Properties

Label 98.6.c.i.79.4
Level 9898
Weight 66
Character 98.79
Analytic conductor 15.71815.718
Analytic rank 00
Dimension 88
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [98,6,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 98=272 98 = 2 \cdot 7^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 98.c (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,-16,0,-64,0,0,0,512,-712] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 15.717614341715.7176143417
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x84x7782x6+2360x5+232083x4468104x330964778x2+31199224x+1568558404 x^{8} - 4x^{7} - 782x^{6} + 2360x^{5} + 232083x^{4} - 468104x^{3} - 30964778x^{2} + 31199224x + 1568558404 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 2274 2^{2}\cdot 7^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 79.4
Root 15.28721.22474i15.2872 - 1.22474i of defining polynomial
Character χ\chi == 98.79
Dual form 98.6.c.i.67.4

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(2.00000+3.46410i)q2+(12.4310+21.5312i)q3+(8.0000013.8564i)q4+(42.242873.1667i)q599.4482q6+64.0000q8+(187.561+324.865i)q9+(168.971+292.667i)q10+(217.183+376.171i)q11+(198.896344.499i)q12+848.786q13+2100.49q15+(128.000+221.703i)q16+(150.723+261.059i)q17+(750.2441299.46i)q18+(1454.96+2520.07i)q191351.77q201737.46q22+(854.7311480.44i)q23+(795.586+1377.99i)q24+(2006.413475.21i)q25+(1697.57+2940.28i)q263284.82q27+3841.63q29+(4200.97+7276.30i)q30+(484.926+839.916i)q31+(512.000886.810i)q32+(5399.61+9352.40i)q331205.78q34+6001.95q36+(1253.55+2171.21i)q37+(5819.8410080.3i)q38+(10551.3+18275.4i)q39+(2703.544682.67i)q4013284.0q41+7781.29q43+(3474.926018.74i)q44+(15846.2+27446.4i)q45+(3418.92+5921.75i)q46+(2744.574753.73i)q476364.69q48+16051.3q50+(3747.27+6490.47i)q51+(6790.2911761.1i)q52+(11429.919797.2i)q53+(6569.6411378.9i)q54+36697.6q5572346.6q57+(7683.27+13307.8i)q58+(5554.94+9621.44i)q59+(16803.929105.2i)q60+(11102.6+19230.2i)q613879.41q62+4096.00q64+(35855.162102.9i)q65+(21598.437409.6i)q66+(3609.29+6251.47i)q67+(2411.564176.95i)q68+42500.7q69+46153.3q71+(12003.9+20791.4i)q72+(33840.658613.7i)q73+(5014.198684.84i)q74+(49883.686400.9i)q75+46558.7q7684410.3q78+(34974.760578.0i)q79+(10814.2+18730.7i)q80+(4743.62+8216.19i)q81+(26568.046017.1i)q823915.73q83+25467.8q85+(15562.6+26955.2i)q86+(47755.5+82714.9i)q87+(13899.7+24075.0i)q88+(26475.6+45857.1i)q89126770.q9027351.4q92+(12056.2+20882.0i)q93+(10978.3+19014.9i)q94+(122923.+212909.i)q95+(12729.422047.9i)q9664.5382q97162940.q99+O(q100)q+(-2.00000 + 3.46410i) q^{2} +(12.4310 + 21.5312i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(42.2428 - 73.1667i) q^{5} -99.4482 q^{6} +64.0000 q^{8} +(-187.561 + 324.865i) q^{9} +(168.971 + 292.667i) q^{10} +(217.183 + 376.171i) q^{11} +(198.896 - 344.499i) q^{12} +848.786 q^{13} +2100.49 q^{15} +(-128.000 + 221.703i) q^{16} +(150.723 + 261.059i) q^{17} +(-750.244 - 1299.46i) q^{18} +(-1454.96 + 2520.07i) q^{19} -1351.77 q^{20} -1737.46 q^{22} +(854.731 - 1480.44i) q^{23} +(795.586 + 1377.99i) q^{24} +(-2006.41 - 3475.21i) q^{25} +(-1697.57 + 2940.28i) q^{26} -3284.82 q^{27} +3841.63 q^{29} +(-4200.97 + 7276.30i) q^{30} +(484.926 + 839.916i) q^{31} +(-512.000 - 886.810i) q^{32} +(-5399.61 + 9352.40i) q^{33} -1205.78 q^{34} +6001.95 q^{36} +(-1253.55 + 2171.21i) q^{37} +(-5819.84 - 10080.3i) q^{38} +(10551.3 + 18275.4i) q^{39} +(2703.54 - 4682.67i) q^{40} -13284.0 q^{41} +7781.29 q^{43} +(3474.92 - 6018.74i) q^{44} +(15846.2 + 27446.4i) q^{45} +(3418.92 + 5921.75i) q^{46} +(2744.57 - 4753.73i) q^{47} -6364.69 q^{48} +16051.3 q^{50} +(-3747.27 + 6490.47i) q^{51} +(-6790.29 - 11761.1i) q^{52} +(-11429.9 - 19797.2i) q^{53} +(6569.64 - 11378.9i) q^{54} +36697.6 q^{55} -72346.6 q^{57} +(-7683.27 + 13307.8i) q^{58} +(5554.94 + 9621.44i) q^{59} +(-16803.9 - 29105.2i) q^{60} +(-11102.6 + 19230.2i) q^{61} -3879.41 q^{62} +4096.00 q^{64} +(35855.1 - 62102.9i) q^{65} +(-21598.4 - 37409.6i) q^{66} +(3609.29 + 6251.47i) q^{67} +(2411.56 - 4176.95i) q^{68} +42500.7 q^{69} +46153.3 q^{71} +(-12003.9 + 20791.4i) q^{72} +(-33840.6 - 58613.7i) q^{73} +(-5014.19 - 8684.84i) q^{74} +(49883.6 - 86400.9i) q^{75} +46558.7 q^{76} -84410.3 q^{78} +(34974.7 - 60578.0i) q^{79} +(10814.2 + 18730.7i) q^{80} +(4743.62 + 8216.19i) q^{81} +(26568.0 - 46017.1i) q^{82} -3915.73 q^{83} +25467.8 q^{85} +(-15562.6 + 26955.2i) q^{86} +(47755.5 + 82714.9i) q^{87} +(13899.7 + 24075.0i) q^{88} +(-26475.6 + 45857.1i) q^{89} -126770. q^{90} -27351.4 q^{92} +(-12056.2 + 20882.0i) q^{93} +(10978.3 + 19014.9i) q^{94} +(122923. + 212909. i) q^{95} +(12729.4 - 22047.9i) q^{96} -64.5382 q^{97} -162940. q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q16q264q4+512q8712q9628q11+10496q151024q162848q18+5024q222624q234224q25+35464q2920992q304096q32+22784q36+709000q99+O(q100) 8 q - 16 q^{2} - 64 q^{4} + 512 q^{8} - 712 q^{9} - 628 q^{11} + 10496 q^{15} - 1024 q^{16} - 2848 q^{18} + 5024 q^{22} - 2624 q^{23} - 4224 q^{25} + 35464 q^{29} - 20992 q^{30} - 4096 q^{32} + 22784 q^{36}+ \cdots - 709000 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/98Z)×\left(\mathbb{Z}/98\mathbb{Z}\right)^\times.

nn 33
χ(n)\chi(n) 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 −2.00000 + 3.46410i −0.353553 + 0.612372i
33 12.4310 + 21.5312i 0.797451 + 1.38123i 0.921271 + 0.388921i 0.127152π0.127152\pi
−0.123820 + 0.992305i 0.539515π0.539515\pi
44 −8.00000 13.8564i −0.250000 0.433013i
55 42.2428 73.1667i 0.755663 1.30885i −0.189381 0.981904i 0.560648π-0.560648\pi
0.945044 0.326943i 0.106018π-0.106018\pi
66 −99.4482 −1.12777
77 0 0
88 64.0000 0.353553
99 −187.561 + 324.865i −0.771856 + 1.33689i
1010 168.971 + 292.667i 0.534334 + 0.925494i
1111 217.183 + 376.171i 0.541182 + 0.937355i 0.998837 + 0.0482248i 0.0153564π0.0153564\pi
−0.457654 + 0.889130i 0.651310π0.651310\pi
1212 198.896 344.499i 0.398725 0.690613i
1313 848.786 1.39296 0.696482 0.717574i 0.254747π-0.254747\pi
0.696482 + 0.717574i 0.254747π0.254747\pi
1414 0 0
1515 2100.49 2.41042
1616 −128.000 + 221.703i −0.125000 + 0.216506i
1717 150.723 + 261.059i 0.126490 + 0.219087i 0.922314 0.386440i 0.126296π-0.126296\pi
−0.795824 + 0.605527i 0.792962π0.792962\pi
1818 −750.244 1299.46i −0.545784 0.945326i
1919 −1454.96 + 2520.07i −0.924628 + 1.60150i −0.132471 + 0.991187i 0.542291π0.542291\pi
−0.792158 + 0.610316i 0.791042π0.791042\pi
2020 −1351.77 −0.755663
2121 0 0
2222 −1737.46 −0.765347
2323 854.731 1480.44i 0.336907 0.583540i −0.646942 0.762539i 0.723953π-0.723953\pi
0.983849 + 0.178999i 0.0572859π0.0572859\pi
2424 795.586 + 1377.99i 0.281941 + 0.488337i
2525 −2006.41 3475.21i −0.642052 1.11207i
2626 −1697.57 + 2940.28i −0.492487 + 0.853013i
2727 −3284.82 −0.867166
2828 0 0
2929 3841.63 0.848245 0.424122 0.905605i 0.360583π-0.360583\pi
0.424122 + 0.905605i 0.360583π0.360583\pi
3030 −4200.97 + 7276.30i −0.852211 + 1.47607i
3131 484.926 + 839.916i 0.0906298 + 0.156975i 0.907776 0.419455i 0.137779π-0.137779\pi
−0.817147 + 0.576430i 0.804445π0.804445\pi
3232 −512.000 886.810i −0.0883883 0.153093i
3333 −5399.61 + 9352.40i −0.863132 + 1.49499i
