Properties

Label 200.6.f.d.149.3
Level 200200
Weight 66
Character 200.149
Analytic conductor 32.07732.077
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,6,Mod(149,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.149");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 200=2352 200 = 2^{3} \cdot 5^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 200.f (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 32.076763962632.0767639626
Analytic rank: 00
Dimension: 4040
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 149.3
Character χ\chi == 200.149
Dual form 200.6.f.d.149.4

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+(5.367681.78549i)q2+29.6034q3+(25.6240+19.1679i)q4+(158.90252.8566i)q690.3364iq7+(103.318148.639i)q8+633.360q9181.932iq11+(758.558+567.435i)q12455.237q13+(161.295+484.897i)q14+(289.182+982.319i)q16615.967iq17+(3399.681130.86i)q182493.63iq192674.26iq21+(324.839+976.555i)q224427.05iq23+(3058.554400.21i)q24+(2443.57+812.823i)q26+11556.0q27+(1731.562314.78i)q28+7659.34iq296767.72q31+(201.6855789.11i)q325385.81iq33+(1099.80+3306.31i)q34+(16229.2+12140.2i)q36+4808.64q37+(4452.35+13385.0i)q3813476.6q39+1885.99q41+(4774.88+14354.6i)q42+8262.94q43+(3487.264661.84i)q44+(7904.46+23763.0i)q46+5728.44iq47+(8560.77+29080.0i)q48+8646.33q4918234.7iq51+(11665.08725.95i)q52+32364.5q53+(62028.920633.1i)q54+(13427.5+9333.33i)q5673819.8iq57+(13675.741112.9i)q58+20848.8iq5913265.1iq61+(36327.0+12083.7i)q6257215.5iq63+(11419.0+30714.0i)q64+(9616.33+28909.3i)q66+9642.36q67+(11806.815783.6i)q68131056.iq6933088.4q71+(65437.294141.9i)q7218595.6iq73+(25811.28585.79i)q74+(47797.663896.7i)q7616435.1q77+(72337.9+24062.3i)q7844201.2q79+188190.q81+(10123.43367.42i)q8280063.0q83+(51260.168525.4i)q84+(44352.814753.4i)q86+226742.iq87+(27042.2+18796.8i)q88+81639.3q89+41124.5iq91+(84857.3113439.i)q92200348.q93+(10228.130748.4i)q94+(5970.56171377.i)q9622224.8iq97+(46410.715438.0i)q98115229.iq99+O(q100)q+(-5.36768 - 1.78549i) q^{2} +29.6034 q^{3} +(25.6240 + 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} -90.3364i q^{7} +(-103.318 - 148.639i) q^{8} +633.360 q^{9} -181.932i q^{11} +(758.558 + 567.435i) q^{12} -455.237 q^{13} +(-161.295 + 484.897i) q^{14} +(289.182 + 982.319i) q^{16} -615.967i q^{17} +(-3399.68 - 1130.86i) q^{18} -2493.63i q^{19} -2674.26i q^{21} +(-324.839 + 976.555i) q^{22} -4427.05i q^{23} +(-3058.55 - 4400.21i) q^{24} +(2443.57 + 812.823i) q^{26} +11556.0 q^{27} +(1731.56 - 2314.78i) q^{28} +7659.34i q^{29} -6767.72 q^{31} +(201.685 - 5789.11i) q^{32} -5385.81i q^{33} +(-1099.80 + 3306.31i) q^{34} +(16229.2 + 12140.2i) q^{36} +4808.64 q^{37} +(-4452.35 + 13385.0i) q^{38} -13476.6 q^{39} +1885.99 q^{41} +(-4774.88 + 14354.6i) q^{42} +8262.94 q^{43} +(3487.26 - 4661.84i) q^{44} +(-7904.46 + 23763.0i) q^{46} +5728.44i q^{47} +(8560.77 + 29080.0i) q^{48} +8646.33 q^{49} -18234.7i q^{51} +(-11665.0 - 8725.95i) q^{52} +32364.5 q^{53} +(-62028.9 - 20633.1i) q^{54} +(-13427.5 + 9333.33i) q^{56} -73819.8i q^{57} +(13675.7 - 41112.9i) q^{58} +20848.8i q^{59} -13265.1i q^{61} +(36327.0 + 12083.7i) q^{62} -57215.5i q^{63} +(-11419.0 + 30714.0i) q^{64} +(-9616.33 + 28909.3i) q^{66} +9642.36 q^{67} +(11806.8 - 15783.6i) q^{68} -131056. i q^{69} -33088.4 q^{71} +(-65437.2 - 94141.9i) q^{72} -18595.6i q^{73} +(-25811.2 - 8585.79i) q^{74} +(47797.6 - 63896.7i) q^{76} -16435.1 q^{77} +(72337.9 + 24062.3i) q^{78} -44201.2 q^{79} +188190. q^{81} +(-10123.4 - 3367.42i) q^{82} -80063.0 q^{83} +(51260.1 - 68525.4i) q^{84} +(-44352.8 - 14753.4i) q^{86} +226742. i q^{87} +(-27042.2 + 18796.8i) q^{88} +81639.3 q^{89} +41124.5i q^{91} +(84857.3 - 113439. i) q^{92} -200348. q^{93} +(10228.1 - 30748.4i) q^{94} +(5970.56 - 171377. i) q^{96} -22224.8i q^{97} +(-46410.7 - 15438.0i) q^{98} -115229. i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q2q4+66q6+3240q9+848q14110q1618918q24+18344q26+14320q31+19182q34+29656q3644904q3911608q41+23186q4475224q46125304q49++115582q96+O(q100) 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/200Z)×\left(\mathbb{Z}/200\mathbb{Z}\right)^\times.

nn 101101 151151 177177
χ(n)\chi(n) 1-1 11 1-1

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 −5.36768 1.78549i −0.948881 0.315633i
33 29.6034 1.89906 0.949529 0.313679i 0.101562π-0.101562\pi
0.949529 + 0.313679i 0.101562π0.101562\pi
44 25.6240 + 19.1679i 0.800751 + 0.598997i
55 0 0
66 −158.902 52.8566i −1.80198 0.599406i
77 90.3364i 0.696816i −0.937343 0.348408i 0.886722π-0.886722\pi
0.937343 0.348408i 0.113278π-0.113278\pi
88 −103.318 148.639i −0.570754 0.821121i
99 633.360 2.60642
1010 0 0
1111 181.932i 0.453344i −0.973971 0.226672i 0.927215π-0.927215\pi
0.973971 0.226672i 0.0727846π-0.0727846\pi
1212 758.558 + 567.435i 1.52067 + 1.13753i
1313 −455.237 −0.747101 −0.373551 0.927610i 0.621860π-0.621860\pi
−0.373551 + 0.927610i 0.621860π0.621860\pi
1414 −161.295 + 484.897i −0.219938 + 0.661195i
1515 0 0
1616 289.182 + 982.319i 0.282404 + 0.959295i
1717 615.967i 0.516934i −0.966020 0.258467i 0.916783π-0.916783\pi
0.966020 0.258467i 0.0832173π-0.0832173\pi
1818 −3399.68 1130.86i −2.47318 0.822674i
1919 2493.63i 1.58470i −0.610067 0.792350i 0.708857π-0.708857\pi
0.610067 0.792350i 0.291143π-0.291143\pi
2020 0 0
2121 2674.26i 1.32329i
2222 −324.839 + 976.555i −0.143091 + 0.430170i
2323 4427.05i 1.74500i −0.488616 0.872499i 0.662498π-0.662498\pi
0.488616 0.872499i 0.337502π-0.337502\pi
2424 −3058.55 4400.21i −1.08389 1.55936i
2525 0 0
2626 2443.57 + 812.823i 0.708910 + 0.235810i
2727 11556.0 3.05069
2828 1731.56 2314.78i 0.417391 0.557976i
2929 7659.34i 1.69121i 0.533813 + 0.845603i 0.320759π0.320759\pi
−0.533813 + 0.845603i 0.679241π0.679241\pi
3030 0 0
3131 −6767.72 −1.26485 −0.632424 0.774622i 0.717940π-0.717940\pi
−0.632424 + 0.774622i 0.717940π0.717940\pi
3232 201.685 5789.11i 0.0348176 0.999394i
3333 5385.81i 0.860927i
3434 −1099.80 + 3306.31i −0.163162 + 0.490509i
3535 0 0
3636 16229.2 + 12140.2i 2.08709 + 1.56124i
3737 4808.64 0.577455 0.288727 0.957411i 0.406768π-0.406768\pi
0.288727 + 0.957411i 0.406768π0.406768\pi
3838 −4452.35 + 13385.0i −0.500185 + 1.50369i
3939 −13476.6 −1.41879
4040 0 0
4141 1885.99 0.175218 0.0876092 0.996155i 0.472077π-0.472077\pi
0.0876092 + 0.996155i 0.472077π0.472077\pi
4242 −4774.88 + 14354.6i −0.417676 + 1.25565i
4343 8262.94 0.681496 0.340748 0.940155i 0.389320π-0.389320\pi
0.340748 + 0.940155i 0.389320π0.389320\pi
4444 3487.26 4661.84i 0.271552 0.363016i
