Properties

Label 525.2.bf.f.368.6
Level 525525
Weight 22
Character 525.368
Analytic conductor 4.1924.192
Analytic rank 00
Dimension 4848
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(32,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 525=3527 525 = 3 \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 525.bf (of order 1212, degree 44, 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: 4.192146106124.19214610612
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 368.6
Character χ\chi == 525.368
Dual form 525.2.bf.f.107.6

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+(0.0799329+0.298314i)q2+(0.540759+1.64547i)q3+(1.64945+0.952310i)q4+(0.4476430.292843i)q6+(2.46856+0.951942i)q7+(0.852694+0.852694i)q8+(2.415161.77961i)q9+(0.660315+0.381233i)q11+(2.45895+2.19915i)q12+(2.27077+2.27077i)q13+(0.481297+0.660315i)q14+(1.71841+2.97637i)q16+(4.694711.25794i)q17+(0.7239320.578226i)q18+(1.41761+0.818455i)q19+(2.90129+3.54718i)q21+(0.166508+0.166508i)q22+(7.390031.98015i)q23+(0.9419831.86419i)q24+(0.858909+0.495891i)q26+(4.234323.01174i)q27+(3.16523+3.92102i)q284.94251q29+(2.964135.13403i)q31+(3.35485+0.898930i)q32+(0.984380+0.880375i)q33+1.50105iq34+(2.288945.23535i)q36+(3.415870.915280i)q37+(0.1308430.488313i)q38+(4.96442+2.50855i)q39+4.35963iq41+(0.8262651.14903i)q42+(2.690372.69037i)q43+(0.726104+1.25765i)q44+(1.181412.04627i)q46+(1.10971+4.14148i)q47+(5.82678+1.21809i)q48+(5.18761+4.69986i)q49+(0.468795+8.40527i)q51+(1.58304+5.90798i)q52+(1.79889+6.71354i)q53+(0.559982+1.50389i)q54+(2.91664+1.29321i)q56+(0.5801622.77522i)q57+(0.3950691.47442i)q58+(3.845016.65975i)q59+(2.196993.80529i)q61+(1.29462+1.29462i)q62+(4.267896.69217i)q63+5.80098iq64+(0.1839440.364025i)q66+(0.01262970.0471345i)q67+(8.94164+2.39591i)q68+(7.2545111.0893i)q6912.4172iq71+(3.576850.541931i)q72+(1.340430.359168i)q73+(0.5460810.945840i)q743.11769q76+(1.26712+1.56968i)q77+(0.3515131.68147i)q78+(3.668082.11777i)q79+(2.66599+8.59607i)q81+(1.300540.348478i)q82+(5.053515.05351i)q83+(8.16355+3.08797i)q84+(1.017620.587525i)q86+(2.672718.13276i)q87+(0.888122+0.237971i)q88+(0.4536000.785658i)q89+(3.44389+7.76716i)q91+(10.303810.3038i)q92+(6.84502+7.65367i)q93+(1.146760.662081i)q94+(0.3350026.00642i)q96+(3.73061+3.73061i)q97+(1.81669+1.17186i)q98+(0.9163212.09584i)q99+O(q100)q+(-0.0799329 + 0.298314i) q^{2} +(-0.540759 + 1.64547i) q^{3} +(1.64945 + 0.952310i) q^{4} +(-0.447643 - 0.292843i) q^{6} +(2.46856 + 0.951942i) q^{7} +(-0.852694 + 0.852694i) q^{8} +(-2.41516 - 1.77961i) q^{9} +(0.660315 + 0.381233i) q^{11} +(-2.45895 + 2.19915i) q^{12} +(2.27077 + 2.27077i) q^{13} +(-0.481297 + 0.660315i) q^{14} +(1.71841 + 2.97637i) q^{16} +(4.69471 - 1.25794i) q^{17} +(0.723932 - 0.578226i) q^{18} +(-1.41761 + 0.818455i) q^{19} +(-2.90129 + 3.54718i) q^{21} +(-0.166508 + 0.166508i) q^{22} +(-7.39003 - 1.98015i) q^{23} +(-0.941983 - 1.86419i) q^{24} +(-0.858909 + 0.495891i) q^{26} +(4.23432 - 3.01174i) q^{27} +(3.16523 + 3.92102i) q^{28} -4.94251 q^{29} +(2.96413 - 5.13403i) q^{31} +(-3.35485 + 0.898930i) q^{32} +(-0.984380 + 0.880375i) q^{33} +1.50105i q^{34} +(-2.28894 - 5.23535i) q^{36} +(-3.41587 - 0.915280i) q^{37} +(-0.130843 - 0.488313i) q^{38} +(-4.96442 + 2.50855i) q^{39} +4.35963i q^{41} +(-0.826265 - 1.14903i) q^{42} +(-2.69037 - 2.69037i) q^{43} +(0.726104 + 1.25765i) q^{44} +(1.18141 - 2.04627i) q^{46} +(-1.10971 + 4.14148i) q^{47} +(-5.82678 + 1.21809i) q^{48} +(5.18761 + 4.69986i) q^{49} +(-0.468795 + 8.40527i) q^{51} +(1.58304 + 5.90798i) q^{52} +(1.79889 + 6.71354i) q^{53} +(0.559982 + 1.50389i) q^{54} +(-2.91664 + 1.29321i) q^{56} +(-0.580162 - 2.77522i) q^{57} +(0.395069 - 1.47442i) q^{58} +(3.84501 - 6.65975i) q^{59} +(-2.19699 - 3.80529i) q^{61} +(1.29462 + 1.29462i) q^{62} +(-4.26789 - 6.69217i) q^{63} +5.80098i q^{64} +(-0.183944 - 0.364025i) q^{66} +(-0.0126297 - 0.0471345i) q^{67} +(8.94164 + 2.39591i) q^{68} +(7.25451 - 11.0893i) q^{69} -12.4172i q^{71} +(3.57685 - 0.541931i) q^{72} +(1.34043 - 0.359168i) q^{73} +(0.546081 - 0.945840i) q^{74} -3.11769 q^{76} +(1.26712 + 1.56968i) q^{77} +(-0.351513 - 1.68147i) q^{78} +(3.66808 - 2.11777i) q^{79} +(2.66599 + 8.59607i) q^{81} +(-1.30054 - 0.348478i) q^{82} +(5.05351 - 5.05351i) q^{83} +(-8.16355 + 3.08797i) q^{84} +(1.01762 - 0.587525i) q^{86} +(2.67271 - 8.13276i) q^{87} +(-0.888122 + 0.237971i) q^{88} +(-0.453600 - 0.785658i) q^{89} +(3.44389 + 7.76716i) q^{91} +(-10.3038 - 10.3038i) q^{92} +(6.84502 + 7.65367i) q^{93} +(-1.14676 - 0.662081i) q^{94} +(0.335002 - 6.00642i) q^{96} +(-3.73061 + 3.73061i) q^{97} +(-1.81669 + 1.17186i) q^{98} +(-0.916321 - 2.09584i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+2q324q6+12q7+10q12+16q138q1614q1828q21+8q2240q27+60q2824q31+4q33+8q364q3714q4216q4332q46++120q97+O(q100) 48 q + 2 q^{3} - 24 q^{6} + 12 q^{7} + 10 q^{12} + 16 q^{13} - 8 q^{16} - 14 q^{18} - 28 q^{21} + 8 q^{22} - 40 q^{27} + 60 q^{28} - 24 q^{31} + 4 q^{33} + 8 q^{36} - 4 q^{37} - 14 q^{42} - 16 q^{43} - 32 q^{46}+ \cdots + 120 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/525Z)×\left(\mathbb{Z}/525\mathbb{Z}\right)^\times.

nn 127127 176176 451451
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 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 −0.0799329 + 0.298314i −0.0565211 + 0.210940i −0.988411 0.151802i 0.951492π-0.951492\pi
0.931890 + 0.362741i 0.118159π0.118159\pi
33 −0.540759 + 1.64547i −0.312207 + 0.950014i
44 1.64945 + 0.952310i 0.824725 + 0.476155i
55 0 0
66 −0.447643 0.292843i −0.182749 0.119553i
77 2.46856 + 0.951942i 0.933029 + 0.359800i
88 −0.852694 + 0.852694i −0.301473 + 0.301473i
99 −2.41516 1.77961i −0.805053 0.593203i
1010 0 0
1111 0.660315 + 0.381233i 0.199092 + 0.114946i 0.596232 0.802812i 0.296664π-0.296664\pi
−0.397140 + 0.917758i 0.629997π0.629997\pi
1212 −2.45895 + 2.19915i −0.709839 + 0.634841i
1313 2.27077 + 2.27077i 0.629797 + 0.629797i 0.948017 0.318220i 0.103085π-0.103085\pi
−0.318220 + 0.948017i 0.603085π0.603085\pi
1414 −0.481297 + 0.660315i −0.128632 + 0.176477i
1515 0 0
1616 1.71841 + 2.97637i 0.429602 + 0.744092i
1717 4.69471 1.25794i 1.13864 0.305096i 0.360233 0.932862i 0.382697π-0.382697\pi
0.778402 + 0.627766i 0.216030π0.216030\pi
1818 0.723932 0.578226i 0.170632 0.136289i
1919 −1.41761 + 0.818455i −0.325221 + 0.187767i −0.653717 0.756739i 0.726791π-0.726791\pi
0.328496 + 0.944505i 0.393458π0.393458\pi
2020 0 0
2121 −2.90129 + 3.54718i −0.633114 + 0.774059i
2222 −0.166508 + 0.166508i −0.0354996 + 0.0354996i
2323 −7.39003 1.98015i −1.54093 0.412890i −0.614363 0.789024i 0.710587π-0.710587\pi
−0.926566 + 0.376133i 0.877253π0.877253\pi
2424 −0.941983 1.86419i −0.192281 0.380525i
2525 0 0
2626 −0.858909 + 0.495891i −0.168446 + 0.0972523i
2727 4.23432 3.01174i 0.814894 0.579610i
2828 3.16523 + 3.92102i 0.598172 + 0.741003i
2929 −4.94251 −0.917801 −0.458900 0.888488i 0.651757π-0.651757\pi
−0.458900 + 0.888488i 0.651757π0.651757\pi
3030 0 0
3131 2.96413 5.13403i 0.532374 0.922099i −0.466911 0.884304i 0.654633π-0.654633\pi
0.999286 0.0377949i 0.0120334π-0.0120334\pi
3232 −3.35485 + 0.898930i −0.593060 + 0.158910i
3333 −0.984380 + 0.880375i −0.171358 + 0.153254i
3434 1.50105i 0.257428i
3535 0 0
3636 −2.28894 5.23535i −0.381491 0.872559i
3737 −3.41587 0.915280i −0.561566 0.150471i −0.0331401 0.999451i 0.510551π-0.510551\pi
−0.528426 + 0.848980i 0.677217π0.677217\pi
3838 −0.130843 0.488313i −0.0212255 0.0792148i
3939 −4.96442 + 2.50855i −0.794943 + 0.401689i
