Properties

Label 63.4.s.a.59.19
Level $63$
Weight $4$
Character 63.59
Analytic conductor $3.717$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,4,Mod(47,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.47");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.19
Character \(\chi\) \(=\) 63.59
Dual form 63.4.s.a.47.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.55689 + 2.05357i) q^{2} +(4.91877 - 1.67502i) q^{3} +(4.43430 + 7.68044i) q^{4} -7.61183 q^{5} +(20.9353 + 4.14318i) q^{6} +(4.76690 + 17.8963i) q^{7} +3.56749i q^{8} +(21.3886 - 16.4781i) q^{9} +O(q^{10})\) \(q+(3.55689 + 2.05357i) q^{2} +(4.91877 - 1.67502i) q^{3} +(4.43430 + 7.68044i) q^{4} -7.61183 q^{5} +(20.9353 + 4.14318i) q^{6} +(4.76690 + 17.8963i) q^{7} +3.56749i q^{8} +(21.3886 - 16.4781i) q^{9} +(-27.0744 - 15.6314i) q^{10} -7.17024i q^{11} +(34.6762 + 30.3508i) q^{12} +(-59.6417 - 34.4342i) q^{13} +(-19.7959 + 73.4442i) q^{14} +(-37.4408 + 12.7500i) q^{15} +(28.1483 - 48.7543i) q^{16} +(11.4334 - 19.8032i) q^{17} +(109.916 - 14.6877i) q^{18} +(-86.1218 + 49.7224i) q^{19} +(-33.7532 - 58.4622i) q^{20} +(53.4239 + 80.0430i) q^{21} +(14.7246 - 25.5037i) q^{22} +122.450i q^{23} +(5.97563 + 17.5477i) q^{24} -67.0601 q^{25} +(-141.426 - 244.957i) q^{26} +(77.6045 - 116.878i) q^{27} +(-116.313 + 115.969i) q^{28} +(143.427 - 82.8076i) q^{29} +(-159.356 - 31.5372i) q^{30} +(-11.9405 + 6.89384i) q^{31} +(224.957 - 129.879i) q^{32} +(-12.0103 - 35.2688i) q^{33} +(81.3346 - 46.9585i) q^{34} +(-36.2848 - 136.223i) q^{35} +(221.403 + 91.2050i) q^{36} +(126.544 + 219.181i) q^{37} -408.434 q^{38} +(-351.042 - 69.4726i) q^{39} -27.1552i q^{40} +(159.598 - 276.433i) q^{41} +(25.6490 + 394.414i) q^{42} +(156.693 + 271.399i) q^{43} +(55.0706 - 31.7950i) q^{44} +(-162.806 + 125.428i) q^{45} +(-251.459 + 435.540i) q^{46} +(-35.3934 + 61.3031i) q^{47} +(56.7906 - 286.960i) q^{48} +(-297.553 + 170.620i) q^{49} +(-238.525 - 137.713i) q^{50} +(23.0674 - 116.559i) q^{51} -610.766i q^{52} +(254.574 + 146.979i) q^{53} +(516.048 - 256.357i) q^{54} +54.5786i q^{55} +(-63.8449 + 17.0059i) q^{56} +(-340.327 + 388.829i) q^{57} +680.205 q^{58} +(230.615 + 399.437i) q^{59} +(-263.949 - 231.025i) q^{60} +(573.665 + 331.205i) q^{61} -56.6280 q^{62} +(396.854 + 304.227i) q^{63} +616.491 q^{64} +(453.983 + 262.107i) q^{65} +(29.7076 - 150.111i) q^{66} +(-359.139 - 622.047i) q^{67} +202.797 q^{68} +(205.106 + 602.302i) q^{69} +(150.683 - 559.045i) q^{70} -92.9435i q^{71} +(58.7855 + 76.3037i) q^{72} +(-882.012 - 509.230i) q^{73} +1039.47i q^{74} +(-329.853 + 112.327i) q^{75} +(-763.780 - 440.969i) q^{76} +(128.321 - 34.1798i) q^{77} +(-1105.95 - 967.996i) q^{78} +(-398.113 + 689.551i) q^{79} +(-214.260 + 371.110i) q^{80} +(185.945 - 704.887i) q^{81} +(1135.35 - 655.493i) q^{82} +(10.7079 + 18.5466i) q^{83} +(-377.868 + 765.254i) q^{84} +(-87.0290 + 150.739i) q^{85} +1287.12i q^{86} +(566.780 - 647.555i) q^{87} +25.5798 q^{88} +(-339.721 - 588.414i) q^{89} +(-836.660 + 111.800i) q^{90} +(331.937 - 1231.51i) q^{91} +(-940.467 + 542.979i) q^{92} +(-47.1852 + 53.9098i) q^{93} +(-251.780 + 145.366i) q^{94} +(655.544 - 378.479i) q^{95} +(888.963 - 1015.65i) q^{96} +(-984.068 + 568.152i) q^{97} +(-1408.74 - 4.17218i) q^{98} +(-118.152 - 153.361i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.55689 + 2.05357i 1.25755 + 0.726047i 0.972598 0.232495i \(-0.0746889\pi\)
0.284952 + 0.958542i \(0.408022\pi\)
\(3\) 4.91877 1.67502i 0.946618 0.322358i
\(4\) 4.43430 + 7.68044i 0.554288 + 0.960055i
\(5\) −7.61183 −0.680823 −0.340411 0.940277i \(-0.610566\pi\)
−0.340411 + 0.940277i \(0.610566\pi\)
\(6\) 20.9353 + 4.14318i 1.42447 + 0.281908i
\(7\) 4.76690 + 17.8963i 0.257388 + 0.966308i
\(8\) 3.56749i 0.157662i
\(9\) 21.3886 16.4781i 0.792171 0.610300i
\(10\) −27.0744 15.6314i −0.856168 0.494309i
\(11\) 7.17024i 0.196537i −0.995160 0.0982686i \(-0.968670\pi\)
0.995160 0.0982686i \(-0.0313304\pi\)
\(12\) 34.6762 + 30.3508i 0.834180 + 0.730126i
\(13\) −59.6417 34.4342i −1.27243 0.734640i −0.296988 0.954881i \(-0.595982\pi\)
−0.975445 + 0.220241i \(0.929316\pi\)
\(14\) −19.7959 + 73.4442i −0.377906 + 1.40206i
\(15\) −37.4408 + 12.7500i −0.644479 + 0.219469i
\(16\) 28.1483 48.7543i 0.439818 0.761787i
\(17\) 11.4334 19.8032i 0.163118 0.282529i −0.772867 0.634568i \(-0.781178\pi\)
0.935985 + 0.352039i \(0.114512\pi\)
\(18\) 109.916 14.6877i 1.43930 0.192329i
\(19\) −86.1218 + 49.7224i −1.03988 + 0.600374i −0.919799 0.392390i \(-0.871648\pi\)
−0.120079 + 0.992764i \(0.538315\pi\)
\(20\) −33.7532 58.4622i −0.377372 0.653627i
\(21\) 53.4239 + 80.0430i 0.555146 + 0.831753i
\(22\) 14.7246 25.5037i 0.142695 0.247155i
\(23\) 122.450i 1.11011i 0.831814 + 0.555055i \(0.187303\pi\)
−0.831814 + 0.555055i \(0.812697\pi\)
\(24\) 5.97563 + 17.5477i 0.0508238 + 0.149246i
\(25\) −67.0601 −0.536481
\(26\) −141.426 244.957i −1.06677 1.84769i
\(27\) 77.6045 116.878i 0.553148 0.833083i
\(28\) −116.313 + 115.969i −0.785042 + 0.782720i
\(29\) 143.427 82.8076i 0.918404 0.530241i 0.0352788 0.999378i \(-0.488768\pi\)
0.883126 + 0.469136i \(0.155435\pi\)
\(30\) −159.356 31.5372i −0.969809 0.191929i
\(31\) −11.9405 + 6.89384i −0.0691798 + 0.0399410i −0.534191 0.845364i \(-0.679384\pi\)
0.465011 + 0.885305i \(0.346050\pi\)
\(32\) 224.957 129.879i 1.24273 0.717488i
\(33\) −12.0103 35.2688i −0.0633553 0.186046i
\(34\) 81.3346 46.9585i 0.410258 0.236862i
\(35\) −36.2848 136.223i −0.175236 0.657884i
\(36\) 221.403 + 91.2050i 1.02501 + 0.422246i
\(37\) 126.544 + 219.181i 0.562263 + 0.973868i 0.997299 + 0.0734549i \(0.0234025\pi\)
−0.435035 + 0.900413i \(0.643264\pi\)
\(38\) −408.434 −1.74360
\(39\) −351.042 69.4726i −1.44133 0.285244i
\(40\) 27.1552i 0.107340i
\(41\) 159.598 276.433i 0.607929 1.05296i −0.383652 0.923478i \(-0.625334\pi\)
0.991581 0.129486i \(-0.0413328\pi\)
\(42\) 25.6490 + 394.414i 0.0942316 + 1.44903i
\(43\) 156.693 + 271.399i 0.555707 + 0.962512i 0.997848 + 0.0655670i \(0.0208856\pi\)
−0.442141 + 0.896945i \(0.645781\pi\)
\(44\) 55.0706 31.7950i 0.188686 0.108938i
\(45\) −162.806 + 125.428i −0.539328 + 0.415506i
\(46\) −251.459 + 435.540i −0.805992 + 1.39602i
\(47\) −35.3934 + 61.3031i −0.109844 + 0.190255i −0.915707 0.401847i \(-0.868368\pi\)
0.805863 + 0.592102i \(0.201702\pi\)
\(48\) 56.7906 286.960i 0.170771 0.862899i
\(49\) −297.553 + 170.620i −0.867502 + 0.497433i
\(50\) −238.525 137.713i −0.674651 0.389510i
\(51\) 23.0674 116.559i 0.0633350 0.320029i
\(52\) 610.766i 1.62881i
\(53\) 254.574 + 146.979i 0.659783 + 0.380926i 0.792194 0.610269i \(-0.208939\pi\)
−0.132412 + 0.991195i \(0.542272\pi\)
\(54\) 516.048 256.357i 1.30047 0.646032i
\(55\) 54.5786i 0.133807i
\(56\) −63.8449 + 17.0059i −0.152351 + 0.0405805i
\(57\) −340.327 + 388.829i −0.790832 + 0.903538i
\(58\) 680.205 1.53992
\(59\) 230.615 + 399.437i 0.508873 + 0.881394i 0.999947 + 0.0102763i \(0.00327112\pi\)
−0.491074 + 0.871118i \(0.663396\pi\)
\(60\) −263.949 231.025i −0.567929 0.497086i
\(61\) 573.665 + 331.205i 1.20410 + 0.695189i 0.961465 0.274928i \(-0.0886541\pi\)
0.242637 + 0.970117i \(0.421987\pi\)
\(62\) −56.6280 −0.115996
\(63\) 396.854 + 304.227i 0.793633 + 0.608397i
\(64\) 616.491 1.20408
\(65\) 453.983 + 262.107i 0.866302 + 0.500159i
\(66\) 29.7076 150.111i 0.0554053 0.279961i
\(67\) −359.139 622.047i −0.654863 1.13426i −0.981928 0.189254i \(-0.939393\pi\)
0.327065 0.945002i \(-0.393940\pi\)
\(68\) 202.797 0.361657
\(69\) 205.106 + 602.302i 0.357853 + 1.05085i
