Properties

Label 37.6.c.a.10.15
Level $37$
Weight $6$
Character 37.10
Analytic conductor $5.934$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 10.15
Character \(\chi\) \(=\) 37.10
Dual form 37.6.c.a.26.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.58532 - 9.67406i) q^{2} +(-1.95144 - 3.38000i) q^{3} +(-46.3916 - 80.3526i) q^{4} +(-1.46163 - 2.53162i) q^{5} -43.5978 q^{6} +(81.6887 + 141.489i) q^{7} -678.988 q^{8} +(113.884 - 197.252i) q^{9} +O(q^{10})\) \(q+(5.58532 - 9.67406i) q^{2} +(-1.95144 - 3.38000i) q^{3} +(-46.3916 - 80.3526i) q^{4} +(-1.46163 - 2.53162i) q^{5} -43.5978 q^{6} +(81.6887 + 141.489i) q^{7} -678.988 q^{8} +(113.884 - 197.252i) q^{9} -32.6548 q^{10} +364.183 q^{11} +(-181.061 + 313.607i) q^{12} +(-397.935 - 689.244i) q^{13} +1825.03 q^{14} +(-5.70460 + 9.88065i) q^{15} +(-2307.83 + 3997.28i) q^{16} +(0.520891 - 0.902211i) q^{17} +(-1272.15 - 2203.44i) q^{18} +(210.290 + 364.234i) q^{19} +(-135.615 + 234.892i) q^{20} +(318.822 - 552.216i) q^{21} +(2034.08 - 3523.13i) q^{22} +2633.59 q^{23} +(1325.01 + 2294.98i) q^{24} +(1558.23 - 2698.93i) q^{25} -8890.38 q^{26} -1837.35 q^{27} +(7579.34 - 13127.8i) q^{28} -2798.83 q^{29} +(63.7240 + 110.373i) q^{30} +5306.84 q^{31} +(14916.2 + 25835.6i) q^{32} +(-710.684 - 1230.94i) q^{33} +(-5.81869 - 10.0783i) q^{34} +(238.798 - 413.610i) q^{35} -21133.0 q^{36} +(3245.84 + 7668.67i) q^{37} +4698.16 q^{38} +(-1553.10 + 2690.04i) q^{39} +(992.432 + 1718.94i) q^{40} +(6879.84 + 11916.2i) q^{41} +(-3561.44 - 6168.60i) q^{42} +2630.80 q^{43} +(-16895.1 - 29263.1i) q^{44} -665.825 q^{45} +(14709.4 - 25477.5i) q^{46} -9382.92 q^{47} +18014.4 q^{48} +(-4942.58 + 8560.79i) q^{49} +(-17406.4 - 30148.8i) q^{50} -4.06596 q^{51} +(-36921.7 + 63950.3i) q^{52} +(-125.722 + 217.756i) q^{53} +(-10262.2 + 17774.7i) q^{54} +(-532.303 - 921.976i) q^{55} +(-55465.6 - 96069.2i) q^{56} +(820.740 - 1421.56i) q^{57} +(-15632.3 + 27076.0i) q^{58} +(-21769.5 + 37705.9i) q^{59} +1058.58 q^{60} +(25810.5 + 44705.1i) q^{61} +(29640.4 - 51338.6i) q^{62} +37212.0 q^{63} +185545. q^{64} +(-1163.27 + 2014.84i) q^{65} -15877.6 q^{66} +(-10987.2 - 19030.4i) q^{67} -96.6600 q^{68} +(-5139.30 - 8901.53i) q^{69} +(-2667.53 - 4620.29i) q^{70} +(-10357.8 - 17940.3i) q^{71} +(-77325.7 + 133932. i) q^{72} -62069.4 q^{73} +(92316.2 + 11431.5i) q^{74} -12163.2 q^{75} +(19511.4 - 33794.8i) q^{76} +(29749.7 + 51527.9i) q^{77} +(17349.1 + 30049.5i) q^{78} +(-16972.4 - 29397.1i) q^{79} +13492.8 q^{80} +(-24088.3 - 41722.1i) q^{81} +153704. q^{82} +(-1882.04 + 3259.79i) q^{83} -59162.6 q^{84} -3.04541 q^{85} +(14693.9 - 25450.5i) q^{86} +(5461.76 + 9460.04i) q^{87} -247276. q^{88} +(20494.6 - 35497.8i) q^{89} +(-3718.85 + 6441.24i) q^{90} +(65013.6 - 112607. i) q^{91} +(-122176. - 211616. i) q^{92} +(-10356.0 - 17937.1i) q^{93} +(-52406.6 + 90771.0i) q^{94} +(614.735 - 1064.75i) q^{95} +(58216.2 - 100833. i) q^{96} +113320. q^{97} +(55211.7 + 95629.5i) q^{98} +(41474.6 - 71836.1i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.58532 9.67406i 0.987355 1.71015i 0.356388 0.934338i \(-0.384008\pi\)
0.630966 0.775810i \(-0.282659\pi\)
\(3\) −1.95144 3.38000i −0.125185 0.216827i 0.796620 0.604480i \(-0.206619\pi\)
−0.921805 + 0.387653i \(0.873286\pi\)
\(4\) −46.3916 80.3526i −1.44974 2.51102i
\(5\) −1.46163 2.53162i −0.0261465 0.0452871i 0.852656 0.522473i \(-0.174990\pi\)
−0.878803 + 0.477186i \(0.841657\pi\)
\(6\) −43.5978 −0.494409
\(7\) 81.6887 + 141.489i 0.630110 + 1.09138i 0.987529 + 0.157439i \(0.0503237\pi\)
−0.357418 + 0.933944i \(0.616343\pi\)
\(8\) −678.988 −3.75091
\(9\) 113.884 197.252i 0.468657 0.811738i
\(10\) −32.6548 −0.103264
\(11\) 364.183 0.907483 0.453742 0.891133i \(-0.350089\pi\)
0.453742 + 0.891133i \(0.350089\pi\)
\(12\) −181.061 + 313.607i −0.362972 + 0.628685i
\(13\) −397.935 689.244i −0.653061 1.13113i −0.982376 0.186915i \(-0.940151\pi\)
0.329315 0.944220i \(-0.393182\pi\)
\(14\) 1825.03 2.48857
\(15\) −5.70460 + 9.88065i −0.00654631 + 0.0113385i
\(16\) −2307.83 + 3997.28i −2.25374 + 3.90360i
\(17\) 0.520891 0.902211i 0.000437144 0.000757156i −0.865807 0.500379i \(-0.833194\pi\)
0.866244 + 0.499621i \(0.166528\pi\)
\(18\) −1272.15 2203.44i −0.925462 1.60295i
\(19\) 210.290 + 364.234i 0.133640 + 0.231471i 0.925077 0.379780i \(-0.124000\pi\)
−0.791437 + 0.611250i \(0.790667\pi\)
\(20\) −135.615 + 234.892i −0.0758112 + 0.131309i
\(21\) 318.822 552.216i 0.157761 0.273250i
\(22\) 2034.08 3523.13i 0.896008 1.55193i
\(23\) 2633.59 1.03807 0.519037 0.854752i \(-0.326291\pi\)
0.519037 + 0.854752i \(0.326291\pi\)
\(24\) 1325.01 + 2294.98i 0.469559 + 0.813300i
\(25\) 1558.23 2698.93i 0.498633 0.863657i
\(26\) −8890.38 −2.57921
\(27\) −1837.35 −0.485046
\(28\) 7579.34 13127.8i 1.82699 3.16444i
\(29\) −2798.83 −0.617989 −0.308995 0.951064i \(-0.599993\pi\)
−0.308995 + 0.951064i \(0.599993\pi\)
\(30\) 63.7240 + 110.373i 0.0129271 + 0.0223903i
\(31\) 5306.84 0.991817 0.495908 0.868375i \(-0.334835\pi\)
0.495908 + 0.868375i \(0.334835\pi\)
\(32\) 14916.2 + 25835.6i 2.57503 + 4.46008i
\(33\) −710.684 1230.94i −0.113603 0.196767i
\(34\) −5.81869 10.0783i −0.000863233 0.00149516i
\(35\) 238.798 413.610i 0.0329504 0.0570717i
\(36\) −21133.0 −2.71772
\(37\) 3245.84 + 7668.67i 0.389784 + 0.920907i
\(38\) 4698.16 0.527799
\(39\) −1553.10 + 2690.04i −0.163507 + 0.283203i
\(40\) 992.432 + 1718.94i 0.0980733 + 0.169868i
\(41\) 6879.84 + 11916.2i 0.639173 + 1.10708i 0.985615 + 0.169009i \(0.0540567\pi\)
−0.346441 + 0.938072i \(0.612610\pi\)
\(42\) −3561.44 6168.60i −0.311532 0.539590i
\(43\) 2630.80 0.216978 0.108489 0.994098i \(-0.465399\pi\)
0.108489 + 0.994098i \(0.465399\pi\)
\(44\) −16895.1 29263.1i −1.31561 2.27871i
\(45\) −665.825 −0.0490150
\(46\) 14709.4 25477.5i 1.02495 1.77526i
\(47\) −9382.92 −0.619575 −0.309787 0.950806i \(-0.600258\pi\)
−0.309787 + 0.950806i \(0.600258\pi\)
\(48\) 18014.4 1.12854
\(49\) −4942.58 + 8560.79i −0.294078 + 0.509359i
\(50\) −17406.4 30148.8i −0.984655 1.70547i
\(51\) −4.06596 −0.000218896
\(52\) −36921.7 + 63950.3i −1.89353 + 3.27970i
\(53\) −125.722 + 217.756i −0.00614781 + 0.0106483i −0.869083 0.494666i \(-0.835290\pi\)
0.862935 + 0.505315i \(0.168624\pi\)
\(54\) −10262.2 + 17774.7i −0.478913 + 0.829501i
\(55\) −532.303 921.976i −0.0237275 0.0410973i
\(56\) −55465.6 96069.2i −2.36349 4.09368i
\(57\) 820.740 1421.56i 0.0334594 0.0579534i
\(58\) −15632.3 + 27076.0i −0.610175 + 1.05685i
\(59\) −21769.5 + 37705.9i −0.814177 + 1.41020i 0.0957404 + 0.995406i \(0.469478\pi\)
−0.909917 + 0.414790i \(0.863855\pi\)
\(60\) 1058.58 0.0379618
\(61\) 25810.5 + 44705.1i 0.888120 + 1.53827i 0.842096 + 0.539328i \(0.181322\pi\)
0.0460241 + 0.998940i \(0.485345\pi\)
\(62\) 29640.4 51338.6i 0.979275 1.69615i
\(63\) 37212.0 1.18122
\(64\) 185545. 5.66239
\(65\) −1163.27 + 2014.84i −0.0341505 + 0.0591505i
\(66\) −15877.6 −0.448668
\(67\) −10987.2 19030.4i −0.299020 0.517918i 0.676892 0.736082i \(-0.263326\pi\)
−0.975912 + 0.218165i \(0.929993\pi\)
\(68\) −96.6600 −0.00253498
\(69\) −5139.30 8901.53i −0.129951 0.225083i
\(70\) −2667.53 4620.29i −0.0650674 0.112700i
\(71\) −10357.8 17940.3i −0.243850 0.422361i 0.717957 0.696087i \(-0.245077\pi\)
−0.961808 + 0.273726i \(0.911744\pi\)
\(72\) −77325.7 + 133932.i −1.75789 + 3.04476i
