Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,10,Mod(1,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 13.a (trivial) |
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: | yes |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Fricke sign: | |
Sato-Tate group: |
Embedding invariants
Embedding label | 1.2 | ||
Root | of defining polynomial | ||
Character | 13.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−24.5360 | −1.08435 | −0.542175 | − | 0.840266i | ||||||
−0.542175 | + | 0.840266i | ||||||||
49.9972 | 0.356369 | 0.178185 | − | 0.983997i | ||||||
0.178185 | + | 0.983997i | ||||||||
90.0171 | 0.175815 | |||||||||
1814.98 | 1.29869 | 0.649346 | − | 0.760493i | ||||||
0.649346 | + | 0.760493i | ||||||||
−1226.73 | −0.386429 | |||||||||
−8707.31 | −1.37070 | −0.685351 | − | 0.728213i | ||||||
−0.685351 | + | 0.728213i | ||||||||
10353.8 | 0.893705 | |||||||||
−17183.3 | −0.873001 | |||||||||
−44532.3 | −1.40824 | |||||||||
−82919.7 | −1.70762 | −0.853809 | − | 0.520587i | ||||||
−0.853809 | + | 0.520587i | ||||||||
4500.61 | 0.0626550 | |||||||||
−28561.0 | −0.277350 | |||||||||
213643. | 1.48632 | |||||||||
90743.8 | 0.462814 | |||||||||
−300130. | −1.14490 | |||||||||
374907. | 1.08869 | 0.544344 | − | 0.838862i | ||||||
0.544344 | + | 0.838862i | ||||||||
421610. | 0.946638 | |||||||||
−361501. | −0.636383 | −0.318191 | − | 0.948026i | ||||||
−0.318191 | + | 0.948026i | ||||||||
163379. | 0.228329 | |||||||||
−435341. | −0.488476 | |||||||||
2.03452e6 | 1.85165 | |||||||||
−2.31340e6 | −1.72376 | −0.861878 | − | 0.507116i | ||||||
−0.861878 | + | 0.507116i | ||||||||
517661. | 0.318489 | |||||||||
1.34101e6 | 0.686599 | |||||||||
700774. | 0.300745 | |||||||||
−1.84321e6 | −0.667480 | |||||||||
−783807. | −0.240989 | |||||||||
−649654. | −0.170565 | −0.0852827 | − | 0.996357i | ||||||
−0.0852827 | + | 0.996357i | ||||||||
−2.22649e6 | −0.501852 | |||||||||
4.32521e6 | 0.841162 | 0.420581 | − | 0.907255i | ||||||
0.420581 | + | 0.907255i | ||||||||
2.06285e6 | 0.347771 | |||||||||
−4.14575e6 | −0.608542 | |||||||||
−9.19873e6 | −1.18052 | |||||||||
−1.58036e7 | −1.78012 | |||||||||
−1.54679e6 | −0.153486 | |||||||||
1.21021e7 | 1.06158 | 0.530790 | − | 0.847503i | ||||||
0.530790 | + | 0.847503i | ||||||||
8.86981e6 | 0.690062 | |||||||||
−1.42797e6 | −0.0988391 | |||||||||
1.87919e7 | 1.16065 | |||||||||
2.59960e6 | 0.143674 | 0.0718372 | − | 0.997416i | ||||||
0.0718372 | + | 0.997416i | ||||||||
1.06816e7 | 0.529679 | |||||||||
3.08318e6 | 0.137528 | 0.0687640 | − | 0.997633i | ||||||
0.0687640 | + | 0.997633i | ||||||||
−7.46419e6 | −0.300224 | |||||||||
−3.11872e7 | −1.13376 | |||||||||
5.67617e7 | 1.86915 | |||||||||
2.60298e7 | 0.778090 | 0.389045 | − | 0.921219i | ||||||
0.389045 | + | 0.921219i | ||||||||
−1.50057e7 | −0.408009 | |||||||||
3.54636e7 | 0.878822 | |||||||||
−3.29032e7 | −0.744513 | |||||||||
1.87443e7 | 0.387975 | |||||||||
−2.57098e6 | −0.0487622 | |||||||||
−1.01982e8 | −1.77535 | −0.887673 | − | 0.460475i | ||||||
−0.887673 | + | 0.460475i | ||||||||
4.52251e7 | 0.723782 | |||||||||
−1.50497e8 | −2.21767 | |||||||||
−9.01536e7 | −1.22500 | |||||||||
−1.80741e7 | −0.226787 | |||||||||
1.59399e7 | 0.184953 | |||||||||
1.37562e8 | 1.47797 | 0.738985 | − | 0.673722i | ||||||
0.738985 | + | 0.673722i | ||||||||
8.16850e6 | 0.0813695 | |||||||||
−4.29579e7 | −0.397245 | −0.198623 | − | 0.980076i | ||||||
−0.198623 | + | 0.980076i | ||||||||
−1.06124e8 | −0.912114 | |||||||||
1.49620e8 | 1.19662 | |||||||||
1.03052e8 | 0.767798 | |||||||||
−5.18375e7 | −0.360192 | |||||||||
1.01720e8 | 0.659873 | |||||||||
5.54479e7 | 0.336162 | 0.168081 | − | 0.985773i | ||||||
0.168081 | + | 0.985773i | ||||||||
3.37480e7 | 0.191407 | |||||||||
−1.15664e8 | −0.614294 | |||||||||
3.87757e8 | 1.93027 | |||||||||
−1.43613e8 | −0.670706 | −0.335353 | − | 0.942093i | ||||||
−0.335353 | + | 0.942093i | ||||||||
−1.77912e8 | −0.780205 | |||||||||
3.37147e7 | 0.138952 | 0.0694762 | − | 0.997584i | ||||||
0.0694762 | + | 0.997584i | ||||||||
−2.96937e8 | −1.15112 | |||||||||
6.70469e7 | 0.244683 | |||||||||
−3.25413e7 | −0.111886 | |||||||||
7.22007e8 | 2.34063 | |||||||||
3.50367e7 | 0.107176 | |||||||||
−2.66652e8 | −0.770236 | −0.385118 | − | 0.922867i | ||||||
−0.385118 | + | 0.922867i | ||||||||
−5.44728e8 | −1.48688 | |||||||||
2.46063e8 | 0.635132 | |||||||||
−6.37839e7 | −0.155793 | |||||||||
−9.89542e7 | −0.228867 | −0.114433 | − | 0.993431i | ||||||
−0.114433 | + | 0.993431i | ||||||||
−3.91882e7 | −0.0858812 | |||||||||
6.80447e8 | 1.41387 | |||||||||
−7.56490e7 | −0.149128 | |||||||||
−3.24809e7 | −0.0607843 | |||||||||
−8.58533e8 | −1.52611 | |||||||||
−5.08803e8 | −0.859597 | −0.429798 | − | 0.902925i | ||||||
−0.429798 | + | 0.902925i | ||||||||
7.65211e8 | 1.22939 | |||||||||
2.48689e8 | 0.380164 | |||||||||
−2.08246e8 | −0.303062 | |||||||||
2.16249e8 | 0.299764 | |||||||||
−6.38667e8 | −0.843722 | |||||||||
−6.56116e8 | −0.826465 | |||||||||
1.03137e8 | 0.123935 | |||||||||
−4.53920e8 | −0.520603 | −0.260301 | − | 0.965527i | ||||||
−0.260301 | + | 0.965527i | ||||||||
−8.70137e8 | −0.952950 | |||||||||
1.42483e9 | 1.49075 | |||||||||
1.20714e8 | 0.120714 | |||||||||
6.44663e8 | 0.616434 | 0.308217 | − | 0.951316i | ||||||
0.308217 | + | 0.951316i | ||||||||
−4.59911e8 | −0.420700 | |||||||||
−1.14825e9 | −1.00524 | −0.502620 | − | 0.864507i | ||||||
−0.502620 | + | 0.864507i | ||||||||
−2.95715e8 | −0.247869 | |||||||||
−7.90134e8 | −0.634379 | |||||||||
2.50224e9 | 1.92510 | |||||||||
5.95299e8 | 0.439044 | 0.219522 | − | 0.975607i | ||||||
0.219522 | + | 0.975607i | ||||||||
−1.65921e8 | −0.117353 | |||||||||
1.00898e9 | 0.684645 | 0.342322 | − | 0.939583i | ||||||