\(70\) 150.683 559.045i 0.257287 0.954552i
\(71\) 92.9435i 0.155357i −0.996978 0.0776787i \(-0.975249\pi\)
0.996978 0.0776787i \(-0.0247508\pi\)
\(72\) 58.7855 + 76.3037i 0.0962214 + 0.124896i
\(73\) −882.012 509.230i −1.41413 0.816450i −0.418358 0.908282i \(-0.637394\pi\)
−0.995774 + 0.0918323i \(0.970728\pi\)
\(74\) 1039.47i 1.63292i
\(75\) −329.853 + 112.327i −0.507842 + 0.172939i
\(76\) −763.780 440.969i −1.15278 0.665560i
\(77\) 128.321 34.1798i 0.189915 0.0505864i
\(78\) −1105.95 967.996i −1.60544 1.40518i
\(79\) −398.113 + 689.551i −0.566977 + 0.982033i 0.429886 + 0.902883i \(0.358554\pi\)
−0.996863 + 0.0791495i \(0.974780\pi\)
\(80\) −214.260 + 371.110i −0.299438 + 0.518641i
\(81\) 185.945 704.887i 0.255069 0.966923i
\(82\) 1135.35 655.493i 1.52900 0.882770i
\(83\) 10.7079 + 18.5466i 0.0141608 + 0.0245272i 0.873019 0.487686i \(-0.162159\pi\)
−0.858858 + 0.512213i \(0.828826\pi\)
\(84\) −377.868 + 765.254i −0.490818 + 0.994001i
\(85\) −87.0290 + 150.739i −0.111054 + 0.192352i
\(86\) 1287.12i 1.61388i
\(87\) 566.780 647.555i 0.698451 0.797991i
\(88\) 25.5798 0.0309865
\(89\) −339.721 588.414i −0.404611 0.700806i 0.589665 0.807648i \(-0.299260\pi\)
−0.994276 + 0.106841i \(0.965926\pi\)
\(90\) −836.660 + 111.800i −0.979908 + 0.130942i
\(91\) 331.937 1231.51i 0.382379 1.41865i
\(92\) −940.467 + 542.979i −1.06577 + 0.615320i
\(93\) −47.1852 + 53.9098i −0.0526116 + 0.0601095i
\(94\) −251.780 + 145.366i −0.276268 + 0.159503i
\(95\) 655.544 378.479i 0.707973 0.408748i
\(96\) 888.963 1015.65i 0.945098 1.07979i
\(97\) −984.068 + 568.152i −1.03007 + 0.594713i −0.917005 0.398875i \(-0.869401\pi\)
−0.113067 + 0.993587i \(0.536067\pi\)
\(98\) −1408.74 4.17218i −1.45209 0.00430054i
\(99\) −118.152 153.361i −0.119947 0.155691i
\(100\) −297.365 515.051i −0.297365 0.515051i
\(101\) −1542.10 −1.51926 −0.759629 0.650357i \(-0.774619\pi\)
−0.759629 + 0.650357i \(0.774619\pi\)
\(102\) 321.410 367.216i 0.312003 0.356468i
\(103\) 418.265i 0.400125i −0.979783 0.200062i \(-0.935885\pi\)
0.979783 0.200062i \(-0.0641145\pi\)
\(104\) 122.844 212.772i 0.115825 0.200615i
\(105\) −406.654 609.274i −0.377956 0.566276i
\(106\) 603.662 + 1045.57i 0.553140 + 0.958066i
\(107\) 1368.79 790.270i 1.23669 0.714003i 0.268273 0.963343i \(-0.413547\pi\)
0.968416 + 0.249340i \(0.0802138\pi\)
\(108\) 1241.80 + 77.7626i 1.10641 + 0.0692843i
\(109\) 234.533 406.222i 0.206093 0.356964i −0.744387 0.667748i \(-0.767258\pi\)
0.950480 + 0.310784i \(0.100592\pi\)
\(110\) −112.081 + 194.130i −0.0971501 + 0.168269i
\(111\) 989.574 + 866.137i 0.846182 + 0.740631i
\(112\) 1006.70 + 271.343i 0.849324 + 0.228924i
\(113\) −1733.74 1000.97i −1.44333 0.833306i −0.445259 0.895402i \(-0.646888\pi\)
−0.998070 + 0.0620958i \(0.980222\pi\)
\(114\) −2008.99 + 684.136i −1.65052 + 0.562063i
\(115\) 932.066i 0.755788i
\(116\) 1272.00 + 734.388i 1.01812 + 0.587813i
\(117\) −1843.06 + 246.283i −1.45634 + 0.194606i
\(118\) 1894.34i 1.47786i
\(119\) 408.906 + 110.215i 0.314994 + 0.0849026i
\(120\) −45.4855 133.570i −0.0346020 0.101610i
\(121\) 1279.59 0.961373
\(122\) 1360.31 + 2356.12i 1.00948 + 1.74847i
\(123\) 321.998 1627.04i 0.236045 1.19273i
\(124\) −105.895 61.1388i −0.0766911 0.0442776i
\(125\) 1461.93 1.04607
\(126\) 786.813 + 1897.07i 0.556309 + 1.34130i
\(127\) 522.832 0.365306 0.182653 0.983177i \(-0.441532\pi\)
0.182653 + 0.983177i \(0.441532\pi\)
\(128\) 393.130 + 226.974i 0.271470 + 0.156733i
\(129\) 1225.33 + 1072.49i 0.836316 + 0.731995i
\(130\) 1076.51 + 1864.57i 0.726278 + 1.25795i
\(131\) 2561.88 1.70864 0.854321 0.519746i \(-0.173973\pi\)
0.854321 + 0.519746i \(0.173973\pi\)
\(132\) 217.622 248.637i 0.143497 0.163947i
\(133\) −1300.38 1304.24i −0.847799 0.850313i
\(134\) 2950.07i 1.90184i
\(135\) −590.712 + 889.658i −0.376596 + 0.567182i
\(136\) 70.6479 + 40.7886i 0.0445441 + 0.0257176i
\(137\) 1.22835i 0.000766021i 1.00000 0.000383011i \(0.000121916\pi\)
−1.00000 0.000383011i \(0.999878\pi\)
\(138\) −507.331 + 2563.52i −0.312948 + 1.58131i
\(139\) 1676.23 + 967.770i 1.02285 + 0.590541i 0.914927 0.403619i \(-0.132248\pi\)
0.107920 + 0.994160i \(0.465581\pi\)
\(140\) 885.357 882.739i 0.534474 0.532893i
\(141\) −71.4078 + 360.821i −0.0426498 + 0.215508i
\(142\) 190.866 330.590i 0.112797 0.195370i
\(143\) −246.901 + 427.645i −0.144384 + 0.250080i
\(144\) −201.325 1506.62i −0.116507 0.871885i
\(145\) −1091.74 + 630.317i −0.625271 + 0.361000i
\(146\) −2091.48 3622.55i −1.18556 2.05345i
\(147\) −1177.81 + 1337.65i −0.660842 + 0.750525i
\(148\) −1122.27 + 1943.83i −0.623311 + 1.07961i
\(149\) 2427.95i 1.33494i −0.744639 0.667468i \(-0.767378\pi\)
0.744639 0.667468i \(-0.232622\pi\)
\(150\) −1403.92 277.842i −0.764199 0.151238i
\(151\) −1396.38 −0.752552 −0.376276 0.926508i \(-0.622796\pi\)
−0.376276 + 0.926508i \(0.622796\pi\)
\(152\) −177.384 307.239i −0.0946565 0.163950i
\(153\) −81.7749 611.964i −0.0432099 0.323362i
\(154\) 526.613 + 141.942i 0.275556 + 0.0742726i
\(155\) 90.8889 52.4747i 0.0470992 0.0271927i
\(156\) −1023.05 3004.22i −0.525059 1.54186i
\(157\) −635.157 + 366.708i −0.322873 + 0.186411i −0.652672 0.757640i \(-0.726352\pi\)
0.329799 + 0.944051i \(0.393019\pi\)
\(158\) −2832.08 + 1635.10i −1.42600 + 0.823304i
\(159\) 1498.38 + 296.536i 0.747356 + 0.147905i
\(160\) −1712.34 + 988.618i −0.846075 + 0.488482i
\(161\) −2191.39 + 583.705i −1.07271 + 0.285729i
\(162\) 2108.92 2125.35i 1.02279 1.03076i
\(163\) −1504.67 2606.16i −0.723036 1.25233i −0.959777 0.280762i \(-0.909413\pi\)
0.236742 0.971573i \(-0.423920\pi\)
\(164\) 2830.83 1.34787
\(165\) 91.4204 + 268.460i 0.0431337 + 0.126664i
\(166\) 87.9577i 0.0411256i
\(167\) 40.1692 69.5751i 0.0186131 0.0322388i −0.856569 0.516033i \(-0.827408\pi\)
0.875182 + 0.483794i \(0.160742\pi\)
\(168\) −285.553 + 190.590i −0.131136 + 0.0875256i
\(169\) 1272.92 + 2204.77i 0.579392 + 1.00354i
\(170\) −619.105 + 357.440i −0.279313 + 0.161261i
\(171\) −1022.69 + 2482.62i −0.457353 + 1.11024i
\(172\) −1389.64 + 2406.94i −0.616043 + 1.06702i
\(173\) −1373.36 + 2378.73i −0.603553 + 1.04538i 0.388725 + 0.921354i \(0.372916\pi\)
−0.992278 + 0.124031i \(0.960418\pi\)
\(174\) 3345.77 1139.36i 1.45772 0.496405i
\(175\) −319.669 1200.13i −0.138084 0.518406i
\(176\) −349.580 201.830i −0.149719 0.0864405i
\(177\) 1803.41 + 1578.45i 0.765833 + 0.670304i
\(178\) 2790.56i 1.17507i
\(179\) −2491.90 1438.70i −1.04052 0.600745i −0.120540 0.992708i \(-0.538463\pi\)
−0.919981 + 0.391964i \(0.871796\pi\)
\(180\) −1685.28 694.237i −0.697851 0.287474i
\(181\) 320.544i 0.131634i −0.997832 0.0658172i \(-0.979035\pi\)
0.997832 0.0658172i \(-0.0209654\pi\)
\(182\) 3709.65 3698.68i 1.51087 1.50640i
\(183\) 3376.50 + 668.223i 1.36392 + 0.269926i
\(184\) −436.839 −0.175023
\(185\) −963.232 1668.37i −0.382801 0.663031i
\(186\) −278.540 + 94.8531i −0.109804 + 0.0373923i
\(187\) −141.994 81.9801i −0.0555273 0.0320587i
\(188\) −627.780 −0.243540
\(189\) 2461.62 + 831.684i 0.947389 + 0.320085i
\(190\) 3108.93 1.18708
\(191\) 818.447 + 472.531i 0.310056 + 0.179011i 0.646952 0.762531i \(-0.276044\pi\)
−0.336895 + 0.941542i \(0.609377\pi\)
\(192\) 3032.38 1032.63i 1.13981 0.388146i
\(193\) −393.384 681.362i −0.146717 0.254122i 0.783295 0.621650i \(-0.213537\pi\)
−0.930012 + 0.367528i \(0.880204\pi\)
\(194\) −4666.96 −1.72716
\(195\) 2672.07 + 528.813i 0.981287 + 0.194201i
\(196\) −2629.87 1528.76i −0.958409 0.557129i
\(197\) 5047.70i 1.82555i 0.408462 + 0.912775i \(0.366065\pi\)
−0.408462 + 0.912775i \(0.633935\pi\)
