Properties

Label 32.4.g.a.13.6
Level $32$
Weight $4$
Character 32.13
Analytic conductor $1.888$
Analytic rank $0$
Dimension $44$
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] = [32,4,Mod(5,32)]
 
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([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("32.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 32.g (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: \(1.88806112018\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 32.13
Dual form 32.4.g.a.5.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.582457 + 2.76780i) q^{2} +(-1.90169 + 4.59109i) q^{3} +(-7.32149 - 3.22425i) q^{4} +(0.188811 - 0.0782080i) q^{5} +(-11.5996 - 7.93763i) q^{6} +(-11.4103 + 11.4103i) q^{7} +(13.1886 - 18.3865i) q^{8} +(1.63019 + 1.63019i) q^{9} +O(q^{10})\) \(q+(-0.582457 + 2.76780i) q^{2} +(-1.90169 + 4.59109i) q^{3} +(-7.32149 - 3.22425i) q^{4} +(0.188811 - 0.0782080i) q^{5} +(-11.5996 - 7.93763i) q^{6} +(-11.4103 + 11.4103i) q^{7} +(13.1886 - 18.3865i) q^{8} +(1.63019 + 1.63019i) q^{9} +(0.106490 + 0.568145i) q^{10} +(18.6604 + 45.0502i) q^{11} +(28.7261 - 27.4821i) q^{12} +(18.9369 + 7.84392i) q^{13} +(-24.9354 - 38.2274i) q^{14} +1.01558i q^{15} +(43.2084 + 47.2127i) q^{16} -85.7028i q^{17} +(-5.46155 + 3.56253i) q^{18} +(110.749 + 45.8739i) q^{19} +(-1.63454 - 0.0361752i) q^{20} +(-30.6868 - 74.0844i) q^{21} +(-135.559 + 25.4085i) q^{22} +(-74.2331 - 74.2331i) q^{23} +(59.3334 + 95.5153i) q^{24} +(-88.3588 + 88.3588i) q^{25} +(-32.7404 + 47.8449i) q^{26} +(-134.544 + 55.7299i) q^{27} +(120.330 - 46.7505i) q^{28} +(64.4881 - 155.688i) q^{29} +(-2.81092 - 0.591529i) q^{30} +36.6720 q^{31} +(-155.842 + 92.0930i) q^{32} -242.316 q^{33} +(237.209 + 49.9182i) q^{34} +(-1.26201 + 3.04676i) q^{35} +(-6.67926 - 17.1915i) q^{36} +(313.271 - 129.761i) q^{37} +(-191.477 + 279.813i) q^{38} +(-72.0243 + 72.0243i) q^{39} +(1.05217 - 4.50302i) q^{40} +(196.689 + 196.689i) q^{41} +(222.925 - 41.7840i) q^{42} +(-20.8770 - 50.4016i) q^{43} +(8.63137 - 390.000i) q^{44} +(0.435291 + 0.180303i) q^{45} +(248.700 - 162.225i) q^{46} -508.601i q^{47} +(-298.927 + 108.590i) q^{48} +82.6118i q^{49} +(-193.095 - 296.025i) q^{50} +(393.469 + 162.980i) q^{51} +(-113.355 - 118.486i) q^{52} +(73.8289 + 178.239i) q^{53} +(-75.8835 - 404.852i) q^{54} +(7.04657 + 7.04657i) q^{55} +(59.3094 + 360.279i) q^{56} +(-421.223 + 421.223i) q^{57} +(393.352 + 269.172i) q^{58} +(40.9489 - 16.9616i) q^{59} +(3.27448 - 7.43553i) q^{60} +(-324.831 + 784.211i) q^{61} +(-21.3598 + 101.501i) q^{62} -37.2017 q^{63} +(-164.124 - 484.982i) q^{64} +4.18895 q^{65} +(141.138 - 670.683i) q^{66} +(-49.4427 + 119.365i) q^{67} +(-276.328 + 627.472i) q^{68} +(481.979 - 199.642i) q^{69} +(-7.69776 - 5.26760i) q^{70} +(-362.308 + 362.308i) q^{71} +(51.4732 - 8.47355i) q^{72} +(239.192 + 239.192i) q^{73} +(176.687 + 942.654i) q^{74} +(-237.632 - 573.695i) q^{75} +(-662.942 - 692.950i) q^{76} +(-726.954 - 301.114i) q^{77} +(-157.398 - 241.300i) q^{78} -1018.36i q^{79} +(11.8506 + 5.53503i) q^{80} -661.438i q^{81} +(-658.960 + 429.834i) q^{82} +(231.267 + 95.7940i) q^{83} +(-14.1942 + 641.350i) q^{84} +(-6.70265 - 16.1816i) q^{85} +(151.662 - 28.4268i) q^{86} +(592.141 + 592.141i) q^{87} +(1074.42 + 251.048i) q^{88} +(1103.08 - 1103.08i) q^{89} +(-0.752583 + 1.09978i) q^{90} +(-305.576 + 126.574i) q^{91} +(304.150 + 782.843i) q^{92} +(-69.7388 + 168.364i) q^{93} +(1407.71 + 296.238i) q^{94} +24.4984 q^{95} +(-126.443 - 890.620i) q^{96} -74.0528 q^{97} +(-228.653 - 48.1178i) q^{98} +(-43.0203 + 103.860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.582457 + 2.76780i −0.205930 + 0.978567i
\(3\) −1.90169 + 4.59109i −0.365981 + 0.883556i 0.628419 + 0.777875i \(0.283702\pi\)
−0.994400 + 0.105681i \(0.966298\pi\)
\(4\) −7.32149 3.22425i −0.915186 0.403032i
\(5\) 0.188811 0.0782080i 0.0168878 0.00699514i −0.374224 0.927339i \(-0.622091\pi\)
0.391111 + 0.920343i \(0.372091\pi\)
\(6\) −11.5996 7.93763i −0.789252 0.540087i
\(7\) −11.4103 + 11.4103i −0.616096 + 0.616096i −0.944528 0.328432i \(-0.893480\pi\)
0.328432 + 0.944528i \(0.393480\pi\)
\(8\) 13.1886 18.3865i 0.582857 0.812574i
\(9\) 1.63019 + 1.63019i 0.0603773 + 0.0603773i
\(10\) 0.106490 + 0.568145i 0.00336752 + 0.0179663i
\(11\) 18.6604 + 45.0502i 0.511483 + 1.23483i 0.943020 + 0.332735i \(0.107971\pi\)
−0.431537 + 0.902095i \(0.642029\pi\)
\(12\) 28.7261 27.4821i 0.691042 0.661116i
\(13\) 18.9369 + 7.84392i 0.404011 + 0.167347i 0.575430 0.817851i \(-0.304835\pi\)
−0.171418 + 0.985198i \(0.554835\pi\)
\(14\) −24.9354 38.2274i −0.476019 0.729764i
\(15\) 1.01558i 0.0174814i
\(16\) 43.2084 + 47.2127i 0.675131 + 0.737698i
\(17\) 85.7028i 1.22270i −0.791359 0.611352i \(-0.790626\pi\)
0.791359 0.611352i \(-0.209374\pi\)
\(18\) −5.46155 + 3.56253i −0.0715167 + 0.0466497i
\(19\) 110.749 + 45.8739i 1.33725 + 0.553905i 0.932713 0.360619i \(-0.117434\pi\)
0.404532 + 0.914524i \(0.367434\pi\)
\(20\) −1.63454 0.0361752i −0.0182747 0.000404451i
\(21\) −30.6868 74.0844i −0.318876 0.769835i
\(22\) −135.559 + 25.4085i −1.31369 + 0.246233i
\(23\) −74.2331 74.2331i −0.672985 0.672985i 0.285418 0.958403i \(-0.407868\pi\)
−0.958403 + 0.285418i \(0.907868\pi\)
\(24\) 59.3334 + 95.5153i 0.504640 + 0.812374i
\(25\) −88.3588 + 88.3588i −0.706871 + 0.706871i
\(26\) −32.7404 + 47.8449i −0.246958 + 0.360890i
\(27\) −134.544 + 55.7299i −0.959000 + 0.397231i
\(28\) 120.330 46.7505i 0.812149 0.315536i
\(29\) 64.4881 155.688i 0.412936 0.996915i −0.571410 0.820665i \(-0.693603\pi\)
0.984345 0.176250i \(-0.0563967\pi\)
\(30\) −2.81092 0.591529i −0.0171067 0.00359993i
\(31\) 36.6720 0.212467 0.106234 0.994341i \(-0.466121\pi\)
0.106234 + 0.994341i \(0.466121\pi\)
\(32\) −155.842 + 92.0930i −0.860916 + 0.508747i
\(33\) −242.316 −1.27824
\(34\) 237.209 + 49.9182i 1.19650 + 0.251791i
\(35\) −1.26201 + 3.04676i −0.00609481 + 0.0147142i
\(36\) −6.67926 17.1915i −0.0309225 0.0795904i
\(37\) 313.271 129.761i 1.39193 0.576557i 0.444287 0.895884i \(-0.353457\pi\)
0.947644 + 0.319328i \(0.103457\pi\)
\(38\) −191.477 + 279.813i −0.817412 + 1.19452i
\(39\) −72.0243 + 72.0243i −0.295721 + 0.295721i
\(40\) 1.05217 4.50302i 0.00415909 0.0177997i
\(41\) 196.689 + 196.689i 0.749211 + 0.749211i 0.974331 0.225120i \(-0.0722773\pi\)
−0.225120 + 0.974331i \(0.572277\pi\)
\(42\) 222.925 41.7840i 0.819001 0.153510i
\(43\) −20.8770 50.4016i −0.0740400 0.178748i 0.882526 0.470263i \(-0.155841\pi\)
−0.956566 + 0.291514i \(0.905841\pi\)
\(44\) 8.63137 390.000i 0.0295734 1.33624i
\(45\) 0.435291 + 0.180303i 0.00144198 + 0.000597290i
\(46\) 248.700 162.225i 0.797149 0.519974i
\(47\) 508.601i 1.57845i −0.614106 0.789224i \(-0.710483\pi\)
0.614106 0.789224i \(-0.289517\pi\)
\(48\) −298.927 + 108.590i −0.898883 + 0.326533i
\(49\) 82.6118i 0.240851i
\(50\) −193.095 296.025i −0.546154 0.837286i
\(51\) 393.469 + 162.980i 1.08033 + 0.447487i
\(52\) −113.355 118.486i −0.302299 0.315983i
\(53\) 73.8289 + 178.239i 0.191343 + 0.461943i 0.990214 0.139560i \(-0.0445689\pi\)
−0.798871 + 0.601503i \(0.794569\pi\)
\(54\) −75.8835 404.852i −0.191230 1.02025i
\(55\) 7.04657 + 7.04657i 0.0172756 + 0.0172756i
\(56\) 59.3094 + 360.279i 0.141528 + 0.859720i
\(57\) −421.223 + 421.223i −0.978813 + 0.978813i
\(58\) 393.352 + 269.172i 0.890512 + 0.609379i
\(59\) 40.9489 16.9616i 0.0903576 0.0374273i −0.337047 0.941488i \(-0.609428\pi\)
0.427404 + 0.904061i \(0.359428\pi\)
\(60\) 3.27448 7.43553i 0.00704555 0.0159987i
\(61\) −324.831 + 784.211i −0.681809 + 1.64603i 0.0788549 + 0.996886i \(0.474874\pi\)
−0.760664 + 0.649146i \(0.775126\pi\)
\(62\) −21.3598 + 101.501i −0.0437533 + 0.207913i
\(63\) −37.2017 −0.0743964
\(64\) −164.124 484.982i −0.320554 0.947230i
\(65\) 4.18895 0.00799346
