Properties

Label 32.4.g.a.21.8
Level $32$
Weight $4$
Character 32.21
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 21.8
Character \(\chi\) \(=\) 32.21
Dual form 32.4.g.a.29.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35043 - 2.48522i) q^{2} +(-1.36212 + 0.564209i) q^{3} +(-4.35267 - 6.71224i) q^{4} +(6.58151 - 15.8892i) q^{5} +(-0.437264 + 4.14710i) q^{6} +(14.5517 + 14.5517i) q^{7} +(-22.5594 + 1.75295i) q^{8} +(-17.5548 + 17.5548i) q^{9} +O(q^{10})\) \(q+(1.35043 - 2.48522i) q^{2} +(-1.36212 + 0.564209i) q^{3} +(-4.35267 - 6.71224i) q^{4} +(6.58151 - 15.8892i) q^{5} +(-0.437264 + 4.14710i) q^{6} +(14.5517 + 14.5517i) q^{7} +(-22.5594 + 1.75295i) q^{8} +(-17.5548 + 17.5548i) q^{9} +(-30.6003 - 37.8138i) q^{10} +(34.4676 + 14.2769i) q^{11} +(9.71598 + 6.68707i) q^{12} +(15.3924 + 37.1606i) q^{13} +(55.8151 - 16.5131i) q^{14} +25.3563i q^{15} +(-26.1085 + 58.4324i) q^{16} -103.310i q^{17} +(19.9211 + 67.3343i) q^{18} +(12.4092 + 29.9584i) q^{19} +(-135.299 + 24.9837i) q^{20} +(-28.0313 - 11.6109i) q^{21} +(82.0275 - 66.3797i) q^{22} +(-72.3950 + 72.3950i) q^{23} +(29.7396 - 15.1160i) q^{24} +(-120.761 - 120.761i) q^{25} +(113.139 + 11.9292i) q^{26} +(29.2409 - 70.5937i) q^{27} +(34.3357 - 161.013i) q^{28} +(23.9061 - 9.90225i) q^{29} +(63.0162 + 34.2420i) q^{30} -124.769 q^{31} +(109.960 + 143.794i) q^{32} -55.0042 q^{33} +(-256.748 - 139.513i) q^{34} +(326.986 - 135.442i) q^{35} +(194.243 + 41.4219i) q^{36} +(18.0425 - 43.5584i) q^{37} +(91.2111 + 9.61717i) q^{38} +(-41.9327 - 41.9327i) q^{39} +(-120.622 + 369.988i) q^{40} +(-45.1360 + 45.1360i) q^{41} +(-66.7101 + 53.9842i) q^{42} +(-457.470 - 189.490i) q^{43} +(-54.1959 - 293.498i) q^{44} +(163.395 + 394.469i) q^{45} +(82.1534 + 277.682i) q^{46} +582.766i q^{47} +(2.59478 - 94.3227i) q^{48} +80.5012i q^{49} +(-463.199 + 137.039i) q^{50} +(58.2884 + 140.721i) q^{51} +(182.433 - 265.066i) q^{52} +(395.810 + 163.950i) q^{53} +(-135.953 - 168.002i) q^{54} +(453.698 - 453.698i) q^{55} +(-353.785 - 302.768i) q^{56} +(-33.8056 - 33.8056i) q^{57} +(7.67429 - 72.7844i) q^{58} +(142.805 - 344.762i) q^{59} +(170.198 - 110.368i) q^{60} +(-34.8958 + 14.4543i) q^{61} +(-168.492 + 310.079i) q^{62} -510.904 q^{63} +(505.854 - 79.0909i) q^{64} +691.757 q^{65} +(-74.2794 + 136.698i) q^{66} +(196.686 - 81.4699i) q^{67} +(-693.442 + 449.674i) q^{68} +(57.7649 - 139.457i) q^{69} +(104.968 - 995.538i) q^{70} +(-520.831 - 520.831i) q^{71} +(365.254 - 426.800i) q^{72} +(-582.329 + 582.329i) q^{73} +(-83.8873 - 103.662i) q^{74} +(232.626 + 96.3570i) q^{75} +(147.075 - 213.693i) q^{76} +(293.807 + 709.314i) q^{77} +(-160.839 + 47.5849i) q^{78} -157.779i q^{79} +(756.610 + 799.416i) q^{80} -557.655i q^{81} +(51.2200 + 173.126i) q^{82} +(54.5324 + 131.653i) q^{83} +(44.0756 + 238.691i) q^{84} +(-1641.51 - 679.936i) q^{85} +(-1088.71 + 881.022i) q^{86} +(-26.9761 + 26.9761i) q^{87} +(-802.596 - 261.660i) q^{88} +(-272.884 - 272.884i) q^{89} +(1201.00 + 126.632i) q^{90} +(-316.763 + 764.733i) q^{91} +(801.045 + 170.821i) q^{92} +(169.951 - 70.3959i) q^{93} +(1448.30 + 786.985i) q^{94} +557.686 q^{95} +(-230.909 - 133.825i) q^{96} +788.873 q^{97} +(200.063 + 108.711i) q^{98} +(-855.703 + 354.444i) 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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35043 2.48522i 0.477449 0.878659i
\(3\) −1.36212 + 0.564209i −0.262140 + 0.108582i −0.509883 0.860244i \(-0.670311\pi\)
0.247743 + 0.968826i \(0.420311\pi\)
\(4\) −4.35267 6.71224i −0.544084 0.839031i
\(5\) 6.58151 15.8892i 0.588669 1.42117i −0.296107 0.955155i \(-0.595689\pi\)
0.884776 0.466017i \(-0.154311\pi\)
\(6\) −0.437264 + 4.14710i −0.0297521 + 0.282174i
\(7\) 14.5517 + 14.5517i 0.785715 + 0.785715i 0.980789 0.195073i \(-0.0624945\pi\)
−0.195073 + 0.980789i \(0.562494\pi\)
\(8\) −22.5594 + 1.75295i −0.996995 + 0.0774700i
\(9\) −17.5548 + 17.5548i −0.650179 + 0.650179i
\(10\) −30.6003 37.8138i −0.967666 1.19578i
\(11\) 34.4676 + 14.2769i 0.944761 + 0.391333i 0.801259 0.598317i \(-0.204164\pi\)
0.143502 + 0.989650i \(0.454164\pi\)
\(12\) 9.71598 + 6.68707i 0.233730 + 0.160866i
\(13\) 15.3924 + 37.1606i 0.328391 + 0.792807i 0.998712 + 0.0507354i \(0.0161565\pi\)
−0.670321 + 0.742071i \(0.733843\pi\)
\(14\) 55.8151 16.5131i 1.06552 0.315237i
\(15\) 25.3563i 0.436465i
\(16\) −26.1085 + 58.4324i −0.407945 + 0.913007i
\(17\) 103.310i 1.47390i −0.675946 0.736951i \(-0.736265\pi\)
0.675946 0.736951i \(-0.263735\pi\)
\(18\) 19.9211 + 67.3343i 0.260858 + 0.881714i
\(19\) 12.4092 + 29.9584i 0.149835 + 0.361733i 0.980920 0.194412i \(-0.0622799\pi\)
−0.831085 + 0.556145i \(0.812280\pi\)
\(20\) −135.299 + 24.9837i −1.51269 + 0.279326i
\(21\) −28.0313 11.6109i −0.291282 0.120653i
\(22\) 82.0275 66.3797i 0.794924 0.643281i
\(23\) −72.3950 + 72.3950i −0.656322 + 0.656322i −0.954508 0.298186i \(-0.903619\pi\)
0.298186 + 0.954508i \(0.403619\pi\)
\(24\) 29.7396 15.1160i 0.252941 0.128564i
\(25\) −120.761 120.761i −0.966091 0.966091i
\(26\) 113.139 + 11.9292i 0.853397 + 0.0899810i
\(27\) 29.2409 70.5937i 0.208422 0.503176i
\(28\) 34.3357 161.013i 0.231744 1.08673i
\(29\) 23.9061 9.90225i 0.153078 0.0634069i −0.304829 0.952407i \(-0.598599\pi\)
0.457907 + 0.889000i \(0.348599\pi\)
\(30\) 63.0162 + 34.2420i 0.383504 + 0.208390i
\(31\) −124.769 −0.722877 −0.361439 0.932396i \(-0.617714\pi\)
−0.361439 + 0.932396i \(0.617714\pi\)
\(32\) 109.960 + 143.794i 0.607449 + 0.794359i
\(33\) −55.0042 −0.290152
\(34\) −256.748 139.513i −1.29506 0.703714i
\(35\) 326.986 135.442i 1.57916 0.654110i
\(36\) 194.243 + 41.4219i 0.899273 + 0.191768i
\(37\) 18.0425 43.5584i 0.0801667 0.193540i −0.878714 0.477348i \(-0.841598\pi\)
0.958881 + 0.283809i \(0.0915980\pi\)
\(38\) 91.2111 + 9.61717i 0.389379 + 0.0410555i
\(39\) −41.9327 41.9327i −0.172169 0.172169i
\(40\) −120.622 + 369.988i −0.476801 + 1.46250i
\(41\) −45.1360 + 45.1360i −0.171928 + 0.171928i −0.787826 0.615898i \(-0.788793\pi\)
0.615898 + 0.787826i \(0.288793\pi\)
\(42\) −66.7101 + 53.9842i −0.245085 + 0.198332i
\(43\) −457.470 189.490i −1.62241 0.672023i −0.628057 0.778168i \(-0.716149\pi\)
−0.994351 + 0.106144i \(0.966149\pi\)
\(44\) −54.1959 293.498i −0.185689 1.00560i
\(45\) 163.395 + 394.469i 0.541276 + 1.30676i
\(46\) 82.1534 + 277.682i 0.263323 + 0.890044i
\(47\) 582.766i 1.80862i 0.426877 + 0.904310i \(0.359614\pi\)
−0.426877 + 0.904310i \(0.640386\pi\)
\(48\) 2.59478 94.3227i 0.00780260 0.283631i
\(49\) 80.5012i 0.234697i
\(50\) −463.199 + 137.039i −1.31012 + 0.387605i
\(51\) 58.2884 + 140.721i 0.160039 + 0.386369i
\(52\) 182.433 265.066i 0.486517 0.706884i
\(53\) 395.810 + 163.950i 1.02582 + 0.424910i 0.831203 0.555969i \(-0.187653\pi\)
0.194620 + 0.980879i \(0.437653\pi\)
\(54\) −135.953 168.002i −0.342609 0.423374i
\(55\) 453.698 453.698i 1.11230 1.11230i
\(56\) −353.785 302.768i −0.844223 0.722485i
\(57\) −33.8056 33.8056i −0.0785555 0.0785555i
\(58\) 7.67429 72.7844i 0.0173738 0.164777i
\(59\) 142.805 344.762i 0.315113 0.760750i −0.684387 0.729119i \(-0.739930\pi\)
0.999500 0.0316306i \(-0.0100700\pi\)
\(60\) 170.198 110.368i 0.366208 0.237474i
\(61\) −34.8958 + 14.4543i −0.0732450 + 0.0303391i −0.419005 0.907984i \(-0.637621\pi\)
0.345760 + 0.938323i \(0.387621\pi\)
\(62\) −168.492 + 310.079i −0.345137 + 0.635163i
\(63\) −510.904 −1.02171
\(64\) 505.854 79.0909i 0.987997 0.154474i
\(65\) 691.757 1.32003
\(66\) −74.2794 + 136.698i −0.138533 + 0.254944i
\(67\) 196.686 81.4699i 0.358642 0.148554i −0.196085 0.980587i \(-0.562823\pi\)
0.554727 + 0.832033i \(0.312823\pi\)
\(68\) −693.442 + 449.674i −1.23665 + 0.801927i
\(69\) 57.7649 139.457i 0.100784 0.243313i