\(198\) −105.314 788.123i −0.0377999 0.282876i
\(199\) 1052.30 + 607.546i 0.374852 + 0.216421i 0.675576 0.737290i \(-0.263895\pi\)
−0.300724 + 0.953711i \(0.597228\pi\)
\(200\) 239.236i 0.0845829i
\(201\) −2808.46 2458.14i −0.985541 0.862606i
\(202\) −5485.09 3166.82i −1.91054 1.10305i
\(203\) 2165.65 + 2172.07i 0.748763 + 0.750984i
\(204\) 997.510 339.689i 0.342351 0.116583i
\(205\) −1214.84 + 2104.16i −0.413892 + 0.716882i
\(206\) 858.937 1487.72i 0.290509 0.503177i
\(207\) 2017.74 + 2619.03i 0.677500 + 0.879396i
\(208\) −3357.63 + 1938.53i −1.11928 + 0.646215i
\(209\) 356.522 + 617.514i 0.117996 + 0.204375i
\(210\) −195.236 3002.21i −0.0641550 0.986534i
\(211\) 312.466 541.206i 0.101948 0.176579i −0.810539 0.585684i \(-0.800826\pi\)
0.912487 + 0.409105i \(0.134159\pi\)
\(212\) 2606.99i 0.844570i
\(213\) −155.682 457.168i −0.0500807 0.147064i
\(214\) 6491.50 2.07360
\(215\) −1192.72 2065.85i −0.378338 0.655300i
\(216\) 416.963 + 276.854i 0.131346 + 0.0872107i
\(217\) −180.293 180.828i −0.0564014 0.0565687i
\(218\) 1668.41 963.259i 0.518345 0.299267i
\(219\) −5191.38 1027.40i −1.60183 0.317009i
\(220\) −419.188 + 242.018i −0.128462 + 0.0741676i
\(221\) −1363.81 + 787.399i −0.415113 + 0.239666i
\(222\) 1741.13 + 5112.91i 0.526384 + 1.54575i
\(223\) 2295.49 1325.30i 0.689316 0.397977i −0.114040 0.993476i \(-0.536379\pi\)
0.803356 + 0.595499i \(0.203046\pi\)
\(224\) 3396.70 + 3406.78i 1.01318 + 1.01618i
\(225\) −1434.32 + 1105.02i −0.424984 + 0.327414i
\(226\) −4111.14 7120.70i −1.21004 2.09585i
\(227\) 817.772 0.239108 0.119554 0.992828i \(-0.461854\pi\)
0.119554 + 0.992828i \(0.461854\pi\)
\(228\) −4495.49 889.676i −1.30579 0.258422i
\(229\) 702.979i 0.202857i −0.994843 0.101428i \(-0.967659\pi\)
0.994843 0.101428i \(-0.0323412\pi\)
\(230\) 1914.06 3315.25i 0.548737 0.950441i
\(231\) 573.928 383.062i 0.163470 0.109107i
\(232\) 295.416 + 511.675i 0.0835991 + 0.144798i
\(233\) −3559.17 + 2054.89i −1.00073 + 0.577769i −0.908463 0.417966i \(-0.862743\pi\)
−0.0922626 + 0.995735i \(0.529410\pi\)
\(234\) −7061.33 2908.86i −1.97271 0.812641i
\(235\) 269.408 466.629i 0.0747841 0.129530i
\(236\) −2045.23 + 3542.45i −0.564125 + 0.977092i
\(237\) −803.211 + 4058.59i −0.220144 + 1.11238i
\(238\) 1228.10 + 1231.74i 0.334478 + 0.335470i
\(239\) −2082.70 1202.45i −0.563677 0.325439i 0.190943 0.981601i \(-0.438845\pi\)
−0.754620 + 0.656162i \(0.772179\pi\)
\(240\) −432.280 + 2184.29i −0.116265 + 0.587481i
\(241\) 726.363i 0.194146i −0.995277 0.0970729i \(-0.969052\pi\)
0.995277 0.0970729i \(-0.0309480\pi\)
\(242\) 4551.35 + 2627.72i 1.20897 + 0.698002i
\(243\) −266.080 3778.64i −0.0702430 0.997530i
\(244\) 5874.66i 1.54134i
\(245\) 2264.92 1298.73i 0.590615 0.338664i
\(246\) 4486.55 5125.95i 1.16281 1.32853i
\(247\) 6848.60 1.76423
\(248\) −24.5937 42.5976i −0.00629720 0.0109071i
\(249\) 83.7357 + 73.2906i 0.0213114 + 0.0186530i
\(250\) 5199.92 + 3002.17i 1.31549 + 0.759496i
\(251\) −529.985 −0.133276 −0.0666382 0.997777i \(-0.521227\pi\)
−0.0666382 + 0.997777i \(0.521227\pi\)
\(252\) −576.826 + 4397.05i −0.144193 + 1.09916i
\(253\) 877.994 0.218178
\(254\) 1859.66 + 1073.67i 0.459390 + 0.265229i
\(255\) −175.585 + 887.224i −0.0431199 + 0.217883i
\(256\) −1533.75 2656.53i −0.374450 0.648567i
\(257\) 1948.86 0.473021 0.236511 0.971629i \(-0.423996\pi\)
0.236511 + 0.971629i \(0.423996\pi\)
\(258\) 2155.95 + 6331.03i 0.520246 + 1.52772i
\(259\) −3319.30 + 3309.48i −0.796337 + 0.793982i
\(260\) 4649.05i 1.10893i
\(261\) 1703.19 4134.54i 0.403927 0.980543i
\(262\) 9112.31 + 5260.99i 2.14870 + 1.24055i
\(263\) 506.885i 0.118844i 0.998233 + 0.0594218i \(0.0189257\pi\)
−0.998233 + 0.0594218i \(0.981074\pi\)
\(264\) 125.821 42.8467i 0.0293324 0.00998876i
\(265\) −1937.78 1118.78i −0.449195 0.259343i
\(266\) −1946.96 7309.45i −0.448782 1.68485i
\(267\) −2656.62 2325.23i −0.608922 0.532966i
\(268\) 3185.06 5516.69i 0.725965 1.25741i
\(269\) 3851.69 6671.33i 0.873018 1.51211i 0.0141598 0.999900i \(-0.495493\pi\)
0.858859 0.512213i \(-0.171174\pi\)
\(270\) −3928.07 + 1951.34i −0.885388 + 0.439833i
\(271\) −4585.66 + 2647.53i −1.02789 + 0.593455i −0.916380 0.400308i \(-0.868903\pi\)
−0.111513 + 0.993763i \(0.535570\pi\)
\(272\) −643.662 1114.85i −0.143484 0.248522i
\(273\) −430.081 6613.51i −0.0953469 1.46618i
\(274\) −2.52250 + 4.36910i −0.000556167 + 0.000963310i
\(275\) 480.837i 0.105438i
\(276\) −3716.44 + 4246.09i −0.810520 + 0.926032i
\(277\) 4216.97 0.914705 0.457353 0.889285i \(-0.348798\pi\)
0.457353 + 0.889285i \(0.348798\pi\)
\(278\) 3974.77 + 6884.50i 0.857521 + 1.48527i
\(279\) −141.793 + 344.206i −0.0304263 + 0.0738605i
\(280\) 485.976 129.446i 0.103724 0.0276281i
\(281\) −7104.37 + 4101.71i −1.50823 + 0.870774i −0.508271 + 0.861197i \(0.669715\pi\)
−0.999954 + 0.00957745i \(0.996951\pi\)
\(282\) −994.960 + 1136.76i −0.210103 + 0.240046i
\(283\) 1358.81 784.511i 0.285417 0.164786i −0.350456 0.936579i \(-0.613973\pi\)
0.635873 + 0.771794i \(0.280640\pi\)
\(284\) 713.847 412.140i 0.149152 0.0861127i
\(285\) 2590.51 2959.70i 0.538416 0.615149i
\(286\) −1756.40 + 1014.06i −0.363140 + 0.209659i
\(287\) 5707.90 + 1538.49i 1.17396 + 0.316426i
\(288\) 2671.36 6484.80i 0.546568 1.32681i
\(289\) 2195.06 + 3801.95i 0.446785 + 0.773854i
\(290\) −5177.61 −1.04841
\(291\) −3888.74 + 4442.95i −0.783374 + 0.895018i
\(292\) 9032.32i 1.81019i
\(293\) 227.022 393.213i 0.0452653 0.0784019i −0.842505 0.538688i \(-0.818920\pi\)
0.887770 + 0.460287i \(0.152253\pi\)
\(294\) −6936.27 + 2339.15i −1.37596 + 0.464021i
\(295\) −1755.40 3040.45i −0.346452 0.600073i
\(296\) −781.927 + 451.446i −0.153542 + 0.0886478i
\(297\) −838.046 556.443i −0.163732 0.108714i
\(298\) 4985.97 8635.94i 0.969226 1.67875i
\(299\) 4216.45 7303.11i 0.815531 1.41254i
\(300\) −2325.39 2035.32i −0.447522 0.391698i
\(301\) −4110.10 + 4097.95i −0.787051 + 0.784723i
\(302\) −4966.75 2867.56i −0.946372 0.546388i
\(303\) −7585.25 + 2583.06i −1.43816 + 0.489745i
\(304\) 5598.41i 1.05622i
\(305\) −4366.64 2521.08i −0.819780 0.473300i
\(306\) 965.846 2344.62i 0.180437 0.438016i
\(307\) 74.2025i 0.0137947i 0.999976 + 0.00689733i \(0.00219550\pi\)
−0.999976 + 0.00689733i \(0.997804\pi\)
\(308\) 831.528 + 833.995i 0.153834 + 0.154290i
\(309\) −700.603 2057.35i −0.128983 0.378765i
\(310\) 431.042 0.0789728
\(311\) 3212.96 + 5565.00i 0.585820 + 1.01467i 0.994773 + 0.102114i \(0.0325608\pi\)
−0.408953 + 0.912556i \(0.634106\pi\)
\(312\) 247.843 1252.34i 0.0449723 0.227243i
\(313\) 6681.09 + 3857.33i 1.20651 + 0.696578i 0.961995 0.273067i \(-0.0880382\pi\)
0.244514 + 0.969646i \(0.421372\pi\)
\(314\) −3012.24 −0.541372
\(315\) −3020.78 2315.72i −0.540323 0.414210i
\(316\) −7061.41 −1.25707
\(317\) −265.053 153.028i −0.0469617 0.0271133i 0.476335 0.879264i \(-0.341965\pi\)
−0.523297 + 0.852150i \(0.675298\pi\)
\(318\) 4720.63 + 4131.79i 0.832452 + 0.728613i
\(319\) −593.751 1028.41i −0.104212 0.180501i
\(320\) −4692.62 −0.819767
\(321\) 5409.03 6179.90i 0.940507 1.07454i
\(322\) −8993.22 2424.01i −1.55644 0.419517i
\(323\) 2273.98i 0.391727i
\(324\) 6238.38 1697.54i 1.06968 0.291074i
\(325\) 3999.58 + 2309.16i 0.682636 + 0.394120i
\(326\) 12359.8i 2.09983i
\(327\) 473.181 2390.96i 0.0800213 0.404344i
\(328\) 986.172 + 569.367i 0.166013 + 0.0958476i
\(329\) −1265.81 341.184i −0.212117 0.0571734i
\(330\) −226.129 + 1142.62i −0.0377212 + 0.190603i
\(331\) 2049.56 3549.94i 0.340344 0.589493i −0.644152 0.764897i \(-0.722790\pi\)