4545 0 0
4646 −7904.46 + 23763.0i −0.550780 + 1.65580i
4747 5728.44i 0.378261i 0.981952 + 0.189130i 0.0605669π0.0605669\pi
−0.981952 + 0.189130i 0.939433π0.939433\pi
4848 8560.77 + 29080.0i 0.536302 + 1.82176i
4949 8646.33 0.514448
5050 0 0
5151 18234.7i 0.981687i
5252 −11665.0 8725.95i −0.598242 0.447512i
5353 32364.5 1.58263 0.791316 0.611408i 0.209396π-0.209396\pi
0.791316 + 0.611408i 0.209396π0.209396\pi
5454 −62028.9 20633.1i −2.89474 0.962899i
5555 0 0
5656 −13427.5 + 9333.33i −0.572170 + 0.397710i
5757 73819.8i 3.00944i
5858 13675.7 41112.9i 0.533801 1.60475i
5959 20848.8i 0.779740i 0.920870 + 0.389870i 0.127480π0.127480\pi
−0.920870 + 0.389870i 0.872520π0.872520\pi
6060 0 0
6161 13265.1i 0.456442i −0.973609 0.228221i 0.926709π-0.926709\pi
0.973609 0.228221i 0.0732909π-0.0732909\pi
6262 36327.0 + 12083.7i 1.20019 + 0.399228i
6363 57215.5i 1.81620i
6464 −11419.0 + 30714.0i −0.348480 + 0.937316i
6565 0 0
6666 −9616.33 + 28909.3i −0.271737 + 0.816918i
6767 9642.36 0.262420 0.131210 0.991355i 0.458114π-0.458114\pi
0.131210 + 0.991355i 0.458114π0.458114\pi
6868 11806.8 15783.6i 0.309642 0.413935i
6969 131056.i 3.31385i
7070 0 0
7171 −33088.4 −0.778986 −0.389493 0.921029i 0.627350π-0.627350\pi
−0.389493 + 0.921029i 0.627350π0.627350\pi
7272 −65437.2 94141.9i −1.48763 2.14019i
7373 18595.6i 0.408417i −0.978927 0.204208i 0.934538π-0.934538\pi
0.978927 0.204208i 0.0654620π-0.0654620\pi
7474 −25811.2 8585.79i −0.547936 0.182264i
7575 0 0
7676 47797.6 63896.7i 0.949231 1.26895i
7777 −16435.1 −0.315897
7878 72337.9 + 24062.3i 1.34626 + 0.447817i
7979 −44201.2 −0.796831 −0.398415 0.917205i 0.630440π-0.630440\pi
−0.398415 + 0.917205i 0.630440π0.630440\pi
8080 0 0
8181 188190. 3.18701
8282 −10123.4 3367.42i −0.166261 0.0553048i
8383 −80063.0 −1.27567 −0.637833 0.770175i 0.720169π-0.720169\pi
−0.637833 + 0.770175i 0.720169π0.720169\pi
8484 51260.1 68525.4i 0.792649 1.05963i
8585 0 0
8686 −44352.8 14753.4i −0.646659 0.215103i
8787 226742.i 3.21170i
8888 −27042.2 + 18796.8i −0.372251 + 0.258748i
8989 81639.3 1.09251 0.546254 0.837620i 0.316053π-0.316053\pi
0.546254 + 0.837620i 0.316053π0.316053\pi
9090 0 0
9191 41124.5i 0.520592i
9292 84857.3 113439.i 1.04525 1.39731i
9393 −200348. −2.40202
9494 10228.1 30748.4i 0.119392 0.358925i
9595 0 0
9696 5970.56 171377.i 0.0661206 1.89791i
9797 22224.8i 0.239833i −0.992784 0.119917i 0.961737π-0.961737\pi
0.992784 0.119917i 0.0382627π-0.0382627\pi
9898 −46410.7 15438.0i −0.488150 0.162377i
9999 115229.i 1.18161i
100100 0 0
101101 38894.0i 0.379384i 0.981844 + 0.189692i 0.0607489π0.0607489\pi
−0.981844 + 0.189692i 0.939251π0.939251\pi
102102 −32557.9 + 97878.1i −0.309853 + 0.931505i
103103 175773.i 1.63253i −0.577681 0.816263i 0.696042π-0.696042\pi
0.577681 0.816263i 0.303958π-0.303958\pi
104104 47034.0 + 67665.9i 0.426411 + 0.613461i
105105 0 0
106106 −173723. 57786.6i −1.50173 0.499531i
107107 128182. 1.08235 0.541175 0.840910i 0.317980π-0.317980\pi
0.541175 + 0.840910i 0.317980π0.317980\pi
108108 296111. + 221504.i 2.44284 + 1.82735i
109109 49566.1i 0.399594i 0.979837 + 0.199797i 0.0640283π0.0640283\pi
−0.979837 + 0.199797i 0.935972π0.935972\pi
110110 0 0
111111 142352. 1.09662
112112 88739.2 26123.7i 0.668452 0.196784i
113113 92377.7i 0.680567i 0.940323 + 0.340283i 0.110523π0.110523\pi
−0.940323 + 0.340283i 0.889477π0.889477\pi
114114 −131805. + 396241.i −0.949879 + 2.85560i
115115 0 0
116116 −146814. + 196263.i −1.01303 + 1.35423i
117117 −288329. −1.94726
118118 37225.3 111909.i 0.246112 0.739881i
119119 −55644.2 −0.360208
120120 0 0
121121 127952. 0.794479
122122 −23684.7 + 71202.9i −0.144069 + 0.433110i
123123 55831.7 0.332750
124124 −173416. 129723.i −1.01283 0.757641i
125125 0 0
126126 −102158. + 307115.i −0.573252 + 1.72335i
127127 137192.i 0.754778i −0.926055 0.377389i 0.876822π-0.876822\pi
0.926055 0.377389i 0.123178π-0.123178\pi
128128 116133. 144474.i 0.626514 0.779410i
129129 244611. 1.29420
130130 0 0
131131 91906.6i 0.467917i −0.972247 0.233958i 0.924832π-0.924832\pi
0.972247 0.233958i 0.0751679π-0.0751679\pi
132132 103235. 138006.i 0.515693 0.689388i
133133 −225265. −1.10424
134134 −51757.1 17216.4i −0.249005 0.0828284i
135135 0 0
136136 −91556.6 + 63640.1i −0.424465 + 0.295042i
137137 220709.i 1.00466i 0.864676 + 0.502330i 0.167524π0.167524\pi
−0.864676 + 0.502330i 0.832476π0.832476\pi
138138 −233999. + 703465.i −1.04596 + 3.14445i
139139 154375.i 0.677706i 0.940839 + 0.338853i 0.110039π0.110039\pi
−0.940839 + 0.338853i 0.889961π0.889961\pi
140140 0 0
141141 169581.i 0.718339i
142142 177608. + 59079.1i 0.739165 + 0.245874i
143143 82822.4i 0.338694i
144144 183157. + 622162.i 0.736065 + 2.50033i
145145 0 0
146146 −33202.4 + 99815.4i −0.128910 + 0.387539i
147147 255961. 0.976967
148148 123217. + 92171.6i 0.462397 + 0.345894i
149149 152976.i 0.564492i 0.959342 + 0.282246i 0.0910794π0.0910794\pi
−0.959342 + 0.282246i 0.908921π0.908921\pi
150150 0 0
151151 −440485. −1.57213 −0.786066 0.618143i 0.787885π-0.787885\pi
−0.786066 + 0.618143i 0.787885π0.787885\pi
152152 −370649. + 257635.i −1.30123 + 0.904474i
153153 390129.i 1.34735i
154154 88218.5 + 29344.8i 0.299749 + 0.0997078i
155155 0 0
156156 −345324. 258318.i −1.13610 0.849851i
157157 433381. 1.40320 0.701601 0.712570i 0.252469π-0.252469\pi
0.701601 + 0.712570i 0.252469π0.252469\pi
158158 237258. + 78920.9i 0.756098 + 0.251507i
159159 958100. 3.00551
160160 0 0
161161 −399924. −1.21594
162162 −1.01014e6 336012.i −3.02410 1.00593i
163163 −201943. −0.595333 −0.297666 0.954670i 0.596208π-0.596208\pi
−0.297666 + 0.954670i 0.596208π0.596208\pi
164164 48326.6 + 36150.5i 0.140306 + 0.104955i
165165 0 0
166166 429753. + 142952.i 1.21046 + 0.402643i
167167 300699.i 0.834337i 0.908829 + 0.417168i 0.136977π0.136977\pi
−0.908829 + 0.417168i 0.863023π0.863023\pi
168168 −397499. + 276298.i −1.08658 + 0.755275i
169169 −164052. −0.441840
170170 0 0
171171 1.57936e6i 4.13040i
172172 211730. + 158383.i 0.545709 + 0.408214i
173173 100504. 0.255311 0.127656 0.991819i 0.459255π-0.459255\pi
0.127656 + 0.991819i 0.459255π0.459255\pi
174174 404847. 1.21708e6i 1.01372 3.04752i
175175 0 0
176176 178715. 52611.6i 0.434891 0.128026i
177177 617194.i 1.48077i
178178 −438214. 145766.i −1.03666 0.344832i
179179 554078.i 1.29252i 0.763116 + 0.646262i 0.223669π0.223669\pi
−0.763116 + 0.646262i 0.776331π0.776331\pi
180180 0 0
181181 227592.i 0.516368i 0.966096 + 0.258184i 0.0831241π0.0831241\pi
