Properties

Label 294.8.e.a.79.1
Level 294294
Weight 88
Character 294.79
Analytic conductor 91.84191.841
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] = [294,8,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 294=2372 294 = 2 \cdot 3 \cdot 7^{2}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 294.e (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: 91.841197492391.8411974923
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,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 79.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 294.79
Dual form 294.8.e.a.67.1

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+(4.00000+6.92820i)q2+(13.500023.3827i)q3+(32.000055.4256i)q4+(235.000+407.032i)q5+216.000q6+512.000q8+(364.500+631.333i)q9+(1880.003256.26i)q10+(3634.00+6294.27i)q11+(864.000+1496.49i)q12+11382.0q13+12690.0q15+(2048.00+3547.24i)q16+(10421.018049.7i)q17+(2916.005050.66i)q18+(6842.0011850.7i)q19+30080.0q2058144.0q22+(23368.040474.6i)q23+(6912.0011971.9i)q24+(71387.5123647.i)q25+(45528.0+78856.8i)q26+19683.0q27+2774.00q29+(50760.0+87918.9i)q30+(5616.00+9727.20i)q31+(16384.028377.9i)q32+(98118.0169945.i)q33+166736.q34+46656.0q36+(119849.207585.i)q37+(54736.0+94805.5i)q38+(153657.266142.i)q39+(120320.+208400.i)q40+52962.0q41874732.q43+(232576.402833.i)q44+(171315.296726.i)q45+(186944.+323797.i)q46+(225648.390834.i)q47+110592.q48+1.14220e6q50+(281367.+487342.i)q51+(364224.630854.i)q52+(971769.+1.68315e6i)q53+(78732.0+136368.i)q543.41596e6q55369468.q57+(11096.0+19218.8i)q58+(781954.1.35438e6i)q59+(406080.703351.i)q60+(1.59185e62.75716e6i)q6189856.0q62+262144.q64+(2.67477e6+4.63284e6i)q65+(784944.+1.35956e6i)q66+(1.06434e61.84349e6i)q67+(666944.+1.15518e6i)q681.26187e6q69+5.69454e6q71+(186624.+323242.i)q72+(1.12694e6+1.95192e6i)q73+(958792.+1.66068e6i)q74+(1.92746e6+3.33846e6i)q75875776.q76+2.45851e6q78+(66456.0+115105.i)q79+(962560.1.66720e6i)q80+(265720.460241.i)q81+(211848.+366931.i)q82+6.95052e6q83+9.79574e6q85+(3.49893e66.06032e6i)q86+(37449.064863.6i)q87+(1.86061e6+3.22267e6i)q88+(5.31326e69.20283e6i)q89+2.74104e6q902.99110e6q92+(151632.262634.i)q93+(1.80518e6+3.12667e6i)q94+(3.21574e6+5.56983e6i)q95+(442368.+766204.i)q96+2.40709e6q975.29837e6q99+O(q100)q+(-4.00000 + 6.92820i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-235.000 + 407.032i) q^{5} +216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(-1880.00 - 3256.26i) q^{10} +(3634.00 + 6294.27i) q^{11} +(-864.000 + 1496.49i) q^{12} +11382.0 q^{13} +12690.0 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-10421.0 - 18049.7i) q^{17} +(-2916.00 - 5050.66i) q^{18} +(6842.00 - 11850.7i) q^{19} +30080.0 q^{20} -58144.0 q^{22} +(23368.0 - 40474.6i) q^{23} +(-6912.00 - 11971.9i) q^{24} +(-71387.5 - 123647. i) q^{25} +(-45528.0 + 78856.8i) q^{26} +19683.0 q^{27} +2774.00 q^{29} +(-50760.0 + 87918.9i) q^{30} +(5616.00 + 9727.20i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(98118.0 - 169945. i) q^{33} +166736. q^{34} +46656.0 q^{36} +(119849. - 207585. i) q^{37} +(54736.0 + 94805.5i) q^{38} +(-153657. - 266142. i) q^{39} +(-120320. + 208400. i) q^{40} +52962.0 q^{41} -874732. q^{43} +(232576. - 402833. i) q^{44} +(-171315. - 296726. i) q^{45} +(186944. + 323797. i) q^{46} +(225648. - 390834. i) q^{47} +110592. q^{48} +1.14220e6 q^{50} +(-281367. + 487342. i) q^{51} +(-364224. - 630854. i) q^{52} +(971769. + 1.68315e6i) q^{53} +(-78732.0 + 136368. i) q^{54} -3.41596e6 q^{55} -369468. q^{57} +(-11096.0 + 19218.8i) q^{58} +(-781954. - 1.35438e6i) q^{59} +(-406080. - 703351. i) q^{60} +(1.59185e6 - 2.75716e6i) q^{61} -89856.0 q^{62} +262144. q^{64} +(-2.67477e6 + 4.63284e6i) q^{65} +(784944. + 1.35956e6i) q^{66} +(-1.06434e6 - 1.84349e6i) q^{67} +(-666944. + 1.15518e6i) q^{68} -1.26187e6 q^{69} +5.69454e6 q^{71} +(-186624. + 323242. i) q^{72} +(1.12694e6 + 1.95192e6i) q^{73} +(958792. + 1.66068e6i) q^{74} +(-1.92746e6 + 3.33846e6i) q^{75} -875776. q^{76} +2.45851e6 q^{78} +(-66456.0 + 115105. i) q^{79} +(-962560. - 1.66720e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-211848. + 366931. i) q^{82} +6.95052e6 q^{83} +9.79574e6 q^{85} +(3.49893e6 - 6.06032e6i) q^{86} +(-37449.0 - 64863.6i) q^{87} +(1.86061e6 + 3.22267e6i) q^{88} +(5.31326e6 - 9.20283e6i) q^{89} +2.74104e6 q^{90} -2.99110e6 q^{92} +(151632. - 262634. i) q^{93} +(1.80518e6 + 3.12667e6i) q^{94} +(3.21574e6 + 5.56983e6i) q^{95} +(-442368. + 766204. i) q^{96} +2.40709e6 q^{97} -5.29837e6 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q8q227q364q4470q5+432q6+1024q8729q93760q10+7268q111728q12+22764q13+25380q154096q1620842q175832q18+13684q19+10596744q99+O(q100) 2 q - 8 q^{2} - 27 q^{3} - 64 q^{4} - 470 q^{5} + 432 q^{6} + 1024 q^{8} - 729 q^{9} - 3760 q^{10} + 7268 q^{11} - 1728 q^{12} + 22764 q^{13} + 25380 q^{15} - 4096 q^{16} - 20842 q^{17} - 5832 q^{18} + 13684 q^{19}+ \cdots - 10596744 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/294Z)×\left(\mathbb{Z}/294\mathbb{Z}\right)^\times.

nn 197197 199199
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{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 −13.5000 23.3827i −0.288675 0.500000i
44 −32.0000 55.4256i −0.250000 0.433013i
55 −235.000 + 407.032i −0.840762 + 1.45624i 0.0484902 + 0.998824i 0.484559π0.484559\pi
−0.889252 + 0.457418i 0.848774π0.848774\pi
66 216.000 0.408248
77 0 0
88 512.000 0.353553
99 −364.500 + 631.333i −0.166667 + 0.288675i
1010 −1880.00 3256.26i −0.594508 1.02972i
1111 3634.00 + 6294.27i 0.823210 + 1.42584i 0.903280 + 0.429052i 0.141152π0.141152\pi
−0.0800700 + 0.996789i 0.525514π0.525514\pi
1212 −864.000 + 1496.49i −0.144338 + 0.250000i
1313 11382.0 1.43687 0.718434 0.695595i 0.244859π-0.244859\pi
0.718434 + 0.695595i 0.244859π0.244859\pi
1414 0 0
1515 12690.0 0.970828
1616 −2048.00 + 3547.24i −0.125000 + 0.216506i
1717 −10421.0 18049.7i −0.514444 0.891043i −0.999860 0.0167597i 0.994665π-0.994665\pi
0.485415 0.874284i 0.338668π-0.338668\pi
1818 −2916.00 5050.66i −0.117851 0.204124i
1919 6842.00 11850.7i 0.228847 0.396375i −0.728620 0.684919i 0.759838π-0.759838\pi
0.957467 + 0.288544i 0.0931711π0.0931711\pi
2020 30080.0 0.840762
2121 0 0
2222 −58144.0 −1.16419
2323 23368.0 40474.6i 0.400474 0.693641i −0.593309 0.804975i 0.702179π-0.702179\pi
0.993783 + 0.111334i 0.0355122π0.0355122\pi
2424 −6912.00 11971.9i −0.102062 0.176777i
2525 −71387.5 123647.i −0.913760 1.58268i
2626 −45528.0 + 78856.8i −0.508010 + 0.879898i
2727 19683.0 0.192450
2828 0 0
2929 2774.00 0.0211210 0.0105605 0.999944i 0.496638π-0.496638\pi
0.0105605 + 0.999944i 0.496638π0.496638\pi
3030 −50760.0 + 87918.9i −0.343239 + 0.594508i
3131 5616.00 + 9727.20i 0.0338580 + 0.0586438i 0.882458 0.470391i 0.155887π-0.155887\pi
−0.848600 + 0.529035i 0.822554π0.822554\pi
3232 −16384.0 28377.9i −0.0883883 0.153093i
3333 98118.0 169945.i 0.475280 0.823210i
3434 166736. 0.727534
3535 0 0
3636 46656.0 0.166667
3737 119849. 207585.i 0.388981 0.673735i −0.603332 0.797490i 0.706161π-0.706161\pi
0.992313 + 0.123755i 0.0394938π0.0394938\pi
3838 54736.0 + 94805.5i 0.161819 + 0.280279i
3939 −153657. 266142.i −0.414788 0.718434i
4040 −120320. + 208400.i −0.297254 + 0.514859i
4141 52962.0 0.120011 0.0600055 0.998198i 0.480888π-0.480888\pi
