Properties

Label 105.4.i.d.16.2
Level $105$
Weight $4$
Character 105.16
Analytic conductor $6.195$
Analytic rank $0$
Dimension $10$
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] = [105,4,Mod(16,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} - 12852 x + 7056 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.2
Root \(-1.33997 + 2.32090i\) of defining polynomial
Character \(\chi\) \(=\) 105.16
Dual form 105.4.i.d.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.83997 + 3.18692i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.77099 - 4.79950i) q^{4} +(-2.50000 + 4.33013i) q^{5} +11.0398 q^{6} +(5.08172 + 17.8094i) q^{7} -9.04535 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.83997 + 3.18692i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.77099 - 4.79950i) q^{4} +(-2.50000 + 4.33013i) q^{5} +11.0398 q^{6} +(5.08172 + 17.8094i) q^{7} -9.04535 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-9.19986 - 15.9346i) q^{10} +(-32.5290 - 56.3418i) q^{11} +(-8.31298 + 14.3985i) q^{12} -6.87328 q^{13} +(-66.1076 - 16.5738i) q^{14} +15.0000 q^{15} +(38.8111 - 67.2229i) q^{16} +(-34.0063 - 58.9006i) q^{17} +(-16.5597 - 28.6823i) q^{18} +(-11.7761 + 20.3968i) q^{19} +27.7099 q^{20} +(38.6477 - 39.9169i) q^{21} +239.409 q^{22} +(2.74967 - 4.76257i) q^{23} +(13.5680 + 23.5005i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(12.6467 - 21.9046i) q^{26} +27.0000 q^{27} +(71.3950 - 73.7396i) q^{28} -138.643 q^{29} +(-27.5996 + 47.8039i) q^{30} +(-125.954 - 218.158i) q^{31} +(106.641 + 184.708i) q^{32} +(-97.5869 + 169.025i) q^{33} +250.282 q^{34} +(-89.8214 - 22.5191i) q^{35} +49.8779 q^{36} +(-63.7644 + 110.443i) q^{37} +(-43.3354 - 75.0591i) q^{38} +(10.3099 + 17.8573i) q^{39} +(22.6134 - 39.1675i) q^{40} -126.581 q^{41} +(56.1014 + 196.613i) q^{42} +91.5924 q^{43} +(-180.275 + 312.245i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(10.1186 + 17.5260i) q^{46} +(-284.233 + 492.306i) q^{47} -232.867 q^{48} +(-291.352 + 181.005i) q^{49} +91.9986 q^{50} +(-102.019 + 176.702i) q^{51} +(19.0458 + 32.9883i) q^{52} +(295.199 + 511.300i) q^{53} +(-49.6792 + 86.0470i) q^{54} +325.290 q^{55} +(-45.9660 - 161.093i) q^{56} +70.6566 q^{57} +(255.099 - 441.844i) q^{58} +(-254.890 - 441.483i) q^{59} +(-41.5649 - 71.9925i) q^{60} +(-130.771 + 226.502i) q^{61} +927.006 q^{62} +(-161.679 - 40.5344i) q^{63} -163.890 q^{64} +(17.1832 - 29.7622i) q^{65} +(-359.114 - 622.004i) q^{66} +(461.391 + 799.152i) q^{67} +(-188.462 + 326.426i) q^{68} -16.4980 q^{69} +(237.036 - 244.820i) q^{70} +519.662 q^{71} +(40.7041 - 70.5015i) q^{72} +(-533.244 - 923.606i) q^{73} +(-234.649 - 406.424i) q^{74} +(-37.5000 + 64.9519i) q^{75} +130.526 q^{76} +(838.113 - 865.636i) q^{77} -75.8799 q^{78} +(56.4067 - 97.6992i) q^{79} +(194.056 + 336.114i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(232.906 - 403.405i) q^{82} -593.552 q^{83} +(-298.674 - 74.8803i) q^{84} +340.063 q^{85} +(-168.527 + 291.898i) q^{86} +(207.964 + 360.205i) q^{87} +(294.236 + 509.631i) q^{88} +(121.163 - 209.860i) q^{89} +165.597 q^{90} +(-34.9281 - 122.409i) q^{91} -30.4773 q^{92} +(-377.862 + 654.475i) q^{93} +(-1045.96 - 1811.66i) q^{94} +(-58.8805 - 101.984i) q^{95} +(319.924 - 554.125i) q^{96} -1536.88 q^{97} +(-40.7705 - 1261.56i) q^{98} +585.521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9} - 15 q^{10} - 43 q^{11} - 75 q^{12} + 246 q^{13} - 23 q^{14} + 150 q^{15} - 161 q^{16} - 124 q^{17} - 27 q^{18} - 37 q^{19} + 250 q^{20} + 3 q^{21} - 442 q^{22} - 77 q^{23} - 63 q^{24} - 125 q^{25} + 79 q^{26} + 270 q^{27} - 71 q^{28} + 720 q^{29} - 45 q^{30} - 314 q^{31} + 59 q^{32} - 129 q^{33} + 352 q^{34} + 155 q^{35} + 450 q^{36} - 225 q^{37} - 759 q^{38} - 369 q^{39} - 105 q^{40} + 682 q^{41} + 354 q^{42} + 64 q^{43} - 679 q^{44} - 225 q^{45} + 331 q^{46} - 25 q^{47} + 966 q^{48} + 710 q^{49} + 150 q^{50} - 372 q^{51} - 2299 q^{52} + 317 q^{53} - 81 q^{54} + 430 q^{55} + 1884 q^{56} + 222 q^{57} - 8 q^{58} - 676 q^{59} - 375 q^{60} + 188 q^{61} - 696 q^{62} + 279 q^{63} - 2206 q^{64} - 615 q^{65} + 663 q^{66} + 1776 q^{67} - 1280 q^{68} + 462 q^{69} - 475 q^{70} - 12 q^{71} - 189 q^{72} - 2006 q^{73} + 2729 q^{74} - 375 q^{75} + 2834 q^{76} + 3731 q^{77} - 474 q^{78} - 200 q^{79} - 805 q^{80} - 405 q^{81} + 539 q^{82} - 664 q^{83} + 1821 q^{84} + 1240 q^{85} - 4262 q^{86} - 1080 q^{87} + 4529 q^{88} - 894 q^{89} + 270 q^{90} + 2016 q^{91} - 7374 q^{92} - 942 q^{93} - 4233 q^{94} - 185 q^{95} + 177 q^{96} - 1152 q^{97} + 2539 q^{98} + 774 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83997 + 3.18692i −0.650528 + 1.12675i 0.332467 + 0.943115i \(0.392119\pi\)
−0.982995 + 0.183633i \(0.941214\pi\)
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −2.77099 4.79950i −0.346374 0.599938i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 11.0398 0.751165
\(7\) 5.08172 + 17.8094i 0.274387 + 0.961619i
\(8\) −9.04535 −0.399752
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) −9.19986 15.9346i −0.290925 0.503897i
\(11\) −32.5290 56.3418i −0.891622 1.54434i −0.837930 0.545778i \(-0.816234\pi\)
−0.0536927 0.998558i \(-0.517099\pi\)
\(12\) −8.31298 + 14.3985i −0.199979 + 0.346374i
\(13\) −6.87328 −0.146639 −0.0733195 0.997309i \(-0.523359\pi\)
−0.0733195 + 0.997309i \(0.523359\pi\)
\(14\) −66.1076 16.5738i −1.26200 0.316395i
\(15\) 15.0000 0.258199
\(16\) 38.8111 67.2229i 0.606424 1.05036i
\(17\) −34.0063 58.9006i −0.485161 0.840323i 0.514694 0.857374i \(-0.327906\pi\)
−0.999855 + 0.0170509i \(0.994572\pi\)
\(18\) −16.5597 28.6823i −0.216843 0.375583i
\(19\) −11.7761 + 20.3968i −0.142191 + 0.246282i −0.928321 0.371779i \(-0.878748\pi\)
0.786131 + 0.618060i \(0.212081\pi\)
\(20\) 27.7099 0.309806
\(21\) 38.6477 39.9169i 0.401601 0.414789i
\(22\) 239.409 2.32010
\(23\) 2.74967 4.76257i 0.0249281 0.0431767i −0.853292 0.521433i \(-0.825398\pi\)
0.878220 + 0.478256i \(0.158731\pi\)
\(24\) 13.5680 + 23.5005i 0.115398 + 0.199876i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 12.6467 21.9046i 0.0953928 0.165225i
\(27\) 27.0000 0.192450
\(28\) 71.3950 73.7396i 0.481871 0.497695i
\(29\) −138.643 −0.887770 −0.443885 0.896084i \(-0.646400\pi\)
−0.443885 + 0.896084i \(0.646400\pi\)
\(30\) −27.5996 + 47.8039i −0.167966 + 0.290925i
\(31\) −125.954 218.158i −0.729741 1.26395i −0.956992 0.290113i \(-0.906307\pi\)
0.227251 0.973836i \(-0.427026\pi\)
\(32\) 106.641 + 184.708i 0.589116 + 1.02038i
\(33\) −97.5869 + 169.025i −0.514778 + 0.891622i
\(34\) 250.282 1.26244
\(35\) −89.8214 22.5191i −0.433788 0.108755i
\(36\) 49.8779 0.230916
\(37\) −63.7644 + 110.443i −0.283319 + 0.490723i −0.972200 0.234152i \(-0.924769\pi\)
0.688881 + 0.724874i \(0.258102\pi\)
\(38\) −43.3354 75.0591i −0.184998 0.320426i
\(39\) 10.3099 + 17.8573i 0.0423310 + 0.0733195i
\(40\) 22.6134 39.1675i 0.0893872 0.154823i
\(41\) −126.581 −0.482163 −0.241082 0.970505i \(-0.577502\pi\)
−0.241082 + 0.970505i \(0.577502\pi\)
\(42\) 56.1014 + 196.613i 0.206110 + 0.722335i
\(43\) 91.5924 0.324830 0.162415 0.986723i \(-0.448072\pi\)
0.162415 + 0.986723i \(0.448072\pi\)
\(44\) −180.275 + 312.245i −0.617670 + 1.06984i
\(45\) −22.5000 38.9711i −0.0745356 0.129099i
\(46\) 10.1186 + 17.5260i 0.0324328 + 0.0561753i
\(47\) −284.233 + 492.306i −0.882119 + 1.52788i −0.0331392 + 0.999451i \(0.510550\pi\)
−0.848980 + 0.528425i \(0.822783\pi\)