−0.966096 + 0.258184i 0.916876π0.916876\pi
182182 73427.5 220743.i 0.164316 0.493980i
183183 392692.i 0.866811i
184184 −658031. + 457392.i −1.43285 + 0.995964i
185185 0 0
186186 1.07540e6 + 357719.i 2.27923 + 0.758158i
187187 −112064. −0.234349
188188 −109802. + 146786.i −0.226577 + 0.302893i
189189 1.04393e6i 2.12577i
190190 0 0
191191 796597. 1.57999 0.789997 0.613111i 0.210082π-0.210082\pi
0.789997 + 0.613111i 0.210082π0.210082\pi
192192 −338041. + 909238.i −0.661783 + 1.78002i
193193 356611.i 0.689131i −0.938762 0.344565i 0.888026π-0.888026\pi
0.938762 0.344565i 0.111974π-0.111974\pi
194194 −39682.3 + 119296.i −0.0756994 + 0.227573i
195195 0 0
196196 221554. + 165732.i 0.411945 + 0.308153i
197197 −226534. −0.415880 −0.207940 0.978142i 0.566676π-0.566676\pi
−0.207940 + 0.978142i 0.566676π0.566676\pi
198198 −205740. + 618511.i −0.372955 + 1.12120i
199199 177886. 0.318427 0.159213 0.987244i 0.449104π-0.449104\pi
0.159213 + 0.987244i 0.449104π0.449104\pi
200200 0 0
201201 285447. 0.498350
202202 69444.9 208770.i 0.119746 0.359990i
203203 691917. 1.17846
204204 349521. 467247.i 0.588028 0.786087i
205205 0 0
206206 −313842. + 943495.i −0.515280 + 1.54907i
207207 2.80392e6i 4.54820i
208208 −131646. 447188.i −0.210985 0.716691i
209209 −453671. −0.718415
210210 0 0
211211 525263.i 0.812215i −0.913825 0.406107i 0.866886π-0.866886\pi
0.913825 0.406107i 0.133114π-0.133114\pi
212212 829310. + 620361.i 1.26729 + 0.947992i
213213 −979528. −1.47934
214214 −688041. 228868.i −1.02702 0.341626i
215215 0 0
216216 −1.19394e6 1.71767e6i −1.74119 2.50498i
217217 611372.i 0.881366i
218218 88500.0 266055.i 0.126125 0.379167i
219219 550494.i 0.775607i
220220 0 0
221221 280411.i 0.386202i
222222 −764100. 254168.i −1.04056 0.346130i
223223 711308.i 0.957846i 0.877857 + 0.478923i 0.158973π0.158973\pi
−0.877857 + 0.478923i 0.841027π0.841027\pi
224224 −522967. 18219.5i −0.696393 0.0242614i
225225 0 0
226226 164940. 495854.i 0.214810 0.645777i
227227 −216347. −0.278668 −0.139334 0.990245i 0.544496π-0.544496\pi
−0.139334 + 0.990245i 0.544496π0.544496\pi
228228 1.41497e6 1.89156e6i 1.80265 2.40981i
229229 759408.i 0.956944i 0.878103 + 0.478472i 0.158809π0.158809\pi
−0.878103 + 0.478472i 0.841191π0.841191\pi
230230 0 0
231231 −486535. −0.599907
232232 1.13848e6 791344.i 1.38868 0.965262i
233233 860736.i 1.03868i 0.854569 + 0.519338i 0.173821π0.173821\pi
−0.854569 + 0.519338i 0.826179π0.826179\pi
234234 1.54766e6 + 514810.i 1.84772 + 0.614621i
235235 0 0
236236 −399627. + 534229.i −0.467062 + 0.624378i
237237 −1.30850e6 −1.51323
238238 298681. + 99352.4i 0.341794 + 0.113694i
239239 348130. 0.394228 0.197114 0.980381i 0.436843π-0.436843\pi
0.197114 + 0.980381i 0.436843π0.436843\pi
240240 0 0
241241 −844167. −0.936237 −0.468119 0.883666i 0.655068π-0.655068\pi
−0.468119 + 0.883666i 0.655068π0.655068\pi
242242 −686804. 228457.i −0.753866 0.250764i
243243 2.76295e6 3.00163
244244 254264. 339905.i 0.273408 0.365497i
245245 0 0
246246 −299687. 99687.0i −0.315740 0.105027i
247247 1.13519e6i 1.18393i
248248 699224. + 1.00595e6i 0.721917 + 1.03859i
249249 −2.37014e6 −2.42256
250250 0 0
251251 1.52042e6i 1.52328i 0.648000 + 0.761640i 0.275606π0.275606\pi
−0.648000 + 0.761640i 0.724394π0.724394\pi
252252 1.09670e6 1.46609e6i 1.08790 1.45432i
253253 −805423. −0.791085
254254 −244955. + 736403.i −0.238233 + 0.716195i
255255 0 0
256256 −881323. + 568138.i −0.840496 + 0.541818i
257257 682391.i 0.644466i 0.946660 + 0.322233i 0.104434π0.104434\pi
−0.946660 + 0.322233i 0.895566π0.895566\pi
258258 −1.31299e6 436751.i −1.22804 0.408493i
259259 434395.i 0.402379i
260260 0 0
261261 4.85112e6i 4.40799i
262262 −164099. + 493326.i −0.147690 + 0.443997i
263263 91394.4i 0.0814761i −0.999170 0.0407381i 0.987029π-0.987029\pi
0.999170 0.0407381i 0.0129709π-0.0129709\pi
264264 −800541. + 556449.i −0.706925 + 0.491378i
265265 0 0
266266 1.20915e6 + 402209.i 1.04780 + 0.348536i
267267 2.41680e6 2.07474
268268 247076. + 184824.i 0.210133 + 0.157189i
269269 935475.i 0.788227i 0.919062 + 0.394114i 0.128948π0.128948\pi
−0.919062 + 0.394114i 0.871052π0.871052\pi
270270 0 0
271271 512294. 0.423737 0.211868 0.977298i 0.432045π-0.432045\pi
0.211868 + 0.977298i 0.432045π0.432045\pi
272272 605076. 178127.i 0.495892 0.145984i
273273 1.21742e6i 0.988634i
274274 394075. 1.18470e6i 0.317105 0.953304i
275275 0 0
276276 2.51206e6 3.35817e6i 1.98499 2.65357i
277277 −615832. −0.482239 −0.241120 0.970495i 0.577515π-0.577515\pi
−0.241120 + 0.970495i 0.577515π0.577515\pi
278278 275636. 828638.i 0.213907 0.643062i
279279 −4.28641e6 −3.29673
280280 0 0
281281 1.22082e6 0.922330 0.461165 0.887314i 0.347432π-0.347432\pi
0.461165 + 0.887314i 0.347432π0.347432\pi
282282 302786. 910258.i 0.226732 0.681619i
283283 −696315. −0.516820 −0.258410 0.966035i 0.583199π-0.583199\pi
−0.258410 + 0.966035i 0.583199π0.583199\pi
284284 −847858. 634235.i −0.623774 0.466611i
285285 0 0
286286 147879. 444564.i 0.106903 0.321380i
287287 170374.i 0.122095i
288288 127739. 3.66659e6i 0.0907493 2.60484i
289289 1.04044e6 0.732779
290290 0 0
291291 657931.i 0.455457i
292292 356439. 476495.i 0.244641 0.327040i
293293 134741. 0.0916922 0.0458461 0.998949i 0.485402π-0.485402\pi
0.0458461 + 0.998949i 0.485402π0.485402\pi
294294 −1.37392e6 457016.i −0.927025 0.308363i
295295 0 0
296296 −496817. 714750.i −0.329584 0.474160i
297297 2.10241e6i 1.38301i
298298 273137. 821126.i 0.178172 0.535636i
299299 2.01536e6i 1.30369i
300300 0 0
301301 746444.i 0.474877i
302302 2.36438e6 + 786483.i 1.49177 + 0.496217i
303303 1.15139e6i 0.720472i
304304 2.44953e6 721112.i 1.52020 0.447526i
305305 0 0
306306 −696572. + 2.09409e6i −0.425268 + 1.27847i
307307 280871. 0.170083 0.0850414 0.996377i 0.472898π-0.472898\pi
0.0850414 + 0.996377i 0.472898π0.472898\pi
308308 −421134. 315027.i −0.252955 0.189222i
309309 5.20348e6i 3.10026i
310310 0 0
311311 −2.40348e6 −1.40909 −0.704547 0.709657i 0.748850π-0.748850\pi
−0.704547 + 0.709657i 0.748850π0.748850\pi
312312 1.39236e6 + 2.00314e6i 0.809779 + 1.16500i
313313 619525.i 0.357436i 0.983900 + 0.178718i 0.0571949π0.0571949\pi
−0.983900 + 0.178718i 0.942805π0.942805\pi
314314 −2.32625e6 773798.i −1.33147 0.442898i
315315 0 0
316316 −1.13261e6 847245.i −0.638063 0.477300i
317317 −913021. −0.510308 −0.255154 0.966900i 0.582126π-0.582126\pi
−0.255154 + 0.966900i 0.582126π0.582126\pi
318318 −5.14278e6 1.71068e6i −2.85187 0.948639i
319319 1.39348e6 0.766698
320320 0 0
321321 3.79462e6 2.05545
