Properties

Label 12.15.d.a.7.9
Level $12$
Weight $15$
Character 12.7
Analytic conductor $14.919$
Analytic rank $0$
Dimension $14$
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] = [12,15,Mod(7,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.7");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\), degree \(1\), 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: \(14.9194761782\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - x^{13} + 9158 x^{12} + 65217 x^{11} + 61148515 x^{10} + 439019974 x^{9} + 189458968156 x^{8} + 1788546506656 x^{7} + 430738312102192 x^{6} + \cdots + 89\!\cdots\!84 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{81}\cdot 3^{41} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 7.9
Root \(-30.4205 + 52.6899i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.15.d.a.7.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(67.3573 - 108.844i) q^{2} +1262.67i q^{3} +(-7309.99 - 14662.9i) q^{4} +30766.3 q^{5} +(137433. + 85049.7i) q^{6} -368697. i q^{7} +(-2.08834e6 - 192002. i) q^{8} -1.59432e6 q^{9} +O(q^{10})\) \(q+(67.3573 - 108.844i) q^{2} +1262.67i q^{3} +(-7309.99 - 14662.9i) q^{4} +30766.3 q^{5} +(137433. + 85049.7i) q^{6} -368697. i q^{7} +(-2.08834e6 - 192002. i) q^{8} -1.59432e6 q^{9} +(2.07234e6 - 3.34873e6i) q^{10} -3.40375e7i q^{11} +(1.85143e7 - 9.23007e6i) q^{12} -3.66786e7 q^{13} +(-4.01305e7 - 2.48344e7i) q^{14} +3.88476e7i q^{15} +(-1.61563e8 + 2.14371e8i) q^{16} -4.79329e8 q^{17} +(-1.07389e8 + 1.73532e8i) q^{18} -3.76963e8i q^{19} +(-2.24902e8 - 4.51122e8i) q^{20} +4.65541e8 q^{21} +(-3.70477e9 - 2.29267e9i) q^{22} -1.93464e9i q^{23} +(2.42434e8 - 2.63688e9i) q^{24} -5.15695e9 q^{25} +(-2.47057e9 + 3.99225e9i) q^{26} -2.01310e9i q^{27} +(-5.40616e9 + 2.69517e9i) q^{28} +2.43110e10 q^{29} +(4.22832e9 + 2.61667e9i) q^{30} -5.84660e9i q^{31} +(1.24505e10 + 3.20246e10i) q^{32} +4.29779e10 q^{33} +(-3.22863e10 + 5.21720e10i) q^{34} -1.13435e10i q^{35} +(1.16545e10 + 2.33773e10i) q^{36} +1.15754e11 q^{37} +(-4.10301e10 - 2.53912e10i) q^{38} -4.63128e10i q^{39} +(-6.42507e10 - 5.90720e9i) q^{40} +2.02030e11 q^{41} +(3.13576e10 - 5.06713e10i) q^{42} -3.29553e11i q^{43} +(-4.99086e11 + 2.48814e11i) q^{44} -4.90515e10 q^{45} +(-2.10574e11 - 1.30312e11i) q^{46} +2.44877e11i q^{47} +(-2.70679e11 - 2.04001e11i) q^{48} +5.42285e11 q^{49} +(-3.47358e11 + 5.61302e11i) q^{50} -6.05231e11i q^{51} +(2.68121e11 + 5.37814e11i) q^{52} -1.47142e12 q^{53} +(-2.19113e11 - 1.35597e11i) q^{54} -1.04721e12i q^{55} +(-7.07906e10 + 7.69967e11i) q^{56} +4.75978e11 q^{57} +(1.63752e12 - 2.64610e12i) q^{58} +2.31401e12i q^{59} +(5.69617e11 - 2.83976e11i) q^{60} +7.16981e11 q^{61} +(-6.36367e11 - 3.93811e11i) q^{62} +5.87823e11i q^{63} +(4.32432e12 + 8.01933e11i) q^{64} -1.12847e12 q^{65} +(2.89487e12 - 4.67788e12i) q^{66} +2.62990e12i q^{67} +(3.50389e12 + 7.02833e12i) q^{68} +2.44280e12 q^{69} +(-1.23467e12 - 7.64065e11i) q^{70} +1.80292e13i q^{71} +(3.32950e12 + 3.06113e11i) q^{72} -1.82099e13 q^{73} +(7.79685e12 - 1.25991e13i) q^{74} -6.51150e12i q^{75} +(-5.52735e12 + 2.75560e12i) q^{76} -1.25495e13 q^{77} +(-5.04087e12 - 3.11951e12i) q^{78} -2.69258e13i q^{79} +(-4.97071e12 + 6.59540e12i) q^{80} +2.54187e12 q^{81} +(1.36082e13 - 2.19897e13i) q^{82} -1.90822e13i q^{83} +(-3.40310e12 - 6.82616e12i) q^{84} -1.47472e13 q^{85} +(-3.58699e13 - 2.21978e13i) q^{86} +3.06966e13i q^{87} +(-6.53526e12 + 7.10819e13i) q^{88} +4.60407e13 q^{89} +(-3.30397e12 + 5.33895e12i) q^{90} +1.35233e13i q^{91} +(-2.83674e13 + 1.41422e13i) q^{92} +7.38230e12 q^{93} +(2.66533e13 + 1.64942e13i) q^{94} -1.15978e13i q^{95} +(-4.04364e13 + 1.57208e13i) q^{96} +1.38373e14 q^{97} +(3.65269e13 - 5.90245e13i) q^{98} +5.42667e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9} + 586324 q^{10} + 621108 q^{12} + 109934140 q^{13} - 200755992 q^{14} + 380631536 q^{16} - 291483380 q^{17} - 290166786 q^{18} + 5316726088 q^{20} - 1117661976 q^{21} - 9373833288 q^{22} + 2880331488 q^{24} + 12506859258 q^{25} - 45510637748 q^{26} + 83579713776 q^{28} - 12126204812 q^{29} - 44941179132 q^{30} + 67974212192 q^{32} - 34345330344 q^{33} - 57269346212 q^{34} - 14839958484 q^{36} + 119365701580 q^{37} + 102957884712 q^{38} - 491601579872 q^{40} + 189318893932 q^{41} + 240539889384 q^{42} - 997611383472 q^{44} + 25706864052 q^{45} + 1368039641184 q^{46} - 465649986384 q^{48} - 769149171250 q^{49} + 2170057449522 q^{50} - 2399333559176 q^{52} + 1251391890964 q^{53} - 90656394426 q^{54} + 2319191796096 q^{56} + 1805052294792 q^{57} - 5157502168892 q^{58} + 2354207329944 q^{60} - 7882441676660 q^{61} - 9161379391272 q^{62} + 17520900128384 q^{64} + 5858206778312 q^{65} - 6614704234440 q^{66} + 18747786717976 q^{68} - 13777261381728 q^{69} - 8213486211792 q^{70} - 6939794663568 q^{72} + 39185062250428 q^{73} - 7698562888484 q^{74} - 9224963770896 q^{76} - 41289727781472 q^{77} + 10470873014172 q^{78} - 57127847610848 q^{80} + 35586121596606 q^{81} + 107070799921084 q^{82} - 28102976768880 q^{84} - 188880254078680 q^{85} + 102443851819896 q^{86} - 83262676567680 q^{88} + 223721333984572 q^{89} - 934789838652 q^{90} - 79895035003584 q^{92} + 12688158423960 q^{93} - 52692266305296 q^{94} - 2264434006752 q^{96} + 282902280361756 q^{97} - 228639957171082 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 67.3573 108.844i 0.526229 0.850343i
\(3\) 1262.67i 0.577350i
\(4\) −7309.99 14662.9i −0.446167 0.894950i
\(5\) 30766.3 0.393809 0.196905 0.980423i \(-0.436911\pi\)
0.196905 + 0.980423i \(0.436911\pi\)
\(6\) 137433. + 85049.7i 0.490946 + 0.303818i
\(7\) 368697.i 0.447696i −0.974624 0.223848i \(-0.928138\pi\)
0.974624 0.223848i \(-0.0718620\pi\)
\(8\) −2.08834e6 192002.i −0.995800 0.0915537i
\(9\) −1.59432e6 −0.333333
\(10\) 2.07234e6 3.34873e6i 0.207234 0.334873i
\(11\) 3.40375e7i 1.74666i −0.487129 0.873330i \(-0.661956\pi\)
0.487129 0.873330i \(-0.338044\pi\)
\(12\) 1.85143e7 9.23007e6i 0.516700 0.257594i
\(13\) −3.66786e7 −0.584534 −0.292267 0.956337i \(-0.594410\pi\)
−0.292267 + 0.956337i \(0.594410\pi\)
\(14\) −4.01305e7 2.48344e7i −0.380696 0.235591i
\(15\) 3.88476e7i 0.227366i
\(16\) −1.61563e8 + 2.14371e8i −0.601871 + 0.798594i
\(17\) −4.79329e8 −1.16813 −0.584065 0.811707i \(-0.698539\pi\)
−0.584065 + 0.811707i \(0.698539\pi\)
\(18\) −1.07389e8 + 1.73532e8i −0.175410 + 0.283448i
\(19\) 3.76963e8i 0.421719i −0.977516 0.210860i \(-0.932374\pi\)
0.977516 0.210860i \(-0.0676263\pi\)
\(20\) −2.24902e8 4.51122e8i −0.175704 0.352439i
\(21\) 4.65541e8 0.258478
\(22\) −3.70477e9 2.29267e9i −1.48526 0.919143i
\(23\) 1.93464e9i 0.568206i −0.958794 0.284103i \(-0.908304\pi\)
0.958794 0.284103i \(-0.0916958\pi\)
\(24\) 2.42434e8 2.63688e9i 0.0528586 0.574925i
\(25\) −5.15695e9 −0.844914
\(26\) −2.47057e9 + 3.99225e9i −0.307599 + 0.497054i
\(27\) 2.01310e9i 0.192450i
\(28\) −5.40616e9 + 2.69517e9i −0.400666 + 0.199747i
\(29\) 2.43110e10 1.40934 0.704671 0.709534i \(-0.251095\pi\)
0.704671 + 0.709534i \(0.251095\pi\)
\(30\) 4.22832e9 + 2.61667e9i 0.193339 + 0.119646i
\(31\) 5.84660e9i 0.212506i −0.994339 0.106253i \(-0.966115\pi\)
0.994339 0.106253i \(-0.0338854\pi\)
\(32\) 1.24505e10 + 3.20246e10i 0.362357 + 0.932039i
\(33\) 4.29779e10 1.00843
\(34\) −3.22863e10 + 5.21720e10i −0.614703 + 0.993311i
\(35\) 1.13435e10i 0.176307i
\(36\) 1.16545e10 + 2.33773e10i 0.148722 + 0.298317i
\(37\) 1.15754e11 1.21933 0.609667 0.792658i \(-0.291303\pi\)