\(48\) −232.867 −0.700238
\(49\) −291.352 + 181.005i −0.849423 + 0.527712i
\(50\) 91.9986 0.260211
\(51\) −102.019 + 176.702i −0.280108 + 0.485161i
\(52\) 19.0458 + 32.9883i 0.0507919 + 0.0879742i
\(53\) 295.199 + 511.300i 0.765071 + 1.32514i 0.940209 + 0.340598i \(0.110629\pi\)
−0.175138 + 0.984544i \(0.556037\pi\)
\(54\) −49.6792 + 86.0470i −0.125194 + 0.216843i
\(55\) 325.290 0.797491
\(56\) −45.9660 161.093i −0.109687 0.384409i
\(57\) 70.6566 0.164188
\(58\) 255.099 441.844i 0.577520 1.00029i
\(59\) −254.890 441.483i −0.562438 0.974172i −0.997283 0.0736665i \(-0.976530\pi\)
0.434844 0.900506i \(-0.356803\pi\)
\(60\) −41.5649 71.9925i −0.0894334 0.154903i
\(61\) −130.771 + 226.502i −0.274483 + 0.475419i −0.970005 0.243086i \(-0.921840\pi\)
0.695521 + 0.718506i \(0.255174\pi\)
\(62\) 927.006 1.89887
\(63\) −161.679 40.5344i −0.323327 0.0810611i
\(64\) −163.890 −0.320099
\(65\) 17.1832 29.7622i 0.0327895 0.0567930i
\(66\) −359.114 622.004i −0.669756 1.16005i
\(67\) 461.391 + 799.152i 0.841311 + 1.45719i 0.888787 + 0.458321i \(0.151549\pi\)
−0.0474760 + 0.998872i \(0.515118\pi\)
\(68\) −188.462 + 326.426i −0.336094 + 0.582132i
\(69\) −16.4980 −0.0287845
\(70\) 237.036 244.820i 0.404731 0.418022i
\(71\) 519.662 0.868627 0.434314 0.900762i \(-0.356991\pi\)
0.434314 + 0.900762i \(0.356991\pi\)
\(72\) 40.7041 70.5015i 0.0666253 0.115398i
\(73\) −533.244 923.606i −0.854952 1.48082i −0.876689 0.481057i \(-0.840253\pi\)
0.0217370 0.999764i \(-0.493080\pi\)
\(74\) −234.649 406.424i −0.368614 0.638458i
\(75\) −37.5000 + 64.9519i −0.0577350 + 0.100000i
\(76\) 130.526 0.197005
\(77\) 838.113 865.636i 1.24041 1.28115i
\(78\) −75.8799 −0.110150
\(79\) 56.4067 97.6992i 0.0803322 0.139139i −0.823060 0.567954i \(-0.807735\pi\)
0.903393 + 0.428814i \(0.141069\pi\)
\(80\) 194.056 + 336.114i 0.271201 + 0.469734i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 232.906 403.405i 0.313661 0.543277i
\(83\) −593.552 −0.784949 −0.392474 0.919763i \(-0.628381\pi\)
−0.392474 + 0.919763i \(0.628381\pi\)
\(84\) −298.674 74.8803i −0.387952 0.0972632i
\(85\) 340.063 0.433941
\(86\) −168.527 + 291.898i −0.211311 + 0.366002i
\(87\) 207.964 + 360.205i 0.256277 + 0.443885i
\(88\) 294.236 + 509.631i 0.356428 + 0.617351i
\(89\) 121.163 209.860i 0.144306 0.249945i −0.784808 0.619739i \(-0.787238\pi\)
0.929114 + 0.369794i \(0.120572\pi\)
\(90\) 165.597 0.193950
\(91\) −34.9281 122.409i −0.0402359 0.141011i
\(92\) −30.4773 −0.0345378
\(93\) −377.862 + 654.475i −0.421316 + 0.729741i
\(94\) −1045.96 1811.66i −1.14769 1.98785i
\(95\) −58.8805 101.984i −0.0635896 0.110140i
\(96\) 319.924 554.125i 0.340126 0.589116i
\(97\) −1536.88 −1.60873 −0.804366 0.594134i \(-0.797495\pi\)
−0.804366 + 0.594134i \(0.797495\pi\)
\(98\) −40.7705 1261.56i −0.0420249 1.30038i
\(99\) 585.521 0.594415
\(100\) −69.2748 + 119.988i −0.0692748 + 0.119988i
\(101\) 857.920 + 1485.96i 0.845210 + 1.46395i 0.885439 + 0.464756i \(0.153858\pi\)
−0.0402290 + 0.999190i \(0.512809\pi\)
\(102\) −375.424 650.253i −0.364436 0.631222i
\(103\) 143.826 249.114i 0.137588 0.238310i −0.788995 0.614400i \(-0.789398\pi\)
0.926583 + 0.376090i \(0.122732\pi\)
\(104\) 62.1713 0.0586192
\(105\) 76.2259 + 267.142i 0.0708465 + 0.248289i
\(106\) −2172.63 −1.99080
\(107\) 525.298 909.842i 0.474602 0.822035i −0.524975 0.851118i \(-0.675925\pi\)
0.999577 + 0.0290827i \(0.00925862\pi\)
\(108\) −74.8168 129.587i −0.0666597 0.115458i
\(109\) 92.4004 + 160.042i 0.0811959 + 0.140635i 0.903764 0.428031i \(-0.140793\pi\)
−0.822568 + 0.568667i \(0.807459\pi\)
\(110\) −598.524 + 1036.67i −0.518791 + 0.898572i
\(111\) 382.586 0.327148
\(112\) 1394.43 + 349.597i 1.17644 + 0.294944i
\(113\) −2100.22 −1.74842 −0.874212 0.485545i \(-0.838621\pi\)
−0.874212 + 0.485545i \(0.838621\pi\)
\(114\) −130.006 + 225.177i −0.106809 + 0.184998i
\(115\) 13.7483 + 23.8128i 0.0111482 + 0.0193092i
\(116\) 384.178 + 665.417i 0.307501 + 0.532607i
\(117\) 30.9298 53.5720i 0.0244398 0.0423310i
\(118\) 1875.96 1.46353
\(119\) 876.176 904.949i 0.674949 0.697114i
\(120\) −135.680 −0.103215
\(121\) −1450.77 + 2512.80i −1.08998 + 1.88790i
\(122\) −481.229 833.514i −0.357118 0.618547i
\(123\) 189.872 + 328.868i 0.139189 + 0.241082i
\(124\) −698.035 + 1209.03i −0.505527 + 0.875599i
\(125\) 125.000 0.0894427
\(126\) 426.664 440.675i 0.301669 0.311575i
\(127\) 760.110 0.531094 0.265547 0.964098i \(-0.414448\pi\)
0.265547 + 0.964098i \(0.414448\pi\)
\(128\) −551.577 + 955.360i −0.380883 + 0.659708i
\(129\) −137.389 237.964i −0.0937704 0.162415i
\(130\) 63.2333 + 109.523i 0.0426609 + 0.0738909i
\(131\) 5.05499 8.75549i 0.00337142 0.00583947i −0.864335 0.502917i \(-0.832260\pi\)
0.867706 + 0.497077i \(0.165594\pi\)
\(132\) 1081.65 0.713224
\(133\) −423.099 106.075i −0.275844 0.0691568i
\(134\) −3395.78 −2.18919
\(135\) −67.5000 + 116.913i −0.0430331 + 0.0745356i
\(136\) 307.599 + 532.777i 0.193944 + 0.335921i
\(137\) −1395.86 2417.70i −0.870485 1.50772i −0.861496 0.507764i \(-0.830472\pi\)
−0.00898882 0.999960i \(-0.502861\pi\)
\(138\) 30.3559 52.5779i 0.0187251 0.0324328i
\(139\) 517.250 0.315630 0.157815 0.987469i \(-0.449555\pi\)
0.157815 + 0.987469i \(0.449555\pi\)
\(140\) 140.814 + 493.498i 0.0850070 + 0.297916i
\(141\) 1705.40 1.01858
\(142\) −956.163 + 1656.12i −0.565067 + 0.978724i
\(143\) 223.581 + 387.253i 0.130747 + 0.226460i
\(144\) 349.300 + 605.006i 0.202141 + 0.350119i
\(145\) 346.607 600.341i 0.198511 0.343832i
\(146\) 3924.62 2.22468
\(147\) 907.294 + 485.447i 0.509063 + 0.272374i
\(148\) 706.762 0.392537
\(149\) 985.657 1707.21i 0.541934 0.938658i −0.456859 0.889539i \(-0.651025\pi\)
0.998793 0.0491184i \(-0.0156412\pi\)
\(150\) −137.998 239.019i −0.0751165 0.130106i
\(151\) 80.8806 + 140.089i 0.0435892 + 0.0754987i 0.886997 0.461775i \(-0.152787\pi\)
−0.843408 + 0.537274i \(0.819454\pi\)
\(152\) 106.519 184.496i 0.0568410 0.0984515i
\(153\) 612.113 0.323441
\(154\) 1216.61 + 4263.75i 0.636607 + 2.23106i
\(155\) 1259.54 0.652700
\(156\) 57.1375 98.9650i 0.0293247 0.0507919i
\(157\) 53.7440 + 93.0873i 0.0273200 + 0.0473196i 0.879362 0.476154i \(-0.157969\pi\)
−0.852042 + 0.523473i \(0.824636\pi\)
\(158\) 207.573 + 359.528i 0.104517 + 0.181028i
\(159\) 885.598 1533.90i 0.441714 0.765071i
\(160\) −1066.41 −0.526921
\(161\) 98.7917 + 24.7680i 0.0483595 + 0.0121242i
\(162\) 298.075 0.144562
\(163\) 1004.14 1739.21i 0.482515 0.835741i −0.517283 0.855814i \(-0.673057\pi\)
0.999799 + 0.0200735i \(0.00639003\pi\)
\(164\) 350.756 + 607.528i 0.167009 + 0.289268i
\(165\) −487.934 845.127i −0.230216 0.398746i
\(166\) 1092.12 1891.60i 0.510632 0.884440i
\(167\) −566.505 −0.262500 −0.131250 0.991349i \(-0.541899\pi\)
−0.131250 + 0.991349i \(0.541899\pi\)
\(168\) −349.582 + 361.062i −0.160541 + 0.165813i
\(169\) −2149.76 −0.978497
\(170\) −625.706 + 1083.75i −0.282291 + 0.488942i
\(171\) −105.985 183.571i −0.0473969 0.0820938i
\(172\) −253.802 439.598i −0.112513 0.194878i
\(173\) 373.967 647.729i 0.164348 0.284659i −0.772076 0.635531i \(-0.780781\pi\)
0.936423 + 0.350872i \(0.114115\pi\)
\(174\) −1530.59 −0.666862
\(175\) 322.064 332.641i 0.139119 0.143687i
\(176\) −5049.94 −2.16281
\(177\) −764.670 + 1324.45i −0.324724 + 0.562438i
\(178\) 445.872 + 772.272i 0.187750 + 0.325192i
\(179\) 2023.57 + 3504.93i 0.844965 + 1.46352i 0.885651 + 0.464351i \(0.153712\pi\)
−0.0406860 + 0.999172i \(0.512954\pi\)
