Properties

Label 961.2.g.p.816.2
Level 961961
Weight 22
Character 961.816
Analytic conductor 7.6747.674
Analytic rank 00
Dimension 1616
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [961,2,Mod(235,961)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(961, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("961.235");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 961=312 961 = 31^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 961.g (of order 1515, degree 88, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.673623634257.67362363425
Analytic rank: 00
Dimension: 1616
Relative dimension: 22 over Q(ζ15)\Q(\zeta_{15})
Coefficient field: 16.0.26873856000000000000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x162x14+8x1016x8+32x6128x2+256 x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Embedding invariants

Embedding label 816.2
Root 0.147826+1.40647i0.147826 + 1.40647i of defining polynomial
Character χ\chi == 961.816
Dual form 961.2.g.p.338.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.3090170.224514i)q2+(0.239187+2.27571i)q3+(0.5729491.76336i)q4+(1.11803+1.93649i)q5+(0.4370160.756934i)q6+(0.978148+0.207912i)q7+(0.454915+1.40008i)q8+(2.18720+0.464905i)q9+(0.08927800.849423i)q10+(2.83888+3.15290i)q11+(3.875851.72564i)q12+(6.271252.79214i)q13+(0.2555850.283856i)q14+(4.13948+3.00750i)q15+(2.54508+1.84911i)q16+(0.3614520.401433i)q17+(0.780261+0.347395i)q18+(0.9135450.406737i)q19+(2.774153.08100i)q20+(0.239187+2.27571i)q21+(1.585130.336930i)q22+(2.12132+6.52875i)q23+(3.295000.700373i)q24+(1.31105+2.27080i)q26+(0.540182+1.66251i)q27+(0.1938061.84395i)q28+(2.995352.17625i)q29+1.95440q30+4.14590q32+(7.854105.70634i)q33+(0.0215675+0.205201i)q34+(0.690983+2.12663i)q35+(2.07295+3.59045i)q36+(2.121323.67423i)q37+(0.3736190.0794152i)q38+(4.8541014.9394i)q39+(3.21986+0.684403i)q40+(0.781051+7.43120i)q41+(0.5848420.649532i)q42+(0.1884930.0839224i)q43+(7.18621+3.19951i)q44+(3.345653.71572i)q45+(2.121321.54123i)q46+(3.00000+2.17963i)q47+(4.816805.34959i)q48+(5.481272.44042i)q49+(0.8270910.918578i)q51+(1.33043+12.6582i)q52+(5.129591.09033i)q53+(0.2063310.635021i)q54+(9.279521.97242i)q55+(0.736068+1.27491i)q56+(1.14412+1.98168i)q57+(0.437016+1.34500i)q58+(0.621346+5.91171i)q59+(7.67501+5.57622i)q604.44897q612.23607q63+(3.80902+2.76741i)q64+(1.6045115.2659i)q65+(1.14590+3.52671i)q66+(3.000005.19615i)q67+(0.500776+0.867369i)q68+(15.36493.26592i)q69+(0.2639320.812299i)q70+(7.30885+1.55354i)q71+(0.3440863.27376i)q72+(2.83888+3.15290i)q73+(1.48044+0.659135i)q74+(1.240641.37787i)q76+(3.43237+2.49376i)q77+(4.85410+3.52671i)q78+(7.43229+8.25439i)q79+(6.426282.86117i)q80+(9.78243+4.35542i)q81+(1.909772.12101i)q82+(0.3305483.14495i)q83+(4.149930.882095i)q84+(0.3732561.14876i)q85+(0.07708920.0163858i)q86+(4.236077.33708i)q87+(3.122875.40897i)q88+(1.81182+5.57622i)q89+(0.199632+1.89937i)q90+(5.553694.03499i)q91+12.7279q92+1.41641q94+(1.80902+1.31433i)q95+(0.991644+9.43486i)q96+(2.163126.65740i)q97+(1.14590+1.98475i)q98+(4.743428.21584i)q99+O(q100)q+(-0.309017 - 0.224514i) q^{2} +(0.239187 + 2.27571i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(1.11803 + 1.93649i) q^{5} +(0.437016 - 0.756934i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-2.18720 + 0.464905i) q^{9} +(0.0892780 - 0.849423i) q^{10} +(-2.83888 + 3.15290i) q^{11} +(3.87585 - 1.72564i) q^{12} +(-6.27125 - 2.79214i) q^{13} +(-0.255585 - 0.283856i) q^{14} +(-4.13948 + 3.00750i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(-0.361452 - 0.401433i) q^{17} +(0.780261 + 0.347395i) q^{18} +(0.913545 - 0.406737i) q^{19} +(2.77415 - 3.08100i) q^{20} +(-0.239187 + 2.27571i) q^{21} +(1.58513 - 0.336930i) q^{22} +(-2.12132 + 6.52875i) q^{23} +(-3.29500 - 0.700373i) q^{24} +(1.31105 + 2.27080i) q^{26} +(0.540182 + 1.66251i) q^{27} +(-0.193806 - 1.84395i) q^{28} +(-2.99535 - 2.17625i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(-7.85410 - 5.70634i) q^{33} +(0.0215675 + 0.205201i) q^{34} +(0.690983 + 2.12663i) q^{35} +(2.07295 + 3.59045i) q^{36} +(2.12132 - 3.67423i) q^{37} +(-0.373619 - 0.0794152i) q^{38} +(4.85410 - 14.9394i) q^{39} +(-3.21986 + 0.684403i) q^{40} +(-0.781051 + 7.43120i) q^{41} +(0.584842 - 0.649532i) q^{42} +(0.188493 - 0.0839224i) q^{43} +(7.18621 + 3.19951i) q^{44} +(-3.34565 - 3.71572i) q^{45} +(2.12132 - 1.54123i) q^{46} +(-3.00000 + 2.17963i) q^{47} +(-4.81680 - 5.34959i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(0.827091 - 0.918578i) q^{51} +(-1.33043 + 12.6582i) q^{52} +(5.12959 - 1.09033i) q^{53} +(0.206331 - 0.635021i) q^{54} +(-9.27952 - 1.97242i) q^{55} +(-0.736068 + 1.27491i) q^{56} +(1.14412 + 1.98168i) q^{57} +(0.437016 + 1.34500i) q^{58} +(0.621346 + 5.91171i) q^{59} +(7.67501 + 5.57622i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(3.80902 + 2.76741i) q^{64} +(-1.60451 - 15.2659i) q^{65} +(1.14590 + 3.52671i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-0.500776 + 0.867369i) q^{68} +(-15.3649 - 3.26592i) q^{69} +(0.263932 - 0.812299i) q^{70} +(-7.30885 + 1.55354i) q^{71} +(0.344086 - 3.27376i) q^{72} +(-2.83888 + 3.15290i) q^{73} +(-1.48044 + 0.659135i) q^{74} +(-1.24064 - 1.37787i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(7.43229 + 8.25439i) q^{79} +(-6.42628 - 2.86117i) q^{80} +(-9.78243 + 4.35542i) q^{81} +(1.90977 - 2.12101i) q^{82} +(0.330548 - 3.14495i) q^{83} +(4.14993 - 0.882095i) q^{84} +(0.373256 - 1.14876i) q^{85} +(-0.0770892 - 0.0163858i) q^{86} +(4.23607 - 7.33708i) q^{87} +(-3.12287 - 5.40897i) q^{88} +(1.81182 + 5.57622i) q^{89} +(0.199632 + 1.89937i) q^{90} +(-5.55369 - 4.03499i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(1.80902 + 1.31433i) q^{95} +(0.991644 + 9.43486i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(1.14590 + 1.98475i) q^{98} +(4.74342 - 8.21584i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+4q236q42q752q810q910q108q14+4q16+10q18+2q19+30q20+12q28+120q3272q33+20q35+60q36+8q38+24q39++72q98+O(q100) 16 q + 4 q^{2} - 36 q^{4} - 2 q^{7} - 52 q^{8} - 10 q^{9} - 10 q^{10} - 8 q^{14} + 4 q^{16} + 10 q^{18} + 2 q^{19} + 30 q^{20} + 12 q^{28} + 120 q^{32} - 72 q^{33} + 20 q^{35} + 60 q^{36} + 8 q^{38} + 24 q^{39}+ \cdots + 72 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/961Z)×\left(\mathbb{Z}/961\mathbb{Z}\right)^\times.

