Properties

Label 294.6.e.z.67.2
Level 294294
Weight 66
Character 294.67
Analytic conductor 47.15347.153
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,6,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, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 294=2372 294 = 2 \cdot 3 \cdot 7^{2}
Weight: k k == 6 6
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: 47.152843025047.1528430250
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(2,3)\Q(\sqrt{2}, \sqrt{-3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 72 7^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 67.2
Root 0.707107+1.22474i-0.707107 + 1.22474i of defining polynomial
Character χ\chi == 294.67
Dual form 294.6.e.z.79.2

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+(2.00000+3.46410i)q2+(4.500007.79423i)q3+(8.00000+13.8564i)q4+(51.7487+89.6314i)q5+36.0000q664.0000q8+(40.500070.1481i)q9+(206.995+358.526i)q10+(120.095+208.011i)q11+(72.0000+124.708i)q12805.477q13+931.477q15+(128.000221.703i)q16+(646.633+1120.00i)q17+(162.000280.592i)q18+(137.688238.483i)q191655.96q20960.764q22+(1898.293287.93i)q23+(288.000+498.831i)q24+(3793.36+6570.30i)q25+(1610.952790.26i)q26729.000q27+1227.52q29+(1862.95+3226.73i)q30+(2812.434871.27i)q31+(512.000886.810i)q32+(1080.86+1872.10i)q335173.06q34+1296.00q36+(4539.25+7862.20i)q37+(550.754953.933i)q38+(3624.65+6278.07i)q39+(3311.925736.41i)q40+18207.4q4111708.2q43+(1921.533328.18i)q44+(4191.657260.15i)q45+(7593.1513151.7i)q46+(11524.319960.7i)q472304.00q4830346.9q50+(5819.70+10080.0i)q51+(6443.8211161.0i)q52+(8831.40+15296.4i)q53+(1458.002525.33i)q5424859.2q552478.39q57+(2455.04+4252.25i)q58+(9188.1515914.3i)q59+(7451.82+12906.9i)q60+(5662.04+9806.95i)q61+22499.5q62+4096.00q64+(41682.472196.1i)q65+(4323.44+7488.41i)q66+(18039.7+31245.6i)q67+(10346.117920.0i)q6834169.2q6963434.2q71+(2592.00+4489.48i)q72+(26491.2+45884.1i)q73+(18157.0+31448.8i)q74+(34140.3+59132.7i)q75+4406.03q7628997.2q78+(24282.0+42057.7i)q79+(13247.722945.6i)q80+(3280.50+5681.99i)q81+(36414.8+63072.3i)q82113161.q83133850.q85+(23416.440558.5i)q86+(5523.839567.56i)q87+(7686.1113312.7i)q88+(54182.9+93847.6i)q89+33533.2q90+60745.2q92+(25311.943841.5i)q93+(46097.279842.7i)q94+(14250.424682.4i)q95+(4608.007981.29i)q9699641.2q97+19455.5q99+O(q100)q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(51.7487 + 89.6314i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-206.995 + 358.526i) q^{10} +(-120.095 + 208.011i) q^{11} +(72.0000 + 124.708i) q^{12} -805.477 q^{13} +931.477 q^{15} +(-128.000 - 221.703i) q^{16} +(-646.633 + 1120.00i) q^{17} +(162.000 - 280.592i) q^{18} +(-137.688 - 238.483i) q^{19} -1655.96 q^{20} -960.764 q^{22} +(-1898.29 - 3287.93i) q^{23} +(-288.000 + 498.831i) q^{24} +(-3793.36 + 6570.30i) q^{25} +(-1610.95 - 2790.26i) q^{26} -729.000 q^{27} +1227.52 q^{29} +(1862.95 + 3226.73i) q^{30} +(2812.43 - 4871.27i) q^{31} +(512.000 - 886.810i) q^{32} +(1080.86 + 1872.10i) q^{33} -5173.06 q^{34} +1296.00 q^{36} +(4539.25 + 7862.20i) q^{37} +(550.754 - 953.933i) q^{38} +(-3624.65 + 6278.07i) q^{39} +(-3311.92 - 5736.41i) q^{40} +18207.4 q^{41} -11708.2 q^{43} +(-1921.53 - 3328.18i) q^{44} +(4191.65 - 7260.15i) q^{45} +(7593.15 - 13151.7i) q^{46} +(-11524.3 - 19960.7i) q^{47} -2304.00 q^{48} -30346.9 q^{50} +(5819.70 + 10080.0i) q^{51} +(6443.82 - 11161.0i) q^{52} +(-8831.40 + 15296.4i) q^{53} +(-1458.00 - 2525.33i) q^{54} -24859.2 q^{55} -2478.39 q^{57} +(2455.04 + 4252.25i) q^{58} +(9188.15 - 15914.3i) q^{59} +(-7451.82 + 12906.9i) q^{60} +(5662.04 + 9806.95i) q^{61} +22499.5 q^{62} +4096.00 q^{64} +(-41682.4 - 72196.1i) q^{65} +(-4323.44 + 7488.41i) q^{66} +(-18039.7 + 31245.6i) q^{67} +(-10346.1 - 17920.0i) q^{68} -34169.2 q^{69} -63434.2 q^{71} +(2592.00 + 4489.48i) q^{72} +(-26491.2 + 45884.1i) q^{73} +(-18157.0 + 31448.8i) q^{74} +(34140.3 + 59132.7i) q^{75} +4406.03 q^{76} -28997.2 q^{78} +(24282.0 + 42057.7i) q^{79} +(13247.7 - 22945.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(36414.8 + 63072.3i) q^{82} -113161. q^{83} -133850. q^{85} +(-23416.4 - 40558.5i) q^{86} +(5523.83 - 9567.56i) q^{87} +(7686.11 - 13312.7i) q^{88} +(54182.9 + 93847.6i) q^{89} +33533.2 q^{90} +60745.2 q^{92} +(-25311.9 - 43841.5i) q^{93} +(46097.2 - 79842.7i) q^{94} +(14250.4 - 24682.4i) q^{95} +(-4608.00 - 7981.29i) q^{96} -99641.2 q^{97} +19455.5 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+8q2+18q332q4+108q5+144q6256q8162q9432q10124q11+288q121440q13+1944q15512q161260q17+648q18+360q19++20088q99+O(q100) 4 q + 8 q^{2} + 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} - 256 q^{8} - 162 q^{9} - 432 q^{10} - 124 q^{11} + 288 q^{12} - 1440 q^{13} + 1944 q^{15} - 512 q^{16} - 1260 q^{17} + 648 q^{18} + 360 q^{19}+ \cdots + 20088 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(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.00000 + 3.46410i 0.353553 + 0.612372i
33 4.50000 7.79423i 0.288675 0.500000i
44 −8.00000 + 13.8564i −0.250000 + 0.433013i
55 51.7487 + 89.6314i 0.925710 + 1.60338i 0.790416 + 0.612570i 0.209864π0.209864\pi
0.135294 + 0.990806i 0.456802π0.456802\pi
66 36.0000 0.408248
77 0 0
88 −64.0000 −0.353553
99 −40.5000 70.1481i −0.166667 0.288675i
1010 −206.995 + 358.526i −0.654576 + 1.13376i
1111 −120.095 + 208.011i −0.299257 + 0.518329i −0.975966 0.217922i 0.930072π-0.930072\pi
0.676709 + 0.736251i 0.263406π0.263406\pi
1212 72.0000 + 124.708i 0.144338 + 0.250000i
1313 −805.477 −1.32189 −0.660944 0.750435i 0.729844π-0.729844\pi
−0.660944 + 0.750435i 0.729844π0.729844\pi
1414 0 0
1515 931.477 1.06892
1616 −128.000 221.703i −0.125000 0.216506i
1717 −646.633 + 1120.00i −0.542670 + 0.939932i 0.456080 + 0.889939i 0.349253π0.349253\pi
−0.998750 + 0.0499927i 0.984080π0.984080\pi
1818 162.000 280.592i 0.117851 0.204124i
1919 −137.688 238.483i −0.0875011 0.151556i 0.818953 0.573860i 0.194555π-0.194555\pi
−0.906454 + 0.422304i 0.861221π0.861221\pi
2020 −1655.96 −0.925710
2121 0 0
2222 −960.764 −0.423214
2323 −1898.29 3287.93i −0.748242 1.29599i −0.948665 0.316284i 0.897565π-0.897565\pi
0.200423 0.979710i 0.435769π-0.435769\pi
2424 −288.000 + 498.831i −0.102062 + 0.176777i
2525 −3793.36 + 6570.30i −1.21388 + 2.10250i
2626 −1610.95 2790.26i −0.467358 0.809488i
2727 −729.000 −0.192450
2828 0 0
2929 1227.52 0.271040 0.135520 0.990775i 0.456730π-0.456730\pi
0.135520 + 0.990775i 0.456730π0.456730\pi
3030 1862.95 + 3226.73i 0.377919 + 0.654576i
3131 2812.43 4871.27i 0.525627 0.910413i −0.473927 0.880564i 0.657164π-0.657164\pi
0.999554 0.0298489i 0.00950261π-0.00950261\pi
3232 512.000 886.810i 0.0883883 0.153093i
3333 1080.86 + 1872.10i 0.172776 + 0.299257i
3434 −5173.06 −0.767451
3535 0 0
3636 1296.00 0.166667
3737 4539.25 + 7862.20i 0.545104 + 0.944148i 0.998600 + 0.0528897i 0.0168432π0.0168432\pi
−0.453496 + 0.891258i 0.649824π0.649824\pi
3838 550.754 953.933i 0.0618726 0.107166i
3939 −3624.65 + 6278.07i −0.381596 + 0.660944i
4040 −3311.92 5736.41i −0.327288 0.566879i
4141 18207.4 1.69156 0.845782 0.533528i 0.179134π-0.179134\pi