0.342322 | + | 0.939583i | ||||||||
3.69261e9 | 2.40473 | |||||||||
6.05071e8 | 0.378315 | |||||||||
2.61332e9 | 1.56932 | |||||||||
−1.59931e9 | −0.922739 | −0.461370 | − | 0.887208i | ||||||
−0.461370 | + | 0.887208i | ||||||||
4.43466e8 | 0.245917 | |||||||||
−4.19877e9 | −2.23863 | |||||||||
−5.84800e7 | −0.0299879 | |||||||||
4.90772e8 | 0.242127 | |||||||||
−3.37524e9 | −1.60264 | |||||||||
−3.26443e9 | −1.49226 | |||||||||
9.39542e8 | 0.413619 | |||||||||
4.51772e9 | 1.91596 | |||||||||
1.05402e9 | 0.430753 | |||||||||
1.29973e8 | 0.0512011 | |||||||||
3.89343e8 | 0.147889 | |||||||||
−1.11097e9 | −0.407011 | |||||||||
−3.67108e9 | −1.29756 | |||||||||
−1.58816e9 | −0.541723 | −0.270861 | − | 0.962618i | ||||||
−0.270861 | + | 0.962618i | ||||||||
−3.58467e9 | −1.18033 | |||||||||
1.54151e8 | 0.0490107 | |||||||||
1.27189e9 | 0.390574 | |||||||||
−3.54703e9 | −1.05231 | −0.526156 | − | 0.850388i | ||||||
−0.526156 | + | 0.850388i | ||||||||
−3.73189e8 | −0.106991 | |||||||||
3.14770e9 | 0.872291 | |||||||||
−1.36047e9 | −0.364517 | |||||||||
−3.34539e9 | −0.866850 | |||||||||
3.88170e9 | 0.972965 | |||||||||
−3.79917e9 | −0.921395 | −0.460697 | − | 0.887557i | ||||||
−0.460697 | + | 0.887557i | ||||||||
2.83793e9 | 0.666109 | |||||||||
3.81526e9 | 0.866878 | 0.433439 | − | 0.901183i | ||||||
0.433439 | + | 0.901183i | ||||||||
−1.42259e9 | −0.312971 | |||||||||
1.30142e9 | 0.277287 | |||||||||
3.52370e9 | 0.727280 | |||||||||
2.36827e9 | 0.473608 | |||||||||
5.15721e9 | 0.999502 | |||||||||
−1.17911e9 | −0.221512 | |||||||||
−8.27225e8 | −0.150673 | |||||||||
1.77308e9 | 0.313185 | |||||||||
1.08940e9 | 0.186641 | |||||||||
1.16149e10 | 1.93054 | 0.965269 | − | 0.261258i | ||||||
0.965269 | + | 0.261258i | ||||||||
−1.64507e9 | −0.265322 | |||||||||
3.19196e9 | 0.499645 | 0.249822 | − | 0.968292i | ||||||
0.249822 | + | 0.968292i | ||||||||
−3.74291e9 | −0.568739 | |||||||||
−6.44213e9 | −0.950425 | |||||||||
−1.77152e10 | −2.53806 | |||||||||
7.85016e9 | 1.09241 | |||||||||
−1.28542e8 | −0.0173774 | |||||||||
−5.05861e9 | −0.664481 | −0.332240 | − | 0.943195i | ||||||
−0.332240 | + | 0.943195i | ||||||||
6.54260e9 | 0.835205 | |||||||||
−5.09883e9 | −0.632679 | |||||||||
3.74403e9 | 0.451647 | |||||||||
2.01435e10 | 2.36275 | |||||||||
−6.03741e9 | −0.688705 | |||||||||
−7.83438e9 | −0.869282 | −0.434641 | − | 0.900604i | ||||||
−0.434641 | + | 0.900604i | ||||||||
2.34009e8 | 0.0252601 | |||||||||
−7.52444e9 | −0.790308 | |||||||||
2.42794e9 | 0.248172 | |||||||||
−1.44048e8 | −0.0143312 | −0.00716559 | − | 0.999974i | ||||||
−0.00716559 | + | 0.999974i | ||||||||
−4.50743e9 | −0.436553 | |||||||||
8.15731e8 | 0.0769231 | |||||||||
−1.66955e10 | −1.53313 | |||||||||
6.21178e9 | 0.555563 | |||||||||
2.77539e8 | 0.0241794 | |||||||||
−1.36123e10 | −1.15538 | −0.577689 | − | 0.816257i | ||||||
−0.577689 | + | 0.816257i | ||||||||
7.96952e8 | 0.0659114 | |||||||||
−1.16766e10 | −0.941122 | |||||||||
2.48867e10 | 1.95506 | |||||||||
6.87774e9 | 0.526703 | |||||||||
1.24840e10 | 0.932104 | |||||||||
4.98195e8 | 0.0362711 | 0.0181355 | − | 0.999836i | ||||||
0.0181355 | + | 0.999836i | ||||||||
−2.80739e9 | −0.199331 | |||||||||
2.86758e9 | 0.198592 | 0.0992961 | − | 0.995058i | ||||||
0.0992961 | + | 0.995058i | ||||||||
−6.10185e9 | −0.412231 | |||||||||
−2.14777e9 | −0.141566 | |||||||||
−2.39525e10 | −1.54053 | |||||||||
2.19650e10 | 1.37866 | |||||||||
−5.30588e9 | −0.325049 | |||||||||
−3.10871e10 | −1.85906 | |||||||||
2.34312e9 | 0.136800 | |||||||||
1.60494e10 | 0.914916 | |||||||||
1.60985e10 | 0.896177 | |||||||||
−2.83331e10 | −1.54044 | −0.770218 | − | 0.637781i | ||||||
−0.770218 | + | 0.637781i | ||||||||
5.15232e9 | 0.273620 | |||||||||
2.44273e10 | 1.26726 | 0.633632 | − | 0.773634i | ||||||
0.633632 | + | 0.773634i | ||||||||
1.11374e10 | 0.564516 | |||||||||
−2.59173e9 | −0.128361 | |||||||||
3.19233e9 | 0.154510 | |||||||||
1.37323e10 | 0.649601 | 0.324800 | − | 0.945783i | ||||||
0.324800 | + | 0.945783i | ||||||||
−3.49597e10 | −1.61650 | |||||||||
−8.56614e9 | −0.387210 | −0.193605 | − | 0.981080i | ||||||
−0.193605 | + | 0.981080i | ||||||||
1.38846e10 | 0.613617 | |||||||||
2.77224e9 | 0.119798 | |||||||||
−1.58175e10 | −0.668430 | |||||||||
5.65673e9 | 0.233794 | |||||||||
1.68731e9 | 0.0682117 | |||||||||
4.71821e9 | 0.186589 | |||||||||
2.81736e10 | 1.09003 | |||||||||
3.97518e10 | 1.50484 | |||||||||
8.57200e9 | 0.317539 | |||||||||
2.99756e10 | 1.08670 | |||||||||
1.93868e10 | 0.687889 | |||||||||
2.70272e9 | 0.0938706 | 0.0469353 | − | 0.998898i | ||||||
0.0469353 | + | 0.998898i | ||||||||
−9.18015e9 | −0.312132 | |||||||||
−7.18027e9 | −0.239019 | |||||||||
−1.46063e10 | −0.476078 | |||||||||
5.59590e9 | 0.178606 | |||||||||
−1.90842e10 | −0.596530 | |||||||||
−3.76610e10 | −1.15298 | |||||||||
−2.47565e10 | −0.742394 | |||||||||
1.68564e9 | 0.0495184 | |||||||||
−1.35473e10 | −0.389899 | |||||||||
−1.07077e10 | −0.301947 | |||||||||
−1.48460e10 | −0.410225 | |||||||||
−3.57969e10 | −0.969333 | −0.484667 | − | 0.874699i | ||||||
−0.484667 | + | 0.874699i | ||||||||
−1.79619e10 | −0.476690 | |||||||||
−2.30430e10 | −0.599401 | |||||||||
3.92407e10 | 1.00057 | |||||||||
−7.55373e10 | −1.88819 | −0.944094 | − | 0.329675i | ||||||
−0.944094 | + | 0.329675i | ||||||||
−1.62698e9 | −0.0398726 | |||||||||
−5.69066e10 | −1.36742 | −0.683711 | − | 0.729753i | ||||||
−0.683711 | + | 0.729753i | ||||||||
1.03021e11 | 2.42745 | |||||||||
3.60984e10 | 0.834130 | |||||||||
−6.72637e9 | −0.152435 | |||||||||
−4.68000e10 | −1.04026 | −0.520132 | − | 0.854086i | ||||||
−0.520132 | + | 0.854086i | ||||||||
−1.20416e10 | −0.262550 | |||||||||
4.72434e10 | 1.01050 | |||||||||
1.23830e10 | 0.259849 | |||||||||