0.984497 + 0.175404i \(0.0561231\pi\)
\(332\) −94.9642 + 164.483i −0.0156983 + 0.0271903i
\(333\) 6318.29 + 2602.77i 1.03976 + 0.428321i
\(334\) 285.755 164.981i 0.0468138 0.0270280i
\(335\) 2733.70 + 4734.91i 0.445845 + 0.772227i
\(336\) 5406.24 351.571i 0.877781 0.0570827i
\(337\) −3390.68 + 5872.83i −0.548078 + 0.949298i 0.450329 + 0.892863i \(0.351307\pi\)
−0.998406 + 0.0564355i \(0.982026\pi\)
\(338\) 10456.2i 1.68266i
\(339\) −10204.5 2019.51i −1.63490 0.323554i
\(340\) −1543.65 −0.246224
\(341\) 49.4305 + 85.6161i 0.00784989 + 0.0135964i
\(342\) −8735.83 + 6730.21i −1.38123 + 1.06412i
\(343\) −4471.86 4511.77i −0.703959 0.710241i
\(344\) −968.216 + 559.000i −0.151752 + 0.0876141i
\(345\) −1561.23 4584.62i −0.243634 0.715442i
\(346\) −9769.78 + 5640.59i −1.51800 + 0.876416i
\(347\) −8450.67 + 4878.99i −1.30736 + 0.754807i −0.981656 0.190663i \(-0.938936\pi\)
−0.325709 + 0.945470i \(0.605603\pi\)
\(348\) 7486.78 + 1481.66i 1.15326 + 0.228234i
\(349\) −2576.08 + 1487.30i −0.395113 + 0.228119i −0.684373 0.729132i \(-0.739924\pi\)
0.289260 + 0.957251i \(0.406591\pi\)
\(350\) 1327.52 4925.18i 0.202739 0.752176i
\(351\) −8653.07 + 4298.58i −1.31586 + 0.653679i
\(352\) −931.265 1613.00i −0.141013 0.244242i
\(353\) 9788.58 1.47590 0.737951 0.674854i \(-0.235793\pi\)
0.737951 + 0.674854i \(0.235793\pi\)
\(354\) 3173.05 + 9317.81i 0.476401 + 1.39897i
\(355\) 707.470i 0.105771i
\(356\) 3012.85 5218.41i 0.448542 0.776897i
\(357\) 2195.93 142.803i 0.325548 0.0211706i
\(358\) −5908.94 10234.6i −0.872338 1.51093i
\(359\) −3444.96 + 1988.95i −0.506456 + 0.292403i −0.731376 0.681975i \(-0.761121\pi\)
0.224919 + 0.974377i \(0.427788\pi\)
\(360\) −447.465 580.811i −0.0655097 0.0850317i
\(361\) 1515.14 2624.30i 0.220898 0.382606i
\(362\) 658.259 1140.14i 0.0955727 0.165537i
\(363\) 6294.00 2143.34i 0.910053 0.309906i
\(364\) 10930.4 2911.46i 1.57393 0.419236i
\(365\) 6713.72 + 3876.17i 0.962773 + 0.555858i
\(366\) 10637.6 + 9310.68i 1.51922 + 1.32972i
\(367\) 3534.28i 0.502692i −0.967897 0.251346i \(-0.919127\pi\)
0.967897 0.251346i \(-0.0808732\pi\)
\(368\) 5969.95 + 3446.75i 0.845667 + 0.488246i
\(369\) −1141.49 8542.39i −0.161040 1.20515i
\(370\) 7912.26i 1.11173i
\(371\) −1416.84 + 5256.56i −0.198271 + 0.735599i
\(372\) −623.284 123.350i −0.0868704 0.0171920i
\(373\) 4725.85 0.656019 0.328010 0.944674i \(-0.393622\pi\)
0.328010 + 0.944674i \(0.393622\pi\)
\(374\) −336.704 583.189i −0.0465523 0.0806309i
\(375\) 7190.89 2448.76i 0.990229 0.337209i
\(376\) −218.698 126.266i −0.0299960 0.0173182i
\(377\) −11405.6 −1.55815
\(378\) 7047.78 + 8013.32i 0.958992 + 1.09037i
\(379\) 5183.61 0.702545 0.351272 0.936273i \(-0.385749\pi\)
0.351272 + 0.936273i \(0.385749\pi\)
\(380\) 5813.76 + 3356.58i 0.784841 + 0.453128i
\(381\) 2571.69 875.755i 0.345805 0.117759i
\(382\) 1940.75 + 3361.48i 0.259941 + 0.450231i
\(383\) 6894.41 0.919811 0.459906 0.887968i \(-0.347883\pi\)
0.459906 + 0.887968i \(0.347883\pi\)
\(384\) 2313.90 + 457.931i 0.307502 + 0.0608559i
\(385\) −976.754 + 260.171i −0.129299 + 0.0344404i
\(386\) 3231.37i 0.426094i
\(387\) 7823.58 + 3222.86i 1.02764 + 0.423326i
\(388\) −8727.32 5038.72i −1.14191 0.659284i
\(389\) 2814.17i 0.366797i 0.983039 + 0.183398i \(0.0587098\pi\)
−0.983039 + 0.183398i \(0.941290\pi\)
\(390\) 8418.30 + 7368.22i 1.09302 + 0.956677i
\(391\) 2424.90 + 1400.02i 0.313638 + 0.181079i
\(392\) −608.684 1061.52i −0.0784265 0.136773i
\(393\) 12601.3 4291.20i 1.61743 0.550795i
\(394\) −10365.8 + 17954.1i −1.32544 + 2.29572i
\(395\) 3030.36 5248.75i 0.386011 0.668590i
\(396\) 653.962 1587.51i 0.0829869 0.201453i
\(397\) −5248.35 + 3030.14i −0.663494 + 0.383068i −0.793607 0.608431i \(-0.791799\pi\)
0.130113 + 0.991499i \(0.458466\pi\)
\(398\) 2495.28 + 4321.95i 0.314264 + 0.544320i
\(399\) −8580.90 4237.08i −1.07665 0.531627i
\(400\) −1887.63 + 3269.47i −0.235954 + 0.408684i
\(401\) 12064.2i 1.50239i −0.660080 0.751196i \(-0.729477\pi\)
0.660080 0.751196i \(-0.270523\pi\)
\(402\) −4941.43 14510.7i −0.613075 1.80032i
\(403\) 949.535 0.117369
\(404\) −6838.15 11844.0i −0.842106 1.45857i
\(405\) −1415.38 + 5365.48i −0.173656 + 0.658303i
\(406\) 3242.47 + 12173.1i 0.396357 + 1.48804i
\(407\) 1571.58 907.352i 0.191401 0.110506i
\(408\) 415.822 + 82.2929i 0.0504566 + 0.00998555i
\(409\) 292.292 168.755i 0.0353372 0.0204019i −0.482227 0.876046i \(-0.660172\pi\)
0.517565 + 0.855644i \(0.326839\pi\)
\(410\) −8642.07 + 4989.50i −1.04098 + 0.601010i
\(411\) 2.05751 + 6.04196i 0.000246933 + 0.000725129i
\(412\) 3212.46 1854.71i 0.384142 0.221784i
\(413\) −6049.11 + 6031.23i −0.720720 + 0.718589i
\(414\) 1798.51 + 13459.2i 0.213507 + 1.59778i
\(415\) −81.5067 141.174i −0.00964098 0.0166987i
\(416\) −17889.1 −2.10838
\(417\) 9866.01 + 1952.52i 1.15861 + 0.229294i
\(418\) 2928.57i 0.342682i
\(419\) 4094.25 7091.45i 0.477368 0.826826i −0.522295 0.852765i \(-0.674924\pi\)
0.999664 + 0.0259386i \(0.00825744\pi\)
\(420\) 2876.26 5824.98i 0.334160 0.676738i
\(421\) 958.165 + 1659.59i 0.110922 + 0.192122i 0.916142 0.400853i \(-0.131286\pi\)
−0.805220 + 0.592976i \(0.797953\pi\)
\(422\) 2222.81 1283.34i 0.256409 0.148038i
\(423\) 253.143 + 1894.40i 0.0290975 + 0.217752i
\(424\) −524.345 + 908.193i −0.0600577 + 0.104023i
\(425\) −766.724 + 1328.01i −0.0875096 + 0.151571i
\(426\) 385.082 1945.80i 0.0437964 0.221301i
\(427\) −3192.74 + 11845.3i −0.361844 + 1.34247i
\(428\) 12139.2 + 7008.59i 1.37096 + 0.791526i
\(429\) −498.135 + 2517.05i −0.0560610 + 0.283274i
\(430\) 9797.31i 1.09876i
\(431\) −8604.78 4967.97i −0.961665 0.555218i −0.0649800 0.997887i \(-0.520698\pi\)
−0.896685 + 0.442669i \(0.854032\pi\)
\(432\) −3513.89 7073.48i −0.391347 0.787785i
\(433\) 4551.00i 0.505098i 0.967584 + 0.252549i \(0.0812688\pi\)
−0.967584 + 0.252549i \(0.918731\pi\)
\(434\) −269.940 1013.43i −0.0298561 0.112088i
\(435\) −4314.23 + 4929.08i −0.475521 + 0.543290i
\(436\) 4159.96 0.456940
\(437\) −6088.49 10545.6i −0.666481 1.15438i
\(438\) −16355.3 14315.2i −1.78422 1.56166i
\(439\) −6424.18 3709.00i −0.698427 0.403237i 0.108335 0.994114i \(-0.465448\pi\)
−0.806761 + 0.590878i \(0.798782\pi\)
\(440\) −194.709 −0.0210963
\(441\) −3552.77 + 8552.42i −0.383627 + 0.923488i
\(442\) −6467.91 −0.696035
\(443\) −5479.67 3163.69i −0.587691 0.339303i 0.176493 0.984302i \(-0.443525\pi\)
−0.764184 + 0.644999i \(0.776858\pi\)
\(444\) −2264.24 + 11441.1i −0.242018 + 1.22290i
\(445\) 2585.90 + 4478.91i 0.275468 + 0.477125i
\(446\) 10886.4 1.15580
\(447\) −4066.87 11942.5i −0.430327 1.26367i
\(448\) 2938.75 + 11032.9i 0.309917 + 1.16352i
\(449\) 14396.4i 1.51316i −0.653904 0.756578i \(-0.726870\pi\)
0.653904 0.756578i \(-0.273130\pi\)
\(450\) −7370.96 + 984.960i −0.772157 + 0.103181i
\(451\) −1982.09 1144.36i −0.206946 0.119481i
\(452\) 17754.5i 1.84757i
\(453\) −6868.45 + 2338.96i −0.712380 + 0.242591i
\(454\) 2908.72 + 1679.35i 0.300690 + 0.173603i
\(455\) −2526.65 + 9374.03i −0.260332 + 0.965849i
\(456\) −1387.15 1214.11i −0.142454 0.124685i
\(457\) −2573.61 + 4457.63i −0.263432 + 0.456278i −0.967152 0.254200i \(-0.918188\pi\)
0.703719 + 0.710478i \(0.251521\pi\)
\(458\) 1443.62 2500.42i 0.147283 0.255102i
\(459\) −1427.28 2873.13i −0.145141 0.292171i
\(460\) 7158.68 4133.06i 0.725598 0.418924i
\(461\) 446.618 + 773.565i 0.0451217 + 0.0781530i 0.887704 0.460414i \(-0.152299\pi\)
−0.842583 + 0.538567i \(0.818966\pi\)
\(462\) 2828.04 183.909i 0.284789 0.0185200i
\(463\) 5520.47 9561.73i 0.554121 0.959765i −0.443851 0.896101i \(-0.646388\pi\)
