Properties

Label 10.11.c.c.3.3
Level $10$
Weight $11$
Character 10.3
Analytic conductor $6.354$
Analytic rank $0$
Dimension $6$
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] = [10,11,Mod(3,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.3");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\), degree \(2\), 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: \(6.35357252674\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 1148x^{3} + 68121x^{2} - 299628x + 658952 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{8}\cdot 5^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.3
Root \(-12.3957 + 12.3957i\) of defining polynomial
Character \(\chi\) \(=\) 10.3
Dual form 10.11.c.c.7.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-16.0000 + 16.0000i) q^{2} +(326.149 + 326.149i) q^{3} -512.000i q^{4} +(3124.94 - 19.4459i) q^{5} -10436.8 q^{6} +(-1507.13 + 1507.13i) q^{7} +(8192.00 + 8192.00i) q^{8} +153697. i q^{9} +O(q^{10})\) \(q+(-16.0000 + 16.0000i) q^{2} +(326.149 + 326.149i) q^{3} -512.000i q^{4} +(3124.94 - 19.4459i) q^{5} -10436.8 q^{6} +(-1507.13 + 1507.13i) q^{7} +(8192.00 + 8192.00i) q^{8} +153697. i q^{9} +(-49687.9 + 50310.2i) q^{10} -71462.1 q^{11} +(166988. - 166988. i) q^{12} +(-300816. - 300816. i) q^{13} -48228.2i q^{14} +(1.02554e6 + 1.01285e6i) q^{15} -262144. q^{16} +(1.11637e6 - 1.11637e6i) q^{17} +(-2.45915e6 - 2.45915e6i) q^{18} +684142. i q^{19} +(-9956.30 - 1.59997e6i) q^{20} -983097. q^{21} +(1.14339e6 - 1.14339e6i) q^{22} +(1.52597e6 + 1.52597e6i) q^{23} +5.34362e6i q^{24} +(9.76487e6 - 121534. i) q^{25} +9.62613e6 q^{26} +(-3.08693e7 + 3.08693e7i) q^{27} +(771651. + 771651. i) q^{28} -2.47039e7i q^{29} +(-3.26142e7 + 202952. i) q^{30} +4.13378e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} +(-2.33073e7 - 2.33073e7i) q^{33} +3.57237e7i q^{34} +(-4.68038e6 + 4.73900e6i) q^{35} +7.86928e7 q^{36} +(2.53176e7 - 2.53176e7i) q^{37} +(-1.09463e7 - 1.09463e7i) q^{38} -1.96222e8i q^{39} +(2.57588e7 + 2.54402e7i) q^{40} -1.32462e8 q^{41} +(1.57296e7 - 1.57296e7i) q^{42} +(-2.46531e7 - 2.46531e7i) q^{43} +3.65886e7i q^{44} +(2.98877e6 + 4.80293e8i) q^{45} -4.88310e7 q^{46} +(5.19304e7 - 5.19304e7i) q^{47} +(-8.54979e7 - 8.54979e7i) q^{48} +2.77932e8i q^{49} +(-1.54293e8 + 1.58182e8i) q^{50} +7.28202e8 q^{51} +(-1.54018e8 + 1.54018e8i) q^{52} +(-3.03473e8 - 3.03473e8i) q^{53} -9.87817e8i q^{54} +(-2.23315e8 + 1.38964e6i) q^{55} -2.46928e7 q^{56} +(-2.23132e8 + 2.23132e8i) q^{57} +(3.95262e8 + 3.95262e8i) q^{58} -6.92655e7i q^{59} +(5.18580e8 - 5.25075e8i) q^{60} +6.38536e8 q^{61} +(-6.61404e8 + 6.61404e8i) q^{62} +(-2.31641e8 - 2.31641e8i) q^{63} +1.34218e8i q^{64} +(-9.45883e8 - 9.34184e8i) q^{65} +7.45832e8 q^{66} +(7.98844e8 - 7.98844e8i) q^{67} +(-5.71579e8 - 5.71579e8i) q^{68} +9.95386e8i q^{69} +(-937840. - 1.50710e8i) q^{70} -4.06392e8 q^{71} +(-1.25908e9 + 1.25908e9i) q^{72} +(-5.91419e8 - 5.91419e8i) q^{73} +8.10163e8i q^{74} +(3.22444e9 + 3.14516e9i) q^{75} +3.50281e8 q^{76} +(1.07703e8 - 1.07703e8i) q^{77} +(3.13955e9 + 3.13955e9i) q^{78} +6.97925e8i q^{79} +(-8.19184e8 + 5.09762e6i) q^{80} -1.10603e10 q^{81} +(2.11939e9 - 2.11939e9i) q^{82} +(-2.76663e9 - 2.76663e9i) q^{83} +5.03346e8i q^{84} +(3.46687e9 - 3.51028e9i) q^{85} +7.88901e8 q^{86} +(8.05714e9 - 8.05714e9i) q^{87} +(-5.85417e8 - 5.85417e8i) q^{88} +3.28276e9i q^{89} +(-7.73251e9 - 7.63687e9i) q^{90} +9.06739e8 q^{91} +(7.81297e8 - 7.81297e8i) q^{92} +(1.34823e10 + 1.34823e10i) q^{93} +1.66177e9i q^{94} +(1.33038e7 + 2.13790e9i) q^{95} +2.73593e9 q^{96} +(-3.71980e9 + 3.71980e9i) q^{97} +(-4.44692e9 - 4.44692e9i) q^{98} -1.09835e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 96 q^{2} + 128 q^{3} + 5460 q^{5} - 4096 q^{6} + 13512 q^{7} + 49152 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 96 q^{2} + 128 q^{3} + 5460 q^{5} - 4096 q^{6} + 13512 q^{7} + 49152 q^{8} - 173280 q^{10} + 647832 q^{11} + 65536 q^{12} - 742902 q^{13} + 1577720 q^{15} - 1572864 q^{16} - 755118 q^{17} - 5683744 q^{18} + 2749440 q^{20} + 12277112 q^{21} - 10365312 q^{22} - 15052992 q^{23} + 42644850 q^{25} + 23772864 q^{26} - 47998120 q^{27} - 6918144 q^{28} - 20357760 q^{30} + 153847152 q^{31} + 25165824 q^{32} - 173025784 q^{33} - 208942440 q^{35} + 181879808 q^{36} - 32574498 q^{37} - 17493120 q^{38} + 737280 q^{40} + 226153272 q^{41} - 196433792 q^{42} - 63628752 q^{43} - 174000230 q^{45} + 481695744 q^{46} - 19700448 q^{47} - 33554432 q^{48} - 788800800 q^{50} + 2388638032 q^{51} - 380365824 q^{52} - 950001042 q^{53} - 135145080 q^{55} + 221380608 q^{56} - 338012560 q^{57} - 310652160 q^{58} - 156344320 q^{60} + 1603984392 q^{61} - 2461554432 q^{62} - 5135206432 q^{63} + 1398176070 q^{65} + 5536825088 q^{66} + 2502647712 q^{67} + 386620416 q^{68} + 174645120 q^{70} - 7137533808 q^{71} - 2910076928 q^{72} + 2304462438 q^{73} + 9497972200 q^{75} + 559779840 q^{76} + 597969864 q^{77} + 11288293632 q^{78} - 1431306240 q^{80} - 26068931054 q^{81} - 3618452352 q^{82} - 88180632 q^{83} + 1729841610 q^{85} + 2036120064 q^{86} + 35176248320 q^{87} + 5307039744 q^{88} - 25065537760 q^{90} - 43718253408 q^{91} - 7707131904 q^{92} + 22042053176 q^{93} - 34456200 q^{95} + 1073741824 q^{96} + 33281088582 q^{97} + 12874047264 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.0000 + 16.0000i −0.500000 + 0.500000i
\(3\) 326.149 + 326.149i 1.34218 + 1.34218i 0.893891 + 0.448284i \(0.147965\pi\)
0.448284 + 0.893891i \(0.352035\pi\)
\(4\) 512.000i 0.500000i
\(5\) 3124.94 19.4459i 0.999981 0.00622269i
\(6\) −10436.8 −1.34218
\(7\) −1507.13 + 1507.13i −0.0896728 + 0.0896728i −0.750520 0.660847i \(-0.770197\pi\)
0.660847 + 0.750520i \(0.270197\pi\)
\(8\) 8192.00 + 8192.00i 0.250000 + 0.250000i
\(9\) 153697.i 2.60287i
\(10\) −49687.9 + 50310.2i −0.496879 + 0.503102i
\(11\) −71462.1 −0.443723 −0.221862 0.975078i \(-0.571213\pi\)
−0.221862 + 0.975078i \(0.571213\pi\)
\(12\) 166988. 166988.i 0.671088 0.671088i
\(13\) −300816. 300816.i −0.810186 0.810186i 0.174475 0.984662i \(-0.444177\pi\)
−0.984662 + 0.174475i \(0.944177\pi\)
\(14\) 48228.2i 0.0896728i
\(15\) 1.02554e6 + 1.01285e6i 1.35050 + 1.33380i
\(16\) −262144. −0.250000
\(17\) 1.11637e6 1.11637e6i 0.786252 0.786252i −0.194626 0.980878i \(-0.562349\pi\)
0.980878 + 0.194626i \(0.0623492\pi\)
\(18\) −2.45915e6 2.45915e6i −1.30143 1.30143i
\(19\) 684142.i 0.276299i 0.990411 + 0.138149i \(0.0441154\pi\)
−0.990411 + 0.138149i \(0.955885\pi\)
\(20\) −9956.30 1.59997e6i −0.00311134 0.499990i
\(21\) −983097. −0.240713
\(22\) 1.14339e6 1.14339e6i 0.221862 0.221862i
\(23\) 1.52597e6 + 1.52597e6i 0.237087 + 0.237087i 0.815643 0.578556i \(-0.196384\pi\)
−0.578556 + 0.815643i \(0.696384\pi\)
\(24\) 5.34362e6i 0.671088i
\(25\) 9.76487e6 121534.i 0.999923 0.0124451i
\(26\) 9.62613e6 0.810186
\(27\) −3.08693e7 + 3.08693e7i −2.15133 + 2.15133i
\(28\) 771651. + 771651.i 0.0448364 + 0.0448364i
\(29\) 2.47039e7i 1.20441i −0.798340 0.602207i \(-0.794288\pi\)
0.798340 0.602207i \(-0.205712\pi\)
\(30\) −3.26142e7 + 202952.i −1.34215 + 0.00835194i
\(31\) 4.13378e7 1.44390 0.721952 0.691943i \(-0.243245\pi\)
0.721952 + 0.691943i \(0.243245\pi\)
\(32\) 4.19430e6 4.19430e6i 0.125000 0.125000i
\(33\) −2.33073e7 2.33073e7i −0.595555 0.595555i
\(34\) 3.57237e7i 0.786252i
\(35\) −4.68038e6 + 4.73900e6i −0.0891130 + 0.0902290i
\(36\) 7.86928e7 1.30143
\(37\) 2.53176e7 2.53176e7i 0.365102 0.365102i −0.500586 0.865687i \(-0.666882\pi\)
0.865687 + 0.500586i \(0.166882\pi\)
\(38\) −1.09463e7 1.09463e7i −0.138149 0.138149i
\(39\) 1.96222e8i 2.17482i
\(40\) 2.57588e7 + 2.54402e7i 0.251551 + 0.248439i
\(41\) −1.32462e8 −1.14333 −0.571664 0.820488i \(-0.693702\pi\)
−0.571664 + 0.820488i \(0.693702\pi\)
\(42\) 1.57296e7 1.57296e7i 0.120357 0.120357i
