Properties

Label 32.3.h.a.3.3
Level $32$
Weight $3$
Character 32.3
Analytic conductor $0.872$
Analytic rank $0$
Dimension $28$
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] = [32,3,Mod(3,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.h (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.871936845953\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 3.3
Character \(\chi\) \(=\) 32.3
Dual form 32.3.h.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.44490 - 1.38284i) q^{2} +(0.936461 - 2.26082i) q^{3} +(0.175499 + 3.99615i) q^{4} +(-3.18221 - 7.68254i) q^{5} +(-4.47945 + 1.97169i) q^{6} +(3.67370 + 3.67370i) q^{7} +(5.27246 - 6.01674i) q^{8} +(2.12963 + 2.12963i) q^{9} +O(q^{10})\) \(q+(-1.44490 - 1.38284i) q^{2} +(0.936461 - 2.26082i) q^{3} +(0.175499 + 3.99615i) q^{4} +(-3.18221 - 7.68254i) q^{5} +(-4.47945 + 1.97169i) q^{6} +(3.67370 + 3.67370i) q^{7} +(5.27246 - 6.01674i) q^{8} +(2.12963 + 2.12963i) q^{9} +(-6.02574 + 15.5010i) q^{10} +(6.10089 + 14.7288i) q^{11} +(9.19891 + 3.34547i) q^{12} +(2.82075 - 6.80990i) q^{13} +(-0.228001 - 10.3883i) q^{14} -20.3488 q^{15} +(-15.9384 + 1.40264i) q^{16} -3.67152i q^{17} +(-0.132171 - 6.02205i) q^{18} +(-1.65751 - 0.686564i) q^{19} +(30.1421 - 14.0649i) q^{20} +(11.7458 - 4.86528i) q^{21} +(11.5525 - 29.7183i) q^{22} +(-8.31529 + 8.31529i) q^{23} +(-8.66529 - 17.5545i) q^{24} +(-31.2172 + 31.2172i) q^{25} +(-13.4927 + 5.93900i) q^{26} +(27.1564 - 11.2485i) q^{27} +(-14.0359 + 15.3254i) q^{28} +(-38.8592 - 16.0960i) q^{29} +(29.4021 + 28.1392i) q^{30} +4.11293i q^{31} +(24.9691 + 20.0136i) q^{32} +39.0124 q^{33} +(-5.07713 + 5.30499i) q^{34} +(16.5328 - 39.9138i) q^{35} +(-8.13657 + 8.88406i) q^{36} +(19.8759 + 47.9847i) q^{37} +(1.44554 + 3.28410i) q^{38} +(-12.7544 - 12.7544i) q^{39} +(-63.0019 - 21.3593i) q^{40} +(21.1187 + 21.1187i) q^{41} +(-23.6995 - 9.21275i) q^{42} +(-0.102495 - 0.247444i) q^{43} +(-57.7879 + 26.9649i) q^{44} +(9.58403 - 23.1379i) q^{45} +(23.5135 - 0.516073i) q^{46} -39.3838 q^{47} +(-11.7546 + 37.3473i) q^{48} -22.0079i q^{49} +(88.2745 - 1.93744i) q^{50} +(-8.30063 - 3.43823i) q^{51} +(27.7084 + 10.0770i) q^{52} +(22.6154 - 9.36759i) q^{53} +(-54.7933 - 21.2999i) q^{54} +(93.7406 - 93.7406i) q^{55} +(41.4731 - 2.73426i) q^{56} +(-3.10439 + 3.10439i) q^{57} +(33.8896 + 76.9933i) q^{58} +(-101.380 + 41.9931i) q^{59} +(-3.57119 - 81.3169i) q^{60} +(-14.0475 - 5.81867i) q^{61} +(5.68753 - 5.94279i) q^{62} +15.6472i q^{63} +(-8.40232 - 63.4460i) q^{64} -61.2936 q^{65} +(-56.3693 - 53.9480i) q^{66} +(3.67448 - 8.87098i) q^{67} +(14.6719 - 0.644346i) q^{68} +(11.0124 + 26.5863i) q^{69} +(-79.0828 + 34.8093i) q^{70} +(75.7712 + 75.7712i) q^{71} +(24.0418 - 1.58504i) q^{72} +(-29.0378 - 29.0378i) q^{73} +(37.6364 - 96.8185i) q^{74} +(41.3427 + 99.8102i) q^{75} +(2.45272 - 6.74415i) q^{76} +(-31.6965 + 76.5221i) q^{77} +(0.791578 + 36.0662i) q^{78} +2.76556 q^{79} +(61.4952 + 117.984i) q^{80} -44.8236i q^{81} +(-1.31069 - 59.7184i) q^{82} +(-79.1972 - 32.8045i) q^{83} +(21.5038 + 46.0842i) q^{84} +(-28.2066 + 11.6835i) q^{85} +(-0.194081 + 0.499267i) q^{86} +(-72.7802 + 72.7802i) q^{87} +(120.786 + 40.9498i) q^{88} +(72.4200 - 72.4200i) q^{89} +(-45.8440 + 20.1788i) q^{90} +(35.3801 - 14.6549i) q^{91} +(-34.6885 - 31.7698i) q^{92} +(9.29858 + 3.85160i) q^{93} +(56.9058 + 54.4615i) q^{94} +14.9187i q^{95} +(68.6297 - 37.7086i) q^{96} +66.0511 q^{97} +(-30.4335 + 31.7993i) q^{98} +(-18.3743 + 44.3596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44490 1.38284i −0.722452 0.691421i
\(3\) 0.936461 2.26082i 0.312154 0.753605i −0.687471 0.726212i \(-0.741279\pi\)
0.999625 0.0273938i \(-0.00872079\pi\)
\(4\) 0.175499 + 3.99615i 0.0438747 + 0.999037i
\(5\) −3.18221 7.68254i −0.636442 1.53651i −0.831387 0.555693i \(-0.812453\pi\)
0.194945 0.980814i \(-0.437547\pi\)
\(6\) −4.47945 + 1.97169i −0.746575 + 0.328615i
\(7\) 3.67370 + 3.67370i 0.524814 + 0.524814i 0.919021 0.394208i \(-0.128981\pi\)
−0.394208 + 0.919021i \(0.628981\pi\)
\(8\) 5.27246 6.01674i 0.659058 0.752092i
\(9\) 2.12963 + 2.12963i 0.236625 + 0.236625i
\(10\) −6.02574 + 15.5010i −0.602574 + 1.55010i
\(11\) 6.10089 + 14.7288i 0.554626 + 1.33899i 0.913971 + 0.405781i \(0.133000\pi\)
−0.359345 + 0.933205i \(0.617000\pi\)
\(12\) 9.19891 + 3.34547i 0.766575 + 0.278789i
\(13\) 2.82075 6.80990i 0.216981 0.523839i −0.777484 0.628902i \(-0.783505\pi\)
0.994466 + 0.105063i \(0.0335046\pi\)
\(14\) −0.228001 10.3883i −0.0162858 0.742020i
\(15\) −20.3488 −1.35659
\(16\) −15.9384 + 1.40264i −0.996150 + 0.0876648i
\(17\) 3.67152i 0.215972i −0.994152 0.107986i \(-0.965560\pi\)
0.994152 0.107986i \(-0.0344401\pi\)
\(18\) −0.132171 6.02205i −0.00734285 0.334558i
\(19\) −1.65751 0.686564i −0.0872375 0.0361349i 0.338638 0.940917i \(-0.390034\pi\)
−0.425875 + 0.904782i \(0.640034\pi\)
\(20\) 30.1421 14.0649i 1.50710 0.703243i
\(21\) 11.7458 4.86528i 0.559325 0.231680i
\(22\) 11.5525 29.7183i 0.525112 1.35083i
\(23\) −8.31529 + 8.31529i −0.361534 + 0.361534i −0.864378 0.502843i \(-0.832287\pi\)
0.502843 + 0.864378i \(0.332287\pi\)
\(24\) −8.66529 17.5545i −0.361054 0.731438i
\(25\) −31.2172 + 31.2172i −1.24869 + 1.24869i
\(26\) −13.4927 + 5.93900i −0.518951 + 0.228423i
\(27\) 27.1564 11.2485i 1.00579 0.416612i
\(28\) −14.0359 + 15.3254i −0.501282 + 0.547334i
\(29\) −38.8592 16.0960i −1.33997 0.555035i −0.406489 0.913656i \(-0.633247\pi\)
−0.933483 + 0.358621i \(0.883247\pi\)
\(30\) 29.4021 + 28.1392i 0.980070 + 0.937973i
\(31\) 4.11293i 0.132675i 0.997797 + 0.0663376i \(0.0211314\pi\)
−0.997797 + 0.0663376i \(0.978869\pi\)
\(32\) 24.9691 + 20.0136i 0.780284 + 0.625425i
\(33\) 39.0124 1.18220
\(34\) −5.07713 + 5.30499i −0.149327 + 0.156029i
\(35\) 16.5328 39.9138i 0.472367 1.14039i
\(36\) −8.13657 + 8.88406i −0.226016 + 0.246779i
\(37\) 19.8759 + 47.9847i 0.537186 + 1.29688i 0.926679 + 0.375853i \(0.122650\pi\)
−0.389493 + 0.921030i \(0.627350\pi\)
\(38\) 1.44554 + 3.28410i 0.0380405 + 0.0864236i
\(39\) −12.7544 12.7544i −0.327036 0.327036i
\(40\) −63.0019 21.3593i −1.57505 0.533984i
\(41\) 21.1187 + 21.1187i 0.515091 + 0.515091i 0.916082 0.400991i \(-0.131334\pi\)
−0.400991 + 0.916082i \(0.631334\pi\)
\(42\) −23.6995 9.21275i −0.564274 0.219351i
\(43\) −0.102495 0.247444i −0.00238360 0.00575451i 0.922683 0.385559i \(-0.125991\pi\)
−0.925067 + 0.379804i \(0.875991\pi\)
\(44\) −57.7879 + 26.9649i −1.31336 + 0.612839i
\(45\) 9.58403 23.1379i 0.212978 0.514175i
\(46\) 23.5135 0.516073i 0.511164 0.0112190i
\(47\) −39.3838 −0.837952 −0.418976 0.907997i \(-0.637611\pi\)
−0.418976 + 0.907997i \(0.637611\pi\)
\(48\) −11.7546 + 37.3473i −0.244887 + 0.778069i
\(49\) 22.0079i 0.449141i
\(50\) 88.2745 1.93744i 1.76549 0.0387488i
\(51\) −8.30063 3.43823i −0.162757 0.0674163i
\(52\) 27.7084 + 10.0770i 0.532854 + 0.193789i
\(53\) 22.6154 9.36759i 0.426705 0.176747i −0.158987 0.987281i \(-0.550823\pi\)
0.585692 + 0.810534i \(0.300823\pi\)
\(54\) −54.7933 21.2999i −1.01469 0.394442i
\(55\) 93.7406 93.7406i 1.70437 1.70437i
\(56\) 41.4731 2.73426i 0.740591 0.0488260i
\(57\) −3.10439 + 3.10439i −0.0544630 + 0.0544630i
\(58\) 33.8896 + 76.9933i 0.584304 + 1.32747i
\(59\) −101.380 + 41.9931i −1.71831 + 0.711747i −0.718441 + 0.695588i \(0.755144\pi\)
−0.999869 + 0.0161592i \(0.994856\pi\)
\(60\) −3.57119 81.3169i −0.0595199 1.35528i
\(61\) −14.0475 5.81867i −0.230287 0.0953880i 0.264556 0.964370i \(-0.414775\pi\)
−0.494843 + 0.868982i \(0.664775\pi\)
\(62\) 5.68753 5.94279i 0.0917344 0.0958515i
\(63\) 15.6472i 0.248369i
\(64\) −8.40232 63.4460i −0.131286 0.991345i
\(65\) −61.2936 −0.942978
\(66\) −56.3693 53.9480i −0.854080 0.817394i
\(67\) 3.67448 8.87098i 0.0548430 0.132403i −0.894083 0.447901i \(-0.852172\pi\)
