Properties

Label 162.8.c.l.55.1
Level 162162
Weight 88
Character 162.55
Analytic conductor 50.60650.606
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,8,Mod(55,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.55");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 162=234 162 = 2 \cdot 3^{4}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 162.c (of order 33, degree 22, 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: 50.606374128450.6063741284
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a25]\Z[a_1, \ldots, a_{25}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 2)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 55.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 162.55
Dual form 162.8.c.l.109.1

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+(4.000006.92820i)q2+(32.000055.4256i)q4+(105.000+181.865i)q5+(508.000+879.882i)q7512.000q8+1680.00q10+(546.000+945.700i)q11+(691.0001196.85i)q13+(4064.00+7039.05i)q14+(2048.00+3547.24i)q16+14706.0q1739940.0q19+(6720.0011639.4i)q20+(4368.00+7565.60i)q22+(34356.059506.3i)q23+(17012.529466.5i)q2511056.0q26+65024.0q28+(51285.088828.2i)q29+(113776.197066.i)q31+(16384.0+28377.9i)q32+(58824.0101886.i)q34213360.q35+160526.q37+(159760.+276712.i)q38+(53760.093115.1i)q40+(5421.009389.45i)q41+(315374.546244.i)q43+69888.0q44549696.q46+(236328.+409332.i)q47+(104357.180751.i)q49+(136100.235732.i)q50+(44224.0+76598.2i)q521.49402e6q53229320.q55+(260096.450499.i)q56+(410280.710626.i)q58+(1.32033e62.28688e6i)q59+(413851.+716811.i)q611.82042e6q62+262144.q64+(145110.251338.i)q65+(63002.0+109123.i)q67+(470592.815089.i)q68+(853440.+1.47820e6i)q701.41473e6q71+980282.q73+(642104.1.11216e6i)q74+(1.27808e6+2.21370e6i)q76+(554736.960831.i)q77+(1.78340e63.08894e6i)q79860160.q8086736.0q82+(2.83645e6+4.91287e6i)q83+(1.54413e6+2.67451e6i)q85+(2.52299e64.36995e6i)q86+(279552.484198.i)q881.19512e7q89+1.40411e6q91+(2.19878e6+3.80841e6i)q92+(1.89062e6+3.27466e6i)q94+(4.19370e67.26370e6i)q95+(4.34107e6+7.51896e6i)q971.66970e6q98+O(q100)q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(105.000 + 181.865i) q^{5} +(-508.000 + 879.882i) q^{7} -512.000 q^{8} +1680.00 q^{10} +(-546.000 + 945.700i) q^{11} +(-691.000 - 1196.85i) q^{13} +(4064.00 + 7039.05i) q^{14} +(-2048.00 + 3547.24i) q^{16} +14706.0 q^{17} -39940.0 q^{19} +(6720.00 - 11639.4i) q^{20} +(4368.00 + 7565.60i) q^{22} +(-34356.0 - 59506.3i) q^{23} +(17012.5 - 29466.5i) q^{25} -11056.0 q^{26} +65024.0 q^{28} +(51285.0 - 88828.2i) q^{29} +(-113776. - 197066. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(58824.0 - 101886. i) q^{34} -213360. q^{35} +160526. q^{37} +(-159760. + 276712. i) q^{38} +(-53760.0 - 93115.1i) q^{40} +(-5421.00 - 9389.45i) q^{41} +(315374. - 546244. i) q^{43} +69888.0 q^{44} -549696. q^{46} +(-236328. + 409332. i) q^{47} +(-104357. - 180751. i) q^{49} +(-136100. - 235732. i) q^{50} +(-44224.0 + 76598.2i) q^{52} -1.49402e6 q^{53} -229320. q^{55} +(260096. - 450499. i) q^{56} +(-410280. - 710626. i) q^{58} +(-1.32033e6 - 2.28688e6i) q^{59} +(-413851. + 716811. i) q^{61} -1.82042e6 q^{62} +262144. q^{64} +(145110. - 251338. i) q^{65} +(63002.0 + 109123. i) q^{67} +(-470592. - 815089. i) q^{68} +(-853440. + 1.47820e6i) q^{70} -1.41473e6 q^{71} +980282. q^{73} +(642104. - 1.11216e6i) q^{74} +(1.27808e6 + 2.21370e6i) q^{76} +(-554736. - 960831. i) q^{77} +(1.78340e6 - 3.08894e6i) q^{79} -860160. q^{80} -86736.0 q^{82} +(-2.83645e6 + 4.91287e6i) q^{83} +(1.54413e6 + 2.67451e6i) q^{85} +(-2.52299e6 - 4.36995e6i) q^{86} +(279552. - 484198. i) q^{88} -1.19512e7 q^{89} +1.40411e6 q^{91} +(-2.19878e6 + 3.80841e6i) q^{92} +(1.89062e6 + 3.27466e6i) q^{94} +(-4.19370e6 - 7.26370e6i) q^{95} +(-4.34107e6 + 7.51896e6i) q^{97} -1.66970e6 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+8q264q4+210q51016q71024q8+3360q101092q111382q13+8128q144096q16+29412q1779880q19+13440q20+8736q2268712q23+3339408q98+O(q100) 2 q + 8 q^{2} - 64 q^{4} + 210 q^{5} - 1016 q^{7} - 1024 q^{8} + 3360 q^{10} - 1092 q^{11} - 1382 q^{13} + 8128 q^{14} - 4096 q^{16} + 29412 q^{17} - 79880 q^{19} + 13440 q^{20} + 8736 q^{22} - 68712 q^{23}+ \cdots - 3339408 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/162Z)×\left(\mathbb{Z}/162\mathbb{Z}\right)^\times.

nn 8383
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\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 4.00000 6.92820i 0.353553 0.612372i
33 0 0
44 −32.0000 55.4256i −0.250000 0.433013i
55 105.000 + 181.865i 0.375659 + 0.650661i 0.990425 0.138048i 0.0440829π-0.0440829\pi
−0.614766 + 0.788709i 0.710750π0.710750\pi
66 0 0
77 −508.000 + 879.882i −0.559784 + 0.969575i 0.437730 + 0.899107i 0.355783π0.355783\pi
−0.997514 + 0.0704680i 0.977551π0.977551\pi
88 −512.000 −0.353553
99 0 0
1010 1680.00 0.531263
1111 −546.000 + 945.700i −0.123685 + 0.214229i −0.921218 0.389046i 0.872805π-0.872805\pi
0.797533 + 0.603275i 0.206138π0.206138\pi
1212 0 0
1313 −691.000 1196.85i −0.0872321 0.151090i 0.819108 0.573639i 0.194469π-0.194469\pi
−0.906340 + 0.422549i 0.861136π0.861136\pi
1414 4064.00 + 7039.05i 0.395827 + 0.685593i
1515 0 0
1616 −2048.00 + 3547.24i −0.125000 + 0.216506i
1717 14706.0 0.725978 0.362989 0.931793i 0.381756π-0.381756\pi
0.362989 + 0.931793i 0.381756π0.381756\pi
1818 0 0
1919 −39940.0 −1.33589 −0.667945 0.744211i 0.732826π-0.732826\pi
−0.667945 + 0.744211i 0.732826π0.732826\pi
2020 6720.00 11639.4i 0.187830 0.325331i
2121 0 0
2222 4368.00 + 7565.60i 0.0874587 + 0.151483i
2323 −34356.0 59506.3i −0.588783 1.01980i −0.994392 0.105755i 0.966274π-0.966274\pi
0.405609 0.914047i 0.367059π-0.367059\pi
2424 0 0
2525 17012.5 29466.5i 0.217760 0.377171i
2626 −11056.0 −0.123365
2727 0 0
2828 65024.0 0.559784
2929 51285.0 88828.2i 0.390479 0.676329i −0.602034 0.798470i 0.705643π-0.705643\pi
0.992513 + 0.122141i 0.0389762π0.0389762\pi
3030 0 0
3131 −113776. 197066.i −0.685938 1.18808i −0.973141 0.230209i 0.926059π-0.926059\pi
0.287203 0.957870i 0.407274π-0.407274\pi
3232 16384.0 + 28377.9i 0.0883883 + 0.153093i
3333 0 0
3434 58824.0 101886.i 0.256672 0.444569i
3535 −213360. −0.841153
3636 0 0
3737 160526. 0.521002 0.260501 0.965474i 0.416112π-0.416112\pi
0.260501 + 0.965474i 0.416112π0.416112\pi
3838 −159760. + 276712.i −0.472308 + 0.818062i
3939 0 0
4040 −53760.0 93115.1i −0.132816 0.230043i
4141 −5421.00 9389.45i −0.0122839 0.0212763i 0.859818 0.510600i 0.170577π-0.170577\pi
−0.872102 + 0.489324i 0.837244π0.837244\pi
4242 0 0
4343 315374. 546244.i 0.604904 1.04772i −0.387163 0.922011i 0.626545π-0.626545\pi
0.992067 0.125713i 0.0401218π-0.0401218\pi
