797i
\(156\) −937318. −3.08372
\(157\) 55274.5 95738.3i 0.178968 0.309982i −0.762559 0.646918i \(-0.776057\pi\)
0.941527 + 0.336936i \(0.109391\pi\)
\(158\) −173954. −0.554361
\(159\) −312364. −0.979870
\(160\) 195054. 337843.i 0.602358 1.04331i
\(161\) 37608.6 + 65140.0i 0.114346 + 0.198054i
\(162\) −619043. −1.85325
\(163\) −55011.9 + 95283.4i −0.162176 + 0.280898i −0.935649 0.352932i \(-0.885185\pi\)
0.773473 + 0.633830i \(0.218518\pi\)
\(164\) −269441. + 466685.i −0.782265 + 1.35492i
\(165\) −16948.7 + 29356.0i −0.0484647 + 0.0839434i
\(166\) 594245. + 1.02926e6i 1.67377 + 2.89905i
\(167\) −170680. 295627.i −0.473579 0.820263i 0.525963 0.850507i \(-0.323705\pi\)
−0.999543 + 0.0302439i \(0.990372\pi\)
\(168\) 84872.8 147004.i 0.232004 0.401843i
\(169\) −98915.2 + 171326.i −0.266407 + 0.461431i
\(170\) −351727. + 609210.i −0.933435 + 1.61676i
\(171\) 4602.20 0.0120358
\(172\) −167469. 290065.i −0.431632 0.747609i
\(173\) −132933. + 230247.i −0.337690 + 0.584895i −0.983998 0.178181i \(-0.942979\pi\)
0.646308 + 0.763076i \(0.276312\pi\)
\(174\) 878220. 2.19903
\(175\) 49597.8 0.122424
\(176\) 108101. 187236.i 0.263055 0.455625i
\(177\) 685187. 1.64390
\(178\) −6154.17 10659.3i −0.0145586 0.0252162i
\(179\) −276376. −0.644715 −0.322358 0.946618i \(-0.604475\pi\)
−0.322358 + 0.946618i \(0.604475\pi\)
\(180\) −2703.91 4683.32i −0.00622030 0.0107739i
\(181\) −89464.1 154956.i −0.202979 0.351571i 0.746508 0.665377i \(-0.231729\pi\)
−0.949487 + 0.313806i \(0.898396\pi\)
\(182\) −85821.5 148647.i −0.192051 0.332643i
\(183\) 188578. 326626.i 0.416258 0.720980i
\(184\) 1.78226e6 3.88086
\(185\) −67406.8 228281.i −0.144802 0.490388i
\(186\) −89858.4 −0.190448
\(187\) −88851.1 + 153895.i −0.185806 + 0.321825i
\(188\) 104245. + 180558.i 0.215110 + 0.372582i
\(189\) −40896.9 70835.5i −0.0832791 0.144244i
\(190\) −294810. 510626.i −0.592458 1.02617i
\(191\) 720024. 1.42812 0.714058 0.700086i \(-0.246855\pi\)
0.714058 + 0.700086i \(0.246855\pi\)
\(192\) −418824. 725425.i −0.819933 1.42017i
\(193\) 119592. 0.231104 0.115552 0.993301i \(-0.463136\pi\)
0.115552 + 0.993301i \(0.463136\pi\)
\(194\) 83960.0 145423.i 0.160165 0.277414i
\(195\) 334505. 0.629965
\(196\) −1.30916e6 −2.43417
\(197\) 313235. 542538.i 0.575048 0.996013i −0.420988 0.907066i \(-0.638317\pi\)
0.996036 0.0889465i \(-0.0283500\pi\)
\(198\) −955.941 1655.74i −0.00173288 0.00300143i
\(199\) −421571. −0.754637 −0.377319 0.926083i \(-0.623154\pi\)
−0.377319 + 0.926083i \(0.623154\pi\)
\(200\) 587607. 1.01776e6i 1.03875 1.79917i
\(201\) 259942. 450233.i 0.453823 0.786044i
\(202\) −913711. + 1.58259e6i −1.57554 + 2.72892i
\(203\) 57455.4 + 99515.6i 0.0978567 + 0.169493i
\(204\) 1.44404e6 + 2.50116e6i 2.42943 + 4.20790i
\(205\) 96156.7 166548.i 0.159807 0.276793i
\(206\) 182302. 315757.i 0.299312 0.518423i
\(207\) 4133.90 7160.12i 0.00670554 0.0116143i
\(208\) −2.13351e6 −3.41930
\(209\) −74472.9 128991.i −0.117932 0.204265i
\(210\) −50442.0 + 87368.1i −0.0789304 + 0.136711i
\(211\) −725830. −1.12235 −0.561176 0.827697i \(-0.689651\pi\)
−0.561176 + 0.827697i \(0.689651\pi\)
\(212\) −1.61280e6 −2.46457
\(213\) 308872. 534983.i 0.466477 0.807961i
\(214\) 1.87620e6 2.80056
\(215\) 59765.6 + 103517.i 0.0881769 + 0.152727i
\(216\) −1.93810e6 −2.82645
\(217\) −5878.76 10182.3i −0.00847494 0.0146790i
\(218\) −563818. 976562.i −0.803523 1.39174i
\(219\) 83643.5 + 144875.i 0.117848 + 0.204119i
\(220\) −87509.6 + 151571.i −0.121899 + 0.211135i
\(221\) 1.75360e6 2.41518
\(222\) −1.32960e6 320415.i −1.81066 0.436345i
\(223\) 253141. 0.340879 0.170440 0.985368i \(-0.445481\pi\)
0.170440 + 0.985368i \(0.445481\pi\)
\(224\) 146645. 253997.i 0.195275 0.338227i
\(225\) −2725.87 4721.34i −0.00358962 0.00621740i
\(226\) −172432. 298661.i −0.224568 0.388963i
\(227\) −49217.5 85247.2i −0.0633950 0.109803i 0.832586 0.553896i \(-0.186859\pi\)
−0.895981 + 0.444093i \(0.853526\pi\)
\(228\) −2.42073e6 −3.08396
\(229\) 675529. + 1.17005e6i 0.851246 + 1.47440i 0.880084 + 0.474818i \(0.157486\pi\)
−0.0288381 + 0.999584i \(0.509181\pi\)
\(230\) −1.05924e6 −1.32031
\(231\) −12742.3 + 22070.4i −0.0157116 + 0.0272132i
\(232\) 2.72280e6 3.32120
\(233\) −1.07960e6 −1.30279 −0.651395 0.758738i \(-0.725816\pi\)
−0.651395 + 0.758738i \(0.725816\pi\)
\(234\) −9433.40 + 16339.1i −0.0112623 + 0.0195069i
\(235\) −37202.4 64436.5i −0.0439442 0.0761136i
\(236\) 3.53777e6 4.13475
\(237\) 127437. 220727.i 0.147375 0.255262i
\(238\) −264435. + 458015.i −0.302606 + 0.524128i
\(239\) 179456. 310827.i 0.203218 0.351984i −0.746345 0.665559i \(-0.768193\pi\)
0.949564 + 0.313575i \(0.101527\pi\)
\(240\) 626992. + 1.08598e6i 0.702642 + 1.21701i
\(241\) 700831. + 1.21387e6i 0.777268 + 1.34627i 0.933511 + 0.358549i \(0.116728\pi\)
−0.156243 + 0.987719i \(0.549938\pi\)
\(242\) 821622. 1.42309e6i 0.901849 1.56205i
\(243\) −8947.41 + 15497.4i −0.00972034 + 0.0168361i
\(244\) 973666. 1.68644e6i 1.04697 1.81341i
\(245\) 467205. 0.497270
\(246\) −552504. 956965.i −0.582100 1.00823i
\(247\) −734912. + 1.27291e6i −0.766466 + 1.32756i
\(248\) −278593. −0.287635
\(249\) −1.74135e6 −1.77986
\(250\) −822086. + 1.42389e6i −0.831893 + 1.44088i
\(251\) −1.42358e6 −1.42625 −0.713127 0.701035i \(-0.752722\pi\)
−0.713127 + 0.701035i \(0.752722\pi\)
\(252\) −2032.85 3521.01i −0.00201653 0.00349273i
\(253\) −267579. −0.262816
\(254\) −1.10569e6 1.91512e6i −1.07535 1.86256i
\(255\) −515343. 892600.i −0.496302 0.859620i
\(256\) 149474. + 258897.i 0.142550 + 0.246903i
\(257\) 576067. 997777.i 0.544052 0.942325i −0.454614 0.890688i \(-0.650223\pi\)
0.998666 0.0516367i \(-0.0164438\pi\)
\(258\) 686811. 0.642374
\(259\) −50677.7 171626.i −0.0469426 0.158977i
\(260\) 1.72712e6 1.58449
\(261\) 6315.43 10938.6i 0.00573854 0.00993945i
\(262\) −927368. 1.60625e6i −0.834639 1.44564i