0.948926 + 0.315498i \(0.102172\pi\)
\(68\) 14.6719 0.644346i 0.215764 0.00947568i
\(69\) 11.0124 + 26.5863i 0.159600 + 0.385309i
\(70\) −79.0828 + 34.8093i −1.12975 + 0.497276i
\(71\) 75.7712 + 75.7712i 1.06720 + 1.06720i 0.997573 + 0.0696271i \(0.0221809\pi\)
0.0696271 + 0.997573i \(0.477819\pi\)
\(72\) 24.0418 1.58504i 0.333914 0.0220144i
\(73\) −29.0378 29.0378i −0.397779 0.397779i 0.479670 0.877449i \(-0.340756\pi\)
−0.877449 + 0.479670i \(0.840756\pi\)
\(74\) 37.6364 96.8185i 0.508600 1.30836i
\(75\) 41.3427 + 99.8102i 0.551237 + 1.33080i
\(76\) 2.45272 6.74415i 0.0322726 0.0887389i
\(77\) −31.6965 + 76.5221i −0.411643 + 0.993793i
\(78\) 0.791578 + 36.0662i 0.0101484 + 0.462388i
\(79\) 2.76556 0.0350072 0.0175036 0.999847i \(-0.494428\pi\)
0.0175036 + 0.999847i \(0.494428\pi\)
\(80\) 61.4952 + 117.984i 0.768690 + 1.47480i
\(81\) 44.8236i 0.553378i
\(82\) −1.31069 59.7184i −0.0159841 0.728273i
\(83\) −79.1972 32.8045i −0.954183 0.395235i −0.149381 0.988780i \(-0.547728\pi\)
−0.804801 + 0.593544i \(0.797728\pi\)
\(84\) 21.5038 + 46.0842i 0.255997 + 0.548622i
\(85\) −28.2066 + 11.6835i −0.331842 + 0.137453i
\(86\) −0.194081 + 0.499267i −0.00225675 + 0.00580543i
\(87\) −72.7802 + 72.7802i −0.836554 + 0.836554i
\(88\) 120.786 + 40.9498i 1.37257 + 0.465339i
\(89\) 72.4200 72.4200i 0.813708 0.813708i −0.171480 0.985188i \(-0.554855\pi\)
0.985188 + 0.171480i \(0.0548548\pi\)
\(90\) −45.8440 + 20.1788i −0.509378 + 0.224209i
\(91\) 35.3801 14.6549i 0.388792 0.161043i
\(92\) −34.6885 31.7698i −0.377048 0.345324i
\(93\) 9.29858 + 3.85160i 0.0999847 + 0.0414150i
\(94\) 56.9058 + 54.4615i 0.605380 + 0.579378i
\(95\) 14.9187i 0.157039i
\(96\) 68.6297 37.7086i 0.714892 0.392798i
\(97\) 66.0511 0.680940 0.340470 0.940255i \(-0.389414\pi\)
0.340470 + 0.940255i \(0.389414\pi\)
\(98\) −30.4335 + 31.7993i −0.310545 + 0.324483i
\(99\) −18.3743 + 44.3596i −0.185599 + 0.448077i
\(100\) −130.227 119.270i −1.30227 1.19270i
\(101\) −7.51179 18.1351i −0.0743742 0.179555i 0.882320 0.470650i \(-0.155981\pi\)
−0.956694 + 0.291095i \(0.905981\pi\)
\(102\) 7.23908 + 16.4464i 0.0709714 + 0.161239i
\(103\) 0.589180 + 0.589180i 0.00572020 + 0.00572020i 0.709961 0.704241i \(-0.248712\pi\)
−0.704241 + 0.709961i \(0.748712\pi\)
\(104\) −26.1011 52.8767i −0.250972 0.508430i
\(105\) −74.7554 74.7554i −0.711956 0.711956i
\(106\) −45.6309 17.7382i −0.430480 0.167341i
\(107\) −55.4567 133.884i −0.518287 1.25126i −0.938955 0.344041i \(-0.888204\pi\)
0.420668 0.907215i \(-0.361796\pi\)
\(108\) 49.7167 + 106.547i 0.460340 + 0.986544i
\(109\) 29.4015 70.9815i 0.269739 0.651207i −0.729732 0.683733i \(-0.760355\pi\)
0.999471 + 0.0325264i \(0.0103553\pi\)
\(110\) −265.075 + 5.81783i −2.40977 + 0.0528894i
\(111\) 127.098 1.14502
\(112\) −63.7057 53.4000i −0.568801 0.476786i
\(113\) 134.274i 1.18826i −0.804368 0.594131i \(-0.797496\pi\)
0.804368 0.594131i \(-0.202504\pi\)
\(114\) 8.77843 0.192668i 0.0770037 0.00169007i
\(115\) 90.3436 + 37.4215i 0.785596 + 0.325405i
\(116\) 57.5023 158.112i 0.495709 1.36303i
\(117\) 20.5097 8.49541i 0.175297 0.0726103i
\(118\) 204.555 + 79.5169i 1.73351 + 0.673872i
\(119\) 13.4880 13.4880i 0.113345 0.113345i
\(120\) −107.288 + 122.434i −0.894070 + 1.02028i
\(121\) −94.1580 + 94.1580i −0.778166 + 0.778166i
\(122\) 12.2510 + 27.8329i 0.100418 + 0.228138i
\(123\) 67.5224 27.9687i 0.548963 0.227388i
\(124\) −16.4359 + 0.721814i −0.132547 + 0.00582108i
\(125\) 147.104 + 60.9325i 1.17683 + 0.487460i
\(126\) 21.6376 22.6087i 0.171727 0.179434i
\(127\) 95.5030i 0.751992i −0.926621 0.375996i \(-0.877301\pi\)
0.926621 0.375996i \(-0.122699\pi\)
\(128\) −75.5953 + 103.293i −0.590588 + 0.806973i
\(129\) −0.655407 −0.00508068
\(130\) 88.5634 + 84.7593i 0.681257 + 0.651995i
\(131\) −67.1188 + 162.039i −0.512357 + 1.23694i 0.430151 + 0.902757i \(0.358460\pi\)
−0.942508 + 0.334183i \(0.891540\pi\)
\(132\) 6.84663 + 155.900i 0.0518684 + 1.18106i
\(133\) −3.56697 8.61142i −0.0268193 0.0647475i
\(134\) −17.5764 + 7.73649i −0.131167 + 0.0577350i
\(135\) −172.835 172.835i −1.28026 1.28026i
\(136\) −22.0906 19.3579i −0.162431 0.142338i
\(137\) 88.7244 + 88.7244i 0.647624 + 0.647624i 0.952418 0.304794i \(-0.0985878\pi\)
−0.304794 + 0.952418i \(0.598588\pi\)
\(138\) 20.8528 53.6431i 0.151107 0.388718i
\(139\) −27.6838 66.8346i −0.199164 0.480824i 0.792469 0.609912i \(-0.208795\pi\)
−0.991633 + 0.129087i \(0.958795\pi\)
\(140\) 162.403 + 59.0628i 1.16002 + 0.421877i
\(141\) −36.8813 + 89.0394i −0.261570 + 0.631485i
\(142\) −4.70260 214.262i −0.0331169 1.50889i
\(143\) 117.511 0.821756
\(144\) −36.9300 30.9558i −0.256458 0.214971i
\(145\) 349.758i 2.41213i
\(146\) 1.80218 + 82.1116i 0.0123437 + 0.562409i
\(147\) −49.7558 20.6095i −0.338475 0.140201i
\(148\) −188.266 + 87.8483i −1.27207 + 0.593569i
\(149\) −100.536 + 41.6433i −0.674737 + 0.279485i −0.693625 0.720336i \(-0.743987\pi\)
0.0188878 + 0.999822i \(0.493987\pi\)
\(150\) 78.2854 201.387i 0.521903 1.34258i
\(151\) −134.706 + 134.706i −0.892096 + 0.892096i −0.994720 0.102624i \(-0.967276\pi\)
0.102624 + 0.994720i \(0.467276\pi\)
\(152\) −12.8700 + 6.35294i −0.0846713 + 0.0417956i
\(153\) 7.81897 7.81897i 0.0511044 0.0511044i
\(154\) 151.616 66.7359i 0.984522 0.433350i
\(155\) 31.5977 13.0882i 0.203856 0.0844401i
\(156\) 48.7302 53.2069i 0.312373 0.341070i
\(157\) −56.0501 23.2167i −0.357007 0.147877i 0.196969 0.980410i \(-0.436890\pi\)
−0.553976 + 0.832533i \(0.686890\pi\)
\(158\) −3.99598 3.82434i −0.0252910 0.0242047i
\(159\) 59.9015i 0.376739i
\(160\) 74.2983 255.514i 0.464365 1.59696i
\(161\) −61.0957 −0.379476
\(162\) −61.9840 + 64.7658i −0.382617 + 0.399789i
\(163\) 85.7621 207.048i 0.526148 1.27023i −0.407881 0.913035i \(-0.633732\pi\)
0.934029 0.357198i \(-0.116268\pi\)
\(164\) −80.6872 + 88.0998i −0.491995 + 0.537194i
\(165\) −124.146 299.715i −0.752399 1.81645i
\(166\) 69.0689 + 156.917i 0.416077 + 0.945280i
\(167\) 72.6395 + 72.6395i 0.434967 + 0.434967i 0.890314 0.455347i \(-0.150485\pi\)
−0.455347 + 0.890314i \(0.650485\pi\)
\(168\) 32.6563 96.3236i 0.194383 0.573355i
\(169\) 81.0829 + 81.0829i 0.479781 + 0.479781i
\(170\) 56.9123 + 22.1236i 0.334778 + 0.130139i
\(171\) −2.06776 4.99201i −0.0120922 0.0291930i
\(172\) 0.970835 0.453010i 0.00564439 0.00263378i
\(173\) −4.05480 + 9.78916i −0.0234382 + 0.0565847i −0.935165 0.354212i \(-0.884749\pi\)
0.911727 + 0.410796i \(0.134749\pi\)
\(174\) 205.804 4.51697i 1.18278 0.0259596i
\(175\) −229.365 −1.31066
\(176\) −117.898 226.197i −0.669873 1.28521i
\(177\) 268.527i 1.51710i
\(178\) −204.785 + 4.49461i −1.15048 + 0.0252506i
\(179\) 214.146 + 88.7024i 1.19635 + 0.495544i 0.889817 0.456317i \(-0.150832\pi\)
0.306531 + 0.951861i \(0.400832\pi\)
\(180\) 94.1444 + 34.2385i 0.523024 + 0.190214i
\(181\) −98.2125 + 40.6810i −0.542611 + 0.224757i −0.637116 0.770768i \(-0.719873\pi\)
0.0945057 + 0.995524i \(0.469873\pi\)
\(182\) −71.3863 27.7501i −0.392233 0.152473i
\(183\) −26.3099 + 26.3099i −0.143770 + 0.143770i
\(184\) 6.18890 + 93.8730i 0.0336353 + 0.510179i
\(185\) 305.395 305.395i 1.65078 1.65078i
\(186\) −8.10941 18.4237i −0.0435990 0.0990519i
\(187\) 54.0772 22.3995i 0.289183 0.119783i
\(188\) −6.91180 157.383i −0.0367649 0.837145i
\(189\) 141.088 + 58.4405i 0.746497 + 0.309209i
\(190\) 20.6302 21.5561i 0.108580 0.113453i
\(191\) 181.842i 0.952052i 0.879431 + 0.476026i \(0.157923\pi\)
−0.879431 + 0.476026i \(0.842077\pi\)
\(192\) −151.308 40.4186i −0.788064 0.210514i
\(193\) −221.267 −1.14646 −0.573230 0.819394i \(-0.694310\pi\)
−0.573230 + 0.819394i \(0.694310\pi\)
\(194\) −95.4376 91.3383i −0.491946 0.470816i
\(195\) −57.3990 + 138.574i −0.294354 + 0.710633i
\(196\) 87.9469 3.86236i 0.448709 0.0197059i