−1.33319e10 | −0.274488 | |||||||||
8.00961e10 | 1.61814 | |||||||||
−8.79993e9 | −0.174457 | −0.0872285 | − | 0.996188i | ||||||
−0.0872285 | + | 0.996188i | ||||||||
−2.72349e10 | −0.529877 | |||||||||
−1.76057e10 | −0.336183 | −0.168092 | − | 0.985771i | ||||||
−0.168092 | + | 0.985771i | ||||||||
−1.10847e11 | −2.07757 | |||||||||
4.85824e10 | 0.893821 | |||||||||
−3.86695e9 | −0.0698415 | |||||||||
6.43656e10 | 1.14132 | |||||||||
−3.18902e9 | −0.0555200 | |||||||||
1.03248e10 | 0.176501 | |||||||||
4.47823e10 | 0.751751 | |||||||||
−4.94743e9 | −0.0815611 | |||||||||
2.72588e10 | 0.441343 | |||||||||
−1.77113e10 | −0.281655 | −0.140828 | − | 0.990034i | ||||||
−0.140828 | + | 0.990034i | ||||||||
1.34684e10 | 0.210384 | |||||||||
1.91826e11 | 2.94351 | |||||||||
3.89671e10 | 0.587417 | |||||||||
3.40204e10 | 0.503859 | |||||||||
3.51910e10 | 0.512096 | |||||||||
−6.26733e10 | −0.896156 | −0.448078 | − | 0.893994i | ||||||
−0.448078 | + | 0.893994i | ||||||||
−3.78224e9 | −0.0531448 | |||||||||
−1.05377e11 | −1.45511 | |||||||||
−4.66627e9 | −0.0633271 | |||||||||
1.11632e10 | 0.148904 | |||||||||
8.70301e10 | 1.14107 | |||||||||
4.49501e10 | 0.579335 | 0.289667 | − | 0.957127i | ||||||
0.289667 | + | 0.957127i | ||||||||
−4.29243e10 | −0.543857 | |||||||||
−1.85095e11 | −2.30563 | |||||||||
−7.72322e10 | −0.945869 | |||||||||
−2.54388e10 | −0.306334 | |||||||||
4.99126e9 | 0.0591023 | |||||||||
−8.65536e10 | −1.00786 | −0.503930 | − | 0.863745i | ||||||
−0.503930 | + | 0.863745i | ||||||||
8.20825e10 | 0.939969 | |||||||||
8.36056e10 | 0.941615 | 0.470808 | − | 0.882236i | ||||||
0.470808 | + | 0.882236i | ||||||||
−1.12521e11 | −1.24644 | |||||||||
1.24338e10 | 0.135479 | |||||||||
9.32165e10 | 0.999114 | |||||||||
−1.11196e11 | −1.17245 | |||||||||
−1.04117e10 | −0.108002 | |||||||||
1.73137e11 | 1.76698 | 0.883489 | − | 0.468452i | ||||||
0.883489 | + | 0.468452i | ||||||||
−9.36114e10 | −0.939999 | |||||||||
−7.43213e10 | −0.734335 | |||||||||
−1.63627e11 | −1.59090 | |||||||||
7.57598e10 | 0.724871 | 0.362435 | − | 0.932009i | ||||||
0.362435 | + | 0.932009i | ||||||||
−3.19316e10 | −0.300676 | |||||||||
1.68901e11 | 1.56528 | 0.782642 | − | 0.622472i | ||||||
0.782642 | + | 0.622472i | ||||||||
−1.29277e10 | −0.117920 | |||||||||
−3.28040e10 | −0.294527 | |||||||||
−5.81079e10 | −0.513557 | |||||||||
−2.26355e10 | −0.196935 | |||||||||
−3.54466e10 | −0.303605 | |||||||||
2.19672e10 | 0.185240 | |||||||||
2.89306e10 | 0.240196 | |||||||||
−2.26947e10 | −0.185527 | |||||||||
3.03490e9 | 0.0244299 | |||||||||
−1.18842e11 | −0.942030 | −0.471015 | − | 0.882125i | ||||||
−0.471015 | + | 0.882125i | ||||||||
−4.35044e10 | −0.339602 | |||||||||
2.49672e11 | 1.91943 | |||||||||
1.25302e11 | 0.948740 | |||||||||
1.52839e11 | 1.13980 | |||||||||
−2.84984e11 | −2.09338 | |||||||||
6.60730e10 | 0.478084 | |||||||||
6.03537e9 | 0.0430188 | |||||||||
−2.68462e10 | −0.188510 | |||||||||
−7.83181e10 | −0.541790 | |||||||||
3.22313e10 | 0.219678 | |||||||||
1.08497e11 | 0.728597 | |||||||||
−7.79675e10 | −0.515899 | |||||||||
1.58064e11 | 1.03059 | |||||||||
−1.99530e11 | −1.28199 | −0.640997 | − | 0.767543i | ||||||
−0.640997 | + | 0.767543i | ||||||||
6.49930e10 | 0.411518 | |||||||||
−5.74095e10 | −0.358237 | |||||||||
−1.92612e11 | −1.18455 | |||||||||
1.90145e11 | 1.15256 | 0.576281 | − | 0.817252i | ||||||
0.576281 | + | 0.817252i | ||||||||
−1.47849e10 | −0.0883330 | |||||||||
−3.39674e10 | −0.200038 | −0.100019 | − | 0.994986i | ||||||
−0.100019 | + | 0.994986i | ||||||||
1.24118e11 | 0.720530 | |||||||||
2.71557e11 | 1.55404 | |||||||||
−2.40033e10 | −0.135419 | |||||||||
−8.53565e9 | −0.0474756 | −0.0237378 | − | 0.999718i | ||||||
−0.0237378 | + | 0.999718i | ||||||||
1.25105e11 | 0.686045 | |||||||||
5.38691e10 | 0.291260 | |||||||||
1.87037e11 | 0.997133 | |||||||||
2.97633e10 | 0.156462 | |||||||||
−4.94242e11 | −2.56205 | |||||||||
−1.35529e11 | −0.692822 | |||||||||
2.21499e10 | 0.111665 | |||||||||
−3.83007e10 | −0.190428 | |||||||||
1.92225e11 | 0.942606 | |||||||||
5.04464e10 | 0.243986 | |||||||||
2.69157e10 | 0.128403 | |||||||||
−2.26649e11 | −1.06653 | |||||||||
1.84620e11 | 0.856971 | |||||||||
5.09528e10 | 0.233315 | 0.116657 | − | 0.993172i | ||||||
0.116657 | + | 0.993172i | ||||||||
−8.90757e9 | −0.0402381 | |||||||||
−2.07954e11 | −0.926760 | |||||||||
3.53436e9 | 0.0155400 | |||||||||
1.00637e11 | 0.436571 | |||||||||
1.30659e11 | 0.559258 | |||||||||
2.31891e11 | 0.979375 | 0.489688 | − | 0.871898i | ||||||
0.489688 | + | 0.871898i | ||||||||
−2.00148e10 | −0.0834115 | |||||||||
−7.99609e10 | −0.328836 | |||||||||
6.12519e10 | 0.248579 | |||||||||
−3.58645e11 | −1.43638 | |||||||||
−1.52412e11 | −0.602425 | |||||||||
4.25786e10 | 0.166099 | |||||||||
3.19226e10 | 0.122909 | |||||||||
−2.09927e11 | −0.797778 | |||||||||
3.33992e11 | 1.25283 | |||||||||
−3.64138e10 | −0.134829 | −0.0674146 | − | 0.997725i | ||||||
−0.0674146 | + | 0.997725i | ||||||||
−2.92384e9 | −0.0106868 | |||||||||
9.86839e10 | 0.356067 | 0.178034 | − | 0.984024i | ||||||
0.178034 | + | 0.984024i | ||||||||
2.86498e11 | 1.02051 | |||||||||
5.26440e10 | 0.185126 | |||||||||
−1.71051e11 | −0.593860 | |||||||||
−3.90458e11 | −1.33841 | −0.669204 | − | 0.743078i | ||||||
−0.669204 | + | 0.743078i | ||||||||
−1.68752e11 | −0.571131 | |||||||||
−2.60655e11 | −0.871040 | |||||||||
−4.58010e10 | −0.151130 | |||||||||
−1.63212e11 | −0.531797 | |||||||||
−1.22237e10 | −0.0393305 | |||||||||
−3.86316e11 | −1.22749 | −0.613744 | − | 0.789505i | ||||||
−0.613744 | + | 0.789505i | ||||||||
−3.22906e11 | −1.01325 | |||||||||
−1.92005e11 | −0.595017 | |||||||||
−7.03591e10 | −0.215343 | |||||||||
2.25874e11 | 0.682788 | |||||||||