0.609667 + 0.792658i \(0.291303\pi\)
\(38\) −4.10301e10 2.53912e10i −0.358606 0.221921i
\(39\) 4.63128e10i 0.337481i
\(40\) −6.42507e10 5.90720e9i −0.392155 0.0360547i
\(41\) 2.02030e11 1.03736 0.518678 0.854970i \(-0.326424\pi\)
0.518678 + 0.854970i \(0.326424\pi\)
\(42\) 3.13576e10 5.06713e10i 0.136018 0.219795i
\(43\) 3.29553e11i 1.21240i −0.795312 0.606201i \(-0.792693\pi\)
0.795312 0.606201i \(-0.207307\pi\)
\(44\) −4.99086e11 + 2.48814e11i −1.56317 + 0.779301i
\(45\) −4.90515e10 −0.131270
\(46\) −2.10574e11 1.30312e11i −0.483170 0.299006i
\(47\) 2.44877e11i 0.483351i 0.970357 + 0.241676i \(0.0776970\pi\)
−0.970357 + 0.241676i \(0.922303\pi\)
\(48\) −2.70679e11 2.04001e11i −0.461068 0.347490i
\(49\) 5.42285e11 0.799568
\(50\) −3.47358e11 + 5.61302e11i −0.444618 + 0.718467i
\(51\) 6.05231e11i 0.674420i
\(52\) 2.68121e11 + 5.37814e11i 0.260800 + 0.523129i
\(53\) −1.47142e12 −1.25258 −0.626288 0.779591i \(-0.715427\pi\)
−0.626288 + 0.779591i \(0.715427\pi\)
\(54\) −2.19113e11 1.35597e11i −0.163649 0.101273i
\(55\) 1.04721e12i 0.687850i
\(56\) −7.07906e10 + 7.69967e11i −0.0409883 + 0.445816i
\(57\) 4.75978e11 0.243480
\(58\) 1.63752e12 2.64610e12i 0.741636 1.19842i
\(59\) 2.31401e12i 0.929826i 0.885356 + 0.464913i \(0.153914\pi\)
−0.885356 + 0.464913i \(0.846086\pi\)
\(60\) 5.69617e11 2.83976e11i 0.203481 0.101443i
\(61\) 7.16981e11 0.228139 0.114069 0.993473i \(-0.463611\pi\)
0.114069 + 0.993473i \(0.463611\pi\)
\(62\) −6.36367e11 3.93811e11i −0.180703 0.111827i
\(63\) 5.87823e11i 0.149232i
\(64\) 4.32432e12 + 8.01933e11i 0.983236 + 0.182338i
\(65\) −1.12847e12 −0.230195
\(66\) 2.89487e12 4.67788e12i 0.530667 0.857515i
\(67\) 2.62990e12i 0.433926i 0.976180 + 0.216963i \(0.0696151\pi\)
−0.976180 + 0.216963i \(0.930385\pi\)
\(68\) 3.50389e12 + 7.02833e12i 0.521180 + 1.04542i
\(69\) 2.44280e12 0.328054
\(70\) −1.23467e12 7.64065e11i −0.149921 0.0927778i
\(71\) 1.80292e13i 1.98229i 0.132771 + 0.991147i \(0.457613\pi\)
−0.132771 + 0.991147i \(0.542387\pi\)
\(72\) 3.32950e12 + 3.06113e11i 0.331933 + 0.0305179i
\(73\) −1.82099e13 −1.64834 −0.824172 0.566339i \(-0.808359\pi\)
−0.824172 + 0.566339i \(0.808359\pi\)
\(74\) 7.79685e12 1.25991e13i 0.641648 1.03685i
\(75\) 6.51150e12i 0.487812i
\(76\) −5.52735e12 + 2.75560e12i −0.377417 + 0.188157i
\(77\) −1.25495e13 −0.781973
\(78\) −5.04087e12 3.11951e12i −0.286975 0.177592i
\(79\) 2.69258e13i 1.40210i −0.713113 0.701049i \(-0.752715\pi\)
0.713113 0.701049i \(-0.247285\pi\)
\(80\) −4.97071e12 + 6.59540e12i −0.237022 + 0.314493i
\(81\) 2.54187e12 0.111111
\(82\) 1.36082e13 2.19897e13i 0.545887 0.882109i
\(83\) 1.90822e13i 0.703205i −0.936149 0.351602i \(-0.885637\pi\)
0.936149 0.351602i \(-0.114363\pi\)
\(84\) −3.40310e12 6.82616e12i −0.115324 0.231325i
\(85\) −1.47472e13 −0.460020
\(86\) −3.58699e13 2.21978e13i −1.03096 0.638001i
\(87\) 3.06966e13i 0.813684i
\(88\) −6.53526e12 + 7.10819e13i −0.159913 + 1.73932i
\(89\) 4.60407e13 1.04091 0.520453 0.853890i \(-0.325763\pi\)
0.520453 + 0.853890i \(0.325763\pi\)
\(90\) −3.30397e12 + 5.33895e12i −0.0690779 + 0.111624i
\(91\) 1.35233e13i 0.261694i
\(92\) −2.83674e13 + 1.41422e13i −0.508516 + 0.253515i
\(93\) 7.38230e12 0.122691
\(94\) 2.66533e13 + 1.64942e13i 0.411014 + 0.254353i
\(95\) 1.15978e13i 0.166077i
\(96\) −4.04364e13 + 1.57208e13i −0.538113 + 0.209207i
\(97\) 1.38373e14 1.71257 0.856286 0.516501i \(-0.172766\pi\)
0.856286 + 0.516501i \(0.172766\pi\)
\(98\) 3.65269e13 5.90245e13i 0.420756 0.679907i
\(99\) 5.42667e13i 0.582220i
\(100\) 3.76973e13 + 7.56156e13i 0.376973 + 0.756156i
\(101\) 1.10297e14 1.02876 0.514382 0.857561i \(-0.328021\pi\)
0.514382 + 0.857561i \(0.328021\pi\)
\(102\) −6.58758e13 4.07667e13i −0.573488 0.354899i
\(103\) 2.02040e14i 1.64277i −0.570372 0.821386i \(-0.693201\pi\)
0.570372 0.821386i \(-0.306799\pi\)
\(104\) 7.65976e13 + 7.04237e12i 0.582079 + 0.0535163i
\(105\) 1.43230e13 0.101791
\(106\) −9.91106e13 + 1.60155e14i −0.659142 + 1.06512i
\(107\) 8.40010e13i 0.523116i −0.965188 0.261558i \(-0.915764\pi\)
0.965188 0.261558i \(-0.0842363\pi\)
\(108\) −2.95177e13 + 1.47157e13i −0.172233 + 0.0858648i
\(109\) −2.83963e14 −1.55337 −0.776687 0.629887i \(-0.783101\pi\)
−0.776687 + 0.629887i \(0.783101\pi\)
\(110\) −1.13982e14 7.05371e13i −0.584909 0.361967i
\(111\) 1.46158e14i 0.703982i
\(112\) 7.90379e13 + 5.95680e13i 0.357527 + 0.269455i
\(113\) 1.45379e14 0.617951 0.308975 0.951070i \(-0.400014\pi\)
0.308975 + 0.951070i \(0.400014\pi\)
\(114\) 3.20606e13 5.18073e13i 0.128126 0.207041i
\(115\) 5.95218e13i 0.223765i
\(116\) −1.77713e14 3.56468e14i −0.628801 1.26129i
\(117\) 5.84776e13 0.194845
\(118\) 2.51866e14 + 1.55866e14i 0.790671 + 0.489301i
\(119\) 1.76727e14i 0.522967i
\(120\) 7.45881e12 8.11271e13i 0.0208162 0.226411i
\(121\) −7.78799e14 −2.05082
\(122\) 4.82939e13 7.80390e13i 0.120053 0.193996i
\(123\) 2.55096e14i 0.598918i
\(124\) −8.57279e13 + 4.27386e13i −0.190182 + 0.0948132i
\(125\) −3.46443e14 −0.726544
\(126\) 6.39809e13 + 3.95941e13i 0.126899 + 0.0785302i
\(127\) 2.92861e14i 0.549586i −0.961503 0.274793i \(-0.911391\pi\)
0.961503 0.274793i \(-0.0886094\pi\)
\(128\) 3.78560e14 4.16660e14i 0.672457 0.740136i
\(129\) 4.16116e14 0.699981
\(130\) −7.60105e13 + 1.22827e14i −0.121135 + 0.195745i
\(131\) 8.92594e14i 1.34820i 0.738639 + 0.674101i \(0.235469\pi\)
−0.738639 + 0.674101i \(0.764531\pi\)
\(132\) −3.14168e14 6.30179e14i −0.449930 0.902498i
\(133\) −1.38985e14 −0.188802
\(134\) 2.86249e14 + 1.77143e14i 0.368986 + 0.228344i
\(135\) 6.19356e13i 0.0757886i
\(136\) 1.00100e15 + 9.20321e13i 1.16322 + 0.106947i
\(137\) 1.11799e14 0.123423 0.0617115 0.998094i \(-0.480344\pi\)
0.0617115 + 0.998094i \(0.480344\pi\)
\(138\) 1.64541e14 2.65884e14i 0.172631 0.278958i
\(139\) 1.36899e15i 1.36552i −0.730645 0.682758i \(-0.760781\pi\)
0.730645 0.682758i \(-0.239219\pi\)
\(140\) −1.66328e14 + 8.29206e13i −0.157786 + 0.0786623i
\(141\) −3.09197e14 −0.279063
\(142\) 1.96237e15 + 1.21440e15i 1.68563 + 1.04314i
\(143\) 1.24845e15i 1.02098i
\(144\) 2.57584e14 3.41776e14i 0.200624 0.266198i
\(145\) 7.47959e14 0.555011
\(146\) −1.22657e15 + 1.98204e15i −0.867406 + 1.40166i
\(147\) 6.84725e14i 0.461631i
\(148\) −8.46158e14 1.69728e15i −0.544026 1.09124i
\(149\) 4.24688e13 0.0260475 0.0130237 0.999915i \(-0.495854\pi\)
0.0130237 + 0.999915i \(0.495854\pi\)
\(150\) −7.08737e14 4.38597e14i −0.414807 0.256700i
\(151\) 4.14395e14i 0.231513i −0.993278 0.115757i \(-0.963071\pi\)
0.993278 0.115757i \(-0.0369292\pi\)
\(152\) −7.23776e13 + 7.87228e14i −0.0386099 + 0.419948i
\(153\) 7.64205e14 0.389376
\(154\) −8.45301e14 + 1.36594e15i −0.411497 + 0.664946i
\(155\) 1.79878e14i 0.0836869i
\(156\) −6.79079e14 + 3.38547e14i −0.302028 + 0.150573i
\(157\) 1.48358e15 0.630977 0.315488 0.948929i \(-0.397832\pi\)
0.315488 + 0.948929i \(0.397832\pi\)
\(158\) −2.93071e15 1.81365e15i −1.19226 0.737825i
\(159\) 1.85791e15i 0.723176i
\(160\) 3.83056e14 + 9.85281e14i 0.142699 + 0.367046i
\(161\) −7.13297e14 −0.254384
\(162\) 1.71213e14 2.76667e14i 0.0584699 0.0944826i
\(163\) 2.98948e15i 0.977873i −0.872319 0.488937i \(-0.837385\pi\)
0.872319 0.488937i \(-0.162615\pi\)
\(164\) −1.47683e15 2.96233e15i −0.462834 0.928382i
\(165\) 1.32227e15 0.397131
\(166\) −2.07698e15 1.28533e15i −0.597965 0.370047i
\(167\) 1.80982e15i 0.499598i −0.968298 0.249799i \(-0.919635\pi\)
0.968298 0.249799i \(-0.0803646\pi\)
\(168\) −9.72210e14 8.93848e13i −0.257392 0.0236646i