322322 2.14666e6 + 714061.i 1.15378 + 0.383792i
323323 −1.53599e6 −0.819185
324324 4.82218e6 + 3.60721e6i 2.55200 + 1.90901i
325325 0 0
326326 1.08397e6 + 360568.i 0.564900 + 0.187907i
327327 1.46733e6i 0.758852i
328328 −194856. 280331.i −0.100007 0.143875i
329329 517487. 0.263578
330330 0 0
331331 3.37863e6i 1.69500i −0.530793 0.847502i 0.678106π-0.678106\pi
0.530793 0.847502i 0.321894π-0.321894\pi
332332 −2.05154e6 1.53464e6i −1.02149 0.764120i
333333 3.04560e6 1.50509
334334 536896. 1.61406e6i 0.263345 0.791686i
335335 0 0
336336 2.62698e6 773349.i 1.26943 0.373704i
337337 3.19536e6i 1.53266i −0.642448 0.766329i 0.722081π-0.722081\pi
0.642448 0.766329i 0.277919π-0.277919\pi
338338 880579. + 292914.i 0.419254 + 0.139459i
339339 2.73469e6i 1.29244i
340340 0 0
341341 1.23127e6i 0.573412i
342342 −2.81994e6 + 8.47752e6i −1.30369 + 3.91926i
343343 2.29936e6i 1.05529i
344344 −853706. 1.22819e6i −0.388966 0.559591i
345345 0 0
346346 −539476. 179450.i −0.242260 0.0805847i
347347 −2.15234e6 −0.959592 −0.479796 0.877380i 0.659289π-0.659289\pi
−0.479796 + 0.877380i 0.659289π0.659289\pi
348348 −4.34618e6 + 5.81006e6i −1.92380 + 2.57177i
349349 2.78827e6i 1.22538i 0.790322 + 0.612692i 0.209913π0.209913\pi
−0.790322 + 0.612692i 0.790087π0.790087\pi
350350 0 0
351351 −5.26072e6 −2.27917
352352 −1.05323e6 36693.0i −0.453069 0.0157843i
353353 3.23259e6i 1.38075i 0.723453 + 0.690373i 0.242554π0.242554\pi
−0.723453 + 0.690373i 0.757446π0.757446\pi
354354 1.10199e6 3.31290e6i 0.467381 1.40508i
355355 0 0
356356 2.09193e6 + 1.56486e6i 0.874826 + 0.654409i
357357 −1.64726e6 −0.684055
358358 989303. 2.97412e6i 0.407964 1.22645i
359359 2.02100e6 0.827620 0.413810 0.910363i 0.364198π-0.364198\pi
0.413810 + 0.910363i 0.364198π0.364198\pi
360360 0 0
361361 −3.74207e6 −1.51128
362362 406363. 1.22164e6i 0.162983 0.489972i
363363 3.78780e6 1.50876
364364 −788271. + 1.05378e6i −0.311833 + 0.416864i
365365 0 0
366366 −701149. + 2.10785e6i −0.273595 + 0.822500i
367367 2.50488e6i 0.970781i 0.874297 + 0.485391i 0.161323π0.161323\pi
−0.874297 + 0.485391i 0.838677π0.838677\pi
368368 4.34877e6 1.28022e6i 1.67397 0.492795i
369369 1.19451e6 0.456693
370370 0 0
371371 2.92370e6i 1.10280i
372372 −5.13371e6 3.84024e6i −1.92342 1.43880i
373373 −495172. −0.184283 −0.0921413 0.995746i 0.529371π-0.529371\pi
−0.0921413 + 0.995746i 0.529371π0.529371\pi
374374 601525. + 200090.i 0.222369 + 0.0739684i
375375 0 0
376376 851468. 591848.i 0.310598 0.215894i
377377 3.48682e6i 1.26350i
378378 −1.86392e6 + 5.60347e6i −0.670963 + 2.01710i
379379 2.19040e6i 0.783294i 0.920116 + 0.391647i 0.128095π0.128095\pi
−0.920116 + 0.391647i 0.871905π0.871905\pi
380380 0 0
381381 4.06135e6i 1.43337i
382382 −4.27588e6 1.42232e6i −1.49923 0.498699i
383383 289759.i 0.100935i 0.998726 + 0.0504674i 0.0160711π0.0160711\pi
−0.998726 + 0.0504674i 0.983929π0.983929\pi
384384 3.43793e6 4.27693e6i 1.18979 1.48014i
385385 0 0
386386 −636726. + 1.91417e6i −0.217513 + 0.653903i
387387 5.23342e6 1.77627
388388 426004. 569490.i 0.143659 0.192047i
389389 2.11554e6i 0.708839i 0.935087 + 0.354420i 0.115322π0.115322\pi
−0.935087 + 0.354420i 0.884678π0.884678\pi
390390 0 0
391391 −2.72692e6 −0.902048
392392 −893317. 1.28518e6i −0.293623 0.422424i
393393 2.72075e6i 0.888601i
394394 1.21596e6 + 404475.i 0.394621 + 0.131266i
395395 0 0
396396 2.20869e6 2.95263e6i 0.707779 0.946173i
397397 1.80742e6 0.575549 0.287774 0.957698i 0.407085π-0.407085\pi
0.287774 + 0.957698i 0.407085π0.407085\pi
398398 −954837. 317615.i −0.302149 0.100506i
399399 −6.66861e6 −2.09702
400400 0 0
401401 −2.59111e6 −0.804683 −0.402342 0.915490i 0.631804π-0.631804\pi
−0.402342 + 0.915490i 0.631804π0.631804\pi
402402 −1.53219e6 509663.i −0.472875 0.157296i
403403 3.08092e6 0.944969
404404 −745516. + 996620.i −0.227250 + 0.303792i
405405 0 0
406406 −3.71399e6 1.23541e6i −1.11822 0.371961i
407407 874847.i 0.261786i
408408 −2.71038e6 + 1.88396e6i −0.806084 + 0.560302i
409409 5.00884e6 1.48057 0.740285 0.672293i 0.234690π-0.234690\pi
0.740285 + 0.672293i 0.234690π0.234690\pi
410410 0 0
411411 6.53375e6i 1.90791i
412412 3.36921e6 4.50402e6i 0.977878 1.30725i
413413 1.88340e6 0.543335
414414 −5.00638e6 + 1.50505e7i −1.43556 + 4.31570i
415415 0 0
416416 −91814.5 + 2.63542e6i −0.0260122 + 0.746648i
417417 4.57003e6i 1.28700i
418418 2.43516e6 + 810026.i 0.681690 + 0.226756i
419419 2.27862e6i 0.634071i −0.948414 0.317035i 0.897313π-0.897313\pi
0.948414 0.317035i 0.102687π-0.102687\pi
420420 0 0
421421 1.30407e6i 0.358587i −0.983796 0.179293i 0.942619π-0.942619\pi
0.983796 0.179293i 0.0573811π-0.0573811\pi
422422 −937853. + 2.81945e6i −0.256362 + 0.770695i
423423 3.62817e6i 0.985907i
424424 −3.34382e6 4.81063e6i −0.903293 1.29953i
425425 0 0
426426 5.25780e6 + 1.74894e6i 1.40372 + 0.466929i
427427 −1.19832e6 −0.318056
428428 3.28454e6 + 2.45698e6i 0.866693 + 0.648325i
429429 2.45182e6i 0.643200i
430430 0 0
431431 3.93997e6 1.02164 0.510822 0.859687i 0.329341π-0.329341\pi
0.510822 + 0.859687i 0.329341π0.329341\pi
432432 3.34179e6 + 1.13517e7i 0.861528 + 2.92651i
433433 5.84454e6i 1.49806i 0.662534 + 0.749032i 0.269481π0.269481\pi
−0.662534 + 0.749032i 0.730519π0.730519\pi
434434 1.09160e6 3.28165e6i 0.278189 0.836311i
435435 0 0
436436 −950080. + 1.27008e6i −0.239356 + 0.319975i
437437 −1.10394e7 −2.76530
438438 −982902. + 2.95487e6i −0.244808 + 0.735959i
439439 7.63016e6 1.88961 0.944805 0.327634i 0.106251π-0.106251\pi
0.944805 + 0.327634i 0.106251π0.106251\pi
440440 0 0
441441 5.47624e6 1.34087
442442 500672. 1.50516e6i 0.121898 0.366460i
443443 −1.99010e6 −0.481798 −0.240899 0.970550i 0.577442π-0.577442\pi
−0.240899 + 0.970550i 0.577442π0.577442\pi
444444 3.64763e6 + 2.72859e6i 0.878119 + 0.656872i
445445 0 0
446446 1.27004e6 3.81808e6i 0.302328 0.908882i
447447 4.52861e6i 1.07200i
448448 2.77459e6 + 1.03155e6i 0.653137 + 0.242826i
449449 2.05507e6 0.481074 0.240537 0.970640i 0.422676π-0.422676\pi
0.240537 + 0.970640i 0.422676π0.422676\pi
450450 0 0
451451 343122.i 0.0794342i
452452 −1.77069e6 + 2.36709e6i −0.407658 + 0.544965i
453453 −1.30398e7 −2.98557
454454 1.16128e6 + 386287.i 0.264423 + 0.0879569i
455455 0 0
456456 −1.09725e7 + 7.62687e6i −2.47111 + 1.71765i
457457 2.74689e6i 0.615250i 0.951508 + 0.307625i 0.0995342π0.0995342\pi
−0.951508 + 0.307625i 0.900466π0.900466\pi
458458 1.35592e6 4.07626e6i 0.302044 0.908026i
459459 7.11811e6i 1.57700i
460460 0 0