nn 33
χ(n)\chi(n) e(715)e\left(\frac{7}{15}\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 −0.309017 0.224514i −0.218508 0.158755i 0.473147 0.880984i 0.343118π-0.343118\pi
−0.691655 + 0.722228i 0.743118π0.743118\pi
33 0.239187 + 2.27571i 0.138095 + 1.31388i 0.815708 + 0.578464i 0.196348π0.196348\pi
−0.677614 + 0.735418i 0.736986π0.736986\pi
44 −0.572949 1.76336i −0.286475 0.881678i
55 1.11803 + 1.93649i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
66 0.437016 0.756934i 0.178411 0.309017i
77 0.978148 + 0.207912i 0.369705 + 0.0785832i 0.389018 0.921230i 0.372814π-0.372814\pi
−0.0193127 + 0.999813i 0.506148π0.506148\pi
88 −0.454915 + 1.40008i −0.160837 + 0.495005i
99 −2.18720 + 0.464905i −0.729068 + 0.154968i
1010 0.0892780 0.849423i 0.0282322 0.268611i
1111 −2.83888 + 3.15290i −0.855955 + 0.950634i −0.999237 0.0390478i 0.987568π-0.987568\pi
0.143283 + 0.989682i 0.454234π0.454234\pi
1212 3.87585 1.72564i 1.11886 0.498149i
1313 −6.27125 2.79214i −1.73933 0.774400i −0.994208 0.107474i 0.965724π-0.965724\pi
−0.745124 0.666926i 0.767610π-0.767610\pi
1414 −0.255585 0.283856i −0.0683080 0.0758637i
1515 −4.13948 + 3.00750i −1.06881 + 0.776534i
1616 −2.54508 + 1.84911i −0.636271 + 0.462278i
1717 −0.361452 0.401433i −0.0876650 0.0973618i 0.697716 0.716374i 0.254200π-0.254200\pi
−0.785381 + 0.619012i 0.787533π0.787533\pi
1818 0.780261 + 0.347395i 0.183909 + 0.0818817i
1919 0.913545 0.406737i 0.209582 0.0933118i −0.299261 0.954171i 0.596740π-0.596740\pi
0.508843 + 0.860859i 0.330073π0.330073\pi
2020 2.77415 3.08100i 0.620318 0.688933i
2121 −0.239187 + 2.27571i −0.0521948 + 0.496601i
2222 1.58513 0.336930i 0.337951 0.0718338i
2323 −2.12132 + 6.52875i −0.442326 + 1.36134i 0.443064 + 0.896490i 0.353891π0.353891\pi
−0.885390 + 0.464849i 0.846109π0.846109\pi
2424 −3.29500 0.700373i −0.672588 0.142963i
2525 0 0
2626 1.31105 + 2.27080i 0.257118 + 0.445341i
2727 0.540182 + 1.66251i 0.103958 + 0.319950i
2828 −0.193806 1.84395i −0.0366260 0.348473i
2929 −2.99535 2.17625i −0.556223 0.404120i 0.273852 0.961772i 0.411702π-0.411702\pi
−0.830075 + 0.557652i 0.811702π0.811702\pi
3030 1.95440 0.356822
3131 0 0
3232 4.14590 0.732898
3333 −7.85410 5.70634i −1.36722 0.993346i
3434 0.0215675 + 0.205201i 0.00369879 + 0.0351916i
3535 0.690983 + 2.12663i 0.116797 + 0.359466i
3636 2.07295 + 3.59045i 0.345492 + 0.598409i
3737 2.12132 3.67423i 0.348743 0.604040i −0.637284 0.770629i 0.719942π-0.719942\pi
0.986026 + 0.166589i 0.0532753π0.0532753\pi
3838 −0.373619 0.0794152i −0.0606090 0.0128828i
3939 4.85410 14.9394i 0.777278 2.39222i
4040 −3.21986 + 0.684403i −0.509105 + 0.108214i
4141 −0.781051 + 7.43120i −0.121980 + 1.16056i 0.746692 + 0.665170i 0.231641π0.231641\pi
−0.868671 + 0.495389i 0.835026π0.835026\pi
4242 0.584842 0.649532i 0.0902430 0.100225i
4343 0.188493 0.0839224i 0.0287449 0.0127980i −0.392314 0.919831i 0.628325π-0.628325\pi
0.421059 + 0.907033i 0.361659π0.361659\pi
4444 7.18621 + 3.19951i 1.08336 + 0.482344i
4545 −3.34565 3.71572i −0.498741 0.553907i
4646 2.12132 1.54123i 0.312772 0.227242i
4747 −3.00000 + 2.17963i −0.437595 + 0.317931i −0.784679 0.619903i 0.787172π-0.787172\pi
0.347084 + 0.937834i 0.387172π0.387172\pi
4848 −4.81680 5.34959i −0.695244 0.772147i
4949 −5.48127 2.44042i −0.783039 0.348631i
5050 0 0
5151 0.827091 0.918578i 0.115816 0.128627i
5252 −1.33043 + 12.6582i −0.184497 + 1.75538i
5353 5.12959 1.09033i 0.704604 0.149768i 0.158344 0.987384i 0.449384π-0.449384\pi
0.546260 + 0.837616i 0.316051π0.316051\pi
5454 0.206331 0.635021i 0.0280781 0.0864155i
5555 −9.27952 1.97242i −1.25125 0.265962i
5656 −0.736068 + 1.27491i −0.0983612 + 0.170367i
5757 1.14412 + 1.98168i 0.151543 + 0.262480i
5858 0.437016 + 1.34500i 0.0573830 + 0.176607i
5959 0.621346 + 5.91171i 0.0808923 + 0.769639i 0.957500 + 0.288433i 0.0931343π0.0931343\pi
−0.876608 + 0.481206i 0.840199π0.840199\pi
6060 7.67501 + 5.57622i 0.990839 + 0.719887i
6161 −4.44897 −0.569632 −0.284816 0.958582i 0.591933π-0.591933\pi
−0.284816 + 0.958582i 0.591933π0.591933\pi
6262 0 0
6363 −2.23607 −0.281718
6464 3.80902 + 2.76741i 0.476127 + 0.345927i
6565 −1.60451 15.2659i −0.199015 1.89351i
6666 1.14590 + 3.52671i 0.141050 + 0.434108i
6767 −3.00000 5.19615i −0.366508 0.634811i 0.622509 0.782613i 0.286114π-0.286114\pi
−0.989017 + 0.147802i 0.952780π0.952780\pi
6868 −0.500776 + 0.867369i −0.0607280 + 0.105184i
6969 −15.3649 3.26592i −1.84972 0.393170i
7070 0.263932 0.812299i 0.0315459 0.0970883i
7171 −7.30885 + 1.55354i −0.867401 + 0.184372i −0.620058 0.784556i 0.712891π-0.712891\pi
−0.247343 + 0.968928i 0.579558π0.579558\pi
7272 0.344086 3.27376i 0.0405510 0.385817i
7373 −2.83888 + 3.15290i −0.332266 + 0.369019i −0.886008 0.463669i 0.846533π-0.846533\pi
0.553742 + 0.832688i 0.313199π0.313199\pi
7474 −1.48044 + 0.659135i −0.172098 + 0.0766229i
7575 0 0
7676 −1.24064 1.37787i −0.142311 0.158052i
7777 −3.43237 + 2.49376i −0.391155 + 0.284191i
7878 −4.85410 + 3.52671i −0.549619 + 0.399321i
7979 7.43229 + 8.25439i 0.836198 + 0.928691i 0.998312 0.0580805i 0.0184980π-0.0184980\pi
−0.162114 + 0.986772i 0.551831π0.551831\pi
8080 −6.42628 2.86117i −0.718480 0.319888i
8181 −9.78243 + 4.35542i −1.08694 + 0.483935i
8282 1.90977 2.12101i 0.210898 0.234226i
8383 0.330548 3.14495i 0.0362824 0.345204i −0.961288 0.275544i 0.911142π-0.911142\pi
0.997571 0.0696596i 0.0221913π-0.0221913\pi
8484 4.14993 0.882095i 0.452794 0.0962444i
8585 0.373256 1.14876i 0.0404853 0.124601i
8686 −0.0770892 0.0163858i −0.00831274 0.00176693i
8787 4.23607 7.33708i 0.454154 0.786618i
8888 −3.12287 5.40897i −0.332899 0.576598i
8989 1.81182 + 5.57622i 0.192053 + 0.591078i 0.999998 + 0.00182083i 0.000579589π0.000579589\pi
−0.807945 + 0.589257i 0.799420π0.799420\pi
9090 0.199632 + 1.89937i 0.0210430 + 0.200211i
9191 −5.55369 4.03499i −0.582185 0.422982i
9292 12.7279 1.32698
9393 0 0
9494 1.41641 0.146091
9595 1.80902 + 1.31433i 0.185601 + 0.134847i
9696 0.991644 + 9.43486i 0.101209 + 0.962942i
9797 −2.16312 6.65740i −0.219631 0.675956i −0.998792 0.0491321i 0.984354π-0.984354\pi
0.779161 0.626824i 0.215646π-0.215646\pi
9898 1.14590 + 1.98475i 0.115753 + 0.200490i
9999 4.74342 8.21584i 0.476731 0.825723i
100100 0 0
101101 −0.690983 + 2.12663i −0.0687554 + 0.211607i −0.979531 0.201295i 0.935485π-0.935485\pi
0.910775 + 0.412902i 0.135485π0.135485\pi
102102 −0.461819 + 0.0981626i −0.0457269 + 0.00971954i
103103 0.283084 2.69337i 0.0278931 0.265385i −0.971683 0.236287i 0.924070π-0.924070\pi
0.999577 0.0290988i 0.00926376π-0.00926376\pi
104104 6.76212 7.51009i 0.663080 0.736425i
105105 −4.67431 + 2.08114i −0.456166 + 0.203098i
106106 −1.82993 0.814735i −0.177738 0.0791341i
107107 −4.99983 5.55288i −0.483352 0.536817i 0.451304 0.892370i 0.350959π-0.350959\pi
−0.934656 + 0.355553i 0.884292π0.884292\pi
108108 2.62210 1.90506i 0.252311 0.183315i
109109 11.8992 8.64527i 1.13974 0.828066i 0.152653 0.988280i 0.451218π-0.451218\pi
