Properties

Label 43.4.e.a.11.9
Level $43$
Weight $4$
Character 43.11
Analytic conductor $2.537$
Analytic rank $0$
Dimension $60$
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] = [43,4,Mod(4,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 43.e (of order \(7\), degree \(6\), 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: \(2.53708213025\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) \(=\) 43.11
Dual form 43.4.e.a.4.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.72209 + 3.41339i) q^{2} +(-2.84196 + 3.56370i) q^{3} +(-2.46131 + 10.7837i) q^{4} +(8.30189 - 3.99798i) q^{5} -19.9004 q^{6} -12.2688 q^{7} +(-12.0406 + 5.79846i) q^{8} +(1.38482 + 6.06730i) q^{9} +O(q^{10})\) \(q+(2.72209 + 3.41339i) q^{2} +(-2.84196 + 3.56370i) q^{3} +(-2.46131 + 10.7837i) q^{4} +(8.30189 - 3.99798i) q^{5} -19.9004 q^{6} -12.2688 q^{7} +(-12.0406 + 5.79846i) q^{8} +(1.38482 + 6.06730i) q^{9} +(36.2452 + 17.4548i) q^{10} +(-3.74140 - 16.3922i) q^{11} +(-31.4349 - 39.4182i) q^{12} +(66.8370 - 32.1870i) q^{13} +(-33.3969 - 41.8784i) q^{14} +(-9.34601 + 40.9475i) q^{15} +(27.1570 + 13.0781i) q^{16} +(-0.640842 - 0.308613i) q^{17} +(-16.9405 + 21.2427i) q^{18} +(-6.96294 + 30.5066i) q^{19} +(22.6795 + 99.3654i) q^{20} +(34.8675 - 43.7225i) q^{21} +(45.7684 - 57.3918i) q^{22} +(-18.6609 - 81.7588i) q^{23} +(13.5550 - 59.3881i) q^{24} +(-24.9987 + 31.3473i) q^{25} +(291.803 + 140.525i) q^{26} +(-136.440 - 65.7059i) q^{27} +(30.1974 - 132.304i) q^{28} +(-142.592 - 178.805i) q^{29} +(-165.211 + 79.5613i) q^{30} +(-151.938 - 190.525i) q^{31} +(53.0733 + 232.529i) q^{32} +(69.0496 + 33.2525i) q^{33} +(-0.691012 - 3.02752i) q^{34} +(-101.855 + 49.0506i) q^{35} -68.8364 q^{36} +82.4344 q^{37} +(-123.085 + 59.2745i) q^{38} +(-75.2429 + 329.661i) q^{39} +(-76.7778 + 96.2764i) q^{40} +(252.021 + 316.025i) q^{41} +244.155 q^{42} +(-163.858 - 229.473i) q^{43} +185.977 q^{44} +(35.7536 + 44.8336i) q^{45} +(228.278 - 286.252i) q^{46} +(-78.0998 + 342.177i) q^{47} +(-123.786 + 59.6120i) q^{48} -192.475 q^{49} -175.049 q^{50} +(2.92105 - 1.40670i) q^{51} +(182.588 + 799.972i) q^{52} +(-95.6110 - 46.0438i) q^{53} +(-147.121 - 644.580i) q^{54} +(-96.5962 - 121.128i) q^{55} +(147.725 - 71.1404i) q^{56} +(-88.9281 - 111.512i) q^{57} +(222.183 - 973.447i) q^{58} +(616.615 + 296.946i) q^{59} +(-418.562 - 201.569i) q^{60} +(315.438 - 395.546i) q^{61} +(236.746 - 1037.25i) q^{62} +(-16.9902 - 74.4387i) q^{63} +(-498.898 + 625.599i) q^{64} +(426.190 - 534.426i) q^{65} +(74.4553 + 326.210i) q^{66} +(-63.7497 + 279.306i) q^{67} +(4.90530 - 6.15106i) q^{68} +(344.397 + 165.853i) q^{69} +(-444.686 - 214.150i) q^{70} +(29.2594 - 128.194i) q^{71} +(-51.8551 - 65.0242i) q^{72} +(-656.788 + 316.292i) q^{73} +(224.394 + 281.381i) q^{74} +(-40.6674 - 178.175i) q^{75} +(-311.836 - 150.172i) q^{76} +(45.9027 + 201.113i) q^{77} +(-1330.08 + 640.533i) q^{78} +818.448 q^{79} +277.741 q^{80} +(470.522 - 226.592i) q^{81} +(-392.692 + 1720.50i) q^{82} +(-540.134 + 677.307i) q^{83} +(385.670 + 483.615i) q^{84} -6.55403 q^{85} +(337.245 - 1183.96i) q^{86} +1042.45 q^{87} +(140.098 + 175.677i) q^{88} +(545.794 - 684.404i) q^{89} +(-55.7101 + 244.082i) q^{90} +(-820.013 + 394.897i) q^{91} +927.593 q^{92} +1110.78 q^{93} +(-1380.58 + 664.853i) q^{94} +(64.1593 + 281.100i) q^{95} +(-979.497 - 471.701i) q^{96} +(207.312 + 908.294i) q^{97} +(-523.935 - 656.994i) q^{98} +(94.2749 - 45.4004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 9 q^{2} - 3 q^{3} - 31 q^{4} - 23 q^{5} + 16 q^{6} + 96 q^{7} + 61 q^{8} - 177 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 9 q^{2} - 3 q^{3} - 31 q^{4} - 23 q^{5} + 16 q^{6} + 96 q^{7} + 61 q^{8} - 177 q^{9} - 61 q^{10} + 83 q^{11} + 33 q^{12} + 107 q^{13} - 299 q^{14} + 109 q^{15} + 41 q^{16} + 181 q^{17} - 414 q^{18} + 284 q^{19} - 363 q^{20} - 88 q^{21} + 421 q^{22} + 231 q^{23} - 937 q^{24} + 213 q^{25} + 139 q^{26} - 27 q^{27} + 29 q^{28} - 367 q^{29} + 1244 q^{30} - 319 q^{31} + 435 q^{32} - 2594 q^{33} - 583 q^{34} - 902 q^{35} + 1552 q^{36} + 1020 q^{37} + 1251 q^{38} - 1571 q^{39} + 1263 q^{40} + 293 q^{41} - 1830 q^{42} + 1661 q^{43} + 6512 q^{44} + 1019 q^{45} - 2786 q^{46} - 287 q^{47} - 95 q^{48} + 772 q^{49} - 282 q^{50} + 1524 q^{51} - 1511 q^{52} - 1505 q^{53} - 3489 q^{54} - 1735 q^{55} - 1237 q^{56} + 1055 q^{57} + 335 q^{58} + 571 q^{59} - 101 q^{60} - 339 q^{61} + 923 q^{62} - 702 q^{63} - 5163 q^{64} + 2463 q^{65} + 985 q^{66} - 241 q^{67} + 2904 q^{68} + 2711 q^{69} - 7698 q^{70} - 2431 q^{71} - 4340 q^{72} - 2157 q^{73} - 1294 q^{74} - 242 q^{75} - 4272 q^{76} - 3962 q^{77} - 2860 q^{78} + 1092 q^{79} + 11618 q^{80} + 12060 q^{81} + 4023 q^{82} - 2664 q^{83} + 3334 q^{84} - 3446 q^{85} + 10055 q^{86} + 11874 q^{87} + 9957 q^{88} - 5811 q^{89} - 1612 q^{90} - 760 q^{91} + 2120 q^{92} + 3994 q^{93} + 6057 q^{94} + 379 q^{95} - 2044 q^{96} - 5509 q^{97} - 9041 q^{98} - 2012 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.72209 + 3.41339i 0.962404 + 1.20682i 0.978353 + 0.206944i \(0.0663517\pi\)
−0.0159488 + 0.999873i \(0.505077\pi\)
\(3\) −2.84196 + 3.56370i −0.546935 + 0.685834i −0.976083 0.217400i \(-0.930242\pi\)
0.429148 + 0.903234i \(0.358814\pi\)
\(4\) −2.46131 + 10.7837i −0.307664 + 1.34796i
\(5\) 8.30189 3.99798i 0.742544 0.357590i −0.0240601 0.999711i \(-0.507659\pi\)
0.766604 + 0.642120i \(0.221945\pi\)
\(6\) −19.9004 −1.35405
\(7\) −12.2688 −0.662455 −0.331228 0.943551i \(-0.607463\pi\)
−0.331228 + 0.943551i \(0.607463\pi\)
\(8\) −12.0406 + 5.79846i −0.532125 + 0.256258i
\(9\) 1.38482 + 6.06730i 0.0512897 + 0.224715i
\(10\) 36.2452 + 17.4548i 1.14617 + 0.551968i
\(11\) −3.74140 16.3922i −0.102552 0.449311i −0.999967 0.00812292i \(-0.997414\pi\)
0.897415 0.441188i \(-0.145443\pi\)
\(12\) −31.4349 39.4182i −0.756207 0.948253i
\(13\) 66.8370 32.1870i 1.42594 0.686697i 0.447703 0.894182i \(-0.352242\pi\)
0.978238 + 0.207485i \(0.0665278\pi\)
\(14\) −33.3969 41.8784i −0.637550 0.799462i
\(15\) −9.34601 + 40.9475i −0.160875 + 0.704841i
\(16\) 27.1570 + 13.0781i 0.424328 + 0.204346i
\(17\) −0.640842 0.308613i −0.00914277 0.00440293i 0.429307 0.903159i \(-0.358758\pi\)
−0.438450 + 0.898756i \(0.644472\pi\)
\(18\) −16.9405 + 21.2427i −0.221828 + 0.278164i
\(19\) −6.96294 + 30.5066i −0.0840741 + 0.368353i −0.999410 0.0343378i \(-0.989068\pi\)
0.915336 + 0.402691i \(0.131925\pi\)
\(20\) 22.6795 + 99.3654i 0.253564 + 1.11094i
\(21\) 34.8675 43.7225i 0.362320 0.454335i
\(22\) 45.7684 57.3918i 0.443539 0.556180i
\(23\) −18.6609 81.7588i −0.169177 0.741213i −0.986329 0.164790i \(-0.947305\pi\)
0.817152 0.576423i \(-0.195552\pi\)
\(24\) 13.5550 59.3881i 0.115287 0.505106i
\(25\) −24.9987 + 31.3473i −0.199989 + 0.250779i
\(26\) 291.803 + 140.525i 2.20105 + 1.05997i
\(27\) −136.440 65.7059i −0.972513 0.468337i
\(28\) 30.1974 132.304i 0.203813 0.892965i
\(29\) −142.592 178.805i −0.913060 1.14494i −0.989013 0.147829i \(-0.952771\pi\)
0.0759532 0.997111i \(-0.475800\pi\)
\(30\) −165.211 + 79.5613i −1.00544 + 0.484194i
\(31\) −151.938 190.525i −0.880289 1.10385i −0.993896 0.110321i \(-0.964812\pi\)
0.113607 0.993526i \(-0.463759\pi\)
\(32\) 53.0733 + 232.529i 0.293192 + 1.28456i
\(33\) 69.0496 + 33.2525i 0.364242 + 0.175410i
\(34\) −0.691012 3.02752i −0.00348551 0.0152710i
\(35\) −101.855 + 49.0506i −0.491902 + 0.236888i
\(36\) −68.8364 −0.318687
\(37\) 82.4344 0.366274 0.183137 0.983087i \(-0.441375\pi\)
0.183137 + 0.983087i \(0.441375\pi\)
\(38\) −123.085 + 59.2745i −0.525447 + 0.253042i
\(39\) −75.2429 + 329.661i −0.308936 + 1.35354i
\(40\) −76.7778 + 96.2764i −0.303491 + 0.380566i
\(41\) 252.021 + 316.025i 0.959979 + 1.20378i 0.978980 + 0.203956i \(0.0653799\pi\)
−0.0190013 + 0.999819i \(0.506049\pi\)
\(42\) 244.155 0.896997