\(66\) 141.138 670.683i 0.263226 1.25084i
\(67\) −49.4427 + 119.365i −0.0901550 + 0.217654i −0.962525 0.271192i \(-0.912582\pi\)
0.872370 + 0.488846i \(0.162582\pi\)
\(68\) −276.328 + 627.472i −0.492789 + 1.11900i
\(69\) 481.979 199.642i 0.840920 0.348321i
\(70\) −7.69776 5.26760i −0.0131437 0.00899426i
\(71\) −362.308 + 362.308i −0.605606 + 0.605606i −0.941795 0.336189i \(-0.890862\pi\)
0.336189 + 0.941795i \(0.390862\pi\)
\(72\) 51.4732 8.47355i 0.0842524 0.0138697i
\(73\) 239.192 + 239.192i 0.383498 + 0.383498i 0.872361 0.488863i \(-0.162588\pi\)
−0.488863 + 0.872361i \(0.662588\pi\)
\(74\) 176.687 + 942.654i 0.277560 + 1.48083i
\(75\) −237.632 573.695i −0.365859 0.883261i
\(76\) −662.942 692.950i −1.00059 1.04588i
\(77\) −726.954 301.114i −1.07590 0.445651i
\(78\) −157.398 241.300i −0.228485 0.350280i
\(79\) 1018.36i 1.45030i −0.688589 0.725152i \(-0.741769\pi\)
0.688589 0.725152i \(-0.258231\pi\)
\(80\) 11.8506 + 5.53503i 0.0165617 + 0.00773544i
\(81\) 661.438i 0.907323i
\(82\) −658.960 + 429.834i −0.887438 + 0.578869i
\(83\) 231.267 + 95.7940i 0.305842 + 0.126684i 0.530326 0.847794i \(-0.322070\pi\)
−0.224484 + 0.974478i \(0.572070\pi\)
\(84\) −14.1942 + 641.350i −0.0184370 + 0.833060i
\(85\) −6.70265 16.1816i −0.00855299 0.0206487i
\(86\) 151.662 28.4268i 0.190164 0.0356435i
\(87\) 592.141 + 592.141i 0.729704 + 0.729704i
\(88\) 1074.42 + 251.048i 1.30151 + 0.304112i
\(89\) 1103.08 1103.08i 1.31378 1.31378i 0.395174 0.918606i \(-0.370684\pi\)
0.918606 0.395174i \(-0.129316\pi\)
\(90\) −0.752583 + 1.09978i −0.000881435 + 0.00128808i
\(91\) −305.576 + 126.574i −0.352012 + 0.145808i
\(92\) 304.150 + 782.843i 0.344672 + 0.887141i
\(93\) −69.7388 + 168.364i −0.0777589 + 0.187727i
\(94\) 1407.71 + 296.238i 1.54462 + 0.325049i
\(95\) 24.4984 0.0264577
\(96\) −126.443 890.620i −0.134427 0.946860i
\(97\) −74.0528 −0.0775147 −0.0387573 0.999249i \(-0.512340\pi\)
−0.0387573 + 0.999249i \(0.512340\pi\)
\(98\) −228.653 48.1178i −0.235689 0.0495983i
\(99\) −43.0203 + 103.860i −0.0436737 + 0.105438i
\(100\) 931.809 362.027i 0.931809 0.362027i
\(101\) 564.281 233.733i 0.555922 0.230270i −0.0869918 0.996209i \(-0.527725\pi\)
0.642914 + 0.765939i \(0.277725\pi\)
\(102\) −680.277 + 994.118i −0.660367 + 0.965023i
\(103\) −504.784 + 504.784i −0.482892 + 0.482892i −0.906054 0.423162i \(-0.860920\pi\)
0.423162 + 0.906054i \(0.360920\pi\)
\(104\) 393.972 244.732i 0.371463 0.230750i
\(105\) −11.5880 11.5880i −0.0107702 0.0107702i
\(106\) −536.332 + 100.528i −0.491445 + 0.0921142i
\(107\) −399.644 964.826i −0.361075 0.871713i −0.995143 0.0984356i \(-0.968616\pi\)
0.634068 0.773277i \(-0.281384\pi\)
\(108\) 1164.75 + 25.7779i 1.03776 + 0.0229674i
\(109\) −1362.55 564.385i −1.19732 0.495948i −0.307191 0.951648i \(-0.599389\pi\)
−0.890133 + 0.455700i \(0.849389\pi\)
\(110\) −23.6079 + 15.3992i −0.0204629 + 0.0133478i
\(111\) 1685.02i 1.44086i
\(112\) −1031.73 45.6902i −0.870439 0.0385475i
\(113\) 1171.99i 0.975681i −0.872933 0.487840i \(-0.837785\pi\)
0.872933 0.487840i \(-0.162215\pi\)
\(114\) −920.519 1411.21i −0.756267 1.15940i
\(115\) −19.8216 8.21039i −0.0160728 0.00665759i
\(116\) −974.126 + 931.942i −0.779701 + 0.745936i
\(117\) 18.0836 + 43.6577i 0.0142892 + 0.0344971i
\(118\) 23.0954 + 123.218i 0.0180179 + 0.0961284i
\(119\) 977.891 + 977.891i 0.753304 + 0.753304i
\(120\) 18.6729 + 13.3940i 0.0142049 + 0.0101891i
\(121\) −740.147 + 740.147i −0.556084 + 0.556084i
\(122\) −1981.34 1355.84i −1.47035 1.00616i
\(123\) −1277.06 + 528.976i −0.936168 + 0.387773i
\(124\) −268.493 118.240i −0.194447 0.0856310i
\(125\) −19.5487 + 47.1948i −0.0139879 + 0.0337699i
\(126\) 21.6684 102.967i 0.0153204 0.0728019i
\(127\) 2033.56 1.42086 0.710432 0.703766i \(-0.248500\pi\)
0.710432 + 0.703766i \(0.248500\pi\)
\(128\) 1437.93 171.782i 0.992940 0.118621i
\(129\) 271.100 0.185031
\(130\) −2.43988 + 11.5942i −0.00164609 + 0.00782214i
\(131\) 268.953 649.310i 0.179378 0.433057i −0.808458 0.588553i \(-0.799698\pi\)
0.987836 + 0.155496i \(0.0496977\pi\)
\(132\) 1774.11 + 781.288i 1.16982 + 0.515169i
\(133\) −1787.11 + 740.247i −1.16513 + 0.482613i
\(134\) −301.581 206.373i −0.194423 0.133044i
\(135\) −21.0448 + 21.0448i −0.0134167 + 0.0134167i
\(136\) −1575.77 1130.30i −0.993539 0.712663i
\(137\) 1077.41 + 1077.41i 0.671894 + 0.671894i 0.958152 0.286259i \(-0.0924116\pi\)
−0.286259 + 0.958152i \(0.592412\pi\)
\(138\) 271.839 + 1450.31i 0.167685 + 0.894626i
\(139\) 285.862 + 690.132i 0.174435 + 0.421124i 0.986783 0.162050i \(-0.0518106\pi\)
−0.812347 + 0.583174i \(0.801811\pi\)
\(140\) 19.0633 18.2378i 0.0115082 0.0110098i
\(141\) 2335.03 + 967.202i 1.39465 + 0.577682i
\(142\) −791.769 1213.83i −0.467914 0.717338i
\(143\) 999.480i 0.584481i
\(144\) −6.52777 + 147.403i −0.00377764 + 0.0853028i
\(145\) 34.4391i 0.0197242i
\(146\) −801.357 + 522.718i −0.454252 + 0.296305i
\(147\) −379.278 157.102i −0.212805 0.0881468i
\(148\) −2711.99 60.0211i −1.50625 0.0333358i
\(149\) −634.226 1531.16i −0.348710 0.841860i −0.996773 0.0802736i \(-0.974421\pi\)
0.648063 0.761587i \(-0.275579\pi\)
\(150\) 1726.29 323.567i 0.939671 0.176128i
\(151\) −805.847 805.847i −0.434297 0.434297i 0.455790 0.890087i \(-0.349357\pi\)
−0.890087 + 0.455790i \(0.849357\pi\)
\(152\) 2304.08 1431.28i 1.22951 0.763764i
\(153\) 139.712 139.712i 0.0738236 0.0738236i
\(154\) 1256.84 1836.68i 0.657659 0.961065i
\(155\) 6.92407 2.86804i 0.00358809 0.00148624i
\(156\) 759.550 295.100i 0.389825 0.151455i
\(157\) −308.064 + 743.733i −0.156600 + 0.378066i −0.982634 0.185554i \(-0.940592\pi\)
0.826034 + 0.563620i \(0.190592\pi\)
\(158\) 2818.61 + 593.149i 1.41922 + 0.298661i
\(159\) −958.710 −0.478180
\(160\) −22.2224 + 29.5763i −0.0109802 + 0.0146138i
\(161\) 1694.04 0.829248
\(162\) 1830.73 + 385.259i 0.887876 + 0.186845i
\(163\) 396.959 958.344i 0.190750 0.460511i −0.799352 0.600863i \(-0.794824\pi\)
0.990102 + 0.140353i \(0.0448236\pi\)
\(164\) −805.881 2074.23i −0.383712 0.987624i
\(165\) −45.7519 + 18.9510i −0.0215865 + 0.00894143i
\(166\) −399.842 + 584.306i −0.186950 + 0.273199i
\(167\) 307.489 307.489i 0.142480 0.142480i −0.632269 0.774749i \(-0.717876\pi\)
0.774749 + 0.632269i \(0.217876\pi\)
\(168\) −1766.86 412.845i −0.811408 0.189594i
\(169\) −1256.43 1256.43i −0.571887 0.571887i
\(170\) 48.6916 9.12652i 0.0219675 0.00411748i
\(171\) 105.759 + 255.325i 0.0472960 + 0.114183i
\(172\) −9.65669 + 436.328i −0.00428090 + 0.193428i
\(173\) 328.204 + 135.946i 0.144236 + 0.0597446i 0.453634 0.891188i \(-0.350127\pi\)
−0.309398 + 0.950933i \(0.600127\pi\)
\(174\) −1983.83 + 1294.04i −0.864331 + 0.563796i
\(175\) 2016.39i 0.871001i
\(176\) −1320.65 + 2827.55i −0.565614 + 1.21099i
\(177\) 220.256i 0.0935337i
\(178\) 2410.62 + 3695.61i 1.01508 + 1.55617i
\(179\) −1270.86 526.407i −0.530662 0.219807i 0.101231 0.994863i \(-0.467722\pi\)
−0.631893 + 0.775056i \(0.717722\pi\)
\(180\) −2.60563 2.72358i −0.00107896 0.00112780i
\(181\) 1449.19 + 3498.66i 0.595125 + 1.43676i 0.878496 + 0.477749i \(0.158547\pi\)
−0.283371 + 0.959010i \(0.591453\pi\)
\(182\) −172.347 919.499i −0.0701933 0.374493i
\(183\) −2982.66 2982.66i −1.20483 1.20483i
\(184\) −2343.91 + 385.856i −0.939105 + 0.154596i
\(185\) 49.0007 49.0007i 0.0194735 0.0194735i
\(186\) −425.380 291.089i −0.167690 0.114751i
\(187\) 3860.92 1599.25i 1.50983 0.625393i
\(188\) −1639.86 + 3723.71i −0.636164 + 1.44457i
\(189\) 899.289 2171.08i 0.346104 0.835569i
\(190\) −14.2693 + 67.8068i −0.00544843 + 0.0258907i
\(191\) −2124.08 −0.804677 −0.402338 0.915491i \(-0.631803\pi\)
−0.402338 + 0.915491i \(0.631803\pi\)
\(192\) 2538.71 + 168.779i 0.954248 + 0.0634403i
\(193\) −2384.50 −0.889328 −0.444664 0.895697i \(-0.646677\pi\)
−0.444664 + 0.895697i \(0.646677\pi\)