0.0600055 + 0.998198i 0.480888π0.480888\pi
4242 0 0
4343 −874732. −1.67778 −0.838891 0.544300i 0.816795π-0.816795\pi
−0.838891 + 0.544300i 0.816795π0.816795\pi
4444 232576. 402833.i 0.411605 0.712921i
4545 −171315. 296726.i −0.280254 0.485414i
4646 186944. + 323797.i 0.283178 + 0.490478i
4747 225648. 390834.i 0.317022 0.549098i −0.662843 0.748758i 0.730651π-0.730651\pi
0.979865 + 0.199660i 0.0639839π0.0639839\pi
4848 110592. 0.144338
4949 0 0
5050 1.14220e6 1.29225
5151 −281367. + 487342.i −0.297014 + 0.514444i
5252 −364224. 630854.i −0.359217 0.622182i
5353 971769. + 1.68315e6i 0.896597 + 1.55295i 0.831815 + 0.555053i 0.187302π0.187302\pi
0.0647824 + 0.997899i 0.479365π0.479365\pi
5454 −78732.0 + 136368.i −0.0680414 + 0.117851i
5555 −3.41596e6 −2.76849
5656 0 0
5757 −369468. −0.264250
5858 −11096.0 + 19218.8i −0.00746738 + 0.0129339i
5959 −781954. 1.35438e6i −0.495677 0.858539i 0.504310 0.863523i 0.331747π-0.331747\pi
−0.999988 + 0.00498408i 0.998414π0.998414\pi
6060 −406080. 703351.i −0.242707 0.420381i
6161 1.59185e6 2.75716e6i 0.897938 1.55527i 0.0678122 0.997698i 0.478398π-0.478398\pi
0.830126 0.557576i 0.188269π-0.188269\pi
6262 −89856.0 −0.0478824
6363 0 0
6464 262144. 0.125000
6565 −2.67477e6 + 4.63284e6i −1.20806 + 2.09243i
6666 784944. + 1.35956e6i 0.336074 + 0.582097i
6767 −1.06434e6 1.84349e6i −0.432334 0.748824i 0.564740 0.825269i 0.308977π-0.308977\pi
−0.997074 + 0.0764445i 0.975643π0.975643\pi
6868 −666944. + 1.15518e6i −0.257222 + 0.445522i
6969 −1.26187e6 −0.462427
7070 0 0
7171 5.69454e6 1.88823 0.944115 0.329617i 0.106920π-0.106920\pi
0.944115 + 0.329617i 0.106920π0.106920\pi
7272 −186624. + 323242.i −0.0589256 + 0.102062i
7373 1.12694e6 + 1.95192e6i 0.339055 + 0.587261i 0.984255 0.176753i 0.0565593π-0.0565593\pi
−0.645200 + 0.764014i 0.723226π0.723226\pi
7474 958792. + 1.66068e6i 0.275051 + 0.476402i
7575 −1.92746e6 + 3.33846e6i −0.527560 + 0.913760i
7676 −875776. −0.228847
7777 0 0
7878 2.45851e6 0.586599
7979 −66456.0 + 115105.i −0.0151649 + 0.0262664i −0.873508 0.486809i 0.838161π-0.838161\pi
0.858343 + 0.513076i 0.171494π0.171494\pi
8080 −962560. 1.66720e6i −0.210190 0.364060i
8181 −265720. 460241.i −0.0555556 0.0962250i
8282 −211848. + 366931.i −0.0424303 + 0.0734914i
8383 6.95052e6 1.33427 0.667136 0.744936i 0.267520π-0.267520\pi
0.667136 + 0.744936i 0.267520π0.267520\pi
8484 0 0
8585 9.79574e6 1.73010
8686 3.49893e6 6.06032e6i 0.593185 1.02743i
8787 −37449.0 64863.6i −0.00609709 0.0105605i
8888 1.86061e6 + 3.22267e6i 0.291049 + 0.504111i
8989 5.31326e6 9.20283e6i 0.798906 1.38375i −0.121423 0.992601i 0.538746π-0.538746\pi
0.920329 0.391145i 0.127921π-0.127921\pi
9090 2.74104e6 0.396339
9191 0 0
9292 −2.99110e6 −0.400474
9393 151632. 262634.i 0.0195479 0.0338580i
9494 1.80518e6 + 3.12667e6i 0.224168 + 0.388271i
9595 3.21574e6 + 5.56983e6i 0.384812 + 0.666513i
9696 −442368. + 766204.i −0.0510310 + 0.0883883i
9797 2.40709e6 0.267788 0.133894 0.990996i 0.457252π-0.457252\pi
0.133894 + 0.990996i 0.457252π0.457252\pi
9898 0 0
9999 −5.29837e6 −0.548807
100100 −4.56880e6 + 7.91339e6i −0.456880 + 0.791339i
101101 −3.88788e6 6.73400e6i −0.375481 0.650351i 0.614918 0.788591i 0.289189π-0.289189\pi
−0.990399 + 0.138239i 0.955856π0.955856\pi
102102 −2.25094e6 3.89874e6i −0.210021 0.363767i
103103 6.61701e6 1.14610e7i 0.596666 1.03346i −0.396643 0.917973i 0.629825π-0.629825\pi
0.993309 0.115484i 0.0368418π-0.0368418\pi
104104 5.82758e6 0.508010
105105 0 0
106106 −1.55483e7 −1.26798
107107 3.60472e6 6.24356e6i 0.284465 0.492708i −0.688014 0.725697i 0.741517π-0.741517\pi
0.972479 + 0.232989i 0.0748508π0.0748508\pi
108108 −629856. 1.09094e6i −0.0481125 0.0833333i
109109 −1.94519e6 3.36916e6i −0.143869 0.249189i 0.785081 0.619393i 0.212621π-0.212621\pi
−0.928951 + 0.370204i 0.879288π0.879288\pi
110110 1.36638e7 2.36665e7i 0.978810 1.69535i
111111 −6.47185e6 −0.449157
112112 0 0
113113 1.46647e7 0.956091 0.478046 0.878335i 0.341345π-0.341345\pi
0.478046 + 0.878335i 0.341345π0.341345\pi
114114 1.47787e6 2.55975e6i 0.0934264 0.161819i
115115 1.09830e7 + 1.90230e7i 0.673406 + 1.16637i
116116 −88768.0 153751.i −0.00528024 0.00914564i
117117 −4.14874e6 + 7.18583e6i −0.239478 + 0.414788i
118118 1.25113e7 0.700994
119119 0 0
120120 6.49728e6 0.343239
121121 −1.66683e7 + 2.88704e7i −0.855349 + 1.48151i
122122 1.27348e7 + 2.20573e7i 0.634938 + 1.09974i
123123 −714987. 1.23839e6i −0.0346442 0.0600055i
124124 359424. 622541.i 0.0169290 0.0293219i
125125 3.03855e7 1.39149
126126 0 0
127127 3.87331e6 0.167791 0.0838957 0.996475i 0.473264π-0.473264\pi
0.0838957 + 0.996475i 0.473264π0.473264\pi
128128 −1.04858e6 + 1.81619e6i −0.0441942 + 0.0765466i
129129 1.18089e7 + 2.04536e7i 0.484334 + 0.838891i
130130 −2.13982e7 3.70627e7i −0.854230 1.47957i
131131 −1.13738e7 + 1.97000e7i −0.442035 + 0.765627i −0.997840 0.0656854i 0.979077π-0.979077\pi
0.555805 + 0.831312i 0.312410π0.312410\pi
132132 −1.25591e7 −0.475280
133133 0 0
134134 1.70295e7 0.611413
135135 −4.62550e6 + 8.01161e6i −0.161805 + 0.280254i
136136 −5.33555e6 9.24145e6i −0.181883 0.315031i
137137 2.11191e7 + 3.65794e7i 0.701703 + 1.21539i 0.967868 + 0.251458i 0.0809100π0.0809100\pi
−0.266165 + 0.963927i 0.585757π0.585757\pi
138138 5.04749e6 8.74251e6i 0.163493 0.283178i
139139 −2.02320e6 −0.0638978 −0.0319489 0.999490i 0.510171π-0.510171\pi
−0.0319489 + 0.999490i 0.510171π0.510171\pi
140140 0 0
141141 −1.21850e7 −0.366065
142142 −2.27782e7 + 3.94530e7i −0.667590 + 1.15630i
143143 4.13622e7 + 7.16414e7i 1.18284 + 2.04875i
144144 −1.49299e6 2.58594e6i −0.0416667 0.0721688i
145145 −651890. + 1.12911e6i −0.0177577 + 0.0307572i
146146 −1.80310e7 −0.479496
147147 0 0
148148 −1.53407e7 −0.388981
149149 −3.16509e7 + 5.48209e7i −0.783851 + 1.35767i 0.145832 + 0.989309i 0.453414π0.453414\pi
−0.929683 + 0.368360i 0.879919π0.879919\pi
150150 −1.54197e7 2.67077e7i −0.373041 0.646126i
151151 2.69813e7 + 4.67330e7i 0.637739 + 1.10460i 0.985928 + 0.167173i 0.0534637π0.0534637\pi
−0.348188 + 0.937425i 0.613203π0.613203\pi
152152 3.50310e6 6.06755e6i 0.0809097 0.140140i
153153 1.51938e7 0.342963
154154 0 0
155155 −5.27904e6 −0.113866
156156 −9.83405e6 + 1.70331e7i −0.207394 + 0.359217i
157157 −2.91683e7 5.05211e7i −0.601538 1.04189i −0.992588 0.121525i 0.961222π-0.961222\pi
0.391050 0.920369i 0.372112π-0.372112\pi
158158 −531648. 920841.i −0.0107232 0.0185731i
159159 2.62378e7 4.54451e7i 0.517651 0.896597i
160160 1.54010e7 0.297254
161161 0 0
162162 4.25153e6 0.0785674
163163 −3.02922e7 + 5.24677e7i −0.547867 + 0.948933i 0.450554 + 0.892749i 0.351227π0.351227\pi
−0.998420 + 0.0561836i 0.982107π0.982107\pi
164164 −1.69478e6 2.93545e6i −0.0300027 0.0519663i
165165 4.61155e7 + 7.98743e7i 0.799195 + 1.38425i
166166 −2.78021e7 + 4.81546e7i −0.471736 + 0.817071i
167167 5.94193e7 0.987234 0.493617 0.869680i 0.335675π-0.335675\pi
0.493617 + 0.869680i 0.335675π0.335675\pi
168168 0 0
169169 6.68014e7 1.06459
170170 −3.91830e7 + 6.78669e7i −0.611682 + 1.05947i
171171 4.98782e6 + 8.63915e6i 0.0762824 + 0.132125i
172172 2.79914e7 + 4.84826e7i 0.419445 + 0.726501i
173173 −2.79283e7 + 4.83732e7i −0.410094 + 0.710303i −0.994900 0.100870i 0.967837π-0.967837\pi
0.584806 + 0.811173i 0.301171π0.301171\pi