\(43\) −163.858 229.473i −0.581118 0.813820i
\(44\) 185.977 0.637206
\(45\) 35.7536 + 44.8336i 0.118441 + 0.148520i
\(46\) 228.278 286.252i 0.731691 0.917512i
\(47\) −78.0998 + 342.177i −0.242383 + 1.06195i 0.696457 + 0.717599i \(0.254759\pi\)
−0.938840 + 0.344353i \(0.888098\pi\)
\(48\) −123.786 + 59.6120i −0.372227 + 0.179255i
\(49\) −192.475 −0.561153
\(50\) −175.049 −0.495114
\(51\) 2.92105 1.40670i 0.00802018 0.00386231i
\(52\) 182.588 + 799.972i 0.486932 + 2.13339i
\(53\) −95.6110 46.0438i −0.247796 0.119332i 0.305864 0.952075i \(-0.401055\pi\)
−0.553660 + 0.832743i \(0.686769\pi\)
\(54\) −147.121 644.580i −0.370753 1.62437i
\(55\) −96.5962 121.128i −0.236819 0.296961i
\(56\) 147.725 71.1404i 0.352509 0.169760i
\(57\) −88.9281 111.512i −0.206646 0.259126i
\(58\) 222.183 973.447i 0.503001 2.20379i
\(59\) 616.615 + 296.946i 1.36062 + 0.655239i 0.964774 0.263079i \(-0.0847381\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(60\) −418.562 201.569i −0.900603 0.433708i
\(61\) 315.438 395.546i 0.662092 0.830238i −0.331477 0.943463i \(-0.607547\pi\)
0.993569 + 0.113226i \(0.0361183\pi\)
\(62\) 236.746 1037.25i 0.484947 2.12469i
\(63\) −16.9902 74.4387i −0.0339771 0.148863i
\(64\) −498.898 + 625.599i −0.974410 + 1.22187i
\(65\) 426.190 534.426i 0.813268 1.01981i
\(66\) 74.4553 + 326.210i 0.138861 + 0.608389i
\(67\) −63.7497 + 279.306i −0.116243 + 0.509293i 0.882963 + 0.469443i \(0.155545\pi\)
−0.999206 + 0.0398502i \(0.987312\pi\)
\(68\) 4.90530 6.15106i 0.00874787 0.0109695i
\(69\) 344.397 + 165.853i 0.600878 + 0.289368i
\(70\) −444.686 214.150i −0.759288 0.365654i
\(71\) 29.2594 128.194i 0.0489078 0.214279i −0.944569 0.328313i \(-0.893520\pi\)
0.993477 + 0.114034i \(0.0363771\pi\)
\(72\) −51.8551 65.0242i −0.0848775 0.106433i
\(73\) −656.788 + 316.292i −1.05303 + 0.507112i −0.878601 0.477557i \(-0.841522\pi\)
−0.174429 + 0.984670i \(0.555808\pi\)
\(74\) 224.394 + 281.381i 0.352503 + 0.442025i
\(75\) −40.6674 178.175i −0.0626115 0.274319i
\(76\) −311.836 150.172i −0.470659 0.226657i
\(77\) 45.9027 + 201.113i 0.0679363 + 0.297648i
\(78\) −1330.08 + 640.533i −1.93079 + 0.929821i
\(79\) 818.448 1.16560 0.582801 0.812615i \(-0.301957\pi\)
0.582801 + 0.812615i \(0.301957\pi\)
\(80\) 277.741 0.388154
\(81\) 470.522 226.592i 0.645435 0.310825i
\(82\) −392.692 + 1720.50i −0.528848 + 2.31704i
\(83\) −540.134 + 677.307i −0.714306 + 0.895712i −0.998001 0.0632031i \(-0.979868\pi\)
0.283695 + 0.958915i \(0.408440\pi\)
\(84\) 385.670 + 483.615i 0.500953 + 0.628176i
\(85\) −6.55403 −0.00836335
\(86\) 337.245 1183.96i 0.422861 1.48453i
\(87\) 1042.45 1.28462
\(88\) 140.098 + 175.677i 0.169710 + 0.212810i
\(89\) 545.794 684.404i 0.650045 0.815131i −0.342174 0.939637i \(-0.611163\pi\)
0.992219 + 0.124506i \(0.0397346\pi\)
\(90\) −55.7101 + 244.082i −0.0652485 + 0.285872i
\(91\) −820.013 + 394.897i −0.944623 + 0.454906i
\(92\) 927.593 1.05118
\(93\) 1110.78 1.23852
\(94\) −1380.58 + 664.853i −1.51485 + 0.729514i
\(95\) 64.1593 + 281.100i 0.0692906 + 0.303582i
\(96\) −979.497 471.701i −1.04135 0.501487i
\(97\) 207.312 + 908.294i 0.217004 + 0.950756i 0.959678 + 0.281103i \(0.0907001\pi\)
−0.742674 + 0.669653i \(0.766443\pi\)
\(98\) −523.935 656.994i −0.540056 0.677208i
\(99\) 94.2749 45.4004i 0.0957069 0.0460900i
\(100\) −276.511 346.733i −0.276511 0.346733i
\(101\) −152.349 + 667.485i −0.150092 + 0.657597i 0.842764 + 0.538283i \(0.180927\pi\)
−0.992857 + 0.119314i \(0.961930\pi\)
\(102\) 12.7530 + 6.14152i 0.0123798 + 0.00596177i
\(103\) −857.904 413.145i −0.820697 0.395227i −0.0240793 0.999710i \(-0.507665\pi\)
−0.796618 + 0.604483i \(0.793380\pi\)
\(104\) −618.124 + 775.103i −0.582808 + 0.730818i
\(105\) 114.665 502.379i 0.106573 0.466925i
\(106\) −103.096 451.693i −0.0944677 0.413890i
\(107\) −1040.23 + 1304.41i −0.939838 + 1.17852i 0.0439222 + 0.999035i \(0.486015\pi\)
−0.983761 + 0.179485i \(0.942557\pi\)
\(108\) 1044.37 1309.60i 0.930508 1.16682i
\(109\) −483.141 2116.78i −0.424555 1.86010i −0.504673 0.863311i \(-0.668387\pi\)
0.0801182 0.996785i \(-0.474470\pi\)
\(110\) 150.513 659.442i 0.130462 0.571593i
\(111\) −234.275 + 293.771i −0.200328 + 0.251203i
\(112\) −333.185 160.453i −0.281099 0.135370i
\(113\) −1496.80 720.820i −1.24608 0.600080i −0.309621 0.950860i \(-0.600202\pi\)
−0.936458 + 0.350780i \(0.885917\pi\)
\(114\) 138.565 607.093i 0.113840 0.498767i
\(115\) −481.791 604.147i −0.390672 0.489887i
\(116\) 2279.14 1097.58i 1.82425 0.878513i
\(117\) 287.845 + 360.947i 0.227447 + 0.285210i
\(118\) 664.888 + 2913.06i 0.518711 + 2.27262i
\(119\) 7.86240 + 3.78633i 0.00605668 + 0.00291674i
\(120\) −124.901 547.226i −0.0950153 0.416289i
\(121\) 944.485 454.840i 0.709606 0.341728i
\(122\) 2208.80 1.63914
\(123\) −1842.45 −1.35064
\(124\) 2428.53 1169.52i 1.75878 0.846982i
\(125\) −338.510 + 1483.11i −0.242218 + 1.06123i
\(126\) 207.840 260.623i 0.146951 0.184271i
\(127\) −408.083 511.720i −0.285130 0.357542i 0.618554 0.785743i \(-0.287719\pi\)
−0.903684 + 0.428201i \(0.859148\pi\)
\(128\) −1585.38 −1.09476
\(129\) 1283.45 + 68.2113i 0.875979 + 0.0465556i
\(130\) 2984.33 2.01341
\(131\) 1632.78 + 2047.44i 1.08898 + 1.36554i 0.925392 + 0.379011i \(0.123736\pi\)
0.163590 + 0.986528i \(0.447693\pi\)
\(132\) −528.538 + 662.765i −0.348510 + 0.437017i
\(133\) 85.4272 374.281i 0.0556953 0.244017i
\(134\) −1126.91 + 542.693i −0.726496 + 0.349862i
\(135\) −1395.40 −0.889606
\(136\) 9.50562 0.00599339
\(137\) −374.805 + 180.496i −0.233735 + 0.112561i −0.547086 0.837077i \(-0.684263\pi\)
0.313350 + 0.949638i \(0.398549\pi\)
\(138\) 371.359 + 1627.03i 0.229074 + 1.00364i
\(139\) 1862.66 + 897.010i 1.13661 + 0.547363i 0.904985 0.425442i \(-0.139882\pi\)
0.231625 + 0.972805i \(0.425596\pi\)
\(140\) −278.251 1219.10i −0.167975 0.735947i
\(141\) −997.462 1250.78i −0.595755 0.747053i
\(142\) 517.223 249.082i 0.305665 0.147200i
\(143\) −777.678 975.177i −0.454774 0.570269i
\(144\) −41.7413 + 182.880i −0.0241558 + 0.105834i
\(145\) −1898.65 914.340i −1.08741 0.523667i
\(146\) −2867.46 1380.90i −1.62543 0.782767i
\(147\) 547.007 685.925i 0.306914 0.384858i
\(148\) −202.896 + 888.947i −0.112689 + 0.493723i
\(149\) 218.150 + 955.778i 0.119943 + 0.525506i 0.998825 + 0.0484659i \(0.0154332\pi\)
−0.878882 + 0.477040i \(0.841710\pi\)
\(150\) 497.482 623.823i 0.270795 0.339566i
\(151\) 6.78596 8.50933i 0.00365718 0.00458596i −0.780000 0.625780i \(-0.784781\pi\)
0.783657 + 0.621194i \(0.213352\pi\)
\(152\) −93.0533 407.693i −0.0496554 0.217555i
\(153\) 0.984997 4.31556i 0.000520473 0.00228034i
\(154\) −561.526 + 704.131i −0.293825 + 0.368445i
\(155\) −2023.09 974.269i −1.04838 0.504872i
\(156\) −3369.77 1622.79i −1.72947 0.832869i
\(157\) 229.073 1003.63i 0.116446 0.510182i −0.882741 0.469860i \(-0.844304\pi\)
0.999187 0.0403224i \(-0.0128385\pi\)
\(158\) 2227.89 + 2793.68i 1.12178 + 1.40667i
\(159\) 435.809 209.874i 0.217370 0.104680i
\(160\) 1370.26 + 1718.25i 0.677052 + 0.848997i
\(161\) 228.948 + 1003.09i 0.112072 + 0.491020i
\(162\) 2054.25 + 989.274i 0.996278 + 0.479782i
\(163\) −208.966 915.539i −0.100414 0.439942i −0.999995 0.00318810i \(-0.998985\pi\)
0.899581 0.436754i \(-0.143872\pi\)
\(164\) −4028.22 + 1939.89i −1.91799 + 0.923657i
\(165\) 706.185 0.333191
\(166\) −3782.21 −1.76841
\(167\) 1566.03 754.162i 0.725649 0.349454i −0.0343224 0.999411i \(-0.510927\pi\)
0.759971 + 0.649957i \(0.225213\pi\)
\(168\) −166.304 + 728.624i −0.0763726 + 0.334610i
\(169\) 2061.37 2584.88i 0.938266 1.17655i
\(170\) −17.8407 22.3715i −0.00804892 0.0100930i
\(171\) −194.735 −0.0870864
\(172\) 2877.87 1202.19i 1.27579 0.532942i
\(173\) −108.791 −0.0478107 −0.0239053 0.999714i \(-0.507610\pi\)
−0.0239053 + 0.999714i \(0.507610\pi\)
\(174\) 2837.64 + 3558.29i 1.23633 + 1.55031i
\(175\) 306.705 384.596i 0.132484 0.166130i
