Properties

Label 308.2.d.a.43.4
Level 308308
Weight 22
Character 308.43
Analytic conductor 2.4592.459
Analytic rank 00
Dimension 1818
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [308,2,Mod(43,308)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(308, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("308.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 308=22711 308 = 2^{2} \cdot 7 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 308.d (of order 22, degree 11, 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: 2.459392382262.45939238226
Analytic rank: 00
Dimension: 1818
Coefficient field: Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x18x172x15+3x143x13+4x1214x11+12x10+16x9++512 x^{18} - x^{17} - 2 x^{15} + 3 x^{14} - 3 x^{13} + 4 x^{12} - 14 x^{11} + 12 x^{10} + 16 x^{9} + \cdots + 512 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 27 2^{7}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 43.4
Root 1.35077+0.418821i1.35077 + 0.418821i of defining polynomial
Character χ\chi == 308.43
Dual form 308.2.d.a.43.3

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+(1.35077+0.418821i)q2+1.57463iq3+(1.649181.13146i)q4+1.58188q5+(0.6594872.12696i)q6+1.00000q7+(1.75378+2.21906i)q8+0.520549q9+(2.13676+0.662524i)q10+(3.038111.33037i)q11+(1.78164+2.59684i)q122.62307iq13+(1.35077+0.418821i)q14+2.49087iq15+(1.439573.73197i)q160.750224iq17+(0.703144+0.218017i)q18+1.14137q19+(2.608801.78984i)q20+1.57463iq21+(3.54662+3.06945i)q22+3.83223iq23+(3.494202.76156i)q242.49766q25+(1.09860+3.54318i)q26+5.54355iq27+(1.649181.13146i)q28+9.02097iq29+(1.043233.36460i)q304.41685iq31+(0.381509+5.64397i)q32+(2.09483+4.78389i)q33+(0.314210+1.01338i)q34+1.58188q35+(0.8584780.588983i)q362.80558q37+(1.54174+0.478031i)q38+4.13036q39+(2.77427+3.51029i)q40+0.250697iq41+(0.6594872.12696i)q42+1.82459q43+(3.505125.63153i)q44+0.823446q45+(1.605025.17647i)q46+4.73143iq47+(5.87647+2.26679i)q48+1.00000q49+(3.373771.04607i)q50+1.18132q51+(2.967914.32591i)q529.11425q53+(2.321767.48808i)q54+(4.805922.10448i)q55+(1.75378+2.21906i)q56+1.79724iq57+(3.7781712.1853i)q5814.5290iq59+(2.81833+4.10788i)q607.65849iq61+(1.84987+5.96616i)q62+0.520549q63+(1.848487.78352i)q644.14938iq65+(4.833245.58460i)q668.00407iq67+(0.8488521.23725i)q686.03433q69+(2.13676+0.662524i)q70+11.4380iq71+(0.912931+1.15513i)q72+0.267868iq73+(3.789701.17503i)q743.93289iq75+(1.882331.29142i)q76+(3.038111.33037i)q77+(5.57918+1.72988i)q786.72244q79+(2.277235.90353i)q807.16738q81+(0.1049970.338635i)q82+1.20081q83+(1.78164+2.59684i)q841.18676iq85+(2.46461+0.764178i)q8614.2047q87+(2.37602+9.07494i)q88+10.6509q89+(1.11229+0.344876i)q902.62307iq91+(4.33603+6.32002i)q92+6.95489q93+(1.981626.39109i)q94+1.80551q95+(8.887160.600735i)q9612.3457q97+(1.35077+0.418821i)q98+(1.581490.692521i)q99+O(q100)q+(-1.35077 + 0.418821i) q^{2} +1.57463i q^{3} +(1.64918 - 1.13146i) q^{4} +1.58188 q^{5} +(-0.659487 - 2.12696i) q^{6} +1.00000 q^{7} +(-1.75378 + 2.21906i) q^{8} +0.520549 q^{9} +(-2.13676 + 0.662524i) q^{10} +(3.03811 - 1.33037i) q^{11} +(1.78164 + 2.59684i) q^{12} -2.62307i q^{13} +(-1.35077 + 0.418821i) q^{14} +2.49087i q^{15} +(1.43957 - 3.73197i) q^{16} -0.750224i q^{17} +(-0.703144 + 0.218017i) q^{18} +1.14137 q^{19} +(2.60880 - 1.78984i) q^{20} +1.57463i q^{21} +(-3.54662 + 3.06945i) q^{22} +3.83223i q^{23} +(-3.49420 - 2.76156i) q^{24} -2.49766 q^{25} +(1.09860 + 3.54318i) q^{26} +5.54355i q^{27} +(1.64918 - 1.13146i) q^{28} +9.02097i q^{29} +(-1.04323 - 3.36460i) q^{30} -4.41685i q^{31} +(-0.381509 + 5.64397i) q^{32} +(2.09483 + 4.78389i) q^{33} +(0.314210 + 1.01338i) q^{34} +1.58188 q^{35} +(0.858478 - 0.588983i) q^{36} -2.80558 q^{37} +(-1.54174 + 0.478031i) q^{38} +4.13036 q^{39} +(-2.77427 + 3.51029i) q^{40} +0.250697i q^{41} +(-0.659487 - 2.12696i) q^{42} +1.82459 q^{43} +(3.50512 - 5.63153i) q^{44} +0.823446 q^{45} +(-1.60502 - 5.17647i) q^{46} +4.73143i q^{47} +(5.87647 + 2.26679i) q^{48} +1.00000 q^{49} +(3.37377 - 1.04607i) q^{50} +1.18132 q^{51} +(-2.96791 - 4.32591i) q^{52} -9.11425 q^{53} +(-2.32176 - 7.48808i) q^{54} +(4.80592 - 2.10448i) q^{55} +(-1.75378 + 2.21906i) q^{56} +1.79724i q^{57} +(-3.77817 - 12.1853i) q^{58} -14.5290i q^{59} +(2.81833 + 4.10788i) q^{60} -7.65849i q^{61} +(1.84987 + 5.96616i) q^{62} +0.520549 q^{63} +(-1.84848 - 7.78352i) q^{64} -4.14938i q^{65} +(-4.83324 - 5.58460i) q^{66} -8.00407i q^{67} +(-0.848852 - 1.23725i) q^{68} -6.03433 q^{69} +(-2.13676 + 0.662524i) q^{70} +11.4380i q^{71} +(-0.912931 + 1.15513i) q^{72} +0.267868i q^{73} +(3.78970 - 1.17503i) q^{74} -3.93289i q^{75} +(1.88233 - 1.29142i) q^{76} +(3.03811 - 1.33037i) q^{77} +(-5.57918 + 1.72988i) q^{78} -6.72244 q^{79} +(2.27723 - 5.90353i) q^{80} -7.16738 q^{81} +(-0.104997 - 0.338635i) q^{82} +1.20081 q^{83} +(1.78164 + 2.59684i) q^{84} -1.18676i q^{85} +(-2.46461 + 0.764178i) q^{86} -14.2047 q^{87} +(-2.37602 + 9.07494i) q^{88} +10.6509 q^{89} +(-1.11229 + 0.344876i) q^{90} -2.62307i q^{91} +(4.33603 + 6.32002i) q^{92} +6.95489 q^{93} +(-1.98162 - 6.39109i) q^{94} +1.80551 q^{95} +(-8.88716 - 0.600735i) q^{96} -12.3457 q^{97} +(-1.35077 + 0.418821i) q^{98} +(1.58149 - 0.692521i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 18qq2+q4+18q77q822q9+6q10+4q118q12q143q16+5q18+8q1910q207q22+28q24+18q2526q26+q28+32q30+4q99+O(q100) 18 q - q^{2} + q^{4} + 18 q^{7} - 7 q^{8} - 22 q^{9} + 6 q^{10} + 4 q^{11} - 8 q^{12} - q^{14} - 3 q^{16} + 5 q^{18} + 8 q^{19} - 10 q^{20} - 7 q^{22} + 28 q^{24} + 18 q^{25} - 26 q^{26} + q^{28} + 32 q^{30}+ \cdots - 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/308Z)×\left(\mathbb{Z}/308\mathbb{Z}\right)^\times.