174174 599184. 0.00862259
175175 0 0
176176 −2.97697e7 −0.411605
177177 −2.11128e7 + 3.65684e7i −0.286180 + 0.495677i
178178 4.25060e7 + 7.36226e7i 0.564912 + 0.978456i
179179 −4.01126e7 6.94771e7i −0.522752 0.905432i −0.999650 0.0264736i 0.991572π-0.991572\pi
0.476898 0.878959i 0.341761π-0.341761\pi
180180 −1.09642e7 + 1.89905e7i −0.140127 + 0.242707i
181181 −7.18632e7 −0.900807 −0.450403 0.892825i 0.648720π-0.648720\pi
−0.450403 + 0.892825i 0.648720π0.648720\pi
182182 0 0
183183 −8.59596e7 −1.03685
184184 1.19644e7 2.07230e7i 0.141589 0.245239i
185185 5.63290e7 + 9.75647e7i 0.654081 + 1.13290i
186186 1.21306e6 + 2.10107e6i 0.0138225 + 0.0239412i
187187 7.57398e7 1.31185e8i 0.846991 1.46703i
188188 −2.88829e7 −0.317022
189189 0 0
190190 −5.14518e7 −0.544206
191191 8.37176e6 1.45003e7i 0.0869361 0.150578i −0.819278 0.573396i 0.805626π-0.805626\pi
0.906215 + 0.422818i 0.138959π0.138959\pi
192192 −3.53894e6 6.12963e6i −0.0360844 0.0625000i
193193 6.73511e7 + 1.16656e8i 0.674364 + 1.16803i 0.976654 + 0.214816i 0.0689153π0.0689153\pi
−0.302291 + 0.953216i 0.597751π0.597751\pi
194194 −9.62836e6 + 1.66768e7i −0.0946774 + 0.163986i
195195 1.44438e8 1.39495
196196 0 0
197197 −5.89413e7 −0.549273 −0.274636 0.961548i 0.588557π-0.588557\pi
−0.274636 + 0.961548i 0.588557π0.588557\pi
198198 2.11935e7 3.67082e7i 0.194032 0.336074i
199199 −6.56866e7 1.13773e8i −0.590869 1.02341i −0.994116 0.108324i 0.965452π-0.965452\pi
0.403247 0.915091i 0.367882π-0.367882\pi
200200 −3.65504e7 6.33071e7i −0.323063 0.559561i
201201 −2.87372e7 + 4.97743e7i −0.249608 + 0.432334i
202202 6.22060e7 0.531010
203203 0 0
204204 3.60150e7 0.297014
205205 −1.24461e7 + 2.15572e7i −0.100901 + 0.174765i
206206 5.29361e7 + 9.16880e7i 0.421907 + 0.730764i
207207 1.70353e7 + 2.95060e7i 0.133491 + 0.231214i
208208 −2.33103e7 + 4.03747e7i −0.179608 + 0.311091i
209209 9.94553e7 0.753557
210210 0 0
211211 −2.96600e7 −0.217362 −0.108681 0.994077i 0.534663π-0.534663\pi
−0.108681 + 0.994077i 0.534663π0.534663\pi
212212 6.21932e7 1.07722e8i 0.448299 0.776476i
213213 −7.68763e7 1.33154e8i −0.545085 0.944115i
214214 2.88378e7 + 4.99485e7i 0.201147 + 0.348397i
215215 2.05562e8 3.56044e8i 1.41061 2.44326i
216216 1.00777e7 0.0680414
217217 0 0
218218 3.11230e7 0.203462
219219 3.04274e7 5.27017e7i 0.195754 0.339055i
220220 1.09311e8 + 1.89332e8i 0.692123 + 1.19879i
221221 −1.18612e8 2.05442e8i −0.739188 1.28031i
222222 2.58874e7 4.48383e7i 0.158801 0.275051i
223223 3.16037e8 1.90841 0.954203 0.299161i 0.0967068π-0.0967068\pi
0.954203 + 0.299161i 0.0967068π0.0967068\pi
224224 0 0
225225 1.04083e8 0.609173
226226 −5.86589e7 + 1.01600e8i −0.338029 + 0.585484i
227227 −2.38028e7 4.12277e7i −0.135063 0.233937i 0.790558 0.612387i 0.209790π-0.209790\pi
−0.925622 + 0.378450i 0.876457π0.876457\pi
228228 1.18230e7 + 2.04780e7i 0.0660625 + 0.114424i
229229 5.21444e7 9.03168e7i 0.286935 0.496986i −0.686142 0.727468i 0.740697π-0.740697\pi
0.973077 + 0.230482i 0.0740303π0.0740303\pi
230230 −1.75727e8 −0.952340
231231 0 0
232232 1.42029e6 0.00746738
233233 −1.17529e8 + 2.03567e8i −0.608697 + 1.05429i 0.382759 + 0.923848i 0.374974π0.374974\pi
−0.991456 + 0.130445i 0.958359π0.958359\pi
234234 −3.31899e7 5.74866e7i −0.169337 0.293299i
235235 1.06055e8 + 1.83692e8i 0.533079 + 0.923320i
236236 −5.00451e7 + 8.66806e7i −0.247839 + 0.429269i
237237 3.58862e6 0.0175109
238238 0 0
239239 3.74362e7 0.177378 0.0886888 0.996059i 0.471732π-0.471732\pi
0.0886888 + 0.996059i 0.471732π0.471732\pi
240240 −2.59891e7 + 4.50145e7i −0.121353 + 0.210190i
241241 −4.93834e6 8.55345e6i −0.0227259 0.0393624i 0.854439 0.519552i 0.173901π-0.173901\pi
−0.877165 + 0.480190i 0.840568π0.840568\pi
242242 −1.33347e8 2.30963e8i −0.604823 1.04758i
243243 −7.17445e6 + 1.24265e7i −0.0320750 + 0.0555556i
244244 −2.03756e8 −0.897938
245245 0 0
246246 1.14398e7 0.0489943
247247 7.78756e7 1.34885e8i 0.328823 0.569538i
248248 2.87539e6 + 4.98033e6i 0.0119706 + 0.0207337i
249249 −9.38321e7 1.62522e8i −0.385171 0.667136i
250250 −1.21542e8 + 2.10517e8i −0.491967 + 0.852113i
251251 1.32438e8 0.528634 0.264317 0.964436i 0.414853π-0.414853\pi
0.264317 + 0.964436i 0.414853π0.414853\pi
252252 0 0
253253 3.39677e8 1.31870
254254 −1.54932e7 + 2.68351e7i −0.0593232 + 0.102751i
255255 −1.32242e8 2.29051e8i −0.499437 0.865050i
256256 −8.38861e6 1.45295e7i −0.0312500 0.0541266i
257257 −1.66334e8 + 2.88098e8i −0.611243 + 1.05870i 0.379788 + 0.925074i 0.375997π0.375997\pi
−0.991031 + 0.133631i 0.957336π0.957336\pi
258258 −1.88942e8 −0.684951
259259 0 0
260260 3.42371e8 1.20806
261261 −1.01112e6 + 1.75132e6i −0.00352016 + 0.00609709i
262262 −9.09905e7 1.57600e8i −0.312566 0.541380i
263263 4.75614e7 + 8.23788e7i 0.161217 + 0.279235i 0.935305 0.353842i 0.115125π-0.115125\pi
−0.774089 + 0.633077i 0.781792π0.781792\pi
264264 5.02364e7 8.70120e7i 0.168037 0.291049i
265265 −9.13463e8 −3.01530
266266 0 0
267267 −2.86916e8 −0.922497
268268 −6.81179e7 + 1.17984e8i −0.216167 + 0.374412i
269269 1.34427e8 + 2.32835e8i 0.421071 + 0.729316i 0.996044 0.0888560i 0.0283211π-0.0283211\pi
−0.574974 + 0.818172i 0.694988π0.694988\pi
270270 −3.70040e7 6.40929e7i −0.114413 0.198169i
271271 −2.26442e8 + 3.92209e8i −0.691137 + 1.19708i 0.280329 + 0.959904i 0.409557π0.409557\pi
−0.971466 + 0.237180i 0.923777π0.923777\pi
272272 8.53688e7 0.257222
273273 0 0
274274 −3.37906e8 −0.992358
275275 5.18844e8 8.98665e8i 1.50443 2.60575i
276276 4.03799e7 + 6.99400e7i 0.115607 + 0.200237i
277277 8.23547e6 + 1.42643e7i 0.0232814 + 0.0403246i 0.877431 0.479702i 0.159255π-0.159255\pi
−0.854150 + 0.520027i 0.825922π0.825922\pi
278278 8.09278e6 1.40171e7i 0.0225913 0.0391293i
279279 −8.18813e6 −0.0225720
280280 0 0
281281 5.08113e8 1.36612 0.683059 0.730363i 0.260649π-0.260649\pi
0.683059 + 0.730363i 0.260649π0.260649\pi
282282 4.87400e7 8.44201e7i 0.129424 0.224168i
283283 1.28748e8 + 2.22998e8i 0.337666 + 0.584855i 0.983993 0.178205i 0.0570291π-0.0570291\pi
−0.646327 + 0.763061i 0.723696π0.723696\pi
284284 −1.82225e8 3.15624e8i −0.472057 0.817627i
285285 8.68250e7 1.50385e8i 0.222171 0.384812i
286286 −6.61795e8 −1.67279
287287 0 0
288288 2.38879e7 0.0589256
289289 −1.20251e7 + 2.08282e7i −0.0293054 + 0.0507585i
290290 −5.21512e6 9.03285e6i −0.0125566 0.0217486i
291291 −3.24957e7 5.62842e7i −0.0773038 0.133894i
292292 7.21241e7 1.24923e8i 0.169528 0.293630i
293293 7.33847e7 0.170439 0.0852195 0.996362i 0.472841π-0.472841\pi
0.0852195 + 0.996362i 0.472841π0.472841\pi
294294 0 0
295295 7.35037e8 1.66699
296296 6.13627e7 1.06283e8i 0.137526 0.238201i
297297 7.15280e7 + 1.23890e8i 0.158427 + 0.274403i
298298 −2.53207e8 4.38567e8i −0.554266 0.960017i
299299 2.65975e8 4.60681e8i 0.575428 0.996670i
300300 2.46715e8 0.527560
301301 0 0
302302 −4.31701e8 −0.901900
303303 −1.04973e8 + 1.81818e8i −0.216784 + 0.375481i
304304 2.80248e7 + 4.85404e7i 0.0572118 + 0.0990937i
305305 7.48167e8 + 1.29586e9i 1.50990 + 2.61523i
306306 −6.07753e7 + 1.05266e8i −0.121256 + 0.210021i
307307 −9.31624e7 −0.183762 −0.0918811 0.995770i 0.529288π-0.529288\pi
−0.0918811 + 0.995770i 0.529288π0.529288\pi
308308 0 0
309309 −3.57319e8 −0.688971
310310 2.11162e7 3.65743e7i 0.0402577 0.0697284i