\(73\) −62069.4 −1.36323 −0.681617 0.731709i \(-0.738723\pi\)
−0.681617 + 0.731709i \(0.738723\pi\)
\(74\) 92316.2 + 11431.5i 1.95974 + 0.242674i
\(75\) −12163.2 −0.249686
\(76\) 19511.4 33794.8i 0.387485 0.671144i
\(77\) 29749.7 + 51527.9i 0.571815 + 0.990412i
\(78\) 17349.1 + 30049.5i 0.322879 + 0.559243i
\(79\) −16972.4 29397.1i −0.305968 0.529953i 0.671508 0.740997i \(-0.265647\pi\)
−0.977476 + 0.211045i \(0.932313\pi\)
\(80\) 13492.8 0.235710
\(81\) −24088.3 41722.1i −0.407937 0.706567i
\(82\) 153704. 2.52436
\(83\) −1882.04 + 3259.79i −0.0299870 + 0.0519391i −0.880629 0.473806i \(-0.842880\pi\)
0.850642 + 0.525745i \(0.176213\pi\)
\(84\) −59162.6 −0.914849
\(85\) −3.04541 −4.57192e−5
\(86\) 14693.9 25450.5i 0.214235 0.371065i
\(87\) 5461.76 + 9460.04i 0.0773632 + 0.133997i
\(88\) −247276. −3.40389
\(89\) 20494.6 35497.8i 0.274262 0.475035i −0.695687 0.718345i \(-0.744900\pi\)
0.969949 + 0.243310i \(0.0782332\pi\)
\(90\) −3718.85 + 6441.24i −0.0483952 + 0.0838229i
\(91\) 65013.6 112607.i 0.823001 1.42548i
\(92\) −122176. 211616.i −1.50493 2.60662i
\(93\) −10356.0 17937.1i −0.124161 0.215053i
\(94\) −52406.6 + 90771.0i −0.611740 + 1.05956i
\(95\) 614.735 1064.75i 0.00698842 0.0121043i
\(96\) 58216.2 100833.i 0.644712 1.11667i
\(97\) 113320. 1.22286 0.611430 0.791299i \(-0.290595\pi\)
0.611430 + 0.791299i \(0.290595\pi\)
\(98\) 55211.7 + 95629.5i 0.580719 + 1.00584i
\(99\) 41474.6 71836.1i 0.425299 0.736639i
\(100\) −289155. −2.89155
\(101\) −119160. −1.16233 −0.581163 0.813787i \(-0.697402\pi\)
−0.581163 + 0.813787i \(0.697402\pi\)
\(102\) −22.7097 + 39.3344i −0.000216128 + 0.000374345i
\(103\) 161486. 1.49983 0.749916 0.661533i \(-0.230094\pi\)
0.749916 + 0.661533i \(0.230094\pi\)
\(104\) 270193. + 467988.i 2.44957 + 4.24279i
\(105\) −1864.00 −0.0164996
\(106\) 1404.39 + 2432.48i 0.0121401 + 0.0210273i
\(107\) −59005.8 102201.i −0.498236 0.862971i 0.501762 0.865006i \(-0.332685\pi\)
−0.999998 + 0.00203537i \(0.999352\pi\)
\(108\) 85237.8 + 147636.i 0.703190 + 1.21796i
\(109\) −34416.9 + 59611.9i −0.277464 + 0.480581i −0.970754 0.240078i \(-0.922827\pi\)
0.693290 + 0.720659i \(0.256160\pi\)
\(110\) −11892.3 −0.0937099
\(111\) 19586.0 25935.9i 0.150882 0.199800i
\(112\) −754095. −5.68043
\(113\) 65282.5 113073.i 0.480951 0.833032i −0.518810 0.854890i \(-0.673625\pi\)
0.999761 + 0.0218580i \(0.00695816\pi\)
\(114\) −9168.20 15879.8i −0.0660727 0.114441i
\(115\) −3849.34 6667.26i −0.0271420 0.0470113i
\(116\) 129842. + 224893.i 0.895923 + 1.55178i
\(117\) −181273. −1.22425
\(118\) 243180. + 421199.i 1.60776 + 2.78473i
\(119\) 170.204 0.00110180
\(120\) 3873.35 6708.84i 0.0245547 0.0425299i
\(121\) −28421.4 −0.176474
\(122\) 576639. 3.50756
\(123\) 26851.3 46507.7i 0.160030 0.277180i
\(124\) −246193. 426418.i −1.43787 2.49047i
\(125\) −18245.4 −0.104443
\(126\) 207841. 359991.i 1.16629 2.02007i
\(127\) −113735. + 196995.i −0.625727 + 1.08379i 0.362673 + 0.931916i \(0.381864\pi\)
−0.988400 + 0.151874i \(0.951469\pi\)
\(128\) 559011. 968236.i 3.01575 5.22344i
\(129\) −5133.86 8892.11i −0.0271625 0.0470468i
\(130\) 12994.5 + 22507.1i 0.0674374 + 0.116805i
\(131\) −60077.9 + 104058.i −0.305870 + 0.529782i −0.977455 0.211146i \(-0.932280\pi\)
0.671585 + 0.740928i \(0.265614\pi\)
\(132\) −65939.6 + 114211.i −0.329391 + 0.570521i
\(133\) −34356.7 + 59507.5i −0.168416 + 0.291704i
\(134\) −245468. −1.18095
\(135\) 2685.54 + 4651.49i 0.0126823 + 0.0219663i
\(136\) −353.679 + 612.590i −0.00163969 + 0.00284003i
\(137\) −154223. −0.702015 −0.351008 0.936373i \(-0.614161\pi\)
−0.351008 + 0.936373i \(0.614161\pi\)
\(138\) −114819. −0.513233
\(139\) 15182.2 26296.3i 0.0666495 0.115440i −0.830775 0.556608i \(-0.812102\pi\)
0.897425 + 0.441168i \(0.145436\pi\)
\(140\) −44312.9 −0.191078
\(141\) 18310.3 + 31714.3i 0.0775616 + 0.134341i
\(142\) −231407. −0.963067
\(143\) −144921. 251011.i −0.592642 1.02649i
\(144\) 525649. + 910451.i 2.11247 + 3.65890i
\(145\) 4090.86 + 7085.58i 0.0161583 + 0.0279869i
\(146\) −346678. + 600463.i −1.34600 + 2.33133i
\(147\) 38580.7 0.147257
\(148\) 465618. 616574.i 1.74733 2.31383i
\(149\) 86305.1 0.318472 0.159236 0.987241i \(-0.449097\pi\)
0.159236 + 0.987241i \(0.449097\pi\)
\(150\) −67935.2 + 117667.i −0.246528 + 0.427000i
\(151\) 73951.5 + 128088.i 0.263940 + 0.457157i 0.967285 0.253691i \(-0.0816447\pi\)
−0.703346 + 0.710848i \(0.748311\pi\)
\(152\) −142785. 247310.i −0.501271 0.868227i
\(153\) −118.642 205.494i −0.000409742 0.000709694i
\(154\) 664646. 2.25833
\(155\) −7756.65 13434.9i −0.0259325 0.0449165i
\(156\) 288203. 0.948170
\(157\) −288931. + 500444.i −0.935504 + 1.62034i −0.161771 + 0.986828i \(0.551720\pi\)
−0.773733 + 0.633512i \(0.781613\pi\)
\(158\) −379186. −1.20840
\(159\) 981.355 0.00307846
\(160\) 43604.0 75524.3i 0.134656 0.233231i
\(161\) 215134. + 372623.i 0.654101 + 1.13294i
\(162\) −538162. −1.61111
\(163\) 51624.8 89416.8i 0.152191 0.263603i −0.779842 0.625977i \(-0.784700\pi\)
0.932033 + 0.362374i \(0.118034\pi\)
\(164\) 638334. 1.10563e6i 1.85327 3.20995i
\(165\) −2077.52 + 3598.37i −0.00594067 + 0.0102895i
\(166\) 21023.6 + 36413.9i 0.0592157 + 0.102565i
\(167\) −248945. 431185.i −0.690735 1.19639i −0.971597 0.236640i \(-0.923954\pi\)
0.280863 0.959748i \(-0.409379\pi\)
\(168\) −216476. + 374948.i −0.591748 + 1.02494i
\(169\) −131058. + 226999.i −0.352977 + 0.611375i
\(170\) −17.0096 + 29.4615i −4.51411e−5 + 7.81866e-5i
\(171\) 95794.6 0.250525
\(172\) −122047. 211392.i −0.314562 0.544837i
\(173\) −130263. + 225622.i −0.330906 + 0.573146i −0.982690 0.185259i \(-0.940688\pi\)
0.651784 + 0.758405i \(0.274021\pi\)
\(174\) 122023. 0.305539
\(175\) 509158. 1.25677
\(176\) −840475. + 1.45574e6i −2.04523 + 3.54245i
\(177\) 169928. 0.407692
\(178\) −228938. 396533.i −0.541587 0.938057i
\(179\) 483532. 1.12796 0.563978 0.825790i \(-0.309270\pi\)
0.563978 + 0.825790i \(0.309270\pi\)
\(180\) 30888.7 + 53500.8i 0.0710589 + 0.123078i
\(181\) 188724. + 326880.i 0.428185 + 0.741638i 0.996712 0.0810267i \(-0.0258199\pi\)
−0.568527 + 0.822665i \(0.692487\pi\)
\(182\) −726243. 1.25789e6i −1.62519 2.81491i
\(183\) 100735. 174479.i 0.222359 0.385137i
\(184\) −1.78817e6 −3.89372
\(185\) 14669.9 19426.0i 0.0315137 0.0417306i
\(186\) −231366. −0.490363
\(187\) 189.700 328.570i 0.000396701 0.000687107i
\(188\) 435289. + 753943.i 0.898221 + 1.55576i
\(189\) −150091. 259965.i −0.305633 0.529372i
\(190\) −6866.99 11894.0i −0.0138001 0.0239025i
\(191\) −307026. −0.608964 −0.304482 0.952518i \(-0.598483\pi\)
−0.304482 + 0.952518i \(0.598483\pi\)
\(192\) −362081. 627143.i −0.708847 1.22776i
\(193\) −262414. −0.507099 −0.253550 0.967322i \(-0.581598\pi\)
−0.253550 + 0.967322i \(0.581598\pi\)
\(194\) 632927. 1.09626e6i 1.20740 2.09127i
\(195\) 9080.23 0.0171006
\(196\) 917176. 1.70535
\(197\) 113555. 196683.i 0.208469 0.361078i −0.742764 0.669554i \(-0.766485\pi\)
0.951232 + 0.308476i \(0.0998188\pi\)
\(198\) −463298. 802455.i −0.839841 1.45465i
\(199\) 438665. 0.785236 0.392618 0.919702i \(-0.371570\pi\)
0.392618 + 0.919702i \(0.371570\pi\)
\(200\) −1.05802e6 + 1.83254e6i −1.87033 + 3.23950i
\(201\) −42881.8 + 74273.5i −0.0748657 + 0.129671i
\(202\) −665549. + 1.15276e6i −1.14763 + 1.98775i
\(203\) −228632. 396003.i −0.389402 0.674463i