461461 4.01666e6i 0.880264i −0.897933 0.440132i 0.854932π-0.854932\pi
0.897933 0.440132i 0.145068π-0.145068\pi
462462 2.61157e6 + 868705.i 0.569241 + 0.189351i
463463 7.77791e6i 1.68620i −0.537753 0.843102i 0.680727π-0.680727\pi
0.537753 0.843102i 0.319273π-0.319273\pi
464464 −7.52391e6 + 2.21494e6i −1.62237 + 0.477604i
465465 0 0
466466 1.53684e6 4.62015e6i 0.327841 0.985580i
467467 −3.81432e6 −0.809329 −0.404664 0.914465i 0.632612π-0.632612\pi
−0.404664 + 0.914465i 0.632612π0.632612\pi
468468 −7.38816e6 5.52667e6i −1.55927 1.16640i
469469 871056.i 0.182858i
470470 0 0
471471 1.28295e7 2.66476
472472 3.09893e6 2.15404e6i 0.640261 0.445040i
473473 1.50330e6i 0.308952i
474474 7.02364e6 + 2.33633e6i 1.43587 + 0.477625i
475475 0 0
476476 −1.42583e6 1.06658e6i −0.288437 0.215763i
477477 2.04984e7 4.12500
478478 −1.86865e6 621584.i −0.374075 0.124431i
479479 2.44255e6 0.486413 0.243206 0.969975i 0.421801π-0.421801\pi
0.243206 + 0.969975i 0.421801π0.421801\pi
480480 0 0
481481 −2.18907e6 −0.431417
482482 4.53122e6 + 1.50725e6i 0.888378 + 0.295508i
483483 −1.18391e7 −2.30914
484484 3.27864e6 + 2.45257e6i 0.636180 + 0.475891i
485485 0 0
486486 −1.48307e7 4.93323e6i −2.84819 0.947416i
487487 8.35163e6i 1.59569i −0.602862 0.797846i 0.705973π-0.705973\pi
0.602862 0.797846i 0.294027π-0.294027\pi
488488 −1.97171e6 + 1.37052e6i −0.374795 + 0.260516i
489489 −5.97820e6 −1.13057
490490 0 0
491491 340069.i 0.0636595i 0.999493 + 0.0318298i 0.0101334π0.0101334\pi
−0.999493 + 0.0318298i 0.989867π0.989867\pi
492492 1.43063e6 + 1.07018e6i 0.266450 + 0.199316i
493493 4.71790e6 0.874241
494494 2.02688e6 6.09335e6i 0.373688 1.12341i
495495 0 0
496496 −1.95710e6 6.64806e6i −0.357199 1.21336i
497497 2.98909e6i 0.542810i
498498 1.27221e7 + 4.23186e6i 2.29872 + 0.764642i
499499 648994.i 0.116678i 0.998297 + 0.0583391i 0.0185805π0.0185805\pi
−0.998297 + 0.0583391i 0.981420π0.981420\pi
500500 0 0
501501 8.90172e6i 1.58445i
502502 2.71470e6 8.16114e6i 0.480798 1.44541i
503503 3.13514e6i 0.552506i 0.961085 + 0.276253i 0.0890928π0.0890928\pi
−0.961085 + 0.276253i 0.910907π0.910907\pi
504504 −8.50445e6 + 5.91137e6i −1.49132 + 1.03660i
505505 0 0
506506 4.32326e6 + 1.43808e6i 0.750645 + 0.249693i
507507 −4.85650e6 −0.839080
508508 2.62968e6 3.51541e6i 0.452110 0.604390i
509509 5.04542e6i 0.863183i −0.902069 0.431591i 0.857952π-0.857952\pi
0.902069 0.431591i 0.142048π-0.142048\pi
510510 0 0
511511 −1.67986e6 −0.284591
512512 5.74507e6 1.47599e6i 0.968546 0.248833i
513513 2.88163e7i 4.83443i
514514 1.21840e6 3.66286e6i 0.203415 0.611522i
515515 0 0
516516 6.26792e6 + 4.68868e6i 1.03633 + 0.775223i
517517 1.04219e6 0.171482
518518 −775610. + 2.33170e6i −0.127004 + 0.381810i
519519 2.97527e6 0.484851
520520 0 0
521521 598792. 0.0966456 0.0483228 0.998832i 0.484612π-0.484612\pi
0.0483228 + 0.998832i 0.484612π0.484612\pi
522522 8.66165e6 2.60393e7i 1.39131 4.18266i
523523 −1.12334e7 −1.79580 −0.897901 0.440197i 0.854909π-0.854909\pi
−0.897901 + 0.440197i 0.854909π0.854909\pi
524524 1.76166e6 2.35502e6i 0.280281 0.374685i
525525 0 0
526526 −163184. + 490576.i −0.0257166 + 0.0773111i
527527 4.16869e6i 0.653843i
528528 5.29058e6 1.55748e6i 0.825884 0.243130i
529529 −1.31624e7 −2.04502
530530 0 0
531531 1.32048e7i 2.03233i
532532 −5.77220e6 4.31786e6i −0.884224 0.661439i
533533 −858572. −0.130906
534534 −1.29726e7 4.31518e6i −1.96868 0.654856i
535535 0 0
536536 −996225. 1.43323e6i −0.149777 0.215478i
537537 1.64026e7i 2.45458i
538538 1.67028e6 5.02133e6i 0.248791 0.747934i
539539 1.57305e6i 0.233222i
540540 0 0
541541 8.05017e6i 1.18253i −0.806478 0.591264i 0.798629π-0.798629\pi
0.806478 0.591264i 0.201371π-0.201371\pi
542542 −2.74983e6 914697.i −0.402076 0.133746i
543543 6.73748e6i 0.980614i
544544 −3.56590e6 124231.i −0.516620 0.0179984i
545545 0 0
546546 2.17370e6 6.53475e6i 0.312046 0.938096i
547547 −6.14990e6 −0.878819 −0.439410 0.898287i 0.644812π-0.644812\pi
−0.439410 + 0.898287i 0.644812π0.644812\pi
548548 −4.23054e6 + 5.65547e6i −0.601789 + 0.804483i
549549 8.40159e6i 1.18968i
550550 0 0
551551 1.90995e7 2.68005
552552 −1.94800e7 + 1.35403e7i −2.72107 + 1.89139i
553553 3.99298e6i 0.555244i
554554 3.30559e6 + 1.09956e6i 0.457588 + 0.152211i
555555 0 0
556556 −2.95905e6 + 3.95572e6i −0.405944 + 0.542673i
557557 6.26714e6 0.855917 0.427959 0.903798i 0.359233π-0.359233\pi
0.427959 + 0.903798i 0.359233π0.359233\pi
558558 2.30081e7 + 7.65335e6i 3.12820 + 1.04056i
559559 −3.76160e6 −0.509146
560560 0 0
561561 −3.31748e6 −0.445042
562562 −6.55298e6 2.17977e6i −0.875182 0.291118i
563563 149874. 0.0199276 0.00996378 0.999950i 0.496828π-0.496828\pi
0.00996378 + 0.999950i 0.496828π0.496828\pi
564564 −3.25052e6 + 4.34535e6i −0.430283 + 0.575211i
565565 0 0
566566 3.73760e6 + 1.24327e6i 0.490401 + 0.163126i
567567 1.70004e7i 2.22076i
568568 3.41861e6 + 4.91822e6i 0.444609 + 0.639642i
569569 −2.10351e6 −0.272373 −0.136186 0.990683i 0.543485π-0.543485\pi
−0.136186 + 0.990683i 0.543485π0.543485\pi
570570 0 0
571571 8.72030e6i 1.11929i −0.828734 0.559643i 0.810938π-0.810938\pi
0.828734 0.559643i 0.189062π-0.189062\pi
572572 −1.58753e6 + 2.12224e6i −0.202877 + 0.271210i
573573 2.35820e7 3.00050
574574 −304201. + 914511.i −0.0385372 + 0.115854i
575575 0 0
576576 −7.23234e6 + 1.94530e7i −0.908285 + 2.44304i
577577 5.44606e6i 0.680993i −0.940246 0.340497i 0.889405π-0.889405\pi
0.940246 0.340497i 0.110595π-0.110595\pi
578578 −5.58476e6 1.85770e6i −0.695321 0.231290i
579579 1.05569e7i 1.30870i
580580 0 0
581581 7.23261e6i 0.888904i
582582 −1.17473e6 + 3.53156e6i −0.143758 + 0.432175i
583583 5.88816e6i 0.717477i
584584 −2.76403e6 + 1.92125e6i −0.335360 + 0.233106i
585585 0 0
586586 −723249. 240580.i −0.0870050 0.0289411i
587587 −1.53801e6 −0.184232 −0.0921158 0.995748i 0.529363π-0.529363\pi
−0.0921158 + 0.995748i 0.529363π0.529363\pi
588588 6.55874e6 + 4.90623e6i 0.782307 + 0.585201i
589589 1.68762e7i 2.00441i
590590 0 0
591591 −6.70618e6 −0.789781
592592 1.39057e6 + 4.72361e6i 0.163076 + 0.553950i
593593 1.23546e7i 1.44275i 0.692542 + 0.721377i 0.256491π0.256491\pi
−0.692542 + 0.721377i 0.743509π0.743509\pi
594594 −3.75383e6 + 1.12851e7i −0.436525 + 1.31231i
595595 0 0
596596 −2.93223e6 + 3.91986e6i −0.338129 + 0.452017i
597597 5.26604e6 0.604711
598598 3.59841e6 1.08178e7i 0.411488 1.23705i
599599 1.46319e7 1.66622 0.833112 0.553105i 0.186557π-0.186557\pi
0.833112 + 0.553105i 0.186557π0.186557\pi
600600 0 0
601601 −1.08262e7 −1.22261 −0.611306 0.791394i 0.709356π-0.709356\pi