\(197\) −15.4361 37.2660i −0.0783556 0.189167i 0.879847 0.475256i \(-0.157645\pi\)
−0.958203 + 0.286089i \(0.907645\pi\)
\(198\) 87.8915 38.6866i 0.443896 0.195387i
\(199\) −135.618 135.618i −0.681498 0.681498i 0.278840 0.960338i \(-0.410050\pi\)
−0.960338 + 0.278840i \(0.910050\pi\)
\(200\) 23.2343 + 352.418i 0.116172 + 1.76209i
\(201\) −16.6146 16.6146i −0.0826599 0.0826599i
\(202\) −14.2241 + 36.5911i −0.0704164 + 0.181144i
\(203\) −83.6250 201.889i −0.411946 0.994526i
\(204\) 12.2829 33.7739i 0.0602105 0.165559i
\(205\) 95.0411 229.450i 0.463615 1.11927i
\(206\) −0.0365664 1.66605i −0.000177507 0.00808763i
\(207\) −35.4170 −0.171096
\(208\) −35.4065 + 112.495i −0.170223 + 0.540844i
\(209\) 28.6019i 0.136851i
\(210\) 4.63955 + 211.389i 0.0220931 + 1.00662i
\(211\) 138.015 + 57.1678i 0.654100 + 0.270937i 0.684954 0.728587i \(-0.259822\pi\)
−0.0308532 + 0.999524i \(0.509822\pi\)
\(212\) 41.4032 + 88.7303i 0.195298 + 0.418539i
\(213\) 242.262 100.348i 1.13738 0.471118i
\(214\) −105.011 + 270.138i −0.490706 + 1.26233i
\(215\) −1.57484 + 1.57484i −0.00732483 + 0.00732483i
\(216\) 75.5014 222.700i 0.349543 1.03102i
\(217\) −15.1097 + 15.1097i −0.0696298 + 0.0696298i
\(218\) −140.639 + 61.9039i −0.645131 + 0.283963i
\(219\) −92.8420 + 38.4564i −0.423936 + 0.175600i
\(220\) 391.053 + 358.150i 1.77751 + 1.62795i
\(221\) −25.0027 10.3564i −0.113134 0.0468618i
\(222\) −183.644 175.756i −0.827224 0.791692i
\(223\) 30.6228i 0.137322i −0.997640 0.0686609i \(-0.978127\pi\)
0.997640 0.0686609i \(-0.0218727\pi\)
\(224\) 18.2050 + 165.253i 0.0812721 + 0.737736i
\(225\) −132.962 −0.590944
\(226\) −185.679 + 194.013i −0.821589 + 0.858463i
\(227\) 8.41171 20.3077i 0.0370560 0.0894611i −0.904268 0.426965i \(-0.859583\pi\)
0.941324 + 0.337504i \(0.109583\pi\)
\(228\) −12.9504 11.8608i −0.0568001 0.0520210i
\(229\) 76.6532 + 185.057i 0.334730 + 0.808110i 0.998204 + 0.0599101i \(0.0190814\pi\)
−0.663474 + 0.748199i \(0.730919\pi\)
\(230\) −78.7898 179.001i −0.342564 0.778267i
\(231\) 143.320 + 143.320i 0.620432 + 0.620432i
\(232\) −301.729 + 148.940i −1.30056 + 0.641983i
\(233\) −127.558 127.558i −0.547461 0.547461i 0.378245 0.925706i \(-0.376528\pi\)
−0.925706 + 0.378245i \(0.876528\pi\)
\(234\) −41.3824 16.0866i −0.176848 0.0687464i
\(235\) 125.327 + 302.567i 0.533308 + 1.28752i
\(236\) −185.603 397.761i −0.786452 1.68543i
\(237\) 2.58984 6.25243i 0.0109276 0.0263816i
\(238\) −38.1408 + 0.837110i −0.160255 + 0.00351727i
\(239\) 397.241 1.66210 0.831048 0.556200i \(-0.187741\pi\)
0.831048 + 0.556200i \(0.187741\pi\)
\(240\) 324.328 28.5420i 1.35137 0.118925i
\(241\) 401.128i 1.66443i −0.554451 0.832216i \(-0.687072\pi\)
0.554451 0.832216i \(-0.312928\pi\)
\(242\) 266.255 5.84374i 1.10023 0.0241477i
\(243\) 143.069 + 59.2612i 0.588763 + 0.243873i
\(244\) 20.7869 57.1571i 0.0851924 0.234250i
\(245\) −169.077 + 70.0338i −0.690109 + 0.285852i
\(246\) −136.240 52.9607i −0.553820 0.215287i
\(247\) −9.35087 + 9.35087i −0.0378578 + 0.0378578i
\(248\) 24.7464 + 21.6853i 0.0997840 + 0.0874406i
\(249\) −148.330 + 148.330i −0.595703 + 0.595703i
\(250\) −128.291 291.463i −0.513166 1.16585i
\(251\) 220.193 91.2070i 0.877264 0.363375i 0.101829 0.994802i \(-0.467531\pi\)
0.775435 + 0.631427i \(0.217531\pi\)
\(252\) −62.5286 + 2.74607i −0.248129 + 0.0108971i
\(253\) −173.205 71.7440i −0.684606 0.283573i
\(254\) −132.066 + 137.993i −0.519943 + 0.543279i
\(255\) 74.7111i 0.292985i
\(256\) 252.065 44.7116i 0.984630 0.174655i
\(257\) 436.624 1.69893 0.849463 0.527648i \(-0.176926\pi\)
0.849463 + 0.527648i \(0.176926\pi\)
\(258\) 0.947001 + 0.906324i 0.00367055 + 0.00351289i
\(259\) −103.263 + 249.299i −0.398699 + 0.962545i
\(260\) −10.7569 244.938i −0.0413729 0.942070i
\(261\) −48.4771 117.034i −0.185736 0.448407i
\(262\) 321.055 141.316i 1.22540 0.539376i
\(263\) −324.662 324.662i −1.23445 1.23445i −0.962235 0.272219i \(-0.912242\pi\)
−0.272219 0.962235i \(-0.587758\pi\)
\(264\) 205.692 234.728i 0.779135 0.889120i
\(265\) −143.934 143.934i −0.543146 0.543146i
\(266\) −6.75430 + 17.3752i −0.0253921 + 0.0653204i
\(267\) −95.9098 231.547i −0.359213 0.867217i
\(268\) 36.0946 + 13.1269i 0.134681 + 0.0489810i
\(269\) −98.7998 + 238.524i −0.367286 + 0.886706i 0.626907 + 0.779094i \(0.284320\pi\)
−0.994193 + 0.107612i \(0.965680\pi\)
\(270\) 10.7266 + 488.732i 0.0397283 + 1.81012i
\(271\) −91.7678 −0.338627 −0.169313 0.985562i \(-0.554155\pi\)
−0.169313 + 0.985562i \(0.554155\pi\)
\(272\) 5.14981 + 58.5181i 0.0189331 + 0.215140i
\(273\) 93.7117i 0.343266i
\(274\) −5.50651 250.890i −0.0200968 0.915658i
\(275\) −650.247 269.341i −2.36453 0.979422i
\(276\) −104.310 + 48.6731i −0.377935 + 0.176352i
\(277\) 42.7749 17.7179i 0.154422 0.0639636i −0.304134 0.952629i \(-0.598367\pi\)
0.458556 + 0.888666i \(0.348367\pi\)
\(278\) −52.4212 + 134.852i −0.188566 + 0.485079i
\(279\) −8.75902 + 8.75902i −0.0313943 + 0.0313943i
\(280\) −152.982 309.918i −0.546365 1.10685i
\(281\) −167.424 + 167.424i −0.595813 + 0.595813i −0.939196 0.343382i \(-0.888427\pi\)
0.343382 + 0.939196i \(0.388427\pi\)
\(282\) 176.417 77.6524i 0.625594 0.275363i
\(283\) −494.380 + 204.779i −1.74693 + 0.723601i −0.748775 + 0.662824i \(0.769358\pi\)
−0.998151 + 0.0607762i \(0.980642\pi\)
\(284\) −289.495 + 316.091i −1.01935 + 1.11300i
\(285\) 33.7284 + 13.9708i 0.118345 + 0.0490202i
\(286\) −169.792 162.499i −0.593679 0.568179i
\(287\) 155.168i 0.540653i
\(288\) 10.5534 + 95.7965i 0.0366436 + 0.332627i
\(289\) 275.520 0.953356
\(290\) 483.660 505.367i 1.66779 1.74265i
\(291\) 61.8543 149.329i 0.212558 0.513160i
\(292\) 110.943 121.136i 0.379943 0.414848i
\(293\) 146.767 + 354.328i 0.500913 + 1.20931i 0.948987 + 0.315314i \(0.102110\pi\)
−0.448075 + 0.893996i \(0.647890\pi\)
\(294\) 43.3927 + 98.5833i 0.147594 + 0.335317i
\(295\) 645.227 + 645.227i 2.18721 + 2.18721i
\(296\) 393.506 + 133.409i 1.32941 + 0.450707i
\(297\) 331.356 + 331.356i 1.11568 + 1.11568i
\(298\) 202.851 + 78.8545i 0.680707 + 0.264613i
\(299\) 33.1709 + 80.0817i 0.110940 + 0.267832i
\(300\) −391.601 + 182.728i −1.30534 + 0.609094i
\(301\) 0.532500 1.28557i 0.00176910 0.00427099i
\(302\) 380.916 8.36030i 1.26131 0.0276831i
\(303\) −48.0346 −0.158530
\(304\) 27.3811 + 8.61784i 0.0900694 + 0.0283482i
\(305\) 126.437i 0.414547i
\(306\) −22.1101 + 0.485269i −0.0722551 + 0.00158585i
\(307\) −53.4306 22.1317i −0.174041 0.0720902i 0.293962 0.955817i \(-0.405026\pi\)
−0.468003 + 0.883727i \(0.655026\pi\)
\(308\) −311.356 113.234i −1.01090 0.367644i
\(309\) 1.88377 0.780284i 0.00609635 0.00252519i
\(310\) −63.7547 24.7835i −0.205660 0.0799466i
\(311\) 274.515 274.515i 0.882685 0.882685i −0.111122 0.993807i \(-0.535444\pi\)
0.993807 + 0.111122i \(0.0354444\pi\)
\(312\) −143.987 + 9.49284i −0.461497 + 0.0304258i
\(313\) −78.4013 + 78.4013i −0.250483 + 0.250483i −0.821169 0.570685i \(-0.806678\pi\)
0.570685 + 0.821169i \(0.306678\pi\)
\(314\) 48.8820 + 111.054i 0.155675 + 0.353676i
\(315\) 120.210 49.7928i 0.381620 0.158072i
\(316\) 0.485353 + 11.0516i 0.00153593 + 0.0349734i
\(317\) −136.520 56.5483i −0.430661 0.178386i 0.156814 0.987628i \(-0.449878\pi\)
−0.587475 + 0.809243i \(0.699878\pi\)
\(318\) −82.8343 + 86.5520i −0.260485 + 0.272176i
\(319\) 670.551i 2.10204i
\(320\) −460.689 + 266.450i −1.43965 + 0.832656i
\(321\) −354.621 −1.10474
\(322\) 88.2775 + 84.4857i 0.274154 + 0.262378i
\(323\) −2.52073 + 6.08558i −0.00780412 + 0.0188408i
\(324\) 179.122 7.86648i 0.552845 0.0242793i
\(325\) 124.530 + 300.643i 0.383170 + 0.925054i
\(326\) −410.232 + 180.569i −1.25838 + 0.553893i
\(327\) −132.943 132.943i −0.406553 0.406553i
\(328\) 238.413 15.7182i 0.726870 0.0479214i
\(329\) −144.684 144.684i −0.439769 0.439769i