\(204\) 188.627 + 326.711i 0.000317342 + 0.000549653i
\(205\) 20111.6 34834.3i 0.0334243 0.0578926i
\(206\) 901953. 1.56223e6i 1.48087 2.56494i
\(207\) 299923. 519481.i 0.486501 0.842644i
\(208\) 3.67347e6 5.88733
\(209\) 76584.3 + 132648.i 0.121276 + 0.210056i
\(210\) −10411.1 + 18032.5i −0.0162910 + 0.0282168i
\(211\) 526124. 0.813546 0.406773 0.913529i \(-0.366654\pi\)
0.406773 + 0.913529i \(0.366654\pi\)
\(212\) 23329.7 0.0356509
\(213\) −40425.5 + 70019.0i −0.0610529 + 0.105747i
\(214\) −1.31827e6 −1.96774
\(215\) −3845.27 6660.20i −0.00567323 0.00982632i
\(216\) 1.24754e6 1.81937
\(217\) 433508. + 750858.i 0.624954 + 1.08245i
\(218\) 384459. + 665903.i 0.547910 + 0.949008i
\(219\) 121125. + 209795.i 0.170657 + 0.295586i
\(220\) −49388.8 + 85543.9i −0.0687974 + 0.119161i
\(221\) −829.124 −0.00114193
\(222\) −141512. 334337.i −0.192712 0.455304i
\(223\) 110253. 0.148466 0.0742329 0.997241i \(-0.476349\pi\)
0.0742329 + 0.997241i \(0.476349\pi\)
\(224\) −2.43696e6 + 4.22095e6i −3.24511 + 5.62069i
\(225\) −354913. 614728.i −0.467376 0.809519i
\(226\) −729248. 1.26309e6i −0.949738 1.64499i
\(227\) 136713. + 236795.i 0.176095 + 0.305005i 0.940540 0.339684i \(-0.110320\pi\)
−0.764445 + 0.644689i \(0.776987\pi\)
\(228\) −152302. −0.194030
\(229\) −220319. 381603.i −0.277627 0.480865i 0.693167 0.720777i \(-0.256215\pi\)
−0.970795 + 0.239912i \(0.922881\pi\)
\(230\) −85999.2 −0.107195
\(231\) 116110. 201108.i 0.143165 0.247970i
\(232\) 1.90037e6 2.31802
\(233\) −1.38173e6 −1.66738 −0.833689 0.552234i \(-0.813775\pi\)
−0.833689 + 0.552234i \(0.813775\pi\)
\(234\) −1.01247e6 + 1.75365e6i −1.20877 + 2.09364i
\(235\) 13714.4 + 23754.0i 0.0161997 + 0.0280587i
\(236\) 4.03969e6 4.72137
\(237\) −66241.5 + 114734.i −0.0766054 + 0.132685i
\(238\) 950.642 1646.56i 0.00108786 0.00188424i
\(239\) 318125. 551009.i 0.360249 0.623970i −0.627753 0.778413i \(-0.716025\pi\)
0.988002 + 0.154443i \(0.0493584\pi\)
\(240\) −26330.5 45605.8i −0.0295074 0.0511083i
\(241\) 357584. + 619353.i 0.396584 + 0.686903i 0.993302 0.115548i \(-0.0368623\pi\)
−0.596718 + 0.802451i \(0.703529\pi\)
\(242\) −158743. + 274950.i −0.174243 + 0.301798i
\(243\) −317252. + 549497.i −0.344658 + 0.596966i
\(244\) 2.39478e6 4.14788e6i 2.57508 4.46017i
\(245\) 28897.0 0.0307565
\(246\) −299946. 519521.i −0.316013 0.547350i
\(247\) 167364. 289883.i 0.174550 0.302329i
\(248\) −3.60328e6 −3.72022
\(249\) 14690.8 0.0150157
\(250\) −101907. + 176508.i −0.103122 + 0.178613i
\(251\) −1.47851e6 −1.48129 −0.740645 0.671896i \(-0.765480\pi\)
−0.740645 + 0.671896i \(0.765480\pi\)
\(252\) −1.72633e6 2.99009e6i −1.71246 2.96608i
\(253\) 959109. 0.942034
\(254\) 1.27049e6 + 2.20056e6i 1.23563 + 2.14017i
\(255\) 5.94295 + 10.2935i 5.72337e−6 + 9.91317e-6i
\(256\) −3.27579e6 5.67384e6i −3.12404 5.41100i
\(257\) 411533. 712796.i 0.388662 0.673182i −0.603608 0.797281i \(-0.706271\pi\)
0.992270 + 0.124099i \(0.0396042\pi\)
\(258\) −114697. −0.107276
\(259\) −819883. + 1.08569e6i −0.759455 + 1.00568i
\(260\) 215864. 0.198037
\(261\) −318741. + 552075.i −0.289625 + 0.501646i
\(262\) 671108. + 1.16239e6i 0.604004 + 1.04616i
\(263\) 175931. + 304721.i 0.156839 + 0.271652i 0.933727 0.357986i \(-0.116536\pi\)
−0.776888 + 0.629638i \(0.783203\pi\)
\(264\) 482546. + 835794.i 0.426117 + 0.738056i
\(265\) 735.036 0.000642975
\(266\) 383786. + 664737.i 0.332572 + 0.576031i
\(267\) −159977. −0.137334
\(268\) −1.01943e6 + 1.76570e6i −0.867001 + 1.50169i
\(269\) 324500. 0.273423 0.136711 0.990611i \(-0.456347\pi\)
0.136711 + 0.990611i \(0.456347\pi\)
\(270\) 59998.4 0.0500876
\(271\) 66098.2 114485.i 0.0546722 0.0946950i −0.837394 0.546600i \(-0.815922\pi\)
0.892066 + 0.451905i \(0.149255\pi\)
\(272\) 2404.26 + 4164.30i 0.00197042 + 0.00341287i
\(273\) −507481. −0.412110
\(274\) −861382. + 1.49196e6i −0.693138 + 1.20055i
\(275\) 567481. 982905.i 0.452501 0.783754i
\(276\) −476841. + 825913.i −0.376791 + 0.652622i
\(277\) 265983. + 460697.i 0.208284 + 0.360758i 0.951174 0.308655i \(-0.0998789\pi\)
−0.742890 + 0.669413i \(0.766546\pi\)
\(278\) −169595. 293747.i −0.131613 0.227961i
\(279\) 604362. 1.04679e6i 0.464822 0.805096i
\(280\) −162141. + 280836.i −0.123594 + 0.214071i
\(281\) −682632. + 1.18235e6i −0.515728 + 0.893267i 0.484105 + 0.875010i \(0.339145\pi\)
−0.999833 + 0.0182572i \(0.994188\pi\)
\(282\) 409075. 0.306323
\(283\) −484759. 839627.i −0.359799 0.623190i 0.628128 0.778110i \(-0.283821\pi\)
−0.987927 + 0.154920i \(0.950488\pi\)
\(284\) −961034. + 1.66456e6i −0.707038 + 1.22463i
\(285\) −4798.49 −0.00349939
\(286\) −3.23773e6 −2.34059
\(287\) −1.12401e6 + 1.94684e6i −0.805500 + 1.39517i
\(288\) 6.79484e6 4.82723
\(289\) 709928. + 1.22963e6i 0.500000 + 0.866025i
\(290\) 91395.1 0.0638158
\(291\) −221137. 383021.i −0.153084 0.265149i
\(292\) 2.87950e6 + 4.98744e6i 1.97633 + 3.42311i
\(293\) −725040. 1.25581e6i −0.493393 0.854582i 0.506578 0.862194i \(-0.330910\pi\)
−0.999971 + 0.00761229i \(0.997577\pi\)
\(294\) 215485. 373232.i 0.145395 0.251831i
\(295\) 127276. 0.0851515
\(296\) −2.20389e6 5.20693e6i −1.46204 3.45424i
\(297\) −669134. −0.440171
\(298\) 482042. 834921.i 0.314445 0.544634i
\(299\) −1.04800e6 1.81518e6i −0.677925 1.17420i
\(300\) 564269. + 977343.i 0.361979 + 0.626966i
\(301\) 214907. + 372229.i 0.136720 + 0.236807i
\(302\) 1.65217e6 1.04241
\(303\) 232535. + 402762.i 0.145506 + 0.252024i
\(304\) −1.94126e6 −1.20476
\(305\) 75451.0 130685.i 0.0464425 0.0804407i
\(306\) −2650.62 −0.00161824
\(307\) 2.10401e6 1.27410 0.637049 0.770823i \(-0.280155\pi\)
0.637049 + 0.770823i \(0.280155\pi\)
\(308\) 2.76027e6 4.78093e6i 1.65796 2.87168i
\(309\) −315132. 545824.i −0.187757 0.325204i
\(310\) −173294. −0.102418
\(311\) 600569. 1.04022e6i 0.352096 0.609849i −0.634520 0.772906i \(-0.718802\pi\)
0.986617 + 0.163057i \(0.0521356\pi\)
\(312\) 1.05453e6 1.82651e6i 0.613301 1.06227i
\(313\) −303047. + 524892.i −0.174843 + 0.302837i −0.940107 0.340879i \(-0.889275\pi\)
0.765264 + 0.643717i \(0.222609\pi\)
\(314\) 3.22755e6 + 5.59028e6i 1.84735 + 3.19970i
\(315\) −54390.4 94206.9i −0.0308849 0.0534942i
\(316\) −1.57476e6 + 2.72756e6i −0.887148 + 1.53659i
\(317\) −24603.8 + 42615.1i −0.0137517 + 0.0238186i −0.872819 0.488043i \(-0.837711\pi\)
0.859068 + 0.511862i \(0.171044\pi\)
\(318\) 5481.19 9493.69i 0.00303953 0.00526462i
\(319\) −1.01929e6 −0.560815
\(320\) −271199. 469731.i −0.148052 0.256433i
\(321\) −230293. + 398879.i −0.124744 + 0.216062i
\(322\) 4.80638e6 2.58332
\(323\) 438.154 0.000233679
\(324\) −2.23499e6 + 3.87111e6i −1.18280 + 2.04867i
\(325\) −2.48029e6 −1.30255
\(326\) −576682. 998843.i −0.300533 0.520539i
\(327\) 268651. 0.138937
\(328\) −4.67133e6 8.09097e6i −2.39748 4.15256i
\(329\) −766479. 1.32758e6i −0.390400 0.676193i
\(330\) 23207.2 + 40196.1i 0.0117311 + 0.0203188i
\(331\) 287884. 498631.i 0.144427 0.250155i −0.784732 0.619835i \(-0.787199\pi\)
0.929159 + 0.369680i \(0.120533\pi\)
\(332\) 349244. 0.173893
\(333\) 1.88231e6 + 233086.i 0.930210 + 0.115187i
\(334\) −5.56174e6 −2.72800
\(335\) −32118.5 + 55630.9i −0.0156366 + 0.0270835i
\(336\) 1.47157e6 + 2.54884e6i 0.711106 + 1.23167i
\(337\) −1.33374e6 2.31010e6i −0.639728 1.10804i −0.985492 0.169720i \(-0.945714\pi\)
0.345765 0.938321i \(-0.387620\pi\)