0.987082 + 0.160214i 0.0512183π0.0512183\pi
110110 2.42469 + 2.69290i 0.231185 + 0.256757i
111111 8.86889 + 3.94868i 0.841797 + 0.374792i
112112 −2.87392 + 1.27955i −0.271560 + 0.120906i
113113 −9.52579 + 10.5795i −0.896111 + 0.995232i 0.103889 + 0.994589i 0.466871π0.466871\pi
−1.00000 0.000643002i 0.999795π0.999795\pi
114114 0.0913612 0.869244i 0.00855676 0.0814122i
115115 −15.0146 + 3.19145i −1.40012 + 0.297604i
116116 −2.12132 + 6.52875i −0.196960 + 0.606179i
117117 15.0146 + 3.19145i 1.38810 + 0.295049i
118118 1.13525 1.96632i 0.104509 0.181014i
119119 −0.270091 0.467811i −0.0247592 0.0428842i
120120 −2.32765 7.16377i −0.212485 0.653960i
121121 −0.731699 6.96165i −0.0665181 0.632878i
122122 1.37481 + 0.998856i 0.124469 + 0.0904322i
123123 −17.0981 −1.54168
124124 0 0
125125 11.1803 1.00000
126126 0.690983 + 0.502029i 0.0615577 + 0.0447243i
127127 0.991644 + 9.43486i 0.0879942 + 0.837209i 0.946130 + 0.323786i 0.104956π0.104956\pi
−0.858136 + 0.513422i 0.828377π0.828377\pi
128128 −3.11803 9.59632i −0.275598 0.848203i
129129 0.236068 + 0.408882i 0.0207846 + 0.0360000i
130130 −2.93159 + 5.07767i −0.257118 + 0.445341i
131131 18.9921 + 4.03690i 1.65935 + 0.352705i 0.939797 0.341733i 0.111014π-0.111014\pi
0.719552 + 0.694439i 0.244347π0.244347\pi
132132 −5.56231 + 17.1190i −0.484137 + 1.49002i
133133 0.978148 0.207912i 0.0848162 0.0180282i
134134 −0.239558 + 2.27924i −0.0206947 + 0.196896i
135135 −2.61549 + 2.90480i −0.225106 + 0.250005i
136136 0.726470 0.323445i 0.0622943 0.0277352i
137137 −6.27125 2.79214i −0.535789 0.238549i 0.120961 0.992657i 0.461403π-0.461403\pi
−0.656750 + 0.754109i 0.728069π0.728069\pi
138138 4.01478 + 4.45887i 0.341761 + 0.379564i
139139 0.810272 0.588697i 0.0687264 0.0499327i −0.552892 0.833253i 0.686476π-0.686476\pi
0.621618 + 0.783321i 0.286476π0.286476\pi
140140 3.35410 2.43690i 0.283473 0.205955i
141141 −5.67776 6.30579i −0.478154 0.531044i
142142 2.60735 + 1.16087i 0.218804 + 0.0974179i
143143 26.6067 11.8460i 2.22496 0.990616i
144144 4.70696 5.22761i 0.392247 0.435634i
145145 0.865386 8.23360i 0.0718664 0.683763i
146146 1.58513 0.336930i 0.131186 0.0278845i
147147 4.24264 13.0575i 0.349927 1.07696i
148148 −7.69439 1.63549i −0.632475 0.134437i
149149 −6.70820 + 11.6190i −0.549557 + 0.951861i 0.448747 + 0.893659i 0.351870π0.351870\pi
−0.998305 + 0.0582028i 0.981463π0.981463\pi
150150 0 0
151151 −0.937792 2.88623i −0.0763164 0.234878i 0.905620 0.424091i 0.139406π-0.139406\pi
−0.981936 + 0.189213i 0.939406π0.939406\pi
152152 0.153880 + 1.46407i 0.0124813 + 0.118752i
153153 0.977198 + 0.709976i 0.0790017 + 0.0573981i
154154 1.62054 0.130587
155155 0 0
156156 −29.1246 −2.33184
157157 3.80902 + 2.76741i 0.303993 + 0.220864i 0.729315 0.684179i 0.239839π-0.239839\pi
−0.425322 + 0.905042i 0.639839π0.639839\pi
158158 −0.443477 4.21940i −0.0352811 0.335677i
159159 3.70820 + 11.4127i 0.294080 + 0.905084i
160160 4.63525 + 8.02850i 0.366449 + 0.634708i
161161 −3.43237 + 5.94504i −0.270509 + 0.468535i
162162 4.00079 + 0.850394i 0.314332 + 0.0668133i
163163 −3.83688 + 11.8087i −0.300528 + 0.924929i 0.680781 + 0.732487i 0.261641π0.261641\pi
−0.981308 + 0.192442i 0.938359π0.938359\pi
164164 13.5514 2.88043i 1.05818 0.224924i
165165 2.26913 21.5893i 0.176651 1.68072i
166166 −0.808231 + 0.897632i −0.0627309 + 0.0696697i
167167 6.76473 3.01185i 0.523470 0.233064i −0.127951 0.991781i 0.540840π-0.540840\pi
0.651421 + 0.758716i 0.274173π0.274173\pi
168168 −3.07738 1.37014i −0.237425 0.105708i
169169 22.8338 + 25.3595i 1.75645 + 1.95073i
170170 −0.373256 + 0.271187i −0.0286274 + 0.0207991i
171171 −1.80902 + 1.31433i −0.138339 + 0.100509i
172172 −0.255982 0.284296i −0.0195184 0.0216774i
173173 16.4438 + 7.32126i 1.25020 + 0.556625i 0.921709 0.387882i 0.126793π-0.126793\pi
0.328491 + 0.944507i 0.393460π0.393460\pi
174174 −2.95630 + 1.31623i −0.224116 + 0.0997829i
175175 0 0
176176 1.39513 13.2738i 0.105162 1.00055i
177177 −13.3047 + 2.82801i −1.00004 + 0.212566i
178178 0.692055 2.12993i 0.0518717 0.159645i
179179 16.0713 + 3.41607i 1.20123 + 0.255329i 0.764715 0.644369i 0.222880π-0.222880\pi
0.436513 + 0.899698i 0.356213π0.356213\pi
180180 −4.63525 + 8.02850i −0.345492 + 0.598409i
181181 9.08922 + 15.7430i 0.675597 + 1.17017i 0.976294 + 0.216448i 0.0694472π0.0694472\pi
−0.300698 + 0.953720i 0.597219π0.597219\pi
182182 0.810272 + 2.49376i 0.0600614 + 0.184850i
183183 −1.06414 10.1246i −0.0786631 0.748430i
184184 −8.17578 5.94006i −0.602727 0.437907i
185185 9.48683 0.697486
186186 0 0
187187 2.29180 0.167593
188188 5.56231 + 4.04125i 0.405673 + 0.294739i
189189 0.182722 + 1.73849i 0.0132911 + 0.126456i
190190 −0.263932 0.812299i −0.0191476 0.0589304i
191191 −7.11803 12.3288i −0.515043 0.892080i −0.999848 0.0174580i 0.994443π-0.994443\pi
0.484805 0.874622i 0.338891π-0.338891\pi
192192 −5.38676 + 9.33015i −0.388756 + 0.673345i
193193 7.13245 + 1.51605i 0.513405 + 0.109128i 0.457327 0.889299i 0.348807π-0.348807\pi
0.0560784 + 0.998426i 0.482140π0.482140\pi
194194 −0.826238 + 2.54290i −0.0593204 + 0.182569i
195195 34.3571 7.30282i 2.46036 0.522966i
196196 −1.16284 + 11.0637i −0.0830599 + 0.790262i
197197 4.95486 5.50293i 0.353019 0.392067i −0.540313 0.841464i 0.681694π-0.681694\pi
0.893332 + 0.449397i 0.148361π0.148361\pi
198198 −3.31037 + 1.47387i −0.235258 + 0.104743i
199199 13.4575 + 5.99165i 0.953974 + 0.424737i 0.823880 0.566765i 0.191805π-0.191805\pi
0.130095 + 0.991502i 0.458472π0.458472\pi
200200 0 0
201201 11.1074 8.06998i 0.783454 0.569213i
202202 0.690983 0.502029i 0.0486174 0.0353226i
203203 −2.47743 2.75146i −0.173881 0.193115i
204204 −2.09366 0.932157i −0.146586 0.0652641i
205205 −15.2637 + 6.79584i −1.06606 + 0.474642i
206206 −0.692177 + 0.768740i −0.0482262 + 0.0535607i
207207 1.60451 15.2659i 0.111521 1.06106i
208208 21.1238 4.49001i 1.46467 0.311326i
209209 −1.31105 + 4.03499i −0.0906871 + 0.279106i
210210 1.91169 + 0.406342i 0.131919 + 0.0280402i
211211 2.50000 4.33013i 0.172107 0.298098i −0.767049 0.641588i 0.778276π-0.778276\pi
0.939156 + 0.343490i 0.111609π0.111609\pi
212212 −4.86163 8.42060i −0.333898 0.578329i
213213 −5.28360 16.2612i −0.362026 1.11420i
214214 0.298335 + 2.83847i 0.0203938 + 0.194034i
215215 0.373256 + 0.271187i 0.0254559 + 0.0184948i
216216 −2.57339 −0.175097
217217 0 0
218218 −5.61803 −0.380501
219219 −7.85410 5.70634i −0.530731 0.385599i
220220 1.83861 + 17.4932i 0.123959 + 1.17939i
221221 1.14590 + 3.52671i 0.0770814 + 0.237232i
222222 −1.85410 3.21140i −0.124439 0.215535i
223223 −10.9010 + 18.8812i −0.729988 + 1.26438i 0.226900 + 0.973918i 0.427141π0.427141\pi
−0.956888 + 0.290458i 0.906192π0.906192\pi
224224 4.05530 + 0.861981i 0.270956 + 0.0575935i
225225 0 0
226226 5.31887 1.13056i 0.353806 0.0752037i
227227 −1.64195 + 15.6222i −0.108980 + 1.03688i 0.794211 + 0.607641i 0.207884π0.207884\pi
−0.903192 + 0.429237i 0.858782π0.858782\pi
228228 2.83888 3.15290i 0.188009 0.208806i