0.997971 0.0636644i \(-0.0202787\pi\)
\(464\) 9323.59i 0.932838i
\(465\) 359.165 410.352i 0.0358191 0.0409239i
\(466\) −16879.4 −1.67795
\(467\) 4900.18 + 8487.36i 0.485553 + 0.841003i 0.999862 0.0166023i \(-0.00528493\pi\)
−0.514309 + 0.857605i \(0.671952\pi\)
\(468\) −10064.3 13063.4i −0.994061 1.29029i
\(469\) 9420.34 9392.49i 0.927486 0.924744i
\(470\) 1916.51 1106.50i 0.188089 0.108593i
\(471\) −2509.95 + 2867.66i −0.245546 + 0.280541i
\(472\) −1424.99 + 822.718i −0.138963 + 0.0802302i
\(473\) 1946.00 1123.52i 0.189169 0.109217i
\(474\) −11191.5 + 12786.5i −1.08448 + 1.23904i
\(475\) 5775.33 3334.39i 0.557875 0.322089i
\(476\) 966.711 + 3629.30i 0.0930864 + 0.349472i
\(477\) 7866.92 1051.23i 0.755139 0.100907i
\(478\) −4938.63 8553.95i −0.472568 0.818512i
\(479\) 138.670 0.0132275 0.00661377 0.999978i \(-0.497895\pi\)
0.00661377 + 0.999978i \(0.497895\pi\)
\(480\) −6766.63 + 7730.98i −0.643444 + 0.735145i
\(481\) 17429.8i 1.65224i
\(482\) 1491.64 2583.59i 0.140959 0.244148i
\(483\) −9801.24 + 6541.74i −0.923337 + 0.616273i
\(484\) 5674.08 + 9827.80i 0.532878 + 0.922971i
\(485\) 7490.56 4324.68i 0.701296 0.404894i
\(486\) 6813.28 13986.6i 0.635919 1.30544i
\(487\) −9148.40 + 15845.5i −0.851239 + 1.47439i 0.0288514 + 0.999584i \(0.490815\pi\)
−0.880091 + 0.474806i \(0.842518\pi\)
\(488\) −1181.57 + 2046.55i −0.109605 + 0.189842i
\(489\) −11766.5 10298.8i −1.08814 0.952406i
\(490\) 10723.1 + 31.7579i 0.988614 + 0.00292791i
\(491\) 5097.03 + 2942.77i 0.468484 + 0.270479i 0.715605 0.698505i \(-0.246151\pi\)
−0.247121 + 0.968985i \(0.579484\pi\)
\(492\) 13924.2 4741.70i 1.27592 0.434497i
\(493\) 3787.09i 0.345967i
\(494\) 24359.7 + 14064.1i 2.21861 + 1.28092i
\(495\) 899.352 + 1167.36i 0.0816623 + 0.105998i
\(496\) 776.201i 0.0702670i
\(497\) 1663.34 443.053i 0.150123 0.0399872i
\(498\) 147.331 + 432.644i 0.0132572 + 0.0389302i
\(499\) 534.725 0.0479711 0.0239856 0.999712i \(-0.492364\pi\)
0.0239856 + 0.999712i \(0.492364\pi\)
\(500\) 6482.63 + 11228.3i 0.579824 + 1.00429i
\(501\) 81.0433 409.508i 0.00722704 0.0365179i
\(502\) −1885.10 1088.36i −0.167602 0.0967649i
\(503\) −10504.5 −0.931155 −0.465578 0.885007i \(-0.654153\pi\)
−0.465578 + 0.885007i \(0.654153\pi\)
\(504\) −1085.33 + 1415.77i −0.0959213 + 0.125126i
\(505\) 11738.2 1.03434
\(506\) 3122.93 + 1803.02i 0.274369 + 0.158407i
\(507\) 9954.25 + 8712.57i 0.871960 + 0.763193i
\(508\) 2318.40 + 4015.58i 0.202485 + 0.350714i
\(509\) 2817.87 0.245383 0.122691 0.992445i \(-0.460847\pi\)
0.122691 + 0.992445i \(0.460847\pi\)
\(510\) −2446.51 + 2795.18i −0.212419 + 0.242692i
\(511\) 4908.85 18212.2i 0.424961 1.57663i
\(512\) 16230.2i 1.40094i
\(513\) −871.962 + 13924.5i −0.0750449 + 1.19840i
\(514\) 6931.87 + 4002.12i 0.594848 + 0.343435i
\(515\) 3183.76i 0.272414i
\(516\) −2803.68 + 14166.8i −0.239196 + 1.20864i
\(517\) 439.558 + 253.779i 0.0373921 + 0.0215884i
\(518\) −18602.6 + 4955.05i −1.57790 + 0.420294i
\(519\) −2770.82 + 14000.8i −0.234346 + 1.18414i
\(520\) −935.065 + 1619.58i −0.0788564 + 0.136583i
\(521\) −5520.76 + 9562.24i −0.464240 + 0.804087i −0.999167 0.0408113i \(-0.987006\pi\)
0.534927 + 0.844898i \(0.320339\pi\)
\(522\) 14548.6 11208.5i 1.21988 0.939812i
\(523\) −4094.57 + 2364.00i −0.342338 + 0.197649i −0.661306 0.750117i \(-0.729997\pi\)
0.318967 + 0.947766i \(0.396664\pi\)
\(524\) 11360.1 + 19676.3i 0.947080 + 1.64039i
\(525\) −3582.61 5367.69i −0.297825 0.446219i
\(526\) −1040.92 + 1802.93i −0.0862860 + 0.149452i
\(527\) 315.280i 0.0260604i
\(528\) −2057.58 407.202i −0.169592 0.0335629i
\(529\) −2826.93 −0.232344
\(530\) −4594.97 7958.72i −0.376590 0.652273i
\(531\) 11514.5 + 4743.30i 0.941029 + 0.387649i
\(532\) 4250.83 15770.9i 0.346423 1.28525i
\(533\) −19037.5 + 10991.3i −1.54710 + 0.893218i
\(534\) −4674.25 13726.1i −0.378792 1.11234i
\(535\) −10419.0 + 6015.40i −0.841966 + 0.486109i
\(536\) 2219.15 1281.23i 0.178830 0.103247i
\(537\) −14666.9 2902.64i −1.17863 0.233256i
\(538\) 27400.1 15819.5i 2.19573 1.26770i
\(539\) 1223.38 + 2133.53i 0.0977641 + 0.170496i
\(540\) −9452.36 591.915i −0.753268 0.0471703i
\(541\) 11254.7 + 19493.8i 0.894415 + 1.54917i 0.834527 + 0.550967i \(0.185741\pi\)
0.0598879 + 0.998205i \(0.480926\pi\)
\(542\) −21747.6 −1.72350
\(543\) −536.917 1576.68i −0.0424334 0.124607i
\(544\) 5939.84i 0.468140i
\(545\) −1785.22 + 3092.10i −0.140313 + 0.243029i
\(546\) 12051.6 24406.7i 0.944614 1.91302i
\(547\) −1219.31 2111.91i −0.0953088 0.165080i 0.814429 0.580264i \(-0.197051\pi\)
−0.909737 + 0.415184i \(0.863717\pi\)
\(548\) −9.43426 + 5.44687i −0.000735422 + 0.000424596i
\(549\) 17727.5 2368.88i 1.37813 0.184155i
\(550\) −987.432 + 1710.28i −0.0765532 + 0.132594i
\(551\) −8234.79 + 14263.1i −0.636686 + 1.10277i
\(552\) −2148.71 + 731.714i −0.165680 + 0.0564200i
\(553\) −14238.2 3837.71i −1.09488 0.295110i
\(554\) 14999.3 + 8659.85i 1.15029 + 0.664119i
\(555\) −7532.47 6592.88i −0.576100 0.504238i
\(556\) 17165.5i 1.30932i
\(557\) 9826.37 + 5673.25i 0.747498 + 0.431568i 0.824789 0.565440i \(-0.191294\pi\)
−0.0772911 + 0.997009i \(0.524627\pi\)
\(558\) −1211.19 + 933.121i −0.0918887 + 0.0707924i
\(559\) 21582.3i 1.63298i
\(560\) −7662.84 2065.42i −0.578239 0.155857i
\(561\) −835.753 165.399i −0.0628976 0.0124477i
\(562\) −33692.6 −2.52889
\(563\) 8427.86 + 14597.5i 0.630891 + 1.09274i 0.987370 + 0.158432i \(0.0506440\pi\)
−0.356478 + 0.934304i \(0.616023\pi\)
\(564\) −3087.90 + 1051.54i −0.230539 + 0.0785071i
\(565\) 13196.9 + 7619.23i 0.982651 + 0.567334i
\(566\) 6444.19 0.478568
\(567\) 13501.2 32.4028i 0.999997 0.00239999i
\(568\) 331.576 0.0244940
\(569\) −10320.6 5958.57i −0.760387 0.439009i 0.0690479 0.997613i \(-0.478004\pi\)
−0.829435 + 0.558604i \(0.811337\pi\)
\(570\) 15292.1 5207.52i 1.12371 0.382665i
\(571\) −10204.7 17675.0i −0.747902 1.29540i −0.948826 0.315798i \(-0.897728\pi\)
0.200924 0.979607i \(-0.435606\pi\)
\(572\) −4379.34 −0.320121
\(573\) 4817.25 + 953.353i 0.351210 + 0.0695059i
\(574\) 17143.0 + 17193.8i 1.24657 + 1.25027i
\(575\) 8211.49i 0.595552i
\(576\) 13185.9 10158.6i 0.953839 0.734852i
\(577\) −3374.84 1948.46i −0.243495 0.140582i 0.373287 0.927716i \(-0.378231\pi\)
−0.616782 + 0.787134i \(0.711564\pi\)
\(578\) 18030.8i 1.29755i
\(579\) −3076.26 2692.53i −0.220803 0.193261i
\(580\) −9682.23 5590.04i −0.693160 0.400196i
\(581\) −280.872 + 280.041i −0.0200560 + 0.0199967i
\(582\) −22955.7 + 7817.26i −1.63496 + 0.556763i
\(583\) 1053.87 1825.36i 0.0748660 0.129672i
\(584\) 1816.67 3146.57i 0.128724 0.222956i
\(585\) 14029.1 1874.66i 0.991506 0.132492i
\(586\) 1614.98 932.410i 0.113847 0.0657295i
\(587\) 8643.77 + 14971.5i 0.607780 + 1.05271i 0.991606 + 0.129300i \(0.0412730\pi\)
−0.383826 + 0.923406i \(0.625394\pi\)
\(588\) −15496.5 3114.53i −1.08684 0.218437i
\(589\) 685.557 1187.42i 0.0479591 0.0830675i
\(590\) 14419.4i 1.00616i
\(591\) 8455.00 + 24828.5i 0.588481 + 1.72810i
\(592\) 14248.0 0.989173
\(593\) 985.742 + 1707.36i 0.0682623 + 0.118234i 0.898136 0.439717i \(-0.144921\pi\)
−0.829874 + 0.557951i \(0.811588\pi\)
\(594\) −1838.14 3700.19i −0.126969 0.255590i
\(595\) −3112.52 838.939i −0.214455 0.0578036i
\(596\) 18647.7 10766.3i 1.28161 0.739939i
\(597\) 6193.68 + 1225.75i 0.424607 + 0.0840314i
\(598\) 29994.9 17317.6i 2.05114 1.18423i
\(599\) 12120.3 6997.65i 0.826747 0.477323i −0.0259904 0.999662i \(-0.508274\pi\)
0.852738 + 0.522339i \(0.174941\pi\)
\(600\) −400.726 1176.75i −0.0272660 0.0800676i