311311 −3.05467e8 5.29085e8i −0.575842 0.997387i −0.995950 0.0899130i 0.971341π-0.971341\pi
0.420108 0.907474i 0.361992π-0.361992\pi
312312 −7.86724e7 1.36265e8i −0.146650 0.254005i
313313 1.06115e8 1.83797e8i 0.195602 0.338793i −0.751496 0.659738i 0.770667π-0.770667\pi
0.947098 + 0.320945i 0.104001π0.104001\pi
314314 4.66694e8 0.850703
315315 0 0
316316 8.50637e6 0.0151649
317317 5.51972e8 9.56044e8i 0.973218 1.68566i 0.287522 0.957774i 0.407168π-0.407168\pi
0.685695 0.727889i 0.259498π-0.259498\pi
318318 2.09902e8 + 3.63561e8i 0.366034 + 0.633990i
319319 1.00807e7 + 1.74603e7i 0.0173870 + 0.0301151i
320320 −6.16038e7 + 1.06701e8i −0.105095 + 0.182030i
321321 −1.94655e8 −0.328472
322322 0 0
323323 −2.85202e8 −0.470916
324324 −1.70061e7 + 2.94555e7i −0.0277778 + 0.0481125i
325325 −8.12533e8 1.40735e9i −1.31295 2.27410i
326326 −2.42338e8 4.19742e8i −0.387400 0.670997i
327327 −5.25200e7 + 9.09674e7i −0.0830631 + 0.143869i
328328 2.71165e7 0.0424303
329329 0 0
330330 −7.37847e8 −1.13023
331331 3.35294e8 5.80746e8i 0.508192 0.880214i −0.491763 0.870729i 0.663647π-0.663647\pi
0.999955 0.00948492i 0.00301919π-0.00301919\pi
332332 −2.22417e8 3.85237e8i −0.333568 0.577757i
333333 8.73699e7 + 1.51329e8i 0.129660 + 0.224578i
334334 −2.37677e8 + 4.11669e8i −0.349040 + 0.604555i
335335 1.00048e9 1.45396
336336 0 0
337337 −6.84122e8 −0.973709 −0.486854 0.873483i 0.661856π-0.661856\pi
−0.486854 + 0.873483i 0.661856π0.661856\pi
338338 −2.67206e8 + 4.62814e8i −0.376389 + 0.651925i
339339 −1.97974e8 3.42901e8i −0.276000 0.478046i
340340 −3.13464e8 5.42935e8i −0.432525 0.749155i
341341 −4.08171e7 + 7.06973e7i −0.0557445 + 0.0965522i
342342 −7.98051e7 −0.107880
343343 0 0
344344 −4.47863e8 −0.593185
345345 2.96540e8 5.13622e8i 0.388791 0.673406i
346346 −2.23426e8 3.86986e8i −0.289980 0.502260i
347347 −2.18776e8 3.78932e8i −0.281091 0.486865i 0.690562 0.723273i 0.257363π-0.257363\pi
−0.971654 + 0.236408i 0.924030π0.924030\pi
348348 −2.39674e6 + 4.15127e6i −0.00304855 + 0.00528024i
349349 9.39833e6 0.0118348 0.00591741 0.999982i 0.498116π-0.498116\pi
0.00591741 + 0.999982i 0.498116π0.498116\pi
350350 0 0
351351 2.24032e8 0.276525
352352 1.19079e8 2.06251e8i 0.145524 0.252055i
353353 −7.07359e8 1.22518e9i −0.855911 1.48248i −0.875797 0.482679i 0.839664π-0.839664\pi
0.0198865 0.999802i 0.493670π-0.493670\pi
354354 −1.68902e8 2.92547e8i −0.202359 0.350497i
355355 −1.33822e9 + 2.31786e9i −1.58755 + 2.74972i
356356 −6.80097e8 −0.798906
357357 0 0
358358 6.41802e8 0.739282
359359 1.53792e8 2.66375e8i 0.175429 0.303852i −0.764881 0.644172i 0.777202π-0.777202\pi
0.940310 + 0.340320i 0.110535π0.110535\pi
360360 −8.77133e7 1.51924e8i −0.0990847 0.171620i
361361 3.53310e8 + 6.11951e8i 0.395258 + 0.684607i
362362 2.87453e8 4.97883e8i 0.318483 0.551629i
363363 9.00090e8 0.987672
364364 0 0
365365 −1.05932e9 −1.14026
366366 3.43839e8 5.95546e8i 0.366582 0.634938i
367367 6.15636e8 + 1.06631e9i 0.650119 + 1.12604i 0.983094 + 0.183103i 0.0586143π0.0586143\pi
−0.332975 + 0.942936i 0.608052π0.608052\pi
368368 9.57153e7 + 1.65784e8i 0.100118 + 0.173410i
369369 −1.93046e7 + 3.34366e7i −0.0200018 + 0.0346442i
370370 −9.01264e8 −0.925010
371371 0 0
372372 −1.94089e7 −0.0195479
373373 −9.17958e8 + 1.58995e9i −0.915887 + 1.58636i −0.110291 + 0.993899i 0.535178π0.535178\pi
−0.805597 + 0.592464i 0.798155π0.798155\pi
374374 6.05919e8 + 1.04948e9i 0.598913 + 1.03735i
375375 −4.10204e8 7.10495e8i −0.401690 0.695747i
376376 1.15532e8 2.00107e8i 0.112084 0.194135i
377377 3.15737e7 0.0303480
378378 0 0
379379 −6.48934e8 −0.612298 −0.306149 0.951984i 0.599041π-0.599041\pi
−0.306149 + 0.951984i 0.599041π0.599041\pi
380380 2.05807e8 3.56469e8i 0.192406 0.333257i
381381 −5.22897e7 9.05684e7i −0.0484372 0.0838957i
382382 6.69741e7 + 1.16003e8i 0.0614731 + 0.106475i
383383 3.40160e8 5.89175e8i 0.309377 0.535857i −0.668849 0.743398i 0.733213π-0.733213\pi
0.978226 + 0.207541i 0.0665462π0.0665462\pi
384384 5.66231e7 0.0510310
385385 0 0
386386 −1.07762e9 −0.953694
387387 3.18840e8 5.52247e8i 0.279630 0.484334i
388388 −7.70269e7 1.33414e8i −0.0669470 0.115956i
389389 −1.36853e8 2.37036e8i −0.117877 0.204169i 0.801049 0.598599i 0.204276π-0.204276\pi
−0.918926 + 0.394430i 0.870942π0.870942\pi
390390 −5.77750e8 + 1.00069e9i −0.493190 + 0.854230i
391391 −9.74072e8 −0.824086
392392 0 0
393393 6.14186e8 0.510418
394394 2.35765e8 4.08357e8i 0.194197 0.336359i
395395 −3.12343e7 5.40994e7i −0.0255001 0.0441675i
396396 1.69548e8 + 2.93666e8i 0.137202 + 0.237640i
397397 6.05171e8 1.04819e9i 0.485413 0.840759i −0.514447 0.857522i 0.672003π-0.672003\pi
0.999859 + 0.0167629i 0.00533605π0.00533605\pi
398398 1.05099e9 0.835615
399399 0 0
400400 5.84806e8 0.456880
401401 2.98551e8 5.17106e8i 0.231214 0.400474i −0.726952 0.686688i 0.759064π-0.759064\pi
0.958166 + 0.286215i 0.0923970π0.0923970\pi
402402 −2.29898e8 3.98195e8i −0.176500 0.305706i
403403 6.39213e7 + 1.10715e8i 0.0486495 + 0.0842633i
404404 −2.48824e8 + 4.30976e8i −0.187740 + 0.325176i
405405 2.49777e8 0.186836
406406 0 0
407407 1.74213e9 1.28085
408408 −1.44060e8 + 2.49519e8i −0.105010 + 0.181883i
409409 5.98836e8 + 1.03721e9i 0.432789 + 0.749612i 0.997112 0.0759416i 0.0241962π-0.0241962\pi
−0.564323 + 0.825554i 0.690863π0.690863\pi
410410 −9.95686e7 1.72458e8i −0.0713475 0.123577i
411411 5.70216e8 9.87643e8i 0.405128 0.701703i
412412 −8.46978e8 −0.596666
413413 0 0
414414 −2.72564e8 −0.188785
415415 −1.63337e9 + 2.82909e9i −1.12180 + 1.94302i
416416 −1.86483e8 3.22997e8i −0.127002 0.219975i
417417 2.73131e7 + 4.73078e7i 0.0184457 + 0.0319489i
418418 −3.97821e8 + 6.89047e8i −0.266423 + 0.461457i
419419 −1.68680e9 −1.12025 −0.560125 0.828408i 0.689247π-0.689247\pi
−0.560125 + 0.828408i 0.689247π0.689247\pi
420420 0 0
421421 −9.60356e8 −0.627256 −0.313628 0.949546i 0.601544π-0.601544\pi
−0.313628 + 0.949546i 0.601544π0.601544\pi
422422 1.18640e8 2.05491e8i 0.0768489 0.133106i
423423 1.64497e8 + 2.84918e8i 0.105674 + 0.183033i
424424 4.97546e8 + 8.61774e8i 0.316995 + 0.549052i
425425 −1.48786e9 + 2.57705e9i −0.940157 + 1.62840i
426426 1.23002e9 0.770866
427427 0 0
428428 −4.61404e8 −0.284465
429429 1.11678e9 1.93432e9i 0.682915 1.18284i
430430 1.64450e9 + 2.84835e9i 0.997455 + 1.72764i
431431 5.15829e7 + 8.93442e7i 0.0310338 + 0.0537522i 0.881125 0.472883i 0.156787π-0.156787\pi
−0.850091 + 0.526635i 0.823453π0.823453\pi
432432 −4.03108e7 + 6.98203e7i −0.0240563 + 0.0416667i
433433 −2.33278e9 −1.38091 −0.690455 0.723375i 0.742590π-0.742590\pi
−0.690455 + 0.723375i 0.742590π0.742590\pi
434434 0 0
435435 3.52021e7 0.0205048
436436 −1.24492e8 + 2.15626e8i −0.0719347 + 0.124595i
437437 −3.19768e8 5.53854e8i −0.183295 0.317475i
438438 2.43419e8 + 4.21614e8i 0.138419 + 0.239748i
439439 7.80794e8 1.35237e9i 0.440464 0.762906i −0.557260 0.830338i 0.688147π-0.688147\pi
0.997724 + 0.0674320i 0.0214806π0.0214806\pi
440440 −1.74897e9 −0.978810
441441 0 0
442442 1.89779e9 1.04537
443443 −8.12404e8 + 1.40712e9i −0.443975 + 0.768988i −0.997980 0.0635255i 0.979766π-0.979766\pi
0.554005 + 0.832513i 0.313099π0.313099\pi
444444 2.07099e8 + 3.58706e8i 0.112289 + 0.194490i
445445 2.49723e9 + 4.32533e9i 1.34338 + 2.32680i
446446 −1.26415e9 + 2.18957e9i −0.674723 + 1.16865i
