Properties

Label 25.4.e.a.14.1
Level $25$
Weight $4$
Character 25.14
Analytic conductor $1.475$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,4,Mod(4,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\), degree \(4\), 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: \(1.47504775014\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 14.1
Character \(\chi\) \(=\) 25.14
Dual form 25.4.e.a.9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.42187 - 3.33341i) q^{2} +(-3.56321 - 1.15776i) q^{3} +(-2.77407 + 8.53772i) q^{4} +(-8.01402 + 7.79587i) q^{5} +(4.77034 + 14.6816i) q^{6} -26.4674i q^{7} +(3.82887 - 1.24408i) q^{8} +(-10.4874 - 7.61952i) q^{9} +O(q^{10})\) \(q+(-2.42187 - 3.33341i) q^{2} +(-3.56321 - 1.15776i) q^{3} +(-2.77407 + 8.53772i) q^{4} +(-8.01402 + 7.79587i) q^{5} +(4.77034 + 14.6816i) q^{6} -26.4674i q^{7} +(3.82887 - 1.24408i) q^{8} +(-10.4874 - 7.61952i) q^{9} +(45.3957 + 7.83348i) q^{10} +(15.6737 - 11.3876i) q^{11} +(19.7692 - 27.2100i) q^{12} +(26.2024 - 36.0645i) q^{13} +(-88.2266 + 64.1004i) q^{14} +(37.5814 - 18.5000i) q^{15} +(44.6809 + 32.4626i) q^{16} +(-70.5478 + 22.9224i) q^{17} +53.4122i q^{18} +(-6.14742 - 18.9198i) q^{19} +(-44.3274 - 90.0477i) q^{20} +(-30.6428 + 94.3088i) q^{21} +(-75.9192 - 24.6676i) q^{22} +(36.2441 + 49.8857i) q^{23} -15.0834 q^{24} +(3.44892 - 124.952i) q^{25} -183.676 q^{26} +(88.0062 + 121.130i) q^{27} +(225.971 + 73.4224i) q^{28} +(88.7735 - 273.217i) q^{29} +(-152.685 - 80.4696i) q^{30} +(25.1347 + 77.3567i) q^{31} -259.767i q^{32} +(-69.0328 + 22.4301i) q^{33} +(247.267 + 179.650i) q^{34} +(206.336 + 212.110i) q^{35} +(94.1461 - 68.4011i) q^{36} +(-230.938 + 317.858i) q^{37} +(-48.1793 + 66.3131i) q^{38} +(-135.119 + 98.1694i) q^{39} +(-20.9860 + 39.8194i) q^{40} +(-176.752 - 128.418i) q^{41} +(388.583 - 126.258i) q^{42} -430.797i q^{43} +(53.7442 + 165.408i) q^{44} +(143.447 - 20.6952i) q^{45} +(78.5113 - 241.633i) q^{46} +(-174.686 - 56.7589i) q^{47} +(-121.624 - 167.401i) q^{48} -357.521 q^{49} +(-424.871 + 291.121i) q^{50} +277.915 q^{51} +(235.221 + 323.754i) q^{52} +(-59.1999 - 19.2352i) q^{53} +(190.638 - 586.722i) q^{54} +(-36.8330 + 213.451i) q^{55} +(-32.9274 - 101.340i) q^{56} +74.5325i q^{57} +(-1125.74 + 365.776i) q^{58} +(299.411 + 217.535i) q^{59} +(53.6947 + 372.180i) q^{60} +(180.255 - 130.963i) q^{61} +(196.989 - 271.132i) q^{62} +(-201.669 + 277.573i) q^{63} +(-508.464 + 369.421i) q^{64} +(71.1676 + 493.291i) q^{65} +(241.957 + 175.792i) q^{66} +(423.363 - 137.559i) q^{67} -665.905i q^{68} +(-71.3898 - 219.715i) q^{69} +(207.332 - 1201.50i) q^{70} +(126.710 - 389.973i) q^{71} +(-49.6341 - 16.1271i) q^{72} +(196.202 + 270.049i) q^{73} +1618.85 q^{74} +(-156.954 + 441.239i) q^{75} +178.585 q^{76} +(-301.400 - 414.841i) q^{77} +(654.478 + 212.653i) q^{78} +(77.3261 - 237.985i) q^{79} +(-611.147 + 88.1707i) q^{80} +(-65.1884 - 200.629i) q^{81} +900.197i q^{82} +(1008.98 - 327.838i) q^{83} +(-720.177 - 523.239i) q^{84} +(386.671 - 733.681i) q^{85} +(-1436.03 + 1043.33i) q^{86} +(-632.638 + 870.752i) q^{87} +(45.8455 - 63.1010i) q^{88} +(-425.441 + 309.101i) q^{89} +(-416.395 - 428.046i) q^{90} +(-954.531 - 693.507i) q^{91} +(-526.453 + 171.055i) q^{92} -304.738i q^{93} +(233.865 + 719.763i) q^{94} +(196.762 + 103.699i) q^{95} +(-300.748 + 925.606i) q^{96} +(469.781 + 152.641i) q^{97} +(865.868 + 1191.77i) q^{98} -251.144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42187 3.33341i −0.856259 1.17854i −0.982449 0.186534i \(-0.940275\pi\)
0.126189 0.992006i \(-0.459725\pi\)
\(3\) −3.56321 1.15776i −0.685741 0.222811i −0.0546337 0.998506i \(-0.517399\pi\)
−0.631107 + 0.775696i \(0.717399\pi\)
\(4\) −2.77407 + 8.53772i −0.346759 + 1.06721i
\(5\) −8.01402 + 7.79587i −0.716795 + 0.697284i
\(6\) 4.77034 + 14.6816i 0.324581 + 0.998956i
\(7\) 26.4674i 1.42910i −0.699583 0.714551i \(-0.746631\pi\)
0.699583 0.714551i \(-0.253369\pi\)
\(8\) 3.82887 1.24408i 0.169214 0.0549809i
\(9\) −10.4874 7.61952i −0.388421 0.282205i
\(10\) 45.3957 + 7.83348i 1.43554 + 0.247716i
\(11\) 15.6737 11.3876i 0.429618 0.312136i −0.351878 0.936046i \(-0.614457\pi\)
0.781496 + 0.623910i \(0.214457\pi\)
\(12\) 19.7692 27.2100i 0.475574 0.654571i
\(13\) 26.2024 36.0645i 0.559018 0.769422i −0.432184 0.901786i \(-0.642257\pi\)
0.991201 + 0.132364i \(0.0422568\pi\)
\(14\) −88.2266 + 64.1004i −1.68425 + 1.22368i
\(15\) 37.5814 18.5000i 0.646898 0.318446i
\(16\) 44.6809 + 32.4626i 0.698139 + 0.507228i
\(17\) −70.5478 + 22.9224i −1.00649 + 0.327029i −0.765457 0.643488i \(-0.777487\pi\)
−0.241035 + 0.970516i \(0.577487\pi\)
\(18\) 53.4122i 0.699410i
\(19\) −6.14742 18.9198i −0.0742271 0.228447i 0.907059 0.421004i \(-0.138322\pi\)
−0.981286 + 0.192556i \(0.938322\pi\)
\(20\) −44.3274 90.0477i −0.495596 1.00676i
\(21\) −30.6428 + 94.3088i −0.318419 + 0.979994i
\(22\) −75.9192 24.6676i −0.735729 0.239053i
\(23\) 36.2441 + 49.8857i 0.328583 + 0.452256i 0.941063 0.338230i \(-0.109828\pi\)
−0.612480 + 0.790486i \(0.709828\pi\)
\(24\) −15.0834 −0.128287
\(25\) 3.44892 124.952i 0.0275913 0.999619i
\(26\) −183.676 −1.38546
\(27\) 88.0062 + 121.130i 0.627289 + 0.863389i
\(28\) 225.971 + 73.4224i 1.52516 + 0.495554i
\(29\) 88.7735 273.217i 0.568442 1.74949i −0.0890523 0.996027i \(-0.528384\pi\)
0.657495 0.753459i \(-0.271616\pi\)
\(30\) −152.685 80.4696i −0.929214 0.489723i
\(31\) 25.1347 + 77.3567i 0.145624 + 0.448183i 0.997091 0.0762249i \(-0.0242867\pi\)
−0.851467 + 0.524408i \(0.824287\pi\)
\(32\) 259.767i 1.43502i
\(33\) −69.0328 + 22.4301i −0.364154 + 0.118321i
\(34\) 247.267 + 179.650i 1.24723 + 0.906169i
\(35\) 206.336 + 212.110i 0.996490 + 1.02437i
\(36\) 94.1461 68.4011i 0.435861 0.316672i
\(37\) −230.938 + 317.858i −1.02611 + 1.41231i −0.118273 + 0.992981i \(0.537736\pi\)
−0.907833 + 0.419332i \(0.862264\pi\)
\(38\) −48.1793 + 66.3131i −0.205677 + 0.283090i
\(39\) −135.119 + 98.1694i −0.554776 + 0.403069i
\(40\) −20.9860 + 39.8194i −0.0829544 + 0.157400i
\(41\) −176.752 128.418i −0.673268 0.489158i 0.197850 0.980232i \(-0.436604\pi\)
−0.871118 + 0.491075i \(0.836604\pi\)
\(42\) 388.583 126.258i 1.42761 0.463859i
\(43\) 430.797i 1.52781i −0.645327 0.763906i \(-0.723279\pi\)
0.645327 0.763906i \(-0.276721\pi\)
\(44\) 53.7442 + 165.408i 0.184142 + 0.566730i
\(45\) 143.447 20.6952i 0.475195 0.0685568i
\(46\) 78.5113 241.633i 0.251649 0.774496i
\(47\) −174.686 56.7589i −0.542139 0.176152i 0.0251299 0.999684i \(-0.492000\pi\)
−0.567269 + 0.823532i \(0.692000\pi\)
\(48\) −121.624 167.401i −0.365727 0.503379i
\(49\) −357.521 −1.04234
\(50\) −424.871 + 291.121i −1.20172 + 0.823416i
\(51\) 277.915 0.763058
\(52\) 235.221 + 323.754i 0.627294 + 0.863396i
\(53\) −59.1999 19.2352i −0.153429 0.0498520i 0.231296 0.972884i \(-0.425704\pi\)
−0.384724 + 0.923031i \(0.625704\pi\)
\(54\) 190.638 586.722i 0.480417 1.47857i
\(55\) −36.8330 + 213.451i −0.0903011 + 0.523303i
\(56\) −32.9274 101.340i −0.0785734 0.241824i
\(57\) 74.5325i 0.173194i
\(58\) −1125.74 + 365.776i −2.54857 + 0.828082i
\(59\) 299.411 + 217.535i 0.660678 + 0.480010i 0.866892 0.498497i \(-0.166114\pi\)
−0.206214 + 0.978507i \(0.566114\pi\)
\(60\) 53.6947 + 372.180i 0.115533 + 0.800803i
\(61\) 180.255 130.963i 0.378348 0.274886i −0.382316 0.924032i \(-0.624873\pi\)
0.760664 + 0.649146i \(0.224873\pi\)
\(62\) 196.989 271.132i 0.403510 0.555384i
\(63\) −201.669 + 277.573i −0.403299 + 0.555094i
\(64\) −508.464 + 369.421i −0.993095 + 0.721526i
\(65\) 71.1676 + 493.291i 0.135804 + 0.941312i
\(66\) 241.957 + 175.792i 0.451256 + 0.327856i
\(67\) 423.363 137.559i 0.771970 0.250828i 0.103562 0.994623i \(-0.466976\pi\)