nn 4545 5757 155155
χ(n)\chi(n) 11 1-1 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 −1.35077 + 0.418821i −0.955141 + 0.296151i
33 1.57463i 0.909111i 0.890718 + 0.454556i 0.150202π0.150202\pi
−0.890718 + 0.454556i 0.849798π0.849798\pi
44 1.64918 1.13146i 0.824589 0.565732i
55 1.58188 0.707437 0.353719 0.935352i 0.384917π-0.384917\pi
0.353719 + 0.935352i 0.384917π0.384917\pi
66 −0.659487 2.12696i −0.269235 0.868330i
77 1.00000 0.377964
88 −1.75378 + 2.21906i −0.620056 + 0.784557i
99 0.520549 0.173516
1010 −2.13676 + 0.662524i −0.675703 + 0.209509i
1111 3.03811 1.33037i 0.916025 0.401121i
1212 1.78164 + 2.59684i 0.514314 + 0.749643i
1313 2.62307i 0.727509i −0.931495 0.363755i 0.881495π-0.881495\pi
0.931495 0.363755i 0.118505π-0.118505\pi
1414 −1.35077 + 0.418821i −0.361009 + 0.111935i
1515 2.49087i 0.643139i
1616 1.43957 3.73197i 0.359894 0.932993i
1717 0.750224i 0.181956i −0.995853 0.0909781i 0.971001π-0.971001\pi
0.995853 0.0909781i 0.0289993π-0.0289993\pi
1818 −0.703144 + 0.218017i −0.165733 + 0.0513871i
1919 1.14137 0.261849 0.130924 0.991392i 0.458205π-0.458205\pi
0.130924 + 0.991392i 0.458205π0.458205\pi
2020 2.60880 1.78984i 0.583345 0.400220i
2121 1.57463i 0.343612i
2222 −3.54662 + 3.06945i −0.756141 + 0.654409i
2323 3.83223i 0.799075i 0.916717 + 0.399537i 0.130829π0.130829\pi
−0.916717 + 0.399537i 0.869171π0.869171\pi
2424 −3.49420 2.76156i −0.713250 0.563700i
2525 −2.49766 −0.499532
2626 1.09860 + 3.54318i 0.215453 + 0.694874i
2727 5.54355i 1.06686i
2828 1.64918 1.13146i 0.311665 0.213827i
2929 9.02097i 1.67515i 0.546321 + 0.837576i 0.316028π0.316028\pi
−0.546321 + 0.837576i 0.683972π0.683972\pi
3030 −1.04323 3.36460i −0.190467 0.614289i
3131 4.41685i 0.793290i −0.917972 0.396645i 0.870174π-0.870174\pi
0.917972 0.396645i 0.129826π-0.129826\pi
3232 −0.381509 + 5.64397i −0.0674419 + 0.997723i
3333 2.09483 + 4.78389i 0.364663 + 0.832769i
3434 0.314210 + 1.01338i 0.0538865 + 0.173794i
3535 1.58188 0.267386
3636 0.858478 0.588983i 0.143080 0.0981639i
3737 −2.80558 −0.461234 −0.230617 0.973045i 0.574074π-0.574074\pi
−0.230617 + 0.973045i 0.574074π0.574074\pi
3838 −1.54174 + 0.478031i −0.250103 + 0.0775469i
3939 4.13036 0.661387
4040 −2.77427 + 3.51029i −0.438651 + 0.555025i
4141 0.250697i 0.0391523i 0.999808 + 0.0195761i 0.00623168π0.00623168\pi
−0.999808 + 0.0195761i 0.993768π0.993768\pi
4242 −0.659487 2.12696i −0.101761 0.328198i
4343 1.82459 0.278248 0.139124 0.990275i 0.455571π-0.455571\pi
0.139124 + 0.990275i 0.455571π0.455571\pi
4444 3.50512 5.63153i 0.528417 0.848985i
4545 0.823446 0.122752
4646 −1.60502 5.17647i −0.236647 0.763229i
4747 4.73143i 0.690150i 0.938575 + 0.345075i 0.112146π0.112146\pi
−0.938575 + 0.345075i 0.887854π0.887854\pi
4848 5.87647 + 2.26679i 0.848195 + 0.327183i
4949 1.00000 0.142857
5050 3.37377 1.04607i 0.477124 0.147937i
5151 1.18132 0.165418
5252 −2.96791 4.32591i −0.411576 0.599896i
5353 −9.11425 −1.25194 −0.625969 0.779848i 0.715296π-0.715296\pi
−0.625969 + 0.779848i 0.715296π0.715296\pi
5454 −2.32176 7.48808i −0.315951 1.01900i
5555 4.80592 2.10448i 0.648031 0.283768i
5656 −1.75378 + 2.21906i −0.234359 + 0.296535i
5757 1.79724i 0.238050i
5858 −3.77817 12.1853i −0.496098 1.60001i
5959 14.5290i 1.89152i −0.324869 0.945759i 0.605320π-0.605320\pi
0.324869 0.945759i 0.394680π-0.394680\pi
6060 2.81833 + 4.10788i 0.363845 + 0.530326i
6161 7.65849i 0.980569i −0.871562 0.490284i 0.836893π-0.836893\pi
0.871562 0.490284i 0.163107π-0.163107\pi
6262 1.84987 + 5.96616i 0.234934 + 0.757704i
6363 0.520549 0.0655830
6464 −1.84848 7.78352i −0.231060 0.972939i
6565 4.14938i 0.514667i
6666 −4.83324 5.58460i −0.594931 0.687416i
6767 8.00407i 0.977853i −0.872325 0.488926i 0.837389π-0.837389\pi
0.872325 0.488926i 0.162611π-0.162611\pi
6868 −0.848852 1.23725i −0.102938 0.150039i
6969 −6.03433 −0.726448
7070 −2.13676 + 0.662524i −0.255392 + 0.0791868i
7171 11.4380i 1.35744i 0.734398 + 0.678719i 0.237464π0.237464\pi
−0.734398 + 0.678719i 0.762536π0.762536\pi
7272 −0.912931 + 1.15513i −0.107590 + 0.136134i
7373 0.267868i 0.0313516i 0.999877 + 0.0156758i 0.00498997π0.00498997\pi
−0.999877 + 0.0156758i 0.995010π0.995010\pi
7474 3.78970 1.17503i 0.440543 0.136595i
7575 3.93289i 0.454130i
7676 1.88233 1.29142i 0.215918 0.148136i
7777 3.03811 1.33037i 0.346225 0.151609i
7878 −5.57918 + 1.72988i −0.631718 + 0.195871i
7979 −6.72244 −0.756334 −0.378167 0.925737i 0.623445π-0.623445\pi
−0.378167 + 0.925737i 0.623445π0.623445\pi
8080 2.27723 5.90353i 0.254602 0.660034i
8181 −7.16738 −0.796376
8282 −0.104997 0.338635i −0.0115950 0.0373960i
8383 1.20081 0.131806 0.0659029 0.997826i 0.479007π-0.479007\pi
0.0659029 + 0.997826i 0.479007π0.479007\pi
8484 1.78164 + 2.59684i 0.194392 + 0.283338i
8585 1.18676i 0.128723i
8686 −2.46461 + 0.764178i −0.265766 + 0.0824035i
8787 −14.2047 −1.52290
8888 −2.37602 + 9.07494i −0.253285 + 0.967392i
8989 10.6509 1.12899 0.564494 0.825437i 0.309071π-0.309071\pi
0.564494 + 0.825437i 0.309071π0.309071\pi
9090 −1.11229 + 0.344876i −0.117245 + 0.0363532i
9191 2.62307i 0.274973i
9292 4.33603 + 6.32002i 0.452063 + 0.658908i
9393 6.95489 0.721189
9494 −1.98162 6.39109i −0.204389 0.659190i
9595 1.80551 0.185242
9696 −8.88716 0.600735i −0.907042 0.0613122i
9797 −12.3457 −1.25352 −0.626758 0.779214i 0.715618π-0.715618\pi
−0.626758 + 0.779214i 0.715618π0.715618\pi
9898 −1.35077 + 0.418821i −0.136449 + 0.0423073i
9999 1.58149 0.692521i 0.158945 0.0696010i
100100 −4.11909 + 2.82602i −0.411909 + 0.282602i
101101 18.5310i 1.84390i −0.387307 0.921951i 0.626595π-0.626595\pi
0.387307 0.921951i 0.373405π-0.373405\pi
102102 −1.59570 + 0.494763i −0.157998 + 0.0489889i
103103 3.44171i 0.339122i 0.985520 + 0.169561i 0.0542349π0.0542349\pi
−0.985520 + 0.169561i 0.945765π0.945765\pi
104104 5.82076 + 4.60030i 0.570773 + 0.451097i
105105 2.49087i 0.243084i
106106 12.3113 3.81724i 1.19578 0.370763i
107107 −13.6088 −1.31561 −0.657807 0.753186i 0.728516π-0.728516\pi
−0.657807 + 0.753186i 0.728516π0.728516\pi
108108 6.27234 + 9.14230i 0.603556 + 0.879719i
109109 4.90234i 0.469559i −0.972049 0.234779i 0.924563π-0.924563\pi
0.972049 0.234779i 0.0754368π-0.0754368\pi
110110 −5.61031 + 4.85550i −0.534922 + 0.462953i
111111 4.41773i 0.419313i
112112 1.43957 3.73197i 0.136027 0.352638i
113113 18.6980 1.75896 0.879480 0.475936i 0.157891π-0.157891\pi
0.879480 + 0.475936i 0.157891π0.157891\pi
114114 −0.752721 2.42766i −0.0704987 0.227371i
115115 6.06212i 0.565295i
116116 10.2069 + 14.8772i 0.947688 + 1.38131i
117117 1.36544i 0.126235i
118118 6.08506 + 19.6254i 0.560175 + 1.80667i
119119 0.750224i 0.0687729i
120120 −5.52739 4.36845i −0.504580 0.398783i
121121 7.46025 8.08361i 0.678204 0.734873i
122122 3.20754 + 10.3449i 0.290397 + 0.936582i
123123 −0.394754 −0.0355938
124124 −4.99751 7.28417i −0.448790 0.654138i
125125 −11.8604 −1.06083
126126 −0.703144 + 0.218017i −0.0626411 + 0.0194225i
127127 0.249900 0.0221751 0.0110875 0.999939i 0.496471π-0.496471\pi
0.0110875 + 0.999939i 0.496471π0.496471\pi
128128 5.75678 + 9.73958i 0.508833 + 0.860866i
129129 2.87305i 0.252958i
130130 1.73785 + 5.60487i 0.152419 + 0.491580i
131131 −16.9727 −1.48292 −0.741458 0.671000i 0.765865π-0.765865\pi
−0.741458 + 0.671000i 0.765865π0.765865\pi
132132 8.86756 + 5.51926i 0.771822 + 0.480390i
133133 1.14137 0.0989696
134134 3.35227 + 10.8117i 0.289592 + 0.933987i
135135 8.76923i 0.754735i
