Properties

Label 81.9.f.a.71.19
Level 8181
Weight 99
Character 81.71
Analytic conductor 32.99832.998
Analytic rank 00
Dimension 138138
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,9,Mod(8,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.8");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: N N == 81=34 81 = 3^{4}
Weight: k k == 9 9
Character orbit: [χ][\chi] == 81.f (of order 1818, degree 66, not 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: 32.997667415032.9976674150
Analytic rank: 00
Dimension: 138138
Relative dimension: 2323 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 71.19
Character χ\chi == 81.71
Dual form 81.9.f.a.8.19

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(21.58263.80559i)q2+(210.76476.7119i)q4+(129.757+154.639i)q5+(1479.28+538.412i)q7+(601.827+347.465i)q8+(2212.01+3831.31i)q10+(5647.40+6730.30i)q11+(2496.75+14159.8i)q13+(33975.6+5990.81i)q14+(55651.7+46697.3i)q16+(48327.4+27901.8i)q17+(24124.8+41785.3i)q19+(15485.6+42546.2i)q20+(147498.+123766.i)q22+(57310.9+157460.i)q23+(60755.1+344560.i)q25+315106.iq26+353081.q28+(52796.69309.47i)q29+(971027.353425.i)q31+(909043.+1.08336e6i)q32+(1.14921e6+418280.i)q34+(275206.+158890.i)q35+(932654.+1.61540e6i)q37+(679693.+810026.i)q38+(24359.9138152.i)q40+(4.40599e6+776896.i)q41+(3.96290e6+3.32527e6i)q43+(1.70656e6+985285.i)q44+(1.83615e6+3.18030e6i)q46+(1.82983e65.02741e6i)q47+(2.51772e62.11262e6i)q49+(2.62251e6+7.20528e6i)q50+(559998.+3.17591e6i)q521.03085e7iq531.77356e6q55+(1.07735e6+189966.i)q56+(1.10406e6401845.i)q58+(555817.662397.i)q59+(1.53716e75.59480e6i)q61+(1.96123e71.13232e7i)q62+(6.19773e6+1.07348e7i)q64+(1.86568e62.22343e6i)q65+(1.38317e67.84434e6i)q67+(1.23261e7+2.17342e6i)q68+(5.33499e6+4.47659e6i)q70+(1.63960e7+9.46623e6i)q71+(2.49290e7+4.31782e7i)q73+(1.39815e7+3.84139e7i)q74+(8.29006e6+6.95619e6i)q76+(4.73038e6+1.29966e7i)q77+(2.63044e61.49180e7i)q791.46652e7iq80+9.80493e7q82+(8.67787e7+1.53014e7i)q83+(1.05855e7+3.85282e6i)q85+(7.28750e7+8.68490e7i)q86+(5.73730e62.08821e6i)q88+(6.02765e73.48007e7i)q89+(1.13172e7+1.96019e7i)q91+(2.41582e7+2.87906e7i)q92+(2.03602e71.15468e8i)q94+(9.59199e61.69133e6i)q95+(2.85952e7+2.39942e7i)q97+(6.23788e73.60144e7i)q98+O(q100)q+(21.5826 - 3.80559i) q^{2} +(210.764 - 76.7119i) q^{4} +(-129.757 + 154.639i) q^{5} +(1479.28 + 538.412i) q^{7} +(-601.827 + 347.465i) q^{8} +(-2212.01 + 3831.31i) q^{10} +(5647.40 + 6730.30i) q^{11} +(-2496.75 + 14159.8i) q^{13} +(33975.6 + 5990.81i) q^{14} +(-55651.7 + 46697.3i) q^{16} +(48327.4 + 27901.8i) q^{17} +(24124.8 + 41785.3i) q^{19} +(-15485.6 + 42546.2i) q^{20} +(147498. + 123766. i) q^{22} +(57310.9 + 157460. i) q^{23} +(60755.1 + 344560. i) q^{25} +315106. i q^{26} +353081. q^{28} +(52796.6 - 9309.47i) q^{29} +(971027. - 353425. i) q^{31} +(-909043. + 1.08336e6i) q^{32} +(1.14921e6 + 418280. i) q^{34} +(-275206. + 158890. i) q^{35} +(-932654. + 1.61540e6i) q^{37} +(679693. + 810026. i) q^{38} +(24359.9 - 138152. i) q^{40} +(4.40599e6 + 776896. i) q^{41} +(-3.96290e6 + 3.32527e6i) q^{43} +(1.70656e6 + 985285. i) q^{44} +(1.83615e6 + 3.18030e6i) q^{46} +(1.82983e6 - 5.02741e6i) q^{47} +(-2.51772e6 - 2.11262e6i) q^{49} +(2.62251e6 + 7.20528e6i) q^{50} +(559998. + 3.17591e6i) q^{52} -1.03085e7i q^{53} -1.77356e6 q^{55} +(-1.07735e6 + 189966. i) q^{56} +(1.10406e6 - 401845. i) q^{58} +(555817. - 662397. i) q^{59} +(-1.53716e7 - 5.59480e6i) q^{61} +(1.96123e7 - 1.13232e7i) q^{62} +(-6.19773e6 + 1.07348e7i) q^{64} +(-1.86568e6 - 2.22343e6i) q^{65} +(1.38317e6 - 7.84434e6i) q^{67} +(1.23261e7 + 2.17342e6i) q^{68} +(-5.33499e6 + 4.47659e6i) q^{70} +(1.63960e7 + 9.46623e6i) q^{71} +(2.49290e7 + 4.31782e7i) q^{73} +(-1.39815e7 + 3.84139e7i) q^{74} +(8.29006e6 + 6.95619e6i) q^{76} +(4.73038e6 + 1.29966e7i) q^{77} +(-2.63044e6 - 1.49180e7i) q^{79} -1.46652e7i q^{80} +9.80493e7 q^{82} +(-8.67787e7 + 1.53014e7i) q^{83} +(-1.05855e7 + 3.85282e6i) q^{85} +(-7.28750e7 + 8.68490e7i) q^{86} +(-5.73730e6 - 2.08821e6i) q^{88} +(6.02765e7 - 3.48007e7i) q^{89} +(-1.13172e7 + 1.96019e7i) q^{91} +(2.41582e7 + 2.87906e7i) q^{92} +(2.03602e7 - 1.15468e8i) q^{94} +(-9.59199e6 - 1.69133e6i) q^{95} +(-2.85952e7 + 2.39942e7i) q^{97} +(-6.23788e7 - 3.60144e7i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 138q+6q26q4+447q56q7+9q83q1028668q116q13+120975q14774q16+9q173q19137913q20185478q2268376q23+507585q25+1293135102q98+O(q100) 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/81Z)×\left(\mathbb{Z}/81\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(1718)e\left(\frac{17}{18}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 21.5826 3.80559i 1.34891 0.237850i 0.547923 0.836529i 0.315419π-0.315419\pi
0.800989 + 0.598679i 0.204308π0.204308\pi
33 0 0
44 210.764 76.7119i 0.823297 0.299656i
55 −129.757 + 154.639i −0.207612 + 0.247422i −0.859795 0.510639i 0.829409π-0.829409\pi
0.652183 + 0.758061i 0.273853π0.273853\pi
66 0 0
77 1479.28 + 538.412i 0.616108 + 0.224245i 0.631174 0.775641i 0.282573π-0.282573\pi
−0.0150656 + 0.999887i 0.504796π0.504796\pi
88 −601.827 + 347.465i −0.146930 + 0.0848304i
99 0 0
1010 −2212.01 + 3831.31i −0.221201 + 0.383131i
1111 5647.40 + 6730.30i 0.385725 + 0.459689i 0.923612 0.383328i 0.125222π-0.125222\pi
−0.537888 + 0.843017i 0.680778π0.680778\pi
1212 0 0
1313 −2496.75 + 14159.8i −0.0874182 + 0.495773i 0.909390 + 0.415944i 0.136549π0.136549\pi
−0.996809 + 0.0798295i 0.974562π0.974562\pi
1414 33975.6 + 5990.81i 0.884412 + 0.155946i
1515 0 0
1616 −55651.7 + 46697.3i −0.849178 + 0.712545i
1717 48327.4 + 27901.8i 0.578626 + 0.334070i 0.760587 0.649236i 0.224911π-0.224911\pi
−0.181961 + 0.983306i 0.558245π0.558245\pi
1818 0 0
1919 24124.8 + 41785.3i 0.185118 + 0.320634i 0.943616 0.331041i 0.107400π-0.107400\pi
−0.758498 + 0.651675i 0.774067π0.774067\pi
2020 −15485.6 + 42546.2i −0.0967847 + 0.265914i
2121 0 0
2222 147498. + 123766.i 0.629645 + 0.528335i
2323 57310.9 + 157460.i 0.204798 + 0.562678i 0.998987 0.0449922i 0.0143263π-0.0143263\pi
−0.794189 + 0.607671i 0.792104π0.792104\pi
2424 0 0
2525 60755.1 + 344560.i 0.155533 + 0.882072i
2626 315106.i 0.689547i
2727 0 0
2828 353081. 0.574437
2929 52796.6 9309.47i 0.0746473 0.0131623i −0.136200 0.990681i 0.543489π-0.543489\pi
0.210847 + 0.977519i 0.432378π0.432378\pi
3030 0 0
3131 971027. 353425.i 1.05144 0.382693i 0.242234 0.970218i 0.422120π-0.422120\pi
0.809206 + 0.587525i 0.199898π0.199898\pi
3232 −909043. + 1.08336e6i −0.866931 + 1.03317i
3333 0 0
3434 1.14921e6 + 418280.i 0.859974 + 0.313005i
3535 −275206. + 158890.i −0.183394 + 0.105883i
3636 0 0
3737 −932654. + 1.61540e6i −0.497638 + 0.861935i −0.999996 0.00272492i 0.999133π-0.999133\pi
0.502358 + 0.864660i 0.332466π0.332466\pi
3838 679693. + 810026.i 0.325970 + 0.388476i
3939 0 0
4040 24359.9 138152.i 0.00951559 0.0539656i
4141 4.40599e6 + 776896.i 1.55922 + 0.274933i 0.885709 0.464241i 0.153673π-0.153673\pi
0.673515 + 0.739174i 0.264784π0.264784\pi