\(330\) −235.079 + 604.733i −0.712360 + 1.83252i
\(331\) 143.690 + 346.898i 0.434109 + 1.04803i 0.977949 + 0.208843i \(0.0669696\pi\)
−0.543841 + 0.839189i \(0.683030\pi\)
\(332\) 117.193 322.241i 0.352990 0.970605i
\(333\) −59.8612 + 144.518i −0.179763 + 0.433987i
\(334\) −4.50823 205.406i −0.0134977 0.614988i
\(335\) −79.8446 −0.238342
\(336\) −180.385 + 94.0199i −0.536861 + 0.279821i
\(337\) 479.136i 1.42177i −0.703310 0.710884i \(-0.748295\pi\)
0.703310 0.710884i \(-0.251705\pi\)
\(338\) −5.03226 229.282i −0.0148883 0.678349i
\(339\) −303.568 125.742i −0.895481 0.370920i
\(340\) −51.6394 110.667i −0.151881 0.325492i
\(341\) −60.5787 + 25.0925i −0.177650 + 0.0735851i
\(342\) −3.91545 + 10.0724i −0.0114487 + 0.0294514i
\(343\) 260.861 260.861i 0.760529 0.760529i
\(344\) −2.02920 0.687955i −0.00589885 0.00199987i
\(345\) 169.206 169.206i 0.490453 0.490453i
\(346\) 19.3957 8.53725i 0.0560568 0.0246741i
\(347\) 172.145 71.3048i 0.496095 0.205489i −0.120585 0.992703i \(-0.538477\pi\)
0.616680 + 0.787214i \(0.288477\pi\)
\(348\) −303.613 278.068i −0.872452 0.799045i
\(349\) 388.120 + 160.765i 1.11209 + 0.460644i 0.861658 0.507490i \(-0.169427\pi\)
0.250434 + 0.968134i \(0.419427\pi\)
\(350\) 331.411 + 317.176i 0.946889 + 0.906217i
\(351\) 216.662i 0.617269i
\(352\) −142.444 + 489.867i −0.404669 + 1.39167i
\(353\) −165.952 −0.470120 −0.235060 0.971981i \(-0.575529\pi\)
−0.235060 + 0.971981i \(0.575529\pi\)
\(354\) 371.330 387.996i 1.04896 1.09603i
\(355\) 340.995 823.235i 0.960550 2.31897i
\(356\) 302.111 + 276.691i 0.848626 + 0.777223i
\(357\) −17.8630 43.1250i −0.0500363 0.120798i
\(358\) −186.760 424.297i −0.521676 1.18519i
\(359\) 100.971 + 100.971i 0.281257 + 0.281257i 0.833610 0.552353i \(-0.186270\pi\)
−0.552353 + 0.833610i \(0.686270\pi\)
\(360\) −88.6832 179.658i −0.246342 0.499050i
\(361\) −252.990 252.990i −0.700802 0.700802i
\(362\) 198.163 + 77.0322i 0.547412 + 0.212796i
\(363\) 124.699 + 301.049i 0.343523 + 0.829337i
\(364\) 64.7724 + 138.812i 0.177946 + 0.381352i
\(365\) −130.680 + 315.489i −0.358027 + 0.864353i
\(366\) 74.3976 1.63287i 0.203272 0.00446140i
\(367\) −651.959 −1.77645 −0.888227 0.459405i \(-0.848063\pi\)
−0.888227 + 0.459405i \(0.848063\pi\)
\(368\) 120.869 144.196i 0.328449 0.391836i
\(369\) 89.9501i 0.243767i
\(370\) −863.579 + 18.9537i −2.33400 + 0.0512263i
\(371\) 117.496 + 48.6683i 0.316700 + 0.131181i
\(372\) −13.7597 + 37.8345i −0.0369884 + 0.101706i
\(373\) 605.919 250.980i 1.62445 0.672868i 0.629854 0.776713i \(-0.283115\pi\)
0.994593 + 0.103845i \(0.0331146\pi\)
\(374\) −109.111 42.4150i −0.291742 0.113409i
\(375\) 275.515 275.515i 0.734705 0.734705i
\(376\) −207.649 + 236.962i −0.552259 + 0.630218i
\(377\) −219.224 + 219.224i −0.581497 + 0.581497i
\(378\) −123.045 279.543i −0.325515 0.739532i
\(379\) −431.591 + 178.771i −1.13876 + 0.471691i −0.870750 0.491725i \(-0.836366\pi\)
−0.268011 + 0.963416i \(0.586366\pi\)
\(380\) −59.6173 + 2.61821i −0.156888 + 0.00689003i
\(381\) −215.915 89.4348i −0.566705 0.234737i
\(382\) 251.459 262.744i 0.658269 0.687812i
\(383\) 583.987i 1.52477i 0.647124 + 0.762385i \(0.275972\pi\)
−0.647124 + 0.762385i \(0.724028\pi\)
\(384\) 162.733 + 267.637i 0.423785 + 0.696970i
\(385\) 688.749 1.78896
\(386\) 319.710 + 305.977i 0.828263 + 0.792687i
\(387\) 0.308688 0.745239i 0.000797644 0.00192568i
\(388\) 11.5919 + 263.950i 0.0298760 + 0.680284i
\(389\) −57.9070 139.800i −0.148861 0.359383i 0.831806 0.555067i \(-0.187307\pi\)
−0.980667 + 0.195684i \(0.937307\pi\)
\(390\) 274.561 120.852i 0.704003 0.309876i
\(391\) 30.5297 + 30.5297i 0.0780812 + 0.0780812i
\(392\) −132.416 116.036i −0.337796 0.296010i
\(393\) 303.487 + 303.487i 0.772231 + 0.772231i
\(394\) −29.2293 + 75.1914i −0.0741860 + 0.190841i
\(395\) −8.80061 21.2466i −0.0222800 0.0537888i
\(396\) −180.492 65.6415i −0.455788 0.165761i
\(397\) 216.482 522.634i 0.545295 1.31646i −0.375649 0.926762i \(-0.622580\pi\)
0.920944 0.389696i \(-0.127420\pi\)
\(398\) 8.41688 + 383.493i 0.0211479 + 0.963551i
\(399\) −22.8092 −0.0571658
\(400\) 453.767 541.340i 1.13442 1.35335i
\(401\) 271.900i 0.678055i −0.940776 0.339028i \(-0.889902\pi\)
0.940776 0.339028i \(-0.110098\pi\)
\(402\) 1.03116 + 46.9820i 0.00256506 + 0.116871i
\(403\) 28.0087 + 11.6016i 0.0695004 + 0.0287880i
\(404\) 71.1521 33.2009i 0.176119 0.0821805i
\(405\) −344.359 + 142.638i −0.850269 + 0.352193i
\(406\) −158.350 + 407.350i −0.390024 + 1.00333i
\(407\) −585.498 + 585.498i −1.43857 + 1.43857i
\(408\) −64.4517 + 31.8148i −0.157970 + 0.0779774i
\(409\) −181.723 + 181.723i −0.444310 + 0.444310i −0.893458 0.449147i \(-0.851728\pi\)
0.449147 + 0.893458i \(0.351728\pi\)
\(410\) −454.618 + 200.106i −1.10882 + 0.488063i
\(411\) 283.677 117.503i 0.690211 0.285895i
\(412\) −2.25105 + 2.45785i −0.00546372 + 0.00596566i
\(413\) −526.710 218.171i −1.27533 0.528258i
\(414\) 51.1741 + 48.9761i 0.123609 + 0.118300i
\(415\) 712.826i 1.71765i
\(416\) 206.722 113.584i 0.496929 0.273038i
\(417\) −177.026 −0.424522
\(418\) −39.5519 + 41.3270i −0.0946217 + 0.0988684i
\(419\) −84.5458 + 204.112i −0.201780 + 0.487140i −0.992084 0.125575i \(-0.959923\pi\)
0.790304 + 0.612715i \(0.209923\pi\)
\(420\) 285.614 311.853i 0.680034 0.742507i
\(421\) 13.1417 + 31.7269i 0.0312155 + 0.0753608i 0.938719 0.344685i \(-0.112014\pi\)
−0.907503 + 0.420045i \(0.862014\pi\)
\(422\) −120.365 273.455i −0.285225 0.647998i
\(423\) −83.8728 83.8728i −0.198281 0.198281i
\(424\) 62.8762 185.461i 0.148293 0.437408i
\(425\) 114.615 + 114.615i 0.269682 + 0.269682i
\(426\) −488.810 190.016i −1.14744 0.446047i
\(427\) −30.2302 72.9823i −0.0707968 0.170919i
\(428\) 525.289 245.110i 1.22731 0.572686i
\(429\) 110.045 265.671i 0.256514 0.619280i
\(430\) 4.45324 0.0977393i 0.0103564 0.000227301i
\(431\) 18.4839 0.0428861 0.0214431 0.999770i \(-0.493174\pi\)
0.0214431 + 0.999770i \(0.493174\pi\)
\(432\) −417.051 + 217.374i −0.965397 + 0.503181i
\(433\) 370.297i 0.855190i 0.903970 + 0.427595i \(0.140639\pi\)
−0.903970 + 0.427595i \(0.859361\pi\)
\(434\) 42.7263 0.937752i 0.0984476 0.00216072i
\(435\) 790.739 + 327.535i 1.81779 + 0.752954i
\(436\) 288.813 + 105.036i 0.662414 + 0.240907i
\(437\) 19.4917 8.07372i 0.0446034 0.0184753i
\(438\) 187.327 + 72.8199i 0.427687 + 0.166256i
\(439\) −1.47108 + 1.47108i −0.00335099 + 0.00335099i −0.708780 0.705429i \(-0.750754\pi\)
0.705429 + 0.708780i \(0.250754\pi\)
\(440\) −69.7691 1058.26i −0.158566 2.40513i
\(441\) 46.8687 46.8687i 0.106278 0.106278i
\(442\) 21.8052 + 49.5388i 0.0493329 + 0.112079i
\(443\) 15.4970 6.41908i 0.0349820 0.0144900i −0.365124 0.930959i \(-0.618973\pi\)
0.400106 + 0.916469i \(0.368973\pi\)
\(444\) 22.3054 + 507.900i 0.0502375 + 1.14392i
\(445\) −786.825 325.914i −1.76815 0.732390i
\(446\) −42.3464 + 44.2470i −0.0949472 + 0.0992085i
\(447\) 266.290i 0.595728i
\(448\) 202.214 263.949i 0.451370 0.589172i
\(449\) −349.645 −0.778719 −0.389359 0.921086i \(-0.627304\pi\)
−0.389359 + 0.921086i \(0.627304\pi\)
\(450\) 192.118 + 183.866i 0.426929 + 0.408591i
\(451\) −182.211 + 439.897i −0.404016 + 0.975382i
\(452\) 536.577 23.5648i 1.18712 0.0521346i
\(453\) 178.399 + 430.694i 0.393817 + 0.950759i
\(454\) −40.2364 + 17.7106i −0.0886264 + 0.0390101i
\(455\) −225.174 225.174i −0.494888 0.494888i
\(456\) 2.31053 + 35.0461i 0.00506696 + 0.0768554i
\(457\) 167.442 + 167.442i 0.366393 + 0.366393i 0.866160 0.499767i \(-0.166581\pi\)
−0.499767 + 0.866160i \(0.666581\pi\)
\(458\) 145.148 373.389i 0.316917 0.815260i
\(459\) −41.2992 99.7051i −0.0899764 0.217222i
\(460\) −133.687 + 367.594i −0.290623 + 0.799117i
\(461\) 299.864 723.935i 0.650463 1.57036i −0.161644 0.986849i \(-0.551680\pi\)
0.812107 0.583508i \(-0.198320\pi\)