2.23863e10 | 0.0668385 | |||||||||
6.11914e10 | 0.180456 | |||||||||
5.26979e10 | 0.153507 | |||||||||
1.48155e11 | 0.426305 | 0.213152 | − | 0.977019i | ||||||
0.213152 | + | 0.977019i | ||||||||
6.94320e11 | 1.97353 | |||||||||
−4.46697e10 | −0.125428 | |||||||||
−5.38934e11 | −1.49495 | |||||||||
8.87991e11 | 2.43347 | |||||||||
1.94661e10 | 0.0527030 | |||||||||
−6.15338e11 | −1.64598 | −0.822989 | − | 0.568057i | ||||||
−0.822989 | + | 0.568057i | ||||||||
7.62755e11 | 2.01587 | |||||||||
−5.55453e10 | −0.145046 | |||||||||
2.69507e11 | 0.695383 | |||||||||
1.85548e10 | 0.0473063 | |||||||||
−3.93789e11 | −0.992089 | |||||||||
2.48822e10 | 0.0619459 | 0.0309729 | − | 0.999520i | ||||||
0.0309729 | + | 0.999520i | ||||||||
−5.90617e10 | −0.145305 | |||||||||
−7.94035e10 | −0.193053 | |||||||||
6.95181e11 | 1.67037 | |||||||||
4.82478e11 | 1.14573 | 0.572866 | − | 0.819649i | ||||||
0.572866 | + | 0.819649i | ||||||||
−1.79224e11 | −0.420634 | |||||||||
1.31043e12 | 3.03976 | |||||||||
−5.99349e11 | −1.37416 | |||||||||
−5.29792e10 | −0.120062 | |||||||||
−4.08606e10 | −0.0915297 | |||||||||
3.80215e11 | 0.841890 | 0.420945 | − | 0.907086i | ||||||
0.420945 | + | 0.907086i | ||||||||
6.35909e10 | 0.139189 | |||||||||
−8.67310e11 | −1.87663 | |||||||||
3.67183e11 | 0.785408 | |||||||||
−1.77342e11 | −0.375012 | |||||||||
−3.36937e11 | −0.704394 | |||||||||
−4.83968e11 | −1.00030 | |||||||||
1.28259e11 | 0.262096 | |||||||||
7.91759e11 | 1.59969 | 0.799845 | − | 0.600207i | ||||||
0.799845 | + | 0.600207i | ||||||||
2.10179e11 | 0.419871 | |||||||||
1.57376e11 | 0.310858 | |||||||||
−4.02478e11 | −0.786090 | |||||||||
−3.06132e11 | −0.591234 | −0.295617 | − | 0.955307i | ||||||
−0.295617 | + | 0.955307i | ||||||||
−6.80199e10 | −0.129903 | |||||||||
−1.23532e11 | −0.233296 | |||||||||
5.80307e10 | 0.108378 | |||||||||
4.46598e11 | 0.824840 | |||||||||
−1.38794e11 | −0.253515 | |||||||||
−1.00350e12 | −1.81277 | |||||||||
1.94074e11 | 0.346735 | |||||||||
9.04916e11 | 1.59902 | 0.799509 | − | 0.600654i | ||||||
0.799509 | + | 0.600654i | ||||||||
−1.15766e11 | −0.202327 | |||||||||
−1.89948e11 | −0.328357 | |||||||||
−1.03362e11 | −0.176736 | |||||||||
−1.19780e12 | −2.02586 | |||||||||
−9.75352e11 | −1.63177 | |||||||||
−1.79599e11 | −0.297227 | |||||||||
−5.89172e10 | −0.0964544 | |||||||||
1.90753e11 | 0.308929 | |||||||||
−7.35482e11 | −1.17836 | |||||||||
3.36210e11 | 0.532903 | 0.266451 | − | 0.963848i | ||||||
0.266451 | + | 0.963848i | ||||||||
−7.11256e10 | −0.111533 | |||||||||
−1.87100e11 | −0.290271 | −0.145135 | − | 0.989412i | ||||||
−0.145135 | + | 0.989412i | ||||||||
−6.63140e10 | −0.101789 | |||||||||
−4.47276e11 | −0.679273 | |||||||||
−1.05590e12 | −1.58664 | |||||||||
5.02755e11 | 0.747491 | |||||||||
1.76175e11 | 0.259180 | |||||||||
3.74048e11 | 0.544504 | |||||||||
5.35872e10 | 0.0771905 | |||||||||
1.18407e11 | 0.168779 | |||||||||
−1.37301e11 | −0.193672 | |||||||||
9.60500e11 | 1.34076 | 0.670378 | − | 0.742020i | ||||||
0.670378 | + | 0.742020i | ||||||||
5.53203e11 | 0.764200 | |||||||||
1.14812e12 | 1.56961 | 0.784806 | − | 0.619741i | ||||||
0.784806 | + | 0.619741i | ||||||||
9.24051e11 | 1.25024 | |||||||||
−5.89520e10 | −0.0789400 | |||||||||
9.08259e10 | 0.120371 | |||||||||
8.36297e11 | 1.09697 | |||||||||
−4.13590e10 | −0.0536953 | |||||||||
5.44277e11 | 0.699407 | 0.349703 | − | 0.936860i | ||||||
0.349703 | + | 0.936860i | ||||||||
−1.55822e12 | −1.98194 | |||||||||
−6.09381e11 | −0.767212 | |||||||||
2.62725e11 | 0.327417 | |||||||||
−1.12065e11 | −0.138247 | −0.0691233 | − | 0.997608i | ||||||
−0.0691233 | + | 0.997608i | ||||||||
5.44668e10 | 0.0665133 | |||||||||
−9.23466e11 | −1.11635 | |||||||||
8.78313e11 | 1.05110 | |||||||||
5.80714e11 | 0.687984 | |||||||||
−8.97307e11 | −1.05242 | |||||||||
−1.11883e12 | −1.29913 | −0.649567 | − | 0.760304i | ||||||
−0.649567 | + | 0.760304i | ||||||||
5.65384e11 | 0.649961 | |||||||||
−2.15558e11 | −0.245341 | |||||||||
−1.43965e11 | −0.162231 | |||||||||
1.59589e11 | 0.178058 | |||||||||
1.85339e12 | 2.04746 | |||||||||
4.51365e11 | 0.493716 | |||||||||
−1.87135e11 | −0.202681 | |||||||||
−1.38914e12 | −1.48978 | −0.744890 | − | 0.667188i | ||||||
−0.744890 | + | 0.667188i | ||||||||
1.39626e12 | 1.48276 | |||||||||
−6.91032e11 | −0.726677 | |||||||||
−3.77961e11 | −0.393583 | |||||||||
1.06041e12 | 1.09350 | 0.546752 | − | 0.837294i | ||||||
0.546752 | + | 0.837294i | ||||||||
−8.85711e11 | −0.904488 | |||||||||
2.81576e11 | 0.284762 | 0.142381 | − | 0.989812i | ||||||
0.142381 | + | 0.989812i | ||||||||
1.94980e11 | 0.195281 | |||||||||
3.92486e11 | 0.389301 | |||||||||
1.14829e12 | 1.12801 | |||||||||
−9.91125e11 | −0.964278 | −0.482139 | − | 0.876095i | ||||||
−0.482139 | + | 0.876095i | ||||||||
4.41779e10 | 0.0425695 | |||||||||
−4.82802e11 | −0.460778 | |||||||||
−1.15917e12 | −1.09573 | |||||||||
−2.52916e11 | −0.236801 | |||||||||
1.42429e12 | 1.32087 | |||||||||
−2.55656e11 | −0.234845 | |||||||||
3.27112e11 | 0.297641 | |||||||||
−4.84778e11 | −0.436940 | |||||||||
−2.93855e11 | −0.262362 | |||||||||
1.75239e12 | 1.54988 | |||||||||
2.15915e11 | 0.189173 | |||||||||
−1.38074e12 | −1.19841 | −0.599203 | − | 0.800597i | ||||||
−0.599203 | + | 0.800597i | ||||||||
1.87191e11 | 0.160953 | |||||||||
−3.45648e11 | −0.294429 | |||||||||
4.31974e11 | 0.364541 | |||||||||
1.00712e12 | 0.842013 | |||||||||
4.06673e11 | 0.336853 | |||||||||
−8.23854e11 | −0.676102 | |||||||||
−1.19202e12 | −0.969215 | |||||||||
9.65212e11 | 0.777575 | 0.388788 | − | 0.921327i | ||||||
0.388788 | + | 0.921327i | ||||||||
−4.44777e11 | −0.355020 | |||||||||
−3.91697e11 | −0.309785 | |||||||||
−1.57928e12 | −1.23759 | |||||||||