\(70\) 104.968 995.538i 0.179230 1.69985i
\(71\) −520.831 520.831i −0.870582 0.870582i 0.121954 0.992536i \(-0.461084\pi\)
−0.992536 + 0.121954i \(0.961084\pi\)
\(72\) 365.254 426.800i 0.597856 0.698595i
\(73\) −582.329 + 582.329i −0.933649 + 0.933649i −0.997932 0.0642823i \(-0.979524\pi\)
0.0642823 + 0.997932i \(0.479524\pi\)
\(74\) −83.8873 103.662i −0.131780 0.162845i
\(75\) 232.626 + 96.3570i 0.358152 + 0.148351i
\(76\) 147.075 213.693i 0.221982 0.322529i
\(77\) 293.807 + 709.314i 0.434837 + 1.04979i
\(78\) −160.839 + 47.5849i −0.233480 + 0.0690760i
\(79\) 157.779i 0.224702i −0.993669 0.112351i \(-0.964162\pi\)
0.993669 0.112351i \(-0.0358381\pi\)
\(80\) 756.610 + 799.416i 1.05739 + 1.11722i
\(81\) 557.655i 0.764959i
\(82\) 51.2200 + 173.126i 0.0689792 + 0.233153i
\(83\) 54.5324 + 131.653i 0.0721170 + 0.174106i 0.955828 0.293928i \(-0.0949626\pi\)
−0.883711 + 0.468034i \(0.844963\pi\)
\(84\) 44.0756 + 238.691i 0.0572505 + 0.310040i
\(85\) −1641.51 679.936i −2.09467 0.867640i
\(86\) −1088.71 + 881.022i −1.36510 + 1.10469i
\(87\) −26.9761 + 26.9761i −0.0332430 + 0.0332430i
\(88\) −802.596 261.660i −0.972238 0.316966i
\(89\) −272.884 272.884i −0.325007 0.325007i 0.525677 0.850684i \(-0.323812\pi\)
−0.850684 + 0.525677i \(0.823812\pi\)
\(90\) 1201.00 + 126.632i 1.40663 + 0.148313i
\(91\) −316.763 + 764.733i −0.364898 + 0.880943i
\(92\) 801.045 + 170.821i 0.907769 + 0.193580i
\(93\) 169.951 70.3959i 0.189495 0.0784915i
\(94\) 1448.30 + 786.985i 1.58916 + 0.863524i
\(95\) 557.686 0.602288
\(96\) −230.909 133.825i −0.245490 0.142275i
\(97\) 788.873 0.825752 0.412876 0.910787i \(-0.364524\pi\)
0.412876 + 0.910787i \(0.364524\pi\)
\(98\) 200.063 + 108.711i 0.206219 + 0.112056i
\(99\) −855.703 + 354.444i −0.868701 + 0.359828i
\(100\) −284.945 + 1336.22i −0.284945 + 1.33622i
\(101\) 585.257 1412.93i 0.576586 1.39200i −0.319272 0.947663i \(-0.603438\pi\)
0.895858 0.444339i \(-0.146562\pi\)
\(102\) 428.437 + 45.1738i 0.415898 + 0.0438517i
\(103\) 1120.20 + 1120.20i 1.07161 + 1.07161i 0.997230 + 0.0743853i \(0.0236995\pi\)
0.0743853 + 0.997230i \(0.476301\pi\)
\(104\) −412.384 811.339i −0.388823 0.764984i
\(105\) −368.977 + 368.977i −0.342937 + 0.342937i
\(106\) 941.965 762.273i 0.863130 0.698476i
\(107\) −1665.63 689.926i −1.50488 0.623343i −0.530388 0.847755i \(-0.677954\pi\)
−0.974494 + 0.224413i \(0.927954\pi\)
\(108\) −601.118 + 110.999i −0.535580 + 0.0988975i
\(109\) −342.786 827.559i −0.301220 0.727209i −0.999930 0.0118047i \(-0.996242\pi\)
0.698710 0.715405i \(-0.253758\pi\)
\(110\) −514.853 1740.23i −0.446267 1.50840i
\(111\) 69.5116i 0.0594392i
\(112\) −1230.21 + 470.367i −1.03789 + 0.396835i
\(113\) 924.353i 0.769521i 0.923016 + 0.384760i \(0.125716\pi\)
−0.923016 + 0.384760i \(0.874284\pi\)
\(114\) −129.667 + 38.3624i −0.106530 + 0.0315172i
\(115\) 673.829 + 1626.77i 0.546390 + 1.31910i
\(116\) −170.522 117.363i −0.136488 0.0939383i
\(117\) −922.559 382.137i −0.728980 0.301953i
\(118\) −663.963 820.481i −0.517989 0.640096i
\(119\) 1503.33 1503.33i 1.15807 1.15807i
\(120\) −44.4483 572.024i −0.0338130 0.435154i
\(121\) 43.0249 + 43.0249i 0.0323253 + 0.0323253i
\(122\) −11.2021 + 106.243i −0.00831307 + 0.0788427i
\(123\) 36.0145 86.9467i 0.0264010 0.0637376i
\(124\) 543.079 + 837.481i 0.393306 + 0.606516i
\(125\) −727.445 + 301.318i −0.520517 + 0.215605i
\(126\) −689.940 + 1269.71i −0.487816 + 0.897737i
\(127\) 569.829 0.398143 0.199072 0.979985i \(-0.436207\pi\)
0.199072 + 0.979985i \(0.436207\pi\)
\(128\) 486.563 1363.97i 0.335988 0.941866i
\(129\) 730.042 0.498268
\(130\) 934.169 1719.17i 0.630247 1.15986i
\(131\) 1171.87 485.406i 0.781581 0.323742i 0.0440278 0.999030i \(-0.485981\pi\)
0.737553 + 0.675289i \(0.235981\pi\)
\(132\) 239.415 + 369.202i 0.157867 + 0.243446i
\(133\) −255.370 + 616.518i −0.166492 + 0.401947i
\(134\) 63.1396 598.828i 0.0407047 0.386051i
\(135\) −929.227 929.227i −0.592408 0.592408i
\(136\) 181.097 + 2330.61i 0.114183 + 1.46947i
\(137\) 946.041 946.041i 0.589969 0.589969i −0.347654 0.937623i \(-0.613022\pi\)
0.937623 + 0.347654i \(0.113022\pi\)
\(138\) −268.574 331.885i −0.165670 0.204724i
\(139\) 1313.93 + 544.249i 0.801772 + 0.332105i 0.745666 0.666320i \(-0.232131\pi\)
0.0561063 + 0.998425i \(0.482131\pi\)
\(140\) −2332.38 1605.27i −1.40802 0.969074i
\(141\) −328.802 793.797i −0.196384 0.474112i
\(142\) −1997.73 + 591.036i −1.18060 + 0.349286i
\(143\) 1500.59i 0.877523i
\(144\) −567.442 1484.10i −0.328381 0.858855i
\(145\) 445.021i 0.254876i
\(146\) 660.822 + 2233.61i 0.374589 + 1.26613i
\(147\) −45.4195 109.652i −0.0254839 0.0615236i
\(148\) −370.908 + 68.4900i −0.206003 + 0.0380395i
\(149\) 2438.15 + 1009.92i 1.34054 + 0.555272i 0.933644 0.358201i \(-0.116610\pi\)
0.406900 + 0.913473i \(0.366610\pi\)
\(150\) 553.614 448.005i 0.301349 0.243863i
\(151\) −872.975 + 872.975i −0.470475 + 0.470475i −0.902068 0.431594i \(-0.857951\pi\)
0.431594 + 0.902068i \(0.357951\pi\)
\(152\) −332.459 654.091i −0.177408 0.349038i
\(153\) 1813.59 + 1813.59i 0.958301 + 0.958301i
\(154\) 2159.57 + 227.702i 1.13002 + 0.119148i
\(155\) −821.170 + 1982.48i −0.425535 + 1.02733i
\(156\) −98.9431 + 463.982i −0.0507807 + 0.238130i
\(157\) −866.489 + 358.912i −0.440467 + 0.182447i −0.591885 0.806022i \(-0.701616\pi\)
0.151418 + 0.988470i \(0.451616\pi\)
\(158\) −392.115 213.069i −0.197437 0.107284i
\(159\) −631.643 −0.315047
\(160\) 3008.48 800.790i 1.48651 0.395675i
\(161\) −2106.94 −1.03136
\(162\) −1385.90 753.074i −0.672138 0.365229i
\(163\) −745.455 + 308.777i −0.358212 + 0.148376i −0.554529 0.832164i \(-0.687102\pi\)
0.196318 + 0.980540i \(0.437102\pi\)
\(164\) 499.426 + 106.501i 0.237796 + 0.0507096i
\(165\) −362.011 + 873.972i −0.170803 + 0.412355i
\(166\) 400.829 + 42.2629i 0.187412 + 0.0197605i
\(167\) −741.751 741.751i −0.343703 0.343703i 0.514055 0.857758i \(-0.328143\pi\)
−0.857758 + 0.514055i \(0.828143\pi\)
\(168\) 652.723 + 212.799i 0.299754 + 0.0977248i
\(169\) 409.532 409.532i 0.186405 0.186405i
\(170\) −3906.54 + 3161.31i −1.76246 + 1.42625i
\(171\) −743.756 308.074i −0.332611 0.137772i
\(172\) 719.313 + 3895.44i 0.318878 + 1.72689i
\(173\) −34.3941 83.0347i −0.0151152 0.0364914i 0.916142 0.400854i \(-0.131287\pi\)
−0.931257 + 0.364363i \(0.881287\pi\)
\(174\) 30.6123 + 103.471i 0.0133374 + 0.0450812i
\(175\) 3514.56i 1.51815i
\(176\) −1734.13 + 1641.28i −0.742700 + 0.702931i
\(177\) 550.180i 0.233639i
\(178\) −1046.69 + 309.666i −0.440744 + 0.130396i
\(179\) −1402.83 3386.73i −0.585768 1.41417i −0.887514 0.460781i \(-0.847570\pi\)
0.301746 0.953388i \(-0.402430\pi\)
\(180\) 1936.57 2813.74i 0.801909 1.16513i
\(181\) 504.860 + 209.120i 0.207326 + 0.0858771i 0.483930 0.875107i \(-0.339209\pi\)
−0.276604 + 0.960984i \(0.589209\pi\)
\(182\) 1472.77 + 1819.94i 0.599828 + 0.741227i
\(183\) 39.3770 39.3770i 0.0159062 0.0159062i
\(184\) 1506.29 1760.09i 0.603504 0.705195i
\(185\) −573.361 573.361i −0.227861 0.227861i
\(186\) 54.5571 517.430i 0.0215071 0.203977i
\(187\) 1474.95 3560.85i 0.576786 1.39249i
\(188\) 3911.67 2536.59i 1.51749 0.984041i
\(189\) 1452.76 601.752i 0.559114 0.231593i
\(190\) 753.116 1385.97i 0.287562 0.529206i
\(191\) −17.6918 −0.00670226 −0.00335113 0.999994i \(-0.501067\pi\)
−0.00335113 + 0.999994i \(0.501067\pi\)
\(192\) −644.411 + 393.139i −0.242221 + 0.147773i
\(193\) −3321.63 −1.23884 −0.619420 0.785059i \(-0.712632\pi\)
−0.619420 + 0.785059i \(0.712632\pi\)
\(194\) 1065.32 1960.53i 0.394255 0.725555i
\(195\) −942.256 + 390.295i −0.346033 + 0.143331i
\(196\) 540.344 350.395i 0.196918 0.127695i
\(197\) −310.402 + 749.376i −0.112260 + 0.271020i −0.970018 0.243035i \(-0.921857\pi\)
0.857758 + 0.514054i \(0.171857\pi\)