\(462\) −8.89488 405.272i −0.0192530 0.877213i
\(463\) −70.4485 −0.152157 −0.0760783 0.997102i \(-0.524240\pi\)
−0.0760783 + 0.997102i \(0.524240\pi\)
\(464\) 641.930 + 202.039i 1.38347 + 0.435429i
\(465\) 83.6933i 0.179986i
\(466\) 7.91667 + 360.703i 0.0169886 + 0.774040i
\(467\) −89.8391 37.2126i −0.192375 0.0796843i 0.284416 0.958701i \(-0.408200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(468\) 37.5483 + 80.4690i 0.0802315 + 0.171942i
\(469\) 46.0882 19.0904i 0.0982691 0.0407044i
\(470\) 237.316 610.489i 0.504928 1.29891i
\(471\) −104.977 + 104.977i −0.222882 + 0.222882i
\(472\) −281.862 + 831.386i −0.597166 + 1.76141i
\(473\) 3.01925 3.01925i 0.00638320 0.00638320i
\(474\) −12.3882 + 5.45283i −0.0261354 + 0.0115039i
\(475\) 73.1756 30.3103i 0.154054 0.0638112i
\(476\) 56.2673 + 51.5331i 0.118209 + 0.108263i
\(477\) 68.1118 + 28.2128i 0.142792 + 0.0591464i
\(478\) −573.975 549.321i −1.20079 1.14921i
\(479\) 900.546i 1.88005i −0.341101 0.940027i \(-0.610800\pi\)
0.341101 0.940027i \(-0.389200\pi\)
\(480\) −508.092 407.253i −1.05852 0.848444i
\(481\) 382.836 0.795917
\(482\) −554.697 + 579.592i −1.15082 + 1.20247i
\(483\) −57.2137 + 138.126i −0.118455 + 0.285976i
\(484\) −392.794 359.745i −0.811558 0.743274i
\(485\) −210.189 507.440i −0.433379 1.04627i
\(486\) −124.773 283.469i −0.256734 0.583270i
\(487\) −175.466 175.466i −0.360301 0.360301i 0.503623 0.863924i \(-0.332000\pi\)
−0.863924 + 0.503623i \(0.832000\pi\)
\(488\) −109.074 + 53.8415i −0.223513 + 0.110331i
\(489\) −387.785 387.785i −0.793015 0.793015i
\(490\) 341.145 + 132.614i 0.696215 + 0.270641i
\(491\) −111.990 270.368i −0.228086 0.550648i 0.767858 0.640620i \(-0.221322\pi\)
−0.995944 + 0.0899713i \(0.971322\pi\)
\(492\) 123.617 + 264.921i 0.251254 + 0.538457i
\(493\) −59.0968 + 142.672i −0.119872 + 0.289396i
\(494\) 26.4419 0.580344i 0.0535261 0.00117478i
\(495\) 399.265 0.806596
\(496\) −5.76895 65.5535i −0.0116309 0.132164i
\(497\) 556.721i 1.12016i
\(498\) 419.440 9.20582i 0.842249 0.0184856i
\(499\) 96.4128 + 39.9355i 0.193212 + 0.0800310i 0.477192 0.878799i \(-0.341655\pi\)
−0.283980 + 0.958830i \(0.591655\pi\)
\(500\) −217.679 + 598.544i −0.435358 + 1.19709i
\(501\) 232.249 96.2005i 0.463570 0.192017i
\(502\) −444.283 172.707i −0.885026 0.344038i
\(503\) 491.151 491.151i 0.976442 0.976442i −0.0232864 0.999729i \(-0.507413\pi\)
0.999729 + 0.0232864i \(0.00741295\pi\)
\(504\) 94.1452 + 82.4994i 0.186796 + 0.163689i
\(505\) −115.419 + 115.419i −0.228553 + 0.228553i
\(506\) 151.055 + 343.179i 0.298527 + 0.678219i
\(507\) 259.245 107.383i 0.511331 0.211800i
\(508\) 381.644 16.7607i 0.751268 0.0329934i
\(509\) 891.336 + 369.204i 1.75115 + 0.725351i 0.997695 + 0.0678534i \(0.0216150\pi\)
0.753457 + 0.657498i \(0.228385\pi\)
\(510\) 103.314 107.950i 0.202576 0.211667i
\(511\) 213.352i 0.417519i
\(512\) −426.039 283.962i −0.832108 0.554614i
\(513\) −52.7348 −0.102797
\(514\) −630.880 603.782i −1.22739 1.17467i
\(515\) 2.65150 6.40130i 0.00514855 0.0124297i
\(516\) −0.115023 2.61910i −0.000222913 0.00507578i
\(517\) −240.276 580.077i −0.464750 1.12201i
\(518\) 493.946 217.417i 0.953564 0.419724i
\(519\) 18.3343 + 18.3343i 0.0353263 + 0.0353263i
\(520\) −323.168 + 368.787i −0.621477 + 0.709207i
\(521\) 285.723 + 285.723i 0.548413 + 0.548413i 0.925982 0.377569i \(-0.123240\pi\)
−0.377569 + 0.925982i \(0.623240\pi\)
\(522\) −91.7949 + 236.139i −0.175852 + 0.452374i
\(523\) 260.696 + 629.375i 0.498462 + 1.20339i 0.950312 + 0.311300i \(0.100764\pi\)
−0.451849 + 0.892094i \(0.649236\pi\)
\(524\) −659.312 239.779i −1.25823 0.457594i
\(525\) −214.792 + 518.553i −0.409127 + 0.987720i
\(526\) 20.1495 + 918.060i 0.0383070 + 1.74536i
\(527\) 15.1007 0.0286541
\(528\) −621.796 + 54.7203i −1.17764 + 0.103637i
\(529\) 390.712i 0.738586i
\(530\) 8.93297 + 407.008i 0.0168547 + 0.767939i
\(531\) −305.332 126.473i −0.575013 0.238178i
\(532\) 33.7865 15.7654i 0.0635085 0.0296343i
\(533\) 203.387 84.2457i 0.381589 0.158059i
\(534\) −181.612 + 467.191i −0.340097 + 0.874890i
\(535\) −852.096 + 852.096i −1.59270 + 1.59270i
\(536\) −34.0008 68.8802i −0.0634343 0.128508i
\(537\) 401.079 401.079i 0.746889 0.746889i
\(538\) 472.597 208.020i 0.878433 0.386654i
\(539\) 324.151 134.268i 0.601393 0.249105i
\(540\) 660.340 721.005i 1.22285 1.33519i
\(541\) 355.077 + 147.078i 0.656335 + 0.271863i 0.685895 0.727700i \(-0.259411\pi\)
−0.0295603 + 0.999563i \(0.509411\pi\)
\(542\) 132.596 + 126.900i 0.244642 + 0.234134i
\(543\) 260.137i 0.479073i
\(544\) 73.4803 91.6745i 0.135074 0.168519i
\(545\) −638.880 −1.17226
\(546\) −129.588 + 135.404i −0.237341 + 0.247994i
\(547\) 404.897 977.508i 0.740214 1.78704i 0.135204 0.990818i \(-0.456831\pi\)
0.605010 0.796218i \(-0.293169\pi\)
\(548\) −338.985 + 370.127i −0.618586 + 0.675414i
\(549\) −17.5244 42.3076i −0.0319205 0.0770630i
\(550\) 567.089 + 1288.36i 1.03107 + 2.34247i
\(551\) 53.3586 + 53.3586i 0.0968396 + 0.0968396i
\(552\) 218.025 + 73.9164i 0.394973 + 0.133907i
\(553\) 10.1598 + 10.1598i 0.0183722 + 0.0183722i
\(554\) −86.3067 33.5501i −0.155788 0.0605598i
\(555\) −404.451 976.431i −0.728741 1.75934i
\(556\) 262.222 122.358i 0.471623 0.220068i
\(557\) −296.952 + 716.907i −0.533128 + 1.28709i 0.396313 + 0.918115i \(0.370289\pi\)
−0.929441 + 0.368970i \(0.879711\pi\)
\(558\) 24.7683 0.543612i 0.0443876 0.000974214i
\(559\) −1.97418 −0.00353163
\(560\) −207.522 + 659.352i −0.370576 + 1.17741i
\(561\) 143.235i 0.255321i
\(562\) 473.431 10.3908i 0.842405 0.0184890i
\(563\) −44.6869 18.5099i −0.0793728 0.0328773i 0.342644 0.939465i \(-0.388678\pi\)
−0.422017 + 0.906588i \(0.638678\pi\)
\(564\) −362.287 131.757i −0.642354 0.233612i
\(565\) −1031.56 + 427.287i −1.82577 + 0.756260i
\(566\) 997.509 + 387.763i 1.76238 + 0.685094i
\(567\) 164.668 164.668i 0.290420 0.290420i
\(568\) 855.396 56.3949i 1.50598 0.0992868i
\(569\) 487.094 487.094i 0.856053 0.856053i −0.134818 0.990870i \(-0.543045\pi\)
0.990870 + 0.134818i \(0.0430449\pi\)
\(570\) −29.4150 66.8275i −0.0516052 0.117241i
\(571\) −252.561 + 104.614i −0.442313 + 0.183212i −0.592714 0.805413i \(-0.701944\pi\)
0.150401 + 0.988625i \(0.451944\pi\)
\(572\) 20.6230 + 469.592i 0.0360543 + 0.820964i
\(573\) 411.111 + 170.288i 0.717472 + 0.297187i
\(574\) 214.572 224.202i 0.373819 0.390596i
\(575\) 519.161i 0.902889i
\(576\) 117.223 153.010i 0.203512 0.265643i
\(577\) 460.004 0.797234 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(578\) −398.100 381.000i −0.688754 0.659170i
\(579\) −207.208 + 500.244i −0.357872 + 0.863979i
\(580\) −1397.69 + 61.3821i −2.40980 + 0.105831i
\(581\) −170.432 411.460i −0.293343 0.708193i
\(582\) −295.873 + 130.232i −0.508372 + 0.223767i
\(583\) 275.947 + 275.947i 0.473323 + 0.473323i
\(584\) −327.814 + 21.6123i −0.561325 + 0.0370073i
\(585\) −130.533 130.533i −0.223133 0.223133i
\(586\) 277.914 714.926i 0.474257 1.22001i
\(587\) 68.3015 + 164.895i 0.116357 + 0.280911i 0.971319 0.237780i \(-0.0764197\pi\)
−0.854962 + 0.518690i \(0.826420\pi\)
\(588\) 73.6267 202.449i 0.125216 0.344300i
\(589\) 2.82379 6.81723i 0.00479421 0.0115742i
\(590\) −40.0448 1824.54i −0.0678725 3.09244i
\(591\) −98.7067 −0.167016
\(592\) −384.095 736.920i −0.648809 1.24480i
\(593\) 167.545i 0.282538i 0.989971 + 0.141269i \(0.0451182\pi\)
−0.989971 + 0.141269i \(0.954882\pi\)
\(594\) −20.5650 936.990i −0.0346211 1.57742i
\(595\) −146.544 60.7006i −0.246293 0.102018i
\(596\) −184.057 394.448i −0.308820 0.661825i
\(597\) −433.609 + 179.607i −0.726313 + 0.300848i
\(598\) 62.8115 161.581i 0.105036 0.270202i
\(599\) −316.998 + 316.998i −0.529213 + 0.529213i −0.920338 0.391125i \(-0.872086\pi\)
0.391125 + 0.920338i \(0.372086\pi\)
\(600\) 818.510 + 277.497i 1.36418 + 0.462495i