4444 69888.0 0.123685
4545 0 0
4646 −549696. −0.832665
4747 −236328. + 409332.i −0.332026 + 0.575087i −0.982909 0.184092i 0.941066π-0.941066\pi
0.650883 + 0.759178i 0.274399π0.274399\pi
4848 0 0
4949 −104357. 180751.i −0.126717 0.219479i
5050 −136100. 235732.i −0.153980 0.266700i
5151 0 0
5252 −44224.0 + 76598.2i −0.0436160 + 0.0755452i
5353 −1.49402e6 −1.37845 −0.689224 0.724548i 0.742048π-0.742048\pi
−0.689224 + 0.724548i 0.742048π0.742048\pi
5454 0 0
5555 −229320. −0.185854
5656 260096. 450499.i 0.197914 0.342796i
5757 0 0
5858 −410280. 710626.i −0.276110 0.478237i
5959 −1.32033e6 2.28688e6i −0.836952 1.44964i −0.892431 0.451183i 0.851002π-0.851002\pi
0.0554795 0.998460i 0.482331π-0.482331\pi
6060 0 0
6161 −413851. + 716811.i −0.233448 + 0.404343i −0.958820 0.284013i 0.908334π-0.908334\pi
0.725373 + 0.688356i 0.241667π0.241667\pi
6262 −1.82042e6 −0.970063
6363 0 0
6464 262144. 0.125000
6565 145110. 251338.i 0.0655391 0.113517i
6666 0 0
6767 63002.0 + 109123.i 0.0255913 + 0.0443255i 0.878537 0.477674i 0.158520π-0.158520\pi
−0.852946 + 0.521999i 0.825186π0.825186\pi
6868 −470592. 815089.i −0.181494 0.314358i
6969 0 0
7070 −853440. + 1.47820e6i −0.297392 + 0.515099i
7171 −1.41473e6 −0.469104 −0.234552 0.972104i 0.575362π-0.575362\pi
−0.234552 + 0.972104i 0.575362π0.575362\pi
7272 0 0
7373 980282. 0.294931 0.147466 0.989067i 0.452888π-0.452888\pi
0.147466 + 0.989067i 0.452888π0.452888\pi
7474 642104. 1.11216e6i 0.184202 0.319047i
7575 0 0
7676 1.27808e6 + 2.21370e6i 0.333972 + 0.578457i
7777 −554736. 960831.i −0.138474 0.239844i
7878 0 0
7979 1.78340e6 3.08894e6i 0.406962 0.704879i −0.587586 0.809162i 0.699921π-0.699921\pi
0.994548 + 0.104283i 0.0332548π0.0332548\pi
8080 −860160. −0.187830
8181 0 0
8282 −86736.0 −0.0173720
8383 −2.83645e6 + 4.91287e6i −0.544504 + 0.943109i 0.454134 + 0.890934i 0.349949π0.349949\pi
−0.998638 + 0.0521754i 0.983385π0.983385\pi
8484 0 0
8585 1.54413e6 + 2.67451e6i 0.272720 + 0.472366i
8686 −2.52299e6 4.36995e6i −0.427732 0.740853i
8787 0 0
8888 279552. 484198.i 0.0437294 0.0757415i
8989 −1.19512e7 −1.79699 −0.898496 0.438982i 0.855339π-0.855339\pi
−0.898496 + 0.438982i 0.855339π0.855339\pi
9090 0 0
9191 1.40411e6 0.195325
9292 −2.19878e6 + 3.80841e6i −0.294391 + 0.509901i
9393 0 0
9494 1.89062e6 + 3.27466e6i 0.234778 + 0.406648i
9595 −4.19370e6 7.26370e6i −0.501839 0.869211i
9696 0 0
9797 −4.34107e6 + 7.51896e6i −0.482943 + 0.836482i −0.999808 0.0195848i 0.993766π-0.993766\pi
0.516865 + 0.856067i 0.327099π0.327099\pi
9898 −1.66970e6 −0.179204
9999 0 0
100100 −2.17760e6 −0.217760
101101 5.03977e6 8.72914e6i 0.486727 0.843037i −0.513156 0.858295i 0.671524π-0.671524\pi
0.999884 + 0.0152586i 0.00485716π0.00485716\pi
102102 0 0
103103 −1.87400e6 3.24586e6i −0.168981 0.292684i 0.769081 0.639152i 0.220714π-0.220714\pi
−0.938062 + 0.346468i 0.887381π0.887381\pi
104104 353792. + 612786.i 0.0308412 + 0.0534185i
105105 0 0
106106 −5.97607e6 + 1.03509e7i −0.487355 + 0.844123i
107107 −1.79856e7 −1.41932 −0.709661 0.704543i 0.751152π-0.751152\pi
−0.709661 + 0.704543i 0.751152π0.751152\pi
108108 0 0
109109 1.22570e7 0.906552 0.453276 0.891370i 0.350255π-0.350255\pi
0.453276 + 0.891370i 0.350255π0.350255\pi
110110 −917280. + 1.58878e6i −0.0657094 + 0.113812i
111111 0 0
112112 −2.08077e6 3.60400e6i −0.139946 0.242394i
113113 −8.29748e6 1.43717e7i −0.540968 0.936984i −0.998849 0.0479706i 0.984725π-0.984725\pi
0.457881 0.889014i 0.348609π-0.348609\pi
114114 0 0
115115 7.21476e6 1.24963e7i 0.442364 0.766196i
116116 −6.56448e6 −0.390479
117117 0 0
118118 −2.11253e7 −1.18363
119119 −7.47065e6 + 1.29395e7i −0.406391 + 0.703890i
120120 0 0
121121 9.14735e6 + 1.58437e7i 0.469404 + 0.813031i
122122 3.31081e6 + 5.73449e6i 0.165072 + 0.285914i
123123 0 0
124124 −7.28166e6 + 1.26122e7i −0.342969 + 0.594040i
125125 2.35515e7 1.07853
126126 0 0
127127 1.16826e6 0.0506087 0.0253043 0.999680i 0.491945π-0.491945\pi
0.0253043 + 0.999680i 0.491945π0.491945\pi
128128 1.04858e6 1.81619e6i 0.0441942 0.0765466i
129129 0 0
130130 −1.16088e6 2.01070e6i −0.0463432 0.0802687i
131131 3.96191e6 + 6.86224e6i 0.153977 + 0.266696i 0.932686 0.360689i 0.117459π-0.117459\pi
−0.778709 + 0.627385i 0.784125π0.784125\pi
132132 0 0
133133 2.02895e7 3.51425e7i 0.747810 1.29524i
134134 1.00803e6 0.0361916
135135 0 0
136136 −7.52947e6 −0.256672
137137 157827. 273364.i 0.00524396 0.00908280i −0.863392 0.504535i 0.831664π-0.831664\pi
0.868635 + 0.495452i 0.164997π0.164997\pi
138138 0 0
139139 −1.96019e7 3.39515e7i −0.619079 1.07228i −0.989654 0.143474i 0.954173π-0.954173\pi
0.370575 0.928803i 0.379161π-0.379161\pi
140140 6.82752e6 + 1.18256e7i 0.210288 + 0.364230i
141141 0 0
142142 −5.65891e6 + 9.80152e6i −0.165853 + 0.287266i
143143 1.50914e6 0.0431573
144144 0 0
145145 2.15397e7 0.586748
146146 3.92113e6 6.79159e6i 0.104274 0.180608i
147147 0 0
148148 −5.13683e6 8.89725e6i −0.130250 0.225600i
149149 1.09430e7 + 1.89539e7i 0.271010 + 0.469403i 0.969121 0.246587i 0.0793090π-0.0793090\pi
−0.698111 + 0.715990i 0.745976π0.745976\pi
150150 0 0
151151 1.47077e7 2.54745e7i 0.347637 0.602125i −0.638192 0.769877i 0.720317π-0.720317\pi
0.985829 + 0.167752i 0.0536508π0.0536508\pi
152152 2.04493e7 0.472308
153153 0 0
154154 −8.87578e6 −0.195832
155155 2.38930e7 4.13838e7i 0.515358 0.892626i
156156 0 0
157157 −3.02775e7 5.24421e7i −0.624412 1.08151i −0.988654 0.150209i 0.952005π-0.952005\pi
0.364243 0.931304i 0.381328π-0.381328\pi
158158 −1.42672e7 2.47115e7i −0.287766 0.498425i
159159 0 0
160160 −3.44064e6 + 5.95936e6i −0.0664078 + 0.115022i
161161 6.98114e7 1.31837
162162 0 0
163163 5.70853e7 1.03245 0.516223 0.856454i 0.327337π-0.327337\pi
0.516223 + 0.856454i 0.327337π0.327337\pi
164164 −346944. + 600925.i −0.00614194 + 0.0106382i
165165 0 0
166166 2.26916e7 + 3.93029e7i 0.385023 + 0.666879i
167167 4.38633e7 + 7.59734e7i 0.728775 + 1.26227i 0.957401 + 0.288760i 0.0932431π0.0932431\pi
−0.228627 + 0.973514i 0.573424π0.573424\pi
168168 0 0
169169 3.04193e7 5.26878e7i 0.484781 0.839666i
170170 2.47061e7 0.385685
171171 0 0
172172 −4.03679e7 −0.604904
173173 −4.28477e6 + 7.42144e6i −0.0629167 + 0.108975i −0.895768 0.444522i 0.853374π-0.853374\pi
0.832851 + 0.553497i 0.186707π0.186707\pi
174174 0 0
175175 1.72847e7 + 2.99380e7i 0.243797 + 0.422269i
176176 −2.23642e6 3.87359e6i −0.0309213 0.0535573i
177177 0 0
178178 −4.78048e7 + 8.28003e7i −0.635333 + 1.10043i
179179 1.88041e7 0.245056 0.122528 0.992465i 0.460900π-0.460900\pi
0.122528 + 0.992465i 0.460900π0.460900\pi
180180 0 0
181181 −5.99625e7 −0.751631 −0.375816 0.926694i 0.622637π-0.622637\pi