0.668408 + 0.743795i \(0.266976\pi\)
\(68\) 665.905i 1.18754i
\(69\) −71.3898 219.715i −0.124555 0.383342i
\(70\) 207.332 1201.50i 0.354012 2.05153i
\(71\) 126.710 389.973i 0.211798 0.651848i −0.787567 0.616229i \(-0.788660\pi\)
0.999365 0.0356193i \(-0.0113404\pi\)
\(72\) −49.6341 16.1271i −0.0812421 0.0263972i
\(73\) 196.202 + 270.049i 0.314571 + 0.432970i 0.936800 0.349865i \(-0.113773\pi\)
−0.622229 + 0.782835i \(0.713773\pi\)
\(74\) 1618.85 2.54308
\(75\) −156.954 + 441.239i −0.241646 + 0.679332i
\(76\) 178.585 0.269541
\(77\) −301.400 414.841i −0.446074 0.613968i
\(78\) 654.478 + 212.653i 0.950065 + 0.308695i
\(79\) 77.3261 237.985i 0.110125 0.338930i −0.880774 0.473537i \(-0.842977\pi\)
0.990899 + 0.134607i \(0.0429772\pi\)
\(80\) −611.147 + 88.1707i −0.854104 + 0.123222i
\(81\) −65.1884 200.629i −0.0894216 0.275212i
\(82\) 900.197i 1.21232i
\(83\) 1008.98 327.838i 1.33434 0.433553i 0.446944 0.894562i \(-0.352512\pi\)
0.887396 + 0.461009i \(0.152512\pi\)
\(84\) −720.177 523.239i −0.935449 0.679644i
\(85\) 386.671 733.681i 0.493417 0.936223i
\(86\) −1436.03 + 1043.33i −1.80059 + 1.30820i
\(87\) −632.638 + 870.752i −0.779608 + 1.07304i
\(88\) 45.8455 63.1010i 0.0555358 0.0764385i
\(89\) −425.441 + 309.101i −0.506704 + 0.368142i −0.811572 0.584252i \(-0.801388\pi\)
0.304868 + 0.952395i \(0.401388\pi\)
\(90\) −416.395 428.046i −0.487687 0.501334i
\(91\) −954.531 693.507i −1.09958 0.798894i
\(92\) −526.453 + 171.055i −0.596593 + 0.193845i
\(93\) 304.738i 0.339784i
\(94\) 233.865 + 719.763i 0.256610 + 0.789764i
\(95\) 196.762 + 103.699i 0.212498 + 0.111993i
\(96\) −300.748 + 925.606i −0.319739 + 0.984055i
\(97\) 469.781 + 152.641i 0.491743 + 0.159777i 0.544383 0.838837i \(-0.316764\pi\)
−0.0526405 + 0.998614i \(0.516764\pi\)
\(98\) 865.868 + 1191.77i 0.892509 + 1.22843i
\(99\) −251.144 −0.254959
\(100\) 1057.24 + 376.073i 1.05724 + 0.376073i
\(101\) −212.047 −0.208906 −0.104453 0.994530i \(-0.533309\pi\)
−0.104453 + 0.994530i \(0.533309\pi\)
\(102\) −673.074 926.407i −0.653375 0.899294i
\(103\) 550.741 + 178.947i 0.526856 + 0.171186i 0.560354 0.828253i \(-0.310665\pi\)
−0.0334986 + 0.999439i \(0.510665\pi\)
\(104\) 55.4586 170.684i 0.0522900 0.160932i
\(105\) −489.647 994.680i −0.455092 0.924484i
\(106\) 79.2553 + 243.923i 0.0726222 + 0.223508i
\(107\) 1045.08i 0.944225i −0.881538 0.472112i \(-0.843492\pi\)
0.881538 0.472112i \(-0.156508\pi\)
\(108\) −1278.31 + 415.348i −1.13894 + 0.370064i
\(109\) −1457.66 1059.05i −1.28091 0.930633i −0.281326 0.959612i \(-0.590774\pi\)
−0.999580 + 0.0289797i \(0.990774\pi\)
\(110\) 800.724 394.169i 0.694055 0.341660i
\(111\) 1190.88 865.227i 1.01832 0.739853i
\(112\) 859.198 1182.58i 0.724880 0.997712i
\(113\) −27.4350 + 37.7611i −0.0228396 + 0.0314360i −0.820284 0.571956i \(-0.806185\pi\)
0.797445 + 0.603392i \(0.206185\pi\)
\(114\) 248.448 180.508i 0.204116 0.148299i
\(115\) −679.363 117.231i −0.550877 0.0950593i
\(116\) 2086.38 + 1515.85i 1.66996 + 1.21330i
\(117\) −549.588 + 178.572i −0.434269 + 0.141102i
\(118\) 1524.90i 1.18965i
\(119\) 606.694 + 1867.21i 0.467358 + 1.43838i
\(120\) 120.879 117.588i 0.0919557 0.0894525i
\(121\) −295.314 + 908.884i −0.221874 + 0.682858i
\(122\) −873.105 283.689i −0.647928 0.210525i
\(123\) 481.128 + 662.215i 0.352698 + 0.485447i
\(124\) −730.175 −0.528804
\(125\) 946.473 + 1028.26i 0.677241 + 0.735762i
\(126\) 1413.68 0.999529
\(127\) 699.634 + 962.963i 0.488838 + 0.672828i 0.980173 0.198143i \(-0.0634909\pi\)
−0.491335 + 0.870971i \(0.663491\pi\)
\(128\) 486.440 + 158.054i 0.335904 + 0.109142i
\(129\) −498.759 + 1535.02i −0.340413 + 1.04768i
\(130\) 1471.99 1431.92i 0.993090 0.966057i
\(131\) −63.5100 195.464i −0.0423580 0.130365i 0.927641 0.373473i \(-0.121833\pi\)
−0.969999 + 0.243108i \(0.921833\pi\)
\(132\) 651.606i 0.429659i
\(133\) −500.757 + 162.706i −0.326475 + 0.106078i
\(134\) −1483.87 1078.09i −0.956618 0.695023i
\(135\) −1649.60 284.654i −1.05167 0.181475i
\(136\) −241.601 + 175.534i −0.152332 + 0.110676i
\(137\) 1310.51 1803.76i 0.817256 1.12486i −0.172907 0.984938i \(-0.555316\pi\)
0.990163 0.139919i \(-0.0446841\pi\)
\(138\) −559.505 + 770.093i −0.345132 + 0.475034i
\(139\) 557.340 404.931i 0.340093 0.247092i −0.404608 0.914490i \(-0.632592\pi\)
0.744701 + 0.667398i \(0.232592\pi\)
\(140\) −2383.32 + 1173.23i −1.43877 + 0.708257i
\(141\) 556.730 + 404.488i 0.332519 + 0.241589i
\(142\) −1606.81 + 522.086i −0.949583 + 0.308538i
\(143\) 863.646i 0.505047i
\(144\) −221.236 680.894i −0.128030 0.394036i
\(145\) 1418.53 + 2881.63i 0.812431 + 1.65039i
\(146\) 425.010 1308.04i 0.240918 0.741470i
\(147\) 1273.92 + 413.923i 0.714772 + 0.232243i
\(148\) −2073.15 2853.44i −1.15143 1.58481i
\(149\) 332.872 0.183020 0.0915098 0.995804i \(-0.470831\pi\)
0.0915098 + 0.995804i \(0.470831\pi\)
\(150\) 1850.95 545.430i 1.00753 0.296895i
\(151\) −3165.59 −1.70604 −0.853020 0.521878i \(-0.825231\pi\)
−0.853020 + 0.521878i \(0.825231\pi\)
\(152\) −47.0754 64.7937i −0.0251205 0.0345754i
\(153\) 914.518 + 297.145i 0.483232 + 0.157011i
\(154\) −652.887 + 2009.38i −0.341631 + 1.05143i
\(155\) −804.493 423.991i −0.416893 0.219715i
\(156\) −463.314 1425.93i −0.237787 0.731833i
\(157\) 790.622i 0.401901i 0.979601 + 0.200951i \(0.0644031\pi\)
−0.979601 + 0.200951i \(0.935597\pi\)
\(158\) −980.577 + 318.609i −0.493737 + 0.160425i
\(159\) 188.672 + 137.078i 0.0941048 + 0.0683711i
\(160\) 2025.11 + 2081.78i 1.00062 + 1.02862i
\(161\) 1320.34 959.285i 0.646320 0.469579i
\(162\) −510.903 + 703.197i −0.247780 + 0.341039i
\(163\) −89.2654 + 122.863i −0.0428945 + 0.0590393i −0.829926 0.557874i \(-0.811617\pi\)
0.787031 + 0.616913i \(0.211617\pi\)
\(164\) 1586.72 1152.82i 0.755498 0.548902i
\(165\) 378.368 717.926i 0.178521 0.338730i
\(166\) −3536.44 2569.38i −1.65350 1.20134i
\(167\) −1707.52 + 554.806i −0.791207 + 0.257079i −0.676618 0.736334i \(-0.736555\pi\)
−0.114589 + 0.993413i \(0.536555\pi\)
\(168\) 399.218i 0.183336i
\(169\) 64.8290 + 199.523i 0.0295080 + 0.0908162i
\(170\) −3382.13 + 487.943i −1.52587 + 0.220138i
\(171\) −79.6896 + 245.259i −0.0356375 + 0.109681i
\(172\) 3678.02 + 1195.06i 1.63050 + 0.529783i
\(173\) 901.648 + 1241.01i 0.396249 + 0.545389i 0.959798 0.280693i \(-0.0905644\pi\)
−0.563549 + 0.826083i \(0.690564\pi\)
\(174\) 4434.74 1.93217
\(175\) −3307.16 91.2837i −1.42856 0.0394308i
\(176\) 1069.99 0.458257
\(177\) −815.012 1121.77i −0.346102 0.476369i
\(178\) 2060.72 + 669.570i 0.867741 + 0.281946i
\(179\) 939.001 2889.95i 0.392091 1.20673i −0.539113 0.842233i \(-0.681241\pi\)
0.931204 0.364498i \(-0.118759\pi\)
\(180\) −221.242 + 1282.12i −0.0916134 + 0.530908i
\(181\) 1076.93 + 3314.44i 0.442250 + 1.36111i 0.885471 + 0.464694i \(0.153836\pi\)
−0.443221 + 0.896413i \(0.646164\pi\)
\(182\) 4861.43i 1.97996i
\(183\) −793.908 + 257.956i −0.320696 + 0.104200i
\(184\) 200.835 + 145.916i 0.0804662 + 0.0584621i
\(185\) −627.244 4347.68i −0.249275 1.72783i
\(186\) −1015.82 + 738.036i −0.400449 + 0.290943i
\(187\) −844.714 + 1162.65i −0.330329 + 0.454659i
\(188\) 969.182 1333.96i 0.375983 0.517497i
\(189\) 3206.00 2329.29i 1.23387 0.896461i
\(190\) −130.859 907.034i −0.0499657 0.346333i
\(191\) 385.738 + 280.255i 0.146131 + 0.106170i 0.658449 0.752626i \(-0.271213\pi\)
−0.512318 + 0.858796i \(0.671213\pi\)
\(192\) 2239.47 727.647i 0.841769 0.273507i
\(193\) 1098.86i 0.409831i 0.978780 + 0.204916i \(0.0656920\pi\)
−0.978780 + 0.204916i \(0.934308\pi\)
\(194\) −628.931 1935.65i −0.232756 0.716349i
\(195\) 317.527 1840.10i 0.116608 0.675754i
\(196\) 991.789 3052.41i 0.361439 1.11240i