4242 0 0
4343 −3.96290e6 + 3.32527e6i −1.15915 + 0.972641i −0.999893 0.0145968i 0.995354π-0.995354\pi
−0.159255 + 0.987238i 0.550909π0.550909\pi
4444 1.70656e6 + 985285.i 0.455315 + 0.262876i
4545 0 0
4646 1.83615e6 + 3.18030e6i 0.410087 + 0.710292i
4747 1.82983e6 5.02741e6i 0.374990 1.03028i −0.598416 0.801186i 0.704203π-0.704203\pi
0.973405 0.229090i 0.0735749π-0.0735749\pi
4848 0 0
4949 −2.51772e6 2.11262e6i −0.436741 0.366469i
5050 2.62251e6 + 7.20528e6i 0.419601 + 1.15284i
5151 0 0
5252 559998. + 3.17591e6i 0.0765901 + 0.434364i
5353 1.03085e7i 1.30645i −0.757163 0.653226i 0.773415π-0.773415\pi
0.757163 0.653226i 0.226585π-0.226585\pi
5454 0 0
5555 −1.77356e6 −0.193818
5656 −1.07735e6 + 189966.i −0.109548 + 0.0193162i
5757 0 0
5858 1.10406e6 401845.i 0.0975620 0.0355097i
5959 555817. 662397.i 0.0458695 0.0546651i −0.742622 0.669711i 0.766418π-0.766418\pi
0.788491 + 0.615046i 0.210862π0.210862\pi
6060 0 0
6161 −1.53716e7 5.59480e6i −1.11020 0.404078i −0.279130 0.960253i 0.590046π-0.590046\pi
−0.831065 + 0.556175i 0.812268π0.812268\pi
6262 1.96123e7 1.13232e7i 1.32728 0.766303i
6363 0 0
6464 −6.19773e6 + 1.07348e7i −0.369414 + 0.639843i
6565 −1.86568e6 2.22343e6i −0.104516 0.124558i
6666 0 0
6767 1.38317e6 7.84434e6i 0.0686398 0.389276i −0.931062 0.364861i 0.881117π-0.881117\pi
0.999702 0.0244149i 0.00777228π-0.00777228\pi
6868 1.23261e7 + 2.17342e6i 0.576487 + 0.101650i
6969 0 0
7070 −5.33499e6 + 4.47659e6i −0.222199 + 0.186447i
7171 1.63960e7 + 9.46623e6i 0.645215 + 0.372515i 0.786620 0.617437i 0.211829π-0.211829\pi
−0.141406 + 0.989952i 0.545162π0.545162\pi
7272 0 0
7373 2.49290e7 + 4.31782e7i 0.877835 + 1.52045i 0.853712 + 0.520745i 0.174346π0.174346\pi
0.0241223 + 0.999709i 0.492321π0.492321\pi
7474 −1.39815e7 + 3.84139e7i −0.466259 + 1.28104i
7575 0 0
7676 8.29006e6 + 6.95619e6i 0.248487 + 0.208505i
7777 4.73038e6 + 1.29966e7i 0.134565 + 0.369715i
7878 0 0
7979 −2.63044e6 1.49180e7i −0.0675336 0.383002i −0.999776 0.0211675i 0.993262π-0.993262\pi
0.932242 0.361834i 0.117849π-0.117849\pi
8080 1.46652e7i 0.358038i
8181 0 0
8282 9.80493e7 2.16865
8383 −8.67787e7 + 1.53014e7i −1.82852 + 0.322418i −0.978802 0.204811i 0.934342π-0.934342\pi
−0.849723 + 0.527229i 0.823231π0.823231\pi
8484 0 0
8585 −1.05855e7 + 3.85282e6i −0.202786 + 0.0738080i
8686 −7.28750e7 + 8.68490e7i −1.33225 + 1.58771i
8787 0 0
8888 −5.73730e6 2.08821e6i −0.0956703 0.0348211i
8989 6.02765e7 3.48007e7i 0.960701 0.554661i 0.0643121 0.997930i 0.479515π-0.479515\pi
0.896389 + 0.443269i 0.146181π0.146181\pi
9090 0 0
9191 −1.13172e7 + 1.96019e7i −0.165034 + 0.285847i
9292 2.41582e7 + 2.87906e7i 0.337220 + 0.401883i
9393 0 0
9494 2.03602e7 1.15468e8i 0.260777 1.47894i
9595 −9.59199e6 1.69133e6i −0.117765 0.0207651i
9696 0 0
9797 −2.85952e7 + 2.39942e7i −0.323003 + 0.271032i −0.789842 0.613311i 0.789837π-0.789837\pi
0.466839 + 0.884343i 0.345393π0.345393\pi
9898 −6.23788e7 3.60144e7i −0.676289 0.390456i
9999 0 0
100100 3.92368e7 + 6.79601e7i 0.392368 + 0.679601i
101101 4.94931e7 1.35981e8i 0.475619 1.30675i −0.437558 0.899190i 0.644157π-0.644157\pi
0.913177 0.407563i 0.133621π-0.133621\pi
102102 0 0
103103 −9.02900e7 7.57623e7i −0.802215 0.673138i 0.146521 0.989208i 0.453192π-0.453192\pi
−0.948736 + 0.316069i 0.897637π0.897637\pi
104104 −3.41742e6 9.38928e6i −0.0292122 0.0802599i
105105 0 0
106106 −3.92301e7 2.22485e8i −0.310739 1.76229i
107107 1.92244e8i 1.46662i −0.679894 0.733311i 0.737974π-0.737974\pi
0.679894 0.733311i 0.262026π-0.262026\pi
108108 0 0
109109 −8.87094e7 −0.628440 −0.314220 0.949350i 0.601743π-0.601743\pi
−0.314220 + 0.949350i 0.601743π0.601743\pi
110110 −3.82779e7 + 6.74943e6i −0.261443 + 0.0460995i
111111 0 0
112112 −1.07467e8 + 3.91147e7i −0.682970 + 0.248581i
113113 1.98236e7 2.36248e7i 0.121582 0.144895i −0.701820 0.712354i 0.747629π-0.747629\pi
0.823402 + 0.567459i 0.192073π0.192073\pi
114114 0 0
115115 −3.17860e7 1.15692e7i −0.181738 0.0661470i
116116 1.04135e7 6.01223e6i 0.0575128 0.0332050i
117117 0 0
118118 9.47516e6 1.64115e7i 0.0488718 0.0846485i
119119 5.64669e7 + 6.72946e7i 0.281583 + 0.335577i
120120 0 0
121121 2.38191e7 1.35085e8i 0.111118 0.630181i
122122 −3.53050e8 6.22523e7i −1.59366 0.281006i
123123 0 0
124124 1.77546e8 1.48979e8i 0.750972 0.630140i
125125 −1.29455e8 7.47411e7i −0.530249 0.306139i
126126 0 0
127127 −3.00728e7 5.20876e7i −0.115600 0.200225i 0.802419 0.596761i 0.203546π-0.203546\pi
−0.918020 + 0.396535i 0.870212π0.870212\pi
128128 3.09142e7 8.49361e7i 0.115164 0.316412i
129129 0 0
130130 −4.87276e7 4.08874e7i −0.170609 0.143158i
131131 3.55348e7 + 9.76311e7i 0.120662 + 0.331515i 0.985288 0.170900i 0.0546674π-0.0546674\pi
−0.864627 + 0.502415i 0.832445π0.832445\pi
132132 0 0
133133 1.31894e7 + 7.48011e7i 0.0421522 + 0.239057i
134134 1.74565e8i 0.541424i
135135 0 0
136136 −3.87797e7 −0.113357
137137 1.72397e8 3.03983e7i 0.489383 0.0862913i 0.0764886 0.997070i 0.475629π-0.475629\pi
0.412894 + 0.910779i 0.364518π0.364518\pi
138138 0 0
139139 −3.82714e8 + 1.39297e8i −1.02522 + 0.373148i −0.799257 0.600989i 0.794774π-0.794774\pi
−0.225959 + 0.974137i 0.572551π0.572551\pi
140140 −4.58148e7 + 5.46000e7i −0.119260 + 0.142128i
141141 0 0
142142 3.89892e8 + 1.41909e8i 0.958940 + 0.349026i
143143 −1.09400e8 + 6.31620e7i −0.261621 + 0.151047i
144144 0 0
145145 −5.41114e6 + 9.37238e6i −0.0122410 + 0.0212020i
146146 7.02350e8 + 8.37028e8i 1.54576 + 1.84217i
147147 0 0
148148 −7.26494e7 + 4.12015e8i −0.151421 + 0.858749i
149149 −2.83527e8 4.99934e7i −0.575240 0.101430i −0.121543 0.992586i 0.538784π-0.538784\pi
−0.453697 + 0.891156i 0.649895π0.649895\pi
150150 0 0
151151 5.12960e8 4.30425e8i 0.986680 0.827922i 0.00159590 0.999999i 0.499492π-0.499492\pi
0.985084 + 0.172076i 0.0550476π0.0550476\pi
152152 −2.90379e7 1.67650e7i −0.0543990 0.0314073i
153153 0 0
154154 1.51554e8 + 2.62498e8i 0.269453 + 0.466706i
155155 −7.13446e7 + 1.96018e8i −0.123605 + 0.339601i
156156 0 0
157157 6.50076e8 + 5.45478e8i 1.06995 + 0.897798i 0.995048 0.0993922i 0.0316898π-0.0316898\pi
0.0749061 + 0.997191i 0.476134π0.476134\pi
158158 −1.13543e8 3.11958e8i −0.182194 0.500573i
159159 0 0
160160 −4.95737e7 2.81147e8i −0.0756435 0.428996i
161161 2.63784e8i 0.392596i
162162 0 0
163163 4.59051e8 0.650296 0.325148 0.945663i 0.394586π-0.394586\pi
0.325148 + 0.945663i 0.394586π0.394586\pi
164164 9.88223e8 1.74250e8i 1.36609 0.240879i
165165 0 0
166166 −1.81468e9 + 6.60489e8i −2.38983 + 0.869827i
167167 −1.44585e8 + 1.72310e8i −0.185890 + 0.221536i −0.850939 0.525265i 0.823966π-0.823966\pi
0.665049 + 0.746800i 0.268411π0.268411\pi
168168 0 0
169169 5.72270e8 + 2.08289e8i 0.701543 + 0.255341i
170170 −2.13801e8 + 1.23438e8i −0.255985 + 0.147793i
171171 0 0
172172 −5.80149e8 + 1.00485e9i −0.662866 + 1.14812i
173173 8.39464e8 + 1.00043e9i 0.937169 + 1.11687i 0.992962 + 0.118432i 0.0377866π0.0377866\pi
−0.0557937 + 0.998442i 0.517769π0.517769\pi