\(198\) −274.695 + 2605.26i −0.0985947 + 0.935091i
\(199\) 1908.35 + 1908.35i 0.679795 + 0.679795i 0.959954 0.280158i \(-0.0903870\pi\)
−0.280158 + 0.959954i \(0.590387\pi\)
\(200\) 2935.99 + 2512.62i 1.03803 + 0.888345i
\(201\) −221.944 + 221.944i −0.0778841 + 0.0778841i
\(202\) −2721.11 3362.56i −0.947805 1.17123i
\(203\) 491.968 + 203.780i 0.170095 + 0.0704559i
\(204\) 690.841 1003.76i 0.237101 0.344495i
\(205\) 420.110 + 1014.24i 0.143131 + 0.345548i
\(206\) 4296.69 1271.19i 1.45323 0.429943i
\(207\) 2541.77i 0.853454i
\(208\) −2573.25 70.7893i −0.857803 0.0235979i
\(209\) 1209.76i 0.400387i
\(210\) 418.712 + 1415.27i 0.137590 + 0.465060i
\(211\) −969.860 2341.45i −0.316435 0.763943i −0.999438 0.0335266i \(-0.989326\pi\)
0.683002 0.730416i \(-0.260674\pi\)
\(212\) −622.360 3370.39i −0.201622 1.09188i
\(213\) 1003.29 + 415.578i 0.322744 + 0.133685i
\(214\) −3963.94 + 3207.76i −1.26621 + 1.02466i
\(215\) −6021.69 + 6021.69i −1.91012 + 1.91012i
\(216\) −535.910 + 1643.81i −0.168815 + 0.517811i
\(217\) −1815.60 1815.60i −0.567976 0.567976i
\(218\) −2519.58 265.661i −0.782787 0.0825359i
\(219\) 464.647 1121.76i 0.143370 0.346125i
\(220\) −5020.13 1070.53i −1.53844 0.328070i
\(221\) 3839.06 1590.19i 1.16852 0.484017i
\(222\) 172.752 + 93.8706i 0.0522268 + 0.0283792i
\(223\) −267.474 −0.0803200 −0.0401600 0.999193i \(-0.512787\pi\)
−0.0401600 + 0.999193i \(0.512787\pi\)
\(224\) −492.345 + 3692.54i −0.146858 + 1.10142i
\(225\) 4239.89 1.25627
\(226\) 2297.23 + 1248.28i 0.676147 + 0.367407i
\(227\) −721.748 + 298.958i −0.211031 + 0.0874120i −0.485695 0.874128i \(-0.661433\pi\)
0.274664 + 0.961540i \(0.411433\pi\)
\(228\) −79.7667 + 374.056i −0.0231696 + 0.108651i
\(229\) −1403.35 + 3387.98i −0.404960 + 0.977660i 0.581484 + 0.813558i \(0.302472\pi\)
−0.986443 + 0.164101i \(0.947528\pi\)
\(230\) 4952.84 + 522.220i 1.41992 + 0.149714i
\(231\) −800.402 800.402i −0.227977 0.227977i
\(232\) −521.950 + 265.295i −0.147706 + 0.0750753i
\(233\) 95.4522 95.4522i 0.0268381 0.0268381i −0.693560 0.720399i \(-0.743959\pi\)
0.720399 + 0.693560i \(0.243959\pi\)
\(234\) −2195.55 + 1776.72i −0.613365 + 0.496358i
\(235\) 9259.67 + 3835.48i 2.57036 + 1.06468i
\(236\) −2935.71 + 542.094i −0.809740 + 0.149523i
\(237\) 89.0201 + 214.913i 0.0243986 + 0.0589035i
\(238\) −1705.97 5766.26i −0.464628 1.57047i
\(239\) 2210.32i 0.598216i 0.954219 + 0.299108i \(0.0966890\pi\)
−0.954219 + 0.299108i \(0.903311\pi\)
\(240\) −1481.63 662.015i −0.398496 0.178054i
\(241\) 3029.15i 0.809645i −0.914395 0.404823i \(-0.867333\pi\)
0.914395 0.404823i \(-0.132667\pi\)
\(242\) 165.029 48.8244i 0.0438366 0.0129692i
\(243\) 1104.14 + 2665.62i 0.291483 + 0.703703i
\(244\) 248.911 + 171.314i 0.0653068 + 0.0449478i
\(245\) 1279.10 + 529.820i 0.333545 + 0.138159i
\(246\) −167.447 206.920i −0.0433985 0.0536289i
\(247\) −922.264 + 922.264i −0.237580 + 0.237580i
\(248\) 2814.72 218.714i 0.720705 0.0560013i
\(249\) −148.560 148.560i −0.0378095 0.0378095i
\(250\) −233.522 + 2214.77i −0.0590770 + 0.560298i
\(251\) −134.300 + 324.230i −0.0337727 + 0.0815346i −0.939866 0.341543i \(-0.889050\pi\)
0.906093 + 0.423078i \(0.139050\pi\)
\(252\) 2223.80 + 3429.31i 0.555897 + 0.857247i
\(253\) −3528.86 + 1461.70i −0.876908 + 0.363227i
\(254\) 769.515 1416.15i 0.190093 0.349832i
\(255\) 2619.56 0.643307
\(256\) −2732.70 3051.16i −0.667162 0.744912i
\(257\) −7459.69 −1.81059 −0.905297 0.424779i \(-0.860352\pi\)
−0.905297 + 0.424779i \(0.860352\pi\)
\(258\) 985.871 1814.32i 0.237898 0.437808i
\(259\) 896.396 371.299i 0.215055 0.0890788i
\(260\) −3010.99 4643.24i −0.718207 1.10754i
\(261\) −245.836 + 593.501i −0.0583022 + 0.140754i
\(262\) 376.192 3567.88i 0.0887070 0.841314i
\(263\) 4192.29 + 4192.29i 0.982919 + 0.982919i 0.999857 0.0169374i \(-0.00539160\pi\)
−0.0169374 + 0.999857i \(0.505392\pi\)
\(264\) 1240.86 96.4195i 0.289280 0.0224781i
\(265\) 5210.05 5210.05i 1.20774 1.20774i
\(266\) 1187.33 + 1467.22i 0.273683 + 0.338199i
\(267\) 525.664 + 217.737i 0.120487 + 0.0499075i
\(268\) −1402.96 965.591i −0.319773 0.220085i
\(269\) −1275.44 3079.18i −0.289088 0.697921i 0.710897 0.703296i \(-0.248289\pi\)
−0.999986 + 0.00537488i \(0.998289\pi\)
\(270\) −3564.19 + 1054.48i −0.803370 + 0.237680i
\(271\) 1188.89i 0.266494i 0.991083 + 0.133247i \(0.0425404\pi\)
−0.991083 + 0.133247i \(0.957460\pi\)
\(272\) 6036.65 + 2697.26i 1.34568 + 0.601271i
\(273\) 1220.38i 0.270552i
\(274\) −1073.56 3628.69i −0.236701 0.800062i
\(275\) −2438.25 5886.46i −0.534662 1.29079i
\(276\) −1187.50 + 219.278i −0.258982 + 0.0478224i
\(277\) 3832.51 + 1587.48i 0.831310 + 0.344340i 0.757421 0.652926i \(-0.226459\pi\)
0.0738890 + 0.997266i \(0.476459\pi\)
\(278\) 3126.96 2530.45i 0.674613 0.545921i
\(279\) 2190.30 2190.30i 0.470000 0.470000i
\(280\) −7139.18 + 3628.68i −1.52374 + 0.774482i
\(281\) 230.048 + 230.048i 0.0488382 + 0.0488382i 0.731104 0.682266i \(-0.239005\pi\)
−0.682266 + 0.731104i \(0.739005\pi\)
\(282\) −2416.79 254.823i −0.510346 0.0538102i
\(283\) −405.744 + 979.554i −0.0852261 + 0.205754i −0.960747 0.277426i \(-0.910519\pi\)
0.875521 + 0.483181i \(0.160519\pi\)
\(284\) −1228.94 + 5762.96i −0.256775 + 1.20411i
\(285\) −759.635 + 314.651i −0.157884 + 0.0653977i
\(286\) 3729.31 + 2026.45i 0.771044 + 0.418973i
\(287\) −1313.61 −0.270173
\(288\) −4454.62 593.956i −0.911426 0.121525i
\(289\) −5759.94 −1.17239
\(290\) −1105.98 600.970i −0.223949 0.121690i
\(291\) −1074.54 + 445.089i −0.216463 + 0.0896619i
\(292\) 6443.42 + 1374.05i 1.29134 + 0.275377i
\(293\) −614.388 + 1483.26i −0.122501 + 0.295744i −0.973220 0.229878i \(-0.926167\pi\)
0.850718 + 0.525622i \(0.176167\pi\)
\(294\) −333.847 35.2003i −0.0662256 0.00698273i
\(295\) −4538.12 4538.12i −0.895659 0.895659i
\(296\) −330.673 + 1014.28i −0.0649323 + 0.199168i
\(297\) 2015.72 2015.72i 0.393819 0.393819i
\(298\) 5802.42 4695.53i 1.12794 0.912768i
\(299\) −3804.58 1575.91i −0.735867 0.304806i
\(300\) −365.775 1980.86i −0.0703934 0.381216i
\(301\) −3899.55 9414.34i −0.746732 1.80277i
\(302\) 990.646 + 3348.43i 0.188759 + 0.638015i
\(303\) 2254.80i 0.427507i
\(304\) −2074.53 57.0695i −0.391389 0.0107670i
\(305\) 649.596i 0.121953i
\(306\) 6956.30 2058.05i 1.29956 0.384480i
\(307\) 2158.05 + 5210.00i 0.401194 + 0.968569i 0.987377 + 0.158390i \(0.0506302\pi\)
−0.586182 + 0.810179i \(0.699370\pi\)
\(308\) 3482.24 5059.52i 0.644218 0.936016i
\(309\) −2157.87 893.819i −0.397272 0.164555i
\(310\) 3817.97 + 4717.99i 0.699504 + 0.864400i
\(311\) 182.317 182.317i 0.0332420 0.0332420i −0.690290 0.723532i \(-0.742517\pi\)
0.723532 + 0.690290i \(0.242517\pi\)
\(312\) 1019.48 + 872.471i 0.184990 + 0.158314i
\(313\) 3731.88 + 3731.88i 0.673924 + 0.673924i 0.958618 0.284694i \(-0.0918921\pi\)
−0.284694 + 0.958618i \(0.591892\pi\)
\(314\) −278.158 + 2638.10i −0.0499916 + 0.474130i
\(315\) −3362.52 + 8117.84i −0.601450 + 1.45203i
\(316\) −1059.05 + 686.758i −0.188532 + 0.122257i
\(317\) 2940.58 1218.03i 0.521007 0.215808i −0.106652 0.994296i \(-0.534013\pi\)
0.627659 + 0.778488i \(0.284013\pi\)
\(318\) −852.990 + 1569.77i −0.150419 + 0.276819i
\(319\) 965.361 0.169435
\(320\) 2072.60 8558.15i 0.362068 1.49505i
\(321\) 2658.05 0.462174
\(322\) −2845.27 + 5236.21i −0.492425 + 0.906218i
\(323\) 3095.00 1281.99i 0.533159 0.220842i
\(324\) −3743.12 + 2427.29i −0.641824 + 0.416202i
\(325\) 2628.75 6346.37i 0.448668 1.08318i
\(326\) −239.304 + 2269.60i −0.0406559 + 0.385588i
\(327\) 933.833 + 933.833i 0.157924 + 0.157924i
\(328\) 939.120 1097.36i 0.158092 0.184731i
\(329\) −8480.20 + 8480.20i −1.42106 + 1.42106i
\(330\) 1683.15 + 2079.92i 0.280770 + 0.346957i
\(331\) −5918.75 2451.63i −0.982852 0.407111i −0.167371 0.985894i \(-0.553528\pi\)