\(338\) 1.46400e6 + 2.53573e6i 0.697027 + 1.20729i
\(339\) −509581. −0.240832
\(340\) 141.282 + 244.707i 6.62809e−5 + 0.000114802i
\(341\) 1.93266e6 0.900057
\(342\) 535044. 926723.i 0.247357 0.428435i
\(343\) 1.13087e6 0.519013
\(344\) −1.78628e6 −0.813867
\(345\) −15023.6 + 26021.6i −0.00679556 + 0.0117702i
\(346\) 1.45512e6 + 2.52034e6i 0.653443 + 1.13180i
\(347\) −1.50599e6 −0.671427 −0.335713 0.941964i \(-0.608977\pi\)
−0.335713 + 0.941964i \(0.608977\pi\)
\(348\) 506759. 877733.i 0.224313 0.388521i
\(349\) 1.05231e6 1.82265e6i 0.462466 0.801015i −0.536617 0.843826i \(-0.680298\pi\)
0.999083 + 0.0428113i \(0.0136314\pi\)
\(350\) 2.84381e6 4.92562e6i 1.24088 2.14927i
\(351\) 731147. + 1.26638e6i 0.316765 + 0.548653i
\(352\) 5.43222e6 + 9.40889e6i 2.33680 + 4.04745i
\(353\) 861986. 1.49300e6i 0.368183 0.637711i −0.621099 0.783732i \(-0.713313\pi\)
0.989281 + 0.146021i \(0.0466468\pi\)
\(354\) 949103. 1.64389e6i 0.402536 0.697213i
\(355\) −30278.8 + 52444.3i −0.0127517 + 0.0220865i
\(356\) −3.80312e6 −1.59043
\(357\) −332.143 575.289i −0.000137929 0.000238900i
\(358\) 2.70068e6 4.67771e6i 1.11369 1.92897i
\(359\) −1.15223e6 −0.471847 −0.235924 0.971772i \(-0.575812\pi\)
−0.235924 + 0.971772i \(0.575812\pi\)
\(360\) 452087. 0.183851
\(361\) 1.14961e6 1.99117e6i 0.464281 0.804158i
\(362\) 4.21634e6 1.69108
\(363\) 55462.8 + 96064.3i 0.0220920 + 0.0382645i
\(364\) −1.20643e7 −4.77254
\(365\) 90722.8 + 157137.i 0.0356438 + 0.0617369i
\(366\) −1.12528e6 1.94904e6i −0.439094 0.760534i
\(367\) 590037. + 1.02197e6i 0.228673 + 0.396072i 0.957415 0.288715i \(-0.0932282\pi\)
−0.728742 + 0.684788i \(0.759895\pi\)
\(368\) −6.07788e6 + 1.05272e7i −2.33955 + 4.05222i
\(369\) 3.13401e6 1.19821
\(370\) −105992. 250419.i −0.0402504 0.0950960i
\(371\) −41080.1 −0.0154952
\(372\) −960863. + 1.66426e6i −0.360001 + 0.623541i
\(373\) 352006. + 609692.i 0.131002 + 0.226902i 0.924063 0.382240i \(-0.124847\pi\)
−0.793061 + 0.609142i \(0.791514\pi\)
\(374\) −2119.07 3670.34i −0.000783369 0.00135684i
\(375\) 35605.0 + 61669.6i 0.0130747 + 0.0226461i
\(376\) 6.37089e6 2.32397
\(377\) 1.11375e6 + 1.92907e6i 0.403585 + 0.699029i
\(378\) −3.35322e6 −1.20707
\(379\) −1.39302e6 + 2.41278e6i −0.498150 + 0.862820i −0.999998 0.00213540i \(-0.999320\pi\)
0.501848 + 0.864956i \(0.332654\pi\)
\(380\) −114074. −0.0405255
\(381\) 887790. 0.313327
\(382\) −1.71484e6 + 2.97019e6i −0.601263 + 1.04142i
\(383\) 1.55836e6 + 2.69916e6i 0.542839 + 0.940224i 0.998740 + 0.0501935i \(0.0159838\pi\)
−0.455901 + 0.890031i \(0.650683\pi\)
\(384\) −4.36352e6 −1.51011
\(385\) 86966.3 150630.i 0.0299019 0.0517916i
\(386\) −1.46566e6 + 2.53861e6i −0.500687 + 0.867215i
\(387\) 299605. 518932.i 0.101689 0.176130i
\(388\) −5.25709e6 9.10554e6i −1.77283 3.07062i
\(389\) −771047. 1.33549e6i −0.258349 0.447473i 0.707451 0.706763i \(-0.249845\pi\)
−0.965800 + 0.259289i \(0.916512\pi\)
\(390\) 50716.0 87842.7i 0.0168843 0.0292445i
\(391\) 1371.81 2376.05i 0.000453788 0.000785984i
\(392\) 3.35595e6 5.81267e6i 1.10306 1.91056i
\(393\) 468955. 0.153161
\(394\) −1.26848e6 2.19707e6i −0.411665 0.713024i
\(395\) −49615.0 + 85935.7i −0.0160000 + 0.0277128i
\(396\) −7.69629e6 −2.46629
\(397\) −957673. −0.304959 −0.152479 0.988307i \(-0.548726\pi\)
−0.152479 + 0.988307i \(0.548726\pi\)
\(398\) 2.45008e6 4.24367e6i 0.775306 1.34287i
\(399\) 268181. 0.0843326
\(400\) 7.19226e6 + 1.24574e7i 2.24758 + 3.89292i
\(401\) 979169. 0.304086 0.152043 0.988374i \(-0.451415\pi\)
0.152043 + 0.988374i \(0.451415\pi\)
\(402\) 479017. + 829683.i 0.147838 + 0.256063i
\(403\) −2.11178e6 3.65770e6i −0.647717 1.12188i
\(404\) 5.52804e6 + 9.57485e6i 1.68507 + 2.91863i
\(405\) −70416.4 + 121965.i −0.0213322 + 0.0369485i
\(406\) −5.10794e6 −1.53791
\(407\) 1.18208e6 + 2.79280e6i 0.353722 + 0.835707i
\(408\) 2760.74 0.000821060
\(409\) 2.00983e6 3.48112e6i 0.594087 1.02899i −0.399588 0.916695i \(-0.630847\pi\)
0.993675 0.112294i \(-0.0358198\pi\)
\(410\) −224660. 389122.i −0.0660033 0.114321i
\(411\) 300957. + 521272.i 0.0878819 + 0.152216i
\(412\) −7.49161e6 1.29759e7i −2.17436 3.76611i
\(413\) −7.11329e6 −2.05209
\(414\) −3.35033e6 5.80294e6i −0.960698 1.66398i
\(415\) 11003.4 0.00313623
\(416\) 1.18713e7 2.05617e7i 3.36330 5.82541i
\(417\) −118509. −0.0333741
\(418\) 1.71099e6 0.478969
\(419\) −965336. + 1.67201e6i −0.268623 + 0.465269i −0.968506 0.248988i \(-0.919902\pi\)
0.699883 + 0.714257i \(0.253235\pi\)
\(420\) 86474.1 + 149778.i 0.0239201 + 0.0414308i
\(421\) 4.99175e6 1.37261 0.686305 0.727314i \(-0.259232\pi\)
0.686305 + 0.727314i \(0.259232\pi\)
\(422\) 2.93857e6 5.08975e6i 0.803258 1.39128i
\(423\) −1.06856e6 + 1.85080e6i −0.290368 + 0.502932i
\(424\) 85363.5 147854.i 0.0230599 0.0399409i
\(425\) −1623.33 2811.70i −0.000435949 0.000755086i
\(426\) 451579. + 782158.i 0.120562 + 0.208819i
\(427\) −4.21685e6 + 7.30379e6i −1.11923 + 1.93856i
\(428\) −5.47475e6 + 9.48255e6i −1.44462 + 2.50216i
\(429\) −565612. + 979669.i −0.148380 + 0.257002i
\(430\) −85908.2 −0.0224060
\(431\) 2.43420e6 + 4.21615e6i 0.631194 + 1.09326i 0.987308 + 0.158817i \(0.0507680\pi\)
−0.356115 + 0.934442i \(0.615899\pi\)
\(432\) 4.24030e6 7.34442e6i 1.09317 1.89343i
\(433\) −941882. −0.241422 −0.120711 0.992688i \(-0.538517\pi\)
−0.120711 + 0.992688i \(0.538517\pi\)
\(434\) 9.68513e6 2.46821
\(435\) 15966.2 27654.2i 0.00404555 0.00700710i
\(436\) 6.38663e6 1.60900
\(437\) 553818. + 959241.i 0.138728 + 0.240284i
\(438\) 2.70609e6 0.673995
\(439\) 1.77079e6 + 3.06710e6i 0.438537 + 0.759568i 0.997577 0.0695727i \(-0.0221636\pi\)
−0.559040 + 0.829141i \(0.688830\pi\)
\(440\) 361427. + 626010.i 0.0889998 + 0.154152i
\(441\) 1.12576e6 + 1.94987e6i 0.275644 + 0.477429i
\(442\) −4630.92 + 8020.99i −0.00112749 + 0.00195287i
\(443\) −4.67617e6 −1.13209 −0.566046 0.824374i \(-0.691527\pi\)
−0.566046 + 0.824374i \(0.691527\pi\)
\(444\) −2.99265e6 370578.i −0.720441 0.0892118i
\(445\) −119823. −0.0286840
\(446\) 615796. 1.06659e6i 0.146588 0.253899i
\(447\) −168420. 291711.i −0.0398680 0.0690533i
\(448\) 1.51569e7 + 2.62526e7i 3.56793 + 6.17983i
\(449\) −643194. 1.11404e6i −0.150566 0.260787i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(450\) −7.92922e6 −1.84586
\(451\) 2.50552e6 + 4.33969e6i 0.580039 + 1.00466i
\(452\) −1.21142e7 −2.78901
\(453\) 288625. 499912.i 0.0660827 0.114459i
\(454\) 3.05435e6 0.695472
\(455\) −380104. −0.0860744
\(456\) −557273. + 965224.i −0.125503 + 0.217378i
\(457\) −1.28737e6 2.22979e6i −0.288346 0.499430i 0.685069 0.728478i \(-0.259772\pi\)
−0.973415 + 0.229048i \(0.926439\pi\)
\(458\) −4.92220e6 −1.09647
\(459\) −957.062 + 1657.68i −0.000212035 + 0.000367256i
\(460\) −357154. + 618610.i −0.0786976 + 0.136308i
\(461\) −3.57807e6 + 6.19741e6i −0.784146 + 1.35818i 0.145362 + 0.989379i \(0.453565\pi\)
−0.929508 + 0.368803i \(0.879768\pi\)
\(462\) −1.29702e6 2.24650e6i −0.282710 0.489668i
\(463\) −3.18060e6 5.50896e6i −0.689535 1.19431i −0.971988 0.235029i \(-0.924481\pi\)
0.282453 0.959281i \(-0.408852\pi\)
\(464\) 6.45923e6 1.11877e7i 1.39279 2.41238i
\(465\) −30273.4 + 52435.0i −0.00649274 + 0.0112458i
\(466\) −7.71742e6 + 1.33670e7i −1.64629 + 2.85146i
\(467\) −1.38751e6 −0.294405 −0.147202 0.989106i \(-0.547027\pi\)
−0.147202 + 0.989106i \(0.547027\pi\)