\(169\) −2.59205e15 −0.658320
\(170\) −9.93330e14 + 1.60514e15i −0.242076 + 0.391175i
\(171\) 6.01000e14i 0.140573i
\(172\) −4.83220e15 + 2.40903e15i −1.08504 + 0.540933i
\(173\) 4.35216e15 0.938387 0.469194 0.883095i \(-0.344545\pi\)
0.469194 + 0.883095i \(0.344545\pi\)
\(174\) 3.34114e15 + 2.06764e15i 0.691910 + 0.428184i
\(175\) 1.90135e15i 0.378265i
\(176\) 7.29664e15 + 5.49921e15i 1.39487 + 1.05126i
\(177\) −2.92182e15 −0.536835
\(178\) 3.10118e15 5.01125e15i 0.547755 0.885128i
\(179\) 5.79613e14i 0.0984390i −0.998788 0.0492195i \(-0.984327\pi\)
0.998788 0.0492195i \(-0.0156734\pi\)
\(180\) 3.58566e14 + 7.19235e14i 0.0585682 + 0.117480i
\(181\) 1.66845e15 0.262158 0.131079 0.991372i \(-0.458156\pi\)
0.131079 + 0.991372i \(0.458156\pi\)
\(182\) 1.47193e15 + 9.10894e14i 0.222530 + 0.137711i
\(183\) 9.05307e14i 0.131716i
\(184\) −3.71455e14 + 4.04020e15i −0.0520214 + 0.565820i
\(185\) 3.56131e15 0.480185
\(186\) 4.97252e14 8.03518e14i 0.0645633 0.104329i
\(187\) 1.63151e16i 2.04032i
\(188\) 3.59059e15 1.79005e15i 0.432575 0.215655i
\(189\) −7.42223e14 −0.0861592
\(190\) −1.26235e15 7.81194e14i −0.141222 0.0873944i
\(191\) 7.74538e15i 0.835235i −0.908623 0.417618i \(-0.862865\pi\)
0.908623 0.417618i \(-0.137135\pi\)
\(192\) −1.01257e15 + 5.46016e15i −0.105273 + 0.567671i
\(193\) −4.19241e14 −0.0420303 −0.0210152 0.999779i \(-0.506690\pi\)
−0.0210152 + 0.999779i \(0.506690\pi\)
\(194\) 9.32042e15 1.50611e16i 0.901205 1.45627i
\(195\) 1.42488e15i 0.132903i
\(196\) −3.96410e15 7.95145e15i −0.356740 0.715573i
\(197\) −1.76103e16 −1.52934 −0.764669 0.644424i \(-0.777097\pi\)
−0.764669 + 0.644424i \(0.777097\pi\)
\(198\) 5.90660e15 + 3.65526e15i 0.495087 + 0.306381i
\(199\) 5.65746e15i 0.457772i 0.973453 + 0.228886i \(0.0735084\pi\)
−0.973453 + 0.228886i \(0.926492\pi\)
\(200\) 1.07695e16 + 9.90145e14i 0.841366 + 0.0773550i
\(201\) −3.32069e15 −0.250527
\(202\) 7.42933e15 1.20052e16i 0.541365 0.874802i
\(203\) 8.96339e15i 0.630957i
\(204\) −8.87442e15 + 4.42424e15i −0.603572 + 0.300904i
\(205\) 6.21571e15 0.408520
\(206\) −2.19909e16 1.36089e16i −1.39692 0.864474i
\(207\) 3.08444e15i 0.189402i
\(208\) 5.92593e15 7.86283e15i 0.351814 0.466805i
\(209\) −1.28309e16 −0.736600
\(210\) 9.64758e14 1.55897e15i 0.0535653 0.0865571i
\(211\) 2.83607e16i 1.52314i 0.648082 + 0.761571i \(0.275572\pi\)
−0.648082 + 0.761571i \(0.724428\pi\)
\(212\) 1.07560e16 + 2.15752e16i 0.558858 + 1.12099i
\(213\) −2.27648e16 −1.14448
\(214\) −9.14300e15 5.65808e15i −0.444828 0.275279i
\(215\) 1.01391e16i 0.477455i
\(216\) −3.86519e14 + 4.20404e15i −0.0176195 + 0.191642i
\(217\) −2.15563e15 −0.0951383
\(218\) −1.91270e16 + 3.09076e16i −0.817430 + 1.32090i
\(219\) 2.29930e16i 0.951672i
\(220\) −1.53551e16 + 7.65508e15i −0.615592 + 0.306896i
\(221\) 1.75811e16 0.682811
\(222\) 1.59084e16 + 9.84481e15i 0.598627 + 0.370456i
\(223\) 3.08803e16i 1.12602i −0.826449 0.563011i \(-0.809643\pi\)
0.826449 0.563011i \(-0.190357\pi\)
\(224\) 1.18074e16 4.59046e15i 0.417271 0.162226i
\(225\) 8.22184e15 0.281638
\(226\) 9.79237e15 1.58237e16i 0.325184 0.525470i
\(227\) 2.50452e16i 0.806386i 0.915115 + 0.403193i \(0.132100\pi\)
−0.915115 + 0.403193i \(0.867900\pi\)
\(228\) −3.47939e15 6.97919e15i −0.108632 0.217902i
\(229\) 4.62302e16 1.39984 0.699919 0.714223i \(-0.253220\pi\)
0.699919 + 0.714223i \(0.253220\pi\)
\(230\) −6.47859e15 4.00923e15i −0.190277 0.117751i
\(231\) 1.58458e16i 0.451473i
\(232\) −5.07697e16 4.66775e15i −1.40342 0.129030i
\(233\) 2.49166e15 0.0668340 0.0334170 0.999441i \(-0.489361\pi\)
0.0334170 + 0.999441i \(0.489361\pi\)
\(234\) 3.93889e15 6.36493e15i 0.102533 0.165685i
\(235\) 7.53396e15i 0.190348i
\(236\) 3.39301e16 1.69154e16i 0.832148 0.414857i
\(237\) 3.39982e16 0.809502
\(238\) 1.92357e16 + 1.19039e16i 0.444702 + 0.275200i
\(239\) 1.31724e16i 0.295718i −0.989008 0.147859i \(-0.952762\pi\)
0.989008 0.147859i \(-0.0472382\pi\)
\(240\) −8.32779e15 6.27635e15i −0.181573 0.136845i
\(241\) 3.30650e16 0.700245 0.350122 0.936704i \(-0.386140\pi\)
0.350122 + 0.936704i \(0.386140\pi\)
\(242\) −5.24578e16 + 8.47675e16i −1.07920 + 1.74390i
\(243\) 3.20953e15i 0.0641500i
\(244\) −5.24113e15 1.05130e16i −0.101788 0.204173i
\(245\) 1.66841e16 0.314877
\(246\) 2.77656e16 + 1.71826e16i 0.509286 + 0.315168i
\(247\) 1.38265e16i 0.246509i
\(248\) −1.12256e15 + 1.22097e16i −0.0194557 + 0.211614i
\(249\) 2.40944e16 0.405995
\(250\) −2.33355e16 + 3.77082e16i −0.382328 + 0.617812i
\(251\) 3.75727e16i 0.598628i 0.954155 + 0.299314i \(0.0967577\pi\)
−0.954155 + 0.299314i \(0.903242\pi\)
\(252\) 8.61916e15 4.29698e15i 0.133555 0.0665824i
\(253\) −6.58503e16 −0.992462
\(254\) −3.18762e16 1.97263e16i −0.467337 0.289208i
\(255\) 1.86208e16i 0.265593i
\(256\) −1.98521e16 6.92690e16i −0.275503 0.961300i
\(257\) 3.46414e16 0.467804 0.233902 0.972260i \(-0.424851\pi\)
0.233902 + 0.972260i \(0.424851\pi\)
\(258\) 2.80284e16 4.52916e16i 0.368350 0.595224i
\(259\) 4.26780e16i 0.545891i
\(260\) 8.24909e15 + 1.65466e16i 0.102705 + 0.206013i
\(261\) −3.87595e16 −0.469780
\(262\) 9.71534e16 + 6.01227e16i 1.14643 + 0.709462i
\(263\) 4.51324e16i 0.518558i −0.965802 0.259279i \(-0.916515\pi\)
0.965802 0.259279i \(-0.0834850\pi\)
\(264\) −8.97527e16 8.25185e15i −1.00420 0.0923259i
\(265\) −4.52701e16 −0.493276
\(266\) −9.36166e15 + 1.51277e16i −0.0993531 + 0.160547i
\(267\) 5.81340e16i 0.600968i
\(268\) 3.85619e16 1.92246e16i 0.388342 0.193603i
\(269\) −1.92854e17 −1.89218 −0.946088 0.323909i \(-0.895003\pi\)
−0.946088 + 0.323909i \(0.895003\pi\)
\(270\) −6.74131e15 4.17181e15i −0.0644463 0.0398821i
\(271\) 1.21122e17i 1.12833i −0.825660 0.564167i \(-0.809197\pi\)
0.825660 0.564167i \(-0.190803\pi\)
\(272\) 7.74420e16 1.02754e17i 0.703063 0.932860i
\(273\) −1.70754e16 −0.151089
\(274\) 7.53051e15 1.21687e16i 0.0649487 0.104952i
\(275\) 1.75529e17i 1.47578i
\(276\) −1.78569e16 3.58185e16i −0.146367 0.293592i
\(277\) −9.92031e16 −0.792806 −0.396403 0.918077i \(-0.629742\pi\)
−0.396403 + 0.918077i \(0.629742\pi\)
\(278\) −1.49006e17 9.22114e16i −1.16116 0.718573i
\(279\) 9.32137e15i 0.0708354i
\(280\) −2.17797e15 + 2.36891e16i −0.0161416 + 0.175566i
\(281\) 1.87290e16 0.135385 0.0676925 0.997706i \(-0.478436\pi\)
0.0676925 + 0.997706i \(0.478436\pi\)
\(282\) −2.08267e16 + 3.36543e16i −0.146851 + 0.237299i
\(283\) 4.34201e16i 0.298666i 0.988787 + 0.149333i \(0.0477126\pi\)
−0.988787 + 0.149333i \(0.952287\pi\)
\(284\) 2.64360e17 1.31793e17i 1.77405 0.884433i
\(285\) 1.46441e16 0.0958845
\(286\) 1.35886e17 + 8.40920e16i 0.868185 + 0.537270i
\(287\) 7.44878e16i 0.464421i
\(288\) −1.98501e16 5.10576e16i −0.120786 0.310680i
\(289\) 6.13781e16 0.364526
\(290\) 5.03805e16 8.14108e16i 0.292063 0.471950i
\(291\) 1.74719e17i 0.988754i
\(292\) 1.33114e17 + 2.67009e17i 0.735436 + 1.47519i
\(293\) 3.03810e17 1.63881 0.819405 0.573215i \(-0.194304\pi\)
0.819405 + 0.573215i \(0.194304\pi\)
\(294\) 7.45281e16 + 4.61212e16i 0.392544 + 0.242923i
\(295\) 7.11937e16i 0.366174i
\(296\) −2.41733e17 2.22249e16i −1.21421 0.111634i
\(297\) −6.85207e16 −0.336145
\(298\) 2.86058e15 4.62247e15i 0.0137069 0.0221493i
\(299\) 7.09600e16i 0.332136i
\(300\) −9.54772e16 + 4.75990e16i −0.436567 + 0.217645i
\(301\) −1.21505e17 −0.542788
\(302\) −4.51043e16 2.79125e16i −0.196865 0.121829i
\(303\) 1.39269e17i 0.593957i
\(304\) 8.08098e16 + 6.09034e16i 0.336782 + 0.253820i
\(305\) 2.20589e16 0.0898430
\(306\) 5.14747e16 8.31790e16i 0.204901 0.331104i