\(180\) −124.695 + 215.978i −0.0516344 + 0.0894334i
\(181\) −2930.28 −1.20335 −0.601673 0.798742i \(-0.705499\pi\)
−0.601673 + 0.798742i \(0.705499\pi\)
\(182\) 454.376 + 113.916i 0.185058 + 0.0463959i
\(183\) 784.625 0.316946
\(184\) −24.8717 + 43.0791i −0.00996504 + 0.0172600i
\(185\) −318.822 552.216i −0.126704 0.219458i
\(186\) −1390.51 2408.43i −0.548156 0.949435i
\(187\) −2212.38 + 3831.95i −0.865160 + 1.49850i
\(188\) 3150.43 1.22217
\(189\) 137.207 + 480.855i 0.0528059 + 0.185064i
\(190\) 433.354 0.165467
\(191\) −1508.61 + 2613.00i −0.571516 + 0.989894i 0.424895 + 0.905243i \(0.360311\pi\)
−0.996411 + 0.0846516i \(0.973022\pi\)
\(192\) 245.836 + 425.800i 0.0924045 + 0.160049i
\(193\) −393.459 681.491i −0.146745 0.254170i 0.783278 0.621672i \(-0.213546\pi\)
−0.930023 + 0.367502i \(0.880213\pi\)
\(194\) 2827.82 4897.94i 1.04653 1.81264i
\(195\) −103.099 −0.0378620
\(196\) 1676.07 + 896.781i 0.610813 + 0.326815i
\(197\) −2009.92 −0.726910 −0.363455 0.931612i \(-0.618403\pi\)
−0.363455 + 0.931612i \(0.618403\pi\)
\(198\) −1077.34 + 1866.01i −0.386684 + 0.669756i
\(199\) −1360.62 2356.66i −0.484681 0.839492i 0.515164 0.857091i \(-0.327731\pi\)
−0.999845 + 0.0175996i \(0.994398\pi\)
\(200\) 113.067 + 195.838i 0.0399752 + 0.0692391i
\(201\) 1384.17 2397.46i 0.485731 0.841311i
\(202\) −6314.19 −2.19933
\(203\) −704.545 2469.15i −0.243593 0.853697i
\(204\) 1130.77 0.388088
\(205\) 316.454 548.114i 0.107815 0.186741i
\(206\) 529.271 + 916.725i 0.179010 + 0.310055i
\(207\) 24.7470 + 42.8631i 0.00830936 + 0.0143922i
\(208\) −266.760 + 462.042i −0.0889254 + 0.154023i
\(209\) 1532.26 0.507122
\(210\) −991.614 248.607i −0.325847 0.0816929i
\(211\) 640.229 0.208887 0.104444 0.994531i \(-0.466694\pi\)
0.104444 + 0.994531i \(0.466694\pi\)
\(212\) 1635.99 2833.62i 0.530002 0.917990i
\(213\) −779.493 1350.12i −0.250751 0.434314i
\(214\) 1933.07 + 3348.17i 0.617484 + 1.06951i
\(215\) −228.981 + 396.607i −0.0726343 + 0.125806i
\(216\) −244.225 −0.0769323
\(217\) 3245.22 3351.79i 1.01521 1.04854i
\(218\) −680.057 −0.211281
\(219\) −1599.73 + 2770.82i −0.493607 + 0.854952i
\(220\) −901.375 1561.23i −0.276230 0.478445i
\(221\) 233.735 + 404.841i 0.0711435 + 0.123224i
\(222\) −703.948 + 1219.27i −0.212819 + 0.368614i
\(223\) −1970.27 −0.591655 −0.295828 0.955241i \(-0.595595\pi\)
−0.295828 + 0.955241i \(0.595595\pi\)
\(224\) −2747.63 + 2837.86i −0.819570 + 0.846484i
\(225\) 225.000 0.0666667
\(226\) 3864.34 6693.24i 1.13740 1.97003i
\(227\) 2298.03 + 3980.31i 0.671920 + 1.16380i 0.977359 + 0.211588i \(0.0678636\pi\)
−0.305439 + 0.952212i \(0.598803\pi\)
\(228\) −195.789 339.116i −0.0568704 0.0985024i
\(229\) 2312.71 4005.73i 0.667371 1.15592i −0.311266 0.950323i \(-0.600753\pi\)
0.978637 0.205598i \(-0.0659138\pi\)
\(230\) −101.186 −0.0290088
\(231\) −3506.16 879.027i −0.998650 0.250371i
\(232\) 1254.07 0.354888
\(233\) 948.296 1642.50i 0.266631 0.461818i −0.701359 0.712808i \(-0.747423\pi\)
0.967990 + 0.250990i \(0.0807563\pi\)
\(234\) 113.820 + 197.142i 0.0317976 + 0.0550750i
\(235\) −1421.16 2461.53i −0.394496 0.683287i
\(236\) −1412.60 + 2446.69i −0.389628 + 0.674856i
\(237\) −338.440 −0.0927596
\(238\) 1271.87 + 4457.39i 0.346398 + 1.21399i
\(239\) 7217.92 1.95351 0.976754 0.214362i \(-0.0687673\pi\)
0.976754 + 0.214362i \(0.0687673\pi\)
\(240\) 582.167 1008.34i 0.156578 0.271201i
\(241\) −480.020 831.419i −0.128302 0.222226i 0.794717 0.606980i \(-0.207619\pi\)
−0.923019 + 0.384755i \(0.874286\pi\)
\(242\) −5338.73 9246.96i −1.41813 2.45627i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 1449.46 0.380296
\(245\) −55.3955 1714.11i −0.0144453 0.446980i
\(246\) −1397.44 −0.362184
\(247\) 80.9405 140.193i 0.0208507 0.0361145i
\(248\) 1139.30 + 1973.32i 0.291715 + 0.505266i
\(249\) 890.328 + 1542.09i 0.226595 + 0.392474i
\(250\) −229.996 + 398.366i −0.0581850 + 0.100779i
\(251\) 2907.61 0.731183 0.365592 0.930775i \(-0.380867\pi\)
0.365592 + 0.930775i \(0.380867\pi\)
\(252\) 253.466 + 888.297i 0.0633604 + 0.222053i
\(253\) −357.775 −0.0889057
\(254\) −1398.58 + 2422.41i −0.345491 + 0.598409i
\(255\) −510.094 883.509i −0.125268 0.216970i
\(256\) −2685.34 4651.14i −0.655599 1.13553i
\(257\) −1839.05 + 3185.32i −0.446368 + 0.773132i −0.998146 0.0608588i \(-0.980616\pi\)
0.551778 + 0.833991i \(0.313949\pi\)
\(258\) 1011.16 0.244001
\(259\) −2290.96 574.366i −0.549627 0.137797i
\(260\) −190.458 −0.0454297
\(261\) 623.893 1080.61i 0.147962 0.256277i
\(262\) 18.6021 + 32.2197i 0.00438641 + 0.00759749i
\(263\) 2934.87 + 5083.35i 0.688107 + 1.19184i 0.972450 + 0.233113i \(0.0748913\pi\)
−0.284343 + 0.958723i \(0.591775\pi\)
\(264\) 882.707 1528.89i 0.205784 0.356428i
\(265\) −2951.99 −0.684300
\(266\) 1116.54 1153.21i 0.257367 0.265819i
\(267\) −726.976 −0.166630
\(268\) 2557.02 4428.89i 0.582817 1.00947i
\(269\) −230.381 399.031i −0.0522177 0.0904438i 0.838735 0.544540i \(-0.183296\pi\)
−0.890953 + 0.454096i \(0.849962\pi\)
\(270\) −248.396 430.235i −0.0559886 0.0969750i
\(271\) 2657.50 4602.93i 0.595689 1.03176i −0.397760 0.917490i \(-0.630212\pi\)
0.993449 0.114275i \(-0.0364544\pi\)
\(272\) −5279.29 −1.17685
\(273\) −265.637 + 274.360i −0.0588903 + 0.0608243i
\(274\) 10273.4 2.26510
\(275\) −813.224 + 1408.54i −0.178324 + 0.308867i
\(276\) 45.7159 + 79.1822i 0.00997019 + 0.0172689i
\(277\) 1190.29 + 2061.65i 0.258187 + 0.447193i 0.965756 0.259451i \(-0.0835415\pi\)
−0.707569 + 0.706644i \(0.750208\pi\)
\(278\) −951.725 + 1648.44i −0.205326 + 0.355635i
\(279\) 2267.17 0.486494
\(280\) 812.467 + 203.693i 0.173408 + 0.0434750i
\(281\) 1769.23 0.375599 0.187800 0.982207i \(-0.439864\pi\)
0.187800 + 0.982207i \(0.439864\pi\)
\(282\) −3137.88 + 5434.97i −0.662618 + 1.14769i
\(283\) −728.463 1261.74i −0.153013 0.265026i 0.779321 0.626625i \(-0.215564\pi\)
−0.932334 + 0.361599i \(0.882231\pi\)
\(284\) −1439.98 2494.12i −0.300870 0.521122i
\(285\) −176.642 + 305.952i −0.0367135 + 0.0635896i
\(286\) −1645.53 −0.340217
\(287\) −643.252 2254.34i −0.132299 0.463658i
\(288\) −1919.55 −0.392744
\(289\) 143.647 248.803i 0.0292381 0.0506418i
\(290\) 1275.49 + 2209.22i 0.258275 + 0.447345i
\(291\) 2305.33 + 3992.94i 0.464401 + 0.804366i
\(292\) −2955.23 + 5118.61i −0.592267 + 1.02584i
\(293\) −2743.56 −0.547032 −0.273516 0.961868i \(-0.588187\pi\)
−0.273516 + 0.961868i \(0.588187\pi\)
\(294\) −3216.48 + 1998.27i −0.638057 + 0.396399i
\(295\) 2548.90 0.503060
\(296\) 576.771 998.997i 0.113257 0.196167i
\(297\) −878.282 1521.23i −0.171593 0.297207i
\(298\) 3627.16 + 6282.43i 0.705087 + 1.22125i
\(299\) −18.8993 + 32.7345i −0.00365543 + 0.00633138i
\(300\) 415.649 0.0799917
\(301\) 465.447 + 1631.21i 0.0891293 + 0.312363i
\(302\) −595.272 −0.113424
\(303\) 2573.76 4457.88i 0.487982 0.845210i
\(304\) 914.088 + 1583.25i 0.172456 + 0.298702i
\(305\) −653.854 1132.51i −0.122753 0.212614i
\(306\) −1126.27 + 1950.76i −0.210407 + 0.364436i
\(307\) 3367.27 0.625995 0.312997 0.949754i \(-0.398667\pi\)
0.312997 + 0.949754i \(0.398667\pi\)
\(308\) −6477.02 1623.85i −1.19826 0.300414i
\(309\) −862.955 −0.158873
\(310\) −2317.52 + 4014.05i −0.424600 + 0.735429i
\(311\) 3100.15 + 5369.61i 0.565251 + 0.979044i 0.997026 + 0.0770626i \(0.0245541\pi\)
−0.431775 + 0.901981i \(0.642113\pi\)
\(312\) −93.2569 161.526i −0.0169219 0.0293096i
\(313\) −5169.97 + 8954.65i −0.933622 + 1.61708i −0.156550 + 0.987670i \(0.550037\pi\)
−0.777072 + 0.629412i \(0.783296\pi\)