\(43\) −2.46531e7 2.46531e7i −0.167699 0.167699i 0.618268 0.785967i \(-0.287835\pi\)
−0.785967 + 0.618268i \(0.787835\pi\)
\(44\) 3.65886e7i 0.221862i
\(45\) 2.98877e6 + 4.80293e8i 0.0161968 + 2.60282i
\(46\) −4.88310e7 −0.237087
\(47\) 5.19304e7 5.19304e7i 0.226429 0.226429i −0.584770 0.811199i \(-0.698815\pi\)
0.811199 + 0.584770i \(0.198815\pi\)
\(48\) −8.54979e7 8.54979e7i −0.335544 0.335544i
\(49\) 2.77932e8i 0.983918i
\(50\) −1.54293e8 + 1.58182e8i −0.493739 + 0.506184i
\(51\) 7.28202e8 2.11058
\(52\) −1.54018e8 + 1.54018e8i −0.405093 + 0.405093i
\(53\) −3.03473e8 3.03473e8i −0.725672 0.725672i 0.244083 0.969754i \(-0.421513\pi\)
−0.969754 + 0.244083i \(0.921513\pi\)
\(54\) 9.87817e8i 2.15133i
\(55\) −2.23315e8 + 1.38964e6i −0.443715 + 0.00276115i
\(56\) −2.46928e7 −0.0448364
\(57\) −2.23132e8 + 2.23132e8i −0.370841 + 0.370841i
\(58\) 3.95262e8 + 3.95262e8i 0.602207 + 0.602207i
\(59\) 6.92655e7i 0.0968851i −0.998826 0.0484426i \(-0.984574\pi\)
0.998826 0.0484426i \(-0.0154258\pi\)
\(60\) 5.18580e8 5.25075e8i 0.666899 0.675251i
\(61\) 6.38536e8 0.756025 0.378012 0.925801i \(-0.376608\pi\)
0.378012 + 0.925801i \(0.376608\pi\)
\(62\) −6.61404e8 + 6.61404e8i −0.721952 + 0.721952i
\(63\) −2.31641e8 2.31641e8i −0.233407 0.233407i
\(64\) 1.34218e8i 0.125000i
\(65\) −9.45883e8 9.34184e8i −0.815212 0.805129i
\(66\) 7.45832e8 0.595555
\(67\) 7.98844e8 7.98844e8i 0.591682 0.591682i −0.346404 0.938085i \(-0.612597\pi\)
0.938085 + 0.346404i \(0.112597\pi\)
\(68\) −5.71579e8 5.71579e8i −0.393126 0.393126i
\(69\) 9.95386e8i 0.636423i
\(70\) −937840. 1.50710e8i −0.000558005 0.0896710i
\(71\) −4.06392e8 −0.225244 −0.112622 0.993638i \(-0.535925\pi\)
−0.112622 + 0.993638i \(0.535925\pi\)
\(72\) −1.25908e9 + 1.25908e9i −0.650717 + 0.650717i
\(73\) −5.91419e8 5.91419e8i −0.285286 0.285286i 0.549927 0.835213i \(-0.314656\pi\)
−0.835213 + 0.549927i \(0.814656\pi\)
\(74\) 8.10163e8i 0.365102i
\(75\) 3.22444e9 + 3.14516e9i 1.35878 + 1.32537i
\(76\) 3.50281e8 0.138149
\(77\) 1.07703e8 1.07703e8i 0.0397899 0.0397899i
\(78\) 3.13955e9 + 3.13955e9i 1.08741 + 1.08741i
\(79\) 6.97925e8i 0.226816i 0.993549 + 0.113408i \(0.0361767\pi\)
−0.993549 + 0.113408i \(0.963823\pi\)
\(80\) −8.19184e8 + 5.09762e6i −0.249995 + 0.00155567i
\(81\) −1.10603e10 −3.17206
\(82\) 2.11939e9 2.11939e9i 0.571664 0.571664i
\(83\) −2.76663e9 2.76663e9i −0.702362 0.702362i 0.262555 0.964917i \(-0.415435\pi\)
−0.964917 + 0.262555i \(0.915435\pi\)
\(84\) 5.03346e8i 0.120357i
\(85\) 3.46687e9 3.51028e9i 0.781344 0.791129i
\(86\) 7.88901e8 0.167699
\(87\) 8.05714e9 8.05714e9i 1.61653 1.61653i
\(88\) −5.85417e8 5.85417e8i −0.110931 0.110931i
\(89\) 3.28276e9i 0.587880i 0.955824 + 0.293940i \(0.0949667\pi\)
−0.955824 + 0.293940i \(0.905033\pi\)
\(90\) −7.73251e9 7.63687e9i −1.30951 1.29331i
\(91\) 9.06739e8 0.145303
\(92\) 7.81297e8 7.81297e8i 0.118543 0.118543i
\(93\) 1.34823e10 + 1.34823e10i 1.93797 + 1.93797i
\(94\) 1.66177e9i 0.226429i
\(95\) 1.33038e7 + 2.13790e9i 0.00171932 + 0.276293i
\(96\) 2.73593e9 0.335544
\(97\) −3.71980e9 + 3.71980e9i −0.433172 + 0.433172i −0.889706 0.456534i \(-0.849091\pi\)
0.456534 + 0.889706i \(0.349091\pi\)
\(98\) −4.44692e9 4.44692e9i −0.491959 0.491959i
\(99\) 1.09835e10i 1.15495i
\(100\) −6.22257e7 4.99961e9i −0.00622257 0.499961i
\(101\) −1.25605e10 −1.19509 −0.597546 0.801834i \(-0.703858\pi\)
−0.597546 + 0.801834i \(0.703858\pi\)
\(102\) −1.16512e10 + 1.16512e10i −1.05529 + 1.05529i
\(103\) 2.20101e9 + 2.20101e9i 0.189861 + 0.189861i 0.795636 0.605775i \(-0.207137\pi\)
−0.605775 + 0.795636i \(0.707137\pi\)
\(104\) 4.92858e9i 0.405093i
\(105\) −3.07212e9 + 1.91172e7i −0.240709 + 0.00149788i
\(106\) 9.71112e9 0.725672
\(107\) −1.14498e10 + 1.14498e10i −0.816358 + 0.816358i −0.985578 0.169220i \(-0.945875\pi\)
0.169220 + 0.985578i \(0.445875\pi\)
\(108\) 1.58051e10 + 1.58051e10i 1.07567 + 1.07567i
\(109\) 2.68242e10i 1.74339i 0.490052 + 0.871693i \(0.336978\pi\)
−0.490052 + 0.871693i \(0.663022\pi\)
\(110\) 3.55080e9 3.59527e9i 0.220477 0.223238i
\(111\) 1.65146e10 0.980061
\(112\) 3.95085e8 3.95085e8i 0.0224182 0.0224182i
\(113\) −2.19648e10 2.19648e10i −1.19216 1.19216i −0.976459 0.215702i \(-0.930796\pi\)
−0.215702 0.976459i \(-0.569204\pi\)
\(114\) 7.14023e9i 0.370841i
\(115\) 4.79824e9 + 4.73889e9i 0.238557 + 0.235607i
\(116\) −1.26484e10 −0.602207
\(117\) 4.62345e10 4.62345e10i 2.10881 2.10881i
\(118\) 1.10825e9 + 1.10825e9i 0.0484426 + 0.0484426i
\(119\) 3.36502e9i 0.141011i
\(120\) 1.03911e8 + 1.66985e10i 0.00417597 + 0.671075i
\(121\) −2.08306e10 −0.803110
\(122\) −1.02166e10 + 1.02166e10i −0.378012 + 0.378012i
\(123\) −4.32022e10 4.32022e10i −1.53455 1.53455i
\(124\) 2.11649e10i 0.721952i
\(125\) 3.05123e10 5.69674e8i 0.999826 0.0186671i
\(126\) 7.41252e9 0.233407
\(127\) −2.16505e10 + 2.16505e10i −0.655313 + 0.655313i −0.954268 0.298954i \(-0.903362\pi\)
0.298954 + 0.954268i \(0.403362\pi\)
\(128\) −2.14748e9 2.14748e9i −0.0625000 0.0625000i
\(129\) 1.60812e10i 0.450163i
\(130\) 3.00811e10 1.87189e8i 0.810170 0.00504153i
\(131\) 6.24374e10 1.61841 0.809204 0.587528i \(-0.199899\pi\)
0.809204 + 0.587528i \(0.199899\pi\)
\(132\) −1.19333e10 + 1.19333e10i −0.297777 + 0.297777i
\(133\) −1.03109e9 1.03109e9i −0.0247765 0.0247765i
\(134\) 2.55630e10i 0.591682i
\(135\) −9.58643e10 + 9.70649e10i −2.13790 + 2.16468i
\(136\) 1.82905e10 0.393126
\(137\) 1.70085e10 1.70085e10i 0.352423 0.352423i −0.508588 0.861010i \(-0.669832\pi\)
0.861010 + 0.508588i \(0.169832\pi\)
\(138\) −1.59262e10 1.59262e10i −0.318212 0.318212i
\(139\) 1.11583e9i 0.0215043i 0.999942 + 0.0107522i \(0.00342259\pi\)
−0.999942 + 0.0107522i \(0.996577\pi\)
\(140\) 2.42637e9 + 2.39636e9i 0.0451145 + 0.0445565i
\(141\) 3.38740e10 0.607815
\(142\) 6.50228e9 6.50228e9i 0.112622 0.112622i
\(143\) 2.14970e10 + 2.14970e10i 0.359499 + 0.359499i
\(144\) 4.02907e10i 0.650717i
\(145\) −4.80389e8 7.71982e10i −0.00749469 1.20439i
\(146\) 1.89254e10 0.285286
\(147\) −9.06473e10 + 9.06473e10i −1.32059 + 1.32059i
\(148\) −1.29626e10 1.29626e10i −0.182551 0.182551i
\(149\) 2.71583e10i 0.369804i −0.982757 0.184902i \(-0.940803\pi\)
0.982757 0.184902i \(-0.0591968\pi\)
\(150\) −1.01914e11 + 1.26843e9i −1.34207 + 0.0167035i
\(151\) 4.49613e9 0.0572735 0.0286368 0.999590i \(-0.490883\pi\)
0.0286368 + 0.999590i \(0.490883\pi\)
\(152\) −5.60450e9 + 5.60450e9i −0.0690746 + 0.0690746i
\(153\) 1.71582e11 + 1.71582e11i 2.04651 + 2.04651i
\(154\) 3.44649e9i 0.0397899i
\(155\) 1.29178e11 8.03850e8i 1.44388 0.00898497i
\(156\) −1.00466e11 −1.08741
\(157\) −8.17410e10 + 8.17410e10i −0.856922 + 0.856922i −0.990974 0.134052i \(-0.957201\pi\)
0.134052 + 0.990974i \(0.457201\pi\)
\(158\) −1.11668e10 1.11668e10i −0.113408 0.113408i
\(159\) 1.97954e11i 1.94796i
\(160\) 1.30254e10 1.31885e10i 0.124220 0.125775i
\(161\) −4.59967e9 −0.0425204
\(162\) 1.76965e11 1.76965e11i 1.58603 1.58603i
\(163\) −1.47684e11 1.47684e11i −1.28350 1.28350i −0.938664 0.344834i \(-0.887935\pi\)
−0.344834 0.938664i \(-0.612065\pi\)
\(164\) 6.78203e10i 0.571664i
\(165\) −7.32870e10 7.23806e10i −0.599249 0.591837i
\(166\) 8.85323e10 0.702362
\(167\) 1.23605e11 1.23605e11i 0.951596 0.951596i −0.0472858 0.998881i \(-0.515057\pi\)
0.998881 + 0.0472858i \(0.0150572\pi\)
\(168\) −8.05353e9 8.05353e9i −0.0601783 0.0601783i
\(169\) 4.31226e10i 0.312803i
\(170\) 6.94679e8 + 1.11634e11i 0.00489260 + 0.786237i
\(171\) −1.05151e11 −0.719169
\(172\) −1.26224e10 + 1.26224e10i −0.0838494 + 0.0838494i
\(173\) −1.80164e10 1.80164e10i −0.116262 0.116262i 0.646582 0.762844i \(-0.276198\pi\)
−0.762844 + 0.646582i \(0.776198\pi\)
\(174\) 2.57829e11i 1.61653i
\(175\) −1.45338e10 + 1.49001e10i −0.0885498 + 0.0907818i
\(176\) 1.87334e10 0.110931