174174 0 0
175175 −9.56415e7 + 5.42410e8i −0.101975 + 0.578330i
176176 −6.28574e8 1.10835e8i −0.655098 0.115511i
177177 0 0
178178 1.16849e9 9.80476e8i 1.16397 0.976691i
179179 1.21670e9 + 7.02464e8i 1.18515 + 0.684245i 0.957200 0.289428i 0.0934652π-0.0934652\pi
0.227948 + 0.973673i 0.426799π0.426799\pi
180180 0 0
181181 5.89616e8 + 1.02124e9i 0.549357 + 0.951514i 0.998319 + 0.0579632i 0.0184606π0.0184606\pi
−0.448962 + 0.893551i 0.648206π0.648206\pi
182182 −1.69657e8 + 4.66129e8i −0.154627 + 0.424835i
183183 0 0
184184 −8.92033e7 7.48505e7i −0.0778233 0.0653015i
185185 −1.28785e8 3.53835e8i −0.109946 0.302074i
186186 0 0
187187 8.51361e7 + 4.82831e8i 0.0696222 + 0.394847i
188188 1.19997e9i 0.960591i
189189 0 0
190190 −2.13457e8 −0.163793
191191 1.37346e9 2.42179e8i 1.03201 0.181971i 0.368102 0.929785i 0.380008π-0.380008\pi
0.663908 + 0.747814i 0.268897π0.268897\pi
192192 0 0
193193 −2.42195e9 + 8.81518e8i −1.74557 + 0.635334i −0.999532 0.0305752i 0.990266π-0.990266\pi
−0.746033 + 0.665909i 0.768044π0.768044\pi
194194 −5.25847e8 + 6.26680e8i −0.371238 + 0.442424i
195195 0 0
196196 −6.92709e8 2.52126e8i −0.469382 0.170841i
197197 1.45799e9 8.41768e8i 0.968029 0.558892i 0.0693939 0.997589i 0.477893π-0.477893\pi
0.898635 + 0.438698i 0.144560π0.144560\pi
198198 0 0
199199 3.37619e8 5.84773e8i 0.215285 0.372885i −0.738076 0.674718i 0.764265π-0.764265\pi
0.953361 + 0.301833i 0.0975986π0.0975986\pi
200200 −1.56287e8 1.86255e8i −0.0976791 0.116409i
201201 0 0
202202 5.50700e8 3.12318e9i 0.330758 1.87582i
203203 8.31131e7 + 1.46551e7i 0.0489424 + 0.00862987i
204204 0 0
205205 −6.91848e8 + 5.80529e8i −0.391738 + 0.328707i
206206 −2.23701e9 1.29154e9i −1.24222 0.717198i
207207 0 0
208208 −5.22275e8 9.04608e8i −0.279027 0.483289i
209209 −1.44986e8 + 3.98345e8i −0.0759872 + 0.208773i
210210 0 0
211211 1.43470e9 + 1.20386e9i 0.723823 + 0.607359i 0.928440 0.371483i 0.121151π-0.121151\pi
−0.204617 + 0.978842i 0.565595π0.565595\pi
212212 −7.90787e8 2.17267e9i −0.391486 1.07560i
213213 0 0
214214 −7.31603e8 4.14913e9i −0.348835 1.97834i
215215 1.04429e9i 0.488730i
216216 0 0
217217 1.62670e9 0.733618
218218 −1.91458e9 + 3.37592e8i −0.847710 + 0.149474i
219219 0 0
220220 −3.73802e8 + 1.36053e8i −0.159570 + 0.0580787i
221221 −5.15746e8 + 6.14642e8i −0.216205 + 0.257664i
222222 0 0
223223 −2.38952e8 8.69713e7i −0.0966252 0.0351687i 0.293255 0.956034i 0.405261π-0.405261\pi
−0.389880 + 0.920865i 0.627484π0.627484\pi
224224 −1.92802e9 + 1.11314e9i −0.765806 + 0.442139i
225225 0 0
226226 3.37937e8 5.85325e8i 0.129540 0.224369i
227227 −2.65807e9 3.16776e9i −1.00106 1.19302i −0.981155 0.193221i 0.938107π-0.938107\pi
−0.0199095 0.999802i 0.506338π-0.506338\pi
228228 0 0
229229 8.13979e8 4.61631e9i 0.295986 1.67862i −0.367181 0.930150i 0.619677π-0.619677\pi
0.663167 0.748472i 0.269212π-0.269212\pi
230230 −7.30052e8 1.28728e8i −0.260881 0.0460003i
231231 0 0
232232 −2.85397e7 + 2.39477e7i −0.00985140 + 0.00826631i
233233 1.81802e9 + 1.04964e9i 0.616844 + 0.356135i 0.775639 0.631176i 0.217428π-0.217428\pi
−0.158795 + 0.987312i 0.550761π0.550761\pi
234234 0 0
235235 5.39999e8 + 9.35306e8i 0.177061 + 0.306678i
236236 6.63326e7 1.82247e8i 0.0213835 0.0587507i
237237 0 0
238238 1.47480e9 + 1.23750e9i 0.459647 + 0.385690i
239239 2.15785e9 + 5.92864e9i 0.661347 + 1.81704i 0.570708 + 0.821153i 0.306669π0.306669\pi
0.0906399 + 0.995884i 0.471109π0.471109\pi
240240 0 0
241241 1.06267e9 + 6.02671e9i 0.315015 + 1.78654i 0.572137 + 0.820158i 0.306115π0.306115\pi
−0.257122 + 0.966379i 0.582774π0.582774\pi
242242 3.00613e9i 0.876488i
243243 0 0
244244 −3.66897e9 −1.03511
245245 6.53386e8 1.15210e8i 0.181345 0.0319760i
246246 0 0
247247 −6.51905e8 + 2.37274e8i −0.175144 + 0.0637473i
248248 −4.61588e8 + 5.50099e8i −0.122025 + 0.145423i
249249 0 0
250250 −3.07841e9 1.12045e9i −0.788074 0.286836i
251251 1.88232e9 1.08676e9i 0.474241 0.273803i −0.243773 0.969832i 0.578385π-0.578385\pi
0.718013 + 0.696029i 0.245052π0.245052\pi
252252 0 0
253253 −7.36100e8 + 1.27496e9i −0.179661 + 0.311182i
254254 −8.47272e8 1.00974e9i −0.203558 0.242591i
255255 0 0
256256 8.95004e8 5.07582e9i 0.208384 1.18181i
257257 3.64585e9 + 6.42861e8i 0.835730 + 0.147362i 0.575106 0.818079i 0.304961π-0.304961\pi
0.260624 + 0.965440i 0.416072π0.416072\pi
258258 0 0
259259 −2.24941e9 + 1.88748e9i −0.499884 + 0.419452i
260260 −5.63782e8 3.25500e8i −0.123372 0.0712290i
261261 0 0
262262 1.13848e9 + 1.97190e9i 0.241612 + 0.418485i
263263 −1.37284e9 + 3.77183e9i −0.286943 + 0.788369i 0.709547 + 0.704658i 0.248900π0.248900\pi
−0.996490 + 0.0837112i 0.973323π0.973323\pi
264264 0 0
265265 1.59410e9 + 1.33761e9i 0.323245 + 0.271235i
266266 5.69325e8 + 1.56421e9i 0.113719 + 0.312441i
267267 0 0
268268 −3.10232e8 1.75941e9i −0.0601377 0.341058i
269269 8.40864e8i 0.160589i −0.996771 0.0802946i 0.974414π-0.974414\pi
0.996771 0.0802946i 0.0255861π-0.0255861\pi
270270 0 0
271271 7.85425e9 1.45622 0.728111 0.685459i 0.240398π-0.240398\pi
0.728111 + 0.685459i 0.240398π0.240398\pi
272272 −3.99244e9 + 7.03976e8i −0.729396 + 0.128612i
273273 0 0
274274 3.60510e9 1.31215e9i 0.639609 0.232799i
275275 −1.97588e9 + 2.35476e9i −0.345486 + 0.411734i
276276 0 0
277277 1.01728e9 + 3.70260e8i 0.172792 + 0.0628910i 0.426967 0.904267i 0.359582π-0.359582\pi
−0.254176 + 0.967158i 0.581804π0.581804\pi
278278 −7.72986e9 + 4.46283e9i −1.29417 + 0.747191i
279279 0 0
280280 1.10418e8 1.91249e8i 0.0179642 0.0311148i
281281 −6.63691e9 7.90956e9i −1.06449 1.26861i −0.961759 0.273897i 0.911687π-0.911687\pi
−0.102728 0.994709i 0.532757π-0.532757\pi
282282 0 0
283283 1.22974e9 6.97420e9i 0.191720 1.08730i −0.725293 0.688440i 0.758296π-0.758296\pi
0.917013 0.398858i 0.130593π-0.130593\pi
284284 4.18186e9 + 7.37374e8i 0.642830 + 0.113348i
285285 0 0
286286 −2.12076e9 + 1.77953e9i −0.316977 + 0.265975i
287287 6.09939e9 + 3.52148e9i 0.898998 + 0.519037i
288288 0 0
289289 −1.93085e9 3.34433e9i −0.276795 0.479422i
290290 −8.11190e7 + 2.22873e8i −0.0114691 + 0.0315112i
291291 0 0
292292 8.56641e9 + 7.18807e9i 1.17833 + 0.988738i
293293 −1.02284e9 2.81023e9i −0.138783 0.381304i 0.850757 0.525559i 0.176144π-0.176144\pi
−0.989541 + 0.144255i 0.953922π0.953922\pi
294294 0 0
295295 3.03109e7 + 1.71902e8i 0.00400231 + 0.0226982i
296296 1.29626e9i 0.168859i
297297 0 0
298298 −6.30950e9 −0.800073
299299 −2.37270e9 + 4.18371e8i −0.296864 + 0.0523451i
300300 0 0
301301 −7.65258e9 + 2.78531e9i −0.932271 + 0.339319i
302302 9.43299e9 1.12418e10i 1.13402 1.35148i
303303 0 0
304304 −3.29385e9 1.19886e9i −0.385664 0.140370i
305305 2.85975e9 1.65108e9i 0.330467 0.190795i
306306 0 0
307307 3.33707e9 5.77997e9i 0.375675 0.650687i −0.614753 0.788720i 0.710744π-0.710744\pi
0.990428 + 0.138032i 0.0440777π0.0440777\pi
308308 1.99399e9 + 2.37634e9i 0.221574 + 0.264062i
309309 0 0
310310 −7.93838e8 + 4.50208e9i −0.0859578 + 0.487491i
311311 −3.83851e9 6.76833e8i −0.410319 0.0723502i −0.0353210 0.999376i 0.511245π-0.511245\pi