\(314\) −395.550 −0.0710897
\(315\) 579.715 598.753i 0.103693 0.107098i
\(316\) −625.210 −0.111300
\(317\) −1488.66 + 2578.43i −0.263758 + 0.456842i −0.967237 0.253873i \(-0.918295\pi\)
0.703480 + 0.710715i \(0.251629\pi\)
\(318\) 3258.95 + 5644.67i 0.574695 + 0.995401i
\(319\) 4509.91 + 7811.39i 0.791556 + 1.37102i
\(320\) 409.726 709.667i 0.0715762 0.123974i
\(321\) −3151.79 −0.548023
\(322\) −260.708 + 269.269i −0.0451201 + 0.0466018i
\(323\) 1601.85 0.275941
\(324\) −224.450 + 388.760i −0.0384860 + 0.0666597i
\(325\) 85.9161 + 148.811i 0.0146639 + 0.0253986i
\(326\) 3695.16 + 6400.21i 0.627779 + 1.08735i
\(327\) 277.201 480.127i 0.0468785 0.0811959i
\(328\) 1144.97 0.192746
\(329\) −10212.1 2560.26i −1.71128 0.429033i
\(330\) 3591.14 0.599048
\(331\) 3378.51 5851.75i 0.561027 0.971727i −0.436381 0.899762i \(-0.643740\pi\)
0.997407 0.0719644i \(-0.0229268\pi\)
\(332\) 1644.73 + 2848.75i 0.271886 + 0.470920i
\(333\) −573.879 993.988i −0.0944396 0.163574i
\(334\) 1042.35 1805.41i 0.170764 0.295771i
\(335\) −4613.91 −0.752491
\(336\) −1183.36 4147.23i −0.192136 0.673363i
\(337\) 10292.1 1.66364 0.831818 0.555048i \(-0.187300\pi\)
0.831818 + 0.555048i \(0.187300\pi\)
\(338\) 3955.49 6851.12i 0.636540 1.10252i
\(339\) 3150.33 + 5456.53i 0.504726 + 0.874212i
\(340\) −942.312 1632.13i −0.150306 0.260338i
\(341\) −8194.29 + 14192.9i −1.30131 + 2.25393i
\(342\) 780.037 0.123332
\(343\) −4704.17 4269.00i −0.740529 0.672024i
\(344\) −828.485 −0.129852
\(345\) 41.2450 71.4385i 0.00643640 0.0111482i
\(346\) 1376.18 + 2383.61i 0.213826 + 0.370357i
\(347\) −4520.22 7829.25i −0.699303 1.21123i −0.968708 0.248201i \(-0.920161\pi\)
0.269406 0.963027i \(-0.413173\pi\)
\(348\) 1152.54 1996.25i 0.177536 0.307501i
\(349\) −7449.27 −1.14255 −0.571275 0.820759i \(-0.693551\pi\)
−0.571275 + 0.820759i \(0.693551\pi\)
\(350\) 467.511 + 1638.44i 0.0713987 + 0.250224i
\(351\) −185.579 −0.0282207
\(352\) 6937.87 12016.7i 1.05054 1.81959i
\(353\) −848.018 1468.81i −0.127862 0.221464i 0.794986 0.606628i \(-0.207478\pi\)
−0.922848 + 0.385164i \(0.874145\pi\)
\(354\) −2813.94 4873.89i −0.422484 0.731764i
\(355\) −1299.16 + 2250.20i −0.194231 + 0.336418i
\(356\) −1342.96 −0.199935
\(357\) −3665.39 918.948i −0.543398 0.136235i
\(358\) −14893.3 −2.19870
\(359\) −2393.00 + 4144.81i −0.351805 + 0.609344i −0.986566 0.163365i \(-0.947765\pi\)
0.634761 + 0.772709i \(0.281099\pi\)
\(360\) 203.520 + 352.508i 0.0297957 + 0.0516077i
\(361\) 3152.15 + 5459.68i 0.459564 + 0.795988i
\(362\) 5391.63 9338.57i 0.782811 1.35587i
\(363\) 8704.59 1.25860
\(364\) −490.718 + 506.833i −0.0706610 + 0.0729815i
\(365\) 5332.44 0.764693
\(366\) −1443.69 + 2500.54i −0.206182 + 0.357118i
\(367\) −956.276 1656.32i −0.136014 0.235583i 0.789970 0.613145i \(-0.210096\pi\)
−0.925984 + 0.377562i \(0.876763\pi\)
\(368\) −213.436 369.681i −0.0302340 0.0523668i
\(369\) 569.616 986.605i 0.0803606 0.139189i
\(370\) 2346.49 0.329698
\(371\) −7605.85 + 7855.62i −1.06436 + 1.09931i
\(372\) 4188.21 0.583732
\(373\) 6402.04 11088.7i 0.888700 1.53927i 0.0472865 0.998881i \(-0.484943\pi\)
0.841413 0.540392i \(-0.181724\pi\)
\(374\) −8141.42 14101.4i −1.12562 1.94964i
\(375\) −187.500 324.760i −0.0258199 0.0447214i
\(376\) 2570.99 4453.08i 0.352629 0.610771i
\(377\) 952.932 0.130182
\(378\) −1784.90 447.492i −0.242872 0.0608903i
\(379\) −5817.74 −0.788489 −0.394244 0.919006i \(-0.628994\pi\)
−0.394244 + 0.919006i \(0.628994\pi\)
\(380\) −326.315 + 565.194i −0.0440516 + 0.0762996i
\(381\) −1140.17 1974.82i −0.153314 0.265547i
\(382\) −5551.62 9615.68i −0.743574 1.28791i
\(383\) 5650.48 9786.92i 0.753854 1.30571i −0.192088 0.981378i \(-0.561526\pi\)
0.945942 0.324335i \(-0.105141\pi\)
\(384\) 3309.46 0.439806
\(385\) 1653.03 + 5793.22i 0.218822 + 0.766883i
\(386\) 2895.81 0.381847
\(387\) −412.166 + 713.892i −0.0541384 + 0.0937704i
\(388\) 4258.70 + 7376.28i 0.557223 + 0.965139i
\(389\) −635.322 1100.41i −0.0828075 0.143427i 0.821647 0.569996i \(-0.193055\pi\)
−0.904455 + 0.426569i \(0.859722\pi\)
\(390\) 189.700 328.570i 0.0246303 0.0426609i
\(391\) −374.024 −0.0483765
\(392\) 2635.38 1637.26i 0.339559 0.210954i
\(393\) −30.3299 −0.00389298
\(394\) 3698.21 6405.48i 0.472875 0.819044i
\(395\) 282.033 + 488.496i 0.0359257 + 0.0622251i
\(396\) −1622.47 2810.21i −0.205890 0.356612i
\(397\) −5657.04 + 9798.28i −0.715161 + 1.23869i 0.247737 + 0.968827i \(0.420313\pi\)
−0.962898 + 0.269867i \(0.913020\pi\)
\(398\) 10014.0 1.26119
\(399\) 359.057 + 1258.35i 0.0450510 + 0.157886i
\(400\) −1940.56 −0.242570
\(401\) 3398.03 5885.57i 0.423166 0.732945i −0.573081 0.819499i \(-0.694252\pi\)
0.996247 + 0.0865533i \(0.0275853\pi\)
\(402\) 5093.67 + 8822.50i 0.631964 + 1.09459i
\(403\) 865.717 + 1499.47i 0.107008 + 0.185344i
\(404\) 4754.58 8235.17i 0.585518 1.01415i
\(405\) 405.000 0.0496904
\(406\) 9165.34 + 2297.84i 1.12037 + 0.280886i
\(407\) 8296.75 1.01045
\(408\) 922.796 1598.33i 0.111974 0.193944i
\(409\) −4012.23 6949.39i −0.485067 0.840160i 0.514786 0.857319i \(-0.327871\pi\)
−0.999853 + 0.0171587i \(0.994538\pi\)
\(410\) 1164.53 + 2017.03i 0.140273 + 0.242961i
\(411\) −4187.58 + 7253.10i −0.502575 + 0.870485i
\(412\) −1594.16 −0.190628
\(413\) 6567.28 6782.94i 0.782457 0.808152i
\(414\) −182.135 −0.0216219
\(415\) 1483.88 2570.15i 0.175520 0.304009i
\(416\) −732.977 1269.55i −0.0863874 0.149627i
\(417\) −775.874 1343.85i −0.0911145 0.157815i
\(418\) −2819.31 + 4883.19i −0.329897 + 0.571398i
\(419\) 2524.40 0.294332 0.147166 0.989112i \(-0.452985\pi\)
0.147166 + 0.989112i \(0.452985\pi\)
\(420\) 1070.92 1106.09i 0.124419 0.128504i
\(421\) −7844.12 −0.908074 −0.454037 0.890983i \(-0.650017\pi\)
−0.454037 + 0.890983i \(0.650017\pi\)
\(422\) −1178.00 + 2040.36i −0.135887 + 0.235363i
\(423\) −2558.09 4430.75i −0.294040 0.509292i
\(424\) −2670.18 4624.89i −0.305839 0.529728i
\(425\) −850.157 + 1472.51i −0.0970322 + 0.168065i
\(426\) 5736.98 0.652483
\(427\) −4698.41 1177.94i −0.532487 0.133500i
\(428\) −5822.38 −0.657560
\(429\) 670.742 1161.76i 0.0754866 0.130747i
\(430\) −842.637 1459.49i −0.0945013 0.163681i
\(431\) −3411.88 5909.55i −0.381310 0.660448i 0.609940 0.792448i \(-0.291193\pi\)
−0.991250 + 0.132000i \(0.957860\pi\)
\(432\) 1047.90 1815.02i 0.116706 0.202141i
\(433\) −9283.82 −1.03037 −0.515187 0.857078i \(-0.672277\pi\)
−0.515187 + 0.857078i \(0.672277\pi\)
\(434\) 4710.79 + 16509.5i 0.521026 + 1.82599i
\(435\) −2079.64 −0.229221
\(436\) 512.082 886.952i 0.0562483 0.0974250i
\(437\) 64.7608 + 112.169i 0.00708908 + 0.0122786i
\(438\) −5886.93 10196.5i −0.642211 1.11234i
\(439\) −334.674 + 579.672i −0.0363852 + 0.0630210i −0.883645 0.468158i \(-0.844918\pi\)
0.847259 + 0.531179i \(0.178251\pi\)
\(440\) −2942.36 −0.318799
\(441\) −99.7119 3085.39i −0.0107669 0.333159i
\(442\) −1720.26 −0.185123
\(443\) −4874.38 + 8442.68i −0.522774 + 0.905472i 0.476875 + 0.878971i \(0.341770\pi\)
−0.999649 + 0.0265002i \(0.991564\pi\)
\(444\) −1060.14 1836.22i −0.113316 0.196269i
\(445\) 605.813 + 1049.30i 0.0645355 + 0.111779i
\(446\) 3625.24 6279.11i 0.384888 0.666646i
\(447\) −5913.94 −0.625772
\(448\) −832.846 2918.80i −0.0878310 0.307813i
\(449\) 5113.54 0.537467 0.268734 0.963215i \(-0.413395\pi\)
0.268734 + 0.963215i \(0.413395\pi\)
\(450\) −413.994 + 717.058i −0.0433686 + 0.0751165i
\(451\) 4117.56 + 7131.82i 0.429908 + 0.744622i