0.845782 + 0.533528i 0.179134π0.179134\pi
4242 0 0
4343 −11708.2 −0.965650 −0.482825 0.875717i 0.660389π-0.660389\pi
−0.482825 + 0.875717i 0.660389π0.660389\pi
4444 −1921.53 3328.18i −0.149629 0.259164i
4545 4191.65 7260.15i 0.308570 0.534459i
4646 7593.15 13151.7i 0.529087 0.916406i
4747 −11524.3 19960.7i −0.760974 1.31805i −0.942349 0.334632i 0.891388π-0.891388\pi
0.181375 0.983414i 0.441945π-0.441945\pi
4848 −2304.00 −0.144338
4949 0 0
5050 −30346.9 −1.71668
5151 5819.70 + 10080.0i 0.313311 + 0.542670i
5252 6443.82 11161.0i 0.330472 0.572395i
5353 −8831.40 + 15296.4i −0.431857 + 0.747998i −0.997033 0.0769720i 0.975475π-0.975475\pi
0.565176 + 0.824970i 0.308808π0.308808\pi
5454 −1458.00 2525.33i −0.0680414 0.117851i
5555 −24859.2 −1.10810
5656 0 0
5757 −2478.39 −0.101038
5858 2455.04 + 4252.25i 0.0958270 + 0.165977i
5959 9188.15 15914.3i 0.343636 0.595194i −0.641469 0.767149i 0.721675π-0.721675\pi
0.985105 + 0.171954i 0.0550082π0.0550082\pi
6060 −7451.82 + 12906.9i −0.267229 + 0.462855i
6161 5662.04 + 9806.95i 0.194827 + 0.337450i 0.946844 0.321694i 0.104252π-0.104252\pi
−0.752017 + 0.659144i 0.770919π0.770919\pi
6262 22499.5 0.743349
6363 0 0
6464 4096.00 0.125000
6565 −41682.4 72196.1i −1.22369 2.11948i
6666 −4323.44 + 7488.41i −0.122171 + 0.211607i
6767 −18039.7 + 31245.6i −0.490955 + 0.850359i −0.999946 0.0104130i 0.996685π-0.996685\pi
0.508991 + 0.860772i 0.330019π0.330019\pi
6868 −10346.1 17920.0i −0.271335 0.469966i
6969 −34169.2 −0.863996
7070 0 0
7171 −63434.2 −1.49341 −0.746703 0.665158i 0.768364π-0.768364\pi
−0.746703 + 0.665158i 0.768364π0.768364\pi
7272 2592.00 + 4489.48i 0.0589256 + 0.102062i
7373 −26491.2 + 45884.1i −0.581828 + 1.00776i 0.413435 + 0.910534i 0.364329π0.364329\pi
−0.995263 + 0.0972215i 0.969004π0.969004\pi
7474 −18157.0 + 31448.8i −0.385447 + 0.667613i
7575 34140.3 + 59132.7i 0.700832 + 1.21388i
7676 4406.03 0.0875011
7777 0 0
7878 −28997.2 −0.539659
7979 24282.0 + 42057.7i 0.437741 + 0.758189i 0.997515 0.0704561i 0.0224455π-0.0224455\pi
−0.559774 + 0.828645i 0.689112π0.689112\pi
8080 13247.7 22945.6i 0.231427 0.400844i
8181 −3280.50 + 5681.99i −0.0555556 + 0.0962250i
8282 36414.8 + 63072.3i 0.598058 + 1.03587i
8383 −113161. −1.80303 −0.901513 0.432753i 0.857542π-0.857542\pi
−0.901513 + 0.432753i 0.857542π0.857542\pi
8484 0 0
8585 −133850. −2.00942
8686 −23416.4 40558.5i −0.341409 0.591337i
8787 5523.83 9567.56i 0.0782424 0.135520i
8888 7686.11 13312.7i 0.105803 0.183257i
8989 54182.9 + 93847.6i 0.725083 + 1.25588i 0.958940 + 0.283609i 0.0915318π0.0915318\pi
−0.233857 + 0.972271i 0.575135π0.575135\pi
9090 33533.2 0.436384
9191 0 0
9292 60745.2 0.748242
9393 −25311.9 43841.5i −0.303471 0.525627i
9494 46097.2 79842.7i 0.538090 0.931999i
9595 14250.4 24682.4i 0.162001 0.280594i
9696 −4608.00 7981.29i −0.0510310 0.0883883i
9797 −99641.2 −1.07525 −0.537625 0.843184i 0.680679π-0.680679\pi
−0.537625 + 0.843184i 0.680679π0.680679\pi
9898 0 0
9999 19455.5 0.199505
100100 −60693.8 105125.i −0.606938 1.05125i
101101 82599.9 143067.i 0.805705 1.39552i −0.110109 0.993920i 0.535120π-0.535120\pi
0.915814 0.401603i 0.131547π-0.131547\pi
102102 −23278.8 + 40320.0i −0.221544 + 0.383725i
103103 −53623.6 92878.8i −0.498038 0.862628i 0.501959 0.864891i 0.332613π-0.332613\pi
−0.999997 + 0.00226355i 0.999279π0.999279\pi
104104 51550.5 0.467358
105105 0 0
106106 −70651.2 −0.610738
107107 48711.2 + 84370.2i 0.411310 + 0.712409i 0.995033 0.0995431i 0.0317381π-0.0317381\pi
−0.583723 + 0.811953i 0.698405π0.698405\pi
108108 5832.00 10101.3i 0.0481125 0.0833333i
109109 −29653.6 + 51361.5i −0.239062 + 0.414068i −0.960445 0.278468i 0.910173π-0.910173\pi
0.721383 + 0.692536i 0.243507π0.243507\pi
110110 −49718.3 86114.6i −0.391773 0.678571i
111111 81706.4 0.629432
112112 0 0
113113 157268. 1.15863 0.579313 0.815105i 0.303321π-0.303321\pi
0.579313 + 0.815105i 0.303321π0.303321\pi
114114 −4956.78 8585.40i −0.0357222 0.0618726i
115115 196468. 340292.i 1.38531 2.39943i
116116 −9820.15 + 17009.0i −0.0677599 + 0.117364i
117117 32621.8 + 56502.7i 0.220315 + 0.381596i
118118 73505.2 0.485974
119119 0 0
120120 −59614.5 −0.377919
121121 51679.7 + 89511.8i 0.320890 + 0.555798i
122122 −22648.2 + 39227.8i −0.137763 + 0.238613i
123123 81933.4 141913.i 0.488313 0.845782i
124124 44998.9 + 77940.4i 0.262814 + 0.455206i
125125 −461778. −2.64337
126126 0 0
127127 −92477.3 −0.508775 −0.254387 0.967102i 0.581874π-0.581874\pi
−0.254387 + 0.967102i 0.581874π0.581874\pi
128128 8192.00 + 14189.0i 0.0441942 + 0.0765466i
129129 −52687.0 + 91256.5i −0.278759 + 0.482825i
130130 166730. 288784.i 0.865276 1.49870i
131131 −36164.2 62638.2i −0.184120 0.318905i 0.759160 0.650904i 0.225610π-0.225610\pi
−0.943280 + 0.331999i 0.892277π0.892277\pi
132132 −34587.5 −0.172776
133133 0 0
134134 −144317. −0.694315
135135 −37724.8 65341.3i −0.178153 0.308570i
136136 41384.5 71680.1i 0.191863 0.332316i
137137 −112831. + 195429.i −0.513602 + 0.889585i 0.486273 + 0.873807i 0.338356π0.338356\pi
−0.999876 + 0.0157784i 0.994977π0.994977\pi
138138 −68338.3 118365.i −0.305469 0.529087i
139139 327971. 1.43979 0.719894 0.694084i 0.244190π-0.244190\pi
0.719894 + 0.694084i 0.244190π0.244190\pi
140140 0 0
141141 −207437. −0.878697
142142 −126868. 219743.i −0.527999 0.914521i
143143 96734.2 167548.i 0.395585 0.685173i
144144 −10368.0 + 17957.9i −0.0416667 + 0.0721688i
145145 63522.5 + 110024.i 0.250904 + 0.434579i
146146 −211930. −0.822829
147147 0 0
148148 −145256. −0.545104
149149 −82005.4 142038.i −0.302606 0.524128i 0.674120 0.738622i 0.264523π-0.264523\pi
−0.976725 + 0.214494i 0.931190π0.931190\pi
150150 −136561. + 236531.i −0.495563 + 0.858340i
151151 −31154.4 + 53961.0i −0.111193 + 0.192592i −0.916251 0.400604i 0.868800π-0.868800\pi
0.805059 + 0.593195i 0.202134π0.202134\pi
152152 8812.06 + 15262.9i 0.0309363 + 0.0535832i
153153 104755. 0.361780
154154 0 0
155155 582159. 1.94631
156156 −57994.4 100449.i −0.190798 0.330472i
157157 −119903. + 207679.i −0.388224 + 0.672423i −0.992211 0.124571i 0.960244π-0.960244\pi
0.603987 + 0.796994i 0.293578π0.293578\pi
158158 −97128.0 + 168231.i −0.309529 + 0.536121i
159159 79482.6 + 137668.i 0.249333 + 0.431857i
160160 105981. 0.327288
161161 0 0
162162 −26244.0 −0.0785674
163163 218397. + 378275.i 0.643841 + 1.11516i 0.984568 + 0.175002i 0.0559933π0.0559933\pi
−0.340727 + 0.940162i 0.610673π0.610673\pi
164164 −145659. + 252289.i −0.422891 + 0.732469i
165165 −111866. + 193758.i −0.319881 + 0.554051i
166166 −226322. 392001.i −0.637466 1.10412i
167167 −38846.7 −0.107786 −0.0538931 0.998547i 0.517163π-0.517163\pi
−0.0538931 + 0.998547i 0.517163π0.517163\pi
168168 0 0
169169 277501. 0.747390
170170 −267700. 463669.i −0.710437 1.23051i
171171 −11152.8 + 19317.1i −0.0291670 + 0.0505188i
172172 93665.7 162234.i 0.241412 0.418139i
173173 198139. + 343186.i 0.503331 + 0.871795i 0.999993 + 0.00385097i 0.00122580π0.00122580\pi
−0.496661 + 0.867944i 0.665441π0.665441\pi
174174 44190.7 0.110652
175175 0 0
176176 61488.9 0.149629
177177 −82693.4 143229.i −0.198398 0.343636i