\(177\) 2.25909e10 2.25909e10i 0.130037 0.130037i
\(178\) −5.25241e10 5.25241e10i −0.293940 0.293940i
\(179\) 3.15130e11i 1.71485i 0.514613 + 0.857423i \(0.327936\pi\)
−0.514613 + 0.857423i \(0.672064\pi\)
\(180\) 2.45910e11 1.53025e9i 1.30141 0.00809842i
\(181\) −2.08416e11 −1.07285 −0.536425 0.843948i \(-0.680226\pi\)
−0.536425 + 0.843948i \(0.680226\pi\)
\(182\) −1.45078e10 + 1.45078e10i −0.0726516 + 0.0726516i
\(183\) 2.08258e11 + 2.08258e11i 1.01472 + 1.01472i
\(184\) 2.50015e10i 0.118543i
\(185\) 7.86236e10 7.96083e10i 0.362823 0.367366i
\(186\) −4.31432e11 −1.93797
\(187\) −7.97778e10 + 7.97778e10i −0.348878 + 0.348878i
\(188\) −2.65883e10 2.65883e10i −0.113215 0.113215i
\(189\) 9.30480e10i 0.385832i
\(190\) −3.44193e10 3.39936e10i −0.139006 0.137287i
\(191\) −3.00305e10 −0.118140 −0.0590699 0.998254i \(-0.518813\pi\)
−0.0590699 + 0.998254i \(0.518813\pi\)
\(192\) −4.37749e10 + 4.37749e10i −0.167772 + 0.167772i
\(193\) −3.12278e10 3.12278e10i −0.116615 0.116615i 0.646391 0.763006i \(-0.276277\pi\)
−0.763006 + 0.646391i \(0.776277\pi\)
\(194\) 1.19034e11i 0.433172i
\(195\) −3.81571e9 6.13181e11i −0.0135332 2.17478i
\(196\) 1.42301e11 0.491959
\(197\) 7.34355e9 7.34355e9i 0.0247500 0.0247500i −0.694623 0.719373i \(-0.744429\pi\)
0.719373 + 0.694623i \(0.244429\pi\)
\(198\) 1.75736e11 + 1.75736e11i 0.577477 + 0.577477i
\(199\) 2.55725e11i 0.819423i 0.912215 + 0.409712i \(0.134371\pi\)
−0.912215 + 0.409712i \(0.865629\pi\)
\(200\) 8.09894e10 + 7.89982e10i 0.253092 + 0.246869i
\(201\) 5.21084e11 1.58828
\(202\) 2.00969e11 2.00969e11i 0.597546 0.597546i
\(203\) 3.72320e10 + 3.72320e10i 0.108003 + 0.108003i
\(204\) 3.72839e11i 1.05529i
\(205\) −4.13934e11 + 2.57583e9i −1.14331 + 0.00711457i
\(206\) −7.04325e10 −0.189861
\(207\) −2.34537e11 + 2.34537e11i −0.617105 + 0.617105i
\(208\) 7.88572e10 + 7.88572e10i 0.202547 + 0.202547i
\(209\) 4.88903e10i 0.122600i
\(210\) 4.88480e10 4.94598e10i 0.119605 0.121103i
\(211\) 5.52308e11 1.32059 0.660297 0.751005i \(-0.270430\pi\)
0.660297 + 0.751005i \(0.270430\pi\)
\(212\) −1.55378e11 + 1.55378e11i −0.362836 + 0.362836i
\(213\) −1.32544e11 1.32544e11i −0.302317 0.302317i
\(214\) 3.66395e11i 0.816358i
\(215\) −7.75190e10 7.65602e10i −0.168739 0.166652i
\(216\) −5.05762e11 −1.07567
\(217\) −6.23014e10 + 6.23014e10i −0.129479 + 0.129479i
\(218\) −4.29186e11 4.29186e11i −0.871693 0.871693i
\(219\) 3.85781e11i 0.765809i
\(220\) 7.11498e8 + 1.14337e11i 0.00138058 + 0.221857i
\(221\) −6.71642e11 −1.27402
\(222\) −2.64233e11 + 2.64233e11i −0.490030 + 0.490030i
\(223\) 7.13397e11 + 7.13397e11i 1.29362 + 1.29362i 0.932531 + 0.361090i \(0.117595\pi\)
0.361090 + 0.932531i \(0.382405\pi\)
\(224\) 1.26427e10i 0.0224182i
\(225\) 1.86795e10 + 1.50083e12i 0.0323931 + 2.60267i
\(226\) 7.02874e11 1.19216
\(227\) 7.15956e11 7.15956e11i 1.18784 1.18784i 0.210173 0.977664i \(-0.432597\pi\)
0.977664 0.210173i \(-0.0674026\pi\)
\(228\) 1.14244e11 + 1.14244e11i 0.185421 + 0.185421i
\(229\) 2.72580e11i 0.432829i 0.976302 + 0.216415i \(0.0694363\pi\)
−0.976302 + 0.216415i \(0.930564\pi\)
\(230\) −1.52594e11 + 9.49563e8i −0.237082 + 0.00147531i
\(231\) 7.02542e10 0.106810
\(232\) 2.02374e11 2.02374e11i 0.301103 0.301103i
\(233\) −3.08559e11 3.08559e11i −0.449323 0.449323i 0.445806 0.895130i \(-0.352917\pi\)
−0.895130 + 0.445806i \(0.852917\pi\)
\(234\) 1.47951e12i 2.10881i
\(235\) 1.61269e11 1.63289e11i 0.225016 0.227834i
\(236\) −3.54640e10 −0.0484426
\(237\) −2.27627e11 + 2.27627e11i −0.304426 + 0.304426i
\(238\) −5.38403e10 5.38403e10i −0.0705054 0.0705054i
\(239\) 1.51966e11i 0.194875i −0.995242 0.0974375i \(-0.968935\pi\)
0.995242 0.0974375i \(-0.0310646\pi\)
\(240\) −2.68838e11 2.65513e11i −0.337625 0.333449i
\(241\) −1.68383e11 −0.207116 −0.103558 0.994623i \(-0.533023\pi\)
−0.103558 + 0.994623i \(0.533023\pi\)
\(242\) 3.33290e11 3.33290e11i 0.401555 0.401555i
\(243\) −1.78450e12 1.78450e12i −2.10613 2.10613i
\(244\) 3.26930e11i 0.378012i
\(245\) 5.40464e9 + 8.68522e11i 0.00612261 + 0.983899i
\(246\) 1.38247e12 1.53455
\(247\) 2.05801e11 2.05801e11i 0.223853 0.223853i
\(248\) 3.38639e11 + 3.38639e11i 0.360976 + 0.360976i
\(249\) 1.80467e12i 1.88539i
\(250\) −4.79081e11 + 4.97311e11i −0.490579 + 0.509246i
\(251\) −1.52960e12 −1.53535 −0.767676 0.640838i \(-0.778587\pi\)
−0.767676 + 0.640838i \(0.778587\pi\)
\(252\) −1.18600e11 + 1.18600e11i −0.116703 + 0.116703i
\(253\) −1.09049e11 1.09049e11i −0.105201 0.105201i
\(254\) 6.92816e11i 0.655313i
\(255\) 2.27559e12 1.41605e10i 2.11054 0.0131335i
\(256\) 6.87195e10 0.0625000
\(257\) −8.15308e11 + 8.15308e11i −0.727203 + 0.727203i −0.970062 0.242858i \(-0.921915\pi\)
0.242858 + 0.970062i \(0.421915\pi\)
\(258\) 2.57299e11 + 2.57299e11i 0.225081 + 0.225081i
\(259\) 7.63138e10i 0.0654793i
\(260\) −4.78302e11 + 4.84292e11i −0.402564 + 0.407606i
\(261\) 3.79691e12 3.13493
\(262\) −9.98998e11 + 9.98998e11i −0.809204 + 0.809204i
\(263\) 4.93450e11 + 4.93450e11i 0.392161 + 0.392161i 0.875457 0.483296i \(-0.160561\pi\)
−0.483296 + 0.875457i \(0.660561\pi\)
\(264\) 3.81866e11i 0.297777i
\(265\) −9.54235e11 9.42432e11i −0.730173 0.721142i
\(266\) 3.29949e10 0.0247765
\(267\) −1.07067e12 + 1.07067e12i −0.789039 + 0.789039i
\(268\) −4.09008e11 4.09008e11i −0.295841 0.295841i
\(269\) 9.86681e11i 0.700512i −0.936654 0.350256i \(-0.886095\pi\)
0.936654 0.350256i \(-0.113905\pi\)
\(270\) −1.92090e10 3.08687e12i −0.0133871 2.15129i
\(271\) −8.14097e11 −0.556967 −0.278484 0.960441i \(-0.589832\pi\)
−0.278484 + 0.960441i \(0.589832\pi\)
\(272\) −2.92648e11 + 2.92648e11i −0.196563 + 0.196563i
\(273\) 2.95732e11 + 2.95732e11i 0.195022 + 0.195022i
\(274\) 5.44273e11i 0.352423i
\(275\) −6.97818e11 + 8.68511e9i −0.443689 + 0.00552219i
\(276\) 5.09638e11 0.318212
\(277\) 1.79975e12 1.79975e12i 1.10360 1.10360i 0.109630 0.993972i \(-0.465033\pi\)
0.993972 0.109630i \(-0.0349666\pi\)
\(278\) −1.78534e10 1.78534e10i −0.0107522 0.0107522i
\(279\) 6.35349e12i 3.75830i
\(280\) −7.71636e10 + 4.80174e8i −0.0448355 + 0.000279003i
\(281\) −2.26906e12 −1.29514 −0.647568 0.762008i \(-0.724214\pi\)
−0.647568 + 0.762008i \(0.724214\pi\)
\(282\) −5.41985e11 + 5.41985e11i −0.303907 + 0.303907i
\(283\) 8.09303e11 + 8.09303e11i 0.445840 + 0.445840i 0.893969 0.448129i \(-0.147909\pi\)
−0.448129 + 0.893969i \(0.647909\pi\)
\(284\) 2.08073e11i 0.112622i
\(285\) −6.92935e11 + 7.01613e11i −0.368526 + 0.373142i
\(286\) −6.87903e11 −0.359499
\(287\) 1.99637e11 1.99637e11i 0.102525 0.102525i
\(288\) 6.44651e11 + 6.44651e11i 0.325359 + 0.325359i
\(289\) 4.76549e11i 0.236384i
\(290\) 1.24286e12 + 1.22748e12i 0.605942 + 0.598448i
\(291\) −2.42641e12 −1.16279
\(292\) −3.02807e11 + 3.02807e11i −0.142643 + 0.142643i
\(293\) 1.68288e12 + 1.68288e12i 0.779318 + 0.779318i 0.979715 0.200397i \(-0.0642231\pi\)
−0.200397 + 0.979715i \(0.564223\pi\)
\(294\) 2.90071e12i 1.32059i
\(295\) −1.34693e9 2.16451e11i −0.000602886 0.0968833i
\(296\) 4.14803e11 0.182551
\(297\) 2.20598e12 2.20598e12i 0.954596 0.954596i
\(298\) 4.34533e11 + 4.34533e11i 0.184902 + 0.184902i
\(299\) 9.18074e11i 0.384168i
\(300\) 1.61032e12 1.65091e12i 0.662684 0.679388i
\(301\) 7.43110e10 0.0300760
\(302\) −7.19381e10 + 7.19381e10i −0.0286368 + 0.0286368i
\(303\) −4.09661e12 4.09661e12i −1.60402 1.60402i
\(304\) 1.79344e11i 0.0690746i
\(305\) 1.99539e12 1.24169e10i 0.756010 0.00470450i
\(306\) −5.49062e12 −2.04651
\(307\) 2.99054e12 2.99054e12i 1.09662 1.09662i 0.101820 0.994803i \(-0.467533\pi\)
0.994803 0.101820i \(-0.0324667\pi\)
\(308\) −5.51438e10 5.51438e10i −0.0198950 0.0198950i
\(309\) 1.43572e12i 0.509655i
\(310\) −2.05399e12 + 2.07971e12i −0.717446 + 0.726431i
\(311\) 3.03633e12 1.04363 0.521815 0.853058i \(-0.325255\pi\)
0.521815 + 0.853058i \(0.325255\pi\)