4040 0 0
4141 4.35963i 0.680860i 0.940270 + 0.340430i 0.110573π0.110573\pi
−0.940270 + 0.340430i 0.889427π0.889427\pi
4242 −0.826265 1.14903i −0.127495 0.177299i
4343 −2.69037 2.69037i −0.410277 0.410277i 0.471558 0.881835i 0.343692π-0.343692\pi
−0.881835 + 0.471558i 0.843692π0.843692\pi
4444 0.726104 + 1.25765i 0.109464 + 0.189598i
4545 0 0
4646 1.18141 2.04627i 0.174190 0.301706i
4747 −1.10971 + 4.14148i −0.161867 + 0.604097i 0.836552 + 0.547888i 0.184568π0.184568\pi
−0.998419 + 0.0562089i 0.982099π0.982099\pi
4848 −5.82678 + 1.21809i −0.841023 + 0.175817i
4949 5.18761 + 4.69986i 0.741088 + 0.671408i
5050 0 0
5151 −0.468795 + 8.40527i −0.0656444 + 1.17697i
5252 1.58304 + 5.90798i 0.219528 + 0.819290i
5353 1.79889 + 6.71354i 0.247096 + 0.922176i 0.972318 + 0.233661i 0.0750705π0.0750705\pi
−0.725222 + 0.688515i 0.758263π0.758263\pi
5454 0.559982 + 1.50389i 0.0762039 + 0.204654i
5555 0 0
5656 −2.91664 + 1.29321i −0.389753 + 0.172813i
5757 −0.580162 2.77522i −0.0768444 0.367587i
5858 0.395069 1.47442i 0.0518751 0.193601i
5959 3.84501 6.65975i 0.500577 0.867026i −0.499422 0.866359i 0.666454π-0.666454\pi
1.00000 0.000666931i 0.000212291π-0.000212291\pi
6060 0 0
6161 −2.19699 3.80529i −0.281295 0.487218i 0.690409 0.723420i 0.257431π-0.257431\pi
−0.971704 + 0.236202i 0.924097π0.924097\pi
6262 1.29462 + 1.29462i 0.164417 + 0.164417i
6363 −4.26789 6.69217i −0.537704 0.843134i
6464 5.80098i 0.725122i
6565 0 0
6666 −0.183944 0.364025i −0.0226419 0.0448084i
6767 −0.0126297 0.0471345i −0.00154296 0.00575840i 0.965150 0.261697i 0.0842821π-0.0842821\pi
−0.966693 + 0.255939i 0.917615π0.917615\pi
6868 8.94164 + 2.39591i 1.08433 + 0.290546i
6969 7.25451 11.0893i 0.873341 1.33500i
7070 0 0
7171 12.4172i 1.47365i −0.676082 0.736826i 0.736324π-0.736324\pi
0.676082 0.736826i 0.263676π-0.263676\pi
7272 3.57685 0.541931i 0.421536 0.0638672i
7373 1.34043 0.359168i 0.156886 0.0420374i −0.179521 0.983754i 0.557455π-0.557455\pi
0.336407 + 0.941717i 0.390788π0.390788\pi
7474 0.546081 0.945840i 0.0634806 0.109952i
7575 0 0
7676 −3.11769 −0.357624
7777 1.26712 + 1.56968i 0.144401 + 0.178882i
7878 −0.351513 1.68147i −0.0398010 0.190389i
7979 3.66808 2.11777i 0.412692 0.238268i −0.279254 0.960217i 0.590087π-0.590087\pi
0.691946 + 0.721950i 0.256754π0.256754\pi
8080 0 0
8181 2.66599 + 8.59607i 0.296221 + 0.955119i
8282 −1.30054 0.348478i −0.143620 0.0384830i
8383 5.05351 5.05351i 0.554695 0.554695i −0.373097 0.927792i 0.621704π-0.621704\pi
0.927792 + 0.373097i 0.121704π0.121704\pi
8484 −8.16355 + 3.08797i −0.890716 + 0.336925i
8585 0 0
8686 1.01762 0.587525i 0.109733 0.0633544i
8787 2.67271 8.13276i 0.286544 0.871924i
8888 −0.888122 + 0.237971i −0.0946741 + 0.0253678i
8989 −0.453600 0.785658i −0.0480815 0.0832796i 0.840983 0.541061i 0.181977π-0.181977\pi
−0.889065 + 0.457782i 0.848644π0.848644\pi
9090 0 0
9191 3.44389 + 7.76716i 0.361018 + 0.814220i
9292 −10.3038 10.3038i −1.07424 1.07424i
9393 6.84502 + 7.65367i 0.709796 + 0.793649i
9494 −1.14676 0.662081i −0.118279 0.0682884i
9595 0 0
9696 0.335002 6.00642i 0.0341910 0.613028i
9797 −3.73061 + 3.73061i −0.378786 + 0.378786i −0.870664 0.491878i 0.836311π-0.836311\pi
0.491878 + 0.870664i 0.336311π0.336311\pi
9898 −1.81669 + 1.17186i −0.183514 + 0.118376i
9999 −0.916321 2.09584i −0.0920937 0.210640i
100100 0 0
101101 16.4444 + 9.49420i 1.63628 + 0.944708i 0.982098 + 0.188373i 0.0603214π0.0603214\pi
0.654185 + 0.756335i 0.273012π0.273012\pi
102102 −2.46993 0.811705i −0.244560 0.0803708i
103103 3.26921 12.2009i 0.322125 1.20219i −0.595046 0.803692i 0.702866π-0.702866\pi
0.917171 0.398494i 0.130467π-0.130467\pi
104104 −3.87254 −0.379733
105105 0 0
106106 −2.14653 −0.208490
107107 0.564395 2.10635i 0.0545621 0.203629i −0.933264 0.359192i 0.883052π-0.883052\pi
0.987826 + 0.155563i 0.0497191π0.0497191\pi
108108 9.85240 0.935331i 0.948047 0.0900023i
109109 −2.04357 1.17986i −0.195739 0.113010i 0.398928 0.916982i 0.369382π-0.369382\pi
−0.594666 + 0.803973i 0.702716π0.702716\pi
110110 0 0
111111 3.35323 5.12578i 0.318275 0.486517i
112112 1.40867 + 8.98318i 0.133107 + 0.848831i
113113 11.9386 11.9386i 1.12309 1.12309i 0.131814 0.991274i 0.457920π-0.457920\pi
0.991274 0.131814i 0.0420801π-0.0420801\pi
114114 0.874260 + 0.0487609i 0.0818819 + 0.00456688i
115115 0 0
116116 −8.15242 4.70680i −0.756933 0.437015i
117117 −1.44319 9.52533i −0.133423 0.880617i
118118 1.67935 + 1.67935i 0.154597 + 0.154597i
119119 12.7867 + 1.36378i 1.17215 + 0.125017i
120120 0 0
121121 −5.20932 9.02281i −0.473575 0.820256i
122122 1.31078 0.351223i 0.118673 0.0317983i
123123 −7.17366 2.35751i −0.646827 0.212570i
124124 9.77837 5.64555i 0.878124 0.506985i
125125 0 0
126126 2.33751 0.738246i 0.208242 0.0657682i
127127 −4.46126 + 4.46126i −0.395873 + 0.395873i −0.876775 0.480901i 0.840309π-0.840309\pi
0.480901 + 0.876775i 0.340309π0.340309\pi
128128 −8.44022 2.26155i −0.746017 0.199895i
129129 5.88177 2.97209i 0.517861 0.261678i
130130 0 0
131131 1.86149 1.07473i 0.162639 0.0938999i −0.416471 0.909149i 0.636733π-0.636733\pi
0.579111 + 0.815249i 0.303400π0.303400\pi
132132 −2.46207 + 0.514699i −0.214296 + 0.0447988i
133133 −4.27857 + 0.670931i −0.370999 + 0.0581771i
134134 0.0150704 0.00130188
135135 0 0
136136 −2.93051 + 5.07580i −0.251289 + 0.435246i
137137 8.51678 2.28207i 0.727638 0.194970i 0.124061 0.992275i 0.460408π-0.460408\pi
0.603577 + 0.797305i 0.293742π0.293742\pi
138138 2.72822 + 3.05052i 0.232241 + 0.259678i
139139 10.3626i 0.878941i 0.898257 + 0.439471i 0.144834π0.144834\pi
−0.898257 + 0.439471i 0.855166π0.855166\pi
140140 0 0
141141 −6.21461 4.06553i −0.523364 0.342380i
142142 3.70423 + 0.992544i 0.310852 + 0.0832925i
143143 0.633730 + 2.36511i 0.0529951 + 0.197780i
144144 1.14654 10.2465i 0.0955452 0.853875i
145145 0 0
146146 0.428578i 0.0354694i
147147 −10.5387 + 5.99459i −0.869220 + 0.494425i
148148 −4.76267 4.76267i −0.391489 0.391489i
149149 8.72716 + 15.1159i 0.714957 + 1.23834i 0.962976 + 0.269586i 0.0868870π0.0868870\pi
−0.248019 + 0.968755i 0.579780π0.579780\pi
150150 0 0
151151 7.60786 13.1772i 0.619119 1.07235i −0.370528 0.928821i 0.620823π-0.620823\pi
0.989647 0.143524i 0.0458434π-0.0458434\pi
152152 0.510892 1.90668i 0.0414388 0.154652i
153153 −13.5771 5.31661i −1.09765 0.429823i
154154 −0.569541 + 0.252530i −0.0458949 + 0.0203494i
155155 0 0
156156 −10.5775 0.589947i −0.846875 0.0472336i
157157 −2.36469 8.82516i −0.188723 0.704324i −0.993803 0.111158i 0.964544π-0.964544\pi
0.805080 0.593167i 0.202122π-0.202122\pi
158158 0.338559 + 1.26352i 0.0269343 + 0.100520i
159159 −12.0197 0.670387i −0.953225 0.0531652i
160160 0 0
161161 −16.3578 11.9230i −1.28917 0.939665i
162162 −2.77743 + 0.108192i −0.218215 + 0.00850040i
163163 −0.700710 + 2.61508i −0.0548838 + 0.204829i −0.987923 0.154946i 0.950480π-0.950480\pi
0.933039 + 0.359775i 0.117146π0.117146\pi
164164 −4.15172 + 7.19099i −0.324195 + 0.561522i
165165 0 0
166166 1.10359 + 1.91147i 0.0856551 + 0.148359i
167167 −3.85551 3.85551i −0.298348 0.298348i 0.542018 0.840367i 0.317660π-0.317660\pi
−0.840367 + 0.542018i 0.817660π0.817660\pi
168168 −0.550747 5.49857i −0.0424911 0.424224i
169169 2.68725i 0.206712i
170170 0 0
171171 4.88027 + 0.546083i 0.373204 + 0.0417600i
172172 −1.87556 6.99969i −0.143010 0.533721i
173173 −1.27815 0.342481i −0.0971763 0.0260383i 0.209903 0.977722i 0.432685π-0.432685\pi
−0.307080 + 0.951684i 0.599352π0.599352\pi
174174 2.21248 + 1.44738i 0.167727 + 0.109726i
175175 0 0
176176 2.62045i 0.197524i