\(452\) 5819.69 + 10080.0i 0.605609 + 1.04895i
\(453\) 242.642 420.268i 0.0251662 0.0435892i
\(454\) −16913.3 −1.74841
\(455\) 617.368 + 154.780i 0.0636103 + 0.0159477i
\(456\) −639.114 −0.0656343
\(457\) 1739.10 3012.20i 0.178012 0.308326i −0.763187 0.646177i \(-0.776367\pi\)
0.941200 + 0.337851i \(0.109700\pi\)
\(458\) 8510.63 + 14740.8i 0.868287 + 1.50392i
\(459\) −918.169 1590.32i −0.0933692 0.161720i
\(460\) 76.1931 131.970i 0.00772288 0.0133764i
\(461\) −996.935 −0.100720 −0.0503600 0.998731i \(-0.516037\pi\)
−0.0503600 + 0.998731i \(0.516037\pi\)
\(462\) 9252.62 9556.47i 0.931755 0.962354i
\(463\) −12681.1 −1.27287 −0.636436 0.771330i \(-0.719592\pi\)
−0.636436 + 0.771330i \(0.719592\pi\)
\(464\) −5380.89 + 9319.97i −0.538365 + 0.932476i
\(465\) −1889.31 3272.38i −0.188418 0.326350i
\(466\) 3489.68 + 6044.30i 0.346902 + 0.600851i
\(467\) 33.5108 58.0425i 0.00332055 0.00575136i −0.864360 0.502873i \(-0.832276\pi\)
0.867681 + 0.497122i \(0.165610\pi\)
\(468\) −342.825 −0.0338613
\(469\) −11887.8 + 12278.2i −1.17042 + 1.20886i
\(470\) 10459.6 1.02652
\(471\) 161.232 279.262i 0.0157732 0.0273200i
\(472\) 2305.57 + 3993.37i 0.224836 + 0.389427i
\(473\) −2979.40 5160.48i −0.289626 0.501647i
\(474\) 622.720 1078.58i 0.0603428 0.104517i
\(475\) 588.805 0.0568763
\(476\) −6771.18 1697.60i −0.652010 0.163465i
\(477\) −5313.59 −0.510047
\(478\) −13280.8 + 23003.0i −1.27081 + 2.20111i
\(479\) −7832.74 13566.7i −0.747155 1.29411i −0.949181 0.314730i \(-0.898086\pi\)
0.202027 0.979380i \(-0.435247\pi\)
\(480\) 1599.62 + 2770.62i 0.152109 + 0.263461i
\(481\) 438.271 759.107i 0.0415456 0.0719590i
\(482\) 3532.89 0.333857
\(483\) −83.8384 293.820i −0.00789809 0.0276797i
\(484\) 16080.2 1.51017
\(485\) 3842.21 6654.91i 0.359723 0.623059i
\(486\) −447.113 774.423i −0.0417314 0.0722809i
\(487\) 5862.43 + 10154.0i 0.545486 + 0.944810i 0.998576 + 0.0533453i \(0.0169884\pi\)
−0.453090 + 0.891465i \(0.649678\pi\)
\(488\) 1182.87 2048.79i 0.109725 0.190050i
\(489\) −6024.81 −0.557160
\(490\) 5564.65 + 2977.36i 0.513031 + 0.274497i
\(491\) 10584.2 0.972823 0.486412 0.873730i \(-0.338306\pi\)
0.486412 + 0.873730i \(0.338306\pi\)
\(492\) 1052.27 1822.58i 0.0964226 0.167009i
\(493\) 4714.73 + 8166.15i 0.430711 + 0.746014i
\(494\) 297.857 + 515.903i 0.0271279 + 0.0469870i
\(495\) −1463.80 + 2535.38i −0.132915 + 0.230216i
\(496\) −19553.7 −1.77013
\(497\) 2640.78 + 9254.89i 0.238340 + 0.835289i
\(498\) −6552.71 −0.589626
\(499\) −5221.55 + 9044.00i −0.468435 + 0.811352i −0.999349 0.0360729i \(-0.988515\pi\)
0.530915 + 0.847425i \(0.321848\pi\)
\(500\) −346.374 599.938i −0.0309806 0.0536601i
\(501\) 849.758 + 1471.82i 0.0757772 + 0.131250i
\(502\) −5349.93 + 9266.35i −0.475655 + 0.823859i
\(503\) −13824.2 −1.22543 −0.612713 0.790305i \(-0.709922\pi\)
−0.612713 + 0.790305i \(0.709922\pi\)
\(504\) 1462.44 + 366.647i 0.129250 + 0.0324043i
\(505\) −8579.20 −0.755979
\(506\) 658.297 1140.20i 0.0578357 0.100174i
\(507\) 3224.64 + 5585.24i 0.282468 + 0.489249i
\(508\) −2106.26 3648.15i −0.183957 0.318623i
\(509\) 2750.71 4764.38i 0.239535 0.414887i −0.721046 0.692887i \(-0.756338\pi\)
0.960581 + 0.278001i \(0.0896717\pi\)
\(510\) 3754.24 0.325961
\(511\) 13739.1 14190.3i 1.18940 1.22846i
\(512\) 10938.5 0.944178
\(513\) −317.955 + 550.714i −0.0273646 + 0.0473969i
\(514\) −6767.59 11721.8i −0.580750 1.00589i
\(515\) 719.130 + 1245.57i 0.0615313 + 0.106575i
\(516\) −761.405 + 1318.79i −0.0649593 + 0.112513i
\(517\) 36983.2 3.14607
\(518\) 6045.77 6244.31i 0.512810 0.529651i
\(519\) −2243.80 −0.189772
\(520\) −155.428 + 269.210i −0.0131076 + 0.0227031i
\(521\) −4102.73 7106.13i −0.344998 0.597553i 0.640356 0.768079i \(-0.278787\pi\)
−0.985353 + 0.170525i \(0.945454\pi\)
\(522\) 2295.89 + 3976.60i 0.192507 + 0.333431i
\(523\) 9320.29 16143.2i 0.779250 1.34970i −0.153125 0.988207i \(-0.548934\pi\)
0.932375 0.361494i \(-0.117733\pi\)
\(524\) −56.0293 −0.00467109
\(525\) −1347.32 337.786i −0.112004 0.0280804i
\(526\) −21600.3 −1.79053
\(527\) −8566.44 + 14837.5i −0.708084 + 1.22644i
\(528\) 7574.91 + 13120.1i 0.624348 + 1.08140i
\(529\) 6068.38 + 10510.7i 0.498757 + 0.863873i
\(530\) 5431.59 9407.78i 0.445157 0.771034i
\(531\) 4588.02 0.374959
\(532\) 663.297 + 2324.59i 0.0540556 + 0.189444i
\(533\) 870.030 0.0707039
\(534\) 1337.61 2316.82i 0.108397 0.187750i
\(535\) 2626.49 + 4549.21i 0.212249 + 0.367625i
\(536\) −4173.44 7228.61i −0.336316 0.582516i
\(537\) 6070.71 10514.8i 0.487841 0.844965i
\(538\) 1695.58 0.135876
\(539\) 19675.5 + 10527.4i 1.57233 + 0.841274i
\(540\) 748.168 0.0596223
\(541\) −2401.26 + 4159.10i −0.190829 + 0.330525i −0.945525 0.325549i \(-0.894451\pi\)
0.754697 + 0.656074i \(0.227784\pi\)
\(542\) 9779.46 + 16938.5i 0.775025 + 1.34238i
\(543\) 4395.42 + 7613.08i 0.347376 + 0.601673i
\(544\) 7252.95 12562.5i 0.571632 0.990096i
\(545\) −924.004 −0.0726238
\(546\) −385.601 1351.38i −0.0302238 0.105922i
\(547\) 1125.69 0.0879913 0.0439956 0.999032i \(-0.485991\pi\)
0.0439956 + 0.999032i \(0.485991\pi\)
\(548\) −7735.84 + 13398.9i −0.603027 + 1.04447i
\(549\) −1176.94 2038.52i −0.0914945 0.158473i
\(550\) −2992.62 5183.37i −0.232010 0.401854i
\(551\) 1632.67 2827.87i 0.126233 0.218641i
\(552\) 149.230 0.0115066
\(553\) 2026.61 + 508.090i 0.155841 + 0.0390709i
\(554\) −8760.43 −0.671832
\(555\) −956.465 + 1656.65i −0.0731526 + 0.126704i
\(556\) −1433.30 2482.54i −0.109326 0.189358i
\(557\) −4482.81 7764.45i −0.341010 0.590647i 0.643611 0.765353i \(-0.277436\pi\)
−0.984621 + 0.174707i \(0.944102\pi\)
\(558\) −4171.53 + 7225.30i −0.316478 + 0.548156i
\(559\) −629.540 −0.0476328
\(560\) −4999.87 + 5164.06i −0.377291 + 0.389681i
\(561\) 13274.3 0.999001
\(562\) −3255.33 + 5638.40i −0.244338 + 0.423206i
\(563\) −6032.82 10449.2i −0.451604 0.782201i 0.546882 0.837210i \(-0.315815\pi\)
−0.998486 + 0.0550087i \(0.982481\pi\)
\(564\) −4725.64 8185.05i −0.352811 0.611087i
\(565\) 5250.55 9094.21i 0.390959 0.677162i
\(566\) 5361.41 0.398157
\(567\) 1043.49 1077.76i 0.0772881 0.0798262i
\(568\) −4700.53 −0.347235
\(569\) −5902.60 + 10223.6i −0.434886 + 0.753244i −0.997286 0.0736208i \(-0.976545\pi\)
0.562401 + 0.826865i \(0.309878\pi\)
\(570\) −650.031 1125.89i −0.0477663 0.0827337i
\(571\) −514.397 890.962i −0.0377003 0.0652988i 0.846560 0.532294i \(-0.178670\pi\)
−0.884260 + 0.466995i \(0.845337\pi\)
\(572\) 1239.08 2146.15i 0.0905745 0.156880i
\(573\) 9051.69 0.659930
\(574\) 8367.99 + 2097.93i 0.608490 + 0.152554i
\(575\) −137.483 −0.00997123
\(576\) 737.507 1277.40i 0.0533498 0.0924045i
\(577\) −5312.66 9201.79i −0.383308 0.663909i 0.608225 0.793765i \(-0.291882\pi\)
−0.991533 + 0.129856i \(0.958549\pi\)
\(578\) 528.612 + 915.582i 0.0380404 + 0.0658879i
\(579\) −1180.38 + 2044.47i −0.0847233 + 0.146745i
\(580\) −3841.78 −0.275037
\(581\) −3016.27 10570.8i −0.215380 0.754822i
\(582\) −16966.9 −1.20842
\(583\) 19205.1 33264.1i 1.36431 2.36305i
\(584\) 4823.38 + 8354.34i 0.341769 + 0.591961i
\(585\) 154.649 + 267.860i 0.0109298 + 0.0189310i
\(586\) 5048.07 8743.51i 0.355860 0.616367i
\(587\) −4881.61 −0.343246 −0.171623 0.985163i \(-0.554901\pi\)
−0.171623 + 0.985163i \(0.554901\pi\)
\(588\) −184.201 5699.73i −0.0129189 0.399750i
\(589\) 5932.98 0.415050
\(590\) −4689.91 + 8123.16i −0.327255 + 0.566822i
\(591\) 3014.89 + 5221.94i 0.209841 + 0.363455i
\(592\) 4949.54 + 8572.85i 0.343623 + 0.595172i