\(197\) −87.3420 28.3791i −0.0315881 0.0102636i 0.293180 0.956057i \(-0.405286\pi\)
−0.324768 + 0.945794i \(0.605286\pi\)
\(198\) 608.237 + 837.167i 0.218311 + 0.300479i
\(199\) 1614.65 0.575174 0.287587 0.957754i \(-0.407147\pi\)
0.287587 + 0.957754i \(0.407147\pi\)
\(200\) −142.245 482.718i −0.0502911 0.170666i
\(201\) −1667.79 −0.585259
\(202\) 513.549 + 706.840i 0.178877 + 0.246203i
\(203\) −7231.33 2349.60i −2.50020 0.812363i
\(204\) −770.957 + 2372.76i −0.264597 + 0.814346i
\(205\) 2417.62 348.792i 0.823677 0.118833i
\(206\) −737.319 2269.23i −0.249376 0.767500i
\(207\) 799.332i 0.268393i
\(208\) 2341.49 760.796i 0.780544 0.253614i
\(209\) −311.804 226.539i −0.103196 0.0749762i
\(210\) −2129.82 + 4041.18i −0.699864 + 1.32794i
\(211\) 2980.05 2165.14i 0.972300 0.706418i 0.0163258 0.999867i \(-0.494803\pi\)
0.955975 + 0.293449i \(0.0948031\pi\)
\(212\) 328.449 452.072i 0.106406 0.146455i
\(213\) −902.988 + 1242.86i −0.290477 + 0.399808i
\(214\) −3483.70 + 2531.05i −1.11281 + 0.808501i
\(215\) 3358.44 + 3452.42i 1.06532 + 1.09513i
\(216\) 487.660 + 354.306i 0.153616 + 0.111609i
\(217\) 2047.43 665.250i 0.640500 0.208111i
\(218\) 7423.88i 2.30646i
\(219\) −386.458 1189.40i −0.119244 0.366995i
\(220\) −1720.20 906.597i −0.527164 0.277831i
\(221\) −1021.84 + 3144.89i −0.311023 + 0.957231i
\(222\) −5768.32 1874.24i −1.74389 0.566625i
\(223\) −2910.64 4006.15i −0.874039 1.20301i −0.978036 0.208434i \(-0.933163\pi\)
0.103997 0.994578i \(-0.466837\pi\)
\(224\) −6875.35 −2.05080
\(225\) −988.248 + 1284.14i −0.292814 + 0.380487i
\(226\) 192.317 0.0566051
\(227\) 216.700 + 298.261i 0.0633606 + 0.0872084i 0.839521 0.543327i \(-0.182835\pi\)
−0.776161 + 0.630535i \(0.782835\pi\)
\(228\) −636.338 206.759i −0.184836 0.0600567i
\(229\) −319.117 + 982.142i −0.0920868 + 0.283414i −0.986484 0.163861i \(-0.947605\pi\)
0.894397 + 0.447274i \(0.147605\pi\)
\(230\) 1254.55 + 2548.51i 0.359663 + 0.730626i
\(231\) 593.666 + 1827.12i 0.169092 + 0.520413i
\(232\) 1156.55i 0.327291i
\(233\) 1338.84 435.017i 0.376440 0.122313i −0.114685 0.993402i \(-0.536586\pi\)
0.491125 + 0.871089i \(0.336586\pi\)
\(234\) 1926.28 + 1399.53i 0.538141 + 0.390982i
\(235\) 1842.42 906.961i 0.511431 0.251760i
\(236\) −2687.84 + 1952.83i −0.741370 + 0.538637i
\(237\) −551.059 + 758.467i −0.151034 + 0.207881i
\(238\) 4754.86 6544.51i 1.29501 1.78243i
\(239\) −3547.06 + 2577.09i −0.960002 + 0.697482i −0.953151 0.302495i \(-0.902181\pi\)
−0.00685049 + 0.999977i \(0.502181\pi\)
\(240\) 2279.73 + 393.390i 0.613149 + 0.105805i
\(241\) 224.103 + 162.820i 0.0598993 + 0.0435194i 0.617332 0.786703i \(-0.288214\pi\)
−0.557433 + 0.830222i \(0.688214\pi\)
\(242\) 3744.90 1216.79i 0.994757 0.323216i
\(243\) 3252.22i 0.858560i
\(244\) 618.082 + 1902.26i 0.162167 + 0.499098i
\(245\) 2865.18 2787.19i 0.747141 0.726803i
\(246\) 1042.21 3207.60i 0.270118 0.831337i
\(247\) −843.410 274.040i −0.217267 0.0705942i
\(248\) 192.475 + 264.919i 0.0492830 + 0.0678323i
\(249\) −3974.78 −1.01161
\(250\) 1135.38 5645.29i 0.287231 1.42816i
\(251\) 6881.24 1.73044 0.865219 0.501393i \(-0.167179\pi\)
0.865219 + 0.501393i \(0.167179\pi\)
\(252\) −1810.40 2491.80i −0.452557 0.622891i
\(253\) 1136.16 + 369.160i 0.282330 + 0.0917347i
\(254\) 1515.54 4664.34i 0.374382 1.15223i
\(255\) −2227.22 + 2166.59i −0.546956 + 0.532068i
\(256\) 902.495 + 2777.59i 0.220336 + 0.678124i
\(257\) 7406.10i 1.79759i −0.438372 0.898794i \(-0.644445\pi\)
0.438372 0.898794i \(-0.355555\pi\)
\(258\) 6324.79 2055.05i 1.52622 0.495898i
\(259\) 8412.87 + 6112.31i 2.01834 + 1.46641i
\(260\) −4409.01 760.817i −1.05167 0.181476i
\(261\) −3012.78 + 2188.92i −0.714508 + 0.519120i
\(262\) −497.749 + 685.093i −0.117370 + 0.161546i
\(263\) −2819.25 + 3880.36i −0.660997 + 0.909784i −0.999514 0.0311762i \(-0.990075\pi\)
0.338517 + 0.940960i \(0.390075\pi\)
\(264\) −236.413 + 171.764i −0.0551145 + 0.0400430i
\(265\) 624.384 307.363i 0.144738 0.0712497i
\(266\) 1755.13 + 1275.18i 0.404564 + 0.293933i
\(267\) 1873.80 608.836i 0.429494 0.139551i
\(268\) 3996.15i 0.910835i
\(269\) −520.192 1600.99i −0.117906 0.362877i 0.874636 0.484780i \(-0.161100\pi\)
−0.992542 + 0.121903i \(0.961100\pi\)
\(270\) 3046.24 + 6188.19i 0.686622 + 1.39482i
\(271\) −1243.61 + 3827.43i −0.278759 + 0.857933i 0.709441 + 0.704765i \(0.248948\pi\)
−0.988200 + 0.153168i \(0.951052\pi\)
\(272\) −3896.26 1265.97i −0.868549 0.282209i
\(273\) 2598.28 + 3576.23i 0.576027 + 0.792833i
\(274\) −9186.54 −2.02547
\(275\) −1368.85 1997.74i −0.300163 0.438067i
\(276\) 2073.91 0.452299
\(277\) −1126.62 1550.66i −0.244376 0.336354i 0.669156 0.743122i \(-0.266656\pi\)
−0.913532 + 0.406768i \(0.866656\pi\)
\(278\) −2699.60 877.155i −0.582416 0.189238i
\(279\) 325.824 1002.78i 0.0699160 0.215179i
\(280\) 1053.91 + 555.444i 0.224941 + 0.118550i
\(281\) −164.991 507.791i −0.0350269 0.107802i 0.932014 0.362421i \(-0.118050\pi\)
−0.967041 + 0.254619i \(0.918050\pi\)
\(282\) 2835.43i 0.598749i
\(283\) 1372.10 445.823i 0.288209 0.0936446i −0.161345 0.986898i \(-0.551583\pi\)
0.449553 + 0.893253i \(0.351583\pi\)
\(284\) 2977.97 + 2163.62i 0.622219 + 0.452069i
\(285\) −581.046 597.305i −0.120766 0.124145i
\(286\) −2878.89 + 2091.63i −0.595218 + 0.432451i
\(287\) −3398.88 + 4678.15i −0.699057 + 0.962169i
\(288\) −1979.30 + 2724.28i −0.404970 + 0.557394i
\(289\) 476.855 346.456i 0.0970599 0.0705181i
\(290\) 6170.18 11707.5i 1.24940 2.37064i
\(291\) −1497.21 1087.79i −0.301608 0.219131i
\(292\) −2849.88 + 925.982i −0.571153 + 0.185579i
\(293\) 3570.98i 0.712009i 0.934484 + 0.356005i \(0.115861\pi\)
−0.934484 + 0.356005i \(0.884139\pi\)
\(294\) −1705.50 5248.98i −0.338322 1.04125i
\(295\) −4095.36 + 590.840i −0.808274 + 0.116610i
\(296\) −488.791 + 1504.34i −0.0959810 + 0.295399i
\(297\) 2758.77 + 896.377i 0.538989 + 0.175128i
\(298\) −806.171 1109.60i −0.156712 0.215696i
\(299\) 2748.78 0.531659
\(300\) −3331.77 2564.06i −0.641200 0.493453i
\(301\) −11402.1 −2.18340
\(302\) 7666.64 + 10552.2i 1.46081 + 2.01064i
\(303\) 755.569 + 245.499i 0.143255 + 0.0465464i
\(304\) 339.513 1044.91i 0.0640540 0.197138i
\(305\) −423.596 + 2454.78i −0.0795247 + 0.460853i
\(306\) −1224.33 3768.11i −0.228727 0.703950i
\(307\) 254.168i 0.0472512i −0.999721 0.0236256i \(-0.992479\pi\)
0.999721 0.0236256i \(-0.00752097\pi\)
\(308\) 4377.90 1422.47i 0.809916 0.263158i
\(309\) −1755.23 1275.25i −0.323145 0.234778i
\(310\) 535.037 + 3708.56i 0.0980259 + 0.679458i
\(311\) 6533.93 4747.18i 1.19134 0.865556i 0.197930 0.980216i \(-0.436578\pi\)
0.993405 + 0.114660i \(0.0365780\pi\)
\(312\) −395.221 + 543.976i −0.0717148 + 0.0987069i
\(313\) 402.923 554.576i 0.0727621 0.100148i −0.771085 0.636732i \(-0.780286\pi\)
0.843847 + 0.536584i \(0.180286\pi\)
\(314\) 2635.47 1914.78i 0.473656 0.344132i
\(315\) −547.747 3796.66i −0.0979747 0.679103i
\(316\) 1817.34 + 1320.38i 0.323524 + 0.235054i
\(317\) −4354.28 + 1414.79i −0.771485 + 0.250671i −0.668201 0.743981i \(-0.732935\pi\)
−0.103285 + 0.994652i \(0.532935\pi\)
\(318\) 960.907i 0.169450i
\(319\) −1719.88 5293.24i −0.301864 0.929042i
\(320\) 1194.89 6924.47i 0.208738 1.20965i
\(321\) −1209.95 + 3723.86i −0.210383 + 0.647493i
\(322\) −6395.38 2077.99i −1.10683 0.359632i
\(323\) 867.374 + 1193.84i 0.149418 + 0.205656i
\(324\) 1893.75 0.324718
\(325\) −4415.97 3398.43i −0.753705 0.580034i
\(326\) 625.743 0.106309
\(327\) 3967.83 + 5461.26i 0.671014 + 0.923572i
\(328\) −836.521 271.802i −0.140821 0.0457554i
\(329\) −1502.26 + 4623.47i −0.251739 + 0.774773i
\(330\) −3309.50 + 477.465i −0.552067 + 0.0796472i
\(331\) −2287.10 7038.96i −0.379789 1.16887i −0.940190 0.340650i \(-0.889353\pi\)