−0.375816 + 0.926694i 0.622637π0.622637\pi
182182 5.61645e6 9.72797e6i 0.0690577 0.119611i
183183 0 0
184184 1.75903e7 + 3.04672e7i 0.208166 + 0.360554i
185185 1.68552e7 + 2.91941e7i 0.195719 + 0.338996i
186186 0 0
187187 −8.02948e6 + 1.39075e7i −0.0897928 + 0.155526i
188188 3.02500e7 0.332026
189189 0 0
190190 −6.70992e7 −0.709708
191191 −4.69931e7 + 8.13944e7i −0.487997 + 0.845235i −0.999905 0.0138052i 0.995606π-0.995606\pi
0.511908 + 0.859040i 0.328939π0.328939\pi
192192 0 0
193193 1.75973e7 + 3.04794e7i 0.176196 + 0.305180i 0.940574 0.339588i 0.110288π-0.110288\pi
−0.764379 + 0.644767i 0.776954π0.776954\pi
194194 3.47286e7 + 6.01517e7i 0.341492 + 0.591482i
195195 0 0
196196 −6.67882e6 + 1.15680e7i −0.0633583 + 0.109740i
197197 1.02985e8 0.959718 0.479859 0.877346i 0.340688π-0.340688\pi
0.479859 + 0.877346i 0.340688π0.340688\pi
198198 0 0
199199 8.36376e7 0.752342 0.376171 0.926550i 0.377240π-0.377240\pi
0.376171 + 0.926550i 0.377240π0.377240\pi
200200 −8.71040e6 + 1.50869e7i −0.0769898 + 0.133350i
201201 0 0
202202 −4.03182e7 6.98331e7i −0.344168 0.596117i
203203 5.21056e7 + 9.02495e7i 0.437168 + 0.757196i
204204 0 0
205205 1.13841e6 1.97178e6i 0.00922912 0.0159853i
206206 −2.99839e7 −0.238975
207207 0 0
208208 5.66067e6 0.0436160
209209 2.18072e7 3.77712e7i 0.165230 0.286187i
210210 0 0
211211 4.87005e7 + 8.43518e7i 0.356899 + 0.618167i 0.987441 0.157988i 0.0505008π-0.0505008\pi
−0.630542 + 0.776155i 0.717167π0.717167\pi
212212 4.78086e7 + 8.28069e7i 0.344612 + 0.596885i
213213 0 0
214214 −7.19423e7 + 1.24608e8i −0.501806 + 0.869153i
215215 1.32457e8 0.908951
216216 0 0
217217 2.31193e8 1.53591
218218 4.90281e7 8.49192e7i 0.320514 0.555147i
219219 0 0
220220 7.33824e6 + 1.27102e7i 0.0464636 + 0.0804773i
221221 −1.01618e7 1.76008e7i −0.0633286 0.109688i
222222 0 0
223223 7.32286e6 1.26836e7i 0.0442195 0.0765904i −0.843069 0.537806i 0.819253π-0.819253\pi
0.887288 + 0.461216i 0.152587π0.152587\pi
224224 −3.32923e7 −0.197914
225225 0 0
226226 −1.32760e8 −0.765045
227227 9.22704e7 1.59817e8i 0.523567 0.906844i −0.476057 0.879414i 0.657934π-0.657934\pi
0.999624 0.0274298i 0.00873228π-0.00873228\pi
228228 0 0
229229 4.37730e6 + 7.58171e6i 0.0240870 + 0.0417199i 0.877818 0.478995i 0.158999π-0.158999\pi
−0.853731 + 0.520715i 0.825665π0.825665\pi
230230 −5.77181e7 9.99706e7i −0.312798 0.541783i
231231 0 0
232232 −2.62579e7 + 4.54801e7i −0.138055 + 0.239118i
233233 −1.19556e8 −0.619193 −0.309597 0.950868i 0.600194π-0.600194\pi
−0.309597 + 0.950868i 0.600194π0.600194\pi
234234 0 0
235235 −9.92578e7 −0.498915
236236 −8.45011e7 + 1.46360e8i −0.418476 + 0.724822i
237237 0 0
238238 5.97652e7 + 1.03516e8i 0.287362 + 0.497725i
239239 −1.98105e8 3.43127e8i −0.938646 1.62578i −0.768000 0.640450i 0.778748π-0.778748\pi
−0.170646 0.985332i 0.554585π-0.554585\pi
240240 0 0
241241 1.28303e8 2.22228e8i 0.590443 1.02268i −0.403730 0.914878i 0.632287π-0.632287\pi
0.994173 0.107799i 0.0343801π-0.0343801\pi
242242 1.46358e8 0.663837
243243 0 0
244244 5.29729e7 0.233448
245245 2.19149e7 3.79577e7i 0.0952045 0.164899i
246246 0 0
247247 2.75985e7 + 4.78021e7i 0.116532 + 0.201840i
248248 5.82533e7 + 1.00898e8i 0.242516 + 0.420049i
249249 0 0
250250 9.42060e7 1.63170e8i 0.381319 0.660464i
251251 −7.34775e7 −0.293290 −0.146645 0.989189i 0.546847π-0.546847\pi
−0.146645 + 0.989189i 0.546847π0.546847\pi
252252 0 0
253253 7.50335e7 0.291295
254254 4.67302e6 8.09391e6i 0.0178929 0.0309914i
255255 0 0
256256 −8.38861e6 1.45295e7i −0.0312500 0.0541266i
257257 1.01351e8 + 1.75544e8i 0.372443 + 0.645091i 0.989941 0.141482i 0.0451868π-0.0451868\pi
−0.617498 + 0.786573i 0.711853π0.711853\pi
258258 0 0
259259 −8.15472e7 + 1.41244e8i −0.291649 + 0.505150i
260260 −1.85741e7 −0.0655391
261261 0 0
262262 6.33906e7 0.217756
263263 −7.71270e7 + 1.33588e8i −0.261434 + 0.452816i −0.966623 0.256203i 0.917529π-0.917529\pi
0.705189 + 0.709019i 0.250862π0.250862\pi
264264 0 0
265265 −1.56872e8 2.71710e8i −0.517827 0.896902i
266266 −1.62316e8 2.81140e8i −0.528781 0.915876i
267267 0 0
268268 4.03213e6 6.98385e6i 0.0127957 0.0221627i
269269 −6.24018e8 −1.95463 −0.977315 0.211793i 0.932070π-0.932070\pi
−0.977315 + 0.211793i 0.932070π0.932070\pi
270270 0 0
271271 −3.87983e8 −1.18419 −0.592094 0.805869i 0.701698π-0.701698\pi
−0.592094 + 0.805869i 0.701698π0.701698\pi
272272 −3.01179e7 + 5.21657e7i −0.0907472 + 0.157179i
273273 0 0
274274 −1.26262e6 2.18692e6i −0.00370804 0.00642251i
275275 1.85776e7 + 3.21774e7i 0.0538674 + 0.0933011i
276276 0 0
277277 −2.26976e8 + 3.93134e8i −0.641654 + 1.11138i 0.343409 + 0.939186i 0.388418π0.388418\pi
−0.985063 + 0.172192i 0.944915π0.944915\pi
278278 −3.13630e8 −0.875510
279279 0 0
280280 1.09240e8 0.297392
281281 −1.66885e8 + 2.89053e8i −0.448689 + 0.777152i −0.998301 0.0582682i 0.981442π-0.981442\pi
0.549612 + 0.835420i 0.314775π0.314775\pi
282282 0 0
283283 −2.68847e8 4.65657e8i −0.705104 1.22128i −0.966654 0.256086i 0.917567π-0.917567\pi
0.261550 0.965190i 0.415766π-0.415766\pi
284284 4.52713e7 + 7.84122e7i 0.117276 + 0.203128i
285285 0 0
286286 6.03658e6 1.04557e7i 0.0152584 0.0264284i
287287 1.10155e7 0.0275053
288288 0 0
289289 −1.94072e8 −0.472956
290290 8.61588e7 1.49231e8i 0.207447 0.359308i
291291 0 0
292292 −3.13690e7 5.43327e7i −0.0737329 0.127709i
293293 −1.67800e8 2.90638e8i −0.389722 0.675019i 0.602690 0.797976i 0.294096π-0.294096\pi
−0.992412 + 0.122957i 0.960762π0.960762\pi
294294 0 0
295295 2.77269e8 4.80245e8i 0.628818 1.08914i
296296 −8.21893e7 −0.184202
297297 0 0
298298 1.75088e8 0.383266
299299 −4.74800e7 + 8.22378e7i −0.102722 + 0.177919i
300300 0 0
301301 3.20420e8 + 5.54984e8i 0.677231 + 1.17300i
302302 −1.17662e8 2.03796e8i −0.245817 0.425767i
303303 0 0
304304 8.17971e7 1.41677e8i 0.166986 0.289229i
305305 −1.73817e8 −0.350787
306306 0 0
307307 2.15029e8 0.424143 0.212072 0.977254i 0.431979π-0.431979\pi
0.212072 + 0.977254i 0.431979π0.431979\pi
308308 −3.55031e7 + 6.14932e7i −0.0692371 + 0.119922i
309309 0 0
310310 −1.91144e8 3.31071e8i −0.364413 0.631182i
311311 −3.96031e8 6.85945e8i −0.746565 1.29309i −0.949460 0.313888i 0.898368π-0.898368\pi
0.202895 0.979200i 0.434965π-0.434965\pi
312312 0 0
313313 5.92287e7 1.02587e8i 0.109176 0.189098i −0.806261 0.591560i 0.798512π-0.798512\pi
0.915437 + 0.402462i 0.131845π0.131845\pi
314314 −4.84440e8 −0.883051
315315 0 0
316316 −2.28275e8 −0.406962
317317 2.53655e7 4.39343e7i 0.0447235 0.0774633i −0.842797 0.538231i 0.819093π-0.819093\pi
0.887521 + 0.460768i 0.152426π0.152426\pi
318318 0 0
319319 5.60032e7 + 9.70004e7i 0.0965930 + 0.167304i