−0.815481 + 0.578783i \(0.803528\pi\)
\(332\) 646.325 939.077i 0.106842 0.155237i
\(333\) 447.928 + 1081.39i 0.0737127 + 0.177958i
\(334\) −2845.10 + 841.734i −0.466099 + 0.137897i
\(335\) 3661.37i 0.597141i
\(336\) 1410.31 1334.79i 0.228984 0.216723i
\(337\) 11283.3i 1.82385i 0.410355 + 0.911926i \(0.365405\pi\)
−0.410355 + 0.911926i \(0.634595\pi\)
\(338\) −464.734 1570.82i −0.0747875 0.252785i
\(339\) −521.529 1259.08i −0.0835562 0.201722i
\(340\) 2581.06 + 13977.8i 0.411699 + 2.22956i
\(341\) −4300.49 1781.32i −0.682946 0.282886i
\(342\) −1770.02 + 1432.37i −0.279859 + 0.226472i
\(343\) 3819.79 3819.79i 0.601310 0.601310i
\(344\) 10652.4 + 3472.87i 1.66959 + 0.544316i
\(345\) −1835.67 1835.67i −0.286462 0.286462i
\(346\) −252.807 26.6556i −0.0392802 0.00414165i
\(347\) 4803.69 11597.1i 0.743157 1.79414i 0.150630 0.988590i \(-0.451870\pi\)
0.592527 0.805550i \(-0.298130\pi\)
\(348\) 298.489 + 63.6521i 0.0459789 + 0.00980491i
\(349\) −5191.29 + 2150.30i −0.796228 + 0.329808i −0.743445 0.668798i \(-0.766809\pi\)
−0.0527834 + 0.998606i \(0.516809\pi\)
\(350\) −8734.46 4746.16i −1.33393 0.724838i
\(351\) 3073.39 0.467366
\(352\) 1737.11 + 6526.14i 0.263035 + 0.988194i
\(353\) 9949.61 1.50018 0.750091 0.661335i \(-0.230010\pi\)
0.750091 + 0.661335i \(0.230010\pi\)
\(354\) 1367.32 + 742.980i 0.205289 + 0.111551i
\(355\) −11703.4 + 4847.72i −1.74973 + 0.724762i
\(356\) −643.888 + 3019.43i −0.0958595 + 0.449522i
\(357\) −1199.53 + 2895.91i −0.177831 + 0.429322i
\(358\) −10311.2 1087.20i −1.52225 0.160504i
\(359\) −3301.10 3301.10i −0.485308 0.485308i 0.421514 0.906822i \(-0.361499\pi\)
−0.906822 + 0.421514i \(0.861499\pi\)
\(360\) −4377.57 8612.58i −0.640884 1.26090i
\(361\) 4106.53 4106.53i 0.598706 0.598706i
\(362\) 1201.49 972.289i 0.174444 0.141167i
\(363\) −82.8802 34.3301i −0.0119837 0.00496381i
\(364\) 6511.84 1202.44i 0.937673 0.173146i
\(365\) 5420.12 + 13085.3i 0.777266 + 1.87649i
\(366\) −44.6847 151.037i −0.00638172 0.0215705i
\(367\) 10621.1i 1.51067i −0.655340 0.755334i \(-0.727474\pi\)
0.655340 0.755334i \(-0.272526\pi\)
\(368\) −2340.09 6120.34i −0.331483 0.866970i
\(369\) 1584.71i 0.223568i
\(370\) −2199.21 + 650.646i −0.309005 + 0.0914202i
\(371\) 3373.95 + 8145.43i 0.472147 + 1.13986i
\(372\) −1212.25 834.340i −0.168958 0.116286i
\(373\) −527.627 218.550i −0.0732426 0.0303381i 0.345761 0.938322i \(-0.387621\pi\)
−0.419004 + 0.907984i \(0.637621\pi\)
\(374\) −6857.68 8474.26i −0.948134 1.17164i
\(375\) 820.862 820.862i 0.113038 0.113038i
\(376\) −1021.56 13146.9i −0.140114 1.80318i
\(377\) 735.947 + 735.947i 0.100539 + 0.100539i
\(378\) 466.360 4423.05i 0.0634576 0.601845i
\(379\) −3589.96 + 8666.94i −0.486554 + 1.17465i 0.469888 + 0.882726i \(0.344294\pi\)
−0.956443 + 0.291920i \(0.905706\pi\)
\(380\) −2427.42 3743.32i −0.327695 0.505338i
\(381\) −776.177 + 321.503i −0.104369 + 0.0432312i
\(382\) −23.8915 + 43.9680i −0.00319999 + 0.00588900i
\(383\) −4350.16 −0.580372 −0.290186 0.956970i \(-0.593717\pi\)
−0.290186 + 0.956970i \(0.593717\pi\)
\(384\) 106.806 + 2132.41i 0.0141938 + 0.283383i
\(385\) 13204.1 1.74791
\(386\) −4485.63 + 8255.00i −0.591484 + 1.08852i
\(387\) 11357.3 4704.34i 1.49179 0.617920i
\(388\) −3433.71 5295.11i −0.449279 0.692831i
\(389\) 763.322 1842.82i 0.0994909 0.240192i −0.866295 0.499533i \(-0.833505\pi\)
0.965786 + 0.259340i \(0.0835051\pi\)
\(390\) −302.481 + 2868.78i −0.0392736 + 0.372478i
\(391\) 7479.13 + 7479.13i 0.967355 + 0.967355i
\(392\) −141.114 1816.06i −0.0181820 0.233992i
\(393\) −1322.36 + 1322.36i −0.169731 + 0.169731i
\(394\) 1443.19 + 1783.40i 0.184535 + 0.228036i
\(395\) −2506.97 1038.42i −0.319340 0.132275i
\(396\) 6103.71 + 4200.91i 0.774553 + 0.533090i
\(397\) 1876.19 + 4529.53i 0.237187 + 0.572621i 0.996990 0.0775330i \(-0.0247043\pi\)
−0.759802 + 0.650154i \(0.774704\pi\)
\(398\) 7319.77 2165.58i 0.921876 0.272741i
\(399\) 983.855i 0.123444i
\(400\) 10209.3 3903.49i 1.27616 0.487936i
\(401\) 14992.8i 1.86710i −0.358450 0.933549i \(-0.616695\pi\)
0.358450 0.933549i \(-0.383305\pi\)
\(402\) 251.860 + 851.300i 0.0312479 + 0.105619i
\(403\) −1920.50 4636.49i −0.237387 0.573102i
\(404\) −12031.4 + 2221.66i −1.48164 + 0.273593i
\(405\) −8860.68 3670.21i −1.08714 0.450307i
\(406\) 1170.81 947.460i 0.143119 0.115817i
\(407\) 1243.76 1243.76i 0.151477 0.151477i
\(408\) −1561.63 3072.40i −0.189490 0.372810i
\(409\) 8450.62 + 8450.62i 1.02165 + 1.02165i 0.999760 + 0.0218936i \(0.00696949\pi\)
0.0218936 + 0.999760i \(0.493031\pi\)
\(410\) 3087.93 + 325.587i 0.371957 + 0.0392186i
\(411\) −754.857 + 1822.39i −0.0905946 + 0.218715i
\(412\) 2643.19 12394.9i 0.316069 1.48217i
\(413\) 7094.91 2938.81i 0.845322 0.350144i
\(414\) −6316.86 3432.48i −0.749895 0.407481i
\(415\) 2450.76 0.289887
\(416\) −3650.93 + 6299.52i −0.430292 + 0.742450i
\(417\) −2096.81 −0.246238
\(418\) 3006.52 + 1633.70i 0.351803 + 0.191164i
\(419\) −3136.96 + 1299.37i −0.365753 + 0.151500i −0.557988 0.829849i \(-0.688426\pi\)
0.192235 + 0.981349i \(0.438426\pi\)
\(420\) 4082.70 + 870.627i 0.474322 + 0.101148i
\(421\) 3434.08 8290.60i 0.397546 0.959760i −0.590701 0.806891i \(-0.701149\pi\)
0.988246 0.152870i \(-0.0488514\pi\)
\(422\) −7128.75 751.645i −0.822327 0.0867050i
\(423\) −10230.4 10230.4i −1.17593 1.17593i
\(424\) −9216.63 3004.78i −1.05566 0.344162i
\(425\) −12475.9 + 12475.9i −1.42392 + 1.42392i
\(426\) 2387.68 1932.20i 0.271558 0.219754i
\(427\) −718.125 297.457i −0.0813876 0.0337118i
\(428\) 2618.99 + 14183.1i 0.295779 + 1.60179i
\(429\) −846.648 2043.99i −0.0952833 0.230034i
\(430\) 6833.37 + 23097.1i 0.766359 + 2.59033i
\(431\) 15375.3i 1.71833i 0.511699 + 0.859165i \(0.329016\pi\)
−0.511699 + 0.859165i \(0.670984\pi\)
\(432\) 3361.53 + 3551.71i 0.374379 + 0.395559i
\(433\) 12522.9i 1.38987i 0.719073 + 0.694934i \(0.244567\pi\)
−0.719073 + 0.694934i \(0.755433\pi\)
\(434\) −6964.00 + 2060.33i −0.770237 + 0.227878i
\(435\) 251.085 + 606.172i 0.0276749 + 0.0668132i
\(436\) −4062.74 + 5902.96i −0.446262 + 0.648396i
\(437\) −3067.20 1270.48i −0.335753 0.139074i
\(438\) −2160.34 2669.61i −0.235674 0.291230i
\(439\) 6689.38 6689.38i 0.727259 0.727259i −0.242814 0.970073i \(-0.578071\pi\)
0.970073 + 0.242814i \(0.0780705\pi\)
\(440\) −9439.85 + 11030.5i −1.02279 + 1.19513i
\(441\) −1413.19 1413.19i −0.152595 0.152595i
\(442\) 1232.40 11688.4i 0.132623 1.25782i
\(443\) 1232.30 2975.03i 0.132163 0.319070i −0.843920 0.536470i \(-0.819758\pi\)
0.976083 + 0.217400i \(0.0697576\pi\)
\(444\) 466.579 302.561i 0.0498713 0.0323399i
\(445\) −6131.88 + 2539.91i −0.653212 + 0.270569i
\(446\) −361.205 + 664.732i −0.0383487 + 0.0705739i
\(447\) −3890.86 −0.411703
\(448\) 8511.92 + 6210.11i 0.897657 + 0.654911i
\(449\) −2465.75 −0.259167 −0.129584 0.991569i \(-0.541364\pi\)
−0.129584 + 0.991569i \(0.541364\pi\)
\(450\) 5725.68 10537.1i 0.599803 1.10383i
\(451\) −2200.13 + 911.324i −0.229712 + 0.0951498i
\(452\) 6204.49 4023.41i 0.645652 0.418684i
\(453\) 696.557 1681.64i 0.0722453 0.174415i
\(454\) −231.694 + 2197.43i −0.0239514 + 0.227159i
\(455\) 10066.2 + 10066.2i 1.03717 + 1.03717i
\(456\) 821.894 + 703.375i 0.0844051 + 0.0722337i
\(457\) 720.641 720.641i 0.0737640 0.0737640i −0.669262 0.743026i \(-0.733390\pi\)
0.743026 + 0.669262i \(0.233390\pi\)
\(458\) 6524.77 + 8062.86i 0.665682 + 0.822605i
\(459\) −7293.03 3020.87i −0.741633 0.307194i
\(460\) 7986.30 11603.7i 0.809485 1.17614i
\(461\) 94.7149 + 228.662i 0.00956900 + 0.0231016i 0.928592 0.371103i \(-0.121020\pi\)
−0.919023 + 0.394204i \(0.871020\pi\)
\(462\) −3070.07 + 908.291i −0.309161 + 0.0914665i
\(463\) 6979.44i 0.700566i 0.936644 + 0.350283i \(0.113915\pi\)
