Properties

Label 128.4.k.a.5.7
Level $128$
Weight $4$
Character 128.5
Analytic conductor $7.552$
Analytic rank $0$
Dimension $752$
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] = [128,4,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.k (of order \(32\), degree \(16\), 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: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(752\)
Relative dimension: \(47\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 5.7
Character \(\chi\) \(=\) 128.5
Dual form 128.4.k.a.77.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.53887 + 1.24665i) q^{2} +(7.58094 + 2.29965i) q^{3} +(4.89175 - 6.33015i) q^{4} +(9.48044 + 0.933742i) q^{5} +(-22.1139 + 3.61223i) q^{6} +(6.95727 + 10.4123i) q^{7} +(-4.52806 + 22.1697i) q^{8} +(29.7326 + 19.8667i) q^{9} +O(q^{10})\) \(q+(-2.53887 + 1.24665i) q^{2} +(7.58094 + 2.29965i) q^{3} +(4.89175 - 6.33015i) q^{4} +(9.48044 + 0.933742i) q^{5} +(-22.1139 + 3.61223i) q^{6} +(6.95727 + 10.4123i) q^{7} +(-4.52806 + 22.1697i) q^{8} +(29.7326 + 19.8667i) q^{9} +(-25.2337 + 9.44810i) q^{10} +(15.2548 - 28.5396i) q^{11} +(51.6412 - 36.7392i) q^{12} +(-2.95490 - 30.0016i) q^{13} +(-30.6441 - 17.7622i) q^{14} +(69.7234 + 28.8804i) q^{15} +(-16.1416 - 61.9310i) q^{16} +(-6.89315 + 2.85523i) q^{17} +(-100.254 - 13.3729i) q^{18} +(-22.5489 + 27.4759i) q^{19} +(52.2866 - 55.4450i) q^{20} +(28.7980 + 94.9343i) q^{21} +(-3.15104 + 91.4758i) q^{22} +(8.93152 + 44.9018i) q^{23} +(-85.3096 + 157.654i) q^{24} +(-33.5913 - 6.68172i) q^{25} +(44.9035 + 72.4865i) q^{26} +(44.0206 + 53.6392i) q^{27} +(99.9446 + 6.89371i) q^{28} +(35.9847 - 19.2342i) q^{29} +(-213.022 + 13.5968i) q^{30} +(220.931 + 220.931i) q^{31} +(118.188 + 137.112i) q^{32} +(181.277 - 181.277i) q^{33} +(13.9414 - 15.8424i) q^{34} +(56.2356 + 105.209i) q^{35} +(271.203 - 91.0291i) q^{36} +(-254.030 + 208.477i) q^{37} +(22.9960 - 97.8682i) q^{38} +(46.5923 - 234.235i) q^{39} +(-63.6288 + 205.951i) q^{40} +(-25.8255 + 5.13701i) q^{41} +(-191.464 - 205.125i) q^{42} +(-377.768 + 114.595i) q^{43} +(-106.038 - 236.174i) q^{44} +(263.328 + 216.107i) q^{45} +(-78.6526 - 102.865i) q^{46} +(-195.297 - 471.489i) q^{47} +(20.0510 - 506.615i) q^{48} +(71.2482 - 172.008i) q^{49} +(93.6138 - 24.9124i) q^{50} +(-58.8226 + 5.79352i) q^{51} +(-204.369 - 128.055i) q^{52} +(229.832 + 122.848i) q^{53} +(-178.632 - 81.3051i) q^{54} +(171.270 - 256.324i) q^{55} +(-262.341 + 107.093i) q^{56} +(-234.127 + 156.438i) q^{57} +(-67.3823 + 93.6935i) q^{58} +(64.2233 - 652.071i) q^{59} +(523.886 - 300.084i) q^{60} +(-101.025 + 333.034i) q^{61} +(-836.337 - 285.492i) q^{62} +447.803i q^{63} +(-470.993 - 200.772i) q^{64} -287.187i q^{65} +(-234.251 + 686.226i) q^{66} +(216.225 - 712.797i) q^{67} +(-15.6455 + 57.6017i) q^{68} +(-35.5492 + 360.937i) q^{69} +(-273.934 - 197.007i) q^{70} +(595.158 - 397.672i) q^{71} +(-575.070 + 569.206i) q^{72} +(-390.085 + 583.803i) q^{73} +(385.053 - 845.982i) q^{74} +(-239.288 - 127.902i) q^{75} +(63.6231 + 277.143i) q^{76} +(403.295 - 39.7211i) q^{77} +(173.717 + 652.778i) q^{78} +(-150.383 + 363.056i) q^{79} +(-95.2023 - 602.205i) q^{80} +(-159.113 - 384.133i) q^{81} +(59.1637 - 45.2375i) q^{82} +(-939.124 - 770.720i) q^{83} +(741.821 + 282.099i) q^{84} +(-68.0161 + 20.6325i) q^{85} +(816.246 - 761.884i) q^{86} +(317.030 - 63.0612i) q^{87} +(563.642 + 467.423i) q^{88} +(-159.699 + 802.864i) q^{89} +(-937.965 - 220.393i) q^{90} +(291.827 - 239.496i) q^{91} +(327.926 + 163.110i) q^{92} +(1166.80 + 2182.93i) q^{93} +(1083.61 + 953.584i) q^{94} +(-239.429 + 239.429i) q^{95} +(580.663 + 1311.23i) q^{96} +(-71.2744 - 71.2744i) q^{97} +(33.5435 + 525.528i) q^{98} +(1020.55 - 545.496i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{32}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53887 + 1.24665i −0.897627 + 0.440756i
\(3\) 7.58094 + 2.29965i 1.45895 + 0.442569i 0.917355 0.398069i \(-0.130320\pi\)
0.541598 + 0.840638i \(0.317820\pi\)
\(4\) 4.89175 6.33015i 0.611468 0.791269i
\(5\) 9.48044 + 0.933742i 0.847956 + 0.0835164i 0.512655 0.858595i \(-0.328662\pi\)
0.335301 + 0.942111i \(0.391162\pi\)
\(6\) −22.1139 + 3.61223i −1.50466 + 0.245781i
\(7\) 6.95727 + 10.4123i 0.375657 + 0.562211i 0.970338 0.241751i \(-0.0777216\pi\)
−0.594681 + 0.803962i \(0.702722\pi\)
\(8\) −4.52806 + 22.1697i −0.200114 + 0.979773i
\(9\) 29.7326 + 19.8667i 1.10121 + 0.735803i
\(10\) −25.2337 + 9.44810i −0.797959 + 0.298775i
\(11\) 15.2548 28.5396i 0.418135 0.782275i −0.581373 0.813637i \(-0.697484\pi\)
0.999508 + 0.0313618i \(0.00998442\pi\)
\(12\) 51.6412 36.7392i 1.24229 0.883808i
\(13\) −2.95490 30.0016i −0.0630416 0.640072i −0.973842 0.227226i \(-0.927035\pi\)
0.910801 0.412847i \(-0.135465\pi\)
\(14\) −30.6441 17.7622i −0.584998 0.339083i
\(15\) 69.7234 + 28.8804i 1.20017 + 0.497125i
\(16\) −16.1416 61.9310i −0.252213 0.967672i
\(17\) −6.89315 + 2.85523i −0.0983431 + 0.0407351i −0.431313 0.902203i \(-0.641949\pi\)
0.332969 + 0.942938i \(0.391949\pi\)
\(18\) −100.254 13.3729i −1.31278 0.175113i
\(19\) −22.5489 + 27.4759i −0.272267 + 0.331758i −0.891136 0.453736i \(-0.850091\pi\)
0.618870 + 0.785494i \(0.287591\pi\)
\(20\) 52.2866 55.4450i 0.584582 0.619894i
\(21\) 28.7980 + 94.9343i 0.299250 + 0.986494i
\(22\) −3.15104 + 91.4758i −0.0305366 + 0.886487i
\(23\) 8.93152 + 44.9018i 0.0809717 + 0.407072i 0.999919 + 0.0126930i \(0.00404042\pi\)
−0.918948 + 0.394379i \(0.870960\pi\)
\(24\) −85.3096 + 157.654i −0.725573 + 1.34088i
\(25\) −33.5913 6.68172i −0.268730 0.0534538i
\(26\) 44.9035 + 72.4865i 0.338704 + 0.546760i
\(27\) 44.0206 + 53.6392i 0.313769 + 0.382329i
\(28\) 99.9446 + 6.89371i 0.674563 + 0.0465282i
\(29\) 35.9847 19.2342i 0.230420 0.123162i −0.352147 0.935945i \(-0.614548\pi\)
0.582567 + 0.812782i \(0.302048\pi\)
\(30\) −213.022 + 13.5968i −1.29641 + 0.0827476i
\(31\) 220.931 + 220.931i 1.28001 + 1.28001i 0.940661 + 0.339349i \(0.110207\pi\)
0.339349 + 0.940661i \(0.389793\pi\)
\(32\) 118.188 + 137.112i 0.652900 + 0.757444i
\(33\) 181.277 181.277i 0.956249 0.956249i
\(34\) 13.9414 15.8424i 0.0703212 0.0799102i
\(35\) 56.2356 + 105.209i 0.271587 + 0.508104i
\(36\) 271.203 91.0291i 1.25557 0.421431i
\(37\) −254.030 + 208.477i −1.12871 + 0.926309i −0.997879 0.0650958i \(-0.979265\pi\)
−0.130832 + 0.991405i \(0.541765\pi\)
\(38\) 22.9960 97.8682i 0.0981696 0.417798i
\(39\) 46.5923 234.235i 0.191301 0.961736i
\(40\) −63.6288 + 205.951i −0.251515 + 0.814092i
\(41\) −25.8255 + 5.13701i −0.0983724 + 0.0195675i −0.244031 0.969767i \(-0.578470\pi\)
0.145659 + 0.989335i \(0.453470\pi\)
\(42\) −191.464 205.125i −0.703418 0.753607i
\(43\) −377.768 + 114.595i −1.33975 + 0.406407i −0.877173 0.480174i \(-0.840574\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(44\) −106.038 236.174i −0.363314 0.809193i
\(45\) 263.328 + 216.107i 0.872324 + 0.715898i
\(46\) −78.6526 102.865i −0.252102 0.329710i
\(47\) −195.297 471.489i −0.606107 1.46327i −0.867201 0.497958i \(-0.834083\pi\)
0.261094 0.965313i \(-0.415917\pi\)
\(48\) 20.0510 506.615i 0.0602940 1.52341i
\(49\) 71.2482 172.008i 0.207721 0.501482i
\(50\) 93.6138 24.9124i 0.264780 0.0704630i
\(51\) −58.8226 + 5.79352i −0.161506 + 0.0159070i
\(52\) −204.369 128.055i −0.545017 0.341501i
\(53\) 229.832 + 122.848i 0.595658 + 0.318386i 0.741532 0.670917i \(-0.234099\pi\)
−0.145874 + 0.989303i \(0.546599\pi\)
\(54\) −178.632 81.3051i −0.450161 0.204893i
\(55\) 171.270 256.324i 0.419893 0.628414i
\(56\) −262.341 + 107.093i −0.626013 + 0.255553i
\(57\) −234.127 + 156.438i −0.544050 + 0.363522i
\(58\) −67.3823 + 93.6935i −0.152547 + 0.212113i
\(59\) 64.2233 652.071i 0.141715 1.43885i −0.616760 0.787151i \(-0.711555\pi\)
0.758475 0.651702i \(-0.225945\pi\)
\(60\) 523.886 300.084i 1.12722 0.645678i
\(61\) −101.025 + 333.034i −0.212047 + 0.699026i 0.784805 + 0.619743i \(0.212763\pi\)
−0.996852 + 0.0792834i \(0.974737\pi\)
\(62\) −836.337 285.492i −1.71314 0.584799i