3434 −1205.78 −0.178884
3535 0 0
3636 6001.95 0.771856
3737 −1253.55 + 2171.21i −0.150535 + 0.260734i −0.931424 0.363935i 0.881433π-0.881433\pi
0.780889 + 0.624669i 0.214766π0.214766\pi
3838 −5819.84 10080.3i −0.653811 1.13243i
3939 10551.3 + 18275.4i 1.11082 + 1.92400i
4040 2703.54 4682.67i 0.267167 0.462747i
4141 −13284.0 −1.23415 −0.617076 0.786904i 0.711683π-0.711683\pi
−0.617076 + 0.786904i 0.711683π0.711683\pi
4242 0 0
4343 7781.29 0.641771 0.320886 0.947118i 0.396019π-0.396019\pi
0.320886 + 0.947118i 0.396019π0.396019\pi
4444 3474.92 6018.74i 0.270591 0.468678i
4545 15846.2 + 27446.4i 1.16652 + 2.02048i
4646 3418.92 + 5921.75i 0.238229 + 0.412625i
4747 2744.57 4753.73i 0.181230 0.313899i −0.761070 0.648670i 0.775326π-0.775326\pi
0.942300 + 0.334771i 0.108659π0.108659\pi
4848 −6364.69 −0.398725
4949 0 0
5050 16051.3 0.907999
5151 −3747.27 + 6490.47i −0.201739 + 0.349422i
5252 −6790.29 11761.1i −0.348241 0.603171i
5353 −11429.9 19797.2i −0.558926 0.968088i −0.997586 0.0694354i 0.977880π-0.977880\pi
0.438660 0.898653i 0.355453π-0.355453\pi
5454 6569.64 11378.9i 0.306589 0.531028i
5555 36697.6 1.63580
5656 0 0
5757 −72346.6 −2.94938
5858 −7683.27 + 13307.8i −0.299900 + 0.519442i
5959 5554.94 + 9621.44i 0.207754 + 0.359841i 0.951007 0.309170i 0.100051π-0.100051\pi
−0.743253 + 0.669011i 0.766718π0.766718\pi
6060 −16803.9 29105.2i −0.602604 1.04374i
6161 −11102.6 + 19230.2i −0.382032 + 0.661699i −0.991353 0.131225i 0.958109π-0.958109\pi
0.609321 + 0.792924i 0.291442π0.291442\pi
6262 −3879.41 −0.128170
6363 0 0
6464 4096.00 0.125000
6565 35855.1 62102.9i 1.05261 1.82318i
6666 −21598.4 37409.6i −0.610327 1.05712i
6767 3609.29 + 6251.47i 0.0982278 + 0.170136i 0.910951 0.412514i 0.135349π-0.135349\pi
−0.812723 + 0.582650i 0.802016π0.802016\pi
6868 2411.56 4176.95i 0.0632450 0.109543i
6969 42500.7 1.07467
7070 0 0
7171 46153.3 1.08657 0.543284 0.839549i 0.317181π-0.317181\pi
0.543284 + 0.839549i 0.317181π0.317181\pi
7272 −12003.9 + 20791.4i −0.272892 + 0.472663i
7373 −33840.6 58613.7i −0.743244 1.28734i −0.951011 0.309157i 0.899953π-0.899953\pi
0.207767 0.978178i 0.433380π-0.433380\pi
7474 −5014.19 8684.84i −0.106444 0.184367i
7575 49883.6 86400.9i 1.02401 1.77364i
7676 46558.7 0.924628
7777 0 0
7878 −84410.3 −1.57094
7979 34974.7 60578.0i 0.630503 1.09206i −0.356946 0.934125i 0.616182π-0.616182\pi
0.987449 0.157938i 0.0504845π-0.0504845\pi
8080 10814.2 + 18730.7i 0.188916 + 0.327212i
8181 4743.62 + 8216.19i 0.0803336 + 0.139142i
8282 26568.0 46017.1i 0.436339 0.755761i
8383 −3915.73 −0.0623903 −0.0311951 0.999513i 0.509931π-0.509931\pi
−0.0311951 + 0.999513i 0.509931π0.509931\pi
8484 0 0
8585 25467.8 0.382335
8686 −15562.6 + 26955.2i −0.226900 + 0.393003i
8787 47755.5 + 82714.9i 0.676433 + 1.17162i
8888 13899.7 + 24075.0i 0.191337 + 0.331405i
8989 −26475.6 + 45857.1i −0.354300 + 0.613665i −0.986998 0.160733i 0.948614π-0.948614\pi
0.632698 + 0.774399i 0.281947π0.281947\pi
9090 −126770. −1.64972
9191 0 0
9292 −27351.4 −0.336907
9393 −12056.2 + 20882.0i −0.144546 + 0.250360i
9494 10978.3 + 19014.9i 0.128149 + 0.221960i
9595 122923. + 212909.i 1.39741 + 2.42039i
9696 12729.4 22047.9i 0.140971 0.244168i
9797 −64.5382 −0.000696447 −0.000348223 1.00000i 0.500111π-0.500111\pi
−0.000348223 1.00000i 0.500111π0.500111\pi
9898 0 0
9999 −162940. −1.67086
100100 −32102.6 + 55603.4i −0.321026 + 0.556034i
101101 −36246.8 62781.3i −0.353563 0.612389i 0.633308 0.773900i 0.281697π-0.281697\pi
−0.986871 + 0.161511i 0.948363π0.948363\pi
102102 −14989.1 25961.9i −0.142651 0.247079i
103103 39493.6 68404.9i 0.366804 0.635322i −0.622260 0.782810i 0.713785π-0.713785\pi
0.989064 + 0.147488i 0.0471188π0.0471188\pi
104104 54322.3 0.492487
105105 0 0
106106 91439.5 0.790441
107107 −63193.0 + 109453.i −0.533592 + 0.924209i 0.465638 + 0.884975i 0.345825π0.345825\pi
−0.999230 + 0.0392333i 0.987508π0.987508\pi
108108 26278.6 + 45515.8i 0.216791 + 0.375494i
109109 −89859.0 155640.i −0.724428 1.25475i −0.959209 0.282698i 0.908771π-0.908771\pi
0.234781 0.972048i 0.424563π-0.424563\pi
110110 −73395.3 + 127124.i −0.578344 + 1.00172i
111111 −62331.6 −0.480176
112112 0 0
113113 258027. 1.90094 0.950471 0.310812i 0.100601π-0.100601\pi
0.950471 + 0.310812i 0.100601π0.100601\pi
114114 144693. 250616.i 1.04276 1.80612i
115115 −72212.5 125076.i −0.509176 0.881918i
116116 −30733.1 53231.3i −0.212061 0.367301i
117117 −159199. + 275741.i −1.07517 + 1.86224i
118118 −44439.5 −0.293809
119119 0 0
120120 134431. 0.852211
121121 −13811.1 + 23921.6i −0.0857563 + 0.148534i
122122 −44410.4 76921.0i −0.270137 0.467892i
123123 −165134. 286020.i −0.984175 1.70464i
124124 7758.81 13438.7i 0.0453149 0.0784877i
125125 −75008.6 −0.429374
126126 0 0
127127 −71222.2 −0.391838 −0.195919 0.980620i 0.562769π-0.562769\pi
−0.195919 + 0.980620i 0.562769π0.562769\pi
128128 −8192.00 + 14189.0i −0.0441942 + 0.0765466i
129129 96729.4 + 167540.i 0.511781 + 0.886431i
130130 143421. + 248412.i 0.744309 + 1.28918i
131131 −68351.3 + 118388.i −0.347991 + 0.602739i −0.985893 0.167380i 0.946469π-0.946469\pi
0.637901 + 0.770118i 0.279803π0.279803\pi
132132 172787. 0.863132
133133 0 0
134134 −28874.3 −0.138915
135135 −138760. + 240339.i −0.655285 + 1.13499i
136136 9646.24 + 16707.8i 0.0447209 + 0.0774589i
137137 −72096.5 124875.i −0.328181 0.568425i 0.653970 0.756520i 0.273102π-0.273102\pi
−0.982151 + 0.188095i 0.939769π0.939769\pi
138138 −85001.5 + 147227.i −0.379952 + 0.658096i
139139 −217792. −0.956102 −0.478051 0.878332i 0.658657π-0.658657\pi
−0.478051 + 0.878332i 0.658657π0.658657\pi
140140 0 0
141141 136471. 0.578087
142142 −92306.5 + 159880.i −0.384160 + 0.665384i
143143 184342. + 319289.i 0.753848 + 1.30570i
144144 −48015.6 83165.4i −0.192964 0.334223i
145145 162282. 281080.i 0.640987 1.11022i
146146 270725. 1.05111
147147 0 0
148148 40113.5 0.150535
149149 −142539. + 246885.i −0.525978 + 0.911021i 0.473564 + 0.880760i 0.342967π0.342967\pi
−0.999542 + 0.0302615i 0.990366π0.990366\pi
150150 199534. + 345603.i 0.724085 + 1.25415i
151151 −50538.1 87534.6i −0.180375 0.312419i 0.761633 0.648008i 0.224398π-0.224398\pi
−0.942008 + 0.335589i 0.891065π0.891065\pi
152152 −93117.5 + 161284.i −0.326906 + 0.566217i
153153 −113079. −0.390528
154154 0 0
155155 81938.5 0.273942
156156 168821. 292406.i 0.555410 0.961999i
157157 −135942. 235459.i −0.440155 0.762371i 0.557546 0.830146i 0.311743π-0.311743\pi
−0.997701 + 0.0677755i 0.978410π0.978410\pi
158158 139899. + 242312.i 0.445833 + 0.772205i
159159 284172. 492200.i 0.891432 1.54401i
160160 −86513.3 −0.267167
161161 0 0
162162 −37949.0 −0.113609
163163 190588. 330108.i 0.561858 0.973167i −0.435476 0.900200i 0.643420π-0.643420\pi
0.997334 0.0729666i 0.0232466π-0.0232466\pi
164164 106272. + 184068.i 0.308538 + 0.534403i
165165 456189. + 790143.i 1.30447 + 2.25941i
166166 7831.45 13564.5i 0.0220583 0.0382061i
167167 216934. 0.601917 0.300958 0.953637i 0.402694π-0.402694\pi
0.300958 + 0.953637i 0.402694π0.402694\pi
168168 0 0
169169 349146. 0.940350
170170 −50935.6 + 88223.0i −0.135176 + 0.234131i
171171 −545787. 945332.i −1.42736 2.47226i
172172 −62250.3 107821.i −0.160443 0.277895i