\(312\) 1.60745e12 1.60745e12i 0.543706 0.543706i
\(313\) 8.96455e11 + 8.96455e11i 0.298405 + 0.298405i 0.840389 0.541984i \(-0.182327\pi\)
−0.541984 + 0.840389i \(0.682327\pi\)
\(314\) 2.61571e12i 0.856922i
\(315\) −7.28369e11 7.19360e11i −0.234854 0.231950i
\(316\) 3.57337e11 0.113408
\(317\) 3.27607e12 3.27607e12i 1.02343 1.02343i 0.0237088 0.999719i \(-0.492453\pi\)
0.999719 0.0237088i \(-0.00754744\pi\)
\(318\) 3.16727e12 + 3.16727e12i 0.973979 + 0.973979i
\(319\) 1.76539e12i 0.534426i
\(320\) 2.60998e9 + 4.19422e11i 0.000777836 + 0.124998i
\(321\) −7.46870e12 −2.19139
\(322\) 7.35947e10 7.35947e10i 0.0212602 0.0212602i
\(323\) 7.63753e11 + 7.63753e11i 0.217240 + 0.217240i
\(324\) 5.66287e12i 1.58603i
\(325\) −2.97399e12 2.90087e12i −0.820206 0.800041i
\(326\) 4.72588e12 1.28350
\(327\) −8.74866e12 + 8.74866e12i −2.33993 + 2.33993i
\(328\) −1.08513e12 1.08513e12i −0.285832 0.285832i
\(329\) 1.56532e11i 0.0406090i
\(330\) 2.33068e12 1.45034e10i 0.595543 0.00370595i
\(331\) 6.48540e11 0.163229 0.0816144 0.996664i \(-0.473992\pi\)
0.0816144 + 0.996664i \(0.473992\pi\)
\(332\) −1.41652e12 + 1.41652e12i −0.351181 + 0.351181i
\(333\) 3.89123e12 + 3.89123e12i 0.950312 + 0.950312i
\(334\) 3.95535e12i 0.951596i
\(335\) 2.48081e12 2.51187e12i 0.587988 0.595352i
\(336\) 2.57713e11 0.0601783
\(337\) −6.16866e11 + 6.16866e11i −0.141919 + 0.141919i −0.774497 0.632578i \(-0.781997\pi\)
0.632578 + 0.774497i \(0.281997\pi\)
\(338\) −6.89961e11 6.89961e11i −0.156402 0.156402i
\(339\) 1.43276e13i 3.20018i
\(340\) −1.79726e12 1.77503e12i −0.395565 0.390672i
\(341\) −2.95408e12 −0.640694
\(342\) 1.68241e12 1.68241e12i 0.359585 0.359585i
\(343\) −8.44607e11 8.44607e11i −0.177903 0.177903i
\(344\) 4.03917e11i 0.0838494i
\(345\) 1.93562e10 + 3.11052e12i 0.00396026 + 0.636411i
\(346\) 5.76526e11 0.116262
\(347\) −5.59961e12 + 5.59961e12i −1.11304 + 1.11304i −0.120302 + 0.992737i \(0.538386\pi\)
−0.992737 + 0.120302i \(0.961614\pi\)
\(348\) −4.12526e12 4.12526e12i −0.808267 0.808267i
\(349\) 6.66328e12i 1.28695i 0.765468 + 0.643474i \(0.222507\pi\)
−0.765468 + 0.643474i \(0.777493\pi\)
\(350\) −5.86139e9 4.70942e11i −0.00111599 0.0896658i
\(351\) 1.85720e13 3.48596
\(352\) −2.99734e11 + 2.99734e11i −0.0554654 + 0.0554654i
\(353\) 4.34264e12 + 4.34264e12i 0.792284 + 0.792284i 0.981865 0.189581i \(-0.0607130\pi\)
−0.189581 + 0.981865i \(0.560713\pi\)
\(354\) 7.22908e11i 0.130037i
\(355\) −1.26995e12 + 7.90266e9i −0.225240 + 0.00140162i
\(356\) 1.68077e12 0.293940
\(357\) −1.09750e12 + 1.09750e12i −0.189261 + 0.189261i
\(358\) −5.04208e12 5.04208e12i −0.857423 0.857423i
\(359\) 4.49607e12i 0.753982i 0.926217 + 0.376991i \(0.123041\pi\)
−0.926217 + 0.376991i \(0.876959\pi\)
\(360\) −3.91008e12 + 3.95905e12i −0.646656 + 0.654754i
\(361\) 5.66302e12 0.923659
\(362\) 3.33466e12 3.33466e12i 0.536425 0.536425i
\(363\) −6.79387e12 6.79387e12i −1.07791 1.07791i
\(364\) 4.64250e11i 0.0726516i
\(365\) −1.85965e12 1.83665e12i −0.287056 0.283506i
\(366\) −6.66424e12 −1.01472
\(367\) 2.25425e12 2.25425e12i 0.338587 0.338587i −0.517248 0.855836i \(-0.673044\pi\)
0.855836 + 0.517248i \(0.173044\pi\)
\(368\) −4.00024e11 4.00024e11i −0.0592716 0.0592716i
\(369\) 2.03589e13i 2.97593i
\(370\) 1.57543e10 + 2.53171e12i 0.00227191 + 0.365095i
\(371\) 9.14746e11 0.130146
\(372\) 6.90292e12 6.90292e12i 0.968987 0.968987i
\(373\) −6.84615e12 6.84615e12i −0.948205 0.948205i 0.0505184 0.998723i \(-0.483913\pi\)
−0.998723 + 0.0505184i \(0.983913\pi\)
\(374\) 2.55289e12i 0.348878i
\(375\) 1.01373e13 + 9.76573e12i 1.36700 + 1.31689i
\(376\) 8.50827e11 0.113215
\(377\) −7.43134e12 + 7.43134e12i −0.975799 + 0.975799i
\(378\) 1.48877e12 + 1.48877e12i 0.192916 + 0.192916i
\(379\) 1.40526e13i 1.79705i 0.438927 + 0.898523i \(0.355359\pi\)
−0.438927 + 0.898523i \(0.644641\pi\)
\(380\) 1.09461e12 6.81153e9i 0.138147 0.000859659i
\(381\) −1.41226e13 −1.75909
\(382\) 4.80489e11 4.80489e11i 0.0590699 0.0590699i
\(383\) −2.81487e12 2.81487e12i −0.341558 0.341558i 0.515395 0.856953i \(-0.327645\pi\)
−0.856953 + 0.515395i \(0.827645\pi\)
\(384\) 1.40080e12i 0.167772i
\(385\) 3.34470e11 3.38659e11i 0.0395415 0.0400367i
\(386\) 9.99290e11 0.116615
\(387\) 3.78911e12 3.78911e12i 0.436498 0.436498i
\(388\) 1.90454e12 + 1.90454e12i 0.216586 + 0.216586i
\(389\) 1.40114e12i 0.157302i −0.996902 0.0786509i \(-0.974939\pi\)
0.996902 0.0786509i \(-0.0250613\pi\)
\(390\) 9.87195e12 + 9.74985e12i 1.09416 + 1.08062i
\(391\) 3.40708e12 0.372819
\(392\) −2.27682e12 + 2.27682e12i −0.245979 + 0.245979i
\(393\) 2.03639e13 + 2.03639e13i 2.17219 + 2.17219i
\(394\) 2.34994e11i 0.0247500i
\(395\) 1.35718e10 + 2.18097e12i 0.00141140 + 0.226811i
\(396\) −5.62355e12 −0.577477
\(397\) 7.93928e12 7.93928e12i 0.805061 0.805061i −0.178821 0.983882i \(-0.557228\pi\)
0.983882 + 0.178821i \(0.0572282\pi\)
\(398\) −4.09161e12 4.09161e12i −0.409712 0.409712i
\(399\) 6.72578e11i 0.0665087i
\(400\) −2.55980e12 + 3.18595e10i −0.249981 + 0.00311128i
\(401\) 3.42032e12 0.329871 0.164936 0.986304i \(-0.447258\pi\)
0.164936 + 0.986304i \(0.447258\pi\)
\(402\) −8.33734e12 + 8.33734e12i −0.794141 + 0.794141i
\(403\) −1.24351e13 1.24351e13i −1.16983 1.16983i
\(404\) 6.43100e12i 0.597546i
\(405\) −3.45628e13 + 2.15077e11i −3.17200 + 0.0197387i
\(406\) −1.19142e12 −0.108003
\(407\) −1.80925e12 + 1.80925e12i −0.162004 + 0.162004i
\(408\) 5.96543e12 + 5.96543e12i 0.527644 + 0.527644i
\(409\) 6.67262e12i 0.583016i 0.956568 + 0.291508i \(0.0941569\pi\)
−0.956568 + 0.291508i \(0.905843\pi\)
\(410\) 6.58174e12 6.66416e12i 0.568095 0.575210i
\(411\) 1.10946e13 0.946026
\(412\) 1.12692e12 1.12692e12i 0.0949307 0.0949307i
\(413\) 1.04392e11 + 1.04392e11i 0.00868796 + 0.00868796i
\(414\) 7.50518e12i 0.617105i
\(415\) −8.69936e12 8.59176e12i −0.706719 0.697978i
\(416\) −2.52343e12 −0.202547
\(417\) −3.63928e11 + 3.63928e11i −0.0288626 + 0.0288626i
\(418\) 7.82244e11 + 7.82244e11i 0.0613001 + 0.0613001i
\(419\) 2.04512e13i 1.58361i −0.610775 0.791804i \(-0.709142\pi\)
0.610775 0.791804i \(-0.290858\pi\)
\(420\) 9.78801e9 + 1.57292e12i 0.000748941 + 0.120354i
\(421\) 1.53655e13 1.16181 0.580906 0.813971i \(-0.302698\pi\)
0.580906 + 0.813971i \(0.302698\pi\)
\(422\) −8.83693e12 + 8.83693e12i −0.660297 + 0.660297i
\(423\) 7.98153e12 + 7.98153e12i 0.589365 + 0.589365i
\(424\) 4.97210e12i 0.362836i
\(425\) 1.07655e13 1.10368e13i 0.776406 0.795976i
\(426\) 4.24142e12 0.302317
\(427\) −9.62356e11 + 9.62356e11i −0.0677948 + 0.0677948i
\(428\) 5.86232e12 + 5.86232e12i 0.408179 + 0.408179i
\(429\) 1.40224e13i 0.965020i
\(430\) 2.46527e12 1.53409e10i 0.167696 0.00104354i
\(431\) −1.77529e13 −1.19367 −0.596834 0.802365i \(-0.703575\pi\)
−0.596834 + 0.802365i \(0.703575\pi\)
\(432\) 8.09219e12 8.09219e12i 0.537833 0.537833i
\(433\) −4.48900e11 4.48900e11i −0.0294924 0.0294924i 0.692207 0.721699i \(-0.256639\pi\)
−0.721699 + 0.692207i \(0.756639\pi\)
\(434\) 1.99365e12i 0.129479i
\(435\) 2.50214e13 2.53348e13i 1.60644 1.62656i
\(436\) 1.37340e13 0.871693
\(437\) −1.04398e12 + 1.04398e12i −0.0655067 + 0.0655067i
\(438\) 6.17250e12 + 6.17250e12i 0.382904 + 0.382904i
\(439\) 9.39701e12i 0.576325i 0.957582 + 0.288162i \(0.0930443\pi\)
−0.957582 + 0.288162i \(0.906956\pi\)
\(440\) −1.84078e12 1.81801e12i −0.111619 0.110238i
\(441\) −4.27173e13 −2.56101
\(442\) 1.07463e13 1.07463e13i 0.637010 0.637010i
\(443\) −4.16887e12 4.16887e12i −0.244343 0.244343i 0.574301 0.818644i \(-0.305274\pi\)
−0.818644 + 0.574301i \(0.805274\pi\)
\(444\) 8.45547e12i 0.490030i
\(445\) 6.38362e10 + 1.02584e13i 0.00365819 + 0.587869i
\(446\) −2.28287e13 −1.29362
\(447\) 8.85765e12 8.85765e12i 0.496342 0.496342i
\(448\) −2.02284e11 2.02284e11i −0.0112091 0.0112091i
\(449\) 8.98571e12i 0.492403i −0.969219 0.246201i \(-0.920818\pi\)