\(601\) −224.198 + 224.198i −0.373042 + 0.373042i −0.868584 0.495542i \(-0.834970\pi\)
0.495542 + 0.868584i \(0.334970\pi\)
\(602\) −2.54715 + 1.12116i −0.00423114 + 0.00186239i
\(603\) 26.7172 11.0666i 0.0443071 0.0183526i
\(604\) −561.948 514.666i −0.930377 0.852096i
\(605\) 1023.00 + 423.742i 1.69091 + 0.700400i
\(606\) 69.4054 + 66.4242i 0.114530 + 0.109611i
\(607\) 89.2468i 0.147029i −0.997294 0.0735146i \(-0.976578\pi\)
0.997294 0.0735146i \(-0.0234216\pi\)
\(608\) −27.6459 50.3157i −0.0454703 0.0827560i
\(609\) −534.745 −0.878070
\(610\) 174.842 182.689i 0.286626 0.299490i
\(611\) −111.092 + 268.200i −0.181820 + 0.438952i
\(612\) 32.6180 + 29.8735i 0.0532974 + 0.0488130i
\(613\) 202.134 + 487.995i 0.329746 + 0.796076i 0.998611 + 0.0526926i \(0.0167803\pi\)
−0.668865 + 0.743384i \(0.733220\pi\)
\(614\) 46.5975 + 105.864i 0.0758918 + 0.172417i
\(615\) −429.741 429.741i −0.698766 0.698766i
\(616\) 293.295 + 594.169i 0.476128 + 0.964560i
\(617\) 380.984 + 380.984i 0.617479 + 0.617479i 0.944884 0.327405i \(-0.106174\pi\)
−0.327405 + 0.944884i \(0.606174\pi\)
\(618\) −3.80088 1.47752i −0.00615029 0.00239081i
\(619\) −371.320 896.447i −0.599871 1.44822i −0.873712 0.486443i \(-0.838294\pi\)
0.273841 0.961775i \(-0.411706\pi\)
\(620\) 57.8478 + 123.972i 0.0933029 + 0.199955i
\(621\) −132.278 + 319.348i −0.213008 + 0.514248i
\(622\) −776.259 + 17.0373i −1.24800 + 0.0273911i
\(623\) 532.098 0.854090
\(624\) 221.175 + 185.395i 0.354447 + 0.297108i
\(625\) 220.337i 0.352539i
\(626\) 221.699 4.86583i 0.354152 0.00777289i
\(627\) −64.6636 26.7845i −0.103132 0.0427186i
\(628\) 82.9407 228.059i 0.132071 0.363151i
\(629\) 176.177 72.9747i 0.280090 0.116017i
\(630\) −242.548 94.2861i −0.384997 0.149660i
\(631\) 384.726 384.726i 0.609708 0.609708i −0.333162 0.942870i \(-0.608115\pi\)
0.942870 + 0.333162i \(0.108115\pi\)
\(632\) 14.5813 16.6397i 0.0230717 0.0263286i
\(633\) 258.492 258.492i 0.408360 0.408360i
\(634\) 119.061 + 270.492i 0.187793 + 0.426643i
\(635\) −733.706 + 303.911i −1.15544 + 0.478600i
\(636\) 239.375 10.5126i 0.376376 0.0165293i
\(637\) −149.872 62.0789i −0.235277 0.0974551i
\(638\) −927.266 + 968.882i −1.45339 + 1.51862i
\(639\) 322.729i 0.505053i
\(640\) 1034.11 + 252.065i 1.61580 + 0.393851i
\(641\) −407.931 −0.636398 −0.318199 0.948024i \(-0.603078\pi\)
−0.318199 + 0.948024i \(0.603078\pi\)
\(642\) 512.393 + 490.385i 0.798121 + 0.763839i
\(643\) −319.302 + 770.863i −0.496582 + 1.19885i 0.454732 + 0.890629i \(0.349735\pi\)
−0.951313 + 0.308226i \(0.900265\pi\)
\(644\) −10.7222 244.148i −0.0166494 0.379111i
\(645\) 2.08564 + 5.03519i 0.00323356 + 0.00780650i
\(646\) 12.0576 5.30732i 0.0186650 0.00821566i
\(647\) −48.6565 48.6565i −0.0752033 0.0752033i 0.668505 0.743708i \(-0.266935\pi\)
−0.743708 + 0.668505i \(0.766935\pi\)
\(648\) −269.692 236.331i −0.416191 0.364708i
\(649\) −1237.02 1237.02i −1.90604 1.90604i
\(650\) 235.807 606.606i 0.362780 0.933239i
\(651\) 20.0106 + 48.3098i 0.0307382 + 0.0742085i
\(652\) 842.445 + 306.381i 1.29209 + 0.469910i
\(653\) −290.106 + 700.378i −0.444267 + 1.07255i 0.530170 + 0.847892i \(0.322128\pi\)
−0.974436 + 0.224663i \(0.927872\pi\)
\(654\) 8.25084 + 375.929i 0.0126160 + 0.574814i
\(655\) 1458.46 2.22665
\(656\) −366.220 306.977i −0.558263 0.467952i
\(657\) 123.680i 0.188249i
\(658\) 8.97953 + 409.129i 0.0136467 + 0.621777i
\(659\) 818.045 + 338.845i 1.24134 + 0.514181i 0.904134 0.427248i \(-0.140517\pi\)
0.337209 + 0.941430i \(0.390517\pi\)
\(660\) 1175.92 548.705i 1.78169 0.831371i
\(661\) −35.2123 + 14.5854i −0.0532712 + 0.0220657i −0.409160 0.912463i \(-0.634178\pi\)
0.355889 + 0.934528i \(0.384178\pi\)
\(662\) 272.087 699.936i 0.411008 1.05730i
\(663\) −46.8281 + 46.8281i −0.0706306 + 0.0706306i
\(664\) −614.940 + 303.548i −0.926115 + 0.457151i
\(665\) −54.8067 + 54.8067i −0.0824161 + 0.0824161i
\(666\) 286.339 126.036i 0.429938 0.189243i
\(667\) 456.969 189.283i 0.685110 0.283782i
\(668\) −277.530 + 303.026i −0.415464 + 0.453632i
\(669\) −69.2325 28.6770i −0.103487 0.0428655i
\(670\) 115.368 + 110.412i 0.172191 + 0.164795i
\(671\) 242.402i 0.361256i
\(672\) 390.654 + 113.595i 0.581331 + 0.169040i
\(673\) 114.199 0.169687 0.0848434 0.996394i \(-0.472961\pi\)
0.0848434 + 0.996394i \(0.472961\pi\)
\(674\) −662.569 + 692.305i −0.983039 + 1.02716i
\(675\) −496.599 + 1198.90i −0.735702 + 1.77614i
\(676\) −309.789 + 338.249i −0.458268 + 0.500369i
\(677\) −212.733 513.583i −0.314229 0.758617i −0.999539 0.0303647i \(-0.990333\pi\)
0.685310 0.728252i \(-0.259667\pi\)
\(678\) 264.746 + 601.472i 0.390480 + 0.887126i
\(679\) 242.652 + 242.652i 0.357366 + 0.357366i
\(680\) −78.4212 + 231.313i −0.115325 + 0.340166i
\(681\) −38.0347 38.0347i −0.0558512 0.0558512i
\(682\) 122.229 + 47.5144i 0.179222 + 0.0696693i
\(683\) 363.453 + 877.454i 0.532142 + 1.28471i 0.930102 + 0.367302i \(0.119719\pi\)
−0.397959 + 0.917403i \(0.630281\pi\)
\(684\) 19.5859 9.13916i 0.0286344 0.0133613i
\(685\) 399.289 963.969i 0.582904 1.40725i
\(686\) −737.650 + 16.1899i −1.07529 + 0.0236004i
\(687\) 490.163 0.713483
\(688\) 1.98067 + 3.80010i 0.00287889 + 0.00552340i
\(689\) 180.432i 0.261875i
\(690\) −478.473 + 10.5015i −0.693439 + 0.0152195i
\(691\) −682.306 282.620i −0.987418 0.409002i −0.170249 0.985401i \(-0.554457\pi\)
−0.817168 + 0.576399i \(0.804457\pi\)
\(692\) −39.8306 14.4856i −0.0575586 0.0209330i
\(693\) −230.465 + 95.4619i −0.332562 + 0.137752i
\(694\) −347.336 135.021i −0.500485 0.194554i
\(695\) −425.364 + 425.364i −0.612034 + 0.612034i
\(696\) 54.1688 + 821.631i 0.0778287 + 1.18050i
\(697\) 77.5377 77.5377i 0.111245 0.111245i
\(698\) −338.485 768.998i −0.484935 1.10172i
\(699\) −407.840 + 168.933i −0.583462 + 0.241678i
\(700\) −40.2533 916.578i −0.0575047 1.30940i
\(701\) −565.621 234.288i −0.806878 0.334220i −0.0591703 0.998248i \(-0.518846\pi\)
−0.747708 + 0.664028i \(0.768846\pi\)
\(702\) −299.609 + 313.055i −0.426793 + 0.445948i
\(703\) 93.1812i 0.132548i
\(704\) 883.225 510.833i 1.25458 0.725616i
\(705\) 801.413 1.13676
\(706\) 239.785 + 229.486i 0.339639 + 0.325051i
\(707\) 39.0267 94.2188i 0.0552004 0.133266i
\(708\) −1073.07 + 47.1262i −1.51564 + 0.0665624i
\(709\) 447.695 + 1080.83i 0.631446 + 1.52444i 0.837806 + 0.545968i \(0.183838\pi\)
−0.206360 + 0.978476i \(0.566162\pi\)
\(710\) −1631.11 + 717.954i −2.29734 + 1.01120i
\(711\) 5.88963 + 5.88963i 0.00828358 + 0.00828358i
\(712\) −53.9007 817.564i −0.0757032 1.14826i
\(713\) −34.2002 34.2002i −0.0479666 0.0479666i
\(714\) −33.8248 + 87.0132i −0.0473736 + 0.121867i
\(715\) −373.945 902.783i −0.523000 1.26263i
\(716\) −316.885 + 871.328i −0.442577 + 1.21694i
\(717\) 372.001 898.089i 0.518829 1.25257i
\(718\) −6.26658 285.521i −0.00872783 0.397661i
\(719\) 122.001 0.169681 0.0848406 0.996395i \(-0.472962\pi\)
0.0848406 + 0.996395i \(0.472962\pi\)
\(720\) −120.300 + 382.224i −0.167083 + 0.530866i
\(721\) 4.32894i 0.00600408i
\(722\) 15.7013 + 715.390i 0.0217470 + 0.990845i
\(723\) −906.877 375.641i −1.25433 0.519559i
\(724\) −179.803 385.332i −0.248347 0.532227i
\(725\) 1715.55 710.604i 2.36628 0.980144i
\(726\) 236.126 607.426i 0.325242 0.836675i
\(727\) 438.189 438.189i 0.602736 0.602736i −0.338301 0.941038i \(-0.609852\pi\)
0.941038 + 0.338301i \(0.109852\pi\)
\(728\) 98.3654 290.140i 0.135117 0.398545i
\(729\) 553.213 553.213i 0.758866 0.758866i
\(730\) 625.091 275.142i 0.856289 0.376907i
\(731\) −0.908495 + 0.376311i −0.00124281 + 0.000514789i
\(732\) −109.755 100.521i −0.149939 0.137323i
\(733\) −629.241 260.640i −0.858446 0.355580i −0.0903463 0.995910i \(-0.528797\pi\)
−0.768099 + 0.640331i \(0.778797\pi\)
\(734\) 942.018 + 901.555i 1.28340 + 1.22828i
\(735\) 447.835i 0.609299i
\(736\) −374.044 + 41.2063i −0.508212 + 0.0559869i