136136 1.66480 + 1.31573i 0.142755 + 0.112823i
137137 8.45260 0.722155 0.361077 0.932536i 0.382409π-0.382409\pi
0.361077 + 0.932536i 0.382409π0.382409\pi
138138 8.15101 2.52730i 0.693860 0.215138i
139139 10.4874 0.889533 0.444766 0.895647i 0.353287π-0.353287\pi
0.444766 + 0.895647i 0.353287π0.353287\pi
140140 2.60880 1.78984i 0.220484 0.151269i
141141 −7.45024 −0.627423
142142 −4.79046 15.4501i −0.402007 1.29654i
143143 −3.48965 7.96919i −0.291819 0.666417i
144144 0.749369 1.94268i 0.0624474 0.161890i
145145 14.2701i 1.18506i
146146 −0.112189 0.361829i −0.00928482 0.0299452i
147147 1.57463i 0.129873i
148148 −4.62689 + 3.17441i −0.380328 + 0.260935i
149149 17.5806i 1.44026i 0.693841 + 0.720128i 0.255917π0.255917\pi
−0.693841 + 0.720128i 0.744083π0.744083\pi
150150 1.64718 + 5.31244i 0.134491 + 0.433759i
151151 1.11949 0.0911028 0.0455514 0.998962i 0.485496π-0.485496\pi
0.0455514 + 0.998962i 0.485496π0.485496\pi
152152 −2.00172 + 2.53278i −0.162361 + 0.205435i
153153 0.390529i 0.0315724i
154154 −3.54662 + 3.06945i −0.285794 + 0.247343i
155155 6.98692i 0.561203i
156156 6.81170 4.67336i 0.545372 0.374168i
157157 8.38807 0.669441 0.334720 0.942318i 0.391358π-0.391358\pi
0.334720 + 0.942318i 0.391358π0.391358\pi
158158 9.08050 2.81550i 0.722406 0.223989i
159159 14.3515i 1.13815i
160160 −0.603501 + 8.92808i −0.0477110 + 0.705827i
161161 3.83223i 0.302022i
162162 9.68151 3.00185i 0.760651 0.235848i
163163 4.32454i 0.338725i 0.985554 + 0.169362i 0.0541708π0.0541708\pi
−0.985554 + 0.169362i 0.945829π0.945829\pi
164164 0.283655 + 0.413444i 0.0221497 + 0.0322845i
165165 3.31377 + 7.56754i 0.257977 + 0.589132i
166166 −1.62202 + 0.502924i −0.125893 + 0.0390345i
167167 −21.2610 −1.64523 −0.822614 0.568600i 0.807485π-0.807485\pi
−0.822614 + 0.568600i 0.807485π0.807485\pi
168168 −3.49420 2.76156i −0.269583 0.213059i
169169 6.11949 0.470730
170170 0.497042 + 1.60305i 0.0381214 + 0.122948i
171171 0.594141 0.0454351
172172 3.00908 2.06446i 0.229440 0.157414i
173173 2.41069i 0.183282i −0.995792 0.0916408i 0.970789π-0.970789\pi
0.995792 0.0916408i 0.0292112π-0.0292112\pi
174174 19.1873 5.94921i 1.45458 0.451009i
175175 −2.49766 −0.188805
176176 −0.591305 13.2533i −0.0445713 0.999006i
177177 22.8778 1.71960
178178 −14.3869 + 4.46080i −1.07834 + 0.334351i
179179 12.5187i 0.935689i 0.883811 + 0.467844i 0.154969π0.154969\pi
−0.883811 + 0.467844i 0.845031π0.845031\pi
180180 1.35801 0.931700i 0.101220 0.0694448i
181181 −24.6700 −1.83371 −0.916854 0.399223i 0.869280π-0.869280\pi
−0.916854 + 0.399223i 0.869280π0.869280\pi
182182 1.09860 + 3.54318i 0.0814335 + 0.262638i
183183 12.0593 0.891446
184184 −8.50396 6.72090i −0.626920 0.495471i
185185 −4.43808 −0.326294
186186 −9.39448 + 2.91286i −0.688837 + 0.213581i
187187 −0.998073 2.27927i −0.0729863 0.166676i
188188 5.35345 + 7.80297i 0.390440 + 0.569090i
189189 5.54355i 0.403234i
190190 −2.43884 + 0.756187i −0.176932 + 0.0548596i
191191 11.8677i 0.858720i −0.903133 0.429360i 0.858739π-0.858739\pi
0.903133 0.429360i 0.141261π-0.141261\pi
192192 12.2561 2.91067i 0.884510 0.210060i
193193 8.28858i 0.596625i 0.954468 + 0.298312i 0.0964237π0.0964237\pi
−0.954468 + 0.298312i 0.903576π0.903576\pi
194194 16.6762 5.17064i 1.19728 0.371230i
195195 6.53373 0.467890
196196 1.64918 1.13146i 0.117798 0.0808189i
197197 19.0013i 1.35379i −0.736081 0.676893i 0.763326π-0.763326\pi
0.736081 0.676893i 0.236674π-0.236674\pi
198198 −1.84619 + 1.59780i −0.131203 + 0.113551i
199199 16.0120i 1.13506i 0.823351 + 0.567532i 0.192102π0.192102\pi
−0.823351 + 0.567532i 0.807898π0.807898\pi
200200 4.38036 5.54247i 0.309738 0.391912i
201201 12.6034 0.888977
202202 7.76117 + 25.0312i 0.546074 + 1.76119i
203203 9.02097i 0.633148i
204204 1.94821 1.33663i 0.136402 0.0935825i
205205 0.396572i 0.0276978i
206206 −1.44146 4.64897i −0.100431 0.323909i
207207 1.99486i 0.138653i
208208 −9.78924 3.77611i −0.678761 0.261826i
209209 3.46762 1.51844i 0.239860 0.105033i
210210 −1.04323 3.36460i −0.0719896 0.232179i
211211 0.980150 0.0674763 0.0337381 0.999431i 0.489259π-0.489259\pi
0.0337381 + 0.999431i 0.489259π0.489259\pi
212212 −15.0310 + 10.3125i −1.03233 + 0.708262i
213213 −18.0105 −1.23406
214214 18.3824 5.69966i 1.25660 0.389621i
215215 2.88628 0.196843
216216 −12.3015 9.72219i −0.837011 0.661511i
217217 4.41685i 0.299835i
218218 2.05320 + 6.62195i 0.139060 + 0.448495i
219219 −0.421793 −0.0285021
220220 5.54468 8.90839i 0.373822 0.600604i
221221 −1.96789 −0.132375
222222 1.85024 + 5.96736i 0.124180 + 0.400503i
223223 7.90537i 0.529383i −0.964333 0.264691i 0.914730π-0.914730\pi
0.964333 0.264691i 0.0852700π-0.0852700\pi
224224 −0.381509 + 5.64397i −0.0254907 + 0.377104i
225225 −1.30016 −0.0866770
226226 −25.2568 + 7.83112i −1.68005 + 0.520918i
227227 −8.91322 −0.591591 −0.295796 0.955251i 0.595585π-0.595585\pi
−0.295796 + 0.955251i 0.595585π0.595585\pi
228228 2.03351 + 2.96396i 0.134672 + 0.196293i
229229 −20.0551 −1.32528 −0.662639 0.748939i 0.730563π-0.730563\pi
−0.662639 + 0.748939i 0.730563π0.730563\pi
230230 −2.53894 8.18855i −0.167413 0.539937i
231231 2.09483 + 4.78389i 0.137830 + 0.314757i
232232 −20.0181 15.8208i −1.31425 1.03869i
233233 7.48274i 0.490210i 0.969496 + 0.245105i 0.0788225π0.0788225\pi
−0.969496 + 0.245105i 0.921177π0.921177\pi
234234 0.571874 + 1.84440i 0.0373846 + 0.120572i
235235 7.48454i 0.488238i
236236 −16.4391 23.9609i −1.07009 1.55972i
237237 10.5853i 0.687592i
238238 0.314210 + 1.01338i 0.0203672 + 0.0656879i
239239 −14.2237 −0.920057 −0.460029 0.887904i 0.652161π-0.652161\pi
−0.460029 + 0.887904i 0.652161π0.652161\pi
240240 9.29586 + 3.58579i 0.600045 + 0.231462i
241241 13.7418i 0.885184i −0.896723 0.442592i 0.854059π-0.854059\pi
0.896723 0.442592i 0.145941π-0.145941\pi
242242 −6.69152 + 14.0436i −0.430147 + 0.902759i
243243 5.34471i 0.342863i
244244 −8.66531 12.6302i −0.554740 0.808566i
245245 1.58188 0.101062
246246 0.533224 0.165331i 0.0339971 0.0105411i
247247 2.99390i 0.190498i
248248 9.80127 + 7.74620i 0.622381 + 0.491884i
249249 1.89083i 0.119826i
250250 16.0207 4.96738i 1.01324 0.314165i
251251 23.6620i 1.49353i −0.665086 0.746767i 0.731605π-0.731605\pi
0.665086 0.746767i 0.268395π-0.268395\pi
252252 0.858478 0.588983i 0.0540790 0.0371025i
253253 5.09827 + 11.6427i 0.320525 + 0.731973i
254254 −0.337559 + 0.104664i −0.0211803 + 0.00656718i
255255 1.86871 0.117023
256256 −11.8553 10.7449i −0.740953 0.671557i
257257 13.6739 0.852952 0.426476 0.904499i 0.359755π-0.359755\pi
0.426476 + 0.904499i 0.359755π0.359755\pi
258258 −1.20330 3.88085i −0.0749139 0.241611i
259259 −2.80558 −0.174330
260260 −4.69488 6.84307i −0.291164 0.424389i
261261 4.69586i 0.290666i
262262 22.9263 7.10854i 1.41639 0.439167i
263263 −1.54709 −0.0953978 −0.0476989 0.998862i 0.515189π-0.515189\pi
−0.0476989 + 0.998862i 0.515189π0.515189\pi
264264 −14.2896 3.74135i −0.879467 0.230264i
265265 −14.4176 −0.885668
266266 −1.54174 + 0.478031i −0.0945299 + 0.0293100i
267267 16.7711i 1.02638i
268268 −9.05632 13.2001i −0.553203 0.806326i
269269 −11.1137 −0.677617 −0.338808 0.940855i 0.610024π-0.610024\pi
−0.338808 + 0.940855i 0.610024π0.610024\pi
270270 −3.67274 11.8452i −0.223516 0.720878i
271271 12.4657 0.757235 0.378617 0.925553i 0.376400π-0.376400\pi
0.378617 + 0.925553i 0.376400π0.376400\pi
272272 −2.79982 1.08000i −0.169764 0.0654848i
273273 4.13036 0.249981
274274 −11.4176 + 3.54013i −0.689760 + 0.213867i