0.969219 0.246201i \(-0.0791825\pi\)
\(450\) −2.43121e13 2.37144e13i −1.31753 1.28514i
\(451\) 9.46598e12 0.507321
\(452\) −1.12460e13 + 1.12460e13i −0.596081 + 0.596081i
\(453\) 1.46641e12 + 1.46641e12i 0.0768711 + 0.0768711i
\(454\) 2.29106e13i 1.18784i
\(455\) 2.83351e12 1.76324e10i 0.145300 0.000904177i
\(456\) −3.65580e12 −0.185421
\(457\) 5.53018e12 5.53018e12i 0.277433 0.277433i −0.554650 0.832084i \(-0.687148\pi\)
0.832084 + 0.554650i \(0.187148\pi\)
\(458\) −4.36128e12 4.36128e12i −0.216415 0.216415i
\(459\) 6.89228e13i 3.38298i
\(460\) 2.42631e12 2.45670e12i 0.117803 0.119279i
\(461\) 1.62906e13 0.782406 0.391203 0.920304i \(-0.372059\pi\)
0.391203 + 0.920304i \(0.372059\pi\)
\(462\) −1.12407e12 + 1.12407e12i −0.0534050 + 0.0534050i
\(463\) 7.68718e12 + 7.68718e12i 0.361295 + 0.361295i 0.864290 0.502994i \(-0.167768\pi\)
−0.502994 + 0.864290i \(0.667768\pi\)
\(464\) 6.47598e12i 0.301103i
\(465\) 4.23934e13 + 4.18691e13i 1.95000 + 1.92588i
\(466\) 9.87390e12 0.449323
\(467\) −1.94981e13 + 1.94981e13i −0.877826 + 0.877826i −0.993309 0.115484i \(-0.963158\pi\)
0.115484 + 0.993309i \(0.463158\pi\)
\(468\) −2.36721e13 2.36721e13i −1.05440 1.05440i
\(469\) 2.40792e12i 0.106115i
\(470\) 3.23146e10 + 5.19294e12i 0.00140900 + 0.226425i
\(471\) −5.33194e13 −2.30028
\(472\) 5.67423e11 5.67423e11i 0.0242213 0.0242213i
\(473\) 1.76177e12 + 1.76177e12i 0.0744119 + 0.0744119i
\(474\) 7.28407e12i 0.304426i
\(475\) 8.31469e10 + 6.68056e12i 0.00343857 + 0.276277i
\(476\) 1.72289e12 0.0705054
\(477\) 4.66428e13 4.66428e13i 1.88883 1.88883i
\(478\) 2.43145e12 + 2.43145e12i 0.0974375 + 0.0974375i
\(479\) 3.68363e13i 1.46083i −0.683006 0.730413i \(-0.739328\pi\)
0.683006 0.730413i \(-0.260672\pi\)
\(480\) 8.54963e12 5.32027e10i 0.335537 0.00208798i
\(481\) −1.52319e13 −0.591600
\(482\) 2.69413e12 2.69413e12i 0.103558 0.103558i
\(483\) −1.50018e12 1.50018e12i −0.0570699 0.0570699i
\(484\) 1.06653e13i 0.401555i
\(485\) −1.15518e13 + 1.16965e13i −0.430469 + 0.435860i
\(486\) 5.71040e13 2.10613
\(487\) −1.50421e13 + 1.50421e13i −0.549116 + 0.549116i −0.926185 0.377069i \(-0.876932\pi\)
0.377069 + 0.926185i \(0.376932\pi\)
\(488\) 5.23088e12 + 5.23088e12i 0.189006 + 0.189006i
\(489\) 9.63338e13i 3.44536i
\(490\) −1.39828e13 1.38099e13i −0.495011 0.488888i
\(491\) −2.16133e13 −0.757380 −0.378690 0.925524i \(-0.623625\pi\)
−0.378690 + 0.925524i \(0.623625\pi\)
\(492\) −2.21195e13 + 2.21195e13i −0.767273 + 0.767273i
\(493\) −2.75786e13 2.75786e13i −0.946972 0.946972i
\(494\) 6.58564e12i 0.223853i
\(495\) −2.13584e11 3.43228e13i −0.00718692 1.15493i
\(496\) −1.08364e13 −0.360976
\(497\) 6.12486e11 6.12486e11i 0.0201983 0.0201983i
\(498\) 2.88747e13 + 2.88747e13i 0.942693 + 0.942693i
\(499\) 5.41692e13i 1.75085i 0.483350 + 0.875427i \(0.339420\pi\)
−0.483350 + 0.875427i \(0.660580\pi\)
\(500\) −2.91673e11 1.56223e13i −0.00933355 0.499913i
\(501\) 8.06270e13 2.55442
\(502\) 2.44735e13 2.44735e13i 0.767676 0.767676i
\(503\) 1.09238e13 + 1.09238e13i 0.339262 + 0.339262i 0.856090 0.516827i \(-0.172887\pi\)
−0.516827 + 0.856090i \(0.672887\pi\)
\(504\) 3.79521e12i 0.116703i
\(505\) −3.92510e13 + 2.44251e11i −1.19507 + 0.00743669i
\(506\) 3.48957e12 0.105201
\(507\) −1.40644e13 + 1.40644e13i −0.419837 + 0.419837i
\(508\) 1.10850e13 + 1.10850e13i 0.327657 + 0.327657i
\(509\) 2.14613e13i 0.628155i 0.949397 + 0.314078i \(0.101695\pi\)
−0.949397 + 0.314078i \(0.898305\pi\)
\(510\) −3.61828e13 + 3.66360e13i −1.04870 + 1.06183i
\(511\) 1.78269e12 0.0511648
\(512\) −1.09951e12 + 1.09951e12i −0.0312500 + 0.0312500i
\(513\) −2.11190e13 2.11190e13i −0.594410 0.594410i
\(514\) 2.60898e13i 0.727203i
\(515\) 6.92084e12 + 6.83524e12i 0.191039 + 0.188676i
\(516\) −8.23357e12 −0.225081
\(517\) −3.71105e12 + 3.71105e12i −0.100472 + 0.100472i
\(518\) −1.22102e12 1.22102e12i −0.0327397 0.0327397i
\(519\) 1.17521e13i 0.312088i
\(520\) −9.58406e10 1.54015e13i −0.00252077 0.405085i
\(521\) 3.08056e13 0.802493 0.401246 0.915970i \(-0.368577\pi\)
0.401246 + 0.915970i \(0.368577\pi\)
\(522\) −6.07506e13 + 6.07506e13i −1.56747 + 1.56747i
\(523\) −5.30765e11 5.30765e11i −0.0135642 0.0135642i 0.700292 0.713856i \(-0.253053\pi\)
−0.713856 + 0.700292i \(0.753053\pi\)
\(524\) 3.19679e13i 0.809204i
\(525\) −9.59981e12 + 1.19480e11i −0.240695 + 0.00299571i
\(526\) −1.57904e13 −0.392161
\(527\) 4.61481e13 4.61481e13i 1.13527 1.13527i
\(528\) 6.10986e12 + 6.10986e12i 0.148889 + 0.148889i
\(529\) 3.67693e13i 0.887580i
\(530\) 3.03467e13 1.88841e11i 0.725658 0.00451563i
\(531\) 1.06459e13 0.252179
\(532\) −5.27919e11 + 5.27919e11i −0.0123882 + 0.0123882i
\(533\) 3.98466e13 + 3.98466e13i 0.926308 + 0.926308i
\(534\) 3.42614e13i 0.789039i
\(535\) −3.55574e13 + 3.60027e13i −0.811262 + 0.821422i
\(536\) 1.30883e13 0.295841
\(537\) −1.02779e14 + 1.02779e14i −2.30162 + 2.30162i
\(538\) 1.57869e13 + 1.57869e13i 0.350256 + 0.350256i
\(539\) 1.98616e13i 0.436587i
\(540\) 4.96972e13 + 4.90825e13i 1.08234 + 1.06895i
\(541\) 1.52125e13 0.328258 0.164129 0.986439i \(-0.447519\pi\)
0.164129 + 0.986439i \(0.447519\pi\)
\(542\) 1.30256e13 1.30256e13i 0.278484 0.278484i
\(543\) −6.79747e13 6.79747e13i −1.43995 1.43995i
\(544\) 9.36475e12i 0.196563i
\(545\) 5.21620e11 + 8.38239e13i 0.0108485 + 1.74335i
\(546\) −9.46342e12 −0.195022
\(547\) 4.79703e13 4.79703e13i 0.979571 0.979571i −0.0202243 0.999795i \(-0.506438\pi\)
0.999795 + 0.0202243i \(0.00643804\pi\)
\(548\) −8.70836e12 8.70836e12i −0.176211 0.176211i
\(549\) 9.81409e13i 1.96783i
\(550\) 1.10261e13 1.13040e13i 0.219083 0.224606i
\(551\) 1.69010e13 0.332778
\(552\) −8.15420e12 + 8.15420e12i −0.159106 + 0.159106i
\(553\) −1.05186e12 1.05186e12i −0.0203392 0.0203392i
\(554\) 5.75919e13i 1.10360i
\(555\) 5.16071e13 3.21141e11i 0.980042 0.00609861i
\(556\) 5.71307e11 0.0107522
\(557\) 4.65821e13 4.65821e13i 0.868846 0.868846i −0.123498 0.992345i \(-0.539411\pi\)
0.992345 + 0.123498i \(0.0394114\pi\)
\(558\) −1.01656e14 1.01656e14i −1.87915 1.87915i
\(559\) 1.48321e13i 0.271735i
\(560\) 1.22693e12 1.24230e12i 0.0222783 0.0225573i
\(561\) −5.20388e13 −0.936512
\(562\) 3.63050e13 3.63050e13i 0.647568 0.647568i
\(563\) 8.88206e12 + 8.88206e12i 0.157026 + 0.157026i 0.781247 0.624221i \(-0.214584\pi\)
−0.624221 + 0.781247i \(0.714584\pi\)
\(564\) 1.73435e13i 0.303907i
\(565\) −6.90658e13 6.82116e13i −1.19956 1.18472i
\(566\) −2.58977e13 −0.445840
\(567\) 1.66693e13 1.66693e13i 0.284448 0.284448i
\(568\) −3.32917e12 3.32917e12i −0.0563111 0.0563111i
\(569\) 2.03394e12i 0.0341018i −0.999855 0.0170509i \(-0.994572\pi\)
0.999855 0.0170509i \(-0.00542773\pi\)
\(570\) −1.38848e11 2.23128e13i −0.00230763 0.370834i
\(571\) 4.37466e13 0.720716 0.360358 0.932814i \(-0.382655\pi\)
0.360358 + 0.932814i \(0.382655\pi\)
\(572\) 1.10064e13 1.10064e13i 0.179749 0.179749i
\(573\) −9.79442e12 9.79442e12i −0.158564 0.158564i
\(574\) 6.38838e12i 0.102525i
\(575\) 1.50864e13 + 1.47154e13i 0.240019 + 0.234118i
\(576\) −2.06288e13 −0.325359
\(577\) 6.55899e12 6.55899e12i 0.102555 0.102555i −0.653967 0.756523i \(-0.726897\pi\)
0.756523 + 0.653967i \(0.226897\pi\)
\(578\) 7.62478e12 + 7.62478e12i 0.118192 + 0.118192i
\(579\) 2.03698e13i 0.313036i
\(580\) −3.95255e13 + 2.45959e11i −0.602195 + 0.00374734i
\(581\) 8.33936e12 0.125966
\(582\) 3.88226e13 3.88226e13i 0.581393 0.581393i
\(583\) 2.16868e13 + 2.16868e13i 0.321997 + 0.321997i
\(584\) 9.68981e12i 0.142643i
\(585\) 1.43581e14 1.45379e14i 2.09565 2.12189i
\(586\) −5.38521e13 −0.779318
\(587\) −3.54072e13 + 3.54072e13i −0.508044 + 0.508044i −0.913925 0.405882i \(-0.866964\pi\)
0.405882 + 0.913925i \(0.366964\pi\)
\(588\) 4.64114e13 + 4.64114e13i 0.660295 + 0.660295i
\(589\) 2.82809e13i 0.398949i
\(590\) 3.48476e12 + 3.44166e12i 0.0487431 + 0.0481402i