173173 −139101. + 240930.i −0.353358 + 0.612034i −0.986836 0.161727i 0.948294π-0.948294\pi
0.633478 + 0.773761i 0.281627π0.281627\pi
174174 −382044. −0.956621
175175 0 0
176176 −111198. −0.270591
177177 −138107. + 239209.i −0.331347 + 0.573910i
178178 −105902. 183428.i −0.250528 0.433927i
179179 −180081. 311909.i −0.420083 0.727605i 0.575864 0.817545i 0.304666π-0.304666\pi
−0.995947 + 0.0899402i 0.971332π0.971332\pi
180180 253539. 439143.i 0.583262 1.01024i
181181 −309871. −0.703047 −0.351524 0.936179i 0.614336π-0.614336\pi
−0.351524 + 0.936179i 0.614336π0.614336\pi
182182 0 0
183183 −552066. −1.21861
184184 54702.8 94748.0i 0.119115 0.206312i
185185 105907. + 183436.i 0.227507 + 0.394054i
186186 −48225.0 83528.1i −0.102209 0.177031i
187187 −65468.7 + 113395.i −0.136908 + 0.237132i
188188 −87826.1 −0.181230
189189 0 0
190190 −983386. −1.97624
191191 480477. 832211.i 0.952992 1.65063i 0.214094 0.976813i 0.431320π-0.431320\pi
0.738898 0.673818i 0.235347π-0.235347\pi
192192 50917.5 + 88191.7i 0.0996813 + 0.172653i
193193 −256503. 444277.i −0.495678 0.858539i 0.504310 0.863523i 0.331747π-0.331747\pi
−0.999988 + 0.00498354i 0.998414π0.998414\pi
194194 129.076 223.567i 0.000246231 0.000426485i
195195 1.78287e6 3.35762
196196 0 0
197197 −768131. −1.41017 −0.705083 0.709125i 0.749090π-0.749090\pi
−0.705083 + 0.709125i 0.749090π0.749090\pi
198198 325880. 564440.i 0.590737 1.02319i
199199 −521064. 902509.i −0.932735 1.61554i −0.778624 0.627491i 0.784082π-0.784082\pi
−0.154111 0.988054i 0.549251π-0.549251\pi
200200 −128410. 222413.i −0.227000 0.393175i
201201 −89734.3 + 155424.i −0.156664 + 0.271350i
202202 289975. 0.500013
203203 0 0
204204 119913. 0.201739
205205 −561153. + 971945.i −0.932602 + 1.61531i
206206 157974. + 273620.i 0.259369 + 0.449241i
207207 320628. + 555344.i 0.520087 + 0.900817i
208208 −108645. + 188178.i −0.174121 + 0.301586i
209209 −1.26397e6 −2.00157
210210 0 0
211211 −813317. −1.25763 −0.628817 0.777554i 0.716460π-0.716460\pi
−0.628817 + 0.777554i 0.716460π0.716460\pi
212212 −182879. + 316756.i −0.279463 + 0.484044i
213213 573733. + 993734.i 0.866484 + 1.50079i
214214 −252772. 437814.i −0.377307 0.653514i
215215 328704. 569331.i 0.484963 0.839980i
216216 −210228. −0.306589
217217 0 0
218218 718872. 1.02450
219219 841347. 1.45726e6i 1.18540 2.05317i
220220 −293581. 508497.i −0.408951 0.708324i
221221 127931. + 221583.i 0.176196 + 0.305180i
222222 124663. 215923.i 0.169768 0.294047i
223223 −238869. −0.321661 −0.160830 0.986982i 0.551417π-0.551417\pi
−0.160830 + 0.986982i 0.551417π0.551417\pi
224224 0 0
225225 1.50530e6 1.98229
226226 −516054. + 893832.i −0.672085 + 1.16408i
227227 292618. + 506829.i 0.376909 + 0.652826i 0.990611 0.136712i 0.0436536π-0.0436536\pi
−0.613702 + 0.789538i 0.710320π0.710320\pi
228228 578773. + 1.00246e6i 0.737346 + 1.27712i
229229 742732. 1.28645e6i 0.935930 1.62108i 0.162962 0.986632i 0.447895π-0.447895\pi
0.772967 0.634446i 0.218772π-0.218772\pi
230230 577700. 0.720083
231231 0 0
232232 245865. 0.299900
233233 560354. 970562.i 0.676196 1.17121i −0.299922 0.953964i 0.596961π-0.596961\pi
0.976118 0.217242i 0.0697061π-0.0697061\pi
234234 −636797. 1.10296e6i −0.760258 1.31681i
235235 −231877. 401622.i −0.273897 0.474403i
236236 88879.1 153943.i 0.103877 0.179920i
237237 1.73909e6 2.01118
238238 0 0
239239 13757.0 0.0155786 0.00778931 0.999970i 0.497521π-0.497521\pi
0.00778931 + 0.999970i 0.497521π0.497521\pi
240240 −268862. + 465683.i −0.301302 + 0.521870i
241241 749382. + 1.29797e6i 0.831114 + 1.43953i 0.897156 + 0.441715i 0.145630π0.145630\pi
−0.0660416 + 0.997817i 0.521037π0.521037\pi
242242 −55244.5 95686.4i −0.0606389 0.105030i
243243 −517042. + 895542.i −0.561707 + 0.972905i
244244 355283. 0.382032
245245 0 0
246246 1.32107e6 1.39183
247247 −1.23495e6 + 2.13900e6i −1.28797 + 2.23084i
248248 31035.2 + 53754.6i 0.0320425 + 0.0554992i
249249 −48676.5 84310.2i −0.0497532 0.0861751i
250250 150017. 259838.i 0.151807 0.262937i
251251 −966842. −0.968660 −0.484330 0.874886i 0.660936π-0.660936\pi
−0.484330 + 0.874886i 0.660936π0.660936\pi
252252 0 0
253253 742531. 0.729312
254254 142444. 246721.i 0.138535 0.239950i
255255 316591. + 548351.i 0.304893 + 0.528091i
256256 −32768.0 56755.8i −0.0312500 0.0541266i
257257 −857425. + 1.48510e6i −0.809774 + 1.40257i 0.103247 + 0.994656i 0.467077π0.467077\pi
−0.913021 + 0.407913i 0.866257π0.866257\pi
258258 −773835. −0.723768
259259 0 0
260260 −1.14736e6 −1.05261
261261 −720540. + 1.24801e6i −0.654722 + 1.13401i
262262 −273405. 473552.i −0.246067 0.426201i
263263 238994. + 413950.i 0.213058 + 0.369027i 0.952670 0.304006i 0.0983244π-0.0983244\pi
−0.739612 + 0.673033i 0.764991π0.764991\pi
264264 −345575. + 598553.i −0.305163 + 0.528558i
265265 −1.93133e6 −1.68944
266266 0 0
267267 −1.31648e6 −1.13015
268268 57748.6 100024.i 0.0491139 0.0850678i
269269 360049. + 623623.i 0.303376 + 0.525462i 0.976898 0.213704i 0.0685529π-0.0685529\pi
−0.673523 + 0.739167i 0.735220π0.735220\pi
270270 −555040. 961358.i −0.463356 0.802557i
271271 190810. 330492.i 0.157826 0.273362i −0.776259 0.630414i 0.782885π-0.782885\pi
0.934084 + 0.357053i 0.116218π0.116218\pi
272272 −77169.9 −0.0632450
273273 0 0
274274 576772. 0.464117
275275 871517. 1.50951e6i 0.694935 1.20366i
276276 −340006. 588907.i −0.268667 0.465344i
277277 −361288. 625770.i −0.282914 0.490021i 0.689187 0.724583i 0.257968π-0.257968\pi
−0.972101 + 0.234562i 0.924634π0.924634\pi
278278 435583. 754452.i 0.338033 0.585490i
279279 −363812. −0.279812
280280 0 0
281281 −51828.2 −0.0391561 −0.0195781 0.999808i 0.506232π-0.506232\pi
−0.0195781 + 0.999808i 0.506232π0.506232\pi
282282 −272942. + 472750.i −0.204385 + 0.354004i
283283 −31080.6 53833.2i −0.0230687 0.0399562i 0.854261 0.519845i 0.174010π-0.174010\pi
−0.877329 + 0.479889i 0.840677π0.840677\pi
284284 −369226. 639518.i −0.271642 0.470497i
285285 −3.05613e6 + 5.29337e6i −2.22874 + 3.86029i
286286 −1.47473e6 −1.06610
287287 0 0
288288 384125. 0.272892
289289 664494. 1.15094e6i 0.468001 0.810601i
290290 649126. + 1.12432e6i 0.453246 + 0.785045i
291291 −802.277 1389.58i −0.000555382 0.000961950i
292292 −541450. + 937819.i −0.371622 + 0.643668i
293293 2.00409e6 1.36379 0.681896 0.731449i 0.261156π-0.261156\pi
0.681896 + 0.731449i 0.261156π0.261156\pi
294294 0 0
295295 938626. 0.627968
296296 −80227.1 + 138957.i −0.0532221 + 0.0921833i
297297 −713406. 1.23566e6i −0.469295 0.812842i
298298 −570156. 987539.i −0.371923 0.644189i
299299 725484. 1.25657e6i 0.469299 0.812850i
300300 −1.59627e6 −1.02401
301301 0 0
302302 404305. 0.255089
303303 901170. 1.56087e6i 0.563898 0.976699i
304304 −372470. 645137.i −0.231157 0.400376i
305305 938010. + 1.62468e6i 0.577375 + 1.00004i
306306 226157. 391716.i 0.138072 0.239148i
307307 2.11066e6 1.27812 0.639061 0.769156i 0.279323π-0.279323\pi
0.639061 + 0.769156i 0.279323π0.279323\pi
308308 0 0
309309 1.96378e6 1.17003
310310 −163877. + 283843.i −0.0968532 + 0.167755i
311311 −521715. 903637.i −0.305867 0.529777i 0.671587 0.740926i 0.265613π-0.265613\pi
−0.977454 + 0.211149i 0.932280π0.932280\pi