\(307\) 6.06880e16i 0.236121i −0.993006 0.118060i \(-0.962332\pi\)
0.993006 0.118060i \(-0.0376676\pi\)
\(308\) 9.17369e16 + 1.84012e17i 0.348890 + 0.699827i
\(309\) 2.55109e17 0.948455
\(310\) −1.95787e16 1.21161e16i −0.0711625 0.0440384i
\(311\) 4.00103e17i 1.42183i −0.703276 0.710917i \(-0.748280\pi\)
0.703276 0.710917i \(-0.251720\pi\)
\(312\) −8.89216e15 + 9.67172e16i −0.0308976 + 0.336064i
\(313\) −2.92916e17 −0.995250 −0.497625 0.867392i \(-0.665794\pi\)
−0.497625 + 0.867392i \(0.665794\pi\)
\(314\) 9.99299e16 1.61479e17i 0.332038 0.536547i
\(315\) 1.80851e16i 0.0587690i
\(316\) −3.94809e17 + 1.96827e17i −1.25481 + 0.625570i
\(317\) 1.65545e17 0.514636 0.257318 0.966327i \(-0.417161\pi\)
0.257318 + 0.966327i \(0.417161\pi\)
\(318\) −2.02222e17 1.25143e17i −0.614947 0.380556i
\(319\) 8.27483e17i 2.46164i
\(320\) 1.33043e17 + 2.46725e16i 0.387207 + 0.0718065i
\(321\) 1.06065e17 0.302021
\(322\) −4.80458e16 + 7.76381e16i −0.133864 + 0.216313i
\(323\) 1.80689e17i 0.492622i
\(324\) −1.85810e16 3.72710e16i −0.0495741 0.0994389i
\(325\) 1.89150e17 0.493881
\(326\) −3.25387e17 2.01363e17i −0.831528 0.514585i
\(327\) 3.58550e17i 0.896841i
\(328\) −4.21907e17 3.87901e16i −1.03300 0.0949738i
\(329\) 9.02854e16 0.216395
\(330\) 8.90647e16 1.43921e17i 0.208982 0.337697i
\(331\) 7.06800e17i 1.62368i 0.583880 + 0.811840i \(0.301534\pi\)
−0.583880 + 0.811840i \(0.698466\pi\)
\(332\) −2.79800e17 + 1.39491e17i −0.629333 + 0.313746i
\(333\) −1.84549e17 −0.406444
\(334\) −1.96988e17 1.21905e17i −0.424830 0.262903i
\(335\) 8.09124e16i 0.170884i
\(336\) −7.52144e16 + 9.97984e16i −0.155570 + 0.206419i
\(337\) 1.03081e17 0.208819 0.104409 0.994534i \(-0.466705\pi\)
0.104409 + 0.994534i \(0.466705\pi\)
\(338\) −1.74594e17 + 2.82129e17i −0.346427 + 0.559798i
\(339\) 1.83566e17i 0.356774i
\(340\) 1.07802e17 + 2.16236e17i 0.205246 + 0.411695i
\(341\) −1.99003e17 −0.371176
\(342\) 6.54152e16 + 4.04818e16i 0.119535 + 0.0739736i
\(343\) 4.49998e17i 0.805660i
\(344\) −6.32749e16 + 6.88221e17i −0.111000 + 1.20731i
\(345\) 7.51561e16 0.129191
\(346\) 2.93150e17 4.73706e17i 0.493806 0.797951i
\(347\) 2.48415e17i 0.410083i 0.978753 + 0.205041i \(0.0657329\pi\)
−0.978753 + 0.205041i \(0.934267\pi\)
\(348\) 4.50100e17 2.24392e17i 0.728206 0.363038i
\(349\) 5.13504e17 0.814265 0.407133 0.913369i \(-0.366529\pi\)
0.407133 + 0.913369i \(0.366529\pi\)
\(350\) 2.06951e17 + 1.28070e17i 0.321655 + 0.199054i
\(351\) 7.38376e16i 0.112494i
\(352\) 1.09004e18 4.23783e17i 1.62796 0.632914i
\(353\) −4.41600e17 −0.646557 −0.323278 0.946304i \(-0.604785\pi\)
−0.323278 + 0.946304i \(0.604785\pi\)
\(354\) −1.96806e17 + 3.18023e17i −0.282498 + 0.456494i
\(355\) 5.54692e17i 0.780645i
\(356\) −3.36557e17 6.75088e17i −0.464418 0.931559i
\(357\) −2.23147e17 −0.301935
\(358\) −6.30874e16 3.90412e16i −0.0837069 0.0518014i
\(359\) 2.62499e17i 0.341559i 0.985309 + 0.170780i \(0.0546286\pi\)
−0.985309 + 0.170780i \(0.945371\pi\)
\(360\) 1.02436e17 + 9.41798e15i 0.130718 + 0.0120182i
\(361\) 6.56906e17 0.822153
\(362\) 1.12382e17 1.81601e17i 0.137955 0.222924i
\(363\) 9.83362e17i 1.18404i
\(364\) 1.98290e17 9.88554e16i 0.234203 0.116759i
\(365\) −5.60252e17 −0.649133
\(366\) 9.85371e16 + 6.09790e16i 0.112004 + 0.0693127i
\(367\) 2.42222e16i 0.0270116i −0.999909 0.0135058i \(-0.995701\pi\)
0.999909 0.0135058i \(-0.00429917\pi\)
\(368\) 4.14731e17 + 3.12567e17i 0.453766 + 0.341987i
\(369\) −3.22100e17 −0.345785
\(370\) 2.39880e17 3.87627e17i 0.252687 0.408322i
\(371\) 5.42507e17i 0.560774i
\(372\) −5.39646e16 1.08246e17i −0.0547404 0.109802i
\(373\) −4.64802e17 −0.462707 −0.231354 0.972870i \(-0.574315\pi\)
−0.231354 + 0.972870i \(0.574315\pi\)
\(374\) 1.77580e18 + 1.09894e18i 1.73498 + 1.07368i
\(375\) 4.37442e17i 0.419470i
\(376\) 4.70168e16 5.11387e17i 0.0442526 0.481321i
\(377\) −8.91693e17 −0.823808
\(378\) −4.99941e16 + 8.07864e16i −0.0453395 + 0.0732649i
\(379\) 1.66809e18i 1.48506i 0.669811 + 0.742532i \(0.266375\pi\)
−0.669811 + 0.742532i \(0.733625\pi\)
\(380\) −1.70056e17 + 8.47796e16i −0.148630 + 0.0740979i
\(381\) 3.69786e17 0.317304
\(382\) −8.43037e17 5.21707e17i −0.710237 0.439525i
\(383\) 3.29986e17i 0.272963i −0.990643 0.136482i \(-0.956420\pi\)
0.990643 0.136482i \(-0.0435795\pi\)
\(384\) 5.26101e17 + 4.77994e17i 0.427318 + 0.388243i
\(385\) −3.86103e17 −0.307948
\(386\) −2.82389e16 + 4.56318e16i −0.0221176 + 0.0357402i
\(387\) 5.25415e17i 0.404134i
\(388\) −1.01151e18 2.02894e18i −0.764093 1.53267i
\(389\) 4.56208e17 0.338466 0.169233 0.985576i \(-0.445871\pi\)
0.169233 + 0.985576i \(0.445871\pi\)
\(390\) −1.55089e17 9.59758e16i −0.113013 0.0699374i
\(391\) 9.27329e17i 0.663738i
\(392\) −1.13248e18 1.04120e17i −0.796210 0.0732034i
\(393\) −1.12705e18 −0.778385
\(394\) −1.18618e18 + 1.91677e18i −0.804781 + 1.30046i
\(395\) 8.28407e17i 0.552159i
\(396\) 7.95705e17 3.96689e17i 0.521058 0.259767i
\(397\) −7.12062e17 −0.458125 −0.229063 0.973412i \(-0.573566\pi\)
−0.229063 + 0.973412i \(0.573566\pi\)
\(398\) 6.15780e17 + 3.81071e17i 0.389264 + 0.240893i
\(399\) 1.75492e17i 0.109005i
\(400\) 8.33174e17 1.10550e18i 0.508529 0.674743i
\(401\) 1.12281e17 0.0673436 0.0336718 0.999433i \(-0.489280\pi\)
0.0336718 + 0.999433i \(0.489280\pi\)
\(402\) −2.23672e17 + 3.61436e17i −0.131835 + 0.213034i
\(403\) 2.14445e17i 0.124217i
\(404\) −8.06274e17 1.61728e18i −0.459000 0.920692i
\(405\) 7.82039e16 0.0437566
\(406\) −9.75610e17 6.03749e17i −0.536530 0.332028i
\(407\) 3.93996e18i 2.12976i
\(408\) −1.16206e17 + 1.26393e18i −0.0617456 + 0.671587i
\(409\) 1.36519e18 0.713065 0.356532 0.934283i \(-0.383959\pi\)
0.356532 + 0.934283i \(0.383959\pi\)
\(410\) 4.18673e17 6.76542e17i 0.214975 0.347382i
\(411\) 1.41165e17i 0.0712583i
\(412\) −2.96249e18 + 1.47691e18i −1.47020 + 0.732950i
\(413\) 8.53170e17 0.416280
\(414\) 3.35723e17 + 2.07760e17i 0.161057 + 0.0996688i
\(415\) 5.87089e17i 0.276928i
\(416\) −4.56667e17 1.17462e18i −0.211810 0.544809i
\(417\) 1.72858e18 0.788381
\(418\) −8.64251e17 + 1.39656e18i −0.387620 + 0.626362i
\(419\) 2.54171e17i 0.112106i 0.998428 + 0.0560528i \(0.0178515\pi\)
−0.998428 + 0.0560528i \(0.982148\pi\)
\(420\) −1.04701e17 2.10016e17i −0.0454157 0.0910977i
\(421\) 1.38924e18 0.592655 0.296328 0.955086i \(-0.404238\pi\)
0.296328 + 0.955086i \(0.404238\pi\)
\(422\) 3.08689e18 + 1.91030e18i 1.29519 + 0.801521i
\(423\) 3.90413e17i 0.161117i
\(424\) 3.07282e18 + 2.82515e17i 1.24732 + 0.114678i
\(425\) 2.47187e18 0.986969
\(426\) −1.53338e18 + 2.47781e18i −0.602257 + 0.973199i
\(427\) 2.64349e17i 0.102137i
\(428\) −1.23169e18 + 6.14047e17i −0.468163 + 0.233397i
\(429\) −1.57637e18 −0.589464
\(430\) −1.10358e18 6.82946e17i −0.406000 0.251250i
\(431\) 6.88298e17i 0.249136i −0.992211 0.124568i \(-0.960246\pi\)
0.992211 0.124568i \(-0.0397544\pi\)
\(432\) 4.31549e17 + 3.25243e17i 0.153689 + 0.115830i
\(433\) 1.64319e18 0.575800 0.287900 0.957661i \(-0.407043\pi\)
0.287900 + 0.957661i \(0.407043\pi\)
\(434\) −1.45197e17 + 2.34627e17i −0.0500645 + 0.0809002i
\(435\) 9.44422e17i 0.320436i
\(436\) 2.07577e18 + 4.16371e18i 0.693063 + 1.39019i
\(437\) −7.29288e17 −0.239623
\(438\) −2.50265e18 1.54875e18i −0.809248 0.500797i
\(439\) 3.97715e18i 1.26567i 0.774287 + 0.632835i \(0.218109\pi\)
−0.774287 + 0.632835i \(0.781891\pi\)
\(440\) −2.01066e17 + 2.18693e18i −0.0629753 + 0.684962i
\(441\) −8.64578e17 −0.266523
\(442\) 1.18422e18 1.91360e18i 0.359315 0.580624i