\(468\) 8.40956e6 + 1.45658e7i 1.77484 + 3.07411i
\(469\) 1.79506e6 3.10913e6i 0.376831 0.652691i
\(470\) 306397. 0.0639794
\(471\) 2.25533e6 0.468445
\(472\) 1.47812e7 2.56019e7i 3.05391 5.28952i
\(473\) 958094. 0.196904
\(474\) 739961. + 1.28165e6i 0.151273 + 0.262013i
\(475\) 1.31072e6 0.266549
\(476\) −7896.03 13676.3i −0.00159732 0.00276663i
\(477\) 28635.3 + 49597.8i 0.00576243 + 0.00998082i
\(478\) −3.55366e6 6.15512e6i −0.711387 1.23216i
\(479\) −457553. + 792505.i −0.0911177 + 0.157820i −0.907982 0.419010i \(-0.862377\pi\)
0.816864 + 0.576830i \(0.195711\pi\)
\(480\) −340363. −0.0674278
\(481\) 3.99394e6 5.28881e6i 0.787117 1.04231i
\(482\) 7.98887e6 1.56628
\(483\) 839645. 1.45431e6i 0.163768 0.283654i
\(484\) 1.31851e6 + 2.28373e6i 0.255842 + 0.443131i
\(485\) −165632. 286883.i −0.0319735 0.0553797i
\(486\) 3.54391e6 + 6.13823e6i 0.680600 + 1.17883i
\(487\) 7.47578e6 1.42835 0.714174 0.699969i \(-0.246803\pi\)
0.714174 + 0.699969i \(0.246803\pi\)
\(488\) −1.75250e7 3.03542e7i −3.33126 5.76991i
\(489\) −402972. −0.0762083
\(490\) 161399. 279551.i 0.0303676 0.0525982i
\(491\) −6.03053e6 −1.12889 −0.564445 0.825471i \(-0.690910\pi\)
−0.564445 + 0.825471i \(0.690910\pi\)
\(492\) −4.98269e6 −0.928007
\(493\) −1457.89 + 2525.13i −0.000270151 + 0.000467915i
\(494\) −1.86956e6 3.23818e6i −0.344685 0.597012i
\(495\) −242483. −0.0444803
\(496\) −1.22473e7 + 2.12129e7i −2.23530 + 3.87165i
\(497\) 1.69224e6 2.93104e6i 0.307305 0.532268i
\(498\) 82052.8 142120.i 0.0148259 0.0256791i
\(499\) 405296. + 701993.i 0.0728653 + 0.126206i 0.900156 0.435568i \(-0.143452\pi\)
−0.827291 + 0.561774i \(0.810119\pi\)
\(500\) 846436. + 1.46607e6i 0.151415 + 0.262259i
\(501\) −971603. + 1.68287e6i −0.172940 + 0.299540i
\(502\) −8.25796e6 + 1.43032e7i −1.46256 + 2.53323i
\(503\) 1.39895e6 2.42306e6i 0.246538 0.427016i −0.716025 0.698075i \(-0.754040\pi\)
0.962563 + 0.271058i \(0.0873737\pi\)
\(504\) −2.52665e7 −4.43067
\(505\) 174169. + 301669.i 0.0303908 + 0.0526384i
\(506\) 5.35693e6 9.27848e6i 0.930122 1.61102i
\(507\) 1.02301e6 0.176750
\(508\) 2.11054e7 3.62856
\(509\) −838785. + 1.45282e6i −0.143501 + 0.248552i −0.928813 0.370549i \(-0.879169\pi\)
0.785311 + 0.619101i \(0.212503\pi\)
\(510\) 132.773 2.26040e−5
\(511\) −5.07037e6 8.78214e6i −0.858988 1.48781i
\(512\) −3.74087e7 −6.30664
\(513\) −386378. 669226.i −0.0648215 0.112274i
\(514\) −4.59709e6 7.96239e6i −0.767494 1.32934i
\(515\) −236034. 408823.i −0.0392154 0.0679230i
\(516\) −476336. + 825038.i −0.0787570 + 0.136411i
\(517\) −3.41711e6 −0.562253
\(518\) 5.92376e6 + 1.39955e7i 0.970003 + 2.29174i
\(519\) 1.01680e6 0.165698
\(520\) 789847. 1.36805e6i 0.128096 0.221868i
\(521\) 3.49607e6 + 6.05537e6i 0.564269 + 0.977342i 0.997117 + 0.0758754i \(0.0241751\pi\)
−0.432849 + 0.901467i \(0.642492\pi\)
\(522\) 3.56054e6 + 6.16704e6i 0.571926 + 0.990604i
\(523\) −5.60809e6 9.71349e6i −0.896521 1.55282i −0.831911 0.554909i \(-0.812753\pi\)
−0.0646101 0.997911i \(-0.520580\pi\)
\(524\) 1.11484e7 1.77372
\(525\) −993594. 1.72095e6i −0.157330 0.272503i
\(526\) 3.93052e6 0.619421
\(527\) 2764.29 4787.88i 0.000433567 0.000750960i
\(528\) 6.56056e6 1.02413
\(529\) 499440. 0.0775969
\(530\) 4105.41 7110.79i 0.000634844 0.00109958i
\(531\) 4.95839e6 + 8.58818e6i 0.763140 + 1.32180i
\(532\) 6.37545e6 0.976634
\(533\) 5.47546e6 9.48377e6i 0.834838 1.44598i
\(534\) −893521. + 1.54762e6i −0.135597 + 0.234862i
\(535\) −172490. + 298761.i −0.0260543 + 0.0451273i
\(536\) 7.46017e6 + 1.29214e7i 1.12160 + 1.94266i
\(537\) −943585. 1.63434e6i −0.141203 0.244572i
\(538\) 1.81244e6 3.13923e6i 0.269965 0.467593i
\(539\) −1.80000e6 + 3.11770e6i −0.266871 + 0.462234i
\(540\) 249173. 431580.i 0.0367719 0.0636909i
\(541\) −3.70126e6 −0.543697 −0.271848 0.962340i \(-0.587635\pi\)
−0.271848 + 0.962340i \(0.587635\pi\)
\(542\) −738359. 1.27888e6i −0.107962 0.186995i
\(543\) 736570. 1.27578e6i 0.107205 0.185684i
\(544\) 31078.8 0.00450264
\(545\) 201220. 0.0290188
\(546\) −2.83445e6 + 4.90941e6i −0.406899 + 0.704770i
\(547\) −6.62509e6 −0.946724 −0.473362 0.880868i \(-0.656960\pi\)
−0.473362 + 0.880868i \(0.656960\pi\)
\(548\) 7.15463e6 + 1.23922e7i 1.01774 + 1.76277i
\(549\) 1.17576e7 1.66490
\(550\) −6.33912e6 1.09797e7i −0.893557 1.54769i
\(551\) −588567. 1.01943e6i −0.0825879 0.143046i
\(552\) 3.48952e6 + 6.04403e6i 0.487437 + 0.844265i
\(553\) 2.77291e6 4.80282e6i 0.385588 0.667857i
\(554\) 5.94241e6 0.822599
\(555\) −94287.7 11675.6i −0.0129934 0.00160896i
\(556\) −2.81730e6 −0.386497
\(557\) 6.65904e6 1.15338e7i 0.909439 1.57520i 0.0945948 0.995516i \(-0.469844\pi\)
0.814845 0.579679i \(-0.196822\pi\)
\(558\) −6.75111e6 1.16933e7i −0.917889 1.58983i
\(559\) −1.04689e6 1.81326e6i −0.141700 0.245432i
\(560\) 1.10221e6 + 1.90909e6i 0.148523 + 0.257250i
\(561\) −1480.76 −0.000198645
\(562\) 7.62543e6 + 1.32076e7i 1.01841 + 1.76394i
\(563\) −1.20161e7 −1.59769 −0.798845 0.601536i \(-0.794556\pi\)
−0.798845 + 0.601536i \(0.794556\pi\)
\(564\) 1.69889e6 2.94256e6i 0.224888 0.389517i
\(565\) −381677. −0.0503008
\(566\) −1.08301e7 −1.42100
\(567\) 3.93547e6 6.81644e6i 0.514090 0.890431i
\(568\) 7.03285e6 + 1.21813e7i 0.914662 + 1.58424i
\(569\) −1.19419e6 −0.154629 −0.0773146 0.997007i \(-0.524635\pi\)
−0.0773146 + 0.997007i \(0.524635\pi\)
\(570\) −26801.1 + 46420.9i −0.00345514 + 0.00598448i
\(571\) −134175. + 232397.i −0.0172219 + 0.0298291i −0.874508 0.485011i \(-0.838815\pi\)
0.857286 + 0.514840i \(0.172149\pi\)
\(572\) −1.34463e7 + 2.32896e7i −1.71835 + 2.97627i
\(573\) 599144. + 1.03775e6i 0.0762333 + 0.132040i
\(574\) 1.25559e7 + 2.17475e7i 1.59063 + 2.75505i
\(575\) 4.10373e6 7.10787e6i 0.517617 0.896540i
\(576\) 2.11306e7 3.65992e7i 2.65372 4.59638i
\(577\) −3.64014e6 + 6.30491e6i −0.455175 + 0.788386i −0.998698 0.0510078i \(-0.983757\pi\)
0.543523 + 0.839394i \(0.317090\pi\)
\(578\) 1.58607e7 1.97471
\(579\) 512086. + 886958.i 0.0634814 + 0.109953i
\(580\) 379563. 657423.i 0.0468505 0.0811475i
\(581\) −614965. −0.0755806
\(582\) −4.94049e6 −0.604592
\(583\) −45785.7 + 79303.2i −0.00557903 + 0.00966317i
\(584\) 4.21444e7 5.11337
\(585\) 264955. + 458916.i 0.0320098 + 0.0554426i
\(586\) −1.61983e7 −1.94862
\(587\) 2.61325e6 + 4.52628e6i 0.313029 + 0.542183i 0.979017 0.203780i \(-0.0653228\pi\)
−0.665987 + 0.745963i \(0.731990\pi\)
\(588\) −1.78982e6 3.10006e6i −0.213484 0.369766i
\(589\) 1.11598e6 + 1.93293e6i 0.132546 + 0.229577i
\(590\) 710879. 1.23128e6i 0.0840748 0.145622i
\(591\) −886385. −0.104389
\(592\) −3.81447e7 4.72344e6i −4.47332 0.553929i
\(593\) −1.44351e7 −1.68571 −0.842853 0.538143i \(-0.819126\pi\)
−0.842853 + 0.538143i \(0.819126\pi\)
\(594\) −3.73733e6 + 6.47324e6i −0.434605 + 0.752758i
\(595\) −248.776 430.892i −2.88082e−5 4.98972e-5i
\(596\) −4.00383e6 6.93485e6i −0.461701 0.799689i
\(597\) −856030. 1.48269e6i −0.0982999 0.170260i
\(598\) −2.34136e7 −2.67741
\(599\) 8.14606e6 + 1.41094e7i 0.927642 + 1.60672i 0.787255 + 0.616627i \(0.211501\pi\)
0.140387 + 0.990097i \(0.455165\pi\)
\(600\) 8.25865e6 0.936550
\(601\) 3.92446e6 6.79737e6i 0.443194 0.767635i −0.554730 0.832030i \(-0.687179\pi\)
0.997924 + 0.0643953i \(0.0205118\pi\)
\(602\) 4.80129e6 0.539966
\(603\) −5.00505e6 −0.560551
\(604\) 6.86146e6 1.18844e7i 0.765287 1.32552i