229229 −3.87585 + 1.72564i −0.256123 + 0.114033i −0.530782 0.847508i 0.678102π-0.678102\pi
0.274659 + 0.961542i 0.411435π0.411435\pi
230230 5.35629 + 2.38477i 0.353183 + 0.157247i
231231 −6.49606 7.21460i −0.427409 0.474686i
232232 4.40957 3.20374i 0.289502 0.210336i
233233 3.66312 2.66141i 0.239979 0.174355i −0.461295 0.887247i 0.652615π-0.652615\pi
0.701274 + 0.712892i 0.252615π0.252615\pi
234234 −3.92324 4.35720i −0.256470 0.284839i
235235 −7.57493 3.37258i −0.494134 0.220003i
236236 10.0684 4.48276i 0.655400 0.291803i
237237 −17.0069 + 18.8881i −1.10472 + 1.22691i
238238 −0.0215675 + 0.205201i −0.00139801 + 0.0133012i
239239 −15.9942 + 3.39968i −1.03458 + 0.219907i −0.693749 0.720217i 0.744042π-0.744042\pi
−0.340833 + 0.940124i 0.610709π0.610709\pi
240240 4.97410 15.3087i 0.321077 0.988173i
241241 14.4091 + 3.06275i 0.928173 + 0.197289i 0.647107 0.762399i 0.275979π-0.275979\pi
0.281066 + 0.959688i 0.409312π0.409312\pi
242242 −1.33688 + 2.31555i −0.0859380 + 0.148849i
243243 −9.62940 16.6786i −0.617727 1.06993i
244244 2.54903 + 7.84512i 0.163185 + 0.502232i
245245 −1.40240 13.3429i −0.0895958 0.852447i
246246 5.28360 + 3.83876i 0.336870 + 0.244750i
247247 −6.86474 −0.436793
248248 0 0
249249 7.23607 0.458567
250250 −3.45492 2.51014i −0.218508 0.158755i
251251 −2.48323 23.6263i −0.156740 1.49128i −0.736468 0.676472i 0.763508π-0.763508\pi
0.579728 0.814810i 0.303159π-0.303159\pi
252252 1.28115 + 3.94298i 0.0807050 + 0.248385i
253253 −14.5623 25.2227i −0.915524 1.58573i
254254 1.81182 3.13817i 0.113684 0.196906i
255255 2.70353 + 0.574654i 0.169302 + 0.0359862i
256256 1.71885 5.29007i 0.107428 0.330629i
257257 −23.4210 + 4.97829i −1.46096 + 0.310537i −0.868753 0.495246i 0.835078π-0.835078\pi
−0.592211 + 0.805783i 0.701745π0.701745\pi
258258 0.0188507 0.179352i 0.00117359 0.0111660i
259259 2.83888 3.15290i 0.176399 0.195911i
260260 −26.0000 + 11.5759i −1.61245 + 0.717909i
261261 7.56320 + 3.36735i 0.468150 + 0.208434i
262262 −4.96255 5.51147i −0.306587 0.340499i
263263 2.18508 1.58755i 0.134738 0.0978928i −0.518375 0.855153i 0.673463π-0.673463\pi
0.653113 + 0.757261i 0.273463π0.273463\pi
264264 11.5623 8.40051i 0.711611 0.517015i
265265 7.84647 + 8.71439i 0.482005 + 0.535321i
266266 −0.348943 0.155360i −0.0213951 0.00952571i
267267 −12.2565 + 5.45694i −0.750086 + 0.333960i
268268 −7.44382 + 8.26720i −0.454704 + 0.504999i
269269 1.54805 14.7287i 0.0943862 0.898025i −0.840197 0.542281i 0.817561π-0.817561\pi
0.934583 0.355744i 0.115773π-0.115773\pi
270270 1.46040 0.310417i 0.0888770 0.0188914i
271271 8.67656 26.7037i 0.527064 1.62213i −0.233135 0.972444i 0.574899π-0.574899\pi
0.760199 0.649690i 0.225101π-0.225101\pi
272272 1.66222 + 0.353316i 0.100787 + 0.0214229i
273273 7.85410 13.6037i 0.475352 0.823334i
274274 1.31105 + 2.27080i 0.0792033 + 0.137184i
275275 0 0
276276 3.04435 + 28.9651i 0.183248 + 1.74349i
277277 15.8508 + 11.5163i 0.952382 + 0.691946i 0.951369 0.308054i 0.0996776π-0.0996776\pi
0.00101288 + 0.999999i 0.499678π0.499678\pi
278278 −0.382559 −0.0229443
279279 0 0
280280 −3.29180 −0.196722
281281 25.3713 + 18.4333i 1.51353 + 1.09964i 0.964582 + 0.263782i 0.0849699π0.0849699\pi
0.548944 + 0.835859i 0.315030π0.315030\pi
282282 0.338786 + 3.22333i 0.0201744 + 0.191947i
283283 7.41641 + 22.8254i 0.440860 + 1.35683i 0.886961 + 0.461844i 0.152812π0.152812\pi
−0.446101 + 0.894982i 0.647188π0.647188\pi
284284 6.92705 + 11.9980i 0.411045 + 0.711951i
285285 −2.55834 + 4.43117i −0.151543 + 0.262480i
286286 −10.8815 2.31294i −0.643437 0.136767i
287287 −2.30902 + 7.10642i −0.136297 + 0.419479i
288288 −9.06793 + 1.92745i −0.534333 + 0.113576i
289289 1.74648 16.6167i 0.102734 0.977451i
290290 −2.11598 + 2.35003i −0.124254 + 0.137999i
291291 14.6329 6.51499i 0.857797 0.381916i
292292 7.18621 + 3.19951i 0.420541 + 0.187237i
293293 −10.5108 11.6735i −0.614050 0.681971i 0.353273 0.935520i 0.385069π-0.385069\pi
−0.967323 + 0.253549i 0.918402π0.918402\pi
294294 −4.24264 + 3.08246i −0.247436 + 0.179773i
295295 −10.7533 + 7.81272i −0.626081 + 0.454874i
296296 4.17922 + 4.64149i 0.242912 + 0.269781i
297297 −6.77523 3.01652i −0.393138 0.175037i
298298 4.68157 2.08437i 0.271196 0.120744i
299299 31.5325 35.0204i 1.82357 2.02528i
300300 0 0
301301 0.201822 0.0428986i 0.0116328 0.00247264i
302302 −0.358205 + 1.10244i −0.0206124 + 0.0634383i
303303 −5.00486 1.06382i −0.287522 0.0611146i
304304 −1.57295 + 2.72443i −0.0902148 + 0.156257i
305305 −4.97410 8.61540i −0.284816 0.493316i
306306 −0.142571 0.438789i −0.00815025 0.0250839i
307307 1.68548 + 16.0363i 0.0961955 + 0.915239i 0.931080 + 0.364814i 0.118867π0.118867\pi
−0.834885 + 0.550425i 0.814466π0.814466\pi
308308 6.36396 + 4.62369i 0.362620 + 0.263459i
309309 6.19704 0.352537
310310 0 0
311311 16.5279 0.937209 0.468605 0.883408i 0.344757π-0.344757\pi
0.468605 + 0.883408i 0.344757π0.344757\pi
312312 18.7082 + 13.5923i 1.05914 + 0.769513i
313313 −2.19582 20.8918i −0.124115 1.18087i −0.862344 0.506324i 0.831004π-0.831004\pi
0.738229 0.674550i 0.235663π-0.235663\pi
314314 −0.555728 1.71036i −0.0313616 0.0965209i
315315 −2.50000 4.33013i −0.140859 0.243975i
316316 10.2971 17.8351i 0.579257 1.00330i
317317 −21.2883 4.52498i −1.19567 0.254148i −0.433278 0.901260i 0.642643π-0.642643\pi
−0.762395 + 0.647113i 0.775976π0.775976\pi
318318 1.41641 4.35926i 0.0794282 0.244455i
319319 15.3649 3.26592i 0.860272 0.182856i
320320 −1.10046 + 10.4702i −0.0615177 + 0.585301i
321321 11.4409 12.7064i 0.638566 0.709199i
322322 2.39540 1.06650i 0.133491 0.0594339i
323323 −0.493480 0.219712i −0.0274580 0.0122251i
324324 13.2850 + 14.7545i 0.738055 + 0.819693i
325325 0 0
326326 3.83688 2.78766i 0.212505 0.154394i
327327 22.5202 + 25.0113i 1.24537 + 1.38313i
328328 −10.0490 4.47410i −0.554863 0.247041i
329329 −3.38761 + 1.50826i −0.186765 + 0.0831532i
330330 −5.54829 + 6.16201i −0.305424 + 0.339207i
331331 −2.67928 + 25.4917i −0.147267 + 1.40115i 0.632249 + 0.774765i 0.282132π0.282132\pi
−0.779516 + 0.626383i 0.784535π0.784535\pi
332332 −5.73506 + 1.21902i −0.314752 + 0.0669027i
333333 −2.93159 + 9.02251i −0.160650 + 0.494431i
334334 −2.76662 0.588063i −0.151383 0.0321774i
335335 6.70820 11.6190i 0.366508 0.634811i
336336 −3.59929 6.23416i −0.196358 0.340101i
337337 1.81182 + 5.57622i 0.0986963 + 0.303756i 0.988199 0.153173i 0.0489492π-0.0489492\pi
−0.889503 + 0.456929i 0.848949π0.848949\pi
338338 −1.36247 12.9630i −0.0741086 0.705096i
339339 −26.3542 19.1475i −1.43137 1.03995i
340340 −2.23954 −0.121456
341341 0 0
342342 0.854102 0.0461845
343343 −10.5172 7.64121i −0.567877 0.412586i
344344 0.0317502 + 0.302083i 0.00171186 + 0.0162872i
345345 −10.8541 33.4055i −0.584365 1.79849i
346346 −3.43769 5.95426i −0.184812 0.320103i
347347 12.9192 22.3767i 0.693539 1.20124i −0.277132 0.960832i 0.589384π-0.589384\pi
0.970671 0.240413i 0.0772829π-0.0772829\pi
348348 −15.3649 3.26592i −0.823647 0.175072i
349349 1.85410 5.70634i 0.0992478 0.305453i −0.889090 0.457733i 0.848662π-0.848662\pi