\(263\) 304165. + 526828.i 0.271156 + 0.469656i 0.969158 0.246440i \(-0.0792607\pi\)
−0.698002 + 0.716096i \(0.745927\pi\)
\(264\) 301928. + 522955.i 0.266621 + 0.461801i
\(265\) 575568. 0.503480
\(266\) −221644. 383898.i −0.192066 0.332668i
\(267\) 18033.9 0.0154814
\(268\) 1.34214e6 2.32465e6i 1.14146 1.97706i
\(269\) −1.07935e6 −0.909452 −0.454726 0.890631i \(-0.650263\pi\)
−0.454726 + 0.890631i \(0.650263\pi\)
\(270\) 1.15186e6 0.961589
\(271\) −557279. + 965236.i −0.460945 + 0.798381i −0.999008 0.0445239i \(-0.985823\pi\)
0.538063 + 0.842905i \(0.319156\pi\)
\(272\) 3.28692e6 + 5.69311e6i 2.69381 + 4.66581i
\(273\) 251487. 0.204225
\(274\) 280648. 486096.i 0.225832 0.391152i
\(275\) −88220.0 + 152802.i −0.0703454 + 0.121842i
\(276\) −2.17440e6 + 3.76618e6i −1.71818 + 2.97597i
\(277\) 347185. + 601342.i 0.271870 + 0.470893i 0.969341 0.245721i \(-0.0790246\pi\)
−0.697471 + 0.716613i \(0.745691\pi\)
\(278\) 1.10339e6 + 1.91113e6i 0.856284 + 1.48313i
\(279\) −646.187 + 1119.23i −0.000496990 + 0.000860812i
\(280\) −156388. + 270873.i −0.119209 + 0.206476i
\(281\) −1.05421e6 + 1.82594e6i −0.796452 + 1.37949i 0.125461 + 0.992098i \(0.459959\pi\)
−0.921913 + 0.387396i \(0.873374\pi\)
\(282\) −427521. −0.320136
\(283\) 90560.8 + 156856.i 0.0672163 + 0.116422i 0.897675 0.440658i \(-0.145255\pi\)
−0.830459 + 0.557080i \(0.811922\pi\)
\(284\) 1.59477e6 2.76223e6i 1.17328 2.03219i
\(285\) 863897. 0.630014
\(286\) 610606. 0.441414
\(287\) 72292.4 125214.i 0.0518069 0.0897322i
\(288\) −32238.2 −0.0229028
\(289\) −1.99168e6 3.44970e6i −1.40274 2.42961i
\(290\) −1.61823e6 −1.12991
\(291\) 123016. + 213070.i 0.0851589 + 0.147500i
\(292\) 431869. + 748019.i 0.296412 + 0.513400i
\(293\) −597994. 1.03576e6i −0.406938 0.704837i 0.587607 0.809146i \(-0.300070\pi\)
−0.994545 + 0.104309i \(0.966737\pi\)
\(294\) 1.34225e6 2.32485e6i 0.905661 1.56865i
\(295\) −1.26254e6 −0.844676
\(296\) −4.12223e6 993402.i −2.73466 0.659015i
\(297\) 290975. 0.191410
\(298\) −1.40664e6 + 2.43637e6i −0.917574 + 1.58928i
\(299\) 1.32026e6 + 2.28676e6i 0.854047 + 1.47925i
\(300\) 1.43379e6 + 2.48339e6i 0.919775 + 1.59310i
\(301\) 44932.9 + 77826.0i 0.0285857 + 0.0495118i
\(302\) 3.22782e6 2.03654
\(303\) −1.33875e6 2.31878e6i −0.837707 1.45095i
\(304\) −5.51004e6 −3.41956
\(305\) −347477. + 601848.i −0.213883 + 0.370456i
\(306\) 58132.9 0.0354910
\(307\) −2.06735e6 −1.25190 −0.625948 0.779865i \(-0.715288\pi\)
−0.625948 + 0.779865i \(0.715288\pi\)
\(308\) −65791.4 + 113954.i −0.0395177 + 0.0684467i
\(309\) 267105. + 462639.i 0.159142 + 0.275643i
\(310\) 165575. 0.0978566
\(311\) −1.25468e6 + 2.17316e6i −0.735582 + 1.27407i 0.218886 + 0.975751i \(0.429758\pi\)
−0.954468 + 0.298315i \(0.903575\pi\)
\(312\) 2.97948e6 5.16062e6i 1.73282 3.00134i
\(313\) 955598. 1.65514e6i 0.551334 0.954938i −0.446845 0.894611i \(-0.647452\pi\)
0.998179 0.0603265i \(-0.0192142\pi\)
\(314\) 585217. + 1.01363e6i 0.334960 + 0.580168i
\(315\) 725.474 + 1256.56i 0.000411951 + 0.000713520i
\(316\) 657984. 1.13966e6i 0.370679 0.642035i
\(317\) 239594. 414989.i 0.133915 0.231947i −0.791268 0.611470i \(-0.790579\pi\)
0.925182 + 0.379523i \(0.123912\pi\)
\(318\) 1.65357e6 2.86407e6i 0.916970 1.58824i
\(319\) −408786. −0.224915
\(320\) 771734. + 1.33668e6i 0.421301 + 0.729715i
\(321\) −1.37448e6 + 2.38068e6i −0.744521 + 1.28955i
\(322\) −796359. −0.428025
\(323\) 4.52886e6 2.41536
\(324\) 2.34153e6 4.05566e6i 1.23919 2.14634i
\(325\) 1.74114e6 0.914378
\(326\) −582436. 1.00881e6i −0.303532 0.525733i
\(327\) 1.65219e6 0.854457
\(328\) −1.71296e6 2.96694e6i −0.879150 1.52273i
\(329\) −27969.5 48444.6i −0.0142461 0.0246749i
\(330\) −179443. 310805.i −0.0907074 0.157110i
\(331\) 495787. 858727.i 0.248728 0.430810i −0.714445 0.699691i \(-0.753321\pi\)
0.963173 + 0.268882i \(0.0866541\pi\)
\(332\) −8.99094e6 −4.47672
\(333\) −13552.3 + 14256.6i −0.00669733 + 0.00704539i
\(334\) 3.61415e6 1.77272
\(335\) −478974. + 829608.i −0.233185 + 0.403888i
\(336\) 471384. + 816462.i 0.227786 + 0.394537i
\(337\) 978872. + 1.69546e6i 0.469517 + 0.813227i 0.999393 0.0348482i \(-0.0110948\pi\)
−0.529876 + 0.848075i \(0.677761\pi\)
\(338\) −1.04726e6 1.81391e6i −0.498613 0.863622i
\(339\) 505288. 0.238803
\(340\) −2.66082e6 4.60868e6i −1.24830 2.16212i
\(341\) 41826.4 0.0194789
\(342\) −24362.8 + 42197.6i −0.0112632 + 0.0195085i
\(343\) 712432. 0.326970
\(344\) 2.12936e6 0.970182
\(345\) 775990. 1.34405e6i 0.351001 0.607952i
\(346\) −1.40742e6 2.43773e6i −0.632025 1.09470i
\(347\) 2.55966e6 1.14119 0.570596 0.821231i \(-0.306712\pi\)
0.570596 + 0.821231i \(0.306712\pi\)
\(348\) −3.32188e6 + 5.75366e6i −1.47040 + 2.54681i
\(349\) −1.42203e6 + 2.46302e6i −0.624948 + 1.08244i 0.363602 + 0.931554i \(0.381547\pi\)
−0.988551 + 0.150888i \(0.951787\pi\)
\(350\) −262557. + 454762.i −0.114565 + 0.198433i
\(351\) −1.43570e6 2.48670e6i −0.622007 1.07735i
\(352\) 521678. + 903574.i 0.224412 + 0.388693i
\(353\) −184527. + 319610.i −0.0788175 + 0.136516i −0.902740 0.430187i \(-0.858448\pi\)
0.823923 + 0.566702i \(0.191781\pi\)
\(354\) −3.62720e6 + 6.28249e6i −1.53838 + 2.66455i
\(355\) −569134. + 985769.i −0.239687 + 0.415149i
\(356\) 93112.8 0.0389390
\(357\) −387445. 671074.i −0.160894 0.278676i
\(358\) 1.46306e6 2.53410e6i 0.603330 1.04500i
\(359\) −413282. −0.169243 −0.0846214 0.996413i \(-0.526968\pi\)
−0.0846214 + 0.996413i \(0.526968\pi\)
\(360\) 34380.1 0.0139814
\(361\) −659944. + 1.14306e6i −0.266525 + 0.461636i
\(362\) 1.89439e6 0.759799
\(363\) 1.20382e6 + 2.08508e6i 0.479508 + 0.830532i
\(364\) 1.29848e6 0.513668
\(365\) −154123. 266949.i −0.0605530 0.104881i
\(366\) 1.99656e6 + 3.45814e6i 0.779075 + 1.34940i
\(367\) 1.41431e6 + 2.44965e6i 0.548124 + 0.949378i 0.998403 + 0.0564906i \(0.0179911\pi\)
−0.450279 + 0.892888i \(0.648676\pi\)