−0.936644 + 0.350283i \(0.886085\pi\)
\(464\) −45.5402 + 1655.43i −0.00455636 + 0.165628i
\(465\) 3163.69i 0.315511i
\(466\) −108.319 366.122i −0.0107677 0.0363954i
\(467\) 795.725 + 1921.05i 0.0788475 + 0.190355i 0.958388 0.285470i \(-0.0921497\pi\)
−0.879540 + 0.475825i \(0.842150\pi\)
\(468\) 1450.61 + 7855.76i 0.143278 + 0.775924i
\(469\) 4047.63 + 1676.58i 0.398512 + 0.165069i
\(470\) 22036.6 17832.8i 2.16270 1.75014i
\(471\) 977.762 977.762i 0.0956537 0.0956537i
\(472\) −2617.25 + 8027.97i −0.255231 + 0.782875i
\(473\) −13062.5 13062.5i −1.26980 1.26980i
\(474\) 654.323 + 68.9909i 0.0634052 + 0.00668536i
\(475\) 2119.27 5116.37i 0.204713 0.494221i
\(476\) −16634.2 3547.21i −1.60174 0.341568i
\(477\) −9826.49 + 4070.26i −0.943237 + 0.390702i
\(478\) 5493.13 + 2984.88i 0.525628 + 0.285618i
\(479\) 973.751 0.0928848 0.0464424 0.998921i \(-0.485212\pi\)
0.0464424 + 0.998921i \(0.485212\pi\)
\(480\) −3646.10 + 2788.18i −0.346710 + 0.265130i
\(481\) 1896.37 0.179766
\(482\) −7528.11 4090.65i −0.711402 0.386565i
\(483\) 2869.90 1188.75i 0.270362 0.111988i
\(484\) 101.520 476.067i 0.00953422 0.0447096i
\(485\) 5191.98 12534.6i 0.486094 1.17354i
\(486\) 8115.73 + 855.711i 0.757484 + 0.0798680i
\(487\) −11379.8 11379.8i −1.05887 1.05887i −0.998155 0.0607112i \(-0.980663\pi\)
−0.0607112 0.998155i \(-0.519337\pi\)
\(488\) 761.890 387.251i 0.0706745 0.0359222i
\(489\) 841.184 841.184i 0.0777907 0.0777907i
\(490\) 3044.05 2463.36i 0.280646 0.227109i
\(491\) −1394.56 577.645i −0.128178 0.0530932i 0.317672 0.948201i \(-0.397099\pi\)
−0.445851 + 0.895107i \(0.647099\pi\)
\(492\) −740.367 + 136.713i −0.0678421 + 0.0125274i
\(493\) −1023.00 2469.74i −0.0934557 0.225622i
\(494\) 1046.58 + 3537.49i 0.0953195 + 0.322184i
\(495\) 15929.2i 1.44639i
\(496\) 3257.53 7290.56i 0.294894 0.659992i
\(497\) 15157.9i 1.36806i
\(498\) −569.823 + 168.584i −0.0512739 + 0.0151696i
\(499\) 5429.65 + 13108.3i 0.487103 + 1.17597i 0.956171 + 0.292809i \(0.0945900\pi\)
−0.469068 + 0.883162i \(0.655410\pi\)
\(500\) 5188.85 + 3571.25i 0.464105 + 0.319422i
\(501\) 1428.86 + 591.852i 0.127418 + 0.0527784i
\(502\) 624.420 + 771.616i 0.0555164 + 0.0686034i
\(503\) 11037.0 11037.0i 0.978362 0.978362i −0.0214085 0.999771i \(-0.506815\pi\)
0.999771 + 0.0214085i \(0.00681506\pi\)
\(504\) 11525.7 895.587i 1.01864 0.0791520i
\(505\) −18598.5 18598.5i −1.63886 1.63886i
\(506\) −1132.83 + 10743.9i −0.0995262 + 0.943926i
\(507\) −326.770 + 788.893i −0.0286240 + 0.0691045i
\(508\) −2480.28 3824.83i −0.216623 0.334054i
\(509\) 13984.8 5792.71i 1.21781 0.504435i 0.321099 0.947046i \(-0.395948\pi\)
0.896714 + 0.442611i \(0.145948\pi\)
\(510\) 3537.54 6510.20i 0.307147 0.565248i
\(511\) −16947.7 −1.46717
\(512\) −11273.1 + 2670.98i −0.973060 + 0.230550i
\(513\) 2477.73 0.213244
\(514\) −10073.8 + 18539.0i −0.864467 + 1.59090i
\(515\) 25171.6 10426.4i 2.15377 0.892123i
\(516\) −3177.63 4900.22i −0.271100 0.418062i
\(517\) −8320.11 + 20086.5i −0.707772 + 1.70871i
\(518\) 287.759 2729.16i 0.0244081 0.231491i
\(519\) 93.6978 + 93.6978i 0.00792462 + 0.00792462i
\(520\) −15605.6 + 1212.61i −1.31606 + 0.102263i
\(521\) 8504.46 8504.46i 0.715139 0.715139i −0.252467 0.967606i \(-0.581242\pi\)
0.967606 + 0.252467i \(0.0812418\pi\)
\(522\) 1143.00 + 1412.44i 0.0958384 + 0.118431i
\(523\) −2991.17 1238.98i −0.250086 0.103589i 0.254119 0.967173i \(-0.418214\pi\)
−0.504205 + 0.863584i \(0.668214\pi\)
\(524\) −8358.95 5753.09i −0.696875 0.479628i
\(525\) 1982.94 + 4787.25i 0.164843 + 0.397967i
\(526\) 16080.2 4757.38i 1.33295 0.394357i
\(527\) 12889.9i 1.06545i
\(528\) 1436.08 3214.03i 0.118366 0.264910i
\(529\) 1684.91i 0.138482i
\(530\) −5912.33 19984.0i −0.484557 1.63783i
\(531\) 3545.33 + 8559.17i 0.289744 + 0.699504i
\(532\) 5249.76 969.395i 0.427831 0.0790012i
\(533\) −2372.03 982.527i −0.192765 0.0798461i
\(534\) 1251.00 1012.35i 0.101378 0.0820390i
\(535\) −21924.7 + 21924.7i −1.77175 + 1.77175i
\(536\) −4294.31 + 2182.69i −0.346055 + 0.175892i
\(537\) 3821.65 + 3821.65i 0.307107 + 0.307107i
\(538\) −9374.83 988.469i −0.751260 0.0792118i
\(539\) −1149.31 + 2774.68i −0.0918448 + 0.221733i
\(540\) −2192.58 + 10281.8i −0.174729 + 0.819369i
\(541\) 4615.58 1911.84i 0.366801 0.151934i −0.191667 0.981460i \(-0.561389\pi\)
0.558468 + 0.829526i \(0.311389\pi\)
\(542\) 2954.66 + 1605.51i 0.234157 + 0.127237i
\(543\) −805.668 −0.0636732
\(544\) 14855.4 11360.0i 1.17081 0.895320i
\(545\) −15405.3 −1.21081
\(546\) −3032.92 1648.04i −0.237723 0.129175i
\(547\) 1759.02 728.609i 0.137496 0.0569526i −0.312875 0.949794i \(-0.601292\pi\)
0.450370 + 0.892842i \(0.351292\pi\)
\(548\) −10467.9 2232.25i −0.815995 0.174009i
\(549\) 358.847 866.332i 0.0278965 0.0673482i
\(550\) −17921.9 1889.66i −1.38944 0.146500i
\(551\) 593.311 + 593.311i 0.0458728 + 0.0458728i
\(552\) −1058.68 + 3247.32i −0.0816313 + 0.250390i
\(553\) 2295.94 2295.94i 0.176552 0.176552i
\(554\) 9120.77 7380.86i 0.699466 0.566034i
\(555\) 1104.48 + 457.492i 0.0844733 + 0.0349900i
\(556\) −2065.99 11188.4i −0.157585 0.853405i
\(557\) 7305.07 + 17636.0i 0.555702 + 1.34158i 0.913140 + 0.407646i \(0.133650\pi\)
−0.357438 + 0.933937i \(0.616350\pi\)
\(558\) −2485.54 8401.24i −0.188569 0.637371i
\(559\) 19916.6i 1.50694i
\(560\) −622.894 + 22642.8i −0.0470037 + 1.70863i
\(561\) 5682.48i 0.427655i
\(562\) 882.386 261.057i 0.0662299 0.0195944i
\(563\) 498.470 + 1203.41i 0.0373144 + 0.0900849i 0.941438 0.337186i \(-0.109475\pi\)
−0.904124 + 0.427271i \(0.859475\pi\)
\(564\) −3897.00 + 5662.14i −0.290945 + 0.422729i
\(565\) 14687.2 + 6083.65i 1.09362 + 0.452993i
\(566\) 1886.48 + 2331.18i 0.140097 + 0.173122i
\(567\) 8114.80 8114.80i 0.601040 0.601040i
\(568\) 12662.6 + 10836.7i 0.935409 + 0.800521i
\(569\) 13188.4 + 13188.4i 0.971684 + 0.971684i 0.999610 0.0279264i \(-0.00889041\pi\)
−0.0279264 + 0.999610i \(0.508890\pi\)
\(570\) −243.856 + 2312.78i −0.0179193 + 0.169950i
\(571\) 5719.51 13808.1i 0.419184 1.01200i −0.563401 0.826184i \(-0.690507\pi\)
0.982585 0.185815i \(-0.0594926\pi\)
\(572\) 10072.3 6531.59i 0.736269 0.477447i
\(573\) 24.0983 9.98186i 0.00175693 0.000727746i
\(574\) −1773.93 + 3264.60i −0.128994 + 0.237390i
\(575\) 17485.1 1.26813
\(576\) −7491.76 + 10268.6i −0.541939 + 0.742811i
\(577\) 7866.08 0.567538 0.283769 0.958893i \(-0.408415\pi\)
0.283769 + 0.958893i \(0.408415\pi\)
\(578\) −7778.40 + 14314.7i −0.559756 + 1.03013i
\(579\) 4524.46 1874.09i 0.324750 0.134516i
\(580\) −2987.09 + 1937.03i −0.213848 + 0.138674i
\(581\) −1122.23 + 2709.30i −0.0801342 + 0.193461i
\(582\) −344.946 + 3271.54i −0.0245678 + 0.233006i
\(583\) 11301.9 + 11301.9i 0.802877 + 0.802877i
\(584\) 12116.2 14157.8i 0.858514 1.00317i
\(585\) −12143.7 + 12143.7i −0.858255 + 0.858255i
\(586\) 2856.55 + 3529.93i 0.201370 + 0.248840i
\(587\) 13370.3 + 5538.16i 0.940122 + 0.389411i 0.799510 0.600653i \(-0.205093\pi\)
0.140613 + 0.990065i \(0.455093\pi\)
\(588\) −538.317 + 782.148i −0.0377548 + 0.0548558i
\(589\) −1548.28 3737.88i −0.108312 0.261489i
\(590\) −17406.6 + 5149.82i −1.21461 + 0.359347i
\(591\) 1195.87i 0.0832346i
\(592\) 2074.16 + 2191.51i 0.143999 + 0.152146i
\(593\) 7176.23i 0.496952i 0.968638 + 0.248476i \(0.0799297\pi\)
−0.968638 + 0.248476i \(0.920070\pi\)
\(594\) −2287.43 7731.62i −0.158004 0.534061i
\(595\) −13992.5 33780.9i −0.964095 2.32753i
\(596\) −3833.68 20761.3i −0.263479 1.42687i
\(597\) −3676.11 1522.69i −0.252015 0.104388i
\(598\) −9054.30 + 7327.07i −0.619160 + 0.501047i
\(599\) −11813.4 + 11813.4i −0.805815 + 0.805815i −0.983997 0.178183i \(-0.942978\pi\)
0.178183 + 0.983997i \(0.442978\pi\)
\(600\) −5416.82 1765.98i −0.368568 0.120159i