\(176\) 112.773 494.092i 0.0482989 0.211611i
\(177\) −2810.62 + 1353.52i −1.19355 + 0.574785i
\(178\) 3821.84 1.60932
\(179\) −1852.75 −0.773637 −0.386819 0.922156i \(-0.626426\pi\)
−0.386819 + 0.922156i \(0.626426\pi\)
\(180\) −571.472 + 275.206i −0.236639 + 0.113959i
\(181\) 275.636 + 1207.64i 0.113193 + 0.495930i 0.999463 + 0.0327617i \(0.0104303\pi\)
−0.886270 + 0.463168i \(0.846713\pi\)
\(182\) −3580.09 1724.08i −1.45810 0.702183i
\(183\) 513.148 + 2248.25i 0.207284 + 0.908172i
\(184\) 698.764 + 876.223i 0.279965 + 0.351065i
\(185\) 684.361 329.571i 0.271974 0.130976i
\(186\) 3023.63 + 3791.51i 1.19195 + 1.49466i
\(187\) −2.66119 + 11.6594i −0.00104067 + 0.00455948i
\(188\) −3497.71 1684.41i −1.35690 0.653447i
\(189\) 1673.96 + 806.136i 0.644246 + 0.310253i
\(190\) −784.859 + 984.182i −0.299682 + 0.375790i
\(191\) 649.569 2845.95i 0.246079 1.07814i −0.689294 0.724482i \(-0.742079\pi\)
0.935373 0.353662i \(-0.115064\pi\)
\(192\) −811.599 3555.85i −0.305063 1.33657i
\(193\) 1949.53 2444.63i 0.727100 0.911755i −0.271616 0.962406i \(-0.587558\pi\)
0.998716 + 0.0506510i \(0.0161296\pi\)
\(194\) −2536.04 + 3180.10i −0.938542 + 1.17689i
\(195\) 693.319 + 3037.63i 0.254613 + 1.11553i
\(196\) 473.741 2075.60i 0.172646 0.756413i
\(197\) −360.369 + 451.888i −0.130331 + 0.163430i −0.842715 0.538360i \(-0.819044\pi\)
0.712384 + 0.701790i \(0.247616\pi\)
\(198\) 411.594 + 198.213i 0.147731 + 0.0711434i
\(199\) −2813.46 1354.89i −1.00221 0.482641i −0.140525 0.990077i \(-0.544879\pi\)
−0.861689 + 0.507436i \(0.830593\pi\)
\(200\) 119.233 522.395i 0.0421553 0.184695i
\(201\) −814.188 1020.96i −0.285713 0.358273i
\(202\) −2693.10 + 1296.93i −0.938048 + 0.451740i
\(203\) 1749.44 + 2193.73i 0.604861 + 0.758472i
\(204\) 7.97986 + 34.9621i 0.00273874 + 0.0119992i
\(205\) 3355.72 + 1616.03i 1.14328 + 0.550577i
\(206\) −925.067 4052.98i −0.312876 1.37080i
\(207\) 470.213 226.443i 0.157884 0.0760331i
\(208\) 2236.04 0.745391
\(209\) 526.120 0.174127
\(210\) 2026.94 976.125i 0.666059 0.320757i
\(211\) 4.05107 17.7489i 0.00132174 0.00579092i −0.974263 0.225415i \(-0.927626\pi\)
0.975584 + 0.219624i \(0.0704832\pi\)
\(212\) 731.851 917.712i 0.237093 0.297305i
\(213\) 373.691 + 468.593i 0.120211 + 0.150739i
\(214\) −7284.04 −2.32676
\(215\) −2277.76 1249.96i −0.722519 0.396495i
\(216\) 2023.81 0.637514
\(217\) 1864.11 + 2337.52i 0.583152 + 0.731249i
\(218\) 5910.24 7411.20i 1.83620 2.30252i
\(219\) 739.391 3239.48i 0.228143 0.999561i
\(220\) 1543.96 743.531i 0.473153 0.227859i
\(221\) −52.7653 −0.0160605
\(222\) −1640.47 −0.495952
\(223\) 1731.66 833.924i 0.520002 0.250420i −0.155423 0.987848i \(-0.549674\pi\)
0.675426 + 0.737428i \(0.263960\pi\)
\(224\) −651.149 2852.87i −0.194226 0.850961i
\(225\) −224.812 108.264i −0.0666110 0.0320782i
\(226\) −1613.98 7071.30i −0.475045 2.08131i
\(227\) −434.006 544.226i −0.126899 0.159126i 0.714323 0.699816i \(-0.246735\pi\)
−0.841222 + 0.540690i \(0.818163\pi\)
\(228\) 1421.39 684.508i 0.412869 0.198827i
\(229\) 1188.11 + 1489.84i 0.342850 + 0.429920i 0.923125 0.384501i \(-0.125626\pi\)
−0.580275 + 0.814421i \(0.697055\pi\)
\(230\) 750.712 3289.08i 0.215220 0.942938i
\(231\) −847.159 407.970i −0.241294 0.116201i
\(232\) 2753.69 + 1326.11i 0.779263 + 0.375273i
\(233\) −2115.56 + 2652.83i −0.594829 + 0.745892i −0.984562 0.175036i \(-0.943996\pi\)
0.389733 + 0.920928i \(0.372567\pi\)
\(234\) −448.512 + 1965.06i −0.125300 + 0.548974i
\(235\) 719.643 + 3152.96i 0.199763 + 0.875219i
\(236\) −4719.86 + 5918.51i −1.30185 + 1.63247i
\(237\) −2325.99 + 2916.70i −0.637508 + 0.799410i
\(238\) 8.47791 + 37.1442i 0.00230900 + 0.0101164i
\(239\) −946.024 + 4144.80i −0.256039 + 1.12178i 0.669406 + 0.742896i \(0.266549\pi\)
−0.925445 + 0.378882i \(0.876309\pi\)
\(240\) −789.327 + 989.784i −0.212295 + 0.266210i
\(241\) −6322.84 3044.92i −1.69000 0.813860i −0.995541 0.0943265i \(-0.969930\pi\)
−0.694457 0.719534i \(-0.744355\pi\)
\(242\) 4123.52 + 1985.78i 1.09533 + 0.527483i
\(243\) 380.142 1665.51i 0.100355 0.439682i
\(244\) 3489.06 + 4375.14i 0.915427 + 1.14791i
\(245\) −1597.91 + 769.513i −0.416681 + 0.200663i
\(246\) −5015.32 6289.01i −1.29986 1.62997i
\(247\) 516.535 + 2263.09i 0.133062 + 0.582983i
\(248\) 2934.18 + 1413.03i 0.751294 + 0.361804i
\(249\) −878.681 3849.75i −0.223631 0.979791i
\(250\) −5983.89 + 2881.69i −1.51382 + 0.729016i
\(251\) 2690.62 0.676616 0.338308 0.941035i \(-0.390145\pi\)
0.338308 + 0.941035i \(0.390145\pi\)
\(252\) 844.543 0.211116
\(253\) −1270.39 + 611.785i −0.315685 + 0.152026i
\(254\) 635.862 2785.89i 0.157077 0.688199i
\(255\) 18.6263 23.3566i 0.00457421 0.00573587i
\(256\) −324.370 406.748i −0.0791920 0.0993036i
\(257\) 652.543 0.158383 0.0791917 0.996859i \(-0.474766\pi\)
0.0791917 + 0.996859i \(0.474766\pi\)
\(258\) 3260.83 + 4566.59i 0.786861 + 1.10195i
\(259\) −1011.37 −0.242640
\(260\) 4714.10 + 5911.29i 1.12445 + 1.41001i
\(261\) 887.399 1112.76i 0.210455 0.263902i
\(262\) −2544.15 + 11146.6i −0.599916 + 2.62840i
\(263\) 4463.63 2149.57i 1.04654 0.503986i 0.170063 0.985433i \(-0.445603\pi\)
0.876475 + 0.481447i \(0.159889\pi\)
\(264\) −1024.21 −0.238773
\(265\) −977.834 −0.226671
\(266\) 1510.11 727.230i 0.348085 0.167629i
\(267\) 887.888 + 3890.09i 0.203512 + 0.891646i
\(268\) −2855.04 1374.92i −0.650744 0.313382i
\(269\) 1566.00 + 6861.10i 0.354947 + 1.55513i 0.765590 + 0.643329i \(0.222447\pi\)
−0.410642 + 0.911797i \(0.634695\pi\)
\(270\) −3798.40 4763.04i −0.856161 1.07359i
\(271\) 77.0982 37.1285i 0.0172819 0.00832250i −0.425223 0.905089i \(-0.639804\pi\)
0.442505 + 0.896766i \(0.354090\pi\)
\(272\) −13.3673 16.7620i −0.00297982 0.00373657i
\(273\) 923.144 4044.56i 0.204657 0.896659i
\(274\) −1636.36 788.028i −0.360788 0.173746i
\(275\) 607.380 + 292.499i 0.133187 + 0.0641394i
\(276\) −2636.18 + 3305.66i −0.574925 + 0.720933i
\(277\) −1665.04 + 7295.02i −0.361165 + 1.58237i 0.389079 + 0.921204i \(0.372793\pi\)
−0.750244 + 0.661161i \(0.770064\pi\)
\(278\) 2008.48 + 8799.74i 0.433312 + 1.89846i
\(279\) 945.563 1185.70i 0.202901 0.254430i
\(280\) 941.975 1181.20i 0.201049 0.252108i
\(281\) 609.148 + 2668.85i 0.129319 + 0.566585i 0.997521 + 0.0703730i \(0.0224190\pi\)
−0.868201 + 0.496212i \(0.834724\pi\)
\(282\) 1554.21 6809.46i 0.328199 1.43793i
\(283\) 4625.89 5800.68i 0.971663 1.21843i −0.00418792 0.999991i \(-0.501333\pi\)
0.975851 0.218436i \(-0.0700955\pi\)
\(284\) 1310.39 + 631.050i 0.273793 + 0.131852i
\(285\) −1184.10 570.230i −0.246104 0.118518i
\(286\) 1211.75 5309.04i 0.250533 1.09766i
\(287\) −3092.01 3877.26i −0.635943 0.797448i
\(288\) −1337.33 + 644.023i −0.273621 + 0.131769i
\(289\) −3062.89 3840.74i −0.623426 0.781751i
\(290\) −2047.28 8969.74i −0.414554 1.81628i
\(291\) −3826.06 1842.53i −0.770748 0.371173i
\(292\) −1794.24 7861.09i −0.359589 1.57546i
\(293\) −1617.83 + 779.105i −0.322575 + 0.155344i −0.588162 0.808743i \(-0.700148\pi\)
0.265587 + 0.964087i \(0.414434\pi\)
\(294\) 3830.33 0.759828
\(295\) 6306.26 1.24463
\(296\) −992.561 + 477.992i −0.194904 + 0.0938606i
\(297\) −566.585 + 2482.37i −0.110696 + 0.484990i
\(298\) −2668.62 + 3346.35i −0.518755 + 0.650499i
\(299\) −3878.81 4863.87i −0.750225 0.940753i
\(300\) 2021.49 0.389035
\(301\) 2010.34 + 2815.36i 0.384965 + 0.539119i
\(302\) 47.5177 0.00905409
\(303\) −1945.75 2439.89i −0.368912 0.462601i
\(304\) −588.062 + 737.407i −0.110946 + 0.139122i
\(305\) 1037.34 4544.89i 0.194748 0.853246i
\(306\) 17.4119 8.38515i 0.00325286 0.00156649i
\(307\) −1176.57 −0.218731 −0.109365 0.994002i \(-0.534882\pi\)
−0.109365 + 0.994002i \(0.534882\pi\)
\(308\) −2281.72 −0.422120
\(309\) 3910.45 1883.17i 0.719928 0.346699i
\(310\) −2181.47 9557.65i −0.399675 1.75109i
\(311\) 5673.77 + 2732.34i 1.03450 + 0.498190i 0.872507 0.488602i \(-0.162493\pi\)