−0.611306 + 0.791394i 0.709356π0.709356\pi
602602 −1.33277e6 + 4.00668e6i −0.149887 + 0.450602i
603603 6.10709e6 0.683976
604604 −1.12870e7 8.44318e6i −1.25889 0.941702i
605605 0 0
606606 2.05580e6 6.18031e6i 0.227405 0.683642i
607607 722652.i 0.0796082i 0.999208 + 0.0398041i 0.0126734π0.0126734\pi
−0.999208 + 0.0398041i 0.987327π0.987327\pi
608608 −1.44359e7 502927.i −1.58374 0.0551754i
609609 2.04831e7 2.23796
610610 0 0
611611 2.60780e6i 0.282599i
612612 7.47796e6 9.99668e6i 0.807058 1.07889i
613613 −1.19951e6 −0.128930 −0.0644648 0.997920i 0.520534π-0.520534\pi
−0.0644648 + 0.997920i 0.520534π0.520534\pi
614614 −1.50762e6 501492.i −0.161388 0.0536838i
615615 0 0
616616 1.69804e6 + 2.44290e6i 0.180300 + 0.259390i
617617 1.26945e7i 1.34246i −0.741249 0.671230i 0.765766π-0.765766\pi
0.741249 0.671230i 0.234234π-0.234234\pi
618618 −9.29078e6 + 2.79307e7i −0.978546 + 2.94178i
619619 9.69565e6i 1.01707i −0.861042 0.508534i 0.830187π-0.830187\pi
0.861042 0.508534i 0.169813π-0.169813\pi
620620 0 0
621621 5.11590e7i 5.32344i
622622 1.29011e7 + 4.29140e6i 1.33706 + 0.444757i
623623 7.37501e6i 0.761276i
624624 −3.89718e6 1.32383e7i −0.400672 1.36104i
625625 0 0
626626 1.10616e6 3.32541e6i 0.112819 0.339164i
627627 −1.34302e7 −1.36431
628628 1.11050e7 + 8.30700e6i 1.12362 + 0.840515i
629629 2.96196e6i 0.298506i
630630 0 0
631631 2.38091e6 0.238051 0.119025 0.992891i 0.462023π-0.462023\pi
0.119025 + 0.992891i 0.462023π0.462023\pi
632632 4.56676e6 + 6.57001e6i 0.454794 + 0.654295i
633633 1.55496e7i 1.54244i
634634 4.90081e6 + 1.63019e6i 0.484222 + 0.161070i
635635 0 0
636636 2.45504e7 + 1.83648e7i 2.40666 + 1.80029i
637637 −3.93613e6 −0.384345
638638 −7.47977e6 2.48805e6i −0.727506 0.241996i
639639 −2.09569e7 −2.03037
640640 0 0
641641 6.37112e6 0.612450 0.306225 0.951959i 0.400934π-0.400934\pi
0.306225 + 0.951959i 0.400934π0.400934\pi
642642 −2.03683e7 6.77527e6i −1.95037 0.648768i
643643 1.64996e7 1.57379 0.786896 0.617086i 0.211687π-0.211687\pi
0.786896 + 0.617086i 0.211687π0.211687\pi
644644 −1.02477e7 7.66571e6i −0.973666 0.728346i
645645 0 0
646646 8.24471e6 + 2.74250e6i 0.777310 + 0.258562i
647647 2.94843e6i 0.276905i 0.990369 + 0.138452i 0.0442128π0.0442128\pi
−0.990369 + 0.138452i 0.955787π0.955787\pi
648648 −1.94433e7 2.79723e7i −1.81900 2.61692i
649649 3.79306e6 0.353491
650650 0 0
651651 1.80987e7i 1.67376i
652652 −5.17460e6 3.87083e6i −0.476713 0.356603i
653653 −1.02662e7 −0.942167 −0.471083 0.882089i 0.656137π-0.656137\pi
−0.471083 + 0.882089i 0.656137π0.656137\pi
654654 2.61990e6 7.87614e6i 0.239519 0.720061i
655655 0 0
656656 545394. + 1.85264e6i 0.0494824 + 0.168086i
657657 1.17777e7i 1.06451i
658658 −2.77770e6 923968.i −0.250104 0.0831941i
659659 7.94727e6i 0.712860i −0.934322 0.356430i 0.883994π-0.883994\pi
0.934322 0.356430i 0.116006π-0.116006\pi
660660 0 0
661661 9.79140e6i 0.871648i 0.900032 + 0.435824i 0.143543π0.143543\pi
−0.900032 + 0.435824i 0.856457π0.856457\pi
662662 −6.03252e6 + 1.81354e7i −0.535000 + 1.60836i
663663 8.30112e6i 0.733420i
664664 8.27191e6 + 1.19005e7i 0.728091 + 1.04748i
665665 0 0
666666 −1.63478e7 5.43790e6i −1.42815 0.475057i
667667 3.39083e7 2.95115
668668 −5.76378e6 + 7.70513e6i −0.499765 + 0.668096i
669669 2.10571e7i 1.81901i
670670 0 0
671671 −2.41335e6 −0.206926
672672 −1.54816e7 539359.i −1.32249 0.0460739i
673673 1.64861e7i 1.40307i −0.712635 0.701535i 0.752498π-0.752498\pi
0.712635 0.701535i 0.247502π-0.247502\pi
674674 −5.70530e6 + 1.71517e7i −0.483758 + 1.45431i
675675 0 0
676676 −4.20368e6 3.14454e6i −0.353804 0.264661i
677677 2.81251e6 0.235843 0.117922 0.993023i 0.462377π-0.462377\pi
0.117922 + 0.993023i 0.462377π0.462377\pi
678678 4.88277e6 1.46790e7i 0.407936 1.22637i
679679 −2.00771e6 −0.167120
680680 0 0
681681 −6.40461e6 −0.529206
682682 2.19842e6 6.60905e6i 0.180988 0.544100i
683683 −1.56071e7 −1.28018 −0.640090 0.768300i 0.721103π-0.721103\pi
−0.640090 + 0.768300i 0.721103π0.721103\pi
684684 3.02731e7 4.04697e7i 2.47410 3.30742i
685685 0 0
686686 −4.10550e6 + 1.23423e7i −0.333085 + 1.00135i
687687 2.24811e7i 1.81729i
688688 2.38949e6 + 8.11684e6i 0.192457 + 0.653756i
689689 −1.47335e7 −1.18239
690690 0 0
691691 1.32611e7i 1.05654i 0.849077 + 0.528269i 0.177159π0.177159\pi
−0.849077 + 0.528269i 0.822841π0.822841\pi
692692 2.57533e6 + 1.92646e6i 0.204441 + 0.152931i
693693 −1.04094e7 −0.823362
694694 1.15531e7 + 3.84298e6i 0.910539 + 0.302879i
695695 0 0
696696 3.37027e7 2.34265e7i 2.63719 1.83309i
697697 1.16171e6i 0.0905763i
698698 4.97844e6 1.49666e7i 0.386772 1.16274i
699699 2.54807e7i 1.97251i
700700 0 0
701701 2.41803e7i 1.85852i −0.369432 0.929258i 0.620448π-0.620448\pi
0.369432 0.929258i 0.379552π-0.379552\pi
702702 2.82379e7 + 9.39297e6i 2.16266 + 0.719383i
703703 1.19909e7i 0.915093i
704704 5.58787e6 + 2.07748e6i 0.424927 + 0.157981i
705705 0 0
706706 5.77177e6 1.73515e7i 0.435810 1.31016i
707707 3.51354e6 0.264361
708708 −1.18303e7 + 1.58150e7i −0.886979 + 1.18573i
709709 3.10586e6i 0.232042i −0.993247 0.116021i 0.962986π-0.962986\pi
0.993247 0.116021i 0.0370140π-0.0370140\pi
710710 0 0
711711 −2.79953e7 −2.07688
712712 −8.43477e6 1.21348e7i −0.623553 0.897081i
713713 2.99610e7i 2.20716i
714714 8.84196e6 + 2.94117e6i 0.649087 + 0.215911i
715715 0 0
716716 −1.06205e7 + 1.41977e7i −0.774219 + 1.03499i
717717 1.03058e7 0.748661
718718 −1.08481e7 3.60849e6i −0.785313 0.261225i
719719 7.95560e6 0.573919 0.286960 0.957943i 0.407355π-0.407355\pi
0.286960 + 0.957943i 0.407355π0.407355\pi
720720 0 0
721721 −1.58787e7 −1.13757
722722 2.00862e7 + 6.68143e6i 1.43402 + 0.477009i
723723 −2.49902e7 −1.77797
724724 −4.36246e6 + 5.83181e6i −0.309303 + 0.413483i
725725 0 0
726726 −2.03317e7 6.76309e6i −1.43164 0.476216i
727727 2.50891e7i 1.76055i 0.474463 + 0.880276i 0.342642π0.342642\pi
−0.474463 + 0.880276i 0.657358π0.657358\pi
728728 6.11270e6 4.24888e6i 0.427469 0.297130i
729729 3.60626e7 2.51327
730730 0 0
731731 5.08969e6i 0.352288i
732732 7.52709e6 1.00624e7i 0.519217 0.694100i
733733 2.58258e7 1.77539 0.887694 0.460434i 0.152306π-0.152306\pi
0.887694 + 0.460434i 0.152306π0.152306\pi
734734 4.47244e6 1.34454e7i 0.306411 0.921156i
735735 0 0
736736 −2.56287e7 892869.i −1.74394 0.0607566i
737737 1.75426e6i 0.118966i
738738 −6.41176e6 2.13279e6i −0.433347 0.144148i
739739 2.15950e7i 1.45459i 0.686323 + 0.727297i 0.259224π0.259224\pi
−0.686323 + 0.727297i 0.740776π0.740776\pi
740740 0 0
741741 3.36055e7i 2.24835i