−0.374998 + 0.927026i 0.622356π0.622356\pi
312312 0 0
313313 −9.12437e9 + 7.65626e9i −0.950661 + 0.797699i −0.979409 0.201887i 0.935293π-0.935293\pi
0.0287476 + 0.999587i 0.490848π0.490848\pi
314314 1.61062e10 + 9.29891e9i 1.65681 + 0.956563i
315315 0 0
316316 −1.69879e9 2.94238e9i −0.170369 0.295088i
317317 2.42078e9 6.65105e9i 0.239728 0.658647i −0.760232 0.649652i 0.774915π-0.774915\pi
0.999960 0.00899508i 0.00286326π-0.00286326\pi
318318 0 0
319319 3.60819e8 + 3.02763e8i 0.0348439 + 0.0292375i
320320 −8.55813e8 2.35133e9i −0.0816167 0.224240i
321321 0 0
322322 1.00386e9 + 5.69315e9i 0.0933787 + 0.529577i
323323 2.69250e9i 0.247369i
324324 0 0
325325 −5.03058e9 −0.450904
326326 9.90752e9 1.74696e9i 0.877192 0.154673i
327327 0 0
328328 −2.92159e9 + 1.06337e9i −0.252420 + 0.0918734i
329329 5.41364e9 6.45173e9i 0.462068 0.550671i
330330 0 0
331331 1.33703e9 + 4.86637e8i 0.111385 + 0.0405409i 0.397112 0.917770i 0.370013π-0.370013\pi
−0.285726 + 0.958311i 0.592235π0.592235\pi
332332 −1.71160e10 + 9.88195e9i −1.40881 + 0.813374i
333333 0 0
334334 −2.46478e9 + 4.26912e9i −0.198058 + 0.343046i
335335 1.03356e9 + 1.23175e9i 0.0820649 + 0.0978012i
336336 0 0
337337 −9.90440e8 + 5.61706e9i −0.0767907 + 0.435502i 0.922037 + 0.387101i 0.126524π0.126524\pi
−0.998828 + 0.0484006i 0.984588π0.984588\pi
338338 1.31437e10 + 2.31760e9i 1.00705 + 0.177571i
339339 0 0
340340 −1.93550e9 + 1.62407e9i −0.144836 + 0.121532i
341341 7.86243e9 + 4.53938e9i 0.581486 + 0.335721i
342342 0 0
343343 −7.12446e9 1.23399e10i −0.514725 0.891530i
344344 1.22957e9 3.37820e9i 0.0878047 0.241242i
345345 0 0
346346 2.19250e10 + 1.83973e10i 1.52981 + 1.28366i
347347 −1.18946e9 3.26801e9i −0.0820412 0.225406i 0.891889 0.452254i 0.149380π-0.149380\pi
−0.973930 + 0.226848i 0.927158π0.927158\pi
348348 0 0
349349 1.12421e9 + 6.37569e9i 0.0757782 + 0.429759i 0.998968 + 0.0454155i 0.0144612π0.0144612\pi
−0.923190 + 0.384344i 0.874428π0.874428\pi
350350 1.20706e10i 0.804370i
351351 0 0
352352 −1.24250e10 −0.809333
353353 −1.33418e10 + 2.35251e9i −0.859240 + 0.151507i −0.585873 0.810403i 0.699248π-0.699248\pi
−0.273366 + 0.961910i 0.588137π0.588137\pi
354354 0 0
355355 −3.59134e9 + 1.30714e9i −0.226122 + 0.0823018i
356356 1.00345e10 1.19587e10i 0.624735 0.744530i
357357 0 0
358358 2.89329e10 + 1.05307e10i 1.76141 + 0.641099i
359359 −1.20904e10 + 6.98039e9i −0.727885 + 0.420244i −0.817648 0.575719i 0.804722π-0.804722\pi
0.0897632 + 0.995963i 0.471389π0.471389\pi
360360 0 0
361361 7.32777e9 1.26921e10i 0.431463 0.747315i
362362 1.66119e10 + 1.97973e10i 0.967351 + 1.15284i
363363 0 0
364364 −8.81555e8 + 4.99955e9i −0.0502162 + 0.284790i
365365 −9.91174e9 1.74771e9i −0.558442 0.0984685i
366366 0 0
367367 3.14341e9 2.63763e9i 0.173275 0.145395i −0.552026 0.833827i 0.686145π-0.686145\pi
0.725301 + 0.688432i 0.241701π0.241701\pi
368368 −1.05424e10 6.08668e9i −0.574843 0.331886i
369369 0 0
370370 −4.12607e9 7.14657e9i −0.220156 0.381321i
371371 5.55024e9 1.52492e10i 0.292965 0.804916i
372372 0 0
373373 −7.37158e9 6.18549e9i −0.380825 0.319550i 0.432201 0.901777i 0.357737π-0.357737\pi
−0.813026 + 0.582227i 0.802181π0.802181\pi
374374 3.67492e9 + 1.00967e10i 0.187828 + 0.516054i
375375 0 0
376376 6.45610e8 + 3.66144e9i 0.0323012 + 0.183189i
377377 7.70832e8i 0.0381588i
378378 0 0
379379 −1.08158e9 −0.0524205 −0.0262102 0.999656i 0.508344π-0.508344\pi
−0.0262102 + 0.999656i 0.508344π0.508344\pi
380380 −2.15139e9 + 3.79349e8i −0.103178 + 0.0181930i
381381 0 0
382382 2.87213e10 1.04537e10i 1.34881 0.490926i
383383 −9.63162e9 + 1.14785e10i −0.447615 + 0.533446i −0.941918 0.335843i 0.890979π-0.890979\pi
0.494303 + 0.869290i 0.335423π0.335423\pi
384384 0 0
385385 −2.62358e9 9.54905e8i −0.119413 0.0434627i
386386 −4.89173e10 + 2.82424e10i −2.20350 + 1.27219i
387387 0 0
388388 −4.18621e9 + 7.25072e9i −0.184711 + 0.319930i
389389 −5.18750e9 6.18222e9i −0.226548 0.269989i 0.640782 0.767723i 0.278610π-0.278610\pi
−0.867330 + 0.497734i 0.834166π0.834166\pi
390390 0 0
391391 −1.62375e9 + 9.20874e9i −0.0694723 + 0.393997i
392392 2.24930e9 + 3.96612e8i 0.0952583 + 0.0167966i
393393 0 0
394394 2.82637e10 2.37160e10i 1.17285 0.984140i
395395 2.64821e9 + 1.52895e9i 0.108784 + 0.0628064i
396396 0 0
397397 −1.52733e10 2.64542e10i −0.614854 1.06496i −0.990410 0.138158i 0.955882π-0.955882\pi
0.375556 0.926800i 0.377452π-0.377452\pi
398398 5.06128e9 1.39057e10i 0.201710 0.554194i
399399 0 0
400400 −1.94711e10 1.63382e10i −0.760591 0.638212i
401401 −6.89815e9 1.89525e10i −0.266781 0.732975i −0.998670 0.0515517i 0.983583π-0.983583\pi
0.731889 0.681424i 0.238639π-0.238639\pi
402402 0 0
403403 2.58001e9 + 1.46319e10i 0.0978139 + 0.554730i
404404 3.24567e10i 1.21837i
405405 0 0
406406 1.84957e9 0.0680716
407407 −1.61392e10 + 2.84578e9i −0.588173 + 0.103711i
408408 0 0
409409 2.42731e10 8.83468e9i 0.867424 0.315717i 0.130301 0.991475i 0.458406π-0.458406\pi
0.737124 + 0.675758i 0.236184π0.236184\pi
410410 −1.27226e10 + 1.51622e10i −0.450237 + 0.536571i
411411 0 0
412412 −2.48418e10 9.04166e9i −0.862171 0.313805i
413413 1.17885e9 6.80609e8i 0.0405189 0.0233936i
414414 0 0
415415 8.89398e9 1.54048e10i 0.299850 0.519355i
416416 −1.30704e10 1.55767e10i −0.436432 0.520119i
417417 0 0
418418 −1.61323e9 + 9.14908e9i −0.0528434 + 0.299690i
419419 1.14285e10 + 2.01516e9i 0.370796 + 0.0653813i 0.355941 0.934508i 0.384160π-0.384160\pi
0.0148546 + 0.999890i 0.495271π0.495271\pi
420420 0 0
421421 −6.33667e9 + 5.31710e9i −0.201713 + 0.169257i −0.738049 0.674748i 0.764252π-0.764252\pi
0.536336 + 0.844005i 0.319808π0.319808\pi
422422 3.55460e10 + 2.05225e10i 1.12083 + 0.647113i
423423 0 0
424424 3.58186e9 + 6.20396e9i 0.110827 + 0.191958i
425425 −6.67771e9 + 1.83469e10i −0.204678 + 0.562349i
426426 0 0
427427 −1.97265e10 1.65525e10i −0.593388 0.497912i
428428 −1.47474e10 4.05182e10i −0.439482 1.20747i
429429 0 0
430430 −3.97416e9 2.25386e10i −0.116244 0.659254i
431431 4.80677e10i 1.39298i −0.717567 0.696490i 0.754744π-0.754744\pi
0.717567 0.696490i 0.245256π-0.245256\pi
432432 0 0
433433 9.18386e9 0.261260 0.130630 0.991431i 0.458300π-0.458300\pi
0.130630 + 0.991431i 0.458300π0.458300\pi
434434 3.51085e10 6.19057e9i 0.989585 0.174491i
435435 0 0
436436 −1.86968e10 + 6.80507e9i −0.517393 + 0.188316i
437437 −5.19692e9 + 6.19345e9i −0.142502 + 0.169827i
438438 0 0
439439 −5.28907e10 1.92506e10i −1.42404 0.518307i −0.488821 0.872384i 0.662573π-0.662573\pi
−0.935216 + 0.354077i 0.884795π0.884795\pi
440440 1.06737e9 6.16249e8i 0.0284778 0.0164417i
441441 0 0
442442 −8.79205e9 + 1.52283e10i −0.230357 + 0.398990i
443443 −2.37382e9 2.82901e9i −0.0616357 0.0734546i 0.734346 0.678776i 0.237489π-0.237489\pi
−0.795981 + 0.605321i 0.793045π0.793045\pi
444444 0 0
445445 −2.43979e9 + 1.38367e10i −0.0622174 + 0.352853i
446446 −5.48817e9 9.67713e8i −0.138704 0.0244572i
447447 0 0