\(601\) −17296.5 + 9986.12i −1.17394 + 0.677774i −0.954605 0.297875i \(-0.903722\pi\)
−0.219335 + 0.975650i \(0.570389\pi\)
\(602\) −23034.6 + 6135.56i −1.55950 + 0.415393i
\(603\) −17931.6 7386.79i −1.21100 0.498861i
\(604\) −6191.95 10724.8i −0.417131 0.722492i
\(605\) −9740.00 −0.654525
\(606\) −32284.4 6389.21i −2.16413 0.428290i
\(607\) 12997.8i 0.869136i 0.900639 + 0.434568i \(0.143099\pi\)
−0.900639 + 0.434568i \(0.856901\pi\)
\(608\) −12915.8 + 22370.8i −0.861522 + 1.49220i
\(609\) 14290.6 + 7056.42i 0.950878 + 0.469525i
\(610\) −10354.4 17934.4i −0.687276 1.19040i
\(611\) 4221.84 2437.48i 0.279538 0.161391i
\(612\) 4337.53 3341.70i 0.286494 0.220719i
\(613\) −3450.80 + 5976.96i −0.227368 + 0.393812i −0.957027 0.289998i \(-0.906345\pi\)
0.729659 + 0.683811i \(0.239679\pi\)
\(614\) −152.380 + 263.930i −0.0100156 + 0.0173475i
\(615\) −2450.99 + 12384.7i −0.160705 + 0.812034i
\(616\) 121.936 + 457.783i 0.00797557 + 0.0299425i
\(617\) −8207.48 4738.59i −0.535528 0.309187i 0.207737 0.978185i \(-0.433390\pi\)
−0.743265 + 0.668998i \(0.766724\pi\)
\(618\) 1732.95 8756.50i 0.112798 0.569964i
\(619\) 15581.4i 1.01174i −0.862609 0.505871i \(-0.831171\pi\)
0.862609 0.505871i \(-0.168829\pi\)
\(620\) 806.058 + 465.378i 0.0522130 + 0.0301452i
\(621\) 14311.7 + 9502.65i 0.924814 + 0.614055i
\(622\) 26392.1i 1.70133i
\(623\) 8911.00 8884.65i 0.573053 0.571358i
\(624\) −13268.3 + 15159.3i −0.851215 + 0.972527i
\(625\) −2745.44 −0.175708
\(626\) 15842.6 + 27440.2i 1.01150 + 1.75196i
\(627\) 2788.00 + 2440.23i 0.177579 + 0.155428i
\(628\) −5632.96 3252.19i −0.357929 0.206651i
\(629\) 5787.32 0.366861
\(630\) −5989.09 14440.2i −0.378748 0.913190i
\(631\) 7028.73 0.443438 0.221719 0.975111i \(-0.428833\pi\)
0.221719 + 0.975111i \(0.428833\pi\)
\(632\) −2459.97 1420.26i −0.154830 0.0893910i
\(633\) 630.415 3185.46i 0.0395841 0.200017i
\(634\) −628.509 1088.61i −0.0393711 0.0681928i
\(635\) −3979.71 −0.248709
\(636\) 4366.76 + 12823.2i 0.272254 + 0.799485i
\(637\) 23621.7 + 69.9588i 1.46927 + 0.00435144i
\(638\) 4877.23i 0.302651i
\(639\) −1531.53 1987.93i −0.0948145 0.123069i
\(640\) −2992.44 1727.69i −0.184823 0.106707i
\(641\) 19240.0i 1.18555i −0.805369 0.592773i \(-0.798033\pi\)
0.805369 0.592773i \(-0.201967\pi\)
\(642\) 31930.2 10873.4i 1.96290 0.668441i
\(643\) 2402.55 + 1387.11i 0.147352 + 0.0850737i 0.571863 0.820349i \(-0.306221\pi\)
−0.424511 + 0.905423i \(0.639554\pi\)
\(644\) −14200.4 14242.5i −0.868905 0.871482i
\(645\) −9327.04 8163.60i −0.569383 0.498359i
\(646\) −4669.79 + 8088.31i −0.284412 + 0.492616i
\(647\) 4830.91 8367.38i 0.293544 0.508432i −0.681101 0.732189i \(-0.738499\pi\)
0.974645 + 0.223757i \(0.0718321\pi\)
\(648\) 2514.68 + 663.358i 0.152447 + 0.0402147i
\(649\) 2864.06 1653.56i 0.173227 0.100012i
\(650\) 9484.04 + 16426.8i 0.572299 + 0.991251i
\(651\) −1189.71 587.456i −0.0716259 0.0353675i
\(652\) 13344.3 23113.0i 0.801540 1.38831i
\(653\) 11885.8i 0.712294i −0.934430 0.356147i \(-0.884090\pi\)
0.934430 0.356147i \(-0.115910\pi\)
\(654\) 6593.06 7532.68i 0.394203 0.450384i
\(655\) −19500.6 −1.16328
\(656\) −8984.86 15562.2i −0.534756 0.926224i
\(657\) −27256.1 + 3642.16i −1.61851 + 0.216277i
\(658\) −3801.71 3812.99i −0.225237 0.225906i
\(659\) 20497.2 11834.1i 1.21162 0.699529i 0.248508 0.968630i \(-0.420060\pi\)
0.963112 + 0.269100i \(0.0867263\pi\)
\(660\) −1656.50 + 1892.58i −0.0976959 + 0.111619i
\(661\) −8316.03 + 4801.26i −0.489344 + 0.282523i −0.724302 0.689483i \(-0.757838\pi\)
0.234959 + 0.972005i \(0.424505\pi\)
\(662\) 14580.1 8417.83i 0.856000 0.494212i
\(663\) −5389.38 + 6157.45i −0.315696 + 0.360687i
\(664\) −66.1650 + 38.2004i −0.00386702 + 0.00223262i
\(665\) 9898.27 + 9927.63i 0.577201 + 0.578913i
\(666\) 17128.5 + 22232.8i 0.996569 + 1.29355i
\(667\) 10139.8 + 17562.6i 0.588626 + 1.01953i
\(668\) 712.490 0.0412681
\(669\) 9071.09 10363.9i 0.524228 0.598939i
\(670\) 22455.4i 1.29482i
\(671\) 2374.82 4113.31i 0.136630 0.236651i
\(672\) 22414.0 + 11067.6i 1.28667 + 0.635330i
\(673\) −3469.40 6009.18i −0.198716 0.344186i 0.749397 0.662121i \(-0.230344\pi\)
−0.948112 + 0.317936i \(0.897010\pi\)
\(674\) −24120.6 + 13926.0i −1.37847 + 0.795860i
\(675\) −5204.16 + 7837.87i −0.296753 + 0.446933i
\(676\) −11289.1 + 19553.2i −0.642300 + 1.11250i
\(677\) 4176.49 7233.90i 0.237098 0.410667i −0.722782 0.691076i \(-0.757137\pi\)
0.959880 + 0.280410i \(0.0904703\pi\)
\(678\) −32149.1 28138.8i −1.82106 1.59390i
\(679\) −14858.8 14902.8i −0.839804 0.842295i
\(680\) −537.759 310.476i −0.0303267 0.0175091i
\(681\) 4022.43 1369.79i 0.226344 0.0770783i
\(682\) 406.036i 0.0227975i
\(683\) 8631.82 + 4983.58i 0.483583 + 0.279197i 0.721908 0.691989i \(-0.243265\pi\)
−0.238325 + 0.971185i \(0.576598\pi\)
\(684\) −23602.5 + 3153.93i −1.31939 + 0.176307i
\(685\) 9.34998i 0.000521524i
\(686\) −6640.67 25231.1i −0.369595 1.40427i
\(687\) −1177.50 3457.79i −0.0653924 0.192028i
\(688\) 17642.5 0.977639
\(689\) −10122.2 17532.1i −0.559686 0.969405i
\(690\) 3861.71 19513.1i 0.213062 1.07659i
\(691\) 4151.78 + 2397.03i 0.228569 + 0.131964i 0.609912 0.792469i \(-0.291205\pi\)
−0.381343 + 0.924434i \(0.624538\pi\)
\(692\) −24359.6 −1.33817
\(693\) 2181.38 2845.54i 0.119573 0.155978i
\(694\) −40077.4 −2.19210
\(695\) −12759.2 7366.50i −0.696377 0.402054i
\(696\) 2310.15 + 2021.98i 0.125813 + 0.110119i
\(697\) −3649.50 6321.12i −0.198328 0.343515i
\(698\) −12217.1 −0.662499
\(699\) −14064.8 + 16069.2i −0.761056 + 0.869518i
\(700\) 7799.98 7776.92i 0.421160 0.419914i
\(701\) 13815.7i 0.744382i 0.928156 + 0.372191i \(0.121393\pi\)
−0.928156 + 0.372191i \(0.878607\pi\)
\(702\) −39605.5 2480.13i −2.12936 0.133343i
\(703\) −21796.4 12584.2i −1.16937 0.675136i
\(704\) 4420.39i 0.236647i
\(705\) 543.544 2746.50i 0.0290370 0.146722i
\(706\) 34816.9 + 20101.5i 1.85602 + 1.07157i
\(707\) −7351.05 27597.9i −0.391039 1.46807i
\(708\) −4126.36 + 20850.3i −0.219037 + 1.10678i
\(709\) −67.3023 + 116.571i −0.00356501 + 0.00617477i −0.867802 0.496909i \(-0.834468\pi\)
0.864237 + 0.503084i \(0.167801\pi\)
\(710\) −1452.84 + 2516.39i −0.0767945 + 0.133012i
\(711\) 2847.42 + 21308.7i 0.150192 + 1.12396i
\(712\) 2099.16 1211.95i 0.110491 0.0637919i
\(713\) −844.149 1462.11i −0.0443389 0.0767972i
\(714\) 8103.92 + 4001.56i 0.424764 + 0.209740i
\(715\) 1879.37 3255.16i 0.0982999 0.170260i
\(716\) 25518.5i 1.33194i
\(717\) −12258.5 2426.00i −0.638494 0.126361i
\(718\) −16337.8 −0.849192
\(719\) −279.689 484.435i −0.0145071 0.0251271i 0.858681 0.512511i \(-0.171285\pi\)
−0.873188 + 0.487384i \(0.837951\pi\)
\(720\) 1532.45 + 11468.1i 0.0793209 + 0.593599i
\(721\) 7485.38 1993.83i 0.386644 0.102988i
\(722\) 10778.4 6222.89i 0.555580 0.320764i
\(723\) −1216.67 3572.81i −0.0625844 0.183782i
\(724\) 2461.92 1421.39i 0.126376 0.0729633i
\(725\) −9618.23 + 5553.09i −0.492706 + 0.284464i
\(726\) 26788.5 + 5301.56i 1.36944 + 0.271018i
\(727\) −6529.04 + 3769.54i −0.333079 + 0.192303i −0.657207 0.753710i \(-0.728262\pi\)
0.324128 + 0.946013i \(0.394929\pi\)
\(728\) 4393.40 + 1184.18i 0.223668 + 0.0602868i
\(729\) −7638.09 18140.6i −0.388055 0.921636i
\(730\) 15920.0 + 27574.2i 0.807157 + 1.39804i
\(731\) 7166.11 0.362583
\(732\) 9840.19 + 28896.1i 0.496863 + 1.45906i
\(733\) 34171.1i 1.72188i 0.508708 + 0.860939i \(0.330123\pi\)
−0.508708 + 0.860939i \(0.669877\pi\)
\(734\) 7257.90 12571.0i 0.364978 0.632161i
\(735\) 8965.25 10181.9i 0.449916 0.510975i
\(736\) 15903.7 + 27545.9i 0.796490 + 1.37956i