\(194\) 43.1326 204.964i 0.0159626 0.0758533i
\(195\) −7.96609 + 19.2319i −0.00292546 + 0.00706268i
\(196\) 266.361 604.841i 0.0970705 0.220423i
\(197\) −3010.53 + 1247.00i −1.08879 + 0.450990i −0.853584 0.520956i \(-0.825576\pi\)
−0.235204 + 0.971946i \(0.575576\pi\)
\(198\) −262.407 179.566i −0.0941841 0.0644504i
\(199\) 2542.97 2542.97i 0.905862 0.905862i −0.0900734 0.995935i \(-0.528710\pi\)
0.995935 + 0.0900734i \(0.0287102\pi\)
\(200\) 459.281 + 2789.93i 0.162380 + 0.986390i
\(201\) −453.992 453.992i −0.159314 0.159314i
\(202\) 318.258 + 1697.96i 0.110854 + 0.591426i
\(203\) 1040.61 + 2512.27i 0.359787 + 0.868604i
\(204\) −2355.29 2461.90i −0.808350 0.844940i
\(205\) 52.5197 + 21.7544i 0.0178933 + 0.00741167i
\(206\) −1103.13 1691.16i −0.373100 0.571984i
\(207\) 242.028i 0.0812661i
\(208\) 447.900 + 1232.98i 0.149309 + 0.411020i
\(209\) 5845.30i 1.93458i
\(210\) 38.8228 25.3238i 0.0127573 0.00832146i
\(211\) 411.497 + 170.448i 0.134259 + 0.0556118i 0.448801 0.893632i \(-0.351851\pi\)
−0.314543 + 0.949243i \(0.601851\pi\)
\(212\) 34.1496 1543.02i 0.0110632 0.499881i
\(213\) −974.390 2352.39i −0.313447 0.756727i
\(214\) 2903.23 544.167i 0.927385 0.173825i
\(215\) −7.88363 7.88363i −0.00250074 0.00250074i
\(216\) −749.765 + 3208.78i −0.236181 + 1.01079i
\(217\) −418.437 + 418.437i −0.130900 + 0.130900i
\(218\) 2355.73 3442.53i 0.731882 1.06953i
\(219\) −1553.02 + 643.284i −0.479195 + 0.198489i
\(220\) −28.8714 74.3113i −0.00884778 0.0227730i
\(221\) 672.246 1622.94i 0.204616 0.493987i
\(222\) −4663.81 981.453i −1.40998 0.296715i
\(223\) −1847.81 −0.554880 −0.277440 0.960743i \(-0.589486\pi\)
−0.277440 + 0.960743i \(0.589486\pi\)
\(224\) 727.399 2829.01i 0.216970 0.843844i
\(225\) −288.083 −0.0853579
\(226\) 3243.85 + 682.636i 0.954769 + 0.200922i
\(227\) −904.304 + 2183.18i −0.264409 + 0.638339i −0.999202 0.0399527i \(-0.987279\pi\)
0.734793 + 0.678291i \(0.237279\pi\)
\(228\) 4442.11 1725.85i 1.29029 0.501303i
\(229\) 4319.52 1789.20i 1.24647 0.516305i 0.340740 0.940158i \(-0.389322\pi\)
0.905731 + 0.423852i \(0.139322\pi\)
\(230\) 34.2700 50.0802i 0.00982477 0.0143574i
\(231\) 2764.89 2764.89i 0.787516 0.787516i
\(232\) −2012.05 3239.01i −0.569385 0.916600i
\(233\) −3523.28 3523.28i −0.990634 0.990634i 0.00932269 0.999957i \(-0.497032\pi\)
−0.999957 + 0.00932269i \(0.997032\pi\)
\(234\) −131.369 + 24.6232i −0.0367003 + 0.00687892i
\(235\) −39.7767 96.0294i −0.0110415 0.0266564i
\(236\) −354.496 7.84560i −0.0977784 0.00216400i
\(237\) 4675.37 + 1936.60i 1.28143 + 0.530784i
\(238\) −3276.19 + 2137.03i −0.892286 + 0.582031i
\(239\) 6222.79i 1.68418i 0.539337 + 0.842090i \(0.318675\pi\)
−0.539337 + 0.842090i \(0.681325\pi\)
\(240\) −47.9481 + 43.8814i −0.0128960 + 0.0118022i
\(241\) 4271.08i 1.14160i 0.821091 + 0.570798i \(0.193366\pi\)
−0.821091 + 0.570798i \(0.806634\pi\)
\(242\) −1617.48 2479.69i −0.429651 0.658679i
\(243\) −595.962 246.856i −0.157329 0.0651679i
\(244\) 4906.74 4694.26i 1.28739 1.23163i
\(245\) 6.46091 + 15.5980i 0.00168478 + 0.00406743i
\(246\) −720.269 3842.76i −0.186677 0.995956i
\(247\) 1737.42 + 1737.42i 0.447568 + 0.447568i
\(248\) 483.651 674.268i 0.123838 0.172645i
\(249\) −879.598 + 879.598i −0.223864 + 0.223864i
\(250\) −119.240 81.5961i −0.0301656 0.0206424i
\(251\) 4861.21 2013.58i 1.22246 0.506358i 0.324267 0.945966i \(-0.394883\pi\)
0.898190 + 0.439608i \(0.144883\pi\)
\(252\) 272.372 + 119.948i 0.0680866 + 0.0299841i
\(253\) 1958.99 4729.43i 0.486802 1.17524i
\(254\) −1184.46 + 5628.51i −0.292598 + 1.39041i
\(255\) 87.0377 0.0213746
\(256\) −362.074 + 4079.97i −0.0883969 + 0.996085i
\(257\) 2043.19 0.495917 0.247958 0.968771i \(-0.420240\pi\)
0.247958 + 0.968771i \(0.420240\pi\)
\(258\) −157.904 + 750.353i −0.0381035 + 0.181066i
\(259\) −2093.90 + 5055.12i −0.502349 + 1.21278i
\(260\) −30.6693 13.5062i −0.00731551 0.00322162i
\(261\) 358.928 148.673i 0.0851230 0.0352591i
\(262\) 1640.51 + 1122.60i 0.386836 + 0.264713i
\(263\) −3376.45 + 3376.45i −0.791638 + 0.791638i −0.981760 0.190123i \(-0.939111\pi\)
0.190123 + 0.981760i \(0.439111\pi\)
\(264\) −3195.80 + 4455.33i −0.745029 + 1.03866i
\(265\) 27.8794 + 27.8794i 0.00646271 + 0.00646271i
\(266\) −1007.94 5377.54i −0.232334 1.23954i
\(267\) 2966.63 + 7162.07i 0.679980 + 1.64162i
\(268\) 746.858 714.515i 0.170230 0.162858i
\(269\) −3758.60 1556.86i −0.851917 0.352876i −0.0863762 0.996263i \(-0.527529\pi\)
−0.765541 + 0.643387i \(0.777529\pi\)
\(270\) −45.9903 70.5057i −0.0103662 0.0158920i
\(271\) 4182.58i 0.937540i −0.883320 0.468770i \(-0.844697\pi\)
0.883320 0.468770i \(-0.155303\pi\)
\(272\) 4046.26 3703.08i 0.901987 0.825486i
\(273\) 1643.63i 0.364385i
\(274\) −3609.61 + 2354.52i −0.795856 + 0.519130i
\(275\) −5629.39 2331.77i −1.23442 0.511313i
\(276\) −4172.50 92.3447i −0.909983 0.0201395i
\(277\) −26.8731 64.8775i −0.00582906 0.0140726i 0.920938 0.389709i \(-0.127424\pi\)
−0.926767 + 0.375636i \(0.877424\pi\)
\(278\) −2076.65 + 389.238i −0.448020 + 0.0839747i
\(279\) 59.7822 + 59.7822i 0.0128282 + 0.0128282i
\(280\) 39.3750 + 63.3862i 0.00840395 + 0.0135287i
\(281\) 3756.73 3756.73i 0.797536 0.797536i −0.185171 0.982706i \(-0.559284\pi\)
0.982706 + 0.185171i \(0.0592837\pi\)
\(282\) −4037.08 + 5899.56i −0.852499 + 1.24579i
\(283\) 47.8634 19.8257i 0.0100536 0.00416436i −0.377651 0.925948i \(-0.623268\pi\)
0.387705 + 0.921784i \(0.373268\pi\)
\(284\) 3820.80 1484.46i 0.798321 0.310164i
\(285\) −46.5885 + 112.474i −0.00968303 + 0.0233769i
\(286\) −2766.37 582.154i −0.571953 0.120362i
\(287\) −4488.55 −0.923173
\(288\) −404.181 103.924i −0.0826965 0.0212630i
\(289\) −2431.97 −0.495007
\(290\) 95.3206 + 20.0593i 0.0193015 + 0.00406180i
\(291\) 140.826 339.983i 0.0283689 0.0684886i
\(292\) −980.027 2522.46i −0.196410 0.505534i
\(293\) −3659.53 + 1515.83i −0.729666 + 0.302238i −0.716415 0.697674i \(-0.754218\pi\)
−0.0132515 + 0.999912i \(0.504218\pi\)
\(294\) 655.742 958.264i 0.130080 0.190092i
\(295\) 6.40507 6.40507i 0.00126413 0.00126413i
\(296\) 1745.75 7471.31i 0.342802 1.46710i
\(297\) −5021.28 5021.28i −0.981025 0.981025i
\(298\) 4607.35 863.580i 0.895626 0.167872i
\(299\) −823.465 1988.02i −0.159272 0.384516i
\(300\) −109.917 + 4966.49i −0.0211535 + 0.955801i
\(301\) 813.309 + 336.883i 0.155742 + 0.0645104i
\(302\) 2699.80 1761.06i 0.514424 0.335554i
\(303\) 3035.16i 0.575463i
\(304\) 2619.47 + 7210.92i 0.494201 + 1.36044i
\(305\) 173.472i 0.0325671i
\(306\) 305.318 + 468.070i 0.0570389 + 0.0874438i
\(307\) 1166.44 + 483.155i 0.216847 + 0.0898211i 0.488463 0.872585i \(-0.337558\pi\)
−0.271615 + 0.962406i \(0.587558\pi\)
\(308\) 4351.52 + 4548.49i 0.805035 + 0.841475i
\(309\) −1357.57 3277.46i −0.249933 0.603391i
\(310\) 3.90521 + 20.8350i 0.000715488 + 0.00381725i
\(311\) 811.491 + 811.491i 0.147960 + 0.147960i 0.777206 0.629246i \(-0.216636\pi\)
−0.629246 + 0.777206i \(0.716636\pi\)
\(312\) 374.375 + 2274.17i 0.0679321 + 0.412658i
\(313\) −748.416 + 748.416i −0.135153 + 0.135153i −0.771447 0.636294i \(-0.780467\pi\)
0.636294 + 0.771447i \(0.280467\pi\)
\(314\) −1879.07 1285.85i −0.337714 0.231099i
\(315\) −7.02409 + 2.90947i −0.00125639 + 0.000520414i
\(316\) −3283.44 + 7455.88i −0.584519 + 1.32730i
\(317\) −1647.93 + 3978.45i −0.291977 + 0.704896i −0.999999 0.00129494i \(-0.999588\pi\)
0.708022 + 0.706191i \(0.249588\pi\)
\(318\) 558.407 2653.52i 0.0984715 0.467931i
\(319\) 8217.14 1.44223
\(320\) −68.9179 78.7341i −0.0120395 0.0137543i
\(321\) 5189.61 0.902354
\(322\) −986.704 + 4688.77i −0.170767 + 0.811474i
\(323\) 3931.52 9491.54i 0.677263 1.63506i
\(324\) −2132.65 + 4842.71i −0.365680 + 0.830369i
\(325\) −2366.32 + 980.162i −0.403876 + 0.167291i
\(326\) 2421.30 + 1656.90i 0.411360 + 0.281494i
\(327\) 5182.29 5182.29i 0.876395 0.876395i