\(368\) −4.94936e6 + 8.57254e6i −1.90515 + 3.29982i
\(369\) −15892.6 −0.00607616
\(370\) 2.44994e6 + 590403.i 0.930361 + 0.224205i
\(371\) 432723. 0.163221
\(372\) 339890. 588707.i 0.127345 0.220568i
\(373\) −1.76435e6 3.05595e6i −0.656619 1.13730i −0.981485 0.191537i \(-0.938653\pi\)
0.324866 0.945760i \(-0.394681\pi\)
\(374\) −940707. 1.62935e6i −0.347757 0.602332i
\(375\) −1.20450e6 2.08626e6i −0.442313 0.766108i
\(376\) −1.32547e6 −0.483504
\(377\) 2.01699e6 + 3.49352e6i 0.730886 + 1.26593i
\(378\) 865989. 0.311733
\(379\) 2.34548e6 4.06248e6i 0.838751 1.45276i −0.0521889 0.998637i \(-0.516620\pi\)
0.890940 0.454122i \(-0.150047\pi\)
\(380\) 4.46048e6 1.58461
\(381\) 3.24007e6 1.14352
\(382\) −3.81161e6 + 6.60191e6i −1.33644 + 2.31479i
\(383\) −904670. 1.56693e6i −0.315133 0.545826i 0.664333 0.747437i \(-0.268716\pi\)
−0.979466 + 0.201611i \(0.935382\pi\)
\(384\) 2.09373e6 0.724591
\(385\) 23479.3 40667.3i 0.00807296 0.0139828i
\(386\) −633086. + 1.09654e6i −0.216269 + 0.374589i
\(387\) 4938.97 8554.55i 0.00167633 0.00290349i
\(388\) 635159. + 1.10013e6i 0.214192 + 0.370991i
\(389\) −1.16201e6 2.01266e6i −0.389347 0.674368i 0.603015 0.797730i \(-0.293966\pi\)
−0.992362 + 0.123362i \(0.960632\pi\)
\(390\) −1.77078e6 + 3.06708e6i −0.589526 + 1.02109i
\(391\) 4.06802e6 7.04602e6i 1.34568 2.33078i
\(392\) 4.16146e6 7.20786e6i 1.36783 2.36914i
\(393\) 2.71752e6 0.887546
\(394\) 3.31636e6 + 5.74410e6i 1.07627 + 1.86415i
\(395\) −234818. + 406717.i −0.0757249 + 0.131159i
\(396\) 14463.4 0.00463482
\(397\) −2.06164e6 −0.656503 −0.328251 0.944590i \(-0.606459\pi\)
−0.328251 + 0.944590i \(0.606459\pi\)
\(398\) 2.23168e6 3.86539e6i 0.706196 1.22317i
\(399\) 649494. 0.204241
\(400\) 3.26357e6 + 5.65268e6i 1.01987 + 1.76646i
\(401\) −4.19444e6 −1.30261 −0.651303 0.758818i \(-0.725777\pi\)
−0.651303 + 0.758818i \(0.725777\pi\)
\(402\) 2.75213e6 + 4.76682e6i 0.849382 + 1.47117i
\(403\) −206375. 357453.i −0.0632988 0.109637i
\(404\) −6.91224e6 1.19723e7i −2.10700 3.64944i
\(405\) −835635. + 1.44736e6i −0.253151 + 0.438470i
\(406\) −1.21661e6 −0.366300
\(407\) 618888. + 149144.i 0.185194 + 0.0446292i
\(408\) −1.83609e7 −5.46065
\(409\) 591244. 1.02407e6i 0.174767 0.302705i −0.765314 0.643657i \(-0.777416\pi\)
0.940081 + 0.340952i \(0.110750\pi\)
\(410\) 1.01806e6 + 1.76332e6i 0.299097 + 0.518051i
\(411\) 411199. + 712217.i 0.120074 + 0.207973i
\(412\) 1.37912e6 + 2.38870e6i 0.400275 + 0.693297i
\(413\) −949201. −0.273831
\(414\) 43767.5 + 75807.5i 0.0125502 + 0.0217376i
\(415\) 3.20864e6 0.914536
\(416\) 5.14802e6 8.91663e6i 1.45850 2.52620i
\(417\) −3.23333e6 −0.910562
\(418\) 1.57696e6 0.441448
\(419\) −959408. + 1.66174e6i −0.266974 + 0.462412i −0.968079 0.250646i \(-0.919357\pi\)
0.701105 + 0.713058i \(0.252690\pi\)
\(420\) −381595. 660942.i −0.105555 0.182827i
\(421\) −6.70176e6 −1.84282 −0.921412 0.388588i \(-0.872963\pi\)
−0.921412 + 0.388588i \(0.872963\pi\)
\(422\) 3.84235e6 6.65515e6i 1.05031 1.81918i
\(423\) −3074.38 + 5324.98i −0.000835422 + 0.00144699i
\(424\) 5.12667e6 8.87965e6i 1.38491 2.39873i
\(425\) −2.68243e6 4.64610e6i −0.720370 1.24772i
\(426\) 3.27017e6 + 5.66411e6i 0.873065 + 1.51219i
\(427\) −261240. + 452480.i −0.0693377 + 0.120096i
\(428\) −7.09675e6 + 1.22919e7i −1.87262 + 3.24348i
\(429\) −447323. + 774786.i −0.117349 + 0.203254i
\(430\) −1.26553e6 −0.330067
\(431\) −940654. 1.62926e6i −0.243914 0.422472i 0.717912 0.696134i \(-0.245098\pi\)
−0.961826 + 0.273663i \(0.911765\pi\)
\(432\) 5.38210e6 9.32207e6i 1.38753 2.40327i
\(433\) −4.92491e6 −1.26235 −0.631173 0.775642i \(-0.717426\pi\)
−0.631173 + 0.775642i \(0.717426\pi\)
\(434\) 124482. 0.0317237
\(435\) 1.18549e6 2.05334e6i 0.300384 0.520280i
\(436\) 8.53059e6 2.14913
\(437\) 3.40972e6 + 5.90581e6i 0.854112 + 1.47937i
\(438\) −1.77115e6 −0.441132
\(439\) −282238. 488850.i −0.0698962 0.121064i 0.828959 0.559309i \(-0.188933\pi\)
−0.898855 + 0.438245i \(0.855600\pi\)
\(440\) −556339. 963608.i −0.136996 0.237284i
\(441\) −19304.7 33436.7i −0.00472680 0.00818705i
\(442\) −9.28307e6 + 1.60788e7i −2.26014 + 3.91468i
\(443\) 5.64681e6 1.36708 0.683540 0.729913i \(-0.260439\pi\)
0.683540 + 0.729913i \(0.260439\pi\)
\(444\) 7.12841e6 7.49888e6i 1.71607 1.80526i
\(445\) −33229.6 −0.00795473
\(446\) −1.34006e6 + 2.32106e6i −0.318998 + 0.552520i
\(447\) −2.06097e6 3.56971e6i −0.487869 0.845014i
\(448\) 580204. + 1.00494e6i 0.136580 + 0.236563i
\(449\) 937316. + 1.62348e6i 0.219417 + 0.380041i 0.954630 0.297795i \(-0.0962512\pi\)
−0.735213 + 0.677836i \(0.762918\pi\)
\(450\) 57720.0 0.0134368
\(451\) 257174. + 445439.i 0.0595369 + 0.103121i
\(452\) 2.60891e6 0.600637
\(453\) −2.36466e6 + 4.09572e6i −0.541407 + 0.937745i
\(454\) 1.04218e6 0.237302
\(455\) −463396. −0.104936
\(456\) 7.69485e6 1.33279e7i 1.73296 3.00157i
\(457\) 149098. + 258245.i 0.0333950 + 0.0578418i 0.882240 0.470800i \(-0.156035\pi\)
−0.848845 + 0.528642i \(0.822701\pi\)
\(458\) −1.43043e7 −3.18641
\(459\) −4.42370e6 + 7.66208e6i −0.980064 + 1.69752i
\(460\) 4.00660e6 6.93963e6i 0.882839 1.52912i
\(461\) 1.01828e6 1.76371e6i 0.223158 0.386522i −0.732607 0.680652i \(-0.761697\pi\)
0.955765 + 0.294130i \(0.0950299\pi\)
\(462\) −134909. 233669.i −0.0294060 0.0509327i
\(463\) −2.64283e6 4.57751e6i −0.572950 0.992378i −0.996261 0.0863937i \(-0.972466\pi\)
0.423311 0.905984i \(-0.360868\pi\)
\(464\) −7.56122e6 + 1.30964e7i −1.63041 + 2.82395i
\(465\) −121298. + 210095.i −0.0260149 + 0.0450591i
\(466\) 5.71513e6 9.89890e6i 1.21916 2.11165i
\(467\) 2.55705e6 0.542558 0.271279 0.962501i \(-0.412553\pi\)
0.271279 + 0.962501i \(0.412553\pi\)
\(468\) −71363.9 123606.i −0.0150613 0.0260870i
\(469\) −360102. + 623715.i −0.0755950 + 0.130934i
\(470\) 787759. 0.164493
\(471\) −1.71489e6 −0.356193