742742 −5.22024e6 + 1.56935e7i −0.348081 + 1.04643i
743743 1.25570e7i 0.834479i −0.908797 0.417239i 0.862998π-0.862998\pi
0.908797 0.417239i 0.137002π-0.137002\pi
744744 2.06994e7 + 2.97794e7i 1.37096 + 1.97235i
745745 0 0
746746 2.65793e6 + 884126.i 0.174862 + 0.0581657i
747747 −5.07088e7 −3.32492
748748 −2.87154e6 2.14804e6i −0.187655 0.140374i
749749 1.15795e7i 0.754199i
750750 0 0
751751 −5.43894e6 −0.351896 −0.175948 0.984399i 0.556299π-0.556299\pi
−0.175948 + 0.984399i 0.556299π0.556299\pi
752752 −5.62715e6 + 1.65656e6i −0.362864 + 0.106823i
753753 4.50097e7i 2.89280i
754754 −6.22569e6 + 1.87161e7i −0.398803 + 1.19891i
755755 0 0
756756 2.00099e7 2.67496e7i 1.27333 1.70221i
757757 −1.06247e7 −0.673873 −0.336937 0.941527i 0.609391π-0.609391\pi
−0.336937 + 0.941527i 0.609391π0.609391\pi
758758 3.91094e6 1.17574e7i 0.247234 0.743253i
759759 −2.38433e7 −1.50232
760760 0 0
761761 2.31511e7 1.44914 0.724570 0.689201i 0.242038π-0.242038\pi
0.724570 + 0.689201i 0.242038π0.242038\pi
762762 −7.25151e6 + 2.18000e7i −0.452419 + 1.36010i
763763 4.47763e6 0.278443
764764 2.04120e7 + 1.52691e7i 1.26518 + 0.946412i
765765 0 0
766766 517363. 1.55534e6i 0.0318584 0.0957751i
767767 9.49113e6i 0.582545i
768768 −2.60902e7 + 1.68188e7i −1.59615 + 1.02894i
769769 −9.09958e6 −0.554888 −0.277444 0.960742i 0.589487π-0.589487\pi
−0.277444 + 0.960742i 0.589487π0.589487\pi
770770 0 0
771771 2.02011e7i 1.22388i
772772 6.83549e6 9.13781e6i 0.412787 0.551822i
773773 1.82799e7 1.10034 0.550169 0.835053i 0.314563π-0.314563\pi
0.550169 + 0.835053i 0.314563π0.314563\pi
774774 −2.80913e7 9.34423e6i −1.68547 0.560649i
775775 0 0
776776 −3.30347e6 + 2.29622e6i −0.196932 + 0.136886i
777777 1.28596e7i 0.764142i
778778 3.77728e6 1.13556e7i 0.223733 0.672604i
779779 4.70295e6i 0.277669i
780780 0 0
781781 6.01985e6i 0.353149i
782782 1.46372e7 + 4.86889e6i 0.855937 + 0.284717i
783783 8.85113e7i 5.15934i
784784 2.50036e6 + 8.49345e6i 0.145282 + 0.493508i
785785 0 0
786786 −4.85787e6 + 1.46041e7i −0.280472 + 0.843177i
787787 3.07594e6 0.177028 0.0885139 0.996075i 0.471788π-0.471788\pi
0.0885139 + 0.996075i 0.471788π0.471788\pi
788788 −5.80472e6 4.34219e6i −0.333017 0.249111i
789789 2.70558e6i 0.154728i
790790 0 0
791791 8.34507e6 0.474230
792792 −1.71275e7 + 1.19051e7i −0.970242 + 0.674407i
793793 6.03877e6i 0.341009i
794794 −9.70164e6 3.22713e6i −0.546127 0.181662i
795795 0 0
796796 4.55816e6 + 3.40971e6i 0.254981 + 0.190737i
797797 2.64996e6 0.147772 0.0738861 0.997267i 0.476460π-0.476460\pi
0.0738861 + 0.997267i 0.476460π0.476460\pi
798798 3.57950e7 + 1.19068e7i 1.98983 + 0.661891i
799799 3.52853e6 0.195536
800800 0 0
801801 5.17071e7 2.84754
802802 1.39083e7 + 4.62641e6i 0.763549 + 0.253985i
803803 −3.38315e6 −0.185153
804804 7.31429e6 + 5.47141e6i 0.399054 + 0.298510i
805805 0 0
806806 −1.65374e7 5.50096e6i −0.896664 0.298264i
807807 2.76932e7i 1.49689i
808808 5.78115e6 4.01843e6i 0.311520 0.216535i
809809 −4.52804e6 −0.243242 −0.121621 0.992577i 0.538809π-0.538809\pi
−0.121621 + 0.992577i 0.538809π0.538809\pi
810810 0 0
811811 2.45669e7i 1.31159i 0.754939 + 0.655795i 0.227666π0.227666\pi
−0.754939 + 0.655795i 0.772334π0.772334\pi
812812 1.77297e7 + 1.32626e7i 0.943652 + 0.705893i
813813 1.51656e7 0.804701
814814 −1.56203e6 + 4.69590e6i −0.0826283 + 0.248404i
815815 0 0
816816 1.79123e7 5.27315e6i 0.941728 0.277233i
817817 2.06047e7i 1.07997i
818818 −2.68859e7 8.94325e6i −1.40489 0.467318i
819819 2.60466e7i 1.35688i
820820 0 0
821821 3.38228e7i 1.75126i 0.482981 + 0.875631i 0.339554π0.339554\pi
−0.482981 + 0.875631i 0.660446π0.660446\pi
822822 1.16660e7 3.50711e7i 0.602200 1.81038i
823823 1.50699e7i 0.775554i −0.921753 0.387777i 0.873243π-0.873243\pi
0.921753 0.387777i 0.126757π-0.126757\pi
824824 −2.61267e7 + 1.81605e7i −1.34050 + 0.931770i
825825 0 0
826826 −1.01095e7 3.36280e6i −0.515561 0.171495i
827827 −1.25312e7 −0.637132 −0.318566 0.947901i 0.603201π-0.603201\pi
−0.318566 + 0.947901i 0.603201π0.603201\pi
828828 5.37453e7 7.18477e7i 2.72436 3.64198i
829829 6.28073e6i 0.317412i −0.987326 0.158706i 0.949268π-0.949268\pi
0.987326 0.158706i 0.0507323π-0.0507323\pi
830830 0 0
831831 −1.82307e7 −0.915801
832832 5.19835e6 1.39821e7i 0.260350 0.700270i
833833 5.32585e6i 0.265936i
834834 8.15976e6 2.45305e7i 0.406221 1.22121i
835835 0 0
836836 −1.16249e7 8.69593e6i −0.575271 0.430329i
837837 −7.82078e7 −3.85866
838838 −4.06847e6 + 1.22309e7i −0.200134 + 0.601658i
839839 −2.04326e7 −1.00212 −0.501058 0.865414i 0.667056π-0.667056\pi
−0.501058 + 0.865414i 0.667056π0.667056\pi
840840 0 0
841841 −3.81543e7 −1.86018
842842 −2.32840e6 + 6.99981e6i −0.113182 + 0.340256i
843843 3.61404e7 1.75156
844844 1.00682e7 1.34594e7i 0.486514 0.650382i
845845 0 0
846846 6.47806e6 1.94748e7i 0.311185 0.935509i
847847 1.15587e7i 0.553605i
848848 9.35924e6 + 3.17923e7i 0.446942 + 1.51821i
849849 −2.06133e7 −0.981472
850850 0 0
851851 2.12881e7i 1.00766i
852852 −2.50995e7 1.87755e7i −1.18458 0.886121i
853853 −2.97962e7 −1.40213 −0.701066 0.713097i 0.747292π-0.747292\pi
−0.701066 + 0.713097i 0.747292π0.747292\pi
854854 6.43221e6 + 2.13960e6i 0.301798 + 0.100389i
855855 0 0
856856 −1.32435e7 1.90528e7i −0.617756 0.888741i
857857 2.06770e7i 0.961690i −0.876806 0.480845i 0.840330π-0.840330\pi
0.876806 0.480845i 0.159670π-0.159670\pi
858858 4.37771e6 1.31606e7i 0.203015 0.610320i
859859 2.17795e7i 1.00708i −0.863971 0.503542i 0.832030π-0.832030\pi
0.863971 0.503542i 0.167970π-0.167970\pi
860860 0 0
861861 5.04363e6i 0.231865i
862862 −2.11485e7 7.03478e6i −0.969419 0.322465i
863863 2.24327e7i 1.02531i −0.858596 0.512654i 0.828663π-0.828663\pi
0.858596 0.512654i 0.171337π-0.171337\pi
864864 2.33067e6 6.68989e7i 0.106218 3.04884i
865865 0 0
866866 1.04354e7 3.13716e7i 0.472839 1.42148i
867867 3.08006e7 1.39159
868868 −1.17187e7 + 1.56658e7i −0.527936 + 0.705755i
869869 8.04162e6i 0.361239i
870870 0 0
871871 −4.38956e6 −0.196054
872872 7.36745e6 5.12105e6i 0.328115 0.228070i
873873 1.40763e7i 0.625107i
874874 5.92560e7 + 1.97108e7i 2.62394 + 0.872821i
875875 0 0
876876 1.05518e7 1.41059e7i 0.464587 0.621068i
877877 3.66024e7 1.60698 0.803491 0.595317i 0.202973π-0.202973\pi
0.803491 + 0.595317i 0.202973π0.202973\pi
878878 −4.09563e7 1.36236e7i −1.79302 0.596424i
879879 3.98880e6 0.174129
880880 0 0
881881 −4.27422e7 −1.85531 −0.927656 0.373436i 0.878179π-0.878179\pi
−0.927656 + 0.373436i 0.878179π0.878179\pi