177177 8.87921 + 9.92818i 0.667403 + 0.746247i
178178 0.270630 0.0725151i 0.0202846 0.00543524i
179179 0.120836 0.209294i 0.00903168 0.0156433i −0.861474 0.507801i 0.830458π-0.830458\pi
0.870506 + 0.492158i 0.163792π0.163792\pi
180180 0 0
181181 18.6864 1.38895 0.694475 0.719517i 0.255637π-0.255637\pi
0.694475 + 0.719517i 0.255637π0.255637\pi
182182 −2.59233 + 0.406508i −0.192156 + 0.0301324i
183183 7.44955 1.55734i 0.550686 0.115122i
184184 7.98990 4.61297i 0.589023 0.340073i
185185 0 0
186186 −2.83034 + 1.43018i −0.207530 + 0.104866i
187187 3.57956 + 0.959140i 0.261763 + 0.0701393i
188188 −5.77437 + 5.77437i −0.421140 + 0.421140i
189189 13.3197 3.40385i 0.968864 0.247594i
190190 0 0
191191 −12.3330 + 7.12049i −0.892388 + 0.515220i −0.874723 0.484624i 0.838957π-0.838957\pi
−0.0176651 + 0.999844i 0.505623π0.505623\pi
192192 −9.54535 3.13693i −0.688876 0.226388i
193193 6.58385 1.76414i 0.473916 0.126985i −0.0139523 0.999903i 0.504441π-0.504441\pi
0.487868 + 0.872917i 0.337775π0.337775\pi
194194 −0.814694 1.41109i −0.0584916 0.101310i
195195 0 0
196196 4.08099 + 12.6924i 0.291499 + 0.906599i
197197 7.65626 + 7.65626i 0.545486 + 0.545486i 0.925132 0.379646i 0.123954π-0.123954\pi
−0.379646 + 0.925132i 0.623954π0.623954\pi
198198 0.698462 0.105824i 0.0496375 0.00752061i
199199 −14.1855 8.19000i −1.00558 0.580573i −0.0956874 0.995411i 0.530505π-0.530505\pi
−0.909895 + 0.414838i 0.863838π0.863838\pi
200200 0 0
201201 0.0843881 + 0.00470666i 0.00595228 + 0.000331982i
202202 −4.14670 + 4.14670i −0.291761 + 0.291761i
203203 −12.2009 4.70498i −0.856335 0.330225i
204204 −8.77767 + 13.4176i −0.614560 + 0.939421i
205205 0 0
206206 3.37836 + 1.95050i 0.235382 + 0.135898i
207207 14.3242 + 17.9337i 0.995601 + 1.24648i
208208 −2.85654 + 10.6607i −0.198065 + 0.739189i
209209 −1.24809 −0.0863321
210210 0 0
211211 −25.5028 −1.75568 −0.877842 0.478950i 0.841018π-0.841018\pi
−0.877842 + 0.478950i 0.841018π0.841018\pi
212212 −3.42620 + 12.7867i −0.235312 + 0.878197i
213213 20.4322 + 6.71472i 1.39999 + 0.460085i
214214 0.583239 + 0.336733i 0.0398694 + 0.0230186i
215215 0 0
216216 −1.04248 + 6.17867i −0.0709320 + 0.420405i
217217 12.2044 9.85200i 0.828492 0.668797i
218218 0.515316 0.515316i 0.0349016 0.0349016i
219219 −0.133850 + 2.39987i −0.00904475 + 0.162168i
220220 0 0
221221 13.5171 + 7.80410i 0.909258 + 0.524960i
222222 1.26106 + 1.41003i 0.0846365 + 0.0946352i
223223 15.4546 + 15.4546i 1.03491 + 1.03491i 0.999368 + 0.0355465i 0.0113172π0.0113172\pi
0.0355465 + 0.999368i 0.488683π0.488683\pi
224224 −9.13740 0.974557i −0.610518 0.0651154i
225225 0 0
226226 2.60716 + 4.51573i 0.173426 + 0.300382i
227227 −12.4101 + 3.32527i −0.823686 + 0.220706i −0.645957 0.763374i 0.723542π-0.723542\pi
−0.177728 + 0.984080i 0.556875π0.556875\pi
228228 1.68592 5.13008i 0.111653 0.339748i
229229 −13.2508 + 7.65038i −0.875641 + 0.505551i −0.869219 0.494428i 0.835378π-0.835378\pi
−0.00642204 + 0.999979i 0.502044π0.502044\pi
230230 0 0
231231 −3.26807 + 1.23619i −0.215023 + 0.0813353i
232232 4.21445 4.21445i 0.276692 0.276692i
233233 6.62761 + 1.77586i 0.434189 + 0.116341i 0.469292 0.883043i 0.344509π-0.344509\pi
−0.0351029 + 0.999384i 0.511176π0.511176\pi
234234 2.95690 + 0.330865i 0.193298 + 0.0216293i
235235 0 0
236236 12.6843 7.32328i 0.825677 0.476705i
237237 1.50118 + 7.18093i 0.0975122 + 0.466452i
238238 −1.42891 + 3.70543i −0.0926225 + 0.240188i
239239 −18.7082 −1.21013 −0.605067 0.796174i 0.706854π-0.706854\pi
−0.605067 + 0.796174i 0.706854π0.706854\pi
240240 0 0
241241 0.986063 1.70791i 0.0635179 0.110016i −0.832518 0.553998i 0.813101π-0.813101\pi
0.896036 + 0.443982i 0.146435π0.146435\pi
242242 3.10802 0.832793i 0.199791 0.0535339i
243243 −15.5863 0.261589i −0.999859 0.0167810i
244244 8.36885i 0.535761i
245245 0 0
246246 1.27669 1.95156i 0.0813987 0.124427i
247247 −5.07757 1.36053i −0.323078 0.0865685i
248248 1.85026 + 6.90525i 0.117491 + 0.438484i
249249 5.58268 + 11.0481i 0.353788 + 0.700148i
250250 0 0
251251 17.9016i 1.12994i 0.825112 + 0.564970i 0.191112π0.191112\pi
−0.825112 + 0.564970i 0.808888π0.808888\pi
252252 −0.666655 15.1027i −0.0419953 0.951383i
253253 −4.12485 4.12485i −0.259327 0.259327i
254254 −0.974254 1.68746i −0.0611301 0.105881i
255255 0 0
256256 −4.45168 + 7.71053i −0.278230 + 0.481908i
257257 5.10358 19.0468i 0.318353 1.18811i −0.602475 0.798138i 0.705819π-0.705819\pi
0.920827 0.389971i 0.127515π-0.127515\pi
258258 0.416467 + 1.99218i 0.0259281 + 0.124028i
259259 −7.56100 5.51114i −0.469818 0.342445i
260260 0 0
261261 11.9369 + 8.79573i 0.738879 + 0.544442i
262262 0.171813 + 0.641215i 0.0106147 + 0.0396144i
263263 1.43607 + 5.35948i 0.0885517 + 0.330480i 0.995963 0.0897640i 0.0286113π-0.0286113\pi
−0.907411 + 0.420244i 0.861945π0.861945\pi
264264 0.0886842 1.59006i 0.00545813 0.0978617i
265265 0 0
266266 0.141851 1.32999i 0.00869744 0.0815467i
267267 1.53807 0.321534i 0.0941281 0.0196776i
268268 0.0240547 0.0897733i 0.00146937 0.00548378i
269269 5.02321 8.70045i 0.306270 0.530476i −0.671273 0.741210i 0.734252π-0.734252\pi
0.977543 + 0.210734i 0.0675855π0.0675855\pi
270270 0 0
271271 2.82028 + 4.88486i 0.171320 + 0.296734i 0.938881 0.344241i 0.111864π-0.111864\pi
−0.767562 + 0.640975i 0.778530π0.778530\pi
272272 11.8115 + 11.8115i 0.716180 + 0.716180i
273273 −14.6430 + 1.46667i −0.886233 + 0.0887667i
274274 2.72309i 0.164508i
275275 0 0
276276 22.5264 11.3827i 1.35593 0.685158i
277277 −2.91038 10.8617i −0.174868 0.652615i −0.996574 0.0827040i 0.973644π-0.973644\pi
0.821707 0.569911i 0.193022π-0.193022\pi
278278 −3.09130 0.828310i −0.185404 0.0496787i
279279 −16.2954 + 7.12451i −0.975581 + 0.426533i
280280 0 0
281281 1.92831i 0.115033i −0.998345 0.0575167i 0.981682π-0.981682\pi
0.998345 0.0575167i 0.0183183π-0.0183183\pi
282282 1.70956 1.52893i 0.101803 0.0910466i
283283 −25.4667 + 6.82379i −1.51384 + 0.405632i −0.917709 0.397254i 0.869963π-0.869963\pi
−0.596132 + 0.802887i 0.703296π0.703296\pi
284284 11.8250 20.4816i 0.701687 1.21536i
285285 0 0
286286 −0.756201 −0.0447151
287287 −4.15012 + 10.7620i −0.244974 + 0.635263i
288288 9.70225 + 3.79926i 0.571710 + 0.223874i
289289 5.73548 3.31138i 0.337381 0.194787i
290290 0 0
291291 −4.12126 8.15598i −0.241592 0.478112i
292292 2.55301 + 0.684078i 0.149404 + 0.0400326i
293293 −7.83332 + 7.83332i −0.457627 + 0.457627i −0.897876 0.440249i 0.854890π-0.854890\pi
0.440249 + 0.897876i 0.354890π0.354890\pi
294294 −0.945876 3.62301i −0.0551646 0.211298i
295295 0 0
296296 3.69315 2.13224i 0.214660 0.123934i
297297 3.94416 0.374436i 0.228863 0.0217270i
298298 −5.20686 + 1.39517i −0.301625 + 0.0808203i
299299 −12.2846 21.2775i −0.710435 1.23051i
300300 0 0
301301 −4.08027 9.20242i −0.235183 0.530418i
302302 3.32282 + 3.32282i 0.191207 + 0.191207i
303303 −24.5149 + 21.9248i −1.40835 + 1.25955i
304304 −4.87205 2.81288i −0.279431 0.161330i
305305 0 0
306306 2.67128 3.62527i 0.152707 0.207243i
307307 17.0769 17.0769i 0.974628 0.974628i −0.0250576 0.999686i 0.507977π-0.507977\pi
0.999686 + 0.0250576i 0.00797691π0.00797691\pi
308308 0.595226 + 3.79579i 0.0339161 + 0.216285i
309309 18.3083 + 11.9771i 1.04152 + 0.681354i
310310 0 0
311311 −20.4797 11.8240i −1.16130 0.670475i −0.209683 0.977769i 0.567243π-0.567243\pi
−0.951615 + 0.307294i 0.900576π0.900576\pi
312312 2.09411 6.37215i 0.118556 0.360752i
313313 3.20409 11.9578i 0.181106 0.675895i −0.814325 0.580409i 0.802893π-0.802893\pi
0.995431 0.0954864i 0.0304406π-0.0304406\pi
314314 2.82168 0.159237