448448 −1.49479e10 + 1.25428e10i −0.371081 + 0.311374i
449449 3.11307e10 + 1.79733e10i 0.765956 + 0.442225i 0.831430 0.555629i 0.187523π-0.187523\pi
−0.0654738 + 0.997854i 0.520856π0.520856\pi
450450 0 0
451451 1.96536e10 + 3.40411e10i 0.475047 + 0.822806i
452452 2.36579e9 6.49997e9i 0.0566791 0.155725i
453453 0 0
454454 −6.94231e10 5.82529e10i −1.63411 1.37118i
455455 −1.56273e9 4.29357e9i −0.0364619 0.100178i
456456 0 0
457457 −8.23273e9 4.66901e10i −0.188747 1.07044i −0.921046 0.389453i 0.872664π-0.872664\pi
0.732300 0.680982i 0.238447π-0.238447\pi
458458 1.02729e11i 2.33471i
459459 0 0
460460 −7.58684e9 −0.169445
461461 −5.56762e10 + 9.81722e9i −1.23272 + 0.217363i −0.751795 0.659397i 0.770812π-0.770812\pi
−0.480930 + 0.876759i 0.659701π0.659701\pi
462462 0 0
463463 3.32703e10 1.21094e10i 0.723990 0.263511i 0.0463714 0.998924i 0.485234π-0.485234\pi
0.677619 + 0.735413i 0.263012π0.263012\pi
464464 −2.50349e9 + 2.98355e9i −0.0540101 + 0.0643667i
465465 0 0
466466 4.32321e10 + 1.57352e10i 0.916775 + 0.333679i
467467 3.69556e10 2.13363e10i 0.776984 0.448592i −0.0583762 0.998295i 0.518592π-0.518592\pi
0.835360 + 0.549703i 0.185259π0.185259\pi
468468 0 0
469469 6.26958e9 1.08592e10i 0.129583 0.224444i
470470 1.52140e10 + 1.81313e10i 0.311782 + 0.371568i
471471 0 0
472472 −1.04346e8 + 5.91776e8i −0.00210236 + 0.0119231i
473473 −4.47601e10 7.89241e9i −0.894224 0.157676i
474474 0 0
475475 −1.29318e10 + 1.08511e10i −0.254030 + 0.213157i
476476 1.70635e10 + 9.85161e9i 0.332384 + 0.191902i
477477 0 0
478478 6.91340e10 + 1.19744e11i 1.32428 + 2.29372i
479479 −1.59069e10 + 4.37038e10i −0.302164 + 0.830189i 0.691959 + 0.721936i 0.256748π0.256748\pi
−0.994123 + 0.108252i 0.965475π0.965475\pi
480480 0 0
481481 −2.05452e10 1.72394e10i −0.383822 0.322065i
482482 4.58704e10 + 1.26028e11i 0.849854 + 2.33495i
483483 0 0
484484 −5.34240e9 3.02983e10i −0.0973543 0.552124i
485485 7.53536e9i 0.136187i
486486 0 0
487487 8.34928e10 1.48434 0.742170 0.670212i 0.233797π-0.233797\pi
0.742170 + 0.670212i 0.233797π0.233797\pi
488488 1.11950e10 1.97399e9i 0.197400 0.0348069i
489489 0 0
490490 1.36633e10 4.97304e9i 0.237013 0.0862657i
491491 −1.56381e10 + 1.86368e10i −0.269066 + 0.320660i −0.883611 0.468221i 0.844895π-0.844895\pi
0.614545 + 0.788882i 0.289339π0.289339\pi
492492 0 0
493493 2.81128e9 + 1.02322e9i 0.0475900 + 0.0173213i
494494 −1.31668e10 + 7.60187e9i −0.221092 + 0.127648i
495495 0 0
496496 −3.75353e10 + 6.50130e10i −0.620173 + 1.07417i
497497 1.91575e10 + 2.28310e10i 0.313987 + 0.374196i
498498 0 0
499499 −9.77907e9 + 5.54599e10i −0.157723 + 0.894493i 0.798531 + 0.601954i 0.205611π0.205611\pi
−0.956254 + 0.292538i 0.905500π0.905500\pi
500500 −3.30181e10 5.82198e9i −0.528289 0.0931516i
501501 0 0
502502 3.64896e10 3.06184e10i 0.574585 0.482134i
503503 6.61060e10 + 3.81663e10i 1.03269 + 0.596223i 0.917754 0.397150i 0.130001π-0.130001\pi
0.114935 + 0.993373i 0.463334π0.463334\pi
504504 0 0
505505 1.46059e10 + 2.52981e10i 0.224575 + 0.388976i
506506 −1.10349e10 + 3.03183e10i −0.168333 + 0.462490i
507507 0 0
508508 −1.03340e10 8.67125e9i −0.155172 0.130205i
509509 2.18554e10 + 6.00473e10i 0.325603 + 0.894586i 0.989210 + 0.146505i 0.0468024π0.0468024\pi
−0.663607 + 0.748081i 0.730975π0.730975\pi
510510 0 0
511511 1.36291e10 + 7.72946e10i 0.199887 + 1.13361i
512512 8.98162e10i 1.30700i
513513 0 0
514514 8.11333e10 1.16238
515515 2.34316e10 4.13162e9i 0.333098 0.0587342i
516516 0 0
517517 4.41698e10 1.60765e10i 0.618249 0.225024i
518518 −4.13650e10 + 4.92969e10i −0.574532 + 0.684701i
519519 0 0
520520 1.89538e9 + 6.89862e8i 0.0259229 + 0.00943516i
521521 −6.91938e10 + 3.99491e10i −0.939110 + 0.542195i −0.889681 0.456582i 0.849073π-0.849073\pi
−0.0494285 + 0.998778i 0.515740π0.515740\pi
522522 0 0
523523 −2.22994e10 + 3.86237e10i −0.298048 + 0.516235i −0.975689 0.219158i 0.929669π-0.929669\pi
0.677641 + 0.735393i 0.263002π0.263002\pi
524524 1.49789e10 + 1.78512e10i 0.198681 + 0.236779i
525525 0 0
526526 −1.52753e10 + 8.66304e10i −0.199547 + 1.13169i
527527 5.67884e10 + 1.00133e10i 0.736236 + 0.129818i
528528 0 0
529529 3.84804e10 3.22889e10i 0.491380 0.412317i
530530 3.94952e10 + 2.28026e10i 0.500542 + 0.288988i
531531 0 0
532532 8.51799e9 + 1.47536e10i 0.106339 + 0.184184i
533533 −2.20013e10 + 6.04482e10i −0.272609 + 0.748987i
534534 0 0
535535 2.97284e10 + 2.49451e10i 0.362874 + 0.304488i
536536 1.89321e9 + 5.20154e9i 0.0229371 + 0.0630192i
537537 0 0
538538 −3.19998e9 1.81480e10i −0.0381961 0.216621i
539539 2.88759e10i 0.342121i
540540 0 0
541541 −1.16720e11 −1.36256 −0.681282 0.732021i 0.738577π-0.738577\pi
−0.681282 + 0.732021i 0.738577π0.738577\pi
542542 1.69515e11 2.98901e10i 1.96432 0.346362i
543543 0 0
544544 −7.41593e10 + 2.69918e10i −0.846779 + 0.308202i
545545 1.15107e10 1.37179e10i 0.130471 0.155490i
546546 0 0
547547 −3.09611e10 1.12689e10i −0.345834 0.125873i 0.163263 0.986583i 0.447798π-0.447798\pi
−0.509097 + 0.860709i 0.670020π0.670020\pi
548548 3.40033e10 1.96318e10i 0.377050 0.217690i
549549 0 0
550550 −3.36834e10 + 5.83413e10i −0.368099 + 0.637566i
551551 1.66271e9 + 1.98154e9i 0.0180389 + 0.0214979i
552552 0 0
553553 4.14087e9 2.34840e10i 0.0442783 0.251115i
554554 2.33646e10 + 4.11982e9i 0.248039 + 0.0437360i
555555 0 0
556556 −6.99767e10 + 5.87175e10i −0.732242 + 0.614424i
557557 −1.80115e10 1.03990e10i −0.187124 0.108036i 0.403511 0.914975i 0.367790π-0.367790\pi
−0.590636 + 0.806938i 0.701123π0.701123\pi
558558 0 0
559559 −3.71907e10 6.44161e10i −0.380879 0.659701i
560560 7.89594e9 2.16939e10i 0.0802882 0.220590i
561561 0 0
562562 −1.73342e11 1.45451e11i −1.73764 1.45805i
563563 −5.32759e10 1.46374e11i −0.530270 1.45690i −0.858750 0.512394i 0.828759π-0.828759\pi
0.328480 0.944511i 0.393464π-0.393464\pi
564564 0 0
565565 1.08106e9 + 6.13098e9i 0.0106085 + 0.0601639i
566566 1.55201e11i 1.51227i
567567 0 0
568568 −1.31567e10 −0.126402
569569 3.54658e10 6.25358e9i 0.338346 0.0596595i −0.00189393 0.999998i 0.500603π-0.500603\pi
0.340240 + 0.940339i 0.389492π0.389492\pi
570570 0 0
571571 8.81956e10 3.21006e10i 0.829664 0.301973i 0.107943 0.994157i 0.465574π-0.465574\pi
0.721721 + 0.692184i 0.243351π0.243351\pi
572572 −1.82123e10 + 2.17045e10i −0.170130 + 0.202753i
573573 0 0
574574 1.45042e11 + 5.27909e10i 1.33612 + 0.486309i
575575 −5.07726e10 + 2.93136e10i −0.464470 + 0.268162i
576576 0 0
577577 6.26865e10 1.08576e11i 0.565549 0.979560i −0.431449 0.902137i 0.641998π-0.641998\pi
0.996998 0.0774229i 0.0246692π-0.0246692\pi
578578 −5.44000e10 6.48313e10i −0.487402 0.580863i
579579 0 0
580580 −4.21503e8 + 2.39046e9i −0.00372467 + 0.0211237i
581581 −1.36608e11 2.40877e10i −1.19887 0.211393i
582582 0 0
583583 6.93796e10 5.82164e10i 0.600562 0.503931i
584584 −3.00059e10 1.73239e10i −0.257961 0.148934i
585585 0 0
586586 −3.27702e10 5.67596e10i −0.277900 0.481336i
587587 5.98853e9 1.64533e10i 0.0504392 0.138580i −0.911915 0.410379i 0.865396π-0.865396\pi