0.988337 + 0.152280i 0.0486615π0.0486615\pi
350350 0 0
351351 1.25434 11.9343i 0.0669518 0.637004i
352352 −11.7697 + 13.0716i −0.627328 + 0.696718i
353353 −14.5164 + 6.46313i −0.772631 + 0.343998i −0.754895 0.655845i 0.772312π-0.772312\pi
−0.0177357 + 0.999843i 0.505646π0.505646\pi
354354 4.74631 + 2.11319i 0.252264 + 0.112315i
355355 −11.1800 12.4166i −0.593371 0.659006i
356356 8.79478 6.38978i 0.466122 0.338658i
357357 1.00000 0.726543i 0.0529256 0.0384527i
358358 −4.19936 4.66386i −0.221943 0.246493i
359359 8.91980 + 3.97135i 0.470769 + 0.209600i 0.628388 0.777900i 0.283715π-0.283715\pi
−0.157619 + 0.987500i 0.550382π0.550382\pi
360360 6.72432 2.99386i 0.354403 0.157790i
361361 −12.0444 + 13.3766i −0.633913 + 0.704032i
362362 0.725798 6.90551i 0.0381471 0.362946i
363363 15.6677 3.33027i 0.822341 0.174794i
364364 −3.93314 + 12.1050i −0.206153 + 0.634473i
365365 −9.27952 1.97242i −0.485712 0.103241i
366366 −1.94427 + 3.36758i −0.101629 + 0.176026i
367367 −6.15763 10.6653i −0.321426 0.556726i 0.659357 0.751830i 0.270829π-0.270829\pi
−0.980782 + 0.195105i 0.937495π0.937495\pi
368368 −6.67346 20.5388i −0.347878 1.07066i
369369 −1.74648 16.6167i −0.0909183 0.865030i
370370 −2.93159 2.12993i −0.152406 0.110730i
371371 5.24419 0.272265
372372 0 0
373373 −22.7082 −1.17579 −0.587893 0.808939i 0.700042π-0.700042\pi
−0.587893 + 0.808939i 0.700042π0.700042\pi
374374 −0.708204 0.514540i −0.0366204 0.0266062i
375375 2.67419 + 25.4432i 0.138095 + 1.31388i
376376 −1.68692 5.19180i −0.0869961 0.267747i
377377 12.7082 + 22.0113i 0.654506 + 1.13364i
378378 0.333851 0.578246i 0.0171714 0.0297418i
379379 18.9921 + 4.03690i 0.975559 + 0.207362i 0.667995 0.744166i 0.267153π-0.267153\pi
0.307564 + 0.951527i 0.400486π0.400486\pi
380380 1.28115 3.94298i 0.0657218 0.202271i
381381 −21.2338 + 4.51339i −1.08784 + 0.231228i
382382 −0.568394 + 5.40791i −0.0290816 + 0.276693i
383383 12.7486 14.1587i 0.651423 0.723478i −0.323449 0.946246i 0.604842π-0.604842\pi
0.974872 + 0.222767i 0.0715090π0.0715090\pi
384384 21.0927 9.39106i 1.07638 0.479235i
385385 −8.66665 3.85864i −0.441694 0.196655i
386386 −1.86367 2.06982i −0.0948585 0.105351i
387387 −0.373256 + 0.271187i −0.0189737 + 0.0137852i
388388 −10.5000 + 7.62870i −0.533057 + 0.387288i
389389 −22.6056 25.1060i −1.14615 1.27293i −0.956713 0.291033i 0.906001π-0.906001\pi
−0.189435 0.981893i 0.560666π-0.560666\pi
390390 −12.2565 5.45694i −0.620632 0.276323i
391391 3.38761 1.50826i 0.171319 0.0762761i
392392 5.91031 6.56406i 0.298516 0.331535i
393393 −4.64415 + 44.1861i −0.234266 + 2.22889i
394394 −2.76662 + 0.588063i −0.139380 + 0.0296262i
395395 −7.67501 + 23.6212i −0.386172 + 1.18851i
396396 −17.2052 3.65707i −0.864593 0.183775i
397397 −0.645898 + 1.11873i −0.0324167 + 0.0561474i −0.881779 0.471664i 0.843654π-0.843654\pi
0.849362 + 0.527811i 0.176987π0.176987\pi
398398 −2.81338 4.87291i −0.141022 0.244257i
399399 0.707107 + 2.17625i 0.0353996 + 0.108949i
400400 0 0
401401 −2.99535 2.17625i −0.149581 0.108677i 0.510478 0.859891i 0.329469π-0.329469\pi
−0.660059 + 0.751214i 0.729469π0.729469\pi
402402 −5.24419 −0.261557
403403 0 0
404404 4.14590 0.206266
405405 −19.3713 14.0741i −0.962569 0.699347i
406406 0.147826 + 1.40647i 0.00733646 + 0.0698018i
407407 5.56231 + 17.1190i 0.275713 + 0.848558i
408408 0.909830 + 1.57587i 0.0450433 + 0.0780173i
409409 −8.67656 + 15.0282i −0.429028 + 0.743099i −0.996787 0.0800961i 0.974477π-0.974477\pi
0.567759 + 0.823195i 0.307811π0.307811\pi
410410 6.24250 + 1.32689i 0.308295 + 0.0655302i
411411 4.85410 14.9394i 0.239435 0.736906i
412412 −4.91156 + 1.04398i −0.241975 + 0.0514334i
413413 −0.621346 + 5.91171i −0.0305744 + 0.290896i
414414 −3.92324 + 4.35720i −0.192817 + 0.214144i
415415 6.45974 2.87606i 0.317096 0.141180i
416416 −26.0000 11.5759i −1.27475 0.567557i
417417 1.53351 + 1.70314i 0.0750964 + 0.0834029i
418418 1.31105 0.952532i 0.0641255 0.0465899i
419419 15.0451 10.9309i 0.735000 0.534009i −0.156141 0.987735i 0.549905π-0.549905\pi
0.891141 + 0.453726i 0.149905π0.149905\pi
420420 6.34793 + 7.05009i 0.309747 + 0.344009i
421421 −0.380408 0.169368i −0.0185399 0.00825451i 0.397446 0.917626i 0.369897π-0.369897\pi
−0.415986 + 0.909371i 0.636563π0.636563\pi
422422 −1.74472 + 0.776798i −0.0849315 + 0.0378139i
423423 5.54829 6.16201i 0.269767 0.299607i
424424 −0.806977 + 7.67787i −0.0391903 + 0.372870i
425425 0 0
426426 −2.01815 + 6.21124i −0.0977799 + 0.300936i
427427 −4.35175 0.924993i −0.210596 0.0447636i
428428 −6.92705 + 11.9980i −0.334832 + 0.579945i
429429 33.3221 + 57.7156i 1.60881 + 2.78654i
430430 −0.0544574 0.167602i −0.00262617 0.00808251i
431431 0.0116503 + 0.110846i 0.000561177 + 0.00533925i 0.994799 0.101858i 0.0324789π-0.0324789\pi
−0.994238 + 0.107198i 0.965812π0.965812\pi
432432 −4.44897 3.23237i −0.214051 0.155517i
433433 −21.5958 −1.03783 −0.518913 0.854827i 0.673663π-0.673663\pi
−0.518913 + 0.854827i 0.673663π0.673663\pi
434434 0 0
435435 18.9443 0.908308
436436 −22.0623 16.0292i −1.05659 0.767660i
437437 0.717560 + 6.82713i 0.0343256 + 0.326586i
438438 1.14590 + 3.52671i 0.0547531 + 0.168513i
439439 12.5000 + 21.6506i 0.596592 + 1.03333i 0.993320 + 0.115392i 0.0368124π0.0368124\pi
−0.396728 + 0.917936i 0.629854π0.629854\pi
440440 6.98295 12.0948i 0.332899 0.576598i
441441 13.1232 + 2.78943i 0.624916 + 0.132830i
442442 0.437694 1.34708i 0.0208190 0.0640742i
443443 −23.4210 + 4.97829i −1.11277 + 0.236526i −0.727384 0.686231i 0.759264π-0.759264\pi
−0.385383 + 0.922757i 0.625931π0.625931\pi
444444 1.88151 17.9014i 0.0892926 0.849563i
445445 −8.77262 + 9.74299i −0.415862 + 0.461862i
446446 7.60769 3.38716i 0.360235 0.160387i
447447 −28.0459 12.4868i −1.32652 0.590607i
448448 3.15040 + 3.49888i 0.148843 + 0.165306i
449449 −34.1324 + 24.7986i −1.61081 + 1.17032i −0.749915 + 0.661535i 0.769905π0.769905\pi
−0.860893 + 0.508786i 0.830095π0.830095\pi
450450 0 0
451451 −21.2125 23.5589i −0.998858 1.10934i
452452 24.1131 + 10.7359i 1.13419 + 0.504973i
453453 6.34391 2.82449i 0.298063 0.132706i
454454 4.01478 4.45887i 0.188423 0.209265i
455455 1.60451 15.2659i 0.0752208 0.715678i
456456 −3.29500 + 0.700373i −0.154302 + 0.0327980i
457457 −3.49613 + 10.7600i −0.163542 + 0.503330i −0.998926 0.0463365i 0.985245π-0.985245\pi
0.835384 + 0.549667i 0.185245π0.185245\pi
458458 1.58513 + 0.336930i 0.0740683 + 0.0157437i
459459 0.472136 0.817763i 0.0220374 0.0381699i
460460 14.2302 + 24.6475i 0.663489 + 1.14920i
461461 12.0846 + 37.1925i 0.562835 + 1.73223i 0.674299 + 0.738459i 0.264446π0.264446\pi
−0.111464 + 0.993768i 0.535554π0.535554\pi
462462 0.387613 + 3.68789i 0.0180334 + 0.171576i
463463 12.2515 + 8.90124i 0.569376 + 0.413676i 0.834878 0.550435i 0.185538π-0.185538\pi
−0.265503 + 0.964110i 0.585538π0.585538\pi
464464 11.6476 0.540724
465465 0 0
466466 −1.72949 −0.0801171
467467 −12.6631 9.20029i −0.585979 0.425739i 0.254895 0.966969i 0.417959π-0.417959\pi