315315 0 0
316316 8.06709 0.453809
317317 −1.13684 + 4.24276i −0.0638515 + 0.238297i −0.990475 0.137694i 0.956031π-0.956031\pi
0.926623 + 0.375991i 0.122698π0.122698\pi
318318 1.16076 3.53206i 0.0650920 0.198068i
319319 −3.26361 1.88425i −0.182727 0.105498i
320320 0 0
321321 3.16074 + 2.06772i 0.176415 + 0.115409i
322322 4.86432 3.92671i 0.271078 0.218827i
323323 −5.62568 + 5.62568i −0.313021 + 0.313021i
324324 −3.78871 + 16.7176i −0.210484 + 0.928758i
325325 0 0
326326 −0.724106 0.418063i −0.0401045 0.0231543i
327327 3.04650 2.72462i 0.168472 0.150672i
328328 −3.71743 3.71743i −0.205261 0.205261i
329329 −6.68183 + 9.16713i −0.368381 + 0.505400i
330330 0 0
331331 3.10933 + 5.38552i 0.170904 + 0.296015i 0.938736 0.344636i 0.111998π-0.111998\pi
−0.767832 + 0.640651i 0.778664π0.778664\pi
332332 13.1480 3.52300i 0.721591 0.193350i
333333 6.62103 + 8.28946i 0.362830 + 0.454259i
334334 1.45833 0.841970i 0.0797965 0.0460705i
335335 0 0
336336 −15.5433 2.53981i −0.847958 0.138558i
337337 −15.0501 + 15.0501i −0.819833 + 0.819833i −0.986084 0.166250i 0.946834π-0.946834\pi
0.166250 + 0.986084i 0.446834π0.446834\pi
338338 0.801644 + 0.214800i 0.0436037 + 0.0116836i
339339 13.1887 + 26.1005i 0.716313 + 1.41759i
340340 0 0
341341 3.91452 2.26005i 0.211983 0.122389i
342342 −0.552999 + 1.41220i −0.0299027 + 0.0763632i
343343 8.33197 + 16.5402i 0.449884 + 0.893087i
344344 4.58812 0.247375
345345 0 0
346346 0.204333 0.353916i 0.0109850 0.0190266i
347347 −18.6057 + 4.98539i −0.998808 + 0.267630i −0.720946 0.692991i 0.756292π-0.756292\pi
−0.277862 + 0.960621i 0.589626π0.589626\pi
348348 12.1534 10.8693i 0.651491 0.582657i
349349 9.24369i 0.494803i 0.968913 + 0.247402i 0.0795767π0.0795767\pi
−0.968913 + 0.247402i 0.920423π0.920423\pi
350350 0 0
351351 16.4541 + 2.77618i 0.878254 + 0.148182i
352352 −2.55796 0.685404i −0.136340 0.0365321i
353353 3.05649 + 11.4070i 0.162681 + 0.607132i 0.998325 + 0.0578609i 0.0184280π0.0184280\pi
−0.835644 + 0.549271i 0.814905π0.814905\pi
354354 −3.67145 + 1.85520i −0.195135 + 0.0986029i
355355 0 0
356356 1.72787i 0.0915769i
357357 −9.15857 + 20.3027i −0.484723 + 1.07453i
358358 0.0527764 + 0.0527764i 0.00278932 + 0.00278932i
359359 −6.98129 12.0920i −0.368459 0.638189i 0.620866 0.783917i 0.286781π-0.286781\pi
−0.989325 + 0.145728i 0.953448π0.953448\pi
360360 0 0
361361 −8.16026 + 14.1340i −0.429487 + 0.743894i
362362 −1.49366 + 5.57441i −0.0785050 + 0.292985i
363363 17.6638 3.69263i 0.927108 0.193813i
364364 −1.71622 + 16.0912i −0.0899544 + 0.843408i
365365 0 0
366366 −0.130889 + 2.34678i −0.00684170 + 0.122668i
367367 3.90370 + 14.5688i 0.203771 + 0.760485i 0.989821 + 0.142321i 0.0454565π0.0454565\pi
−0.786049 + 0.618164i 0.787877π0.787877\pi
368368 −6.80542 25.3982i −0.354757 1.32397i
369369 7.75844 10.5292i 0.403888 0.548129i
370370 0 0
371371 −1.95023 + 18.2852i −0.101251 + 0.949323i
372372 4.00185 + 19.1429i 0.207486 + 0.992515i
373373 9.01635 33.6495i 0.466849 1.74230i −0.183837 0.982957i 0.558852π-0.558852\pi
0.650686 0.759347i 0.274481π-0.274481\pi
374374 −0.572249 + 0.991165i −0.0295903 + 0.0512519i
375375 0 0
376376 −2.58517 4.47765i −0.133320 0.230917i
377377 −11.2233 11.2233i −0.578028 0.578028i
378378 −0.0492653 + 4.24552i −0.00253393 + 0.218366i
379379 19.0602i 0.979056i −0.871988 0.489528i 0.837169π-0.837169\pi
0.871988 0.489528i 0.162831π-0.162831\pi
380380 0 0
381381 −4.92842 9.75335i −0.252491 0.499680i
382382 −1.13832 4.24828i −0.0582417 0.217361i
383383 −9.81007 2.62860i −0.501271 0.134315i −0.000681261 1.00000i 0.500217π-0.500217\pi
−0.500590 + 0.865685i 0.666884π0.666884\pi
384384 8.28544 12.6652i 0.422815 0.646318i
385385 0 0
386386 2.10507i 0.107145i
387387 1.70987 + 11.2855i 0.0869174 + 0.573672i
388388 −9.70615 + 2.60076i −0.492755 + 0.132033i
389389 −18.6290 + 32.2664i −0.944528 + 1.63597i −0.187835 + 0.982201i 0.560147π0.560147\pi
−0.756693 + 0.653770i 0.773186π0.773186\pi
390390 0 0
391391 −37.1850 −1.88053
392392 −8.43099 + 0.415908i −0.425829 + 0.0210065i
393393 0.761825 + 3.64421i 0.0384290 + 0.183826i
394394 −2.89595 + 1.67198i −0.145896 + 0.0842331i
395395 0 0
396396 0.484465 4.32960i 0.0243453 0.217571i
397397 −8.58658 2.30077i −0.430948 0.115472i 0.0368231 0.999322i 0.488276π-0.488276\pi
−0.467771 + 0.883850i 0.654943π0.654943\pi
398398 3.57708 3.57708i 0.179303 0.179303i
399399 1.20968 7.40309i 0.0605597 0.370618i
400400 0 0
401401 −4.02832 + 2.32575i −0.201165 + 0.116142i −0.597199 0.802093i 0.703720π-0.703720\pi
0.396034 + 0.918236i 0.370386π0.370386\pi
402402 −0.00814945 + 0.0247979i −0.000406458 + 0.00123681i
403403 18.3890 4.92733i 0.916023 0.245448i
404404 18.0828 + 31.3204i 0.899655 + 1.55825i
405405 0 0
406406 2.37881 3.26361i 0.118059 0.161970i
407407 −1.90662 1.90662i −0.0945074 0.0945074i
408408 −6.76738 7.56686i −0.335035 0.374615i
409409 −23.0006 13.2794i −1.13731 0.656626i −0.191546 0.981484i 0.561350π-0.561350\pi
−0.945763 + 0.324858i 0.894683π0.894683\pi
410410 0 0
411411 −0.850451 + 15.2482i −0.0419497 + 0.752137i
412412 17.0114 17.0114i 0.838091 0.838091i
413413 15.8313 12.7798i 0.779009 0.628853i
414414 −6.49486 + 2.83961i −0.319205 + 0.139559i
415415 0 0
416416 −9.65934 5.57682i −0.473588 0.273426i
417417 −17.0513 5.60365i −0.835007 0.274412i
418418 0.0997634 0.372322i 0.00487959 0.0182109i
419419 25.8278 1.26177 0.630885 0.775876i 0.282692π-0.282692\pi
0.630885 + 0.775876i 0.282692π0.282692\pi
420420 0 0
421421 0.432430 0.0210753 0.0105377 0.999944i 0.496646π-0.496646\pi
0.0105377 + 0.999944i 0.496646π0.496646\pi
422422 2.03851 7.60783i 0.0992332 0.370343i
423423 10.0503 8.02749i 0.488664 0.390310i
424424 −7.25850 4.19070i −0.352504 0.203518i
425425 0 0
426426 −3.63630 + 5.55847i −0.176179 + 0.269309i
427427 −1.80099 11.4850i −0.0871558 0.555799i
428428 2.93684 2.93684i 0.141957 0.141957i
429429 −4.23442 0.236170i −0.204440 0.0114024i
430430 0 0
431431 14.1264 + 8.15586i 0.680443 + 0.392854i 0.800022 0.599971i 0.204821π-0.204821\pi
−0.119579 + 0.992825i 0.538154π0.538154\pi
432432 16.2403 + 7.42749i 0.781363 + 0.357355i
433433 0.514238 + 0.514238i 0.0247127 + 0.0247127i 0.719355 0.694642i 0.244437π-0.244437\pi
−0.694642 + 0.719355i 0.744437π0.744437\pi
434434 1.96345 + 4.42825i 0.0942486 + 0.212563i
435435 0 0
436436 −2.24718 3.89223i −0.107620 0.186404i
437437 12.0968 3.24133i 0.578669 0.155054i
438438 −0.705214 0.231758i −0.0336964 0.0110738i
439439 13.2487 7.64917i 0.632328 0.365075i −0.149325 0.988788i 0.547710π-0.547710\pi
0.781653 + 0.623713i 0.214377π0.214377\pi
440440 0 0
441441 −4.16501 20.5828i −0.198334 0.980135i
442442 −3.40853 + 3.40853i −0.162127 + 0.162127i
443443 8.81439 + 2.36181i 0.418784 + 0.112213i 0.462057 0.886850i 0.347112π-0.347112\pi
−0.0432723 + 0.999063i 0.513778π0.513778\pi
444444 10.4123 5.26139i 0.494146 0.249695i
445445 0 0
446446 −5.84564 + 3.37498i −0.276799 + 0.159810i
447447 −29.5921 + 6.18625i −1.39966 + 0.292600i
448448 −5.52219 + 14.3201i −0.260899 + 0.676560i
449449 9.40891 0.444034 0.222017 0.975043i 0.428736π-0.428736\pi
0.222017 + 0.975043i 0.428736π0.428736\pi
450450 0 0
451451 −1.66204 + 2.87873i −0.0782622 + 0.135554i
452452 31.0613 8.32286i 1.46100 0.391474i
453453 17.5687 + 19.6442i 0.825450 + 0.922966i
454454 3.96789i 0.186222i
455455 0 0
456456 2.86111 + 1.87171i 0.133984 + 0.0876509i
457457 −33.3520 8.93665i −1.56014 0.418039i −0.627434 0.778670i 0.715895π-0.715895\pi
−0.932708 + 0.360631i 0.882561π0.882561\pi