0.161995 + 0.986792i \(0.448207\pi\)
\(312\) −1005.55 4405.62i −0.182462 0.799420i
\(313\) 731.410 + 917.159i 0.132082 + 0.165626i 0.843474 0.537169i \(-0.180506\pi\)
−0.711392 + 0.702795i \(0.751935\pi\)
\(314\) 4049.35 1950.06i 0.727765 0.350473i
\(315\) −438.655 550.056i −0.0784616 0.0983878i
\(316\) −2014.45 + 8825.90i −0.358613 + 1.57119i
\(317\) 1122.29 + 540.467i 0.198846 + 0.0957591i 0.530657 0.847587i \(-0.321945\pi\)
−0.331811 + 0.943346i \(0.607660\pi\)
\(318\) 1902.69 + 916.289i 0.335528 + 0.161582i
\(319\) −2397.51 + 3006.38i −0.420798 + 0.527664i
\(320\) −1640.67 + 7188.24i −0.286613 + 1.25573i
\(321\) −1692.23 7414.13i −0.294239 1.28915i
\(322\) −2800.71 + 3511.98i −0.484713 + 0.607811i
\(323\) 13.8769 17.4011i 0.00239050 0.00299759i
\(324\) 1285.39 + 5631.68i 0.220404 + 0.965652i
\(325\) −661.859 + 2899.79i −0.112964 + 0.494928i
\(326\) 2556.27 3205.46i 0.434291 0.544583i
\(327\) 8916.62 + 4294.02i 1.50792 + 0.726177i
\(328\) −4866.95 2343.80i −0.819306 0.394557i
\(329\) 958.194 4198.12i 0.160568 0.703495i
\(330\) 1922.30 + 2410.49i 0.320664 + 0.402100i
\(331\) −888.205 + 427.737i −0.147493 + 0.0710288i −0.506174 0.862431i \(-0.668941\pi\)
0.358681 + 0.933460i \(0.383226\pi\)
\(332\) −5974.43 7491.70i −0.987619 1.23844i
\(333\) 114.157 + 500.154i 0.0187861 + 0.0823071i
\(334\) 6837.14 + 3292.59i 1.12009 + 0.539409i
\(335\) 587.416 + 2573.64i 0.0958029 + 0.419740i
\(336\) 1518.71 731.370i 0.246584 0.118749i
\(337\) −11334.6 −1.83214 −0.916072 0.401014i \(-0.868658\pi\)
−0.916072 + 0.401014i \(0.868658\pi\)
\(338\) 14434.4 2.32287
\(339\) 6822.62 3285.60i 1.09308 0.526399i
\(340\) 16.1315 70.6767i 0.00257310 0.0112735i
\(341\) −2554.65 + 3203.43i −0.405695 + 0.508725i
\(342\) −530.087 664.708i −0.0838123 0.105097i
\(343\) 6569.67 1.03419
\(344\) 3303.54 + 1812.87i 0.517775 + 0.284138i
\(345\) 3522.23 0.549653
\(346\) −296.140 371.347i −0.0460132 0.0576987i
\(347\) 3244.83 4068.89i 0.501994 0.629480i −0.464684 0.885476i \(-0.653832\pi\)
0.966678 + 0.255997i \(0.0824036\pi\)
\(348\) −2565.79 + 11241.5i −0.395232 + 1.73162i
\(349\) −4995.61 + 2405.76i −0.766214 + 0.368989i −0.775812 0.630965i \(-0.782659\pi\)
0.00959725 + 0.999954i \(0.496945\pi\)
\(350\) 2147.65 0.327991
\(351\) −11234.1 −1.70835
\(352\) 3613.09 1739.97i 0.547098 0.263468i
\(353\) −613.931 2689.81i −0.0925672 0.405563i 0.907322 0.420436i \(-0.138123\pi\)
−0.999889 + 0.0148726i \(0.995266\pi\)
\(354\) −12270.9 5909.34i −1.84234 0.887225i
\(355\) −269.608 1181.23i −0.0403080 0.176601i
\(356\) 6037.03 + 7570.20i 0.898770 + 1.12702i
\(357\) −35.8379 + 17.2586i −0.00531301 + 0.00255861i
\(358\) −5043.35 6324.16i −0.744552 0.933638i
\(359\) 92.3117 404.444i 0.0135711 0.0594588i −0.967689 0.252147i \(-0.918863\pi\)
0.981260 + 0.192688i \(0.0617205\pi\)
\(360\) −690.461 332.508i −0.101085 0.0486798i
\(361\) 5297.57 + 2551.18i 0.772354 + 0.371946i
\(362\) −3371.85 + 4228.16i −0.489559 + 0.613888i
\(363\) −1063.27 + 4658.50i −0.153739 + 0.673575i
\(364\) −2240.15 9814.73i −0.322571 1.41327i
\(365\) −4188.05 + 5251.65i −0.600582 + 0.753106i
\(366\) −6277.32 + 7871.51i −0.896505 + 1.12418i
\(367\) −475.812 2084.67i −0.0676762 0.296509i 0.929752 0.368187i \(-0.120022\pi\)
−0.997428 + 0.0716787i \(0.977164\pi\)
\(368\) 562.477 2464.37i 0.0796771 0.349088i
\(369\) −1568.41 + 1966.73i −0.221269 + 0.277463i
\(370\) 2987.85 + 1438.87i 0.419813 + 0.202171i
\(371\) 1173.04 + 564.905i 0.164154 + 0.0790523i
\(372\) −2733.96 + 11978.3i −0.381046 + 1.66947i
\(373\) 3295.55 + 4132.49i 0.457472 + 0.573651i 0.956054 0.293191i \(-0.0947172\pi\)
−0.498582 + 0.866842i \(0.666146\pi\)
\(374\) −47.0422 + 22.6543i −0.00650400 + 0.00313216i
\(375\) −4323.32 5421.28i −0.595348 0.746543i
\(376\) −1043.73 4572.89i −0.143155 0.627204i
\(377\) −15285.6 7361.18i −2.08820 1.00562i
\(378\) 1805.01 + 7908.25i 0.245607 + 1.07608i
\(379\) 11184.1 5385.99i 1.51581 0.729973i 0.523297 0.852150i \(-0.324702\pi\)
0.992508 + 0.122177i \(0.0389875\pi\)
\(380\) −3189.22 −0.430535
\(381\) 2983.37 0.401162
\(382\) 11482.5 5529.69i 1.53795 0.740637i
\(383\) −1854.07 + 8123.21i −0.247359 + 1.08375i 0.686786 + 0.726859i \(0.259021\pi\)
−0.934146 + 0.356892i \(0.883836\pi\)
\(384\) 4505.59 5649.83i 0.598763 0.750825i
\(385\) 1185.12 + 1486.10i 0.156882 + 0.196724i
\(386\) 13651.3 1.80008
\(387\) 1165.36 1311.95i 0.153072 0.172326i
\(388\) −10305.0 −1.34835
\(389\) −4564.21 5723.34i −0.594896 0.745976i 0.389677 0.920952i \(-0.372587\pi\)
−0.984573 + 0.174976i \(0.944015\pi\)
\(390\) −8481.34 + 10635.3i −1.10120 + 1.38087i
\(391\) −13.2732 + 58.1535i −0.00171676 + 0.00752161i
\(392\) 2317.52 1116.06i 0.298604 0.143800i
\(393\) −11936.8 −1.53214
\(394\) −2523.43 −0.322661
\(395\) 6794.67 3272.14i 0.865511 0.416808i
\(396\) 257.544 + 1128.38i 0.0326821 + 0.143189i
\(397\) 3464.66 + 1668.49i 0.438001 + 0.210930i 0.639871 0.768482i \(-0.278988\pi\)
−0.201870 + 0.979412i \(0.564702\pi\)
\(398\) −3033.71 13291.6i −0.382076 1.67398i
\(399\) 1091.05 + 1368.13i 0.136894 + 0.171659i
\(400\) −1088.85 + 524.364i −0.136107 + 0.0655455i
\(401\) 3121.68 + 3914.46i 0.388751 + 0.487478i 0.937243 0.348678i \(-0.113369\pi\)
−0.548492 + 0.836156i \(0.684798\pi\)
\(402\) 1268.64 5558.29i 0.157398 0.689607i
\(403\) −16287.5 7843.66i −2.01325 0.969530i
\(404\) −6822.98 3285.77i −0.840238 0.404637i
\(405\) 3000.32 3762.28i 0.368116 0.461603i
\(406\) −2725.93 + 11943.1i −0.333216 + 1.45991i
\(407\) −308.420 1351.28i −0.0375622 0.164571i
\(408\) −27.0146 + 33.8752i −0.00327799 + 0.00411047i
\(409\) 8370.93 10496.8i 1.01202 1.26903i 0.0492267 0.998788i \(-0.484324\pi\)
0.962792 0.270244i \(-0.0871043\pi\)
\(410\) 3618.42 + 15853.3i 0.435856 + 1.90961i
\(411\) 421.943 1848.65i 0.0506397 0.221867i
\(412\) 6566.80 8234.50i 0.785250 0.984672i
\(413\) −7565.15 3643.19i −0.901348 0.434067i
\(414\) 2052.90 + 988.625i 0.243707 + 0.117363i
\(415\) −1776.28 + 7782.37i −0.210106 + 0.920534i
\(416\) 11031.7 + 13833.3i 1.30018 + 1.63037i
\(417\) −8490.28 + 4088.70i −0.997052 + 0.480155i
\(418\) 1432.15 + 1795.86i 0.167580 + 0.210139i
\(419\) 431.243 + 1889.40i 0.0502807 + 0.220294i 0.993826 0.110949i \(-0.0353891\pi\)
−0.943545 + 0.331243i \(0.892532\pi\)
\(420\) 5135.28 + 2473.02i 0.596609 + 0.287312i
\(421\) 2894.60 + 12682.1i 0.335093 + 1.46814i 0.809129 + 0.587632i \(0.199940\pi\)
−0.474036 + 0.880505i \(0.657203\pi\)
\(422\) 71.6113 34.4862i 0.00826063 0.00397811i
\(423\) −2184.25 −0.251068
\(424\) 1418.20 0.162438
\(425\) 25.6944 12.3738i 0.00293262 0.00141227i
\(426\) −582.273 + 2551.11i −0.0662236 + 0.290144i
\(427\) −3870.05 + 4852.90i −0.438607 + 0.549995i
\(428\) −11506.0 14428.1i −1.29945 1.62945i
\(429\) 5685.37 0.639842
\(430\) −1933.66 11177.4i −0.216859 1.25354i
\(431\) 445.930 0.0498368 0.0249184 0.999689i \(-0.492067\pi\)
0.0249184 + 0.999689i \(0.492067\pi\)
\(432\) −2845.98 3568.75i −0.316962 0.397458i
\(433\) −3091.47 + 3876.58i −0.343110 + 0.430246i −0.923208 0.384300i \(-0.874443\pi\)
0.580098 + 0.814547i \(0.303014\pi\)
\(434\) −2904.60 + 12725.9i −0.321256 + 1.40751i
\(435\) 8654.30 4167.69i 0.953889 0.459369i
\(436\) 24015.8 2.63796
\(437\) 2624.12 0.287251
\(438\) 13070.3 6294.33i 1.42585 0.686655i
\(439\) −499.408 2188.05i −0.0542949 0.237881i 0.940498 0.339799i \(-0.110359\pi\)
−0.994793 + 0.101918i \(0.967502\pi\)
\(440\) 1865.43 + 898.345i 0.202116 + 0.0973339i
\(441\) −266.544 1167.81i −0.0287813 0.126099i
\(442\) −143.632 180.109i −0.0154567 0.0193821i
\(443\) −1375.31 + 662.315i −0.147501 + 0.0710328i −0.506178 0.862429i \(-0.668942\pi\)
0.358677 + 0.933462i \(0.383228\pi\)
\(444\) −2591.32 3249.41i −0.276979 0.347320i
\(445\) 1794.89 7863.92i 0.191204 0.837720i
\(446\) 7560.24 + 3640.82i 0.802663 + 0.386542i
\(447\) −4026.08 1938.86i −0.426011 0.205156i