447447 1.70915e9 0.905113
448448 0 0
449449 −8.18478e8 −0.426722 −0.213361 0.976973i 0.568441π-0.568441\pi
−0.213361 + 0.976973i 0.568441π0.568441\pi
450450 −4.16332e8 + 7.21108e8i −0.215375 + 0.373041i
451451 1.92464e8 + 3.33357e8i 0.0987942 + 0.171117i
452452 −4.69271e8 8.12801e8i −0.239023 0.414000i
453453 7.28495e8 1.26179e9i 0.368199 0.637739i
454454 3.80845e8 0.191008
455455 0 0
456456 −1.89168e8 −0.0934264
457457 7.66628e8 1.32784e9i 0.375732 0.650786i −0.614705 0.788757i 0.710725π-0.710725\pi
0.990436 + 0.137971i 0.0440581π0.0440581\pi
458458 4.17155e8 + 7.22534e8i 0.202894 + 0.351422i
459459 −2.05117e8 3.55272e8i −0.0990048 0.171481i
460460 7.02909e8 1.21747e9i 0.336703 0.583187i
461461 3.43507e9 1.63299 0.816494 0.577354i 0.195915π-0.195915\pi
0.816494 + 0.577354i 0.195915π0.195915\pi
462462 0 0
463463 1.73200e9 0.810990 0.405495 0.914097i 0.367099π-0.367099\pi
0.405495 + 0.914097i 0.367099π0.367099\pi
464464 −5.68115e6 + 9.84004e6i −0.00264012 + 0.00457282i
465465 7.12670e7 + 1.23438e8i 0.0328703 + 0.0569330i
466466 −9.40236e8 1.62854e9i −0.430414 0.745498i
467467 2.40744e8 4.16980e8i 0.109382 0.189455i −0.806138 0.591728i 0.798446π-0.798446\pi
0.915520 + 0.402272i 0.131779π0.131779\pi
468468 5.31039e8 0.239478
469469 0 0
470470 −1.69687e9 −0.753888
471471 −7.87545e8 + 1.36407e9i −0.347298 + 0.601538i
472472 −4.00360e8 6.93445e8i −0.175248 0.303539i
473473 −3.17878e9 5.50580e9i −1.38117 2.39225i
474474 −1.43545e7 + 2.48627e7i −0.00619104 + 0.0107232i
475475 −1.95373e9 −0.836445
476476 0 0
477477 −1.41684e9 −0.597732
478478 −1.49745e8 + 2.59365e8i −0.0627125 + 0.108621i
479479 8.29697e8 + 1.43708e9i 0.344941 + 0.597456i 0.985343 0.170584i 0.0545655π-0.0545655\pi
−0.640402 + 0.768040i 0.721232π0.721232\pi
480480 −2.07913e8 3.60116e8i −0.0858099 0.148627i
481481 1.36412e9 2.36273e9i 0.558914 0.968068i
482482 7.90134e7 0.0321393
483483 0 0
484484 2.13355e9 0.855349
485485 −5.65666e8 + 9.79763e8i −0.225146 + 0.389964i
486486 −5.73956e7 9.94121e7i −0.0226805 0.0392837i
487487 −8.60083e8 1.48971e9i −0.337434 0.584453i 0.646515 0.762901i 0.276226π-0.276226\pi
−0.983949 + 0.178448i 0.942892π0.942892\pi
488488 8.15025e8 1.41166e9i 0.317469 0.549872i
489489 1.63578e9 0.632622
490490 0 0
491491 −6.67098e8 −0.254334 −0.127167 0.991881i 0.540588π-0.540588\pi
−0.127167 + 0.991881i 0.540588π0.540588\pi
492492 −4.57592e7 + 7.92572e7i −0.0173221 + 0.0300027i
493493 −2.89079e7 5.00699e7i −0.0108655 0.0188197i
494494 6.23005e8 + 1.07908e9i 0.232513 + 0.402724i
495495 1.24512e9 2.15661e9i 0.461415 0.799195i
496496 −4.60063e7 −0.0169290
497497 0 0
498498 1.50131e9 0.544714
499499 2.72989e8 4.72830e8i 0.0983541 0.170354i −0.812649 0.582753i 0.801976π-0.801976\pi
0.911004 + 0.412399i 0.135309π0.135309\pi
500500 −9.72336e8 1.68414e9i −0.347874 0.602535i
501501 −8.02161e8 1.38938e9i −0.284990 0.493617i
502502 −5.29753e8 + 9.17559e8i −0.186900 + 0.323721i
503503 4.13284e9 1.44797 0.723987 0.689813i 0.242307π-0.242307\pi
0.723987 + 0.689813i 0.242307π0.242307\pi
504504 0 0
505505 3.65460e9 1.26276
506506 −1.35871e9 + 2.35335e9i −0.466229 + 0.807533i
507507 −9.01819e8 1.56200e9i −0.307320 0.532295i
508508 −1.23946e8 2.14681e8i −0.0419478 0.0726558i
509509 9.56065e8 1.65595e9i 0.321348 0.556590i −0.659419 0.751776i 0.729198π-0.729198\pi
0.980766 + 0.195185i 0.0625309π0.0625309\pi
510510 2.11588e9 0.706310
511511 0 0
512512 1.34218e8 0.0441942
513513 1.34671e8 2.33257e8i 0.0440417 0.0762824i
514514 −1.33067e9 2.30479e9i −0.432214 0.748617i
515515 3.11000e9 + 5.38667e9i 1.00331 + 1.73778i
516516 7.55768e8 1.30903e9i 0.242167 0.419445i
517517 3.28002e9 1.04390
518518 0 0
519519 1.50813e9 0.473536
520520 −1.36948e9 + 2.37201e9i −0.427115 + 0.739785i
521521 −3.10587e7 5.37952e7i −0.00962169 0.0166652i 0.861174 0.508309i 0.169729π-0.169729\pi
−0.870796 + 0.491644i 0.836396π0.836396\pi
522522 −8.08898e6 1.40105e7i −0.00248913 0.00431130i
523523 −3.41037e8 + 5.90694e8i −0.104243 + 0.180554i −0.913429 0.406999i 0.866575π-0.866575\pi
0.809186 + 0.587553i 0.199909π0.199909\pi
524524 1.45585e9 0.442035
525525 0 0
526526 −7.60983e8 −0.227995
527527 1.17049e8 2.02734e8i 0.0348361 0.0603379i
528528 4.01891e8 + 6.96096e8i 0.118820 + 0.205802i
529529 6.10286e8 + 1.05705e9i 0.179241 + 0.310455i
530530 3.65385e9 6.32866e9i 1.06607 1.84649i
531531 1.14009e9 0.330452
532532 0 0
533533 6.02813e8 0.172440
534534 1.14766e9 1.98781e9i 0.326152 0.564912i
535535 1.69422e9 + 2.93447e9i 0.478334 + 0.828499i
536536 −5.44943e8 9.43869e8i −0.152853 0.264749i
537537 −1.08304e9 + 1.87588e9i −0.301811 + 0.522752i
538538 −2.15084e9 −0.595484
539539 0 0
540540 5.92065e8 0.161805
541541 −1.10271e8 + 1.90994e8i −0.0299412 + 0.0518597i −0.880608 0.473846i 0.842865π-0.842865\pi
0.850667 + 0.525706i 0.176199π0.176199\pi
542542 −1.81153e9 3.13767e9i −0.488708 0.846466i
543543 9.70153e8 + 1.68036e9i 0.260041 + 0.450403i
544544 −3.41475e8 + 5.91453e8i −0.0909417 + 0.157516i
545545 1.82848e9 0.483840
546546 0 0
547547 5.39461e9 1.40930 0.704652 0.709553i 0.251103π-0.251103\pi
0.704652 + 0.709553i 0.251103π0.251103\pi
548548 1.35162e9 2.34108e9i 0.350852 0.607693i
549549 1.16046e9 + 2.00997e9i 0.299313 + 0.518425i
550550 4.15075e9 + 7.18932e9i 1.06379 + 1.84255i
551551 1.89797e7 3.28738e7i 0.00483347 0.00837181i
552552 −6.46078e8 −0.163493
553553 0 0
554554 −1.31768e8 −0.0329249
555555 1.52088e9 2.63425e9i 0.377634 0.654081i
556556 6.47423e7 + 1.12137e8i 0.0159745 + 0.0276686i
557557 6.11934e8 + 1.05990e9i 0.150041 + 0.259879i 0.931242 0.364400i 0.118726π-0.118726\pi
−0.781201 + 0.624280i 0.785393π0.785393\pi
558558 3.27525e7 5.67290e7i 0.00798040 0.0138225i
559559 −9.95620e9 −2.41075
560560 0 0
561561 −4.08995e9 −0.978021
562562 −2.03245e9 + 3.52031e9i −0.482996 + 0.836574i
563563 1.83547e9 + 3.17913e9i 0.433479 + 0.750807i 0.997170 0.0751784i 0.0239526π-0.0239526\pi
−0.563691 + 0.825985i 0.690619π0.690619\pi
564564 3.89920e8 + 6.75361e8i 0.0915163 + 0.158511i
565565 −3.44621e9 + 5.96901e9i −0.803845 + 1.39230i
566566 −2.05997e9 −0.477532
567567 0 0
568568 2.91561e9 0.667590
569569 −2.50185e9 + 4.33333e9i −0.569335 + 0.986118i 0.427296 + 0.904112i 0.359466π0.359466\pi
−0.996632 + 0.0820062i 0.973867π0.973867\pi
570570 6.94600e8 + 1.20308e9i 0.157099 + 0.272103i
571571 −7.55829e8 1.30913e9i −0.169902 0.294278i 0.768484 0.639870i 0.221012π-0.221012\pi
−0.938385 + 0.345591i 0.887678π0.887678\pi
572572 2.64718e9 4.58505e9i 0.591422 1.02437i
573573 −4.52075e8 −0.100385
574574 0 0
575575 −6.67273e9 −1.46375
576576 −9.55515e7 + 1.65500e8i −0.0208333 + 0.0360844i
577577 2.19560e9 + 3.80289e9i 0.475814 + 0.824135i 0.999616 0.0277054i 0.00882004π-0.00882004\pi
−0.523802 + 0.851840i 0.675487π0.675487\pi
578578 −9.62012e7 1.66625e8i −0.0207221 0.0358917i
579579 1.81848e9 3.14970e9i 0.389344 0.674364i
580580 8.34419e7 0.0177577
581581 0 0
582582 5.19931e8 0.109324
583583 −7.06282e9 + 1.22332e10i −1.47618 + 2.55681i
584584 5.76993e8 + 9.99381e8i 0.119874 + 0.207628i
585585 −1.94991e9 3.37734e9i −0.402688 0.697476i
586586 −2.93539e8 + 5.08424e8i −0.0602593 + 0.104372i
587587 −6.47628e9 −1.32158 −0.660789 0.750572i 0.729778π-0.729778\pi
−0.660789 + 0.750572i 0.729778π0.729778\pi
588588 0 0
589589 1.53699e8 0.0309932