\(328\) 6210.46 1022.37i 1.04547 0.172107i
\(329\) 5803.27 + 5803.27i 0.972476 + 0.972476i
\(330\) −25.8043 137.670i −0.00430448 0.0229652i
\(331\) −2379.90 5745.58i −0.395199 0.954095i −0.988788 0.149327i \(-0.952289\pi\)
0.593589 0.804769i \(-0.297711\pi\)
\(332\) −1384.35 1447.02i −0.228844 0.239203i
\(333\) 722.225 + 299.156i 0.118852 + 0.0492301i
\(334\) 671.970 + 1030.17i 0.110086 + 0.168767i
\(335\) 26.4043i 0.00430633i
\(336\) 2171.80 4649.87i 0.352623 0.754974i
\(337\) 10731.5i 1.73466i −0.497730 0.867332i \(-0.665833\pi\)
0.497730 0.867332i \(-0.334167\pi\)
\(338\) 4209.39 2745.75i 0.677398 0.441861i
\(339\) 5380.73 + 2228.77i 0.862069 + 0.357081i
\(340\) −3.10031 + 140.085i −0.000494524 + 0.0223446i
\(341\) 684.313 + 1652.08i 0.108673 + 0.262361i
\(342\) −768.291 + 144.005i −0.121475 + 0.0227687i
\(343\) −4856.34 4856.34i −0.764484 0.764484i
\(344\) −1202.05 280.870i −0.188401 0.0440218i
\(345\) 75.3893 75.3893i 0.0117647 0.0117647i
\(346\) −567.438 + 829.221i −0.0881666 + 0.128842i
\(347\) −5414.63 + 2242.81i −0.837673 + 0.346976i −0.759936 0.649998i \(-0.774770\pi\)
−0.0777376 + 0.996974i \(0.524770\pi\)
\(348\) −2426.14 6244.57i −0.373721 0.961908i
\(349\) −443.942 + 1071.77i −0.0680907 + 0.164385i −0.954261 0.298973i \(-0.903356\pi\)
0.886171 + 0.463359i \(0.153356\pi\)
\(350\) 5580.99 + 1174.46i 0.852332 + 0.179365i
\(351\) −2984.99 −0.453922
\(352\) −7056.88 5302.24i −1.06856 0.802870i
\(353\) 812.561 0.122516 0.0612582 0.998122i \(-0.480489\pi\)
0.0612582 + 0.998122i \(0.480489\pi\)
\(354\) −609.626 128.290i −0.0915290 0.0192614i
\(355\) −40.0723 + 96.7430i −0.00599103 + 0.0144636i
\(356\) −11632.8 + 4519.58i −1.73185 + 0.672858i
\(357\) −6349.24 + 2629.94i −0.941281 + 0.389891i
\(358\) 2197.21 3210.88i 0.324375 0.474023i
\(359\) −3733.47 + 3733.47i −0.548871 + 0.548871i −0.926114 0.377243i \(-0.876872\pi\)
0.377243 + 0.926114i \(0.376872\pi\)
\(360\) 9.05600 5.62552i 0.00132581 0.000823585i
\(361\) 5310.98 + 5310.98i 0.774308 + 0.774308i
\(362\) −10527.7 + 1973.26i −1.52852 + 0.286498i
\(363\) −1990.55 4805.62i −0.287815 0.694847i
\(364\) 2645.38 + 58.5467i 0.380922 + 0.00843045i
\(365\) 63.8689 + 26.4554i 0.00915904 + 0.00379380i
\(366\) 9992.69 6518.15i 1.42712 0.930899i
\(367\) 6820.92i 0.970161i 0.874469 + 0.485081i \(0.161210\pi\)
−0.874469 + 0.485081i \(0.838790\pi\)
\(368\) 297.252 6712.23i 0.0421069 0.950813i
\(369\) 641.280i 0.0904707i
\(370\) 107.083 + 164.165i 0.0150460 + 0.0230663i
\(371\) −2876.16 1191.34i −0.402487 0.166716i
\(372\) 1053.44 1007.82i 0.146824 0.140466i
\(373\) 3875.45 + 9356.15i 0.537970 + 1.29878i 0.926137 + 0.377186i \(0.123108\pi\)
−0.388167 + 0.921589i \(0.626892\pi\)
\(374\) 2177.58 + 11617.8i 0.301070 + 1.60626i
\(375\) −179.500 179.500i −0.0247183 0.0247183i
\(376\) −9351.37 6707.71i −1.28261 0.920010i
\(377\) 2442.41 2442.41i 0.333661 0.333661i
\(378\) 5485.32 + 3753.61i 0.746387 + 0.510754i
\(379\) −4336.19 + 1796.11i −0.587692 + 0.243430i −0.656657 0.754189i \(-0.728030\pi\)
0.0689653 + 0.997619i \(0.478030\pi\)
\(380\) −179.365 78.9891i −0.0242137 0.0106633i
\(381\) −3867.22 + 9336.29i −0.520009 + 1.25541i
\(382\) 1237.19 5879.05i 0.165707 0.787430i
\(383\) 8452.79 1.12772 0.563861 0.825870i \(-0.309315\pi\)
0.563861 + 0.825870i \(0.309315\pi\)
\(384\) −1945.84 + 6928.35i −0.258588 + 0.920731i
\(385\) −160.806 −0.0212869
\(386\) 1388.87 6599.84i 0.183139 0.870267i
\(387\) 48.1306 116.198i 0.00632201 0.0152627i
\(388\) 542.177 + 238.765i 0.0709403 + 0.0312409i
\(389\) −468.925 + 194.235i −0.0611194 + 0.0253165i −0.413034 0.910716i \(-0.635531\pi\)
0.351914 + 0.936032i \(0.385531\pi\)
\(390\) −48.5901 33.2503i −0.00630886 0.00431717i
\(391\) −6361.98 + 6361.98i −0.822862 + 0.822862i
\(392\) 1518.94 + 1089.53i 0.195709 + 0.140382i
\(393\) 2469.58 + 2469.58i 0.316981 + 0.316981i
\(394\) −1697.95 9058.87i −0.217111 1.15832i
\(395\) −79.6437 192.277i −0.0101451 0.0244924i
\(396\) 649.844 621.702i 0.0824643 0.0788932i
\(397\) −3306.01 1369.40i −0.417945 0.173118i 0.163793 0.986495i \(-0.447627\pi\)
−0.581738 + 0.813376i \(0.697627\pi\)
\(398\) 5557.28 + 8519.62i 0.699902 + 1.07299i
\(399\) 9612.53i 1.20609i
\(400\) −7989.50 353.816i −0.998687 0.0442270i
\(401\) 3887.84i 0.484164i 0.970256 + 0.242082i \(0.0778303\pi\)
−0.970256 + 0.242082i \(0.922170\pi\)
\(402\) 1520.99 992.131i 0.188707 0.123092i
\(403\) 694.453 + 287.652i 0.0858392 + 0.0355557i
\(404\) −4884.99 108.113i −0.601578 0.0133140i
\(405\) −51.7298 124.887i −0.00634685 0.0153227i
\(406\) −7559.58 + 1416.93i −0.924078 + 0.173205i
\(407\) 11691.5 + 11691.5i 1.42390 + 1.42390i
\(408\) 8185.93 5085.03i 0.993294 0.617026i
\(409\) −7188.15 + 7188.15i −0.869025 + 0.869025i −0.992365 0.123339i \(-0.960640\pi\)
0.123339 + 0.992365i \(0.460640\pi\)
\(410\) −90.8023 + 132.693i −0.0109376 + 0.0159836i
\(411\) −6995.40 + 2897.59i −0.839556 + 0.347756i
\(412\) 5323.32 2068.22i 0.636557 0.247315i
\(413\) −273.702 + 660.775i −0.0326101 + 0.0787278i
\(414\) 669.885 + 140.971i 0.0795243 + 0.0167351i
\(415\) 51.1576 0.00605115
\(416\) −3673.54 + 521.539i −0.432957 + 0.0614677i
\(417\) −3712.08 −0.435927
\(418\) −16178.7 3404.64i −1.89312 0.398388i
\(419\) 4190.33 10116.4i 0.488571 1.17951i −0.466869 0.884327i \(-0.654618\pi\)
0.955439 0.295187i \(-0.0953821\pi\)
\(420\) 47.4787 + 122.204i 0.00551601 + 0.0141975i
\(421\) 14568.6 6034.51i 1.68653 0.698584i 0.686927 0.726726i \(-0.258959\pi\)
0.999604 + 0.0281419i \(0.00895901\pi\)
\(422\) −711.445 + 1039.66i −0.0820677 + 0.119929i
\(423\) 829.114 829.114i 0.0953024 0.0953024i
\(424\) 4250.87 + 993.259i 0.486888 + 0.113766i
\(425\) 7572.60 + 7572.60i 0.864294 + 0.864294i
\(426\) 7078.49 1326.76i 0.805056 0.150896i
\(427\) −5241.65 12654.5i −0.594054 1.43417i
\(428\) −184.856 + 8352.52i −0.0208769 + 0.943304i
\(429\) −4588.71 1900.70i −0.516422 0.213909i
\(430\) 26.4122 17.2285i 0.00296212 0.00193216i
\(431\) 844.040i 0.0943295i −0.998887 0.0471647i \(-0.984981\pi\)
0.998887 0.0471647i \(-0.0150186\pi\)
\(432\) −8444.58 3944.18i −0.940487 0.439270i
\(433\) 11447.7i 1.27053i −0.772293 0.635266i \(-0.780890\pi\)
0.772293 0.635266i \(-0.219110\pi\)
\(434\) −914.430 1401.87i −0.101138 0.155051i
\(435\) 158.113 + 65.4925i 0.0174274 + 0.00721868i
\(436\) 8156.15 + 8525.34i 0.895891 + 0.936444i
\(437\) −4815.91 11626.6i −0.527177 1.27272i
\(438\) −875.914 4673.15i −0.0955543 0.509799i
\(439\) 2040.34 + 2040.34i 0.221823 + 0.221823i 0.809266 0.587443i \(-0.199865\pi\)
−0.587443 + 0.809266i \(0.699865\pi\)
\(440\) 222.496 36.6274i 0.0241070 0.00396850i
\(441\) −134.673 + 134.673i −0.0145419 + 0.0145419i
\(442\) 4100.44 + 2805.94i 0.441262 + 0.301957i
\(443\) 12477.8 5168.47i 1.33823 0.554315i 0.405241 0.914210i \(-0.367187\pi\)
0.932993 + 0.359895i \(0.117187\pi\)
\(444\) 5432.94 12336.9i 0.580712 1.31865i
\(445\) 122.004 294.544i 0.0129967 0.0313769i
\(446\) 1076.27 5114.37i 0.114266 0.542987i
\(447\) 8235.78 0.871452
\(448\) 7406.47 + 3661.07i 0.781077 + 0.386093i
\(449\) −3601.74 −0.378567 −0.189283 0.981922i \(-0.560616\pi\)
−0.189283 + 0.981922i \(0.560616\pi\)
\(450\) 167.796 797.357i 0.0175777 0.0835284i
\(451\) −5190.58 + 12531.2i −0.541940 + 1.30836i
\(452\) −3778.81 + 8580.74i −0.393230 + 0.892930i
\(453\) 5232.19 2167.25i 0.542671 0.224782i
\(454\) −5515.90 3774.55i −0.570207 0.390194i
\(455\) −47.7970 + 47.7970i −0.00492474 + 0.00492474i
\(456\) 2189.48 + 13300.1i 0.224850 + 1.36587i
\(457\) −10018.4 10018.4i −1.02547 1.02547i −0.999667 0.0258078i \(-0.991784\pi\)
−0.0258078 0.999667i \(-0.508216\pi\)
\(458\) 2436.23 + 12997.7i 0.248554 + 1.32608i
\(459\) 4776.21 + 11530.8i 0.485696 + 1.17257i
\(460\) 118.651 + 124.022i 0.0120264 + 0.0125708i
\(461\) −1495.66 619.524i −0.151106 0.0625902i 0.305849 0.952080i \(-0.401060\pi\)