\(448\) 6120.90 7675.37i 0.645504 0.809436i
\(449\) −1871.60 + 8200.00i −0.196717 + 0.861875i 0.776157 + 0.630540i \(0.217167\pi\)
−0.972874 + 0.231335i \(0.925691\pi\)
\(450\) −242.412 1062.08i −0.0253942 0.111259i
\(451\) 4237.41 5313.55i 0.442421 0.554779i
\(452\) 11457.2 14366.9i 1.19226 1.49504i
\(453\) 11.0393 + 48.3663i 0.00114497 + 0.00501644i
\(454\) 676.255 2962.87i 0.0699080 0.306287i
\(455\) −5228.86 + 6556.79i −0.538754 + 0.675576i
\(456\) 1717.35 + 827.032i 0.176365 + 0.0849327i
\(457\) 13711.3 + 6603.03i 1.40348 + 0.675879i 0.973864 0.227134i \(-0.0729354\pi\)
0.429614 + 0.903013i \(0.358650\pi\)
\(458\) −1851.28 + 8110.98i −0.188875 + 0.827514i
\(459\) 67.1586 + 84.2143i 0.00682940 + 0.00856380i
\(460\) 7700.77 3708.50i 0.780544 0.375890i
\(461\) −9474.08 11880.1i −0.957162 1.20024i −0.979694 0.200497i \(-0.935744\pi\)
0.0225322 0.999746i \(-0.492827\pi\)
\(462\) −913.480 4002.22i −0.0919890 0.403030i
\(463\) −16427.2 7910.91i −1.64889 0.794063i −0.999433 0.0336624i \(-0.989283\pi\)
−0.649455 0.760400i \(-0.725003\pi\)
\(464\) −1533.94 6720.65i −0.153473 0.672410i
\(465\) 9221.54 4440.86i 0.919653 0.442881i
\(466\) −14813.9 −1.47262
\(467\) 358.288 0.0355024 0.0177512 0.999842i \(-0.494349\pi\)
0.0177512 + 0.999842i \(0.494349\pi\)
\(468\) −4600.81 + 2215.64i −0.454429 + 0.218841i
\(469\) 782.136 3426.76i 0.0770057 0.337384i
\(470\) −8803.36 + 11039.1i −0.863976 + 1.08339i
\(471\) 2925.63 + 3668.63i 0.286212 + 0.358899i
\(472\) −9146.26 −0.891929
\(473\) −3148.49 + 3544.53i −0.306063 + 0.344562i
\(474\) −16287.4 −1.57828
\(475\) −782.237 980.895i −0.0755611 0.0947506i
\(476\) −60.1824 + 75.4664i −0.00579508 + 0.00726680i
\(477\) 146.957 643.863i 0.0141063 0.0618039i
\(478\) −16723.0 + 8053.37i −1.60019 + 0.770613i
\(479\) 9899.32 0.944283 0.472141 0.881523i \(-0.343481\pi\)
0.472141 + 0.881523i \(0.343481\pi\)
\(480\) −10017.5 −0.952574
\(481\) 5509.66 2653.31i 0.522285 0.251519i
\(482\) −6817.83 29870.9i −0.644281 2.82278i
\(483\) −4225.36 2034.83i −0.398055 0.191693i
\(484\) 2580.19 + 11304.5i 0.242317 + 1.06166i
\(485\) 5352.43 + 6711.73i 0.501116 + 0.628379i
\(486\) 6719.83 3236.10i 0.627197 0.302042i
\(487\) 7565.88 + 9487.31i 0.703989 + 0.882775i 0.997314 0.0732381i \(-0.0233333\pi\)
−0.293325 + 0.956013i \(0.594762\pi\)
\(488\) −1504.51 + 6591.67i −0.139561 + 0.611457i
\(489\) 3856.58 + 1857.23i 0.356647 + 0.171752i
\(490\) −6976.30 3359.61i −0.643178 0.309738i
\(491\) −9408.62 + 11798.0i −0.864776 + 1.08440i 0.130890 + 0.991397i \(0.458217\pi\)
−0.995666 + 0.0929984i \(0.970355\pi\)
\(492\) 4534.84 19868.4i 0.415542 1.82061i
\(493\) 36.1975 + 158.592i 0.00330681 + 0.0144881i
\(494\) −6318.75 + 7923.46i −0.575494 + 0.721647i
\(495\) 601.150 753.818i 0.0545852 0.0684477i
\(496\) −1634.49 7161.15i −0.147965 0.648277i
\(497\) −358.980 + 1572.79i −0.0323993 + 0.141950i
\(498\) 10748.9 13478.6i 0.967205 1.21284i
\(499\) −2430.19 1170.32i −0.218017 0.104991i 0.321688 0.946846i \(-0.395750\pi\)
−0.539705 + 0.841854i \(0.681464\pi\)
\(500\) −15160.2 7300.78i −1.35597 0.653001i
\(501\) −1762.99 + 7724.17i −0.157215 + 0.688803i
\(502\) 7324.12 + 9184.15i 0.651178 + 0.816551i
\(503\) 1243.30 598.744i 0.110211 0.0530749i −0.377966 0.925820i \(-0.623376\pi\)
0.488177 + 0.872745i \(0.337662\pi\)
\(504\) 636.202 + 797.772i 0.0562276 + 0.0705071i
\(505\) 1403.81 + 6150.48i 0.123700 + 0.541966i
\(506\) −5546.36 2670.99i −0.487285 0.234664i
\(507\) 3353.40 + 14692.2i 0.293747 + 1.28699i
\(508\) 6522.65 3141.14i 0.569677 0.274342i
\(509\) 21509.0 1.87302 0.936512 0.350636i \(-0.114035\pi\)
0.936512 + 0.350636i \(0.114035\pi\)
\(510\) 130.428 0.0113244
\(511\) 8058.03 3880.54i 0.697585 0.335939i
\(512\) −2316.82 + 10150.7i −0.199981 + 0.876173i
\(513\) 2954.49 3704.81i 0.254276 0.318853i
\(514\) 1776.28 + 2227.39i 0.152429 + 0.191140i
\(515\) −8773.97 −0.750733
\(516\) −3894.53 + 13672.4i −0.332262 + 1.16646i
\(517\) 5901.23 0.502003
\(518\) −2753.05 3452.22i −0.233518 0.292822i
\(519\) 309.180 387.699i 0.0261493 0.0327902i
\(520\) −2032.75 + 8906.07i −0.171427 + 0.751071i
\(521\) 10369.4 4993.63i 0.871959 0.419913i 0.0562779 0.998415i \(-0.482077\pi\)
0.815681 + 0.578502i \(0.196362\pi\)
\(522\) 6213.88 0.521023
\(523\) 7328.63 0.612732 0.306366 0.951914i \(-0.400887\pi\)
0.306366 + 0.951914i \(0.400887\pi\)
\(524\) −26097.8 + 12568.0i −2.17574 + 1.04778i
\(525\) 498.942 + 2186.01i 0.0414774 + 0.181724i
\(526\) 19487.7 + 9384.80i 1.61541 + 0.777941i
\(527\) 38.5701 + 168.987i 0.00318812 + 0.0139681i
\(528\) 1440.30 + 1806.08i 0.118714 + 0.148863i
\(529\) 4625.81 2227.67i 0.380193 0.183091i
\(530\) −2661.75 3337.73i −0.218149 0.273551i
\(531\) −947.759 + 4152.40i −0.0774562 + 0.339358i
\(532\) 3825.87 + 1842.44i 0.311791 + 0.150150i
\(533\) 27016.2 + 13010.3i 2.19550 + 1.05730i
\(534\) −10861.5 + 13619.9i −0.880192 + 1.10373i
\(535\) −3420.88 + 14987.9i −0.276444 + 1.21118i
\(536\) −851.957 3732.67i −0.0686547 0.300796i
\(537\) 5265.43 6602.65i 0.423129 0.530587i
\(538\) −19156.8 + 24021.9i −1.53515 + 1.92502i
\(539\) 720.128 + 3155.09i 0.0575475 + 0.252132i
\(540\) 3434.51 15047.6i 0.273699 1.19916i
\(541\) −4490.93 + 5631.45i −0.356895 + 0.447532i −0.927573 0.373642i \(-0.878109\pi\)
0.570678 + 0.821174i \(0.306680\pi\)
\(542\) 336.603 + 162.099i 0.0266759 + 0.0128464i
\(543\) −5087.02 2449.78i −0.402035 0.193610i
\(544\) 37.7501 165.394i 0.00297522 0.0130353i
\(545\) −12473.8 15641.7i −0.980403 1.22939i
\(546\) 16318.5 7858.60i 1.27906 0.615965i
\(547\) −2592.19 3250.51i −0.202622 0.254080i 0.670130 0.742244i \(-0.266238\pi\)
−0.872752 + 0.488164i \(0.837667\pi\)
\(548\) −1023.91 4486.04i −0.0798161 0.349697i
\(549\) 2836.72 + 1366.09i 0.220525 + 0.106199i
\(550\) 654.930 + 2869.43i 0.0507751 + 0.222460i
\(551\) 6447.60 3105.00i 0.498507 0.240068i
\(552\) −5108.45 −0.393895
\(553\) −10041.4 −0.772160
\(554\) −29433.2 + 14174.3i −2.25721 + 1.08702i
\(555\) −770.432 + 3375.48i −0.0589244 + 0.258165i
\(556\) −14257.7 + 17878.6i −1.08752 + 1.36370i
\(557\) −13921.1 17456.6i −1.05899 1.32793i −0.942302 0.334763i \(-0.891344\pi\)
−0.116688 0.993169i \(-0.537228\pi\)
\(558\) 6621.16 0.502323
\(559\) −18337.8 10063.2i −1.38749 0.761407i
\(560\) −3407.56 −0.257135
\(561\) −33.9877 42.6193i −0.00255787 0.00320746i
\(562\) −7451.68 + 9344.12i −0.559307 + 0.701348i
\(563\) 3020.32 13232.9i 0.226095 0.990586i −0.726696 0.686959i \(-0.758945\pi\)
0.952791 0.303627i \(-0.0981976\pi\)
\(564\) 15943.1 7677.78i 1.19029 0.573214i
\(565\) −15308.1 −1.13985
\(566\) 32392.1 2.40555
\(567\) −5772.76 + 2780.02i −0.427572 + 0.205908i
\(568\) 391.026 + 1713.19i 0.0288857 + 0.126556i
\(569\) −5067.93 2440.59i −0.373390 0.179815i 0.237771 0.971321i \(-0.423583\pi\)
−0.611161 + 0.791506i \(0.709297\pi\)
\(570\) −1276.79 5594.00i −0.0938229 0.411065i
\(571\) −9489.95 11900.0i −0.695520 0.872155i 0.301160 0.953574i \(-0.402626\pi\)
−0.996680 + 0.0814190i \(0.974055\pi\)
\(572\) 12430.1 5986.03i 0.908618 0.437567i
\(573\) 8296.05 + 10402.9i 0.604839 + 0.758444i
\(574\) 4817.88 21108.5i 0.350339 1.53493i
\(575\) 3029.42 + 1458.89i 0.219714 + 0.105809i
\(576\) −4486.58 2160.62i −0.324550 0.156295i
\(577\) 425.039 532.982i 0.0306666 0.0384547i −0.766262 0.642529i \(-0.777885\pi\)
0.796928 + 0.604074i \(0.206457\pi\)
\(578\) 4772.50 20909.7i 0.343443 1.50472i
\(579\) 3171.46 + 13895.1i 0.227636 + 0.997340i
\(580\) 14533.1 18223.9i 1.04044 1.30467i
\(581\) 6626.82 8309.77i 0.473196 0.593369i
\(582\) −4125.59 18075.4i −0.293834 1.28737i
\(583\) −397.038 + 1739.54i −0.0282052 + 0.123575i
\(584\) 6074.13 7616.71i 0.430392 0.539695i
\(585\) 3832.72 + 1845.74i 0.270878 + 0.130448i
\(586\) −7063.26 3401.49i −0.497919 0.239785i
\(587\) 1188.47 5207.05i 0.0835666 0.366129i −0.915803 0.401627i \(-0.868445\pi\)