\(593\) −6931.35 + 12005.4i −0.479994 + 0.831373i −0.999737 0.0229493i \(-0.992694\pi\)
0.519743 + 0.854323i \(0.326028\pi\)
\(594\) 6464.05 0.446504
\(595\) 1728.10 + 6056.33i 0.119068 + 0.417286i
\(596\) −10925.0 −0.750848
\(597\) −4081.85 + 7069.97i −0.279831 + 0.484681i
\(598\) −69.5482 120.461i −0.00475592 0.00823749i
\(599\) −12524.5 21693.1i −0.854320 1.47973i −0.877274 0.479989i \(-0.840641\pi\)
0.0229544 0.999737i \(-0.492693\pi\)
\(600\) 339.201 587.513i 0.0230797 0.0399752i
\(601\) 20281.5 1.37654 0.688268 0.725457i \(-0.258371\pi\)
0.688268 + 0.725457i \(0.258371\pi\)
\(602\) −6054.95 1518.03i −0.409936 0.102775i
\(603\) −8305.03 −0.560874
\(604\) 448.239 776.373i 0.0301963 0.0523016i
\(605\) −7253.83 12564.0i −0.487454 0.844296i
\(606\) 9471.29 + 16404.8i 0.634892 + 1.09967i
\(607\) 681.260 1179.98i 0.0455544 0.0789025i −0.842349 0.538932i \(-0.818828\pi\)
0.887904 + 0.460030i \(0.152161\pi\)
\(608\) −5023.28 −0.335067
\(609\) −5358.23 + 5534.19i −0.356529 + 0.368238i
\(610\) 4812.29 0.319416
\(611\) 1953.61 3383.76i 0.129353 0.224046i
\(612\) −1696.16 2937.84i −0.112031 0.194044i
\(613\) 6988.02 + 12103.6i 0.460430 + 0.797488i 0.998982 0.0451040i \(-0.0143619\pi\)
−0.538552 + 0.842592i \(0.681029\pi\)
\(614\) −6195.68 + 10731.2i −0.407227 + 0.705338i
\(615\) −1898.72 −0.124494
\(616\) −7581.02 + 7829.98i −0.495857 + 0.512141i
\(617\) −3529.04 −0.230265 −0.115133 0.993350i \(-0.536729\pi\)
−0.115133 + 0.993350i \(0.536729\pi\)
\(618\) 1587.81 2750.17i 0.103352 0.179010i
\(619\) −4348.23 7531.36i −0.282343 0.489032i 0.689618 0.724173i \(-0.257778\pi\)
−0.971961 + 0.235141i \(0.924445\pi\)
\(620\) −3490.17 6045.16i −0.226079 0.391580i
\(621\) 74.2411 128.589i 0.00479741 0.00830936i
\(622\) −22816.7 −1.47085
\(623\) 4353.20 + 1091.39i 0.279948 + 0.0701855i
\(624\) 1600.56 0.102682
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −19025.2 32952.6i −1.21470 2.10391i
\(627\) −2298.39 3980.92i −0.146393 0.253561i
\(628\) 297.848 515.889i 0.0189259 0.0327806i
\(629\) 8673.55 0.549821
\(630\) 841.521 + 2949.20i 0.0532174 + 0.186506i
\(631\) −24940.4 −1.57347 −0.786737 0.617289i \(-0.788231\pi\)
−0.786737 + 0.617289i \(0.788231\pi\)
\(632\) −510.218 + 883.724i −0.0321129 + 0.0556213i
\(633\) −960.344 1663.36i −0.0603006 0.104444i
\(634\) −5478.17 9488.47i −0.343164 0.594377i
\(635\) −1900.28 + 3291.37i −0.118756 + 0.205692i
\(636\) −9815.95 −0.611993
\(637\) 2002.55 1244.10i 0.124559 0.0773832i
\(638\) −33192.4 −2.05972
\(639\) −2338.48 + 4050.36i −0.144771 + 0.250751i
\(640\) −2757.89 4776.80i −0.170336 0.295031i
\(641\) −10589.4 18341.3i −0.652503 1.13017i −0.982514 0.186191i \(-0.940386\pi\)
0.330011 0.943977i \(-0.392948\pi\)
\(642\) 5799.20 10044.5i 0.356505 0.617484i
\(643\) 27000.8 1.65600 0.828001 0.560727i \(-0.189478\pi\)
0.828001 + 0.560727i \(0.189478\pi\)
\(644\) −154.877 542.783i −0.00947672 0.0332122i
\(645\) 1373.89 0.0838708
\(646\) −2947.35 + 5104.96i −0.179508 + 0.310916i
\(647\) −7642.44 13237.1i −0.464382 0.804334i 0.534791 0.844984i \(-0.320390\pi\)
−0.999173 + 0.0406506i \(0.987057\pi\)
\(648\) 366.337 + 634.514i 0.0222084 + 0.0384661i
\(649\) −16582.6 + 28721.9i −1.00297 + 1.73719i
\(650\) −632.333 −0.0381571
\(651\) −13576.0 3403.64i −0.817337 0.204914i
\(652\) −11129.8 −0.668523
\(653\) −138.967 + 240.698i −0.00832802 + 0.0144246i −0.870159 0.492770i \(-0.835984\pi\)
0.861831 + 0.507195i \(0.169318\pi\)
\(654\) 1020.09 + 1766.84i 0.0609916 + 0.105640i
\(655\) 25.2749 + 43.7775i 0.00150775 + 0.00261149i
\(656\) −4912.77 + 8509.17i −0.292395 + 0.506444i
\(657\) 9598.40 0.569968
\(658\) 26949.3 27834.3i 1.59665 1.64908i
\(659\) 31344.1 1.85280 0.926398 0.376545i \(-0.122888\pi\)
0.926398 + 0.376545i \(0.122888\pi\)
\(660\) −2704.12 + 4683.68i −0.159482 + 0.276230i
\(661\) 16157.6 + 27985.8i 0.950768 + 1.64678i 0.743768 + 0.668438i \(0.233037\pi\)
0.207000 + 0.978341i \(0.433630\pi\)
\(662\) 12432.7 + 21534.1i 0.729927 + 1.26427i
\(663\) 701.204 1214.52i 0.0410747 0.0711435i
\(664\) 5368.88 0.313785
\(665\) 1517.06 1566.88i 0.0884650 0.0913701i
\(666\) 4223.69 0.245743
\(667\) −381.222 + 660.296i −0.0221304 + 0.0383310i
\(668\) 1569.78 + 2718.94i 0.0909232 + 0.157484i
\(669\) 2955.41 + 5118.91i 0.170796 + 0.295828i
\(670\) 8489.46 14704.2i 0.489517 0.847868i
\(671\) 17015.4 0.978942
\(672\) 11494.4 + 2881.76i 0.659832 + 0.165426i
\(673\) 19454.9 1.11431 0.557156 0.830408i \(-0.311892\pi\)
0.557156 + 0.830408i \(0.311892\pi\)
\(674\) −18937.1 + 32800.1i −1.08224 + 1.87450i
\(675\) −337.500 584.567i −0.0192450 0.0333333i
\(676\) 5956.96 + 10317.8i 0.338926 + 0.587037i
\(677\) −2611.65 + 4523.51i −0.148263 + 0.256799i −0.930585 0.366075i \(-0.880701\pi\)
0.782323 + 0.622873i \(0.214035\pi\)
\(678\) −23186.1 −1.31336
\(679\) −7810.02 27371.1i −0.441416 1.54699i
\(680\) −3075.99 −0.173469
\(681\) 6894.10 11940.9i 0.387933 0.671920i
\(682\) −30154.5 52229.2i −1.69307 2.93249i
\(683\) 9508.03 + 16468.4i 0.532672 + 0.922614i 0.999272 + 0.0381462i \(0.0121452\pi\)
−0.466601 + 0.884468i \(0.654521\pi\)
\(684\) −587.367 + 1017.35i −0.0328341 + 0.0568704i
\(685\) 13958.6 0.778585
\(686\) 22260.5 7137.01i 1.23894 0.397219i
\(687\) −13876.2 −0.770614
\(688\) 3554.80 6157.10i 0.196985 0.341188i
\(689\) −2028.99 3514.31i −0.112189 0.194317i
\(690\) 151.779 + 262.890i 0.00837412 + 0.0145044i
\(691\) −2024.13 + 3505.90i −0.111435 + 0.193011i −0.916349 0.400380i \(-0.868878\pi\)
0.804914 + 0.593391i \(0.202211\pi\)
\(692\) −4145.04 −0.227703
\(693\) 2975.46 + 10427.8i 0.163100 + 0.571601i
\(694\) 33268.3 1.81967
\(695\) −1293.12 + 2239.76i −0.0705770 + 0.122243i
\(696\) −1881.11 3258.18i −0.102447 0.177444i
\(697\) 4304.56 + 7455.72i 0.233927 + 0.405173i
\(698\) 13706.4 23740.3i 0.743261 1.28737i
\(699\) −5689.78 −0.307879
\(700\) −2488.95 624.002i −0.134390 0.0336930i
\(701\) 12385.2 0.667306 0.333653 0.942696i \(-0.391719\pi\)
0.333653 + 0.942696i \(0.391719\pi\)
\(702\) 341.460 591.425i 0.0183583 0.0317976i
\(703\) −1501.79 2601.18i −0.0805706 0.139552i
\(704\) 5331.19 + 9233.88i 0.285407 + 0.494340i
\(705\) −4263.49 + 7384.58i −0.227762 + 0.394496i
\(706\) 6241.32 0.332713
\(707\) −22104.4 + 22830.3i −1.17584 + 1.21446i
\(708\) 8475.59 0.449904
\(709\) 2630.05 4555.37i 0.139314 0.241298i −0.787923 0.615773i \(-0.788844\pi\)
0.927237 + 0.374475i \(0.122177\pi\)
\(710\) −4780.82 8280.62i −0.252705 0.437699i
\(711\) 507.660 + 879.293i 0.0267774 + 0.0463798i
\(712\) −1095.96 + 1898.26i −0.0576865 + 0.0999159i
\(713\) −1385.33 −0.0727642
\(714\) 9672.84 9990.49i 0.506998 0.523648i
\(715\) −2235.81 −0.116943
\(716\) 11214.6 19424.3i 0.585348 1.01385i
\(717\) −10826.9 18752.7i −0.563929 0.976754i
\(718\) −8806.12 15252.7i −0.457718 0.792791i
\(719\) −676.337 + 1171.45i −0.0350808 + 0.0607618i −0.883033 0.469311i \(-0.844502\pi\)
0.847952 + 0.530073i \(0.177836\pi\)
\(720\) −3493.00 −0.180801
\(721\) 5167.46 + 1295.53i 0.266916 + 0.0669183i
\(722\) −23199.4 −1.19584
\(723\) −1440.06 + 2494.26i −0.0740753 + 0.128302i
\(724\) 8119.78 + 14063.9i 0.416808 + 0.721933i
\(725\) 1733.04 + 3001.71i 0.0887770 + 0.153766i
\(726\) −16016.2 + 27740.9i −0.818756 + 1.41813i
\(727\) −2491.53 −0.127106 −0.0635528 0.997978i \(-0.520243\pi\)
−0.0635528 + 0.997978i \(0.520243\pi\)
\(728\) 315.937 + 1107.24i 0.0160844 + 0.0563693i
\(729\) 729.000 0.0370370
\(730\) −9811.54 + 16994.1i −0.497454 + 0.861616i