312312 675282. + 1.16962e6i 0.392734 + 0.680236i
313313 459959. 796673.i 0.265374 0.459642i −0.702287 0.711894i 0.747838π-0.747838\pi
0.967662 + 0.252252i 0.0811712π0.0811712\pi
314314 1.08754e6 0.622473
315315 0 0
316316 −1.11919e6 −0.630503
317317 −976484. + 1.69132e6i −0.545779 + 0.945317i 0.452778 + 0.891623i 0.350433π0.350433\pi
−0.998557 + 0.0536941i 0.982900π0.982900\pi
318318 1.13669e6 + 1.96880e6i 0.630338 + 1.09178i
319319 834337. + 1.44511e6i 0.459055 + 0.795106i
320320 173027. 299691.i 0.0944578 0.163606i
321321 −3.14221e6 −1.70205
322322 0 0
323323 −877181. −0.467825
324324 75897.9 131459.i 0.0401668 0.0695709i
325325 −1.70302e6 2.94971e6i −0.894356 1.54907i
326326 762352. + 1.32043e6i 0.397294 + 0.688133i
327327 2.23408e6 3.86954e6i 1.15539 2.00120i
328328 −850175. −0.436339
329329 0 0
330330 −3.64952e6 −1.84480
331331 −1.92519e6 + 3.33452e6i −0.965836 + 1.67288i −0.258483 + 0.966016i 0.583223π0.583223\pi
−0.707353 + 0.706861i 0.750111π0.750111\pi
332332 31325.8 + 54257.9i 0.0155976 + 0.0270158i
333333 −470233. 814468.i −0.232382 0.402498i
334334 −433868. + 751481.i −0.212810 + 0.368597i
335335 609866. 0.296908
336336 0 0
337337 3.34682e6 1.60531 0.802653 0.596447i 0.203421π-0.203421\pi
0.802653 + 0.596447i 0.203421π0.203421\pi
338338 −698291. + 1.20948e6i −0.332464 + 0.575845i
339339 3.20754e6 + 5.55562e6i 1.51591 + 2.62563i
340340 −203742. 352892.i −0.0955837 0.165556i
341341 −210635. + 364830.i −0.0980945 + 0.169905i
342342 4.36630e6 2.01859
343343 0 0
344344 498002. 0.226900
345345 1.79535e6 3.10964e6i 0.812085 1.40657i
346346 −556404. 963720.i −0.249862 0.432773i
347347 603294. + 1.04494e6i 0.268971 + 0.465871i 0.968596 0.248638i 0.0799831π-0.0799831\pi
−0.699625 + 0.714510i 0.746650π0.746650\pi
348348 764087. 1.32344e6i 0.338217 0.585808i
349349 398849. 0.175285 0.0876426 0.996152i 0.472067π-0.472067\pi
0.0876426 + 0.996152i 0.472067π0.472067\pi
350350 0 0
351351 −2.78811e6 −1.20793
352352 222395. 385200.i 0.0956684 0.165703i
353353 −420973. 729147.i −0.179812 0.311443i 0.762004 0.647572i 0.224215π-0.224215\pi
−0.941816 + 0.336129i 0.890882π0.890882\pi
354354 −552429. 956835.i −0.234298 0.405816i
355355 1.94964e6 3.37688e6i 0.821078 1.42215i
356356 847219. 0.354300
357357 0 0
358358 1.44065e6 0.594087
359359 534970. 926596.i 0.219075 0.379450i −0.735450 0.677579i 0.763029π-0.763029\pi
0.954526 + 0.298129i 0.0963626π0.0963626\pi
360360 1.01416e6 + 1.75657e6i 0.412429 + 0.714348i
361361 −2.99577e6 5.18883e6i −1.20988 2.09557i
362362 619742. 1.07342e6i 0.248565 0.430527i
363363 −686747. −0.273546
364364 0 0
365365 −5.71809e6 −2.24657
366366 1.10413e6 1.91241e6i 0.430843 0.746241i
367367 −1.66760e6 2.88837e6i −0.646290 1.11941i −0.984002 0.178157i 0.942986π-0.942986\pi
0.337712 0.941249i 0.390347π-0.390347\pi
368368 218811. + 378992.i 0.0842267 + 0.145885i
369369 2.49156e6 4.31550e6i 0.952587 1.64993i
370370 −847255. −0.321743
371371 0 0
372372 385800. 0.144546
373373 359560. 622777.i 0.133813 0.231772i −0.791330 0.611389i 0.790611π-0.790611\pi
0.925144 + 0.379617i 0.123944π0.123944\pi
374374 −261875. 453580.i −0.0968087 0.167678i
375375 −932434. 1.61502e6i −0.342405 0.593063i
376376 175652. 304239.i 0.0640743 0.110980i
377377 3.26073e6 1.18157
378378 0 0
379379 1.33953e6 0.479022 0.239511 0.970894i 0.423013π-0.423013\pi
0.239511 + 0.970894i 0.423013π0.423013\pi
380380 1.96677e6 3.40655e6i 0.698707 1.21020i
381381 −885365. 1.53350e6i −0.312471 0.541216i
382382 1.92191e6 + 3.32884e6i 0.673867 + 1.16717i
383383 −2.12438e6 + 3.67953e6i −0.740005 + 1.28173i 0.212487 + 0.977164i 0.431844π0.431844\pi
−0.952492 + 0.304562i 0.901490π0.901490\pi
384384 −407340. −0.140971
385385 0 0
386386 2.05203e6 0.700994
387387 −1.45947e6 + 2.52787e6i −0.495355 + 0.857980i
388388 516.306 + 894.268i 0.000174112 + 0.000301570i
389389 904866. + 1.56727e6i 0.303187 + 0.525135i 0.976856 0.213898i 0.0686160π-0.0686160\pi
−0.673669 + 0.739033i 0.735283π0.735283\pi
390390 −3.56573e6 + 6.17603e6i −1.18710 + 2.05612i
391391 515309. 0.170461
392392 0 0
393393 −3.39871e6 −1.11002
394394 1.53626e6 2.66089e6i 0.498569 0.863546i
395395 −2.95486e6 5.11798e6i −0.952895 1.65046i
396396 1.30352e6 + 2.25776e6i 0.417714 + 0.723503i
397397 −1.97083e6 + 3.41359e6i −0.627587 + 1.08701i 0.360447 + 0.932780i 0.382624π0.382624\pi
−0.988034 + 0.154233i 0.950709π0.950709\pi
398398 4.16851e6 1.31909
399399 0 0
400400 1.02728e6 0.321026
401401 −82270.6 + 142497.i −0.0255496 + 0.0442532i −0.878517 0.477710i 0.841467π-0.841467\pi
0.852968 + 0.521963i 0.174800π0.174800\pi
402402 −358937. 621698.i −0.110778 0.191873i
403403 411598. + 712909.i 0.126244 + 0.218661i
404404 −579949. + 1.00450e6i −0.176781 + 0.306194i
405405 801536. 0.242820
406406 0 0
407407 −1.08900e6 −0.325867
408408 −239825. + 415390.i −0.0713255 + 0.123539i
409409 1.19537e6 + 2.07043e6i 0.353340 + 0.612002i 0.986832 0.161746i 0.0517126π-0.0517126\pi
−0.633493 + 0.773749i 0.718379π0.718379\pi
410410 −2.24461e6 3.88778e6i −0.659450 1.14220i
411411 1.79247e6 3.10465e6i 0.523416 0.906583i
412412 −1.26379e6 −0.366804
413413 0 0
414414 −2.56502e6 −0.735514
415415 −165411. + 286501.i −0.0471460 + 0.0816593i
416416 −434579. 752712.i −0.123122 0.213253i
417417 −2.70737e6 4.68931e6i −0.762444 1.32059i
418418 2.52794e6 4.37852e6i 0.707662 1.22571i
419419 −3.45750e6 −0.962114 −0.481057 0.876689i 0.659747π-0.659747\pi
−0.481057 + 0.876689i 0.659747π0.659747\pi
420420 0 0
421421 −3.69055e6 −1.01481 −0.507406 0.861707i 0.669396π-0.669396\pi
−0.507406 + 0.861707i 0.669396π0.669396\pi
422422 1.62663e6 2.81741e6i 0.444640 0.770140i
423423 1.02955e6 + 1.78323e6i 0.279766 + 0.484569i
424424 −731516. 1.26702e6i −0.197610 0.342271i
425425 604823. 1.04758e6i 0.162426 0.281331i
426426 −4.58986e6 −1.22539
427427 0 0
428428 2.02218e6 0.533592
429429 −4.58311e6 + 7.93819e6i −1.20231 + 2.08247i
430430 1.31481e6 + 2.27733e6i 0.342920 + 0.593956i
431431 2.63090e6 + 4.55686e6i 0.682200 + 1.18160i 0.974308 + 0.225220i 0.0723099π0.0723099\pi
−0.292108 + 0.956385i 0.594357π0.594357\pi
432432 420457. 728253.i 0.108396 0.187747i
433433 −5.01353e6 −1.28506 −0.642530 0.766260i 0.722115π-0.722115\pi
−0.642530 + 0.766260i 0.722115π0.722115\pi
434434 0 0
435435 8.06930e6 2.04462
436436 −1.43774e6 + 2.49024e6i −0.362214 + 0.627373i
437437 2.48720e6 + 4.30796e6i 0.623027 + 1.07911i
438438 3.36539e6 + 5.82903e6i 0.838205 + 1.45181i
439439 −2.97080e6 + 5.14558e6i −0.735720 + 1.27430i 0.218687 + 0.975795i 0.429823π0.429823\pi
−0.954407 + 0.298509i 0.903511π0.903511\pi
440440 2.34865e6 0.578344
441441 0 0
442442 −1.02345e6 −0.249179
443443 631667. 1.09408e6i 0.152925 0.264874i −0.779377 0.626556i 0.784464π-0.784464\pi
0.932302 + 0.361682i 0.117797π0.117797\pi
444444 498652. + 863691.i 0.120044 + 0.207922i
445445 2.23681e6 + 3.87427e6i 0.535462 + 0.927448i
446446 477738. 827467.i 0.113724 0.196976i
447447 −7.08762e6 −1.67777
448448 0 0
449449 6.37580e6 1.49252 0.746258 0.665657i 0.231849π-0.231849\pi
0.746258 + 0.665657i 0.231849π0.231849\pi
450450 −3.01060e6 + 5.21451e6i −0.700844 + 1.21390i
451451 −2.88505e6 4.99705e6i −0.667901 1.15684i