178178 −216732. + 375390.i −0.512711 + 0.888041i
179179 −121942. + 211209.i −0.284459 + 0.492698i −0.972478 0.232995i 0.925147π-0.925147\pi
0.688019 + 0.725693i 0.258481π0.258481\pi
180180 67066.4 + 116162.i 0.154285 + 0.267229i
181181 299273. 0.679002 0.339501 0.940606i 0.389742π-0.389742\pi
0.339501 + 0.940606i 0.389742π0.389742\pi
182182 0 0
183183 101917. 0.224967
184184 121490. + 210427.i 0.264544 + 0.458203i
185185 −469800. + 813718.i −1.00922 + 1.74801i
186186 101248. 175366.i 0.214586 0.371675i
187187 −155315. 269014.i −0.324796 0.562563i
188188 368778. 0.760974
189189 0 0
190190 114003. 0.229104
191191 388498. + 672899.i 0.770558 + 1.33465i 0.937257 + 0.348639i 0.113356π0.113356\pi
−0.166699 + 0.986008i 0.553311π0.553311\pi
192192 18432.0 31925.2i 0.0360844 0.0625000i
193193 −138211. + 239388.i −0.267084 + 0.462603i −0.968108 0.250535i 0.919393π-0.919393\pi
0.701023 + 0.713138i 0.252727π0.252727\pi
194194 −199282. 345167.i −0.380159 0.658454i
195195 −750284. −1.41299
196196 0 0
197197 −131615. −0.241624 −0.120812 0.992675i 0.538550π-0.538550\pi
−0.120812 + 0.992675i 0.538550π0.538550\pi
198198 38910.9 + 67395.7i 0.0705356 + 0.122171i
199199 282480. 489270.i 0.505656 0.875822i −0.494322 0.869279i 0.664584π-0.664584\pi
0.999979 0.00654355i 0.00208289π-0.00208289\pi
200200 242775. 420499.i 0.429170 0.743344i
201201 162357. + 281211.i 0.283453 + 0.490955i
202202 660799. 1.13944
203203 0 0
204204 −186230. −0.313311
205205 942211. + 1.63196e6i 1.56590 + 2.71221i
206206 214494. 371515.i 0.352166 0.609970i
207207 −153761. + 266322.i −0.249414 + 0.431998i
208208 103101. + 178576.i 0.165236 + 0.286197i
209209 66143.0 0.104741
210210 0 0
211211 313637. 0.484977 0.242489 0.970154i 0.422036π-0.422036\pi
0.242489 + 0.970154i 0.422036π0.422036\pi
212212 −141302. 244743.i −0.215928 0.373999i
213213 −285454. + 494421.i −0.431109 + 0.746703i
214214 −194845. + 337481.i −0.290840 + 0.503750i
215215 −605886. 1.04942e6i −0.893911 1.54830i
216216 46656.0 0.0680414
217217 0 0
218218 −237229. −0.338085
219219 238421. + 412957.i 0.335918 + 0.581828i
220220 198873. 344459.i 0.277025 0.479822i
221221 520848. 902136.i 0.717349 1.24248i
222222 163413. + 283039.i 0.222538 + 0.385447i
223223 279483. 0.376351 0.188176 0.982135i 0.439743π-0.439743\pi
0.188176 + 0.982135i 0.439743π0.439743\pi
224224 0 0
225225 614525. 0.809251
226226 314535. + 544791.i 0.409636 + 0.709511i
227227 −611754. + 1.05959e6i −0.787974 + 1.36481i 0.139232 + 0.990260i 0.455537π0.455537\pi
−0.927206 + 0.374551i 0.877797π0.877797\pi
228228 19827.1 34341.6i 0.0252594 0.0437505i
229229 127387. + 220641.i 0.160523 + 0.278034i 0.935056 0.354499i 0.115349π-0.115349\pi
−0.774533 + 0.632533i 0.782015π0.782015\pi
230230 1.57174e6 1.95912
231231 0 0
232232 −78561.2 −0.0958270
233233 −373086. 646204.i −0.450215 0.779794i 0.548184 0.836357i 0.315319π-0.315319\pi
−0.998399 + 0.0565630i 0.981986π0.981986\pi
234234 −130487. + 226011.i −0.155786 + 0.269829i
235235 1.19274e6 2.06588e6i 1.40888 2.44026i
236236 147010. + 254630.i 0.171818 + 0.297597i
237237 437076. 0.505459
238238 0 0
239239 321036. 0.363546 0.181773 0.983341i 0.441816π-0.441816\pi
0.181773 + 0.983341i 0.441816π0.441816\pi
240240 −119229. 206511.i −0.133615 0.231427i
241241 621268. 1.07607e6i 0.689027 1.19343i −0.283125 0.959083i 0.591371π-0.591371\pi
0.972153 0.234348i 0.0752954π-0.0752954\pi
242242 −206719. + 358047.i −0.226904 + 0.393008i
243243 29524.5 + 51137.9i 0.0320750 + 0.0555556i
244244 −181185. −0.194827
245245 0 0
246246 655467. 0.690578
247247 110905. + 192093.i 0.115667 + 0.200341i
248248 −179996. + 311762.i −0.185837 + 0.321880i
249249 −509225. + 882003.i −0.520489 + 0.901513i
250250 −923555. 1.59964e6i −0.934572 1.61873i
251251 −690235. −0.691532 −0.345766 0.938321i 0.612381π-0.612381\pi
−0.345766 + 0.938321i 0.612381π0.612381\pi
252252 0 0
253253 911902. 0.895668
254254 −184955. 320351.i −0.179879 0.311560i
255255 −602324. + 1.04326e6i −0.580069 + 1.00471i
256256 −32768.0 + 56755.8i −0.0312500 + 0.0541266i
257257 6893.35 + 11939.6i 0.00651024 + 0.0112761i 0.869262 0.494351i 0.164594π-0.164594\pi
−0.862752 + 0.505627i 0.831261π0.831261\pi
258258 −421496. −0.394225
259259 0 0
260260 1.33384e6 1.22369
261261 −49714.5 86108.0i −0.0451733 0.0782424i
262262 144657. 250553.i 0.130192 0.225500i
263263 −287417. + 497820.i −0.256226 + 0.443796i −0.965228 0.261411i 0.915812π-0.915812\pi
0.709002 + 0.705206i 0.249146π0.249146\pi
264264 −69175.0 119815.i −0.0610857 0.105803i
265265 −1.82806e6 −1.59910
266266 0 0
267267 975293. 0.837253
268268 −288635. 499930.i −0.245477 0.425179i
269269 −559464. + 969020.i −0.471402 + 0.816492i −0.999465 0.0327131i 0.989585π-0.989585\pi
0.528063 + 0.849205i 0.322919π0.322919\pi
270270 150899. 261365.i 0.125973 0.218192i
271271 347435. + 601775.i 0.287376 + 0.497749i 0.973183 0.230034i 0.0738839π-0.0738839\pi
−0.685807 + 0.727784i 0.740551π0.740551\pi
272272 331076. 0.271335
273273 0 0
274274 −902648. −0.726343
275275 −911131. 1.57813e6i −0.726523 1.25837i
276276 273353. 473462.i 0.215999 0.374121i
277277 418827. 725429.i 0.327971 0.568062i −0.654138 0.756375i 0.726969π-0.726969\pi
0.982109 + 0.188313i 0.0603019π0.0603019\pi
278278 655942. + 1.13613e6i 0.509042 + 0.881687i
279279 −455614. −0.350418
280280 0 0
281281 −917687. −0.693312 −0.346656 0.937992i 0.612683π-0.612683\pi
−0.346656 + 0.937992i 0.612683π0.612683\pi
282282 −414875. 718584.i −0.310666 0.538090i
283283 −207632. + 359629.i −0.154109 + 0.266924i −0.932734 0.360565i 0.882584π-0.882584\pi
0.778625 + 0.627489i 0.215917π0.215917\pi
284284 507474. 878971.i 0.373352 0.646664i
285285 −128254. 222142.i −0.0935314 0.162001i
286286 773873. 0.559442
287287 0 0
288288 −82944.0 −0.0589256
289289 −126340. 218828.i −0.0889809 0.154119i
290290 −254090. + 440097.i −0.177416 + 0.307293i
291291 −448386. + 776627.i −0.310398 + 0.537625i
292292 −423859. 734145.i −0.290914 0.503878i
293293 1.21491e6 0.826752 0.413376 0.910561i 0.364350π-0.364350\pi
0.413376 + 0.910561i 0.364350π0.364350\pi
294294 0 0
295295 1.90190e6 1.27243
296296 −290512. 503181.i −0.192723 0.333807i
297297 87549.6 151640.i 0.0575921 0.0997525i
298298 328022. 568150.i 0.213974 0.370615i
299299 1.52903e6 + 2.64835e6i 0.989093 + 1.71316i
300300 −1.09249e6 −0.700832
301301 0 0
302302 −249235. −0.157250
303303 −743399. 1.28761e6i −0.465174 0.805705i
304304 −35248.2 + 61051.7i −0.0218753 + 0.0378891i
305305 −586007. + 1.01499e6i −0.360706 + 0.624761i
306306 209509. + 362880.i 0.127908 + 0.221544i
307307 2.60119e6 1.57517 0.787584 0.616207i 0.211332π-0.211332\pi
0.787584 + 0.616207i 0.211332π0.211332\pi
308308 0 0
309309 −965225. −0.575085
310310 1.16432e6 + 2.01666e6i 0.688125 + 1.19187i
311311 −409582. + 709417.i −0.240126 + 0.415911i −0.960750 0.277415i 0.910522π-0.910522\pi
0.720624 + 0.693326i 0.243856π0.243856\pi
312312 231977. 401797.i 0.134915 0.233679i
313313 −440970. 763782.i −0.254418 0.440665i 0.710319 0.703880i 0.248551π-0.248551\pi
−0.964737 + 0.263215i 0.915217π0.915217\pi
314314 −959226. −0.549031