−1.10735e12 | −0.859841 | −0.429920 | − | 0.902867i | ||||||
−0.429920 | + | 0.902867i | ||||||||
1.16998e10 | 0.00900191 | |||||||||
−2.43559e11 | −0.185692 | |||||||||
−2.53331e11 | −0.191389 | |||||||||
2.58604e12 | 1.93603 | |||||||||
−1.29812e12 | −0.963050 | |||||||||
1.25049e12 | 0.919338 | |||||||||
1.21390e11 | 0.0884407 | |||||||||
−2.24583e12 | −1.62153 | −0.810763 | − | 0.585374i | ||||||
−0.810763 | + | 0.585374i | ||||||||
−1.00006e11 | −0.0715586 | |||||||||
−7.20198e9 | −0.00510719 | |||||||||
4.34564e11 | 0.305413 | |||||||||
3.98259e11 | 0.277402 | 0.138701 | − | 0.990334i | ||||||
0.138701 | + | 0.990334i | ||||||||
1.54913e12 | 1.06943 | |||||||||
1.17005e12 | 0.800557 | |||||||||
−4.70666e12 | −3.19180 | |||||||||
4.07843e10 | 0.0274130 | |||||||||
−1.42961e11 | −0.0952428 | |||||||||
2.66411e12 | 1.75923 | 0.879615 | − | 0.475687i | ||||||
0.879615 | + | 0.475687i | ||||||||
−8.34727e11 | −0.546360 | |||||||||
−2.93564e11 | −0.190462 | |||||||||
9.71905e11 | 0.625042 | |||||||||
6.66323e11 | 0.424773 | |||||||||
1.53775e12 | 0.971747 | |||||||||
−2.08405e12 | −1.30550 | |||||||||
1.38762e10 | 0.00861681 | |||||||||
−2.15838e12 | −1.32868 | |||||||||
2.58553e12 | 1.57785 | |||||||||
−6.80577e11 | −0.411741 | |||||||||
−5.36715e11 | −0.321906 | |||||||||
−3.11961e12 | −1.85494 | −0.927472 | − | 0.373894i | ||||||
−0.927472 | + | 0.373894i | ||||||||
−2.73900e11 | −0.161464 | |||||||||
−2.05566e12 | −1.20142 | −0.600709 | − | 0.799468i | ||||||
−0.600709 | + | 0.799468i | ||||||||
−3.19294e11 | −0.185012 | |||||||||
−5.83798e11 | −0.335387 | |||||||||
−1.10290e12 | −0.628202 | |||||||||
1.62155e12 | 0.915762 | |||||||||
1.24426e12 | 0.696722 | |||||||||
3.55067e12 | 1.97133 | |||||||||
4.54150e12 | 2.50011 | |||||||||
−2.36377e12 | −1.29027 | |||||||||
2.83347e11 | 0.153362 | |||||||||
−7.42472e10 | −0.0398481 | |||||||||
6.24166e11 | 0.332173 | |||||||||
1.08045e12 | 0.570183 | |||||||||
5.74096e11 | 0.300430 | |||||||||
2.49083e10 | 0.0129259 | |||||||||
2.12368e12 | 1.09287 | |||||||||
−2.94063e12 | −1.50069 | |||||||||
−3.01142e11 | −0.152405 | |||||||||
8.06876e11 | 0.404966 | 0.202483 | − | 0.979286i | ||||||
0.202483 | + | 0.979286i | ||||||||
−2.05135e12 | −1.02104 | |||||||||
1.43371e11 | 0.0707721 | |||||||||
7.73378e11 | 0.378614 | |||||||||
1.83128e12 | 0.889142 | |||||||||
−3.05076e11 | −0.146906 | |||||||||
1.93370e12 | 0.923521 | 0.461760 | − | 0.887005i | ||||||
0.461760 | + | 0.887005i | ||||||||
−3.41990e11 | −0.161995 | |||||||||
7.38157e11 | 0.346795 | |||||||||
2.72832e12 | 1.27134 | |||||||||
2.34851e11 | 0.108545 | |||||||||
−1.19756e12 | −0.548997 | |||||||||
2.32183e12 | 1.05576 | |||||||||
−4.24810e12 | −1.91602 | |||||||||
1.09819e12 | 0.491314 | |||||||||
3.43439e11 | 0.152410 | |||||||||
3.06623e12 | 1.34976 | 0.674879 | − | 0.737928i | ||||||
0.674879 | + | 0.737928i | ||||||||
1.82355e12 | 0.796276 | |||||||||
−8.80587e10 | −0.0381434 | |||||||||
4.74312e12 | 2.03806 | |||||||||
−1.55427e12 | −0.662512 | |||||||||
−1.85885e12 | −0.786013 | |||||||||
−2.59944e12 | −1.09042 | −0.545208 | − | 0.838301i | ||||||
−0.545208 | + | 0.838301i | ||||||||
1.17150e11 | 0.0487512 | |||||||||
−2.90270e12 | −1.19835 | |||||||||
−4.14416e12 | −1.69732 | |||||||||
−2.14255e12 | −0.870576 | |||||||||
−1.48694e12 | −0.599413 | |||||||||
−1.63182e12 | −0.652632 | −0.326316 | − | 0.945261i | ||||||
−0.326316 | + | 0.945261i | ||||||||
8.04880e11 | 0.319370 | |||||||||
−1.05673e12 | −0.416010 | −0.208005 | − | 0.978128i | ||||||
−0.208005 | + | 0.978128i | ||||||||
2.13185e11 | 0.0832672 | |||||||||
−1.41658e12 | −0.548964 | |||||||||
5.55386e11 | 0.213546 | |||||||||
−3.10230e12 | −1.18353 | |||||||||
−1.77077e12 | −0.670289 | |||||||||
−8.51110e11 | −0.319665 | −0.159832 | − | 0.987144i | ||||||
−0.159832 | + | 0.987144i | ||||||||
−5.38987e11 | −0.200865 | |||||||||
1.22130e12 | 0.451614 | |||||||||
−1.06140e11 | −0.0389450 | |||||||||
8.61624e11 | 0.313708 | |||||||||
5.56839e11 | 0.201176 | |||||||||
8.45633e12 | 3.03161 | |||||||||
3.49075e11 | 0.124183 | |||||||||
8.90739e11 | 0.314448 | |||||||||
2.91591e12 | 1.02149 | |||||||||
6.19927e11 | 0.215511 | 0.107755 | − | 0.994177i | ||||||
0.107755 | + | 0.994177i | ||||||||
1.59608e11 | 0.0550626 | |||||||||
−1.56357e12 | −0.535301 | |||||||||
−6.12597e12 | −2.08133 | |||||||||
6.86579e11 | 0.231498 | |||||||||
−3.63220e12 | −1.21541 | |||||||||
−3.79034e12 | −1.25873 | −0.629364 | − | 0.777110i | ||||||
−0.629364 | + | 0.777110i | ||||||||
−3.75005e12 | −1.23594 | |||||||||
−5.92486e12 | −1.93799 | |||||||||
1.04554e12 | 0.339417 | |||||||||
−4.28283e11 | −0.137990 | |||||||||
−1.62117e12 | −0.518410 | |||||||||
2.62045e12 | 0.831679 | 0.415839 | − | 0.909438i | ||||||
0.415839 | + | 0.909438i | ||||||||
6.94190e11 | 0.218674 | |||||||||
1.11042e12 | 0.347178 | 0.173589 | − | 0.984818i | ||||||
0.173589 | + | 0.984818i | ||||||||
6.58700e11 | 0.204411 | |||||||||
−9.52777e11 | −0.293470 | |||||||||
2.87331e11 | 0.0878449 | |||||||||
8.19956e12 | 2.48824 | |||||||||
−7.90829e11 | −0.238208 | |||||||||
4.57077e12 | 1.36660 | 0.683298 | − | 0.730140i | ||||||
0.683298 | + | 0.730140i | ||||||||
−7.45724e11 | −0.221316 | |||||||||
2.82821e11 | 0.0833171 | |||||||||
1.91301e12 | 0.559415 | |||||||||
−7.43436e11 | −0.215803 | |||||||||
−5.79902e11 | −0.167099 | |||||||||
−5.61998e12 | −1.60754 | −0.803772 | − | 0.594938i | ||||||
−0.803772 | + | 0.594938i | ||||||||
4.89568e12 | 1.39013 | |||||||||
2.35898e11 | 0.0664945 | |||||||||
7.47551e12 | 2.09184 | |||||||||
2.17420e12 | 0.603970 | 0.301985 | − | 0.953313i | ||||||
0.301985 | + | 0.953313i | ||||||||
1.40860e12 | 0.388454 | |||||||||
5.91455e12 | 1.61925 | 0.809625 | − | 0.586947i | ||||||