452452 −2.06422e6 3.57533e6i −0.475236 0.823132i
453453 1.25648e6 2.17629e6i 0.287681 0.498278i
454454 −2.34094e6 −0.533030
455455 0 0
456456 −4.63018e6 −1.04276
457457 520330. 901238.i 0.116544 0.201859i −0.801852 0.597522i 0.796152π-0.796152\pi
0.918396 + 0.395663i 0.129485π0.129485\pi
458458 2.97093e6 + 5.14580e6i 0.661802 + 1.14628i
459459 −495096. 857532.i −0.109688 0.189985i
460460 −1.15540e6 + 2.00121e6i −0.254588 + 0.440959i
461461 −4.79707e6 −1.05129 −0.525647 0.850703i 0.676177π-0.676177\pi
−0.525647 + 0.850703i 0.676177π0.676177\pi
462462 0 0
463463 1.28428e6 0.278424 0.139212 0.990263i 0.455543π-0.455543\pi
0.139212 + 0.990263i 0.455543π0.455543\pi
464464 −491729. + 851700.i −0.106031 + 0.183650i
465465 1.01858e6 + 1.76423e6i 0.218455 + 0.378376i
466466 2.24142e6 + 3.88225e6i 0.478143 + 0.828168i
467467 543295. 941014.i 0.115277 0.199666i −0.802613 0.596500i 0.796558π-0.796558\pi
0.917891 + 0.396834i 0.129891π0.129891\pi
468468 5.09437e6 1.07517
469469 0 0
470470 1.85501e6 0.387349
471471 3.37981e6 5.85400e6i 0.702004 1.21591i
472472 355516. + 615772.i 0.0734522 + 0.127223i
473473 1.68996e6 + 2.92710e6i 0.347315 + 0.601568i
474474 −3.47818e6 + 6.02438e6i −0.711059 + 1.23159i
475475 1.16770e7 2.37464
476476 0 0
477477 8.57524e6 1.72564
478478 −27514.0 + 47655.6i −0.00550787 + 0.00953991i
479479 −646682. 1.12009e6i −0.128781 0.223055i 0.794424 0.607364i 0.207773π-0.207773\pi
−0.923205 + 0.384309i 0.874440π0.874440\pi
480480 −1.07545e6 1.86273e6i −0.213053 0.369018i
481481 −1.06399e6 + 1.84289e6i −0.209690 + 0.363193i
482482 −5.99506e6 −1.17537
483483 0 0
484484 441956. 0.0857563
485485 −2726.28 + 4722.05i −0.000526279 + 0.000911541i
486486 −2.06817e6 3.58217e6i −0.397187 0.687948i
487487 −4.80813e6 8.32793e6i −0.918658 1.59116i −0.801456 0.598054i 0.795941π-0.795941\pi
−0.117202 0.993108i 0.537393π-0.537393\pi
488488 −710566. + 1.23074e6i −0.135069 + 0.233946i
489489 9.47682e6 1.79222
490490 0 0
491491 7.37274e6 1.38015 0.690074 0.723739i 0.257578π-0.257578\pi
0.690074 + 0.723739i 0.257578π0.257578\pi
492492 −2.64214e6 + 4.57631e6i −0.492088 + 0.852321i
493493 579021. + 1.00289e6i 0.107294 + 0.185839i
494494 −4.93980e6 8.55599e6i −0.910736 1.57744i
495495 −6.88304e6 + 1.19218e7i −1.26260 + 2.18690i
496496 −248282. −0.0453149
497497 0 0
498498 389412. 0.0703616
499499 −2.71007e6 + 4.69398e6i −0.487224 + 0.843897i −0.999892 0.0146897i 0.995324π-0.995324\pi
0.512668 + 0.858587i 0.328657π0.328657\pi
500500 600069. + 1.03935e6i 0.107344 + 0.185925i
501501 2.69671e6 + 4.67084e6i 0.479999 + 0.831382i
502502 1.93368e6 3.34924e6i 0.342473 0.593180i
503503 410131. 0.0722774 0.0361387 0.999347i 0.488494π-0.488494\pi
0.0361387 + 0.999347i 0.488494π0.488494\pi
504504 0 0
505505 −6.12467e6 −1.06870
506506 −1.48506e6 + 2.57220e6i −0.257851 + 0.446610i
507507 4.34024e6 + 7.51751e6i 0.749883 + 1.29884i
508508 569778. + 986884.i 0.0979594 + 0.169671i
509509 2.56191e6 4.43736e6i 0.438298 0.759155i −0.559260 0.828992i 0.688915π-0.688915\pi
0.997558 + 0.0698374i 0.0222480π0.0222480\pi
510510 −2.53273e6 −0.431184
511511 0 0
512512 262144. 0.0441942
513513 4.77928e6 8.27796e6i 0.801806 1.38877i
514514 −3.42970e6 5.94042e6i −0.572596 0.991766i
515515 −3.33664e6 5.77923e6i −0.554360 0.960179i
516516 1.54767e6 2.68064e6i 0.255891 0.443215i
517517 2.38429e6 0.392313
518518 0 0
519519 −6.91667e6 −1.12714
520520 2.29473e6 3.97459e6i 0.372154 0.644590i
521521 −3.33701e6 5.77987e6i −0.538596 0.932876i −0.998980 0.0451557i 0.985622π-0.985622\pi
0.460384 0.887720i 0.347712π-0.347712\pi
522522 −2.88216e6 4.99205e6i −0.462959 0.801868i
523523 −4.70208e6 + 8.14424e6i −0.751685 + 1.30196i 0.195320 + 0.980739i 0.437425π0.437425\pi
−0.947005 + 0.321217i 0.895908π0.895908\pi
524524 2.18724e6 0.347991
525525 0 0
526526 −1.91195e6 −0.301309
527527 −146178. + 253189.i −0.0229275 + 0.0397116i
528528 −1.38230e6 2.39421e6i −0.215783 0.373747i
529529 1.75704e6 + 3.04329e6i 0.272988 + 0.472829i
530530 3.86266e6 6.69033e6i 0.597307 1.03457i
531531 −4.16756e6 −0.641425
532532 0 0
533533 −1.12753e7 −1.71913
534534 2.63295e6 4.56041e6i 0.399567 0.692070i
535535 5.33890e6 + 9.24725e6i 0.806431 + 1.39678i
536536 230994. + 400094.i 0.0347288 + 0.0601520i
537537 4.47718e6 7.75471e6i 0.669991 1.16046i
538538 −2.88039e6 −0.429038
539539 0 0
540540 4.44032e6 0.655285
541541 2.30474e6 3.99192e6i 0.338554 0.586393i −0.645607 0.763670i 0.723395π-0.723395\pi
0.984161 + 0.177277i 0.0567288π0.0567288\pi
542542 763239. + 1.32197e6i 0.111600 + 0.193296i
543543 −3.85202e6 6.67189e6i −0.560646 0.971067i
544544 154340. 267325.i 0.0223605 0.0387295i
545545 −1.51836e7 −2.18969
546546 0 0
547547 −31688.1 −0.00452822 −0.00226411 0.999997i 0.500721π-0.500721\pi
−0.00226411 + 0.999997i 0.500721π0.500721\pi
548548 −1.15354e6 + 1.99800e6i −0.164090 + 0.284213i
549549 −4.16482e6 7.21369e6i −0.589747 1.02147i
550550 3.48607e6 + 6.03804e6i 0.491393 + 0.851117i
551551 −5.58943e6 + 9.68117e6i −0.784311 + 1.35847i
552552 2.72005e6 0.379952
553553 0 0
554554 2.89031e6 0.400101
555555 −2.63306e6 + 4.56060e6i −0.362851 + 0.628477i
556556 1.74233e6 + 3.01781e6i 0.239025 + 0.414004i
557557 543101. + 940679.i 0.0741725 + 0.128471i 0.900726 0.434387i 0.143035π-0.143035\pi
−0.826554 + 0.562858i 0.809702π0.809702\pi
558558 727625. 1.26028e6i 0.0989286 0.171349i
559559 6.60465e6 0.893965
560560 0 0
561561 −3.25537e6 −0.436710
562562 103656. 179538.i 0.0138438 0.0239781i
563563 3.78462e6 + 6.55515e6i 0.503212 + 0.871589i 0.999993 + 0.00371329i 0.00118198π0.00118198\pi
−0.496781 + 0.867876i 0.665485π0.665485\pi
564564 −1.09177e6 1.89100e6i −0.144522 0.250319i
565565 1.08998e7 1.88790e7i 1.43647 2.48804i
566566 248645. 0.0326241
567567 0 0
568568 2.95381e6 0.384160
569569 −7.29078e6 + 1.26280e7i −0.944046 + 1.63514i −0.186396 + 0.982475i 0.559681π0.559681\pi
−0.757650 + 0.652661i 0.773653π0.773653\pi
570570 −1.22245e7 2.11735e7i −1.57596 2.72964i
571571 5.76078e6 + 9.97796e6i 0.739419 + 1.28071i 0.952757 + 0.303733i 0.0982332π0.0982332\pi
−0.213338 + 0.976979i 0.568433π0.568433\pi
572572 2.94947e6 5.10863e6i 0.376924 0.652851i
573573 2.38913e7 3.03986
574574 0 0
575575 −6.85977e6 −0.865247
576576 −768249. + 1.33065e6i −0.0964819 + 0.167112i
577577 7.69266e6 + 1.33241e7i 0.961916 + 1.66609i 0.717683 + 0.696370i 0.245203π0.245203\pi
0.244233 + 0.969717i 0.421464π0.421464\pi
578578 2.65798e6 + 4.60375e6i 0.330926 + 0.573181i
579579 6.37720e6 1.10456e7i 0.790558 1.36929i
580580 −5.19301e6 −0.640987
581581 0 0
582582 6418.21 0.000785429
583583 4.96477e6 8.59924e6i 0.604962 1.04782i
584584 −2.16580e6 3.75128e6i −0.262776 0.455142i
585585 1.34500e7 + 2.32962e7i 1.62493 + 2.81446i
586586 −4.00818e6 + 6.94237e6i −0.482173 + 0.835149i
587587 −5.34856e6 −0.640680 −0.320340 0.947303i 0.603797π-0.603797\pi
−0.320340 + 0.947303i 0.603797π0.603797\pi
588588 0 0
589589 −2.82219e6 −0.335195
590590 −1.87725e6 + 3.25150e6i −0.222020 + 0.384550i
591591 −9.54866e6 1.65388e7i −1.12454 1.94776i
592592 −320908. 555829.i −0.0376337 0.0651834i
593593 −2.59654e6 + 4.49734e6i −0.303221 + 0.525194i −0.976864 0.213863i 0.931395π-0.931395\pi