−0.456955 + 0.889490i \(0.651060\pi\)
\(462\) 6042.24 + 9263.09i 0.608464 + 0.932810i
\(463\) 14517.8i 1.45724i −0.684921 0.728618i \(-0.740163\pi\)
0.684921 0.728618i \(-0.259837\pi\)
\(464\) 10136.9 3682.37i 1.01421 0.368426i
\(465\) 37.2432i 0.00371422i
\(466\) 11803.9 7699.59i 1.17340 0.765401i
\(467\) 5649.95 + 2340.29i 0.559847 + 0.231896i 0.644619 0.764504i \(-0.277016\pi\)
−0.0847717 + 0.996400i \(0.527016\pi\)
\(468\) 8.36459 377.946i 0.000826182 0.0373302i
\(469\) −797.835 1926.14i −0.0785513 0.189640i
\(470\) 288.959 54.1611i 0.0283589 0.00531546i
\(471\) −2828.70 2828.70i −0.276730 0.276730i
\(472\) 228.194 976.605i 0.0222531 0.0952371i
\(473\) 1881.03 1881.03i 0.182854 0.182854i
\(474\) −8083.34 + 11812.5i −0.783291 + 1.14466i
\(475\) −13839.1 + 5732.32i −1.33680 + 0.553720i
\(476\) −4006.65 10312.6i −0.385808 0.993018i
\(477\) −170.207 + 410.917i −0.0163381 + 0.0394436i
\(478\) −17223.5 3624.51i −1.64808 0.346823i
\(479\) −10244.1 −0.977172 −0.488586 0.872516i \(-0.662487\pi\)
−0.488586 + 0.872516i \(0.662487\pi\)
\(480\) −93.5274 158.270i −0.00889359 0.0150500i
\(481\) 6950.22 0.658841
\(482\) −11821.5 2487.72i −1.11713 0.235088i
\(483\) −3221.54 + 7777.48i −0.303489 + 0.732687i
\(484\) 7805.40 3032.56i 0.733039 0.284801i
\(485\) −13.9820 + 5.79153i −0.00130905 + 0.000542226i
\(486\) 1030.37 1505.72i 0.0961699 0.140537i
\(487\) −12510.0 + 12510.0i −1.16403 + 1.16403i −0.180446 + 0.983585i \(0.557754\pi\)
−0.983585 + 0.180446i \(0.942246\pi\)
\(488\) 10134.8 + 16315.1i 0.940126 + 1.51342i
\(489\) 3644.95 + 3644.95i 0.337076 + 0.337076i
\(490\) −46.9355 + 8.79736i −0.00432720 + 0.000811070i
\(491\) −4847.78 11703.6i −0.445575 1.07571i −0.973962 0.226710i \(-0.927203\pi\)
0.528387 0.849004i \(-0.322797\pi\)
\(492\) 11055.5 + 244.678i 1.01305 + 0.0224206i
\(493\) −13342.9 5526.81i −1.21893 0.504898i
\(494\) −5820.81 + 3796.86i −0.530143 + 0.345808i
\(495\) 22.9744i 0.00208611i
\(496\) 1584.54 + 1731.38i 0.143443 + 0.156737i
\(497\) 8268.05i 0.746223i
\(498\) −1922.23 2946.88i −0.172966 0.265167i
\(499\) 18011.3 + 7460.51i 1.61582 + 0.669295i 0.993538 0.113498i \(-0.0362055\pi\)
0.622282 + 0.782793i \(0.286206\pi\)
\(500\) 295.294 282.506i 0.0264119 0.0252681i
\(501\) 826.961 + 1996.46i 0.0737443 + 0.178034i
\(502\) 2741.75 + 14627.7i 0.243765 + 1.30053i
\(503\) −3687.97 3687.97i −0.326915 0.326915i 0.524497 0.851412i \(-0.324253\pi\)
−0.851412 + 0.524497i \(0.824253\pi\)
\(504\) −490.637 + 684.008i −0.0433625 + 0.0604527i
\(505\) 88.2627 88.2627i 0.00777750 0.00777750i
\(506\) 11949.1 + 8176.80i 1.04981 + 0.718386i
\(507\) 8157.76 3379.06i 0.714594 0.295994i
\(508\) −14888.7 6556.73i −1.30035 0.572653i
\(509\) 1071.88 2587.76i 0.0933407 0.225344i −0.870313 0.492499i \(-0.836083\pi\)
0.963654 + 0.267155i \(0.0860835\pi\)
\(510\) −50.6957 + 240.903i −0.00440166 + 0.0209164i
\(511\) −5458.49 −0.472543
\(512\) −11081.7 3378.55i −0.956532 0.291626i
\(513\) −17457.2 −1.50245
\(514\) −1190.07 + 5655.15i −0.102124 + 0.485287i
\(515\) −55.8306 + 134.787i −0.00477707 + 0.0115329i
\(516\) −1984.86 874.097i −0.169338 0.0745736i
\(517\) 22912.5 9490.68i 1.94911 0.807350i
\(518\) −12772.0 8739.89i −1.08334 0.741329i
\(519\) −1248.29 + 1248.29i −0.105575 + 0.105575i
\(520\) 55.2462 77.0199i 0.00465905 0.00649528i
\(521\) −8038.89 8038.89i −0.675988 0.675988i 0.283102 0.959090i \(-0.408637\pi\)
−0.959090 + 0.283102i \(0.908637\pi\)
\(522\) 202.437 + 1080.04i 0.0169740 + 0.0905594i
\(523\) 7860.76 + 18977.6i 0.657222 + 1.58667i 0.802076 + 0.597222i \(0.203729\pi\)
−0.144854 + 0.989453i \(0.546271\pi\)
\(524\) −4062.68 + 3886.74i −0.338700 + 0.324033i
\(525\) 9257.45 + 3834.56i 0.769578 + 0.318770i
\(526\) −7378.71 11312.0i −0.611649 0.937692i
\(527\) 3142.89i 0.259785i
\(528\) −10470.1 11440.4i −0.862976 0.942952i
\(529\) 1145.90i 0.0941813i
\(530\) −93.4033 + 60.9262i −0.00765505 + 0.00499333i
\(531\) 94.4050 + 39.1038i 0.00771531 + 0.00319579i
\(532\) 15471.1 + 342.402i 1.26082 + 0.0279041i
\(533\) 2181.87 + 5267.49i 0.177312 + 0.428068i
\(534\) −21551.2 + 4039.45i −1.74646 + 0.327348i
\(535\) −150.914 150.914i −0.0121955 0.0121955i
\(536\) 1542.63 + 2483.33i 0.124312 + 0.200119i
\(537\) 4833.57 4833.57i 0.388424 0.388424i
\(538\) 6498.31 9496.26i 0.520748 0.760991i
\(539\) −3721.67 + 1541.57i −0.297410 + 0.123191i
\(540\) 221.933 86.2256i 0.0176861 0.00687141i
\(541\) −1316.22 + 3177.63i −0.104600 + 0.252527i −0.967511 0.252829i \(-0.918639\pi\)
0.862911 + 0.505356i \(0.168639\pi\)
\(542\) 11576.6 + 2436.17i 0.917446 + 0.193067i
\(543\) −18818.6 −1.48726
\(544\) 7892.63 + 13356.1i 0.622047 + 1.05265i
\(545\) −301.403 −0.0236893
\(546\) 4549.25 + 957.345i 0.356575 + 0.0750377i
\(547\) −6431.02 + 15525.9i −0.502689 + 1.21360i 0.445325 + 0.895369i \(0.353088\pi\)
−0.948014 + 0.318229i \(0.896912\pi\)
\(548\) −4414.41 11362.1i −0.344113 0.885702i
\(549\) −1807.95 + 748.876i −0.140549 + 0.0582172i
\(550\) 9732.76 14222.9i 0.754557 1.10267i
\(551\) 14284.0 14284.0i 1.10439 1.10439i
\(552\) 2685.90 11494.9i 0.207100 0.886332i
\(553\) 11619.7 + 11619.7i 0.893527 + 0.893527i
\(554\) 195.221 36.5912i 0.0149713 0.00280616i
\(555\) 131.782 + 318.151i 0.0100790 + 0.0243329i
\(556\) 132.226 5974.49i 0.0100856 0.455710i
\(557\) −5335.11 2209.88i −0.405846 0.168107i 0.170416 0.985372i \(-0.445489\pi\)
−0.576261 + 0.817266i \(0.695489\pi\)
\(558\) −200.286 + 130.645i −0.0151949 + 0.00991154i
\(559\) 1118.21i 0.0846068i
\(560\) −198.375 + 72.0626i −0.0149694 + 0.00543786i
\(561\) 20767.1i 1.56290i
\(562\) 8209.76 + 12586.0i 0.616206 + 0.944678i
\(563\) 5228.46 + 2165.70i 0.391391 + 0.162120i 0.569696 0.821856i \(-0.307061\pi\)
−0.178304 + 0.983975i \(0.557061\pi\)
\(564\) −13977.4 14610.1i −1.04354 1.09077i
\(565\) −91.6594 221.285i −0.00682502 0.0164771i
\(566\) 26.9952 + 144.024i 0.00200476 + 0.0106957i
\(567\) 7547.18 + 7547.18i 0.558998 + 0.558998i
\(568\) 1883.24 + 11439.9i 0.139118 + 0.845082i
\(569\) −4183.25 + 4183.25i −0.308209 + 0.308209i −0.844215 0.536005i \(-0.819933\pi\)
0.536005 + 0.844215i \(0.319933\pi\)
\(570\) −284.172 194.459i −0.0208818 0.0142895i
\(571\) 7441.94 3082.55i 0.545421 0.225921i −0.0929211 0.995673i \(-0.529620\pi\)
0.638342 + 0.769753i \(0.279620\pi\)
\(572\) 3222.58 7317.68i 0.235564 0.534909i
\(573\) 4039.35 9751.87i 0.294496 0.710977i
\(574\) 2614.39 12423.4i 0.190109 0.903386i
\(575\) 13118.3 0.951427
\(576\) 523.058 1058.16i 0.0378370 0.0765454i
\(577\) 2828.16 0.204052 0.102026 0.994782i \(-0.467468\pi\)
0.102026 + 0.994782i \(0.467468\pi\)
\(578\) 1416.52 6731.21i 0.101937 0.484397i
\(579\) 4534.59 10947.5i 0.325477 0.785771i
\(580\) −111.040 + 252.145i −0.00794948 + 0.0180513i
\(581\) −3731.85 + 1545.78i −0.266477 + 0.110379i
\(582\) 858.983 + 587.804i 0.0611786 + 0.0418647i
\(583\) −6652.00 + 6652.00i −0.472552 + 0.472552i
\(584\) 7552.50 1243.30i 0.535145 0.0880960i
\(585\) 6.82877 + 6.82877i 0.000482624 + 0.000482624i
\(586\) −2064.00 11011.8i −0.145500 0.776267i
\(587\) 1835.52 + 4431.34i 0.129063 + 0.311586i 0.975181 0.221410i \(-0.0710659\pi\)
−0.846118 + 0.532996i \(0.821066\pi\)
\(588\) 2270.35 + 2373.11i 0.159230 + 0.166438i
\(589\) 4061.40 + 1682.29i 0.284121 + 0.117687i
\(590\) 13.9973 + 21.4587i 0.000976713 + 0.00149736i
\(591\) 16193.0i 1.12706i
\(592\) 19662.3 + 9183.60i 1.36506 + 0.637574i
\(593\) 13545.0i 0.937989i 0.883201 + 0.468995i \(0.155384\pi\)
−0.883201 + 0.468995i \(0.844616\pi\)
\(594\) 16822.6 10973.3i 1.16202 0.757976i
\(595\) 261.116 + 108.158i 0.0179911 + 0.00745215i
\(596\) −293.361 + 13255.2i −0.0201620 + 0.911000i
\(597\) 6839.07 + 16511.0i 0.468852 + 1.13191i
\(598\) 5982.09 1121.25i 0.409073 0.0766748i
\(599\) −12379.3 12379.3i −0.844414 0.844414i 0.145015 0.989429i \(-0.453677\pi\)