\(605\) 41541.7 + 71952.3i 0.00461419 + 0.00799201i
\(606\) 5.19513e6 0.574665
\(607\) −633076. + 1.09652e6i −0.0697404 + 0.120794i −0.898787 0.438386i \(-0.855550\pi\)
0.829047 + 0.559180i \(0.188884\pi\)
\(608\) −6.27346e6 + 1.08659e7i −0.688253 + 1.19209i
\(609\) −892327. + 1.54556e6i −0.0974947 + 0.168866i
\(610\) −842836. 1.45983e6i −0.0917104 0.158847i
\(611\) 3.73379e6 + 6.46712e6i 0.404620 + 0.700822i
\(612\) −11008.0 + 19066.4i −0.00118804 + 0.00205774i
\(613\) −1.26207e6 + 2.18597e6i −0.135654 + 0.234960i −0.925847 0.377898i \(-0.876647\pi\)
0.790193 + 0.612858i \(0.209980\pi\)
\(614\) 1.17516e7 2.03544e7i 1.25799 2.17890i
\(615\) −156987. −0.0167369
\(616\) −2.01997e7 3.49868e7i −2.14483 3.71495i
\(617\) −2.10647e6 + 3.64852e6i −0.222763 + 0.385837i −0.955646 0.294518i \(-0.904841\pi\)
0.732883 + 0.680355i \(0.238174\pi\)
\(618\) −7.04044e6 −0.741530
\(619\) −1.54773e7 −1.62356 −0.811781 0.583961i \(-0.801502\pi\)
−0.811781 + 0.583961i \(0.801502\pi\)
\(620\) −719687. + 1.24654e6i −0.0751908 + 0.130234i
\(621\) −4.83883e6 −0.503514
\(622\) −6.70874e6 1.16199e7i −0.695288 1.20427i
\(623\) 6.69672e6 0.691261
\(624\) −7.16857e6 1.24163e7i −0.737006 1.27653i
\(625\) −4.84279e6 8.38796e6i −0.495902 0.858927i
\(626\) 3.38523e6 + 5.86339e6i 0.345265 + 0.598016i
\(627\) 298900. 517710.i 0.0303639 0.0525918i
\(628\) 5.36160e7 5.42494
\(629\) 8609.48 + 1066.11i 0.000867662 + 0.000107442i
\(630\) −1.21515e6 −0.121977
\(631\) 6.45032e6 1.11723e7i 0.644923 1.11704i −0.339397 0.940643i \(-0.610223\pi\)
0.984319 0.176395i \(-0.0564437\pi\)
\(632\) 1.15241e7 + 1.99603e7i 1.14766 + 1.98781i
\(633\) −1.02670e6 1.77830e6i −0.101844 0.176399i
\(634\) 274841. + 476038.i 0.0271555 + 0.0470347i
\(635\) 664956. 0.0654423
\(636\) −45526.7 78854.5i −0.00446296 0.00773007i
\(637\) 7.86730e6 0.768205
\(638\) −5.69304e6 + 9.86064e6i −0.553723 + 0.959077i
\(639\) −4.71836e6 −0.457129
\(640\) −3.26828e6 −0.315406
\(641\) −7.46246e6 + 1.29254e7i −0.717360 + 1.24250i 0.244682 + 0.969603i \(0.421316\pi\)
−0.962042 + 0.272901i \(0.912017\pi\)
\(642\) 2.57252e6 + 4.45574e6i 0.246332 + 0.426660i
\(643\) 9.16285e6 0.873983 0.436992 0.899466i \(-0.356044\pi\)
0.436992 + 0.899466i \(0.356044\pi\)
\(644\) 1.99609e7 3.45732e7i 1.89655 3.28492i
\(645\) −15007.7 + 25994.0i −0.00142041 + 0.00246022i
\(646\) 2447.23 4238.73i 0.000230724 0.000399626i
\(647\) 9.68563e6 + 1.67760e7i 0.909635 + 1.57553i 0.814571 + 0.580064i \(0.196972\pi\)
0.0950643 + 0.995471i \(0.469694\pi\)
\(648\) 1.63556e7 + 2.83288e7i 1.53013 + 2.65027i
\(649\) −7.92810e6 + 1.37319e7i −0.738852 + 1.27973i
\(650\) −1.38532e7 + 2.39945e7i −1.28608 + 2.22755i
\(651\) 1.69194e6 2.93052e6i 0.156470 0.271014i
\(652\) −9.57983e6 −0.882549
\(653\) −5.00319e6 8.66578e6i −0.459160 0.795289i 0.539757 0.841821i \(-0.318516\pi\)
−0.998917 + 0.0465323i \(0.985183\pi\)
\(654\) 1.50050e6 2.59895e6i 0.137180 0.237603i
\(655\) 351248. 0.0319897
\(656\) −6.35101e7 −5.76213
\(657\) −7.06870e6 + 1.22433e7i −0.638890 + 1.10659i
\(658\) −1.71241e7 −1.54185
\(659\) −6.78824e6 1.17576e7i −0.608897 1.05464i −0.991423 0.130695i \(-0.958279\pi\)
0.382526 0.923945i \(-0.375054\pi\)
\(660\) 385518. 0.0344497
\(661\) 9.12568e6 + 1.58061e7i 0.812384 + 1.40709i 0.911191 + 0.411984i \(0.135164\pi\)
−0.0988070 + 0.995107i \(0.531503\pi\)
\(662\) −3.21585e6 5.57002e6i −0.285201 0.493983i
\(663\) 1617.99 + 2802.44i 0.000142953 + 0.000247601i
\(664\) 1.27788e6 2.21336e6i 0.112479 0.194819i
\(665\) 200868. 0.0176139
\(666\) 1.27682e7 1.69077e7i 1.11543 1.47707i
\(667\) −7.37096e6 −0.641519
\(668\) −2.30979e7 + 4.00067e7i −2.00277 + 3.46890i
\(669\) −215152. 372654.i −0.0185857 0.0321914i
\(670\) 358785. + 621433.i 0.0308778 + 0.0534820i
\(671\) 9.39975e6 + 1.62808e7i 0.805954 + 1.39595i
\(672\) 1.90224e7 1.62496
\(673\) 1.91614e6 + 3.31885e6i 0.163076 + 0.282455i 0.935970 0.352079i \(-0.114525\pi\)
−0.772895 + 0.634534i \(0.781192\pi\)
\(674\) −2.97974e7 −2.52655
\(675\) −2.86301e6 + 4.95889e6i −0.241860 + 0.418914i
\(676\) 2.43200e7 2.04690
\(677\) −1.26925e7 −1.06433 −0.532164 0.846641i \(-0.678621\pi\)
−0.532164 + 0.846641i \(0.678621\pi\)
\(678\) −2.84617e6 + 4.92972e6i −0.237786 + 0.411858i
\(679\) 9.25694e6 + 1.60335e7i 0.770536 + 1.33461i
\(680\) 2067.80 0.000171489
\(681\) 533578. 924183.i 0.0440890 0.0763643i
\(682\) 1.07945e7 1.86967e7i 0.888675 1.53923i
\(683\) 9.60314e6 1.66331e7i 0.787701 1.36434i −0.139671 0.990198i \(-0.544605\pi\)
0.927372 0.374140i \(-0.122062\pi\)
\(684\) −4.44407e6 7.69735e6i −0.363195 0.629073i
\(685\) 225417. + 390434.i 0.0183552 + 0.0317922i
\(686\) 6.31629e6 1.09401e7i 0.512450 0.887590i
\(687\) −859879. + 1.48935e6i −0.0695097 + 0.120394i
\(688\) −6.07145e6 + 1.05161e7i −0.489014 + 0.846997i
\(689\) 200116. 0.0160596
\(690\) 167823. + 290678.i 0.0134192 + 0.0232428i
\(691\) 9.21884e6 1.59675e7i 0.734482 1.27216i −0.220469 0.975394i \(-0.570759\pi\)
0.954950 0.296766i \(-0.0959080\pi\)
\(692\) 2.41724e7 1.91891
\(693\) 1.35520e7 1.07194
\(694\) −8.41144e6 + 1.45690e7i −0.662936 + 1.14824i
\(695\) −88763.1 −0.00697061
\(696\) −3.70847e6 6.42325e6i −0.290182 0.502611i
\(697\) 14334.6 0.00111764
\(698\) −1.17550e7 2.03602e7i −0.913236 1.58177i
\(699\) 2.69637e6 + 4.67026e6i 0.208731 + 0.361533i
\(700\) −2.36207e7 4.09122e7i −1.82199 3.15579i
\(701\) 5.49806e6 9.52292e6i 0.422585 0.731939i −0.573606 0.819131i \(-0.694456\pi\)
0.996192 + 0.0871920i \(0.0277894\pi\)
\(702\) 1.63348e7 1.25104
\(703\) −2.11062e6 + 2.79489e6i −0.161072 + 0.213293i
\(704\) 6.75724e7 5.13852
\(705\) 53525.8 92709.4i 0.00405593 0.00702508i
\(706\) −9.62893e6 1.66778e7i −0.727054 1.25929i
\(707\) −9.73405e6 1.68599e7i −0.732394 1.26854i
\(708\) −7.88324e6 1.36542e7i −0.591046 1.02372i
\(709\) −5.13350e6 −0.383529 −0.191764 0.981441i \(-0.561421\pi\)
−0.191764 + 0.981441i \(0.561421\pi\)
\(710\) 338233. + 585837.i 0.0251808 + 0.0436145i
\(711\) −7.73154e6 −0.573577
\(712\) −1.39156e7 + 2.41025e7i −1.02873 + 1.78182i
\(713\) 1.39760e7 1.02958
\(714\) −7420.50 −0.000544738
\(715\) −423644. + 733773.i −0.0309910 + 0.0536780i
\(716\) −2.24318e7 3.88530e7i −1.63524 2.83232i
\(717\) −2.48321e6 −0.180391
\(718\) −6.43555e6 + 1.11467e7i −0.465881 + 0.806929i
\(719\) 5.89947e6 1.02182e7i 0.425589 0.737142i −0.570886 0.821029i \(-0.693400\pi\)
0.996475 + 0.0838874i \(0.0267336\pi\)
\(720\) 1.53661e6 2.66149e6i 0.110467 0.191335i
\(721\) 1.31916e7 + 2.28485e7i 0.945060 + 1.63689i
\(722\) −1.28418e7 2.22427e7i −0.916820 1.58798i
\(723\) 1.39561e6 2.41727e6i 0.0992929 0.171980i
\(724\) 1.75104e7 3.03290e7i 1.24151 2.15036i
\(725\) −4.36121e6 + 7.55384e6i −0.308150 + 0.533731i
\(726\) 1.23911e6 0.0872506
\(727\) −107117. 185533.i −0.00751665 0.0130192i 0.862243 0.506495i \(-0.169059\pi\)
−0.869759 + 0.493476i \(0.835726\pi\)
\(728\) −4.41434e7 + 7.64586e7i −3.08701 + 5.34685i
\(729\) −9.23049e6 −0.643289
\(730\) 2.02686e6 0.140772
\(731\) 1370.36 2373.54i 9.48509e−5 0.000164287i
\(732\) −1.86931e7 −1.28945
\(733\) 5.77161e6 + 9.99672e6i 0.396768 + 0.687223i 0.993325 0.115348i \(-0.0367984\pi\)
−0.596557 + 0.802571i \(0.703465\pi\)
\(734\) 1.31822e7 0.903124
\(735\) −56390.8 97671.7i −0.00385026 0.00666884i
\(736\) 3.92830e7 + 6.80402e7i 2.67307 + 4.62990i