\(737\) 153.077 0.207703
\(738\) 124.387 129.969i 0.168546 0.176110i
\(739\) 55.5902 134.207i 0.0752235 0.181606i −0.881795 0.471633i \(-0.843665\pi\)
0.957018 + 0.290028i \(0.0936646\pi\)
\(740\) 1274.00 + 1166.81i 1.72162 + 1.57676i
\(741\) 12.3839 + 29.8973i 0.0167124 + 0.0403473i
\(742\) −102.469 232.799i −0.138099 0.313745i
\(743\) −180.295 180.295i −0.242658 0.242658i 0.575291 0.817949i \(-0.304889\pi\)
−0.817949 + 0.575291i \(0.804889\pi\)
\(744\) 72.2005 35.6397i 0.0970436 0.0479029i
\(745\) 639.853 + 639.853i 0.858863 + 0.858863i
\(746\) −1222.56 475.248i −1.63882 0.637062i
\(747\) −98.7991 238.522i −0.132261 0.319307i
\(748\) 99.0022 + 212.169i 0.132356 + 0.283649i
\(749\) 288.119 695.581i 0.384672 0.928680i
\(750\) −779.085 + 17.0993i −1.03878 + 0.0227990i
\(751\) −264.213 −0.351815 −0.175908 0.984407i \(-0.556286\pi\)
−0.175908 + 0.984407i \(0.556286\pi\)
\(752\) 627.714 55.2411i 0.834726 0.0734589i
\(753\) 583.228i 0.774539i
\(754\) 619.911 13.6057i 0.822163 0.0180448i
\(755\) 1463.55 + 606.223i 1.93848 + 0.802945i
\(756\) −208.776 + 574.064i −0.276159 + 0.759345i
\(757\) −691.098 + 286.262i −0.912944 + 0.378154i −0.789183 0.614158i \(-0.789496\pi\)
−0.123761 + 0.992312i \(0.539496\pi\)
\(758\) 870.819 + 338.515i 1.14884 + 0.446590i
\(759\) −324.400 + 324.400i −0.427404 + 0.427404i
\(760\) 89.7619 + 78.6582i 0.118108 + 0.103498i
\(761\) 287.342 287.342i 0.377585 0.377585i −0.492645 0.870230i \(-0.663970\pi\)
0.870230 + 0.492645i \(0.163970\pi\)
\(762\) 188.302 + 427.801i 0.247116 + 0.561418i
\(763\) 368.777 152.752i 0.483325 0.200200i
\(764\) −726.667 + 31.9130i −0.951135 + 0.0417710i
\(765\) −84.9511 35.1879i −0.111047 0.0459973i
\(766\) 807.561 843.805i 1.05426 1.10157i
\(767\) 808.842i 1.05455i
\(768\) 134.964 611.744i 0.175735 0.796541i
\(769\) −1240.31 −1.61289 −0.806446 0.591308i \(-0.798612\pi\)
−0.806446 + 0.591308i \(0.798612\pi\)
\(770\) −995.176 952.430i −1.29244 1.23692i
\(771\) 408.881 987.127i 0.530326 1.28032i
\(772\) −38.8321 884.215i −0.0503006 1.14536i
\(773\) −318.633 769.248i −0.412203 0.995146i −0.984545 0.175131i \(-0.943965\pi\)
0.572342 0.820015i \(-0.306035\pi\)
\(774\) −1.47657 + 0.649933i −0.00190772 + 0.000839706i
\(775\) −128.394 128.394i −0.165670 0.165670i
\(776\) 348.252 397.413i 0.448778 0.512130i
\(777\) 466.918 + 466.918i 0.600924 + 0.600924i
\(778\) −109.651 + 282.074i −0.140940 + 0.362563i
\(779\) −20.5052 49.5039i −0.0263224 0.0635480i
\(780\) −563.834 205.056i −0.722864 0.262892i
\(781\) −653.751 + 1578.29i −0.837069 + 2.02086i
\(782\) −1.89477 86.3304i −0.00242298 0.110397i
\(783\) −1236.33 −1.57897
\(784\) 30.8691 + 350.771i 0.0393739 + 0.447412i
\(785\) 504.487i 0.642659i
\(786\) −18.8353 858.183i −0.0239635 1.09184i
\(787\) 584.664 + 242.176i 0.742902 + 0.307720i 0.721842 0.692058i \(-0.243296\pi\)
0.0210600 + 0.999778i \(0.493296\pi\)
\(788\) 146.211 68.2249i 0.185547 0.0865798i
\(789\) −1038.03 + 429.967i −1.31563 + 0.544952i
\(790\) −16.6646 + 42.8691i −0.0210944 + 0.0542647i
\(791\) 493.280 493.280i 0.623616 0.623616i
\(792\) 170.022 + 344.438i 0.214674 + 0.434896i
\(793\) −79.2491 + 79.2491i −0.0999358 + 0.0999358i
\(794\) −1035.52 + 455.796i −1.30418 + 0.574050i
\(795\) −460.196 + 190.619i −0.578863 + 0.239773i
\(796\) 518.149 565.751i 0.650941 0.710742i
\(797\) −651.965 270.053i −0.818024 0.338837i −0.0658733 0.997828i \(-0.520983\pi\)
−0.752150 + 0.658991i \(0.770983\pi\)
\(798\) 32.9571 + 31.5415i 0.0412996 + 0.0395256i
\(799\) 144.598i 0.180974i
\(800\) −1404.24 + 154.697i −1.75530 + 0.193371i
\(801\) 308.455 0.385088
\(802\) −375.995 + 392.870i −0.468822 + 0.489863i
\(803\) 250.537 604.850i 0.312002 0.753238i
\(804\) 63.4787 69.3104i 0.0789536 0.0862070i
\(805\) 194.419 + 469.370i 0.241515 + 0.583068i
\(806\) −24.4267 55.4947i −0.0303061 0.0688520i
\(807\) 446.737 + 446.737i 0.553577 + 0.553577i
\(808\) −148.720 50.4200i −0.184059 0.0624009i
\(809\) −734.385 734.385i −0.907769 0.907769i 0.0883227 0.996092i \(-0.471849\pi\)
−0.996092 + 0.0883227i \(0.971849\pi\)
\(810\) 694.812 + 270.095i 0.857793 + 0.333451i
\(811\) 430.173 + 1038.53i 0.530423 + 1.28055i 0.931243 + 0.364398i \(0.118725\pi\)
−0.400820 + 0.916157i \(0.631275\pi\)
\(812\) 792.101 369.609i 0.975494 0.455184i
\(813\) −85.9370 + 207.470i −0.105704 + 0.255191i
\(814\) 1655.64 36.3378i 2.03395 0.0446410i
\(815\) −1863.57 −2.28658
\(816\) 137.121 + 43.1572i 0.168041 + 0.0528887i
\(817\) 0.480510i 0.000588140i
\(818\) 513.866 11.2783i 0.628199 0.0137876i
\(819\) 106.556 + 44.1370i 0.130105 + 0.0538913i
\(820\) 933.594 + 339.530i 1.13853 + 0.414061i
\(821\) 30.8969 12.7979i 0.0376333 0.0155882i −0.363787 0.931482i \(-0.618517\pi\)
0.401421 + 0.915894i \(0.368517\pi\)
\(822\) −572.373 222.500i −0.696318 0.270681i
\(823\) 581.324 581.324i 0.706348 0.706348i −0.259417 0.965765i \(-0.583530\pi\)
0.965765 + 0.259417i \(0.0835305\pi\)
\(824\) 6.65138 0.438515i 0.00807206 0.000532178i
\(825\) −1217.86 + 1217.86i −1.47620 + 1.47620i
\(826\) 459.351 + 1043.59i 0.556115 + 1.26343i
\(827\) 625.862 259.241i 0.756786 0.313471i 0.0292791 0.999571i \(-0.490679\pi\)
0.727507 + 0.686100i \(0.240679\pi\)
\(828\) −6.21563 141.531i −0.00750680 0.170932i
\(829\) 1209.84 + 501.131i 1.45939 + 0.604500i 0.964412 0.264403i \(-0.0851750\pi\)
0.494981 + 0.868904i \(0.335175\pi\)
\(830\) 985.726 1029.97i 1.18762 1.24092i
\(831\) 113.298i 0.136340i
\(832\) −455.762 121.747i −0.547791 0.146330i
\(833\) −80.8024 −0.0970017
\(834\) 255.785 + 244.798i 0.306697 + 0.293523i
\(835\) 326.901 789.210i 0.391499 0.945162i
\(836\) 114.297 5.01959i 0.136719 0.00600430i
\(837\) 46.2644 + 111.692i 0.0552741 + 0.133444i
\(838\) 404.415 178.008i 0.482595 0.212421i
\(839\) −92.2651 92.2651i −0.109970 0.109970i 0.649981 0.759951i \(-0.274777\pi\)
−0.759951 + 0.649981i \(0.774777\pi\)
\(840\) −843.929 + 55.6389i −1.00468 + 0.0662368i
\(841\) 656.279 + 656.279i 0.780355 + 0.780355i
\(842\) 24.8848 64.0152i 0.0295543 0.0760276i
\(843\) 221.728 + 535.300i 0.263023 + 0.634994i
\(844\) −204.229 + 561.562i −0.241978 + 0.665358i
\(845\) 364.900 880.946i 0.431834 1.04254i
\(846\) 5.20540 + 237.171i 0.00615296 + 0.280344i
\(847\) −691.816 −0.816784
\(848\) −347.313 + 181.025i −0.409567 + 0.213473i
\(849\) 1309.47i 1.54237i
\(850\) −7.11334 324.101i −0.00836864 0.381296i
\(851\) −564.280 233.733i −0.663079 0.274656i
\(852\) 443.522 + 950.502i 0.520566 + 1.11561i
\(853\) 404.566 167.577i 0.474286 0.196456i −0.132719 0.991154i \(-0.542371\pi\)
0.607005 + 0.794698i \(0.292371\pi\)
\(854\) −57.2431 + 147.256i −0.0670294 + 0.172431i
\(855\) −31.7713 + 31.7713i −0.0371594 + 0.0371594i
\(856\) −1097.94 372.231i −1.28264 0.434850i
\(857\) −870.817 + 870.817i −1.01612 + 1.01612i −0.0162551 + 0.999868i \(0.505174\pi\)
−0.999868 + 0.0162551i \(0.994826\pi\)
\(858\) −526.385 + 231.695i −0.613502 + 0.270041i
\(859\) −1000.98 + 414.619i −1.16528 + 0.482677i −0.879631 0.475657i \(-0.842211\pi\)
−0.285653 + 0.958333i \(0.592211\pi\)
\(860\) −6.56967 6.01690i −0.00763915 0.00699640i
\(861\) 350.805 + 145.308i 0.407439 + 0.168767i
\(862\) −26.7075 25.5603i −0.0309832 0.0296524i
\(863\) 130.559i 0.151285i −0.997135 0.0756423i \(-0.975899\pi\)
0.997135 0.0756423i \(-0.0241007\pi\)
\(864\) 903.193 + 262.631i 1.04536 + 0.303971i
\(865\) 88.1088 0.101860
\(866\) 512.062 535.044i 0.591296 0.617834i
\(867\) 258.014 622.900i 0.297594 0.718455i
\(868\) −63.0322 57.7287i −0.0726177 0.0665077i
\(869\) 16.8724 + 40.7336i 0.0194159 + 0.0468741i
\(870\) −689.614 1566.72i −0.792659 1.80083i
\(871\) −50.0457 50.0457i −0.0574577 0.0574577i
\(872\) −272.059 551.149i −0.311994 0.632051i
\(873\) 140.664 + 140.664i 0.161128 + 0.161128i