458458 −1.22303 4.56443i −0.0571486 0.213282i
459459 16.0903 19.4658i 0.751031 0.908585i
460460 0 0
461461 36.9326i 1.72012i −0.510192 0.860061i 0.670426π-0.670426\pi
0.510192 0.860061i 0.329574π-0.329574\pi
462462 −0.107546 1.07372i −0.00500349 0.0499541i
463463 −26.3687 26.3687i −1.22546 1.22546i −0.965664 0.259794i 0.916345π-0.916345\pi
−0.259794 0.965664i 0.583655π-0.583655\pi
464464 −8.49325 14.7107i −0.394289 0.682929i
465465 0 0
466466 −1.05953 + 1.83516i −0.0490817 + 0.0850120i
467467 −2.63979 + 9.85183i −0.122155 + 0.455888i −0.999722 0.0235650i 0.992498π-0.992498\pi
0.877567 + 0.479453i 0.159165π0.159165\pi
468468 6.69060 17.0859i 0.309273 0.789797i
469469 0.0136922 0.128377i 0.000632247 0.00592791i
470470 0 0
471471 15.8003 + 0.881244i 0.728039 + 0.0406056i
472472 2.40011 + 8.95734i 0.110474 + 0.412295i
473473 −0.750833 2.80215i −0.0345233 0.128843i
474474 −2.26216 0.126170i −0.103905 0.00579517i
475475 0 0
476476 19.7923 + 14.4264i 0.907177 + 0.661232i
477477 7.60287 19.4156i 0.348112 0.888979i
478478 1.49540 5.58092i 0.0683981 0.255265i
479479 6.85350 11.8706i 0.313144 0.542382i −0.665897 0.746044i 0.731951π-0.731951\pi
0.979041 + 0.203662i 0.0652843π0.0652843\pi
480480 0 0
481481 −5.67825 9.83503i −0.258906 0.448439i
482482 0.430674 + 0.430674i 0.0196167 + 0.0196167i
483483 28.4646 20.4688i 1.29518 0.931362i
484484 19.8436i 0.901980i
485485 0 0
486486 1.32389 4.62869i 0.0600529 0.209961i
487487 5.91662 + 22.0811i 0.268108 + 1.00059i 0.960321 + 0.278898i 0.0899692π0.0899692\pi
−0.692213 + 0.721693i 0.743364π0.743364\pi
488488 5.11811 + 1.37139i 0.231686 + 0.0620800i
489489 −3.92413 2.56713i −0.177455 0.116090i
490490 0 0
491491 23.7476i 1.07172i −0.844308 0.535858i 0.819988π-0.819988\pi
0.844308 0.535858i 0.180012π-0.180012\pi
492492 −9.58750 10.7201i −0.432238 0.483301i
493493 −23.2037 + 6.21740i −1.04504 + 0.280018i
494494 0.811730 1.40596i 0.0365215 0.0632570i
495495 0 0
496496 20.3744 0.914836
497497 11.8205 30.6527i 0.530220 1.37496i
498498 −3.74205 + 0.782280i −0.167685 + 0.0350548i
499499 −2.80187 + 1.61766i −0.125429 + 0.0724165i −0.561402 0.827543i 0.689738π-0.689738\pi
0.435973 + 0.899960i 0.356404π0.356404\pi
500500 0 0
501501 8.42904 4.25924i 0.376582 0.190289i
502502 −5.34029 1.43093i −0.238349 0.0638654i
503503 2.62851 2.62851i 0.117199 0.117199i −0.646075 0.763274i 0.723591π-0.723591\pi
0.763274 + 0.646075i 0.223591π0.223591\pi
504504 9.34558 + 2.06716i 0.416285 + 0.0920788i
505505 0 0
506506 1.56021 0.900788i 0.0693598 0.0400449i
507507 4.42180 + 1.45316i 0.196379 + 0.0645369i
508508 −11.6071 + 3.11012i −0.514983 + 0.137989i
509509 6.91189 + 11.9717i 0.306364 + 0.530638i 0.977564 0.210638i 0.0675541π-0.0675541\pi
−0.671200 + 0.741276i 0.734221π0.734221\pi
510510 0 0
511511 3.65085 + 0.389385i 0.161504 + 0.0172254i
512512 −14.3017 14.3017i −0.632050 0.632050i
513513 −3.53762 + 7.73506i −0.156190 + 0.341511i
514514 5.27399 + 3.04494i 0.232626 + 0.134306i
515515 0 0
516516 12.5320 + 0.698960i 0.551691 + 0.0307700i
517517 −2.31162 + 2.31162i −0.101665 + 0.101665i
518518 2.24842 1.81503i 0.0987899 0.0797478i
519519 1.25472 1.91797i 0.0550759 0.0841895i
520520 0 0
521521 9.49156 + 5.47996i 0.415833 + 0.240081i 0.693293 0.720656i 0.256159π-0.256159\pi
−0.277460 + 0.960737i 0.589493π0.589493\pi
522522 −3.57804 + 2.85789i −0.156607 + 0.125086i
523523 −3.54814 + 13.2418i −0.155149 + 0.579026i 0.843943 + 0.536433i 0.180229π0.180229\pi
−0.999093 + 0.0425929i 0.986438π0.986438\pi
524524 4.09392 0.178844
525525 0 0
526526 −1.71360 −0.0747163
527527 7.45743 27.8315i 0.324851 1.21236i
528528 −4.31189 1.41703i −0.187651 0.0616685i
529529 30.7730 + 17.7668i 1.33796 + 0.772469i
530530 0 0
531531 −21.1381 + 9.24175i −0.917313 + 0.401058i
532532 −7.69622 2.96786i −0.333674 0.128673i
533533 −9.89970 + 9.89970i −0.428804 + 0.428804i
534534 −0.0270240 + 0.484527i −0.00116944 + 0.0209676i
535535 0 0
536536 0.0509605 + 0.0294221i 0.00220116 + 0.00127084i
537537 0.279044 + 0.312009i 0.0120416 + 0.0134642i
538538 2.19394 + 2.19394i 0.0945876 + 0.0945876i
539539 1.63372 + 5.08108i 0.0703692 + 0.218857i
540540 0 0
541541 −3.53276 6.11892i −0.151885 0.263073i 0.780035 0.625735i 0.215201π-0.215201\pi
−0.931920 + 0.362663i 0.881868π0.881868\pi
542542 −1.68265 + 0.450866i −0.0722762 + 0.0193663i
543543 −10.1048 + 30.7480i −0.433640 + 1.31952i
544544 −14.6193 + 8.44044i −0.626796 + 0.361881i
545545 0 0
546546 0.732928 4.48543i 0.0313664 0.191959i
547547 19.7665 19.7665i 0.845154 0.845154i −0.144370 0.989524i 0.546115π-0.546115\pi
0.989524 + 0.144370i 0.0461154π0.0461154\pi
548548 16.2212 + 4.34647i 0.692937 + 0.185672i
549549 −1.46586 + 13.1002i −0.0625612 + 0.559101i
550550 0 0
551551 7.00653 4.04522i 0.298488 0.172332i
552552 3.26991 + 15.6417i 0.139176 + 0.665753i
553553 11.0709 1.73605i 0.470782 0.0738242i
554554 3.47282 0.147546
555555 0 0
556556 −9.86837 + 17.0925i −0.418512 + 0.724884i
557557 −42.2902 + 11.3316i −1.79189 + 0.480137i −0.992666 0.120891i 0.961425π-0.961425\pi
−0.799228 + 0.601028i 0.794758π0.794758\pi
558558 −0.822798 5.43063i −0.0348318 0.229897i
559559 12.2184i 0.516783i
560560 0 0
561561 −3.51392 + 5.37140i −0.148358 + 0.226781i
562562 0.575242 + 0.154136i 0.0242651 + 0.00650182i
563563 −2.87110 10.7151i −0.121002 0.451587i 0.878663 0.477442i 0.158436π-0.158436\pi
−0.999666 + 0.0258549i 0.991769π0.991769\pi
564564 −6.37903 12.6241i −0.268606 0.531571i
565565 0 0
566566 8.14252i 0.342256i
567567 −1.60179 + 23.7578i −0.0672689 + 0.997735i
568568 10.5881 + 10.5881i 0.444266 + 0.444266i
569569 −6.90318 11.9567i −0.289396 0.501249i 0.684269 0.729229i 0.260121π-0.260121\pi
−0.973666 + 0.227980i 0.926788π0.926788\pi
570570 0 0
571571 6.56260 11.3668i 0.274636 0.475684i −0.695407 0.718616i 0.744776π-0.744776\pi
0.970043 + 0.242932i 0.0781092π0.0781092\pi
572572 −1.20701 + 4.50464i −0.0504678 + 0.188348i
573573 −5.04736 24.1442i −0.210857 1.00864i
574574 −2.87873 2.09828i −0.120156 0.0875804i
575575 0 0
576576 10.3235 14.0103i 0.430144 0.583762i
577577 3.94772 + 14.7331i 0.164346 + 0.613347i 0.998123 + 0.0612453i 0.0195072π0.0195072\pi
−0.833777 + 0.552101i 0.813826π0.813826\pi
578578 0.529377 + 1.97566i 0.0220192 + 0.0821767i
579579 −0.657437 + 11.7875i −0.0273221 + 0.489873i
580580 0 0
581581 17.2856 7.66426i 0.717126 0.317967i
582582 2.76247 0.577496i 0.114508 0.0239380i
583583 −1.37159 + 5.11885i −0.0568055 + 0.212001i
584584 −0.836718 + 1.44924i −0.0346236 + 0.0599699i
585585 0 0
586586 −1.71065 2.96293i −0.0706662 0.122397i
587587 5.54217 + 5.54217i 0.228750 + 0.228750i 0.812170 0.583421i 0.198286π-0.198286\pi
−0.583421 + 0.812170i 0.698286π0.698286\pi
588588 −23.0918 0.148375i −0.952290 0.00611888i
589589 9.70404i 0.399848i
590590 0 0
591591 −16.7384 + 8.45798i −0.688524 + 0.347915i
592592 −3.14565 11.7397i −0.129285 0.482499i
593593 8.37814 + 2.24492i 0.344049 + 0.0921877i 0.426706 0.904390i 0.359674π-0.359674\pi
−0.0826570 + 0.996578i 0.526341π0.526341\pi
594594 −0.203568 + 1.20653i −0.00835252 + 0.0495043i
595595 0 0
596596 33.2438i 1.36172i
597597 21.1473 18.9130i 0.865503 0.774058i
598598 7.32931 1.96388i 0.299718 0.0803091i
599599 −7.93869 + 13.7502i −0.324366 + 0.561819i −0.981384 0.192056i 0.938484π-0.938484\pi
0.657018 + 0.753875i 0.271818π0.271818\pi
600600 0 0
601601 41.5249 1.69384 0.846919 0.531722i 0.178455π-0.178455\pi
0.846919 + 0.531722i 0.178455π0.178455\pi
602602 3.07135 0.481625i 0.125179 0.0196296i
603603 −0.0533783 + 0.136313i −0.00217373 + 0.00555110i