0.809625 | + | 0.586947i | ||||||||
7.06649e11 | 0.192062 | |||||||||
4.26409e12 | 1.15057 | |||||||||
−4.66542e12 | −1.24978 | |||||||||
4.43031e12 | 1.17825 | |||||||||
4.28576e11 | 0.113161 | |||||||||
−4.63555e12 | −1.21518 | |||||||||
8.33426e11 | 0.216912 | |||||||||
1.49869e12 | 0.387266 | |||||||||
−4.55361e11 | −0.116826 | |||||||||
4.53716e12 | 1.15573 | |||||||||
−6.66293e12 | −1.68513 | |||||||||
−5.05658e12 | −1.26977 | −0.634884 | − | 0.772607i | ||||||
−0.634884 | + | 0.772607i | ||||||||
−2.76086e12 | −0.688364 | |||||||||
1.35128e11 | 0.0334526 | |||||||||
2.09431e11 | 0.0514801 | |||||||||
−2.88247e12 | −0.703530 | |||||||||
−4.58982e11 | −0.111234 | |||||||||
−1.01288e12 | −0.243741 | |||||||||
−1.32173e12 | −0.315828 | |||||||||
2.46775e12 | 0.585527 | |||||||||
−6.50609e12 | −1.53289 | |||||||||
1.51370e12 | 0.354142 | 0.177071 | − | 0.984198i | ||||||
0.177071 | + | 0.984198i | ||||||||
−7.30274e11 | −0.169660 | |||||||||
3.90178e12 | 0.900146 | 0.450073 | − | 0.892992i | ||||||
0.450073 | + | 0.892992i | ||||||||
1.81326e12 | 0.415407 | |||||||||
2.79779e11 | 0.0636498 | |||||||||
3.32535e12 | 0.751261 | |||||||||
7.88115e12 | 1.76815 | 0.884077 | − | 0.467341i | ||||||
0.884077 | + | 0.467341i | ||||||||
2.54768e12 | 0.567620 | |||||||||
−1.14066e13 | −2.52381 | |||||||||
9.39747e11 | 0.206491 | |||||||||
−1.88294e12 | −0.410887 | |||||||||
−7.05229e11 | −0.152833 | |||||||||
−5.10697e12 | −1.09914 | −0.549571 | − | 0.835447i | ||||||
−0.549571 | + | 0.835447i | ||||||||
−1.23776e12 | −0.264567 | |||||||||
−6.43778e12 | −1.36663 | |||||||||
−7.80217e11 | −0.164493 | |||||||||
−5.79329e11 | −0.121306 | |||||||||
5.56107e12 | 1.15649 | |||||||||
−5.45308e11 | −0.112631 | −0.0563154 | − | 0.998413i | ||||||
−0.0563154 | + | 0.998413i | ||||||||
−6.77329e11 | −0.138948 | |||||||||
−3.05503e12 | −0.622456 | −0.311228 | − | 0.950335i | ||||||
−0.311228 | + | 0.950335i | ||||||||
−1.25018e12 | −0.252995 | |||||||||
−5.35356e11 | −0.107605 | |||||||||
−1.02455e12 | −0.204539 | |||||||||
5.71301e12 | 1.13284 | |||||||||
5.10236e12 | 1.00493 | |||||||||
1.50291e12 | 0.294013 | |||||||||
−1.29668e10 | −0.00251963 | |||||||||
−1.78974e12 | −0.345441 | |||||||||
−2.46923e12 | −0.473395 | |||||||||
3.56205e12 | 0.678343 | |||||||||
−8.98046e11 | −0.169878 | |||||||||
−1.57419e12 | −0.295795 | −0.147897 | − | 0.989003i | ||||||
−0.147897 | + | 0.989003i | ||||||||
−5.68968e12 | −1.06199 | |||||||||
−2.47177e12 | −0.458291 | |||||||||
7.34298e10 | 0.0135242 | |||||||||
−2.62249e11 | −0.0479805 | −0.0239903 | − | 0.999712i | ||||||
−0.0239903 | + | 0.999712i | ||||||||
1.96192e12 | 0.356573 | |||||||||
3.95242e12 | 0.713591 | |||||||||
7.04520e12 | 1.26358 | |||||||||
−3.77666e12 | −0.672892 | |||||||||
8.79973e12 | 1.55754 | |||||||||
−3.64995e12 | −0.641791 | −0.320896 | − | 0.947115i | ||||||
−0.320896 | + | 0.947115i | ||||||||
5.59166e11 | 0.0976762 | |||||||||
−6.89539e12 | −1.19661 | |||||||||
−1.04471e12 | −0.180110 | |||||||||
−2.84517e12 | −0.487307 | |||||||||
−9.25354e11 | −0.157456 | |||||||||
2.91271e12 | 0.492392 | |||||||||
5.15077e12 | 0.865070 | |||||||||
−1.69603e12 | −0.282998 | −0.141499 | − | 0.989938i | ||||||
−0.141499 | + | 0.989938i | ||||||||
−1.22534e12 | −0.203132 | |||||||||
−1.24065e13 | −2.04337 | |||||||||
8.93451e11 | 0.146202 | |||||||||
6.92461e12 | 1.12581 | |||||||||
−3.36300e11 | −0.0543232 | |||||||||
9.74608e11 | 0.156416 | |||||||||
−2.42131e12 | −0.386101 | |||||||||
−2.33987e12 | −0.370718 | |||||||||
−1.05110e12 | −0.165463 | |||||||||
1.15906e13 | 1.81291 | 0.906454 | − | 0.422304i | ||||||
0.906454 | + | 0.422304i | ||||||||
−1.29167e12 | −0.200741 | |||||||||
−4.37492e12 | −0.675571 | |||||||||
−8.54505e12 | −1.31111 | |||||||||
2.36204e12 | 0.360111 | |||||||||
9.58030e12 | 1.45130 | |||||||||
−5.61328e12 | −0.844946 | |||||||||
6.19114e11 | 0.0926022 | |||||||||
−6.98541e12 | −1.03821 | −0.519104 | − | 0.854711i | ||||||
−0.519104 | + | 0.854711i | ||||||||
6.39544e12 | 0.944512 | |||||||||
4.58196e12 | 0.672417 | |||||||||
−5.26804e12 | −0.768226 | |||||||||
−1.00059e13 | −1.44996 | |||||||||
4.00459e12 | 0.576654 | |||||||||
4.29835e12 | 0.615070 | |||||||||
4.48461e10 | 0.00637699 | |||||||||
−4.39972e11 | −0.0621711 | |||||||||
9.47866e12 | 1.33103 | |||||||||
−3.43730e12 | −0.479665 | −0.239832 | − | 0.970814i | ||||||
−0.239832 | + | 0.970814i | ||||||||
9.36022e12 | 1.29804 | |||||||||
9.99820e12 | 1.37788 | |||||||||
4.71103e12 | 0.645206 | |||||||||
−8.80236e11 | −0.119805 | |||||||||
2.58131e11 | 0.0349154 | |||||||||
−8.71194e11 | −0.117110 | |||||||||
−5.54205e12 | −0.740381 | |||||||||
1.25723e12 | 0.166920 | 0.0834601 | − | 0.996511i | ||||||
0.0834601 | + | 0.996511i | ||||||||
2.57488e12 | 0.339755 | |||||||||
−2.41427e12 | −0.316601 | |||||||||
−1.50139e12 | −0.195678 | |||||||||
1.15591e12 | 0.149725 | |||||||||
−1.93337e11 | −0.0248894 | |||||||||
−1.51950e12 | −0.194416 | −0.0972079 | − | 0.995264i | ||||||
−0.0972079 | + | 0.995264i | ||||||||
−3.63515e12 | −0.462264 | |||||||||
3.21810e12 | 0.406731 | |||||||||
−4.77221e12 | −0.599473 | |||||||||
−4.59772e12 | −0.574036 | |||||||||
1.09602e12 | 0.136008 | |||||||||
1.19661e13 | 1.47589 | 0.737944 | − | 0.674862i | ||||||
0.737944 | + | 0.674862i | ||||||||
1.97723e12 | 0.242390 | |||||||||
5.16213e11 | 0.0628995 | |||||||||
−2.17878e13 | −2.63873 | |||||||||
1.52097e12 | 0.183093 | 0.0915465 | − | 0.995801i | ||||||
0.0915465 | + | 0.995801i | ||||||||
2.23899e12 | 0.267901 | |||||||||
2.10808e13 | 2.50717 | |||||||||
1.50980e13 | 1.78482 | |||||||||
1.70036e12 | 0.199801 | |||||||||
−2.79838e12 | −0.326850 | |||||||||
−5.18346e12 | −0.601799 | |||||||||
1.36286e12 | 0.157281 | |||||||||