275275 −7.58817 + 3.32281i −0.457584 + 0.200373i
276276 −9.95168 + 6.82763i −0.599021 + 0.410975i
277277 21.0155i 1.26270i −0.775498 0.631350i 0.782501π-0.782501\pi
0.775498 0.631350i 0.217499π-0.217499\pi
278278 −14.1662 + 4.39236i −0.849629 + 0.263436i
279279 2.29919i 0.137649i
280280 −2.77427 + 3.51029i −0.165795 + 0.209780i
281281 17.7260i 1.05744i 0.848795 + 0.528721i 0.177328π0.177328\pi
−0.848795 + 0.528721i 0.822672π0.822672\pi
282282 10.0636 3.12032i 0.599278 0.185812i
283283 32.9128 1.95646 0.978232 0.207513i 0.0665370π-0.0665370\pi
0.978232 + 0.207513i 0.0665370π0.0665370\pi
284284 12.9417 + 18.8632i 0.767946 + 1.11933i
285285 2.84301i 0.168405i
286286 8.05139 + 9.30303i 0.476089 + 0.550100i
287287 0.250697i 0.0147982i
288288 −0.198594 + 2.93797i −0.0117023 + 0.173121i
289289 16.4372 0.966892
290290 −5.97661 19.2756i −0.350958 1.13190i
291291 19.4399i 1.13958i
292292 0.303084 + 0.441762i 0.0177366 + 0.0258522i
293293 29.4803i 1.72226i −0.508386 0.861130i 0.669757π-0.669757\pi
0.508386 0.861130i 0.330243π-0.330243\pi
294294 −0.659487 2.12696i −0.0384621 0.124047i
295295 22.9831i 1.33813i
296296 4.92037 6.22575i 0.285991 0.361864i
297297 7.37496 + 16.8419i 0.427938 + 0.977268i
298298 −7.36311 23.7474i −0.426534 1.37565i
299299 10.0522 0.581334
300300 −4.44992 6.48603i −0.256916 0.374471i
301301 1.82459 0.105168
302302 −1.51218 + 0.468866i −0.0870160 + 0.0269802i
303303 29.1794 1.67631
304304 1.64309 4.25957i 0.0942377 0.244303i
305305 12.1148i 0.693691i
306306 0.163562 + 0.527516i 0.00935020 + 0.0301561i
307307 22.5952 1.28958 0.644789 0.764361i 0.276945π-0.276945\pi
0.644789 + 0.764361i 0.276945π0.276945\pi
308308 3.50512 5.63153i 0.199723 0.320886i
309309 −5.41941 −0.308299
310310 2.92627 + 9.43774i 0.166201 + 0.536028i
311311 8.11720i 0.460284i −0.973157 0.230142i 0.926081π-0.926081\pi
0.973157 0.230142i 0.0739191π-0.0739191\pi
312312 −7.24376 + 9.16553i −0.410097 + 0.518896i
313313 −22.3289 −1.26210 −0.631052 0.775741i 0.717376π-0.717376\pi
−0.631052 + 0.775741i 0.717376π0.717376\pi
314314 −11.3304 + 3.51310i −0.639410 + 0.198256i
315315 0.823446 0.0463959
316316 −11.0865 + 7.60621i −0.623665 + 0.427883i
317317 −4.24834 −0.238611 −0.119305 0.992858i 0.538067π-0.538067\pi
−0.119305 + 0.992858i 0.538067π0.538067\pi
318318 6.01073 + 19.3857i 0.337065 + 1.08710i
319319 12.0012 + 27.4067i 0.671938 + 1.53448i
320320 −2.92408 12.3126i −0.163461 0.688294i
321321 21.4288i 1.19604i
322322 −1.60502 5.17647i −0.0894442 0.288473i
323323 0.856286i 0.0476450i
324324 −11.8203 + 8.10964i −0.656682 + 0.450536i
325325 6.55155i 0.363414i
326326 −1.81121 5.84148i −0.100314 0.323530i
327327 7.71935 0.426881
328328 −0.556313 0.439668i −0.0307172 0.0242766i
329329 4.73143i 0.260852i
330330 −7.64559 8.83415i −0.420876 0.486304i
331331 0.144143i 0.00792284i −0.999992 0.00396142i 0.998739π-0.998739\pi
0.999992 0.00396142i 0.00126096π-0.00126096\pi
332332 1.98035 1.35867i 0.108686 0.0745669i
333333 −1.46044 −0.0800316
334334 28.7188 8.90457i 1.57142 0.487236i
335335 12.6615i 0.691770i
336336 5.87647 + 2.26679i 0.320588 + 0.123664i
337337 28.5950i 1.55767i 0.627230 + 0.778834i 0.284189π0.284189\pi
−0.627230 + 0.778834i 0.715811π0.715811\pi
338338 −8.26604 + 2.56297i −0.449614 + 0.139407i
339339 29.4424i 1.59909i
340340 −1.34278 1.95718i −0.0728225 0.106143i
341341 −5.87603 13.4189i −0.318205 0.726673i
342342 −0.802549 + 0.248839i −0.0433969 + 0.0134557i
343343 1.00000 0.0539949
344344 −3.19994 + 4.04889i −0.172529 + 0.218301i
345345 −9.54558 −0.513917
346346 1.00965 + 3.25630i 0.0542791 + 0.175060i
347347 −23.0033 −1.23488 −0.617442 0.786616i 0.711831π-0.711831\pi
−0.617442 + 0.786616i 0.711831π0.711831\pi
348348 −23.4260 + 16.0721i −1.25577 + 0.861554i
349349 23.7790i 1.27286i 0.771334 + 0.636430i 0.219590π0.219590\pi
−0.771334 + 0.636430i 0.780410π0.780410\pi
350350 3.37377 1.04607i 0.180336 0.0559150i
351351 14.5411 0.776149
352352 6.34949 + 17.6546i 0.338429 + 0.940992i
353353 −1.29117 −0.0687220 −0.0343610 0.999409i 0.510940π-0.510940\pi
−0.0343610 + 0.999409i 0.510940π0.510940\pi
354354 −30.9027 + 9.58170i −1.64246 + 0.509262i
355355 18.0935i 0.960302i
356356 17.5652 12.0511i 0.930951 0.638705i
357357 1.18132 0.0625223
358358 −5.24308 16.9099i −0.277105 0.893715i
359359 25.2115 1.33061 0.665306 0.746571i 0.268301π-0.268301\pi
0.665306 + 0.746571i 0.268301π0.268301\pi
360360 −1.44415 + 1.82728i −0.0761132 + 0.0963060i
361361 −17.6973 −0.931435
362362 33.3236 10.3323i 1.75145 0.543055i
363363 12.7287 + 11.7471i 0.668082 + 0.616563i
364364 −2.96791 4.32591i −0.155561 0.226739i
365365 0.423735i 0.0221793i
366366 −16.2893 + 5.05067i −0.851457 + 0.264003i
367367 1.10279i 0.0575651i 0.999586 + 0.0287825i 0.00916303π0.00916303\pi
−0.999586 + 0.0287825i 0.990837π0.990837\pi
368368 14.3018 + 5.51678i 0.745531 + 0.287582i
369369 0.130500i 0.00679357i
370370 5.99484 1.85876i 0.311657 0.0966324i
371371 −9.11425 −0.473188
372372 11.4699 7.86922i 0.594684 0.408000i
373373 19.1952i 0.993888i 0.867783 + 0.496944i 0.165545π0.165545\pi
−0.867783 + 0.496944i 0.834455π0.834455\pi
374374 2.30278 + 2.66076i 0.119074 + 0.137584i
375375 18.6757i 0.964408i
376376 −10.4993 8.29790i −0.541462 0.427932i
377377 23.6627 1.21869
378378 −2.32176 7.48808i −0.119418 0.385145i
379379 7.61066i 0.390933i −0.980710 0.195467i 0.937378π-0.937378\pi
0.980710 0.195467i 0.0626221π-0.0626221\pi
380380 2.97761 2.04287i 0.152748 0.104797i
381381 0.393500i 0.0201596i
382382 4.97046 + 16.0306i 0.254311 + 0.820199i
383383 22.0885i 1.12867i 0.825546 + 0.564335i 0.190867π0.190867\pi
−0.825546 + 0.564335i 0.809133π0.809133\pi
384384 −15.3362 + 9.06479i −0.782623 + 0.462585i
385385 4.80592 2.10448i 0.244933 0.107254i
386386 −3.47143 11.1960i −0.176691 0.569861i
387387 0.949791 0.0482806
388388 −20.3602 + 13.9687i −1.03363 + 0.709154i
389389 −27.1911 −1.37865 −0.689323 0.724454i 0.742092π-0.742092\pi
−0.689323 + 0.724454i 0.742092π0.742092\pi
390390 −8.82559 + 2.73646i −0.446901 + 0.138566i
391391 2.87503 0.145397
392392 −1.75378 + 2.21906i −0.0885795 + 0.112080i
393393 26.7257i 1.34814i
394394 7.95814 + 25.6664i 0.400925 + 1.29306i
395395 −10.6341 −0.535059
396396 1.82459 2.93149i 0.0916891 0.147313i
397397 13.6761 0.686383 0.343192 0.939265i 0.388492π-0.388492\pi
0.343192 + 0.939265i 0.388492π0.388492\pi
398398 −6.70618 21.6286i −0.336151 1.08415i
399399 1.79724i 0.0899744i
400400 −3.59557 + 9.32121i −0.179778 + 0.466060i
401401 3.77907 0.188718 0.0943588 0.995538i 0.469920π-0.469920\pi
0.0943588 + 0.995538i 0.469920π0.469920\pi
402402 −17.0244 + 5.27858i −0.849098 + 0.263272i
403403 −11.5857 −0.577126
404404 −20.9672 30.5609i −1.04315 1.52046i
405405 −11.3379 −0.563386
406406 −3.77817 12.1853i −0.187508 0.604745i
407407 −8.52365 + 3.73244i −0.422502 + 0.185010i
408408 −2.07179 + 2.62143i −0.102569 + 0.129780i
409409 28.8350i 1.42580i 0.701267 + 0.712899i 0.252618π0.252618\pi
−0.701267 + 0.712899i 0.747382π0.747382\pi
410410 −0.166093 0.535679i −0.00820274 0.0264553i
411411 13.3097i 0.656519i
412412 3.89417 + 5.67599i 0.191852 + 0.279636i
413413 14.5290i 0.714927i
414414 −0.835491 2.69461i −0.0410621 0.132433i
415415 1.89953 0.0932444
416416 14.8046 + 1.00073i 0.725853 + 0.0490646i
417417 16.5138i 0.808684i
418418 −4.04801 + 3.50339i −0.197995 + 0.171356i
419419 20.7473i 1.01357i 0.862072 + 0.506786i 0.169166π0.169166\pi