\(731\) −3114.71 5394.84i −0.157595 0.272962i
\(732\) −2174.19 3765.81i −0.109782 0.190148i
\(733\) −13868.1 + 24020.2i −0.698811 + 1.21038i 0.270068 + 0.962841i \(0.412954\pi\)
−0.968879 + 0.247535i \(0.920380\pi\)
\(734\) 7038.08 0.353924
\(735\) −4370.28 + 2715.08i −0.219320 + 0.136255i
\(736\) 1172.91 0.0587421
\(737\) 30017.1 51991.1i 1.50026 2.59853i
\(738\) 2096.16 + 3630.65i 0.104554 + 0.181092i
\(739\) −19681.8 34089.9i −0.979713 1.69691i −0.663414 0.748253i \(-0.730893\pi\)
−0.316299 0.948659i \(-0.602440\pi\)
\(740\) −1766.91 + 3060.37i −0.0877740 + 0.152029i
\(741\) −485.643 −0.0240763
\(742\) −11040.7 38693.4i −0.546251 1.91439i
\(743\) −14854.4 −0.733451 −0.366725 0.930329i \(-0.619521\pi\)
−0.366725 + 0.930329i \(0.619521\pi\)
\(744\) 3417.89 5919.96i 0.168422 0.291715i
\(745\) 4928.29 + 8536.04i 0.242360 + 0.419780i
\(746\) 23559.1 + 40805.6i 1.15625 + 2.00268i
\(747\) 2670.98 4626.28i 0.130825 0.226595i
\(748\) 24521.9 1.19868
\(749\) 18873.2 + 4731.69i 0.920710 + 0.230831i
\(750\) 1379.98 0.0671863
\(751\) −19784.3 + 34267.4i −0.961302 + 1.66502i −0.242065 + 0.970260i \(0.577825\pi\)
−0.719237 + 0.694765i \(0.755508\pi\)
\(752\) 22062.8 + 38213.9i 1.06988 + 1.85308i
\(753\) −4361.42 7554.20i −0.211074 0.365592i
\(754\) −1753.37 + 3036.92i −0.0846869 + 0.146682i
\(755\) −808.806 −0.0389874
\(756\) 1927.66 1990.97i 0.0927361 0.0957815i
\(757\) −8043.85 −0.386207 −0.193103 0.981178i \(-0.561855\pi\)
−0.193103 + 0.981178i \(0.561855\pi\)
\(758\) 10704.5 18540.7i 0.512934 0.888428i
\(759\) 536.663 + 929.528i 0.0256649 + 0.0444529i
\(760\) 532.595 + 922.482i 0.0254201 + 0.0440288i
\(761\) −16112.9 + 27908.4i −0.767532 + 1.32940i 0.171365 + 0.985208i \(0.445182\pi\)
−0.938897 + 0.344197i \(0.888151\pi\)
\(762\) 8391.49 0.398939
\(763\) −2380.71 + 2458.89i −0.112959 + 0.116668i
\(764\) 16721.4 0.791833
\(765\) −1530.28 + 2650.53i −0.0723235 + 0.125268i
\(766\) 20793.4 + 36015.3i 0.980806 + 1.69881i
\(767\) 1751.93 + 3034.44i 0.0824754 + 0.142852i
\(768\) −8056.01 + 13953.4i −0.378511 + 0.655599i
\(769\) 11196.5 0.525041 0.262521 0.964926i \(-0.415446\pi\)
0.262521 + 0.964926i \(0.415446\pi\)
\(770\) −21504.1 5391.28i −1.00643 0.252322i
\(771\) 11034.3 0.515421
\(772\) −2180.54 + 3776.81i −0.101657 + 0.176076i
\(773\) 10198.4 + 17664.1i 0.474528 + 0.821907i 0.999575 0.0291664i \(-0.00928527\pi\)
−0.525046 + 0.851074i \(0.675952\pi\)
\(774\) −1516.75 2627.08i −0.0704371 0.122001i
\(775\) −3148.85 + 5453.96i −0.145948 + 0.252790i
\(776\) 13901.7 0.643094
\(777\) 1944.20 + 6813.64i 0.0897654 + 0.314592i
\(778\) 4675.90 0.215474
\(779\) 1490.64 2581.86i 0.0685591 0.118748i
\(780\) 285.687 + 494.825i 0.0131144 + 0.0227148i
\(781\) −16904.1 29278.7i −0.774488 1.34145i
\(782\) 688.194 1191.99i 0.0314703 0.0545081i
\(783\) −3743.36 −0.170851
\(784\) 859.985 + 26610.5i 0.0391757 + 1.21222i
\(785\) −537.440 −0.0244357
\(786\) 55.8062 96.6592i 0.00253250 0.00438641i
\(787\) −11037.5 19117.5i −0.499928 0.865901i 0.500072 0.865984i \(-0.333307\pi\)
−1.00000 8.30685e-5i \(0.999974\pi\)
\(788\) 5569.49 + 9646.64i 0.251783 + 0.436100i
\(789\) 8804.62 15250.1i 0.397279 0.688107i
\(790\) −2075.73 −0.0934826
\(791\) −10672.7 37403.7i −0.479745 1.68132i
\(792\) −5296.24 −0.237619
\(793\) 898.825 1556.81i 0.0402500 0.0697150i
\(794\) −20817.6 36057.1i −0.930465 1.61161i
\(795\) 4427.99 + 7669.51i 0.197540 + 0.342150i
\(796\) −7540.51 + 13060.6i −0.335762 + 0.581557i
\(797\) 9131.50 0.405840 0.202920 0.979195i \(-0.434957\pi\)
0.202920 + 0.979195i \(0.434957\pi\)
\(798\) −4670.94 1171.05i −0.207205 0.0519482i
\(799\) 38662.8 1.71188
\(800\) 2666.04 4617.71i 0.117823 0.204076i
\(801\) 1090.46 + 1888.74i 0.0481019 + 0.0833150i
\(802\) 12504.6 + 21658.6i 0.550563 + 0.953604i
\(803\) −34691.8 + 60087.9i −1.52459 + 2.64067i
\(804\) −15342.1 −0.672979
\(805\) −354.228 + 365.861i −0.0155092 + 0.0160185i
\(806\) −6371.58 −0.278448
\(807\) −691.143 + 1197.09i −0.0301479 + 0.0522177i
\(808\) −7760.19 13441.0i −0.337874 0.585215i
\(809\) 9548.26 + 16538.1i 0.414956 + 0.718724i 0.995424 0.0955587i \(-0.0304638\pi\)
−0.580468 + 0.814283i \(0.697130\pi\)
\(810\) −745.189 + 1290.70i −0.0323250 + 0.0559886i
\(811\) −9090.20 −0.393588 −0.196794 0.980445i \(-0.563053\pi\)
−0.196794 + 0.980445i \(0.563053\pi\)
\(812\) −9898.41 + 10223.5i −0.427791 + 0.441839i
\(813\) −15945.0 −0.687843
\(814\) −15265.8 + 26441.1i −0.657329 + 1.13853i
\(815\) 5020.68 + 8696.07i 0.215787 + 0.373755i
\(816\) 7918.93 + 13716.0i 0.339728 + 0.588426i
\(817\) −1078.60 + 1868.19i −0.0461878 + 0.0799997i
\(818\) 29529.6 1.26220
\(819\) 1111.26 + 278.604i 0.0474123 + 0.0118867i
\(820\) −3507.56 −0.149377
\(821\) −10587.9 + 18338.8i −0.450085 + 0.779571i −0.998391 0.0567074i \(-0.981940\pi\)
0.548305 + 0.836278i \(0.315273\pi\)
\(822\) −15410.1 26691.0i −0.653878 1.13255i
\(823\) −7456.89 12915.7i −0.315833 0.547040i 0.663781 0.747927i \(-0.268951\pi\)
−0.979614 + 0.200888i \(0.935617\pi\)
\(824\) −1300.96 + 2253.32i −0.0550012 + 0.0952648i
\(825\) 4879.34 0.205911
\(826\) 9533.13 + 33409.8i 0.401574 + 1.40736i
\(827\) −36795.0 −1.54714 −0.773571 0.633710i \(-0.781531\pi\)
−0.773571 + 0.633710i \(0.781531\pi\)
\(828\) 137.148 237.547i 0.00575629 0.00997019i
\(829\) −6029.62 10443.6i −0.252614 0.437541i 0.711631 0.702554i \(-0.247957\pi\)
−0.964245 + 0.265013i \(0.914624\pi\)
\(830\) 5460.59 + 9458.02i 0.228361 + 0.395533i
\(831\) 3570.88 6184.95i 0.149064 0.258187i
\(832\) 1126.47 0.0469389
\(833\) 20569.1 + 11005.5i 0.855556 + 0.457765i
\(834\) 5710.35 0.237090
\(835\) 1416.26 2453.04i 0.0586968 0.101666i
\(836\) −4245.87 7354.07i −0.175654 0.304241i
\(837\) −3400.75 5890.28i −0.140439 0.243247i
\(838\) −4644.82 + 8045.07i −0.191471 + 0.331638i
\(839\) −30556.5 −1.25736 −0.628681 0.777663i \(-0.716405\pi\)
−0.628681 + 0.777663i \(0.716405\pi\)
\(840\) −689.490 2416.39i −0.0283210 0.0992540i
\(841\) −5167.15 −0.211864
\(842\) 14433.0 24998.6i 0.590728 1.02317i
\(843\) −2653.84 4596.59i −0.108426 0.187800i
\(844\) −1774.07 3072.78i −0.0723531 0.125319i
\(845\) 5374.39 9308.73i 0.218799 0.378970i
\(846\) 18827.3 0.765125
\(847\) −52123.9 13068.0i −2.11452 0.530130i
\(848\) 45828.1 1.85583
\(849\) −2185.39 + 3785.21i −0.0883420 + 0.153013i
\(850\) −3128.53 5418.77i −0.126244 0.218662i
\(851\) 350.662 + 607.364i 0.0141252 + 0.0244655i
\(852\) −4319.94 + 7482.35i −0.173707 + 0.300870i
\(853\) −42918.6 −1.72275 −0.861375 0.507969i \(-0.830396\pi\)
−0.861375 + 0.507969i \(0.830396\pi\)
\(854\) 12398.9 12806.1i 0.496818 0.513134i
\(855\) 1059.85 0.0423931
\(856\) −4751.50 + 8229.84i −0.189723 + 0.328610i
\(857\) 3089.36 + 5350.92i 0.123139 + 0.213284i 0.921004 0.389553i \(-0.127370\pi\)
−0.797865 + 0.602837i \(0.794037\pi\)
\(858\) 2468.29 + 4275.21i 0.0982123 + 0.170109i
\(859\) −2545.27 + 4408.53i −0.101098 + 0.175107i −0.912137 0.409885i \(-0.865569\pi\)
0.811039 + 0.584992i \(0.198902\pi\)
\(860\) 2538.02 0.100635
\(861\) −4892.08 + 5052.73i −0.193637 + 0.199996i
\(862\) 25111.0 0.992211
\(863\) −5734.20 + 9931.92i −0.226181 + 0.391757i −0.956673 0.291164i \(-0.905957\pi\)
0.730492 + 0.682921i \(0.239291\pi\)
\(864\) 2879.32 + 4987.12i 0.113375 + 0.196372i
\(865\) 1869.83 + 3238.65i 0.0734985 + 0.127303i
\(866\) 17082.0 29586.8i 0.670287 1.16097i
\(867\) −861.880 −0.0337612
\(868\) −25079.4 6287.64i −0.980703 0.245871i
\(869\) −7339.40 −0.286504