\(591\) 4.79018e12 0.0664376
\(592\) −6.63685e12 + 6.63685e12i −0.0912754 + 0.0912754i
\(593\) 1.82645e13 + 1.82645e13i 0.249077 + 0.249077i 0.820592 0.571515i \(-0.193644\pi\)
−0.571515 + 0.820592i \(0.693644\pi\)
\(594\) 7.05914e13i 0.954596i
\(595\) 6.54357e10 + 1.05155e13i 0.000877466 + 0.141008i
\(596\) −1.39051e13 −0.184902
\(597\) −8.34045e13 + 8.34045e13i −1.09981 + 1.09981i
\(598\) 1.46892e13 + 1.46892e13i 0.192084 + 0.192084i
\(599\) 7.75562e13i 1.00573i −0.864364 0.502866i \(-0.832279\pi\)
0.864364 0.502866i \(-0.167721\pi\)
\(600\) 6.49434e11 + 5.21797e13i 0.00835177 + 0.671036i
\(601\) −6.85036e13 −0.873657 −0.436829 0.899545i \(-0.643898\pi\)
−0.436829 + 0.899545i \(0.643898\pi\)
\(602\) −1.18898e12 + 1.18898e12i −0.0150380 + 0.0150380i
\(603\) 1.22780e14 + 1.22780e14i 1.54007 + 1.54007i
\(604\) 2.30202e12i 0.0286368i
\(605\) −6.50943e13 + 4.05070e11i −0.803094 + 0.00499750i
\(606\) 1.31091e14 1.60402
\(607\) −1.16409e14 + 1.16409e14i −1.41268 + 1.41268i −0.673414 + 0.739265i \(0.735173\pi\)
−0.739265 + 0.673414i \(0.764827\pi\)
\(608\) 2.86950e12 + 2.86950e12i 0.0345373 + 0.0345373i
\(609\) 2.42863e13i 0.289918i
\(610\) −3.17275e13 + 3.21248e13i −0.375653 + 0.380357i
\(611\) −3.12430e13 −0.366899
\(612\) 8.78499e13 8.78499e13i 1.02326 1.02326i
\(613\) −7.77875e13 7.77875e13i −0.898685 0.898685i 0.0966345 0.995320i \(-0.469192\pi\)
−0.995320 + 0.0966345i \(0.969192\pi\)
\(614\) 9.56972e13i 1.09662i
\(615\) −1.35844e14 1.34164e14i −1.54407 1.52497i
\(616\) 1.76460e12 0.0198950
\(617\) −6.34760e12 + 6.34760e12i −0.0709878 + 0.0709878i −0.741709 0.670722i \(-0.765985\pi\)
0.670722 + 0.741709i \(0.265985\pi\)
\(618\) −2.29714e13 2.29714e13i −0.254827 0.254827i
\(619\) 8.98265e13i 0.988443i −0.869336 0.494221i \(-0.835453\pi\)
0.869336 0.494221i \(-0.164547\pi\)
\(620\) −4.11571e11 6.61392e13i −0.00449248 0.721939i
\(621\) −9.42112e13 −1.02010
\(622\) −4.85813e13 + 4.85813e13i −0.521815 + 0.521815i
\(623\) −4.94755e12 4.94755e12i −0.0527169 0.0527169i
\(624\) 5.14384e13i 0.543706i
\(625\) 9.53379e13 2.37354e12i 0.999690 0.0248883i
\(626\) −2.86866e13 −0.298405
\(627\) 1.59455e13 1.59455e13i 0.164551 0.164551i
\(628\) 4.18514e13 + 4.18514e13i 0.428461 + 0.428461i
\(629\) 5.65274e13i 0.574124i
\(630\) 2.31637e13 1.44143e11i 0.233402 0.00145242i
\(631\) 1.81926e14 1.81865 0.909324 0.416089i \(-0.136599\pi\)
0.909324 + 0.416089i \(0.136599\pi\)
\(632\) −5.71740e12 + 5.71740e12i −0.0567039 + 0.0567039i
\(633\) 1.80135e14 + 1.80135e14i 1.77247 + 1.77247i
\(634\) 1.04834e14i 1.02343i
\(635\) −6.72354e13 + 6.80775e13i −0.651223 + 0.659379i
\(636\) −1.01353e14 −0.973979
\(637\) 8.36066e13 8.36066e13i 0.797156 0.797156i
\(638\) −2.82463e13 2.82463e13i −0.267213 0.267213i
\(639\) 6.24612e13i 0.586281i
\(640\) −6.75252e12 6.66900e12i −0.0628877 0.0621099i
\(641\) −1.99408e14 −1.84269 −0.921344 0.388748i \(-0.872908\pi\)
−0.921344 + 0.388748i \(0.872908\pi\)
\(642\) 1.19499e14 1.19499e14i 1.09570 1.09570i
\(643\) 1.52095e14 + 1.52095e14i 1.38376 + 1.38376i 0.837841 + 0.545914i \(0.183818\pi\)
0.545914 + 0.837841i \(0.316182\pi\)
\(644\) 2.35503e12i 0.0212602i
\(645\) −3.12713e11 5.02527e13i −0.00280122 0.450154i
\(646\) −2.44401e13 −0.217240
\(647\) 8.79654e13 8.79654e13i 0.775873 0.775873i −0.203253 0.979126i \(-0.565151\pi\)
0.979126 + 0.203253i \(0.0651515\pi\)
\(648\) −9.06059e13 9.06059e13i −0.793015 0.793015i
\(649\) 4.94986e12i 0.0429902i
\(650\) 9.39979e13 1.16991e12i 0.810123 0.0100829i
\(651\) −4.06390e13 −0.347567
\(652\) −7.56142e13 + 7.56142e13i −0.641749 + 0.641749i
\(653\) −1.01299e14 1.01299e14i −0.853173 0.853173i 0.137349 0.990523i \(-0.456142\pi\)
−0.990523 + 0.137349i \(0.956142\pi\)
\(654\) 2.79957e14i 2.33993i
\(655\) 1.95113e14 1.21415e12i 1.61838 0.0100708i
\(656\) 3.47240e13 0.285832
\(657\) 9.08993e13 9.08993e13i 0.742563 0.742563i
\(658\) −2.50451e12 2.50451e12i −0.0203045 0.0203045i
\(659\) 4.67893e11i 0.00376461i 0.999998 + 0.00188230i \(0.000599156\pi\)
−0.999998 + 0.00188230i \(0.999401\pi\)
\(660\) −3.70588e13 + 3.75230e13i −0.295919 + 0.299624i
\(661\) −1.34088e13 −0.106263 −0.0531317 0.998588i \(-0.516920\pi\)
−0.0531317 + 0.998588i \(0.516920\pi\)
\(662\) −1.03766e13 + 1.03766e13i −0.0816144 + 0.0816144i
\(663\) −2.19055e14 2.19055e14i −1.70996 1.70996i
\(664\) 4.53285e13i 0.351181i
\(665\) −3.24215e12 3.20205e12i −0.0249302 0.0246218i
\(666\) −1.24519e14 −0.950312
\(667\) 3.76974e13 3.76974e13i 0.285550 0.285550i
\(668\) −6.32856e13 6.32856e13i −0.475798 0.475798i
\(669\) 4.65347e14i 3.47253i
\(670\) 4.97096e11 + 7.98829e13i 0.00368185 + 0.591670i
\(671\) −4.56311e13 −0.335466
\(672\) −4.12341e12 + 4.12341e12i −0.0300891 + 0.0300891i
\(673\) −1.01893e14 1.01893e14i −0.738024 0.738024i 0.234171 0.972195i \(-0.424762\pi\)
−0.972195 + 0.234171i \(0.924762\pi\)
\(674\) 1.97397e13i 0.141919i
\(675\) −2.97683e14 + 3.05186e14i −2.12439 + 2.17794i
\(676\) 2.20788e13 0.156402
\(677\) −5.83118e13 + 5.83118e13i −0.410028 + 0.410028i −0.881748 0.471720i \(-0.843633\pi\)
0.471720 + 0.881748i \(0.343633\pi\)
\(678\) 2.29241e14 + 2.29241e14i 1.60009 + 1.60009i
\(679\) 1.12124e13i 0.0776875i
\(680\) 5.71568e13 3.55676e11i 0.393118 0.00244630i
\(681\) 4.67016e14 3.18857
\(682\) 4.72653e13 4.72653e13i 0.320347 0.320347i
\(683\) −6.32645e13 6.32645e13i −0.425654 0.425654i 0.461491 0.887145i \(-0.347315\pi\)
−0.887145 + 0.461491i \(0.847315\pi\)
\(684\) 5.38371e13i 0.359585i
\(685\) 5.28199e13 5.34813e13i 0.350223 0.354609i
\(686\) 2.70274e13 0.177903
\(687\) −8.89016e13 + 8.89016e13i −0.580933 + 0.580933i
\(688\) 6.46268e12 + 6.46268e12i 0.0419247 + 0.0419247i
\(689\) 1.82579e14i 1.17586i
\(690\) −5.00780e13 4.94586e13i −0.320186 0.316225i
\(691\) 1.47937e14 0.939047 0.469524 0.882920i \(-0.344426\pi\)
0.469524 + 0.882920i \(0.344426\pi\)
\(692\) −9.22441e12 + 9.22441e12i −0.0581311 + 0.0581311i
\(693\) 1.65536e13 + 1.65536e13i 0.103568 + 0.103568i
\(694\) 1.79188e14i 1.11304i
\(695\) 2.16984e10 + 3.48692e12i 0.000133815 + 0.0215039i
\(696\) 1.32008e14 0.808267
\(697\) −1.47875e14 + 1.47875e14i −0.898943 + 0.898943i
\(698\) −1.06612e14 1.06612e14i −0.643474 0.643474i
\(699\) 2.01272e14i 1.20614i
\(700\) 7.62885e12 + 7.44129e12i 0.0453909 + 0.0442749i
\(701\) 1.82732e13 0.107951 0.0539753 0.998542i \(-0.482811\pi\)
0.0539753 + 0.998542i \(0.482811\pi\)
\(702\) −2.97151e14 + 2.97151e14i −1.74298 + 1.74298i
\(703\) 1.73208e13 + 1.73208e13i 0.100877 + 0.100877i
\(704\) 9.59148e12i 0.0554654i
\(705\) 1.05854e14 6.58711e11i 0.607803 0.00378224i
\(706\) −1.38965e14 −0.792284
\(707\) 1.89304e13 1.89304e13i 0.107167 0.107167i
\(708\) −1.15665e13 1.15665e13i −0.0650184 0.0650184i
\(709\) 3.45145e14i 1.92650i −0.268598 0.963252i \(-0.586560\pi\)
0.268598 0.963252i \(-0.413440\pi\)
\(710\) 2.01928e13 2.04457e13i 0.111919 0.113321i
\(711\) −1.07269e14 −0.590372
\(712\) −2.68924e13 + 2.68924e13i −0.146970 + 0.146970i
\(713\) 6.30802e13 + 6.30802e13i 0.342330 + 0.342330i
\(714\) 3.51199e13i 0.189261i
\(715\) 6.75948e13 + 6.67587e13i 0.361729 + 0.357254i
\(716\) 1.61347e14 0.857423
\(717\) 4.95634e13 4.95634e13i 0.261556 0.261556i
\(718\) −7.19372e13 7.19372e13i −0.376991 0.376991i
\(719\) 1.61283e14i 0.839354i 0.907673 + 0.419677i \(0.137857\pi\)
−0.907673 + 0.419677i \(0.862143\pi\)
\(720\) −7.83489e11 1.25906e14i −0.00404921 0.650705i
\(721\) −6.63443e12 −0.0340508
\(722\) −9.06082e13 + 9.06082e13i −0.461830 + 0.461830i
\(723\) −5.49178e13 5.49178e13i −0.277985 0.277985i
\(724\) 1.06709e14i 0.536425i
\(725\) −3.00238e12 2.41230e14i −0.0149891 1.20432i
\(726\) 2.17404e14 1.07791
\(727\) −4.18604e13 + 4.18604e13i −0.206125 + 0.206125i −0.802618 0.596493i \(-0.796560\pi\)
0.596493 + 0.802618i \(0.296560\pi\)