315315 0 0
316316 −777024. −0.437741
317317 802191. + 1.38944e6i 0.448363 + 0.776587i 0.998280 0.0586323i 0.0186740π-0.0186740\pi
−0.549917 + 0.835219i 0.685341π0.685341\pi
318318 −317930. + 550672.i −0.176305 + 0.305369i
319319 −147419. + 255338.i −0.0811106 + 0.140488i
320320 211963. + 367130.i 0.115714 + 0.200422i
321321 876801. 0.474940
322322 0 0
323323 356135. 0.189937
324324 −52488.0 90911.9i −0.0277778 0.0481125i
325325 3.05547e6 5.29223e6i 1.60461 2.77927i
326326 −873589. + 1.51310e6i −0.455264 + 0.788540i
327327 266882. + 462254.i 0.138023 + 0.239062i
328328 −1.16527e6 −0.598058
329329 0 0
330330 −894929. −0.452381
331331 −501540. 868693.i −0.251614 0.435809i 0.712356 0.701818i 0.247628π-0.247628\pi
−0.963970 + 0.266009i 0.914295π0.914295\pi
332332 905288. 1.56801e6i 0.450756 0.780733i
333333 367679. 636839.i 0.181701 0.314716i
334334 −77693.4 134569.i −0.0381082 0.0660053i
335335 −3.73412e6 −1.81793
336336 0 0
337337 −2.62317e6 −1.25821 −0.629103 0.777322i 0.716578π-0.716578\pi
−0.629103 + 0.777322i 0.716578π0.716578\pi
338338 555001. + 961290.i 0.264242 + 0.457681i
339339 707705. 1.22578e6i 0.334467 0.579313i
340340 1.07080e6 1.85468e6i 0.502355 0.870104i
341341 675521. + 1.17004e6i 0.314596 + 0.544896i
342342 −89222.1 −0.0412484
343343 0 0
344344 749326. 0.341409
345345 −1.76821e6 3.06263e6i −0.799809 1.38531i
346346 −792555. + 1.37274e6i −0.355909 + 0.616452i
347347 −113117. + 195924.i −0.0504317 + 0.0873503i −0.890139 0.455689i 0.849393π-0.849393\pi
0.839708 + 0.543039i 0.182726π0.182726\pi
348348 88381.3 + 153081.i 0.0391212 + 0.0677599i
349349 1.46280e6 0.642866 0.321433 0.946932i 0.395835π-0.395835\pi
0.321433 + 0.946932i 0.395835π0.395835\pi
350350 0 0
351351 587193. 0.254398
352352 122978. + 213004.i 0.0529017 + 0.0916285i
353353 1.40479e6 2.43316e6i 0.600031 1.03928i −0.392785 0.919630i 0.628488π-0.628488\pi
0.992816 0.119653i 0.0381783π-0.0381783\pi
354354 330773. 572916.i 0.140289 0.242987i
355355 −3.28264e6 5.68570e6i −1.38246 2.39449i
356356 −1.73385e6 −0.725083
357357 0 0
358358 −975534. −0.402286
359359 1.84950e6 + 3.20343e6i 0.757388 + 1.31183i 0.944178 + 0.329435i 0.106858π0.106858\pi
−0.186790 + 0.982400i 0.559808π0.559808\pi
360360 −268265. + 464649.i −0.109096 + 0.188960i
361361 1.20013e6 2.07869e6i 0.484687 0.839503i
362362 598546. + 1.03671e6i 0.240063 + 0.415802i
363363 930234. 0.370532
364364 0 0
365365 −5.48354e6 −2.15441
366366 203834. + 353050.i 0.0795377 + 0.137763i
367367 584623. 1.01260e6i 0.226574 0.392438i −0.730216 0.683216i 0.760581π-0.760581\pi
0.956791 + 0.290778i 0.0939141π0.0939141\pi
368368 −485961. + 841710.i −0.187061 + 0.323998i
369369 −737400. 1.27721e6i −0.281927 0.488313i
370370 −3.75840e6 −1.42725
371371 0 0
372372 809980. 0.303471
373373 2.28845e6 + 3.96371e6i 0.851666 + 1.47513i 0.879704 + 0.475523i 0.157741π0.157741\pi
−0.0280372 + 0.999607i 0.508926π0.508926\pi
374374 621262. 1.07606e6i 0.229665 0.397792i
375375 −2.07800e6 + 3.59920e6i −0.763075 + 1.32168i
376376 737555. + 1.27748e6i 0.269045 + 0.466000i
377377 −988738. −0.358284
378378 0 0
379379 −2.35520e6 −0.842229 −0.421114 0.907007i 0.638361π-0.638361\pi
−0.421114 + 0.907007i 0.638361π0.638361\pi
380380 228006. + 394919.i 0.0810006 + 0.140297i
381381 −416148. + 720789.i −0.146871 + 0.254387i
382382 −1.55399e6 + 2.69159e6i −0.544867 + 0.943738i
383383 1.51973e6 + 2.63225e6i 0.529382 + 0.916916i 0.999413 + 0.0342662i 0.0109094π0.0109094\pi
−0.470031 + 0.882650i 0.655757π0.655757\pi
384384 147456. 0.0510310
385385 0 0
386386 −1.10568e6 −0.377714
387387 474183. + 821309.i 0.160942 + 0.278759i
388388 797130. 1.38067e6i 0.268813 0.465597i
389389 229637. 397742.i 0.0769426 0.133269i −0.824987 0.565152i 0.808818π-0.808818\pi
0.901929 + 0.431883i 0.142151π0.142151\pi
390390 −1.50057e6 2.59906e6i −0.499567 0.865276i
391391 4.90998e6 1.62419
392392 0 0
393393 −650956. −0.212603
394394 −263231. 455929.i −0.0854272 0.147964i
395395 −2.51313e6 + 4.35286e6i −0.810441 + 1.40373i
396396 −155644. + 269583.i −0.0498762 + 0.0863882i
397397 2.71250e6 + 4.69819e6i 0.863761 + 1.49608i 0.868272 + 0.496089i 0.165231π0.165231\pi
−0.00451026 + 0.999990i 0.501436π0.501436\pi
398398 2.25984e6 0.715106
399399 0 0
400400 1.94220e6 0.606938
401401 −1.05564e6 1.82841e6i −0.327833 0.567824i 0.654248 0.756280i 0.272985π-0.272985\pi
−0.982082 + 0.188456i 0.939652π0.939652\pi
402402 −649428. + 1.12484e6i −0.200432 + 0.347158i
403403 −2.26535e6 + 3.92370e6i −0.694821 + 1.20346i
404404 1.32160e6 + 2.28908e6i 0.402853 + 0.697761i
405405 −679047. −0.205713
406406 0 0
407407 −2.18057e6 −0.652506
408408 −372461. 645121.i −0.110772 0.191863i
409409 1.27872e6 2.21481e6i 0.377980 0.654680i −0.612788 0.790247i 0.709952π-0.709952\pi
0.990768 + 0.135567i 0.0432856π0.0432856\pi
410410 −3.76884e6 + 6.52783e6i −1.10726 + 1.91783i
411411 1.01548e6 + 1.75886e6i 0.296528 + 0.513602i
412412 1.71595e6 0.498038
413413 0 0
414414 −1.23009e6 −0.352725
415415 −5.85594e6 1.01428e7i −1.66908 2.89093i
416416 −412404. + 714305.i −0.116840 + 0.202372i
417417 1.47587e6 2.55628e6i 0.415631 0.719894i
418418 132286. + 229126.i 0.0370317 + 0.0641407i
419419 −2.17401e6 −0.604959 −0.302480 0.953156i 0.597814π-0.597814\pi
−0.302480 + 0.953156i 0.597814π0.597814\pi
420420 0 0
421421 −5.47930e6 −1.50668 −0.753338 0.657633i 0.771558π-0.771558\pi
−0.753338 + 0.657633i 0.771558π0.771558\pi
422422 627274. + 1.08647e6i 0.171465 + 0.296987i
423423 −933468. + 1.61681e6i −0.253658 + 0.439349i
424424 565210. 978972.i 0.152684 0.264457i
425425 −4.90583e6 8.49714e6i −1.31747 2.28192i
426426 −2.28363e6 −0.609680
427427 0 0
428428 −1.55876e6 −0.411310
429429 −870607. 1.50794e6i −0.228391 0.395585i
430430 2.42354e6 4.19770e6i 0.632091 1.09481i
431431 3.08437e6 5.34229e6i 0.799785 1.38527i −0.119971 0.992777i 0.538280π-0.538280\pi
0.919756 0.392491i 0.128387π-0.128387\pi
432432 93312.0 + 161621.i 0.0240563 + 0.0416667i
433433 −4.89596e6 −1.25493 −0.627463 0.778647i 0.715907π-0.715907\pi
−0.627463 + 0.778647i 0.715907π0.715907\pi
434434 0 0
435435 1.14341e6 0.289719
436436 −474458. 821785.i −0.119531 0.207034i
437437 −522744. + 905419.i −0.130944 + 0.226802i
438438 −953683. + 1.65183e6i −0.237530 + 0.411414i
439439 −1.77294e6 3.07082e6i −0.439069 0.760489i 0.558549 0.829471i 0.311358π-0.311358\pi
−0.997618 + 0.0689822i 0.978025π0.978025\pi
440440 1.59099e6 0.391773
441441 0 0
442442 4.16679e6 1.01448
443443 −3.02826e6 5.24510e6i −0.733134 1.26983i −0.955537 0.294871i 0.904723π-0.904723\pi
0.222403 0.974955i 0.428610π-0.428610\pi
444444 −653651. + 1.13216e6i −0.157358 + 0.272552i
445445 −5.60780e6 + 9.71299e6i −1.34243 + 2.32516i
446446 558966. + 968158.i 0.133060 + 0.230467i
447447 −1.47610e6 −0.349419
448448 0 0
449449 −1.20801e6 −0.282783 −0.141392 0.989954i 0.545158π-0.545158\pi
−0.141392 + 0.989954i 0.545158π0.545158\pi
450450 1.22905e6 + 2.12878e6i 0.286113 + 0.495563i
451451 −2.18663e6 + 3.78735e6i −0.506213 + 0.876787i
452452 −1.25814e6 + 2.17917e6i −0.289657 + 0.501700i
453453 280390. + 485649.i 0.0641972 + 0.111193i