\(737\) −4.00136e6 6.93055e6i −0.271355 0.470001i
\(738\) 1.75044e7 3.03186e7i 1.18306 2.04912i
\(739\) −2.35473e7 −1.58610 −0.793048 0.609159i \(-0.791507\pi\)
−0.793048 + 0.609159i \(0.791507\pi\)
\(740\) −2.24150e6 277563.i −0.150473 0.0186330i
\(741\) −1.30641e6 −0.0874042
\(742\) −229446. + 397412.i −0.0152993 + 0.0264991i
\(743\) −1.38303e7 2.39547e7i −0.919091 1.59191i −0.800798 0.598934i \(-0.795591\pi\)
−0.118293 0.992979i \(-0.537742\pi\)
\(744\) 7.03160e6 + 1.21791e7i 0.465716 + 0.806644i
\(745\) −126147. 218492.i −0.00832693 0.0144227i
\(746\) 7.86426e6 0.517382
\(747\) 428667. + 742474.i 0.0281073 + 0.0486833i
\(748\) −35202.0 −0.00230045
\(749\) 9.64021e6 1.66973e7i 0.627888 1.08753i
\(750\) 795461. 0.0516376
\(751\) 2.45156e7 1.58614 0.793072 0.609128i \(-0.208480\pi\)
0.793072 + 0.609128i \(0.208480\pi\)
\(752\) 2.16542e7 3.75062e7i 1.39636 2.41857i
\(753\) 2.88523e6 + 4.99737e6i 0.185436 + 0.321184i
\(754\) 2.48826e7 1.59393
\(755\) 216180. 374435.i 0.0138022 0.0239061i
\(756\) −1.39259e7 + 2.41204e7i −0.886175 + 1.53490i
\(757\) −1.33213e7 + 2.30732e7i −0.844906 + 1.46342i 0.0407977 + 0.999167i \(0.487010\pi\)
−0.885703 + 0.464252i \(0.846323\pi\)
\(758\) 1.55609e7 + 2.69523e7i 0.983700 + 1.70382i
\(759\) −1.87165e6 3.24179e6i −0.117929 0.204259i
\(760\) −417398. + 722954.i −0.0262130 + 0.0454022i
\(761\) −6.27905e6 + 1.08756e7i −0.393036 + 0.680758i −0.992848 0.119383i \(-0.961908\pi\)
0.599813 + 0.800141i \(0.295242\pi\)
\(762\) 4.95859e6 8.58853e6i 0.309365 0.535836i
\(763\) −1.12459e7 −0.699331
\(764\) 1.42434e7 + 2.46703e7i 0.882838 + 1.52912i
\(765\) −346.823 + 600.715i −2.14266e−5 + 3.71120e-5i
\(766\) 3.48158e7 2.14390
\(767\) 3.46514e7 2.12683
\(768\) −1.27851e7 + 2.21444e7i −0.782168 + 1.35475i
\(769\) 2.46945e6 0.150586 0.0752930 0.997161i \(-0.476011\pi\)
0.0752930 + 0.997161i \(0.476011\pi\)
\(770\) −971469. 1.68263e6i −0.0590476 0.102273i
\(771\) −3.21233e6 −0.194619
\(772\) 1.21738e7 + 2.10856e7i 0.735161 + 1.27334i
\(773\) −1.09133e7 1.89024e7i −0.656913 1.13781i −0.981411 0.191920i \(-0.938529\pi\)
0.324498 0.945886i \(-0.394805\pi\)
\(774\) −3.34678e6 5.79680e6i −0.200805 0.347805i
\(775\) 8.26926e6 1.43228e7i 0.494552 0.856590i
\(776\) −7.69427e7 −4.58684
\(777\) 5.26960e6 + 652532.i 0.313131 + 0.0387748i
\(778\) −1.72262e7 −1.02033
\(779\) −2.89353e6 + 5.01174e6i −0.170838 + 0.295900i
\(780\) −421247. 729621.i −0.0247913 0.0429399i
\(781\) −3.77215e6 6.53356e6i −0.221290 0.383286i
\(782\) −15324.0 26542.0i −0.000896100 0.00155209i
\(783\) 5.14243e6 0.299754
\(784\) −2.28133e7 3.95138e7i −1.32555 2.29593i
\(785\) 1.68925e6 0.0978406
\(786\) 2.61926e6 4.53669e6i 0.151225 0.261929i
\(787\) 1.00902e7 0.580714 0.290357 0.956918i \(-0.406226\pi\)
0.290357 + 0.956918i \(0.406226\pi\)
\(788\) −2.10720e7 −1.20890
\(789\) 686639. 1.18929e6i 0.0392677 0.0680137i
\(790\) 554231. + 959957.i 0.0315954 + 0.0547248i
\(791\) 2.13314e7 1.21221
\(792\) −2.81607e7 + 4.87758e7i −1.59526 + 2.76307i
\(793\) 2.05418e7 3.55794e7i 1.15999 2.00917i
\(794\) −5.34891e6 + 9.26458e6i −0.301102 + 0.521524i
\(795\) −1434.38 2484.42i −8.04910e−5 0.000139414i
\(796\) −2.03504e7 3.52479e7i −1.13839 1.97174i
\(797\) −1.04554e7 + 1.81092e7i −0.583034 + 1.00984i 0.412084 + 0.911146i \(0.364801\pi\)
−0.995117 + 0.0986979i \(0.968532\pi\)
\(798\) 1.49788e6 2.59440e6i 0.0832661 0.144221i
\(799\) −4887.49 + 8465.37i −0.000270844 + 0.000469115i
\(800\) 9.29711e7 5.13598
\(801\) −4.66801e6 8.08524e6i −0.257070 0.445258i
\(802\) 5.46898e6 9.47254e6i 0.300241 0.520033i
\(803\) −2.26047e7 −1.23711
\(804\) 7.95743e6 0.434143
\(805\) 628895. 1.08928e6i 0.0342049 0.0592447i
\(806\) −4.71798e7 −2.55810
\(807\) −633244. 1.09681e6i −0.0342285 0.0592854i
\(808\) 8.09084e7 4.35979
\(809\) 1.03848e7 + 1.79870e7i 0.557863 + 0.966248i 0.997675 + 0.0681574i \(0.0217120\pi\)
−0.439811 + 0.898090i \(0.644955\pi\)
\(810\) 786597. + 1.36243e6i 0.0421250 + 0.0729626i
\(811\) 6.40458e6 + 1.10931e7i 0.341931 + 0.592242i 0.984791 0.173741i \(-0.0555857\pi\)
−0.642860 + 0.765984i \(0.722252\pi\)
\(812\) −2.12133e7 + 3.67424e7i −1.12906 + 1.95559i
\(813\) −515948. −0.0273766
\(814\) 3.36200e7 + 4.16315e6i 1.77843 + 0.220222i
\(815\) −301826. −0.0159171
\(816\) 9383.56 16252.8i 0.000493336 0.000854482i
\(817\) 553232. + 958226.i 0.0289969 + 0.0502242i
\(818\) −2.24510e7 3.88863e7i −1.17315 2.03195i
\(819\) −1.48080e7 2.56482e7i −0.771411 1.33612i
\(820\) −3.73204e6 −0.193826
\(821\) 4.94783e6 + 8.56988e6i 0.256187 + 0.443728i 0.965217 0.261450i \(-0.0842005\pi\)
−0.709031 + 0.705178i \(0.750867\pi\)
\(822\) 6.72376e6 0.347082
\(823\) −2.59111e6 + 4.48794e6i −0.133348 + 0.230966i −0.924965 0.380052i \(-0.875906\pi\)
0.791617 + 0.611017i \(0.209239\pi\)
\(824\) −1.09647e8 −5.62574
\(825\) −4.42963e6 −0.226586
\(826\) −3.97300e7 + 6.88144e7i −2.02614 + 3.50937i
\(827\) 8.56896e6 + 1.48419e7i 0.435677 + 0.754614i 0.997351 0.0727444i \(-0.0231757\pi\)
−0.561674 + 0.827359i \(0.689842\pi\)
\(828\) −5.56556e7 −2.82120
\(829\) 150003. 259813.i 0.00758078 0.0131303i −0.862210 0.506551i \(-0.830920\pi\)
0.869791 + 0.493420i \(0.164254\pi\)
\(830\) 61457.6 106448.i 0.00309657 0.00536341i
\(831\) 1.03810e6 1.79805e6i 0.0521481 0.0903231i
\(832\) −7.38349e7 1.27886e8i −3.69788 6.40492i
\(833\) 5149.09 + 8918.49i 0.000257109 + 0.000445327i
\(834\) −661909. + 1.14646e6i −0.0329521 + 0.0570747i
\(835\) −727732. + 1.26047e6i −0.0361206 + 0.0625627i
\(836\) 7.10574e6 1.23075e7i 0.351636 0.609052i
\(837\) −9.75053e6 −0.481077
\(838\) 1.07834e7 + 1.86774e7i 0.530452 + 0.918770i
\(839\) 1.13452e7 1.96505e7i 0.556428 0.963761i −0.441363 0.897329i \(-0.645505\pi\)
0.997791 0.0664325i \(-0.0211617\pi\)
\(840\) 1.26564e6 0.0618886
\(841\) −1.26777e7 −0.618089
\(842\) 2.78805e7 4.82904e7i 1.35525 2.34737i
\(843\) 5.32847e6 0.258246
\(844\) −2.44077e7 4.22754e7i −1.17943 2.04283i
\(845\) 766235. 0.0369165
\(846\) 1.19365e7 + 2.06747e7i 0.573393 + 0.993145i
\(847\) −2.32171e6 4.02131e6i −0.111198 0.192601i
\(848\) −580289. 1.00509e6i −0.0277112 0.0479971i
\(849\) −1.89196e6 + 3.27697e6i −0.0900830 + 0.156028i
\(850\) −36267.4 −0.00172175
\(851\) 8.54822e6 + 2.01961e7i 0.404624 + 0.955969i
\(852\) 7.50162e6 0.354043
\(853\) −1.38424e7 + 2.39758e7i −0.651388 + 1.12824i 0.331398 + 0.943491i \(0.392480\pi\)
−0.982786 + 0.184746i \(0.940854\pi\)
\(854\) 4.71049e7 + 8.15881e7i 2.21015 + 3.82809i
\(855\) −140017. 242516.i −0.00655035 0.0113455i
\(856\) 4.00642e7 + 6.93933e7i 1.86884 + 3.23693i
\(857\) −2.40254e7 −1.11743 −0.558714 0.829361i \(-0.688705\pi\)
−0.558714 + 0.829361i \(0.688705\pi\)
\(858\) 6.31825e6 + 1.09435e7i 0.293007 + 0.507504i
\(859\) −1.54867e7 −0.716106 −0.358053 0.933701i \(-0.616559\pi\)
−0.358053 + 0.933701i \(0.616559\pi\)
\(860\) −356776. + 617955.i −0.0164494 + 0.0284912i
\(861\) 8.77377e6 0.403347
\(862\) 5.43831e7 2.49285
\(863\) 4.76679e6 8.25633e6i 0.217871 0.377364i −0.736286 0.676671i \(-0.763422\pi\)
0.954157 + 0.299307i \(0.0967555\pi\)
\(864\) −2.74063e7 4.74691e7i −1.24901 2.16335i
\(865\) 761586. 0.0346082
\(866\) −5.26071e6 + 9.11182e6i −0.238369 + 0.412867i
\(867\) 2.77077e6 4.79911e6i 0.125185 0.216827i
\(868\) 4.02223e7 6.96671e7i 1.81204 3.13854i
\(869\) −6.18108e6 1.07059e7i −0.277661 0.480923i