590590 −2.94015e9 + 5.09248e9i −0.589369 + 1.02082i
591591 7.95708e8 + 1.37821e9i 0.158561 + 0.274636i
592592 4.90902e8 + 8.50266e8i 0.0972452 + 0.168434i
593593 −2.64092e8 + 4.57420e8i −0.0520072 + 0.0900791i −0.890857 0.454284i 0.849895π-0.849895\pi
0.838850 + 0.544363i 0.183229π0.183229\pi
594594 −1.14445e9 −0.224049
595595 0 0
596596 4.05131e9 0.783851
597597 −1.77354e9 + 3.07186e9i −0.341138 + 0.590869i
598598 2.12780e9 + 3.68545e9i 0.406889 + 0.704752i
599599 4.51711e9 + 7.82387e9i 0.858751 + 1.48740i 0.873121 + 0.487503i 0.162092π0.162092\pi
−0.0143708 + 0.999897i 0.504575π0.504575\pi
600600 −9.86861e8 + 1.70929e9i −0.186520 + 0.323063i
601601 5.03992e9 0.947028 0.473514 0.880786i 0.342985π-0.342985\pi
0.473514 + 0.880786i 0.342985π0.342985\pi
602602 0 0
603603 1.55181e9 0.288223
604604 1.72680e9 2.99091e9i 0.318870 0.552299i
605605 −7.83411e9 1.35691e10i −1.43829 2.49119i
606606 −8.39781e8 1.45454e9i −0.153289 0.265505i
607607 −2.98281e9 + 5.16638e9i −0.541334 + 0.937617i 0.457494 + 0.889213i 0.348747π0.348747\pi
−0.998828 + 0.0484046i 0.984586π0.984586\pi
608608 −4.48397e8 −0.0809097
609609 0 0
610610 −1.19707e10 −2.13533
611611 2.56833e9 4.44847e9i 0.455518 0.788981i
612612 −4.86202e8 8.42127e8i −0.0857407 0.148507i
613613 −2.71175e9 4.69689e9i −0.475487 0.823567i 0.524119 0.851645i 0.324395π-0.324395\pi
−0.999606 + 0.0280780i 0.991061π0.991061\pi
614614 3.72649e8 6.45448e8i 0.0649697 0.112531i
615615 6.72088e8 0.116510
616616 0 0
617617 2.18073e9 0.373770 0.186885 0.982382i 0.440161π-0.440161\pi
0.186885 + 0.982382i 0.440161π0.440161\pi
618618 1.42927e9 2.47558e9i 0.243588 0.421907i
619619 2.67868e9 + 4.63960e9i 0.453945 + 0.786255i 0.998627 0.0523875i 0.0166831π-0.0166831\pi
−0.544682 + 0.838642i 0.683350π0.683350\pi
620620 1.68929e8 + 2.92594e8i 0.0284665 + 0.0493054i
621621 4.59952e8 7.96661e8i 0.0770712 0.133491i
622622 4.88747e9 0.814363
623623 0 0
624624 1.25876e9 0.207394
625625 −1.56344e9 + 2.70796e9i −0.256155 + 0.443673i
626626 8.48924e8 + 1.47038e9i 0.138312 + 0.239563i
627627 −1.34265e9 2.32553e9i −0.217533 0.376778i
628628 −1.86677e9 + 3.23335e9i −0.300769 + 0.520947i
629629 −4.99579e9 −0.800436
630630 0 0
631631 1.14559e10 1.81521 0.907607 0.419822i 0.137907π-0.137907\pi
0.907607 + 0.419822i 0.137907π0.137907\pi
632632 −3.40255e7 + 5.89338e7i −0.00536160 + 0.00928656i
633633 4.00410e8 + 6.93531e8i 0.0627469 + 0.108681i
634634 4.41578e9 + 7.64836e9i 0.688169 + 1.19194i
635635 −9.10228e8 + 1.57656e9i −0.141072 + 0.244345i
636636 −3.35843e9 −0.517651
637637 0 0
638638 −1.61291e8 −0.0245889
639639 −2.07566e9 + 3.59515e9i −0.314705 + 0.545085i
640640 −4.92831e8 8.53608e8i −0.0743135 0.128715i
641641 −5.06437e9 8.77175e9i −0.759491 1.31548i −0.943110 0.332480i 0.892115π-0.892115\pi
0.183619 0.982997i 0.441219π-0.441219\pi
642642 7.78620e8 1.34861e9i 0.116132 0.201147i
643643 −4.99152e9 −0.740448 −0.370224 0.928943i 0.620719π-0.620719\pi
−0.370224 + 0.928943i 0.620719π0.620719\pi
644644 0 0
645645 −1.11003e10 −1.62884
646646 1.14081e9 1.97594e9i 0.166494 0.288376i
647647 2.77118e9 + 4.79983e9i 0.402254 + 0.696724i 0.993998 0.109402i 0.0348936π-0.0348936\pi
−0.591744 + 0.806126i 0.701560π0.701560\pi
648648 −1.36049e8 2.35644e8i −0.0196419 0.0340207i
649649 5.68324e9 9.84366e9i 0.816093 1.41351i
650650 1.30005e10 1.85680
651651 0 0
652652 3.87741e9 0.547867
653653 3.71295e9 6.43101e9i 0.521822 0.903822i −0.477856 0.878438i 0.658586π-0.658586\pi
0.999678 0.0253840i 0.00808085π-0.00808085\pi
654654 −4.20160e8 7.27739e8i −0.0587345 0.101731i
655655 −5.34569e9 9.25901e9i −0.743292 1.28742i
656656 −1.08466e8 + 1.87869e8i −0.0150014 + 0.0259831i
657657 −1.64308e9 −0.226037
658658 0 0
659659 8.68127e8 0.118164 0.0590819 0.998253i 0.481183π-0.481183\pi
0.0590819 + 0.998253i 0.481183π0.481183\pi
660660 2.95139e9 5.11196e9i 0.399597 0.692123i
661661 −1.68460e9 2.91781e9i −0.226878 0.392964i 0.730003 0.683443i 0.239518π-0.239518\pi
−0.956881 + 0.290480i 0.906185π0.906185\pi
662662 2.68235e9 + 4.64597e9i 0.359346 + 0.622405i
663663 −3.20252e9 + 5.54693e9i −0.426771 + 0.739188i
664664 3.55867e9 0.471736
665665 0 0
666666 −1.39792e9 −0.183367
667667 6.48228e7 1.12276e8i 0.00845839 0.0146504i
668668 −1.90142e9 3.29335e9i −0.246808 0.427485i
669669 −4.26650e9 7.38979e9i −0.550909 0.954203i
670670 −4.00193e9 + 6.93154e9i −0.514052 + 0.890365i
671671 2.31391e10 2.95677
672672 0 0
673673 −3.43406e9 −0.434265 −0.217133 0.976142i 0.569670π-0.569670\pi
−0.217133 + 0.976142i 0.569670π0.569670\pi
674674 2.73649e9 4.73974e9i 0.344258 0.596272i
675675 −1.40512e9 2.43374e9i −0.175853 0.304587i
676676 −2.13765e9 3.70251e9i −0.266147 0.460981i
677677 −6.44496e9 + 1.11630e10i −0.798289 + 1.38268i 0.122441 + 0.992476i 0.460928π0.460928\pi
−0.920730 + 0.390201i 0.872406π0.872406\pi
678678 3.16758e9 0.390323
679679 0 0
680680 5.01542e9 0.611682
681681 −6.42676e8 + 1.11315e9i −0.0779789 + 0.135063i
682682 −3.26537e8 5.65578e8i −0.0394173 0.0682727i
683683 3.26006e9 + 5.64659e9i 0.391519 + 0.678131i 0.992650 0.121019i 0.0386163π-0.0386163\pi
−0.601131 + 0.799151i 0.705283π0.705283\pi
684684 3.19220e8 5.52906e8i 0.0381412 0.0660625i
685685 −1.98520e10 −2.35986
686686 0 0
687687 −2.81580e9 −0.331324
688688 1.79145e9 3.10288e9i 0.209723 0.363250i
689689 1.10607e10 + 1.91577e10i 1.28829 + 2.23139i
690690 2.37232e9 + 4.10898e9i 0.274917 + 0.476170i
691691 7.56322e9 1.30999e10i 0.872035 1.51041i 0.0121462 0.999926i 0.496134π-0.496134\pi
0.859888 0.510482i 0.170533π-0.170533\pi
692692 3.57482e9 0.410094
693693 0 0
694694 3.50042e9 0.397523
695695 4.75451e8 8.23505e8i 0.0537228 0.0930507i
696696 −1.91739e7 3.32101e7i −0.00215565 0.00373369i
697697 −5.51917e8 9.55948e8i −0.0617389 0.106935i
698698 −3.75933e7 + 6.51135e7i −0.00418424 + 0.00724732i
699699 6.34659e9 0.702862
700700 0 0
701701 −8.52704e9 −0.934943 −0.467472 0.884008i 0.654835π-0.654835\pi
−0.467472 + 0.884008i 0.654835π0.654835\pi
702702 −8.96128e8 + 1.55214e9i −0.0977665 + 0.169337i
703703 −1.64001e9 2.84059e9i −0.178034 0.308365i
704704 9.52631e8 + 1.65001e9i 0.102901 + 0.178230i
705705 2.86347e9 4.95968e9i 0.307773 0.533079i
706706 1.13177e10 1.21044
707707 0 0
708708 2.70243e9 0.286180
709709 4.92290e9 8.52671e9i 0.518751 0.898503i −0.481012 0.876714i 0.659731π-0.659731\pi
0.999763 0.0217886i 0.00693609π-0.00693609\pi
710710 −1.07057e10 1.85429e10i −1.12257 1.94434i
711711 −4.84464e7 8.39117e7i −0.00505496 0.00875546i
712712 2.72039e9 4.71185e9i 0.282456 0.489228i
713713 5.24939e8 0.0542370
714714 0 0
715715 −3.88805e10 −3.97796
716716 −2.56721e9 + 4.44653e9i −0.261376 + 0.452716i
717717 −5.05388e8 8.75359e8i −0.0512045 0.0886888i
718718 1.23033e9 + 2.13100e9i 0.124047 + 0.214856i
719719 −2.01398e9 + 3.48831e9i −0.202071 + 0.349997i −0.949195 0.314687i 0.898100π-0.898100\pi
0.747125 + 0.664684i 0.231434π0.231434\pi
720720 1.40341e9 0.140127
721721 0 0
722722 −5.65296e9 −0.558979
723723 −1.33335e8 + 2.30943e8i −0.0131208 + 0.0227259i
724724 2.29962e9 + 3.98306e9i 0.225202 + 0.390061i
725725 −1.98029e8 3.42996e8i −0.0192995 0.0334277i
726726 −3.60036e9 + 6.23600e9i −0.349195 + 0.604823i
727727 −5.95463e9 −0.574757 −0.287379 0.957817i 0.592784π-0.592784\pi
−0.287379 + 0.957817i 0.592784π0.592784\pi