454454 −4.89403e6 −1.11436
455455 0 0
456456 158617. 0.0357222
457457 2.73275e6 + 4.73326e6i 0.612082 + 1.06016i 0.990889 + 0.134681i 0.0430011π0.0430011\pi
−0.378807 + 0.925476i 0.623666π0.623666\pi
458458 −509549. + 882565.i −0.113507 + 0.196600i
459459 471396. 816481.i 0.104437 0.180890i
460460 3.14349e6 + 5.44468e6i 0.692655 + 1.19971i
461461 −1.15956e6 −0.254121 −0.127061 0.991895i 0.540554π-0.540554\pi
−0.127061 + 0.991895i 0.540554π0.540554\pi
462462 0 0
463463 −4.31335e6 −0.935108 −0.467554 0.883964i 0.654865π-0.654865\pi
−0.467554 + 0.883964i 0.654865π0.654865\pi
464464 −157122. 272144.i −0.0338800 0.0586818i
465465 2.61972e6 4.53748e6i 0.561852 0.973156i
466466 1.49235e6 2.58482e6i 0.318350 0.551398i
467467 −2.99462e6 5.18683e6i −0.635403 1.10055i −0.986430 0.164184i 0.947501π-0.947501\pi
0.351027 0.936365i 0.385833π-0.385833\pi
468468 −1.04390e6 −0.220315
469469 0 0
470470 9.54189e6 1.99246
471471 1.07913e6 + 1.86911e6i 0.224141 + 0.388224i
472472 −588042. + 1.01852e6i −0.121494 + 0.210433i
473473 1.40610e6 2.43544e6i 0.288978 0.500524i
474474 874152. + 1.51408e6i 0.178707 + 0.309529i
475475 2.08921e6 0.424862
476476 0 0
477477 1.43069e6 0.287905
478478 642073. + 1.11210e6i 0.128533 + 0.222626i
479479 1.77326e6 3.07138e6i 0.353129 0.611638i −0.633667 0.773606i 0.718451π-0.718451\pi
0.986796 + 0.161968i 0.0517843π0.0517843\pi
480480 476916. 826043.i 0.0944798 0.163644i
481481 −3.65626e6 6.33283e6i −0.720567 1.24806i
482482 4.97015e6 0.974432
483483 0 0
484484 −1.65375e6 −0.320890
485485 −5.15631e6 8.93099e6i −0.995370 1.72403i
486486 −118098. + 204552.i −0.0226805 + 0.0392837i
487487 4.39160e6 7.60648e6i 0.839074 1.45332i −0.0515950 0.998668i 0.516430π-0.516430\pi
0.890669 0.454651i 0.150236π-0.150236\pi
488488 −362371. 627645.i −0.0688817 0.119307i
489489 3.93115e6 0.743443
490490 0 0
491491 −586608. −0.109811 −0.0549053 0.998492i 0.517486π-0.517486\pi
−0.0549053 + 0.998492i 0.517486π0.517486\pi
492492 1.31093e6 + 2.27060e6i 0.244156 + 0.422891i
493493 −793754. + 1.37482e6i −0.147085 + 0.254759i
494494 −443619. + 768371.i −0.0817887 + 0.141662i
495495 1.00680e6 + 1.74382e6i 0.184684 + 0.319881i
496496 −1.43997e6 −0.262814
497497 0 0
498498 −4.07380e6 −0.736082
499499 4.79886e6 + 8.31187e6i 0.862753 + 1.49433i 0.869261 + 0.494353i 0.164595π0.164595\pi
−0.00650801 + 0.999979i 0.502072π0.502072\pi
500500 3.69422e6 6.39858e6i 0.660842 1.14461i
501501 −174810. + 302780.i −0.0311152 + 0.0538931i
502502 −1.38047e6 2.39104e6i −0.244494 0.423475i
503503 7.21481e6 1.27147 0.635733 0.771909i 0.280698π-0.280698\pi
0.635733 + 0.771909i 0.280698π0.280698\pi
504504 0 0
505505 1.70978e7 2.98340
506506 1.82380e6 + 3.15892e6i 0.316666 + 0.548482i
507507 1.24875e6 2.16290e6i 0.215753 0.373695i
508508 739818. 1.28140e6i 0.127194 0.220306i
509509 2.19210e6 + 3.79682e6i 0.375029 + 0.649569i 0.990331 0.138722i 0.0442994π-0.0442994\pi
−0.615302 + 0.788291i 0.710966π0.710966\pi
510510 −4.81859e6 −0.820342
511511 0 0
512512 −262144. −0.0441942
513513 100375. + 173854.i 0.0168396 + 0.0291670i
514514 −27573.4 + 47758.5i −0.00460344 + 0.00797339i
515515 5.54991e6 9.61272e6i 0.922078 1.59709i
516516 −842992. 1.46010e6i −0.139380 0.241412i
517517 5.53606e6 0.910909
518518 0 0
519519 3.56650e6 0.581197
520520 2.66768e6 + 4.62055e6i 0.432638 + 0.749351i
521521 1.03291e6 1.78905e6i 0.166712 0.288753i −0.770550 0.637380i 0.780018π-0.780018\pi
0.937262 + 0.348626i 0.113352π0.113352\pi
522522 198858. 344432.i 0.0319423 0.0553258i
523523 3.98285e6 + 6.89850e6i 0.636707 + 1.10281i 0.986151 + 0.165852i 0.0530373π0.0530373\pi
−0.349444 + 0.936957i 0.613629π0.613629\pi
524524 1.15725e6 0.184120
525525 0 0
526526 −2.29933e6 −0.362358
527527 3.63722e6 + 6.29985e6i 0.570484 + 0.988107i
528528 276700. 479258.i 0.0431941 0.0748143i
529529 −3.98881e6 + 6.90882e6i −0.619732 + 1.07341i
530530 −3.65611e6 6.33257e6i −0.565366 0.979242i
531531 −1.48848e6 −0.229090
532532 0 0
533533 −1.46657e7 −2.23606
534534 1.95059e6 + 3.37851e6i 0.296014 + 0.512711i
535535 −5.04148e6 + 8.73210e6i −0.761507 + 1.31897i
536536 1.15454e6 1.99972e6i 0.173579 0.300647i
537537 1.09748e6 + 1.90088e6i 0.164233 + 0.284459i
538538 −4.47571e6 −0.666663
539539 0 0
540540 1.20719e6 0.178153
541541 −4.11712e6 7.13105e6i −0.604784 1.04752i −0.992086 0.125563i 0.959926π-0.959926\pi
0.387302 0.921953i 0.373407π-0.373407\pi
542542 −1.38974e6 + 2.40710e6i −0.203205 + 0.351962i
543543 1.34673e6 2.33260e6i 0.196011 0.339501i
544544 662152. + 1.14688e6i 0.0959314 + 0.166158i
545545 −6.13815e6 −0.885209
546546 0 0
547547 5.20365e6 0.743601 0.371800 0.928313i 0.378741π-0.378741\pi
0.371800 + 0.928313i 0.378741π0.378741\pi
548548 −1.80530e6 3.12686e6i −0.256801 0.444793i
549549 458626. 794363.i 0.0649423 0.112483i
550550 3.64453e6 6.31250e6i 0.513729 0.889805i
551551 −169015. 292743.i −0.0237163 0.0410778i
552552 2.18683e6 0.305469
553553 0 0
554554 3.35061e6 0.463821
555555 4.22820e6 + 7.32346e6i 0.582671 + 1.00922i
556556 −2.62377e6 + 4.54450e6i −0.359947 + 0.623447i
557557 2.04583e6 3.54347e6i 0.279403 0.483940i −0.691834 0.722057i 0.743197π-0.743197\pi
0.971236 + 0.238117i 0.0765302π0.0765302\pi
558558 −911228. 1.57829e6i −0.123892 0.214586i
559559 9.43070e6 1.27648
560560 0 0
561561 −2.79568e6 −0.375042
562562 −1.83537e6 3.17896e6i −0.245123 0.424565i
563563 −1.79526e6 + 3.10948e6i −0.238702 + 0.413444i −0.960342 0.278824i 0.910055π-0.910055\pi
0.721640 + 0.692269i 0.243389π0.243389\pi
564564 1.65950e6 2.87434e6i 0.219674 0.380487i
565565 8.13841e6 + 1.40961e7i 1.07255 + 1.85771i
566566 −1.66105e6 −0.217943
567567 0 0
568568 4.05979e6 0.527999
569569 −4.89858e6 8.48459e6i −0.634293 1.09863i −0.986665 0.162767i 0.947958π-0.947958\pi
0.352372 0.935860i 0.385375π-0.385375\pi
570570 513014. 888567.i 0.0661367 0.114552i
571571 1.10902e6 1.92088e6i 0.142347 0.246552i −0.786033 0.618185i 0.787868π-0.787868\pi
0.928380 + 0.371632i 0.121202π0.121202\pi
572572 1.54775e6 + 2.68078e6i 0.197792 + 0.342587i
573573 6.99297e6 0.889764
574574 0 0
575575 2.88036e7 3.63309
576576 −165888. 287326.i −0.0208333 0.0360844i
577577 −1.32767e6 + 2.29959e6i −0.166016 + 0.287548i −0.937016 0.349288i 0.886424π-0.886424\pi
0.771000 + 0.636836i 0.219757π0.219757\pi
578578 505361. 875310.i 0.0629190 0.108979i
579579 1.24390e6 + 2.15449e6i 0.154201 + 0.267084i
580580 −2.03272e6 −0.250904
581581 0 0
582582 −3.58708e6 −0.438969
583583 −2.12122e6 3.67406e6i −0.258473 0.447688i
584584 1.69544e6 2.93658e6i 0.205707 0.356295i
585585 −3.37628e6 + 5.84788e6i −0.407895 + 0.706495i
586586 2.42982e6 + 4.20857e6i 0.292301 + 0.506280i
587587 2.62690e6 0.314665 0.157332 0.987546i 0.449711π-0.449711\pi
0.157332 + 0.987546i 0.449711π0.449711\pi
588588 0 0
589589 −1.54896e6 −0.183972
590590 3.80380e6 + 6.58838e6i 0.449871 + 0.779199i
591591 −592269. + 1.02584e6i −0.0697510 + 0.120812i
592592 1.16205e6 2.01272e6i 0.136276 0.236037i
593593 −5.75310e6 9.96467e6i −0.671839 1.16366i −0.977382 0.211481i 0.932171π-0.932171\pi
0.305543 0.952178i 0.401162π-0.401162\pi