604604 25.0976 14.4901i 1.02120 0.589593i
605605 0 0
606606 −4.58092 9.06565i −0.186087 0.368267i
607607 −14.7681 3.95710i −0.599418 0.160614i −0.0536641 0.998559i 0.517090π-0.517090\pi
−0.545754 + 0.837945i 0.683757π0.683757\pi
608608 4.02013 4.02013i 0.163038 0.163038i
609609 14.3397 17.5320i 0.581072 0.710432i
610610 0 0
611611 −11.9242 + 6.88444i −0.482402 + 0.278515i
612612 −17.3317 21.6991i −0.700593 0.877135i
613613 29.7879 7.98165i 1.20312 0.322376i 0.399063 0.916924i 0.369336π-0.369336\pi
0.804060 + 0.594548i 0.202669π0.202669\pi
614614 3.72926 + 6.45927i 0.150501 + 0.260675i
615615 0 0
616616 −2.41892 0.257992i −0.0974611 0.0103948i
617617 13.2098 + 13.2098i 0.531808 + 0.531808i 0.921110 0.389302i 0.127284π-0.127284\pi
−0.389302 + 0.921110i 0.627284π0.627284\pi
618618 −5.03637 + 4.50426i −0.202593 + 0.181188i
619619 −14.7495 8.51561i −0.592831 0.342271i 0.173385 0.984854i 0.444529π-0.444529\pi
−0.766216 + 0.642583i 0.777863π0.777863\pi
620620 0 0
621621 −37.2554 + 13.8723i −1.49501 + 0.556675i
622622 5.16425 5.16425i 0.207068 0.207068i
623623 −0.371840 2.37125i −0.0148974 0.0950020i
624624 −15.9973 10.4652i −0.640403 0.418945i
625625 0 0
626626 3.31107 + 1.91165i 0.132337 + 0.0764047i
627627 0.674915 2.05370i 0.0269535 0.0820167i
628628 4.50384 16.8086i 0.179723 0.670735i
629629 −17.1879 −0.685327
630630 0 0
631631 6.51082 0.259191 0.129596 0.991567i 0.458632π-0.458632\pi
0.129596 + 0.991567i 0.458632π0.458632\pi
632632 −1.32194 + 4.93356i −0.0525841 + 0.196247i
633633 13.7909 41.9641i 0.548138 1.66792i
634634 −1.17480 0.678272i −0.0466573 0.0269376i
635635 0 0
636636 −19.1875 12.5523i −0.760834 0.497730i
637637 1.10758 + 22.4521i 0.0438840 + 0.889586i
638638 0.822967 0.822967i 0.0325816 0.0325816i
639639 −22.0978 + 29.9896i −0.874174 + 1.18637i
640640 0 0
641641 −36.6801 21.1773i −1.44878 0.836451i −0.450367 0.892843i 0.648707π-0.648707\pi
−0.998409 + 0.0563924i 0.982040π0.982040\pi
642642 −0.869478 + 0.777613i −0.0343155 + 0.0306899i
643643 −11.2098 11.2098i −0.442072 0.442072i 0.450636 0.892708i 0.351197π-0.351197\pi
−0.892708 + 0.450636i 0.851197π0.851197\pi
644644 −15.6269 35.2441i −0.615787 1.38881i
645645 0 0
646646 −1.22854 2.12790i −0.0483363 0.0837209i
647647 −22.9610 + 6.15237i −0.902689 + 0.241875i −0.680171 0.733054i 0.738094π-0.738094\pi
−0.222518 + 0.974929i 0.571428π0.571428\pi
648648 −9.60309 5.05655i −0.377245 0.198640i
649649 5.07783 2.93169i 0.199322 0.115079i
650650 0 0
651651 9.61153 + 25.4096i 0.376705 + 0.995882i
652652 −3.64616 + 3.64616i −0.142794 + 0.142794i
653653 21.0505 + 5.64046i 0.823769 + 0.220728i 0.645994 0.763343i 0.276443π-0.276443\pi
0.177775 + 0.984071i 0.443110π0.443110\pi
654654 0.569277 + 1.12660i 0.0222605 + 0.0440535i
655655 0 0
656656 −12.9759 + 7.49163i −0.506623 + 0.292499i
657657 −3.87653 1.51800i −0.151238 0.0592227i
658658 −2.20058 2.72604i −0.0857876 0.106272i
659659 42.6184 1.66018 0.830088 0.557632i 0.188290π-0.188290\pi
0.830088 + 0.557632i 0.188290π0.188290\pi
660660 0 0
661661 −22.7467 + 39.3985i −0.884744 + 1.53242i −0.0387381 + 0.999249i 0.512334π0.512334\pi
−0.846006 + 0.533173i 0.821000π0.821000\pi
662662 −1.85511 + 0.497076i −0.0721010 + 0.0193194i
663663 −20.1509 + 18.0219i −0.782597 + 0.699911i
664664 8.61819i 0.334451i
665665 0 0
666666 −3.00210 + 1.31254i −0.116329 + 0.0508601i
667667 36.5253 + 9.78693i 1.41427 + 0.378951i
668668 −2.68783 10.0311i −0.103995 0.388115i
669669 −33.7873 + 17.0729i −1.30629 + 0.660075i
670670 0 0
671671 3.35026i 0.129335i
672672 6.54474 14.5083i 0.252469 0.559671i
673673 32.1249 + 32.1249i 1.23832 + 1.23832i 0.960686 + 0.277636i 0.0895508π0.0895508\pi
0.277636 + 0.960686i 0.410449π0.410449\pi
674674 −3.28666 5.69266i −0.126597 0.219273i
675675 0 0
676676 2.55910 4.43248i 0.0984268 0.170480i
677677 −11.0202 + 41.1280i −0.423542 + 1.58068i 0.343545 + 0.939136i 0.388372π0.388372\pi
−0.767087 + 0.641543i 0.778295π0.778295\pi
678678 −8.84036 + 1.84809i −0.339512 + 0.0709753i
679679 −12.7606 + 5.65793i −0.489706 + 0.217131i
680680 0 0
681681 1.23922 22.2186i 0.0474870 0.851419i
682682 0.361305 + 1.34841i 0.0138351 + 0.0516332i
683683 −0.603360 2.25177i −0.0230869 0.0861617i 0.953421 0.301642i 0.0975348π-0.0975348\pi
−0.976508 + 0.215481i 0.930868π0.930868\pi
684684 7.52972 + 5.54827i 0.287906 + 0.212143i
685685 0 0
686686 −5.60017 + 1.16343i −0.213815 + 0.0444201i
687687 −5.42298 25.9409i −0.206899 0.989708i
688688 3.38438 12.6307i 0.129028 0.481540i
689689 −11.1600 + 19.3297i −0.425163 + 0.736404i
690690 0 0
691691 8.27824 + 14.3383i 0.314919 + 0.545456i 0.979420 0.201831i 0.0646893π-0.0646893\pi
−0.664501 + 0.747287i 0.731356π0.731356\pi
692692 −1.78210 1.78210i −0.0677454 0.0677454i
693693 −0.266878 6.04600i −0.0101379 0.229669i
694694 5.94884i 0.225815i
695695 0 0
696696 4.65576 + 9.21376i 0.176476 + 0.349247i
697697 5.48418 + 20.4672i 0.207728 + 0.775252i
698698 −2.75752 0.738875i −0.104374 0.0279668i
699699 −6.50607 + 9.94523i −0.246082 + 0.376163i
700700 0 0
701701 26.5973i 1.00457i 0.864703 + 0.502284i 0.167507π0.167507\pi
−0.864703 + 0.502284i 0.832493π0.832493\pi
702702 −2.14340 + 4.68657i −0.0808973 + 0.176883i
703703 5.59148 1.49823i 0.210886 0.0565069i
704704 −2.21152 + 3.83047i −0.0833500 + 0.144366i
705705 0 0
706706 −3.64717 −0.137263
707707 31.5562 + 39.0912i 1.18679 + 1.47017i
708708 5.19111 + 24.8318i 0.195094 + 0.933235i
709709 −13.7850 + 7.95880i −0.517708 + 0.298899i −0.735997 0.676985i 0.763286π-0.763286\pi
0.218288 + 0.975884i 0.429953π0.429953\pi
710710 0 0
711711 −12.6278 1.41300i −0.473580 0.0529917i
712712 1.05671 + 0.283144i 0.0396018 + 0.0106113i
713713 −32.0712 + 32.0712i −1.20108 + 1.20108i
714714 −5.32449 4.35498i −0.199264 0.162981i
715715 0 0
716716 0.398625 0.230146i 0.0148973 0.00860096i
717717 10.1166 30.7839i 0.377813 1.14964i
718718 4.16523 1.11607i 0.155445 0.0416514i
719719 −10.6906 18.5167i −0.398694 0.690558i 0.594871 0.803821i 0.297203π-0.297203\pi
−0.993565 + 0.113263i 0.963870π0.963870\pi
720720 0 0
721721 19.6848 27.0065i 0.733099 1.00577i
722722 −3.56409 3.56409i −0.132642 0.132642i
723723 2.27710 + 2.54611i 0.0846862 + 0.0946907i
724724 30.8223 + 17.7952i 1.14550 + 0.661355i
725725 0 0
726726 −0.310355 + 5.56451i −0.0115183 + 0.206518i
727727 −7.43836 + 7.43836i −0.275873 + 0.275873i −0.831459 0.555586i 0.812494π-0.812494\pi
0.555586 + 0.831459i 0.312494π0.312494\pi
728728 −9.55960 3.68643i −0.354302 0.136628i
729729 8.85885 25.5053i 0.328106 0.944641i
730730 0 0
731731 −16.0148 9.24617i −0.592330 0.341982i
732732 13.7707 + 4.52553i 0.508980 + 0.167268i
733733 −9.45077 + 35.2708i −0.349072 + 1.30276i 0.538710 + 0.842491i 0.318912π0.318912\pi
−0.887782 + 0.460264i 0.847755π0.847755\pi
734734 −4.65810 −0.171934
735735 0 0
736736 26.5725 0.979475
737737 0.00962968 0.0359385i 0.000354714 0.00132381i
738738 2.52085 + 3.15608i 0.0927939 + 0.116177i
739739 33.2198 + 19.1794i 1.22201 + 0.705527i 0.965346 0.260974i 0.0840437π-0.0840437\pi
0.256663 + 0.966501i 0.417377π0.417377\pi
740740 0 0
741741 4.98446 7.61928i 0.183109 0.279901i
742742 −5.29885 2.04337i −0.194527 0.0750146i
743743 −30.8182 + 30.8182i −1.13061 + 1.13061i −0.140534 + 0.990076i 0.544882π0.544882\pi
−0.990076 + 0.140534i 0.955118π0.955118\pi
744744 −12.3630 0.689531i −0.453248 0.0252794i
745745 0 0
746746 9.31740 + 5.37940i 0.341134 + 0.196954i
747747 −21.1983 + 3.21177i −0.775605 + 0.117512i
748748 4.99090 + 4.99090i 0.182485 + 0.182485i