\(443\) 3.21465e18i 0.960079i 0.877247 + 0.480040i \(0.159378\pi\)
−0.877247 + 0.480040i \(0.840622\pi\)
\(444\) 2.14309e18 1.06841e18i 0.630029 0.314093i
\(445\) 1.41650e18 0.409919
\(446\) −3.36113e18 2.08001e18i −0.957506 0.592546i
\(447\) 5.36238e16i 0.0150385i
\(448\) 2.95670e17 1.59436e18i 0.0816322 0.440191i
\(449\) 6.29446e18 1.71094 0.855469 0.517855i \(-0.173269\pi\)
0.855469 + 0.517855i \(0.173269\pi\)
\(450\) 5.53801e17 8.94897e17i 0.148206 0.239489i
\(451\) 6.87657e18i 1.81191i
\(452\) −1.06272e18 2.13168e18i −0.275709 0.553035i
\(453\) 5.23242e17 0.133664
\(454\) 2.72601e18 + 1.68697e18i 0.685705 + 0.424344i
\(455\) 4.16063e17i 0.103057i
\(456\) −9.94005e17 9.13887e16i −0.242457 0.0222915i
\(457\) −7.34945e18 −1.76539 −0.882697 0.469942i \(-0.844275\pi\)
−0.882697 + 0.469942i \(0.844275\pi\)
\(458\) 3.11394e18 5.03188e18i 0.736634 1.19034i
\(459\) 9.64934e17i 0.224807i
\(460\) −8.72760e17 + 4.35104e17i −0.200258 + 0.0998363i
\(461\) −8.27064e18 −1.86910 −0.934550 0.355832i \(-0.884197\pi\)
−0.934550 + 0.355832i \(0.884197\pi\)
\(462\) −1.72472e18 1.06733e18i −0.383907 0.237578i
\(463\) 2.96915e18i 0.650976i −0.945546 0.325488i \(-0.894471\pi\)
0.945546 0.325488i \(-0.105529\pi\)
\(464\) −3.92776e18 + 5.21156e18i −0.848241 + 1.12549i
\(465\) 2.27126e17 0.0483166
\(466\) 1.67831e17 2.71202e17i 0.0351700 0.0568318i
\(467\) 1.84642e17i 0.0381164i −0.999818 0.0190582i \(-0.993933\pi\)
0.999818 0.0190582i \(-0.00606678\pi\)
\(468\) −4.27471e17 8.57449e17i −0.0869332 0.174376i
\(469\) 9.69638e17 0.194267
\(470\) 8.20026e17 + 5.07467e17i 0.161861 + 0.100167i
\(471\) 1.87326e18i 0.364294i
\(472\) 4.44295e17 4.83246e18i 0.0851290 0.925921i
\(473\) −1.12172e19 −2.11765
\(474\) 2.29003e18 3.70050e18i 0.425983 0.688354i
\(475\) 1.94398e18i 0.356317i
\(476\) 2.59133e18 1.29187e18i 0.468030 0.233331i
\(477\) 2.34591e18 0.417526
\(478\) −1.43373e18 8.87254e17i −0.251462 0.155615i
\(479\) 9.34485e18i 1.61519i 0.589737 + 0.807596i \(0.299232\pi\)
−0.589737 + 0.807596i \(0.700768\pi\)
\(480\) −1.24408e18 + 4.83671e17i −0.211914 + 0.0823875i
\(481\) −4.24569e18 −0.712742
\(482\) 2.22717e18 3.59893e18i 0.368489 0.595448i
\(483\) 9.00655e17i 0.146869i
\(484\) 5.69301e18 + 1.14194e19i 0.915007 + 1.83538i
\(485\) 4.25723e18 0.674427
\(486\) 3.49337e17 + 2.16185e17i 0.0545495 + 0.0337576i
\(487\) 7.97764e18i 1.22792i −0.789336 0.613962i \(-0.789575\pi\)
0.789336 0.613962i \(-0.210425\pi\)
\(488\) −1.49730e18 1.37662e17i −0.227180 0.0208869i
\(489\) 3.77471e18 0.564575
\(490\) 1.12380e18 1.81597e18i 0.165697 0.267754i
\(491\) 6.36977e17i 0.0925876i 0.998928 + 0.0462938i \(0.0147410\pi\)
−0.998928 + 0.0462938i \(0.985259\pi\)
\(492\) 3.74043e18 1.86475e18i 0.536002 0.267217i
\(493\) −1.16529e19 −1.64629
\(494\) 1.50493e18 + 9.31314e17i 0.209617 + 0.129720i
\(495\) 1.66959e18i 0.229283i
\(496\) 1.25334e18 + 9.44597e17i 0.169706 + 0.127901i
\(497\) 6.64732e18 0.887466
\(498\) 1.62294e18 2.62253e18i 0.213646 0.345235i
\(499\) 1.24967e18i 0.162215i −0.996705 0.0811075i \(-0.974154\pi\)
0.996705 0.0811075i \(-0.0258457\pi\)
\(500\) 2.53250e18 + 5.07985e18i 0.324160 + 0.650221i
\(501\) 2.28520e18 0.288443
\(502\) 4.08956e18 + 2.53080e18i 0.509039 + 0.315015i
\(503\) 1.01888e19i 1.25069i 0.780349 + 0.625344i \(0.215041\pi\)
−0.780349 + 0.625344i \(0.784959\pi\)
\(504\) 1.12863e17 1.22758e18i 0.0136628 0.148605i
\(505\) 3.39345e18 0.405137
\(506\) −4.43550e18 + 7.16740e18i −0.522262 + 0.843934i
\(507\) 3.27290e18i 0.380081i
\(508\) −4.29418e18 + 2.14081e18i −0.491852 + 0.245207i
\(509\) 1.16612e19 1.31741 0.658704 0.752402i \(-0.271105\pi\)
0.658704 + 0.752402i \(0.271105\pi\)
\(510\) −2.02676e18 1.25424e18i −0.225845 0.139762i
\(511\) 6.71395e18i 0.737958i
\(512\) −8.87669e18 2.50499e18i −0.962413 0.271591i
\(513\) −7.58862e17 −0.0811599
\(514\) 2.33335e18 3.77051e18i 0.246172 0.397794i
\(515\) 6.21604e18i 0.646939i
\(516\) −3.04180e18 6.10144e18i −0.312308 0.626448i
\(517\) 8.33498e18 0.844250
\(518\) −4.64524e18 2.87468e18i −0.464195 0.287264i
\(519\) 5.49532e18i 0.541778i
\(520\) 2.35663e18 + 2.16668e17i 0.229228 + 0.0210752i
\(521\) 2.34671e18 0.225214 0.112607 0.993640i \(-0.464080\pi\)
0.112607 + 0.993640i \(0.464080\pi\)
\(522\) −2.61074e18 + 4.21874e18i −0.247212 + 0.399475i
\(523\) 1.95230e19i 1.82404i −0.410147 0.912020i \(-0.634523\pi\)
0.410147 0.912020i \(-0.365477\pi\)
\(524\) 1.30880e19 6.52486e18i 1.20657 0.601523i
\(525\) −2.40077e18 −0.218392
\(526\) −4.91238e18 3.03999e18i −0.440953 0.272880i
\(527\) 2.80244e18i 0.248235i
\(528\) −6.94366e18 + 9.21321e18i −0.606947 + 0.805329i
\(529\) 7.85000e18 0.677142
\(530\) −3.04927e18 + 4.92737e18i −0.259576 + 0.419454i
\(531\) 3.68928e18i 0.309942i
\(532\) 1.01598e18 + 2.03792e18i 0.0842372 + 0.168968i
\(533\) −7.41017e18 −0.606370
\(534\) 6.32753e18 + 3.91575e18i 0.511029 + 0.316247i
\(535\) 2.58440e18i 0.206008i
\(536\) 5.04947e17 5.49214e18i 0.0397276 0.432104i
\(537\) 7.31857e17 0.0568338
\(538\) −1.29901e19 + 2.09909e19i −0.995718 + 1.60900i
\(539\) 1.84580e19i 1.39657i
\(540\) −9.08153e17 + 4.52749e17i −0.0678270 + 0.0338143i
\(541\) 1.02621e19 0.756583 0.378291 0.925687i \(-0.376512\pi\)
0.378291 + 0.925687i \(0.376512\pi\)
\(542\) −1.31834e19 8.15845e18i −0.959472 0.593762i
\(543\) 2.10670e18i 0.151357i
\(544\) −5.96787e18 1.53503e19i −0.423280 1.08874i
\(545\) −8.73649e18 −0.611733
\(546\) −1.15015e18 + 1.85856e18i −0.0795074 + 0.128477i
\(547\) 2.17511e19i 1.48447i 0.670141 + 0.742233i \(0.266233\pi\)
−0.670141 + 0.742233i \(0.733767\pi\)
\(548\) −8.17253e17 1.63930e18i −0.0550672 0.110457i
\(549\) −1.14310e18 −0.0760462
\(550\) 1.91053e19 + 1.18232e19i 1.25492 + 0.776597i
\(551\) 9.16433e18i 0.594346i
\(552\) −5.10142e18 4.69024e17i −0.326676 0.0300345i
\(553\) −9.92746e18 −0.627715
\(554\) −6.68205e18 + 1.07976e19i −0.417197 + 0.674157i
\(555\) 4.49675e18i 0.277235i
\(556\) −2.00733e19 + 1.00073e19i −1.22207 + 0.609247i
\(557\) 5.10549e17 0.0306938 0.0153469 0.999882i \(-0.495115\pi\)
0.0153469 + 0.999882i \(0.495115\pi\)
\(558\) 1.01457e18 + 6.27862e17i 0.0602344 + 0.0372756i
\(559\) 1.20876e19i 0.708690i
\(560\) 2.43171e18 + 1.83269e18i 0.140798 + 0.106114i
\(561\) −2.06005e19 −1.17798
\(562\) 1.26154e18 2.03854e18i 0.0712435 0.115124i
\(563\) 2.78917e19i 1.55566i −0.628472 0.777832i \(-0.716319\pi\)
0.628472 0.777832i \(-0.283681\pi\)
\(564\) 2.26023e18 + 4.53372e18i 0.124509 + 0.249747i
\(565\) 4.47279e18 0.243355
\(566\) 4.72601e18 + 2.92466e18i 0.253969 + 0.157167i
\(567\) 9.37179e17i 0.0497440i
\(568\) 3.46164e18 3.76512e19i 0.181486 1.97397i
\(569\) 2.07494e19 1.07453 0.537266 0.843413i \(-0.319457\pi\)
0.537266 + 0.843413i \(0.319457\pi\)
\(570\) 9.86386e17 1.59392e18i 0.0504572 0.0815347i
\(571\) 1.24535e19i 0.629274i −0.949212 0.314637i \(-0.898117\pi\)
0.949212 0.314637i \(-0.101883\pi\)
\(572\) 1.83058e19 9.12615e18i 0.913728 0.455528i
\(573\) 9.77981e18 0.482223
\(574\) −8.10754e18 5.01729e18i −0.394917 0.244392i
\(575\) 9.97685e18i 0.480085i
\(576\) −6.89436e18 1.27854e18i −0.327745 0.0607795i
\(577\) −9.37091e18 −0.440099 −0.220050 0.975489i \(-0.570622\pi\)
−0.220050 + 0.975489i \(0.570622\pi\)
\(578\) 4.13426e18 6.68063e18i 0.191824 0.309972i
\(579\) 5.29361e17i 0.0242662i
\(580\) −5.46758e18 1.09672e19i −0.247628 0.496707i
\(581\) −7.03556e18 −0.314822
\(582\) 1.90171e19 + 1.17686e19i 0.840780 + 0.520311i
\(583\) 5.00833e19i 2.18783i
\(584\) 3.80286e19 + 3.49634e18i 1.64142 + 0.150912i