882882 −2.93947e7 9.77779e6i −1.27233 0.423223i
883883 −1.39684e7 −0.602901 −0.301451 0.953482i 0.597471π-0.597471\pi
−0.301451 + 0.953482i 0.597471π0.597471\pi
884884 −5.37489e6 + 7.18526e6i −0.231334 + 0.309252i
885885 0 0
886886 1.06822e7 + 3.55330e6i 0.457169 + 0.152071i
887887 8.75249e6i 0.373528i 0.982405 + 0.186764i 0.0597999π0.0597999\pi
−0.982405 + 0.186764i 0.940200π0.940200\pi
888888 −1.47075e7 2.11590e7i −0.625900 0.900458i
889889 −1.23934e7 −0.525941
890890 0 0
891891 3.42378e7i 1.44481i
892892 −1.36343e7 + 1.82266e7i −0.573747 + 0.766996i
893893 1.42846e7 0.599430
894894 8.08579e6 2.43081e7i 0.338360 1.01720i
895895 0 0
896896 −1.30513e7 1.04910e7i −0.543105 0.436565i
897897 5.96614e7i 2.47578i
898898 −1.10310e7 3.66932e6i −0.456482 0.151843i
899899 5.18363e7i 2.13912i
900900 0 0
901901 1.99355e7i 0.818116i
902902 −612642. + 1.84177e6i −0.0250721 + 0.0753736i
903903 2.20973e7i 0.901819i
904904 1.37309e7 9.54423e6i 0.558828 0.388436i
905905 0 0
906906 6.99938e7 + 2.32826e7i 2.83295 + 0.942345i
907907 4.22342e7 1.70469 0.852345 0.522979i 0.175180π-0.175180\pi
0.852345 + 0.522979i 0.175180π0.175180\pi
908908 −5.54369e6 4.14693e6i −0.223144 0.166921i
909909 2.46339e7i 0.988834i
910910 0 0
911911 3.59551e7 1.43537 0.717686 0.696367i 0.245201π-0.245201\pi
0.717686 + 0.696367i 0.245201π0.245201\pi
912912 7.25145e7 2.13473e7i 2.88694 0.849878i
913913 1.45661e7i 0.578316i
914914 4.90456e6 1.47445e7i 0.194193 0.583799i
915915 0 0
916916 −1.45563e7 + 1.94591e7i −0.573207 + 0.766274i
917917 −8.30252e6 −0.326052
918918 −1.27093e7 + 3.82077e7i −0.497755 + 1.49639i
919919 −4.72565e6 −0.184575 −0.0922875 0.995732i 0.529418π-0.529418\pi
−0.0922875 + 0.995732i 0.529418π0.529418\pi
920920 0 0
921921 8.31472e6 0.322997
922922 −7.17172e6 + 2.15602e7i −0.277841 + 0.835266i
923923 1.50631e7 0.581981
924924 −1.24670e7 9.32586e6i −0.480376 0.359343i
925925 0 0
926926 −1.38874e7 + 4.17493e7i −0.532223 + 1.60001i
927927 1.11328e8i 4.25505i
928928 4.43407e7 + 1.54477e6i 1.69018 + 0.0588837i
929929 3.52534e7 1.34018 0.670088 0.742282i 0.266256π-0.266256\pi
0.670088 + 0.742282i 0.266256π0.266256\pi
930930 0 0
931931 2.15607e7i 0.815246i
932932 −1.64985e7 + 2.20555e7i −0.622164 + 0.831721i
933933 −7.11513e7 −2.67595
934934 2.04741e7 + 6.81044e6i 0.767957 + 0.255451i
935935 0 0
936936 2.97895e7 + 4.28569e7i 1.11141 + 1.59894i
937937 4.46076e7i 1.65982i 0.557899 + 0.829909i 0.311607π0.311607\pi
−0.557899 + 0.829909i 0.688393π0.688393\pi
938938 −1.55526e6 + 4.67555e6i −0.0577161 + 0.173511i
939939 1.83400e7i 0.678791i
940940 0 0
941941 901496.i 0.0331886i 0.999862 + 0.0165943i 0.00528238π0.00528238\pi
−0.999862 + 0.0165943i 0.994718π0.994718\pi
942942 −6.88649e7 2.29070e7i −2.52854 0.841089i
943943 8.34937e6i 0.305756i
944944 −2.04801e7 + 6.02909e6i −0.748001 + 0.220202i
945945 0 0
946946 −2.68412e6 + 8.06921e6i −0.0975157 + 0.293159i
947947 −1.66417e7 −0.603006 −0.301503 0.953465i 0.597488π-0.597488\pi
−0.301503 + 0.953465i 0.597488π0.597488\pi
948948 −3.35292e7 2.50813e7i −1.21172 0.906420i
949949 8.46542e6i 0.305129i
950950 0 0
951951 −2.70285e7 −0.969105
952952 5.74902e6 + 8.27089e6i 0.205590 + 0.295774i
953953 1.76926e7i 0.631043i −0.948918 0.315522i 0.897821π-0.897821\pi
0.948918 0.315522i 0.102179π-0.102179\pi
954954 −1.10029e8 3.65998e7i −3.91414 1.30199i
955955 0 0
956956 8.92050e6 + 6.67293e6i 0.315678 + 0.236141i
957957 4.12518e7 1.45600
958958 −1.31108e7 4.36116e6i −0.461548 0.153528i
959959 1.99381e7 0.700063
960960 0 0
961961 1.71729e7 0.599841
962962 1.17502e7 + 3.90857e6i 0.409363 + 0.136170i
963963 8.11855e7 2.82106
964964 −2.16310e7 1.61809e7i −0.749693 0.560804i
965965 0 0
966966 6.35485e7 + 2.11386e7i 2.19110 + 0.728843i
967967 1.08926e7i 0.374598i −0.982303 0.187299i 0.940027π-0.940027\pi
0.982303 0.187299i 0.0599733π-0.0599733\pi
968968 −1.32196e7 1.90186e7i −0.453452 0.652363i
969969 −4.54705e7 −1.55568
970970 0 0
971971 1.33282e7i 0.453654i −0.973935 0.226827i 0.927165π-0.927165\pi
0.973935 0.226827i 0.0728351π-0.0728351\pi
972972 7.07980e7 + 5.29600e7i 2.40356 + 1.79797i
973973 1.39457e7 0.472236
974974 −1.49118e7 + 4.48289e7i −0.503654 + 1.51412i
975975 0 0
976976 1.30306e7 3.83603e6i 0.437863 0.128901i
977977 5.24537e7i 1.75808i −0.476745 0.879042i 0.658184π-0.658184\pi
0.476745 0.879042i 0.341816π-0.341816\pi
978978 3.20891e7 + 1.06740e7i 1.07278 + 0.356846i
979979 1.48528e7i 0.495282i
980980 0 0
981981 3.13932e7i 1.04151i
982982 607191. 1.82538e6i 0.0200931 0.0604053i
983983 9.86355e6i 0.325574i −0.986661 0.162787i 0.947952π-0.947952\pi
0.986661 0.162787i 0.0520483π-0.0520483\pi
984984 −5.76839e6 8.29875e6i −0.189918 0.273228i
985985 0 0
986986 −2.53242e7 8.42377e6i −0.829551 0.275940i
987987 1.53194e7 0.500550
988988 −2.17592e7 + 2.90882e7i −0.709172 + 0.948034i
989989 3.65804e7i 1.18921i
990990 0 0
991991 2.89033e7 0.934897 0.467448 0.884020i 0.345173π-0.345173\pi
0.467448 + 0.884020i 0.345173π0.345173\pi
992992 −1.36495e6 + 3.91791e7i −0.0440389 + 1.26408i
993993 1.00019e8i 3.21891i
994994 5.33699e6 1.60445e7i 0.171329 0.515062i
995995 0 0
996996 −6.07325e7 4.54306e7i −1.93987 1.45111i
997997 4.81768e6 0.153497 0.0767485 0.997050i 0.475546π-0.475546\pi
0.0767485 + 0.997050i 0.475546π0.475546\pi
998998 1.15877e6 3.48360e6i 0.0368275 0.110714i
999999 5.55686e7 1.76163
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 200.6.f.d.149.3 40
4.3 odd 2 800.6.f.d.49.2 40
5.2 odd 4 200.6.d.c.101.11 20
5.3 odd 4 200.6.d.d.101.10 yes 20
5.4 even 2 inner 200.6.f.d.149.38 40
8.3 odd 2 800.6.f.d.49.40 40
8.5 even 2 inner 200.6.f.d.149.37 40
20.3 even 4 800.6.d.b.401.1 20
20.7 even 4 800.6.d.d.401.20 20
20.19 odd 2 800.6.f.d.49.39 40
40.3 even 4 800.6.d.b.401.20 20
40.13 odd 4 200.6.d.d.101.9 yes 20
40.19 odd 2 800.6.f.d.49.1 40
40.27 even 4 800.6.d.d.401.1 20
40.29 even 2 inner 200.6.f.d.149.4 40
40.37 odd 4 200.6.d.c.101.12 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.6.d.c.101.11 20 5.2 odd 4
200.6.d.c.101.12 yes 20 40.37 odd 4
200.6.d.d.101.9 yes 20 40.13 odd 4
200.6.d.d.101.10 yes 20 5.3 odd 4
200.6.f.d.149.3 40 1.1 even 1 trivial
200.6.f.d.149.4 40 40.29 even 2 inner
200.6.f.d.149.37 40 8.5 even 2 inner
200.6.f.d.149.38 40 5.4 even 2 inner
800.6.d.b.401.1 20 20.3 even 4
800.6.d.b.401.20 20 40.3 even 4
800.6.d.d.401.1 20 40.27 even 4
800.6.d.d.401.20 20 20.7 even 4
800.6.f.d.49.1 40 40.19 odd 2
800.6.f.d.49.2 40 4.3 odd 2
800.6.f.d.49.39 40 20.19 odd 2
800.6.f.d.49.40 40 8.3 odd 2