\(601\) −1438.92 1438.92i −0.0976618 0.0976618i 0.656588 0.754250i \(-0.271999\pi\)
−0.754250 + 0.656588i \(0.771999\pi\)
\(602\) −28662.8 3022.17i −1.94055 0.204609i
\(603\) −2022.60 + 4882.98i −0.136595 + 0.329768i
\(604\) 9659.39 + 2059.85i 0.650720 + 0.138765i
\(605\) 966.800 400.462i 0.0649686 0.0269109i
\(606\) 5603.67 + 3044.94i 0.375633 + 0.204113i
\(607\) −19331.1 −1.29263 −0.646314 0.763071i \(-0.723691\pi\)
−0.646314 + 0.763071i \(0.723691\pi\)
\(608\) −2943.33 + 5078.59i −0.196329 + 0.338757i
\(609\) −785.094 −0.0522391
\(610\) 1614.39 + 877.234i 0.107155 + 0.0582265i
\(611\) −21655.9 + 8970.17i −1.43389 + 0.593935i
\(612\) 4279.29 20067.2i 0.282647 1.32544i
\(613\) 2013.56 4861.15i 0.132670 0.320294i −0.843559 0.537037i \(-0.819543\pi\)
0.976229 + 0.216743i \(0.0695435\pi\)
\(614\) 15862.3 + 1672.50i 1.04259 + 0.109929i
\(615\) −1144.48 1144.48i −0.0750406 0.0750406i
\(616\) −7871.51 15486.7i −0.514857 1.01295i
\(617\) −6574.52 + 6574.52i −0.428979 + 0.428979i −0.888281 0.459301i \(-0.848100\pi\)
0.459301 + 0.888281i \(0.348100\pi\)
\(618\) −5135.39 + 4155.75i −0.334265 + 0.270500i
\(619\) 2395.09 + 992.077i 0.155520 + 0.0644183i 0.459085 0.888392i \(-0.348177\pi\)
−0.303566 + 0.952810i \(0.598177\pi\)
\(620\) 16881.2 3117.19i 1.09349 0.201918i
\(621\) 2993.74 + 7227.53i 0.193454 + 0.467038i
\(622\) −206.892 699.306i −0.0133370 0.0450797i
\(623\) 7941.81i 0.510726i
\(624\) 3545.02 1355.43i 0.227427 0.0869561i
\(625\) 7806.17i 0.499595i
\(626\) 14314.2 4234.91i 0.913914 0.270385i
\(627\) −682.557 1647.84i −0.0434748 0.104957i
\(628\) 6180.65 + 4253.86i 0.392730 + 0.270299i
\(629\) −4500.02 1863.97i −0.285258 0.118158i
\(630\) 15633.8 + 19319.2i 0.988676 + 1.22174i
\(631\) −2820.94 + 2820.94i −0.177971 + 0.177971i −0.790471 0.612500i \(-0.790164\pi\)
0.612500 + 0.790471i \(0.290164\pi\)
\(632\) 276.577 + 3559.39i 0.0174077 + 0.224027i
\(633\) 2642.13 + 2642.13i 0.165901 + 0.165901i
\(634\) 943.976 8952.85i 0.0591326 0.560825i
\(635\) 3750.34 9054.12i 0.234374 0.565830i
\(636\) 2749.33 + 4239.74i 0.171412 + 0.264334i
\(637\) −2991.47 + 1239.11i −0.186070 + 0.0770726i
\(638\) 1303.65 2399.14i 0.0808968 0.148876i
\(639\) 18286.2 1.13207
\(640\) −18470.0 16708.1i −1.14077 1.03194i
\(641\) 8220.77 0.506553 0.253277 0.967394i \(-0.418492\pi\)
0.253277 + 0.967394i \(0.418492\pi\)
\(642\) 3589.51 6605.85i 0.220665 0.406094i
\(643\) −21031.3 + 8711.45i −1.28988 + 0.534286i −0.918950 0.394374i \(-0.870962\pi\)
−0.370932 + 0.928660i \(0.620962\pi\)
\(644\) 9170.80 + 14142.3i 0.561149 + 0.865347i
\(645\) 4804.78 11599.8i 0.293315 0.708124i
\(646\) 993.549 9423.01i 0.0605119 0.573906i
\(647\) −14749.1 14749.1i −0.896208 0.896208i 0.0988901 0.995098i \(-0.468471\pi\)
−0.995098 + 0.0988901i \(0.968471\pi\)
\(648\) 977.539 + 12580.4i 0.0592614 + 0.762660i
\(649\) 9844.31 9844.31i 0.595413 0.595413i
\(650\) −12222.2 15103.4i −0.737530 0.911390i
\(651\) 3497.44 + 1448.69i 0.210561 + 0.0872174i
\(652\) 5317.31 + 3659.67i 0.319389 + 0.219821i
\(653\) −4279.06 10330.6i −0.256436 0.619091i 0.742262 0.670110i \(-0.233753\pi\)
−0.998698 + 0.0510191i \(0.983753\pi\)
\(654\) 3581.86 1059.71i 0.214162 0.0633606i
\(655\) 21814.8i 1.30134i
\(656\) −1458.97 3815.83i −0.0868343 0.227109i
\(657\) 20445.4i 1.21408i
\(658\) 9623.28 + 32527.1i 0.570143 + 1.92711i
\(659\) −11437.1 27611.6i −0.676063 1.63216i −0.771121 0.636689i \(-0.780304\pi\)
0.0950580 0.995472i \(-0.469696\pi\)
\(660\) 7442.03 1374.21i 0.438910 0.0810469i
\(661\) 19843.3 + 8219.36i 1.16765 + 0.483655i 0.880414 0.474205i \(-0.157265\pi\)
0.287233 + 0.957861i \(0.407265\pi\)
\(662\) −14085.7 + 11398.7i −0.826974 + 0.669218i
\(663\) −4332.06 + 4332.06i −0.253761 + 0.253761i
\(664\) −1461.00 2874.42i −0.0853883 0.167996i
\(665\) 8115.25 + 8115.25i 0.473227 + 0.473227i
\(666\) 3292.40 + 347.146i 0.191559 + 0.0201977i
\(667\) −1013.81 + 2447.56i −0.0588530 + 0.142084i
\(668\) −1750.21 + 8207.41i −0.101374 + 0.475381i
\(669\) 364.332 150.911i 0.0210551 0.00872132i
\(670\) −9099.33 4944.43i −0.524683 0.285104i
\(671\) −1409.14 −0.0810717
\(672\) −1412.73 5307.48i −0.0810972 0.304673i
\(673\) −13639.3 −0.781216 −0.390608 0.920557i \(-0.627735\pi\)
−0.390608 + 0.920557i \(0.627735\pi\)
\(674\) 28041.4 + 15237.3i 1.60254 + 0.870797i
\(675\) −12056.2 + 4993.82i −0.687469 + 0.284759i
\(676\) −4531.43 966.319i −0.257819 0.0549795i
\(677\) −10163.0 + 24535.6i −0.576951 + 1.39288i 0.318586 + 0.947894i \(0.396792\pi\)
−0.895537 + 0.444988i \(0.853208\pi\)
\(678\) −3833.39 404.187i −0.217139 0.0228948i
\(679\) 11479.4 + 11479.4i 0.648806 + 0.648806i
\(680\) 38223.4 + 12461.5i 2.15559 + 0.702758i
\(681\) 814.433 814.433i 0.0458284 0.0458284i
\(682\) −10234.5 + 8282.13i −0.574632 + 0.465014i
\(683\) −12279.3 5086.25i −0.687928 0.284949i 0.0112089 0.999937i \(-0.496432\pi\)
−0.699136 + 0.714988i \(0.746432\pi\)
\(684\) 1169.46 + 6333.22i 0.0653735 + 0.354030i
\(685\) −8805.43 21258.2i −0.491151 1.18574i
\(686\) −4334.67 14651.4i −0.241252 0.815442i
\(687\) 5406.62i 0.300255i
\(688\) 23016.2 21783.8i 1.27541 1.20712i
\(689\) 17232.1i 0.952817i
\(690\) −7041.01 + 2083.11i −0.388473 + 0.114931i
\(691\) 12427.1 + 30001.7i 0.684153 + 1.65169i 0.756241 + 0.654293i \(0.227034\pi\)
−0.0720884 + 0.997398i \(0.522966\pi\)
\(692\) −407.643 + 592.284i −0.0223934 + 0.0325365i
\(693\) −17609.6 7294.15i −0.965273 0.399829i
\(694\) −22334.4 27599.4i −1.22162 1.50959i
\(695\) 17295.3 17295.3i 0.943956 0.943956i
\(696\) 561.278 655.853i 0.0305678 0.0357185i
\(697\) 4662.99 + 4662.99i 0.253405 + 0.253405i
\(698\) −1666.50 + 15805.4i −0.0903693 + 0.857080i
\(699\) −76.1625 + 183.873i −0.00412122 + 0.00994950i
\(700\) −23590.6 + 15297.7i −1.27377 + 0.825999i
\(701\) −24563.9 + 10174.7i −1.32349 + 0.548207i −0.928791 0.370605i \(-0.879150\pi\)
−0.394697 + 0.918811i \(0.629150\pi\)
\(702\) 4150.40 7638.06i 0.223144 0.410655i
\(703\) 1528.83 0.0820214
\(704\) 18564.8 + 4495.98i 0.993872 + 0.240694i
\(705\) −14776.8 −0.789399
\(706\) 13436.3 24727.0i 0.716261 1.31815i
\(707\) 29077.0 12044.1i 1.54675 0.640685i
\(708\) 3692.94 2394.75i 0.196030 0.127119i
\(709\) −4032.81 + 9736.05i −0.213618 + 0.515720i −0.993974 0.109616i \(-0.965038\pi\)
0.780356 + 0.625336i \(0.215038\pi\)
\(710\) −3757.01 + 35632.2i −0.198589 + 1.88345i
\(711\) 2769.78 + 2769.78i 0.146097 + 0.146097i
\(712\) 6634.44 + 5677.74i 0.349208 + 0.298852i
\(713\) 9032.67 9032.67i 0.474440 0.474440i
\(714\) 5577.11 + 6891.82i 0.292322 + 0.361232i
\(715\) 23843.2 + 9876.17i 1.24711 + 0.516570i
\(716\) −16626.5 + 24157.5i −0.867824 + 1.26090i
\(717\) −1247.08 3010.72i −0.0649555 0.156816i
\(718\) −12661.9 + 3746.07i −0.658130 + 0.194710i
\(719\) 2159.37i 0.112004i −0.998431 0.0560021i \(-0.982165\pi\)
0.998431 0.0560021i \(-0.0178353\pi\)
\(720\) −27315.8 751.448i −1.41389 0.0388956i
\(721\) 32601.4i 1.68397i
\(722\) −4660.06 15751.2i −0.240207 0.811911i
\(723\) 1709.07 + 4126.06i 0.0879129 + 0.212241i
\(724\) −793.828 4298.98i −0.0407491 0.220677i
\(725\) −4082.75 1691.13i −0.209144 0.0866303i
\(726\) −197.242 + 159.615i −0.0100831 + 0.00815962i
\(727\) −15999.3 + 15999.3i −0.816204 + 0.816204i −0.985556 0.169352i \(-0.945833\pi\)
0.169352 + 0.985556i \(0.445833\pi\)
\(728\) 5805.45 17807.2i 0.295555 0.906564i
\(729\) 7638.74 + 7638.74i 0.388088 + 0.388088i
\(730\) 39839.5 + 4200.62i 2.01990 + 0.212975i
\(731\) −19576.2 + 47261.2i −0.990497 + 2.39127i
\(732\) −435.703 92.9128i −0.0220001 0.00469147i
\(733\) −2232.08 + 924.559i −0.112475 + 0.0465885i −0.438211 0.898872i \(-0.644388\pi\)
0.325737 + 0.945461i \(0.394388\pi\)
\(734\) −26395.7 14343.0i −1.32736 0.721268i
\(735\) −2041.22 −0.102437