0.673643 + 0.739057i 0.264729π0.264729\pi
594594 5.70725e6 0.663683
595595 0 0
596596 4.56125e6 0.525978
597597 1.29547e7 2.24382e7i 1.48762 2.57663i
598598 2.90194e6 + 5.02630e6i 0.331845 + 0.574772i
599599 5.64643e6 + 9.77991e6i 0.642994 + 1.11370i 0.984761 + 0.173914i 0.0556415π0.0556415\pi
−0.341766 + 0.939785i 0.611025π0.611025\pi
600600 3.19255e6 5.52966e6i 0.362042 0.627076i
601601 3.49678e6 0.394895 0.197447 0.980313i 0.436735π-0.436735\pi
0.197447 + 0.980313i 0.436735π0.436735\pi
602602 0 0
603603 −2.70785e6 −0.303271
604604 −808610. + 1.40055e6i −0.0901876 + 0.156210i
605605 1.16684e6 + 2.02103e6i 0.129606 + 0.224484i
606606 3.60468e6 + 6.24349e6i 0.398736 + 0.690631i
607607 4.21966e6 7.30866e6i 0.464842 0.805131i −0.534352 0.845262i 0.679444π-0.679444\pi
0.999194 + 0.0401314i 0.0127777π0.0127777\pi
608608 2.97976e6 0.326906
609609 0 0
610610 −7.50408e6 −0.816531
611611 2.32955e6 4.03490e6i 0.252446 0.437250i
612612 904629. + 1.56686e6i 0.0976319 + 0.169103i
613613 −7.94116e6 1.37545e7i −0.853557 1.47840i −0.877977 0.478703i 0.841107π-0.841107\pi
0.0244199 0.999702i 0.492226π-0.492226\pi
614614 −4.22132e6 + 7.31155e6i −0.451885 + 0.782687i
615615 −2.79028e7 −2.97482
616616 0 0
617617 −1.68397e6 −0.178082 −0.0890412 0.996028i 0.528380π-0.528380\pi
−0.0890412 + 0.996028i 0.528380π0.528380\pi
618618 −3.92757e6 + 6.80275e6i −0.413668 + 0.716495i
619619 7.29394e6 + 1.26335e7i 0.765131 + 1.32525i 0.940177 + 0.340685i 0.110659π0.110659\pi
−0.175046 + 0.984560i 0.556008π0.556008\pi
620620 −655508. 1.13537e6i −0.0684856 0.118620i
621621 −2.80764e6 + 4.86297e6i −0.292154 + 0.506026i
622622 4.17372e6 0.432561
623623 0 0
624624 −5.40226e6 −0.555410
625625 3.10146e6 5.37189e6i 0.317590 0.550082i
626626 1.83984e6 + 3.18669e6i 0.187648 + 0.325016i
627627 −1.57124e7 2.72147e7i −1.59615 2.76462i
628628 −2.17508e6 + 3.76734e6i −0.220077 + 0.381185i
629629 −755752. −0.0761645
630630 0 0
631631 −7.42899e6 −0.742773 −0.371387 0.928478i 0.621118π-0.621118\pi
−0.371387 + 0.928478i 0.621118π0.621118\pi
632632 2.23838e6 3.87699e6i 0.222916 0.386102i
633633 −1.01104e7 1.75117e7i −1.00290 1.73707i
634634 −3.90594e6 6.76528e6i −0.385924 0.668440i
635635 −3.00863e6 + 5.21109e6i −0.296097 + 0.512855i
636636 −9.09350e6 −0.891432
637637 0 0
638638 −6.67469e6 −0.649202
639639 −8.65655e6 + 1.49936e7i −0.838673 + 1.45262i
640640 692107. + 1.19876e6i 0.0667918 + 0.115687i
641641 −5.27112e6 9.12984e6i −0.506708 0.877644i −0.999970 0.00776283i 0.997529π-0.997529\pi
0.493262 0.869881i 0.335804π-0.335804\pi
642642 6.28443e6 1.08850e7i 0.601767 1.04229i
643643 8.53482e6 0.814080 0.407040 0.913410i 0.366561π-0.366561\pi
0.407040 + 0.913410i 0.366561π0.366561\pi
644644 0 0
645645 1.63445e7 1.54694
646646 1.75436e6 3.03865e6i 0.165401 0.286483i
647647 −4.74804e6 8.22385e6i −0.445917 0.772351i 0.552199 0.833713i 0.313789π-0.313789\pi
−0.998116 + 0.0613619i 0.980456π0.980456\pi
648648 303592. + 525836.i 0.0284022 + 0.0491941i
649649 −2.41287e6 + 4.17922e6i −0.224866 + 0.389479i
650650 1.36241e7 1.26481
651651 0 0
652652 −6.09882e6 −0.561858
653653 −3.31526e6 + 5.74220e6i −0.304253 + 0.526982i −0.977095 0.212805i 0.931740π-0.931740\pi
0.672842 + 0.739787i 0.265074π0.265074\pi
654654 8.93631e6 + 1.54781e7i 0.816985 + 1.41506i
655655 5.77470e6 + 1.00021e7i 0.525928 + 0.910934i
656656 1.70035e6 2.94509e6i 0.154269 0.267202i
657657 2.53887e7 2.29471
658658 0 0
659659 7.54914e6 0.677149 0.338574 0.940940i 0.390055π-0.390055\pi
0.338574 + 0.940940i 0.390055π0.390055\pi
660660 7.29903e6 1.26423e7i 0.652237 1.12971i
661661 930337. + 1.61139e6i 0.0828203 + 0.143449i 0.904460 0.426558i 0.140274π-0.140274\pi
−0.821640 + 0.570007i 0.806941π0.806941\pi
662662 −7.70075e6 1.33381e7i −0.682949 1.18290i
663663 −3.18063e6 + 5.50902e6i −0.281015 + 0.486733i
664664 −250606. −0.0220583
665665 0 0
666666 3.76187e6 0.328638
667667 3.28356e6 5.68730e6i 0.285779 0.494984i
668668 −1.73547e6 3.00592e6i −0.150479 0.260638i
669669 −2.96939e6 5.14313e6i −0.256508 0.444286i
670670 −1.21973e6 + 2.11264e6i −0.104973 + 0.181819i
671671 −9.64516e6 −0.826996
672672 0 0
673673 −1.14956e6 −0.0978350 −0.0489175 0.998803i 0.515577π-0.515577\pi
−0.0489175 + 0.998803i 0.515577π0.515577\pi
674674 −6.69364e6 + 1.15937e7i −0.567561 + 0.983045i
675675 6.59071e6 + 1.14154e7i 0.556766 + 0.964346i
676676 −2.79316e6 4.83790e6i −0.235088 0.407184i
677677 −1.00789e6 + 1.74573e6i −0.0845169 + 0.146388i −0.905185 0.425017i 0.860268π-0.860268\pi
0.820668 + 0.571405i 0.193601π0.193601\pi
678678 −2.56603e7 −2.14382
679679 0 0
680680 1.62994e6 0.135176
681681 −7.27509e6 + 1.26008e7i −0.601133 + 1.04119i
682682 −842540. 1.45932e6i −0.0693633 0.120141i
683683 3.73215e6 + 6.46427e6i 0.306131 + 0.530234i 0.977512 0.210878i 0.0676322π-0.0676322\pi
−0.671382 + 0.741112i 0.734299π0.734299\pi
684684 −8.73260e6 + 1.51253e7i −0.713680 + 1.23613i
685685 −1.21822e7 −0.991975
686686 0 0
687687 3.69317e7 2.98543
688688 −996005. + 1.72513e6i −0.0802214 + 0.138948i
689689 −9.70158e6 1.68036e7i −0.778564 1.34851i
690690 7.18140e6 + 1.24386e7i 0.574231 + 0.994597i
691691 −9.42851e6 + 1.63307e7i −0.751187 + 1.30109i 0.196061 + 0.980592i 0.437185π0.437185\pi
−0.947248 + 0.320502i 0.896149π0.896149\pi
692692 4.45123e6 0.353358
693693 0 0
694694 −4.82635e6 −0.380382
695695 −9.20014e6 + 1.59351e7i −0.722491 + 1.25139i
696696 3.05635e6 + 5.29375e6i 0.239155 + 0.414229i
697697 −2.00220e6 3.46790e6i −0.156108 0.270387i
698698 −797699. + 1.38165e6i −0.0619727 + 0.107340i
699699 2.78631e7 2.15693
700700 0 0
701701 −1.66789e7 −1.28195 −0.640976 0.767561i 0.721470π-0.721470\pi
−0.640976 + 0.767561i 0.721470π0.721470\pi
702702 5.57622e6 9.65830e6i 0.427068 0.739704i
703703 −3.64773e6 6.31805e6i −0.278377 0.482164i
704704 889580. + 1.54080e6i 0.0676478 + 0.117169i
705705 5.76493e6 9.98515e6i 0.436839 0.756627i
706706 3.36778e6 0.254292
707707 0 0
708708 4.41943e6 0.331347
709709 7.99121e6 1.38412e7i 0.597031 1.03409i −0.396226 0.918153i 0.629680π-0.629680\pi
0.993257 0.115935i 0.0369865π-0.0369865\pi
710710 7.79858e6 + 1.35075e7i 0.580590 + 1.00561i
711711 1.31198e7 + 2.27241e7i 0.973314 + 1.68583i
712712 −1.69444e6 + 2.93485e6i −0.125264 + 0.216963i
713713 1.65792e6 0.122135
714714 0 0
715715 3.11485e7 2.27862
716716 −2.88129e6 + 4.99055e6i −0.210042 + 0.363803i
717717 171014. + 296204.i 0.0124232 + 0.0215176i
718718 2.13988e6 + 3.70638e6i 0.154910 + 0.268312i
719719 5.89067e6 1.02029e7i 0.424954 0.736042i −0.571462 0.820629i 0.693623π-0.693623\pi
0.996416 + 0.0845862i 0.0269568π0.0269568\pi
720720 −8.11326e6 −0.583262
721721 0 0
722722 2.39662e7 1.71102
723723 −1.86312e7 + 3.22701e7i −1.32555 + 2.29591i
724724 2.47897e6 + 4.29370e6i 0.175762 + 0.304428i
725725 −7.70791e6 1.33505e7i −0.544617 0.943305i
726726 1.37349e6 2.37896e6i 0.0967130 0.167512i
727727 −1.26528e7 −0.887870 −0.443935 0.896059i 0.646418π-0.646418\pi
−0.443935 + 0.896059i 0.646418π0.646418\pi
728728 0 0
729729 −2.34040e7 −1.63107
730730 1.14362e7 1.98081e7i 0.794281 1.37574i
731731 1.17282e6 + 2.03138e6i 0.0811776 + 0.140604i