0.560401 0.828221i \(-0.310647\pi\)
\(332\) 9523.85i 1.57437i
\(333\) 4843.86 1573.86i 0.797122 0.259001i
\(334\) 5984.78 + 4348.19i 0.980456 + 0.712343i
\(335\) −2320.45 + 4402.88i −0.378446 + 0.718075i
\(336\) −4430.65 + 3219.06i −0.719381 + 0.522661i
\(337\) 802.653 1104.76i 0.129743 0.178576i −0.739203 0.673482i \(-0.764798\pi\)
0.868946 + 0.494907i \(0.164798\pi\)
\(338\) 508.086 699.320i 0.0817640 0.112539i
\(339\) 141.475 102.788i 0.0226663 0.0164680i
\(340\) 5191.31 + 5336.58i 0.828054 + 0.851225i
\(341\) 1274.86 + 926.241i 0.202456 + 0.147093i
\(342\) 1010.55 328.347i 0.159778 0.0519152i
\(343\) 384.331i 0.0605012i
\(344\) −535.944 1649.47i −0.0840005 0.258527i
\(345\) 2284.99 + 1204.26i 0.356579 + 0.187927i
\(346\) 1953.13 6011.13i 0.303472 0.933990i
\(347\) 10055.8 + 3267.32i 1.55568 + 0.505472i 0.955651 0.294503i \(-0.0951539\pi\)
0.600033 + 0.799975i \(0.295154\pi\)
\(348\) −5679.25 7816.81i −0.874826 1.20410i
\(349\) 1310.55 0.201008 0.100504 0.994937i \(-0.467954\pi\)
0.100504 + 0.994937i \(0.467954\pi\)
\(350\) 7705.21 + 11245.2i 1.17675 + 1.71738i
\(351\) 6674.47 1.01498
\(352\) −2958.13 4071.51i −0.447922 0.616512i
\(353\) −4073.40 1323.53i −0.614179 0.199559i −0.0146250 0.999893i \(-0.504655\pi\)
−0.599554 + 0.800334i \(0.704655\pi\)
\(354\) −1765.47 + 5433.55i −0.265066 + 0.815790i
\(355\) 2024.72 + 4113.06i 0.302707 + 0.614925i
\(356\) −1458.81 4489.77i −0.217183 0.668419i
\(357\) 7355.69i 1.09049i
\(358\) −11907.5 + 3868.99i −1.75791 + 0.571180i
\(359\) −309.644 224.970i −0.0455220 0.0330737i 0.564792 0.825234i \(-0.308957\pi\)
−0.610314 + 0.792160i \(0.708957\pi\)
\(360\) 523.493 257.698i 0.0766403 0.0377274i
\(361\) 5228.88 3799.00i 0.762338 0.553871i
\(362\) 8440.23 11617.0i 1.22544 1.68667i
\(363\) 2104.54 2896.65i 0.304296 0.418828i
\(364\) 8568.91 6225.67i 1.23388 0.896467i
\(365\) −3677.63 634.611i −0.527386 0.0910057i
\(366\) 2782.62 + 2021.69i 0.397403 + 0.288731i
\(367\) −850.776 + 276.434i −0.121009 + 0.0393181i −0.368895 0.929471i \(-0.620264\pi\)
0.247887 + 0.968789i \(0.420264\pi\)
\(368\) 3405.51i 0.482404i
\(369\) 875.180 + 2693.53i 0.123469 + 0.379999i
\(370\) −12973.5 + 12620.4i −1.82287 + 1.77325i
\(371\) −509.105 + 1566.86i −0.0712437 + 0.219266i
\(372\) 2601.77 + 845.366i 0.362622 + 0.117823i
\(373\) 1239.91 + 1706.59i 0.172118 + 0.236900i 0.886358 0.463001i \(-0.153227\pi\)
−0.714240 + 0.699901i \(0.753227\pi\)
\(374\) 5921.37 0.818682
\(375\) −2182.01 4759.69i −0.300476 0.655438i
\(376\) −739.462 −0.101422
\(377\) −7527.34 10360.5i −1.02832 1.41537i
\(378\) −15529.0 5045.67i −2.11303 0.686565i
\(379\) 667.344 2053.88i 0.0904464 0.278365i −0.895594 0.444873i \(-0.853249\pi\)
0.986040 + 0.166507i \(0.0532489\pi\)
\(380\) −1431.19 + 1392.23i −0.193206 + 0.187947i
\(381\) −1378.07 4241.25i −0.185303 0.570304i
\(382\) 1964.57i 0.263131i
\(383\) 1520.78 494.130i 0.202893 0.0659239i −0.205808 0.978592i \(-0.565982\pi\)
0.408700 + 0.912669i \(0.365982\pi\)
\(384\) −1550.30 1126.36i −0.206025 0.149686i
\(385\) 5649.47 + 974.872i 0.747854 + 0.129050i
\(386\) 3662.95 2661.29i 0.483003 0.350922i
\(387\) −3282.47 + 4517.93i −0.431156 + 0.593435i
\(388\) −2606.41 + 3587.42i −0.341032 + 0.469391i
\(389\) −8141.92 + 5915.45i −1.06121 + 0.771016i −0.974312 0.225201i \(-0.927696\pi\)
−0.0868999 + 0.996217i \(0.527696\pi\)
\(390\) −6902.81 + 3398.02i −0.896250 + 0.441194i
\(391\) −3700.44 2688.52i −0.478617 0.347735i
\(392\) −1368.90 + 444.783i −0.176378 + 0.0573085i
\(393\) 770.008i 0.0988341i
\(394\) 116.931 + 359.877i 0.0149516 + 0.0460162i
\(395\) 1235.61 + 2510.04i 0.157393 + 0.319731i
\(396\) 696.692 2144.20i 0.0884093 0.272096i
\(397\) 12486.1 + 4056.99i 1.57849 + 0.512882i 0.961667 0.274220i \(-0.0884195\pi\)
0.616823 + 0.787102i \(0.288419\pi\)
\(398\) −3910.47 5382.30i −0.492498 0.677866i
\(399\) 1972.68 0.247513
\(400\) 4210.38 5471.02i 0.526297 0.683878i
\(401\) −3357.62 −0.418133 −0.209067 0.977901i \(-0.567043\pi\)
−0.209067 + 0.977901i \(0.567043\pi\)
\(402\) 4039.17 + 5559.44i 0.501133 + 0.689751i
\(403\) 3448.42 + 1120.46i 0.426248 + 0.138496i
\(404\) 588.234 1810.40i 0.0724399 0.222947i
\(405\) 2086.50 + 1099.65i 0.255997 + 0.134918i
\(406\) 9681.12 + 29795.4i 1.18341 + 3.64217i
\(407\) 7611.84i 0.927039i
\(408\) 1064.10 345.748i 0.129120 0.0419536i
\(409\) −12519.4 9095.91i −1.51356 1.09967i −0.964566 0.263842i \(-0.915010\pi\)
−0.548996 0.835825i \(-0.684990\pi\)
\(410\) −7017.82 7214.20i −0.845330 0.868985i
\(411\) −6757.93 + 4909.92i −0.811056 + 0.589267i
\(412\) −3055.59 + 4205.66i −0.365384 + 0.502908i
\(413\) 5757.57 7924.61i 0.685984 0.944176i
\(414\) −2664.50 + 1935.88i −0.316312 + 0.229814i
\(415\) −5530.22 + 10493.2i −0.654139 + 1.24118i
\(416\) −9368.36 6806.51i −1.10414 0.802204i
\(417\) −2454.73 + 797.591i −0.288270 + 0.0936647i
\(418\) 1588.02i 0.185820i
\(419\) 3839.41 + 11816.5i 0.447655 + 1.37774i 0.879546 + 0.475814i \(0.157847\pi\)
−0.431891 + 0.901926i \(0.642153\pi\)
\(420\) 9850.61 1421.16i 1.14443 0.165108i
\(421\) 5200.54 16005.6i 0.602040 1.85289i 0.0860563 0.996290i \(-0.472573\pi\)
0.515984 0.856598i \(-0.327427\pi\)
\(422\) −14434.6 4690.08i −1.66508 0.541018i
\(423\) 1399.52 + 1926.27i 0.160868 + 0.221415i
\(424\) −250.599 −0.0287032
\(425\) 2620.89 + 8894.17i 0.299134 + 1.01513i
\(426\) 6329.87 0.719914
\(427\) −3466.23 4770.86i −0.392840 0.540698i
\(428\) 8922.63 + 2899.14i 1.00769 + 0.327418i
\(429\) −999.893 + 3077.35i −0.112530 + 0.346331i
\(430\) 3374.64 19556.3i 0.378464 2.19323i
\(431\) −3856.90 11870.3i −0.431044 1.32662i −0.897086 0.441855i \(-0.854320\pi\)
0.466042 0.884763i \(-0.345680\pi\)
\(432\) 8269.11i 0.920944i
\(433\) −3965.44 + 1288.45i −0.440109 + 0.143000i −0.520686 0.853748i \(-0.674324\pi\)
0.0805771 + 0.996748i \(0.474324\pi\)
\(434\) −7176.15 5213.78i −0.793701 0.576657i
\(435\) −1718.29 11910.2i −0.189393 1.31276i
\(436\) 13085.6 9507.22i 1.43735 1.04430i
\(437\) 721.020 992.399i 0.0789269 0.108634i
\(438\) −3028.80 + 4168.78i −0.330415 + 0.454777i
\(439\) 11333.0 8233.91i 1.23211 0.895178i 0.235060 0.971981i \(-0.424471\pi\)
0.997046 + 0.0768033i \(0.0244713\pi\)
\(440\) 124.520 + 863.098i 0.0134915 + 0.0935150i
\(441\) 3749.46 + 2724.14i 0.404865 + 0.294152i
\(442\) 12958.0 4210.30i 1.39445 0.453085i
\(443\) 7372.11i 0.790653i −0.918541 0.395327i \(-0.870631\pi\)
0.918541 0.395327i \(-0.129369\pi\)
\(444\) 4083.47 + 12567.6i 0.436470 + 1.34332i
\(445\) 999.782 5793.83i 0.106504 0.617199i
\(446\) −6304.98 + 19404.7i −0.669393 + 2.06018i
\(447\) −1186.09 385.385i −0.125504 0.0407787i
\(448\) 9777.60 + 13457.7i 1.03113 + 1.41923i
\(449\) −4449.29 −0.467650 −0.233825 0.972279i \(-0.575124\pi\)
−0.233825 + 0.972279i \(0.575124\pi\)
\(450\) 6673.99 + 184.214i 0.699144 + 0.0192977i
\(451\) −4232.72 −0.441932
\(452\) −246.287 338.984i −0.0256291 0.0352754i
\(453\) 11279.7 + 3664.99i 1.16990 + 0.380124i
\(454\) 469.411 1444.70i 0.0485255 0.149346i
\(455\) 13056.1 1883.62i 1.34523 0.194078i
\(456\) 92.7241 + 285.376i 0.00952238 + 0.0293069i
\(457\) 6349.09i 0.649886i 0.945734 + 0.324943i \(0.105345\pi\)
−0.945734 + 0.324943i \(0.894655\pi\)
\(458\) 4046.75 1314.87i 0.412865 0.134148i
\(459\) −8985.24 6528.16i −0.913714 0.663852i
\(460\) 2885.48 5475.00i 0.292470 0.554942i
\(461\) −12414.6 + 9019.70i −1.25424 + 0.911257i −0.998460 0.0554788i \(-0.982331\pi\)
−0.255778 + 0.966736i \(0.582331\pi\)
\(462\) 4652.75 6403.97i 0.468541 0.644891i
\(463\) −672.343 + 925.400i −0.0674868 + 0.0928877i −0.841426 0.540372i \(-0.818284\pi\)
0.773939 + 0.633260i \(0.218284\pi\)