\(63\) 447.803i 0.895521i
\(64\) −470.993 200.772i −0.919909 0.392132i
\(65\) 287.187i 0.548018i
\(66\) −234.251 + 686.226i −0.436882 + 1.27983i
\(67\) 216.225 712.797i 0.394269 1.29973i −0.505296 0.862946i \(-0.668617\pi\)
0.899565 0.436786i \(-0.143883\pi\)
\(68\) −15.6455 + 57.6017i −0.0279013 + 0.102724i
\(69\) −35.5492 + 360.937i −0.0620235 + 0.629735i
\(70\) −273.934 197.007i −0.467734 0.336384i
\(71\) 595.158 397.672i 0.994820 0.664718i 0.0522182 0.998636i \(-0.483371\pi\)
0.942602 + 0.333918i \(0.108371\pi\)
\(72\) −575.070 + 569.206i −0.941287 + 0.931688i
\(73\) −390.085 + 583.803i −0.625424 + 0.936014i 0.374537 + 0.927212i \(0.377802\pi\)
−0.999961 + 0.00880164i \(0.997198\pi\)
\(74\) 385.053 845.982i 0.604885 1.32897i
\(75\) −239.288 127.902i −0.368408 0.196918i
\(76\) 63.6231 + 277.143i 0.0960273 + 0.418295i
\(77\) 403.295 39.7211i 0.596879 0.0587875i
\(78\) 173.717 + 652.778i 0.252174 + 0.947597i
\(79\) −150.383 + 363.056i −0.214169 + 0.517051i −0.994056 0.108870i \(-0.965277\pi\)
0.779887 + 0.625921i \(0.215277\pi\)
\(80\) −95.2023 602.205i −0.133049 0.841607i
\(81\) −159.113 384.133i −0.218262 0.526932i
\(82\) 59.1637 45.2375i 0.0796772 0.0609225i
\(83\) −939.124 770.720i −1.24196 1.01925i −0.998786 0.0492627i \(-0.984313\pi\)
−0.243170 0.969984i \(-0.578187\pi\)
\(84\) 741.821 + 282.099i 0.963564 + 0.366423i
\(85\) −68.0161 + 20.6325i −0.0867927 + 0.0263283i
\(86\) 816.246 761.884i 1.02347 0.955303i
\(87\) 317.030 63.0612i 0.390680 0.0777112i
\(88\) 563.642 + 467.423i 0.682777 + 0.566221i
\(89\) −159.699 + 802.864i −0.190203 + 0.956218i 0.761258 + 0.648449i \(0.224582\pi\)
−0.951461 + 0.307768i \(0.900418\pi\)
\(90\) −937.965 220.393i −1.09856 0.258127i
\(91\) 291.827 239.496i 0.336174 0.275891i
\(92\) 327.926 + 163.110i 0.371615 + 0.184841i
\(93\) 1166.80 + 2182.93i 1.30098 + 2.43397i
\(94\) 1083.61 + 953.584i 1.18900 + 1.04633i
\(95\) −239.429 + 239.429i −0.258577 + 0.258577i
\(96\) 580.663 + 1311.23i 0.617330 + 1.39403i
\(97\) −71.2744 71.2744i −0.0746064 0.0746064i 0.668819 0.743425i \(-0.266800\pi\)
−0.743425 + 0.668819i \(0.766800\pi\)
\(98\) 33.5435 + 525.528i 0.0345756 + 0.541698i
\(99\) 1020.55 545.496i 1.03605 0.553782i
\(100\) −206.616 + 179.953i −0.206616 + 0.179953i
\(101\) 646.243 + 787.449i 0.636669 + 0.775783i 0.986979 0.160851i \(-0.0514237\pi\)
−0.350310 + 0.936634i \(0.613924\pi\)
\(102\) 142.121 88.0400i 0.137961 0.0854633i
\(103\) 178.270 + 35.4602i 0.170539 + 0.0339223i 0.279621 0.960110i \(-0.409791\pi\)
−0.109082 + 0.994033i \(0.534791\pi\)
\(104\) 678.507 + 70.3396i 0.639741 + 0.0663209i
\(105\) 184.374 + 926.909i 0.171362 + 0.861496i
\(106\) −736.662 25.3756i −0.675009 0.0232519i
\(107\) −625.617 2062.38i −0.565240 1.86335i −0.501070 0.865407i \(-0.667060\pi\)
−0.0641693 0.997939i \(-0.520440\pi\)
\(108\) 554.882 16.2674i 0.494385 0.0144938i
\(109\) 524.176 638.710i 0.460614 0.561260i −0.489965 0.871742i \(-0.662990\pi\)
0.950579 + 0.310482i \(0.100490\pi\)
\(110\) −115.288 + 864.288i −0.0999298 + 0.749152i
\(111\) −2405.21 + 996.272i −2.05669 + 0.851909i
\(112\) 532.542 598.942i 0.449290 0.505310i
\(113\) −1635.52 677.456i −1.36157 0.563980i −0.422078 0.906559i \(-0.638699\pi\)
−0.939489 + 0.342580i \(0.888699\pi\)
\(114\) 399.394 689.050i 0.328129 0.566101i
\(115\) 42.7481 + 434.028i 0.0346633 + 0.351942i
\(116\) 54.2725 321.878i 0.0434403 0.257634i
\(117\) 508.175 950.729i 0.401545 0.751238i
\(118\) 649.846 + 1735.59i 0.506976 + 1.35402i
\(119\) −77.6871 51.9088i −0.0598451 0.0399872i
\(120\) −955.981 + 1414.98i −0.727240 + 1.07641i
\(121\) 157.660 + 235.955i 0.118453 + 0.177277i
\(122\) −158.687 971.472i −0.117761 0.720926i
\(123\) −207.595 20.4463i −0.152181 0.0149885i
\(124\) 2479.26 317.788i 1.79552 0.230147i
\(125\) −1451.74 440.379i −1.03878 0.315110i
\(126\) −558.251 1136.91i −0.394706 0.803844i
\(127\) −2310.04 −1.61404 −0.807018 0.590527i \(-0.798920\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(128\) 1446.08 77.4285i 0.998570 0.0534670i
\(129\) −3127.36 −2.13449
\(130\) 358.021 + 729.132i 0.241542 + 0.491916i
\(131\) 1341.61 + 406.973i 0.894786 + 0.271430i 0.703999 0.710201i \(-0.251396\pi\)
0.190787 + 0.981631i \(0.438896\pi\)
\(132\) −260.749 2034.27i −0.171934 1.34137i
\(133\) −442.966 43.6283i −0.288797 0.0284440i
\(134\) 339.639 + 2079.26i 0.218958 + 1.34045i
\(135\) 367.249 + 549.627i 0.234132 + 0.350403i
\(136\) −32.0872 165.748i −0.0202313 0.104506i
\(137\) 201.103 + 134.373i 0.125412 + 0.0837975i 0.616694 0.787203i \(-0.288472\pi\)
−0.491282 + 0.871001i \(0.663472\pi\)
\(138\) −359.706 960.691i −0.221886 0.592604i
\(139\) 55.1769 103.229i 0.0336694 0.0629909i −0.864524 0.502592i \(-0.832380\pi\)
0.898193 + 0.439601i \(0.144880\pi\)
\(140\) 941.082 + 158.678i 0.568114 + 0.0957909i
\(141\) −396.275 4023.45i −0.236684 2.40309i
\(142\) −1015.27 + 1751.59i −0.599999 + 1.03514i
\(143\) −901.310 373.335i −0.527072 0.218321i
\(144\) 750.431 2162.05i 0.434277 1.25119i
\(145\) 359.111 148.749i 0.205673 0.0851924i
\(146\) 262.580 1968.50i 0.148844 1.11585i
\(147\) 935.688 1140.14i 0.524995 0.639708i
\(148\) 77.0410 + 2627.87i 0.0427887 + 1.45952i
\(149\) −520.164 1714.75i −0.285997 0.942805i −0.975774 0.218783i \(-0.929791\pi\)
0.689777 0.724022i \(-0.257709\pi\)
\(150\) 766.970 + 26.4196i 0.417486 + 0.0143810i
\(151\) 260.033 + 1307.28i 0.140141 + 0.704534i 0.985410 + 0.170195i \(0.0544396\pi\)
−0.845270 + 0.534340i \(0.820560\pi\)
\(152\) −507.030 624.315i −0.270563 0.333149i
\(153\) −261.675 52.0504i −0.138269 0.0275034i
\(154\) −974.396 + 603.613i −0.509864 + 0.315847i
\(155\) 1888.23 + 2300.81i 0.978490 + 1.19229i
\(156\) −1254.83 1440.76i −0.644017 0.739441i
\(157\) −544.892 + 291.251i −0.276988 + 0.148053i −0.604042 0.796952i \(-0.706444\pi\)
0.327054 + 0.945006i \(0.393944\pi\)
\(158\) −70.7999 1109.23i −0.0356490 0.558515i
\(159\) 1459.84 + 1459.84i 0.728129 + 0.728129i
\(160\) 992.443 + 1410.24i 0.490372 + 0.696807i
\(161\) −405.392 + 405.392i −0.198443 + 0.198443i
\(162\) 882.847 + 776.908i 0.428167 + 0.376788i
\(163\) 952.509 + 1782.02i 0.457707 + 0.856310i 0.999871 + 0.0160375i \(0.00510513\pi\)
−0.542164 + 0.840273i \(0.682395\pi\)
\(164\) −93.8138 + 188.608i −0.0446685 + 0.0898039i
\(165\) 1887.85 1549.32i 0.890720 0.730995i
\(166\) 3345.13 + 786.003i 1.56405 + 0.367504i
\(167\) −60.9305 + 306.318i −0.0282332 + 0.141938i −0.992331 0.123610i \(-0.960553\pi\)
0.964098 + 0.265548i \(0.0855528\pi\)
\(168\) −2235.07 + 208.576i −1.02642 + 0.0957856i
\(169\) 1263.42 251.310i 0.575067 0.114388i
\(170\) 146.963 137.175i 0.0663031 0.0618874i
\(171\) −1216.29 + 368.958i −0.543930 + 0.164999i
\(172\) −1122.54 + 2951.90i −0.497634 + 1.30860i
\(173\) 2742.56 + 2250.76i 1.20528 + 0.989147i 0.999945 + 0.0104552i \(0.00332805\pi\)
0.205334 + 0.978692i \(0.434172\pi\)
\(174\) −726.284 + 555.329i −0.316434 + 0.241950i
\(175\) −164.132 396.249i −0.0708983 0.171164i
\(176\) −2013.73 484.066i −0.862445 0.207317i
\(177\) 1986.41 4795.62i 0.843546 2.03650i
\(178\) −595.430 2237.46i −0.250727 0.942160i
\(179\) 2466.21 242.900i 1.02979 0.101426i 0.431018 0.902343i \(-0.358155\pi\)
0.598775 + 0.800918i \(0.295655\pi\)
\(180\) 2656.13 609.761i 1.09987 0.252494i
\(181\) −2448.02 1308.50i −1.00530 0.537347i −0.115316 0.993329i \(-0.536788\pi\)
−0.889989 + 0.455982i \(0.849288\pi\)
\(182\) −442.345 + 971.856i −0.180158 + 0.395817i
\(183\) −1531.72 + 2292.39i −0.618734 + 0.926001i
\(184\) −1035.90 5.30859i −0.415042 0.00212692i
\(185\) −2602.98 + 1739.26i −1.03446 + 0.691204i
\(186\) −5683.69 4087.58i −2.24058 1.61138i
\(187\) −23.6659 + 240.284i −0.00925466 + 0.0939641i
\(188\) −3939.94 1070.14i −1.52846 0.415151i
\(189\) −252.244 + 831.538i −0.0970798 + 0.320029i
\(190\) 309.396 906.361i 0.118136 0.346076i
\(191\) 636.302i 0.241053i 0.992710 + 0.120527i \(0.0384583\pi\)
−0.992710 + 0.120527i \(0.961542\pi\)
\(192\) −3108.87 2605.16i −1.16856 0.979225i