−0.862072 + 0.506786i 0.830834π0.830834\pi
420420 2.81833 + 4.10788i 0.137520 + 0.200444i
421421 22.2373 1.08378 0.541890 0.840449i 0.317709π-0.317709\pi
0.541890 + 0.840449i 0.317709π0.317709\pi
422422 −1.32396 + 0.410507i −0.0644494 + 0.0199832i
423423 2.46294i 0.119752i
424424 15.9844 20.2251i 0.776272 0.982217i
425425 1.87381i 0.0908929i
426426 24.3282 7.54319i 1.17870 0.365469i
427427 7.65849i 0.370620i
428428 −22.4434 + 15.3979i −1.08484 + 0.744286i
429429 12.5485 5.49489i 0.605847 0.265296i
430430 −3.89872 + 1.20884i −0.188013 + 0.0582953i
431431 −12.3696 −0.595823 −0.297912 0.954593i 0.596290π-0.596290\pi
−0.297912 + 0.954593i 0.596290π0.596290\pi
432432 20.6884 + 7.98036i 0.995371 + 0.383955i
433433 14.3230 0.688318 0.344159 0.938911i 0.388164π-0.388164\pi
0.344159 + 0.938911i 0.388164π0.388164\pi
434434 1.84987 + 5.96616i 0.0887966 + 0.286385i
435435 −22.4700 −1.07736
436436 −5.54682 8.08483i −0.265645 0.387193i
437437 4.37400i 0.209237i
438438 0.569746 0.176656i 0.0272235 0.00844093i
439439 −6.33190 −0.302205 −0.151103 0.988518i 0.548282π-0.548282\pi
−0.151103 + 0.988518i 0.548282π0.548282\pi
440440 −3.75858 + 14.3554i −0.179183 + 0.684369i
441441 0.520549 0.0247881
442442 2.65818 0.824195i 0.126437 0.0392030i
443443 25.6345i 1.21793i −0.793197 0.608965i 0.791585π-0.791585\pi
0.793197 0.608965i 0.208415π-0.208415\pi
444444 −4.99851 7.28563i −0.237219 0.345761i
445445 16.8484 0.798689
446446 3.31093 + 10.6784i 0.156777 + 0.505635i
447447 −27.6828 −1.30935
448448 −1.84848 7.78352i −0.0873326 0.367737i
449449 4.53508 0.214024 0.107012 0.994258i 0.465872π-0.465872\pi
0.107012 + 0.994258i 0.465872π0.465872\pi
450450 1.75622 0.544533i 0.0827888 0.0256695i
451451 0.333519 + 0.761646i 0.0157048 + 0.0358645i
452452 30.8363 21.1561i 1.45042 0.995101i
453453 1.76278i 0.0828226i
454454 12.0397 3.73304i 0.565053 0.175200i
455455 4.14938i 0.194526i
456456 −3.98818 3.15196i −0.186764 0.147604i
457457 17.6778i 0.826932i −0.910520 0.413466i 0.864318π-0.864318\pi
0.910520 0.413466i 0.135682π-0.135682\pi
458458 27.0899 8.39949i 1.26583 0.392483i
459459 4.15891 0.194121
460460 6.85907 + 9.99751i 0.319806 + 0.466136i
461461 33.9977i 1.58343i 0.610890 + 0.791716i 0.290812π0.290812\pi
−0.610890 + 0.791716i 0.709188π0.709188\pi
462462 −4.83324 5.58460i −0.224863 0.259819i
463463 2.00783i 0.0933117i 0.998911 + 0.0466559i 0.0148564π0.0148564\pi
−0.998911 + 0.0466559i 0.985144π0.985144\pi
464464 33.6660 + 12.9864i 1.56291 + 0.602876i
465465 11.0018 0.510196
466466 −3.13393 10.1075i −0.145176 0.468220i
467467 28.6605i 1.32625i −0.748508 0.663125i 0.769230π-0.769230\pi
0.748508 0.663125i 0.230770π-0.230770\pi
468468 −1.54495 2.25185i −0.0714151 0.104092i
469469 8.00407i 0.369594i
470470 −3.13469 10.1099i −0.144592 0.466336i
471471 13.2081i 0.608596i
472472 32.2408 + 25.4808i 1.48400 + 1.17285i
473473 5.54332 2.42738i 0.254882 0.111611i
474474 4.43336 + 14.2984i 0.203631 + 0.656747i
475475 −2.85076 −0.130802
476476 −0.848852 1.23725i −0.0389071 0.0567094i
477477 −4.74441 −0.217232
478478 19.2131 5.95720i 0.878785 0.272476i
479479 19.7590 0.902811 0.451405 0.892319i 0.350923π-0.350923\pi
0.451405 + 0.892319i 0.350923π0.350923\pi
480480 −14.0584 0.950289i −0.641675 0.0433746i
481481 7.35923i 0.335552i
482482 5.75534 + 18.5620i 0.262149 + 0.845476i
483483 −6.03433 −0.274572
484484 3.15696 21.7723i 0.143498 0.989651i
485485 −19.5294 −0.886784
486486 −2.23848 7.21949i −0.101539 0.327483i
487487 15.3754i 0.696727i −0.937359 0.348364i 0.886737π-0.886737\pi
0.937359 0.348364i 0.113263π-0.113263\pi
488488 16.9947 + 13.4313i 0.769313 + 0.608008i
489489 −6.80955 −0.307938
490490 −2.13676 + 0.662524i −0.0965289 + 0.0299298i
491491 −11.0024 −0.496532 −0.248266 0.968692i 0.579861π-0.579861\pi
−0.248266 + 0.968692i 0.579861π0.579861\pi
492492 −0.651020 + 0.446651i −0.0293502 + 0.0201366i
493493 6.76775 0.304804
494494 1.25391 + 4.04409i 0.0564161 + 0.181952i
495495 2.50172 1.09548i 0.112444 0.0492384i
496496 −16.4836 6.35838i −0.740134 0.285500i
497497 11.4380i 0.513063i
498498 −0.791918 2.55408i −0.0354867 0.114451i
499499 2.31056i 0.103435i −0.998662 0.0517175i 0.983530π-0.983530\pi
0.998662 0.0517175i 0.0164695π-0.0164695\pi
500500 −19.5599 + 13.4196i −0.874745 + 0.600143i
501501 33.4782i 1.49570i
502502 9.91016 + 31.9620i 0.442312 + 1.42654i
503503 −25.2485 −1.12578 −0.562888 0.826533i 0.690310π-0.690310\pi
−0.562888 + 0.826533i 0.690310π0.690310\pi
504504 −0.912931 + 1.15513i −0.0406652 + 0.0514537i
505505 29.3138i 1.30444i
506506 −11.7628 13.5914i −0.522922 0.604213i
507507 9.63592i 0.427946i
508508 0.412130 0.282754i 0.0182853 0.0125452i
509509 33.9007 1.50262 0.751310 0.659949i 0.229422π-0.229422\pi
0.751310 + 0.659949i 0.229422π0.229422\pi
510510 −2.52420 + 0.782655i −0.111774 + 0.0346566i
511511 0.267868i 0.0118498i
512512 20.5140 + 9.54870i 0.906597 + 0.421997i
513513 6.32726i 0.279355i
514514 −18.4703 + 5.72690i −0.814690 + 0.252603i
515515 5.44437i 0.239907i
516516 3.25076 + 4.73818i 0.143107 + 0.208587i
517517 6.29453 + 14.3746i 0.276833 + 0.632195i
518518 3.78970 1.17503i 0.166510 0.0516280i
519519 3.79594 0.166623
520520 9.20774 + 7.27712i 0.403786 + 0.319123i
521521 −39.3095 −1.72218 −0.861090 0.508453i 0.830217π-0.830217\pi
−0.861090 + 0.508453i 0.830217π0.830217\pi
522522 −1.96672 6.34304i −0.0860812 0.277627i
523523 −21.6105 −0.944962 −0.472481 0.881341i 0.656641π-0.656641\pi
−0.472481 + 0.881341i 0.656641π0.656641\pi
524524 −27.9911 + 19.2041i −1.22280 + 0.838933i
525525 3.93289i 0.171645i
526526 2.08977 0.647955i 0.0911184 0.0282522i
527527 −3.31363 −0.144344
528528 20.8690 0.931085i 0.908208 0.0405203i
529529 8.31403 0.361480
530530 19.4750 6.03841i 0.845938 0.262292i
531531 7.56307i 0.328209i
532532 1.88233 1.29142i 0.0816092 0.0559903i
533533 0.657596 0.0284837
534534 −7.02410 22.6540i −0.303963 0.980334i
535535 −21.5275 −0.930715
536536 17.7615 + 14.0374i 0.767181 + 0.606324i
537537 −19.7122 −0.850645
538538 15.0121 4.65467i 0.647220 0.200677i
539539 3.03811 1.33037i 0.130861 0.0573029i
540540 9.92207 + 14.4620i 0.426978 + 0.622346i
541541 14.4449i 0.621036i 0.950568 + 0.310518i 0.100502π0.100502\pi
−0.950568 + 0.310518i 0.899498π0.899498\pi
542542 −16.8383 + 5.22088i −0.723266 + 0.224256i
543543 38.8461i 1.66704i
544544 4.23425 + 0.286217i 0.181542 + 0.0122715i
545545 7.75490i 0.332183i
546546 −5.57918 + 1.72988i −0.238767 + 0.0740321i
547547 −39.5985 −1.69311 −0.846555 0.532301i 0.821327π-0.821327\pi
−0.846555 + 0.532301i 0.821327π0.821327\pi
548548 13.9398 9.56382i 0.595481 0.408546i
549549 3.98662i 0.170145i
550550 8.85824 7.66644i 0.377717 0.326898i
551551 10.2963i 0.438637i
552552 10.5829 13.3906i 0.450439 0.569940i
553553 −6.72244 −0.285867
554554 8.80174 + 28.3872i 0.373950 + 1.20606i
555555 6.98832i 0.296638i
556556 17.2956 11.8662i 0.733499 0.503238i
557557 1.26393i 0.0535543i −0.999641 0.0267771i 0.991476π-0.991476\pi
0.999641 0.0267771i 0.00852445π-0.00852445\pi
558558 0.962949 + 3.10568i 0.0407649 + 0.131474i
559559 4.78604i 0.202428i
560560 2.27723 5.90353i 0.0962306 0.249470i
561561 3.58899 1.57159i 0.151527 0.0663527i
562562 −7.42401 23.9438i −0.313163 1.01001i
563563 38.8614 1.63781 0.818906 0.573928i 0.194581π-0.194581\pi
0.818906 + 0.573928i 0.194581π0.194581\pi
564564 −12.2868 + 8.42968i −0.517366 + 0.354954i
565565 29.5780 1.24435