\(870\) −178352. 308916.i −0.00798879 0.0138370i
\(871\) −8.74438e6 + 1.51457e7i −0.390556 + 0.676463i
\(872\) 2.33687e7 4.04757e7i 1.04074 1.80262i
\(873\) 1.29053e7 2.23526e7i 0.573102 0.992641i
\(874\) 1.23730e7 0.547894
\(875\) −1.49045e6 2.58153e6i −0.0658107 0.113987i
\(876\) 1.12384e7 1.94654e7i 0.494815 0.857046i
\(877\) −2.76664e7 −1.21466 −0.607328 0.794451i \(-0.707759\pi\)
−0.607328 + 0.794451i \(0.707759\pi\)
\(878\) 3.95617e7 1.73196
\(879\) −2.82975e6 + 4.90127e6i −0.123531 + 0.213962i
\(880\) 4.91387e6 0.213903
\(881\) 9.76484e6 + 1.69132e7i 0.423863 + 0.734152i 0.996314 0.0857870i \(-0.0273404\pi\)
−0.572450 + 0.819939i \(0.694007\pi\)
\(882\) 2.51509e7 1.08863
\(883\) 217317. + 376405.i 0.00937978 + 0.0162463i 0.870677 0.491855i \(-0.163681\pi\)
−0.861297 + 0.508101i \(0.830348\pi\)
\(884\) 38464.4 + 66622.3i 0.00165550 + 0.00286740i
\(885\) −248373. 430194.i −0.0106597 0.0184632i
\(886\) −2.61179e7 + 4.52376e7i −1.11778 + 1.93604i
\(887\) −1.99392e7 −0.850942 −0.425471 0.904972i \(-0.639891\pi\)
−0.425471 + 0.904972i \(0.639891\pi\)
\(888\) −1.32987e7 + 1.76102e7i −0.565947 + 0.749431i
\(889\) −3.71634e7 −1.57711
\(890\) −669248. + 1.15917e6i −0.0283212 + 0.0490538i
\(891\) −8.77254e6 1.51945e7i −0.370196 0.641198i
\(892\) −5.11480e6 8.85909e6i −0.215237 0.372801i
\(893\) −1.97314e6 3.41758e6i −0.0827998 0.143413i
\(894\) −3.76271e6 −0.157455
\(895\) −706746. 1.22412e6i −0.0294921 0.0510818i
\(896\) 1.82660e8 7.60103
\(897\) −4.09021e6 + 7.08446e6i −0.169733 + 0.293985i
\(898\) −1.43698e7 −0.594647
\(899\) −1.48529e7 −0.612932
\(900\) −3.29300e7 + 5.70365e7i −1.35514 + 2.34718i
\(901\) 130.975 + 226.855i 5.37496e−6 + 9.30971e-6i
\(902\) 5.59766e7 2.29082
\(903\) 838756. 1.45277e6i 0.0342308 0.0592894i
\(904\) −4.43260e7 + 7.67749e7i −1.80401 + 3.12463i
\(905\) 551692. 955558.i 0.0223911 0.0387825i
\(906\) −3.22412e6 5.58434e6i −0.130494 0.226022i
\(907\) −4.34752e6 7.53013e6i −0.175478 0.303938i 0.764848 0.644210i \(-0.222814\pi\)
−0.940327 + 0.340273i \(0.889481\pi\)
\(908\) 1.26847e7 2.19706e7i 0.510583 0.884355i
\(909\) −1.35704e7 + 2.35047e7i −0.544733 + 0.943505i
\(910\) −2.12300e6 + 3.67715e6i −0.0849860 + 0.147200i
\(911\) 1.01465e7 0.405061 0.202531 0.979276i \(-0.435083\pi\)
0.202531 + 0.979276i \(0.435083\pi\)
\(912\) 3.78826e6 + 6.56146e6i 0.150818 + 0.261224i
\(913\) −685408. + 1.18716e6i −0.0272127 + 0.0471338i
\(914\) −2.87615e7 −1.13880
\(915\) −588954. −0.0232556
\(916\) −2.04419e7 + 3.54064e7i −0.804974 + 1.39426i
\(917\) −1.96307e7 −0.770927
\(918\) 10691.0 + 18517.3i 0.000418708 + 0.000725224i
\(919\) 3.60671e7 1.40871 0.704355 0.709847i \(-0.251236\pi\)
0.704355 + 0.709847i \(0.251236\pi\)
\(920\) 2.61366e6 + 4.52699e6i 0.101807 + 0.176335i
\(921\) −4.10587e6 7.11157e6i −0.159498 0.276259i
\(922\) 3.99694e7 + 6.92290e7i 1.54846 + 2.68201i
\(923\) −8.24350e6 + 1.42782e7i −0.318498 + 0.551655i
\(924\) −2.15461e7 −0.830210
\(925\) 2.57549e7 + 3.18922e6i 0.989706 + 0.122555i
\(926\) −7.10587e7 −2.72326
\(927\) 1.83907e7 3.18536e7i 0.702907 1.21747i
\(928\) −4.17478e7 7.23093e7i −1.59134 2.75628i
\(929\) 878565. + 1.52172e6i 0.0333991 + 0.0578489i 0.882242 0.470797i \(-0.156033\pi\)
−0.848843 + 0.528646i \(0.822700\pi\)
\(930\) 338173. + 585733.i 0.0128213 + 0.0222071i
\(931\) −4.15751e6 −0.157202
\(932\) 6.41008e7 + 1.11026e8i 2.41726 + 4.18682i
\(933\) −4.68791e6 −0.176309
\(934\) −7.74971e6 + 1.34229e7i −0.290682 + 0.503476i
\(935\) −1109.09 −4.14894e−5
\(936\) 1.23082e8 4.59204
\(937\) 1.23212e7 2.13409e7i 0.458461 0.794078i −0.540419 0.841396i \(-0.681734\pi\)
0.998880 + 0.0473181i \(0.0150675\pi\)
\(938\) −2.00520e7 3.47310e7i −0.744132 1.28887i
\(939\) 2.36552e6 0.0875512
\(940\) 1.27247e6 2.20398e6i 0.0469707 0.0813556i
\(941\) 2.13160e7 3.69204e7i 0.784751 1.35923i −0.144397 0.989520i \(-0.546124\pi\)
0.929148 0.369709i \(-0.120543\pi\)
\(942\) 1.25968e7 2.18182e7i 0.462521 0.801110i
\(943\) 1.81187e7 + 3.13824e7i 0.663509 + 1.14923i
\(944\) −1.00481e8 1.74038e8i −3.66989 6.35644i
\(945\) −438756. + 759948.i −0.0159825 + 0.0276824i
\(946\) 5.35126e6 9.26866e6i 0.194414 0.336736i
\(947\) −9.10385e6 + 1.57683e7i −0.329875 + 0.571361i −0.982487 0.186332i \(-0.940340\pi\)
0.652611 + 0.757693i \(0.273673\pi\)
\(948\) 1.22922e7 0.444231
\(949\) 2.46996e7 + 4.27810e7i 0.890275 + 1.54200i
\(950\) 7.32080e6 1.26800e7i 0.263178 0.455837i
\(951\) 192052. 0.00688601
\(952\) −115566. −0.00413275
\(953\) −1.64848e7 + 2.85525e7i −0.587964 + 1.01838i 0.406534 + 0.913635i \(0.366737\pi\)
−0.994499 + 0.104749i \(0.966596\pi\)
\(954\) 639749. 0.0227583
\(955\) 448759. + 777274.i 0.0159223 + 0.0275782i
\(956\) −5.90333e7 −2.08907
\(957\) 1.98908e6 + 3.44519e6i 0.0702058 + 0.121600i
\(958\) 5.11116e6 + 8.85279e6i 0.179931 + 0.311649i
\(959\) −1.25982e7 2.18208e7i −0.442347 0.766168i
\(960\) −1.05846e6 + 1.83331e6i −0.0370678 + 0.0642032i
\(961\) −466646. −0.0162997
\(962\) −2.88568e7 6.81773e7i −1.00533 2.37521i
\(963\) −2.68792e7 −0.934008
\(964\) 3.31778e7 5.74656e7i 1.14989 1.99166i
\(965\) 383553. + 664333.i 0.0132589 + 0.0229651i
\(966\) −9.37938e6 1.62456e7i −0.323393 0.560134i
\(967\) −2.48466e7 4.30356e7i −0.854478 1.48000i −0.877128 0.480257i \(-0.840544\pi\)
0.0226496 0.999743i \(-0.492790\pi\)
\(968\) 1.92978e7 0.661940
\(969\) −855.033 1480.96i −2.92532e−5 5.06681e-5i
\(970\) −3.70043e6 −0.126277
\(971\) 1.13766e7 1.97049e7i 0.387226 0.670696i −0.604849 0.796340i \(-0.706767\pi\)
0.992075 + 0.125644i \(0.0400998\pi\)
\(972\) 5.88714e7 1.99866
\(973\) 4.96085e6 0.167986
\(974\) 4.17546e7 7.23211e7i 1.41029 2.44269i
\(975\) 4.84015e6 + 8.38339e6i 0.163060 + 0.282428i
\(976\) −2.38265e8 −8.00637
\(977\) 2.62371e7 4.54439e7i 0.879385 1.52314i 0.0273674 0.999625i \(-0.491288\pi\)
0.852017 0.523514i \(-0.175379\pi\)
\(978\) −2.25073e6 + 3.89837e6i −0.0752446 + 0.130328i
\(979\) 7.46381e6 1.29277e7i 0.248888 0.431087i
\(980\) −1.34058e6 2.32195e6i −0.0445889 0.0772302i
\(981\) 7.83906e6 + 1.35776e7i 0.260071 + 0.450456i
\(982\) −3.36824e7 + 5.83397e7i −1.11461 + 1.93057i
\(983\) −2.71054e7 + 4.69479e7i −0.894689 + 1.54965i −0.0605002 + 0.998168i \(0.519270\pi\)
−0.834189 + 0.551479i \(0.814064\pi\)
\(984\) −1.82317e7 + 3.15782e7i −0.600259 + 1.03968i
\(985\) −663903. −0.0218029
\(986\) 16285.5 + 28207.3i 0.000533469 + 0.000923995i
\(987\) −2.99148e6 + 5.18140e6i −0.0977447 + 0.169299i
\(988\) −3.10571e7 −1.01221
\(989\) 6.92844e6 0.225240
\(990\) −1.35434e6 + 2.34579e6i −0.0439178 + 0.0760679i
\(991\) 4.13018e7 1.33593 0.667966 0.744191i \(-0.267165\pi\)
0.667966 + 0.744191i \(0.267165\pi\)
\(992\) 7.91577e7 + 1.37105e8i 2.55396 + 4.42359i
\(993\) −2.24716e6 −0.0723205
\(994\) −1.89034e7 3.27416e7i −0.606839 1.05108i
\(995\) −641167. 1.11053e6i −0.0205312 0.0355610i
\(996\) −681529. 1.18044e6i −0.0217689 0.0377048i
\(997\) 6.24004e6 1.08081e7i 0.198815 0.344358i −0.749329 0.662197i \(-0.769624\pi\)
0.948145 + 0.317840i \(0.102957\pi\)
\(998\) 9.05483e6 0.287776
\(999\) −5.96376e6 1.40901e7i −0.189063 0.446682i
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.10.15 30
37.26 even 3 inner 37.6.c.a.26.15 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.6.c.a.10.15 30 1.1 even 1 trivial
37.6.c.a.26.15 yes 30 37.26 even 3 inner