320320 2.75251e7 + 4.76749e7i 0.0469574 + 0.0813327i
321321 0 0
322322 2.79246e8 4.83668e8i 0.466112 0.807331i
323323 −5.87358e8 −0.969826
324324 0 0
325325 −4.70226e7 −0.0759826
326326 2.28341e8 3.95499e8i 0.365025 0.632242i
327327 0 0
328328 2.77555e6 + 4.80740e6i 0.00434301 + 0.00752232i
329329 −2.40109e8 4.15881e8i −0.371726 0.643849i
330330 0 0
331331 −1.36878e8 + 2.37080e8i −0.207461 + 0.359334i −0.950914 0.309455i 0.899853π-0.899853\pi
0.743453 + 0.668788i 0.233187π0.233187\pi
332332 3.63065e8 0.544504
333333 0 0
334334 7.01812e8 1.03064
335335 −1.32304e7 + 2.29158e7i −0.0192272 + 0.0333025i
336336 0 0
337337 4.59256e7 + 7.95455e7i 0.0653658 + 0.113217i 0.896856 0.442322i 0.145845π-0.145845\pi
−0.831490 + 0.555539i 0.812512π0.812512\pi
338338 −2.43354e8 4.21502e8i −0.342792 0.593733i
339339 0 0
340340 9.88243e7 1.71169e8i 0.136360 0.236183i
341341 2.48487e8 0.339362
342342 0 0
343343 −6.24667e8 −0.835833
344344 −1.61471e8 + 2.79677e8i −0.213866 + 0.370426i
345345 0 0
346346 3.42782e7 + 5.93715e7i 0.0444889 + 0.0770570i
347347 6.83502e8 + 1.18386e9i 0.878187 + 1.52106i 0.853329 + 0.521373i 0.174580π0.174580\pi
0.0248578 + 0.999691i 0.492087π0.492087\pi
348348 0 0
349349 −5.65716e8 + 9.79849e8i −0.712377 + 1.23387i 0.251586 + 0.967835i 0.419048π0.419048\pi
−0.963963 + 0.266038i 0.914285π0.914285\pi
350350 2.76555e8 0.344781
351351 0 0
352352 −3.57827e7 −0.0437294
353353 2.24198e7 3.88322e7i 0.0271281 0.0469873i −0.852143 0.523310i 0.824697π-0.824697\pi
0.879271 + 0.476322i 0.158030π0.158030\pi
354354 0 0
355355 −1.48546e8 2.57290e8i −0.176223 0.305227i
356356 3.82438e8 + 6.62402e8i 0.449248 + 0.778120i
357357 0 0
358358 7.52162e7 1.30278e8i 0.0866405 0.150066i
359359 3.98281e8 0.454317 0.227158 0.973858i 0.427057π-0.427057\pi
0.227158 + 0.973858i 0.427057π0.427057\pi
360360 0 0
361361 7.01332e8 0.784600
362362 −2.39850e8 + 4.15432e8i −0.265742 + 0.460278i
363363 0 0
364364 −4.49316e7 7.78238e7i −0.0488311 0.0845780i
365365 1.02930e8 + 1.78279e8i 0.110794 + 0.191900i
366366 0 0
367367 −8.17359e8 + 1.41571e9i −0.863140 + 1.49500i 0.00574132 + 0.999984i 0.498172π0.498172\pi
−0.868882 + 0.495020i 0.835161π0.835161\pi
368368 2.81444e8 0.294391
369369 0 0
370370 2.69684e8 0.276789
371371 7.58961e8 1.31456e9i 0.771633 1.33651i
372372 0 0
373373 7.73166e8 + 1.33916e9i 0.771421 + 1.33614i 0.936784 + 0.349908i 0.113787π0.113787\pi
−0.165363 + 0.986233i 0.552879π0.552879\pi
374374 6.42358e7 + 1.11260e8i 0.0634931 + 0.109973i
375375 0 0
376376 1.21000e8 2.09578e8i 0.117389 0.203324i
377377 −1.41752e8 −0.136249
378378 0 0
379379 −1.05688e9 −0.997216 −0.498608 0.866828i 0.666155π-0.666155\pi
−0.498608 + 0.866828i 0.666155π0.666155\pi
380380 −2.68397e8 + 4.64877e8i −0.250920 + 0.434606i
381381 0 0
382382 3.75944e8 + 6.51155e8i 0.345066 + 0.597671i
383383 −1.12455e8 1.94778e8i −0.102278 0.177151i 0.810345 0.585953i 0.199280π-0.199280\pi
−0.912623 + 0.408802i 0.865947π0.865947\pi
384384 0 0
385385 1.16495e8 2.01774e8i 0.104038 0.180200i
386386 2.81556e8 0.249178
387387 0 0
388388 5.55657e8 0.482943
389389 −5.08941e8 + 8.81512e8i −0.438373 + 0.759284i −0.997564 0.0697544i 0.977778π-0.977778\pi
0.559191 + 0.829039i 0.311112π0.311112\pi
390390 0 0
391391 −5.05239e8 8.75100e8i −0.427443 0.740353i
392392 5.34305e7 + 9.25444e7i 0.0448011 + 0.0775977i
393393 0 0
394394 4.11941e8 7.13503e8i 0.339311 0.587705i
395395 7.49028e8 0.611517
396396 0 0
397397 −1.47565e9 −1.18363 −0.591817 0.806072i 0.701589π-0.701589\pi
−0.591817 + 0.806072i 0.701589π0.701589\pi
398398 3.34550e8 5.79458e8i 0.265993 0.460714i
399399 0 0
400400 6.96832e7 + 1.20695e8i 0.0544400 + 0.0942928i
401401 −1.37456e8 2.38081e8i −0.106453 0.184382i 0.807878 0.589350i 0.200616π-0.200616\pi
−0.914331 + 0.404968i 0.867283π0.867283\pi
402402 0 0
403403 −1.57238e8 + 2.72345e8i −0.119672 + 0.207277i
404404 −6.45090e8 −0.486727
405405 0 0
406406 8.33689e8 0.618248
407407 −8.76472e7 + 1.51809e8i −0.0644403 + 0.111614i
408408 0 0
409409 8.17136e8 + 1.41532e9i 0.590558 + 1.02288i 0.994157 + 0.107941i 0.0344258π0.0344258\pi
−0.403599 + 0.914936i 0.632241π0.632241\pi
410410 −9.10728e6 1.57743e7i −0.00652597 0.0113033i
411411 0 0
412412 −1.19936e8 + 2.07735e8i −0.0844906 + 0.146342i
413413 2.68291e9 1.87405
414414 0 0
415415 −1.19131e9 −0.818192
416416 2.26427e7 3.92183e7i 0.0154206 0.0267093i
417417 0 0
418418 −1.74458e8 3.02170e8i −0.116835 0.202365i
419419 5.56399e8 + 9.63711e8i 0.369519 + 0.640026i 0.989490 0.144598i 0.0461890π-0.0461890\pi
−0.619971 + 0.784625i 0.712856π0.712856\pi
420420 0 0
421421 −4.61264e8 + 7.98933e8i −0.301274 + 0.521823i −0.976425 0.215857i 0.930745π-0.930745\pi
0.675150 + 0.737680i 0.264079π0.264079\pi
422422 7.79208e8 0.504731
423423 0 0
424424 7.64937e8 0.487355
425425 2.50186e8 4.33335e8i 0.158089 0.273818i
426426 0 0
427427 −4.20473e8 7.28280e8i −0.261361 0.452690i
428428 5.75538e8 + 9.96861e8i 0.354830 + 0.614584i
429429 0 0
430430 5.29828e8 9.17690e8i 0.321363 0.556617i
431431 −9.81508e8 −0.590505 −0.295252 0.955419i 0.595404π-0.595404\pi
−0.295252 + 0.955419i 0.595404π0.595404\pi
432432 0 0
433433 2.84998e9 1.68707 0.843537 0.537071i 0.180469π-0.180469\pi
0.843537 + 0.537071i 0.180469π0.180469\pi
434434 9.24771e8 1.60175e9i 0.543026 0.940548i
435435 0 0
436436 −3.92225e8 6.79354e8i −0.226638 0.392548i
437437 1.37218e9 + 2.37668e9i 0.786549 + 1.36234i
438438 0 0
439439 5.28109e8 9.14712e8i 0.297919 0.516011i −0.677741 0.735301i 0.737041π-0.737041\pi
0.975660 + 0.219290i 0.0703742π0.0703742\pi
440440 1.17412e8 0.0657094
441441 0 0
442442 −1.62590e8 −0.0895601
443443 −9.11627e8 + 1.57899e9i −0.498201 + 0.862909i −0.999998 0.00207637i 0.999339π-0.999339\pi
0.501797 + 0.864985i 0.332672π0.332672\pi
444444 0 0
445445 −1.25487e9 2.17351e9i −0.675057 1.16923i
446446 −5.85829e7 1.01469e8i −0.0312679 0.0541576i
447447 0 0
448448 −1.33169e8 + 2.30656e8i −0.0699730 + 0.121197i
449449 1.84846e9 0.963713 0.481856 0.876250i 0.339963π-0.339963\pi
0.481856 + 0.876250i 0.339963π0.339963\pi
450450 0 0
451451 1.18395e7 0.00607735
452452 −5.31039e8 + 9.19786e8i −0.270484 + 0.468492i
453453 0 0
454454 −7.38164e8 1.27854e9i −0.370218 0.641236i
455455 1.47432e8 + 2.55359e8i 0.0733755 + 0.127090i
456456 0 0
457457 1.49033e9 2.58133e9i 0.730425 1.26513i −0.226276 0.974063i 0.572655π-0.572655\pi
0.956702 0.291071i 0.0940114π-0.0940114\pi
458458 7.00369e7 0.0340642
459459 0 0
460460 −9.23489e8 −0.442364
461461 1.26390e9 2.18915e9i 0.600843 1.04069i −0.391851 0.920029i 0.628165π-0.628165\pi
0.992694 0.120661i 0.0385015π-0.0385015\pi
462462 0 0