0.999370 + 0.0354982i \(0.0113018\pi\)
\(588\) 6050.45 + 7587.03i 0.424348 + 0.532115i
\(589\) 6870.21 3308.52i 0.480615 0.231452i
\(590\) 17166.2 + 21525.7i 1.19783 + 1.50203i
\(591\) −586.242 2568.49i −0.0408033 0.178771i
\(592\) 2238.67 + 1078.09i 0.155420 + 0.0748464i
\(593\) −4785.69 20967.5i −0.331408 1.45199i −0.816406 0.577478i \(-0.804037\pi\)
0.484999 0.874515i \(-0.338820\pi\)
\(594\) −10015.6 + 4823.26i −0.691827 + 0.333166i
\(595\) 80.4104 0.00554035
\(596\) −10843.8 −0.745264
\(597\) 12824.1 6175.78i 0.879157 0.423380i
\(598\) 6043.84 26479.8i 0.413296 1.81077i
\(599\) 8819.93 11059.8i 0.601624 0.754413i −0.384006 0.923331i \(-0.625456\pi\)
0.985630 + 0.168918i \(0.0540273\pi\)
\(600\) 1522.80 + 1909.54i 0.103614 + 0.129927i
\(601\) −1655.86 −0.112386 −0.0561930 0.998420i \(-0.517896\pi\)
−0.0561930 + 0.998420i \(0.517896\pi\)
\(602\) −4137.60 + 14525.8i −0.280126 + 0.983432i
\(603\) −1782.91 −0.120408
\(604\) 75.0597 + 94.1219i 0.00505651 + 0.00634067i
\(605\) 6022.57 7552.07i 0.404715 0.507496i
\(606\) 3031.80 13283.2i 0.203232 0.890418i
\(607\) −14307.3 + 6890.03i −0.956697 + 0.460721i −0.846029 0.533136i \(-0.821013\pi\)
−0.110668 + 0.993857i \(0.535299\pi\)
\(608\) −7463.24 −0.497820
\(609\) −12789.6 −0.851006
\(610\) 18337.2 8830.75i 1.21714 0.586142i
\(611\) 5793.71 + 25383.9i 0.383614 + 1.68072i
\(612\) 44.1133 + 21.2438i 0.00291368 + 0.00140315i
\(613\) 3733.91 + 16359.3i 0.246021 + 1.07789i 0.935428 + 0.353516i \(0.115014\pi\)
−0.689407 + 0.724374i \(0.742129\pi\)
\(614\) −3202.73 4016.10i −0.210508 0.263968i
\(615\) −15295.8 + 7366.08i −1.00291 + 0.482974i
\(616\) −1718.84 2155.36i −0.112425 0.140977i
\(617\) 3117.65 13659.3i 0.203423 0.891254i −0.765411 0.643542i \(-0.777464\pi\)
0.968834 0.247712i \(-0.0796786\pi\)
\(618\) 17072.6 + 8221.74i 1.11126 + 0.535156i
\(619\) 735.485 + 354.191i 0.0477571 + 0.0229986i 0.457610 0.889153i \(-0.348706\pi\)
−0.409853 + 0.912152i \(0.634420\pi\)
\(620\) 15485.7 19418.4i 1.00310 1.25784i
\(621\) −2825.95 + 12381.3i −0.182611 + 0.800071i
\(622\) 6117.95 + 26804.5i 0.394385 + 1.72791i
\(623\) −6696.26 + 8396.84i −0.430626 + 0.539988i
\(624\) −6354.72 + 7968.57i −0.407680 + 0.511215i
\(625\) 2003.93 + 8779.78i 0.128251 + 0.561906i
\(626\) −1139.66 + 4993.18i −0.0727635 + 0.318798i
\(627\) −1495.21 + 1874.94i −0.0952360 + 0.119422i
\(628\) 10259.1 + 4940.50i 0.651881 + 0.313929i
\(629\) −52.8274 25.4403i −0.00334876 0.00161268i
\(630\) 683.499 2994.60i 0.0432242 0.189378i
\(631\) −7468.39 9365.07i −0.471176 0.590836i 0.488283 0.872685i \(-0.337623\pi\)
−0.959459 + 0.281850i \(0.909052\pi\)
\(632\) −9854.63 + 4745.74i −0.620247 + 0.298695i
\(633\) 51.7388 + 64.8784i 0.00324871 + 0.00407375i
\(634\) 1210.15 + 5302.02i 0.0758064 + 0.332129i
\(635\) −5433.71 2616.73i −0.339575 0.163531i
\(636\) 1190.56 + 5216.19i 0.0742278 + 0.325213i
\(637\) −12864.5 + 6195.20i −0.800171 + 0.385342i
\(638\) −16788.2 −1.04177
\(639\) 818.310 0.0506602
\(640\) −13161.7 + 6338.33i −0.812908 + 0.391476i
\(641\) 3240.50 14197.6i 0.199676 0.874836i −0.771454 0.636285i \(-0.780470\pi\)
0.971130 0.238551i \(-0.0766724\pi\)
\(642\) 20700.9 25958.1i 1.27259 1.59577i
\(643\) 2111.82 + 2648.14i 0.129521 + 0.162415i 0.842363 0.538910i \(-0.181164\pi\)
−0.712842 + 0.701325i \(0.752592\pi\)
\(644\) −11380.5 −0.696357
\(645\) 10927.8 4564.92i 0.667100 0.278672i
\(646\) 97.1709 0.00591817
\(647\) −10156.2 12735.5i −0.617127 0.773853i 0.370810 0.928709i \(-0.379080\pi\)
−0.987937 + 0.154856i \(0.950509\pi\)
\(648\) −4351.50 + 5456.61i −0.263801 + 0.330796i
\(649\) 2560.58 11218.6i 0.154871 0.678536i
\(650\) −11699.8 + 5634.31i −0.706004 + 0.339994i
\(651\) −13627.9 −0.820462
\(652\) 10387.2 0.623919
\(653\) −14308.7 + 6890.73i −0.857495 + 0.412948i −0.810354 0.585940i \(-0.800725\pi\)
−0.0471411 + 0.998888i \(0.515011\pi\)
\(654\) 9614.67 + 42124.6i 0.574868 + 2.51866i
\(655\) 21740.8 + 10469.8i 1.29692 + 0.624564i
\(656\) 2711.13 + 11878.3i 0.161360 + 0.706963i
\(657\) −2828.57 3546.92i −0.167965 0.210622i
\(658\) 16938.1 8156.97i 1.00352 0.483270i
\(659\) 17874.5 + 22413.9i 1.05659 + 1.32492i 0.943514 + 0.331331i \(0.107498\pi\)
0.113072 + 0.993587i \(0.463931\pi\)
\(660\) −1738.14 + 7615.29i −0.102511 + 0.449128i
\(661\) −28338.8 13647.2i −1.66755 0.803050i −0.998192 0.0601107i \(-0.980855\pi\)
−0.669359 0.742939i \(-0.733431\pi\)
\(662\) −3877.81 1867.45i −0.227667 0.109638i
\(663\) 149.957 188.040i 0.00878406 0.0110149i
\(664\) 2576.22 11287.1i 0.150567 0.659678i
\(665\) −787.161 3448.78i −0.0459020 0.201110i
\(666\) −1396.48 + 1751.13i −0.0812498 + 0.101884i
\(667\) −11958.0 + 14994.9i −0.694176 + 0.870469i
\(668\) 4278.16 + 18743.9i 0.247795 + 1.08566i
\(669\) −1949.45 + 8541.09i −0.112661 + 0.493599i
\(670\) −7185.83 + 9010.75i −0.414348 + 0.519576i
\(671\) −7664.03 3690.80i −0.440934 0.212343i
\(672\) 12017.3 + 5787.23i 0.689848 + 0.332213i
\(673\) 2791.50 12230.4i 0.159888 0.700514i −0.829894 0.557921i \(-0.811599\pi\)
0.989782 0.142592i \(-0.0455438\pi\)
\(674\) −30853.7 38689.3i −1.76326 2.21106i
\(675\) 5470.52 2634.46i 0.311941 0.150223i
\(676\) 22800.9 + 28591.4i 1.29727 + 1.62673i
\(677\) 3217.63 + 14097.4i 0.182664 + 0.800304i 0.980356 + 0.197238i \(0.0631973\pi\)
−0.797691 + 0.603066i \(0.793946\pi\)
\(678\) 29786.8 + 14344.6i 1.68725 + 0.812537i
\(679\) −2543.48 11143.7i −0.143755 0.629833i
\(680\) 78.9147 38.0033i 0.00445035 0.00214318i
\(681\) 3172.89 0.178539
\(682\) −17888.5 −1.00438
\(683\) −18601.3 + 8957.93i −1.04211 + 0.501853i −0.875019 0.484089i \(-0.839151\pi\)
−0.167089 + 0.985942i \(0.553437\pi\)
\(684\) 479.304 2099.97i 0.0267933 0.117389i
\(685\) −2389.97 + 2996.92i −0.133308 + 0.167163i
\(686\) 17883.2 + 22424.8i 0.995313 + 1.24808i
\(687\) −8685.92 −0.482370
\(688\) −1448.81 8374.74i −0.0802841 0.464075i
\(689\) −7872.36 −0.435287
\(690\) 9587.82 + 12022.7i 0.528988 + 0.663331i
\(691\) 17952.3 22511.5i 0.988334 1.23933i 0.0174342 0.999848i \(-0.494450\pi\)
0.970900 0.239484i \(-0.0769783\pi\)
\(692\) 267.769 1173.17i 0.0147096 0.0644470i
\(693\) −1156.64 + 557.010i −0.0634016 + 0.0305326i
\(694\) 22721.4 1.24279
\(695\) 19049.8 1.03971
\(696\) −12551.7 + 6044.60i −0.683581 + 0.329195i
\(697\) −63.9765 280.299i −0.00347673 0.0152326i
\(698\) −21810.3 10503.3i −1.18271 0.569563i
\(699\) −3441.56 15078.5i −0.186226 0.815908i
\(700\) 3392.47 + 4254.02i 0.183176 + 0.229695i
\(701\) −30214.8 + 14550.7i −1.62795 + 0.783981i −0.627970 + 0.778238i \(0.716114\pi\)
−0.999984 + 0.00574352i \(0.998172\pi\)
\(702\) −30580.2 38346.4i −1.64413 2.06167i
\(703\) −573.985 + 2514.79i −0.0307941 + 0.134918i
\(704\) 12121.5 + 5837.40i 0.648928 + 0.312507i
\(705\) −13281.4 6395.99i −0.709513 0.341683i
\(706\) 7510.19 9417.48i 0.400354 0.502028i
\(707\) 1869.15 8189.27i 0.0994294 0.435628i
\(708\) −7678.18 33640.3i −0.407576 1.78571i
\(709\) 20668.0 25916.8i 1.09478 1.37282i 0.173087 0.984907i \(-0.444626\pi\)
0.921697 0.387910i \(-0.126803\pi\)
\(710\) 3298.11 4135.70i 0.174332 0.218605i
\(711\) 1133.40 + 4965.77i 0.0597834 + 0.261928i
\(712\) −2603.21 + 11405.4i −0.137022 + 0.600331i
\(713\) −12741.8 + 15977.7i −0.669261 + 0.839227i
\(714\) −156.465 75.3493i −0.00820103 0.00394941i
\(715\) −10354.9 4986.67i −0.541612 0.260827i
\(716\) 4560.19 19979.5i 0.238020 1.04283i
\(717\) −12082.3 15150.7i −0.629318 0.789140i
\(718\) 1631.81 785.836i 0.0848168 0.0408456i
\(719\) 18412.9 + 23089.1i 0.955058 + 1.19760i 0.980218 + 0.197921i \(0.0634189\pi\)
−0.0251604 + 0.999683i \(0.508010\pi\)
\(720\) 384.621 + 1685.13i 0.0199083 + 0.0872240i
\(721\) 10525.5 + 5068.81i 0.543675 + 0.261820i
\(722\) 5712.30 + 25027.2i 0.294446 + 1.29005i
\(723\) 28820.4 13879.2i 1.48249 0.713931i
\(724\) −13701.3 −0.703320
\(725\) 9169.68 0.469729