\(472\) −1.12456e7 + 1.94780e7i −2.32342 + 4.02428i
\(473\) −319690. −0.0657017
\(474\) 1.34923e6 + 2.33694e6i 0.275830 + 0.477752i
\(475\) 4.49669e6 0.914449
\(476\) −2.00046e6 3.46489e6i −0.404680 0.700927i
\(477\) −23782.2 41192.0i −0.00478582 0.00828929i
\(478\) 1.89998e6 + 3.29086e6i 0.380347 + 0.658780i
\(479\) −1.28242e6 + 2.22122e6i −0.255383 + 0.442336i −0.964999 0.262252i \(-0.915535\pi\)
0.709617 + 0.704588i \(0.248868\pi\)
\(480\) −6.05155e6 −1.19885
\(481\) −1.77905e6 6.02497e6i −0.350612 1.18739i
\(482\) −1.48400e7 −2.90949
\(483\) 583404. 1.01049e6i 0.113789 0.197089i
\(484\) 6.21559e6 + 1.07657e7i 1.20606 + 2.08896i
\(485\) −226672. 392608.i −0.0437566 0.0757887i
\(486\) −94730.3 164078.i −0.0181928 0.0315108i
\(487\) 3.95740e6 0.756115 0.378058 0.925782i \(-0.376592\pi\)
0.378058 + 0.925782i \(0.376592\pi\)
\(488\) 6.19005e6 + 1.07215e7i 1.17664 + 2.03800i
\(489\) 1.70674e6 0.322772
\(490\) −2.47326e6 + 4.28381e6i −0.465350 + 0.806009i
\(491\) −320564. −0.0600083 −0.0300042 0.999550i \(-0.509552\pi\)
−0.0300042 + 0.999550i \(0.509552\pi\)
\(492\) 8.35941e6 1.55691
\(493\) 6.21479e6 1.07643e7i 1.15162 1.99466i
\(494\) −7.78086e6 1.34768e7i −1.43453 2.48468i
\(495\) −5161.63 −0.000946835
\(496\) 773655. 1.34001e6i 0.141203 0.244570i
\(497\) −427886. + 741120.i −0.0777028 + 0.134585i
\(498\) 9.21822e6 1.59664e7i 1.66561 2.88492i
\(499\) 122595. + 212341.i 0.0220406 + 0.0381754i 0.876835 0.480791i \(-0.159650\pi\)
−0.854795 + 0.518966i \(0.826317\pi\)
\(500\) −6.21910e6 1.07718e7i −1.11251 1.92692i
\(501\) −2.64768e6 + 4.58592e6i −0.471272 + 0.816267i
\(502\) 7.53603e6 1.30528e7i 1.33470 2.31177i
\(503\) −2.82627e6 + 4.89524e6i −0.498073 + 0.862688i −0.999998 0.00222327i \(-0.999292\pi\)
0.501924 + 0.864912i \(0.332626\pi\)
\(504\) 25847.6 0.00453256
\(505\) 2.46680e6 + 4.27263e6i 0.430434 + 0.745533i
\(506\) 1.41649e6 2.45344e6i 0.245945 0.425989i
\(507\) 3.06885e6 0.530219
\(508\) 1.67292e7 2.87618
\(509\) −1.47273e6 + 2.55084e6i −0.251958 + 0.436403i −0.964065 0.265667i \(-0.914408\pi\)
0.712107 + 0.702071i \(0.247741\pi\)
\(510\) 1.09123e7 1.85777
\(511\) −115873. 200697.i −0.0196304 0.0340008i
\(512\) −7.48416e6 −1.26174
\(513\) −3.70785e6 6.42218e6i −0.622054 1.07743i
\(514\) 6.09909e6 + 1.05639e7i 1.01826 + 1.76367i
\(515\) −492173. 852469.i −0.0817711 0.141632i
\(516\) −2.59787e6 + 4.49964e6i −0.429529 + 0.743967i
\(517\) 198998. 0.0327434
\(518\) 1.84191e6 + 443876.i 0.301609 + 0.0726838i
\(519\) 4.12425e6 0.672088
\(520\) −5.49006e6 + 9.50906e6i −0.890366 + 1.54216i
\(521\) 4.06862e6 + 7.04705e6i 0.656678 + 1.13740i 0.981470 + 0.191614i \(0.0613723\pi\)
−0.324792 + 0.945785i \(0.605294\pi\)
\(522\) 66864.4 + 115812.i 0.0107403 + 0.0186028i
\(523\) 3.24409e6 + 5.61893e6i 0.518607 + 0.898254i 0.999766 + 0.0216208i \(0.00688265\pi\)
−0.481159 + 0.876633i \(0.659784\pi\)
\(524\) 1.40311e7 2.23236
\(525\) −384693. 666307.i −0.0609138 0.105506i
\(526\) −6.44066e6 −1.01500
\(527\) −635889. + 1.10139e6i −0.0997367 + 0.172749i
\(528\) −3.35383e6 −0.523547
\(529\) 5.81469e6 0.903415
\(530\) −3.04690e6 + 5.27739e6i −0.471161 + 0.816074i
\(531\) 52167.6 + 90356.9i 0.00802905 + 0.0139067i
\(532\) 3.35347e6 0.513708
\(533\) 2.53784e6 4.39567e6i 0.386943 0.670205i
\(534\) −95466.6 + 165353.i −0.0144877 + 0.0250934i
\(535\) 2.53265e6 4.38668e6i 0.382552 0.662600i
\(536\) 8.53258e6 + 1.47789e7i 1.28283 + 2.22192i
\(537\) 2.14364e6 + 3.71290e6i 0.320787 + 0.555619i
\(538\) 5.71376e6 9.89653e6i 0.851073 1.47410i
\(539\) −624779. + 1.08215e6i −0.0926305 + 0.160441i
\(540\) −4.35691e6 + 7.54640e6i −0.642976 + 1.11367i
\(541\) −1.22611e7 −1.80110 −0.900550 0.434753i \(-0.856836\pi\)
−0.900550 + 0.434753i \(0.856836\pi\)
\(542\) −5.90017e6 1.02194e7i −0.862713 1.49426i
\(543\) −1.38781e6 + 2.40376e6i −0.201991 + 0.349858i
\(544\) −3.17244e7 −4.59617
\(545\) −3.04435e6 −0.439040
\(546\) −1.33131e6 + 2.30589e6i −0.191116 + 0.331022i
\(547\) −4.98338e6 −0.712124 −0.356062 0.934462i \(-0.615881\pi\)
−0.356062 + 0.934462i \(0.615881\pi\)
\(548\) 2.12311e6 + 3.67733e6i 0.302009 + 0.523095i
\(549\) 57430.4 0.00813225
\(550\) −934026. 1.61778e6i −0.131660 0.228041i
\(551\) 5.20909e6 + 9.02241e6i 0.730942 + 1.26603i
\(552\) −1.38237e7 2.39433e7i −1.93097 3.34455i
\(553\) −176541. + 305777.i −0.0245489 + 0.0425199i
\(554\) −7.35161e6 −1.01767
\(555\) −2.54395e6 + 2.67616e6i −0.350571 + 0.368791i
\(556\) −1.66944e7 −2.29025
\(557\) −3.93877e6 + 6.82215e6i −0.537926 + 0.931715i 0.461089 + 0.887354i \(0.347459\pi\)
−0.999016 + 0.0443617i \(0.985875\pi\)
\(558\) −6841.48 11849.8i −0.000930175 0.00161111i
\(559\) 1.57738e6 + 2.73210e6i 0.213505 + 0.369801i
\(560\) −868582. 1.50443e6i −0.117042 0.202722i
\(561\) 2.75661e6 0.369801
\(562\) −1.11614e7 1.93320e7i −1.49065 2.58189i
\(563\) 9.07153e6 1.20617 0.603087 0.797676i \(-0.293937\pi\)
0.603087 + 0.797676i \(0.293937\pi\)
\(564\) 1.61710e6 2.80090e6i 0.214062 0.370766i
\(565\) −931053. −0.122702
\(566\) −1.91762e6 −0.251606
\(567\) −628246. + 1.08815e6i −0.0820677 + 0.142145i
\(568\) 1.01387e7 + 1.75608e7i 1.31860 + 2.28388i
\(569\) 353751. 0.0458054 0.0229027 0.999738i \(-0.492709\pi\)
0.0229027 + 0.999738i \(0.492709\pi\)
\(570\) −4.57324e6 + 7.92108e6i −0.589572 + 1.02117i
\(571\) −3.37774e6 + 5.85043e6i −0.433547 + 0.750926i −0.997176 0.0751023i \(-0.976072\pi\)
0.563628 + 0.826028i \(0.309405\pi\)
\(572\) −2.30962e6 + 4.00038e6i −0.295156 + 0.511225i
\(573\) −5.58469e6 9.67297e6i −0.710579 1.23076i
\(574\) 765393. + 1.32570e6i 0.0969627 + 0.167944i
\(575\) 4.03913e6 6.99597e6i 0.509469 0.882426i
\(576\) 63775.4 110462.i 0.00800934 0.0138726i
\(577\) 3.01054e6 5.21441e6i 0.376448 0.652027i −0.614095 0.789232i \(-0.710479\pi\)
0.990543 + 0.137205i \(0.0438120\pi\)
\(578\) 4.21738e7 5.25077