566566 −44.4578 + 13.7846i −1.86870 + 0.579409i
567567 −7.16738 −0.301002
568568 −25.3816 20.0597i −1.06499 0.841688i
569569 21.3750i 0.896085i −0.894012 0.448042i 0.852121π-0.852121\pi
0.894012 0.448042i 0.147879π-0.147879\pi
570570 −1.19071 3.84026i −0.0498735 0.160851i
571571 26.0093 1.08846 0.544228 0.838937i 0.316823π-0.316823\pi
0.544228 + 0.838937i 0.316823π0.316823\pi
572572 −14.7719 9.19419i −0.617644 0.384429i
573573 18.6873 0.780672
574574 −0.104997 0.338635i −0.00438250 0.0141343i
575575 9.57161i 0.399164i
576576 −0.962227 4.05170i −0.0400928 0.168821i
577577 11.9433 0.497206 0.248603 0.968605i 0.420029π-0.420029\pi
0.248603 + 0.968605i 0.420029π0.420029\pi
578578 −22.2029 + 6.88423i −0.923518 + 0.286346i
579579 −13.0514 −0.542399
580580 16.1461 + 23.5339i 0.670430 + 0.977191i
581581 1.20081 0.0498179
582582 8.14183 + 26.2588i 0.337490 + 1.08846i
583583 −27.6901 + 12.1253i −1.14681 + 0.502178i
584584 −0.594417 0.469783i −0.0245971 0.0194398i
585585 2.15996i 0.0893032i
586586 12.3470 + 39.8212i 0.510049 + 1.64500i
587587 16.6576i 0.687533i 0.939055 + 0.343767i 0.111703π0.111703\pi
−0.939055 + 0.343767i 0.888297π0.888297\pi
588588 1.78164 + 2.59684i 0.0734734 + 0.107092i
589589 5.04127i 0.207722i
590590 9.62583 + 31.0450i 0.396289 + 1.27810i
591591 29.9200 1.23074
592592 −4.03883 + 10.4703i −0.165995 + 0.430328i
593593 25.5783i 1.05037i 0.850987 + 0.525187i 0.176005π0.176005\pi
−0.850987 + 0.525187i 0.823995π0.823995\pi
594594 −17.0157 19.6608i −0.698161 0.806694i
595595 1.18676i 0.0486526i
596596 19.8918 + 28.9935i 0.814800 + 1.18762i
597597 −25.2130 −1.03190
598598 −13.5783 + 4.21008i −0.555256 + 0.172163i
599599 9.69854i 0.396272i 0.980175 + 0.198136i 0.0634887π0.0634887\pi
−0.980175 + 0.198136i 0.936511π0.936511\pi
600600 8.72732 + 6.89743i 0.356291 + 0.281586i
601601 23.1097i 0.942664i −0.881956 0.471332i 0.843773π-0.843773\pi
0.881956 0.471332i 0.156227π-0.156227\pi
602602 −2.46461 + 0.764178i −0.100450 + 0.0311456i
603603 4.16651i 0.169673i
604604 1.84624 1.26666i 0.0751224 0.0515398i
605605 11.8012 12.7873i 0.479787 0.519877i
606606 −39.4147 + 12.2209i −1.60111 + 0.496442i
607607 3.90145 0.158355 0.0791775 0.996861i 0.474771π-0.474771\pi
0.0791775 + 0.996861i 0.474771π0.474771\pi
608608 −0.435444 + 6.44188i −0.0176596 + 0.261253i
609609 −14.2047 −0.575602
610610 5.07393 + 16.3643i 0.205438 + 0.662573i
611611 12.4109 0.502090
612612 −0.441869 0.644051i −0.0178615 0.0260342i
613613 26.4674i 1.06901i 0.845165 + 0.534505i 0.179502π0.179502\pi
−0.845165 + 0.534505i 0.820498π0.820498\pi
614614 −30.5210 + 9.46336i −1.23173 + 0.381910i
615615 −0.624453 −0.0251804
616616 −2.37602 + 9.07494i −0.0957328 + 0.365640i
617617 3.74920 0.150937 0.0754685 0.997148i 0.475955π-0.475955\pi
0.0754685 + 0.997148i 0.475955π0.475955\pi
618618 7.32040 2.26976i 0.294469 0.0913033i
619619 1.06345i 0.0427436i 0.999772 + 0.0213718i 0.00680338π0.00680338\pi
−0.999772 + 0.0213718i 0.993197π0.993197\pi
620620 −7.90545 11.5227i −0.317491 0.462762i
621621 −21.2442 −0.852499
622622 3.39966 + 10.9645i 0.136314 + 0.439636i
623623 10.6509 0.426717
624624 5.94596 15.4144i 0.238029 0.617070i
625625 −6.27338 −0.250935
626626 30.1613 9.35181i 1.20549 0.373773i
627627 2.39098 + 5.46021i 0.0954867 + 0.218060i
628628 13.8334 9.49080i 0.552013 0.378724i
629629 2.10481i 0.0839243i
630630 −1.11229 + 0.344876i −0.0443146 + 0.0137402i
631631 45.3102i 1.80377i 0.431975 + 0.901885i 0.357817π0.357817\pi
−0.431975 + 0.901885i 0.642183π0.642183\pi
632632 11.7897 14.9175i 0.468970 0.593387i
633633 1.54337i 0.0613435i
634634 5.73855 1.77930i 0.227907 0.0706649i
635635 0.395312 0.0156875
636636 −16.2383 23.6682i −0.643889 0.938507i
637637 2.62307i 0.103930i
638638 −27.6894 31.9939i −1.09623 1.26665i
639639 5.95403i 0.235538i
640640 9.10653 + 15.4068i 0.359967 + 0.609009i
641641 −11.3560 −0.448535 −0.224268 0.974528i 0.571999π-0.571999\pi
−0.224268 + 0.974528i 0.571999π0.571999\pi
642642 8.97484 + 28.9455i 0.354209 + 1.14239i
643643 24.4202i 0.963040i 0.876435 + 0.481520i 0.159915π0.159915\pi
−0.876435 + 0.481520i 0.840085π0.840085\pi
644644 4.33603 + 6.32002i 0.170864 + 0.249044i
645645 4.54482i 0.178952i
646646 0.358630 + 1.15665i 0.0141101 + 0.0455077i
647647 41.2607i 1.62213i −0.584959 0.811063i 0.698890π-0.698890\pi
0.584959 0.811063i 0.301110π-0.301110\pi
648648 12.5700 15.9049i 0.493798 0.624802i
649649 −19.3289 44.1408i −0.758727 1.73268i
650650 −2.74393 8.84965i −0.107626 0.347112i
651651 6.95489 0.272584
652652 4.89307 + 7.13194i 0.191627 + 0.279308i
653653 −39.0128 −1.52669 −0.763345 0.645991i 0.776444π-0.776444\pi
−0.763345 + 0.645991i 0.776444π0.776444\pi
654654 −10.4271 + 3.23303i −0.407732 + 0.126421i
655655 −26.8488 −1.04907
656656 0.935595 + 0.360897i 0.0365288 + 0.0140907i
657657 0.139439i 0.00544002i
658658 −1.98162 6.39109i −0.0772517 0.249151i
659659 19.6952 0.767217 0.383609 0.923496i 0.374681π-0.374681\pi
0.383609 + 0.923496i 0.374681π0.374681\pi
660660 14.0274 + 8.73080i 0.546016 + 0.339846i
661661 2.52788 0.0983233 0.0491616 0.998791i 0.484345π-0.484345\pi
0.0491616 + 0.998791i 0.484345π0.484345\pi
662662 0.0603703 + 0.194705i 0.00234636 + 0.00756743i
663663 3.09870i 0.120343i
664664 −2.10596 + 2.66467i −0.0817271 + 0.103409i
665665 1.80551 0.0700148
666666 1.97272 0.611663i 0.0764415 0.0237015i
667667 −34.5704 −1.33857
668668 −35.0632 + 24.0561i −1.35664 + 0.930759i
669669 12.4480 0.481268
670670 5.30289 + 17.1028i 0.204868 + 0.660737i
671671 −10.1886 23.2673i −0.393326 0.898226i
672672 −8.88716 0.600735i −0.342829 0.0231738i
673673 46.2104i 1.78128i −0.454708 0.890640i 0.650256π-0.650256\pi
0.454708 0.890640i 0.349744π-0.349744\pi
674674 −11.9762 38.6253i −0.461305 1.48779i
675675 13.8459i 0.532930i
676676 10.0921 6.92399i 0.388159 0.266307i
677677 21.2646i 0.817263i 0.912699 + 0.408632i 0.133994π0.133994\pi
−0.912699 + 0.408632i 0.866006π0.866006\pi
678678 −12.3311 39.7700i −0.473573 1.52736i
679679 −12.3457 −0.473784
680680 2.63350 + 2.08133i 0.100990 + 0.0798152i
681681 14.0350i 0.537822i
682682 13.5573 + 15.6649i 0.519136 + 0.599839i
683683 5.77734i 0.221064i 0.993873 + 0.110532i 0.0352555π0.0352555\pi
−0.993873 + 0.110532i 0.964745π0.964745\pi
684684 0.979844 0.672249i 0.0374653 0.0257041i
685685 13.3710 0.510879
686686 −1.35077 + 0.418821i −0.0515728 + 0.0159907i
687687 31.5793i 1.20482i
688688 2.62664 6.80933i 0.100140 0.259603i
689689 23.9073i 0.910797i
690690 12.8939 3.99789i 0.490863 0.152197i
691691 45.1630i 1.71808i −0.511907 0.859041i 0.671061π-0.671061\pi
0.511907 0.859041i 0.328939π-0.328939\pi
692692 −2.72762 3.97566i −0.103688 0.151132i
693693 1.58149 0.692521i 0.0600757 0.0263067i
694694 31.0723 9.63429i 1.17949 0.365713i
695695 16.5899 0.629289
696696 24.9119 31.5210i 0.944283 1.19480i
697697 0.188079 0.00712400
698698 −9.95914 32.1200i −0.376959 1.21576i
699699 −11.7825 −0.445656
700700 −4.11909 + 2.82602i −0.155687 + 0.106813i
701701 4.89016i 0.184699i 0.995727 + 0.0923494i 0.0294377π0.0294377\pi
−0.995727 + 0.0923494i 0.970562π0.970562\pi
702702 −19.6418 + 6.09014i −0.741331 + 0.229857i
703703 −3.20221 −0.120774
704704 −15.9708 21.1880i −0.601923 0.798554i
705705 −11.7854 −0.443863
706706 1.74408 0.540769i 0.0656392 0.0203521i
707707 18.5310i 0.696929i
708708 37.7296 25.8854i 1.41796 0.972834i
709709 15.6950 0.589436 0.294718 0.955584i 0.404774π-0.404774\pi