−0.989429 + 0.145015i \(0.953677\pi\)
\(600\) −13682.2 3196.99i −0.930959 0.217528i
\(601\) −17513.1 + 17513.1i −1.18864 + 1.18864i −0.211202 + 0.977442i \(0.567738\pi\)
−0.977442 + 0.211202i \(0.932262\pi\)
\(602\) −1406.14 + 2054.86i −0.0951997 + 0.139119i
\(603\) −275.189 + 113.987i −0.0185846 + 0.00769801i
\(604\) 3301.74 + 8498.26i 0.222427 + 0.572499i
\(605\) −81.8624 + 197.633i −0.00550112 + 0.0132809i
\(606\) −8400.72 1767.85i −0.563129 0.118505i
\(607\) 21984.1 1.47003 0.735013 0.678053i \(-0.237176\pi\)
0.735013 + 0.678053i \(0.237176\pi\)
\(608\) −21484.1 + 3050.14i −1.43305 + 0.203453i
\(609\) −13513.0 −0.899135
\(610\) −480.137 101.040i −0.0318691 0.00670654i
\(611\) 3989.42 9631.31i 0.264148 0.637711i
\(612\) −1473.36 + 572.431i −0.0973156 + 0.0378091i
\(613\) −13582.2 + 5625.93i −0.894910 + 0.370684i −0.782261 0.622951i \(-0.785934\pi\)
−0.112649 + 0.993635i \(0.535934\pi\)
\(614\) −2016.68 + 2947.06i −0.132551 + 0.193703i
\(615\) −199.753 + 199.753i −0.0130972 + 0.0130972i
\(616\) −15123.9 + 9394.85i −0.989220 + 0.614496i
\(617\) −4045.14 4045.14i −0.263941 0.263941i 0.562712 0.826653i \(-0.309758\pi\)
−0.826653 + 0.562712i \(0.809758\pi\)
\(618\) 9862.08 1848.50i 0.641927 0.120320i
\(619\) −4901.51 11833.3i −0.318268 0.768368i −0.999346 0.0361568i \(-0.988488\pi\)
0.681078 0.732211i \(-0.261512\pi\)
\(620\) −59.9418 1.32662i −0.00388278 8.59325e-5i
\(621\) 14124.6 + 5850.61i 0.912723 + 0.378062i
\(622\) −2718.71 + 1773.39i −0.175258 + 0.114319i
\(623\) 25172.9i 1.61883i
\(624\) −6512.51 288.407i −0.417803 0.0185025i
\(625\) 15609.3i 0.998998i
\(626\) −1635.55 2507.39i −0.104424 0.160089i
\(627\) −26836.3 11116.0i −1.70931 0.708021i
\(628\) 4653.47 4451.95i 0.295691 0.282886i
\(629\) −11120.9 26848.2i −0.704959 1.70192i
\(630\) −3.96163 21.1360i −0.000250532 0.00133663i
\(631\) −14073.2 14073.2i −0.887870 0.887870i 0.106448 0.994318i \(-0.466052\pi\)
−0.994318 + 0.106448i \(0.966052\pi\)
\(632\) −18724.0 13430.7i −1.17848 0.845321i
\(633\) −1565.08 + 1565.08i −0.0982723 + 0.0982723i
\(634\) −10051.7 6878.42i −0.629661 0.430878i
\(635\) 383.959 159.041i 0.0239952 0.00993914i
\(636\) 7019.18 + 3091.12i 0.437624 + 0.192722i
\(637\) −648.000 + 1564.41i −0.0403057 + 0.0973065i
\(638\) −4786.13 + 22743.4i −0.296998 + 1.41132i
\(639\) −1181.26 −0.0731297
\(640\) 258.062 144.892i 0.0159388 0.00894900i
\(641\) 14401.9 0.887430 0.443715 0.896168i \(-0.353660\pi\)
0.443715 + 0.896168i \(0.353660\pi\)
\(642\) −3022.72 + 14363.8i −0.185821 + 0.883014i
\(643\) 3465.77 8367.12i 0.212561 0.513168i −0.781254 0.624213i \(-0.785420\pi\)
0.993815 + 0.111045i \(0.0354198\pi\)
\(644\) −12402.9 5462.01i −0.758916 0.334213i
\(645\) 51.1867 21.2022i 0.00312477 0.00129432i
\(646\) 23980.8 + 16410.1i 1.46054 + 0.999453i
\(647\) 17607.8 17607.8i 1.06991 1.06991i 0.0725490 0.997365i \(-0.476887\pi\)
0.997365 0.0725490i \(-0.0231134\pi\)
\(648\) −12161.5 8723.42i −0.737267 0.528840i
\(649\) 1528.25 + 1528.25i 0.0924328 + 0.0924328i
\(650\) −1334.62 7120.42i −0.0805354 0.429670i
\(651\) −1125.34 2716.82i −0.0677507 0.163565i
\(652\) −5996.27 + 5736.60i −0.360172 + 0.344575i
\(653\) 25243.9 + 10456.4i 1.51282 + 0.626629i 0.976137 0.217157i \(-0.0696782\pi\)
0.536680 + 0.843786i \(0.319678\pi\)
\(654\) 11325.1 + 17362.0i 0.677136 + 1.03809i
\(655\) 143.631i 0.00856814i
\(656\) −787.604 + 17784.8i −0.0468761 + 1.05851i
\(657\) 779.856i 0.0463091i
\(658\) −19442.5 + 12682.2i −1.15189 + 0.751371i
\(659\) −2555.01 1058.32i −0.151030 0.0625588i 0.305888 0.952068i \(-0.401047\pi\)
−0.456918 + 0.889509i \(0.651047\pi\)
\(660\) 396.075 + 8.76581i 0.0233594 + 0.000516983i
\(661\) −1008.92 2435.76i −0.0593685 0.143328i 0.891412 0.453195i \(-0.149716\pi\)
−0.950780 + 0.309866i \(0.899716\pi\)
\(662\) 17288.8 3240.54i 1.01503 0.190252i
\(663\) 6172.68 + 6172.68i 0.361579 + 0.361579i
\(664\) 4811.39 2988.80i 0.281202 0.174681i
\(665\) −279.533 + 279.533i −0.0163005 + 0.0163005i
\(666\) −1248.67 + 1824.73i −0.0726501 + 0.106167i
\(667\) −16344.3 + 6770.05i −0.948809 + 0.393009i
\(668\) −3242.70 + 1259.85i −0.187820 + 0.0729719i
\(669\) 3513.96 8483.45i 0.203076 0.490268i
\(670\) −73.0819 15.3794i −0.00421403 0.000886801i
\(671\) −41390.3 −2.38130
\(672\) 11605.0 + 8719.46i 0.666177 + 0.500536i
\(673\) 23085.3 1.32225 0.661125 0.750276i \(-0.270079\pi\)
0.661125 + 0.750276i \(0.270079\pi\)
\(674\) 29702.7 + 6250.64i 1.69749 + 0.357219i
\(675\) 6963.91 16812.4i 0.397098 0.958679i
\(676\) 5147.91 + 13250.0i 0.292894 + 0.753871i
\(677\) −29890.9 + 12381.2i −1.69690 + 0.702879i −0.999899 0.0141909i \(-0.995483\pi\)
−0.697001 + 0.717070i \(0.745483\pi\)
\(678\) −9302.86 + 13594.7i −0.526953 + 0.770059i
\(679\) 844.962 844.962i 0.0477565 0.0477565i
\(680\) −385.921 90.1743i −0.0217638 0.00508533i
\(681\) −8303.48 8303.48i −0.467240 0.467240i
\(682\) −4971.21 + 931.781i −0.279117 + 0.0523163i
\(683\) 4968.96 + 11996.1i 0.278378 + 0.672063i 0.999791 0.0204414i \(-0.00650715\pi\)
−0.721413 + 0.692505i \(0.756507\pi\)
\(684\) 48.9190 2210.36i 0.00273460 0.123560i
\(685\) 287.689 + 119.165i 0.0160468 + 0.00664679i
\(686\) 16270.0 10612.8i 0.905528 0.590668i
\(687\) 23233.8i 1.29029i
\(688\) 1477.53 3163.43i 0.0818756 0.175298i
\(689\) 3954.39i 0.218651i
\(690\) 164.752 + 252.574i 0.00908985 + 0.0139353i
\(691\) −7791.33 3227.27i −0.428938 0.177672i 0.157760 0.987477i \(-0.449573\pi\)
−0.586698 + 0.809805i \(0.699573\pi\)
\(692\) −1964.61 2053.54i −0.107924 0.112809i
\(693\) −694.198 1675.94i −0.0380525 0.0918670i
\(694\) −3053.88 16293.0i −0.167037 0.891172i
\(695\) 107.948 + 107.948i 0.00589165 + 0.00589165i
\(696\) 18696.9 3077.89i 1.01825 0.167625i
\(697\) 16856.8 16856.8i 0.916064 0.916064i
\(698\) −2707.87 1853.00i −0.146840 0.100483i
\(699\) 22875.9 9475.51i 1.23783 0.512728i
\(700\) −6501.37 + 14763.0i −0.351041 + 0.797128i
\(701\) −3402.06 + 8213.30i −0.183301 + 0.442528i −0.988643 0.150283i \(-0.951982\pi\)
0.805342 + 0.592810i \(0.201982\pi\)
\(702\) 1738.63 8261.86i 0.0934760 0.444193i
\(703\) 40647.3 2.18071
\(704\) 18785.9 16443.8i 1.00571 0.880323i
\(705\) 516.523 0.0275934
\(706\) −473.282 + 2249.01i −0.0252298 + 0.119890i
\(707\) −3771.64 + 9105.55i −0.200633 + 0.484370i
\(708\) 710.162 1612.60i 0.0376971 0.0856008i
\(709\) −6190.43 + 2564.16i −0.327908 + 0.135824i −0.540563 0.841303i \(-0.681789\pi\)
0.212656 + 0.977127i \(0.431789\pi\)
\(710\) −244.426 167.261i −0.0129199 0.00884111i
\(711\) 1660.11 1660.11i 0.0875655 0.0875655i
\(712\) −5733.71 34829.8i −0.301798 1.83329i
\(713\) −2722.27 2722.27i −0.142987 0.142987i
\(714\) −3581.01 19105.3i −0.187697 1.00140i
\(715\) 78.1674 + 188.713i 0.00408852 + 0.00987057i
\(716\) 7607.31 + 7951.65i 0.397065 + 0.415038i
\(717\) −28569.4 11833.8i −1.48807 0.616378i
\(718\) −8158.92 12508.1i −0.424078 0.650136i
\(719\) 7000.41i 0.363103i −0.983381 0.181552i \(-0.941888\pi\)
0.983381 0.181552i \(-0.0581120\pi\)
\(720\) 10.2956 + 28.3419i 0.000532909 + 0.00146700i
\(721\) 11519.4i 0.595016i
\(722\) −17793.2 + 11606.3i −0.917165 + 0.598259i
\(723\) −19608.9 8122.29i −1.00866 0.417802i
\(724\) 670.325 30288.0i 0.0344094 1.55476i
\(725\) 8058.32 + 19454.5i 0.412798 + 0.996582i
\(726\) 14460.4 2710.39i 0.739224 0.138557i
\(727\) −4176.48 4176.48i −0.213063 0.213063i 0.592504 0.805567i \(-0.298139\pi\)
−0.805567 + 0.592504i \(0.798139\pi\)
\(728\) −1702.86 + 7287.79i −0.0866928 + 0.371021i
\(729\) 14894.8 14894.8i 0.756733 0.756733i
\(730\) −110.424 + 161.367i −0.00559860 + 0.00818148i
\(731\) −4319.56 + 1789.22i −0.218556 + 0.0905291i
\(732\) 12220.6 + 31454.3i 0.617060 + 1.58823i
\(733\) 8727.96 21071.2i 0.439801 1.06177i −0.536216 0.844081i \(-0.680147\pi\)
0.976017 0.217694i \(-0.0698533\pi\)
\(734\) −18879.0 3972.89i −0.949367 0.199785i