\(193\) 2857.57i 1.06577i 0.846189 + 0.532883i \(0.178891\pi\)
−0.846189 + 0.532883i \(0.821109\pi\)
\(194\) 269.811 + 92.1027i 0.0998520 + 0.0340855i
\(195\) 660.431 2177.15i 0.242536 0.799533i
\(196\) −740.311 1292.43i −0.269792 0.471003i
\(197\) −115.169 + 1169.33i −0.0416519 + 0.422899i 0.951636 + 0.307229i \(0.0994017\pi\)
−0.993288 + 0.115671i \(0.963098\pi\)
\(198\) −1911.01 + 2657.21i −0.685907 + 0.953737i
\(199\) 1397.60 933.845i 0.497855 0.332656i −0.281161 0.959661i \(-0.590719\pi\)
0.779015 + 0.627005i \(0.215719\pi\)
\(200\) 300.235 714.455i 0.106149 0.252598i
\(201\) 3278.37 4906.43i 1.15044 1.72176i
\(202\) −2622.40 1193.60i −0.913422 0.415748i
\(203\) 450.628 + 240.866i 0.155802 + 0.0832781i
\(204\) −251.071 + 400.696i −0.0861692 + 0.137521i
\(205\) −249.634 + 24.5868i −0.0850497 + 0.00837666i
\(206\) −496.812 + 132.211i −0.168032 + 0.0447165i
\(207\) −626.492 + 1512.49i −0.210359 + 0.507850i
\(208\) −1810.33 + 667.274i −0.603480 + 0.222438i
\(209\) 440.174 + 1062.67i 0.145682 + 0.351707i
\(210\) −1623.63 2123.46i −0.533529 0.697773i
\(211\) −1176.74 965.729i −0.383935 0.315088i 0.422552 0.906339i \(-0.361134\pi\)
−0.806488 + 0.591251i \(0.798634\pi\)
\(212\) 1901.93 853.932i 0.616155 0.276643i
\(213\) 5426.36 1646.07i 1.74558 0.529516i
\(214\) 4159.42 + 4456.20i 1.32866 + 1.42346i
\(215\) −3688.41 + 733.670i −1.16999 + 0.232725i
\(216\) −1388.49 + 733.042i −0.437385 + 0.230913i
\(217\) −763.320 + 3837.47i −0.238790 + 1.20048i
\(218\) −534.570 + 2275.07i −0.166081 + 0.706821i
\(219\) −4299.76 + 3528.72i −1.32671 + 1.08881i
\(220\) −784.760 2338.04i −0.240493 0.716503i
\(221\) 106.030 + 198.368i 0.0322731 + 0.0603787i
\(222\) 4864.53 5527.86i 1.47066 1.67120i
\(223\) 4209.84 4209.84i 1.26418 1.26418i 0.315131 0.949048i \(-0.397952\pi\)
0.949048 0.315131i \(-0.102048\pi\)
\(224\) −605.387 + 2184.53i −0.180576 + 0.651607i
\(225\) −866.013 866.013i −0.256596 0.256596i
\(226\) 4996.93 318.945i 1.47076 0.0938756i
\(227\) 1006.61 538.044i 0.294322 0.157318i −0.317627 0.948216i \(-0.602886\pi\)
0.611949 + 0.790897i \(0.290386\pi\)
\(228\) −155.009 + 2247.31i −0.0450251 + 0.652772i
\(229\) 3342.86 + 4073.29i 0.964640 + 1.17542i 0.984459 + 0.175614i \(0.0561910\pi\)
−0.0198190 + 0.999804i \(0.506309\pi\)
\(230\) −649.612 1048.65i −0.186235 0.300635i
\(231\) 3148.70 + 626.315i 0.896836 + 0.178392i
\(232\) 263.477 + 884.865i 0.0745607 + 0.250406i
\(233\) 840.035 + 4223.14i 0.236191 + 1.18741i 0.898770 + 0.438421i \(0.144462\pi\)
−0.662579 + 0.748992i \(0.730538\pi\)
\(234\) −104.969 + 3047.29i −0.0293250 + 0.851315i
\(235\) −1411.25 4652.28i −0.391745 1.29141i
\(236\) −3813.54 3596.31i −1.05187 0.991948i
\(237\) −1974.95 + 2406.48i −0.541294 + 0.659568i
\(238\) 261.949 + 34.9416i 0.0713431 + 0.00951651i
\(239\) −1309.50 + 542.411i −0.354411 + 0.146802i −0.552784 0.833325i \(-0.686434\pi\)
0.198373 + 0.980127i \(0.436434\pi\)
\(240\) 663.140 4784.21i 0.178356 1.28675i
\(241\) −5610.30 2323.86i −1.49955 0.621134i −0.526179 0.850374i \(-0.676376\pi\)
−0.973370 + 0.229240i \(0.926376\pi\)
\(242\) −694.433 402.514i −0.184462 0.106920i
\(243\) −506.493 5142.51i −0.133710 1.35758i
\(244\) 1613.97 + 2268.62i 0.423458 + 0.595219i
\(245\) 836.075 1564.19i 0.218020 0.407887i
\(246\) 552.547 206.887i 0.143208 0.0536205i
\(247\) 890.949 + 595.313i 0.229513 + 0.153356i
\(248\) −5898.36 + 3897.58i −1.51027 + 0.997971i
\(249\) −5347.06 8002.44i −1.36087 2.03668i
\(250\) 4234.77 691.734i 1.07132 0.174996i
\(251\) 6487.20 + 638.933i 1.63135 + 0.160674i 0.871829 0.489811i \(-0.162934\pi\)
0.759519 + 0.650485i \(0.225434\pi\)
\(252\) 2834.66 + 2190.54i 0.708598 + 0.547583i
\(253\) 1417.73 + 430.063i 0.352300 + 0.106869i
\(254\) 5864.89 2879.80i 1.44880 0.711396i
\(255\) −563.074 −0.138279
\(256\) −3574.89 + 1999.34i −0.872777 + 0.488119i
\(257\) 3055.64 0.741657 0.370828 0.928701i \(-0.379074\pi\)
0.370828 + 0.928701i \(0.379074\pi\)
\(258\) 7939.98 3898.72i 1.91598 0.940789i
\(259\) −3938.08 1194.60i −0.944790 0.286599i
\(260\) −1817.94 1404.85i −0.433630 0.335096i
\(261\) 1452.04 + 143.013i 0.344364 + 0.0339169i
\(262\) −3913.53 + 639.260i −0.922818 + 0.150739i
\(263\) 3653.18 + 5467.37i 0.856519 + 1.28187i 0.957923 + 0.287026i \(0.0926667\pi\)
−0.101403 + 0.994845i \(0.532333\pi\)
\(264\) 3198.02 + 4839.69i 0.745548 + 1.12827i
\(265\) 2064.20 + 1379.26i 0.478501 + 0.319724i
\(266\) 1179.02 441.455i 0.271769 0.101757i
\(267\) −3056.98 + 5719.21i −0.700690 + 1.31090i
\(268\) −3454.40 4855.56i −0.787354 1.10672i
\(269\) 153.376 + 1557.25i 0.0347639 + 0.352964i 0.996793 + 0.0800185i \(0.0254979\pi\)
−0.962029 + 0.272946i \(0.912002\pi\)
\(270\) −1617.59 937.604i −0.364605 0.211336i
\(271\) −5976.78 2475.66i −1.33972 0.554929i −0.406307 0.913737i \(-0.633184\pi\)
−0.933412 + 0.358807i \(0.883184\pi\)
\(272\) 288.094 + 380.811i 0.0642216 + 0.0848900i
\(273\) 2763.08 1144.51i 0.612562 0.253732i
\(274\) −678.092 90.4511i −0.149507 0.0199429i
\(275\) −703.121 + 856.756i −0.154181 + 0.187870i
\(276\) 2110.89 + 1990.64i 0.460364 + 0.434140i
\(277\) −504.483 1663.06i −0.109428 0.360735i 0.885075 0.465449i \(-0.154107\pi\)
−0.994502 + 0.104714i \(0.966607\pi\)
\(278\) −11.3974 + 330.870i −0.00245889 + 0.0713823i
\(279\) 2179.68 + 10958.0i 0.467721 + 2.35139i
\(280\) −2587.10 + 770.334i −0.552175 + 0.164415i
\(281\) 287.308 + 57.1490i 0.0609941 + 0.0121325i 0.225493 0.974245i \(-0.427601\pi\)
−0.164499 + 0.986377i \(0.552601\pi\)
\(282\) 6021.91 + 9721.01i 1.27163 + 2.05276i
\(283\) 4915.71 + 5989.81i 1.03254 + 1.25815i 0.965500 + 0.260403i \(0.0838555\pi\)
0.0670400 + 0.997750i \(0.478644\pi\)
\(284\) 394.039 5712.75i 0.0823306 1.19362i
\(285\) −2365.70 + 1264.49i −0.491690 + 0.262814i
\(286\) 2753.73 175.765i 0.569341 0.0363399i
\(287\) −233.163 233.163i −0.0479554 0.0479554i
\(288\) 790.064 + 6424.69i 0.161649 + 1.31451i
\(289\) −3434.65 + 3434.65i −0.699095 + 0.699095i
\(290\) −726.299 + 825.337i −0.147068 + 0.167122i
\(291\) −376.421 704.234i −0.0758288 0.141866i
\(292\) 1787.37 + 5325.11i 0.358211 + 1.06722i
\(293\) 4727.92 3880.11i 0.942690 0.773646i −0.0314698 0.999505i \(-0.510019\pi\)
0.974160 + 0.225859i \(0.0725188\pi\)
\(294\) −954.242 + 4061.14i −0.189294 + 0.805614i
\(295\) 1217.73 6121.95i 0.240336 1.20825i
\(296\) −3471.62 6575.77i −0.681701 1.29125i
\(297\) 2202.37 438.078i 0.430284 0.0855888i
\(298\) 3458.32 + 3705.08i 0.672265 + 0.720232i
\(299\) 1320.73 400.640i 0.255451 0.0774903i
\(300\) −1980.18 + 889.065i −0.381085 + 0.171101i
\(301\) −3821.43 3136.17i −0.731772 0.600550i
\(302\) −2289.90 2994.84i −0.436322 0.570641i
\(303\) 3088.27 + 7455.74i 0.585533 + 1.41360i
\(304\) 2065.58 + 952.968i 0.389702 + 0.179791i
\(305\) −1268.73 + 3062.98i −0.238187 + 0.575034i
\(306\) 729.248 194.067i 0.136236 0.0362551i
\(307\) −3649.68 + 359.462i −0.678495 + 0.0668259i −0.431394 0.902164i \(-0.641978\pi\)
−0.247101 + 0.968990i \(0.579478\pi\)
\(308\) 1721.38 2747.22i 0.318456 0.508239i
\(309\) 1269.91 + 678.781i 0.233795 + 0.124966i
\(310\) −7662.26 3487.51i −1.40383 0.638960i
\(311\) −229.529 + 343.515i −0.0418502 + 0.0626332i −0.851805 0.523859i \(-0.824492\pi\)
0.809955 + 0.586493i \(0.199492\pi\)
\(312\) 4981.96 + 2093.57i 0.904000 + 0.379888i
\(313\) 2231.25 1490.88i 0.402933 0.269231i −0.337548 0.941308i \(-0.609598\pi\)
0.740481 + 0.672077i \(0.234598\pi\)
\(314\) 1020.32 1418.74i 0.183377 0.254981i
\(315\) −418.132 + 4245.37i −0.0747907 + 0.759363i
\(316\) 1562.57 + 2727.92i 0.278168 + 0.485626i
\(317\) −2267.67 + 7475.49i −0.401782 + 1.32450i 0.489878 + 0.871791i \(0.337041\pi\)
−0.891660 + 0.452706i \(0.850459\pi\)
\(318\) −5526.24 1886.44i −0.974516 0.332661i
\(319\) 1320.40i 0.231751i
\(320\) −4277.76 2343.19i −0.747293 0.409338i
\(321\) 17073.5i 2.96869i
\(322\) 523.858 1534.62i 0.0906629 0.265593i
\(323\) 76.9826 253.778i 0.0132614 0.0437169i
\(324\) −3209.96 871.872i −0.550405 0.149498i