−0.840875 + 0.541230i 0.817959π0.817959\pi
468468 −2.97493 28.3046i −0.137516 1.30838i
469469 −1.85410 5.70634i −0.0856145 0.263494i
470470 1.58359 + 2.74286i 0.0730457 + 0.126519i
471471 −5.38676 + 9.33015i −0.248209 + 0.429911i
472472 −8.55955 1.81939i −0.393985 0.0837442i
473473 −0.270510 + 0.832544i −0.0124381 + 0.0382804i
474474 9.49606 2.01845i 0.436168 0.0927104i
475475 0 0
476476 −0.670169 + 0.744298i −0.0307171 + 0.0341148i
477477 −10.7126 + 4.76954i −0.490495 + 0.218382i
478478 5.70577 + 2.54037i 0.260976 + 0.116194i
479479 17.0442 + 18.9295i 0.778769 + 0.864910i 0.993741 0.111710i 0.0356327π-0.0356327\pi
−0.214972 + 0.976620i 0.568966π0.568966\pi
480480 −17.1618 + 12.4688i −0.783327 + 0.569121i
481481 −23.5623 + 17.1190i −1.07435 + 0.780560i
482482 −3.76503 4.18149i −0.171492 0.190462i
483483 −14.3502 6.38910i −0.652955 0.290714i
484484 −11.8566 + 5.27892i −0.538938 + 0.239951i
485485 10.4736 11.6321i 0.475579 0.528184i
486486 −0.768933 + 7.31591i −0.0348795 + 0.331857i
487487 18.1848 3.86531i 0.824034 0.175154i 0.223450 0.974715i 0.428268π-0.428268\pi
0.600584 + 0.799562i 0.294935π0.294935\pi
488488 2.02390 6.22894i 0.0916178 0.281971i
489489 −27.7909 5.90714i −1.25675 0.267130i
490490 −2.56231 + 4.43804i −0.115753 + 0.200490i
491491 −4.78282 8.28409i −0.215846 0.373856i 0.737688 0.675142i 0.235917π-0.235917\pi
−0.953534 + 0.301286i 0.902584π0.902584\pi
492492 9.79633 + 30.1500i 0.441653 + 1.35927i
493493 0.209057 + 1.98904i 0.00941545 + 0.0895820i
494494 2.12132 + 1.54123i 0.0954427 + 0.0693432i
495495 21.2132 0.953463
496496 0 0
497497 −7.47214 −0.335171
498498 −2.23607 1.62460i −0.100201 0.0728000i
499499 1.92173 + 18.2841i 0.0860286 + 0.818507i 0.949428 + 0.313986i 0.101664π0.101664\pi
−0.863399 + 0.504521i 0.831669π0.831669\pi
500500 −6.40576 19.7149i −0.286475 0.881678i
501501 8.47214 + 14.6742i 0.378507 + 0.655594i
502502 −4.53709 + 7.85846i −0.202500 + 0.350740i
503503 −2.82542 0.600562i −0.125979 0.0267777i 0.144490 0.989506i 0.453846π-0.453846\pi
−0.270470 + 0.962728i 0.587179π0.587179\pi
504504 1.01722 3.13068i 0.0453106 0.139452i
505505 −4.89074 + 1.03956i −0.217635 + 0.0462597i
506506 −1.16284 + 11.0637i −0.0516945 + 0.491840i
507507 −52.2494 + 58.0288i −2.32048 + 2.57715i
508508 16.0689 7.15432i 0.712940 0.317421i
509509 4.36933 + 1.94535i 0.193667 + 0.0862261i 0.501279 0.865286i 0.332863π-0.332863\pi
−0.307612 + 0.951512i 0.599530π0.599530\pi
510510 −0.706420 0.784559i −0.0312808 0.0347409i
511511 −3.43237 + 2.49376i −0.151839 + 0.110318i
512512 −18.0451 + 13.1105i −0.797488 + 0.579409i
513513 1.16968 + 1.29906i 0.0516428 + 0.0573551i
514514 8.35519 + 3.71997i 0.368532 + 0.164081i
515515 5.53218 2.46309i 0.243777 0.108537i
516516 0.585749 0.650540i 0.0257862 0.0286384i
517517 1.64450 15.6464i 0.0723251 0.688128i
518518 −1.58513 + 0.336930i −0.0696467 + 0.0148039i
519519 −12.7279 + 39.1725i −0.558694 + 1.71948i
520520 22.1035 + 4.69825i 0.969303 + 0.206032i
521521 −6.70820 + 11.6190i −0.293892 + 0.509035i −0.974726 0.223402i 0.928284π-0.928284\pi
0.680835 + 0.732437i 0.261617π0.261617\pi
522522 −1.58114 2.73861i −0.0692046 0.119866i
523523 −8.98606 27.6562i −0.392933 1.20932i −0.930560 0.366140i 0.880679π-0.880679\pi
0.537627 0.843183i 0.319321π-0.319321\pi
524524 −3.76302 35.8028i −0.164388 1.56405i
525525 0 0
526526 −1.03165 −0.0449823
527527 0 0
528528 30.5410 1.32913
529529 −19.5172 14.1801i −0.848575 0.616526i
530530 −0.468191 4.45454i −0.0203369 0.193493i
531531 −4.10739 12.6412i −0.178246 0.548583i
532532 −0.927051 1.60570i −0.0401928 0.0696159i
533533 25.6471 44.4221i 1.11090 1.92414i
534534 5.01263 + 1.06547i 0.216918 + 0.0461073i
535535 5.16312 15.8904i 0.223221 0.687004i
536536 8.63980 1.83645i 0.373182 0.0793224i
537537 −3.92993 + 37.3908i −0.169589 + 1.61353i
538538 −3.78517 + 4.20386i −0.163190 + 0.181241i
539539 23.2551 10.3538i 1.00167 0.445971i
540540 6.62073 + 2.94774i 0.284911 + 0.126851i
541541 −18.6238 20.6838i −0.800699 0.889267i 0.195104 0.980782i 0.437495π-0.437495\pi
−0.995804 + 0.0915159i 0.970829π0.970829\pi
542542 −8.67656 + 6.30389i −0.372690 + 0.270775i
543543 −33.6525 + 24.4500i −1.44417 + 1.04925i
544544 −1.49854 1.66430i −0.0642495 0.0713563i
545545 30.0452 + 13.3770i 1.28699 + 0.573007i
546546 −5.48127 + 2.44042i −0.234577 + 0.104440i
547547 −16.3378 + 18.1449i −0.698552 + 0.775821i −0.983145 0.182827i 0.941475π-0.941475\pi
0.284593 + 0.958649i 0.408142π0.408142\pi
548548 −1.33043 + 12.6582i −0.0568332 + 0.540731i
549549 9.73081 2.06835i 0.415301 0.0882749i
550550 0 0
551551 −3.62155 0.769785i −0.154283 0.0327939i
552552 11.5623 20.0265i 0.492124 0.852384i
553553 5.55369 + 9.61927i 0.236167 + 0.409053i
554554 −2.31260 7.11745i −0.0982529 0.302391i
555555 2.26913 + 21.5893i 0.0963190 + 0.916414i
556556 −1.50233 1.09150i −0.0637129 0.0462901i
557557 23.2951 0.987046 0.493523 0.869733i 0.335709π-0.335709\pi
0.493523 + 0.869733i 0.335709π0.335709\pi
558558 0 0
559559 −1.41641 −0.0599077
560560 −5.69098 4.13474i −0.240488 0.174725i
561561 0.548167 + 5.21546i 0.0231436 + 0.220197i
562562 −3.70163 11.3924i −0.156144 0.480561i
563563 −7.11803 12.3288i −0.299989 0.519597i 0.676144 0.736770i 0.263650π-0.263650\pi
−0.976133 + 0.217173i 0.930316π0.930316\pi
564564 −7.86629 + 13.6248i −0.331230 + 0.573708i
565565 −31.1372 6.61841i −1.30995 0.278439i
566566 2.83282 8.71851i 0.119072 0.366466i
567567 −10.4742 + 2.22636i −0.439875 + 0.0934984i
568568 1.14981 10.9397i 0.0482451 0.459021i
569569 20.5423 22.8146i 0.861179 0.956437i −0.138244 0.990398i 0.544146π-0.544146\pi
0.999423 + 0.0339616i 0.0108124π0.0108124\pi
570570 1.78543 0.794924i 0.0747834 0.0332957i
571571 −6.27125 2.79214i −0.262444 0.116847i 0.271297 0.962496i 0.412547π-0.412547\pi
−0.533741 + 0.845648i 0.679214π0.679214\pi
572572 −36.1331 40.1298i −1.51080 1.67791i
573573 26.3542 19.1475i 1.10096 0.799897i
574574 2.30902 1.67760i 0.0963765 0.0700216i
575575 0 0
576576 −9.61768 4.28207i −0.400737 0.178420i
577577 −27.4064 + 12.2021i −1.14094 + 0.507980i −0.888156 0.459542i 0.848013π-0.848013\pi
−0.252786 + 0.967522i 0.581347π0.581347\pi
578578 −4.27037 + 4.74273i −0.177624 + 0.197271i
579579 −1.74410 + 16.5940i −0.0724824 + 0.689624i
580580 −15.0146 + 3.19145i −0.623447 + 0.132518i
581581 0.977198 3.00750i 0.0405410 0.124772i
582582 −5.98453 1.27205i −0.248067 0.0527282i
583583 −11.1246 + 19.2684i −0.460734 + 0.798015i
584584 −3.12287 5.40897i −0.129225 0.223825i
585585 10.6066 + 32.6438i 0.438529 + 1.34965i
586586 0.627171 + 5.96713i 0.0259082 + 0.246500i
587587 33.3221 + 24.2099i 1.37535 + 0.999251i 0.997298 + 0.0734679i 0.0234066π0.0234066\pi
0.378054 + 0.925784i 0.376593π0.376593\pi
588588 −25.4558 −1.04978
589589 0 0
590590 5.07701 0.209017
591591 13.7082 + 9.95959i 0.563880 + 0.409683i
592592 1.39513 + 13.2738i 0.0573396 + 0.545550i
593593 −5.30902 16.3395i −0.218015 0.670982i −0.998926 0.0463389i 0.985245π-0.985245\pi