\(726\) −18795.6 + 9051.48i −0.960840 + 0.462716i
\(727\) 5450.30 23879.3i 0.278047 1.21820i −0.622211 0.782849i \(-0.713766\pi\)
0.900259 0.435356i \(-0.143377\pi\)
\(728\) 7583.67 9509.62i 0.386084 0.484134i
\(729\) 13646.6 + 17112.2i 0.693317 + 0.869392i
\(730\) −29326.2 −1.48686
\(731\) 34.1886 + 197.624i 0.00172984 + 0.00999918i
\(732\) −25507.5 −1.28795
\(733\) 5246.15 + 6578.46i 0.264353 + 0.331488i 0.896238 0.443574i \(-0.146290\pi\)
−0.631884 + 0.775063i \(0.717718\pi\)
\(734\) 5820.58 7298.78i 0.292700 0.367034i
\(735\) 1798.88 7881.39i 0.0902756 0.395523i
\(736\) 18020.9 8678.43i 0.902528 0.434635i
\(737\) 4816.94 0.240752
\(738\) −10982.6 −0.547797
\(739\) −22447.9 + 10810.4i −1.11740 + 0.538113i −0.899089 0.437766i \(-0.855770\pi\)
−0.218314 + 0.975879i \(0.570056\pi\)
\(740\) 1869.57 + 8191.12i 0.0928740 + 0.406907i
\(741\) −9532.93 4590.82i −0.472606 0.227595i
\(742\) 1264.87 + 5541.75i 0.0625806 + 0.274184i
\(743\) 2771.96 + 3475.92i 0.136868 + 0.171628i 0.845542 0.533909i \(-0.179277\pi\)
−0.708674 + 0.705537i \(0.750706\pi\)
\(744\) −13374.4 + 6440.79i −0.659046 + 0.317380i
\(745\) 5632.24 + 7062.61i 0.276979 + 0.347321i
\(746\) −5135.02 + 22498.0i −0.252019 + 1.10417i
\(747\) −4857.41 2339.21i −0.237916 0.114574i
\(748\) −119.182 57.3949i −0.00582582 0.00280557i
\(749\) 12762.4 16003.6i 0.622601 0.780717i
\(750\) 6736.47 29514.4i 0.327975 1.43695i
\(751\) −1140.76 4997.99i −0.0554286 0.242848i 0.939623 0.342213i \(-0.111176\pi\)
−0.995051 + 0.0993641i \(0.968319\pi\)
\(752\) −6596.00 + 8271.12i −0.319855 + 0.401086i
\(753\) −7646.63 + 9588.57i −0.370065 + 0.464047i
\(754\) −16482.3 72213.7i −0.796087 3.48789i
\(755\) 22.3162 97.7737i 0.00107572 0.00471304i
\(756\) −12813.3 + 16067.3i −0.616420 + 0.772966i
\(757\) 6032.34 + 2905.02i 0.289629 + 0.139478i 0.573057 0.819516i \(-0.305757\pi\)
−0.283428 + 0.958994i \(0.591472\pi\)
\(758\) 48828.7 + 23514.7i 2.33976 + 1.12677i
\(759\) 1430.16 6265.94i 0.0683946 0.299656i
\(760\) −2402.47 3012.60i −0.114667 0.143787i
\(761\) −25622.8 + 12339.3i −1.22054 + 0.587779i −0.929461 0.368922i \(-0.879727\pi\)
−0.291075 + 0.956700i \(0.594013\pi\)
\(762\) 8121.00 + 10183.4i 0.386080 + 0.484129i
\(763\) 5927.58 + 25970.4i 0.281249 + 1.23223i
\(764\) 29091.0 + 14009.5i 1.37759 + 0.663411i
\(765\) −9.07616 39.7653i −0.000428953 0.00187937i
\(766\) −32774.7 + 15783.4i −1.54595 + 0.744490i
\(767\) 50770.5 2.39011
\(768\) 2371.37 0.111419
\(769\) 30040.4 14466.7i 1.40869 0.678390i 0.433788 0.901015i \(-0.357177\pi\)
0.974904 + 0.222625i \(0.0714625\pi\)
\(770\) −1846.62 + 8090.59i −0.0864256 + 0.378655i
\(771\) −1854.50 + 2325.47i −0.0866254 + 0.108625i
\(772\) 21563.8 + 27040.1i 1.00531 + 1.26062i
\(773\) 31381.8 1.46019 0.730094 0.683347i \(-0.239476\pi\)
0.730094 + 0.683347i \(0.239476\pi\)
\(774\) 7650.43 + 406.597i 0.355283 + 0.0188822i
\(775\) 9770.70 0.452870
\(776\) −7762.87 9734.34i −0.359112 0.450312i
\(777\) 2874.28 3604.23i 0.132708 0.166411i
\(778\) 7111.81 31158.9i 0.327726 1.43586i
\(779\) −11395.7 + 5487.86i −0.524123 + 0.252404i
\(780\) −34463.3 −1.58203
\(781\) −2210.85 −0.101294
\(782\) −234.632 + 112.993i −0.0107294 + 0.00516702i
\(783\) 7706.71 + 33765.3i 0.351744 + 1.54109i
\(784\) −5227.06 2517.22i −0.238113 0.114669i
\(785\) −2110.77 9247.88i −0.0959702 0.420473i
\(786\) −32492.9 40744.8i −1.47453 1.84901i
\(787\) −552.575 + 266.106i −0.0250282 + 0.0120529i −0.446356 0.894855i \(-0.647278\pi\)
0.421328 + 0.906908i \(0.361564\pi\)
\(788\) −3986.05 4998.35i −0.180199 0.225963i
\(789\) −5025.02 + 22016.0i −0.226737 + 0.993399i
\(790\) 29664.8 + 14285.8i 1.33598 + 0.643375i
\(791\) 18364.0 + 8843.63i 0.825472 + 0.397526i
\(792\) −871.876 + 1093.30i −0.0391171 + 0.0490513i
\(793\) 8351.45 36590.1i 0.373983 1.63853i
\(794\) 3735.90 + 16368.0i 0.166980 + 0.731587i
\(795\) 2778.96 3484.71i 0.123974 0.155459i
\(796\) 21535.5 27004.7i 0.958926 1.20246i
\(797\) −743.793 3258.77i −0.0330571 0.144833i 0.955706 0.294323i \(-0.0950940\pi\)
−0.988763 + 0.149490i \(0.952237\pi\)
\(798\) −1700.03 + 7448.33i −0.0754142 + 0.330411i
\(799\) 155.650 195.179i 0.00689175 0.00864198i
\(800\) −8615.94 4149.22i −0.380774 0.183371i
\(801\) 4908.31 + 2363.72i 0.216512 + 0.104267i
\(802\) −4864.10 + 21311.0i −0.214161 + 0.938302i
\(803\) 7642.02 + 9582.79i 0.335842 + 0.421132i
\(804\) 13013.7 6267.06i 0.570843 0.274903i
\(805\) 5911.02 + 7412.19i 0.258803 + 0.324528i
\(806\) −17562.6 76946.8i −0.767515 3.36270i
\(807\) −28901.4 13918.2i −1.26069 0.607117i
\(808\) −2036.01 8920.33i −0.0886466 0.388386i
\(809\) −4116.04 + 1982.18i −0.178878 + 0.0861430i −0.521180 0.853447i \(-0.674508\pi\)
0.342302 + 0.939590i \(0.388794\pi\)
\(810\) 21009.3 0.911346
\(811\) −42027.8 −1.81972 −0.909861 0.414913i \(-0.863812\pi\)
−0.909861 + 0.414913i \(0.863812\pi\)
\(812\) −27962.5 + 13466.0i −1.20849 + 0.581976i
\(813\) −86.7947 + 380.273i −0.00374419 + 0.0164044i
\(814\) 3772.89 4731.05i 0.162457 0.203714i
\(815\) −5395.12 6765.26i −0.231881 0.290769i
\(816\) 97.7240 0.00419243
\(817\) 8141.37 3400.94i 0.348630 0.145635i
\(818\) 58616.1 2.50546
\(819\) −3531.53 4428.40i −0.150674 0.188939i
\(820\) −25686.2 + 32209.5i −1.09390 + 1.37171i
\(821\) 4613.95 20215.0i 0.196136 0.859329i −0.777073 0.629410i \(-0.783297\pi\)
0.973210 0.229919i \(-0.0738462\pi\)
\(822\) 7458.75 3591.94i 0.316489 0.152413i
\(823\) −25400.2 −1.07582 −0.537908 0.843003i \(-0.680785\pi\)
−0.537908 + 0.843003i \(0.680785\pi\)
\(824\) 12725.3 0.537994
\(825\) −2768.53 + 1333.25i −0.116834 + 0.0562641i
\(826\) −8157.40 35739.9i −0.343623 1.50551i
\(827\) −1089.89 524.861i −0.0458271 0.0220692i 0.410830 0.911712i \(-0.365239\pi\)
−0.456657 + 0.889643i \(0.650953\pi\)
\(828\) 1284.55 + 5627.98i 0.0539145 + 0.236215i
\(829\) 9201.80 + 11538.7i 0.385515 + 0.483420i 0.936287 0.351235i \(-0.114238\pi\)
−0.550772 + 0.834655i \(0.685667\pi\)
\(830\) −31399.5 + 15121.2i −1.31312 + 0.632366i
\(831\) −21265.3 26665.8i −0.887707 1.11315i
\(832\) −13208.7 + 57871.1i −0.550396 + 2.41144i
\(833\) 123.346 + 59.4005i 0.00513049 + 0.00247071i
\(834\) −37067.6 17850.8i −1.53903 0.741156i
\(835\) 9985.92 12521.9i 0.413865 0.518970i
\(836\) −1294.94 + 5673.52i −0.0535725 + 0.234716i
\(837\) 8211.84 + 35978.4i 0.339119 + 1.48578i
\(838\) −5275.38 + 6615.12i −0.217464 + 0.272692i
\(839\) 26601.6 33357.3i 1.09462 1.37261i 0.172819 0.984954i \(-0.444712\pi\)
0.921803 0.387659i \(-0.126716\pi\)
\(840\) 1532.39 + 6713.84i 0.0629434 + 0.275773i
\(841\) −6211.64 + 27215.0i −0.254690 + 1.11587i
\(842\) −35409.5 + 44402.1i −1.44928 + 1.81734i
\(843\) −11242.2 5413.94i −0.459313 0.221193i
\(844\) 181.428 + 87.3710i 0.00739929 + 0.00356331i
\(845\) 6778.99 29700.7i 0.275981 1.20915i
\(846\) −5945.72 7455.69i −0.241629 0.302993i
\(847\) −11587.7 + 5580.36i −0.470082 + 0.226380i
\(848\) −1994.34 2500.82i −0.0807617 0.101272i
\(849\) 7525.32 + 32970.6i 0.304203 + 1.33280i
\(850\) 112.179 + 54.0226i 0.00452672 + 0.00217995i
\(851\) −1538.30 6739.74i −0.0619651 0.271487i
\(852\) −5972.94 + 2876.42i −0.240175 + 0.115662i
\(853\) −5852.96 −0.234937 −0.117469 0.993077i \(-0.537478\pi\)
−0.117469 + 0.993077i \(0.537478\pi\)
\(854\) −27099.5 −1.08586
\(855\) −1616.67 + 778.548i −0.0646655 + 0.0311413i
\(856\) 4961.46 21737.6i 0.198107 0.867962i
\(857\) −2129.85 + 2670.75i −0.0848943 + 0.106454i −0.822465 0.568816i \(-0.807402\pi\)
0.737570 + 0.675270i \(0.235973\pi\)
\(858\) 15476.1 + 19406.4i 0.615786 + 0.772171i
\(859\) −4064.51 −0.161443 −0.0807213 0.996737i \(-0.525722\pi\)
−0.0807213 + 0.996737i \(0.525722\pi\)
\(860\) 19085.4 21486.1i 0.756753 0.851942i
\(861\) 22604.8 0.894736
\(862\) 1213.86 + 1522.13i 0.0479632 + 0.0601439i
\(863\) −15256.2 + 19130.6i −0.601769 + 0.754594i −0.985652 0.168787i \(-0.946015\pi\)