\(325\) −101.203 + 1027.54i −0.0172731 + 0.175377i
\(326\) −4639.85 3336.88i −0.788274 0.566910i
\(327\) 5442.56 3636.60i 0.920411 0.614999i
\(328\) 3.05326 595.805i 0.000513989 0.100298i
\(329\) 3550.55 5313.77i 0.594979 0.890449i
\(330\) −2861.56 + 6287.00i −0.477344 + 1.04875i
\(331\) 1891.61 + 1011.09i 0.314115 + 0.167898i 0.620919 0.783875i \(-0.286760\pi\)
−0.306804 + 0.951773i \(0.599260\pi\)
\(332\) −9472.73 + 2174.64i −1.56591 + 0.359484i
\(333\) −11694.7 + 1151.83i −1.92453 + 0.189549i
\(334\) −227.176 853.662i −0.0372171 0.139851i
\(335\) 2715.47 6555.73i 0.442872 1.06919i
\(336\) 5414.53 3315.89i 0.879127 0.538382i
\(337\) 13.8137 + 33.3492i 0.00223288 + 0.00539064i 0.924992 0.379986i \(-0.124071\pi\)
−0.922759 + 0.385377i \(0.874071\pi\)
\(338\) −2894.37 + 2213.09i −0.465778 + 0.356142i
\(339\) −10840.9 8896.89i −1.73686 1.42541i
\(340\) −202.111 + 531.481i −0.0322382 + 0.0847753i
\(341\) 9675.52 2935.04i 1.53654 0.466103i
\(342\) 2628.05 2453.02i 0.415522 0.387849i
\(343\) 6499.47 1292.82i 1.02314 0.203516i
\(344\) −829.976 8893.90i −0.130085 1.39397i
\(345\) −674.044 + 3388.65i −0.105186 + 0.528808i
\(346\) −9768.93 2295.40i −1.51786 0.356651i
\(347\) −5717.94 + 4692.59i −0.884596 + 0.725970i −0.962584 0.270985i \(-0.912651\pi\)
0.0779872 + 0.996954i \(0.475151\pi\)
\(348\) 1151.64 2315.33i 0.177398 0.356651i
\(349\) −72.7933 136.187i −0.0111649 0.0208880i 0.876277 0.481808i \(-0.160020\pi\)
−0.887442 + 0.460920i \(0.847520\pi\)
\(350\) 910.692 + 801.412i 0.139082 + 0.122392i
\(351\) 1479.18 1479.18i 0.224937 0.224937i
\(352\) 5716.05 1281.42i 0.865530 0.194034i
\(353\) −105.287 105.287i −0.0158750 0.0158750i 0.699125 0.715000i \(-0.253573\pi\)
−0.715000 + 0.699125i \(0.753573\pi\)
\(354\) 935.198 + 14651.8i 0.140410 + 2.19982i
\(355\) 6013.68 3214.38i 0.899079 0.480568i
\(356\) 4301.04 + 4938.33i 0.640322 + 0.735199i
\(357\) −469.569 572.171i −0.0696140 0.0848250i
\(358\) −5958.57 + 3691.18i −0.879666 + 0.544930i
\(359\) −6231.98 1239.62i −0.916187 0.182241i −0.285590 0.958352i \(-0.592190\pi\)
−0.630596 + 0.776111i \(0.717190\pi\)
\(360\) −5983.41 + 4859.36i −0.875981 + 0.711418i
\(361\) 1091.65 + 5488.11i 0.159156 + 0.800132i
\(362\) 7846.45 + 270.285i 1.13923 + 0.0392427i
\(363\) 652.599 + 2151.33i 0.0943596 + 0.311062i
\(364\) −88.5040 3018.87i −0.0127441 0.434702i
\(365\) −4243.30 + 5170.47i −0.608505 + 0.741465i
\(366\) 1031.06 7729.60i 0.147252 1.10391i
\(367\) 4169.83 1727.20i 0.593089 0.245665i −0.0658902 0.997827i \(-0.520989\pi\)
0.658979 + 0.752162i \(0.270989\pi\)
\(368\) 2636.64 1277.93i 0.373490 0.181023i
\(369\) −869.915 360.331i −0.122726 0.0508349i
\(370\) 4440.40 7660.75i 0.623906 1.07639i
\(371\) 319.877 + 3247.77i 0.0447633 + 0.454490i
\(372\) 19525.9 + 3292.31i 2.72143 + 0.458866i
\(373\) −1900.86 + 3556.26i −0.263868 + 0.493663i −0.978610 0.205726i \(-0.934044\pi\)
0.714741 + 0.699389i \(0.246544\pi\)
\(374\) −239.464 639.553i −0.0331080 0.0884238i
\(375\) −9992.80 6676.98i −1.37607 0.919460i
\(376\) 11337.1 2194.75i 1.55496 0.301026i
\(377\) −683.388 1022.76i −0.0933588 0.139721i
\(378\) −396.218 2425.63i −0.0539133 0.330055i
\(379\) 297.843 + 29.3350i 0.0403672 + 0.00397582i 0.118181 0.992992i \(-0.462294\pi\)
−0.0778134 + 0.996968i \(0.524794\pi\)
\(380\) 344.395 + 2686.84i 0.0464924 + 0.362716i
\(381\) −17512.2 5312.28i −2.35480 0.714322i
\(382\) −793.244 1615.49i −0.106246 0.216376i
\(383\) −10921.1 −1.45703 −0.728514 0.685031i \(-0.759789\pi\)
−0.728514 + 0.685031i \(0.759789\pi\)
\(384\) 11140.7 + 2738.51i 1.48053 + 0.363930i
\(385\) 3860.50 0.511037
\(386\) −3562.38 7255.02i −0.469742 0.956660i
\(387\) −13508.6 4097.80i −1.77437 0.538250i
\(388\) −799.835 + 102.522i −0.104653 + 0.0134143i
\(389\) −5645.36 556.020i −0.735813 0.0724712i −0.276833 0.960918i \(-0.589285\pi\)
−0.458980 + 0.888447i \(0.651785\pi\)
\(390\) 1037.39 + 6350.83i 0.134692 + 0.824581i
\(391\) −189.771 284.013i −0.0245451 0.0367344i
\(392\) 3490.76 + 2358.42i 0.449770 + 0.303872i
\(393\) 9234.77 + 6170.47i 1.18532 + 0.792008i
\(394\) −1165.34 3112.35i −0.149008 0.397964i
\(395\) −1764.70 + 3301.51i −0.224789 + 0.420550i
\(396\) 1539.21 9128.67i 0.195323 1.15842i
\(397\) −951.749 9663.27i −0.120320 1.22163i −0.845844 0.533430i \(-0.820903\pi\)
0.725525 0.688196i \(-0.241597\pi\)
\(398\) −2384.15 + 4113.22i −0.300268 + 0.518033i
\(399\) −3257.77 1349.41i −0.408753 0.169311i
\(400\) 128.413 + 2188.20i 0.0160516 + 0.273525i
\(401\) −3597.47 + 1490.12i −0.448003 + 0.185569i −0.595266 0.803528i \(-0.702953\pi\)
0.147264 + 0.989097i \(0.452953\pi\)
\(402\) −2206.79 + 16543.8i −0.273792 + 2.05256i
\(403\) 5975.44 7281.09i 0.738605 0.899992i
\(404\) 8145.93 238.814i 1.00316 0.0294095i
\(405\) −1149.78 3790.32i −0.141070 0.465044i
\(406\) −1444.36 49.7535i −0.176558 0.00608184i
\(407\) 2074.69 + 10430.2i 0.252675 + 1.27028i
\(408\) 137.911 1330.31i 0.0167344 0.161422i
\(409\) −10192.9 2027.48i −1.23228 0.245116i −0.464353 0.885650i \(-0.653713\pi\)
−0.767930 + 0.640534i \(0.778713\pi\)
\(410\) 603.138 373.628i 0.0726508 0.0450053i
\(411\) 1215.54 + 1481.14i 0.145884 + 0.177760i
\(412\) 1096.52 955.016i 0.131121 0.114200i
\(413\) 7236.37 3867.92i 0.862176 0.460842i
\(414\) −294.951 4621.02i −0.0350146 0.548577i
\(415\) −8183.66 8183.66i −0.968000 0.968000i
\(416\) 3764.34 3950.97i 0.443659 0.465654i
\(417\) 655.683 655.683i 0.0769998 0.0769998i
\(418\) −2442.32 2149.25i −0.285785 0.251491i
\(419\) 4143.08 + 7751.17i 0.483062 + 0.903745i 0.998892 + 0.0470544i \(0.0149834\pi\)
−0.515831 + 0.856691i \(0.672517\pi\)
\(420\) 6769.38 + 3367.09i 0.786458 + 0.391184i
\(421\) −159.437 + 130.846i −0.0184572 + 0.0151474i −0.643577 0.765382i \(-0.722550\pi\)
0.625119 + 0.780529i \(0.285050\pi\)
\(422\) 4191.52 + 984.879i 0.483508 + 0.113609i
\(423\) 3560.23 17898.5i 0.409230 2.05734i
\(424\) −3764.20 + 4539.05i −0.431145 + 0.519896i
\(425\) 250.628 49.8529i 0.0286052 0.00568994i
\(426\) −11724.8 + 10943.9i −1.33349 + 1.24468i
\(427\) −4170.50 + 1265.11i −0.472658 + 0.143379i
\(428\) −16115.5 6128.40i −1.82003 0.692120i
\(429\) −5974.24 4902.93i −0.672352 0.551785i
\(430\) 8449.77 6460.83i 0.947637 0.724579i
\(431\) 3836.38 + 9261.84i 0.428752 + 1.03510i 0.979684 + 0.200548i \(0.0642722\pi\)
−0.550932 + 0.834550i \(0.685728\pi\)
\(432\) 2611.37 3592.06i 0.290832 0.400054i
\(433\) −6275.95 + 15151.5i −0.696542 + 1.68160i 0.0346220 + 0.999400i \(0.488977\pi\)
−0.731164 + 0.682201i \(0.761023\pi\)
\(434\) −2845.99 10694.4i −0.314774 1.18283i
\(435\) 3064.47 301.824i 0.337770 0.0332674i
\(436\) −1479.00 6442.52i −0.162457 0.707663i
\(437\) −1435.11 767.083i −0.157095 0.0839692i
\(438\) 6517.47 14319.2i 0.710997 1.56210i
\(439\) 5742.46 8594.20i 0.624311 0.934348i −0.375660 0.926758i \(-0.622584\pi\)
0.999971 0.00759012i \(-0.00241603\pi\)
\(440\) 4907.12 + 4957.67i 0.531676 + 0.537154i
\(441\) 5535.63 3698.79i 0.597735 0.399394i
\(442\) −516.492 371.450i −0.0555815 0.0399730i
\(443\) 205.522 2086.70i 0.0220421 0.223797i −0.977853 0.209294i \(-0.932883\pi\)
0.999895 0.0145029i \(-0.00461658\pi\)
\(444\) −5459.14 + 20098.9i −0.583512 + 2.14831i
\(445\) −2263.69 + 7462.38i −0.241144 + 0.794946i
\(446\) −5440.07 + 15936.4i −0.577567 + 1.69196i
\(447\) 14195.6i 1.50208i
\(448\) −1186.34 6300.95i −0.125110 0.664490i
\(449\) 10395.4i 1.09263i −0.837580 0.546314i \(-0.816031\pi\)
0.837580 0.546314i \(-0.183969\pi\)
\(450\) 3278.31 + 1119.08i 0.343424 + 0.117231i
\(451\) −247.353 + 815.415i −0.0258258 + 0.0851361i
\(452\) −12289.0 + 7039.17i −1.27881 + 0.732510i
\(453\) −1034.98 + 10508.4i −0.107346 + 1.08990i
\(454\) −1884.90 + 2620.91i −0.194852 + 0.270937i
\(455\) 2990.28 1998.04i 0.308102 0.205867i
\(456\) −2408.06 5898.89i −0.247297 0.605791i
\(457\) −983.909 + 1472.52i −0.100712 + 0.150726i −0.878403 0.477920i \(-0.841391\pi\)
0.777691 + 0.628646i \(0.216391\pi\)
\(458\) −13565.1 6174.20i −1.38396 0.629915i
\(459\) −456.593 244.054i −0.0464312 0.0248180i