\(464\) 12835.8 9325.75i 1.28424 0.933054i
\(465\) 2375.70 + 2442.18i 0.236926 + 0.243556i
\(466\) −4692.59 3409.37i −0.466481 0.338918i
\(467\) −10104.8 + 3283.25i −1.00127 + 0.325334i −0.763375 0.645956i \(-0.776459\pi\)
−0.237899 + 0.971290i \(0.576459\pi\)
\(468\) 5187.60i 0.512386i
\(469\) −3640.82 11205.3i −0.358459 1.10322i
\(470\) −7485.37 3945.01i −0.734626 0.387169i
\(471\) 915.349 2817.15i 0.0895478 0.275600i
\(472\) 1417.04 + 460.423i 0.138187 + 0.0448997i
\(473\) −4905.75 6752.18i −0.476885 0.656376i
\(474\) 3862.88 0.374320
\(475\) −2385.28 + 702.882i −0.230409 + 0.0678957i
\(476\) −17624.8 −1.69712
\(477\) 474.288 + 652.801i 0.0455265 + 0.0626619i
\(478\) 17181.0 + 5582.45i 1.64402 + 0.534175i
\(479\) −4475.35 + 13773.7i −0.426897 + 1.31385i 0.474268 + 0.880380i \(0.342713\pi\)
−0.901166 + 0.433475i \(0.857287\pi\)
\(480\) −4805.70 9762.41i −0.456978 0.928315i
\(481\) 5412.28 + 16657.3i 0.513053 + 1.57902i
\(482\) 1141.36i 0.107858i
\(483\) −5815.28 + 1889.50i −0.547835 + 0.178002i
\(484\) −6940.57 5042.62i −0.651819 0.473575i
\(485\) −4954.80 + 2439.08i −0.463889 + 0.228357i
\(486\) −10841.0 + 7876.45i −1.01185 + 0.735150i
\(487\) −3465.52 + 4769.88i −0.322460 + 0.443828i −0.939216 0.343326i \(-0.888446\pi\)
0.616756 + 0.787154i \(0.288446\pi\)
\(488\) 527.244 725.689i 0.0489082 0.0673164i
\(489\) 460.318 334.441i 0.0425691 0.0309283i
\(490\) −16229.9 2800.63i −1.49631 0.258203i
\(491\) 13594.4 + 9876.90i 1.24950 + 0.907817i 0.998193 0.0600899i \(-0.0191387\pi\)
0.251310 + 0.967907i \(0.419139\pi\)
\(492\) −6988.49 + 2270.70i −0.640377 + 0.208071i
\(493\) 21309.7i 1.94674i
\(494\) 1129.14 + 3475.12i 0.102838 + 0.316504i
\(495\) 2012.67 1957.89i 0.182753 0.177779i
\(496\) −1388.16 + 4272.30i −0.125665 + 0.386758i
\(497\) −10321.5 3353.67i −0.931558 0.302682i
\(498\) 9626.38 + 13249.6i 0.866202 + 1.19222i
\(499\) 6860.80 0.615494 0.307747 0.951468i \(-0.400425\pi\)
0.307747 + 0.951468i \(0.400425\pi\)
\(500\) −11404.6 + 5228.25i −1.02005 + 0.467629i
\(501\) 6726.58 0.599843
\(502\) −16665.5 22938.0i −1.48170 2.03939i
\(503\) 11835.9 + 3845.71i 1.04918 + 0.340898i 0.782345 0.622846i \(-0.214024\pi\)
0.266831 + 0.963743i \(0.414024\pi\)
\(504\) −426.841 + 1313.68i −0.0377243 + 0.116103i
\(505\) 1699.35 1653.09i 0.149743 0.145666i
\(506\) −1521.06 4681.34i −0.133635 0.411286i
\(507\) 786.000i 0.0688510i
\(508\) −10162.3 + 3301.95i −0.887561 + 0.288386i
\(509\) 12853.9 + 9338.90i 1.11933 + 0.813241i 0.984107 0.177574i \(-0.0568250\pi\)
0.135223 + 0.990815i \(0.456825\pi\)
\(510\) 12616.2 + 2177.04i 1.09540 + 0.189022i
\(511\) 7147.48 5192.95i 0.618759 0.449555i
\(512\) 9478.24 13045.7i 0.818131 1.12606i
\(513\) 1750.75 2409.70i 0.150677 0.207389i
\(514\) −24687.6 + 17936.6i −2.11853 + 1.53920i
\(515\) −5808.69 + 2859.42i −0.497013 + 0.244663i
\(516\) −11722.0 8516.52i −1.00006 0.726587i
\(517\) −3384.32 + 1099.63i −0.287896 + 0.0935431i
\(518\) 42846.8i 3.63432i
\(519\) −1775.97 5465.88i −0.150205 0.462284i
\(520\) 886.183 + 1800.21i 0.0747341 + 0.151816i
\(521\) −602.662 + 1854.80i −0.0506777 + 0.155970i −0.973193 0.229991i \(-0.926130\pi\)
0.922515 + 0.385961i \(0.126130\pi\)
\(522\) 14593.1 + 4741.59i 1.22361 + 0.397574i
\(523\) −12465.9 17157.8i −1.04225 1.43453i −0.895342 0.445380i \(-0.853069\pi\)
−0.146905 0.989151i \(-0.546931\pi\)
\(524\) 1845.00 0.153815
\(525\) 11678.4 + 4154.15i 0.970835 + 0.345337i
\(526\) 19762.7 1.63820
\(527\) −3546.40 4881.20i −0.293138 0.403469i
\(528\) −3812.59 1238.78i −0.314245 0.102105i
\(529\) 2584.86 7955.39i 0.212449 0.653849i
\(530\) −2536.74 1336.94i −0.207904 0.109571i
\(531\) −1482.52 4562.74i −0.121160 0.372892i
\(532\) 4726.68i 0.385202i
\(533\) −9262.63 + 3009.61i −0.752737 + 0.244579i
\(534\) −6567.60 4771.64i −0.532225 0.386684i
\(535\) 8147.33 + 8375.32i 0.658392 + 0.676816i
\(536\) 1449.87 1053.39i 0.116837 0.0848872i
\(537\) −6691.72 + 9210.37i −0.537745 + 0.740143i
\(538\) −4076.91 + 5611.39i −0.326707 + 0.449673i
\(539\) −5603.68 + 4071.31i −0.447806 + 0.325350i
\(540\) 7006.40 13294.2i 0.558347 1.05942i
\(541\) 13101.0 + 9518.41i 1.04114 + 0.756430i 0.970507 0.241073i \(-0.0774993\pi\)
0.0706293 + 0.997503i \(0.477499\pi\)
\(542\) 15770.3 5124.07i 1.24980 0.406084i
\(543\) 13056.9i 1.03190i
\(544\) 5954.48 + 18326.0i 0.469294 + 1.44434i
\(545\) 19938.0 2876.47i 1.56706 0.226081i
\(546\) 5628.36 17322.3i 0.441157 1.35774i
\(547\) 11147.3 + 3621.97i 0.871340 + 0.283116i 0.710357 0.703841i \(-0.248533\pi\)
0.160983 + 0.986957i \(0.448533\pi\)
\(548\) 11764.5 + 16192.5i 0.917073 + 1.26224i
\(549\) −2888.27 −0.224532
\(550\) −3344.12 + 9401.21i −0.259261 + 0.728853i
\(551\) −5714.94 −0.441859
\(552\) −546.685 752.447i −0.0421530 0.0580186i
\(553\) −6298.84 2046.62i −0.484365 0.157380i
\(554\) −2440.47 + 7510.98i −0.187158 + 0.576013i
\(555\) −2798.56 + 16217.9i −0.214040 + 1.24038i
\(556\) 1911.08 + 5881.71i 0.145770 + 0.448634i
\(557\) 5469.05i 0.416034i −0.978125 0.208017i \(-0.933299\pi\)
0.978125 0.208017i \(-0.0667009\pi\)
\(558\) −4131.79 + 1342.50i −0.313464 + 0.101851i
\(559\) −15536.5 11287.9i −1.17553 0.854074i
\(560\) 2333.65 + 16175.4i 0.176097 + 1.22060i
\(561\) 4355.96 3164.79i 0.327823 0.238178i
\(562\) −1293.09 + 1779.79i −0.0970565 + 0.133587i
\(563\) −7900.29 + 10873.8i −0.591399 + 0.813991i −0.994887 0.100994i \(-0.967798\pi\)
0.403488 + 0.914985i \(0.367798\pi\)
\(564\) −4997.81 + 3631.12i −0.373131 + 0.271095i
\(565\) −74.5156 516.498i −0.00554848 0.0384588i
\(566\) −4809.16 3494.06i −0.357145 0.259481i
\(567\) −5310.12 + 1725.36i −0.393306 + 0.127793i
\(568\) 1650.79i 0.121947i
\(569\) −4456.10 13714.5i −0.328312 1.01044i −0.969924 0.243410i \(-0.921734\pi\)
0.641612 0.767029i \(-0.278266\pi\)
\(570\) −583.849 + 3383.46i −0.0429031 + 0.248627i
\(571\) −3187.96 + 9811.54i −0.233646 + 0.719089i 0.763652 + 0.645628i \(0.223404\pi\)
−0.997298 + 0.0734610i \(0.976596\pi\)
\(572\) 7373.56 + 2395.82i 0.538993 + 0.175130i
\(573\) −1050.00 1445.20i −0.0765522 0.105365i
\(574\) 23825.8 1.73253
\(575\) 6358.34 4356.73i 0.461150 0.315980i
\(576\) 8147.27 0.589357
\(577\) 14966.0 + 20599.0i 1.07980 + 1.48622i 0.859742 + 0.510728i \(0.170624\pi\)
0.220057 + 0.975487i \(0.429376\pi\)
\(578\) −2309.76 750.487i −0.166217 0.0540071i
\(579\) 1272.21 3915.46i 0.0913148 0.281038i
\(580\) −28537.7 + 4117.15i −2.04304 + 0.294751i
\(581\) −8677.01 26705.1i −0.619592 1.90691i
\(582\) 7625.29i 0.543090i
\(583\) −1146.92 + 372.658i −0.0814764 + 0.0264733i
\(584\) 1087.19 + 789.892i 0.0770349 + 0.0559691i
\(585\) 3012.28 5715.59i 0.212893 0.403950i
\(586\) 11903.5 8648.43i 0.839131 0.609665i
\(587\) 11481.1 15802.4i 0.807286 1.11113i −0.184450 0.982842i \(-0.559050\pi\)
0.991736 0.128293i \(-0.0409497\pi\)
\(588\) −7067.91 + 9728.15i −0.495707 + 0.682282i
\(589\) 1309.06 951.088i 0.0915771 0.0665346i
\(590\) 11887.9 + 12220.6i 0.829522 + 0.852734i
\(591\) 278.362 + 202.242i 0.0193744 + 0.0140763i
\(592\) −20637.0 + 6705.37i −1.43273 + 0.465522i
\(593\) 12614.9i 0.873582i −0.899563 0.436791i \(-0.856115\pi\)
0.899563 0.436791i \(-0.143885\pi\)
\(594\) −3693.37 11367.0i −0.255119 0.785176i
\(595\) −19418.6 10234.2i −1.33796 0.705143i
\(596\) −923.411 + 2841.97i −0.0634637 + 0.195321i
\(597\) −5753.35 1869.38i −0.394420 0.128155i
\(598\) −6657.18 9162.82i −0.455238 0.626581i
\(599\) −662.584 −0.0451961 −0.0225981 0.999745i \(-0.507194\pi\)
−0.0225981 + 0.999745i \(0.507194\pi\)
\(600\) −52.0215 + 1884.71i −0.00353961 + 0.128238i
\(601\) −9643.41 −0.654514 −0.327257 0.944935i \(-0.606124\pi\)
−0.327257 + 0.944935i \(0.606124\pi\)