0.780911 0.624643i 0.214755π-0.214755\pi
594594 1.41641 + 2.45329i 0.0581159 + 0.100660i
595595 0.603941 1.04606i 0.0247592 0.0428842i
596596 24.3318 + 5.17188i 0.996669 + 0.211849i
597597 −10.4164 + 32.0584i −0.426315 + 1.31206i
598598 −17.6067 + 3.74241i −0.719990 + 0.153039i
599599 −2.50286 + 23.8131i −0.102264 + 0.972977i 0.816280 + 0.577657i 0.196033π0.196033\pi
−0.918544 + 0.395320i 0.870634π0.870634\pi
600600 0 0
601601 −7.94018 + 3.53520i −0.323887 + 0.144204i −0.562238 0.826975i 0.690060π-0.690060\pi
0.238352 + 0.971179i 0.423393π0.423393\pi
602602 −0.0719978 0.0320555i −0.00293441 0.00130648i
603603 8.97733 + 9.97033i 0.365585 + 0.406023i
604604 −4.55214 + 3.30732i −0.185224 + 0.134573i
605605 12.6631 9.20029i 0.514829 0.374045i
606606 1.30775 + 1.45240i 0.0531235 + 0.0589997i
607607 −22.9525 10.2191i −0.931612 0.414780i −0.115915 0.993259i 0.536980π-0.536980\pi
−0.815697 + 0.578479i 0.803647π0.803647\pi
608608 3.78747 1.68629i 0.153602 0.0683880i
609609 5.66897 6.29602i 0.229718 0.255128i
610610 −0.397195 + 3.77906i −0.0160820 + 0.153010i
611611 24.8996 5.29257i 1.00733 0.214114i
612612 0.692055 2.12993i 0.0279747 0.0860972i
613613 −36.5421 7.76726i −1.47592 0.313717i −0.601495 0.798877i 0.705428π-0.705428\pi
−0.874425 + 0.485160i 0.838761π0.838761\pi
614614 3.07953 5.33390i 0.124280 0.215259i
615615 −19.1162 33.1103i −0.770841 1.33514i
616616 −1.93004 5.94006i −0.0777636 0.239332i
617617 4.92586 + 46.8665i 0.198308 + 1.88677i 0.413949 + 0.910300i 0.364149π0.364149\pi
−0.215641 + 0.976473i 0.569184π0.569184\pi
618618 −1.91499 1.39132i −0.0770322 0.0559671i
619619 21.5958 0.868007 0.434003 0.900911i 0.357101π-0.357101\pi
0.434003 + 0.900911i 0.357101π0.357101\pi
620620 0 0
621621 −12.0000 −0.481543
622622 −5.10739 3.71074i −0.204788 0.148787i
623623 0.612870 + 5.83107i 0.0245541 + 0.233617i
624624 15.2705 + 46.9978i 0.611310 + 1.88142i
625625 12.5000 + 21.6506i 0.500000 + 0.866025i
626626 −4.01196 + 6.94891i −0.160350 + 0.277734i
627627 −9.49606 2.01845i −0.379236 0.0806091i
628628 2.69756 8.30224i 0.107644 0.331295i
629629 −2.24171 + 0.476491i −0.0893830 + 0.0189989i
630630 −0.199632 + 1.89937i −0.00795351 + 0.0756726i
631631 3.11501 3.45956i 0.124006 0.137723i −0.677944 0.735113i 0.737129π-0.737129\pi
0.801951 + 0.597390i 0.203796π0.203796\pi
632632 −14.9379 + 6.65078i −0.594198 + 0.264554i
633633 10.4521 + 4.65357i 0.415433 + 0.184963i
634634 5.56254 + 6.17782i 0.220917 + 0.245353i
635635 −17.1618 + 12.4688i −0.681047 + 0.494810i
636636 18.0000 13.0778i 0.713746 0.518567i
637637 27.5604 + 30.6090i 1.09198 + 1.21277i
638638 −5.48127 2.44042i −0.217006 0.0966171i
639639 15.2637 6.79584i 0.603823 0.268839i
640640 15.0971 16.7671i 0.596766 0.662776i
641641 −0.886953 + 8.43880i −0.0350326 + 0.333312i 0.962943 + 0.269707i 0.0869267π0.0869267\pi
−0.997975 + 0.0636059i 0.979740π0.979740\pi
642642 −6.38817 + 1.35785i −0.252121 + 0.0535900i
643643 7.30175 22.4725i 0.287953 0.886228i −0.697545 0.716541i 0.745724π-0.745724\pi
0.985498 0.169687i 0.0542758π-0.0542758\pi
644644 12.4498 + 2.64628i 0.490590 + 0.104278i
645645 −0.527864 + 0.914287i −0.0207846 + 0.0360000i
646646 0.103165 + 0.178688i 0.00405899 + 0.00703038i
647647 −5.91189 18.1949i −0.232421 0.715317i −0.997453 0.0713252i 0.977277π-0.977277\pi
0.765033 0.643992i 0.222723π-0.222723\pi
648648 −1.64778 15.6776i −0.0647309 0.615873i
649649 −20.4029 14.8236i −0.800885 0.581877i
650650 0 0
651651 0 0
652652 23.0213 0.901583
653653 5.38197 + 3.91023i 0.210613 + 0.153019i 0.688091 0.725625i 0.258449π-0.258449\pi
−0.477478 + 0.878644i 0.658449π0.658449\pi
654654 −1.34376 12.7850i −0.0525452 0.499934i
655655 13.4164 + 41.2915i 0.524222 + 1.61339i
656656 −11.7533 20.3573i −0.458889 0.794819i
657657 4.74342 8.21584i 0.185058 0.320530i
658658 1.38546 + 0.294488i 0.0540107 + 0.0114803i
659659 14.5795 44.8712i 0.567938 1.74793i −0.0911197 0.995840i 0.529045π-0.529045\pi
0.659057 0.752093i 0.270955π-0.270955\pi
660660 −39.3697 + 8.36828i −1.53246 + 0.325735i
661661 4.79083 45.5817i 0.186342 1.77292i −0.357671 0.933848i 0.616429π-0.616429\pi
0.544013 0.839077i 0.316904π-0.316904\pi
662662 6.55118 7.27582i 0.254619 0.282783i
663663 −7.75169 + 3.45127i −0.301051 + 0.134036i
664664 4.25283 + 1.89348i 0.165042 + 0.0734814i
665665 1.49622 + 1.66172i 0.0580210 + 0.0644388i
666666 2.93159 2.12993i 0.113597 0.0825330i
667667 20.5623 14.9394i 0.796176 0.578455i
668668 −9.18681 10.2030i −0.355448 0.394765i
669669 −45.5755 20.2915i −1.76205 0.784515i
670670 −4.68157 + 2.08437i −0.180865 + 0.0805261i
671671 12.6301 14.0271i 0.487580 0.541512i
672672 −0.991644 + 9.43486i −0.0382535 + 0.363958i
673673 −7.29075 + 1.54970i −0.281038 + 0.0597364i −0.346274 0.938133i 0.612553π-0.612553\pi
0.0652363 + 0.997870i 0.479220π0.479220\pi
674674 0.692055 2.12993i 0.0266570 0.0820417i
675675 0 0
676676 31.6353 54.7939i 1.21674 2.10746i
677677 −10.6066 18.3712i −0.407645 0.706062i 0.586981 0.809601i 0.300317π-0.300317\pi
−0.994625 + 0.103540i 0.966983π0.966983\pi
678678 3.84503 + 11.8338i 0.147668 + 0.454474i
679679 −0.731699 6.96165i −0.0280800 0.267164i
680680 1.43857 + 1.04518i 0.0551666 + 0.0400808i
681681 −35.9442 −1.37739
682682 0 0
683683 −18.8197 −0.720114 −0.360057 0.932930i 0.617243π-0.617243\pi
−0.360057 + 0.932930i 0.617243π0.617243\pi
684684 3.35410 + 2.43690i 0.128247 + 0.0931771i
685685 −1.60451 15.2659i −0.0613053 0.583281i
686686 1.53444 + 4.72253i 0.0585853 + 0.180307i
687687 −4.85410 8.40755i −0.185196 0.320768i
688688 −0.324548 + 0.562134i −0.0123733 + 0.0214312i
689689 −35.2133 7.48482i −1.34152 0.285149i
690690 −4.14590 + 12.7598i −0.157832 + 0.485756i
691691 21.1119 4.48748i 0.803136 0.170712i 0.211985 0.977273i 0.432007π-0.432007\pi
0.591151 + 0.806561i 0.298674π0.298674\pi
692692 3.48852 33.1910i 0.132613 1.26173i
693693 6.34793 7.05009i 0.241138 0.267811i
694694 −9.01614 + 4.01424i −0.342248 + 0.152379i
695695 2.04592 + 0.910902i 0.0776061 + 0.0345525i
696696 8.34549 + 9.26860i 0.316335 + 0.351326i
697697 3.26544 2.37248i 0.123687 0.0898642i
698698 −1.85410 + 1.34708i −0.0701788 + 0.0509879i
699699 6.93277 + 7.69962i 0.262222 + 0.291226i
700700 0 0
701701 25.2618 11.2473i 0.954125 0.424804i 0.130190 0.991489i 0.458441π-0.458441\pi
0.823934 + 0.566685i 0.191774π0.191774\pi
702702 −3.06702 + 3.40627i −0.115757 + 0.128561i
703703 0.443477 4.21940i 0.0167260 0.159138i
704704 −19.5387 + 4.15308i −0.736393 + 0.156525i
705705 5.86319 18.0450i 0.220820 0.679615i
706706 5.93688 + 1.26192i 0.223438 + 0.0474931i
707707 −1.11803 + 1.93649i −0.0420480 + 0.0728293i
708708 12.6097 + 21.8406i 0.473902 + 0.820822i
709709 −4.86163 14.9626i −0.182582 0.561931i 0.817316 0.576190i 0.195461π-0.195461\pi
−0.999898 + 0.0142588i 0.995461π0.995461\pi
710710 0.667097 + 6.34700i 0.0250357 + 0.238199i
711711 −20.0934 14.5987i −0.753563 0.547495i
712712 −8.63141 −0.323476
713713 0 0
714714 −0.472136 −0.0176692