\(460\) 2956.58 + 1852.55i 0.299676 + 0.187773i
\(461\) 5529.21 544.580i 0.558614 0.0550187i 0.185229 0.982695i \(-0.440697\pi\)
0.373385 + 0.927677i \(0.378197\pi\)
\(462\) −8774.94 + 2335.18i −0.883652 + 0.235157i
\(463\) 2546.87 6148.70i 0.255644 0.617180i −0.742997 0.669295i \(-0.766596\pi\)
0.998641 + 0.0521151i \(0.0165963\pi\)
\(464\) −1772.05 1918.10i −0.177296 0.191908i
\(465\) 9023.47 + 21784.6i 0.899900 + 2.17255i
\(466\) −7397.51 9674.80i −0.735371 0.961752i
\(467\) 8949.24 + 7344.46i 0.886770 + 0.727753i 0.963047 0.269333i \(-0.0868033\pi\)
−0.0762769 + 0.997087i \(0.524303\pi\)
\(468\) −3532.39 7867.55i −0.348899 0.777089i
\(469\) 8926.19 2707.73i 0.878834 0.266591i
\(470\) 9382.74 + 10052.2i 0.920838 + 0.986541i
\(471\) −4800.57 + 954.893i −0.469636 + 0.0934165i
\(472\) 14165.4 + 4376.43i 1.38139 + 0.426783i
\(473\) −2492.27 + 12529.5i −0.242272 + 1.21798i
\(474\) 2014.11 8571.81i 0.195171 0.830625i
\(475\) 941.032 772.285i 0.0909000 0.0745997i
\(476\) −708.616 + 237.846i −0.0682340 + 0.0229026i
\(477\) 4392.93 + 8218.59i 0.421674 + 0.788896i
\(478\) 2648.45 3009.59i 0.253425 0.287982i
\(479\) −2293.18 + 2293.18i −0.218743 + 0.218743i −0.807969 0.589225i \(-0.799433\pi\)
0.589225 + 0.807969i \(0.299433\pi\)
\(480\) 4280.59 + 12973.2i 0.407045 + 1.23363i
\(481\) 7005.27 + 7005.27i 0.664060 + 0.664060i
\(482\) 17140.9 1094.07i 1.61980 0.103389i
\(483\) −4005.51 + 2140.99i −0.377344 + 0.201694i
\(484\) 2264.87 + 156.220i 0.212704 + 0.0146713i
\(485\) −609.161 742.265i −0.0570321 0.0694939i
\(486\) 7696.81 + 12424.8i 0.718383 + 1.15967i
\(487\) 786.298 + 156.404i 0.0731634 + 0.0145531i 0.231536 0.972826i \(-0.425625\pi\)
−0.158373 + 0.987379i \(0.550625\pi\)
\(488\) −6925.82 3747.69i −0.642453 0.347643i
\(489\) 3122.89 + 15699.8i 0.288798 + 1.45188i
\(490\) −172.701 + 5013.56i −0.0159221 + 0.462224i
\(491\) −705.851 2326.88i −0.0648770 0.213871i 0.918508 0.395402i \(-0.129395\pi\)
−0.983385 + 0.181531i \(0.941895\pi\)
\(492\) −1144.93 + 1214.09i −0.104914 + 0.111251i
\(493\) −193.130 + 235.329i −0.0176432 + 0.0214984i
\(494\) −3004.15 400.726i −0.273610 0.0364970i
\(495\) 10184.6 4218.61i 0.924778 0.383056i
\(496\) 10116.3 17248.6i 0.915794 1.56146i
\(497\) 8281.35 + 3430.25i 0.747423 + 0.309593i
\(498\) 23551.7 + 13651.3i 2.11923 + 1.22837i
\(499\) 1017.85 + 10334.4i 0.0913128 + 0.927114i 0.926285 + 0.376823i \(0.122983\pi\)
−0.834973 + 0.550292i \(0.814517\pi\)
\(500\) −9889.19 + 7035.48i −0.884516 + 0.629273i
\(501\) −1166.34 + 2182.06i −0.104008 + 0.194586i
\(502\) −17266.7 + 6465.07i −1.53516 + 0.574801i
\(503\) −2861.62 1912.07i −0.253664 0.169493i 0.422236 0.906486i \(-0.361245\pi\)
−0.675901 + 0.736993i \(0.736245\pi\)
\(504\) −9927.66 2027.68i −0.877407 0.179206i
\(505\) 5391.39 + 8068.79i 0.475077 + 0.711003i
\(506\) −4135.57 + 675.530i −0.363337 + 0.0593498i
\(507\) 10155.9 + 1000.26i 0.889620 + 0.0876199i
\(508\) −11300.1 + 14622.9i −0.986932 + 1.27714i
\(509\) 13418.6 + 4070.49i 1.16851 + 0.354463i 0.814154 0.580649i \(-0.197201\pi\)
0.354353 + 0.935112i \(0.384701\pi\)
\(510\) 1429.57 701.954i 0.124123 0.0609471i
\(511\) −8792.66 −0.761183
\(512\) 6583.74 9532.69i 0.568287 0.822831i
\(513\) −2466.40 −0.212269
\(514\) −7757.89 + 3809.31i −0.665731 + 0.326890i
\(515\) 1656.97 + 502.636i 0.141776 + 0.0430074i
\(516\) −15298.3 + 19796.7i −1.30517 + 1.68896i
\(517\) −16435.3 1618.74i −1.39812 0.137702i
\(518\) 11487.5 1876.45i 0.974389 0.159163i
\(519\) 15615.2 + 23369.9i 1.32068 + 1.97654i
\(520\) 6366.86 + 1300.40i 0.536933 + 0.109666i
\(521\) 8039.26 + 5371.66i 0.676020 + 0.451702i 0.845602 0.533814i \(-0.179242\pi\)
−0.169582 + 0.985516i \(0.554242\pi\)
\(522\) −3864.83 + 1447.09i −0.324059 + 0.121336i
\(523\) 1920.49 3592.99i 0.160569 0.300403i −0.788752 0.614711i \(-0.789273\pi\)
0.949321 + 0.314308i \(0.101773\pi\)
\(524\) 9139.01 6501.78i 0.761908 0.542045i
\(525\) −333.038 3381.39i −0.0276856 0.281097i
\(526\) −16090.8 9326.73i −1.33383 0.773127i
\(527\) −2153.71 892.098i −0.178021 0.0737389i
\(528\) −14152.7 8300.54i −1.16651 0.684157i
\(529\) 9304.45 3854.03i 0.764728 0.316761i
\(530\) −6960.19 928.424i −0.570436 0.0760909i
\(531\) 14864.0 18111.8i 1.21477 1.48020i
\(532\) −2443.05 + 2590.62i −0.199097 + 0.211123i
\(533\) 230.430 + 759.627i 0.0187262 + 0.0617319i
\(534\) 631.454 18331.3i 0.0511717 1.48553i
\(535\) −4005.39 20136.5i −0.323679 1.62724i
\(536\) 14823.4 + 8021.23i 1.19454 + 0.646389i
\(537\) 19254.8 + 3830.01i 1.54731 + 0.307778i
\(538\) −2330.75 3762.46i −0.186776 0.301508i
\(539\) −3822.18 4657.34i −0.305442 0.372182i
\(540\) 5275.71 + 363.894i 0.420427 + 0.0289991i
\(541\) 14392.4 7692.88i 1.14376 0.611355i 0.213028 0.977046i \(-0.431667\pi\)
0.930736 + 0.365691i \(0.119167\pi\)
\(542\) 18260.6 1165.54i 1.44716 0.0923692i
\(543\) −15549.2 15549.2i −1.22888 1.22888i
\(544\) −1206.17 607.679i −0.0950628 0.0478935i
\(545\) 5565.81 5565.81i 0.437455 0.437455i
\(546\) −5588.32 + 6350.35i −0.438019 + 0.497747i
\(547\) 5490.07 + 10271.2i 0.429138 + 0.802861i 0.999833 0.0183018i \(-0.00582596\pi\)
−0.570695 + 0.821162i \(0.693326\pi\)
\(548\) 1834.35 615.697i 0.142992 0.0479950i
\(549\) −9620.00 + 7894.93i −0.747854 + 0.613748i
\(550\) 717.064 3051.74i 0.0555922 0.236594i
\(551\) −282.937 + 1422.42i −0.0218757 + 0.109977i
\(552\) −7840.91 2422.46i −0.604585 0.186788i
\(553\) −4826.50 + 960.051i −0.371146 + 0.0738256i
\(554\) 3354.06 + 3593.38i 0.257221 + 0.275574i
\(555\) −23732.7 + 7199.25i −1.81513 + 0.550614i
\(556\) −383.542 854.246i −0.0292550 0.0651585i
\(557\) −2519.05 2067.33i −0.191626 0.157263i 0.533688 0.845681i \(-0.320806\pi\)
−0.725314 + 0.688418i \(0.758306\pi\)
\(558\) −19194.7 25103.7i −1.45623 1.90452i
\(559\) 4554.29 + 10995.0i 0.344590 + 0.831914i
\(560\) 5607.99 5180.98i 0.423180 0.390958i
\(561\) −731.979 + 1767.15i −0.0550877 + 0.132993i
\(562\) −800.682 + 213.077i −0.0600974 + 0.0159931i
\(563\) 17771.9 1750.38i 1.33037 0.131030i 0.592278 0.805734i \(-0.298229\pi\)
0.738088 + 0.674704i \(0.235729\pi\)
\(564\) −27407.5 17173.2i −2.04621 1.28213i
\(565\) −14872.9 7949.74i −1.10745 0.591943i
\(566\) −19947.5 9079.22i −1.48137 0.674254i
\(567\) 2892.72 4329.26i 0.214255 0.320656i
\(568\) 6121.36 + 14995.2i 0.452195 + 1.10772i
\(569\) −518.063 + 346.159i −0.0381693 + 0.0255039i −0.574509 0.818499i \(-0.694807\pi\)
0.536339 + 0.844003i \(0.319807\pi\)
\(570\) 4429.83 6159.57i 0.325518 0.452624i
\(571\) 1441.94 14640.2i 0.105680 1.07298i −0.785354 0.619047i \(-0.787519\pi\)
0.891034 0.453937i \(-0.149981\pi\)
\(572\) −6772.25 + 3879.17i −0.495038 + 0.283560i
\(573\) −1463.27 + 4823.77i −0.106683 + 0.351686i
\(574\) 882.644 + 301.300i 0.0641827 + 0.0219094i
\(575\) 1567.99i 0.113721i
\(576\) −10015.2 15326.5i −0.724478 1.10869i
\(577\) 22999.0i 1.65938i −0.558228 0.829688i \(-0.688518\pi\)
0.558228 0.829688i \(-0.311482\pi\)
\(578\) 4438.35 13001.9i 0.319396 0.935657i
\(579\) −6571.43 + 21663.1i −0.471674 + 1.55490i
\(580\) 815.078 3000.86i 0.0583522 0.214835i
\(581\) 1491.21 15140.5i 0.106482 1.08113i
\(582\) 1833.62 + 1318.70i 0.130594 + 0.0939205i
\(583\) 7012.07 4685.31i 0.498131 0.332840i
\(584\) −11176.4 11291.6i −0.791925 0.800083i
\(585\) 5705.46 8538.82i 0.403234 0.603482i
\(586\) −7166.47 + 15745.1i −0.505195 + 1.10994i
\(587\) 13137.0 + 7021.86i 0.923716 + 0.493736i 0.863443 0.504446i \(-0.168303\pi\)
0.0602722 + 0.998182i \(0.480803\pi\)
\(588\) −2640.10 11500.3i −0.185163 0.806573i
\(589\) −11052.0 + 1088.53i −0.773157 + 0.0761493i
\(590\) 4540.24 + 17060.9i 0.316811 + 1.19049i
\(591\) −3562.14 + 8599.76i −0.247930 + 0.598556i
\(592\) 17011.7 + 12367.2i 1.18104 + 0.858594i
\(593\) −4485.39 10828.7i −0.310612 0.749884i −0.999683 0.0251899i \(-0.991981\pi\)
0.689070 0.724694i \(-0.258019\pi\)
\(594\) −5045.40 + 3857.80i −0.348511 + 0.266477i
\(595\) −688.038 564.658i −0.0474064 0.0389054i
\(596\) −13399.2 5095.41i −0.920890 0.350195i