463463 4.45145e8 + 7.71014e8i 0.208434 + 0.361018i 0.951221 0.308509i 0.0998300π-0.0998300\pi
−0.742787 + 0.669527i 0.766497π0.766497\pi
464464 2.10063e8 + 3.63840e8i 0.0976197 + 0.169082i
465465 0 0
466466 −4.78225e8 + 8.28310e8i −0.218918 + 0.379177i
467467 2.65667e9 1.20706 0.603529 0.797341i 0.293761π-0.293761\pi
0.603529 + 0.797341i 0.293761π0.293761\pi
468468 0 0
469469 −1.28020e8 −0.0573024
470470 −3.97031e8 + 6.87678e8i −0.176393 + 0.305522i
471471 0 0
472472 6.76009e8 + 1.17088e9i 0.295907 + 0.512526i
473473 3.44388e8 + 5.96498e8i 0.149635 + 0.259176i
474474 0 0
475475 −6.79479e8 + 1.17689e9i −0.290903 + 0.503859i
476476 9.56243e8 0.406391
477477 0 0
478478 −3.16967e9 −1.32745
479479 −6.50467e8 + 1.12664e9i −0.270428 + 0.468394i −0.968971 0.247173i 0.920498π-0.920498\pi
0.698544 + 0.715567i 0.253832π0.253832\pi
480480 0 0
481481 −1.10923e8 1.92125e8i −0.0454481 0.0787184i
482482 −1.02643e9 1.77782e9i −0.417506 0.723142i
483483 0 0
484484 5.85431e8 1.01400e9i 0.234702 0.406516i
485485 −1.82325e9 −0.725689
486486 0 0
487487 −1.07447e9 −0.421542 −0.210771 0.977535i 0.567598π-0.567598\pi
−0.210771 + 0.977535i 0.567598π0.567598\pi
488488 2.11892e8 3.67007e8i 0.0825362 0.142957i
489489 0 0
490490 −1.75319e8 3.03661e8i −0.0673198 0.116601i
491491 3.91672e8 + 6.78396e8i 0.149327 + 0.258641i 0.930979 0.365073i 0.118956π-0.118956\pi
−0.781652 + 0.623715i 0.785623π0.785623\pi
492492 0 0
493493 7.54197e8 1.30631e9i 0.283479 0.491000i
494494 4.41577e8 0.164802
495495 0 0
496496 9.32053e8 0.342969
497497 7.18682e8 1.24479e9i 0.262597 0.454831i
498498 0 0
499499 3.11594e8 + 5.39697e8i 0.112263 + 0.194445i 0.916682 0.399617i 0.130857π-0.130857\pi
−0.804419 + 0.594062i 0.797523π0.797523\pi
500500 −7.53648e8 1.30536e9i −0.269633 0.467019i
501501 0 0
502502 −2.93910e8 + 5.09067e8i −0.103694 + 0.179602i
503503 −2.70927e9 −0.949215 −0.474607 0.880198i 0.657410π-0.657410\pi
−0.474607 + 0.880198i 0.657410π0.657410\pi
504504 0 0
505505 2.11670e9 0.731375
506506 3.00134e8 5.19847e8i 0.102988 0.178381i
507507 0 0
508508 −3.73842e7 6.47513e7i −0.0126522 0.0219142i
509509 −1.74972e9 3.03060e9i −0.588106 1.01863i −0.994480 0.104923i 0.966540π-0.966540\pi
0.406374 0.913707i 0.366793π-0.366793\pi
510510 0 0
511511 −4.97983e8 + 8.62532e8i −0.165098 + 0.285958i
512512 −1.34218e8 −0.0441942
513513 0 0
514514 1.62161e9 0.526714
515515 3.93539e8 6.81630e8i 0.126959 0.219899i
516516 0 0
517517 −2.58070e8 4.46991e8i −0.0821336 0.142260i
518518 6.52378e8 + 1.12995e9i 0.206227 + 0.357195i
519519 0 0
520520 −7.42963e7 + 1.28685e8i −0.0231716 + 0.0401343i
521521 −1.37683e9 −0.426530 −0.213265 0.976994i 0.568410π-0.568410\pi
−0.213265 + 0.976994i 0.568410π0.568410\pi
522522 0 0
523523 −2.86154e9 −0.874669 −0.437334 0.899299i 0.644077π-0.644077\pi
−0.437334 + 0.899299i 0.644077π0.644077\pi
524524 2.53562e8 4.39183e8i 0.0769884 0.133348i
525525 0 0
526526 6.17016e8 + 1.06870e9i 0.184862 + 0.320190i
527527 −1.67319e9 2.89805e9i −0.497976 0.862519i
528528 0 0
529529 −6.58257e8 + 1.14013e9i −0.193331 + 0.334858i
530530 −2.50995e9 −0.732318
531531 0 0
532532 −2.59706e9 −0.747810
533533 −7.49182e6 + 1.29762e7i −0.00214310 + 0.00371196i
534534 0 0
535535 −1.88848e9 3.27095e9i −0.533182 0.923498i
536536 −3.22570e7 5.58708e7i −0.00904789 0.0156714i
537537 0 0
538538 −2.49607e9 + 4.32333e9i −0.691066 + 1.19696i
539539 2.27915e8 0.0626919
540540 0 0
541541 5.34467e9 1.45121 0.725605 0.688111i 0.241560π-0.241560\pi
0.725605 + 0.688111i 0.241560π0.241560\pi
542542 −1.55193e9 + 2.68803e9i −0.418673 + 0.725164i
543543 0 0
544544 2.40943e8 + 4.17326e8i 0.0641680 + 0.111142i
545545 1.28699e9 + 2.22913e9i 0.340555 + 0.589858i
546546 0 0
547547 1.68567e9 2.91967e9i 0.440370 0.762743i −0.557347 0.830280i 0.688181π-0.688181\pi
0.997717 + 0.0675365i 0.0215139π0.0215139\pi
548548 −2.02019e7 −0.00524396
549549 0 0
550550 2.97242e8 0.0761801
551551 −2.04832e9 + 3.54780e9i −0.521636 + 0.903501i
552552 0 0
553553 1.81193e9 + 3.13836e9i 0.455622 + 0.789160i
554554 1.81581e9 + 3.14507e9i 0.453718 + 0.785863i
555555 0 0
556556 −1.25452e9 + 2.17289e9i −0.309540 + 0.536138i
557557 −5.61106e9 −1.37579 −0.687894 0.725811i 0.741465π-0.741465\pi
−0.687894 + 0.725811i 0.741465π0.741465\pi
558558 0 0
559559 −8.71694e8 −0.211068
560560 4.36961e8 7.56839e8i 0.105144 0.182115i
561561 0 0
562562 1.33508e9 + 2.31243e9i 0.317271 + 0.549529i
563563 −3.34845e9 5.79968e9i −0.790795 1.36970i −0.925475 0.378809i 0.876334π-0.876334\pi
0.134680 0.990889i 0.456999π-0.456999\pi
564564 0 0
565565 1.74247e9 3.01805e9i 0.406440 0.703974i
566566 −4.30156e9 −0.997168
567567 0 0
568568 7.24341e8 0.165853
569569 −9.84251e8 + 1.70477e9i −0.223982 + 0.387948i −0.956013 0.293323i 0.905239π-0.905239\pi
0.732032 + 0.681271i 0.238572π0.238572\pi
570570 0 0
571571 −5.14629e8 8.91363e8i −0.115682 0.200368i 0.802370 0.596827i 0.203572π-0.203572\pi
−0.918052 + 0.396459i 0.870239π0.870239\pi
572572 −4.82926e7 8.36453e7i −0.0107893 0.0186877i
573573 0 0
574574 4.40619e7 7.63174e7i 0.00972459 0.0168435i
575575 −2.33793e9 −0.512853
576576 0 0
577577 3.31179e9 0.717708 0.358854 0.933394i 0.383168π-0.383168\pi
0.358854 + 0.933394i 0.383168π0.383168\pi
578578 −7.76289e8 + 1.34457e9i −0.167215 + 0.289625i
579579 0 0
580580 −6.89270e8 1.19385e9i −0.146687 0.254069i
581581 −2.88183e9 4.99147e9i −0.609610 1.05587i
582582 0 0
583583 8.15734e8 1.41289e9i 0.170494 0.295304i
584584 −5.01904e8 −0.104274
585585 0 0
586586 −2.68480e9 −0.551151
587587 2.79705e8 4.84464e8i 0.0570778 0.0988617i −0.836075 0.548616i 0.815155π-0.815155\pi
0.893152 + 0.449754i 0.148488π0.148488\pi
588588 0 0
589589 4.54421e9 + 7.87081e9i 0.916337 + 1.58714i
590590 −2.21815e9 3.84196e9i −0.444641 0.770141i
591591 0 0
592592 −3.28757e8 + 5.69424e8i −0.0651252 + 0.112800i
593593 −3.02459e9 −0.595628 −0.297814 0.954624i 0.596258π-0.596258\pi
−0.297814 + 0.954624i 0.596258π0.596258\pi
594594 0 0
595595 −3.13767e9 −0.610658
596596 7.00354e8 1.21305e9i 0.135505 0.234702i
597597 0 0
598598 3.79840e8 + 6.57902e8i 0.0726351 + 0.125808i
599599 2.81623e9 + 4.87785e9i 0.535395 + 0.927331i 0.999144 + 0.0413648i 0.0131706π0.0131706\pi
−0.463749 + 0.885967i 0.653496π0.653496\pi
600600 0 0
601601 −1.70396e8 + 2.95134e8i −0.0320183 + 0.0554573i −0.881591 0.472015i 0.843527π-0.843527\pi
0.849572 + 0.527472i 0.176860π0.176860\pi
602602 5.12672e9 0.957749
603603 0 0
604604 −1.88259e9 −0.347637
605605 −1.92094e9 + 3.32717e9i −0.352672 + 0.610846i
606606 0 0
607607 −1.92710e9 3.33783e9i −0.349739 0.605765i 0.636464 0.771306i 0.280396π-0.280396\pi
−0.986203 + 0.165541i 0.947063π0.947063\pi
608608 −6.54377e8 1.13341e9i −0.118077 0.204515i