0.383884 + 0.923381i \(0.374586\pi\)
\(864\) 8037.25 35213.5i 0.316473 1.38656i
\(865\) −903.173 + 434.945i −0.0355015 + 0.0170966i
\(866\) −21647.6 −0.849439
\(867\) 22391.9 0.877125
\(868\) −29795.2 + 14348.6i −1.16511 + 0.561088i
\(869\) −3062.14 13416.1i −0.119535 0.523718i
\(870\) 37783.7 + 18195.7i 1.47240 + 0.709071i
\(871\) 4729.17 + 20719.9i 0.183975 + 0.806046i
\(872\) 18091.4 + 22685.8i 0.702581 + 0.881009i
\(873\) −5223.80 + 2515.65i −0.202519 + 0.0975279i
\(874\) 7143.09 + 8957.16i 0.276452 + 0.346659i
\(875\) 4153.13 18196.0i 0.160459 0.703015i
\(876\) 33113.7 + 15946.7i 1.27718 + 0.615057i
\(877\) −11535.6 5555.25i −0.444161 0.213897i 0.198416 0.980118i \(-0.436420\pi\)
−0.642577 + 0.766221i \(0.722135\pi\)
\(878\) 6109.24 7660.74i 0.234825 0.294462i
\(879\) 1821.30 7979.64i 0.0698873 0.306196i
\(880\) −1039.14 4552.77i −0.0398061 0.174402i
\(881\) −16750.4 + 21004.3i −0.640561 + 0.803238i −0.991073 0.133320i \(-0.957436\pi\)
0.350512 + 0.936558i \(0.386008\pi\)
\(882\) 3260.62 4088.69i 0.124479 0.156092i
\(883\) 3136.18 + 13740.5i 0.119525 + 0.523675i 0.998872 + 0.0474922i \(0.0151229\pi\)
−0.879346 + 0.476183i \(0.842020\pi\)
\(884\) 129.872 569.005i 0.00494124 0.0216490i
\(885\) −17922.1 + 22473.6i −0.680729 + 0.853607i
\(886\) −6004.46 2891.60i −0.227679 0.109645i
\(887\) −2305.26 1110.15i −0.0872637 0.0420240i 0.389743 0.920924i \(-0.372564\pi\)
−0.477007 + 0.878900i \(0.658278\pi\)
\(888\) 1117.39 4895.62i 0.0422267 0.185007i
\(889\) 5006.71 + 6278.21i 0.188886 + 0.236855i
\(890\) 31728.5 15279.6i 1.19499 0.575477i
\(891\) −5474.74 6865.10i −0.205848 0.258125i
\(892\) 4730.63 + 20726.2i 0.177571 + 0.777989i
\(893\) −9894.88 4765.12i −0.370794 0.178565i
\(894\) −4341.27 19020.3i −0.162409 0.711560i
\(895\) −15381.3 + 7407.26i −0.574459 + 0.276645i
\(896\) 19450.8 0.725230
\(897\) 28356.8 1.05552
\(898\) −33084.5 + 15932.6i −1.22945 + 0.592071i
\(899\) −12401.6 + 54334.7i −0.460083 + 2.01576i
\(900\) 1720.82 2157.84i 0.0637340 0.0799199i
\(901\) 47.0618 + 59.0137i 0.00174013 + 0.00218205i
\(902\) 29671.8 1.09530
\(903\) −15746.4 836.874i −0.580297 0.0308410i
\(904\) 22202.0 0.816846
\(905\) 7116.43 + 8923.72i 0.261390 + 0.327773i
\(906\) −135.043 + 169.339i −0.00495200 + 0.00620961i
\(907\) −5101.35 + 22350.5i −0.186756 + 0.818231i 0.791557 + 0.611096i \(0.209271\pi\)
−0.978312 + 0.207135i \(0.933586\pi\)
\(908\) 6937.00 3340.68i 0.253538 0.122097i
\(909\) −4260.81 −0.155470
\(910\) −36614.3 −1.33379
\(911\) 4400.08 2118.97i 0.160023 0.0770631i −0.352158 0.935941i \(-0.614552\pi\)
0.512181 + 0.858878i \(0.328838\pi\)
\(912\) −956.649 4191.35i −0.0347344 0.152182i
\(913\) 13123.4 + 6319.88i 0.475707 + 0.229088i
\(914\) 14784.7 + 64776.2i 0.535050 + 2.34421i
\(915\) 13248.6 + 16613.2i 0.478671 + 0.600234i
\(916\) −18990.3 + 9145.27i −0.684998 + 0.329878i
\(917\) −20032.3 25119.7i −0.721402 0.904609i
\(918\) −104.645 + 458.478i −0.00376229 + 0.0164837i
\(919\) 14504.5 + 6984.98i 0.520629 + 0.250722i 0.675694 0.737183i \(-0.263844\pi\)
−0.155064 + 0.987904i \(0.549558\pi\)
\(920\) 9304.19 + 4480.66i 0.333424 + 0.160568i
\(921\) 3343.76 4192.94i 0.119632 0.150013i
\(922\) 14762.2 64677.5i 0.527297 2.31024i
\(923\) −2170.57 9509.87i −0.0774052 0.339135i
\(924\) 6484.55 8131.36i 0.230872 0.289505i
\(925\) −2060.75 + 2584.10i −0.0732508 + 0.0918536i
\(926\) −17713.2 77606.6i −0.628609 2.75411i
\(927\) 1318.63 5777.29i 0.0467200 0.204694i
\(928\) 34009.6 42646.7i 1.20304 1.50856i
\(929\) −22902.2 11029.1i −0.808822 0.389508i −0.0166919 0.999861i \(-0.505313\pi\)
−0.792130 + 0.610353i \(0.791028\pi\)
\(930\) 40260.2 + 19388.3i 1.41955 + 0.683621i
\(931\) 1340.19 5871.78i 0.0471784 0.206702i
\(932\) −23400.3 29343.0i −0.822427 1.03129i
\(933\) −25861.9 + 12454.4i −0.907481 + 0.437020i
\(934\) 975.293 + 1222.98i 0.0341676 + 0.0428448i
\(935\) 24.5213 + 107.435i 0.000857681 + 0.00375774i
\(936\) −5558.77 2676.96i −0.194118 0.0934821i
\(937\) 4180.34 + 18315.3i 0.145748 + 0.638564i 0.994038 + 0.109032i \(0.0347751\pi\)
−0.848290 + 0.529532i \(0.822368\pi\)
\(938\) 13825.9 6658.21i 0.481271 0.231768i
\(939\) −5347.11 −0.185832
\(940\) −35771.8 −1.24122
\(941\) 11586.0 5579.51i 0.401373 0.193291i −0.222297 0.974979i \(-0.571355\pi\)
0.623670 + 0.781688i \(0.285641\pi\)
\(942\) −4558.63 + 19972.7i −0.157673 + 0.690812i
\(943\) 21134.9 26502.3i 0.729847 0.915200i
\(944\) 12861.9 + 16128.3i 0.443453 + 0.556073i
\(945\) 17119.9 0.589324
\(946\) −20669.3 1098.51i −0.710379 0.0377544i
\(947\) 56380.9 1.93467 0.967336 0.253498i \(-0.0815813\pi\)
0.967336 + 0.253498i \(0.0815813\pi\)
\(948\) −25727.9 32261.7i −0.881437 1.10529i
\(949\) −33717.2 + 42280.0i −1.15333 + 1.44623i
\(950\) 1218.86 5340.17i 0.0416263 0.182377i
\(951\) −5115.56 + 2463.53i −0.174431 + 0.0840014i
\(952\) −116.623 −0.00397035
\(953\) −7899.32 −0.268504 −0.134252 0.990947i \(-0.542863\pi\)
−0.134252 + 0.990947i \(0.542863\pi\)
\(954\) 2597.79 1251.03i 0.0881619 0.0424565i
\(955\) −5985.39 26223.7i −0.202809 0.888564i
\(956\) −42367.8 20403.3i −1.43334 0.690261i
\(957\) −3900.22 17088.0i −0.131741 0.577195i
\(958\) 26946.8 + 33790.3i 0.908781 + 1.13958i
\(959\) 4598.42 2214.48i 0.154839 0.0745666i
\(960\) −20954.0 26275.5i −0.704466 0.883373i
\(961\) −6585.28 + 28852.0i −0.221049 + 0.968480i
\(962\) 24054.6 + 11584.1i 0.806186 + 0.388239i
\(963\) −9354.75 4505.01i −0.313035 0.150750i
\(964\) 48397.9 60689.1i 1.61700 2.02766i
\(965\) 6411.19 28089.3i 0.213869 0.937022i
\(966\) −4556.15 19961.8i −0.151751 0.664865i
\(967\) 28717.7 36010.8i 0.955014 1.19755i −0.0252145 0.999682i \(-0.508027\pi\)
0.980229 0.197868i \(-0.0634017\pi\)
\(968\) −8734.82 + 10953.1i −0.290029 + 0.363684i
\(969\) 22.5747 + 98.9062i 0.000748404 + 0.00327897i
\(970\) −8339.99 + 36539.9i −0.276063 + 1.20951i
\(971\) 29781.9 37345.3i 0.984291 1.23426i 0.0121353 0.999926i \(-0.496137\pi\)
0.972156 0.234336i \(-0.0752914\pi\)
\(972\) 17024.7 + 8198.68i 0.561799 + 0.270548i
\(973\) −22852.7 11005.3i −0.752954 0.362603i
\(974\) −11788.9 + 51650.6i −0.387825 + 1.69917i
\(975\) −8453.02 10599.7i −0.277655 0.348168i
\(976\) 13739.3 6616.52i 0.450600 0.216998i
\(977\) −10974.5 13761.6i −0.359372 0.450639i 0.568974 0.822356i \(-0.307341\pi\)
−0.928346 + 0.371717i \(0.878769\pi\)
\(978\) 4158.50 + 18219.6i 0.135965 + 0.595703i
\(979\) −13260.9 6386.10i −0.432911 0.208479i
\(980\) −4365.24 19125.4i −0.142288 0.623406i
\(981\) 12174.1 5862.71i 0.396216 0.190807i
\(982\) −65882.5 −2.14093
\(983\) 35830.0 1.16256 0.581281 0.813703i \(-0.302552\pi\)
0.581281 + 0.813703i \(0.302552\pi\)
\(984\) 22184.3 10683.4i 0.718708 0.346111i
\(985\) −1185.10 + 5192.28i −0.0383356 + 0.167959i
\(986\) −442.803 + 555.257i −0.0143019 + 0.0179341i
\(987\) 12237.7 + 15345.6i 0.394661 + 0.494889i
\(988\) −25675.8 −0.826777
\(989\) −15703.7 + 17679.0i −0.504902 + 0.568411i
\(990\) 4209.46 0.135137
\(991\) −10240.0 12840.5i −0.328237 0.411596i 0.590141 0.807300i \(-0.299072\pi\)
−0.918378 + 0.395704i \(0.870501\pi\)
\(992\) 36238.7 45441.9i 1.15986 1.45442i
\(993\) 999.913 4380.90i 0.0319550 0.140004i
\(994\) −6345.73 + 3055.94i −0.202489 + 0.0975137i
\(995\) −28773.8 −0.916776
\(996\) 43677.3 1.38952
\(997\) −21226.8 + 10222.3i −0.674282 + 0.324717i −0.739503 0.673154i \(-0.764939\pi\)
0.0652205 + 0.997871i \(0.479225\pi\)
\(998\) −2620.45 11480.9i −0.0831150 0.364150i
\(999\) −11247.3 5416.42i −0.356206 0.171540i
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 43.4.e.a.11.9 yes 60
43.2 odd 14 1849.4.a.g.1.6 30
43.4 even 7 inner 43.4.e.a.4.9 60
43.41 even 7 1849.4.a.h.1.25 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.e.a.4.9 60 43.4 even 7 inner
43.4.e.a.11.9 yes 60 1.1 even 1 trivial
1849.4.a.g.1.6 30 43.2 odd 14
1849.4.a.h.1.25 30 43.41 even 7