\(874\) −39.3283 15.2881i −0.0449980 0.0174922i
\(875\) 316.568 + 764.264i 0.361792 + 0.873444i
\(876\) −169.971 364.261i −0.194031 0.415824i
\(877\) −251.771 + 607.829i −0.287082 + 0.693077i −0.999966 0.00820433i \(-0.997388\pi\)
0.712884 + 0.701282i \(0.247388\pi\)
\(878\) 4.15985 0.0912999i 0.00473787 0.000103986i
\(879\) 938.512 1.06770
\(880\) −1362.59 + 1625.56i −1.54840 + 1.84723i
\(881\) 349.331i 0.396516i 0.980150 + 0.198258i \(0.0635284\pi\)
−0.980150 + 0.198258i \(0.936472\pi\)
\(882\) −132.533 + 2.90882i −0.150264 + 0.00329798i
\(883\) −1394.24 577.514i −1.57898 0.654036i −0.590731 0.806869i \(-0.701161\pi\)
−0.988252 + 0.152832i \(0.951161\pi\)
\(884\) 36.9980 101.732i 0.0418529 0.115081i
\(885\) 2062.97 854.510i 2.33104 0.965548i
\(886\) −31.2683 12.1550i −0.0352916 0.0137189i
\(887\) −980.070 + 980.070i −1.10493 + 1.10493i −0.111120 + 0.993807i \(0.535444\pi\)
−0.993807 + 0.111120i \(0.964556\pi\)
\(888\) 670.117 764.713i 0.754636 0.861163i
\(889\) 350.849 350.849i 0.394656 0.394656i
\(890\) 686.200 + 1558.97i 0.771012 + 1.75165i
\(891\) 660.200 273.464i 0.740965 0.306918i
\(892\) 122.373 5.37426i 0.137190 0.00602495i
\(893\) 65.2790 + 27.0395i 0.0731008 + 0.0302793i
\(894\) 368.237 384.764i 0.411899 0.430385i
\(895\) 1927.46i 2.15358i
\(896\) −657.180 + 101.751i −0.733459 + 0.113562i
\(897\) 212.113 0.236470
\(898\) 505.203 + 483.503i 0.562587 + 0.538422i
\(899\) 66.2018 159.825i 0.0736393 0.177781i
\(900\) −23.3347 531.337i −0.0259275 0.590375i
\(901\) −34.3933 83.0327i −0.0381723 0.0921561i
\(902\) 871.586 383.640i 0.966282 0.425321i
\(903\) −2.40777 2.40777i −0.00266641 0.00266641i
\(904\) −807.889 707.952i −0.893683 0.783133i
\(905\) 625.066 + 625.066i 0.690681 + 0.690681i
\(906\) 337.812 869.010i 0.372860 0.959172i
\(907\) 64.9162 + 156.722i 0.0715725 + 0.172791i 0.955617 0.294611i \(-0.0951900\pi\)
−0.884045 + 0.467402i \(0.845190\pi\)
\(908\) 82.6287 + 30.0505i 0.0910007 + 0.0330952i
\(909\) 22.6236 54.6183i 0.0248885 0.0600861i
\(910\) 13.9750 + 636.735i 0.0153571 + 0.699709i
\(911\) −989.468 −1.08613 −0.543067 0.839689i \(-0.682737\pi\)
−0.543067 + 0.839689i \(0.682737\pi\)
\(912\) 45.1247 53.8333i 0.0494788 0.0590278i
\(913\) 1366.62i 1.49684i
\(914\) −10.3919 473.482i −0.0113697 0.518033i
\(915\) 285.850 + 118.403i 0.312405 + 0.129402i
\(916\) −726.063 + 338.795i −0.792645 + 0.369863i
\(917\) −841.857 + 348.708i −0.918055 + 0.380271i
\(918\) −78.2029 + 201.175i −0.0851884 + 0.219144i
\(919\) 594.043 594.043i 0.646402 0.646402i −0.305720 0.952122i \(-0.598897\pi\)
0.952122 + 0.305720i \(0.0988970\pi\)
\(920\) 701.488 346.270i 0.762487 0.376381i
\(921\) −100.071 + 100.071i −0.108655 + 0.108655i
\(922\) −1434.36 + 631.353i −1.55571 + 0.684764i
\(923\) 729.727 302.263i 0.790603 0.327478i
\(924\) −547.575 + 597.880i −0.592614 + 0.647056i
\(925\) −2118.42 877.478i −2.29018 0.948625i
\(926\) 101.791 + 97.4191i 0.109926 + 0.105204i
\(927\) 2.50947i 0.00270709i
\(928\) −648.140 1179.62i −0.698427 1.27114i
\(929\) 1637.29 1.76242 0.881209 0.472726i \(-0.156730\pi\)
0.881209 + 0.472726i \(0.156730\pi\)
\(930\) −115.735 + 120.929i −0.124446 + 0.130031i
\(931\) −15.1098 + 36.4784i −0.0162297 + 0.0391819i
\(932\) 487.356 532.129i 0.522914 0.570954i
\(933\) −363.556 877.701i −0.389663 0.940730i
\(934\) 78.3498 + 178.002i 0.0838863 + 0.190580i
\(935\) −344.170 344.170i −0.368096 0.368096i
\(936\) 57.0221 168.193i 0.0609210 0.179694i
\(937\) −407.126 407.126i −0.434500 0.434500i 0.455656 0.890156i \(-0.349405\pi\)
−0.890156 + 0.455656i \(0.849405\pi\)
\(938\) −92.9920 36.1489i −0.0991386 0.0385383i
\(939\) 103.831 + 250.671i 0.110576 + 0.266955i
\(940\) −1187.11 + 553.927i −1.26288 + 0.589284i
\(941\) 510.935 1233.51i 0.542970 1.31085i −0.379648 0.925131i \(-0.623955\pi\)
0.922618 0.385715i \(-0.126045\pi\)
\(942\) 296.850 6.51522i 0.315127 0.00691637i
\(943\) −351.217 −0.372446
\(944\) 1556.94 811.503i 1.64930 0.859643i
\(945\) 1269.88i 1.34379i
\(946\) −8.53768 + 0.187384i −0.00902503 + 0.000198081i
\(947\) −627.458 259.902i −0.662574 0.274447i 0.0259471 0.999663i \(-0.491740\pi\)
−0.688521 + 0.725216i \(0.741740\pi\)
\(948\) 25.4402 + 9.25210i 0.0268356 + 0.00975960i
\(949\) −279.654 + 115.836i −0.294682 + 0.122061i
\(950\) −147.646 57.3947i −0.155417 0.0604155i
\(951\) −255.691 + 255.691i −0.268865 + 0.268865i
\(952\) −10.0389 152.269i −0.0105450 0.159947i
\(953\) −1189.93 + 1189.93i −1.24862 + 1.24862i −0.292290 + 0.956330i \(0.594417\pi\)
−0.956330 + 0.292290i \(0.905583\pi\)
\(954\) −59.4012 134.953i −0.0622654 0.141460i
\(955\) 1397.01 578.660i 1.46284 0.605926i
\(956\) 69.7153 + 1587.43i 0.0729239 + 1.66050i
\(957\) −1515.99 627.945i −1.58411 0.656159i
\(958\) −1245.31 + 1301.20i −1.29991 + 1.35825i
\(959\) 651.893i 0.679764i
\(960\) 170.977 + 1291.05i 0.178101 + 1.34485i
\(961\) 944.084 0.982397
\(962\) −553.161 529.401i −0.575012 0.550313i
\(963\) 167.022 403.226i 0.173439 0.418719i
\(964\) 1602.97 70.3975i 1.66283 0.0730264i
\(965\) 704.118 + 1699.89i 0.729656 + 1.76155i
\(966\) 273.675 120.462i 0.283307 0.124701i
\(967\) 633.832 + 633.832i 0.655462 + 0.655462i 0.954303 0.298841i \(-0.0965999\pi\)
−0.298841 + 0.954303i \(0.596600\pi\)
\(968\) 70.0798 + 1062.97i 0.0723965 + 1.09811i
\(969\) 11.3978 + 11.3978i 0.0117625 + 0.0117625i
\(970\) −398.007 + 1023.86i −0.410317 + 1.05553i
\(971\) −399.517 964.518i −0.411449 0.993325i −0.984749 0.173980i \(-0.944337\pi\)
0.573301 0.819345i \(-0.305663\pi\)
\(972\) −211.708 + 582.126i −0.217807 + 0.598895i
\(973\) 143.828 347.232i 0.147819 0.356867i
\(974\) 10.8900 + 496.174i 0.0111807 + 0.509419i
\(975\) 796.316 0.816734
\(976\) 232.056 + 73.0367i 0.237762 + 0.0748327i
\(977\) 122.057i 0.124931i −0.998047 0.0624653i \(-0.980104\pi\)
0.998047 0.0624653i \(-0.0198963\pi\)
\(978\) 24.0671 + 1096.56i 0.0246085 + 1.12122i
\(979\) 1508.49 + 624.837i 1.54085 + 0.638240i
\(980\) −309.538 663.364i −0.315855 0.676902i
\(981\) 213.779 88.5500i 0.217919 0.0902650i
\(982\) −212.061 + 545.521i −0.215948 + 0.555521i
\(983\) 1257.94 1257.94i 1.27970 1.27970i 0.338864 0.940835i \(-0.389957\pi\)
0.940835 0.338864i \(-0.110043\pi\)
\(984\) 187.729 553.729i 0.190781 0.562732i
\(985\) −237.176 + 237.176i −0.240788 + 0.240788i
\(986\) 282.682 124.426i 0.286696 0.126193i
\(987\) −462.595 + 191.613i −0.468688 + 0.194137i
\(988\) −39.0085 35.7264i −0.0394823 0.0361603i
\(989\) 2.90984 + 1.20530i 0.00294220 + 0.00121870i
\(990\) −576.900 552.121i −0.582727 0.557698i
\(991\) 1409.81i 1.42261i 0.702884 + 0.711304i \(0.251895\pi\)
−0.702884 + 0.711304i \(0.748105\pi\)
\(992\) −82.3146 + 102.696i −0.0829784 + 0.103524i
\(993\) 918.834 0.925311
\(994\) 769.857 804.409i 0.774504 0.809264i
\(995\) −610.326 + 1473.46i −0.613393 + 1.48086i
\(996\) −618.781 566.717i −0.621266 0.568993i
\(997\) −60.9825 147.225i −0.0611660 0.147668i 0.890341 0.455293i \(-0.150466\pi\)
−0.951508 + 0.307625i \(0.900466\pi\)
\(998\) −84.0828 191.027i −0.0842513 0.191409i
\(999\) 1079.51 + 1079.51i 1.08059 + 1.08059i
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 32.3.h.a.3.3 28
3.2 odd 2 288.3.u.a.163.5 28
4.3 odd 2 128.3.h.a.47.2 28
8.3 odd 2 256.3.h.a.95.6 28
8.5 even 2 256.3.h.b.95.2 28
32.5 even 8 256.3.h.a.159.6 28
32.11 odd 8 inner 32.3.h.a.11.3 yes 28
32.21 even 8 128.3.h.a.79.2 28
32.27 odd 8 256.3.h.b.159.2 28
96.11 even 8 288.3.u.a.235.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.3.3 28 1.1 even 1 trivial
32.3.h.a.11.3 yes 28 32.11 odd 8 inner
128.3.h.a.47.2 28 4.3 odd 2
128.3.h.a.79.2 28 32.21 even 8
256.3.h.a.95.6 28 8.3 odd 2
256.3.h.a.159.6 28 32.5 even 8
256.3.h.b.95.2 28 8.5 even 2
256.3.h.b.159.2 28 32.27 odd 8
288.3.u.a.163.5 28 3.2 odd 2
288.3.u.a.235.5 28 96.11 even 8