594594 700397. 0.0814475
595595 0 0
596596 2.62417e6 0.302606
597597 −2.54232e6 4.40343e6i −0.291941 0.505656i
598598 −6.11611e6 + 1.05934e7i −0.699394 + 1.21139i
599599 −3.23132e6 + 5.59681e6i −0.367970 + 0.637343i −0.989248 0.146247i 0.953281π-0.953281\pi
0.621278 + 0.783590i 0.286614π0.286614\pi
600600 −2.18498e6 3.78449e6i −0.247781 0.429170i
601601 −8.55332e6 −0.965937 −0.482968 0.875638i 0.660441π-0.660441\pi
−0.482968 + 0.875638i 0.660441π0.660441\pi
602602 0 0
603603 2.92243e6 0.327303
604604 −498470. 863376.i −0.0555964 0.0962958i
605605 −5.34871e6 + 9.26425e6i −0.594102 + 1.02901i
606606 2.97360e6 5.15042e6i 0.328928 0.569720i
607607 1.49521e6 + 2.58978e6i 0.164714 + 0.285293i 0.936554 0.350524i 0.113997π-0.113997\pi
−0.771840 + 0.635817i 0.780663π0.780663\pi
608608 −281986. −0.0309363
609609 0 0
610610 −4.68806e6 −0.510115
611611 9.28256e6 + 1.60779e7i 1.00592 + 1.74231i
612612 −838036. + 1.45152e6i −0.0904450 + 0.156655i
613613 885724. 1.53412e6i 0.0952023 0.164895i −0.814491 0.580177i 0.802984π-0.802984\pi
0.909693 + 0.415281i 0.136317π0.136317\pi
614614 5.20239e6 + 9.01080e6i 0.556906 + 0.964589i
615615 1.69598e7 1.80814
616616 0 0
617617 1.40871e7 1.48974 0.744869 0.667210i 0.232512π-0.232512\pi
0.744869 + 0.667210i 0.232512π0.232512\pi
618618 −1.93045e6 3.34364e6i −0.203323 0.352166i
619619 −5.67152e6 + 9.82336e6i −0.594940 + 1.03047i 0.398616 + 0.917118i 0.369491π0.369491\pi
−0.993555 + 0.113348i 0.963843π0.963843\pi
620620 −4.65727e6 + 8.06663e6i −0.486578 + 0.842778i
621621 1.38385e6 + 2.39690e6i 0.143999 + 0.249414i
622622 −3.27666e6 −0.339590
623623 0 0
624624 1.85582e6 0.190798
625625 −1.20421e7 2.08576e7i −1.23312 2.13582i
626626 1.76388e6 3.05513e6i 0.179901 0.311597i
627627 297643. 515534.i 0.0302362 0.0523707i
628628 −1.91845e6 3.32286e6i −0.194112 0.336211i
629629 −1.17409e7 −1.18325
630630 0 0
631631 −2.32628e6 −0.232588 −0.116294 0.993215i 0.537102π-0.537102\pi
−0.116294 + 0.993215i 0.537102π0.537102\pi
632632 −1.55405e6 2.69169e6i −0.154765 0.268060i
633633 1.41137e6 2.44456e6i 0.140001 0.242489i
634634 −3.20876e6 + 5.55774e6i −0.317040 + 0.549130i
635635 −4.78558e6 8.28887e6i −0.470978 0.815758i
636636 −2.54344e6 −0.249333
637637 0 0
638638 −1.17935e6 −0.114708
639639 2.56909e6 + 4.44979e6i 0.248901 + 0.431109i
640640 −847851. + 1.46852e6i −0.0818219 + 0.141720i
641641 1.28193e6 2.22036e6i 0.123230 0.213441i −0.797809 0.602910i 0.794008π-0.794008\pi
0.921040 + 0.389468i 0.127341π0.127341\pi
642642 1.75360e6 + 3.03733e6i 0.167917 + 0.290840i
643643 5.95343e6 0.567858 0.283929 0.958845i 0.408362π-0.408362\pi
0.283929 + 0.958845i 0.408362π0.408362\pi
644644 0 0
645645 −1.09059e7 −1.03220
646646 712271. + 1.23369e6i 0.0671528 + 0.116312i
647647 −767611. + 1.32954e6i −0.0720909 + 0.124865i −0.899818 0.436266i 0.856301π-0.856301\pi
0.827727 + 0.561132i 0.189634π0.189634\pi
648648 209952. 363648.i 0.0196419 0.0340207i
649649 2.20691e6 + 3.82248e6i 0.205671 + 0.356233i
650650 2.44437e7 2.26926
651651 0 0
652652 −6.98871e6 −0.643841
653653 9.97909e6 + 1.72843e7i 0.915815 + 1.58624i 0.805703 + 0.592319i 0.201788π0.201788\pi
0.110112 + 0.993919i 0.464879π0.464879\pi
654654 −1.06753e6 + 1.84902e6i −0.0975968 + 0.169043i
655655 3.74290e6 6.48290e6i 0.340883 0.590427i
656656 −2.33055e6 4.03663e6i −0.211446 0.366235i
657657 4.29157e6 0.387885
658658 0 0
659659 −1.05477e7 −0.946119 −0.473060 0.881030i 0.656850π-0.656850\pi
−0.473060 + 0.881030i 0.656850π0.656850\pi
660660 −1.78986e6 3.10013e6i −0.159941 0.277025i
661661 −6.10220e6 + 1.05693e7i −0.543229 + 0.940900i 0.455487 + 0.890242i 0.349465π0.349465\pi
−0.998716 + 0.0506576i 0.983868π0.983868\pi
662662 2.00616e6 3.47477e6i 0.177918 0.308164i
663663 −4.68763e6 8.11922e6i −0.414162 0.717349i
664664 7.24231e6 0.637466
665665 0 0
666666 2.94143e6 0.256964
667667 −2.33018e6 4.03599e6i −0.202803 0.351266i
668668 310774. 538276.i 0.0269466 0.0466728i
669669 1.25767e6 2.17836e6i 0.108643 0.188176i
670670 −7.46824e6 1.29354e7i −0.642734 1.11325i
671671 −2.71994e6 −0.233213
672672 0 0
673673 −7.97959e6 −0.679114 −0.339557 0.940585i 0.610277π-0.610277\pi
−0.339557 + 0.940585i 0.610277π0.610277\pi
674674 −5.24634e6 9.08693e6i −0.444843 0.770491i
675675 2.76536e6 4.78975e6i 0.233611 0.404625i
676676 −2.22001e6 + 3.84516e6i −0.186847 + 0.323629i
677677 2.54190e6 + 4.40271e6i 0.213151 + 0.369188i 0.952699 0.303915i 0.0982940π-0.0982940\pi
−0.739548 + 0.673104i 0.764961π0.764961\pi
678678 5.66164e6 0.473007
679679 0 0
680680 8.56639e6 0.710437
681681 5.50578e6 + 9.53629e6i 0.454937 + 0.787974i
682682 −2.70208e6 + 4.68014e6i −0.222453 + 0.385299i
683683 8.01654e6 1.38850e7i 0.657559 1.13893i −0.323686 0.946165i 0.604922π-0.604922\pi
0.981246 0.192762i 0.0617445π-0.0617445\pi
684684 −178444. 309074.i −0.0145835 0.0252594i
685685 −2.33554e7 −1.90179
686686 0 0
687687 2.29297e6 0.185356
688688 1.49865e6 + 2.59574e6i 0.120706 + 0.209069i
689689 7.11349e6 1.23209e7i 0.570867 0.988770i
690690 7.07284e6 1.22505e7i 0.565550 0.979562i
691691 −5.50657e6 9.53766e6i −0.438719 0.759883i 0.558872 0.829254i 0.311234π-0.311234\pi
−0.997591 + 0.0693705i 0.977901π0.977901\pi
692692 −6.34044e6 −0.503331
693693 0 0
694694 −904935. −0.0713212
695695 1.69721e7 + 2.93965e7i 1.33283 + 2.30852i
696696 −353525. + 612324.i −0.0276629 + 0.0479135i
697697 −1.17735e7 + 2.03923e7i −0.917961 + 1.58996i
698698 2.92560e6 + 5.06728e6i 0.227288 + 0.393674i
699699 −6.71555e6 −0.519863
700700 0 0
701701 −3.10660e6 −0.238776 −0.119388 0.992848i 0.538093π-0.538093\pi
−0.119388 + 0.992848i 0.538093π0.538093\pi
702702 1.17439e6 + 2.03410e6i 0.0899431 + 0.155786i
703703 1.25000e6 2.16507e6i 0.0953943 0.165228i
704704 −491911. + 852015.i −0.0374072 + 0.0647911i
705705 −1.07346e7 1.85929e7i −0.813418 1.40888i
706706 1.12383e7 0.848571
707707 0 0
708708 2.64619e6 0.198398
709709 6.90180e6 + 1.19543e7i 0.515640 + 0.893115i 0.999835 + 0.0181549i 0.00577922π0.00577922\pi
−0.484195 + 0.874960i 0.660887π0.660887\pi
710710 1.31306e7 2.27428e7i 0.977547 1.69316i
711711 1.96684e6 3.40667e6i 0.145914 0.252730i
712712 −3.46771e6 6.00625e6i −0.256355 0.444021i
713713 −2.13552e7 −1.57319
714714 0 0
715715 2.00235e7 1.46479
716716 −1.95107e6 3.37935e6i −0.142230 0.246349i
717717 1.44466e6 2.50223e6i 0.104947 0.181773i
718718 −7.39800e6 + 1.28137e7i −0.535554 + 0.927607i
719719 −6.49275e6 1.12458e7i −0.468389 0.811273i 0.530959 0.847398i 0.321832π-0.321832\pi
−0.999347 + 0.0361248i 0.988499π0.988499\pi
720720 −2.14612e6 −0.154285
721721 0 0
722722 9.60107e6 0.685451
723723 −5.59141e6 9.68461e6i −0.397810 0.689027i
724724 −2.39418e6 + 4.14685e6i −0.169751 + 0.294017i
725725 −4.65642e6 + 8.06516e6i −0.329009 + 0.569860i
726726 1.86047e6 + 3.22242e6i 0.131003 + 0.226904i
727727 8.61224e6 0.604338 0.302169 0.953254i 0.402289π-0.402289\pi
0.302169 + 0.953254i 0.402289π0.402289\pi
728728 0 0
729729 531441. 0.0370370
730730 −1.09671e7 1.89956e7i −0.761700 1.31930i
731731 7.57092e6 1.31132e7i 0.524029 0.907645i
732732 −815334. + 1.41220e6i −0.0562416 + 0.0974134i