\(735\) −83.8986 −0.00421040
\(736\) 18405.0 + 4732.32i 0.921763 + 0.237005i
\(737\) −6300.04 −0.314878
\(738\) −1774.94 373.518i −0.0885316 0.0186306i
\(739\) −1771.01 + 4275.60i −0.0881566 + 0.212829i −0.961809 0.273722i \(-0.911745\pi\)
0.873652 + 0.486551i \(0.161745\pi\)
\(740\) −516.748 + 200.767i −0.0256703 + 0.00997344i
\(741\) −11280.7 + 4672.61i −0.559253 + 0.231650i
\(742\) 4972.64 7266.73i 0.246026 0.359529i
\(743\) 331.818 331.818i 0.0163839 0.0163839i −0.698867 0.715251i \(-0.746312\pi\)
0.715251 + 0.698867i \(0.246312\pi\)
\(744\) 2175.87 + 3502.73i 0.107220 + 0.172603i
\(745\) −239.497 239.497i −0.0117779 0.0117779i
\(746\) −28153.3 + 5276.92i −1.38172 + 0.258984i
\(747\) 220.846 + 533.171i 0.0108171 + 0.0261147i
\(748\) −33424.1 739.733i −1.63383 0.0361595i
\(749\) 15569.0 + 6448.88i 0.759516 + 0.314602i
\(750\) 601.373 392.270i 0.0292787 0.0190983i
\(751\) 35952.8i 1.74692i 0.486897 + 0.873459i \(0.338129\pi\)
−0.486897 + 0.873459i \(0.661871\pi\)
\(752\) 24012.4 21975.8i 1.16442 1.06566i
\(753\) 26147.5i 1.26543i
\(754\) 5337.51 + 8182.70i 0.257799 + 0.395221i
\(755\) −215.177 89.1290i −0.0103723 0.00429634i
\(756\) −13584.2 + 12996.0i −0.653510 + 0.625210i
\(757\) 8248.62 + 19913.9i 0.396038 + 0.956121i 0.988596 + 0.150593i \(0.0481183\pi\)
−0.592557 + 0.805528i \(0.701882\pi\)
\(758\) −2445.64 13047.9i −0.117189 0.625225i
\(759\) 17987.8 + 17987.8i 0.860234 + 0.860234i
\(760\) 323.099 450.439i 0.0154211 0.0214989i
\(761\) 20845.8 20845.8i 0.992983 0.992983i −0.00699229 0.999976i \(-0.502226\pi\)
0.999976 + 0.00699229i \(0.00222573\pi\)
\(762\) −23588.5 16141.7i −1.12142 0.767390i
\(763\) 21986.8 9107.23i 1.04322 0.432115i
\(764\) 15551.5 + 6848.59i 0.736429 + 0.324310i
\(765\) 15.4525 37.3056i 0.000730309 0.00176312i
\(766\) −4923.38 + 23395.7i −0.232231 + 1.10355i
\(767\) 908.491 0.0427689
\(768\) −18042.9 9421.16i −0.847746 0.442652i
\(769\) 14131.4 0.662669 0.331335 0.943513i \(-0.392501\pi\)
0.331335 + 0.943513i \(0.392501\pi\)
\(770\) 93.6628 445.081i 0.00438360 0.0208306i
\(771\) −3885.52 + 9380.46i −0.181496 + 0.438170i
\(772\) 17458.1 + 7688.25i 0.813901 + 0.358428i
\(773\) −15774.0 + 6533.82i −0.733962 + 0.304017i −0.718179 0.695858i \(-0.755024\pi\)
−0.0157831 + 0.999875i \(0.505024\pi\)
\(774\) 293.578 + 200.896i 0.0136337 + 0.00932954i
\(775\) −3240.29 + 3240.29i −0.150187 + 0.150187i
\(776\) −976.650 + 1361.57i −0.0451800 + 0.0629864i
\(777\) −19226.6 19226.6i −0.887708 0.887708i
\(778\) −264.476 1411.03i −0.0121876 0.0650228i
\(779\) 12760.3 + 30806.1i 0.586888 + 1.41687i
\(780\) 120.332 115.121i 0.00552382 0.00528461i
\(781\) −23082.8 9561.22i −1.05758 0.438063i
\(782\) −13903.1 21314.3i −0.635774 0.974678i
\(783\) 24540.8i 1.12007i
\(784\) −3900.32 + 3569.52i −0.177675 + 0.162606i
\(785\) 164.518i 0.00748013i
\(786\) −8273.73 + 5396.88i −0.375463 + 0.244912i
\(787\) 9893.89 + 4098.18i 0.448131 + 0.185622i 0.595324 0.803486i \(-0.297024\pi\)
−0.147193 + 0.989108i \(0.547024\pi\)
\(788\) 26062.2 + 576.801i 1.17821 + 0.0260757i
\(789\) −9080.62 21922.6i −0.409732 0.989181i
\(790\) 578.574 108.445i 0.0260566 0.00488393i
\(791\) 13372.8 + 13372.8i 0.601113 + 0.601113i
\(792\) 1342.24 + 2160.75i 0.0602204 + 0.0969433i
\(793\) −12302.6 + 12302.6i −0.550917 + 0.550917i
\(794\) 5715.83 8352.79i 0.255475 0.373337i
\(795\) −181.015 + 74.9788i −0.00807539 + 0.00334494i
\(796\) −26817.5 + 10419.1i −1.19412 + 0.463941i
\(797\) −10234.0 + 24707.0i −0.454838 + 1.09807i 0.515623 + 0.856815i \(0.327560\pi\)
−0.970461 + 0.241259i \(0.922440\pi\)
\(798\) 26605.6 + 5598.88i 1.18024 + 0.248369i
\(799\) −43588.5 −1.92998
\(800\) 5632.83 21907.3i 0.248938 0.968174i
\(801\) 3596.46 0.158645
\(802\) −10760.8 2264.50i −0.473787 0.0997037i
\(803\) −6312.23 + 15239.1i −0.277402 + 0.669707i
\(804\) 1860.11 + 4787.68i 0.0815934 + 0.210011i
\(805\) 319.853 132.487i 0.0140041 0.00580070i
\(806\) −1200.65 + 1754.57i −0.0524705 + 0.0766774i
\(807\) 14295.4 14295.4i 0.623571 0.623571i
\(808\) 3144.54 13457.7i 0.136911 0.585943i
\(809\) −4366.67 4366.67i −0.189770 0.189770i 0.605827 0.795597i \(-0.292843\pi\)
−0.795597 + 0.605827i \(0.792843\pi\)
\(810\) 375.793 70.4368i 0.0163012 0.00305543i
\(811\) −16742.8 40420.6i −0.724930 1.75014i −0.658792 0.752325i \(-0.728932\pi\)
−0.0661382 0.997810i \(-0.521068\pi\)
\(812\) 481.337 21748.7i 0.0208025 0.939940i
\(813\) 19202.6 + 7953.98i 0.828370 + 0.343122i
\(814\) −39169.7 + 25550.0i −1.68660 + 1.10016i
\(815\) 211.991i 0.00911132i
\(816\) 9306.43 + 25618.9i 0.399253 + 1.09907i
\(817\) 6539.67i 0.280042i
\(818\) −15708.6 24082.2i −0.671441 1.02936i
\(819\) −704.485 291.807i −0.0300570 0.0124500i
\(820\) −314.381 328.611i −0.0133886 0.0139946i
\(821\) −2730.75 6592.63i −0.116083 0.280249i 0.855150 0.518381i \(-0.173465\pi\)
−0.971233 + 0.238132i \(0.923465\pi\)
\(822\) −3945.44 21049.6i −0.167413 0.893175i
\(823\) −7832.94 7832.94i −0.331761 0.331761i 0.521494 0.853255i \(-0.325375\pi\)
−0.853255 + 0.521494i \(0.825375\pi\)
\(824\) 2623.82 + 15938.6i 0.110928 + 0.673843i
\(825\) 21410.7 21410.7i 0.903547 0.903547i
\(826\) −1669.48 1142.43i −0.0703251 0.0481236i
\(827\) −18116.8 + 7504.23i −0.761769 + 0.315535i −0.729533 0.683945i \(-0.760263\pi\)
−0.0322359 + 0.999480i \(0.510263\pi\)
\(828\) −780.358 + 1772.00i −0.0327528 + 0.0743736i
\(829\) −3888.12 + 9386.75i −0.162895 + 0.393264i −0.984160 0.177284i \(-0.943269\pi\)
0.821265 + 0.570547i \(0.193269\pi\)
\(830\) −29.7971 + 141.594i −0.00124611 + 0.00592146i
\(831\) 348.963 0.0145673
\(832\) 696.161 10471.4i 0.0290085 0.436336i
\(833\) 7080.06 0.294489
\(834\) 2162.13 10274.3i 0.0897703 0.426584i
\(835\) 34.0092 82.1054i 0.00140950 0.00340284i
\(836\) 18846.7 42796.3i 0.779699 1.77050i
\(837\) −4933.99 + 2043.73i −0.203756 + 0.0843985i
\(838\) 25559.4 + 17490.4i 1.05362 + 0.720996i
\(839\) −4919.87 + 4919.87i −0.202447 + 0.202447i −0.801047 0.598601i \(-0.795724\pi\)
0.598601 + 0.801047i \(0.295724\pi\)
\(840\) −365.891 + 60.2332i −0.0150291 + 0.00247410i
\(841\) −2834.41 2834.41i −0.116217 0.116217i
\(842\) 8216.76 + 43837.9i 0.336305 + 1.79424i
\(843\) 10103.3 + 24391.6i 0.412785 + 0.996551i
\(844\) −2463.20 2574.70i −0.100458 0.105006i
\(845\) −335.492 138.965i −0.0136583 0.00565746i
\(846\) 1811.90 + 2777.75i 0.0736342 + 0.112885i
\(847\) 16890.5i 0.685202i
\(848\) −5225.10 + 11187.1i −0.211593 + 0.453025i
\(849\) 257.447i 0.0104070i
\(850\) −25370.2 + 16548.8i −1.02375 + 0.667786i
\(851\) −32887.6 13622.5i −1.32476 0.548735i
\(852\) −450.705 + 20364.7i −0.0181231 + 0.818875i
\(853\) −2809.03 6781.60i −0.112754 0.272213i 0.857422 0.514614i \(-0.172065\pi\)
−0.970176 + 0.242401i \(0.922065\pi\)
\(854\) 38078.1 7137.19i 1.52577 0.285983i
\(855\) 39.9370 + 39.9370i 0.00159745 + 0.00159745i
\(856\) −23010.5 5376.63i −0.918787 0.214684i
\(857\) −7846.03 + 7846.03i −0.312737 + 0.312737i −0.845969 0.533232i \(-0.820977\pi\)
0.533232 + 0.845969i \(0.320977\pi\)
\(858\) 7933.50 11593.6i 0.315671 0.461303i
\(859\) 10278.4 4257.47i 0.408261 0.169107i −0.169095 0.985600i \(-0.554085\pi\)
0.577356 + 0.816493i \(0.304085\pi\)
\(860\) 32.3011 + 83.1387i 0.00128076 + 0.00329652i
\(861\) 8535.84 20607.3i 0.337864 0.815675i
\(862\) 2336.14 + 491.617i 0.0923077 + 0.0194252i
\(863\) 28549.2 1.12610 0.563050 0.826423i \(-0.309628\pi\)
0.563050 + 0.826423i \(0.309628\pi\)
\(864\) 15835.3 21075.6i 0.623529 0.829870i
\(865\) 72.6005 0.00285375
\(866\) 31685.0 + 6667.78i 1.24330 + 0.261640i
\(867\) 4624.86 11165.4i 0.181163 0.437366i
\(868\) 4412.73 1714.43i 0.172555 0.0670411i
\(869\) 45877.1 19002.9i 1.79088 0.741807i
\(870\) −273.365 + 399.479i −0.0106528 + 0.0155674i
\(871\) −1872.58 + 1872.58i −0.0728473 + 0.0728473i