\(870\) 3826.48 6627.67i 0.149115 0.258275i
\(871\) −3171.27 5492.80i −0.123369 0.213681i
\(872\) −835.794 1447.64i −0.0324582 0.0562193i
\(873\) 6915.98 11978.8i 0.268122 0.464401i
\(874\) −476.632 −0.0184466
\(875\) 635.215 + 2226.18i 0.0245419 + 0.0860098i
\(876\) 17731.4 0.683891
\(877\) 2773.13 4803.21i 0.106775 0.184940i −0.807687 0.589612i \(-0.799281\pi\)
0.914462 + 0.404671i \(0.132614\pi\)
\(878\) −1231.58 2133.16i −0.0473392 0.0819939i
\(879\) 4115.33 + 7127.97i 0.157914 + 0.273516i
\(880\) 12624.9 21866.9i 0.483618 0.837651i
\(881\) 1259.32 0.0481586 0.0240793 0.999710i \(-0.492335\pi\)
0.0240793 + 0.999710i \(0.492335\pi\)
\(882\) 10016.4 + 5359.26i 0.382391 + 0.204598i
\(883\) −155.096 −0.00591100 −0.00295550 0.999996i \(-0.500941\pi\)
−0.00295550 + 0.999996i \(0.500941\pi\)
\(884\) 1295.36 2243.62i 0.0492845 0.0853633i
\(885\) −3823.35 6622.24i −0.145221 0.251530i
\(886\) −17937.5 31068.6i −0.680159 1.17807i
\(887\) 10447.4 18095.5i 0.395479 0.684990i −0.597683 0.801733i \(-0.703912\pi\)
0.993162 + 0.116742i \(0.0372451\pi\)
\(888\) −3460.63 −0.130778
\(889\) 3862.67 + 13537.1i 0.145725 + 0.510710i
\(890\) −4458.72 −0.167929
\(891\) −2634.84 + 4563.69i −0.0990692 + 0.171593i
\(892\) 5459.61 + 9456.32i 0.204934 + 0.354956i
\(893\) −6694.31 11594.9i −0.250858 0.434499i
\(894\) 10881.5 18847.3i 0.407082 0.705087i
\(895\) −20235.7 −0.755760
\(896\) −19817.4 4968.41i −0.738898 0.185249i
\(897\) 113.396 0.00422092
\(898\) −9408.77 + 16296.5i −0.349638 + 0.605590i
\(899\) 17462.6 + 30246.1i 0.647843 + 1.12210i
\(900\) −623.473 1079.89i −0.0230916 0.0399958i
\(901\) 20077.3 34774.8i 0.742365 1.28581i
\(902\) −30304.8 −1.11867
\(903\) 3539.83 3656.08i 0.130452 0.134736i
\(904\) 18997.2 0.698936
\(905\) 7325.69 12688.5i 0.269077 0.466054i
\(906\) 892.908 + 1546.56i 0.0327427 + 0.0567120i
\(907\) 19876.3 + 34426.7i 0.727653 + 1.26033i 0.957873 + 0.287193i \(0.0927220\pi\)
−0.230220 + 0.973139i \(0.573945\pi\)
\(908\) 12735.7 22058.8i 0.465472 0.806221i
\(909\) −15442.6 −0.563473
\(910\) −1629.21 + 1682.72i −0.0593493 + 0.0612983i
\(911\) 494.980 0.0180015 0.00900077 0.999959i \(-0.497135\pi\)
0.00900077 + 0.999959i \(0.497135\pi\)
\(912\) 2742.26 4749.74i 0.0995674 0.172456i
\(913\) 19307.6 + 33441.8i 0.699878 + 1.21222i
\(914\) 6399.78 + 11084.7i 0.231604 + 0.401149i
\(915\) −1961.56 + 3397.53i −0.0708713 + 0.122753i
\(916\) −25634.0 −0.924640
\(917\) 181.618 + 45.5335i 0.00654043 + 0.00163975i
\(918\) 6757.62 0.242957
\(919\) 16893.8 29260.9i 0.606393 1.05030i −0.385437 0.922734i \(-0.625949\pi\)
0.991830 0.127569i \(-0.0407173\pi\)
\(920\) −124.359 215.395i −0.00445650 0.00771889i
\(921\) −5050.91 8748.43i −0.180709 0.312997i
\(922\) 1834.33 3177.16i 0.0655212 0.113486i
\(923\) −3571.78 −0.127375
\(924\) 5496.65 + 19263.6i 0.195700 + 0.685850i
\(925\) 3188.22 0.113328
\(926\) 23332.8 40413.6i 0.828039 1.43421i
\(927\) 1294.43 + 2242.02i 0.0458627 + 0.0794366i
\(928\) −14785.1 25608.5i −0.523000 0.905862i
\(929\) 19884.7 34441.3i 0.702256 1.21634i −0.265416 0.964134i \(-0.585509\pi\)
0.967673 0.252210i \(-0.0811573\pi\)
\(930\) 13905.1 0.490286
\(931\) −260.937 8074.19i −0.00918569 0.284233i
\(932\) −10510.9 −0.369416
\(933\) 9300.44 16108.8i 0.326348 0.565251i
\(934\) 123.318 + 213.593i 0.00432022 + 0.00748284i
\(935\) −11061.9 19159.7i −0.386912 0.670150i
\(936\) −279.771 + 484.577i −0.00976987 + 0.0169219i
\(937\) 16823.9 0.586568 0.293284 0.956025i \(-0.405252\pi\)
0.293284 + 0.956025i \(0.405252\pi\)
\(938\) −17256.4 60477.0i −0.600685 2.10516i
\(939\) 31019.8 1.07805
\(940\) −7876.07 + 13641.8i −0.273286 + 0.473346i
\(941\) 307.746 + 533.031i 0.0106612 + 0.0184658i 0.871307 0.490739i \(-0.163273\pi\)
−0.860646 + 0.509204i \(0.829940\pi\)
\(942\) 593.324 + 1027.67i 0.0205218 + 0.0355448i
\(943\) −348.057 + 602.852i −0.0120194 + 0.0208182i
\(944\) −39570.3 −1.36430
\(945\) −2425.18 608.015i −0.0834826 0.0209299i
\(946\) 21928.1 0.753640
\(947\) −21017.8 + 36403.9i −0.721211 + 1.24917i 0.239303 + 0.970945i \(0.423081\pi\)
−0.960515 + 0.278230i \(0.910252\pi\)
\(948\) 937.815 + 1624.34i 0.0321295 + 0.0556500i
\(949\) 3665.14 + 6348.21i 0.125369 + 0.217146i
\(950\) −1083.38 + 1876.48i −0.0369996 + 0.0640852i
\(951\) 8931.93 0.304561
\(952\) −7925.32 + 8185.58i −0.269812 + 0.278673i
\(953\) −16830.2 −0.572070 −0.286035 0.958219i \(-0.592337\pi\)
−0.286035 + 0.958219i \(0.592337\pi\)
\(954\) 9776.86 16934.0i 0.331800 0.574695i
\(955\) −7543.07 13065.0i −0.255590 0.442694i
\(956\) −20000.8 34642.4i −0.676645 1.17198i
\(957\) 13529.7 23434.2i 0.457005 0.791556i
\(958\) 57648.1 1.94418
\(959\) 35964.5 37145.6i 1.21101 1.25078i
\(960\) −2458.36 −0.0826491
\(961\) −16833.3 + 29156.0i −0.565045 + 0.978686i
\(962\) 1612.81 + 2793.47i 0.0540531 + 0.0936228i
\(963\) 4727.68 + 8188.58i 0.158201 + 0.274012i
\(964\) −2660.27 + 4607.71i −0.0888811 + 0.153947i
\(965\) 3934.59 0.131253
\(966\) 1090.64 + 273.435i 0.0363260 + 0.00910726i
\(967\) −3695.45 −0.122893 −0.0614466 0.998110i \(-0.519571\pi\)
−0.0614466 + 0.998110i \(0.519571\pi\)
\(968\) 13122.7 22729.2i 0.435722 0.754693i
\(969\) −2402.77 4161.72i −0.0796574 0.137971i
\(970\) 14139.1 + 24489.7i 0.468020 + 0.810635i
\(971\) −11182.2 + 19368.1i −0.369571 + 0.640115i −0.989498 0.144544i \(-0.953829\pi\)
0.619928 + 0.784659i \(0.287162\pi\)
\(972\) 1346.70 0.0444398
\(973\) 2628.52 + 9211.93i 0.0866048 + 0.303516i
\(974\) −43146.8 −1.41942
\(975\) 257.748 446.433i 0.00846620 0.0146639i
\(976\) 10150.7 + 17581.6i 0.332907 + 0.576611i
\(977\) 17216.9 + 29820.6i 0.563786 + 0.976505i 0.997162 + 0.0752921i \(0.0239889\pi\)
−0.433376 + 0.901213i \(0.642678\pi\)
\(978\) 11085.5 19200.6i 0.362449 0.627779i
\(979\) −15765.2 −0.514665
\(980\) −8073.35 + 5015.64i −0.263157 + 0.163489i
\(981\) −1663.21 −0.0541306
\(982\) −19474.6 + 33730.9i −0.632849 + 1.09613i
\(983\) −3696.27 6402.13i −0.119932 0.207728i 0.799809 0.600255i \(-0.204934\pi\)
−0.919740 + 0.392527i \(0.871601\pi\)
\(984\) −1717.46 2974.73i −0.0556409 0.0963729i
\(985\) 5024.81 8703.23i 0.162542 0.281531i
\(986\) −34699.9 −1.12076
\(987\) 8666.35 + 30372.2i 0.279486 + 0.979490i
\(988\) −897.142 −0.0288886
\(989\) 251.849 436.215i 0.00809739 0.0140251i
\(990\) −5386.71 9330.06i −0.172930 0.299524i
\(991\) −20793.5 36015.4i −0.666526 1.15446i −0.978869 0.204487i \(-0.934447\pi\)
0.312344 0.949969i \(-0.398886\pi\)
\(992\) 26863.8 46529.5i 0.859805 1.48923i
\(993\) −20271.1 −0.647818
\(994\) −34353.6 8612.77i −1.09621 0.274829i
\(995\) 13606.2 0.433512
\(996\) 4934.18 8546.26i 0.156973 0.271886i
\(997\) 5336.16 + 9242.51i 0.169507 + 0.293594i 0.938246 0.345968i \(-0.112449\pi\)
−0.768740 + 0.639561i \(0.779116\pi\)
\(998\) −19215.0 33281.4i −0.609460 1.05562i
\(999\) −1721.64 + 2981.96i −0.0545247 + 0.0944396i
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 105.4.i.d.16.2 10
3.2 odd 2 315.4.j.h.226.4 10
7.2 even 3 735.4.a.ba.1.4 5
7.4 even 3 inner 105.4.i.d.46.2 yes 10
7.5 odd 6 735.4.a.z.1.4 5
21.2 odd 6 2205.4.a.br.1.2 5
21.5 even 6 2205.4.a.bs.1.2 5
21.11 odd 6 315.4.j.h.46.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.i.d.16.2 10 1.1 even 1 trivial
105.4.i.d.46.2 yes 10 7.4 even 3 inner
315.4.j.h.46.4 10 21.11 odd 6
315.4.j.h.226.4 10 3.2 odd 2
735.4.a.z.1.4 5 7.5 odd 6
735.4.a.ba.1.4 5 7.2 even 3
2205.4.a.br.1.2 5 21.2 odd 6
2205.4.a.bs.1.2 5 21.5 even 6