\(579\) −927583. 1.60662e6i −0.114989 0.199167i
\(580\) 6.12095e6 1.06018e7i 0.755525 1.30861i
\(581\) 2.41232e6 0.296479
\(582\) −2.60486e6 −0.318770
\(583\) −769689. + 1.33314e6i −0.0937873 + 0.162444i
\(584\) −5.49119e6 −0.666245
\(585\) 25468.0 + 44111.8i 0.00307684 + 0.00532924i
\(586\) 1.26625e7 1.52326
\(587\) 3.49288e6 + 6.04985e6i 0.418397 + 0.724685i 0.995778 0.0917895i \(-0.0292587\pi\)
−0.577381 + 0.816475i \(0.695925\pi\)
\(588\) 1.01542e7 + 1.75875e7i 1.21116 + 2.09779i
\(589\) −532988. 923162.i −0.0633037 0.109645i
\(590\) 6.68354e6 1.15762e7i 0.790454 1.36911i
\(591\) −9.71811e6 −1.14449
\(592\) 1.62256e7 1.70689e7i 1.90282 2.00171i
\(593\) 1.07245e7 1.25239 0.626196 0.779666i \(-0.284611\pi\)
0.626196 + 0.779666i \(0.284611\pi\)
\(594\) −1.54034e6 + 2.66795e6i −0.179123 + 0.310250i
\(595\) 713913. + 1.23653e6i 0.0826709 + 0.143190i
\(596\) −1.06412e7 1.84311e7i −1.22709 2.12538i
\(597\) 3.26981e6 + 5.66348e6i 0.375480 + 0.650351i
\(598\) −2.79564e7 −3.19690
\(599\) −7.60627e6 1.31745e7i −0.866173 1.50026i −0.865877 0.500257i \(-0.833239\pi\)
−0.000296251 1.00000i \(-0.500094\pi\)
\(600\) −1.82305e7 −2.06738
\(601\) 3.39170e6 5.87459e6i 0.383028 0.663425i −0.608465 0.793581i \(-0.708214\pi\)
0.991494 + 0.130156i \(0.0415478\pi\)
\(602\) −951450. −0.107003
\(603\) 79164.0 0.00886614
\(604\) −1.22093e7 + 2.11471e7i −1.36175 + 2.35862i
\(605\) −2.21819e6 3.84201e6i −0.246382 0.426747i
\(606\) 2.83479e7 3.13573
\(607\) −1.49874e6 + 2.59590e6i −0.165103 + 0.285967i −0.936692 0.350155i \(-0.886129\pi\)
0.771589 + 0.636122i \(0.219462\pi\)
\(608\) 1.32953e7 2.30282e7i 1.45861 2.52639i
\(609\) 891277. 1.54374e6i 0.0973799 0.168667i
\(610\) −3.67890e6 6.37204e6i −0.400307 0.693352i
\(611\) −981877. 1.70066e6i −0.106403 0.184295i
\(612\) −219888. + 380857.i −0.0237314 + 0.0411040i
\(613\) 5.95491e6 1.03142e7i 0.640064 1.10862i −0.345354 0.938473i \(-0.612241\pi\)
0.985418 0.170151i \(-0.0544257\pi\)
\(614\) 1.09440e7 1.89556e7i 1.17153 2.02916i
\(615\) −2.98326e6 −0.318056
\(616\) −418266. 724458.i −0.0444121 0.0769240i
\(617\) −2.90618e6 + 5.03364e6i −0.307333 + 0.532316i −0.977778 0.209643i \(-0.932770\pi\)
0.670445 + 0.741959i \(0.266103\pi\)
\(618\) −5.65593e6 −0.595707
\(619\) −1.28133e7 −1.34410 −0.672052 0.740504i \(-0.734587\pi\)
−0.672052 + 0.740504i \(0.734587\pi\)
\(620\) −626288. + 1.08476e6i −0.0654328 + 0.113333i
\(621\) −1.33222e7 −1.38627
\(622\) −1.32838e7 2.30083e7i −1.37673 2.38456i
\(623\) −24982.6 −0.00257880
\(624\) 1.65481e7 + 2.86621e7i 1.70132 + 2.94677i
\(625\) −1.38677e6 2.40196e6i −0.142005 0.245961i
\(626\) 1.01174e7 + 1.75238e7i 1.03189 + 1.78728i
\(627\) −1.15526e6 + 2.00097e6i −0.117358 + 0.203269i
\(628\) −8.85436e6 −0.895897
\(629\) −1.33363e7 + 1.40294e7i −1.34403 + 1.41388i
\(630\) −15361.9 −0.00154203
\(631\) −2.67993e6 + 4.64178e6i −0.267948 + 0.464100i −0.968332 0.249667i \(-0.919679\pi\)
0.700384 + 0.713767i \(0.253012\pi\)
\(632\) 4.18311e6 + 7.24536e6i 0.416588 + 0.721552i
\(633\) 5.62972e6 + 9.75097e6i 0.558442 + 0.967250i
\(634\) 2.53669e6 + 4.39368e6i 0.250637 + 0.434115i
\(635\) −5.97022e6 −0.587566
\(636\) 1.25093e7 + 2.16667e7i 1.22628 + 2.12398i
\(637\) 1.23309e7 1.20405
\(638\) 2.16400e6 3.74816e6i 0.210478 0.364558i
\(639\) 94065.5 0.00911335
\(640\) −3.85795e6 −0.372312
\(641\) 1.89308e6 3.27891e6i 0.181980 0.315198i −0.760575 0.649250i \(-0.775083\pi\)
0.942555 + 0.334052i \(0.108416\pi\)
\(642\) −1.45523e7 2.52053e7i −1.39346 2.41354i
\(643\) 5.89964e6 0.562727 0.281364 0.959601i \(-0.409213\pi\)
0.281364 + 0.959601i \(0.409213\pi\)
\(644\) 3.01224e6 5.21735e6i 0.286203 0.495718i
\(645\) 927114. 1.60581e6i 0.0877473 0.151983i
\(646\) −2.39746e7 + 4.15252e7i −2.26032 + 3.91498i
\(647\) −4.68157e6 8.10871e6i −0.439674 0.761537i 0.557990 0.829847i \(-0.311573\pi\)
−0.997664 + 0.0683102i \(0.978239\pi\)
\(648\) 1.48862e7 + 2.57837e7i 1.39267 + 2.41217i
\(649\) 1.68835e6 2.92431e6i 0.157345 0.272529i
\(650\) −9.21714e6 + 1.59646e7i −0.855683 + 1.48209i
\(651\) −91194.3 + 157953.i −0.00843365 + 0.0146075i
\(652\) 8.81228e6 0.811838
\(653\) 747407. + 1.29455e6i 0.0685921 + 0.118805i 0.898282 0.439420i \(-0.144816\pi\)
−0.829690 + 0.558225i \(0.811483\pi\)
\(654\) −8.74624e6 + 1.51489e7i −0.799608 + 1.38496i
\(655\) −5.00735e6 −0.456042
\(656\) 1.90276e7 1.72633
\(657\) −12736.6 + 22060.4i −0.00115117 + 0.00199389i
\(658\) 592252. 0.0533263
\(659\) 5.66570e6 + 9.81328e6i 0.508206 + 0.880239i 0.999955 + 0.00950180i \(0.00302456\pi\)
−0.491749 + 0.870737i \(0.663642\pi\)
\(660\) 2.71499e6 0.242609
\(661\) 3.65486e6 + 6.33040e6i 0.325362 + 0.563544i 0.981586 0.191023i \(-0.0611804\pi\)
−0.656223 + 0.754567i \(0.727847\pi\)
\(662\) 5.24912e6 + 9.09174e6i 0.465524 + 0.806310i
\(663\) −1.36013e7 2.35582e7i −1.20171 2.08141i
\(664\) 2.85798e7 4.95017e7i 2.51558 4.35712i
\(665\) −1.19677e6 −0.104944
\(666\) −58976.8 199732.i −0.00515223 0.0174486i
\(667\) 1.87161e7 1.62893
\(668\) −1.36705e7 + 2.36781e7i −1.18534 + 2.05308i
\(669\) −1.96343e6 3.40076e6i −0.169609 0.293772i
\(670\) −5.07112e6 8.78344e6i −0.436432 0.755923i
\(671\) −929339. 1.60966e6i −0.0796834 0.138016i
\(672\) −4.54967e6 −0.388648
\(673\) −3.82120e6 6.61852e6i −0.325209 0.563279i 0.656346 0.754460i \(-0.272101\pi\)
−0.981555 + 0.191182i \(0.938768\pi\)
\(674\) −2.07275e7 −1.75751
\(675\) −4.39229e6 + 7.60766e6i −0.371049 + 0.642676i
\(676\) 1.58451e7 1.33361
\(677\) −8.48703e6 −0.711679 −0.355840 0.934547i \(-0.615805\pi\)
−0.355840 + 0.934547i \(0.615805\pi\)
\(678\) −2.67486e6 + 4.63299e6i −0.223474 + 0.387068i
\(679\) −170416. 295170.i −0.0141853 0.0245696i
\(680\) 3.38322e7 2.80581
\(681\) −763487. + 1.32240e6i −0.0630861 + 0.109268i
\(682\) −221418. + 383507.i −0.0182285 + 0.0315728i