\(597\) 12742.6 3865.43i 0.873570 0.264994i
\(598\) −2853.71 + 2663.66i −0.195146 + 0.182149i
\(599\) −9805.39 + 1950.41i −0.668844 + 0.133041i −0.517821 0.855489i \(-0.673257\pi\)
−0.151023 + 0.988530i \(0.548257\pi\)
\(600\) 3919.06 4725.80i 0.266659 0.321550i
\(601\) −4911.42 + 24691.4i −0.333346 + 1.67584i 0.343059 + 0.939314i \(0.388537\pi\)
−0.676405 + 0.736530i \(0.736463\pi\)
\(602\) 13611.8 + 3198.35i 0.921555 + 0.216537i
\(603\) 20589.8 16897.6i 1.39052 1.14117i
\(604\) 9547.28 + 4748.81i 0.643168 + 0.319911i
\(605\) 1274.37 + 2384.18i 0.0856371 + 0.160216i
\(606\) −17135.4 15079.2i −1.14864 1.01081i
\(607\) −10446.0 + 10446.0i −0.698503 + 0.698503i −0.964088 0.265584i \(-0.914435\pi\)
0.265584 + 0.964088i \(0.414435\pi\)
\(608\) −6432.27 + 155.588i −0.429051 + 0.0103782i
\(609\) 2862.28 + 2862.28i 0.190452 + 0.190452i
\(610\) −597.314 9358.16i −0.0396468 0.621149i
\(611\) −13568.3 + 7252.43i −0.898390 + 0.480199i
\(612\) −1609.54 + 1401.83i −0.106310 + 0.0925906i
\(613\) −117.499 143.173i −0.00774185 0.00943348i 0.769125 0.639098i \(-0.220692\pi\)
−0.776867 + 0.629665i \(0.783192\pi\)
\(614\) 8817.94 5462.48i 0.579582 0.359036i
\(615\) −1949.00 387.680i −0.127791 0.0254192i
\(616\) −945.537 + 9120.79i −0.0618454 + 0.596570i
\(617\) −3122.24 15696.6i −0.203722 1.02418i −0.938344 0.345704i \(-0.887640\pi\)
0.734621 0.678477i \(-0.237360\pi\)
\(618\) −4070.34 140.210i −0.264940 0.00912633i
\(619\) −3424.66 11289.6i −0.222373 0.733065i −0.995148 0.0983858i \(-0.968632\pi\)
0.772775 0.634680i \(-0.218868\pi\)
\(620\) 23801.2 697.779i 1.54174 0.0451991i
\(621\) −2015.33 + 2455.68i −0.130229 + 0.158685i
\(622\) 154.504 1158.28i 0.00995988 0.0746670i
\(623\) −9470.73 + 3922.90i −0.609048 + 0.252276i
\(624\) −15258.5 + 895.435i −0.978893 + 0.0574457i
\(625\) −9396.60 3892.20i −0.601382 0.249101i
\(626\) −3806.27 + 6566.73i −0.243018 + 0.419264i
\(627\) 893.152 + 9068.32i 0.0568884 + 0.577598i
\(628\) −821.812 + 4873.98i −0.0522195 + 0.309702i
\(629\) 1155.82 2162.38i 0.0732677 0.137074i
\(630\) −4230.88 11299.7i −0.267560 0.714589i
\(631\) −5956.70 3980.14i −0.375804 0.251104i 0.353296 0.935512i \(-0.385061\pi\)
−0.729100 + 0.684407i \(0.760061\pi\)
\(632\) −7367.91 4977.89i −0.463734 0.313306i
\(633\) −6699.98 10027.2i −0.420696 0.629616i
\(634\) −3561.98 21806.3i −0.223130 1.36599i
\(635\) −21900.2 2156.98i −1.36863 0.134798i
\(636\) 16382.1 2099.84i 1.02137 0.130918i
\(637\) −5371.05 1629.29i −0.334080 0.101342i
\(638\) 1646.08 + 3352.34i 0.102145 + 0.208026i
\(639\) 25596.0 1.58460
\(640\) 13781.8 + 616.212i 0.851209 + 0.0380592i
\(641\) −15716.0 −0.968400 −0.484200 0.874957i \(-0.660889\pi\)
−0.484200 + 0.874957i \(0.660889\pi\)
\(642\) 21284.6 + 43347.4i 1.30847 + 2.66478i
\(643\) −7703.48 2336.83i −0.472466 0.143321i 0.0450674 0.998984i \(-0.485650\pi\)
−0.517534 + 0.855663i \(0.673150\pi\)
\(644\) 583.117 + 4549.26i 0.0356802 + 0.278363i
\(645\) −29648.8 2920.15i −1.80995 0.178265i
\(646\) 120.922 + 740.279i 0.00736472 + 0.0450865i
\(647\) 4537.55 + 6790.93i 0.275718 + 0.412641i 0.943324 0.331874i \(-0.107681\pi\)
−0.667606 + 0.744515i \(0.732681\pi\)
\(648\) 9236.61 1788.12i 0.559951 0.108401i
\(649\) −17630.1 11780.1i −1.06632 0.712494i
\(650\) −1024.03 2734.95i −0.0617935 0.165036i
\(651\) −14611.5 + 27336.3i −0.879679 + 1.64576i
\(652\) 15939.9 + 2687.66i 0.957445 + 0.161437i
\(653\) 2791.49 + 28342.5i 0.167289 + 1.69851i 0.602448 + 0.798158i \(0.294192\pi\)
−0.435160 + 0.900353i \(0.643308\pi\)
\(654\) −9284.41 + 16017.8i −0.555121 + 0.957716i
\(655\) 12339.0 + 5111.00i 0.736070 + 0.304890i
\(656\) 735.007 + 1516.48i 0.0437457 + 0.0902570i
\(657\) −23196.5 + 9608.29i −1.37744 + 0.570556i
\(658\) −2390.00 + 17917.3i −0.141598 + 1.06153i
\(659\) 15096.6 18395.3i 0.892385 1.08737i −0.103306 0.994650i \(-0.532942\pi\)
0.995692 0.0927252i \(-0.0295578\pi\)
\(660\) −572.538 19529.2i −0.0337667 1.15178i
\(661\) −4966.51 16372.4i −0.292247 0.963408i −0.972982 0.230879i \(-0.925840\pi\)
0.680736 0.732529i \(-0.261660\pi\)
\(662\) −6063.02 208.851i −0.355960 0.0122617i
\(663\) 347.629 + 1747.65i 0.0203632 + 0.102373i
\(664\) 21339.1 17330.3i 1.24716 1.01287i
\(665\) −4158.77 827.231i −0.242512 0.0482386i
\(666\) 28255.5 17503.5i 1.64396 1.01839i
\(667\) 1185.05 + 1443.99i 0.0687935 + 0.0838251i
\(668\) 1640.99 + 1884.13i 0.0950473 + 0.109131i
\(669\) 41595.7 22233.4i 2.40386 1.28489i
\(670\) 1278.44 + 20029.4i 0.0737171 + 1.15493i
\(671\) 7963.56 + 7963.56i 0.458167 + 0.458167i
\(672\) −9613.06 + 15168.6i −0.551833 + 0.870747i
\(673\) 6028.57 6028.57i 0.345296 0.345296i −0.513058 0.858354i \(-0.671487\pi\)
0.858354 + 0.513058i \(0.171487\pi\)
\(674\) −76.6458 67.4485i −0.00438025 0.00385463i
\(675\) −1120.31 2095.94i −0.0638824 0.119515i
\(676\) 4589.51 9227.00i 0.261124 0.524977i
\(677\) −1954.06 + 1603.66i −0.110932 + 0.0910393i −0.688224 0.725498i \(-0.741609\pi\)
0.577292 + 0.816538i \(0.304109\pi\)
\(678\) 38614.9 + 9073.31i 2.18731 + 0.513950i
\(679\) 246.255 1238.01i 0.0139181 0.0699710i
\(680\) −149.435 1601.32i −0.00842731 0.0903058i
\(681\) 8868.37 1764.03i 0.499026 0.0992624i
\(682\) −20906.0 + 19513.6i −1.17380 + 1.09562i
\(683\) −23404.0 + 7099.52i −1.31117 + 0.397739i −0.867046 0.498227i \(-0.833984\pi\)
−0.444122 + 0.895966i \(0.646484\pi\)
\(684\) −3614.23 + 9504.15i −0.202037 + 0.531287i
\(685\) 1781.08 + 1461.69i 0.0993453 + 0.0815306i
\(686\) −14889.6 + 11384.9i −0.828701 + 0.633638i
\(687\) 15974.9 + 38566.8i 0.887162 + 2.14180i
\(688\) 13194.8 + 21545.8i 0.731171 + 1.19393i
\(689\) 3006.50 7258.33i 0.166239 0.401336i
\(690\) −2513.13 9443.64i −0.138657 0.521034i
\(691\) 20862.2 2054.75i 1.14853 0.113121i 0.494214 0.869340i \(-0.335456\pi\)
0.654318 + 0.756220i \(0.272956\pi\)
\(692\) 27663.6 6350.68i 1.51967 0.348868i
\(693\) 12780.1 + 6831.12i 0.700544 + 0.374448i
\(694\) 8667.11 19042.1i 0.474062 1.04154i
\(695\) 619.490 927.132i 0.0338109 0.0506016i
\(696\) −37.4814 + 7314.01i −0.00204128 + 0.398329i
\(697\) 163.352 109.148i 0.00887717 0.00593153i
\(698\) 354.590 + 255.013i 0.0192284 + 0.0138286i
\(699\) −3343.51 + 33947.2i −0.180920 + 1.83691i
\(700\) −3311.21 899.371i −0.178788 0.0485615i
\(701\) 4658.24 15356.2i 0.250983 0.827381i −0.737407 0.675448i \(-0.763950\pi\)
0.988391 0.151933i \(-0.0485498\pi\)
\(702\) −1911.44 + 5599.48i −0.102767 + 0.301052i
\(703\) 11680.6i 0.626661i
\(704\) −12914.8 + 10379.3i −0.691401 + 0.555658i
\(705\) 38514.1i 2.05748i
\(706\) 398.566 + 136.055i 0.0212468 + 0.00725281i
\(707\) −3703.07 + 12207.4i −0.196985 + 0.649371i
\(708\) −20640.0 36033.2i −1.09562 1.91273i
\(709\) 16.7751 170.320i 0.000888579 0.00902189i −0.994730 0.102527i \(-0.967307\pi\)
0.995619 + 0.0935052i \(0.0298072\pi\)
\(710\) −11260.8 + 15657.8i −0.595224 + 0.827645i
\(711\) −11684.0 + 7807.00i −0.616293 + 0.411794i
\(712\) −17076.1 7175.91i −0.898813 0.377709i
\(713\) −7946.93 + 11893.4i −0.417412 + 0.624701i
\(714\) 1905.47 + 867.283i 0.0998746 + 0.0454584i
\(715\) −8196.22 4380.97i −0.428701 0.229145i
\(716\) 10526.5 16799.7i 0.549431 0.876862i
\(717\) −11174.6 + 1100.60i −0.582039 + 0.0573258i
\(718\) 17367.6 4621.84i 0.902718 0.240231i
\(719\) −819.170 + 1977.65i −0.0424894 + 0.102579i −0.943699 0.330804i \(-0.892680\pi\)
0.901210 + 0.433383i \(0.142680\pi\)
\(720\) 9133.21 19796.5i 0.472742 1.02468i
\(721\) 871.054 + 2102.91i 0.0449927 + 0.108622i
\(722\) −9613.29 12572.7i −0.495526 0.648071i
\(723\) −37187.3 30518.8i −1.91288 1.56986i
\(724\) −20258.1 + 9095.53i −1.03990 + 0.466896i
\(725\) −1337.29 + 405.663i −0.0685045 + 0.0207806i
\(726\) −4338.81 4648.39i −0.221802 0.237628i
\(727\) 9664.54 1922.40i 0.493037 0.0980711i 0.0576912 0.998334i \(-0.481626\pi\)
0.435346 + 0.900263i \(0.356626\pi\)
\(728\) 3988.16 + 7554.18i 0.203037 + 0.384583i
\(729\) 5796.18 29139.4i 0.294477 1.48043i
\(730\) 4327.44 18417.1i 0.219405 0.933762i