\(585\) 1.79914e18 0.0767316
\(586\) 2.04638e19 3.30679e19i 0.862389 1.39355i
\(587\) 2.05232e19i 0.854631i 0.904103 + 0.427315i \(0.140541\pi\)
−0.904103 + 0.427315i \(0.859459\pi\)
\(588\) 1.00400e19 5.00533e18i 0.413136 0.205964i
\(589\) −2.20395e18 −0.0896179
\(590\) 7.74900e18 + 4.79541e18i 0.311374 + 0.192691i
\(591\) 2.22359e19i 0.882963i
\(592\) −1.87016e19 + 2.48142e19i −0.733881 + 0.973752i
\(593\) −1.53306e19 −0.594535 −0.297268 0.954794i \(-0.596075\pi\)
−0.297268 + 0.954794i \(0.596075\pi\)
\(594\) −4.61537e18 + 7.45806e18i −0.176889 + 0.285838i
\(595\) 5.43725e18i 0.205949i
\(596\) −3.10446e17 6.22714e17i −0.0116215 0.0233112i
\(597\) −7.14347e18 −0.264295
\(598\) 7.72357e18 + 4.77968e18i 0.282429 + 0.174779i
\(599\) 1.55665e19i 0.562605i 0.959619 + 0.281302i \(0.0907664\pi\)
−0.959619 + 0.281302i \(0.909234\pi\)
\(600\) −1.25022e18 + 1.35983e19i −0.0446610 + 0.485763i
\(601\) 6.07039e18 0.214336 0.107168 0.994241i \(-0.465822\pi\)
0.107168 + 0.994241i \(0.465822\pi\)
\(602\) −8.18428e18 + 1.32251e19i −0.285631 + 0.461556i
\(603\) 4.19291e18i 0.144642i
\(604\) −6.07621e18 + 3.02922e18i −0.207193 + 0.103293i
\(605\) −2.39608e19 −0.807632
\(606\) 1.51586e19 + 9.38076e18i 0.505067 + 0.312557i
\(607\) 3.31096e19i 1.09052i 0.838267 + 0.545260i \(0.183569\pi\)
−0.838267 + 0.545260i \(0.816431\pi\)
\(608\) 1.20721e19 4.69337e18i 0.393059 0.152813i
\(609\) 1.13178e19 0.364283
\(610\) 1.48583e18 2.40097e18i 0.0472780 0.0763974i
\(611\) 8.98175e18i 0.282535i
\(612\) −5.58633e18 1.12054e19i −0.173727 0.348472i
\(613\) −2.86054e18 −0.0879479 −0.0439739 0.999033i \(-0.514002\pi\)
−0.0439739 + 0.999033i \(0.514002\pi\)
\(614\) −6.60552e18 4.08778e18i −0.200784 0.124253i
\(615\) 7.84836e18i 0.235859i
\(616\) 2.62077e19 + 2.40953e18i 0.778689 + 0.0715926i
\(617\) 1.58813e19 0.466541 0.233271 0.972412i \(-0.425057\pi\)
0.233271 + 0.972412i \(0.425057\pi\)
\(618\) 1.71835e19 2.77671e19i 0.499104 0.806512i
\(619\) 2.38745e19i 0.685646i −0.939400 0.342823i \(-0.888617\pi\)
0.939400 0.342823i \(-0.111383\pi\)
\(620\) −2.63753e18 + 1.31491e18i −0.0748955 + 0.0373383i
\(621\) −3.89462e18 −0.109351
\(622\) −4.35488e19 2.69499e19i −1.20905 0.748210i
\(623\) 1.69751e19i 0.466010i
\(624\) 9.92812e18 + 7.48246e18i 0.269510 + 0.203120i
\(625\) 2.08167e19 0.558795
\(626\) −1.97300e19 + 3.18821e19i −0.523729 + 0.846304i
\(627\) 1.62011e19i 0.425276i
\(628\) −1.08450e19 2.17535e19i −0.281521 0.564692i
\(629\) −5.54840e19 −1.42434
\(630\) 1.96846e18 + 1.21817e18i 0.0499738 + 0.0309259i
\(631\) 5.06382e19i 1.27137i −0.771948 0.635686i \(-0.780717\pi\)
0.771948 0.635686i \(-0.219283\pi\)
\(632\) −5.16980e18 + 5.62303e19i −0.128367 + 1.39621i
\(633\) −3.58101e19 −0.879386
\(634\) 1.11506e19 1.80185e19i 0.270816 0.437617i
\(635\) 9.01027e18i 0.216432i
\(636\) −2.72422e19 + 1.35813e19i −0.647206 + 0.322657i
\(637\) −1.98903e19 −0.467375
\(638\) −9.00665e19 5.57370e19i −2.09324 1.29539i
\(639\) 2.87444e19i 0.660765i
\(640\) 1.16469e19 1.28191e19i 0.264820 0.291472i
\(641\) 2.72200e19 0.612183 0.306092 0.952002i \(-0.400979\pi\)
0.306092 + 0.952002i \(0.400979\pi\)
\(642\) 7.14426e18 1.15445e19i 0.158932 0.256822i
\(643\) 4.50961e18i 0.0992343i −0.998768 0.0496172i \(-0.984200\pi\)
0.998768 0.0496172i \(-0.0158001\pi\)
\(644\) 5.21420e18 + 1.04590e19i 0.113498 + 0.227661i
\(645\) 1.28023e19 0.275659
\(646\) 1.96669e19 + 1.21707e19i 0.418898 + 0.259232i
\(647\) 2.95245e19i 0.622089i 0.950395 + 0.311045i \(0.100679\pi\)
−0.950395 + 0.311045i \(0.899321\pi\)
\(648\) −5.30829e18 4.88043e17i −0.110644 0.0101726i
\(649\) 7.87631e19 1.62409
\(650\) 1.27406e19 2.05878e19i 0.259895 0.419968i
\(651\) 2.72183e18i 0.0549281i
\(652\) −4.38343e19 + 2.18531e19i −0.875147 + 0.436294i
\(653\) 1.20764e19 0.238531 0.119266 0.992862i \(-0.461946\pi\)
0.119266 + 0.992862i \(0.461946\pi\)
\(654\) −3.90260e19 2.41509e19i −0.762622 0.471943i
\(655\) 2.74618e19i 0.530934i
\(656\) −3.26406e19 + 4.33092e19i −0.624354 + 0.828426i
\(657\) 2.90325e19 0.549448
\(658\) 6.08138e18 9.82702e18i 0.113873 0.184010i
\(659\) 4.66830e19i 0.864890i 0.901660 + 0.432445i \(0.142349\pi\)
−0.901660 + 0.432445i \(0.857651\pi\)
\(660\) −9.66580e18 1.93883e19i −0.177186 0.355412i
\(661\) 6.58636e19 1.19464 0.597318 0.802005i \(-0.296233\pi\)
0.597318 + 0.802005i \(0.296233\pi\)
\(662\) 7.69308e19 + 4.76081e19i 1.38068 + 0.854427i
\(663\) 2.21991e19i 0.394221i
\(664\) −3.66382e18 + 3.98502e19i −0.0643810 + 0.700251i
\(665\) −4.27606e18 −0.0743520
\(666\) −1.24307e19 + 2.00870e19i −0.213883 + 0.345617i
\(667\) 4.70330e19i 0.800796i
\(668\) −2.65372e19 + 1.32298e19i −0.447115 + 0.222904i
\(669\) 3.89915e19 0.650110
\(670\) 8.80683e18 + 5.45004e18i 0.145310 + 0.0899241i
\(671\) 2.44042e19i 0.398480i
\(672\) 5.79621e18 + 1.49088e19i 0.0936611 + 0.240911i
\(673\) −8.37485e19 −1.33928 −0.669640 0.742686i \(-0.733552\pi\)
−0.669640 + 0.742686i \(0.733552\pi\)
\(674\) 6.94325e18 1.12197e19i 0.109886 0.177567i
\(675\) 1.03814e19i 0.162604i
\(676\) 1.89479e19 + 3.80069e19i 0.293720 + 0.589163i
\(677\) 7.84417e19 1.20344 0.601722 0.798705i \(-0.294481\pi\)
0.601722 + 0.798705i \(0.294481\pi\)
\(678\) 1.99800e19 + 1.23645e19i 0.303380 + 0.187745i
\(679\) 5.10177e19i 0.766713i
\(680\) 3.07972e19 + 2.83149e18i 0.458088 + 0.0421165i
\(681\) −3.16237e19 −0.465567
\(682\) −1.34043e19 + 2.16603e19i −0.195323 + 0.315627i
\(683\) 6.47022e18i 0.0933198i −0.998911 0.0466599i \(-0.985142\pi\)
0.998911 0.0466599i \(-0.0148577\pi\)
\(684\) 8.81238e18 4.39331e18i 0.125806 0.0627190i
\(685\) 3.43966e18 0.0486051
\(686\) −4.89796e19 3.03107e19i −0.685087 0.423962i
\(687\) 5.83733e19i 0.808196i
\(688\) 7.06466e19 + 5.32438e19i 0.968216 + 0.729709i
\(689\) 5.39695e19 0.732174
\(690\) 5.06231e18 8.18029e18i 0.0679838 0.109856i
\(691\) 4.17252e19i 0.554692i 0.960770 + 0.277346i \(0.0894548\pi\)
−0.960770 + 0.277346i \(0.910545\pi\)
\(692\) −3.18143e19 6.38151e19i −0.418677 0.839810i
\(693\) 2.00080e19 0.260658
\(694\) 2.70385e19 + 1.67326e19i 0.348711 + 0.215797i
\(695\) 4.21188e19i 0.537752i
\(696\) 5.89381e18 6.41051e19i 0.0744958 0.810266i
\(697\) −9.68386e19 −1.21177
\(698\) 3.45882e19 5.58918e19i 0.428490 0.692405i
\(699\) 3.14613e18i 0.0385866i
\(700\) 2.78793e19 1.38989e19i 0.338528 0.168769i
\(701\) −2.45302e19 −0.294900 −0.147450 0.989069i \(-0.547107\pi\)
−0.147450 + 0.989069i \(0.547107\pi\)
\(702\) 8.03678e18 + 4.97350e18i 0.0956582 + 0.0591974i
\(703\) 4.36348e19i 0.514216i
\(704\) 2.72957e19 1.47189e20i 0.318483 1.71738i
\(705\) −9.51287e18 −0.109897
\(706\) −2.97450e19 + 4.80655e19i −0.340237 + 0.549795i
\(707\) 4.06664e19i 0.460574i
\(708\) 2.13585e19 + 4.28423e19i 0.239518 + 0.480441i
\(709\) −1.36131e20 −1.51158 −0.755792 0.654812i \(-0.772748\pi\)
−0.755792 + 0.654812i \(0.772748\pi\)
\(710\) 6.03749e19 + 3.73626e19i 0.663816 + 0.410798i
\(711\) 4.29284e19i 0.467366i
\(712\) −9.61488e19 8.83991e18i −1.03654 0.0952989i
\(713\) −1.13111e19 −0.120747
\(714\) −1.50306e19 + 2.42882e19i −0.158887 + 0.256749i
\(715\) 3.84102e19i 0.402072i
\(716\) −8.49879e18 + 4.23697e18i −0.0880979 + 0.0439202i
\(717\) 1.66323e19 0.170733
\(718\) 2.85714e19 + 1.76812e19i 0.290443 + 0.179738i
\(719\) 7.37506e19i 0.742443i 0.928544 + 0.371221i \(0.121061\pi\)
−0.928544 + 0.371221i \(0.878939\pi\)
\(720\) 7.92492e18 1.05152e19i 0.0790074 0.104831i
\(721\) −7.44917e19 −0.735464
\(722\) 4.42474e19 7.15002e19i 0.432641 0.699112i