\(683\) −6.73670e6 + 1.16683e7i −0.552580 + 0.957097i 0.445507 + 0.895278i \(0.353023\pi\)
−0.998087 + 0.0618183i \(0.980310\pi\)
\(684\) −184305. 319226.i −0.0150625 0.0260890i
\(685\) −757683. 1.31235e6i −0.0616966 0.106862i
\(686\) −3.77142e6 + 6.53229e6i −0.305981 + 0.529975i
\(687\) 1.04791e7 1.81504e7i 0.847099 1.46722i
\(688\) −5.91324e6 + 1.02420e7i −0.476272 + 0.824927i
\(689\) 1.51909e7 1.21909
\(690\) 8.21576e6 + 1.42301e7i 0.656939 + 1.13785i
\(691\) −6.96227e6 + 1.20590e7i −0.554697 + 0.960763i 0.443230 + 0.896408i \(0.353832\pi\)
−0.997927 + 0.0643554i \(0.979501\pi\)
\(692\) 2.12944e7 1.69044
\(693\) −3880.61 −0.000306950
\(694\) −1.35501e7 + 2.34695e7i −1.06794 + 1.84972i
\(695\) 5.95779e6 0.467868
\(696\) −2.11187e7 3.65787e7i −1.65251 2.86223i
\(697\) −1.56393e7 −1.21937
\(698\) −1.50557e7 2.60772e7i −1.16966 2.02592i
\(699\) 8.37368e6 + 1.45036e7i 0.648222 + 1.12275i
\(700\) −1.98625e6 3.44029e6i −0.153211 0.265368i
\(701\) −7.36436e6 + 1.27554e7i −0.566031 + 0.980394i 0.430922 + 0.902389i \(0.358188\pi\)
−0.996953 + 0.0780047i \(0.975145\pi\)
\(702\) 3.04008e7 2.32832
\(703\) −4.59461e6 1.55602e7i −0.350639 1.18748i
\(704\) −4.12806e6 −0.313916
\(705\) −577103. + 999572.i −0.0437301 + 0.0757428i
\(706\) −1.95367e6 3.38385e6i −0.147516 0.255505i
\(707\) 1.85459e6 + 3.21224e6i 0.139540 + 0.241691i
\(708\) −2.74398e7 4.75271e7i −2.05730 3.56335i
\(709\) 1.44039e7 1.07613 0.538065 0.842904i \(-0.319156\pi\)
0.538065 + 0.842904i \(0.319156\pi\)
\(710\) −6.02569e6 1.04368e7i −0.448601 0.777000i
\(711\) 38810.3 0.00287921
\(712\) −295981. + 512654.i −0.0218808 + 0.0378987i
\(713\) −1.91501e6 −0.141074
\(714\) 8.20411e6 0.602263
\(715\) 824246. 1.42764e6i 0.0602965 0.104437i
\(716\) 1.10681e7 + 1.91705e7i 0.806844 + 1.39750i
\(717\) −5.56762e6 −0.404456
\(718\) 2.18780e6 3.78939e6i 0.158379 0.274320i
\(719\) 8.97005e6 1.55366e7i 0.647102 1.12081i −0.336710 0.941609i \(-0.609314\pi\)
0.983812 0.179205i \(-0.0573526\pi\)
\(720\) −95473.6 + 165365.i −0.00686360 + 0.0118881i
\(721\) −370025. 640902.i −0.0265090 0.0459149i
\(722\) −6.98713e6 1.21021e7i −0.498834 0.864005i
\(723\) 1.08716e7 1.88302e7i 0.773481 1.33971i
\(724\) −7.16556e6 + 1.24111e7i −0.508047 + 0.879963i
\(725\) 6.17065e6 1.06879e7i 0.435999 0.755173i
\(726\) −2.54908e7 −1.79491
\(727\) −441525. 764744.i −0.0309827 0.0536636i 0.850118 0.526592i \(-0.176530\pi\)
−0.881101 + 0.472928i \(0.843197\pi\)
\(728\) −4.12753e6 + 7.14909e6i −0.288643 + 0.499945i
\(729\) 1.44857e7 1.00953
\(730\) 3.26355e6 0.226664
\(731\) 4.86027e6 8.41823e6i 0.336408 0.582676i
\(732\) −3.02080e7 −2.08374
\(733\) 3.31214e6 + 5.73680e6i 0.227693 + 0.394375i 0.957124 0.289679i \(-0.0935486\pi\)
−0.729431 + 0.684054i \(0.760215\pi\)
\(734\) −2.99479e7 −2.05176
\(735\) −3.62376e6 6.27654e6i −0.247424 0.428551i
\(736\) −2.38849e7 4.13698e7i −1.62528 2.81507i
\(737\) −1.28103e6 2.21881e6i −0.0868744 0.150471i
\(738\) 84131.2 145719.i 0.00568612 0.00984865i
\(739\) 9.80466e6 0.660422 0.330211 0.943907i \(-0.392880\pi\)
0.330211 + 0.943907i \(0.392880\pi\)
\(740\) −1.31350e7 + 1.38176e7i −0.881758 + 0.927583i
\(741\) 2.28007e7 1.52546
\(742\) −2.29072e6 + 3.96764e6i −0.152743 + 0.264559i
\(743\) 2.45829e6 + 4.25788e6i 0.163365 + 0.282957i 0.936074 0.351804i \(-0.114432\pi\)
−0.772708 + 0.634761i \(0.781098\pi\)
\(744\) 2.16084e6 + 3.74269e6i 0.143117 + 0.247885i
\(745\) 3.79759e6 + 6.57761e6i 0.250678 + 0.434188i
\(746\) 3.73600e7 2.45788
\(747\) −132580. 229635.i −0.00869311 0.0150569i
\(748\) 1.42329e7 0.930123
\(749\) 1.90410e6 3.29799e6i 0.124018 0.214805i
\(750\) 2.55052e7 1.65568
\(751\) −4.91589e6 −0.318055 −0.159027 0.987274i \(-0.550836\pi\)
−0.159027 + 0.987274i \(0.550836\pi\)
\(752\) 3.68083e6 6.37539e6i 0.237357 0.411114i
\(753\) 1.10416e7 + 1.91247e7i 0.709652 + 1.22915i
\(754\) −4.27095e7 −2.73588
\(755\) 4.35718e6 7.54685e6i 0.278188 0.481835i
\(756\) −3.27561e6 + 5.67352e6i −0.208443 + 0.361034i
\(757\) 1.08114e6 1.87258e6i 0.0685710 0.118768i −0.829702 0.558207i \(-0.811489\pi\)
0.898272 + 0.439439i \(0.144823\pi\)
\(758\) 2.48326e7 + 4.30114e7i 1.56982 + 2.71901i
\(759\) 2.07541e6 + 3.59472e6i 0.130768 + 0.226496i
\(760\) −1.41787e7 + 2.45582e7i −0.890434 + 1.54228i
\(761\) 1.09080e7 1.88932e7i 0.682785 1.18262i −0.291343 0.956619i \(-0.594102\pi\)
0.974128 0.225999i \(-0.0725646\pi\)
\(762\) −1.71521e7 + 2.97083e7i −1.07011 + 1.85349i
\(763\) −2.28880e6 −0.142330
\(764\) −2.88349e7 4.99436e7i −1.78725 3.09561i
\(765\) 78472.5 135918.i 0.00484802 0.00839701i
\(766\) 1.91563e7 1.17961
\(767\) −3.33220e7 −2.04523
\(768\) 2.31872e6 4.01614e6i 0.141855 0.245700i
\(769\) 1.35196e7 0.824416 0.412208 0.911090i \(-0.364758\pi\)
0.412208 + 0.911090i \(0.364758\pi\)
\(770\) 248586. + 430564.i 0.0151095 + 0.0261704i
\(771\) −1.78725e7 −1.08280
\(772\) −4.78931e6 8.29532e6i −0.289221 0.500945i
\(773\) 2.33662e6 + 4.04715e6i 0.140650 + 0.243613i 0.927742 0.373223i \(-0.121747\pi\)
−0.787091 + 0.616836i \(0.788414\pi\)
\(774\) 52291.2 + 90571.0i 0.00313744 + 0.00543421i
\(775\) −631373. + 1.09357e6i −0.0377600 + 0.0654022i
\(776\) −8.07600e6 −0.481440
\(777\) −1.91259e6 + 2.01199e6i −0.113650 + 0.119556i
\(778\) 2.46055e7 1.45742
\(779\) 6.55427e6 1.13523e7i 0.386973 0.670256i
\(780\) −1.33960e7 2.32025e7i −0.788385 1.36552i
\(781\) −1.52217e6 2.63648e6i −0.0892967 0.154666i
\(782\) 4.30700e7 + 7.45994e7i 2.51859 + 4.36233i
\(783\) −2.03526e7 −1.18635
\(784\) 2.31128e7 + 4.00325e7i 1.34296 + 2.32607i
\(785\) 3.15990e6 0.183020
\(786\) −1.43858e7 + 2.49169e7i −0.830573 + 1.43859i
\(787\) −1.44587e7 −0.832133 −0.416066 0.909334i \(-0.636592\pi\)
−0.416066 + 0.909334i \(0.636592\pi\)
\(788\) −5.01766e7 −2.87863
\(789\) 4.71835e6 8.17243e6i 0.269835 0.467368i
\(790\) −2.48613e6 4.30610e6i −0.141728 0.245480i
\(791\) −699983. −0.0397783