0.294718 + 0.955584i 0.404774π0.404774\pi
710710 −7.57793 24.4402i −0.284395 0.917224i
711711 −3.49936 −0.131236
712712 −18.6793 + 23.6349i −0.700036 + 0.885756i
713713 16.9264 0.633898
714714 −1.59570 + 0.494763i −0.0597176 + 0.0185160i
715715 −5.52020 12.6063i −0.206444 0.471448i
716716 14.1644 + 20.6455i 0.529349 + 0.771558i
717717 22.3971i 0.836435i
718718 −34.0550 + 10.5591i −1.27092 + 0.394062i
719719 11.7761i 0.439176i 0.975593 + 0.219588i 0.0704713π0.0704713\pi
−0.975593 + 0.219588i 0.929529π0.929529\pi
720720 1.18541 3.07308i 0.0441777 0.114527i
721721 3.44171i 0.128176i
722722 23.9050 7.41199i 0.889652 0.275846i
723723 21.6381 0.804731
724724 −40.6852 + 27.9133i −1.51206 + 1.03739i
725725 22.5313i 0.836792i
726726 −22.1135 10.5367i −0.820708 0.391052i
727727 10.6509i 0.395019i −0.980301 0.197509i 0.936715π-0.936715\pi
0.980301 0.197509i 0.0632853π-0.0632853\pi
728728 5.82076 + 4.60030i 0.215732 + 0.170499i
729729 −29.9181 −1.10808
730730 −0.177469 0.572370i −0.00656843 0.0211844i
731731 1.36885i 0.0506289i
732732 19.8879 13.6446i 0.735077 0.504320i
733733 27.9850i 1.03365i −0.856091 0.516824i 0.827114π-0.827114\pi
0.856091 0.516824i 0.172886π-0.172886\pi
734734 −0.461871 1.48962i −0.0170480 0.0549828i
735735 2.49087i 0.0918771i
736736 −21.6290 1.46203i −0.797255 0.0538911i
737737 −10.6483 24.3173i −0.392237 0.895738i
738738 −0.0546562 0.176276i −0.00201192 0.00648881i
739739 25.9409 0.954252 0.477126 0.878835i 0.341679π-0.341679\pi
0.477126 + 0.878835i 0.341679π0.341679\pi
740740 −7.31918 + 5.02153i −0.269058 + 0.184595i
741741 4.71428 0.173183
742742 12.3113 3.81724i 0.451961 0.140135i
743743 12.3792 0.454147 0.227074 0.973878i 0.427084π-0.427084\pi
0.227074 + 0.973878i 0.427084π0.427084\pi
744744 −12.1974 + 15.4333i −0.447178 + 0.565814i
745745 27.8103i 1.01889i
746746 −8.03934 25.9283i −0.294341 0.949304i
747747 0.625080 0.0228705
748748 −4.22491 2.62963i −0.154478 0.0961487i
749749 −13.6088 −0.497255
750750 7.82177 + 25.2266i 0.285611 + 0.921146i
751751 11.2531i 0.410632i 0.978696 + 0.205316i 0.0658223π0.0658223\pi
−0.978696 + 0.205316i 0.934178π0.934178\pi
752752 17.6576 + 6.81124i 0.643905 + 0.248380i
753753 37.2589 1.35779
754754 −31.9629 + 9.91042i −1.16402 + 0.360916i
755755 1.77090 0.0644495
756756 6.27234 + 9.14230i 0.228123 + 0.332502i
757757 −23.9144 −0.869184 −0.434592 0.900627i 0.643107π-0.643107\pi
−0.434592 + 0.900627i 0.643107π0.643107\pi
758758 3.18750 + 10.2803i 0.115775 + 0.373396i
759759 −18.3330 + 8.02787i −0.665445 + 0.291393i
760760 −3.16648 + 4.00655i −0.114860 + 0.145333i
761761 43.0293i 1.55981i 0.625897 + 0.779905i 0.284733π0.284733\pi
−0.625897 + 0.779905i 0.715267π0.715267\pi
762762 −0.164806 0.531529i −0.00597029 0.0192553i
763763 4.90234i 0.177477i
764764 −13.4279 19.5720i −0.485806 0.708091i
765765 0.617769i 0.0223355i
766766 −9.25114 29.8366i −0.334257 1.07804i
767767 −38.1107 −1.37610
768768 16.9192 18.6676i 0.610520 0.673609i
769769 43.5881i 1.57183i 0.618337 + 0.785913i 0.287807π0.287807\pi
−0.618337 + 0.785913i 0.712193π0.712193\pi
770770 −5.61031 + 4.85550i −0.202182 + 0.174980i
771771 21.5312i 0.775429i
772772 9.37824 + 13.6693i 0.337530 + 0.491970i
773773 −34.7584 −1.25017 −0.625087 0.780555i 0.714937π-0.714937\pi
−0.625087 + 0.780555i 0.714937π0.714937\pi
774774 −1.28295 + 0.397792i −0.0461148 + 0.0142984i
775775 11.0318i 0.396274i
776776 21.6517 27.3959i 0.777250 0.983454i
777777 4.41773i 0.158485i
778778 36.7291 11.3882i 1.31680 0.408288i
779779 0.286139i 0.0102520i
780780 10.7753 7.39269i 0.385817 0.264701i
781781 15.2167 + 34.7498i 0.544496 + 1.24345i
782782 −3.88351 + 1.20412i −0.138874 + 0.0430594i
783783 −50.0082 −1.78715
784784 1.43957 3.73197i 0.0514134 0.133285i
785785 13.2689 0.473587
786786 11.1933 + 36.1004i 0.399252 + 1.28766i
787787 2.81410 0.100312 0.0501560 0.998741i 0.484028π-0.484028\pi
0.0501560 + 0.998741i 0.484028π0.484028\pi
788788 −21.4993 31.3365i −0.765881 1.11632i
789789 2.43609i 0.0867273i
790790 14.3642 4.45378i 0.511057 0.158458i
791791 18.6980 0.664824
792792 −1.23684 + 4.72395i −0.0439491 + 0.167858i
793793 −20.0888 −0.713373
794794 −18.4733 + 5.72784i −0.655593 + 0.203273i
795795 22.7024i 0.805171i
796796 18.1171 + 26.4067i 0.642142 + 0.935961i
797797 43.2960 1.53362 0.766811 0.641872i 0.221842π-0.221842\pi
0.766811 + 0.641872i 0.221842π0.221842\pi
798798 −0.752721 2.42766i −0.0266460 0.0859382i
799799 3.54963 0.125577
800800 0.952881 14.0967i 0.0336894 0.498395i
801801 5.54429 0.195898
802802 −5.10467 + 1.58275i −0.180252 + 0.0558890i
803803 0.356363 + 0.813814i 0.0125758 + 0.0287189i
804804 20.7853 14.2603i 0.733040 0.502923i
805805 6.06212i 0.213662i
806806 15.6497 4.85234i 0.551236 0.170917i
807807 17.5000i 0.616029i
808808 41.1214 + 32.4993i 1.44665 + 1.14332i
809809 3.65797i 0.128607i −0.997930 0.0643037i 0.979517π-0.979517\pi
0.997930 0.0643037i 0.0204826π-0.0204826\pi
810810 15.3150 4.74856i 0.538113 0.166847i
811811 43.8841 1.54098 0.770489 0.637453i 0.220012π-0.220012\pi
0.770489 + 0.637453i 0.220012π0.220012\pi
812812 10.2069 + 14.8772i 0.358192 + 0.522087i
813813 19.6288i 0.688411i
814814 9.95030 8.61157i 0.348758 0.301835i
815815 6.84090i 0.239626i
816816 1.70060 4.40867i 0.0595330 0.154334i
817817 2.08254 0.0728589
818818 −12.0767 38.9495i −0.422252 1.36184i
819819 1.36544i 0.0477123i
820820 0.448707 + 0.654018i 0.0156695 + 0.0228393i
821821 4.70257i 0.164121i −0.996627 0.0820604i 0.973850π-0.973850\pi
0.996627 0.0820604i 0.0261500π-0.0261500\pi
822822 −5.57438 17.9784i −0.194429 0.627068i
823823 27.6445i 0.963627i 0.876274 + 0.481814i 0.160022π0.160022\pi
−0.876274 + 0.481814i 0.839978π0.839978\pi
824824 −7.63737 6.03602i −0.266060 0.210275i
825825 −5.23218 11.9485i −0.182161 0.415995i
826826 6.08506 + 19.6254i 0.211726 + 0.682856i
827827 38.9620 1.35484 0.677422 0.735595i 0.263097π-0.263097\pi
0.677422 + 0.735595i 0.263097π0.263097\pi
828828 2.25712 + 3.28988i 0.0784403 + 0.114331i
829829 45.2248 1.57072 0.785361 0.619038i 0.212478π-0.212478\pi
0.785361 + 0.619038i 0.212478π0.212478\pi
830830 −2.56584 + 0.795565i −0.0890616 + 0.0276145i
831831 33.0916 1.14793
832832 −20.4167 + 4.84871i −0.707823 + 0.168099i
833833 0.750224i 0.0259937i
834834 −6.91633 22.3064i −0.239493 0.772408i
835835 −33.6324 −1.16390
836836 4.00065 6.42767i 0.138365 0.222306i
837837 24.4850 0.846327
838838 −8.68940 28.0249i −0.300170 0.968104i
839839 49.5274i 1.70987i 0.518732 + 0.854937i 0.326404π0.326404\pi
−0.518732 + 0.854937i 0.673596π0.673596\pi
840840 −5.52739 4.36845i −0.190713 0.150726i
841841 −52.3778 −1.80613
842842 −30.0376 + 9.31345i −1.03516 + 0.320963i
843843 −27.9118 −0.961333
844844 1.61644 1.10901i 0.0556402 0.0381735i
845845 9.68029 0.333012
846846 −1.03153 3.32688i −0.0354648 0.114380i
847847 7.46025 8.08361i 0.256337 0.277756i
848848 −13.1206 + 34.0141i −0.450565 + 1.16805i
849849 51.8254i 1.77864i
850850 −0.784790 2.53109i −0.0269181 0.0868156i
851851 10.7516i 0.368560i
852852 −29.7026 + 20.3783i −1.01759 + 0.698149i
853853 6.05040i 0.207162i 0.994621 + 0.103581i 0.0330301π0.0330301\pi
−0.994621 + 0.103581i 0.966970π0.966970\pi
854854 3.20754 + 10.3449i 0.109760 + 0.353995i
855855 0.939858 0.0321425
856856 23.8669 30.1988i 0.815755 1.03217i
857857 54.7756i 1.87110i −0.353198 0.935549i 0.614906π-0.614906\pi
0.353198 0.935549i 0.385094π-0.385094\pi
858858 −14.6488 + 12.6779i −0.500102 + 0.432818i