609609 0 0
610610 −6.95270e8 + 1.20424e9i −0.124022 + 0.214812i
611611 6.53211e8 0.115853
612612 0 0
613613 9.22245e9 1.61709 0.808545 0.588434i 0.200255π-0.200255\pi
0.808545 + 0.588434i 0.200255π0.200255\pi
614614 8.60116e8 1.48976e9i 0.149957 0.259734i
615615 0 0
616616 2.84025e8 + 4.91945e8i 0.0489580 + 0.0847978i
617617 −3.26806e9 5.66044e9i −0.560133 0.970179i −0.997484 0.0708885i 0.977417π-0.977417\pi
0.437351 0.899291i 0.355917π-0.355917\pi
618618 0 0
619619 −6.82793e8 + 1.18263e9i −0.115710 + 0.200416i −0.918063 0.396434i 0.870248π-0.870248\pi
0.802353 + 0.596849i 0.203581π0.203581\pi
620620 −3.05830e9 −0.515358
621621 0 0
622622 −6.33649e9 −1.05580
623623 6.07120e9 1.05156e10i 1.00593 1.74232i
624624 0 0
625625 1.14381e9 + 1.98113e9i 0.187401 + 0.324588i
626626 −4.73830e8 8.20697e8i −0.0771991 0.133713i
627627 0 0
628628 −1.93776e9 + 3.35630e9i −0.312206 + 0.540756i
629629 2.36070e9 0.378236
630630 0 0
631631 1.54079e9 0.244141 0.122070 0.992521i 0.461047π-0.461047\pi
0.122070 + 0.992521i 0.461047π0.461047\pi
632632 −9.13101e8 + 1.58154e9i −0.143883 + 0.249212i
633633 0 0
634634 −2.02924e8 3.51474e8i −0.0316243 0.0547749i
635635 1.22667e8 + 2.12465e8i 0.0190116 + 0.0329291i
636636 0 0
637637 −1.44221e8 + 2.49798e8i −0.0221075 + 0.0382913i
638638 8.96052e8 0.136603
639639 0 0
640640 4.40402e8 0.0664078
641641 2.27009e9 3.93191e9i 0.340440 0.589659i −0.644075 0.764963i 0.722757π-0.722757\pi
0.984514 + 0.175304i 0.0560908π0.0560908\pi
642642 0 0
643643 −5.70269e9 9.87735e9i −0.845944 1.46522i −0.884799 0.465973i 0.845705π-0.845705\pi
0.0388554 0.999245i 0.487629π-0.487629\pi
644644 −2.23396e9 3.86934e9i −0.329591 0.570869i
645645 0 0
646646 −2.34943e9 + 4.06933e9i −0.342885 + 0.593895i
647647 −1.26393e10 −1.83468 −0.917338 0.398109i 0.869666π-0.869666\pi
−0.917338 + 0.398109i 0.869666π0.869666\pi
648648 0 0
649649 2.88360e9 0.414075
650650 −1.88090e8 + 3.25782e8i −0.0268639 + 0.0465297i
651651 0 0
652652 −1.82673e9 3.16399e9i −0.258112 0.447063i
653653 5.25022e9 + 9.09365e9i 0.737873 + 1.27803i 0.953451 + 0.301547i 0.0975029π0.0975029\pi
−0.215579 + 0.976486i 0.569164π0.569164\pi
654654 0 0
655655 −8.32002e8 + 1.44107e9i −0.115686 + 0.200374i
656656 4.44088e7 0.00614194
657657 0 0
658658 −3.84175e9 −0.525700
659659 −4.82409e9 + 8.35557e9i −0.656624 + 1.13731i 0.324861 + 0.945762i 0.394683π0.394683\pi
−0.981484 + 0.191543i 0.938651π0.938651\pi
660660 0 0
661661 3.29149e9 + 5.70103e9i 0.443290 + 0.767801i 0.997931 0.0642888i 0.0204779π-0.0204779\pi
−0.554641 + 0.832089i 0.687145π0.687145\pi
662662 1.09503e9 + 1.89664e9i 0.146697 + 0.254087i
663663 0 0
664664 1.45226e9 2.51539e9i 0.192511 0.333439i
665665 8.52160e9 1.12369
666666 0 0
667667 −7.04779e9 −0.919629
668668 2.80725e9 4.86230e9i 0.364387 0.631137i
669669 0 0
670670 1.05843e8 + 1.83326e8i 0.0135957 + 0.0235485i
671671 −4.51925e8 7.82758e8i −0.0577481 0.100023i
672672 0 0
673673 4.27324e9 7.40148e9i 0.540387 0.935978i −0.458494 0.888697i 0.651611π-0.651611\pi
0.998882 0.0472808i 0.0150556π-0.0150556\pi
674674 7.34810e8 0.0924411
675675 0 0
676676 −3.89367e9 −0.484781
677677 −4.35652e9 + 7.54572e9i −0.539610 + 0.934631i 0.459315 + 0.888273i 0.348095π0.348095\pi
−0.998925 + 0.0463581i 0.985238π0.985238\pi
678678 0 0
679679 −4.41053e9 7.63926e9i −0.540688 0.936499i
680680 −7.90595e8 1.36935e9i −0.0964212 0.167006i
681681 0 0
682682 9.93947e8 1.72157e9i 0.119983 0.207816i
683683 1.46109e10 1.75470 0.877351 0.479849i 0.159308π-0.159308\pi
0.877351 + 0.479849i 0.159308π0.159308\pi
684684 0 0
685685 6.62873e7 0.00787977
686686 −2.49867e9 + 4.32782e9i −0.295511 + 0.511841i
687687 0 0
688688 1.29177e9 + 2.23741e9i 0.151226 + 0.261931i
689689 1.03237e9 + 1.78811e9i 0.120245 + 0.208270i
690690 0 0
691691 7.36738e9 1.27607e10i 0.849454 1.47130i −0.0322413 0.999480i 0.510265π-0.510265\pi
0.881696 0.471818i 0.156402π-0.156402\pi
692692 5.48451e8 0.0629167
693693 0 0
694694 1.09360e10 1.24194
695695 4.11640e9 7.12981e9i 0.465126 0.805622i
696696 0 0
697697 −7.97212e7 1.38081e8i −0.00891783 0.0154461i
698698 4.52573e9 + 7.83879e9i 0.503726 + 0.872480i
699699 0 0
700700 1.10622e9 1.91603e9i 0.121899 0.211135i
701701 1.31502e9 0.144185 0.0720923 0.997398i 0.477032π-0.477032\pi
0.0720923 + 0.997398i 0.477032π0.477032\pi
702702 0 0
703703 −6.41141e9 −0.696001
704704 −1.43131e8 + 2.47910e8i −0.0154607 + 0.0267787i
705705 0 0
706706 −1.79358e8 3.10657e8i −0.0191825 0.0332250i
707707 5.12041e9 + 8.86880e9i 0.544925 + 0.943837i
708708 0 0
709709 −3.32014e8 + 5.75065e8i −0.0349860 + 0.0605976i −0.882988 0.469395i 0.844472π-0.844472\pi
0.848002 + 0.529993i 0.177805π0.177805\pi
710710 −2.37674e9 −0.249217
711711 0 0
712712 6.11901e9 0.635333
713713 −7.81778e9 + 1.35408e10i −0.807737 + 1.39904i
714714 0 0
715715 1.58460e8 + 2.74461e8i 0.0162125 + 0.0280808i
716716 −6.01730e8 1.04223e9i −0.0612641 0.106113i
717717 0 0
718718 1.59312e9 2.75937e9i 0.160625 0.278211i
719719 4.95034e9 0.496689 0.248344 0.968672i 0.420114π-0.420114\pi
0.248344 + 0.968672i 0.420114π0.420114\pi
720720 0 0
721721 3.80796e9 0.378372
722722 2.80533e9 4.85897e9i 0.277398 0.480467i
723723 0 0
724724 1.91880e9 + 3.32346e9i 0.187908 + 0.325466i
725725 −1.74497e9 3.02238e9i −0.170061 0.294555i
726726 0 0
727727 −4.40550e9 + 7.63056e9i −0.425231 + 0.736522i −0.996442 0.0842813i 0.973141π-0.973141\pi
0.571211 + 0.820803i 0.306474π0.306474\pi
728728 −7.18905e8 −0.0690577
729729 0 0
730730 1.64687e9 0.156686
731731 4.63789e9 8.03306e9i 0.439147 0.760624i
732732 0 0
733733 7.47069e7 + 1.29396e8i 0.00700643 + 0.0121355i 0.869507 0.493920i 0.164436π-0.164436\pi
−0.862501 + 0.506055i 0.831103π0.831103\pi
734734 6.53887e9 + 1.13257e10i 0.610332 + 1.05713i
735735 0 0
736736 1.12578e9 1.94990e9i 0.104083 0.180277i
737737 −1.37596e8 −0.0126611
738738 0 0
739739 −4.70806e9 −0.429127 −0.214564 0.976710i 0.568833π-0.568833\pi
−0.214564 + 0.976710i 0.568833π0.568833\pi
740740 1.07873e9 1.86842e9i 0.0978596 0.169498i
741741 0 0
742742 −6.07169e9 1.05165e10i −0.545627 0.945054i
743743 −8.48381e8 1.46944e9i −0.0758805 0.131429i 0.825588 0.564273i 0.190843π-0.190843\pi
−0.901469 + 0.432844i 0.857510π0.857510\pi
744744 0 0
745745 −2.29804e9 + 3.98031e9i −0.203615 + 0.352671i
746746 1.23707e10 1.09095
747747 0 0
748748 1.02777e9 0.0897928
749749 9.13667e9 1.58252e10i 0.794514 1.37614i
750750 0 0
751751 −5.33250e9 9.23616e9i −0.459400 0.795704i 0.539529 0.841967i 0.318602π-0.318602\pi
−0.998929 + 0.0462626i 0.985269π0.985269\pi
752752 −9.67999e8 1.67662e9i −0.0830066 0.143772i
753753 0 0