−8.06595e12 | −0.925286 | −0.462643 | − | 0.886545i | ||||||
−0.462643 | + | 0.886545i | ||||||||
−7.81230e12 | −0.890838 | |||||||||
−8.85513e11 | −0.100373 | |||||||||
−4.55260e11 | −0.0512966 | |||||||||
5.79333e12 | 0.648884 | |||||||||
1.44472e12 | 0.160856 | |||||||||
8.72882e12 | 0.966104 | 0.483052 | − | 0.875592i | ||||||
0.483052 | + | 0.875592i | ||||||||
−6.10511e11 | −0.0671710 | |||||||||
9.59079e12 | 1.04898 | |||||||||
−6.79329e12 | −0.738616 | |||||||||
7.63407e11 | 0.0825135 | 0.0412568 | − | 0.999149i | ||||||
0.0412568 | + | 0.999149i | ||||||||
1.94825e12 | 0.209337 | |||||||||
−8.78554e12 | −0.938443 | |||||||||
−2.55046e12 | −0.270831 | |||||||||
−1.16923e13 | −1.23431 | |||||||||
−1.18381e13 | −1.24237 | |||||||||
−3.92892e12 | −0.409915 | |||||||||
1.75945e12 | 0.182495 | |||||||||
−5.30538e12 | −0.547076 | −0.273538 | − | 0.961861i | ||||||
−0.273538 | + | 0.961861i | ||||||||
−3.21527e13 | −3.29616 | |||||||||
−3.13349e12 | −0.319363 | |||||||||
2.19887e12 | 0.222804 | |||||||||
−1.53974e12 | −0.155110 | −0.0775550 | − | 0.996988i | ||||||
−0.0775550 | + | 0.996988i | ||||||||
1.29990e12 | 0.130189 | |||||||||
5.80017e12 | 0.577541 | |||||||||
−4.69979e12 | −0.465266 | |||||||||
−5.26854e12 | −0.518556 | |||||||||
−9.32896e12 | −0.912904 | |||||||||
−9.39759e11 | −0.0914319 | |||||||||
−2.33300e11 | −0.0225678 | |||||||||
1.19084e13 | 1.14531 | |||||||||
2.12803e13 | 2.03492 | |||||||||
1.19745e12 | 0.113849 | |||||||||
−1.06437e13 | −1.00617 | |||||||||
−9.18125e12 | −0.862955 | |||||||||
4.35127e12 | 0.406644 | |||||||||
−2.94759e12 | −0.273893 | −0.136946 | − | 0.990578i | ||||||
−0.136946 | + | 0.990578i | ||||||||
1.23615e12 | 0.114209 | |||||||||
2.24738e12 | 0.206457 | |||||||||
1.18747e13 | 1.08467 | |||||||||
1.39257e13 | 1.26480 | |||||||||
1.47524e13 | 1.33229 | |||||||||
1.22692e12 | 0.110176 | |||||||||
−1.94266e13 | −1.73462 | |||||||||
−9.25425e12 | −0.821654 | |||||||||
−7.71099e11 | −0.0680772 | |||||||||
−1.83481e13 | −1.61075 | −0.805376 | − | 0.592764i | ||||||
−0.805376 | + | 0.592764i | ||||||||
−3.86139e12 | −0.337079 | |||||||||
9.75873e12 | 0.847096 | |||||||||
2.76632e12 | 0.238779 | |||||||||
8.74291e12 | 0.750429 | |||||||||
7.51127e12 | 0.641104 | |||||||||
−2.79561e12 | −0.237278 | |||||||||
2.49549e11 | 0.0210622 | |||||||||
3.65600e13 | 3.06849 | |||||||||
3.03099e12 | 0.252975 | |||||||||
−4.32744e12 | −0.359170 | |||||||||
6.67470e12 | 0.550910 | |||||||||
−9.70701e12 | −0.796741 | −0.398371 | − | 0.917225i | ||||||
−0.398371 | + | 0.917225i | ||||||||
−1.09578e13 | −0.894415 | |||||||||
6.14421e12 | 0.498738 | 0.249369 | − | 0.968409i | ||||||
0.249369 | + | 0.968409i | ||||||||
5.09203e11 | 0.0411045 | |||||||||
4.18005e12 | 0.335563 | |||||||||
2.46220e13 | 1.96568 | |||||||||
−1.42192e13 | −1.12893 | |||||||||
−5.62572e12 | −0.444194 | |||||||||
−1.11457e12 | −0.0875205 | |||||||||
−2.22030e13 | −1.73389 | |||||||||
−4.27330e12 | −0.331884 | |||||||||
4.24720e11 | 0.0328050 | |||||||||
1.41092e13 | 1.08383 | 0.541913 | − | 0.840434i | ||||||
0.541913 | + | 0.840434i | ||||||||
4.66057e12 | 0.356054 | |||||||||
7.99374e12 | 0.607366 | 0.303683 | − | 0.952773i | ||||||
0.303683 | + | 0.952773i | ||||||||
−1.18888e13 | −0.898389 | |||||||||
−5.55951e12 | −0.417824 | |||||||||
2.93892e13 | 2.19674 | |||||||||
−4.82994e12 | −0.359060 | −0.179530 | − | 0.983752i | ||||||
−0.179530 | + | 0.983752i | ||||||||
3.57834e12 | 0.264573 | |||||||||
1.41648e13 | 1.04163 | 0.520816 | − | 0.853669i | ||||||
0.520816 | + | 0.853669i | ||||||||
4.40666e12 | 0.322298 | |||||||||
8.65637e12 | 0.629697 | |||||||||
−2.94327e12 | −0.212949 | |||||||||
1.32956e13 | 0.956762 | |||||||||
−4.68031e12 | −0.334987 | |||||||||
−2.61443e11 | −0.0186118 | |||||||||
2.69831e12 | 0.191058 | |||||||||
−7.97228e12 | −0.561459 | |||||||||
−8.24927e12 | −0.577853 | |||||||||
1.79477e13 | 1.25049 | 0.625246 | − | 0.780428i | ||||||
0.625246 | + | 0.780428i | ||||||||
−8.18088e12 | −0.566948 | |||||||||
−1.40851e13 | −0.970907 | |||||||||
4.59068e12 | 0.314755 | |||||||||
3.78778e12 | 0.258322 | |||||||||
2.43291e11 | 0.0165038 | |||||||||
1.48053e12 | 0.0998993 | |||||||||
1.09744e13 | 0.736570 | |||||||||
−3.93372e13 | −2.62620 | |||||||||
3.06079e13 | 2.03260 | |||||||||
8.44458e12 | 0.557819 | |||||||||
−1.23356e13 | −0.810542 | |||||||||
−2.79970e13 | −1.82990 | |||||||||
−6.46347e11 | −0.0420231 | |||||||||
−8.65463e12 | −0.559729 | −0.279865 | − | 0.960039i | ||||||
−0.279865 | + | 0.960039i | ||||||||
−9.17764e12 | −0.590433 | |||||||||
1.12742e13 | 0.721505 | |||||||||
6.16360e12 | 0.392376 | |||||||||
−1.17199e13 | −0.742185 | −0.371092 | − | 0.928596i | ||||||
−0.371092 | + | 0.928596i | ||||||||
−2.90524e12 | −0.183016 | |||||||||
−2.70022e13 | −1.69211 | −0.846057 | − | 0.533092i | ||||||
−0.846057 | + | 0.533092i | ||||||||
5.03727e11 | 0.0314016 | |||||||||
−1.13171e12 | −0.0701815 | |||||||||
−2.35669e13 | −1.45385 | |||||||||
2.11111e13 | 1.29557 | 0.647786 | − | 0.761823i | ||||||
0.647786 | + | 0.761823i | ||||||||
−3.80228e12 | −0.232130 | |||||||||
−2.47060e13 | −1.50048 | |||||||||
−2.81704e13 | −1.70201 | |||||||||
1.09830e12 | 0.0660137 | |||||||||
−3.39013e12 | −0.202711 | |||||||||
2.21107e13 | 1.31527 | |||||||||
1.44645e12 | 0.0855986 | |||||||||
−1.58365e12 | −0.0932346 | |||||||||
1.04468e13 | 0.611870 | |||||||||
7.79984e12 | 0.454487 | |||||||||
−2.05194e13 | −1.18950 | |||||||||
9.67354e12 | 0.557891 | |||||||||
1.51737e11 | 0.00870606 | |||||||||
−1.48840e13 | −0.849614 | −0.424807 | − | 0.905284i | ||||||
−0.424807 | + | 0.905284i | ||||||||
−1.33544e13 | −0.758402 | |||||||||
−5.94176e12 | −0.335711 | |||||||||
4.51687e13 | 2.53902 | |||||||||