749749 3.39837 4.66239i 0.124174 0.170360i
750750 0 0
751751 −19.9356 34.5294i −0.727459 1.26000i −0.957954 0.286923i 0.907368π-0.907368\pi
0.230495 0.973074i 0.425966π-0.425966\pi
752752 −14.2335 + 3.81385i −0.519042 + 0.139077i
753753 −29.4566 9.68045i −1.07346 0.352775i
754754 4.24517 2.45095i 0.154600 0.0892583i
755755 0 0
756756 25.2116 + 7.06998i 0.916939 + 0.257133i
757757 −0.798673 + 0.798673i −0.0290283 + 0.0290283i −0.721472 0.692444i 0.756534π-0.756534\pi
0.692444 + 0.721472i 0.256534π0.256534\pi
758758 5.68591 + 1.52354i 0.206522 + 0.0553373i
759759 9.01787 4.55678i 0.327328 0.165401i
760760 0 0
761761 −37.3941 + 21.5895i −1.35554 + 0.782619i −0.989019 0.147791i 0.952784π-0.952784\pi
−0.366518 + 0.930411i 0.619450π0.619450\pi
762762 3.30350 0.690601i 0.119673 0.0250178i
763763 −3.92153 4.85791i −0.141969 0.175868i
764764 −27.1236 −0.981299
765765 0 0
766766 1.56829 2.71637i 0.0566648 0.0981463i
767767 23.8538 6.39162i 0.861312 0.230788i
768768 −10.2802 11.4946i −0.370954 0.414777i
769769 44.1875i 1.59344i 0.604348 + 0.796720i 0.293434π0.293434\pi
−0.604348 + 0.796720i 0.706566π0.706566\pi
770770 0 0
771771 28.5812 + 18.6975i 1.02933 + 0.673376i
772772 12.5397 + 3.36001i 0.451315 + 0.120929i
773773 −5.66214 21.1314i −0.203653 0.760043i −0.989856 0.142075i 0.954623π-0.954623\pi
0.786203 0.617968i 0.212044π-0.212044\pi
774774 −3.50328 0.392003i −0.125923 0.0140903i
775775 0 0
776776 6.36214i 0.228388i
777777 13.1571 9.46122i 0.472008 0.339420i
778778 −8.13643 8.13643i −0.291705 0.291705i
779779 −3.56817 6.18024i −0.127843 0.221430i
780780 0 0
781781 4.73385 8.19927i 0.169391 0.293393i
782782 2.97231 11.0928i 0.106289 0.396678i
783783 −20.9281 + 14.8856i −0.747911 + 0.531966i
784784 −5.07407 + 23.5165i −0.181217 + 0.839876i
785785 0 0
786786 −1.14801 0.0640291i −0.0409482 0.00228384i
787787 −0.0780372 0.291239i −0.00278173 0.0103815i 0.964521 0.264006i 0.0850439π-0.0850439\pi
−0.967303 + 0.253625i 0.918377π0.918377\pi
788788 5.33748 + 19.9197i 0.190140 + 0.709612i
789789 −9.59544 0.535176i −0.341607 0.0190528i
790790 0 0
791791 40.8360 18.1063i 1.45196 0.643787i
792792 2.56845 + 1.00577i 0.0912659 + 0.0357385i
793793 3.65209 13.6298i 0.129689 0.484007i
794794 1.37270 2.37759i 0.0487153 0.0843774i
795795 0 0
796796 −15.5988 27.0180i −0.552886 0.957626i
797797 −8.45240 8.45240i −0.299399 0.299399i 0.541379 0.840779i 0.317902π-0.317902\pi
−0.840779 + 0.541379i 0.817902π0.817902\pi
798798 2.11175 + 0.952614i 0.0747551 + 0.0337222i
799799 20.8390i 0.737231i
800800 0 0
801801 −0.302647 + 2.70472i −0.0106935 + 0.0955665i
802802 −0.371808 1.38761i −0.0131290 0.0489981i
803803 1.02203 + 0.273853i 0.0360668 + 0.00966407i
804804 0.134712 + 0.0881271i 0.00475092 + 0.00310800i
805805 0 0
806806 5.87955i 0.207098i
807807 11.6000 + 12.9704i 0.408340 + 0.456579i
808808 −22.1177 + 5.92642i −0.778098 + 0.208491i
809809 18.5676 32.1600i 0.652801 1.13068i −0.329640 0.944107i 0.606927π-0.606927\pi
0.982440 0.186577i 0.0597394π-0.0597394\pi
810810 0 0
811811 23.5491 0.826921 0.413461 0.910522i 0.364320π-0.364320\pi
0.413461 + 0.910522i 0.364320π0.364320\pi
812812 −15.6442 19.3797i −0.549003 0.680093i
813813 −9.56300 + 1.99915i −0.335389 + 0.0701134i
814814 0.721171 0.416368i 0.0252770 0.0145937i
815815 0 0
816816 −25.8228 + 13.0484i −0.903977 + 0.456784i
817817 6.01583 + 1.61194i 0.210467 + 0.0563945i
818818 5.79994 5.79994i 0.202790 0.202790i
819819 5.50496 24.8877i 0.192359 0.869647i
820820 0 0
821821 35.4996 20.4957i 1.23895 0.715306i 0.270067 0.962842i 0.412954π-0.412954\pi
0.968879 + 0.247536i 0.0796208π0.0796208\pi
822822 −4.48076 1.47253i −0.156285 0.0513605i
823823 −24.8888 + 6.66893i −0.867568 + 0.232464i −0.665036 0.746812i 0.731584π-0.731584\pi
−0.202532 + 0.979276i 0.564917π0.564917\pi
824824 7.61596 + 13.1912i 0.265315 + 0.459538i
825825 0 0
826826 2.54694 + 5.74423i 0.0886195 + 0.199867i
827827 19.5668 + 19.5668i 0.680404 + 0.680404i 0.960091 0.279687i 0.0902308π-0.0902308\pi
−0.279687 + 0.960091i 0.590231π0.590231\pi
828828 6.54857 + 43.2219i 0.227579 + 1.50206i
829829 21.9279 + 12.6601i 0.761588 + 0.439703i 0.829866 0.557963i 0.188417π-0.188417\pi
−0.0682778 + 0.997666i 0.521750π0.521750\pi
830830 0 0
831831 19.4464 + 1.08460i 0.674588 + 0.0376245i
832832 −13.1727 + 13.1727i −0.456680 + 0.456680i
833833 30.2665 + 15.5388i 1.04867 + 0.538386i
834834 3.03461 4.63873i 0.105080 0.160626i
835835 0 0
836836 −2.05866 1.18857i −0.0712002 0.0411075i
837837 −2.91129 30.6663i −0.100629 1.05998i
838838 −2.06449 + 7.70479i −0.0713167 + 0.266157i
839839 −50.7484 −1.75203 −0.876014 0.482286i 0.839807π-0.839807\pi
−0.876014 + 0.482286i 0.839807π0.839807\pi
840840 0 0
841841 −4.57160 −0.157641
842842 −0.0345654 + 0.129000i −0.00119120 + 0.00444563i
843843 3.17299 + 1.04275i 0.109283 + 0.0359143i
844844 −42.0656 24.2866i −1.44796 0.835978i
845845 0 0
846846 1.59136 + 3.63981i 0.0547120 + 0.125139i
847847 −4.27036 27.2324i −0.146731 0.935715i
848848 −16.8908 + 16.8908i −0.580031 + 0.580031i
849849 2.54300 45.5948i 0.0872757 1.56481i
850850 0 0
851851 23.4310 + 13.5279i 0.803204 + 0.463730i
852852 27.3074 + 30.5334i 0.935535 + 1.04606i
853853 18.8448 + 18.8448i 0.645233 + 0.645233i 0.951837 0.306604i 0.0991928π-0.0991928\pi
−0.306604 + 0.951837i 0.599193π0.599193\pi
854854 3.57009 + 0.380772i 0.122166 + 0.0130297i
855855 0 0
856856 1.31482 + 2.27733i 0.0449395 + 0.0778375i
857857 12.0212 3.22108i 0.410637 0.110030i −0.0475860 0.998867i 0.515153π-0.515153\pi
0.458223 + 0.888837i 0.348486π0.348486\pi
858858 0.408922 1.24431i 0.0139604 0.0424800i
859859 3.33705 1.92665i 0.113859 0.0657364i −0.441989 0.897020i 0.645727π-0.645727\pi
0.555848 + 0.831284i 0.312394π0.312394\pi
860860 0 0
861861 −15.4644 12.6486i −0.527026 0.431062i
862862 −3.56217 + 3.56217i −0.121328 + 0.121328i
863863 −48.2127 12.9186i −1.64118 0.439753i −0.684056 0.729429i 0.739786π-0.739786\pi
−0.957125 + 0.289676i 0.906452π0.906452\pi
864864 −11.4982 + 13.9103i −0.391175 + 0.473238i
865865 0 0
866866 −0.194509 + 0.112300i −0.00660967 + 0.00381610i
867867 2.34727 + 11.2282i 0.0797176 + 0.381331i
868868 29.5128 4.62795i 1.00173 0.157083i
869869 3.22945 0.109552
870870 0 0
871871 0.0783524 0.135710i 0.00265487 0.00459837i
872872 2.74860 0.736484i 0.0930793 0.0249405i
873873 15.6491 2.37100i 0.529640 0.0802461i
874874 3.86774i 0.130828i
875875 0 0
876876 −2.50620 + 3.83099i −0.0846765 + 0.129437i
877877 −43.6713 11.7017i −1.47467 0.395138i −0.570143 0.821546i 0.693112π-0.693112\pi
−0.904531 + 0.426408i 0.859779π0.859779\pi
878878 1.22284 + 4.56370i 0.0412689 + 0.154018i
879879 −8.65357 17.1254i −0.291878 0.577627i
880880 0 0
881881 25.2055i 0.849195i 0.905382 + 0.424597i 0.139584π0.139584\pi
−0.905382 + 0.424597i 0.860416π0.860416\pi
882882 6.47306 + 0.402765i 0.217959 + 0.0135618i
883883 14.2942 + 14.2942i 0.481039 + 0.481039i 0.905463 0.424424i 0.139524π-0.139524\pi
−0.424424 + 0.905463i 0.639524π0.639524\pi
884884 14.8638 + 25.7449i 0.499925 + 0.865895i
885885 0 0
886886 −1.40912 + 2.44067i −0.0473403 + 0.0819958i
887887 10.0709 37.5853i 0.338149 1.26199i −0.562266 0.826957i 0.690070π-0.690070\pi
0.900415 0.435033i 0.143263π-0.143263\pi
888888 1.51144 + 7.23000i 0.0507206 + 0.242623i
889889 −15.2598 + 6.76605i −0.511796 + 0.226926i
890890 0 0
891891 −1.51671 + 6.69248i −0.0508118 + 0.224207i
892892 10.7740 + 40.2091i 0.360740 + 1.34630i
893893 −1.81649 6.77923i −0.0607865 0.226858i
894894 0.519936 9.32220i 0.0173893 0.311781i