\(737\) −4460.23 + 2575.11i −0.222923 + 0.128705i
\(738\) 13482.2 32728.4i 0.672476 1.63245i
\(739\) −5524.56 + 9568.82i −0.274999 + 0.476312i −0.970135 0.242566i \(-0.922011\pi\)
0.695136 + 0.718878i \(0.255344\pi\)
\(740\) 8542.53 14796.1i 0.424364 0.735021i
\(741\) 33686.7 11471.6i 1.67006 0.568715i
\(742\) −15834.3 + 15787.4i −0.783415 + 0.781098i
\(743\) −5588.14 3226.32i −0.275921 0.159303i 0.355655 0.934617i \(-0.384258\pi\)
−0.631575 + 0.775315i \(0.717591\pi\)
\(744\) −192.323 168.333i −0.00947702 0.00829487i
\(745\) 18481.1i 0.908854i
\(746\) 16809.3 + 9704.87i 0.824977 + 0.476301i
\(747\) 534.640 + 220.241i 0.0261867 + 0.0107874i
\(748\) 1454.10i 0.0710791i
\(749\) 20667.8 + 20729.1i 1.00826 + 1.01125i
\(750\) 30605.9 + 6057.03i 1.49009 + 0.294895i
\(751\) −1687.78 −0.0820081 −0.0410041 0.999159i \(-0.513056\pi\)
−0.0410041 + 0.999159i \(0.513056\pi\)
\(752\) 1992.53 + 3451.16i 0.0966224 + 0.167355i
\(753\) −2606.88 + 887.737i −0.126162 + 0.0429627i
\(754\) −40568.6 23422.3i −1.95945 1.13129i
\(755\) 10629.0 0.512355
\(756\) 4527.87 + 22594.3i 0.217827 + 1.08696i
\(757\) 10839.9 0.520453 0.260226 0.965548i \(-0.416203\pi\)
0.260226 + 0.965548i \(0.416203\pi\)
\(758\) 18437.5 + 10644.9i 0.883485 + 0.510080i
\(759\) 4318.65 1470.66i 0.206531 0.0703314i
\(760\) 1350.22 + 2338.65i 0.0644443 + 0.111621i
\(761\) 9058.83 0.431514 0.215757 0.976447i \(-0.430778\pi\)
0.215757 + 0.976447i \(0.430778\pi\)
\(762\) 10945.6 + 2166.19i 0.520366 + 0.102982i
\(763\) 8387.86 + 2260.84i 0.397983 + 0.107271i
\(764\) 8381.38i 0.396895i
\(765\) 622.456 + 4658.16i 0.0294182 + 0.220152i
\(766\) 24522.6 + 14158.2i 1.15671 + 0.667826i
\(767\) 31764.1i 1.49535i
\(768\) −11993.9 10497.8i −0.563532 0.493238i
\(769\) 10991.2 + 6345.79i 0.515415 + 0.297575i 0.735057 0.678006i \(-0.237156\pi\)
−0.219642 + 0.975581i \(0.570489\pi\)
\(770\) −4008.48 1080.43i −0.187605 0.0505665i
\(771\) 9585.98 3264.38i 0.447770 0.152482i
\(772\) 3488.77 6042.73i 0.162647 0.281713i
\(773\) 10423.9 18054.8i 0.485023 0.840085i −0.514829 0.857293i \(-0.672145\pi\)
0.999852 + 0.0172084i \(0.00547788\pi\)
\(774\) 21209.2 + 27529.6i 0.984948 + 1.27847i
\(775\) 800.730 462.302i 0.0371136 0.0214276i
\(776\) −2026.88 3510.66i −0.0937639 0.162404i
\(777\) −10783.4 + 21838.5i −0.497880 + 1.00830i
\(778\) −5779.09 + 10009.7i −0.266312 + 0.461265i
\(779\) 31742.5i 1.45994i
\(780\) 7787.25 + 22867.6i 0.357472 + 1.04973i
\(781\) −666.427 −0.0305335
\(782\) 5750.06 + 9959.40i 0.262943 + 0.455431i
\(783\) 1452.16 23189.8i 0.0662785 1.05841i
\(784\) −57.1881 + 19309.7i −0.00260514 + 0.879631i
\(785\) 4834.71 2791.32i 0.219819 0.126913i
\(786\) 53633.6 + 10614.3i 2.43390 + 0.481679i
\(787\) 4472.89 2582.42i 0.202594 0.116968i −0.395271 0.918565i \(-0.629349\pi\)
0.597865 + 0.801597i \(0.296016\pi\)
\(788\) −38768.5 + 22383.0i −1.75263 + 1.01188i
\(789\) 849.043 + 2493.25i 0.0383102 + 0.112499i
\(790\) 21557.3 12446.1i 0.970855 0.560524i
\(791\) 9649.14 35799.0i 0.433734 1.60918i
\(792\) 547.116 421.506i 0.0245466 0.0189111i
\(793\) −22809.6 39507.3i −1.02143 1.76916i
\(794\) −24890.4 −1.11250
\(795\) −11405.4 2257.18i −0.508817 0.100697i
\(796\) 10776.2i 0.479838i
\(797\) −3686.20 + 6384.68i −0.163829 + 0.283760i −0.936239 0.351364i \(-0.885718\pi\)
0.772410 + 0.635125i \(0.219051\pi\)
\(798\) −21820.2 32692.3i −0.967951 1.45024i
\(799\) 809.332 + 1401.80i 0.0358349 + 0.0620679i
\(800\) −15085.7 + 8709.70i −0.666698 + 0.384918i
\(801\) −16962.1 6987.40i −0.748223 0.308224i
\(802\) 24774.7 42911.1i 1.09081 1.88933i
\(803\) −3651.30 + 6324.24i −0.160463 + 0.277930i
\(804\) 6426.02 32470.4i 0.281876 1.42431i
\(805\) 16680.5 4443.07i 0.730324 0.194531i
\(806\) 3377.39 + 1949.94i 0.147597 + 0.0852154i
\(807\) 7770.98 39266.4i 0.338973 1.71282i
\(808\) 5501.45i 0.239530i
\(809\) −15808.7 9127.15i −0.687026 0.396655i 0.115471 0.993311i \(-0.463162\pi\)
−0.802497 + 0.596656i \(0.796496\pi\)
\(810\) −16052.7 + 16177.8i −0.696340 + 0.701766i
\(811\) 32302.9i 1.39865i −0.714802 0.699327i \(-0.753483\pi\)
0.714802 0.699327i \(-0.246517\pi\)
\(812\) −7079.33 + 26264.8i −0.305955 + 1.13511i
\(813\) −18121.1 + 20703.7i −0.781717 + 0.893124i
\(814\) 7453.25 0.320929
\(815\) 11453.3 + 19837.7i 0.492259 + 0.852618i
\(816\) −5033.43 4405.57i −0.215938 0.189002i
\(817\) −26989.3 15582.3i −1.15573 0.667264i
\(818\) 1386.20 0.0592510
\(819\) −13193.2 31810.0i −0.562893 1.35718i
\(820\) −21547.8 −0.917661
\(821\) 15044.6 + 8686.02i 0.639538 + 0.369238i 0.784437 0.620209i \(-0.212952\pi\)
−0.144898 + 0.989447i \(0.546286\pi\)
\(822\) −5.08927 + 25.7158i −0.000215947 + 0.00109117i
\(823\) 6448.43 + 11169.0i 0.273120 + 0.473058i 0.969659 0.244461i \(-0.0786109\pi\)
−0.696539 + 0.717519i \(0.745278\pi\)
\(824\) 1492.16 0.0630847
\(825\) 805.412 + 2365.13i 0.0339889 + 0.0998098i
\(826\) −33901.6 + 9030.11i −1.42807 + 0.380385i
\(827\) 34437.8i 1.44803i 0.689785 + 0.724014i \(0.257705\pi\)
−0.689785 + 0.724014i \(0.742295\pi\)
\(828\) −11168.0 + 27110.7i −0.468739 + 1.13788i
\(829\) −37770.2 21806.6i −1.58240 0.913601i −0.994508 0.104664i \(-0.966623\pi\)
−0.587896 0.808937i \(-0.700043\pi\)
\(830\) 669.519i 0.0279992i
\(831\) 20742.3 7063.52i 0.865876 0.294863i
\(832\) −36768.6 21228.3i −1.53212 0.884568i
\(833\) −23.2289 + 7843.27i −0.000966185 + 0.326234i
\(834\) 31082.7 + 27205.5i 1.29053 + 1.12955i
\(835\) −305.761 + 529.594i −0.0126722 + 0.0219489i
\(836\) −3161.85 + 5476.49i −0.130807 + 0.226565i
\(837\) −120.895 + 1930.58i −0.00499250 + 0.0797258i
\(838\) 29125.6 16815.7i 1.20063 0.693183i
\(839\) −15073.9 26108.8i −0.620274 1.07435i −0.989434 0.144981i \(-0.953688\pi\)
0.369160 0.929366i \(-0.379645\pi\)
\(840\) 2173.58 1450.74i 0.0892805 0.0595894i
\(841\) 1519.71 2632.21i 0.0623112 0.107926i
\(842\) 7870.64i 0.322138i
\(843\) −28074.3 + 32075.4i −1.14701 + 1.31048i
\(844\) 5542.27 0.226034
\(845\) −9689.27 16782.3i −0.394463 0.683230i
\(846\) −2989.89 + 7258.03i −0.121506 + 0.294960i
\(847\) 6099.67 + 22899.9i 0.247446 + 0.928983i
\(848\) 14331.7 8274.40i 0.580368 0.335076i
\(849\) 5369.62 6134.87i 0.217061 0.247996i
\(850\) −5454.30 + 3149.04i −0.220095 + 0.127072i
\(851\) −26838.6 + 15495.3i −1.08110 + 0.624174i
\(852\) 2820.91 3222.93i 0.113430 0.129596i
\(853\) −23967.5 + 13837.6i −0.962053 + 0.555441i −0.896804 0.442428i \(-0.854117\pi\)
−0.0652484 + 0.997869i \(0.520784\pi\)
\(854\) −35681.4 + 35575.8i −1.42973 + 1.42550i
\(855\) 7784.57 18897.2i 0.311376 0.755874i
\(856\) 2819.28 + 4883.14i 0.112571 + 0.194979i
\(857\) 16486.5 0.657140 0.328570 0.944480i \(-0.393433\pi\)
0.328570 + 0.944480i \(0.393433\pi\)
\(858\) −6940.76 + 7929.93i −0.276170 + 0.315528i
\(859\) 20081.3i 0.797633i −0.917031 0.398817i \(-0.869421\pi\)
0.917031 0.398817i \(-0.130579\pi\)
\(860\) 10577.7 18321.2i 0.419416 0.726450i
\(861\) 30652.9 1993.38i 1.21330 0.0789014i
\(862\) −20404.2 35341.0i −0.806228 1.39643i
\(863\) 23674.1 13668.3i 0.933808 0.539134i 0.0457940 0.998951i \(-0.485418\pi\)
0.888014 + 0.459817i \(0.152085\pi\)
\(864\) 2277.64 36371.8i 0.0896838 1.43217i
\(865\) 10453.8 18106.5i 0.410913 0.711721i
\(866\) −9345.81 + 16187.4i −0.366725 + 0.635186i
\(867\) 17165.3 + 15024.1i 0.672393 + 0.588520i
\(868\) 589.363 2186.58i 0.0230464 0.0855038i
\(869\) 4944.25 + 2854.56i 0.193006 + 0.111432i
\(870\) −25467.5 + 8672.60i −0.992445 + 0.337964i
\(871\) 49466.6i 1.92435i
\(872\) 1449.20 + 836.694i 0.0562798 + 0.0324932i
\(873\) −11685.8 + 28367.6i −0.453040 + 1.09977i