732732 4.41653e6 + 7.64966e6i 0.304652 + 0.527672i
733733 2.67169e6 4.62751e6i 0.183665 0.318117i −0.759461 0.650553i 0.774537π-0.774537\pi
0.943126 + 0.332436i 0.107870π0.107870\pi
734734 1.33408e7 0.913992
735735 0 0
736736 −1.75049e6 −0.119115
737737 −1.56775e6 + 2.71542e6i −0.106318 + 0.184149i
738738 9.96622e6 + 1.72620e7i 0.673581 + 1.16668i
739739 2.11245e6 + 3.65888e6i 0.142290 + 0.246454i 0.928359 0.371685i 0.121220π-0.121220\pi
−0.786068 + 0.618140i 0.787887π0.787887\pi
740740 1.69451e6 2.93498e6i 0.113753 0.197027i
741741 −6.14068e7 −4.10839
742742 0 0
743743 1.70227e7 1.13124 0.565622 0.824665i 0.308636π-0.308636\pi
0.565622 + 0.824665i 0.308636π0.308636\pi
744744 −771600. + 1.33645e6i −0.0511046 + 0.0885157i
745745 1.20425e7 + 2.08582e7i 0.794924 + 1.37685i
746746 1.43824e6 + 2.49111e6i 0.0946204 + 0.163887i
747747 734437. 1.27208e6i 0.0481563 0.0834092i
748748 2.09500e6 0.136908
749749 0 0
750750 7.45948e6 0.484234
751751 1.19717e6 2.07355e6i 0.0774560 0.134158i −0.824696 0.565577i 0.808654π-0.808654\pi
0.902152 + 0.431419i 0.141987π0.141987\pi
752752 702609. + 1.21695e6i 0.0453074 + 0.0784747i
753753 −1.20188e7 2.08172e7i −0.772458 1.33794i
754754 −6.52146e6 + 1.12955e7i −0.417750 + 0.723564i
755755 −8.53950e6 −0.545211
756756 0 0
757757 3.82315e6 0.242483 0.121242 0.992623i 0.461312π-0.461312\pi
0.121242 + 0.992623i 0.461312π0.461312\pi
758758 −2.67907e6 + 4.64028e6i −0.169360 + 0.293340i
759759 9.23042e6 + 1.59876e7i 0.581590 + 1.00734i
760760 7.86709e6 + 1.36262e7i 0.494061 + 0.855738i
761761 −9.18198e6 + 1.59037e7i −0.574745 + 0.995487i 0.421325 + 0.906910i 0.361565π0.361565\pi
−0.996069 + 0.0885770i 0.971768π0.971768\pi
762762 7.08292e6 0.441901
763763 0 0
764764 −1.53753e7 −0.952992
765765 −4.77676e6 + 8.27359e6i −0.295107 + 0.511141i
766766 −8.49751e6 1.47181e7i −0.523263 0.906317i
767767 4.71496e6 + 8.16655e6i 0.289394 + 0.501245i
768768 814680. 1.41107e6i 0.0498407 0.0863266i
769769 1.24704e7 0.760441 0.380220 0.924896i 0.375848π-0.375848\pi
0.380220 + 0.924896i 0.375848π0.375848\pi
770770 0 0
771771 −4.26347e7 −2.58302
772772 −4.10405e6 + 7.10843e6i −0.247839 + 0.429270i
773773 −8.27062e6 1.43251e7i −0.497840 0.862284i 0.502157 0.864776i 0.332540π-0.332540\pi
−0.999997 + 0.00249268i 0.999207π0.999207\pi
774774 −5.83786e6 1.01115e7i −0.350269 0.606683i
775775 1.94592e6 3.37044e6i 0.116378 0.201573i
776776 −4130.45 −0.000246231
777777 0 0
778778 −7.23893e6 −0.428771
779779 1.93277e7 3.34765e7i 1.14113 1.97650i
780780 −1.42629e7 2.47041e7i −0.839406 1.45389i
781781 1.00237e7 + 1.73615e7i 0.588031 + 1.01850i
782782 −1.03062e6 + 1.78508e6i −0.0602671 + 0.104386i
783783 −1.26191e7 −0.735569
784784 0 0
785785 −2.29704e7 −1.33043
786786 6.79741e6 1.17735e7i 0.392453 0.679748i
787787 −3.83182e6 6.63691e6i −0.220530 0.381970i 0.734439 0.678675i 0.237445π-0.237445\pi
−0.954969 + 0.296705i 0.904112π0.904112\pi
788788 6.14505e6 + 1.06435e7i 0.352541 + 0.610619i
789789 −5.94188e6 + 1.02916e7i −0.339806 + 0.588562i
790790 2.36389e7 1.34760
791791 0 0
792792 −1.04282e7 −0.590737
793793 −9.42373e6 + 1.63224e7i −0.532157 + 0.921723i
794794 −7.88334e6 1.36543e7i −0.443771 0.768634i
795795 −2.40084e7 4.15838e7i −1.34724 2.33349i
796796 −8.33702e6 + 1.44401e7i −0.466367 + 0.807772i
797797 −8.13707e6 −0.453756 −0.226878 0.973923i 0.572852π-0.572852\pi
−0.226878 + 0.973923i 0.572852π0.572852\pi
798798 0 0
799799 1.65467e6 0.0916949
800800 −2.05457e6 + 3.55862e6i −0.113500 + 0.196588i
801801 −9.93157e6 1.72020e7i −0.546936 0.947322i
802802 −329082. 569988.i −0.0180663 0.0312917i
803803 1.46992e7 2.54598e7i 0.804460 1.39337i
804804 2.87150e6 0.156664
805805 0 0
806806 −3.29279e6 −0.178536
807807 −8.95156e6 + 1.55045e7i −0.483854 + 0.838060i
808808 −2.31980e6 4.01800e6i −0.125003 0.216512i
809809 −6.97675e6 1.20841e7i −0.374784 0.649146i 0.615510 0.788129i 0.288950π-0.288950\pi
−0.990295 + 0.138983i 0.955617π0.955617\pi
810810 −1.60307e6 + 2.77660e6i −0.0858500 + 0.148697i
811811 1.92110e7 1.02564 0.512822 0.858495i 0.328600π-0.328600\pi
0.512822 + 0.858495i 0.328600π0.328600\pi
812812 0 0
813813 9.48784e6 0.503432
814814 2.17799e6 3.77239e6i 0.115211 0.199552i
815815 −1.61020e7 2.78894e7i −0.849150 1.47077i
816816 −959302. 1.66156e6i −0.0504347 0.0873555i
817817 −1.13215e7 + 1.96094e7i −0.593400 + 1.02780i
818818 −9.56293e6 −0.499698
819819 0 0
820820 1.79569e7 0.932602
821821 1.68847e7 2.92452e7i 0.874249 1.51424i 0.0166893 0.999861i 0.494687π-0.494687\pi
0.857560 0.514384i 0.171979π-0.171979\pi
822822 7.16987e6 + 1.24186e7i 0.370111 + 0.641051i
823823 6.35702e6 + 1.10107e7i 0.327156 + 0.566650i 0.981946 0.189160i 0.0605766π-0.0605766\pi
−0.654791 + 0.755810i 0.727243π0.727243\pi
824824 2.52759e6 4.37791e6i 0.129685 0.224620i
825825 4.33354e7 2.21670
826826 0 0
827827 2.85821e7 1.45322 0.726608 0.687053i 0.241096π-0.241096\pi
0.726608 + 0.687053i 0.241096π0.241096\pi
828828 5.13005e6 8.88551e6i 0.260043 0.450408i
829829 4.02286e6 + 6.96779e6i 0.203305 + 0.352135i 0.949591 0.313490i 0.101498π-0.101498\pi
−0.746286 + 0.665625i 0.768165π0.768165\pi
830830 −661645. 1.14600e6i −0.0333373 0.0577418i
831831 8.98237e6 1.55579e7i 0.451220 0.781536i
832832 3.47663e6 0.174121
833833 0 0
834834 2.16590e7 1.07826
835835 9.16390e6 1.58723e7i 0.454846 0.787816i
836836 1.01118e7 + 1.75141e7i 0.500392 + 0.866705i
837837 −1.59289e6 2.75897e6i −0.0785910 0.136124i
838838 6.91499e6 1.19771e7i 0.340159 0.589172i
839839 4.26854e6 0.209351 0.104675 0.994506i 0.466620π-0.466620\pi
0.104675 + 0.994506i 0.466620π0.466620\pi
840840 0 0
841841 −5.75299e6 −0.280481
842842 7.38110e6 1.27844e7i 0.358790 0.621443i
843843 −644277. 1.11592e6i −0.0312251 0.0540835i
844844 6.50654e6 + 1.12697e7i 0.314408 + 0.544571i
845845 1.47489e7 2.55458e7i 0.710588 1.23077i
846846 −8.23637e6 −0.395649
847847 0 0
848848 5.85213e6 0.279463
849849 772728. 1.33840e6i 0.0367923 0.0637262i
850850 2.41929e6 + 4.19034e6i 0.114853 + 0.198931i
851851 2.14289e6 + 3.71160e6i 0.101432 + 0.175686i
852852 9.17972e6 1.58997e7i 0.433242 0.750397i
853853 6.37238e6 0.299867 0.149934 0.988696i 0.452094π-0.452094\pi
0.149934 + 0.988696i 0.452094π0.452094\pi
854854 0 0
855855 −9.22224e7 −4.31441
856856 −4.04435e6 + 7.00502e6i −0.188653 + 0.326757i
857857 1.03338e7 + 1.78986e7i 0.480625 + 0.832468i 0.999753 0.0222292i 0.00707635π-0.00707635\pi
−0.519127 + 0.854697i 0.673743π0.673743\pi
858858 −1.83325e7 3.17527e7i −0.850163 1.47253i
859859 1.05274e7 1.82339e7i 0.486784 0.843135i −0.513100 0.858329i 0.671503π-0.671503\pi
0.999885 + 0.0151935i 0.00483642π0.00483642\pi
860860 −1.05185e7 −0.484963
861861 0 0
862862 −2.10472e7 −0.964776
863863 1.03530e7 1.79318e7i 0.473192 0.819593i −0.526337 0.850276i 0.676435π-0.676435\pi
0.999529 + 0.0306833i 0.00976833π0.00976833\pi
864864 1.68183e6 + 2.91301e6i 0.0766473 + 0.132757i
865865 1.17520e7 + 2.03551e7i 0.534039 + 0.924982i
866866 1.00271e7 1.73674e7i 0.454337 0.786936i
867867 3.30414e7 1.49283
868868 0 0
869869 3.03836e7 1.36487
870870 −1.61386e7 + 2.79529e7i −0.722883 + 1.25207i
871871 3.06352e6 + 5.30616e6i 0.136828 + 0.236993i
872872 −5.75097e6 9.96098e6i −0.256124 0.443620i