\(731\) 2276.82 1868.53i 0.115200 0.0945420i
\(732\) 7018.36 + 20909.8i 0.354380 + 1.05581i
\(733\) 16398.6 + 30679.7i 0.826327 + 1.54595i 0.837775 + 0.546015i \(0.183856\pi\)
−0.0114483 + 0.999934i \(0.503644\pi\)
\(734\) −8433.46 + 9583.45i −0.424094 + 0.481923i
\(735\) 9935.33 9935.33i 0.498599 0.498599i
\(736\) −5100.98 + 6531.45i −0.255468 + 0.327109i
\(737\) −17044.5 17044.5i −0.851890 0.851890i
\(738\) 2657.81 169.643i 0.132568 0.00846158i
\(739\) −27467.4 + 14681.6i −1.36726 + 0.730814i −0.981442 0.191761i \(-0.938580\pi\)
−0.385816 + 0.922576i \(0.626080\pi\)
\(740\) −1723.37 + 24985.3i −0.0856111 + 1.24118i
\(741\) 5385.22 + 6561.91i 0.266978 + 0.325314i
\(742\) −4860.94 7846.89i −0.240500 0.388232i
\(743\) 23741.1 + 4722.40i 1.17224 + 0.233174i 0.742543 0.669798i \(-0.233620\pi\)
0.429699 + 0.902972i \(0.358620\pi\)
\(744\) −53678.2 + 15983.2i −2.64508 + 0.787596i
\(745\) −3330.25 16742.3i −0.163773 0.823343i
\(746\) 392.644 11398.6i 0.0192704 0.559426i
\(747\) −12611.0 41572.8i −0.617686 2.03624i
\(748\) 1405.27 + 1325.22i 0.0686920 + 0.0647790i
\(749\) 17121.5 20862.7i 0.835257 1.01776i
\(750\) 33694.3 + 4494.50i 1.64045 + 0.218821i
\(751\) −10120.1 + 4191.87i −0.491727 + 0.203680i −0.614747 0.788724i \(-0.710742\pi\)
0.123020 + 0.992404i \(0.460742\pi\)
\(752\) −26047.4 + 19705.6i −1.26310 + 0.955569i
\(753\) 47709.8 + 19762.0i 2.30895 + 0.956399i
\(754\) 3010.06 + 1744.72i 0.145384 + 0.0842692i
\(755\) 1244.57 + 12636.4i 0.0599929 + 0.609118i
\(756\) 4029.85 + 5664.42i 0.193868 + 0.272504i
\(757\) −5110.30 + 9560.69i −0.245359 + 0.459035i −0.974212 0.225636i \(-0.927554\pi\)
0.728852 + 0.684671i \(0.240054\pi\)
\(758\) −792.756 + 296.827i −0.0379871 + 0.0142233i
\(759\) 9758.72 + 6520.57i 0.466692 + 0.311834i
\(760\) −4223.92 6392.21i −0.201602 0.305092i
\(761\) −13976.9 20917.9i −0.665784 0.996417i −0.998572 0.0534152i \(-0.982989\pi\)
0.332788 0.943002i \(-0.392011\pi\)
\(762\) 51083.9 8344.37i 2.42858 0.396699i
\(763\) 10297.3 + 1014.19i 0.488580 + 0.0481209i
\(764\) 4027.89 + 3112.63i 0.190738 + 0.147397i
\(765\) −2432.19 737.798i −0.114949 0.0348695i
\(766\) 27727.3 13614.7i 1.30787 0.642194i
\(767\) −19752.9 −0.929904
\(768\) −31698.8 + 6935.83i −1.48937 + 0.325879i
\(769\) −2363.19 −0.110818 −0.0554088 0.998464i \(-0.517646\pi\)
−0.0554088 + 0.998464i \(0.517646\pi\)
\(770\) −9801.32 + 4812.68i −0.458721 + 0.225243i
\(771\) 23164.7 + 7026.92i 1.08204 + 0.328234i
\(772\) 18088.9 + 13978.5i 0.843307 + 0.651682i
\(773\) −19658.9 1936.23i −0.914723 0.0900924i −0.370309 0.928909i \(-0.620748\pi\)
−0.544415 + 0.838816i \(0.683248\pi\)
\(774\) 39405.2 6436.70i 1.82996 0.298918i
\(775\) −5945.15 8897.54i −0.275556 0.412399i
\(776\) 1902.87 1257.40i 0.0880271 0.0581676i
\(777\) −27107.2 18112.5i −1.25156 0.836268i
\(778\) 15026.0 5626.11i 0.692428 0.259262i
\(779\) 441.192 825.412i 0.0202918 0.0379634i
\(780\) −10551.0 14830.7i −0.484343 0.680800i
\(781\) −2270.42 23052.0i −0.104023 1.05616i
\(782\) 835.869 + 484.495i 0.0382233 + 0.0221554i
\(783\) 2615.78 + 1083.49i 0.119387 + 0.0494518i
\(784\) −11802.7 1635.97i −0.537660 0.0745250i
\(785\) −5437.77 + 2252.40i −0.247239 + 0.102410i
\(786\) −31138.3 4153.56i −1.41306 0.188489i
\(787\) −18291.0 + 22287.6i −0.828467 + 1.00949i 0.171238 + 0.985230i \(0.445223\pi\)
−0.999706 + 0.0242606i \(0.992277\pi\)
\(788\) 6838.65 + 6449.09i 0.309158 + 0.291547i
\(789\) 15121.5 + 49848.8i 0.682305 + 2.24926i
\(790\) 364.518 10582.1i 0.0164164 0.476574i
\(791\) −4324.91 21742.8i −0.194407 0.977351i
\(792\) 7472.38 + 25095.4i 0.335252 + 1.12592i
\(793\) 10290.1 + 2046.82i 0.460795 + 0.0916579i
\(794\) 14463.0 + 23347.3i 0.646441 + 1.04353i
\(795\) 12476.8 + 15203.0i 0.556611 + 0.678233i
\(796\) 925.313 13415.1i 0.0412021 0.597345i
\(797\) −5054.73 + 2701.81i −0.224652 + 0.120079i −0.579884 0.814699i \(-0.696902\pi\)
0.355231 + 0.934778i \(0.384402\pi\)
\(798\) 9953.29 635.300i 0.441532 0.0281822i
\(799\) 2692.42 + 2692.42i 0.119213 + 0.119213i
\(800\) −3053.93 5395.47i −0.134966 0.238448i
\(801\) −20698.5 + 20698.5i −0.913041 + 0.913041i
\(802\) 7275.87 8268.00i 0.320349 0.364032i
\(803\) 10710.9 + 20038.7i 0.470709 + 0.880634i
\(804\) −15021.5 44753.6i −0.658914 1.96311i
\(805\) −4221.82 + 3464.76i −0.184844 + 0.151698i
\(806\) −6093.93 + 25935.0i −0.266314 + 1.13340i
\(807\) −2418.41 + 12158.2i −0.105492 + 0.530344i
\(808\) −20383.8 + 10761.4i −0.887498 + 0.468546i
\(809\) 39417.5 7840.64i 1.71304 0.340744i 0.761473 0.648196i \(-0.224476\pi\)
0.951564 + 0.307452i \(0.0994763\pi\)
\(810\) 7644.35 + 8189.78i 0.331599 + 0.355259i
\(811\) 38786.3 11765.7i 1.67937 0.509433i 0.700458 0.713694i \(-0.252979\pi\)
0.978916 + 0.204261i \(0.0654792\pi\)
\(812\) 3729.07 1674.29i 0.161164 0.0723597i
\(813\) −39616.5 32512.4i −1.70899 1.40253i
\(814\) −18270.2 23894.5i −0.786693 1.02887i
\(815\) 7366.26 + 17783.7i 0.316600 + 0.764340i
\(816\) 1308.29 + 3549.42i 0.0561267 + 0.152273i
\(817\) 5369.65 12963.5i 0.229939 0.555122i
\(818\) 28405.9 7559.36i 1.21417 0.323113i
\(819\) 13434.8 1323.21i 0.573198 0.0564551i
\(820\) −1065.51 + 1700.49i −0.0453770 + 0.0724193i
\(821\) 4694.17 + 2509.09i 0.199547 + 0.106660i 0.568144 0.822929i \(-0.307662\pi\)
−0.368597 + 0.929589i \(0.620162\pi\)
\(822\) −4932.57 2245.08i −0.209298 0.0952630i
\(823\) −12891.6 + 19293.7i −0.546019 + 0.817175i −0.997163 0.0752764i \(-0.976016\pi\)
0.451144 + 0.892451i \(0.351016\pi\)
\(824\) −1593.36 + 3791.64i −0.0673633 + 0.160301i
\(825\) −7300.56 + 4878.08i −0.308088 + 0.205858i
\(826\) −13550.3 + 18841.4i −0.570793 + 0.793674i
\(827\) 3718.42 37753.7i 0.156351 1.58746i −0.522149 0.852854i \(-0.674869\pi\)
0.678499 0.734601i \(-0.262631\pi\)
\(828\) 6509.62 + 11364.5i 0.273219 + 0.476985i
\(829\) −2160.23 + 7121.31i −0.0905039 + 0.298351i −0.990493 0.137560i \(-0.956074\pi\)
0.899990 + 0.435912i \(0.143574\pi\)
\(830\) 30979.4 + 10575.1i 1.29555 + 0.442251i
\(831\) 13767.7i 0.574724i
\(832\) −4631.73 + 14723.8i −0.193000 + 0.613529i
\(833\) 1389.11i 0.0577788i
\(834\) −847.290 + 2482.10i −0.0351790 + 0.103055i
\(835\) −863.670 + 2847.14i −0.0357947 + 0.117999i
\(836\) 8880.11 + 2411.96i 0.367374 + 0.0997841i
\(837\) −2125.05 + 21576.0i −0.0877570 + 0.891012i
\(838\) −20181.7 14514.3i −0.831940 0.598314i
\(839\) −25731.1 + 17193.0i −1.05880 + 0.707470i −0.957806 0.287417i \(-0.907203\pi\)
−0.100998 + 0.994887i \(0.532203\pi\)
\(840\) −21384.2 109.585i −0.878362 0.00450126i
\(841\) −12624.9 + 18894.4i −0.517646 + 0.774711i
\(842\) 241.670 530.963i 0.00989135 0.0217318i
\(843\) 2046.64 + 1093.95i 0.0836180 + 0.0446948i
\(844\) −11869.5 + 2724.87i −0.484083 + 0.111130i
\(845\) 12212.5 1202.82i 0.497185 0.0489684i
\(846\) 13274.1 + 49880.4i 0.539449 + 2.02710i
\(847\) −1359.95 + 3283.21i −0.0551694 + 0.133191i
\(848\) 3898.22 16216.7i 0.157860 0.656702i
\(849\) 23491.2 + 56712.9i 0.949608 + 2.29256i
\(850\) −574.163 + 439.014i −0.0231690 + 0.0177154i
\(851\) −11629.9 9544.38i −0.468468 0.384462i
\(852\) 16124.5 42401.9i 0.648377 1.70500i
\(853\) −5025.74 + 1524.54i −0.201733 + 0.0611949i −0.389534 0.921012i \(-0.627364\pi\)
0.187801 + 0.982207i \(0.439864\pi\)
\(854\) 9011.23 8411.09i 0.361075 0.337028i
\(855\) −11875.5 + 2362.18i −0.475009 + 0.0944852i
\(856\) 48555.3 4531.16i 1.93877 0.180925i
\(857\) −903.695 + 4543.18i −0.0360206 + 0.181088i −0.994607 0.103713i \(-0.966928\pi\)
0.958587 + 0.284801i \(0.0919275\pi\)
\(858\) 21280.1 + 5000.16i 0.846724 + 0.198954i
\(859\) 29811.1 24465.3i 1.18410 0.971765i 0.184161 0.982896i \(-0.441043\pi\)
0.999938 + 0.0111309i \(0.00354314\pi\)
\(860\) −13398.5 + 26937.1i −0.531262 + 1.06808i
\(861\) −1231.40 2303.79i −0.0487411 0.0911882i
\(862\) −21286.3 18732.0i −0.841084 0.740157i
\(863\) −5533.39 + 5533.39i −0.218261 + 0.218261i −0.807765 0.589504i \(-0.799323\pi\)
0.589504 + 0.807765i \(0.299323\pi\)
\(864\) −2151.89 + 12375.2i −0.0847325 + 0.487285i
\(865\) 23899.1 + 23899.1i 0.939414 + 0.939414i