\(728\) 7.42801e12 + 7.42801e12i 0.0363258 + 0.0363258i
\(729\) 5.10925e14i 2.48153i
\(730\) 5.91408e13 3.68022e11i 0.285281 0.00177525i
\(731\) −5.50438e13 −0.263707
\(732\) 1.06628e14 1.06628e14i 0.507359 0.507359i
\(733\) −6.68708e13 6.68708e13i −0.316022 0.316022i 0.531215 0.847237i \(-0.321736\pi\)
−0.847237 + 0.531215i \(0.821736\pi\)
\(734\) 7.21359e13i 0.338587i
\(735\) −2.81504e14 + 2.85030e14i −1.31235 + 1.32878i
\(736\) 1.28008e13 0.0592716
\(737\) −5.70871e13 + 5.70871e13i −0.262543 + 0.262543i
\(738\) 3.25743e14 + 3.25743e14i 1.48797 + 1.48797i
\(739\) 2.11418e14i 0.959223i 0.877481 + 0.479612i \(0.159222\pi\)
−0.877481 + 0.479612i \(0.840778\pi\)
\(740\) −4.07594e13 4.02553e13i −0.183683 0.181411i
\(741\) 1.34244e14 0.600901
\(742\) −1.46359e13 + 1.46359e13i −0.0650730 + 0.0650730i
\(743\) 1.26357e14 + 1.26357e14i 0.558028 + 0.558028i 0.928746 0.370717i \(-0.120888\pi\)
−0.370717 + 0.928746i \(0.620888\pi\)
\(744\) 2.20893e14i 0.968987i
\(745\) −5.28118e11 8.48681e13i −0.00230117 0.369797i
\(746\) 2.19077e14 0.948205
\(747\) 4.25223e14 4.25223e14i 1.82816 1.82816i
\(748\) 4.08462e13 + 4.08462e13i 0.174439 + 0.174439i
\(749\) 3.45128e13i 0.146410i
\(750\) −3.18449e14 + 5.94555e12i −1.34194 + 0.0250545i
\(751\) −4.63669e14 −1.94092 −0.970461 0.241258i \(-0.922440\pi\)
−0.970461 + 0.241258i \(0.922440\pi\)
\(752\) −1.36132e13 + 1.36132e13i −0.0566073 + 0.0566073i
\(753\) −4.98876e14 4.98876e14i −2.06071 2.06071i
\(754\) 2.37803e14i 0.975799i
\(755\) 1.40501e13 8.74312e10i 0.0572724 0.000356395i
\(756\) −4.76406e13 −0.192916
\(757\) 6.74662e12 6.74662e12i 0.0271398 0.0271398i −0.693407 0.720546i \(-0.743891\pi\)
0.720546 + 0.693407i \(0.243891\pi\)
\(758\) −2.24841e14 2.24841e14i −0.898523 0.898523i
\(759\) 7.11324e13i 0.282396i
\(760\) −1.74047e13 + 1.76227e13i −0.0686435 + 0.0695031i
\(761\) 1.52599e14 0.597900 0.298950 0.954269i \(-0.403364\pi\)
0.298950 + 0.954269i \(0.403364\pi\)
\(762\) 2.25961e14 2.25961e14i 0.879546 0.879546i
\(763\) −4.04275e13 4.04275e13i −0.156334 0.156334i
\(764\) 1.53756e13i 0.0590699i
\(765\) 5.39519e14 + 5.32846e14i 2.05921 + 2.03374i
\(766\) 9.00759e13 0.341558
\(767\) −2.08362e13 + 2.08362e13i −0.0784950 + 0.0784950i
\(768\) 2.24128e13 + 2.24128e13i 0.0838860 + 0.0838860i
\(769\) 3.85474e14i 1.43338i 0.697389 + 0.716692i \(0.254345\pi\)
−0.697389 + 0.716692i \(0.745655\pi\)
\(770\) 6.70200e10 + 1.07701e13i 0.000247600 + 0.0397891i
\(771\) −5.31823e14 −1.95207
\(772\) −1.59886e13 + 1.59886e13i −0.0583076 + 0.0583076i
\(773\) 2.19032e14 + 2.19032e14i 0.793616 + 0.793616i 0.982080 0.188464i \(-0.0603510\pi\)
−0.188464 + 0.982080i \(0.560351\pi\)
\(774\) 1.21252e14i 0.436498i
\(775\) 4.03658e14 5.02396e12i 1.44379 0.0179696i
\(776\) −6.09452e13 −0.216586
\(777\) −2.48896e13 + 2.48896e13i −0.0878848 + 0.0878848i
\(778\) 2.24183e13 + 2.24183e13i 0.0786509 + 0.0786509i
\(779\) 9.06226e13i 0.315900i
\(780\) −3.13949e14 + 1.95364e12i −1.08739 + 0.00676662i
\(781\) 2.90416e13 0.0999461
\(782\) −5.45133e13 + 5.45133e13i −0.186410 + 0.186410i
\(783\) 7.62591e14 + 7.62591e14i 2.59109 + 2.59109i
\(784\) 7.28583e13i 0.245979i
\(785\) −2.53846e14 + 2.57025e14i −0.851574 + 0.862238i
\(786\) −6.51643e14 −2.17219
\(787\) −3.33654e14 + 3.33654e14i −1.10515 + 1.10515i −0.111375 + 0.993778i \(0.535525\pi\)
−0.993778 + 0.111375i \(0.964475\pi\)
\(788\) −3.75990e12 3.75990e12i −0.0123750 0.0123750i
\(789\) 3.21876e14i 1.05270i
\(790\) −3.51127e13 3.46784e13i −0.114111 0.112700i
\(791\) 6.62076e13 0.213809
\(792\) 8.99768e13 8.99768e13i 0.288739 0.288739i
\(793\) −1.92082e14 1.92082e14i −0.612521 0.612521i
\(794\) 2.54057e14i 0.805061i
\(795\) −3.84940e12 6.18595e14i −0.0121215 1.94792i
\(796\) 1.30931e14 0.409712
\(797\) 3.59536e14 3.59536e14i 1.11802 1.11802i 0.125993 0.992031i \(-0.459788\pi\)
0.992031 0.125993i \(-0.0402118\pi\)
\(798\) 1.07613e13 + 1.07613e13i 0.0332543 + 0.0332543i
\(799\) 1.15947e14i 0.356061i
\(800\) 4.04471e13 4.14666e13i 0.123435 0.126546i
\(801\) −5.04550e14 −1.53018
\(802\) −5.47250e13 + 5.47250e13i −0.164936 + 0.164936i
\(803\) 4.22640e13 + 4.22640e13i 0.126588 + 0.126588i
\(804\) 2.66795e14i 0.794141i
\(805\) −1.43737e13 + 8.94447e10i −0.0425196 + 0.000264591i
\(806\) 3.97923e14 1.16983
\(807\) 3.21805e14 3.21805e14i 0.940210 0.940210i
\(808\) −1.02896e14 1.02896e14i −0.298773 0.298773i
\(809\) 3.41953e14i 0.986789i 0.869806 + 0.493394i \(0.164244\pi\)
−0.869806 + 0.493394i \(0.835756\pi\)
\(810\) 5.49563e14 5.56445e14i 1.57613 1.59587i
\(811\) −4.43760e14 −1.26486 −0.632431 0.774616i \(-0.717943\pi\)
−0.632431 + 0.774616i \(0.717943\pi\)
\(812\) 1.90628e13 1.90628e13i 0.0540015 0.0540015i
\(813\) −2.65517e14 2.65517e14i −0.747548 0.747548i
\(814\) 5.78959e13i 0.162004i
\(815\) −4.64375e14 4.58631e14i −1.29146 1.27549i
\(816\) −1.90894e14 −0.527644
\(817\) 1.68663e13 1.68663e13i 0.0463349 0.0463349i
\(818\) −1.06762e14 1.06762e14i −0.291508 0.291508i
\(819\) 1.39363e14i 0.378206i
\(820\) 1.31883e12 + 2.11934e14i 0.00355728 + 0.571653i
\(821\) 4.33407e14 1.16193 0.580965 0.813929i \(-0.302675\pi\)
0.580965 + 0.813929i \(0.302675\pi\)
\(822\) −1.77514e14 + 1.77514e14i −0.473013 + 0.473013i
\(823\) 3.52407e14 + 3.52407e14i 0.933352 + 0.933352i 0.997914 0.0645613i \(-0.0205648\pi\)
−0.0645613 + 0.997914i \(0.520565\pi\)
\(824\) 3.60614e13i 0.0949307i
\(825\) −2.30425e14 2.24760e14i −0.602920 0.588097i
\(826\) −3.34055e12 −0.00868796
\(827\) 2.80216e14 2.80216e14i 0.724379 0.724379i −0.245115 0.969494i \(-0.578826\pi\)
0.969494 + 0.245115i \(0.0788258\pi\)
\(828\) 1.20083e14 + 1.20083e14i 0.308553 + 0.308553i
\(829\) 5.19271e14i 1.32624i −0.748514 0.663119i \(-0.769232\pi\)
0.748514 0.663119i \(-0.230768\pi\)
\(830\) 2.76658e14 1.72159e12i 0.702349 0.00437058i
\(831\) 1.17397e15 2.96246
\(832\) 4.03749e13 4.03749e13i 0.101273 0.101273i
\(833\) 3.10274e14 + 3.10274e14i 0.773607 + 0.773607i
\(834\) 1.16457e13i 0.0288626i
\(835\) 3.83853e14 3.88661e14i 0.945656 0.957499i
\(836\) −2.50318e13 −0.0613001
\(837\) −1.27607e15 + 1.27607e15i −3.10632 + 3.10632i
\(838\) 3.27219e14 + 3.27219e14i 0.791804 + 0.791804i
\(839\) 4.00090e14i 0.962384i −0.876615 0.481192i \(-0.840204\pi\)
0.876615 0.481192i \(-0.159796\pi\)
\(840\) −2.53234e13 2.50102e13i −0.0605516 0.0598027i
\(841\) −1.89575e14 −0.450611
\(842\) −2.45848e14 + 2.45848e14i −0.580906 + 0.580906i
\(843\) −7.40052e14 7.40052e14i −1.73830 1.73830i
\(844\) 2.82782e14i 0.660297i
\(845\) 8.38557e11 + 1.34755e14i 0.00194648 + 0.312797i
\(846\) −2.55409e14 −0.589365
\(847\) 3.13944e13 3.13944e13i 0.0720171 0.0720171i
\(848\) 7.95535e13 + 7.95535e13i 0.181418 + 0.181418i
\(849\) 5.27906e14i 1.19679i
\(850\) 4.34166e12 + 3.48837e14i 0.00978501 + 0.786191i
\(851\) 7.72678e13 0.173121
\(852\) −6.78627e13 + 6.78627e13i −0.151159 + 0.151159i
\(853\) 2.04891e13 + 2.04891e13i 0.0453709 + 0.0453709i 0.729428 0.684057i \(-0.239786\pi\)
−0.684057 + 0.729428i \(0.739786\pi\)
\(854\) 3.07954e13i 0.0677948i
\(855\) −3.28589e14 + 2.04475e12i −0.719155 + 0.00447516i
\(856\) −1.87594e14 −0.408179
\(857\) 2.95150e14 2.95150e14i 0.638467 0.638467i −0.311711 0.950177i \(-0.600902\pi\)
0.950177 + 0.311711i \(0.100902\pi\)
\(858\) −2.24359e14 2.24359e14i −0.482510 0.482510i
\(859\) 3.11199e14i 0.665384i 0.943036 + 0.332692i \(0.107957\pi\)
−0.943036 + 0.332692i \(0.892043\pi\)
\(860\) −3.91988e13 + 3.96897e13i −0.0833260 + 0.0843696i
\(861\) 1.30223e14 0.275214
\(862\) 2.84047e14 2.84047e14i 0.596834 0.596834i
\(863\) 1.34806e14 + 1.34806e14i 0.281614 + 0.281614i 0.833752 0.552138i \(-0.186188\pi\)
−0.552138 + 0.833752i \(0.686188\pi\)
\(864\) 2.58950e14i 0.537833i
\(865\) −5.66506e13 5.59499e13i −0.116983 0.115536i
\(866\) 1.43648e13 0.0294924
\(867\) 1.55426e14 1.55426e14i 0.317269 0.317269i