728728 0 0
729729 3.87420e8 0.0370370
730730 4.23729e9 7.33920e9i 0.403142 0.698263i
731731 9.11558e9 + 1.57887e10i 0.863125 + 1.49498i
732732 2.75071e9 + 4.76437e9i 0.259212 + 0.448969i
733733 −8.27724e9 + 1.43366e10i −0.776286 + 1.34457i 0.157783 + 0.987474i 0.449565π0.449565\pi
−0.934069 + 0.357092i 0.883768π0.883768\pi
734734 −9.85018e9 −0.919407
735735 0 0
736736 −1.53145e9 −0.141589
737737 7.73564e9 1.33985e10i 0.711803 1.23288i
738738 −1.54437e8 2.67493e8i −0.0141434 0.0244971i
739739 −5.72231e9 9.91134e9i −0.521574 0.903393i −0.999685 0.0250936i 0.992012π-0.992012\pi
0.478111 0.878299i 0.341322π-0.341322\pi
740740 3.60506e9 6.24414e9i 0.327040 0.566450i
741741 −4.20528e9 −0.379692
742742 0 0
743743 −4.25895e8 −0.0380927 −0.0190464 0.999819i 0.506063π-0.506063\pi
−0.0190464 + 0.999819i 0.506063π0.506063\pi
744744 7.76356e7 1.34469e8i 0.00691123 0.0119706i
745745 −1.48759e10 2.57658e10i −1.31806 2.28295i
746746 −7.34367e9 1.27196e10i −0.647630 1.12173i
747747 −2.53347e9 + 4.38809e9i −0.222379 + 0.385171i
748748 −9.69470e9 −0.846991
749749 0 0
750750 6.56327e9 0.568075
751751 1.47518e8 2.55508e8i 0.0127088 0.0220123i −0.859601 0.510966i 0.829288π-0.829288\pi
0.872310 + 0.488953i 0.162621π0.162621\pi
752752 9.24254e8 + 1.60086e9i 0.0792554 + 0.137274i
753753 −1.78792e9 3.09676e9i −0.152604 0.264317i
754754 −1.26295e8 + 2.18749e8i −0.0107296 + 0.0185843i
755755 −2.53624e10 −2.14475
756756 0 0
757757 1.87377e10 1.56994 0.784968 0.619537i 0.212680π-0.212680\pi
0.784968 + 0.619537i 0.212680π0.212680\pi
758758 2.59573e9 4.49594e9i 0.216480 0.374955i
759759 −4.58564e9 7.94257e9i −0.380675 0.659348i
760760 1.64646e9 + 2.85175e9i 0.136051 + 0.235648i
761761 −2.03748e9 + 3.52902e9i −0.167590 + 0.290274i −0.937572 0.347792i 0.886932π-0.886932\pi
0.769982 + 0.638065i 0.220265π0.220265\pi
762762 8.36635e8 0.0685005
763763 0 0
764764 −1.07159e9 −0.0869361
765765 −3.57055e9 + 6.18437e9i −0.288350 + 0.499437i
766766 2.72128e9 + 4.71340e9i 0.218763 + 0.378908i
767767 −8.90020e9 1.54156e10i −0.712223 1.23361i
768768 −2.26492e8 + 3.92296e8i −0.0180422 + 0.0312500i
769769 1.19604e10 0.948425 0.474213 0.880410i 0.342733π-0.342733\pi
0.474213 + 0.880410i 0.342733π0.342733\pi
770770 0 0
771771 8.98201e9 0.705803
772772 4.31047e9 7.46595e9i 0.337182 0.584016i
773773 −2.33651e8 4.04696e8i −0.0181945 0.0315138i 0.856785 0.515674i 0.172458π-0.172458\pi
−0.874979 + 0.484160i 0.839125π0.839125\pi
774774 2.55072e9 + 4.41797e9i 0.197728 + 0.342476i
775775 8.01824e8 1.38880e9i 0.0618762 0.107173i
776776 1.23243e9 0.0946774
777777 0 0
778778 2.18964e9 0.166703
779779 3.62366e8 6.27636e8i 0.0274642 0.0475693i
780780 −4.62200e9 8.00554e9i −0.348738 0.604032i
781781 2.06940e10 + 3.58430e10i 1.55441 + 2.69232i
782782 3.89629e9 6.74857e9i 0.291358 0.504647i
783783 5.46006e7 0.00406473
784784 0 0
785785 2.74182e10 2.02300
786786 −2.45674e9 + 4.25521e9i −0.180460 + 0.312566i
787787 4.03993e9 + 6.99737e9i 0.295436 + 0.511709i 0.975086 0.221827i 0.0712019π-0.0712019\pi
−0.679651 + 0.733536i 0.737869π0.737869\pi
788788 1.88612e9 + 3.26686e9i 0.137318 + 0.237842i
789789 1.28416e9 2.22423e9i 0.0930784 0.161217i
790790 4.99749e8 0.0360626
791791 0 0
792792 −2.71277e9 −0.194032
793793 1.81184e10 3.13820e10i 1.29022 2.23472i
794794 4.84137e9 + 8.38549e9i 0.343239 + 0.594507i
795795 1.23317e10 + 2.13592e10i 0.870442 + 1.50765i
796796 −4.20394e9 + 7.28144e9i −0.295434 + 0.511707i
797797 −1.48799e10 −1.04111 −0.520555 0.853828i 0.674275π-0.674275\pi
−0.520555 + 0.853828i 0.674275π0.674275\pi
798798 0 0
799799 −9.40591e9 −0.652360
800800 −2.33923e9 + 4.05166e9i −0.161531 + 0.279781i
801801 3.87336e9 + 6.70886e9i 0.266302 + 0.461249i
802802 2.38841e9 + 4.13685e9i 0.163493 + 0.283178i
803803 −8.19059e9 + 1.41865e10i −0.558227 + 0.966878i
804804 3.67837e9 0.249608
805805 0 0
806806 −1.02274e9 −0.0688007
807807 3.62954e9 6.28655e9i 0.243105 0.421071i
808808 −1.99059e9 3.44781e9i −0.132752 0.229934i
809809 −3.57566e9 6.19323e9i −0.237431 0.411242i 0.722546 0.691323i 0.242972π-0.242972\pi
−0.959976 + 0.280081i 0.909639π0.909639\pi
810810 −9.99109e8 + 1.73051e9i −0.0660565 + 0.114413i
811811 2.13058e9 0.140257 0.0701286 0.997538i 0.477659π-0.477659\pi
0.0701286 + 0.997538i 0.477659π0.477659\pi
812812 0 0
813813 1.22279e10 0.798056
814814 −6.96850e9 + 1.20698e10i −0.452850 + 0.784358i
815815 −1.42374e10 2.46598e10i −0.921250 1.59565i
816816 −1.15248e9 1.99615e9i −0.0742536 0.128611i
817817 −5.98492e9 + 1.03662e10i −0.383955 + 0.665030i
818818 −9.58137e9 −0.612056
819819 0 0
820820 1.59310e9 0.100901
821821 −1.02026e9 + 1.76714e9i −0.0643442 + 0.111447i −0.896403 0.443240i 0.853829π-0.853829\pi
0.832059 + 0.554688i 0.187162π0.187162\pi
822822 4.56173e9 + 7.90114e9i 0.286469 + 0.496179i
823823 −1.49569e10 2.59062e10i −0.935283 1.61996i −0.774128 0.633029i 0.781812π-0.781812\pi
−0.161155 0.986929i 0.551522π-0.551522\pi
824824 3.38791e9 5.86803e9i 0.210953 0.365382i
825825 −2.80176e10 −1.73717
826826 0 0
827827 1.05103e10 0.646170 0.323085 0.946370i 0.395280π-0.395280\pi
0.323085 + 0.946370i 0.395280π0.395280\pi
828828 1.09026e9 1.88838e9i 0.0667456 0.115607i
829829 −9.55730e9 1.65537e10i −0.582632 1.00915i −0.995166 0.0982059i 0.968690π-0.968690\pi
0.412534 0.910942i 0.364644π-0.364644\pi
830830 −1.30670e10 2.26327e10i −0.793235 1.37392i
831831 2.22358e8 3.85135e8i 0.0134415 0.0232814i
832832 2.98372e9 0.179608
833833 0 0
834834 −4.37010e8 −0.0260862
835835 −1.39635e10 + 2.41856e10i −0.830028 + 1.43765i
836836 −3.18257e9 5.51237e9i −0.188389 0.326300i
837837 1.10540e8 + 1.91460e8i 0.00651597 + 0.0112860i
838838 6.74720e9 1.16865e10i 0.396068 0.686010i
839839 2.31635e9 0.135406 0.0677028 0.997706i 0.478433π-0.478433\pi
0.0677028 + 0.997706i 0.478433π0.478433\pi
840840 0 0
841841 −1.72422e10 −0.999554
842842 3.84142e9 6.65354e9i 0.221768 0.384114i
843843 −6.85953e9 1.18811e10i −0.394365 0.683059i
844844 9.49121e8 + 1.64393e9i 0.0543404 + 0.0941203i
845845 −1.56983e10 + 2.71903e10i −0.895066 + 1.55030i
846846 −2.63196e9 −0.149445
847847 0 0
848848 −7.96073e9 −0.448299
849849 3.47619e9 6.02095e9i 0.194952 0.337666i
850850 −1.19029e10 2.06164e10i −0.664791 1.15145i
851851 −5.60126e9 9.70167e9i −0.311553 0.539626i
852852 −4.92009e9 + 8.52184e9i −0.272542 + 0.472057i
853853 −8.57597e8 −0.0473110 −0.0236555 0.999720i 0.507530π-0.507530\pi
−0.0236555 + 0.999720i 0.507530π0.507530\pi
854854 0 0
855855 −4.68855e9 −0.256541
856856 1.84562e9 3.19670e9i 0.100573 0.174198i
857857 1.36933e10 + 2.37174e10i 0.743146 + 1.28717i 0.951056 + 0.309018i 0.100000π0.100000\pi
−0.207911 + 0.978148i 0.566666π0.566666\pi
858858 8.93423e9 + 1.54745e10i 0.482894 + 0.836397i
859859 5.09578e9 8.82615e9i 0.274306 0.475111i −0.695654 0.718377i 0.744885π-0.744885\pi
0.969960 + 0.243266i 0.0782187π0.0782187\pi
860860 −2.63119e10 −1.41061
861861 0 0
862862 −8.25327e8 −0.0438885
863863 −1.85337e9 + 3.21014e9i −0.0981578 + 0.170014i −0.910922 0.412578i 0.864628π-0.864628\pi
0.812764 + 0.582593i 0.197962π0.197962\pi
864864 −3.22486e8 5.58563e8i −0.0170103 0.0294628i
865865 −1.31263e10 2.27354e10i −0.689582 1.19439i
866866 9.33110e9 1.61619e10i 0.488225 0.845631i
867867 6.49358e8 0.0338390
868868 0 0