\(602\) 27614.3 + 38007.8i 1.86956 + 2.57323i
\(603\) −5488.10 1783.19i −0.370634 0.120426i
\(604\) 8781.57 27026.9i 0.591585 1.82071i
\(605\) −4718.89 9586.05i −0.317107 0.644179i
\(606\) −1011.54 3113.19i −0.0678067 0.208688i
\(607\) 18733.3i 1.25265i −0.779560 0.626327i \(-0.784557\pi\)
0.779560 0.626327i \(-0.215443\pi\)
\(608\) −4914.75 + 1596.90i −0.327828 + 0.106518i
\(609\) 23046.5 + 16744.3i 1.53348 + 1.11414i
\(610\) 9208.68 4533.12i 0.611227 0.300886i
\(611\) −6624.16 + 4812.73i −0.438600 + 0.318662i
\(612\) −5073.88 + 6983.60i −0.335130 + 0.461267i
\(613\) 12241.1 16848.4i 0.806547 1.11012i −0.185299 0.982682i \(-0.559326\pi\)
0.991847 0.127435i \(-0.0406745\pi\)
\(614\) −847.247 + 615.561i −0.0556875 + 0.0404593i
\(615\) −9018.31 1556.20i −0.591306 0.102036i
\(616\) −1670.12 1213.41i −0.109238 0.0793664i
\(617\) 7351.50 2388.65i 0.479676 0.155856i −0.0591916 0.998247i \(-0.518852\pi\)
0.538868 + 0.842390i \(0.318852\pi\)
\(618\) 8939.40i 0.581870i
\(619\) 6894.63 + 21219.5i 0.447688 + 1.37784i 0.879509 + 0.475882i \(0.157871\pi\)
−0.431822 + 0.901959i \(0.642129\pi\)
\(620\) 5851.64 5692.35i 0.379044 0.368726i
\(621\) −2852.96 + 8780.50i −0.184356 + 0.567390i
\(622\) −31648.6 10283.3i −2.04018 0.662896i
\(623\) 8181.09 + 11260.3i 0.526113 + 0.724133i
\(624\) −9224.04 −0.591759
\(625\) −15601.2 861.901i −0.998477 0.0551617i
\(626\) −2824.45 −0.180332
\(627\) 848.747 + 1168.20i 0.0540601 + 0.0744074i
\(628\) −6750.10 2193.24i −0.428915 0.139363i
\(629\) 9006.07 27717.8i 0.570899 1.75705i
\(630\) −11329.3 + 11020.9i −0.716458 + 0.696955i
\(631\) −3369.80 10371.2i −0.212599 0.654311i −0.999315 0.0369969i \(-0.988221\pi\)
0.786717 0.617314i \(-0.211779\pi\)
\(632\) 1007.41i 0.0634063i
\(633\) −13125.3 + 4264.66i −0.824143 + 0.267780i
\(634\) 15261.6 + 11088.2i 0.956017 + 0.694587i
\(635\) −13114.0 2262.95i −0.819549 0.141421i
\(636\) −1693.73 + 1230.56i −0.105598 + 0.0767217i
\(637\) −9367.89 + 12893.8i −0.582684 + 0.801995i
\(638\) −13479.2 + 18552.6i −0.836439 + 1.15126i
\(639\) −4300.26 + 3124.32i −0.266222 + 0.193421i
\(640\) −5130.51 + 2525.58i −0.316877 + 0.155988i
\(641\) 14924.6 + 10843.4i 0.919635 + 0.668154i 0.943433 0.331563i \(-0.107576\pi\)
−0.0237979 + 0.999717i \(0.507576\pi\)
\(642\) 15343.5 4985.41i 0.943239 0.306477i
\(643\) 13279.7i 0.814462i 0.913325 + 0.407231i \(0.133506\pi\)
−0.913325 + 0.407231i \(0.866494\pi\)
\(644\) 4527.38 + 13933.8i 0.277024 + 0.852593i
\(645\) −7969.77 16189.9i −0.486526 0.988339i
\(646\) 1878.89 5782.63i 0.114433 0.352190i
\(647\) −14829.3 4818.32i −0.901080 0.292779i −0.178397 0.983959i \(-0.557091\pi\)
−0.722683 + 0.691180i \(0.757091\pi\)
\(648\) −499.196 687.084i −0.0302628 0.0416531i
\(649\) 7170.08 0.433667
\(650\) −633.484 + 22950.8i −0.0382266 + 1.38493i
\(651\) −8065.62 −0.485586
\(652\) −801.344 1102.95i −0.0481335 0.0662501i
\(653\) 12519.9 + 4067.98i 0.750296 + 0.243786i 0.659109 0.752048i \(-0.270934\pi\)
0.0911876 + 0.995834i \(0.470934\pi\)
\(654\) 8595.06 26452.9i 0.513904 1.58163i
\(655\) 2032.78 + 1071.33i 0.121263 + 0.0639091i
\(656\) −3728.66 11475.6i −0.221920 0.683000i
\(657\) 4327.07i 0.256948i
\(658\) 19050.2 6189.79i 1.12865 0.366722i
\(659\) 3206.77 + 2329.85i 0.189557 + 0.137721i 0.678516 0.734586i \(-0.262623\pi\)
−0.488959 + 0.872307i \(0.662623\pi\)
\(660\) 5079.83 + 5221.98i 0.299594 + 0.307978i
\(661\) −18655.1 + 13553.7i −1.09773 + 0.797548i −0.980688 0.195579i \(-0.937341\pi\)
−0.117043 + 0.993127i \(0.537341\pi\)
\(662\) −17924.7 + 24671.3i −1.05236 + 1.44845i
\(663\) 7282.04 10022.9i 0.426563 0.587113i
\(664\) 3455.41 2510.50i 0.201952 0.146726i
\(665\) 2744.64 5207.77i 0.160049 0.303682i
\(666\) −16977.5 12334.9i −0.987786 0.717669i
\(667\) 16847.1 5473.96i 0.977996 0.317770i
\(668\) 16117.4i 0.933532i
\(669\) 5733.07 + 17644.6i 0.331321 + 1.01970i
\(670\) 20296.4 2928.18i 1.17033 0.168844i
\(671\) 1333.90 4105.34i 0.0767434 0.236192i
\(672\) 24498.3 + 7959.99i 1.40632 + 0.456940i
\(673\) 9288.82 + 12785.0i 0.532032 + 0.732279i 0.987438 0.158004i \(-0.0505060\pi\)
−0.455406 + 0.890284i \(0.650506\pi\)
\(674\) −5626.53 −0.321552
\(675\) 15439.0 10578.8i 0.880369 0.603228i
\(676\) −1883.31 −0.107153
\(677\) 13063.6 + 17980.5i 0.741616 + 1.02075i 0.998524 + 0.0543109i \(0.0172962\pi\)
−0.256908 + 0.966436i \(0.582704\pi\)
\(678\) −685.267 222.657i −0.0388164 0.0126122i
\(679\) 4040.01 12433.9i 0.228338 0.702751i
\(680\) 567.760 3290.22i 0.0320185 0.185550i
\(681\) −426.832 1313.65i −0.0240180 0.0739198i
\(682\) 6492.88i 0.364553i
\(683\) 3031.22 984.903i 0.169819 0.0551775i −0.222873 0.974847i \(-0.571544\pi\)
0.392692 + 0.919670i \(0.371544\pi\)
\(684\) −1872.89 1360.74i −0.104696 0.0760658i
\(685\) 3559.43 + 24671.9i 0.198539 + 1.37615i
\(686\) 1281.13 930.798i 0.0713030 0.0518047i
\(687\) 2274.17 3130.12i 0.126295 0.173831i
\(688\) 13984.8 19248.4i 0.774949 1.06663i
\(689\) −2244.88 + 1631.00i −0.124127 + 0.0901833i
\(690\) −1519.66 10533.4i −0.0838440 0.581157i
\(691\) −14136.7 10270.9i −0.778271 0.565447i 0.126189 0.992006i \(-0.459725\pi\)
−0.904459 + 0.426560i \(0.859725\pi\)
\(692\) −13096.6 + 4255.36i −0.719450 + 0.233764i
\(693\) 6647.12i 0.364362i
\(694\) −13462.4 41433.1i −0.736350 2.26625i
\(695\) −1309.74 + 7590.07i −0.0714839 + 0.414256i
\(696\) −1339.01 + 4121.05i −0.0729239 + 0.224437i
\(697\) 15413.1 + 5008.01i 0.837607 + 0.272155i
\(698\) −3173.97 4368.59i −0.172115 0.236896i
\(699\) −5274.23 −0.285393
\(700\) 9953.65 27982.4i 0.537447 1.51091i
\(701\) 16491.0 0.888526 0.444263 0.895896i \(-0.353466\pi\)
0.444263 + 0.895896i \(0.353466\pi\)
\(702\) −16164.7 22248.8i −0.869083 1.19619i
\(703\) 7433.49 + 2415.29i 0.398804 + 0.129579i
\(704\) −3762.70 + 11580.4i −0.201437 + 0.619961i
\(705\) −7614.98 + 1098.62i −0.406804 + 0.0586899i
\(706\) 5453.37 + 16783.7i 0.290709 + 0.894709i
\(707\) 5612.32i 0.298548i
\(708\) 11838.2 3846.48i 0.628402 0.204180i
\(709\) 14071.7 + 10223.7i 0.745380 + 0.541550i 0.894391 0.447285i \(-0.147609\pi\)
−0.149011 + 0.988835i \(0.547609\pi\)
\(710\) 8806.92 16710.5i 0.465518 0.883288i
\(711\) −2624.28 + 1906.65i −0.138422 + 0.100570i
\(712\) −1244.42 + 1712.79i −0.0655006 + 0.0901539i
\(713\) −2948.01 + 4057.58i −0.154844 + 0.213124i
\(714\) −24519.5 + 17814.5i −1.28518 + 0.933740i
\(715\) 6732.87 + 6921.27i 0.352161 + 0.362015i
\(716\) 22068.7 + 16033.9i 1.15188 + 0.836890i
\(717\) 15622.6 5076.09i 0.813719 0.264393i
\(718\) 1577.02i 0.0819691i
\(719\) −345.403 1063.04i −0.0179157 0.0551388i 0.941699 0.336457i \(-0.109229\pi\)
−0.959615 + 0.281318i \(0.909229\pi\)
\(720\) 7081.15 + 3731.97i 0.366526 + 0.193170i
\(721\) 4736.25 14576.7i 0.244642 0.752931i
\(722\) −25327.3 8229.34i −1.30552 0.424189i
\(723\) −610.019 839.620i −0.0313788 0.0431892i
\(724\) −31285.2 −1.60595
\(725\) −33832.9 12034.8i −1.73314 0.616497i
\(726\) −14752.6 −0.754162
\(727\) −14331.2 19725.2i −0.731108 1.00628i −0.999081 0.0428572i \(-0.986354\pi\)
0.267973 0.963426i \(-0.413646\pi\)
\(728\) −4517.55 1467.84i −0.229989 0.0747278i
\(729\) −5525.37 + 17005.3i −0.280718 + 0.863961i
\(730\) 6791.31 + 13796.0i 0.344326 + 0.699470i
\(731\) 9874.89 + 30391.8i 0.499639 + 1.53773i
\(732\) 7493.75i 0.378384i
\(733\) −26041.7 + 8461.46i −1.31224 + 0.426373i −0.879823 0.475301i \(-0.842339\pi\)
−0.432417 + 0.901674i \(0.642339\pi\)
\(734\) 2981.93 + 2166.50i 0.149953 + 0.108947i
\(735\) −13436.1 + 6614.15i −0.674285 + 0.331928i
\(736\) 12958.7 9415.02i 0.648998 0.471525i
\(737\) 5069.19 6977.15i 0.253360 0.348720i
\(738\) 6859.07 9440.70i 0.342122 0.470890i