0.962354 + 0.271799i 0.0876185π0.0876185\pi
588588 0 0
589589 3.81938e10 + 3.20484e10i 0.317345 + 0.266284i
590590 1.30838e9 + 3.59473e9i 0.0107975 + 0.0296660i
591591 0 0
592592 −2.35313e10 1.33452e11i −0.191584 1.08653i
593593 8.13815e10i 0.658123i 0.944309 + 0.329061i 0.106732π0.106732\pi
−0.944309 + 0.329061i 0.893268π0.893268\pi
594594 0 0
595595 −1.77333e10 −0.141489
596596 −6.35924e10 + 1.12131e10i −0.503988 + 0.0888666i
597597 0 0
598598 −4.96168e10 + 1.80590e10i −0.387993 + 0.141218i
599599 1.44379e11 1.72064e11i 1.12149 1.33654i 0.186260 0.982500i 0.440363π-0.440363\pi
0.935230 0.354040i 0.115192π-0.115192\pi
600600 0 0
601601 −1.43492e11 5.22268e10i −1.09984 0.400309i −0.272583 0.962132i 0.587878π-0.587878\pi
−0.827257 + 0.561823i 0.810100π0.810100\pi
602602 −1.54563e11 + 8.92368e10i −1.17684 + 0.679451i
603603 0 0
604604 7.50950e10 1.30068e11i 0.564239 0.977291i
605605 1.77987e10 + 2.12116e10i 0.132851 + 0.158326i
606606 0 0
607607 −2.34613e10 + 1.33056e11i −0.172821 + 0.980119i 0.767807 + 0.640681i 0.221348π0.221348\pi
−0.940628 + 0.339438i 0.889763π0.889763\pi
608608 −6.71988e10 1.18490e10i −0.491753 0.0867094i
609609 0 0
610610 5.54374e10 4.65175e10i 0.400391 0.335968i
611611 6.66185e10 + 3.84622e10i 0.478002 + 0.275975i
612612 0 0
613613 −8.05944e10 1.39594e11i −0.570772 0.988606i −0.996487 0.0837489i 0.973311π-0.973311\pi
0.425715 0.904857i 0.360023π-0.360023\pi
614614 5.00264e10 1.37446e11i 0.351986 0.967074i
615615 0 0
616616 −7.36274e9 6.17807e9i −0.0511348 0.0429072i
617617 −6.78498e10 1.86416e11i −0.468175 1.28630i −0.919201 0.393789i 0.871164π-0.871164\pi
0.451026 0.892511i 0.351058π-0.351058\pi
618618 0 0
619619 −5.42660e9 3.07758e10i −0.0369628 0.209626i 0.960733 0.277475i 0.0894976π-0.0894976\pi
−0.997696 + 0.0678486i 0.978386π0.978386\pi
620620 4.67865e10i 0.316631i
621621 0 0
622622 −8.54207e10 −0.570692
623623 1.07903e11 1.90262e10i 0.716276 0.126299i
624624 0 0
625625 −1.00072e11 + 3.64232e10i −0.655832 + 0.238703i
626626 −1.67791e11 + 1.99966e11i −1.09263 + 1.30214i
627627 0 0
628628 1.78857e11 + 6.50987e10i 1.14992 + 0.418537i
629629 −9.01456e10 + 5.20456e10i −0.575893 + 0.332492i
630630 0 0
631631 −6.49274e10 + 1.12458e11i −0.409553 + 0.709367i −0.994840 0.101460i 0.967649π-0.967649\pi
0.585286 + 0.810827i 0.300982π0.300982\pi
632632 6.76654e9 + 8.06405e9i 0.0424129 + 0.0505458i
633633 0 0
634634 2.69356e10 1.52759e11i 0.166713 0.945476i
635635 1.19569e10 + 2.10833e9i 0.0735401 + 0.0129671i
636636 0 0
637637 3.62004e10 3.03757e10i 0.219865 0.184488i
638638 8.93960e9 + 5.16128e9i 0.0539555 + 0.0311512i
639639 0 0
640640 9.12307e9 + 1.58016e10i 0.0543777 + 0.0941850i
641641 −4.87804e10 + 1.34023e11i −0.288944 + 0.793867i 0.707271 + 0.706943i 0.249926π0.249926\pi
−0.996215 + 0.0869244i 0.972296π0.972296\pi
642642 0 0
643643 1.87640e11 + 1.57449e11i 1.09770 + 0.921076i 0.997268 0.0738681i 0.0235344π-0.0235344\pi
0.100428 + 0.994944i 0.467979π0.467979\pi
644644 2.02354e10 + 5.55963e10i 0.117644 + 0.323223i
645645 0 0
646646 1.02466e10 + 5.81112e10i 0.0588367 + 0.333679i
647647 3.75157e9i 0.0214090i 0.999943 + 0.0107045i 0.00340741π0.00340741\pi
−0.999943 + 0.0107045i 0.996593π0.996593\pi
648648 0 0
649649 7.59705e9 0.0428219
650650 −1.08573e11 + 1.91443e10i −0.608230 + 0.107247i
651651 0 0
652652 9.67516e10 3.52147e10i 0.535387 0.194865i
653653 1.12531e11 1.34110e11i 0.618900 0.737577i −0.361981 0.932186i 0.617899π-0.617899\pi
0.980881 + 0.194609i 0.0623438π0.0623438\pi
654654 0 0
655655 −1.97085e10 7.17329e9i −0.107075 0.0389721i
656656 −2.81480e11 + 1.62513e11i −1.51996 + 0.877549i
657657 0 0
658658 9.22878e10 1.59847e11i 0.492312 0.852710i
659659 1.07843e11 + 1.28523e11i 0.571810 + 0.681457i 0.972001 0.234975i 0.0755008π-0.0755008\pi
−0.400191 + 0.916432i 0.631056π0.631056\pi
660660 0 0
661661 −3.24693e10 + 1.84143e11i −0.170086 + 0.964603i 0.773579 + 0.633700i 0.218465π0.218465\pi
−0.943665 + 0.330903i 0.892647π0.892647\pi
662662 3.07084e10 + 5.41472e9i 0.159891 + 0.0281932i
663663 0 0
664664 4.69091e10 3.93614e10i 0.241315 0.202487i
665665 −1.32786e10 7.66639e9i −0.0678992 0.0392016i
666666 0 0
667667 4.49170e9 + 7.77985e9i 0.0226938 + 0.0393068i
668668 −1.72551e10 + 4.74080e10i −0.0866587 + 0.238093i
669669 0 0
670670 2.69945e10 + 2.26511e10i 0.133960 + 0.112406i
671671 −4.91547e10 1.35052e11i −0.242480 0.666207i
672672 0 0
673673 −8.32962e8 4.72396e9i −0.00406037 0.0230275i 0.982710 0.185150i 0.0592771π-0.0592771\pi
−0.986771 + 0.162123i 0.948166π0.948166\pi
674674 1.25000e11i 0.605718i
675675 0 0
676676 1.36592e11 0.654093
677677 −1.91119e11 + 3.36994e10i −0.909807 + 0.160423i −0.608916 0.793235i 0.708395π-0.708395\pi
−0.300891 + 0.953659i 0.597284π0.597284\pi
678678 0 0
679679 −5.52190e10 + 2.00981e10i −0.259782 + 0.0945531i
680680 5.03195e9 5.99684e9i 0.0235343 0.0280470i
681681 0 0
682682 1.86967e11 + 6.80503e10i 0.864224 + 0.314552i
683683 2.62322e11 1.51452e11i 1.20546 0.695972i 0.243695 0.969852i 0.421640π-0.421640\pi
0.961764 + 0.273880i 0.0883071π0.0883071\pi
684684 0 0
685685 −1.76691e10 + 3.06037e10i −0.0802512 + 0.138999i
686686 −2.00725e11 2.39215e11i −0.906369 1.08017i
687687 0 0
688688 6.52610e10 3.70113e11i 0.291273 1.65189i
689689 1.45967e11 + 2.57379e10i 0.647704 + 0.114208i
690690 0 0
691691 −2.26657e11 + 1.90187e11i −0.994160 + 0.834199i −0.986165 0.165769i 0.946989π-0.946989\pi
−0.00799511 + 0.999968i 0.502545π0.502545\pi
692692 2.53674e11 + 1.46459e11i 1.10625 + 0.638691i
693693 0 0
694694 −3.81083e10 6.60056e10i −0.164279 0.284540i
695695 2.81193e10 7.72572e10i 0.120522 0.331131i
696696 0 0
697697 1.91253e11 + 1.60481e11i 0.810360 + 0.679973i
698698 4.85265e10 + 1.33326e11i 0.204436 + 0.561684i
699699 0 0
700700 2.14515e10 + 1.21657e11i 0.0893439 + 0.506695i
701701 2.45235e10i 0.101557i 0.998710 + 0.0507785i 0.0161703π0.0161703\pi
−0.998710 + 0.0507785i 0.983830π0.983830\pi
702702 0 0
703703 −9.00003e10 −0.368487
704704 −1.07249e11 + 1.89110e10i −0.436621 + 0.0769880i
705705 0 0
706706 −2.78997e11 + 1.01547e11i −1.12300 + 0.408739i
707707 1.46428e11 1.74506e11i 0.586066 0.698446i
708708 0 0
709709 −3.53052e11 1.28500e11i −1.39718 0.508533i −0.469843 0.882750i 0.655689π-0.655689\pi
−0.927341 + 0.374217i 0.877912π0.877912\pi
710710 −7.25360e10 + 4.18787e10i −0.285444 + 0.164801i
711711 0 0
712712 −2.41840e10 + 4.18880e10i −0.0941042 + 0.162993i
713713 1.11301e11 + 1.32643e11i 0.430666 + 0.513248i
714714 0 0
715715 4.42813e9 2.51132e10i 0.0169432 0.0960899i
716716 3.10325e11 + 5.47186e10i 1.18077 + 0.208201i
717717 0 0
718718 −2.34377e11 + 1.96666e11i −0.881897 + 0.739999i
719719 1.30207e11 + 7.51752e10i 0.487214 + 0.281293i 0.723418 0.690410i 0.242570π-0.242570\pi
−0.236204 + 0.971703i 0.575903π0.575903\pi
720720 0 0
721721 −9.27725e10 1.60687e11i −0.343303 0.594619i
722722 1.09851e11 3.01814e11i 0.404256 1.11069i
723723 0 0
724724 2.02611e11 + 1.70011e11i 0.737411 + 0.618761i