8.21496e11 | 0.0459424 | 0.0229712 | − | 0.999736i | ||||||
0.0229712 | + | 0.999736i | ||||||||
1.49518e13 | 0.831926 | |||||||||
−5.06069e12 | −0.280147 | −0.140074 | − | 0.990141i | ||||||
−0.140074 | + | 0.990141i | ||||||||
−9.63878e11 | −0.0530868 | |||||||||
1.24829e13 | 0.684025 | |||||||||
2.74964e12 | 0.149908 | |||||||||
−4.00796e12 | −0.217404 | −0.108702 | − | 0.994074i | ||||||
−0.108702 | + | 0.994074i | ||||||||
6.26478e12 | 0.338102 | |||||||||
1.38286e13 | 0.742540 | |||||||||
2.26582e13 | 1.21051 | |||||||||
−2.04035e13 | −1.08456 | |||||||||
−3.22233e12 | −0.170423 | |||||||||
−9.40979e12 | −0.495163 | |||||||||
−1.42484e13 | −0.746016 | |||||||||
9.04211e11 | 0.0471049 | |||||||||
3.12129e13 | 1.61788 | |||||||||
3.30347e12 | 0.170374 | |||||||||
2.74516e13 | 1.40872 | |||||||||
−2.80989e12 | −0.143473 | |||||||||
−2.07427e12 | −0.105384 | |||||||||
−3.82338e13 | −1.93280 | |||||||||
5.28894e12 | 0.266035 | |||||||||
−1.34224e12 | −0.0671791 | |||||||||
−1.65589e13 | −0.824657 | |||||||||
5.20459e12 | 0.257910 | |||||||||
−3.91569e12 | −0.193077 | |||||||||
4.52189e12 | 0.221864 | 0.110932 | − | 0.993828i | ||||||
0.110932 | + | 0.993828i | ||||||||
−6.79966e12 | −0.331971 | |||||||||
−1.10774e13 | −0.538147 | |||||||||
−1.10747e13 | −0.535361 | |||||||||
−5.68437e12 | −0.273432 | −0.136716 | − | 0.990610i | ||||||
−0.136716 | + | 0.990610i | ||||||||
5.42456e12 | 0.259650 | |||||||||
8.20525e12 | 0.390817 | |||||||||
3.40839e13 | 1.61544 | |||||||||
−3.89816e12 | −0.183850 | |||||||||
−5.12257e12 | −0.240413 | |||||||||
3.08851e13 | 1.44241 | |||||||||
1.69552e13 | 0.787972 | |||||||||
3.28047e13 | 1.51711 | 0.758555 | − | 0.651609i | ||||||
0.758555 | + | 0.651609i | ||||||||
−4.34731e13 | −2.00067 | |||||||||
−9.97597e12 | −0.456864 | |||||||||
−2.60183e13 | −1.18574 | |||||||||
4.10174e12 | 0.186020 | |||||||||
3.24947e12 | 0.146652 | |||||||||
1.62291e13 | 0.728880 | |||||||||
−6.90877e12 | −0.308782 | |||||||||
1.97308e13 | 0.877576 | |||||||||
−1.34014e12 | −0.0593177 | |||||||||
1.82868e13 | 0.805504 | 0.402752 | − | 0.915309i | ||||||
0.402752 | + | 0.915309i | ||||||||
−9.63005e12 | −0.422139 | |||||||||
−1.28201e13 | −0.559267 | |||||||||
−4.21280e12 | −0.182894 | |||||||||
9.50675e12 | 0.410738 | |||||||||
2.43183e13 | 1.04562 | |||||||||
−5.64224e13 | −2.41435 | |||||||||
5.08134e12 | 0.216390 | |||||||||
2.71335e13 | 1.14995 | 0.574974 | − | 0.818171i | ||||||
0.574974 | + | 0.818171i | ||||||||
1.18461e13 | 0.499644 | |||||||||
−1.69828e12 | −0.0712875 | |||||||||
4.25271e12 | 0.177660 | |||||||||
−9.48833e12 | −0.394490 | −0.197245 | − | 0.980354i | ||||||
−0.197245 | + | 0.980354i | ||||||||
6.20556e12 | 0.256775 | |||||||||
−6.01392e12 | −0.247660 | |||||||||
−4.12866e13 | −1.69213 | |||||||||
2.91293e13 | 1.18819 | |||||||||
6.27279e12 | 0.254654 | |||||||||
1.99262e13 | 0.805100 | 0.402550 | − | 0.915398i | ||||||
0.402550 | + | 0.915398i | ||||||||
−1.20010e12 | −0.0482591 | |||||||||
−9.62925e11 | −0.0385385 | |||||||||
1.18945e13 | 0.473796 | |||||||||
−4.26759e11 | −0.0169188 | |||||||||
−3.37992e13 | −1.33364 | |||||||||
2.48922e13 | 0.977565 | 0.488782 | − | 0.872406i | ||||||
0.488782 | + | 0.872406i | ||||||||
−4.29967e13 | −1.68061 | |||||||||
−5.14238e13 | −2.00055 | |||||||||
−7.92144e11 | −0.0306721 | |||||||||
2.69330e12 | 0.103796 | |||||||||
3.38780e13 | 1.29949 | |||||||||
3.30805e13 | 1.26296 | |||||||||
9.35134e12 | 0.355347 | |||||||||
−7.73217e12 | −0.292446 | |||||||||
8.48083e12 | 0.319264 | |||||||||
−1.02292e13 | −0.383286 | |||||||||
−1.58481e12 | −0.0591060 | |||||||||
4.43349e13 | 1.64579 | |||||||||
−2.47107e13 | −0.913037 | |||||||||
−4.20642e13 | −1.54701 | −0.773505 | − | 0.633790i | ||||||
−0.773505 | + | 0.633790i | ||||||||
4.67756e13 | 1.71230 | |||||||||
−6.77609e12 | −0.246900 | |||||||||
2.02141e13 | 0.733132 | |||||||||
−1.34740e12 | −0.0486418 | −0.0243209 | − | 0.999704i | ||||||
−0.0243209 | + | 0.999704i | ||||||||
4.37325e12 | 0.157147 | |||||||||
−3.32207e13 | −1.18823 | |||||||||
−2.36825e13 | −0.843164 | |||||||||
−1.91493e12 | −0.0678628 | |||||||||
1.28929e13 | 0.454807 | |||||||||
−2.05822e13 | −0.722714 | −0.361357 | − | 0.932428i | ||||||
−0.361357 | + | 0.932428i | ||||||||
9.61070e12 | 0.335916 | |||||||||
4.21898e13 | 1.46786 | |||||||||
5.79401e12 | 0.200661 | |||||||||
−1.73377e13 | −0.597695 | |||||||||
2.71700e13 | 0.932368 | |||||||||
−5.72322e13 | −1.95501 | −0.977506 | − | 0.210906i | ||||||
−0.977506 | + | 0.210906i | ||||||||
1.34571e12 | 0.0457587 | |||||||||
2.49239e13 | 0.843631 | |||||||||
5.97598e12 | 0.201355 | |||||||||
−1.13318e13 | −0.380078 | |||||||||
9.29412e11 | 0.0310315 | |||||||||
−7.13263e12 | −0.237065 | |||||||||
−6.34511e13 | −2.09933 | |||||||||
1.46766e13 | 0.483386 | 0.241693 | − | 0.970353i | ||||||
0.241693 | + | 0.970353i | ||||||||
8.92228e12 | 0.292532 | |||||||||
2.54750e12 | 0.0831462 | |||||||||
−3.06820e13 | −0.996884 | |||||||||
−1.55473e13 | −0.502866 | |||||||||
−4.45354e11 | −0.0143396 | |||||||||
−5.31286e13 | −1.70294 | −0.851471 | − | 0.524402i | ||||||
−0.851471 | + | 0.524402i | ||||||||
5.51037e13 | 1.75830 | |||||||||
−2.23067e13 | −0.708583 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 13.10.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 117.10.a.c.1.3 | 4 | |||
4.3 | odd | 2 | 208.10.a.g.1.1 | 4 | |||
5.4 | even | 2 | 325.10.a.a.1.3 | 4 | |||
13.12 | even | 2 | 169.10.a.a.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.10.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
117.10.a.c.1.3 | 4 | 3.2 | odd | 2 | |||
169.10.a.a.1.3 | 4 | 13.12 | even | 2 | |||
208.10.a.g.1.1 | 4 | 4.3 | odd | 2 | |||
325.10.a.a.1.3 | 4 | 5.4 | even | 2 |