873873 12104.9 20966.2i 0.000537556 0.000931075i
874874 −1.98976e7 −0.881093
875875 0 0
876876 −2.69231e7 −1.18540
877877 −4.23808e6 + 7.34057e6i −0.186067 + 0.322278i −0.943936 0.330130i 0.892908π-0.892908\pi
0.757868 + 0.652407i 0.226241π0.226241\pi
878878 −1.18832e7 2.05823e7i −0.520232 0.901069i
879879 2.49129e7 + 4.31504e7i 1.08756 + 1.88370i
880880 −4.69730e6 + 8.13596e6i −0.204476 + 0.354162i
881881 652358. 0.0283169 0.0141585 0.999900i 0.495493π-0.495493\pi
0.0141585 + 0.999900i 0.495493π0.495493\pi
882882 0 0
883883 1.20036e7 0.518097 0.259049 0.965864i 0.416591π-0.416591\pi
0.259049 + 0.965864i 0.416591π0.416591\pi
884884 2.04690e6 3.54534e6i 0.0880980 0.152590i
885885 1.16681e7 + 2.02097e7i 0.500774 + 0.867365i
886886 2.52667e6 + 4.37631e6i 0.108134 + 0.187294i
887887 −1.51650e6 + 2.62666e6i −0.0647193 + 0.112097i −0.896569 0.442903i 0.853949π-0.853949\pi
0.831850 + 0.555000i 0.187282π0.187282\pi
888888 −3.98922e6 −0.169768
889889 0 0
890890 −1.78945e7 −0.757258
891891 −2.06046e6 + 3.56883e6i −0.0869502 + 0.150602i
892892 1.91095e6 + 3.30987e6i 0.0804151 + 0.139283i
893893 7.98647e6 + 1.38330e7i 0.335140 + 0.580480i
894894 1.41752e7 2.45522e7i 0.593180 1.02742i
895895 −3.04285e7 −1.26976
896896 0 0
897897 3.60740e7 1.49697
898898 −1.27516e7 + 2.20864e7i −0.527684 + 0.913975i
899899 1.86291e6 + 3.22665e6i 0.0768762 + 0.133154i
900900 −1.20424e7 2.08580e7i −0.495572 0.858355i
901901 3.44550e6 5.96778e6i 0.141397 0.244907i
902902 2.30804e7 0.944555
903903 0 0
904904 1.65137e7 0.672085
905905 −1.30898e7 + 2.26723e7i −0.531267 + 0.920181i
906906 5.02593e6 + 8.70516e6i 0.203421 + 0.352335i
907907 −1.97815e7 3.42625e7i −0.798436 1.38293i −0.920634 0.390427i 0.872328π-0.872328\pi
0.122198 0.992506i 0.461006π-0.461006\pi
908908 4.68189e6 8.10927e6i 0.188455 0.326413i
909909 2.71939e7 1.09160
910910 0 0
911911 −8.51152e6 −0.339790 −0.169895 0.985462i 0.554343π-0.554343\pi
−0.169895 + 0.985462i 0.554343π0.554343\pi
912912 9.26037e6 1.60394e7i 0.368673 0.638560i
913913 −850428. 1.47298e6i −0.0337645 0.0584819i
914914 2.08132e6 + 3.60495e6i 0.0824087 + 0.142736i
915915 −2.33208e7 + 4.03929e7i −0.920856 + 1.59497i
916916 −2.37674e7 −0.935930
917917 0 0
918918 3.96077e6 0.155122
919919 2.75942e6 4.77946e6i 0.107778 0.186677i −0.807092 0.590426i 0.798960π-0.798960\pi
0.914870 + 0.403749i 0.132293π0.132293\pi
920920 −4.62160e6 8.00485e6i −0.180021 0.311805i
921921 2.62377e7 + 4.54450e7i 1.01924 + 1.76538i
922922 9.59415e6 1.66176e7i 0.371689 0.643783i
923923 3.91743e7 1.51355
924924 0 0
925925 1.00605e7 0.386605
926926 −2.56856e6 + 4.44887e6i −0.0984378 + 0.170499i
927927 1.48149e7 + 2.56602e7i 0.566239 + 0.980754i
928928 −1.96692e6 3.40680e6i −0.0749749 0.129860i
929929 2.06763e7 3.58124e7i 0.786019 1.36143i −0.142369 0.989814i 0.545472π-0.545472\pi
0.928388 0.371612i 0.121195π-0.121195\pi
930930 −8.14864e6 −0.308943
931931 0 0
932932 −1.79313e7 −0.676196
933933 1.29709e7 2.24663e7i 0.487827 0.844942i
934934 2.17318e6 + 3.76406e6i 0.0815133 + 0.141185i
935935 5.53116e6 + 9.58025e6i 0.206913 + 0.358384i
936936 −1.01887e7 + 1.76474e7i −0.380129 + 0.658403i
937937 1.56526e7 0.582421 0.291210 0.956659i 0.405942π-0.405942\pi
0.291210 + 0.956659i 0.405942π0.405942\pi
938938 0 0
939939 2.28711e7 0.846492
940940 −3.71002e6 + 6.42595e6i −0.136948 + 0.237202i
941941 1.67088e6 + 2.89405e6i 0.0615137 + 0.106545i 0.895142 0.445781i 0.147074π-0.147074\pi
−0.833629 + 0.552326i 0.813741π0.813741\pi
942942 1.35192e7 + 2.34160e7i 0.496392 + 0.859776i
943943 −1.13542e7 + 1.96661e7i −0.415794 + 0.720176i
944944 −2.84413e6 −0.103877
945945 0 0
946946 −1.35197e7 −0.491178
947947 −7.52817e6 + 1.30392e7i −0.272781 + 0.472471i −0.969573 0.244803i 0.921277π-0.921277\pi
0.696792 + 0.717273i 0.254610π0.254610\pi
948948 −1.39127e7 2.40975e7i −0.502795 0.870866i
949949 −2.87235e7 4.97505e7i −1.03531 1.79321i
950950 −2.33540e7 + 4.04503e7i −0.839562 + 1.45416i
951951 −4.85548e7 −1.74093
952952 0 0
953953 1.17556e7 0.419289 0.209644 0.977778i 0.432769π-0.432769\pi
0.209644 + 0.977778i 0.432769π0.432769\pi
954954 −1.71505e7 + 2.97055e7i −0.610106 + 1.05673i
955955 −4.05934e7 7.03099e7i −1.44028 2.49464i
956956 −110056. 190622.i −0.00389465 0.00674574i
957957 −2.07433e7 + 3.59285e7i −0.732147 + 1.26812i
958958 5.17345e6 0.182124
959959 0 0
960960 8.60360e6 0.301302
961961 1.38443e7 2.39790e7i 0.483572 0.837572i
962962 −4.25598e6 7.37157e6i −0.148273 0.256816i
963963 −2.37051e7 4.10584e7i −0.823712 1.42671i
964964 1.19901e7 2.07675e7i 0.415557 0.719766i
965965 −4.33417e7 −1.49826
966966 0 0
967967 −3.35850e7 −1.15499 −0.577496 0.816394i 0.695970π-0.695970\pi
−0.577496 + 0.816394i 0.695970π0.695970\pi
968968 −883913. + 1.53098e6i −0.0303194 + 0.0525148i
969969 −1.09043e7 1.88867e7i −0.373067 0.646171i
970970 −10905.1 18888.2i −0.000372135 0.000644557i
971971 −1.45780e7 + 2.52498e7i −0.496192 + 0.859430i −0.999990 0.00439139i 0.998602π-0.998602\pi
0.503798 + 0.863821i 0.331936π0.331936\pi
972972 1.65453e7 0.561707
973973 0 0
974974 3.84650e7 1.29918
975975 4.23405e7 7.33359e7i 1.42641 2.47061i
976976 −2.84226e6 4.92294e6i −0.0955080 0.165425i
977977 1.76284e7 + 3.05333e7i 0.590850 + 1.02338i 0.994118 + 0.108300i 0.0345408π0.0345408\pi
−0.403268 + 0.915082i 0.632126π0.632126\pi
978978 −1.89536e7 + 3.28287e7i −0.633644 + 1.09750i
979979 −2.30002e7 −0.766963
980980 0 0
981981 6.74161e7 2.23661
982982 −1.47455e7 + 2.55399e7i −0.487956 + 0.845164i
983983 1.80652e7 + 3.12898e7i 0.596291 + 1.03281i 0.993363 + 0.115020i 0.0366931π0.0366931\pi
−0.397072 + 0.917788i 0.629974π0.629974\pi
984984 −1.05685e7 1.83053e7i −0.347959 0.602682i
985985 −3.24480e7 + 5.62017e7i −1.06561 + 1.84569i
986986 −4.63217e6 −0.151737
987987 0 0
988988 3.95184e7 1.28797
989989 6.65091e6 1.15197e7i 0.216217 0.374499i
990990 −2.75322e7 4.76871e7i −0.892797 1.54637i
991991 1.16458e6 + 2.01711e6i 0.0376692 + 0.0652449i 0.884245 0.467023i 0.154673π-0.154673\pi
−0.846576 + 0.532268i 0.821340π0.821340\pi
992992 496564. 860074.i 0.0160212 0.0277496i
993993 −9.57283e7 −3.08083
994994 0 0
995995 −8.80449e7 −2.81933
996996 −778824. + 1.34896e6i −0.0248766 + 0.0430875i
997997 1.53275e7 + 2.65480e7i 0.488352 + 0.845851i 0.999910 0.0133980i 0.00426484π-0.00426484\pi
−0.511558 + 0.859249i 0.670932π0.670932\pi
998998 −1.08403e7 1.87759e7i −0.344520 0.596726i
999999 4.11768e6 7.13203e6i 0.130539 0.226099i
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 98.6.c.i.79.4 8
7.2 even 3 98.6.a.i.1.1 4
7.3 odd 6 inner 98.6.c.i.67.1 8
7.4 even 3 inner 98.6.c.i.67.4 8
7.5 odd 6 98.6.a.i.1.4 yes 4
7.6 odd 2 inner 98.6.c.i.79.1 8
21.2 odd 6 882.6.a.bv.1.4 4
21.5 even 6 882.6.a.bv.1.1 4
28.19 even 6 784.6.a.bg.1.1 4
28.23 odd 6 784.6.a.bg.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.6.a.i.1.1 4 7.2 even 3
98.6.a.i.1.4 yes 4 7.5 odd 6
98.6.c.i.67.1 8 7.3 odd 6 inner
98.6.c.i.67.4 8 7.4 even 3 inner
98.6.c.i.79.1 8 7.6 odd 2 inner
98.6.c.i.79.4 8 1.1 even 1 trivial
784.6.a.bg.1.1 4 28.19 even 6
784.6.a.bg.1.4 4 28.23 odd 6
882.6.a.bv.1.1 4 21.5 even 6
882.6.a.bv.1.4 4 21.2 odd 6