725725 6.41533e9 + 1.76260e10i 0.0232203 + 0.0637972i
726726 0 0
727727 7.72535e10 + 4.38126e11i 0.276554 + 1.56842i 0.733981 + 0.679170i 0.237660π0.237660\pi
−0.457427 + 0.889247i 0.651229π0.651229\pi
728728 1.57293e10i 0.0559995i
729729 0 0
730730 −2.20572e11 −0.776710
731731 −2.84298e11 + 5.01293e10i −0.995643 + 0.175559i
732732 0 0
733733 2.01572e11 7.33664e10i 0.698257 0.254145i 0.0315904 0.999501i 0.489943π-0.489943\pi
0.666666 + 0.745356i 0.267721π0.267721\pi
734734 5.78051e10 6.88894e10i 0.199151 0.237338i
735735 0 0
736736 −2.22684e11 8.10503e10i −0.758888 0.276212i
737737 6.06061e10 3.49909e10i 0.205422 0.118600i
738738 0 0
739739 5.48728e10 9.50425e10i 0.183984 0.318669i −0.759250 0.650799i 0.774434π-0.774434\pi
0.943234 + 0.332130i 0.107767π0.107767\pi
740740 −5.42867e10 6.46964e10i −0.181037 0.215751i
741741 0 0
742742 6.17565e10 3.50239e11i 0.203736 1.15544i
743743 3.62815e11 + 6.39740e10i 1.19050 + 0.209917i 0.733588 0.679594i 0.237844π-0.237844\pi
0.456912 + 0.889512i 0.348955π0.348955\pi
744744 0 0
745745 4.45206e10 3.73572e10i 0.144523 0.121269i
746746 −1.82637e11 1.05446e11i −0.589704 0.340466i
747747 0 0
748748 5.49825e10 + 9.52325e10i 0.175638 + 0.304214i
749749 1.03507e11 2.84382e11i 0.328883 0.903597i
750750 0 0
751751 4.65384e11 + 3.90504e11i 1.46303 + 1.22762i 0.922329 + 0.386406i 0.126284π0.126284\pi
0.540696 + 0.841218i 0.318161π0.318161\pi
752752 1.32934e11 + 3.65232e11i 0.415684 + 1.14208i
753753 0 0
754754 2.93347e9 + 1.66366e10i 0.00907605 + 0.0514728i
755755 1.35174e11i 0.416013i
756756 0 0
757757 −7.74160e10 −0.235747 −0.117874 0.993029i 0.537608π-0.537608\pi
−0.117874 + 0.993029i 0.537608π0.537608\pi
758758 −2.33432e10 + 4.11604e9i −0.0707106 + 0.0124682i
759759 0 0
760760 6.36040e9 2.31500e9i 0.0190647 0.00693899i
761761 −2.33613e11 + 2.78409e11i −0.696560 + 0.830128i −0.992132 0.125193i 0.960045π-0.960045\pi
0.295573 + 0.955320i 0.404490π0.404490\pi
762762 0 0
763763 −1.31226e11 4.77622e10i −0.387187 0.140925i
764764 2.70899e11 1.56404e11i 0.795122 0.459064i
765765 0 0
766766 −1.64193e11 + 2.84390e11i −0.476913 + 0.826037i
767767 7.99166e9 + 9.52409e9i 0.0230917 + 0.0275196i
768768 0 0
769769 1.08599e11 6.15897e11i 0.310543 1.76117i −0.285651 0.958334i 0.592210π-0.592210\pi
0.596193 0.802841i 0.296679π-0.296679\pi
770770 −6.02576e10 1.06250e10i −0.171415 0.0302251i
771771 0 0
772772 −4.42838e11 + 3.71585e11i −1.24674 + 1.04614i
773773 −1.31183e11 7.57386e10i −0.367418 0.212129i 0.304912 0.952381i 0.401373π-0.401373\pi
−0.672330 + 0.740252i 0.734706π0.734706\pi
774774 0 0
775775 1.80771e11 + 3.13104e11i 0.501096 + 0.867925i
776776 8.87223e9 2.43762e10i 0.0244673 0.0672233i
777777 0 0
778778 −1.35487e11 1.13687e11i −0.369810 0.310307i
779779 7.38307e10 + 2.02848e11i 0.200488 + 0.550835i
780780 0 0
781781 2.88840e10 + 1.63810e11i 0.0776343 + 0.440286i
782782 2.04928e11i 0.547991i
783783 0 0
784784 2.38769e11 0.631996
785785 −1.68704e11 + 2.97471e10i −0.444270 + 0.0783368i
786786 0 0
787787 2.31521e11 8.42667e10i 0.603520 0.219663i −0.0221457 0.999755i 0.507050π-0.507050\pi
0.625665 + 0.780092i 0.284828π0.284828\pi
788788 2.42717e11 2.89259e11i 0.629500 0.750209i
789789 0 0
790790 6.29738e10 + 2.29206e10i 0.161678 + 0.0588461i
791791 4.20444e10 2.42744e10i 0.107400 0.0620071i
792792 0 0
793793 1.17600e11 2.03690e11i 0.297382 0.515081i
794794 −4.30312e11 5.12826e11i −1.08268 1.29029i
795795 0 0
796796 2.62989e10 1.49148e11i 0.0655066 0.371507i
797797 −5.26169e10 9.27778e9i −0.130404 0.0229938i 0.108065 0.994144i 0.465535π-0.465535\pi
−0.238469 + 0.971150i 0.576646π0.576646\pi
798798 0 0
799799 2.28705e11 1.91906e11i 0.561163 0.470871i
800800 −4.28510e11 2.47400e11i −1.04617 0.604004i
801801 0 0
802802 −2.21006e11 3.82793e11i −0.534202 0.925265i
803803 −1.49819e11 + 4.11624e11i −0.360333 + 0.990008i
804804 0 0
805805 −4.07913e10 3.42280e10i −0.0971368 0.0815075i
806806 1.11366e11 + 3.05977e11i 0.263885 + 0.725017i
807807 0 0
808808 1.74624e10 + 9.90344e10i 0.0409694 + 0.232349i
809809 1.30189e11i 0.303935i 0.988385 + 0.151968i 0.0485610π0.0485610\pi
−0.988385 + 0.151968i 0.951439π0.951439\pi
810810 0 0
811811 1.10741e11 0.255990 0.127995 0.991775i 0.459146π-0.459146\pi
0.127995 + 0.991775i 0.459146π0.459146\pi
812812 1.86415e10 3.28700e9i 0.0428802 0.00756093i
813813 0 0
814814 −3.37496e11 + 1.22839e11i −0.768726 + 0.279793i
815815 −5.95653e10 + 7.09871e10i −0.135009 + 0.160897i
816816 0 0
817817 −2.34551e11 8.53697e10i −0.526441 0.191609i
818818 4.90255e11 2.83049e11i 1.09499 0.632190i
819819 0 0
820820 −1.01283e11 + 1.75428e11i −0.224018 + 0.388010i
821821 −1.21666e11 1.44996e11i −0.267792 0.319142i 0.615344 0.788258i 0.289017π-0.289017\pi
−0.883136 + 0.469116i 0.844572π0.844572\pi
822822 0 0
823823 4.72310e10 2.67860e11i 0.102950 0.583860i −0.889069 0.457773i 0.848647π-0.848647\pi
0.992019 0.126087i 0.0402418π-0.0402418\pi
824824 8.06638e10 + 1.42232e10i 0.174972 + 0.0308524i
825825 0 0
826826 2.28525e10 1.91755e10i 0.0490923 0.0411933i
827827 4.83513e11 + 2.79156e11i 1.03368 + 0.596795i 0.918037 0.396496i 0.129774π-0.129774\pi
0.115643 + 0.993291i 0.463107π0.463107\pi
828828 0 0
829829 3.05847e11 + 5.29743e11i 0.647569 + 1.12162i 0.983702 + 0.179808i 0.0575477π0.0575477\pi
−0.336132 + 0.941815i 0.609119π0.609119\pi
830830 1.33331e11 3.66323e11i 0.280942 0.771883i
831831 0 0
832832 −1.36528e11 1.14561e11i −0.284924 0.239079i
833833 −6.27291e10 1.72347e11i −0.130283 0.357951i
834834 0 0
835835 −7.88478e9 4.47168e10i −0.0162197 0.0919867i
836836 9.50790e10i 0.194652i
837837 0 0
838838 2.54326e11 0.515722
839839 9.49572e10 1.67435e10i 0.191637 0.0337908i −0.0770056 0.997031i 0.524536π-0.524536\pi
0.268643 + 0.963240i 0.413425π0.413425\pi
840840 0 0
841841 −4.67377e11 + 1.70111e11i −0.934294 + 0.340055i
842842 −1.16527e11 + 1.38872e11i −0.231835 + 0.276290i
843843 0 0
844844 3.94734e11 + 1.43671e11i 0.777920 + 0.283140i
845845 −1.06466e11 + 6.14681e10i −0.208826 + 0.120565i
846846 0 0
847847 1.07966e11 1.87003e11i 0.209776 0.363342i
848848 4.81381e11 + 5.73688e11i 0.930906 + 1.10941i
849849 0 0
850850 −7.43016e10 + 4.21385e11i −0.142338 + 0.807242i
851851 −3.07814e11 5.42759e10i −0.586908 0.103488i
852852 0 0
853853 −3.15446e10 + 2.64690e10i −0.0595839 + 0.0499968i −0.672093 0.740467i 0.734605π-0.734605\pi
0.612509 + 0.790463i 0.290160π0.290160\pi
854854 −4.88741e11 2.82175e11i −0.918856 0.530502i
855855 0 0
856856 6.67981e10 + 1.15698e11i 0.124414 + 0.215491i
857857 −3.20388e11 + 8.80260e11i −0.593955 + 1.63188i 0.169140 + 0.985592i 0.445901π0.445901\pi
−0.763095 + 0.646286i 0.776321π0.776321\pi
858858 0 0
859859 4.21815e11 + 3.53945e11i 0.774728 + 0.650074i 0.941915 0.335851i 0.109024π-0.109024\pi
−0.167187 + 0.985925i 0.553468π0.553468\pi
860860 −8.01098e10 2.20100e11i −0.146451 0.402370i
861861 0 0
862862 −1.82926e11 1.03743e12i −0.331319 1.87901i
863863 1.57375e11i 0.283722i 0.989887 + 0.141861i 0.0453086π0.0453086\pi