754754 −5.67007e8 + 9.82085e8i −0.0481713 + 0.0834352i
755755 6.17724e9 0.522373
756756 0 0
757757 6.22876e9 0.521874 0.260937 0.965356i 0.415968π-0.415968\pi
0.260937 + 0.965356i 0.415968π0.415968\pi
758758 −4.22753e9 + 7.32229e9i −0.352569 + 0.610668i
759759 0 0
760760 2.14717e9 + 3.71902e9i 0.177427 + 0.307313i
761761 4.19167e9 + 7.26019e9i 0.344779 + 0.597175i 0.985314 0.170755i 0.0546205π-0.0546205\pi
−0.640535 + 0.767929i 0.721287π0.721287\pi
762762 0 0
763763 −6.22657e9 + 1.07847e10i −0.507473 + 0.878969i
764764 6.01511e9 0.487997
765765 0 0
766766 −1.79928e9 −0.144643
767767 −1.82470e9 + 3.16047e9i −0.146018 + 0.252911i
768768 0 0
769769 5.93244e9 + 1.02753e10i 0.470426 + 0.814802i 0.999428 0.0338188i 0.0107669π-0.0107669\pi
−0.529002 + 0.848621i 0.677434π0.677434\pi
770770 −9.31956e8 1.61420e9i −0.0735662 0.127420i
771771 0 0
772772 1.12623e9 1.95068e9i 0.0880978 0.152590i
773773 5.56680e9 0.433488 0.216744 0.976228i 0.430456π-0.430456\pi
0.216744 + 0.976228i 0.430456π0.430456\pi
774774 0 0
775775 −7.74246e9 −0.597479
776776 2.22263e9 3.84971e9i 0.170746 0.295741i
777777 0 0
778778 4.07153e9 + 7.05209e9i 0.309977 + 0.536895i
779779 2.16515e8 + 3.75015e8i 0.0164099 + 0.0284228i
780780 0 0
781781 7.72441e8 1.33791e9i 0.0580212 0.100496i
782782 −8.08383e9 −0.604496
783783 0 0
784784 8.54888e8 0.0633583
785785 6.35827e9 1.10128e10i 0.469132 0.812561i
786786 0 0
787787 −6.73056e7 1.16577e8i −0.00492198 0.00852512i 0.863554 0.504257i 0.168233π-0.168233\pi
−0.868476 + 0.495731i 0.834900π0.834900\pi
788788 −3.29553e9 5.70803e9i −0.239929 0.415570i
789789 0 0
790790 2.99611e9 5.18942e9i 0.216204 0.374476i
791791 1.68605e10 1.21130
792792 0 0
793793 1.14388e9 0.0814565
794794 −5.90261e9 + 1.02236e10i −0.418478 + 0.724825i
795795 0 0
796796 −2.67640e9 4.63566e9i −0.188086 0.325774i
797797 3.70774e9 + 6.42199e9i 0.259421 + 0.449330i 0.966087 0.258217i 0.0831350π-0.0831350\pi
−0.706666 + 0.707547i 0.749802π0.749802\pi
798798 0 0
799799 −3.47544e9 + 6.01964e9i −0.241044 + 0.417500i
800800 1.11493e9 0.0769898
801801 0 0
802802 −2.19930e9 −0.150548
803803 −5.35234e8 + 9.27052e8i −0.0364787 + 0.0631829i
804804 0 0
805805 7.33020e9 + 1.26963e10i 0.495256 + 0.857809i
806806 1.25791e9 + 2.17876e9i 0.0846206 + 0.146567i
807807 0 0
808808 −2.58036e9 + 4.46932e9i −0.172084 + 0.298058i
809809 −1.41542e10 −0.939863 −0.469932 0.882703i 0.655721π-0.655721\pi
−0.469932 + 0.882703i 0.655721π0.655721\pi
810810 0 0
811811 −2.63708e10 −1.73600 −0.868001 0.496563i 0.834595π-0.834595\pi
−0.868001 + 0.496563i 0.834595π0.834595\pi
812812 3.33476e9 5.77597e9i 0.218584 0.378598i
813813 0 0
814814 7.01178e8 + 1.21448e9i 0.0455662 + 0.0789229i
815815 5.99396e9 + 1.03818e10i 0.387848 + 0.671773i
816816 0 0
817817 −1.25960e10 + 2.18170e10i −0.808084 + 1.39964i
818818 1.30742e10 0.835176
819819 0 0
820820 −1.45716e8 −0.00922912
821821 −4.03132e9 + 6.98245e9i −0.254241 + 0.440359i −0.964689 0.263391i 0.915159π-0.915159\pi
0.710448 + 0.703750i 0.248492π0.248492\pi
822822 0 0
823823 1.17101e10 + 2.02825e10i 0.732253 + 1.26830i 0.955918 + 0.293633i 0.0948643π0.0948643\pi
−0.223666 + 0.974666i 0.571802π0.571802\pi
824824 9.59486e8 + 1.66188e9i 0.0597439 + 0.103479i
825825 0 0
826826 1.07316e10 1.85877e10i 0.662576 1.14762i
827827 5.55722e9 0.341655 0.170828 0.985301i 0.445356π-0.445356\pi
0.170828 + 0.985301i 0.445356π0.445356\pi
828828 0 0
829829 2.84256e10 1.73288 0.866440 0.499281i 0.166403π-0.166403\pi
0.866440 + 0.499281i 0.166403π0.166403\pi
830830 −4.76523e9 + 8.25362e9i −0.289275 + 0.501039i
831831 0 0
832832 −1.81142e8 3.13746e8i −0.0109040 0.0188863i
833833 −1.53467e9 2.65812e9i −0.0919934 0.159337i
834834 0 0
835835 −9.21128e9 + 1.59544e10i −0.547542 + 0.948371i
836836 −2.79133e9 −0.165230
837837 0 0
838838 8.90238e9 0.522579
839839 −5.20178e9 + 9.00975e9i −0.304078 + 0.526679i −0.977056 0.212984i 0.931682π-0.931682\pi
0.672977 + 0.739663i 0.265015π0.265015\pi
840840 0 0
841841 3.36464e9 + 5.82772e9i 0.195053 + 0.337841i
842842 3.69011e9 + 6.39146e9i 0.213033 + 0.368984i
843843 0 0
844844 3.11683e9 5.39851e9i 0.178449 0.309083i
845845 1.27761e10 0.728450
846846 0 0
847847 −1.85874e10 −1.05106
848848 3.05975e9 5.29964e9i 0.172306 0.298443i
849849 0 0
850850 −2.00149e9 3.46668e9i −0.111786 0.193619i
851851 −5.51503e9 9.55231e9i −0.306757 0.531319i
852852 0 0
853853 9.02901e9 1.56387e10i 0.498102 0.862739i −0.501895 0.864928i 0.667364π-0.667364\pi
0.999998 + 0.00218977i 0.000697026π0.000697026\pi
854854 −6.72756e9 −0.369620
855855 0 0
856856 9.20861e9 0.501806
857857 3.17017e9 5.49090e9i 0.172048 0.297996i −0.767088 0.641542i 0.778295π-0.778295\pi
0.939136 + 0.343546i 0.111628π0.111628\pi
858858 0 0
859859 −6.07444e9 1.05212e10i −0.326987 0.566358i 0.654926 0.755693i 0.272700π-0.272700\pi
−0.981912 + 0.189336i 0.939367π0.939367\pi
860860 −4.23863e9 7.34152e9i −0.227238 0.393587i
861861 0 0
862862 −3.92603e9 + 6.80009e9i −0.208775 + 0.361609i
863863 −2.87111e10 −1.52059 −0.760295 0.649578i 0.774946π-0.774946\pi
−0.760295 + 0.649578i 0.774946π0.774946\pi
864864 0 0
865865 −1.79960e9 −0.0945411
866866 1.13999e10 1.97452e10i 0.596471 1.03312i
867867 0 0
868868 −7.39817e9 1.28140e10i −0.383977 0.665068i
869869 1.94747e9 + 3.37312e9i 0.100670 + 0.174366i
870870 0 0
871871 8.70688e7 1.50808e8i 0.00446477 0.00773320i
872872 −6.27560e9 −0.320514
873873 0 0
874874 2.19549e10 1.11235
875875 −1.19642e10 + 2.07225e10i −0.603746 + 1.04572i
876876 0 0
877877 −1.23011e10 2.13061e10i −0.615806 1.06661i −0.990243 0.139355i 0.955497π-0.955497\pi
0.374437 0.927253i 0.377836π-0.377836\pi
878878 −4.22487e9 7.31770e9i −0.210660 0.364875i
879879 0 0
880880 4.69647e8 8.13453e8i 0.0232318 0.0402386i
881881 −1.25378e10 −0.617738 −0.308869 0.951105i 0.599951π-0.599951\pi
−0.308869 + 0.951105i 0.599951π0.599951\pi
882882 0 0
883883 1.93097e10 0.943873 0.471937 0.881633i 0.343555π-0.343555\pi
0.471937 + 0.881633i 0.343555π0.343555\pi
884884 −6.50358e8 + 1.12645e9i −0.0316643 + 0.0548441i
885885 0 0
886886 7.29302e9 + 1.26319e10i 0.352281 + 0.610169i
887887 −1.60134e10 2.77360e10i −0.770462 1.33448i −0.937310 0.348496i 0.886692π-0.886692\pi
0.166848 0.985983i 0.446641π-0.446641\pi
888888 0 0
889889 −5.93474e8 + 1.02793e9i −0.0283299 + 0.0490689i
890890 −2.00780e10 −0.954675
891891 0 0
892892 −9.37327e8 −0.0442195
893893 9.43894e9 1.63487e10i 0.443551 0.768252i
894894 0 0
895895 1.97443e9 + 3.41981e9i 0.0920577 + 0.159449i
896896 1.06535e9 + 1.84525e9i 0.0494784 + 0.0856991i
897897 0 0
898898 7.39384e9 1.28065e10i 0.340724 0.590151i
899899 −2.33400e10 −1.07138
900900 0 0