\(736\) −18370.6 2449.44i −0.920037 0.122673i
\(737\) 7942.43 0.396965
\(738\) −3938.36 2140.04i −0.196440 0.106742i
\(739\) −15900.0 + 6585.99i −0.791462 + 0.327834i −0.741531 0.670919i \(-0.765900\pi\)
−0.0499305 + 0.998753i \(0.515900\pi\)
\(740\) −1352.89 + 6344.19i −0.0672069 + 0.315158i
\(741\) 735.886 1776.59i 0.0364824 0.0880762i
\(742\) 24799.5 + 2614.82i 1.22698 + 0.129371i
\(743\) −6184.20 6184.20i −0.305352 0.305352i 0.537751 0.843103i \(-0.319274\pi\)
−0.843103 + 0.537751i \(0.819274\pi\)
\(744\) −3710.59 + 1886.00i −0.182845 + 0.0929358i
\(745\) 32093.4 32093.4i 1.57827 1.57827i
\(746\) −1255.67 + 1016.13i −0.0616265 + 0.0498704i
\(747\) −3268.45 1353.84i −0.160089 0.0663110i
\(748\) −30321.2 + 5598.97i −1.48216 + 0.273688i
\(749\) −14198.1 34277.2i −0.692639 1.67218i
\(750\) −931.509 3148.54i −0.0453518 0.153291i
\(751\) 11095.5i 0.539122i −0.962983 0.269561i \(-0.913121\pi\)
0.962983 0.269561i \(-0.0868786\pi\)
\(752\) −34052.4 15215.1i −1.65128 0.737817i
\(753\) 517.413i 0.0250406i
\(754\) 2822.84 835.147i 0.136342 0.0403372i
\(755\) 8125.36 + 19616.3i 0.391672 + 0.945579i
\(756\) −10362.5 7132.04i −0.498519 0.343108i
\(757\) 25020.9 + 10364.0i 1.20132 + 0.497604i 0.891426 0.453167i \(-0.149706\pi\)
0.309896 + 0.950771i \(0.399706\pi\)
\(758\) 16691.3 + 20626.0i 0.799808 + 0.988349i
\(759\) 3982.03 3982.03i 0.190433 0.190433i
\(760\) −12581.1 + 977.593i −0.600478 + 0.0466593i
\(761\) 2393.12 + 2393.12i 0.113995 + 0.113995i 0.761804 0.647808i \(-0.224314\pi\)
−0.647808 + 0.761804i \(0.724314\pi\)
\(762\) −249.166 + 2363.14i −0.0118456 + 0.112346i
\(763\) 7054.25 17030.5i 0.334706 0.808053i
\(764\) 77.0065 + 118.752i 0.00364660 + 0.00562340i
\(765\) 40752.6 16880.3i 1.92603 0.797788i
\(766\) −5874.59 + 10811.1i −0.277098 + 0.509950i
\(767\) 15009.7 0.706608
\(768\) 5443.76 + 2614.24i 0.255774 + 0.122830i
\(769\) −33544.1 −1.57299 −0.786496 0.617595i \(-0.788107\pi\)
−0.786496 + 0.617595i \(0.788107\pi\)
\(770\) 17831.2 32815.2i 0.834537 1.53581i
\(771\) 10161.0 4208.82i 0.474630 0.196598i
\(772\) 14458.0 + 22295.6i 0.674034 + 1.03943i
\(773\) 9560.71 23081.6i 0.444857 1.07398i −0.529366 0.848394i \(-0.677570\pi\)
0.974223 0.225587i \(-0.0724300\pi\)
\(774\) 3645.89 34578.3i 0.169313 1.60580i
\(775\) 15067.3 + 15067.3i 0.698365 + 0.698365i
\(776\) −17796.5 + 1382.85i −0.823270 + 0.0639710i
\(777\) −1011.51 + 1011.51i −0.0467023 + 0.0467023i
\(778\) −3549.01 4385.63i −0.163545 0.202098i
\(779\) −1912.30 792.101i −0.0879529 0.0364313i
\(780\) 6721.09 + 4625.83i 0.308530 + 0.212348i
\(781\) −10515.9 25387.7i −0.481804 1.16318i
\(782\) 28687.3 8487.26i 1.31184 0.388112i
\(783\) 1977.17i 0.0902406i
\(784\) −4703.88 2101.76i −0.214280 0.0957435i
\(785\) 16130.0i 0.733381i
\(786\) 1500.61 + 5072.13i 0.0680979 + 0.230174i
\(787\) −6144.82 14834.9i −0.278321 0.671927i 0.721468 0.692448i \(-0.243468\pi\)
−0.999789 + 0.0205203i \(0.993468\pi\)
\(788\) 6381.08 1178.30i 0.288473 0.0532679i
\(789\) −8075.74 3345.08i −0.364390 0.150935i
\(790\) −5966.20 + 4828.07i −0.268694 + 0.217437i
\(791\) −13450.9 + 13450.9i −0.604624 + 0.604624i
\(792\) 18682.8 9496.04i 0.838214 0.426044i
\(793\) −1074.26 1074.26i −0.0481060 0.0481060i
\(794\) 13790.6 + 1454.06i 0.616384 + 0.0649906i
\(795\) −4157.17 + 10036.3i −0.185458 + 0.447736i
\(796\) 4502.89 21115.7i 0.200503 0.940235i
\(797\) −15066.3 + 6240.66i −0.669605 + 0.277359i −0.691474 0.722401i \(-0.743038\pi\)
0.0218691 + 0.999761i \(0.493038\pi\)
\(798\) −2445.10 1328.63i −0.108466 0.0589385i
\(799\) 60205.5 2.66573
\(800\) 4085.88 30643.7i 0.180572 1.35427i
\(801\) 9580.85 0.422625
\(802\) −37260.5 20246.8i −1.64054 0.891445i
\(803\) −28385.3 + 11757.6i −1.24744 + 0.516708i
\(804\) 2455.79 + 523.692i 0.107723 + 0.0229716i
\(805\) −13866.8 + 33477.5i −0.607132 + 1.46575i
\(806\) −14116.2 1488.39i −0.616902 0.0650452i
\(807\) 3474.60 + 3474.60i 0.151563 + 0.151563i
\(808\) −10726.2 + 32900.9i −0.467015 + 1.43249i
\(809\) 2211.65 2211.65i 0.0961154 0.0961154i −0.657414 0.753529i \(-0.728350\pi\)
0.753529 + 0.657414i \(0.228350\pi\)
\(810\) −21087.0 + 17064.4i −0.914720 + 0.740225i
\(811\) 19941.1 + 8259.86i 0.863410 + 0.357636i 0.770040 0.637995i \(-0.220236\pi\)
0.0933697 + 0.995632i \(0.470236\pi\)
\(812\) −773.556 4189.20i −0.0334317 0.181049i
\(813\) −670.782 1619.41i −0.0289365 0.0698588i
\(814\) −1411.41 4770.65i −0.0607740 0.205419i
\(815\) 13876.9i 0.596425i
\(816\) −9744.47 268.067i −0.418045 0.0115003i
\(817\) 16056.5i 0.687571i
\(818\) 32413.7 9589.71i 1.38547 0.409898i
\(819\) −7864.04 18985.5i −0.335521 0.810020i
\(820\) 4979.20 7234.52i 0.212050 0.308098i
\(821\) −13446.8 5569.86i −0.571617 0.236772i 0.0781027 0.996945i \(-0.475114\pi\)
−0.649720 + 0.760174i \(0.725114\pi\)
\(822\) 3509.66 + 4337.00i 0.148921 + 0.184027i
\(823\) 23548.4 23548.4i 0.997383 0.997383i −0.00261392 0.999997i \(-0.500832\pi\)
0.999997 + 0.00261392i \(0.000832037\pi\)
\(824\) −27234.6 23307.4i −1.15141 0.985376i
\(825\) 6642.39 + 6642.39i 0.280313 + 0.280313i
\(826\) 2277.59 21601.1i 0.0959413 0.909926i
\(827\) −6650.02 + 16054.6i −0.279618 + 0.675057i −0.999825 0.0187017i \(-0.994047\pi\)
0.720207 + 0.693759i \(0.244047\pi\)
\(828\) −17061.0 + 11063.5i −0.716074 + 0.464351i
\(829\) 1367.19 566.309i 0.0572792 0.0237258i −0.353860 0.935298i \(-0.615131\pi\)
0.411139 + 0.911573i \(0.365131\pi\)
\(830\) 3309.59 6090.69i 0.138406 0.254712i
\(831\) −6116.00 −0.255309
\(832\) 10725.4 + 17580.4i 0.446918 + 0.732563i
\(833\) 8316.57 0.345921
\(834\) −2831.59 + 5211.03i −0.117566 + 0.216359i
\(835\) −16667.7 + 6903.97i −0.690788 + 0.286134i
\(836\) 8120.20 5265.69i 0.335937 0.217844i
\(837\) −3648.36 + 8807.91i −0.150664 + 0.363735i
\(838\) −1007.02 + 9550.75i −0.0415117 + 0.393705i
\(839\) −10926.4 10926.4i −0.449609 0.449609i 0.445616 0.895224i \(-0.352985\pi\)
−0.895224 + 0.445616i \(0.852985\pi\)
\(840\) 7677.10 8970.69i 0.315339 0.368474i
\(841\) −16772.2 + 16772.2i −0.687694 + 0.687694i
\(842\) −15966.5 19730.3i −0.653494 0.807544i
\(843\) −443.149 183.558i −0.0181054 0.00749951i
\(844\) −11494.9 + 16701.5i −0.468804 + 0.681148i
\(845\) −3811.78 9202.46i −0.155183 0.374644i
\(846\) −39240.1 + 11609.3i −1.59468 + 0.471793i
\(847\) 1252.17i 0.0507969i
\(848\) −19914.0 + 18847.6i −0.806425 + 0.763244i
\(849\) 1563.20i 0.0631905i
\(850\) 14157.5 + 47853.1i 0.571292 + 1.93100i
\(851\) 1847.23 + 4459.60i 0.0744091 + 0.179640i
\(852\) −1577.55 8543.22i −0.0634342 0.343528i
\(853\) −8874.25 3675.84i −0.356212 0.147548i 0.197399 0.980323i \(-0.436751\pi\)
−0.553611 + 0.832775i \(0.686751\pi\)
\(854\) −1709.02 + 1383.01i −0.0684797 + 0.0554162i
\(855\) −9790.08 + 9790.08i −0.391595 + 0.391595i
\(856\) 38785.0 + 12644.6i 1.54865 + 0.504886i
\(857\) −16585.9 16585.9i −0.661100 0.661100i 0.294539 0.955639i \(-0.404834\pi\)
−0.955639 + 0.294539i \(0.904834\pi\)
\(858\) −6223.11 656.156i −0.247615 0.0261081i
\(859\) 8809.72 21268.5i 0.349923 0.844788i −0.646706 0.762740i \(-0.723854\pi\)
0.996628 0.0820486i \(-0.0261463\pi\)
\(860\) 66629.5 + 14208.6i 2.64192 + 0.563383i
\(861\) 1789.29 741.148i 0.0708233 0.0293360i
\(862\) 38210.9 + 20763.2i 1.50983 + 0.820415i
\(863\) −19940.2 −0.786527 −0.393263 0.919426i \(-0.628654\pi\)
−0.393263 + 0.919426i \(0.628654\pi\)
\(864\) 13366.3 3557.81i 0.526309 0.140092i
\(865\) −1545.72 −0.0607584
\(866\) 31122.3 + 16911.3i 1.22122 + 0.663592i
\(867\) 7845.74 3249.81i 0.307330 0.127300i
\(868\) −4284.03 + 20089.4i −0.167522 + 0.785576i
\(869\) 2252.60 5438.25i 0.0879333 0.212290i
\(870\) 1845.55 + 194.592i 0.0719194 + 0.00758308i
\(871\) 6054.94 + 6054.94i 0.235550 + 0.235550i
\(872\) 9183.73 + 18068.4i 0.356652 + 0.701688i