895895 0 0
896896 −18.6823 13.6174i −0.624133 0.454924i
897897 41.6545 8.70792i 1.39080 0.290749i
898898 −0.752081 + 2.80681i −0.0250973 + 0.0936643i
899899 −14.6503 + 25.3750i −0.488613 + 0.846303i
900900 0 0
901901 16.8905 + 29.2553i 0.562705 + 0.974634i
902902 −0.725914 0.725914i −0.0241703 0.0241703i
903903 17.3488 1.73768i 0.577331 0.0578265i
904904 20.3599i 0.677161i
905905 0 0
906906 −7.26446 + 3.67077i −0.241345 + 0.121953i
907907 −0.623721 2.32776i −0.0207103 0.0772920i 0.954797 0.297258i 0.0960721π-0.0960721\pi
−0.975508 + 0.219966i 0.929405π0.929405\pi
908908 −23.6365 6.33337i −0.784404 0.210180i
909909 −22.8200 52.1946i −0.756891 1.73119i
910910 0 0
911911 19.3662i 0.641631i 0.947142 + 0.320815i 0.103957π0.103957\pi
−0.947142 + 0.320815i 0.896043π0.896043\pi
912912 7.26312 6.49574i 0.240506 0.215095i
913913 5.26347 1.41034i 0.174196 0.0466755i
914914 5.33185 9.23503i 0.176362 0.305468i
915915 0 0
916916 −29.1421 −0.962883
917917 5.61830 0.881015i 0.185533 0.0290937i
918918 4.52077 + 6.35591i 0.149208 + 0.209776i
919919 29.5591 17.0659i 0.975063 0.562953i 0.0742872 0.997237i 0.476332π-0.476332\pi
0.900776 + 0.434284i 0.142998π0.142998\pi
920920 0 0
921921 18.8650 + 37.3340i 0.621625 + 1.23020i
922922 11.0175 + 2.95213i 0.362842 + 0.0972231i
923923 28.1966 28.1966i 0.928102 0.928102i
924924 −6.56775 1.07318i −0.216063 0.0353051i
925925 0 0
926926 9.97388 5.75842i 0.327762 0.189233i
927927 −29.6084 + 23.6491i −0.972467 + 0.776738i
928928 16.5814 4.44297i 0.544311 0.145848i
929929 −9.86232 17.0820i −0.323572 0.560443i 0.657650 0.753323i 0.271550π-0.271550\pi
−0.981222 + 0.192880i 0.938217π0.938217\pi
930930 0 0
931931 −11.2006 2.41672i −0.367085 0.0792047i
932932 9.24073 + 9.24073i 0.302690 + 0.302690i
933933 30.5306 27.3049i 0.999527 0.893922i
934934 −2.72793 1.57497i −0.0892606 0.0515346i
935935 0 0
936936 9.35279 + 6.89159i 0.305706 + 0.225259i
937937 17.3041 17.3041i 0.565300 0.565300i −0.365508 0.930808i 0.619105π-0.619105\pi
0.930808 + 0.365508i 0.119105π0.119105\pi
938938 0.0372022 + 0.0143461i 0.00121470 + 0.000468418i
939939 17.9436 + 11.7385i 0.585568 + 0.383072i
940940 0 0
941941 −3.89269 2.24744i −0.126898 0.0732646i 0.435207 0.900330i 0.356675π-0.356675\pi
−0.562105 + 0.827066i 0.690008π0.690008\pi
942942 −1.52585 + 4.64300i −0.0497149 + 0.151277i
943943 8.63274 32.2178i 0.281121 1.04916i
944944 26.4292 0.860196
945945 0 0
946946 0.895935 0.0291294
947947 −3.88234 + 14.4891i −0.126159 + 0.470832i −0.999878 0.0155984i 0.995035π-0.995035\pi
0.873719 + 0.486431i 0.161701π0.161701\pi
948948 −4.36235 + 13.2742i −0.141683 + 0.431125i
949949 3.85939 + 2.22822i 0.125281 + 0.0723311i
950950 0 0
951951 −6.36658 4.16495i −0.206451 0.135058i
952952 −12.0660 + 9.74025i −0.391062 + 0.315683i
953953 21.6181 21.6181i 0.700277 0.700277i −0.264193 0.964470i 0.585105π-0.585105\pi
0.964470 + 0.264193i 0.0851054π0.0851054\pi
954954 5.18422 + 3.81999i 0.167845 + 0.123677i
955955 0 0
956956 −30.8583 17.8160i −0.998028 0.576212i
957957 4.86531 4.35126i 0.157273 0.140656i
958958 2.99334 + 2.99334i 0.0967106 + 0.0967106i
959959 23.1966 + 2.47406i 0.749058 + 0.0798915i
960960 0 0
961961 −2.07218 3.58912i −0.0668444 0.115778i
962962 3.38780 0.907759i 0.109227 0.0292673i
963963 −5.11158 + 4.08277i −0.164718 + 0.131565i
964964 3.25292 1.87807i 0.104769 0.0604887i
965965 0 0
966966 3.83086 + 10.1275i 0.123256 + 0.325847i
967967 −16.1911 + 16.1911i −0.520672 + 0.520672i −0.917774 0.397102i 0.870016π-0.870016\pi
0.397102 + 0.917774i 0.370016π0.370016\pi
968968 12.1357 + 3.25174i 0.390055 + 0.104515i
969969 −6.21477 12.2990i −0.199647 0.395102i
970970 0 0
971971 −15.8437 + 9.14738i −0.508450 + 0.293553i −0.732196 0.681094i 0.761505π-0.761505\pi
0.223747 + 0.974647i 0.428171π0.428171\pi
972972 −25.4596 15.2744i −0.816618 0.489928i
973973 −9.86456 + 25.5807i −0.316243 + 0.820078i
974974 −7.06004 −0.226218
975975 0 0
976976 7.55064 13.0781i 0.241690 0.418619i
977977 −14.3951 + 3.85716i −0.460540 + 0.123401i −0.481627 0.876376i 0.659954π-0.659954\pi
0.0210868 + 0.999778i 0.493287π0.493287\pi
978978 1.07948 0.965425i 0.0345179 0.0308709i
979979 0.691709i 0.0221071i
980980 0 0
981981 2.83587 + 6.48630i 0.0905423 + 0.207092i
982982 7.08425 + 1.89822i 0.226067 + 0.0605746i
983983 −3.04352 11.3586i −0.0970733 0.362283i 0.900252 0.435368i 0.143382π-0.143382\pi
−0.997326 + 0.0730860i 0.976715π0.976715\pi
984984 8.12717 4.10670i 0.259085 0.130917i
985985 0 0
986986 7.41895i 0.236267i
987987 −11.4710 15.9520i −0.365126 0.507757i
988988 −7.07955 7.07955i −0.225230 0.225230i
989989 14.5546 + 25.2092i 0.462808 + 0.801607i
990990 0 0
991991 −5.02003 + 8.69495i −0.159467 + 0.276204i −0.934676 0.355499i 0.884311π-0.884311\pi
0.775210 + 0.631704i 0.217644π0.217644\pi
992992 −5.32910 + 19.8885i −0.169199 + 0.631459i
993993 −10.5431 + 2.20405i −0.334576 + 0.0699434i
994994 8.19927 + 5.97636i 0.260065 + 0.189559i
995995 0 0
996996 −1.31291 + 23.5398i −0.0416010 + 0.745887i
997997 3.64290 + 13.5955i 0.115372 + 0.430574i 0.999314 0.0370216i 0.0117870π-0.0117870\pi
−0.883943 + 0.467596i 0.845120π0.845120\pi
998998 −0.258609 0.965142i −0.00818612 0.0305510i
999999 −17.2205 + 6.41213i −0.544831 + 0.202871i
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 525.2.bf.f.368.6 48
3.2 odd 2 inner 525.2.bf.f.368.7 48
5.2 odd 4 inner 525.2.bf.f.32.6 48
5.3 odd 4 105.2.x.a.32.7 yes 48
5.4 even 2 105.2.x.a.53.7 yes 48
7.2 even 3 inner 525.2.bf.f.443.7 48
15.2 even 4 inner 525.2.bf.f.32.7 48
15.8 even 4 105.2.x.a.32.6 yes 48
15.14 odd 2 105.2.x.a.53.6 yes 48
21.2 odd 6 inner 525.2.bf.f.443.6 48
35.2 odd 12 inner 525.2.bf.f.107.7 48
35.3 even 12 735.2.j.e.197.6 24
35.4 even 6 735.2.j.g.638.7 24
35.9 even 6 105.2.x.a.23.6 yes 48
35.13 even 4 735.2.y.i.557.7 48
35.18 odd 12 735.2.j.g.197.6 24
35.19 odd 6 735.2.y.i.128.6 48
35.23 odd 12 105.2.x.a.2.6 48
35.24 odd 6 735.2.j.e.638.7 24
35.33 even 12 735.2.y.i.422.6 48
35.34 odd 2 735.2.y.i.263.7 48
105.2 even 12 inner 525.2.bf.f.107.6 48
105.23 even 12 105.2.x.a.2.7 yes 48
105.38 odd 12 735.2.j.e.197.7 24
105.44 odd 6 105.2.x.a.23.7 yes 48
105.53 even 12 735.2.j.g.197.7 24
105.59 even 6 735.2.j.e.638.6 24
105.68 odd 12 735.2.y.i.422.7 48
105.74 odd 6 735.2.j.g.638.6 24
105.83 odd 4 735.2.y.i.557.6 48
105.89 even 6 735.2.y.i.128.7 48
105.104 even 2 735.2.y.i.263.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.6 48 35.23 odd 12
105.2.x.a.2.7 yes 48 105.23 even 12
105.2.x.a.23.6 yes 48 35.9 even 6
105.2.x.a.23.7 yes 48 105.44 odd 6
105.2.x.a.32.6 yes 48 15.8 even 4
105.2.x.a.32.7 yes 48 5.3 odd 4
105.2.x.a.53.6 yes 48 15.14 odd 2
105.2.x.a.53.7 yes 48 5.4 even 2
525.2.bf.f.32.6 48 5.2 odd 4 inner
525.2.bf.f.32.7 48 15.2 even 4 inner
525.2.bf.f.107.6 48 105.2 even 12 inner
525.2.bf.f.107.7 48 35.2 odd 12 inner
525.2.bf.f.368.6 48 1.1 even 1 trivial
525.2.bf.f.368.7 48 3.2 odd 2 inner
525.2.bf.f.443.6 48 21.2 odd 6 inner
525.2.bf.f.443.7 48 7.2 even 3 inner
735.2.j.e.197.6 24 35.3 even 12
735.2.j.e.197.7 24 105.38 odd 12
735.2.j.e.638.6 24 105.59 even 6
735.2.j.e.638.7 24 35.24 odd 6
735.2.j.g.197.6 24 35.18 odd 12
735.2.j.g.197.7 24 105.53 even 12
735.2.j.g.638.6 24 105.74 odd 6
735.2.j.g.638.7 24 35.4 even 6
735.2.y.i.128.6 48 35.19 odd 6
735.2.y.i.128.7 48 105.89 even 6
735.2.y.i.263.6 48 105.104 even 2
735.2.y.i.263.7 48 35.34 odd 2
735.2.y.i.422.6 48 35.33 even 12
735.2.y.i.422.7 48 105.68 odd 12
735.2.y.i.557.6 48 105.83 odd 4
735.2.y.i.557.7 48 35.13 even 4