\(868\) 3.18983e13 + 3.18983e13i 0.0647395 + 0.0647395i
\(869\) 4.98752e13i 0.100643i
\(870\) 5.01371e12 + 8.05699e14i 0.0100592 + 1.61650i
\(871\) −4.80611e14 −0.958745
\(872\) −2.19743e14 + 2.19743e14i −0.435847 + 0.435847i
\(873\) −5.71721e14 5.71721e14i −1.12749 1.12749i
\(874\) 3.34074e13i 0.0655067i
\(875\) −4.51274e13 + 4.68445e13i −0.0879832 + 0.0913311i
\(876\) −1.97520e14 −0.382904
\(877\) 8.27935e13 8.27935e13i 0.159587 0.159587i −0.622797 0.782384i \(-0.714004\pi\)
0.782384 + 0.622797i \(0.214004\pi\)
\(878\) −1.50352e14 1.50352e14i −0.288162 0.288162i
\(879\) 1.09774e15i 2.09196i
\(880\) 5.85406e13 3.64287e11i 0.110929 0.000690288i
\(881\) 2.97854e14 0.561208 0.280604 0.959824i \(-0.409465\pi\)
0.280604 + 0.959824i \(0.409465\pi\)
\(882\) 6.83477e14 6.83477e14i 1.28050 1.28050i
\(883\) 1.59243e14 + 1.59243e14i 0.296658 + 0.296658i 0.839704 0.543045i \(-0.182729\pi\)
−0.543045 + 0.839704i \(0.682729\pi\)
\(884\) 3.43881e14i 0.637010i
\(885\) 7.01558e13 7.10344e13i 0.129225 0.130844i
\(886\) 1.33404e14 0.244343
\(887\) −1.95156e14 + 1.95156e14i −0.355437 + 0.355437i −0.862128 0.506691i \(-0.830869\pi\)
0.506691 + 0.862128i \(0.330869\pi\)
\(888\) 1.35288e14 + 1.35288e14i 0.245015 + 0.245015i
\(889\) 6.52602e13i 0.117528i
\(890\) −1.65156e14 1.63113e14i −0.295764 0.292105i
\(891\) 7.90392e14 1.40752
\(892\) 3.65259e14 3.65259e14i 0.646811 0.646811i
\(893\) 3.55278e13 + 3.55278e13i 0.0625620 + 0.0625620i
\(894\) 2.83445e14i 0.496342i
\(895\) 6.12799e12 + 9.84763e14i 0.0106709 + 1.71481i
\(896\) 6.47308e12 0.0112091
\(897\) 2.99429e14 2.99429e14i 0.515621 0.515621i
\(898\) 1.43771e14 + 1.43771e14i 0.246201 + 0.246201i
\(899\) 1.02120e15i 1.73906i
\(900\) 7.68425e14 9.56389e12i 1.30133 0.0161965i
\(901\) −6.77573e14 −1.14112
\(902\) −1.51456e14 + 1.51456e14i −0.253661 + 0.253661i
\(903\) 2.42364e13 + 2.42364e13i 0.0403673 + 0.0403673i
\(904\) 3.59871e14i 0.596081i
\(905\) −6.51289e14 + 4.05284e12i −1.07283 + 0.00667601i
\(906\) −4.69250e13 −0.0768711
\(907\) −2.14673e14 + 2.14673e14i −0.349737 + 0.349737i −0.860011 0.510275i \(-0.829544\pi\)
0.510275 + 0.860011i \(0.329544\pi\)
\(908\) −3.66569e14 3.66569e14i −0.593918 0.593918i
\(909\) 1.93052e15i 3.11067i
\(910\) −4.50540e13 + 4.56182e13i −0.0721981 + 0.0731023i
\(911\) −1.02617e15 −1.63542 −0.817709 0.575631i \(-0.804756\pi\)
−0.817709 + 0.575631i \(0.804756\pi\)
\(912\) 5.84927e13 5.84927e13i 0.0927103 0.0927103i
\(913\) 1.97709e14 + 1.97709e14i 0.311655 + 0.311655i
\(914\) 1.76966e14i 0.277433i
\(915\) 6.54842e14 + 6.46742e14i 1.02101 + 1.00838i
\(916\) 1.39561e14 0.216415
\(917\) −9.41012e13 + 9.41012e13i −0.145127 + 0.145127i
\(918\) −1.10276e15 1.10276e15i −1.69149 1.69149i
\(919\) 1.06960e15i 1.63172i −0.578250 0.815859i \(-0.696264\pi\)
0.578250 0.815859i \(-0.303736\pi\)
\(920\) 4.86176e11 + 7.81282e13i 0.000737657 + 0.118541i
\(921\) 1.95072e15 2.94372
\(922\) −2.60650e14 + 2.60650e14i −0.391203 + 0.391203i
\(923\) 1.22249e14 + 1.22249e14i 0.182490 + 0.182490i
\(924\) 3.59701e13i 0.0534050i
\(925\) 2.44146e14 2.50300e14i 0.360530 0.369617i
\(926\) −2.45990e14 −0.361295
\(927\) −3.38289e14 + 3.38289e14i −0.494185 + 0.494185i
\(928\) −1.03616e14 1.03616e14i −0.150552 0.150552i
\(929\) 1.65091e14i 0.238585i 0.992859 + 0.119293i \(0.0380627\pi\)
−0.992859 + 0.119293i \(0.961937\pi\)
\(930\) −1.34820e15 + 8.38959e12i −1.93794 + 0.0120594i
\(931\) −1.90145e14 −0.271855
\(932\) −1.57982e14 + 1.57982e14i −0.224662 + 0.224662i
\(933\) 9.90295e14 + 9.90295e14i 1.40074 + 1.40074i
\(934\) 6.23940e14i 0.877826i
\(935\) −2.47749e14 + 2.50852e14i −0.346701 + 0.351043i
\(936\) 7.57507e14 1.05440
\(937\) −4.68468e14 + 4.68468e14i −0.648608 + 0.648608i −0.952657 0.304049i \(-0.901662\pi\)
0.304049 + 0.952657i \(0.401662\pi\)
\(938\) −3.85268e13 3.85268e13i −0.0530577 0.0530577i
\(939\) 5.84755e14i 0.801025i
\(940\) −8.36040e13 8.25699e13i −0.113917 0.112508i
\(941\) −4.34456e14 −0.588840 −0.294420 0.955676i \(-0.595126\pi\)
−0.294420 + 0.955676i \(0.595126\pi\)
\(942\) 8.53111e14 8.53111e14i 1.15014 1.15014i
\(943\) −2.02132e14 2.02132e14i −0.271068 0.271068i
\(944\) 1.81575e13i 0.0242213i
\(945\) −1.80940e12 2.90769e14i −0.00240091 0.385824i
\(946\) −5.63765e13 −0.0744119
\(947\) −3.62573e14 + 3.62573e14i −0.476043 + 0.476043i −0.903864 0.427821i \(-0.859281\pi\)
0.427821 + 0.903864i \(0.359281\pi\)
\(948\) 1.16545e14 + 1.16545e14i 0.152213 + 0.152213i
\(949\) 3.55817e14i 0.462270i
\(950\) −1.08219e14 1.05559e14i −0.139858 0.136419i
\(951\) 2.13697e15 2.74724
\(952\) −2.75662e13 + 2.75662e13i −0.0352527 + 0.0352527i
\(953\) 7.02985e14 + 7.02985e14i 0.894297 + 0.894297i 0.994924 0.100627i \(-0.0320849\pi\)
−0.100627 + 0.994924i \(0.532085\pi\)
\(954\) 1.49257e15i 1.88883i
\(955\) −9.38436e13 + 5.83971e11i −0.118138 + 0.000735147i
\(956\) −7.78064e13 −0.0974375
\(957\) −5.75780e14 + 5.75780e14i −0.717294 + 0.717294i
\(958\) 5.89381e14 + 5.89381e14i 0.730413 + 0.730413i
\(959\) 5.12681e13i 0.0632054i
\(960\) −1.35943e14 + 1.37645e14i −0.166725 + 0.168813i
\(961\) 8.89183e14 1.08486
\(962\) 2.43710e14 2.43710e14i 0.295800 0.295800i
\(963\) −1.75980e15 1.75980e15i −2.12487 2.12487i
\(964\) 8.62120e13i 0.103558i
\(965\) −9.81923e13 9.69778e13i −0.117339 0.115887i
\(966\) 4.80057e13 0.0570699
\(967\) −4.96692e14 + 4.96692e14i −0.587428 + 0.587428i −0.936934 0.349506i \(-0.886349\pi\)
0.349506 + 0.936934i \(0.386349\pi\)
\(968\) −1.70644e14 1.70644e14i −0.200777 0.200777i
\(969\) 4.98194e14i 0.583149i
\(970\) −2.31471e12 3.71973e14i −0.00269550 0.433164i
\(971\) −8.90045e14 −1.03114 −0.515568 0.856849i \(-0.672419\pi\)
−0.515568 + 0.856849i \(0.672419\pi\)
\(972\) −9.13664e14 + 9.13664e14i −1.05307 + 1.05307i
\(973\) −1.68171e12 1.68171e12i −0.00192835 0.00192835i
\(974\) 4.81348e14i 0.549116i
\(975\) −2.38477e13 1.91608e15i −0.0270660 2.17466i
\(976\) −1.67388e14 −0.189006
\(977\) 5.13225e14 5.13225e14i 0.576548 0.576548i −0.357403 0.933950i \(-0.616338\pi\)
0.933950 + 0.357403i \(0.116338\pi\)
\(978\) 1.54134e15 + 1.54134e15i 1.72268 + 1.72268i
\(979\) 2.34593e14i 0.260856i
\(980\) 4.44683e14 2.76718e12i 0.491949 0.00306130i
\(981\) −4.12279e15 −4.53781
\(982\) 3.45813e14 3.45813e14i 0.378690 0.378690i
\(983\) 3.69731e14 + 3.69731e14i 0.402827 + 0.402827i 0.879228 0.476401i \(-0.158059\pi\)
−0.476401 + 0.879228i \(0.658059\pi\)
\(984\) 7.07824e14i 0.767273i
\(985\) 2.28053e13 2.30909e13i 0.0245955 0.0249035i
\(986\) 8.82514e14 0.946972
\(987\) −5.10526e13 + 5.10526e13i −0.0545045 + 0.0545045i
\(988\) −1.05370e14 1.05370e14i −0.111927 0.111927i
\(989\) 7.52399e13i 0.0795183i
\(990\) 5.52582e14 + 5.45747e14i 0.581059 + 0.573872i
\(991\) 1.22959e15 1.28645 0.643224 0.765678i \(-0.277597\pi\)
0.643224 + 0.765678i \(0.277597\pi\)
\(992\) 1.73383e14 1.73383e14i 0.180488 0.180488i
\(993\) 2.11520e14 + 2.11520e14i 0.219082 + 0.219082i
\(994\) 1.95996e13i 0.0201983i
\(995\) 4.97281e12 + 7.99126e14i 0.00509901 + 0.819408i
\(996\) −9.23990e14 −0.942693
\(997\) 1.01829e15 1.01829e15i 1.03370 1.03370i 0.0342927 0.999412i \(-0.489082\pi\)
0.999412 0.0342927i \(-0.0109179\pi\)
\(998\) −8.66708e14 8.66708e14i −0.875427 0.875427i
\(999\) 1.56307e15i 1.57091i
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 10.11.c.c.3.3 6
3.2 odd 2 90.11.g.c.73.1 6
4.3 odd 2 80.11.p.c.33.1 6
5.2 odd 4 inner 10.11.c.c.7.3 yes 6
5.3 odd 4 50.11.c.e.7.1 6
5.4 even 2 50.11.c.e.43.1 6
15.2 even 4 90.11.g.c.37.1 6
20.7 even 4 80.11.p.c.17.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.11.c.c.3.3 6 1.1 even 1 trivial
10.11.c.c.7.3 yes 6 5.2 odd 4 inner
50.11.c.e.7.1 6 5.3 odd 4
50.11.c.e.43.1 6 5.4 even 2
80.11.p.c.17.1 6 20.7 even 4
80.11.p.c.33.1 6 4.3 odd 2
90.11.g.c.37.1 6 15.2 even 4
90.11.g.c.73.1 6 3.2 odd 2