\(723\) 4.17501e19i 0.404286i
\(724\) −1.21964e19 2.44643e19i −0.116966 0.234619i
\(725\) −1.25370e20 −1.19077
\(726\) −1.07033e20 6.62366e19i −1.00684 0.623077i
\(727\) 1.10896e20i 1.03318i −0.856234 0.516589i \(-0.827202\pi\)
0.856234 0.516589i \(-0.172798\pi\)
\(728\) 2.59650e18 2.82413e19i 0.0239590 0.260595i
\(729\) −4.05256e18 −0.0370370
\(730\) −3.77371e19 + 6.09801e19i −0.341592 + 0.551986i
\(731\) 1.57964e20i 1.41624i
\(732\) 1.32744e19 6.61779e18i 0.117879 0.0587672i
\(733\) −8.60133e18 −0.0756550 −0.0378275 0.999284i \(-0.512044\pi\)
−0.0378275 + 0.999284i \(0.512044\pi\)
\(734\) −2.63644e18 1.63154e18i −0.0229692 0.0142143i
\(735\) 2.10665e19i 0.181794i
\(736\) 6.19562e19 2.40872e19i 0.529590 0.205893i
\(737\) 8.95152e19 0.757922
\(738\) −2.16958e19 + 3.50587e19i −0.181962 + 0.294036i
\(739\) 9.08303e19i 0.754605i 0.926090 + 0.377302i \(0.123148\pi\)
−0.926090 + 0.377302i \(0.876852\pi\)
\(740\) −2.60332e19 5.22190e19i −0.214242 0.429741i
\(741\) −1.74582e19 −0.142322
\(742\) 5.90486e19 + 3.65418e19i 0.476850 + 0.295095i
\(743\) 9.43891e19i 0.755093i −0.925991 0.377546i \(-0.876768\pi\)
0.925991 0.377546i \(-0.123232\pi\)
\(744\) −1.54168e19 1.41742e18i −0.122175 0.0112328i
\(745\) 1.30661e18 0.0102577
\(746\) −3.13078e19 + 5.05909e19i −0.243490 + 0.393460i
\(747\) 3.04232e19i 0.234402i
\(748\) 2.39226e20 1.19263e20i 1.82599 0.910325i
\(749\) −3.09709e19 −0.234197
\(750\) −4.76129e19 2.94649e19i −0.356694 0.220737i
\(751\) 1.32469e20i 0.983182i −0.870826 0.491591i \(-0.836415\pi\)
0.870826 0.491591i \(-0.163585\pi\)
\(752\) −5.24944e19 3.95631e19i −0.386001 0.290915i
\(753\) −4.74418e19 −0.345618
\(754\) −6.00620e19 + 9.70554e19i −0.433511 + 0.700519i
\(755\) 1.27494e19i 0.0911719i
\(756\) 5.42565e18 + 1.08831e19i 0.0384414 + 0.0771082i
\(757\) 9.32107e19 0.654327 0.327163 0.944968i \(-0.393907\pi\)
0.327163 + 0.944968i \(0.393907\pi\)
\(758\) 1.81562e20 + 1.12358e20i 1.26281 + 0.781483i
\(759\) 8.31469e19i 0.572998i
\(760\) −2.22679e18 + 2.42201e19i −0.0152049 + 0.165379i
\(761\) 1.19531e20 0.808702 0.404351 0.914604i \(-0.367497\pi\)
0.404351 + 0.914604i \(0.367497\pi\)
\(762\) 2.49078e19 4.02489e19i 0.166974 0.269817i
\(763\) 1.04696e20i 0.695440i
\(764\) −1.13569e20 + 5.66186e19i −0.747494 + 0.372654i
\(765\) 2.35118e19 0.153340
\(766\) −3.59170e19 2.22270e19i −0.232113 0.143641i
\(767\) 8.48749e19i 0.543515i
\(768\) 8.74635e19 2.50666e19i 0.555007 0.159062i
\(769\) −8.80481e19 −0.553651 −0.276825 0.960920i \(-0.589282\pi\)
−0.276825 + 0.960920i \(0.589282\pi\)
\(770\) −2.60068e19 + 4.20249e19i −0.162051 + 0.261862i
\(771\) 4.37405e19i 0.270087i
\(772\) 3.06465e18 + 6.14727e18i 0.0187525 + 0.0376150i
\(773\) −7.84083e19 −0.475451 −0.237725 0.971332i \(-0.576402\pi\)
−0.237725 + 0.971332i \(0.576402\pi\)
\(774\) 5.71882e19 + 3.53905e19i 0.343652 + 0.212667i
\(775\) 3.01506e19i 0.179550i
\(776\) −2.88970e20 2.65679e19i −1.70538 0.156792i
\(777\) 5.38881e19 0.315170
\(778\) 3.07289e19 4.96554e19i 0.178111 0.287813i
\(779\) 7.61576e19i 0.437473i
\(780\) −2.08928e19 + 1.04158e19i −0.118942 + 0.0592969i
\(781\) 6.13668e20 3.46239
\(782\) 1.00934e20 + 6.24624e19i 0.564405 + 0.349278i
\(783\) 4.89403e19i 0.271228i
\(784\) −8.76135e19 + 1.16250e20i −0.481237 + 0.638530i
\(785\) 4.56443e19 0.248484
\(786\) −7.59148e19 + 1.22672e20i −0.409608 + 0.661894i
\(787\) 1.07032e20i 0.572390i −0.958171 0.286195i \(-0.907610\pi\)
0.958171 0.286195i \(-0.0923905\pi\)
\(788\) 1.28731e20 + 2.58217e20i 0.682339 + 1.36868i
\(789\) 5.69870e19 0.299390
\(790\) −9.01671e19 5.57993e19i −0.469525 0.290562i
\(791\) 5.36010e19i 0.276654i
\(792\) 1.04193e19 1.13328e20i 0.0533044 0.579775i
\(793\) −2.62979e19 −0.133355
\(794\) −4.79626e19 + 7.75036e19i −0.241079 + 0.389564i
\(795\) 5.71609e19i 0.284793i
\(796\) 8.29545e19 4.13560e19i 0.409683 0.204243i
\(797\) −1.83071e20 −0.896213 −0.448106 0.893980i \(-0.647901\pi\)
−0.448106 + 0.893980i \(0.647901\pi\)
\(798\) −1.91012e19 1.18206e19i −0.0926916 0.0573615i
\(799\) 1.17376e20i 0.564616i
\(800\) −6.42065e19 1.65149e20i −0.306160 0.787494i
\(801\) −7.34037e19 −0.346969
\(802\) 7.56295e18 1.22211e19i 0.0354381 0.0572651i
\(803\) 6.19819e20i 2.87910i
\(804\) 2.42742e19 + 4.86907e19i 0.111777 + 0.224210i
\(805\) −2.19455e19 −0.100179
\(806\) 2.33411e19 + 1.44445e19i 0.105627 + 0.0653666i
\(807\) 2.43509e20i 1.09245i
\(808\) −2.30339e20 2.11773e19i −1.02444 0.0941872i
\(809\) 2.61524e20 1.15311 0.576557 0.817057i \(-0.304396\pi\)
0.576557 + 0.817057i \(0.304396\pi\)
\(810\) 5.26760e18 8.51202e18i 0.0230260 0.0372081i
\(811\) 8.41939e19i 0.364867i 0.983218 + 0.182434i \(0.0583974\pi\)
−0.983218 + 0.182434i \(0.941603\pi\)
\(812\) −1.31429e20 + 6.55223e19i −0.564675 + 0.281512i
\(813\) 1.52937e20 0.651444
\(814\) −4.28840e20 2.65385e20i −1.81103 1.12074i
\(815\) 9.19754e19i 0.385095i
\(816\) 1.29744e20 + 9.77833e19i 0.538587 + 0.405913i
\(817\) −1.24229e20 −0.511293
\(818\) 9.19553e19 1.48592e20i 0.375235 0.606350i
\(819\) 2.15605e19i 0.0872313i
\(820\) −4.54368e19 9.11401e19i −0.182268 0.365605i
\(821\) −6.50000e19 −0.258530 −0.129265 0.991610i \(-0.541262\pi\)
−0.129265 + 0.991610i \(0.541262\pi\)
\(822\) 1.53650e19 + 9.50851e18i 0.0605940 + 0.0374981i
\(823\) 2.68219e20i 1.04880i 0.851473 + 0.524398i \(0.175710\pi\)
−0.851473 + 0.524398i \(0.824290\pi\)
\(824\) −3.87922e19 + 4.21930e20i −0.150402 + 1.63587i
\(825\) −2.21635e20 −0.852041
\(826\) 5.74672e19 9.28624e19i 0.219058 0.353981i
\(827\) 3.15873e20i 1.19392i −0.802272 0.596958i \(-0.796376\pi\)
0.802272 0.596958i \(-0.203624\pi\)
\(828\) 4.52268e19 2.25473e19i 0.169505 0.0845048i
\(829\) −4.92038e20 −1.82859 −0.914296 0.405047i \(-0.867255\pi\)
−0.914296 + 0.405047i \(0.867255\pi\)
\(830\) −6.39011e19 3.95447e19i −0.235484 0.145728i
\(831\) 1.25260e20i 0.457726i
\(832\) −1.58610e20 2.94138e19i −0.574735 0.106583i
\(833\) −2.59933e20 −0.933999
\(834\) 1.16432e20 1.88145e20i 0.414868 0.670394i
\(835\) 5.56816e19i 0.196746i
\(836\) 9.37935e19 + 1.88137e20i 0.328646 + 0.659220i
\(837\) −1.17698e19 −0.0408968
\(838\) 2.76650e19 + 1.71203e19i 0.0953283 + 0.0589932i
\(839\) 3.72904e20i 1.27428i −0.770750 0.637138i \(-0.780118\pi\)
0.770750 0.637138i \(-0.219882\pi\)
\(840\) −2.99113e19 2.75004e18i −0.101363 0.00931933i
\(841\) 2.93465e20 0.986243
\(842\) 9.35753e19 1.51210e20i 0.311872 0.503960i
\(843\) 2.36485e19i 0.0781646i
\(844\) 4.15849e20 2.07317e20i 1.36314 0.679575i
\(845\) −7.97480e19 −0.259252
\(846\) −4.24940e19 2.62971e19i −0.137005 0.0847844i
\(847\) 2.87141e20i 0.918145i
\(848\) 2.37727e20 3.15429e20i 0.753889 1.00030i
\(849\) −5.48251e19 −0.172435
\(850\) 1.66499e20 2.69048e20i 0.519372 0.839262i
\(851\) 2.23942e20i 0.692832i
\(852\) 1.66411e20 + 3.33798e20i 0.510628 + 1.02425i
\(853\) 9.24649e19 0.281406 0.140703 0.990052i \(-0.455064\pi\)
0.140703 + 0.990052i \(0.455064\pi\)
\(854\) −2.87728e19 1.78058e19i −0.0868513 0.0537473i
\(855\) 1.84906e19i 0.0553589i
\(856\) −1.61284e19 + 1.75423e20i −0.0478932 + 0.520919i
\(857\) 2.60110e20 0.766110 0.383055 0.923726i \(-0.374872\pi\)
0.383055 + 0.923726i \(0.374872\pi\)
\(858\) −1.06180e20 + 1.71578e20i −0.310193 + 0.501247i
\(859\) 4.50661e20i 1.30586i 0.757417 + 0.652931i \(0.226461\pi\)
−0.757417 + 0.652931i \(0.773539\pi\)
\(860\) −1.48669e20 + 7.41171e19i −0.427298 + 0.213024i
\(861\) 9.40531e19 0.268133
\(862\) −7.49171e19 4.63619e19i −0.211851 0.131102i