\(872\) −28347.1 + 17609.0i −1.10086 + 0.683848i
\(873\) −120.720 120.720i −0.00468013 0.00468013i
\(874\) 34985.3 6557.48i 1.35400 0.253787i
\(875\) −315.449 761.562i −0.0121876 0.0294234i
\(876\) 13444.6 + 297.551i 0.518550 + 0.0114764i
\(877\) −8149.22 3375.52i −0.313774 0.129969i 0.220239 0.975446i \(-0.429316\pi\)
−0.534012 + 0.845477i \(0.679316\pi\)
\(878\) −6835.68 + 4458.86i −0.262748 + 0.171389i
\(879\) 19683.9i 0.755315i
\(880\) −28.2166 + 637.158i −0.00108089 + 0.0244075i
\(881\) 22699.0i 0.868046i 0.900902 + 0.434023i \(0.142906\pi\)
−0.900902 + 0.434023i \(0.857094\pi\)
\(882\) −294.307 451.189i −0.0112356 0.0172248i
\(883\) −3173.59 1314.54i −0.120951 0.0500995i 0.321387 0.946948i \(-0.395851\pi\)
−0.442338 + 0.896848i \(0.645851\pi\)
\(884\) −10154.6 + 9714.88i −0.386354 + 0.369623i
\(885\) 17.2258 + 41.5868i 0.000654282 + 0.00157958i
\(886\) 7037.54 + 37546.5i 0.266852 + 1.42370i
\(887\) 389.896 + 389.896i 0.0147592 + 0.0147592i 0.714448 0.699689i \(-0.246678\pi\)
−0.699689 + 0.714448i \(0.746678\pi\)
\(888\) 30981.6 + 22223.0i 1.17080 + 0.839815i
\(889\) −23203.5 + 23203.5i −0.875389 + 0.875389i
\(890\) 744.178 + 509.242i 0.0280280 + 0.0191796i
\(891\) 29797.9 12342.7i 1.12039 0.464081i
\(892\) 13528.7 + 5957.80i 0.507818 + 0.223634i
\(893\) 23331.5 56327.2i 0.874310 2.11077i
\(894\) −4796.99 + 22795.0i −0.179458 + 0.852774i
\(895\) −281.121 −0.0104993
\(896\) −14447.1 + 18367.2i −0.538664 + 0.684828i
\(897\) 10693.2 0.398032
\(898\) 2097.86 9968.91i 0.0779581 0.370453i
\(899\) 2364.91 5709.39i 0.0877353 0.211812i
\(900\) 2109.19 + 928.852i 0.0781183 + 0.0344019i
\(901\) 15275.6 6327.34i 0.564820 0.233956i
\(902\) −31660.5 21665.4i −1.16871 0.799754i
\(903\) −3093.33 + 3093.33i −0.113997 + 0.113997i
\(904\) −21548.8 15456.9i −0.792813 0.568683i
\(905\) 547.247 + 547.247i 0.0201007 + 0.0201007i
\(906\) 2950.99 + 15744.0i 0.108212 + 0.577329i
\(907\) −14791.8 35710.6i −0.541516 1.30733i −0.923653 0.383229i \(-0.874812\pi\)
0.382138 0.924105i \(-0.375188\pi\)
\(908\) 13660.0 13068.4i 0.499254 0.477634i
\(909\) 1300.91 + 538.856i 0.0474682 + 0.0196620i
\(910\) −104.453 160.132i −0.00380504 0.00583334i
\(911\) 26874.8i 0.977388i −0.872455 0.488694i \(-0.837473\pi\)
0.872455 0.488694i \(-0.162527\pi\)
\(912\) −38087.4 1686.71i −1.38289 0.0612417i
\(913\) 12206.2i 0.442459i
\(914\) 33564.3 21893.7i 1.21467 0.792320i
\(915\) −796.426 329.891i −0.0287749 0.0119190i
\(916\) −37394.2 827.597i −1.34884 0.0298522i
\(917\) 4339.97 + 10477.6i 0.156291 + 0.377319i
\(918\) −34696.9 + 6503.43i −1.24746 + 0.233818i
\(919\) 9495.37 + 9495.37i 0.340831 + 0.340831i 0.856680 0.515849i \(-0.172523\pi\)
−0.515849 + 0.856680i \(0.672523\pi\)
\(920\) −412.379 + 256.167i −0.0147780 + 0.00917996i
\(921\) −4436.42 + 4436.42i −0.158724 + 0.158724i
\(922\) 2585.88 3778.86i 0.0923660 0.134978i
\(923\) −9702.89 + 4019.07i −0.346018 + 0.143325i
\(924\) −29157.8 + 11328.4i −1.03812 + 0.403330i
\(925\) −16214.7 + 39145.8i −0.576364 + 1.39147i
\(926\) 40182.5 + 8456.00i 1.42600 + 0.300088i
\(927\) −1645.79 −0.0583114
\(928\) 4287.79 + 30201.7i 0.151674 + 1.06834i
\(929\) −51635.3 −1.82357 −0.911786 0.410665i \(-0.865297\pi\)
−0.911786 + 0.410665i \(0.865297\pi\)
\(930\) −103.082 21.6926i −0.00363461 0.000764868i
\(931\) −3789.73 + 9149.21i −0.133409 + 0.322077i
\(932\) 14435.7 + 37155.6i 0.507357 + 1.30587i
\(933\) −5268.84 + 2182.42i −0.184881 + 0.0765803i
\(934\) −9768.31 + 14274.8i −0.342215 + 0.500093i
\(935\) 603.911 603.911i 0.0211230 0.0211230i
\(936\) 1041.21 + 243.289i 0.0363600 + 0.00849587i
\(937\) 3704.24 + 3704.24i 0.129149 + 0.129149i 0.768726 0.639578i \(-0.220891\pi\)
−0.639578 + 0.768726i \(0.720891\pi\)
\(938\) 5795.89 1086.36i 0.201751 0.0378153i
\(939\) −2012.79 4859.30i −0.0699520 0.168879i
\(940\) −18.3987 + 831.328i −0.000638404 + 0.0288457i
\(941\) 6682.02 + 2767.78i 0.231485 + 0.0958843i 0.495411 0.868659i \(-0.335017\pi\)
−0.263926 + 0.964543i \(0.585017\pi\)
\(942\) 9476.90 6181.70i 0.327786 0.213812i
\(943\) 29201.7i 1.00842i
\(944\) 2570.14 + 1200.43i 0.0886133 + 0.0413883i
\(945\) 480.254i 0.0165319i
\(946\) 4110.70 + 6301.94i 0.141280 + 0.216589i
\(947\) 494.002 + 204.622i 0.0169513 + 0.00702147i 0.391143 0.920330i \(-0.372080\pi\)
−0.374192 + 0.927351i \(0.622080\pi\)
\(948\) −27986.6 29253.4i −0.958820 1.00222i
\(949\) 2653.35 + 6405.76i 0.0907603 + 0.219115i
\(950\) −7805.30 41642.6i −0.266566 1.42217i
\(951\) −15131.6 15131.6i −0.515957 0.515957i
\(952\) 30876.9 5082.98i 1.05118 0.173047i
\(953\) −28698.0 + 28698.0i −0.975465 + 0.975465i −0.999706 0.0242408i \(-0.992283\pi\)
0.0242408 + 0.999706i \(0.492283\pi\)
\(954\) −1038.20 710.443i −0.0352337 0.0241105i
\(955\) −401.050 + 166.120i −0.0135892 + 0.00562883i
\(956\) 20063.9 45560.1i 0.678778 1.54134i
\(957\) −15626.5 + 37725.6i −0.527829 + 1.27429i
\(958\) 5966.75 28353.7i 0.201229 0.956228i
\(959\) −24587.1 −0.827903
\(960\) 492.536 166.680i 0.0165589 0.00560373i
\(961\) −28446.2 −0.954858
\(962\) −4048.20 + 19236.8i −0.135675 + 0.644720i
\(963\) 921.352 2224.34i 0.0308309 0.0744324i
\(964\) 13771.1 31270.7i 0.460099 1.04477i
\(965\) −450.220 + 186.487i −0.0150188 + 0.00622098i
\(966\) −19650.1 13446.6i −0.654486 0.447866i
\(967\) 22689.5 22689.5i 0.754544 0.754544i −0.220780 0.975324i \(-0.570860\pi\)
0.975324 + 0.220780i \(0.0708603\pi\)
\(968\) 3847.21 + 23370.2i 0.127742 + 0.775977i
\(969\) 36100.0 + 36100.0i 1.19680 + 1.19680i
\(970\) −7.88591 42.0727i −0.000261032 0.00139265i
\(971\) 18313.2 + 44211.9i 0.605250 + 1.46120i 0.868111 + 0.496369i \(0.165334\pi\)
−0.262861 + 0.964834i \(0.584666\pi\)
\(972\) 3567.40 + 3728.88i 0.117721 + 0.123049i
\(973\) −11136.4 4612.83i −0.366922 0.151984i
\(974\) −27338.7 41911.8i −0.899374 1.37879i
\(975\) 12728.0i 0.418073i
\(976\) −51060.1 + 18548.4i −1.67458 + 0.608318i
\(977\) 3076.94i 0.100757i 0.998730 + 0.0503787i \(0.0160428\pi\)
−0.998730 + 0.0503787i \(0.983957\pi\)
\(978\) −12211.5 + 7965.48i −0.399266 + 0.260438i
\(979\) 70277.9 + 29110.1i 2.29427 + 0.950319i
\(980\) 2.98850 135.032i 9.74123e−5 0.00440148i
\(981\) −1301.15 3141.26i −0.0423472 0.102235i
\(982\) 35216.9 6600.89i 1.14441 0.214504i
\(983\) −40340.6 40340.6i −1.30892 1.30892i −0.922197 0.386722i \(-0.873607\pi\)
−0.386722 0.922197i \(-0.626393\pi\)
\(984\) −7116.59 + 30457.0i −0.230558 + 0.986722i
\(985\) −470.895 + 470.895i −0.0152324 + 0.0152324i
\(986\) 23068.8 33711.4i 0.745091 1.08883i
\(987\) −37679.4 + 15607.3i −1.21514 + 0.503329i
\(988\) −7118.61 18322.4i −0.229224 0.589992i
\(989\) −2191.70 + 5291.24i −0.0704672 + 0.170123i
\(990\) −63.5888 13.3816i −0.00204140 0.000429592i
\(991\) 19825.3 0.635492 0.317746 0.948176i \(-0.397074\pi\)
0.317746 + 0.948176i \(0.397074\pi\)
\(992\) −5715.05 + 3377.23i −0.182916 + 0.108092i
\(993\) 30904.3 0.987632
\(994\) 22884.4 + 4815.79i 0.730229 + 0.153669i
\(995\) 281.260 679.022i 0.00896135 0.0216346i
\(996\) 9276.01 3603.92i 0.295102 0.114653i
\(997\) −12624.9 + 5229.39i −0.401036 + 0.166115i −0.574079 0.818800i \(-0.694640\pi\)
0.173043 + 0.984914i \(0.444640\pi\)
\(998\) −31140.0 + 45506.2i −0.987695 + 1.44336i
\(999\) −34917.2 + 34917.2i −1.10584 + 1.10584i
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 32.4.g.a.13.6 yes 44
4.3 odd 2 128.4.g.a.17.9 44
8.3 odd 2 256.4.g.a.33.3 44
8.5 even 2 256.4.g.b.33.9 44
32.5 even 8 inner 32.4.g.a.5.6 44
32.11 odd 8 256.4.g.a.225.3 44
32.21 even 8 256.4.g.b.225.9 44
32.27 odd 8 128.4.g.a.113.9 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.g.a.5.6 44 32.5 even 8 inner
32.4.g.a.13.6 yes 44 1.1 even 1 trivial
128.4.g.a.17.9 44 4.3 odd 2
128.4.g.a.113.9 44 32.27 odd 8
256.4.g.a.33.3 44 8.3 odd 2
256.4.g.a.225.3 44 32.11 odd 8
256.4.g.b.33.9 44 8.5 even 2
256.4.g.b.225.9 44 32.21 even 8