\(873\) −13848.5 + 13848.5i −0.536887 + 0.536887i
\(874\) −7299.46 + 5906.99i −0.282504 + 0.228612i
\(875\) −14970.2 6200.86i −0.578383 0.239574i
\(876\) −9551.97 + 1763.82i −0.368414 + 0.0680296i
\(877\) 11501.0 + 27765.8i 0.442828 + 1.06908i 0.974952 + 0.222414i \(0.0713938\pi\)
−0.532125 + 0.846666i \(0.678606\pi\)
\(878\) −7591.06 25658.1i −0.291783 0.986242i
\(879\) 2367.03i 0.0908280i
\(880\) 14665.3 + 38356.0i 0.561782 + 1.46930i
\(881\) 18012.3i 0.688821i −0.938819 0.344410i \(-0.888079\pi\)
0.938819 0.344410i \(-0.111921\pi\)
\(882\) −5420.49 + 1603.67i −0.206936 + 0.0612228i
\(883\) −6581.16 15888.3i −0.250819 0.605532i 0.747451 0.664317i \(-0.231277\pi\)
−0.998271 + 0.0587851i \(0.981277\pi\)
\(884\) −27383.9 18847.1i −1.04188 0.717078i
\(885\) 8741.91 + 3621.02i 0.332041 + 0.137536i
\(886\) −5729.48 7080.11i −0.217252 0.268466i
\(887\) −2226.45 + 2226.45i −0.0842806 + 0.0842806i −0.747990 0.663710i \(-0.768981\pi\)
0.663710 + 0.747990i \(0.268981\pi\)
\(888\) −121.850 1568.14i −0.00460476 0.0592606i
\(889\) 8291.96 + 8291.96i 0.312827 + 0.312827i
\(890\) −1968.44 + 18669.1i −0.0741374 + 0.703133i
\(891\) 7961.61 19221.0i 0.299353 0.722703i
\(892\) 1164.23 + 1795.35i 0.0437009 + 0.0673910i
\(893\) −17458.7 + 7231.64i −0.654237 + 0.270994i
\(894\) −5254.34 + 9669.66i −0.196567 + 0.361747i
\(895\) −63045.1 −2.35460
\(896\) 26928.3 12767.7i 1.00403 0.476048i
\(897\) 6071.43 0.225997
\(898\) −3329.83 + 6127.95i −0.123739 + 0.227720i
\(899\) −2982.75 + 1235.49i −0.110657 + 0.0458354i
\(900\) −18454.9 28459.2i −0.683514 1.05404i
\(901\) 16937.6 40891.1i 0.626276 1.51196i
\(902\) −706.280 + 6698.50i −0.0260716 + 0.247268i
\(903\) 10623.3 + 10623.3i 0.391497 + 0.391497i
\(904\) −1620.34 20852.9i −0.0596148 0.767208i
\(905\) 6645.49 6645.49i 0.244092 0.244092i
\(906\) −3238.59 4002.03i −0.118758 0.146754i
\(907\) 43002.0 + 17812.0i 1.57427 + 0.652082i 0.987492 0.157668i \(-0.0503977\pi\)
0.586774 + 0.809751i \(0.300398\pi\)
\(908\) 5148.21 + 3543.28i 0.188160 + 0.129502i
\(909\) 14529.8 + 35077.9i 0.530167 + 1.27994i
\(910\) 38610.5 11423.1i 1.40651 0.416121i
\(911\) 13008.4i 0.473094i −0.971620 0.236547i \(-0.923984\pi\)
0.971620 0.236547i \(-0.0760156\pi\)
\(912\) 2857.96 1092.73i 0.103768 0.0396754i
\(913\) 5316.32i 0.192710i
\(914\) −817.778 2764.13i −0.0295948 0.100032i
\(915\) −366.508 884.828i −0.0132419 0.0319689i
\(916\) 28849.3 5327.16i 1.04062 0.192155i
\(917\) 24116.2 + 9989.25i 0.868469 + 0.359732i
\(918\) −17356.3 + 14045.3i −0.624011 + 0.504973i
\(919\) −16677.5 + 16677.5i −0.598628 + 0.598628i −0.939947 0.341319i \(-0.889126\pi\)
0.341319 + 0.939947i \(0.389126\pi\)
\(920\) −18052.8 35517.7i −0.646939 1.27281i
\(921\) −5879.06 5879.06i −0.210338 0.210338i
\(922\) 696.182 + 73.4044i 0.0248672 + 0.00262196i
\(923\) 11337.5 27371.2i 0.404312 0.976095i
\(924\) −1888.61 + 8856.39i −0.0672409 + 0.315318i
\(925\) −7439.02 + 3081.34i −0.264425 + 0.109529i
\(926\) 17345.5 + 9425.25i 0.615559 + 0.334485i
\(927\) −39329.8 −1.39348
\(928\) 4052.61 + 2348.72i 0.143355 + 0.0830823i
\(929\) 24373.6 0.860786 0.430393 0.902642i \(-0.358375\pi\)
0.430393 + 0.902642i \(0.358375\pi\)
\(930\) −7862.47 4272.34i −0.277226 0.150640i
\(931\) −2411.69 + 998.953i −0.0848978 + 0.0351658i
\(932\) −1056.17 225.226i −0.0371202 0.00791581i
\(933\) −145.473 + 351.203i −0.00510458 + 0.0123235i
\(934\) 5848.81 + 616.690i 0.204902 + 0.0216046i
\(935\) −46871.5 46871.5i −1.63942 1.63942i
\(936\) 21482.3 + 7003.58i 0.750181 + 0.244572i
\(937\) −3495.17 + 3495.17i −0.121859 + 0.121859i −0.765406 0.643547i \(-0.777462\pi\)
0.643547 + 0.765406i \(0.277462\pi\)
\(938\) 9632.72 7795.15i 0.335309 0.271344i
\(939\) −7188.83 2977.71i −0.249839 0.103487i
\(940\) −14559.6 78847.8i −0.505195 2.73588i
\(941\) 15711.1 + 37929.9i 0.544279 + 1.31401i 0.921678 + 0.387955i \(0.126818\pi\)
−0.377400 + 0.926050i \(0.623182\pi\)
\(942\) −1109.56 3750.36i −0.0383772 0.129717i
\(943\) 6535.24i 0.225680i
\(944\) 16416.9 + 17345.7i 0.566021 + 0.598044i
\(945\) 27043.6i 0.930928i
\(946\) −50103.4 + 14823.3i −1.72199 + 0.509457i
\(947\) 3104.11 + 7493.99i 0.106515 + 0.257151i 0.968147 0.250384i \(-0.0805568\pi\)
−0.861631 + 0.507535i \(0.830557\pi\)
\(948\) 1055.08 1532.97i 0.0361469 0.0525197i
\(949\) −30603.1 12676.2i −1.04681 0.433601i
\(950\) −9853.39 12176.2i −0.336512 0.415839i
\(951\) −3318.20 + 3318.20i −0.113144 + 0.113144i
\(952\) −31279.0 + 36549.5i −1.06487 + 1.24430i
\(953\) −16440.0 16440.0i −0.558808 0.558808i 0.370160 0.928968i \(-0.379303\pi\)
−0.928968 + 0.370160i \(0.879303\pi\)
\(954\) −3154.47 + 29917.6i −0.107054 + 1.01532i
\(955\) −116.439 + 281.108i −0.00394541 + 0.00952506i
\(956\) 14836.2 9620.79i 0.501921 0.325480i
\(957\) −1314.94 + 544.665i −0.0444158 + 0.0183976i
\(958\) 1314.98 2419.99i 0.0443478 0.0816141i
\(959\) 27532.9 0.927095
\(960\) 2005.46 + 12826.6i 0.0674227 + 0.431226i
\(961\) −14223.7 −0.477449
\(962\) 2560.92 4712.92i 0.0858290 0.157953i
\(963\) 41351.4 17128.3i 1.38373 0.573159i
\(964\) −20332.4 + 13184.9i −0.679317 + 0.440515i
\(965\) −21861.4 + 52778.0i −0.729267 + 1.76061i
\(966\) 921.288 8737.67i 0.0306853 0.291025i
\(967\) 25408.6 + 25408.6i 0.844968 + 0.844968i 0.989500 0.144532i \(-0.0461677\pi\)
−0.144532 + 0.989500i \(0.546168\pi\)
\(968\) −1046.04 895.197i −0.0347324 0.0297239i
\(969\) −3492.45 + 3492.45i −0.115783 + 0.115783i
\(970\) −24139.8 29830.3i −0.799052 0.987415i
\(971\) −33005.6 13671.4i −1.09083 0.451838i −0.236536 0.971623i \(-0.576012\pi\)
−0.854297 + 0.519785i \(0.826012\pi\)
\(972\) 13086.4 19013.8i 0.431837 0.627437i
\(973\) 11200.2 + 27039.6i 0.369025 + 0.890905i
\(974\) −43649.0 + 12913.7i −1.43594 + 0.424828i
\(975\) 10127.7i 0.332662i
\(976\) 66.4749 2416.42i 0.00218013 0.0792498i
\(977\) 23994.9i 0.785738i −0.919594 0.392869i \(-0.871483\pi\)
0.919594 0.392869i \(-0.128517\pi\)
\(978\) −954.570 3226.49i −0.0312104 0.105493i
\(979\) −5509.70 13301.6i −0.179868 0.434239i
\(980\) −2011.22 10891.8i −0.0655571 0.355025i
\(981\) 20545.2 + 8510.11i 0.668663 + 0.276969i
\(982\) −3318.83 + 2685.72i −0.107849 + 0.0872757i
\(983\) 11434.9 11434.9i 0.371023 0.371023i −0.496827 0.867850i \(-0.665502\pi\)
0.867850 + 0.496827i \(0.165502\pi\)
\(984\) −660.053 + 2024.60i −0.0213839 + 0.0655913i
\(985\) 9864.06 + 9864.06i 0.319081 + 0.319081i
\(986\) −7519.35 792.830i −0.242865 0.0256074i
\(987\) 6766.46 16335.7i 0.218215 0.526819i
\(988\) 10204.8 + 2176.15i 0.328600 + 0.0700734i
\(989\) 46836.7 19400.4i 1.50589 0.623758i
\(990\) 39587.6 + 21511.3i 1.27089 + 0.690579i
\(991\) 49651.4 1.59155 0.795777 0.605590i \(-0.207063\pi\)
0.795777 + 0.605590i \(0.207063\pi\)
\(992\) −13719.6 17941.1i −0.439111 0.574224i
\(993\) 9445.29 0.301850
\(994\) −37670.8 20469.7i −1.20206 0.653179i
\(995\) 42881.9 17762.3i 1.36628 0.565932i
\(996\) −350.537 + 1643.80i −0.0111518 + 0.0522949i
\(997\) 13807.6 33334.5i 0.438607 1.05889i −0.537823 0.843058i \(-0.680753\pi\)
0.976430 0.215833i \(-0.0692468\pi\)
\(998\) 39909.5 + 4208.00i 1.26585 + 0.133469i
\(999\) −2547.37 2547.37i −0.0806760 0.0806760i
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.21.8 44
4.3 odd 2 128.4.g.a.49.6 44
8.3 odd 2 256.4.g.a.97.6 44
8.5 even 2 256.4.g.b.97.6 44
32.3 odd 8 128.4.g.a.81.6 44
32.13 even 8 256.4.g.b.161.6 44
32.19 odd 8 256.4.g.a.161.6 44
32.29 even 8 inner 32.4.g.a.29.8 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.g.a.21.8 44 1.1 even 1 trivial
32.4.g.a.29.8 yes 44 32.29 even 8 inner
128.4.g.a.49.6 44 4.3 odd 2
128.4.g.a.81.6 44 32.3 odd 8
256.4.g.a.97.6 44 8.3 odd 2
256.4.g.a.161.6 44 32.19 odd 8
256.4.g.b.97.6 44 8.5 even 2
256.4.g.b.161.6 44 32.13 even 8