\(739\) −12941.1 + 9402.24i −0.644175 + 0.468020i −0.861282 0.508127i \(-0.830338\pi\)
0.217107 + 0.976148i \(0.430338\pi\)
\(740\) 38859.3 + 6705.55i 1.93040 + 0.333109i
\(741\) 2687.98 + 1952.93i 0.133259 + 0.0968187i
\(742\) 6455.99 2097.68i 0.319416 0.103785i
\(743\) 13607.9i 0.671906i 0.941879 + 0.335953i \(0.109058\pi\)
−0.941879 + 0.335953i \(0.890942\pi\)
\(744\) −379.118 1166.80i −0.0186816 0.0574961i
\(745\) −2667.64 + 2595.02i −0.131188 + 0.127617i
\(746\) 2685.87 8266.26i 0.131819 0.405696i
\(747\) −13079.5 4249.80i −0.640637 0.208155i
\(748\) −7583.07 10437.2i −0.370674 0.510190i
\(749\) −27660.6 −1.34939
\(750\) −10581.5 + 18800.9i −0.515174 + 0.915348i
\(751\) 29048.3 1.41143 0.705717 0.708493i \(-0.250625\pi\)
0.705717 + 0.708493i \(0.250625\pi\)
\(752\) −5962.58 8206.79i −0.289139 0.397966i
\(753\) −24519.3 7966.82i −1.18663 0.385560i
\(754\) −16305.6 + 50183.5i −0.787553 + 2.42384i
\(755\) 25369.1 24678.5i 1.22288 1.18959i
\(756\) 10993.2 + 33833.5i 0.528860 + 1.62766i
\(757\) 12825.4i 0.615782i −0.951422 0.307891i \(-0.900377\pi\)
0.951422 0.307891i \(-0.0996232\pi\)
\(758\) −8462.63 + 2749.68i −0.405510 + 0.131758i
\(759\) −3620.97 2630.79i −0.173166 0.125812i
\(760\) 882.386 + 152.264i 0.0421151 + 0.00726738i
\(761\) 14330.7 10411.9i 0.682638 0.495966i −0.191594 0.981474i \(-0.561366\pi\)
0.874232 + 0.485509i \(0.161366\pi\)
\(762\) −10800.4 + 14865.4i −0.513459 + 0.706715i
\(763\) −28030.4 + 38580.5i −1.32997 + 1.83055i
\(764\) −3462.81 + 2515.88i −0.163979 + 0.119138i
\(765\) −9645.47 + 4748.14i −0.455860 + 0.224404i
\(766\) −5330.25 3872.66i −0.251423 0.182669i
\(767\) 15690.5 5098.17i 0.738661 0.240005i
\(768\) 10942.0i 0.514110i
\(769\) 635.990 + 1957.38i 0.0298236 + 0.0917877i 0.964860 0.262763i \(-0.0846338\pi\)
−0.935037 + 0.354551i \(0.884634\pi\)
\(770\) −10432.6 21193.0i −0.488267 0.991875i
\(771\) −8574.48 + 26389.5i −0.400522 + 1.23268i
\(772\) −9381.73 3048.31i −0.437378 0.142113i
\(773\) −8418.84 11587.5i −0.391726 0.539165i 0.566917 0.823775i \(-0.308136\pi\)
−0.958643 + 0.284610i \(0.908136\pi\)
\(774\) 23009.8 1.06857
\(775\) 9752.60 2873.85i 0.452030 0.133202i
\(776\) 1988.63 0.0919944
\(777\) −22900.3 31519.5i −1.05733 1.45529i
\(778\) 39437.3 + 12813.9i 1.81735 + 0.590491i
\(779\) −1343.07 + 4133.55i −0.0617721 + 0.190115i
\(780\) 14829.4 + 7815.52i 0.680740 + 0.358770i
\(781\) −2454.84 7555.23i −0.112473 0.346156i
\(782\) 18846.3i 0.861820i
\(783\) 40907.4 13291.6i 1.86707 0.606646i
\(784\) −15974.4 11606.0i −0.727695 0.528701i
\(785\) −6163.58 6336.05i −0.280239 0.288081i
\(786\) 2566.76 1864.86i 0.116480 0.0846276i
\(787\) 14804.9 20377.1i 0.670567 0.922956i −0.329206 0.944258i \(-0.606781\pi\)
0.999773 + 0.0213017i \(0.00678105\pi\)
\(788\) 484.586 666.975i 0.0219069 0.0301523i
\(789\) 14538.1 10562.5i 0.655982 0.476599i
\(790\) 5374.53 10197.8i 0.242047 0.459267i
\(791\) 999.436 + 726.133i 0.0449252 + 0.0326401i
\(792\) −961.599 + 312.442i −0.0431426 + 0.0140179i
\(793\) 9932.31i 0.444775i
\(794\) −16716.1 51446.9i −0.747144 2.29947i
\(795\) −2580.66 + 372.315i −0.115128 + 0.0166096i
\(796\) −4479.16 + 13785.4i −0.199447 + 0.613834i
\(797\) −10935.0 3553.00i −0.485995 0.157909i 0.0557627 0.998444i \(-0.482241\pi\)
−0.541758 + 0.840535i \(0.682241\pi\)
\(798\) −4777.57 6575.76i −0.211935 0.291703i
\(799\) 13624.7 0.603265
\(800\) −32458.5 895.915i −1.43448 0.0395942i
\(801\) 6816.97 0.300706
\(802\) 8131.70 + 11192.3i 0.358030 + 0.492787i
\(803\) 6150.42 + 1998.39i 0.270291 + 0.0878229i
\(804\) 4626.58 14239.1i 0.202944 0.624596i
\(805\) −3102.79 + 17980.9i −0.135850 + 0.787260i
\(806\) −4616.66 14208.6i −0.201755 0.620939i
\(807\) 6306.91i 0.275110i
\(808\) −811.901 + 263.803i −0.0353497 + 0.0114858i
\(809\) 1971.05 + 1432.05i 0.0856593 + 0.0622351i 0.629791 0.776765i \(-0.283141\pi\)
−0.544131 + 0.839000i \(0.683141\pi\)
\(810\) −1387.65 9618.36i −0.0601939 0.417228i
\(811\) −24879.8 + 18076.2i −1.07725 + 0.782666i −0.977201 0.212317i \(-0.931899\pi\)
−0.100047 + 0.994983i \(0.531899\pi\)
\(812\) 40120.5 55221.1i 1.73393 2.38655i
\(813\) 8862.48 12198.2i 0.382313 0.526209i
\(814\) 25373.4 18434.9i 1.09255 0.793786i
\(815\) −242.452 1680.53i −0.0104205 0.0722287i
\(816\) 12417.5 + 9021.85i 0.532720 + 0.387044i
\(817\) −8150.60 + 2648.29i −0.349025 + 0.113405i
\(818\) 63761.6i 2.72539i
\(819\) 4726.33 + 14546.1i 0.201650 + 0.620614i
\(820\) −3728.76 + 21608.5i −0.158798 + 0.920247i
\(821\) 3820.85 11759.4i 0.162422 0.499885i −0.836415 0.548097i \(-0.815352\pi\)
0.998837 + 0.0482124i \(0.0153524\pi\)
\(822\) 32733.6 + 10635.8i 1.38895 + 0.451297i
\(823\) 3253.78 + 4478.45i 0.137813 + 0.189683i 0.872345 0.488891i \(-0.162598\pi\)
−0.734532 + 0.678574i \(0.762598\pi\)
\(824\) 2331.34 0.0985633
\(825\) 2564.61 + 8703.18i 0.108228 + 0.367280i
\(826\) −40360.1 −1.70013
\(827\) 12038.4 + 16569.4i 0.506185 + 0.696703i 0.983270 0.182154i \(-0.0583068\pi\)
−0.477085 + 0.878857i \(0.658307\pi\)
\(828\) 6824.47 + 2217.41i 0.286433 + 0.0930678i
\(829\) −9881.86 + 30413.2i −0.414006 + 1.27418i 0.499130 + 0.866527i \(0.333653\pi\)
−0.913137 + 0.407653i \(0.866347\pi\)
\(830\) 48371.6 6978.61i 2.02290 0.291845i
\(831\) 2219.10 + 6829.68i 0.0926350 + 0.285101i
\(832\) 28017.2i 1.16745i
\(833\) 25222.3 8195.23i 1.04910 0.340874i
\(834\) 8603.73 + 6250.98i 0.357222 + 0.259537i
\(835\) 9358.87 17757.8i 0.387877 0.735969i
\(836\) 2799.09 2033.66i 0.115800 0.0841335i
\(837\) −7158.22 + 9852.45i −0.295609 + 0.406870i
\(838\) 30090.7 41416.3i 1.24041 1.70728i
\(839\) 11465.9 8330.46i 0.471808 0.342788i −0.326338 0.945253i \(-0.605815\pi\)
0.798145 + 0.602465i \(0.205815\pi\)
\(840\) −3112.25 3199.34i −0.127837 0.131414i
\(841\) −47035.6 34173.4i −1.92856 1.40118i
\(842\) −65948.4 + 21427.9i −2.69921 + 0.877025i
\(843\) 2000.39i 0.0817284i
\(844\) 10218.4 + 31449.1i 0.416745 + 1.28261i
\(845\) −2075.00 1093.58i −0.0844758 0.0445212i
\(846\) 3031.62 9330.36i 0.123202 0.379178i
\(847\) 24055.8 + 7816.19i 0.975875 + 0.317081i
\(848\) −2020.68 2781.23i −0.0818283 0.112627i
\(849\) −5405.25 −0.218501
\(850\) 23300.5 30277.0i 0.940236 1.22176i
\(851\) −24226.7 −0.975888
\(852\) −8106.20 11157.2i −0.325955 0.448639i
\(853\) −32931.0 10699.9i −1.32185 0.429494i −0.438717 0.898625i \(-0.644567\pi\)
−0.883128 + 0.469131i \(0.844567\pi\)
\(854\) −7508.50 + 23108.8i −0.300861 + 0.925956i
\(855\) −1273.38 2586.76i −0.0509340 0.103468i
\(856\) −1300.16 4001.49i −0.0519143 0.159776i
\(857\) 18153.2i 0.723573i 0.932261 + 0.361787i \(0.117833\pi\)
−0.932261 + 0.361787i \(0.882167\pi\)
\(858\) 12679.7 4119.88i 0.504520 0.163928i
\(859\) −9103.82 6614.31i −0.361604 0.262721i 0.392117 0.919916i \(-0.371743\pi\)
−0.753721 + 0.657195i \(0.771743\pi\)
\(860\) −38792.3 + 19096.1i −1.53815 + 0.757178i
\(861\) 17527.1 12734.2i 0.693753 0.504041i
\(862\) −30227.7 + 41604.9i −1.19439 + 1.64393i
\(863\) −3397.50 + 4676.26i −0.134012 + 0.184452i −0.870749 0.491728i \(-0.836366\pi\)
0.736737 + 0.676179i \(0.236366\pi\)
\(864\) 31465.6 22861.1i 1.23899 0.900175i
\(865\) −16900.6 2916.36i −0.664320 0.114635i
\(866\) 13898.7 + 10098.0i 0.545378 + 0.396240i
\(867\) −2100.25 + 682.412i −0.0822701 + 0.0267312i
\(868\) 19325.8i 0.755715i
\(869\) −1498.10 4610.67i −0.0584804 0.179984i
\(870\) −35540.1 + 34572.7i −1.38497 + 1.34727i
\(871\) 6132.12 18872.7i 0.238552 0.734188i
\(872\) −6898.75 2241.54i −0.267914 0.0870505i
\(873\) −3763.72 5180.31i −0.145914 0.200833i
\(874\) −5054.29 −0.195611
\(875\) 27215.3 25050.6i 1.05148 0.967847i
\(876\) 11226.8 0.433012
\(877\) 4802.82 + 6610.52i 0.184926 + 0.254528i 0.891407 0.453203i \(-0.149719\pi\)