901901 −2.19710e10 −1.00072
902902 4.73579e7 8.20262e7i 0.00214867 0.00372160i
903903 0 0
904904 4.24831e9 + 7.35829e9i 0.191261 + 0.331274i
905905 −6.29606e9 1.09051e10i −0.282357 0.489057i
906906 0 0
907907 −1.16852e9 + 2.02393e9i −0.0520008 + 0.0900679i −0.890854 0.454290i 0.849893π-0.849893\pi
0.838853 + 0.544357i 0.183226π0.183226\pi
908908 −1.18106e10 −0.523567
909909 0 0
910910 2.35891e9 0.103769
911911 −1.10172e10 + 1.90823e10i −0.482786 + 0.836211i −0.999805 0.0197638i 0.993709π-0.993709\pi
0.517018 + 0.855974i 0.327042π0.327042\pi
912912 0 0
913913 −3.09740e9 5.36485e9i −0.134694 0.233297i
914914 −1.19226e10 2.06506e10i −0.516489 0.894585i
915915 0 0
916916 2.80148e8 4.85230e8i 0.0120435 0.0208599i
917917 −8.05061e9 −0.344775
918918 0 0
919919 −1.43277e10 −0.608938 −0.304469 0.952522i 0.598479π-0.598479\pi
−0.304469 + 0.952522i 0.598479π0.598479\pi
920920 −3.69396e9 + 6.39812e9i −0.156399 + 0.270891i
921921 0 0
922922 −1.01112e10 1.75132e10i −0.424860 0.735879i
923923 9.77577e8 + 1.69321e9i 0.0409209 + 0.0708771i
924924 0 0
925925 2.73095e9 4.73014e9i 0.113453 0.196507i
926926 7.12233e9 0.294770
927927 0 0
928928 3.36101e9 0.138055
929929 −6.56399e9 + 1.13692e10i −0.268604 + 0.465236i −0.968502 0.249007i 0.919896π-0.919896\pi
0.699898 + 0.714243i 0.253229π0.253229\pi
930930 0 0
931931 4.16800e9 + 7.21919e9i 0.169279 + 0.293200i
932932 3.82580e9 + 6.62648e9i 0.154798 + 0.268119i
933933 0 0
934934 1.06267e10 1.84059e10i 0.426759 0.739169i
935935 −3.37238e9 −0.134926
936936 0 0
937937 −3.87626e10 −1.53930 −0.769652 0.638463i 0.779571π-0.779571\pi
−0.769652 + 0.638463i 0.779571π0.779571\pi
938938 −5.12080e8 + 8.86949e8i −0.0202595 + 0.0350904i
939939 0 0
940940 3.17625e9 + 5.50142e9i 0.124729 + 0.216037i
941941 −1.03140e10 1.78643e10i −0.403517 0.698912i 0.590630 0.806942i 0.298879π-0.298879\pi
−0.994148 + 0.108030i 0.965546π0.965546\pi
942942 0 0
943943 −3.72488e8 + 6.45168e8i −0.0144651 + 0.0250543i
944944 1.08161e10 0.418476
945945 0 0
946946 5.51021e9 0.211617
947947 1.05853e10 1.83342e10i 0.405020 0.701516i −0.589304 0.807912i 0.700598π-0.700598\pi
0.994324 + 0.106396i 0.0339311π0.0339311\pi
948948 0 0
949949 −6.77375e8 1.17325e9i −0.0257275 0.0445613i
950950 5.43583e9 + 9.41514e9i 0.205700 + 0.356282i
951951 0 0
952952 3.82497e9 6.62505e9i 0.143681 0.248863i
953953 2.14876e10 0.804196 0.402098 0.915597i 0.368281π-0.368281\pi
0.402098 + 0.915597i 0.368281π0.368281\pi
954954 0 0
955955 −1.97371e10 −0.733282
956956 −1.26787e10 + 2.19601e10i −0.469323 + 0.812891i
957957 0 0
958958 5.20374e9 + 9.01313e9i 0.191221 + 0.331205i
959959 1.60352e8 + 2.77738e8i 0.00587097 + 0.0101688i
960960 0 0
961961 −1.21336e10 + 2.10161e10i −0.441021 + 0.763871i
962962 −1.77478e9 −0.0642733
963963 0 0
964964 −1.64228e10 −0.590443
965965 −3.69543e9 + 6.40067e9i −0.132379 + 0.229287i
966966 0 0
967967 −1.96313e10 3.40023e10i −0.698161 1.20925i −0.969103 0.246655i 0.920669π-0.920669\pi
0.270943 0.962596i 0.412665π-0.412665\pi
968968 −4.68344e9 8.11196e9i −0.165959 0.287450i
969969 0 0
970970 −7.29300e9 + 1.26319e10i −0.256570 + 0.444392i
971971 −5.62647e10 −1.97228 −0.986140 0.165917i 0.946941π-0.946941\pi
−0.986140 + 0.165917i 0.946941π0.946941\pi
972972 0 0
973973 3.98310e10 1.38620
974974 −4.29786e9 + 7.44412e9i −0.149038 + 0.258141i
975975 0 0
976976 −1.69513e9 2.93606e9i −0.0583619 0.101086i
977977 4.21718e9 + 7.30438e9i 0.144674 + 0.250583i 0.929251 0.369448i 0.120453π-0.120453\pi
−0.784577 + 0.620031i 0.787120π0.787120\pi
978978 0 0
979979 6.52535e9 1.13022e10i 0.222262 0.384968i
980980 −2.80510e9 −0.0952045
981981 0 0
982982 6.26675e9 0.211180
983983 1.12115e10 1.94189e10i 0.376466 0.652058i −0.614079 0.789244i 0.710473π-0.710473\pi
0.990545 + 0.137186i 0.0438059π0.0438059\pi
984984 0 0
985985 1.08135e10 + 1.87295e10i 0.360527 + 0.624451i
986986 −6.03358e9 1.04505e10i −0.200450 0.347189i
987987 0 0
988988 1.76631e9 3.05933e9i 0.0582662 0.100920i
989989 −4.33400e10 −1.42463
990990 0 0
991991 3.46728e10 1.13170 0.565849 0.824509i 0.308548π-0.308548\pi
0.565849 + 0.824509i 0.308548π0.308548\pi
992992 3.72821e9 6.45745e9i 0.121258 0.210025i
993993 0 0
994994 −5.74945e9 9.95835e9i −0.185684 0.321614i
995995 8.78194e9 + 1.52108e10i 0.282625 + 0.489520i
996996 0 0
997997 1.48237e10 2.56754e10i 0.473722 0.820511i −0.525825 0.850593i 0.676243π-0.676243\pi
0.999547 + 0.0300818i 0.00957679π0.00957679\pi
998998 4.98550e9 0.158764
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 162.8.c.l.55.1 2
3.2 odd 2 162.8.c.a.55.1 2
9.2 odd 6 18.8.a.b.1.1 1
9.4 even 3 inner 162.8.c.l.109.1 2
9.5 odd 6 162.8.c.a.109.1 2
9.7 even 3 2.8.a.a.1.1 1
36.7 odd 6 16.8.a.b.1.1 1
36.11 even 6 144.8.a.i.1.1 1
45.2 even 12 450.8.c.g.199.2 2
45.7 odd 12 50.8.b.c.49.1 2
45.29 odd 6 450.8.a.c.1.1 1
45.34 even 6 50.8.a.g.1.1 1
45.38 even 12 450.8.c.g.199.1 2
45.43 odd 12 50.8.b.c.49.2 2
63.16 even 3 98.8.c.d.67.1 2
63.25 even 3 98.8.c.d.79.1 2
63.34 odd 6 98.8.a.a.1.1 1
63.52 odd 6 98.8.c.e.79.1 2
63.61 odd 6 98.8.c.e.67.1 2
72.11 even 6 576.8.a.f.1.1 1
72.29 odd 6 576.8.a.g.1.1 1
72.43 odd 6 64.8.a.e.1.1 1
72.61 even 6 64.8.a.c.1.1 1
99.43 odd 6 242.8.a.e.1.1 1
117.25 even 6 338.8.a.d.1.1 1
117.34 odd 12 338.8.b.d.337.1 2
117.70 odd 12 338.8.b.d.337.2 2
144.43 odd 12 256.8.b.f.129.2 2
144.61 even 12 256.8.b.b.129.2 2
144.115 odd 12 256.8.b.f.129.1 2
144.133 even 12 256.8.b.b.129.1 2
153.16 even 6 578.8.a.b.1.1 1
180.7 even 12 400.8.c.j.49.2 2
180.43 even 12 400.8.c.j.49.1 2
180.79 odd 6 400.8.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2.8.a.a.1.1 1 9.7 even 3
16.8.a.b.1.1 1 36.7 odd 6
18.8.a.b.1.1 1 9.2 odd 6
50.8.a.g.1.1 1 45.34 even 6
50.8.b.c.49.1 2 45.7 odd 12
50.8.b.c.49.2 2 45.43 odd 12
64.8.a.c.1.1 1 72.61 even 6
64.8.a.e.1.1 1 72.43 odd 6
98.8.a.a.1.1 1 63.34 odd 6
98.8.c.d.67.1 2 63.16 even 3
98.8.c.d.79.1 2 63.25 even 3
98.8.c.e.67.1 2 63.61 odd 6
98.8.c.e.79.1 2 63.52 odd 6
144.8.a.i.1.1 1 36.11 even 6
162.8.c.a.55.1 2 3.2 odd 2
162.8.c.a.109.1 2 9.5 odd 6
162.8.c.l.55.1 2 1.1 even 1 trivial
162.8.c.l.109.1 2 9.4 even 3 inner
242.8.a.e.1.1 1 99.43 odd 6
256.8.b.b.129.1 2 144.133 even 12
256.8.b.b.129.2 2 144.61 even 12
256.8.b.f.129.1 2 144.115 odd 12
256.8.b.f.129.2 2 144.43 odd 12
338.8.a.d.1.1 1 117.25 even 6
338.8.b.d.337.1 2 117.34 odd 12
338.8.b.d.337.2 2 117.70 odd 12
400.8.a.l.1.1 1 180.79 odd 6
400.8.c.j.49.1 2 180.43 even 12
400.8.c.j.49.2 2 180.7 even 12
450.8.a.c.1.1 1 45.29 odd 6
450.8.c.g.199.1 2 45.38 even 12
450.8.c.g.199.2 2 45.2 even 12
576.8.a.f.1.1 1 72.11 even 6
576.8.a.g.1.1 1 72.29 odd 6
578.8.a.b.1.1 1 153.16 even 6