\(866\) −2954.70 46291.6i −0.115941 1.81646i
\(867\) −33936.4 + 18139.4i −1.32934 + 0.710549i
\(868\) 20557.8 + 23603.9i 0.803890 + 0.923003i
\(869\) 8067.44 + 9830.21i 0.314924 + 0.383736i
\(870\) −7404.02 + 4586.60i −0.288529 + 0.178736i
\(871\) −22024.0 4380.84i −0.856778 0.170424i
\(872\) 11786.5 + 14513.0i 0.457732 + 0.563613i
\(873\) −703.187 3535.16i −0.0272615 0.137053i
\(874\) 4599.84 + 158.450i 0.178023 + 0.00613231i
\(875\) −5514.76 18179.7i −0.213066 0.702385i
\(876\) 1304.01 + 44479.7i 0.0502950 + 1.71556i
\(877\) 9511.67 11590.0i 0.366233 0.446256i −0.556991 0.830519i \(-0.688044\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(878\) −3865.45 + 28978.4i −0.148579 + 1.11386i
\(879\) 44765.0 18542.3i 1.71773 0.711508i
\(880\) −18639.0 6469.45i −0.714001 0.247824i
\(881\) −10321.4 4275.28i −0.394708 0.163493i 0.176496 0.984301i \(-0.443524\pi\)
−0.571204 + 0.820808i \(0.693524\pi\)
\(882\) −9443.17 + 16291.7i −0.360508 + 0.621962i
\(883\) −3832.90 38916.1i −0.146079 1.48316i −0.736704 0.676215i \(-0.763619\pi\)
0.590626 0.806946i \(-0.298881\pi\)
\(884\) 1774.37 + 299.181i 0.0675098 + 0.0113830i
\(885\) 23309.9 43609.8i 0.885372 1.65641i
\(886\) 2079.58 + 5554.08i 0.0788543 + 0.210601i
\(887\) −28759.0 19216.2i −1.08865 0.727414i −0.124355 0.992238i \(-0.539686\pi\)
−0.964297 + 0.264824i \(0.914686\pi\)
\(888\) −11196.1 57834.1i −0.423105 2.18557i
\(889\) −16071.6 24052.8i −0.606325 0.907429i
\(890\) −3555.73 21768.1i −0.133920 0.819850i
\(891\) −13390.3 1318.83i −0.503469 0.0495874i
\(892\) −6055.46 47242.4i −0.227300 1.77331i
\(893\) 17358.3 + 5265.58i 0.650474 + 0.197319i
\(894\) 17696.9 + 36040.9i 0.662051 + 1.34831i
\(895\) 23607.5 0.881690
\(896\) 10867.0 + 14518.4i 0.405180 + 0.541322i
\(897\) 10933.7 0.406986
\(898\) 12959.4 + 26392.6i 0.481582 + 0.980772i
\(899\) 12199.5 + 3700.69i 0.452589 + 0.137291i
\(900\) −9718.31 + 1245.68i −0.359937 + 0.0461362i
\(901\) −1935.03 190.583i −0.0715483 0.00704690i
\(902\) −388.535 2378.60i −0.0143424 0.0878033i
\(903\) −21757.9 32563.1i −0.801837 1.20003i
\(904\) 22424.8 33191.5i 0.825040 1.22117i
\(905\) −21986.5 14690.9i −0.807577 0.539606i
\(906\) −10472.5 27969.7i −0.384025 1.02564i
\(907\) 9676.49 18103.4i 0.354248 0.662751i −0.640174 0.768230i \(-0.721138\pi\)
0.994422 + 0.105479i \(0.0336376\pi\)
\(908\) 1518.18 9003.97i 0.0554874 0.329083i
\(909\) 3570.47 + 36251.6i 0.130281 + 1.32276i
\(910\) −5101.09 + 8800.59i −0.185823 + 0.320590i
\(911\) −26188.2 10847.5i −0.952419 0.394505i −0.148279 0.988946i \(-0.547373\pi\)
−0.804139 + 0.594441i \(0.797373\pi\)
\(912\) 13467.6 + 11974.5i 0.488987 + 0.434776i
\(913\) −36322.2 + 15045.1i −1.31664 + 0.545368i
\(914\) 662.303 4965.14i 0.0239683 0.179685i
\(915\) −16661.9 + 20302.6i −0.601996 + 0.733534i
\(916\) 42137.0 1235.33i 1.51992 0.0445594i
\(917\) 5096.42 + 16800.7i 0.183532 + 0.605023i
\(918\) 1463.48 + 50.4121i 0.0526166 + 0.00181247i
\(919\) 7906.79 + 39750.1i 0.283810 + 1.42681i 0.814954 + 0.579526i \(0.196762\pi\)
−0.531144 + 0.847281i \(0.678238\pi\)
\(920\) −9815.85 1017.59i −0.351760 0.0364664i
\(921\) −28494.6 5667.93i −1.01947 0.202785i
\(922\) −13359.1 + 8275.59i −0.477177 + 0.295599i
\(923\) −13689.4 16680.6i −0.488182 0.594852i
\(924\) 19367.3 16868.0i 0.689543 0.600558i
\(925\) 9926.19 5305.66i 0.352834 0.188593i
\(926\) 1199.06 + 18785.8i 0.0425525 + 0.666674i
\(927\) 4595.96 + 4595.96i 0.162838 + 0.162838i
\(928\) 6890.19 + 2660.69i 0.243730 + 0.0941178i
\(929\) 17955.2 17955.2i 0.634114 0.634114i −0.314983 0.949097i \(-0.601999\pi\)
0.949097 + 0.314983i \(0.101999\pi\)
\(930\) −50067.1 44059.2i −1.76534 1.55350i
\(931\) 3119.51 + 5836.20i 0.109815 + 0.205450i
\(932\) 30842.4 + 15341.0i 1.08399 + 0.539175i
\(933\) −2530.01 + 2076.33i −0.0887770 + 0.0728574i
\(934\) −31876.9 7490.09i −1.11675 0.262402i
\(935\) −448.726 + 2255.90i −0.0156951 + 0.0789046i
\(936\) 18776.3 + 15571.1i 0.655688 + 0.543756i
\(937\) −12248.6 + 2436.40i −0.427049 + 0.0849452i −0.403935 0.914788i \(-0.632358\pi\)
−0.0231134 + 0.999733i \(0.507358\pi\)
\(938\) −19286.9 + 18002.4i −0.671363 + 0.626651i
\(939\) 20343.5 6171.13i 0.707013 0.214470i
\(940\) −36353.1 13824.3i −1.26139 0.479681i
\(941\) −11458.2 9403.54i −0.396948 0.325767i 0.414652 0.909980i \(-0.363903\pi\)
−0.811600 + 0.584213i \(0.801403\pi\)
\(942\) 10997.6 8408.97i 0.380384 0.290848i
\(943\) −461.322 1113.73i −0.0159308 0.0384603i
\(944\) −41420.0 + 6548.07i −1.42808 + 0.225764i
\(945\) −3167.83 + 7647.82i −0.109047 + 0.263263i
\(946\) −9292.27 34917.7i −0.319364 1.20008i
\(947\) −24271.9 + 2390.57i −0.832872 + 0.0820307i −0.505459 0.862851i \(-0.668677\pi\)
−0.327413 + 0.944881i \(0.606177\pi\)
\(948\) 5572.44 + 24273.6i 0.190912 + 0.831614i
\(949\) 18667.7 + 9978.08i 0.638544 + 0.341309i
\(950\) −1426.39 + 3133.87i −0.0487140 + 0.107027i
\(951\) −34382.1 + 51456.4i −1.17236 + 1.75456i
\(952\) 1502.58 1487.25i 0.0511542 0.0506326i
\(953\) −24795.2 + 16567.6i −0.842806 + 0.563145i −0.900334 0.435199i \(-0.856678\pi\)
0.0575282 + 0.998344i \(0.481678\pi\)
\(954\) −21398.8 15389.5i −0.726216 0.522279i
\(955\) −594.142 + 6032.42i −0.0201319 + 0.204403i
\(956\) −2972.18 + 10942.6i −0.100551 + 0.370199i
\(957\) 3036.47 10009.9i 0.102566 0.338113i
\(958\) 2963.31 8680.87i 0.0999374 0.292762i
\(959\) 3028.82i 0.101987i
\(960\) −27040.9 27600.9i −0.909105 0.927934i
\(961\) 67829.6i 2.27685i
\(962\) −26518.6 9052.40i −0.888767 0.303390i
\(963\) 22371.5 73748.9i 0.748609 2.46783i
\(964\) −42154.6 + 24146.3i −1.40841 + 0.806743i
\(965\) −2668.24 + 27091.1i −0.0890089 + 0.903722i
\(966\) 7500.42 10429.2i 0.249816 0.347363i
\(967\) 32964.7 22026.3i 1.09625 0.732490i 0.130365 0.991466i \(-0.458385\pi\)
0.965884 + 0.258976i \(0.0833850\pi\)
\(968\) −5944.96 + 2426.87i −0.197395 + 0.0805811i
\(969\) 1167.20 1746.84i 0.0386954 0.0579118i
\(970\) 2471.92 + 1125.11i 0.0818234 + 0.0372423i
\(971\) 31697.9 + 16942.9i 1.04761 + 0.559962i 0.903051 0.429534i \(-0.141322\pi\)
0.144564 + 0.989495i \(0.453822\pi\)
\(972\) −35030.5 21949.7i −1.15597 0.724317i
\(973\) 1458.73 143.672i 0.0480624 0.00473373i
\(974\) −2191.29 + 583.144i −0.0720878 + 0.0191839i
\(975\) −3130.19 + 7556.95i −0.102817 + 0.248222i
\(976\) 22255.8 + 880.848i 0.729909 + 0.0288886i
\(977\) −17846.6 43085.5i −0.584404 1.41088i −0.888784 0.458325i \(-0.848449\pi\)
0.304380 0.952551i \(-0.401551\pi\)
\(978\) −27500.8 35966.7i −0.899159 1.17596i
\(979\) 20477.3 + 16805.3i 0.668494 + 0.548619i
\(980\) −5811.67 12944.1i −0.189436 0.421922i
\(981\) 28274.2 8576.88i 0.920209 0.279142i
\(982\) 4692.86 + 5027.71i 0.152500 + 0.163381i
\(983\) −20958.3 + 4168.86i −0.680025 + 0.135265i −0.523005 0.852330i \(-0.675189\pi\)
−0.157021 + 0.987595i \(0.550189\pi\)
\(984\) 1393.29 4509.74i 0.0451388 0.146103i
\(985\) −2183.70 + 10978.2i −0.0706381 + 0.355122i
\(986\) 196.959 838.235i 0.00636152 0.0270739i
\(987\) 39136.3 32118.4i 1.26213 1.03580i
\(988\) 8126.72 2727.72i 0.261686 0.0878344i
\(989\) −8519.54 15938.9i −0.273919 0.512466i
\(990\) −20598.4 + 23407.1i −0.661272 + 0.751442i
\(991\) −32167.8 + 32167.8i −1.03113 + 1.03113i −0.0316254 + 0.999500i \(0.510068\pi\)
−0.999500 + 0.0316254i \(0.989932\pi\)
\(992\) −4180.97 + 56403.5i −0.133816 + 1.80525i
\(993\) 12015.0 + 12015.0i 0.383973 + 0.383973i
\(994\) −25301.6 + 1614.95i −0.807362 + 0.0515324i
\(995\) 14121.8 7548.27i 0.449941 0.240499i
\(996\) −76813.1 5298.21i −2.44369 0.168554i
\(997\) −14282.9 17403.8i −0.453705 0.552841i 0.495046 0.868867i \(-0.335151\pi\)
−0.948751 + 0.316026i \(0.897651\pi\)
\(998\) −15467.5 24968.8i −0.490596 0.791956i
\(999\) −22365.1 4448.70i −0.708309 0.140891i
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 128.4.k.a.5.7 752
128.77 even 32 inner 128.4.k.a.77.7 yes 752
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.k.a.5.7 752 1.1 even 1 trivial
128.4.k.a.77.7 yes 752 128.77 even 32 inner