\(792\) −45975.4 + 79631.7i −0.00260443 + 0.00451100i
\(793\) −9.17089e6 + 1.58844e7i −0.517879 + 0.896993i
\(794\) 1.09138e7 1.89032e7i 0.614361 1.06410i
\(795\) −4.46425e6 7.73232e6i −0.250513 0.433902i
\(796\) 1.68827e7 + 2.92418e7i 0.944409 + 1.63576i
\(797\) 2.86989e6 4.97080e6i 0.160037 0.277192i −0.774845 0.632151i \(-0.782172\pi\)
0.934882 + 0.354960i \(0.115505\pi\)
\(798\) −3.43825e6 + 5.95522e6i −0.191130 + 0.331048i
\(799\) −3.02538e6 + 5.24012e6i −0.167654 + 0.290385i
\(800\) −3.14991e7 −1.74009
\(801\) 1373.03 + 2378.16i 7.56135e−5 + 0.000130966i
\(802\) 2.22042e7 3.84588e7i 1.21899 2.11135i
\(803\) 824416. 0.0451188
\(804\) −4.16398e7 −2.27179
\(805\) −1.07499e6 + 1.86194e6i −0.0584676 + 0.101269i
\(806\) 4.36998e6 0.236942
\(807\) 8.37168e6 + 1.45002e7i 0.452510 + 0.783771i
\(808\) 8.78886e7 4.73592
\(809\) −6.71156e6 1.16248e7i −0.360539 0.624472i 0.627511 0.778608i \(-0.284074\pi\)
−0.988050 + 0.154136i \(0.950741\pi\)
\(810\) −8.84725e6 1.53239e7i −0.473801 0.820647i
\(811\) 1.23269e7 + 2.13509e7i 0.658117 + 1.13989i 0.981103 + 0.193488i \(0.0619801\pi\)
−0.322986 + 0.946404i \(0.604687\pi\)
\(812\) 4.60185e6 7.97064e6i 0.244930 0.424231i
\(813\) 1.72896e7 0.917399
\(814\) −4.64373e6 + 4.88507e6i −0.245644 + 0.258410i
\(815\) −3.14488e6 −0.165848
\(816\) 5.09883e7 8.83144e7i 2.68068 4.64308i
\(817\) 4.07376e6 + 7.05596e6i 0.213521 + 0.369829i
\(818\) 6.25978e6 + 1.08423e7i 0.327096 + 0.566547i
\(819\) 19147.3 + 33164.1i 0.000997465 + 0.00172766i
\(820\) −1.54032e7 −0.799975
\(821\) −1.41101e6 2.44394e6i −0.0730587 0.126541i 0.827182 0.561934i \(-0.189943\pi\)
−0.900240 + 0.435393i \(0.856609\pi\)
\(822\) −8.70710e6 −0.449463
\(823\) −1.23503e7 + 2.13914e7i −0.635593 + 1.10088i 0.350796 + 0.936452i \(0.385911\pi\)
−0.986389 + 0.164428i \(0.947422\pi\)
\(824\) −1.75354e7 −0.899700
\(825\) 2.73703e6 0.140005
\(826\) 5.02481e6 8.70323e6i 0.256254 0.443844i
\(827\) 4.43566e6 + 7.68279e6i 0.225525 + 0.390621i 0.956477 0.291808i \(-0.0942569\pi\)
−0.730952 + 0.682429i \(0.760924\pi\)
\(828\) −662203. −0.0335672
\(829\) −1.35873e7 + 2.35339e7i −0.686669 + 1.18935i 0.286240 + 0.958158i \(0.407594\pi\)
−0.972909 + 0.231188i \(0.925739\pi\)
\(830\) −1.69857e7 + 2.94201e7i −0.855830 + 1.48234i
\(831\) 5.38571e6 9.32832e6i 0.270545 0.468599i
\(832\) 2.03682e7 + 3.52788e7i 1.02010 + 1.76687i
\(833\) −1.89971e7 3.29039e7i −0.948580 1.64299i
\(834\) 1.71164e7 2.96464e7i 0.852112 1.47590i
\(835\) 4.87867e6 8.45011e6i 0.242151 0.419417i
\(836\) −5.96486e6 + 1.03314e7i −0.295178 + 0.511264i
\(837\) 2.08245e6 0.102745
\(838\) −1.01577e7 1.75936e7i −0.499672 0.865457i
\(839\) −4.43563e6 + 7.68274e6i −0.217546 + 0.376801i −0.954057 0.299625i \(-0.903139\pi\)
0.736511 + 0.676425i \(0.236472\pi\)
\(840\) 4.85195e6 0.237257
\(841\) 8.08181e6 0.394020
\(842\) 3.54773e7 6.14485e7i 1.72453 2.98697i
\(843\) 3.27067e7 1.58514
\(844\) 2.90675e7 + 5.03463e7i 1.40459 + 2.43283i
\(845\) −5.65472e6 −0.272439
\(846\) −32549.8 56378.0i −0.00156359 0.00270822i
\(847\) −1.66768e6 2.88850e6i −0.0798735 0.138345i
\(848\) 2.84735e7 + 4.93176e7i 1.35973 + 2.35512i
\(849\) 1.40483e6 2.43323e6i 0.0668888 0.115855i
\(850\) 5.68002e7 2.69651
\(851\) −2.83356e7 6.82850e6i −1.34125 0.323222i
\(852\) −4.94778e7 −2.33513
\(853\) −3.55767e6 + 6.16207e6i −0.167415 + 0.289970i −0.937510 0.347958i \(-0.886875\pi\)
0.770096 + 0.637929i \(0.220208\pi\)
\(854\) −2.76587e6 4.79062e6i −0.129774 0.224774i
\(855\) 65773.9 + 113924.i 0.00307707 + 0.00532965i
\(856\) −4.51173e7 7.81455e7i −2.10455 3.64519i
\(857\) −2.59467e7 −1.20679 −0.603393 0.797444i \(-0.706185\pi\)
−0.603393 + 0.797444i \(0.706185\pi\)
\(858\) −4.73602e6 8.20302e6i −0.219632 0.380413i
\(859\) −1.01345e7 −0.468620 −0.234310 0.972162i \(-0.575283\pi\)
−0.234310 + 0.972162i \(0.575283\pi\)
\(860\) 4.78688e6 8.29113e6i 0.220702 0.382268i
\(861\) −2.24287e6 −0.103109
\(862\) 1.99183e7 0.913027
\(863\) 2.08330e7 3.60839e7i 0.952195 1.64925i 0.211534 0.977371i \(-0.432154\pi\)
0.740661 0.671879i \(-0.234513\pi\)
\(864\) 2.59733e7 + 4.49870e7i 1.18370 + 2.05023i
\(865\) −7.59942e6 −0.345335
\(866\) 2.60711e7 4.51565e7i 1.18131 2.04609i
\(867\) −3.08960e7 + 5.35135e7i −1.39590 + 2.41777i
\(868\) −470855. + 815546.i −0.0212123 + 0.0367408i
\(869\) −628029. 1.08778e6i −0.0282118 0.0488642i
\(870\) 1.25514e7 + 2.17396e7i 0.562203 + 0.973764i
\(871\) −1.26415e7 + 2.18957e7i −0.564615 + 0.977941i
\(872\) −2.71165e7 + 4.69671e7i −1.20765 + 2.09172i
\(873\) −18732.0 + 32444.8i −0.000831856 + 0.00144082i
\(874\) −7.22005e7 −3.19714
\(875\) 1.66862e6 + 2.89013e6i 0.0736777 + 0.127614i
\(876\) 6.69937e6 1.16037e7i 0.294967 0.510898i
\(877\) 1.00493e7 0.441203 0.220601 0.975364i \(-0.429198\pi\)
0.220601 + 0.975364i \(0.429198\pi\)
\(878\) 5.97636e6 0.261638
\(879\) −9.27639e6 + 1.60672e7i −0.404955 + 0.701403i
\(880\) 6.17982e6 0.269011
\(881\) 1.72792e7 + 2.99284e7i 0.750038 + 1.29910i 0.947804 + 0.318855i \(0.103298\pi\)
−0.197765 + 0.980249i \(0.563368\pi\)
\(882\) 408776. 0.0176935
\(883\) −6.08836e6 1.05453e7i −0.262784 0.455155i 0.704197 0.710005i \(-0.251307\pi\)
−0.966981 + 0.254850i \(0.917974\pi\)
\(884\) −7.02266e7 1.21636e8i −3.02253 5.23518i
\(885\) 9.79258e6 + 1.69612e7i 0.420280 + 0.727946i
\(886\) −2.98927e7 + 5.17757e7i −1.27933 + 2.21586i
\(887\) −5.36818e6 −0.229096 −0.114548 0.993418i \(-0.536542\pi\)
−0.114548 + 0.993418i \(0.536542\pi\)
\(888\) 1.86275e7 + 6.30840e7i 0.792723 + 2.68465i
\(889\) −4.48853e6 −0.190480
\(890\) 175909. 304683.i 0.00744410 0.0128936i
\(891\) −2.23493e6 3.87102e6i −0.0943128 0.163355i
\(892\) −1.01376e7 1.75588e7i −0.426602 0.738896i
\(893\) −2.53581e6 4.39214e6i −0.106411 0.184310i
\(894\) 4.36409e7 1.82621
\(895\) −3.94992e6 6.84146e6i −0.164828 0.285490i