−0.706482 + 0.707731i \(0.749719\pi\)
\(878\) −54894.0 17836.2i −2.11000 0.685582i
\(879\) 4134.33 12724.2i 0.158643 0.488254i
\(880\) −8574.88 + 8341.47i −0.328476 + 0.319535i
\(881\) 4845.20 + 14912.0i 0.185288 + 0.570259i 0.999953 0.00967301i \(-0.00307906\pi\)
−0.814665 + 0.579932i \(0.803079\pi\)
\(882\) 19096.0i 0.729020i
\(883\) −5689.20 + 1848.53i −0.216825 + 0.0704508i −0.415415 0.909632i \(-0.636364\pi\)
0.198590 + 0.980083i \(0.436364\pi\)
\(884\) −24015.5 17448.3i −0.913721 0.663857i
\(885\) 15276.7 + 2636.14i 0.580248 + 0.100128i
\(886\) −24574.3 + 17854.3i −0.931816 + 0.677004i
\(887\) −14454.3 + 19894.7i −0.547158 + 0.753099i −0.989623 0.143687i \(-0.954104\pi\)
0.442465 + 0.896786i \(0.354104\pi\)
\(888\) 3483.33 4794.39i 0.131636 0.181182i
\(889\) 25487.1 18517.5i 0.961541 0.698600i
\(890\) −21734.6 + 10699.2i −0.818589 + 0.402964i
\(891\) −3306.43 2402.26i −0.124320 0.0903241i
\(892\) 42277.7 13736.9i 1.58695 0.515632i
\(893\) 3653.94i 0.136926i
\(894\) 1587.91 + 4887.09i 0.0594046 + 0.182829i
\(895\) 15004.5 + 30480.4i 0.560385 + 1.13838i
\(896\) 4183.27 12874.8i 0.155975 0.480041i
\(897\) −9794.49 3182.42i −0.364580 0.118459i
\(898\) 10775.6 + 14831.3i 0.400430 + 0.551145i
\(899\) 23366.5 0.866869
\(900\) −8222.18 11999.7i −0.304525 0.444433i
\(901\) 4617.34 0.170728
\(902\) 10251.1 + 14109.4i 0.378408 + 0.520834i
\(903\) 40628.0 + 13200.8i 1.49725 + 0.486485i
\(904\) −58.0676 + 178.714i −0.00213639 + 0.00657514i
\(905\) −34469.4 18166.4i −1.26608 0.667261i
\(906\) −15100.9 46475.9i −0.553747 1.70426i
\(907\) 2239.16i 0.0819737i 0.999160 + 0.0409868i \(0.0130502\pi\)
−0.999160 + 0.0409868i \(0.986950\pi\)
\(908\) −3147.61 + 1022.72i −0.115041 + 0.0373791i
\(909\) 2223.82 + 1615.70i 0.0811433 + 0.0589541i
\(910\) −37899.0 38959.6i −1.38059 1.41923i
\(911\) 8447.01 6137.11i 0.307203 0.223196i −0.423492 0.905900i \(-0.639196\pi\)
0.730695 + 0.682704i \(0.239196\pi\)
\(912\) −2419.52 + 3330.18i −0.0878489 + 0.120914i
\(913\) 12081.2 16628.3i 0.437929 0.602757i
\(914\) 21164.1 15376.6i 0.765916 0.556471i
\(915\) 4351.40 8256.47i 0.157216 0.298307i
\(916\) −7500.00 5449.07i −0.270532 0.196553i
\(917\) −5173.41 + 1680.94i −0.186304 + 0.0605339i
\(918\) 45761.8i 1.64528i
\(919\) −11493.8 35374.2i −0.412562 1.26973i −0.914414 0.404781i \(-0.867348\pi\)
0.501852 0.864953i \(-0.332652\pi\)
\(920\) −2747.04 + 396.317i −0.0984425 + 0.0142024i
\(921\) −294.265 + 905.654i −0.0105281 + 0.0324021i
\(922\) 60132.8 + 19538.3i 2.14790 + 0.697897i
\(923\) −10744.1 14787.9i −0.383147 0.527357i
\(924\) −17246.3 −0.614027
\(925\) 38920.7 + 29952.5i 1.38346 + 1.06468i
\(926\) 4713.07 0.167258
\(927\) −4412.34 6073.07i −0.156333 0.215173i
\(928\) −70972.8 23060.5i −2.51056 0.815729i
\(929\) −1682.80 + 5179.13i −0.0594305 + 0.182908i −0.976364 0.216131i \(-0.930656\pi\)
0.916934 + 0.399039i \(0.130656\pi\)
\(930\) 2387.16 13833.8i 0.0841700 0.487773i
\(931\) 2197.83 + 6764.23i 0.0773695 + 0.238119i
\(932\) 12637.4i 0.444155i
\(933\) −28777.9 + 9350.50i −1.00980 + 0.328105i
\(934\) 35416.9 + 25731.9i 1.24077 + 0.901471i
\(935\) −2294.31 15902.8i −0.0802479 0.556231i
\(936\) −1882.14 + 1367.46i −0.0657263 + 0.0477530i
\(937\) 16010.7 22036.8i 0.558214 0.768315i −0.432884 0.901449i \(-0.642504\pi\)
0.991098 + 0.133134i \(0.0425041\pi\)
\(938\) −28534.3 + 39274.1i −0.993260 + 1.36711i
\(939\) −2077.76 + 1509.58i −0.0722101 + 0.0524637i
\(940\) 2632.37 + 18246.0i 0.0913388 + 0.633106i
\(941\) 16926.4 + 12297.7i 0.586381 + 0.426031i 0.841019 0.541006i \(-0.181956\pi\)
−0.254638 + 0.967037i \(0.581956\pi\)
\(942\) −11607.6 + 3771.53i −0.401482 + 0.130449i
\(943\) 13471.8i 0.465218i
\(944\) 6316.21 + 19439.3i 0.217770 + 0.670228i
\(945\) −7534.05 + 43660.5i −0.259347 + 1.50294i
\(946\) −10626.8 + 32705.8i −0.365228 + 1.12406i
\(947\) −2549.10 828.252i −0.0874705 0.0284209i 0.264955 0.964261i \(-0.414643\pi\)
−0.352425 + 0.935840i \(0.614643\pi\)
\(948\) −4946.90 6808.83i −0.169481 0.233271i
\(949\) 14880.1 0.508988
\(950\) 8119.82 + 6248.83i 0.277307 + 0.213409i
\(951\) 17153.2 0.584891
\(952\) 4645.91 + 6394.55i 0.158167 + 0.217698i
\(953\) −34211.1 11115.9i −1.16286 0.377837i −0.336888 0.941545i \(-0.609374\pi\)
−0.825974 + 0.563708i \(0.809374\pi\)
\(954\) 1027.39 3162.00i 0.0348670 0.107310i
\(955\) −5276.15 + 761.194i −0.178777 + 0.0257923i
\(956\) −12162.7 37432.9i −0.411474 1.26639i
\(957\) 20852.1i 0.704340i
\(958\) 56752.1 18439.9i 1.91396 0.621885i
\(959\) −47740.7 34685.6i −1.60754 1.16794i
\(960\) −12274.5 + 23290.0i −0.412664 + 0.783001i
\(961\) 18749.1 13622.0i 0.629355 0.457253i
\(962\) 42417.8 58383.1i 1.42163 1.95670i
\(963\) −7963.04 + 10960.2i −0.266465 + 0.366757i
\(964\) −2011.79 + 1461.65i −0.0672151 + 0.0488346i
\(965\) −8566.55 8806.26i −0.285769 0.293765i
\(966\) 20382.3 + 14808.6i 0.678872 + 0.493229i
\(967\) −55891.5 + 18160.2i −1.85868 + 0.603923i −0.863687 + 0.504029i \(0.831851\pi\)
−0.994998 + 0.0998944i \(0.968149\pi\)
\(968\) 3847.40i 0.127748i
\(969\) −1708.46 5258.11i −0.0566395 0.174319i
\(970\) 20130.3 + 10609.3i 0.666337 + 0.351179i
\(971\) −9169.69 + 28221.4i −0.303058 + 0.932717i 0.677337 + 0.735673i \(0.263134\pi\)
−0.980395 + 0.197044i \(0.936866\pi\)
\(972\) 27766.5 + 9021.90i 0.916268 + 0.297714i
\(973\) −10717.5 14751.3i −0.353120 0.486028i
\(974\) 24293.0 0.799178
\(975\) 11800.5 + 17222.0i 0.387608 + 0.565686i
\(976\) 12305.3 0.403569
\(977\) 22514.1 + 30988.0i 0.737247 + 1.01473i 0.998772 + 0.0495366i \(0.0157744\pi\)
−0.261526 + 0.965197i \(0.584226\pi\)
\(978\) −2229.66 724.460i −0.0729004 0.0236868i
\(979\) −3148.32 + 9689.52i −0.102779 + 0.316321i
\(980\) 15848.0 + 32193.9i 0.516577 + 1.04939i
\(981\) 7217.57 + 22213.4i 0.234902 + 0.722955i
\(982\) 69236.2i 2.24992i
\(983\) 10808.9 3512.01i 0.350711 0.113953i −0.128363 0.991727i \(-0.540972\pi\)
0.479075 + 0.877774i \(0.340972\pi\)
\(984\) 2666.02 + 1936.98i 0.0863716 + 0.0627527i
\(985\) 921.200 453.476i 0.0297989 0.0146690i
\(986\) 71034.2 51609.4i 2.29431 1.66691i
\(987\) 10705.7 14735.2i 0.345255 0.475203i
\(988\) 4679.36 6440.58i 0.150678 0.207391i
\(989\) 21490.6 15613.8i 0.690962 0.502013i
\(990\) −11400.9 1967.33i −0.366003 0.0631575i
\(991\) 22004.4 + 15987.1i 0.705340 + 0.512459i 0.881667 0.471872i \(-0.156422\pi\)
−0.176327 + 0.984332i \(0.556422\pi\)
\(992\) 20094.7 6529.18i 0.643154 0.208973i
\(993\) 27729.2i 0.886164i
\(994\) 13818.2 + 42528.1i 0.440933 + 1.35705i
\(995\) −12939.9 + 12587.6i −0.412282 + 0.401060i
\(996\) 11026.3 33935.5i 0.350785 1.07961i
\(997\) −33121.2 10761.7i −1.05211 0.341853i −0.268617 0.963247i \(-0.586567\pi\)
−0.783498 + 0.621394i \(0.786567\pi\)
\(998\) −16615.9 22869.9i −0.527023 0.725385i
\(999\) −58826.2 −1.86304
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 25.4.e.a.14.1 yes 24
3.2 odd 2 225.4.m.a.64.6 24
5.2 odd 4 125.4.d.b.51.11 48
5.3 odd 4 125.4.d.b.51.2 48
5.4 even 2 125.4.e.a.74.6 24
25.3 odd 20 625.4.a.g.1.22 24
25.9 even 10 inner 25.4.e.a.9.1 24
25.12 odd 20 125.4.d.b.76.11 48
25.13 odd 20 125.4.d.b.76.2 48
25.16 even 5 125.4.e.a.49.6 24
25.22 odd 20 625.4.a.g.1.3 24
75.59 odd 10 225.4.m.a.109.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.4.e.a.9.1 24 25.9 even 10 inner
25.4.e.a.14.1 yes 24 1.1 even 1 trivial
125.4.d.b.51.2 48 5.3 odd 4
125.4.d.b.51.11 48 5.2 odd 4
125.4.d.b.76.2 48 25.13 odd 20
125.4.d.b.76.11 48 25.12 odd 20
125.4.e.a.49.6 24 25.16 even 5
125.4.e.a.74.6 24 5.4 even 2
225.4.m.a.64.6 24 3.2 odd 2
225.4.m.a.109.6 24 75.59 odd 10
625.4.a.g.1.3 24 25.22 odd 20
625.4.a.g.1.22 24 25.3 odd 20