\(874\) 50012.6i 1.93559i
\(875\) 6968.87 + 26163.1i 0.269246 + 1.01083i
\(876\) −15129.3 44427.9i −0.583530 1.71356i
\(877\) −43336.3 −1.66860 −0.834300 0.551310i \(-0.814128\pi\)
−0.834300 + 0.551310i \(0.814128\pi\)
\(878\) −15233.4 26385.0i −0.585538 1.01418i
\(879\) 458.027 2314.39i 0.0175755 0.0888082i
\(880\) 2660.94 + 1536.30i 0.101932 + 0.0588506i
\(881\) −48.3703 −0.00184976 −0.000924878 1.00000i \(-0.500294\pi\)
−0.000924878 1.00000i \(0.500294\pi\)
\(882\) −30199.8 + 23124.2i −1.15293 + 0.882802i
\(883\) 36776.7 1.40162 0.700812 0.713346i \(-0.252821\pi\)
0.700812 + 0.713346i \(0.252821\pi\)
\(884\) −12095.1 6983.13i −0.460185 0.265688i
\(885\) −13727.2 12014.9i −0.521396 0.456358i
\(886\) −12993.7 22505.8i −0.492700 0.853382i
\(887\) 27950.3 1.05804 0.529019 0.848610i \(-0.322560\pi\)
0.529019 + 0.848610i \(0.322560\pi\)
\(888\) −3089.94 + 3530.30i −0.116770 + 0.133411i
\(889\) 2492.29 + 9356.75i 0.0940255 + 0.352998i
\(890\) 21241.3i 0.800011i
\(891\) −5054.21 1333.27i −0.190036 0.0501304i
\(892\) 20357.8 + 11753.6i 0.764159 + 0.441188i
\(893\) 7039.37i 0.263789i
\(894\) 10059.4 50829.8i 0.376328 1.90157i
\(895\) 18967.9 + 10951.1i 0.708410 + 0.409001i
\(896\) −2187.97 + 8117.53i −0.0815793 + 0.302665i
\(897\) 8506.90 42985.0i 0.316652 1.60003i
\(898\) 29564.0 51206.3i 1.09862 1.90287i
\(899\) −1141.73 + 1977.53i −0.0423567 + 0.0733640i
\(900\) −14847.3 6116.22i −0.549899 0.226527i
\(901\) 5821.30 3360.93i 0.215245 0.124272i
\(902\) −4700.04 8140.71i −0.173497 0.300506i
\(903\) −13352.5 + 27041.4i −0.492075 + 0.996545i
\(904\) 3570.97 6185.09i 0.131381 0.227559i
\(905\) 2439.92i 0.0896196i
\(906\) −29233.5 5785.43i −1.07199 0.212150i
\(907\) 21610.8 0.791153 0.395576 0.918433i \(-0.370545\pi\)
0.395576 + 0.918433i \(0.370545\pi\)
\(908\) 3626.25 + 6280.85i 0.132535 + 0.229557i
\(909\) −32983.4 + 25410.9i −1.20351 + 0.927202i
\(910\) −28237.2 + 28153.7i −1.02863 + 1.02559i
\(911\) −5927.13 + 3422.03i −0.215560 + 0.124453i −0.603892 0.797066i \(-0.706384\pi\)
0.388333 + 0.921519i \(0.373051\pi\)
\(912\) 9377.46 + 27537.3i 0.340481 + 0.999837i
\(913\) 132.984 76.7782i 0.00482050 0.00278312i
\(914\) −18308.1 + 10570.2i −0.662559 + 0.382528i
\(915\) −25701.3 5086.40i −0.928590 0.183772i
\(916\) 5399.19 3117.22i 0.194753 0.112441i
\(917\) 12212.2 + 45848.0i 0.439785 + 1.65107i
\(918\) 823.493 13150.4i 0.0296071 0.472799i
\(919\) 14558.6 + 25216.3i 0.522573 + 0.905124i 0.999655 + 0.0262648i \(0.00836130\pi\)
−0.477082 + 0.878859i \(0.658305\pi\)
\(920\) 3325.14 0.119159
\(921\) 124.291 + 364.985i 0.00444682 + 0.0130583i
\(922\) 3668.65i 0.131042i
\(923\) −3200.43 + 5543.31i −0.114132 + 0.197682i
\(924\) 5487.06 + 2709.40i 0.195358 + 0.0964640i
\(925\) −8486.06 14698.3i −0.301643 0.522461i
\(926\) 39271.4 22673.3i 1.39367 0.804635i
\(927\) −6892.21 8946.10i −0.244196 0.316967i
\(928\) 21510.0 37256.4i 0.760883 1.31789i
\(929\) −11238.9 + 19466.3i −0.396917 + 0.687480i −0.993344 0.115187i \(-0.963253\pi\)
0.596427 + 0.802667i \(0.296587\pi\)
\(930\) 2120.20 722.005i 0.0747570 0.0254575i
\(931\) 17142.2 29489.1i 0.603451 1.03810i
\(932\) −31564.9 18224.0i −1.10938 0.640501i
\(933\) 25125.3 + 21991.2i 0.881635 + 0.771661i
\(934\) 40251.5i 1.41014i
\(935\) 1080.83 + 624.019i 0.0378043 + 0.0218263i
\(936\) −878.613 6575.12i −0.0306820 0.229609i
\(937\) 25912.1i 0.903426i 0.892163 + 0.451713i \(0.149187\pi\)
−0.892163 + 0.451713i \(0.850813\pi\)
\(938\) 52795.3 14062.7i 1.83777 0.489513i
\(939\) 39323.8 + 7782.34i 1.36665 + 0.270466i
\(940\) 4778.55 0.165808
\(941\) −19906.3 34478.8i −0.689615 1.19445i −0.971962 0.235136i \(-0.924446\pi\)
0.282347 0.959312i \(-0.408887\pi\)
\(942\) −14816.5 + 5045.57i −0.512472 + 0.174516i
\(943\) 33849.1 + 19542.8i 1.16891 + 0.674868i
\(944\) 25965.7 0.895246
\(945\) −18737.4 6330.64i −0.645004 0.217921i
\(946\) 9228.94 0.317187
\(947\) −32618.1 18832.1i −1.11927 0.646209i −0.178053 0.984021i \(-0.556980\pi\)
−0.941213 + 0.337812i \(0.890313\pi\)
\(948\) −34733.5 + 11828.0i −1.18997 + 0.405228i
\(949\) 35069.8 + 60742.7i 1.19959 + 2.07776i
\(950\) 27389.6 0.935407
\(951\) −1560.06 308.742i −0.0531950 0.0105275i
\(952\) −393.192 + 1458.77i −0.0133860 + 0.0496628i
\(953\) 18055.8i 0.613730i 0.951753 + 0.306865i \(0.0992801\pi\)
−0.951753 + 0.306865i \(0.900720\pi\)
\(954\) 30140.5 + 12416.1i 1.02289 + 0.421371i
\(955\) −6229.88 3596.82i −0.211093 0.121875i
\(956\) 21328.1i 0.721548i
\(957\) −4643.12 4063.95i −0.156835 0.137271i
\(958\) 493.233 + 284.768i 0.0166343 + 0.00960381i
\(959\) −21.9829 + 5.85541i −0.000740212 + 0.000197165i
\(960\) −23081.9 + 7860.24i −0.776006 + 0.264258i
\(961\) −14800.4 + 25635.1i −0.496809 + 0.860499i
\(962\) 35793.3 61995.8i 1.19961 2.07778i
\(963\) 16254.3 39457.8i 0.543913 1.32036i
\(964\) 5578.78 3220.91i 0.186391 0.107613i
\(965\) 2994.37 + 5186.41i 0.0998884 + 0.173012i
\(966\) −48295.9 + 3140.71i −1.60859 + 0.104607i
\(967\) −15995.7 + 27705.3i −0.531940 + 0.921348i 0.467364 + 0.884065i \(0.345204\pi\)
−0.999305 + 0.0372829i \(0.988130\pi\)
\(968\) 4564.92i 0.151572i
\(969\) 3808.97 + 11185.2i 0.126276 + 0.370816i
\(970\) 35524.1 1.17589
\(971\) 13431.5 + 23264.0i 0.443910 + 0.768874i 0.997976 0.0635987i \(-0.0202578\pi\)
−0.554066 + 0.832473i \(0.686924\pi\)
\(972\) 27841.7 18799.2i 0.918749 0.620356i
\(973\) −9329.07 + 34611.5i −0.307376 + 1.14038i
\(974\) −65079.7 + 37573.8i −2.14095 + 1.23608i
\(975\) 23540.9 + 4658.84i 0.773243 + 0.153028i
\(976\) 32295.4 18645.8i 1.05917 0.611513i
\(977\) 25359.6 14641.4i 0.830427 0.479447i −0.0235720 0.999722i \(-0.507504\pi\)
0.853999 + 0.520275i \(0.174171\pi\)
\(978\) −20702.9 60794.9i −0.676897 1.98774i
\(979\) −4219.07 + 2435.88i −0.137734 + 0.0795210i
\(980\) 20018.2 + 11636.7i 0.652507 + 0.379306i
\(981\) −1677.44 12553.2i −0.0545940 0.408555i
\(982\) 12086.4 + 20934.2i 0.392761 + 0.680283i
\(983\) 1993.91 0.0646958 0.0323479 0.999477i \(-0.489702\pi\)
0.0323479 + 0.999477i \(0.489702\pi\)
\(984\) 5804.45 + 1148.72i 0.188048 + 0.0372154i
\(985\) 38422.2i 1.24288i
\(986\) 7777.05 13470.2i 0.251188 0.435071i
\(987\) −6797.74 + 442.061i −0.219224 + 0.0142563i
\(988\) 30368.8 + 52600.3i 0.977894 + 1.69376i
\(989\) −33232.8 + 19187.0i −1.06849 + 0.616896i
\(990\) 801.636 + 5999.05i 0.0257350 + 0.192588i
\(991\) −8752.81 + 15160.3i −0.280567 + 0.485957i −0.971525 0.236939i \(-0.923856\pi\)
0.690957 + 0.722896i \(0.257189\pi\)
\(992\) −1790.73 + 3101.64i −0.0573143 + 0.0992713i
\(993\) 4135.08 20894.4i 0.132148 0.667738i
\(994\) 6826.17 + 1839.90i 0.217820 + 0.0587105i
\(995\) −8009.93 4624.53i −0.255208 0.147344i
\(996\) −191.595 + 968.120i −0.00609529 + 0.0307992i
\(997\) 30841.0i 0.979684i −0.871811 0.489842i \(-0.837054\pi\)
0.871811 0.489842i \(-0.162946\pi\)
\(998\) 1901.96 + 1098.10i 0.0603261 + 0.0348293i
\(999\) 35437.9 + 2219.15i 1.12233 + 0.0702812i
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 63.4.s.a.59.19 yes 44
3.2 odd 2 189.4.s.a.17.4 44
7.5 odd 6 63.4.i.a.5.4 44
9.2 odd 6 63.4.i.a.38.19 yes 44
9.7 even 3 189.4.i.a.143.4 44
21.5 even 6 189.4.i.a.152.19 44
63.47 even 6 inner 63.4.s.a.47.19 yes 44
63.61 odd 6 189.4.s.a.89.4 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.4 44 7.5 odd 6
63.4.i.a.38.19 yes 44 9.2 odd 6
63.4.s.a.47.19 yes 44 63.47 even 6 inner
63.4.s.a.59.19 yes 44 1.1 even 1 trivial
189.4.i.a.143.4 44 9.7 even 3
189.4.i.a.152.19 44 21.5 even 6
189.4.s.a.17.4 44 3.2 odd 2
189.4.s.a.89.4 44 63.61 odd 6