\(863\) 5.88823e20i 1.65162i 0.563952 + 0.825808i \(0.309280\pi\)
−0.563952 + 0.825808i \(0.690720\pi\)
\(864\) 6.44687e19 2.50640e19i 0.179371 0.0697356i
\(865\) 1.33900e20 0.369545
\(866\) 1.10681e20 1.78851e20i 0.303002 0.489627i
\(867\) 7.74999e19i 0.210459i
\(868\) 1.57576e19 + 3.16076e19i 0.0424475 + 0.0851440i
\(869\) −9.16485e20 −2.44899
\(870\) 1.02795e20 + 6.36137e19i 0.272481 + 0.168623i
\(871\) 9.64612e19i 0.253645i
\(872\) 5.93012e20 + 5.45214e19i 1.54685 + 0.142217i
\(873\) −2.20611e20 −0.570858
\(874\) −4.91229e19 + 7.93786e19i −0.126097 + 0.203762i
\(875\) 1.27733e20i 0.325271i
\(876\) −3.37144e20 + 1.68079e20i −0.851699 + 0.424604i
\(877\) 1.50279e20 0.376618 0.188309 0.982110i \(-0.439699\pi\)
0.188309 + 0.982110i \(0.439699\pi\)
\(878\) 4.32889e20 + 2.67890e20i 1.07625 + 0.666032i
\(879\) 3.83610e20i 0.946168i
\(880\) 2.24491e20 + 1.69190e20i 0.549313 + 0.413997i
\(881\) 5.39574e20 1.30984 0.654922 0.755697i \(-0.272701\pi\)
0.654922 + 0.755697i \(0.272701\pi\)
\(882\) −5.82356e19 + 9.41041e19i −0.140252 + 0.226636i
\(883\) 5.23695e20i 1.25128i 0.780113 + 0.625639i \(0.215162\pi\)
−0.780113 + 0.625639i \(0.784838\pi\)
\(884\) −1.28518e20 2.57790e20i −0.304648 0.611082i
\(885\) −8.98938e19 −0.211411
\(886\) 3.49895e20 + 2.16530e20i 0.816397 + 0.505221i
\(887\) 5.41727e20i 1.25405i −0.778998 0.627026i \(-0.784272\pi\)
0.778998 0.627026i \(-0.215728\pi\)
\(888\) 2.80626e19 3.05228e20i 0.0644522 0.701026i
\(889\) −1.07977e20 −0.246048
\(890\) 9.54118e19 1.54178e20i 0.215711 0.348571i
\(891\) 8.65186e19i 0.194073i
\(892\) −4.52793e20 + 2.25735e20i −1.00773 + 0.502394i
\(893\) 9.23094e19 0.203838
\(894\) 5.83663e18 + 3.61195e18i 0.0127879 + 0.00791370i
\(895\) 1.78326e19i 0.0387662i
\(896\) −1.53621e20 1.39574e20i −0.331356 0.301057i
\(897\) −8.95988e19 −0.191759
\(898\) 4.23978e20 6.85114e20i 0.900344 1.45488i
\(899\) 1.42137e20i 0.299494i
\(900\) −6.01016e19 1.20556e20i −0.125658 0.252052i
\(901\) 7.05292e20 1.46317
\(902\) −7.48473e20 4.63187e20i −1.54074 0.953478i
\(903\) 1.53421e20i 0.313379i
\(904\) −3.03602e20 2.79132e19i −0.615356 0.0565757i
\(905\) 5.13321e19 0.103240
\(906\) 3.52441e19 5.69517e19i 0.0703379 0.113660i
\(907\) 4.02735e20i 0.797570i −0.917045 0.398785i \(-0.869432\pi\)
0.917045 0.398785i \(-0.130568\pi\)
\(908\) 3.67234e20 1.83080e20i 0.721675 0.359783i
\(909\) −1.75850e20 −0.342921
\(910\) 4.52859e19 + 2.80249e19i 0.0876341 + 0.0542318i
\(911\) 4.59442e19i 0.0882271i −0.999027 0.0441135i \(-0.985954\pi\)
0.999027 0.0441135i \(-0.0140463\pi\)
\(912\) −7.69006e19 + 1.02036e20i −0.146543 + 0.194441i
\(913\) −6.49510e20 −1.22826
\(914\) −4.95039e20 + 7.99943e20i −0.929001 + 1.50119i
\(915\) 2.78530e19i 0.0518709i
\(916\) −3.37943e20 6.77867e20i −0.624561 1.25278i
\(917\) 3.29097e20 0.603585
\(918\) 1.05027e20 + 6.49954e19i 0.191163 + 0.118300i
\(919\) 6.77369e20i 1.22354i −0.791037 0.611768i \(-0.790459\pi\)
0.791037 0.611768i \(-0.209541\pi\)
\(920\) −1.14283e19 + 1.24302e20i −0.0204865 + 0.222825i
\(921\) 7.66286e19 0.136324
\(922\) −5.57088e20 + 9.00208e20i −0.983574 + 1.58938i
\(923\) 6.61287e20i 1.15872i
\(924\) −2.32345e20 + 1.15833e20i −0.404045 + 0.201432i
\(925\) −5.96935e20 −1.03023
\(926\) −3.23174e20 1.99994e20i −0.553553 0.342562i
\(927\) 3.22118e20i 0.547591i
\(928\) 3.02683e20 + 7.78550e20i 0.510684 + 1.31356i
\(929\) 7.95494e20 1.33207 0.666035 0.745921i \(-0.267990\pi\)
0.666035 + 0.745921i \(0.267990\pi\)
\(930\) 1.52986e19 2.47213e19i 0.0254256 0.0410857i
\(931\) 2.04421e20i 0.337193i
\(932\) −1.82140e19 3.65349e19i −0.0298191 0.0598131i
\(933\) 5.05196e20 0.820897
\(934\) −2.00971e19 1.24370e19i −0.0324120 0.0200579i
\(935\) 5.01957e20i 0.803498i
\(936\) −1.22121e20 1.12278e19i −0.194026 0.0178388i
\(937\) −7.01109e20 −1.10563 −0.552814 0.833305i \(-0.686446\pi\)
−0.552814 + 0.833305i \(0.686446\pi\)
\(938\) 6.53122e19 1.05539e20i 0.102229 0.165194i
\(939\) 3.69854e20i 0.574608i
\(940\) 1.10469e20 5.50732e19i 0.170352 0.0849269i
\(941\) −5.22508e20 −0.799771 −0.399885 0.916565i \(-0.630950\pi\)
−0.399885 + 0.916565i \(0.630950\pi\)
\(942\) 2.03893e20 + 1.26178e20i 0.309775 + 0.191702i
\(943\) 3.90855e20i 0.589432i
\(944\) −4.96057e20 3.73860e20i −0.742553 0.559635i
\(945\) −2.28355e19 −0.0339303
\(946\) −7.55557e20 + 1.22092e21i −1.11437 + 1.80073i
\(947\) 8.65791e20i 1.26755i 0.773519 + 0.633773i \(0.218494\pi\)
−0.773519 + 0.633773i \(0.781506\pi\)
\(948\) −2.48527e20 4.98511e20i −0.361173 0.724464i
\(949\) 6.67915e20 0.963514
\(950\) 2.11590e20 + 1.30941e20i 0.302991 + 0.187504i
\(951\) 2.09027e20i 0.297125i
\(952\) 3.39320e19 3.69067e20i 0.0478796 0.520771i
\(953\) −9.85667e19 −0.138064 −0.0690319 0.997614i \(-0.521991\pi\)
−0.0690319 + 0.997614i \(0.521991\pi\)
\(954\) 1.58014e20 2.55338e20i 0.219714 0.355040i
\(955\) 2.38297e20i 0.328923i
\(956\) −1.93144e20 + 9.62899e19i −0.264653 + 0.131940i
\(957\) 1.04483e21 1.42123
\(958\) 1.01713e21 + 6.29444e20i 1.37347 + 0.849960i
\(959\) 4.12202e19i 0.0552560i
\(960\) −3.11531e19 + 1.67989e20i −0.0414575 + 0.223554i
\(961\) 7.22761e20 0.954841
\(962\) −2.85978e20 + 4.62117e20i −0.375065 + 0.606075i
\(963\) 1.33925e20i 0.174372i
\(964\) −2.41705e20 4.84828e20i −0.312426 0.626684i
\(965\) −1.28985e19 −0.0165519
\(966\) −9.80309e19 6.06657e19i −0.124889 0.0772864i
\(967\) 1.44990e20i 0.183380i 0.995788 + 0.0916902i \(0.0292269\pi\)
−0.995788 + 0.0916902i \(0.970773\pi\)
\(968\) 1.62640e21 + 1.49531e20i 2.04221 + 0.187760i
\(969\) −2.28150e20 −0.284416
\(970\) 2.86755e20 4.63373e20i 0.354903 0.573494i
\(971\) 4.14638e20i 0.509489i −0.967008 0.254745i \(-0.918009\pi\)
0.967008 0.254745i \(-0.0819914\pi\)
\(972\) 4.70608e19 2.34616e19i 0.0574111 0.0286216i
\(973\) −5.04743e20 −0.611336
\(974\) −8.68317e20 5.37352e20i −1.04416 0.646169i
\(975\) 2.38833e20i 0.285142i
\(976\) −1.15838e20 + 1.53700e20i −0.137310 + 0.182190i
\(977\) 1.07505e21 1.26522 0.632610 0.774470i \(-0.281983\pi\)
0.632610 + 0.774470i \(0.281983\pi\)
\(978\) 2.54254e20 4.10854e20i 0.297096 0.480083i
\(979\) 1.56711e21i 1.81811i
\(980\) −1.21961e20 2.44637e20i −0.140488 0.281799i
\(981\) 4.52728e20 0.517791
\(982\) 6.93310e19 + 4.29050e19i 0.0787313 + 0.0487223i
\(983\) 1.75429e21i 1.97800i 0.147904 + 0.989002i \(0.452747\pi\)
−0.147904 + 0.989002i \(0.547253\pi\)
\(984\) 4.89789e19 5.32728e20i 0.0548332 0.596403i
\(985\) −5.41805e20 −0.602267
\(986\) −7.84910e20 + 1.26835e21i −0.866327 + 1.39991i
\(987\) 1.14000e20i 0.124935i
\(988\) 2.02736e20 1.01072e20i 0.220613 0.109984i
\(989\) −6.37568e20 −0.688894
\(990\) 1.81724e20 + 1.12459e20i 0.194970 + 0.120656i
\(991\) 1.15921e21i 1.23494i 0.786595 + 0.617469i \(0.211842\pi\)
−0.786595 + 0.617469i \(0.788158\pi\)
\(992\) 1.87235e20 7.27930e19i 0.198064 0.0770031i
\(993\) −8.92451e20 −0.937432
\(994\) 4.47745e20 7.23520e20i 0.467010 0.754650i
\(995\) 1.74059e20i 0.180275i
\(996\) −1.76130e20 3.53293e20i −0.181142 0.363346i
\(997\) 6.04030e20 0.616869 0.308434 0.951246i \(-0.400195\pi\)
0.308434 + 0.951246i \(0.400195\pi\)
\(998\) −1.36019e20 8.41742e19i −0.137938 0.0853622i
\(999\) 2.33023e20i 0.234661i
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 12.15.d.a.7.9 14
3.2 odd 2 36.15.d.e.19.6 14
4.3 odd 2 inner 12.15.d.a.7.10 yes 14
12.11 even 2 36.15.d.e.19.5 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.15.d.a.7.9 14 1.1 even 1 trivial
12.15.d.a.7.10 yes 14 4.3 odd 2 inner
36.15.d.e.19.5 14 12.11 even 2
36.15.d.e.19.6 14 3.2 odd 2