733733 3.01000e6 + 5.21348e6i 0.206922 + 0.358400i 0.950743 0.309979i 0.100322π-0.100322\pi
−0.743821 + 0.668379i 0.766989π0.766989\pi
734734 4.67698e6 0.320424
735735 0 0
736736 −3.88769e6 −0.264544
737737 −4.33297e6 7.50492e6i −0.293844 0.508952i
738738 2.94960e6 5.10886e6i 0.199353 0.345289i
739739 46846.3 81140.1i 0.00315547 0.00546543i −0.864443 0.502730i 0.832329π-0.832329\pi
0.867599 + 0.497265i 0.165662π0.165662\pi
740740 −7.51681e6 1.30195e7i −0.504608 0.874007i
741741 1.99629e6 0.133560
742742 0 0
743743 −1.29874e7 −0.863081 −0.431541 0.902094i 0.642030π-0.642030\pi
−0.431541 + 0.902094i 0.642030π0.642030\pi
744744 1.61996e6 + 2.80585e6i 0.107293 + 0.185837i
745745 8.48735e6 1.47005e7i 0.560250 0.970381i
746746 −9.15380e6 + 1.58549e7i −0.602219 + 1.04307i
747747 4.58302e6 + 7.93803e6i 0.300504 + 0.520489i
748748 4.97009e6 0.324796
749749 0 0
750750 −1.66240e7 −1.07915
751751 318720. + 552040.i 0.0206210 + 0.0357166i 0.876152 0.482035i 0.160102π-0.160102\pi
−0.855531 + 0.517752i 0.826769π0.826769\pi
752752 −2.95022e6 + 5.10993e6i −0.190244 + 0.329511i
753753 −3.10606e6 + 5.37985e6i −0.199628 + 0.345766i
754754 −1.97748e6 3.42509e6i −0.126673 0.219403i
755755 −6.44880e6 −0.411729
756756 0 0
757757 −4.86768e6 −0.308732 −0.154366 0.988014i 0.549334π-0.549334\pi
−0.154366 + 0.988014i 0.549334π0.549334\pi
758758 −4.71040e6 8.15866e6i −0.297773 0.515758i
759759 4.10356e6 7.10757e6i 0.258557 0.447834i
760760 −912026. + 1.57967e6i −0.0572760 + 0.0992050i
761761 2.90894e6 + 5.03842e6i 0.182084 + 0.315379i 0.942590 0.333952i 0.108382π-0.108382\pi
−0.760506 + 0.649331i 0.775049π0.775049\pi
762762 −3.32918e6 −0.207706
763763 0 0
764764 −1.24319e7 −0.770558
765765 5.42092e6 + 9.38930e6i 0.334903 + 0.580069i
766766 −6.07891e6 + 1.05290e7i −0.374329 + 0.648358i
767767 −7.40085e6 + 1.28186e7i −0.454248 + 0.786781i
768768 294912. + 510803.i 0.0180422 + 0.0312500i
769769 −1.94310e7 −1.18490 −0.592448 0.805609i 0.701839π-0.701839\pi
−0.592448 + 0.805609i 0.701839π0.701839\pi
770770 0 0
771771 124080. 0.00751738
772772 −2.21137e6 3.83020e6i −0.133542 0.231302i
773773 4.12089e6 7.13760e6i 0.248052 0.429639i −0.714933 0.699193i 0.753543π-0.753543\pi
0.962985 + 0.269554i 0.0868763π0.0868763\pi
774774 −1.89673e6 + 3.28524e6i −0.113803 + 0.197112i
775775 2.13372e7 + 3.69570e7i 1.27609 + 2.21026i
776776 6.37704e6 0.380159
777777 0 0
778778 1.83709e6 0.108813
779779 −2.50695e6 4.34216e6i −0.148014 0.256367i
780780 6.00227e6 1.03962e7i 0.353247 0.611843i
781781 7.61816e6 1.31950e7i 0.446913 0.774076i
782782 9.81996e6 + 1.70087e7i 0.574239 + 0.994611i
783783 −894861. −0.0521616
784784 0 0
785785 −2.48194e7 −1.43753
786786 −1.30191e6 2.25498e6i −0.0751666 0.130192i
787787 −7.39314e6 + 1.28053e7i −0.425493 + 0.736975i −0.996466 0.0839932i 0.973233π-0.973233\pi
0.570973 + 0.820969i 0.306566π0.306566\pi
788788 1.05292e6 1.82372e6i 0.0604061 0.104626i
789789 2.58675e6 + 4.48038e6i 0.147932 + 0.256226i
790790 −2.01050e7 −1.14614
791791 0 0
792792 −1.24515e6 −0.0705356
793793 −4.56065e6 7.89927e6i −0.257539 0.446071i
794794 −1.08500e7 + 1.87928e7i −0.610772 + 1.05789i
795795 −8.22625e6 + 1.42483e7i −0.461619 + 0.799548i
796796 4.51968e6 + 7.82832e6i 0.252828 + 0.437911i
797797 1.58158e7 0.881956 0.440978 0.897518i 0.354632π-0.354632\pi
0.440978 + 0.897518i 0.354632π0.354632\pi
798798 0 0
799799 2.98080e7 1.65183
800800 3.88440e6 + 6.72799e6i 0.214585 + 0.371672i
801801 4.38882e6 7.60166e6i 0.241694 0.418627i
802802 4.22254e6 7.31366e6i 0.231813 0.401512i
803803 −6.36294e6 1.10209e7i −0.348232 0.603156i
804804 −5.19543e6 −0.283453
805805 0 0
806806 −1.81228e7 −0.982625
807807 5.03518e6 + 8.72118e6i 0.272164 + 0.471402i
808808 −5.28639e6 + 9.15630e6i −0.284860 + 0.493392i
809809 −5.96518e6 + 1.03320e7i −0.320444 + 0.555026i −0.980580 0.196121i 0.937166π-0.937166\pi
0.660136 + 0.751147i 0.270499π0.270499\pi
810810 −1.35809e6 2.35229e6i −0.0727306 0.125973i
811811 −1.89393e7 −1.01114 −0.505571 0.862785i 0.668718π-0.668718\pi
−0.505571 + 0.862785i 0.668718π0.668718\pi
812812 0 0
813813 6.25382e6 0.331833
814814 −4.36114e6 7.55372e6i −0.230696 0.399576i
815815 −2.26036e7 + 3.91505e7i −1.19202 + 2.06464i
816816 1.48984e6 2.58048e6i 0.0783276 0.135667i
817817 1.61209e6 + 2.79221e6i 0.0844954 + 0.146350i
818818 1.02298e7 0.534544
819819 0 0
820820 −3.01507e7 −1.56590
821821 −1.60044e7 2.77204e7i −0.828667 1.43529i −0.899084 0.437776i 0.855766π-0.855766\pi
0.0704167 0.997518i 0.477567π-0.477567\pi
822822 −4.06192e6 + 7.03544e6i −0.209677 + 0.363172i
823823 −1.80715e7 + 3.13008e7i −0.930025 + 1.61085i −0.146753 + 0.989173i 0.546882π0.546882\pi
−0.783273 + 0.621678i 0.786451π0.786451\pi
824824 3.43191e6 + 5.94424e6i 0.176083 + 0.304985i
825825 −1.64004e7 −0.838916
826826 0 0
827827 −2.45831e7 −1.24989 −0.624946 0.780668i 0.714879π-0.714879\pi
−0.624946 + 0.780668i 0.714879π0.714879\pi
828828 −2.46018e6 4.26116e6i −0.124707 0.215999i
829829 1.05212e7 1.82232e7i 0.531715 0.920957i −0.467600 0.883940i 0.654881π-0.654881\pi
0.999315 0.0370169i 0.0117856π-0.0117856\pi
830830 2.34238e7 4.05712e7i 1.18022 2.04419i
831831 −3.76944e6 6.52886e6i −0.189354 0.327971i
832832 −3.29923e6 −0.165236
833833 0 0
834834 1.18070e7 0.587791
835835 −2.01027e6 3.48189e6i −0.0997787 0.172822i
836836 −529144. + 916504.i −0.0261853 + 0.0453543i
837837 −2.05026e6 + 3.55116e6i −0.101157 + 0.175209i
838838 −4.34802e6 7.53099e6i −0.213885 0.370460i
839839 −1.12403e7 −0.551283 −0.275642 0.961260i 0.588890π-0.588890\pi
−0.275642 + 0.961260i 0.588890π0.588890\pi
840840 0 0
841841 −1.90043e7 −0.926537
842842 −1.09586e7 1.89809e7i −0.532691 0.922647i
843843 −4.12959e6 + 7.15266e6i −0.200142 + 0.346656i
844844 −2.50910e6 + 4.34588e6i −0.121244 + 0.210001i
845845 1.43603e7 + 2.48728e7i 0.691866 + 1.19835i
846846 −7.46775e6 −0.358727
847847 0 0
848848 4.52168e6 0.215928
849849 1.86868e6 + 3.23666e6i 0.0889748 + 0.154109i
850850 1.96233e7 3.39886e7i 0.931591 1.61356i
851851 1.72336e7 2.98494e7i 0.815739 1.41290i
852852 −4.56727e6 7.91074e6i −0.215555 0.373352i
853853 2.63779e7 1.24127 0.620636 0.784099i 0.286874π-0.286874\pi
0.620636 + 0.784099i 0.286874π0.286874\pi
854854 0 0
855855 −2.30856e6 −0.108001
856856 −3.11751e6 5.39969e6i −0.145420 0.251875i
857857 2.13331e7 3.69501e7i 0.992208 1.71855i 0.388201 0.921575i 0.373097π-0.373097\pi
0.604006 0.796979i 0.293570π-0.293570\pi
858858 3.48243e6 6.03175e6i 0.161497 0.279721i
859859 1.46309e7 + 2.53414e7i 0.676530 + 1.17179i 0.976019 + 0.217685i 0.0698506π0.0698506\pi
−0.299489 + 0.954100i 0.596816π0.596816\pi
860860 1.93883e7 0.893911
861861 0 0
862862 2.46750e7 1.13107
863863 −6.97238e6 1.20765e7i −0.318680 0.551969i 0.661533 0.749916i 0.269906π-0.269906\pi
−0.980213 + 0.197947i 0.936573π0.936573\pi
864864 −373248. + 646484.i −0.0170103 + 0.0294628i
865865 −2.05069e7 + 3.55189e7i −0.931877 + 1.61406i
866866 −9.79192e6 1.69601e7i −0.443683 0.768482i
867867 −2.27412e6 −0.102746
868868 0 0
869869 −1.16646e7 −0.523988
870870 2.28681e6 + 3.96087e6i 0.102431 + 0.177416i