\(896\) −2.90048e6 −0.120698
\(897\) 2.04805e7 3.54734e7i 0.849886 1.47205i
\(898\) −1.98476e7 −0.821329
\(899\) −2.92560e6 −0.120730
\(900\) −218326. + 378152.i −0.00898462 + 0.0155618i
\(901\) −2.34032e7 4.05356e7i −0.960426 1.66351i
\(902\) −5.44565e6 −0.222861
\(903\) 697022. 1.20728e6i 0.0284464 0.0492706i
\(904\) −8.29301e6 + 1.43639e7i −0.337514 + 0.584591i
\(905\) 2.55721e6 4.42922e6i 0.103787 0.179765i
\(906\) −2.50358e7 4.33633e7i −1.01331 1.75510i
\(907\) 1.91740e7 + 3.32103e7i 0.773915 + 1.34046i 0.935402 + 0.353586i \(0.115038\pi\)
−0.161487 + 0.986875i \(0.551629\pi\)
\(908\) −3.94204e6 + 6.82782e6i −0.158674 + 0.274832i
\(909\) 203854. 353086.i 0.00818296 0.0141733i
\(910\) 2.45309e6 4.24888e6i 0.0981997 0.170087i
\(911\) −1.36375e7 −0.544427 −0.272213 0.962237i \(-0.587756\pi\)
−0.272213 + 0.962237i \(0.587756\pi\)
\(912\) 4.27373e7 + 7.40231e7i 1.70145 + 2.94700i
\(913\) −4.29081e6 + 7.43190e6i −0.170358 + 0.295069i
\(914\) −3.15714e6 −0.125005
\(915\) 1.07805e7 0.425682
\(916\) 5.41060e7 9.37144e7i 2.13062 3.69035i
\(917\) −3.76462e6 −0.147842
\(918\) −4.68358e7 8.11220e7i −1.83430 3.17711i
\(919\) −2.47693e7 −0.967441 −0.483720 0.875223i \(-0.660715\pi\)
−0.483720 + 0.875223i \(0.660715\pi\)
\(920\) 2.54718e7 + 4.41185e7i 0.992180 + 1.71851i
\(921\) 1.60349e7 + 2.77732e7i 0.622898 + 1.07889i
\(922\) 1.07810e7 + 1.86732e7i 0.417667 + 0.723421i
\(923\) −1.50210e7 + 2.60172e7i −0.580358 + 1.00521i
\(924\) 2.04118e6 0.0786504
\(925\) −1.32416e7 + 1.39298e7i −0.508845 + 0.535290i
\(926\) 5.59617e7 2.14468
\(927\) −40672.7 + 70447.2i −0.00155455 + 0.00269256i
\(928\) −3.64894e7 6.32014e7i −1.39090 2.40911i
\(929\) 1.85401e7 + 3.21124e7i 0.704811 + 1.22077i 0.966760 + 0.255686i \(0.0823013\pi\)
−0.261949 + 0.965082i \(0.584365\pi\)
\(930\) −1.28424e6 2.22437e6i −0.0486899 0.0843334i
\(931\) 3.18458e7 1.20414
\(932\) 4.32351e7 + 7.48854e7i 1.63041 + 2.82395i
\(933\) 3.89264e7 1.46400
\(934\) −1.35363e7 + 2.34456e7i −0.507730 + 0.879415i
\(935\) −5.07938e6 −0.190012
\(936\) 907387. 0.0338534
\(937\) −2.28844e7 + 3.96370e7i −0.851512 + 1.47486i 0.0283307 + 0.999599i \(0.490981\pi\)
−0.879843 + 0.475264i \(0.842352\pi\)
\(938\) −3.81256e6 6.60355e6i −0.141485 0.245059i
\(939\) −2.96474e7 −1.09729
\(940\) −2.97970e6 + 5.16100e6i −0.109990 + 0.190508i
\(941\) 1.54209e7 2.67098e7i 0.567723 0.983326i −0.429067 0.903273i \(-0.641158\pi\)
0.996791 0.0800531i \(-0.0255090\pi\)
\(942\) 9.07818e6 1.57239e7i 0.333328 0.577341i
\(943\) −1.17747e7 2.03943e7i −0.431190 0.746843i
\(944\) −6.24582e7 1.08181e8i −2.28118 3.95112i
\(945\) 1.16898e6 2.02474e6i 0.0425823 0.0737546i
\(946\) 1.69235e6 2.93124e6i 0.0614842 0.106494i
\(947\) −1.95006e6 + 3.37760e6i −0.0706598 + 0.122386i −0.899191 0.437557i \(-0.855844\pi\)
0.828531 + 0.559943i \(0.189177\pi\)
\(948\) −2.04140e7 −0.737746
\(949\) −4.06774e6 7.04554e6i −0.146618 0.253950i
\(950\) −2.38043e7 + 4.12302e7i −0.855749 + 1.48220i
\(951\) −7.43341e6 −0.266524
\(952\) 2.54357e7 0.909601
\(953\) 7.91777e6 1.37140e7i 0.282404 0.489138i −0.689573 0.724217i \(-0.742202\pi\)
0.971976 + 0.235079i \(0.0755349\pi\)
\(954\) 503587. 0.0179144
\(955\) 1.02905e7 + 1.78236e7i 0.365112 + 0.632393i
\(956\) −2.87468e7 −1.01729
\(957\) 3.17065e6 + 5.49172e6i 0.111910 + 0.193833i
\(958\) −1.35776e7 2.35170e7i −0.477979 0.827883i
\(959\) −569640. 986646.i −0.0200011 0.0346430i
\(960\) 1.19715e7 2.07353e7i 0.419248 0.726159i
\(961\) −2.83298e7 −0.989544
\(962\) 6.46608e7 + 1.55824e7i 2.25270 + 0.542871i
\(963\) −418592. −0.0145454
\(964\) 5.61326e7 9.72245e7i 1.94546 3.36964i
\(965\) 1.70918e6 + 2.96039e6i 0.0590840 + 0.102337i
\(966\) 6.17677e6 + 1.06985e7i 0.212970 + 0.368875i
\(967\) −1.99527e7 3.45591e7i −0.686177 1.18849i −0.973065 0.230529i \(-0.925954\pi\)
0.286889 0.957964i \(-0.407379\pi\)
\(968\) −7.90308e7 −2.71086
\(969\) −3.51270e7 6.08417e7i −1.20180 2.08158i
\(970\) 4.79977e6 0.163791
\(971\) 1.23977e7 2.14734e7i 0.421981 0.730893i −0.574152 0.818749i \(-0.694668\pi\)
0.996133 + 0.0878560i \(0.0280015\pi\)
\(972\) 1.43327e6 0.0486590
\(973\) 4.47918e6 0.151676
\(974\) −2.09494e7 + 3.62855e7i −0.707579 + 1.22556i
\(975\) −1.35047e7 2.33909e7i −0.454962 0.788017i
\(976\) −6.87592e7 −2.31050
\(977\) −1.15986e7 + 2.00894e7i −0.388750 + 0.673334i −0.992282 0.124005i \(-0.960426\pi\)
0.603532 + 0.797339i \(0.293760\pi\)
\(978\) −9.03504e6 + 1.56492e7i −0.302053 + 0.523171i
\(979\) 44436.9 76966.9i 0.00148179 0.00256654i
\(980\) −1.87102e7 3.24071e7i −0.622321 1.07789i
\(981\) 125791. + 217877.i 0.00417329 + 0.00722834i
\(982\) 1.69698e6 2.93926e6i 0.0561563 0.0972655i
\(983\) 3.71950e6 6.44236e6i 0.122772 0.212648i −0.798088 0.602541i \(-0.794155\pi\)
0.920860 + 0.389893i \(0.127488\pi\)
\(984\) −2.65723e7 + 4.60246e7i −0.874866 + 1.51531i
\(985\) 1.79068e7 0.588067
\(986\) 6.57988e7 + 1.13967e8i 2.15539 + 3.73324i
\(987\) −433877. + 751497.i −0.0141767 + 0.0245547i
\(988\) 1.17725e8 3.83685
\(989\) 1.46369e7 0.475838
\(990\) 27324.3 47327.1i 0.000886056 0.00153469i
\(991\) 7.22842e6 0.233808 0.116904 0.993143i \(-0.462703\pi\)
0.116904 + 0.993143i \(0.462703\pi\)
\(992\) 3.73355e6 + 6.46669e6i 0.120460 + 0.208643i
\(993\) −1.53818e7 −0.495032
\(994\) −4.53022e6 7.84658e6i −0.145430 0.251892i
\(995\) −6.02502e6 1.04356e7i −0.192931 0.334166i
\(996\) 6.97360e7 + 1.20786e8i 2.22745 + 3.85806i
\(997\) 2.92362e7 5.06387e7i 0.931502 1.61341i 0.150745 0.988573i \(-0.451833\pi\)
0.780756 0.624836i \(-0.214834\pi\)
\(998\) −2.59595e6 −0.0825030
\(999\) 3.08131e7 + 7.42555e6i 0.976837 + 0.235405i
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 37.6.c.a.10.1 30
37.26 even 3 inner 37.6.c.a.26.1 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.6.c.a.10.1 30 1.1 even 1 trivial
37.6.c.a.26.1 yes 30 37.26 even 3 inner