859859 13.9017i 0.474318i −0.971471 0.237159i 0.923784π-0.923784\pi
0.971471 0.237159i 0.0762163π-0.0762163\pi
860860 4.76000 3.26573i 0.162315 0.111360i
861861 −0.394754 −0.0134532
862862 16.7085 5.18065i 0.569095 0.176454i
863863 55.7602i 1.89810i 0.315128 + 0.949049i 0.397953π0.397953\pi
−0.315128 + 0.949049i 0.602047π0.602047\pi
864864 −31.2877 2.11492i −1.06443 0.0719509i
865865 3.81342i 0.129660i
866866 −19.3471 + 5.99876i −0.657441 + 0.203846i
867867 25.8824i 0.879013i
868868 −4.99751 7.28417i −0.169627 0.247241i
869869 −20.4235 + 8.94331i −0.692821 + 0.303381i
870870 30.3519 9.41093i 1.02903 0.319060i
871871 −20.9953 −0.711397
872872 10.8786 + 8.59764i 0.368396 + 0.291153i
873873 −6.42654 −0.217505
874874 −1.83192 5.90828i −0.0619657 0.199851i
875875 −11.8604 −0.400954
876876 −0.695611 + 0.477244i −0.0235025 + 0.0161246i
877877 11.2468i 0.379777i −0.981806 0.189888i 0.939187π-0.939187\pi
0.981806 0.189888i 0.0608126π-0.0608126\pi
878878 8.55297 2.65193i 0.288649 0.0894985i
879879 46.4205 1.56573
880880 −0.935373 20.9651i −0.0315314 0.706734i
881881 15.3650 0.517662 0.258831 0.965923i 0.416663π-0.416663\pi
0.258831 + 0.965923i 0.416663π0.416663\pi
882882 −0.703144 + 0.218017i −0.0236761 + 0.00734102i
883883 20.8359i 0.701183i −0.936528 0.350592i 0.885981π-0.885981\pi
0.936528 0.350592i 0.114019π-0.114019\pi
884884 −3.24540 + 2.22660i −0.109155 + 0.0748887i
885885 36.1899 1.21651
886886 10.7363 + 34.6264i 0.360692 + 1.16330i
887887 14.5362 0.488079 0.244039 0.969765i 0.421527π-0.421527\pi
0.244039 + 0.969765i 0.421527π0.421527\pi
888888 9.80323 + 7.74775i 0.328975 + 0.259998i
889889 0.249900 0.00838139
890890 −22.7583 + 7.05645i −0.762860 + 0.236533i
891891 −21.7753 + 9.53524i −0.729500 + 0.319443i
892892 −8.94465 13.0374i −0.299489 0.436523i
893893 5.40032i 0.180715i
894894 37.3932 11.5942i 1.25062 0.387767i
895895 19.8030i 0.661941i
896896 5.75678 + 9.73958i 0.192321 + 0.325377i
897897 15.8285i 0.528498i
898898 −6.12586 + 1.89939i −0.204423 + 0.0633834i
899899 39.8443 1.32888
900900 −2.14419 + 1.47108i −0.0714729 + 0.0490360i
901901 6.83773i 0.227798i
902902 −0.769502 0.889126i −0.0256216 0.0296047i
903903 2.87305i 0.0956093i
904904 −32.7923 + 41.4920i −1.09065 + 1.38000i
905905 −39.0250 −1.29723
906906 −0.738289 2.38112i −0.0245280 0.0791073i
907907 53.5839i 1.77922i 0.456718 + 0.889611i 0.349025π0.349025\pi
−0.456718 + 0.889611i 0.650975π0.650975\pi
908908 −14.6995 + 10.0850i −0.487819 + 0.334682i
909909 9.64629i 0.319947i
910910 1.73785 + 5.60487i 0.0576091 + 0.185800i
911911 31.4308i 1.04135i 0.853755 + 0.520675i 0.174320π0.174320\pi
−0.853755 + 0.520675i 0.825680π0.825680\pi
912912 6.70724 + 2.58726i 0.222099 + 0.0856726i
913913 3.64819 1.59752i 0.120738 0.0528701i
914914 7.40383 + 23.8787i 0.244897 + 0.789837i
915915 19.0763 0.630643
916916 −33.0744 + 22.6916i −1.09281 + 0.749752i
917917 −16.9727 −0.560489
918918 −5.61774 + 1.74184i −0.185413 + 0.0574892i
919919 40.2618 1.32811 0.664057 0.747682i 0.268833π-0.268833\pi
0.664057 + 0.747682i 0.268833π0.268833\pi
920920 −13.4522 10.6316i −0.443507 0.350515i
921921 35.5791i 1.17237i
922922 −14.2390 45.9232i −0.468935 1.51240i
923923 30.0026 0.987549
924924 8.86756 + 5.51926i 0.291721 + 0.181570i
925925 7.00738 0.230401
926926 −0.840921 2.71212i −0.0276344 0.0891258i
927927 1.79158i 0.0588432i
928928 −50.9141 3.44158i −1.67134 0.112975i
929929 −7.61834 −0.249950 −0.124975 0.992160i 0.539885π-0.539885\pi
−0.124975 + 0.992160i 0.539885π0.539885\pi
930930 −14.8609 + 4.60778i −0.487309 + 0.151095i
931931 1.14137 0.0374070
932932 8.46646 + 12.3404i 0.277328 + 0.404222i
933933 12.7816 0.418450
934934 12.0036 + 38.7139i 0.392771 + 1.26676i
935935 −1.57883 3.60552i −0.0516333 0.117913i
936936 3.02999 + 2.39468i 0.0990385 + 0.0782727i
937937 2.79736i 0.0913858i 0.998956 + 0.0456929i 0.0145496π0.0145496\pi
−0.998956 + 0.0456929i 0.985450π0.985450\pi
938938 3.35227 + 10.8117i 0.109456 + 0.353014i
939939 35.1597i 1.14739i
940940 8.46850 + 12.3433i 0.276212 + 0.402595i
941941 32.7923i 1.06900i 0.845169 + 0.534499i 0.179500π0.179500\pi
−0.845169 + 0.534499i 0.820500π0.820500\pi
942942 −5.53182 17.8411i −0.180236 0.581295i
943943 −0.960728 −0.0312856
944944 −54.2219 20.9156i −1.76477 0.680745i
945945 8.76923i 0.285263i
946946 −6.47113 + 5.60050i −0.210395 + 0.182088i
947947 7.15816i 0.232609i −0.993214 0.116305i 0.962895π-0.962895\pi
0.993214 0.116305i 0.0371049π-0.0371049\pi
948948 −11.9769 17.4571i −0.388993 0.566981i
949949 0.702638 0.0228086
950950 3.85073 1.19396i 0.124934 0.0387372i
951951 6.68956i 0.216924i
952952 1.66480 + 1.31573i 0.0539563 + 0.0426431i
953953 38.2832i 1.24011i 0.784557 + 0.620057i 0.212891π0.212891\pi
−0.784557 + 0.620057i 0.787109π0.787109\pi
954954 6.40863 1.98706i 0.207487 0.0643335i
955955 18.7733i 0.607491i
956956 −23.4575 + 16.0937i −0.758669 + 0.520506i
957957 −43.1553 + 18.8974i −1.39501 + 0.610866i
958958 −26.6899 + 8.27548i −0.862312 + 0.267369i
959959 8.45260 0.272949
960960 19.3877 4.60433i 0.625736 0.148604i
961961 11.4914 0.370691
962962 −3.08220 9.94065i −0.0993741 0.320499i
963963 −7.08406 −0.228281
964964 −15.5483 22.6626i −0.500778 0.729913i
965965 13.1115i 0.422075i
966966 8.15101 2.52730i 0.262255 0.0813147i
967967 60.3137 1.93956 0.969778 0.243988i 0.0784559π-0.0784559\pi
0.969778 + 0.243988i 0.0784559π0.0784559\pi
968968 4.85437 + 30.7317i 0.156025 + 0.987753i
969969 1.34833 0.0433146
970970 26.3798 8.17932i 0.847003 0.262622i
971971 7.52865i 0.241606i 0.992676 + 0.120803i 0.0385469π0.0385469\pi
−0.992676 + 0.120803i 0.961453π0.961453\pi
972972 6.04735 + 8.81437i 0.193969 + 0.282721i
973973 10.4874 0.336212
974974 6.43955 + 20.7687i 0.206337 + 0.665473i
975975 −10.3162 −0.330384
976976 −28.5813 11.0250i −0.914864 0.352900i
977977 36.8738 1.17970 0.589849 0.807513i 0.299187π-0.299187\pi
0.589849 + 0.807513i 0.299187π0.299187\pi
978978 9.19815 2.85198i 0.294125 0.0911963i
979979 32.3585 14.1695i 1.03418 0.452861i
980980 2.60880 1.78984i 0.0833350 0.0571743i
981981 2.55191i 0.0814762i
982982 14.8618 4.60805i 0.474258 0.147049i
983983 5.97352i 0.190526i 0.995452 + 0.0952628i 0.0303691π0.0303691\pi
−0.995452 + 0.0952628i 0.969631π0.969631\pi
984984 0.692314 0.875985i 0.0220702 0.0279254i
985985 30.0577i 0.957719i
986986 −9.14169 + 2.83448i −0.291131 + 0.0902681i
987987 −7.45024 −0.237144
988988 −3.38750 4.93748i −0.107771 0.157082i
989989 6.99226i 0.222341i
990990 −2.92044 + 2.52752i −0.0928178 + 0.0803300i
991991 17.3869i 0.552312i 0.961113 + 0.276156i 0.0890606π0.0890606\pi
−0.961113 + 0.276156i 0.910939π0.910939\pi
992992 24.9286 + 1.68507i 0.791484 + 0.0535010i
993993 0.226972 0.00720274
994994 −4.79046 15.4501i −0.151944 0.490048i
995995 25.3291i 0.802987i
996996 2.13940 + 3.11831i 0.0677896 + 0.0988074i
997997 39.6637i 1.25616i −0.778148 0.628081i 0.783841π-0.783841\pi
0.778148 0.628081i 0.216159π-0.216159\pi
998998 0.967713 + 3.12105i 0.0306324 + 0.0987950i
999999 15.5529i 0.492071i
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 308.2.d.a.43.4 yes 18
4.3 odd 2 308.2.d.b.43.16 yes 18
11.10 odd 2 308.2.d.b.43.15 yes 18
44.43 even 2 inner 308.2.d.a.43.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
308.2.d.a.43.3 18 44.43 even 2 inner
308.2.d.a.43.4 yes 18 1.1 even 1 trivial
308.2.d.b.43.15 yes 18 11.10 odd 2
308.2.d.b.43.16 yes 18 4.3 odd 2