871871 1.45305e7 2.51676e7i 0.648988 1.12408i
872872 1.89783e6 3.28714e6i 0.0845213 0.146395i
873873 4.03547e6 + 6.98964e6i 0.179208 + 0.310398i
874874 −4.18195e6 −0.185183
875875 0 0
876876 −7.62946e6 −0.335918
877877 −1.70386e6 2.95117e6i −0.0748057 0.129567i 0.826196 0.563383i 0.190500π-0.190500\pi
−0.901002 + 0.433815i 0.857167π0.857167\pi
878878 7.09175e6 1.22833e7i 0.310468 0.537747i
879879 5.46710e6 9.46929e6i 0.238663 0.413376i
880880 3.18197e6 + 5.51134e6i 0.138513 + 0.239911i
881881 3.51391e6 0.152528 0.0762641 0.997088i 0.475701π-0.475701\pi
0.0762641 + 0.997088i 0.475701π0.475701\pi
882882 0 0
883883 2.14895e7 0.927524 0.463762 0.885960i 0.346499π-0.346499\pi
0.463762 + 0.885960i 0.346499π0.346499\pi
884884 8.33357e6 + 1.44342e7i 0.358675 + 0.621242i
885885 8.55855e6 1.48239e7i 0.367318 0.636213i
886886 1.21130e7 2.09804e7i 0.518404 0.897903i
887887 1.22678e7 + 2.12485e7i 0.523550 + 0.906816i 0.999624 + 0.0274107i 0.00872618π0.00872618\pi
−0.476074 + 0.879405i 0.657940π0.657940\pi
888888 −5.22921e6 −0.222538
889889 0 0
890890 −4.48624e7 −1.89849
891891 −787946. 1.36476e6i −0.0332508 0.0575921i
892892 −2.23587e6 + 3.87263e6i −0.0940879 + 0.162965i
893893 −3.17352e6 + 5.49671e6i −0.133172 + 0.230661i
894894 −2.95220e6 5.11335e6i −0.123538 0.213974i
895895 −2.52413e7 −1.05331
896896 0 0
897897 2.75225e7 1.14211
898898 −2.41602e6 4.18466e6i −0.0999791 0.173169i
899899 3.45231e6 5.97958e6i 0.142466 0.246758i
900900 −4.91620e6 + 8.51511e6i −0.202313 + 0.350416i
901901 −1.14214e7 1.97824e7i −0.468711 0.811832i
902902 −1.74930e7 −0.715894
903903 0 0
904904 −1.00651e7 −0.409636
905905 1.54870e7 + 2.68243e7i 0.628559 + 1.08870i
906906 −1.12156e6 + 1.94260e6i −0.0453943 + 0.0786252i
907907 4.07073e6 7.05071e6i 0.164306 0.284587i −0.772102 0.635498i 0.780795π-0.780795\pi
0.936409 + 0.350911i 0.114128π0.114128\pi
908908 −9.78806e6 1.69534e7i −0.393987 0.682405i
909909 −1.33812e7 −0.537137
910910 0 0
911911 1.01384e7 0.404739 0.202370 0.979309i 0.435136π-0.435136\pi
0.202370 + 0.979309i 0.435136π0.435136\pi
912912 317234. + 549465.i 0.0126297 + 0.0218753i
913913 1.35901e7 2.35388e7i 0.539569 0.934560i
914914 −1.09310e7 + 1.89331e7i −0.432807 + 0.749644i
915915 5.27407e6 + 9.13495e6i 0.208254 + 0.360706i
916916 −4.07639e6 −0.160523
917917 0 0
918918 3.77116e6 0.147696
919919 5.05880e6 + 8.76211e6i 0.197587 + 0.342231i 0.947746 0.319027i 0.103356π-0.103356\pi
−0.750158 + 0.661258i 0.770023π0.770023\pi
920920 −1.25739e7 + 2.17787e7i −0.489781 + 0.848325i
921921 1.17054e7 2.02743e7i 0.454712 0.787584i
922922 −2.31912e6 4.01683e6i −0.0898454 0.155617i
923923 5.10948e7 1.97412
924924 0 0
925925 −6.88760e7 −2.64676
926926 −8.62669e6 1.49419e7i −0.330611 0.572634i
927927 −4.34351e6 + 7.52318e6i −0.166013 + 0.287543i
928928 628489. 1.08858e6i 0.0239568 0.0414943i
929929 1.02555e7 + 1.77631e7i 0.389870 + 0.675274i 0.992432 0.122798i 0.0391868π-0.0391868\pi
−0.602562 + 0.798072i 0.705853π0.705853\pi
930930 2.09577e7 0.794579
931931 0 0
932932 1.19388e7 0.450215
933933 3.68624e6 + 6.38475e6i 0.138637 + 0.240126i
934934 1.19785e7 2.07473e7i 0.449298 0.778206i
935935 1.60748e7 2.78423e7i 0.601333 1.04154i
936936 −2.08780e6 3.61617e6i −0.0778930 0.134915i
937937 1.46527e7 0.545218 0.272609 0.962125i 0.412114π-0.412114\pi
0.272609 + 0.962125i 0.412114π0.412114\pi
938938 0 0
939939 −7.93745e6 −0.293777
940940 1.90838e7 + 3.30541e7i 0.704441 + 1.22013i
941941 1.29670e7 2.24596e7i 0.477382 0.826851i −0.522282 0.852773i 0.674919π-0.674919\pi
0.999664 + 0.0259225i 0.00825231π0.00825231\pi
942942 −4.31652e6 + 7.47643e6i −0.158492 + 0.274515i
943943 −3.45629e7 5.98647e7i −1.26570 2.19226i
944944 −4.70433e6 −0.171818
945945 0 0
946946 1.12488e7 0.408676
947947 −5.22448e6 9.04906e6i −0.189307 0.327890i 0.755712 0.654904i 0.227291π-0.227291\pi
−0.945020 + 0.327014i 0.893958π0.893958\pi
948948 −3.49661e6 + 6.05630e6i −0.126365 + 0.218870i
949949 2.13381e7 3.69586e7i 0.769111 1.33214i
950950 4.17842e6 + 7.23723e6i 0.150211 + 0.260174i
951951 1.44394e7 0.517725
952952 0 0
953953 1.15666e6 0.0412548 0.0206274 0.999787i 0.493434π-0.493434\pi
0.0206274 + 0.999787i 0.493434π0.493434\pi
954954 2.86137e6 + 4.95604e6i 0.101790 + 0.176305i
955955 −4.02086e7 + 6.96433e7i −1.42663 + 2.47099i
956956 −2.56829e6 + 4.44841e6i −0.0908865 + 0.157420i
957957 1.32677e6 + 2.29804e6i 0.0468292 + 0.0811106i
958958 1.41861e7 0.499400
959959 0 0
960960 3.81533e6 0.133615
961961 −1.50497e6 2.60668e6i −0.0525677 0.0910500i
962962 1.46250e7 2.53313e7i 0.509518 0.882511i
963963 3.94560e6 6.83399e6i 0.137103 0.237470i
964964 9.94029e6 + 1.72171e7i 0.344514 + 0.596715i
965965 −2.86089e7 −0.988969
966966 0 0
967967 2.00516e7 0.689577 0.344789 0.938680i 0.387951π-0.387951\pi
0.344789 + 0.938680i 0.387951π0.387951\pi
968968 −3.30750e6 5.72876e6i −0.113452 0.196504i
969969 1.60261e6 2.77580e6i 0.0548300 0.0949684i
970970 2.06252e7 3.57240e7i 0.703833 1.21907i
971971 3.05104e6 + 5.28456e6i 0.103849 + 0.179871i 0.913267 0.407361i 0.133551π-0.133551\pi
−0.809419 + 0.587232i 0.800218π0.800218\pi
972972 −944784. −0.0320750
973973 0 0
974974 3.51328e7 1.18663
975975 −2.74992e7 4.76300e7i −0.926422 1.60461i
976976 1.44948e6 2.51058e6i 0.0487067 0.0843625i
977977 −6.83716e6 + 1.18423e7i −0.229160 + 0.396917i −0.957559 0.288236i 0.906931π-0.906931\pi
0.728399 + 0.685153i 0.240265π0.240265\pi
978978 7.86230e6 + 1.36179e7i 0.262847 + 0.455264i
979979 −2.60285e7 −0.867945
980980 0 0
981981 4.80388e6 0.159375
982982 −1.17322e6 2.03207e6i −0.0388239 0.0672450i
983983 −8.35164e6 + 1.44655e7i −0.275669 + 0.477473i −0.970304 0.241890i 0.922233π-0.922233\pi
0.694635 + 0.719363i 0.255566π0.255566\pi
984984 −5.24374e6 + 9.08242e6i −0.172645 + 0.299029i
985985 −6.81093e6 1.17969e7i −0.223674 0.387415i
986986 −6.35003e6 −0.208010
987987 0 0
988988 −3.54896e6 −0.115667
989989 2.22256e7 + 3.84958e7i 0.722540 + 1.25148i
990990 −4.02718e6 + 6.97529e6i −0.130591 + 0.226190i
991991 −2.87453e7 + 4.97883e7i −0.929785 + 1.61044i −0.146107 + 0.989269i 0.546674π0.546674\pi
−0.783679 + 0.621166i 0.786659π0.786659\pi
992992 −2.87993e6 4.98819e6i −0.0929186 0.160940i
993993 −9.02772e6 −0.290539
994994 0 0
995995 5.84720e7 1.87236
996996 −8.14760e6 1.41121e7i −0.260244 0.450756i
997997 1.97244e7 3.41637e7i 0.628444 1.08850i −0.359420 0.933176i 0.617025π-0.617025\pi
0.987864 0.155321i 0.0496412π-0.0496412\pi
998998 −1.91954e7 + 3.32475e7i −0.610059 + 1.05665i
999999 −3.30911e6 5.73155e6i −0.104905 0.181701i
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 294.6.e.z.67.2 4
7.2 even 3 inner 294.6.e.z.79.2 4
7.3 odd 6 294.6.a.q.1.2 yes 2
7.4 even 3 294.6.a.n.1.1 2
7.5 odd 6 294.6.e.x.79.1 4
7.6 odd 2 294.6.e.x.67.1 4
21.11 odd 6 882.6.a.bu.1.2 2
21.17 even 6 882.6.a.bk.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.6.a.n.1.1 2 7.4 even 3
294.6.a.q.1.2 yes 2 7.3 odd 6
294.6.e.x.67.1 4 7.6 odd 2
294.6.e.x.79.1 4 7.5 odd 6
294.6.e.z.67.2 4 1.1 even 1 trivial
294.6.e.z.79.2 4 7.2 even 3 inner
882.6.a.bk.1.1 2 21.17 even 6
882.6.a.bu.1.2 2 21.11 odd 6