−0.989887 + 0.141861i 0.954691π0.954691\pi
864864 0 0
865865 −2.63632e11 −0.470906
866866 1.98211e11 3.49500e10i 0.352417 0.0621407i
867867 0 0
868868 3.42851e11 1.24788e11i 0.603985 0.219833i
869869 8.55473e10 1.01951e11i 0.150012 0.178778i
870870 0 0
871871 1.07621e11 + 3.91707e10i 0.186992 + 0.0680596i
872872 5.33877e10 3.08234e10i 0.0923370 0.0533108i
873873 0 0
874874 −8.85933e10 + 1.53448e11i −0.151829 + 0.262976i
875875 −1.51259e11 1.80263e11i −0.258041 0.307521i
876876 0 0
877877 −6.44658e10 + 3.65604e11i −0.108976 + 0.618034i 0.880581 + 0.473895i 0.157152π0.157152\pi
−0.989557 + 0.144139i 0.953959π0.953959\pi
878878 −1.21478e12 2.14198e11i −2.04418 0.360444i
879879 0 0
880880 9.87015e10 8.28204e10i 0.164586 0.138104i
881881 −3.48108e11 2.00980e11i −0.577844 0.333618i 0.182432 0.983218i 0.441603π-0.441603\pi
−0.760276 + 0.649600i 0.774936π0.774936\pi
882882 0 0
883883 −3.70632e11 6.41954e11i −0.609677 1.05599i −0.991293 0.131671i 0.957966π-0.957966\pi
0.381616 0.924321i 0.375368π-0.375368\pi
884884 −6.15504e10 + 1.69108e11i −0.100791 + 0.276921i
885885 0 0
886886 −6.19992e10 5.20235e10i −0.100612 0.0844237i
887887 −8.13054e10 2.23385e11i −0.131348 0.360877i 0.856532 0.516094i 0.172614π-0.172614\pi
−0.987880 + 0.155217i 0.950392π0.950392\pi
888888 0 0
889889 −1.64413e10 9.32434e10i −0.0263227 0.149283i
890890 3.07917e11i 0.490765i
891891 0 0
892892 −5.70342e10 −0.0900898
893893 2.54216e11 4.48252e10i 0.399758 0.0704882i
894894 0 0
895895 −2.66504e11 + 9.69996e10i −0.415348 + 0.151174i
896896 9.14613e10 1.08999e11i 0.141908 0.169119i
897897 0 0
898898 7.40281e11 + 2.69440e11i 1.13839 + 0.414340i
899899 4.79767e10 2.76994e10i 0.0734500 0.0424064i
900900 0 0
901901 2.87627e11 4.98185e11i 0.436446 0.755947i
902902 5.53723e11 + 6.59902e11i 0.836501 + 0.996903i
903903 0 0
904904 −3.72157e9 + 2.11061e10i −0.00557253 + 0.0316034i
905905 −2.34431e11 4.13365e10i −0.349478 0.0616225i
906906 0 0
907907 7.52329e11 6.31279e11i 1.11168 0.932807i 0.113522 0.993535i 0.463787π-0.463787\pi
0.998154 + 0.0607281i 0.0193423π0.0193423\pi
908908 −8.03229e11 4.63745e11i −1.18167 0.682238i
909909 0 0
910910 −5.00674e10 8.67192e10i −0.0730112 0.126459i
911911 −1.30412e10 + 3.58304e10i −0.0189341 + 0.0520210i −0.948800 0.315879i 0.897701π-0.897701\pi
0.929866 + 0.367900i 0.119923π0.119923\pi
912912 0 0
913913 −5.93057e11 4.97634e11i −0.853519 0.716188i
914914 −3.55367e11 9.76364e11i −0.509205 1.39903i
915915 0 0
916916 −1.82568e11 1.03539e12i −0.259324 1.47070i
917917 1.63556e11i 0.231307i
918918 0 0
919919 8.74067e11 1.22541 0.612707 0.790310i 0.290081π-0.290081\pi
0.612707 + 0.790310i 0.290081π0.290081\pi
920920 2.31496e10 4.08189e9i 0.0323141 0.00569784i
921921 0 0
922922 −1.16428e12 + 4.23762e11i −1.61114 + 0.586406i
923923 −1.74976e11 + 2.08529e11i −0.241086 + 0.287316i
924924 0 0
925925 −6.13267e11 2.23211e11i −0.837688 0.304894i
926926 6.71976e11 3.87965e11i 0.913923 0.527654i
927927 0 0
928928 −3.79090e10 + 6.56602e10i −0.0511152 + 0.0885341i
929929 −8.86492e11 1.05648e12i −1.19018 1.41840i −0.884675 0.466208i 0.845620π-0.845620\pi
−0.305503 0.952191i 0.598825π-0.598825\pi
930930 0 0
931931 2.75371e10 1.56170e11i 0.0366538 0.207874i
932932 4.63693e11 + 8.17616e10i 0.614564 + 0.108364i
933933 0 0
934934 7.16399e11 6.01130e11i 0.941386 0.789916i
935935 −8.57114e10 4.94855e10i −0.112148 0.0647488i
936936 0 0
937937 −4.16564e11 7.21510e11i −0.540410 0.936018i −0.998880 0.0473080i 0.984936π-0.984936\pi
0.458470 0.888710i 0.348398π-0.348398\pi
938938 9.39879e10 2.58230e11i 0.121412 0.333576i
939939 0 0
940940 1.85562e11 + 1.55705e11i 0.237671 + 0.199430i
941941 −2.80549e11 7.70802e11i −0.357808 0.983070i −0.979788 0.200037i 0.935894π-0.935894\pi
0.621980 0.783033i 0.286328π-0.286328\pi
942942 0 0
943943 1.30181e11 + 7.38295e11i 0.164627 + 0.933647i
944944 6.28187e10i 0.0791045i
945945 0 0
946946 −9.96074e11 −1.24373
947947 9.44642e11 1.66566e11i 1.17454 0.207103i 0.447875 0.894096i 0.352181π-0.352181\pi
0.726664 + 0.686993i 0.241070π0.241070\pi
948948 0 0
949949 −6.73636e11 + 2.45183e11i −0.830539 + 0.302292i
950950 −2.37807e11 + 2.83408e11i −0.291965 + 0.347950i
951951 0 0
952952 −5.73658e10 2.08795e10i −0.0698402 0.0254198i
953953 2.03870e11 1.17705e11i 0.247162 0.142699i −0.371302 0.928512i 0.621088π-0.621088\pi
0.618464 + 0.785813i 0.287755π0.287755\pi
954954 0 0
955955 −1.40767e11 + 2.43815e11i −0.169234 + 0.293121i
956956 9.09595e11 + 1.08401e12i 1.08897 + 1.29779i
957957 0 0
958958 −1.76993e11 + 1.00378e12i −0.210133 + 1.19172i
959959 2.71390e11 + 4.78534e10i 0.320863 + 0.0565768i
960960 0 0
961961 1.64631e11 1.38142e11i 0.193027 0.161969i
962962 −5.09024e11 2.93885e11i −0.594344 0.343145i
963963 0 0
964964 6.86293e11 + 1.18869e12i 0.794697 + 1.37646i
965965 1.77949e11 4.88911e11i 0.205204 0.563794i
966966 0 0
967967 −1.27323e12 1.06837e12i −1.45613 1.22184i −0.927948 0.372709i 0.878429π-0.878429\pi
−0.528183 0.849130i 0.677127π-0.677127\pi
968968 3.26023e10 + 8.95741e10i 0.0371319 + 0.102019i
969969 0 0
970970 −2.86765e10 1.62633e11i −0.0323921 0.183705i
971971 7.56001e11i 0.850443i −0.905089 0.425222i 0.860196π-0.860196\pi
0.905089 0.425222i 0.139804π-0.139804\pi
972972 0 0
973973 −6.41139e11 −0.715321
974974 1.80199e12 3.17740e11i 2.00224 0.353049i
975975 0 0
976976 1.11672e12 4.06452e11i 1.23068 0.447930i
977977 −6.91971e11 + 8.24659e11i −0.759468 + 0.905099i −0.997814 0.0660815i 0.978950π-0.978950\pi
0.238346 + 0.971180i 0.423395π0.423395\pi
978978 0 0
979979 5.74624e11 + 2.09146e11i 0.625537 + 0.227677i
980980 1.28872e11 7.44046e10i 0.139719 0.0806669i
981981 0 0
982982 −2.66587e11 + 4.61743e11i −0.286677 + 0.496540i
983983 5.84236e11 + 6.96265e11i 0.625711 + 0.745694i 0.982041 0.188667i 0.0604165π-0.0604165\pi
−0.356330 + 0.934360i 0.615972π0.615972\pi
984984 0 0
985985 −5.90143e10 + 3.34687e11i −0.0626920 + 0.355544i
986986 6.45686e10 + 1.13852e10i 0.0683146 + 0.0120457i
987987 0 0
988988 −1.19196e11 + 1.00018e11i −0.125094 + 0.104966i
989989 −7.50715e11 4.33426e11i −0.784675 0.453033i
990990 0 0
991991 8.93401e10 + 1.54742e11i 0.0926300 + 0.160440i 0.908617 0.417630i 0.137139π-0.137139\pi
−0.815987 + 0.578070i 0.803806π0.803806\pi
992992 −4.99821e11 + 1.37325e12i −0.516140 + 1.41808i
993993 0 0
994994 5.00353e11 + 4.19846e11i 0.512543 + 0.430075i
995995 4.66200e10 + 1.28087e11i 0.0475642 + 0.130682i
996996 0 0
997997 1.88373e11 + 1.06831e12i 0.190650 + 1.08123i 0.918478 + 0.395471i 0.129419π0.129419\pi
−0.727828 + 0.685759i 0.759470π0.759470\pi
998998 1.23418e12i 1.24411i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 81.9.f.a.71.19 138
3.2 odd 2 27.9.f.a.14.5 yes 138
27.2 odd 18 inner 81.9.f.a.8.19 138
27.25 even 9 27.9.f.a.2.5 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.5 138 27.25 even 9
27.9.f.a.14.5 yes 138 3.2 odd 2
81.9.f.a.8.19 138 27.2 odd 18 inner
81.9.f.a.71.19 138 1.1 even 1 trivial