869869 −9.66004e8 −0.0499356
870870 −1.40808e8 + 2.43887e8i −0.00724954 + 0.0125566i
871871 −1.21143e10 2.09827e10i −0.621207 1.07596i
872872 −9.95936e8 1.72501e9i −0.0508655 0.0881017i
873873 −8.77384e8 + 1.51967e9i −0.0446313 + 0.0773038i
874874 5.11628e9 0.259218
875875 0 0
876876 −3.89470e9 −0.195754
877877 −1.09341e9 + 1.89383e9i −0.0547372 + 0.0948076i −0.892096 0.451847i 0.850765π-0.850765\pi
0.837358 + 0.546654i 0.184099π0.184099\pi
878878 6.24635e9 + 1.08190e10i 0.311455 + 0.539456i
879879 −9.90694e8 1.71593e9i −0.0492015 0.0852195i
880880 6.99589e9 1.21172e10i 0.346062 0.599396i
881881 −9.10532e9 −0.448621 −0.224310 0.974518i 0.572013π-0.572013\pi
−0.224310 + 0.974518i 0.572013π0.572013\pi
882882 0 0
883883 1.99391e10 0.974639 0.487319 0.873224i 0.337975π-0.337975\pi
0.487319 + 0.873224i 0.337975π0.337975\pi
884884 −7.59116e9 + 1.31483e10i −0.369594 + 0.640156i
885885 −9.92300e9 1.71871e10i −0.481217 0.833493i
886886 −6.49923e9 1.12570e10i −0.313938 0.543757i
887887 3.62213e9 6.27371e9i 0.174273 0.301850i −0.765636 0.643274i 0.777576π-0.777576\pi
0.939910 + 0.341424i 0.110909π0.110909\pi
888888 −3.31359e9 −0.158801
889889 0 0
890890 −3.99557e10 −1.89982
891891 1.93126e9 3.34503e9i 0.0914678 0.158427i
892892 −1.01132e10 1.75165e10i −0.477101 0.826364i
893893 −3.08777e9 5.34817e9i −0.145099 0.251319i
894894 −6.83658e9 + 1.18413e10i −0.320006 + 0.554266i
895895 3.77059e10 1.75804
896896 0 0
897897 −1.43626e10 −0.664447
898898 3.27391e9 5.67058e9i 0.150869 0.261313i
899899 1.55788e7 + 2.69832e7i 0.000715113 + 0.00123861i
900900 −3.33066e9 5.76886e9i −0.152293 0.263780i
901901 2.02536e10 3.50803e10i 0.922498 1.59781i
902902 −3.07942e9 −0.139716
903903 0 0
904904 7.50834e9 0.338029
905905 1.68879e10 2.92506e10i 0.757364 1.31179i
906906 5.82796e9 + 1.00943e10i 0.260356 + 0.450950i
907907 −4.37667e9 7.58061e9i −0.194768 0.337349i 0.752056 0.659099i 0.229062π-0.229062\pi
−0.946825 + 0.321750i 0.895729π0.895729\pi
908908 −1.52338e9 + 2.63857e9i −0.0675317 + 0.116968i
909909 5.66852e9 0.250320
910910 0 0
911911 1.99869e10 0.875853 0.437926 0.899011i 0.355713π-0.355713\pi
0.437926 + 0.899011i 0.355713π0.355713\pi
912912 7.56670e8 1.31059e9i 0.0330312 0.0572118i
913913 2.52582e10 + 4.37485e10i 1.09839 + 1.90246i
914914 6.13302e9 + 1.06227e10i 0.265682 + 0.460176i
915915 2.02005e10 3.49883e10i 0.871743 1.50990i
916916 −6.67449e9 −0.286935
917917 0 0
918918 3.28186e9 0.140014
919919 4.96537e9 8.60028e9i 0.211032 0.365518i −0.741006 0.671498i 0.765651π-0.765651\pi
0.952038 + 0.305981i 0.0989843π0.0989843\pi
920920 5.62328e9 + 9.73980e9i 0.238085 + 0.412375i
921921 1.25769e9 + 2.17839e9i 0.0530476 + 0.0918811i
922922 −1.37403e10 + 2.37989e10i −0.577348 + 0.999996i
923923 6.48153e10 2.71314
924924 0 0
925925 −3.42229e10 −1.42174
926926 −6.92802e9 + 1.19997e10i −0.286728 + 0.496628i
927927 4.82380e9 + 8.35507e9i 0.198889 + 0.344486i
928928 −4.54492e7 7.87204e7i −0.00186685 0.00323347i
929929 −9.79538e9 + 1.69661e10i −0.400836 + 0.694267i −0.993827 0.110941i 0.964613π-0.964613\pi
0.592991 + 0.805209i 0.297947π0.297947\pi
930930 −1.14027e9 −0.0464856
931931 0 0
932932 1.50438e10 0.608697
933933 −8.24761e9 + 1.42853e10i −0.332462 + 0.575842i
934934 1.92595e9 + 3.33584e9i 0.0773448 + 0.133965i
935935 3.55977e10 + 6.16571e10i 1.42423 + 2.46685i
936936 −2.12415e9 + 3.67914e9i −0.0846683 + 0.146650i
937937 4.20286e10 1.66900 0.834500 0.551009i 0.185757π-0.185757\pi
0.834500 + 0.551009i 0.185757π0.185757\pi
938938 0 0
939939 −5.73024e9 −0.225862
940940 6.78749e9 1.17563e10i 0.266540 0.461660i
941941 4.97715e9 + 8.62068e9i 0.194723 + 0.337270i 0.946810 0.321794i 0.104286π-0.104286\pi
−0.752087 + 0.659064i 0.770953π0.770953\pi
942942 −6.30036e9 1.09125e10i −0.245577 0.425352i
943943 1.23762e9 2.14361e9i 0.0480612 0.0832445i
944944 6.40577e9 0.247839
945945 0 0
946946 5.08604e10 1.95326
947947 1.21725e10 2.10834e10i 0.465751 0.806705i −0.533484 0.845810i 0.679117π-0.679117\pi
0.999235 + 0.0391052i 0.0124507π0.0124507\pi
948948 −1.14836e8 1.98902e8i −0.00437773 0.00758245i
949949 1.28268e10 + 2.22167e10i 0.487178 + 0.843816i
950950 7.81493e9 1.35359e10i 0.295728 0.512216i
951951 −2.98065e10 −1.12378
952952 0 0
953953 1.71198e10 0.640727 0.320364 0.947295i 0.396195π-0.396195\pi
0.320364 + 0.947295i 0.396195π0.396195\pi
954954 5.66736e9 9.81615e9i 0.211330 0.366034i
955955 3.93473e9 + 6.81515e9i 0.146185 + 0.253200i
956956 −1.19796e9 2.07492e9i −0.0443444 0.0768068i
957957 2.72179e8 4.71428e8i 0.0100384 0.0173870i
958958 −1.32751e10 −0.487821
959959 0 0
960960 3.32661e9 0.121353
961961 1.36932e10 2.37174e10i 0.497707 0.862054i
962962 1.09130e10 + 1.89018e10i 0.395212 + 0.684527i
963963 2.62784e9 + 4.55156e9i 0.0948216 + 0.164236i
964964 −3.16054e8 + 5.47421e8i −0.0113629 + 0.0196812i
965965 −6.33100e10 −2.26792
966966 0 0
967967 −5.29443e10 −1.88290 −0.941448 0.337157i 0.890535π-0.890535\pi
−0.941448 + 0.337157i 0.890535π0.890535\pi
968968 −8.53418e9 + 1.47816e10i −0.302411 + 0.523792i
969969 3.85023e9 + 6.66879e9i 0.135942 + 0.235458i
970970 −4.52533e9 7.83810e9i −0.159202 0.275746i
971971 1.22361e10 2.11936e10i 0.428920 0.742912i −0.567857 0.823127i 0.692227π-0.692227\pi
0.996778 + 0.0802153i 0.0255608π0.0255608\pi
972972 9.18330e8 0.0320750
973973 0 0
974974 1.37613e10 0.477204
975975 −2.19384e10 + 3.79984e10i −0.758033 + 1.31295i
976976 6.52020e9 + 1.12933e10i 0.224485 + 0.388819i
977977 1.60839e10 + 2.78582e10i 0.551774 + 0.955700i 0.998147 + 0.0608529i 0.0193821π0.0193821\pi
−0.446373 + 0.894847i 0.647285π0.647285\pi
978978 −6.54313e9 + 1.13330e10i −0.223666 + 0.387400i
979979 7.72335e10 2.63067
980980 0 0
981981 2.83608e9 0.0959130
982982 2.66839e9 4.62179e9i 0.0899206 0.155747i
983983 −9.27819e9 1.60703e10i −0.311549 0.539618i 0.667149 0.744924i 0.267514π-0.267514\pi
−0.978698 + 0.205306i 0.934181π0.934181\pi
984984 −3.66073e8 6.34058e8i −0.0122486 0.0212151i
985985 1.38512e10 2.39910e10i 0.461807 0.799874i
986986 4.62526e8 0.0153662
987987 0 0
988988 −9.96808e9 −0.328823
989989 −2.04407e10 + 3.54044e10i −0.671908 + 1.16378i
990990 9.96094e9 + 1.72529e10i 0.326270 + 0.565116i
991991 −8.00744e9 1.38693e10i −0.261358 0.452685i 0.705245 0.708964i 0.250837π-0.250837\pi
−0.966603 + 0.256278i 0.917504π0.917504\pi
992992 1.84025e8 3.18741e8i 0.00598530 0.0103668i
993993 −1.81059e10 −0.586809
994994 0 0
995995 6.17454e10 1.98712
996996 −6.00525e9 + 1.04014e10i −0.192586 + 0.333568i
997997 −1.60482e10 2.77964e10i −0.512855 0.888290i −0.999889 0.0149074i 0.995255π-0.995255\pi
0.487034 0.873383i 0.338079π-0.338079\pi
998998 2.18391e9 + 3.78264e9i 0.0695469 + 0.120459i
999999 2.35899e9 4.08589e9i 0.0748594 0.129660i
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 294.8.e.a.79.1 2
7.2 even 3 42.8.a.f.1.1 1
7.3 odd 6 294.8.e.f.67.1 2
7.4 even 3 inner 294.8.e.a.67.1 2
7.5 odd 6 294.8.a.k.1.1 1
7.6 odd 2 294.8.e.f.79.1 2
21.2 odd 6 126.8.a.a.1.1 1
28.23 odd 6 336.8.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.8.a.f.1.1 1 7.2 even 3
126.8.a.a.1.1 1 21.2 odd 6
294.8.a.k.1.1 1 7.5 odd 6
294.8.e.a.67.1 2 7.4 even 3 inner
294.8.e.a.79.1 2 1.1 even 1 trivial
294.8.e.f.67.1 2 7.3 odd 6
294.8.e.f.79.1 2 7.6 odd 2
336.8.a.f.1.1 1 28.23 odd 6