715715 52.6869 + 38.2793i 1.97038 + 1.43156i
716716 −3.18431 30.2967i −0.119003 1.13224i
717717 −11.5623 35.5851i −0.431802 1.32895i
718718 −1.86475 3.22983i −0.0695917 0.120536i
719719 −4.55214 + 7.88453i −0.169766 + 0.294043i −0.938338 0.345720i 0.887635π-0.887635\pi
0.768571 + 0.639764i 0.220968π0.220968\pi
720720 15.3858 + 3.27034i 0.573394 + 0.121879i
721721 0.836881 2.57565i 0.0311671 0.0959224i
722722 6.72514 1.42947i 0.250284 0.0531995i
723723 −3.52347 + 33.5235i −0.131039 + 1.24675i
724724 22.5528 25.0475i 0.838170 0.930882i
725725 0 0
726726 −5.58928 2.48851i −0.207437 0.0923571i
727727 −2.39789 2.66313i −0.0889329 0.0987699i 0.697036 0.717036i 0.254502π-0.254502\pi
−0.785969 + 0.618267i 0.787835π0.787835\pi
728728 8.17578 5.94006i 0.303015 0.220153i
729729 9.66312 7.02067i 0.357893 0.260025i
730730 2.42469 + 2.69290i 0.0897419 + 0.0996685i
731731 −0.101820 0.0453333i −0.00376596 0.00167671i
732732 −17.2435 + 7.67731i −0.637339 + 0.283762i
733733 8.30820 9.22719i 0.306870 0.340814i −0.569908 0.821708i 0.693021π-0.693021\pi
0.876779 + 0.480894i 0.159688π0.159688\pi
734734 −0.491703 + 4.67824i −0.0181491 + 0.172677i
735735 30.0292 6.38290i 1.10764 0.235437i
736736 −8.79478 + 27.0675i −0.324180 + 0.997723i
737737 24.8996 + 5.29257i 0.917188 + 0.194954i
738738 −3.19098 + 5.52694i −0.117462 + 0.203450i
739739 −12.8311 22.2241i −0.471999 0.817527i 0.527488 0.849563i 0.323134π-0.323134\pi
−0.999487 + 0.0320362i 0.989801π0.989801\pi
740740 −5.43547 16.7287i −0.199812 0.614958i
741741 −1.64195 15.6222i −0.0603187 0.573894i
742742 −1.62054 1.17739i −0.0594921 0.0432235i
743743 1.69936 0.0623433 0.0311717 0.999514i 0.490076π-0.490076\pi
0.0311717 + 0.999514i 0.490076π0.490076\pi
744744 0 0
745745 −30.0000 −1.09911
746746 7.01722 + 5.09831i 0.256919 + 0.186662i
747747 0.739128 + 7.03233i 0.0270433 + 0.257300i
748748 −1.31308 4.04125i −0.0480110 0.147763i
749749 −3.73607 6.47106i −0.136513 0.236447i
750750 4.88599 8.46278i 0.178411 0.309017i
751751 −28.8955 6.14192i −1.05441 0.224122i −0.352078 0.935971i 0.614525π-0.614525\pi
−0.702333 + 0.711849i 0.747858π0.747858\pi
752752 3.60488 11.0947i 0.131456 0.404581i
753753 53.1728 11.3022i 1.93772 0.411876i
754754 1.01478 9.65502i 0.0369562 0.351615i
755755 4.54067 5.04293i 0.165252 0.183531i
756756 2.96088 1.31827i 0.107686 0.0479450i
757757 17.5218 + 7.80121i 0.636841 + 0.283540i 0.699650 0.714486i 0.253339π-0.253339\pi
−0.0628093 + 0.998026i 0.520006π0.520006\pi
758758 −4.96255 5.51147i −0.180248 0.200185i
759759 53.9163 39.1725i 1.95704 1.42187i
760760 −2.66312 + 1.93487i −0.0966015 + 0.0701851i
761761 −1.49854 1.66430i −0.0543221 0.0603309i 0.715371 0.698745i 0.246258π-0.246258\pi
−0.769693 + 0.638414i 0.779591π0.779591\pi
762762 7.57493 + 3.37258i 0.274411 + 0.122176i
763763 13.4366 5.98237i 0.486438 0.216576i
764764 −17.6618 + 19.6154i −0.638981 + 0.709660i
765765 −0.282322 + 2.68611i −0.0102074 + 0.0971166i
766766 −7.11837 + 1.51306i −0.257197 + 0.0546689i
767767 12.6097 38.8087i 0.455310 1.40130i
768768 12.4498 + 2.64628i 0.449243 + 0.0954895i
769769 −6.93769 + 12.0164i −0.250180 + 0.433324i −0.963575 0.267438i 0.913823π-0.913823\pi
0.713395 + 0.700762i 0.247156π0.247156\pi
770770 1.81182 + 3.13817i 0.0652936 + 0.113092i
771771 −16.9312 52.1087i −0.609761 1.87665i
772772 −1.41320 13.4457i −0.0508621 0.483920i
773773 −21.8415 15.8688i −0.785584 0.570760i 0.121066 0.992645i 0.461369π-0.461369\pi
−0.906650 + 0.421884i 0.861369π0.861369\pi
774774 0.176228 0.00633437
775775 0 0
776776 10.3050 0.369926
777777 7.85410 + 5.70634i 0.281764 + 0.204714i
778778 1.34885 + 12.8335i 0.0483586 + 0.460102i
779779 2.30902 + 7.10642i 0.0827291 + 0.254614i
780780 −32.5623 56.3996i −1.16592 2.01943i
781781 15.8508 27.4544i 0.567186 0.982395i
782782 −1.38546 0.294488i −0.0495438 0.0105309i
783783 2.00000 6.15537i 0.0714742 0.219975i
784784 18.4629 3.92441i 0.659390 0.140158i
785785 −1.10046 + 10.4702i −0.0392772 + 0.373697i
786786 11.3555 12.6116i 0.405038 0.449840i
787787 8.31717 3.70304i 0.296475 0.131999i −0.253109 0.967438i 0.581453π-0.581453\pi
0.549584 + 0.835439i 0.314786π0.314786\pi
788788 −12.5425 5.58428i −0.446808 0.198932i
789789 4.13545 + 4.59289i 0.147226 + 0.163511i
790790 7.67501 5.57622i 0.273065 0.198393i
791791 −11.5172 + 8.36775i −0.409505 + 0.297523i
792792 9.34502 + 10.3787i 0.332061 + 0.368791i
793793 27.9006 + 12.4222i 0.990780 + 0.441124i
794794 0.450764 0.200693i 0.0159970 0.00712232i
795795 −17.9547 + 19.9407i −0.636786 + 0.707223i
796796 2.85497 27.1632i 0.101192 0.962774i
797797 5.12959 1.09033i 0.181700 0.0386214i −0.116163 0.993230i 0.537060π-0.537060\pi
0.297863 + 0.954609i 0.403726π0.403726\pi
798798 0.270091 0.831254i 0.00956111 0.0294261i
799799 1.95933 + 0.416469i 0.0693161 + 0.0147336i
800800 0 0
801801 −6.55524 11.3540i −0.231618 0.401174i
802802 0.437016 + 1.34500i 0.0154316 + 0.0474935i
803803 −1.88151 17.9014i −0.0663971 0.631726i
804804 −20.5942 14.9626i −0.726302 0.527689i
805805 −15.3500 −0.541017
806806 0 0
807807 33.8885 1.19293
808808 −2.66312 1.93487i −0.0936882 0.0680685i
809809 −2.30560 21.9363i −0.0810605 0.771239i −0.957248 0.289269i 0.906588π-0.906588\pi
0.876187 0.481971i 0.160079π-0.160079\pi
810810 2.82624 + 8.69827i 0.0993039 + 0.305626i
811811 21.7082 + 37.5997i 0.762278 + 1.32030i 0.941674 + 0.336527i 0.109252π0.109252\pi
−0.179396 + 0.983777i 0.557414π0.557414\pi
812812 −3.43237 + 5.94504i −0.120453 + 0.208630i
813813 62.8452 + 13.3582i 2.20408 + 0.468491i
814814 2.12461 6.53888i 0.0744676 0.229188i
815815 −27.1572 + 5.77245i −0.951276 + 0.202200i
816816 −0.406464 + 3.86724i −0.0142291 + 0.135381i
817817 0.138062 0.153334i 0.00483019 0.00536447i
818818 6.05526 2.69597i 0.211717 0.0942625i
819819 14.0229 + 6.24341i 0.490001 + 0.218163i
820820 20.7288 + 23.0217i 0.723881 + 0.803952i
821821 11.6082 8.43382i 0.405127 0.294342i −0.366499 0.930419i 0.619444π-0.619444\pi
0.771626 + 0.636076i 0.219444π0.219444\pi
822822 −4.85410 + 3.52671i −0.169306 + 0.123008i
823823 −9.99504 11.1006i −0.348405 0.386943i 0.543316 0.839528i 0.317169π-0.317169\pi
−0.891721 + 0.452585i 0.850502π0.850502\pi
824824 3.64216 + 1.62160i 0.126881 + 0.0564910i
825825 0 0
826826 1.51927 1.68732i 0.0528621 0.0587093i
827827 5.02292 47.7899i 0.174664 1.66182i −0.459169 0.888349i 0.651853π-0.651853\pi
0.633834 0.773470i 0.281480π-0.281480\pi
828828 −27.8386 + 5.91727i −0.967457 + 0.205639i
829829 1.80252 5.54759i 0.0626042 0.192676i −0.914863 0.403765i 0.867701π-0.867701\pi
0.977467 + 0.211090i 0.0677012π0.0677012\pi
830830 −2.64189 0.561550i −0.0917012 0.0194917i
831831 −22.4164 + 38.8264i −0.777617 + 1.34687i
832832 −16.1603 27.9904i −0.560257 0.970394i
833833 1.00155 + 3.08246i 0.0347017 + 0.106801i
834834 −0.0915030 0.870593i −0.00316849 0.0301462i
835835 13.3956 + 9.73249i 0.463575 + 0.336807i
836836 7.86629 0.272061
837837 0 0
838838 −7.10333 −0.245380
839839 −6.00000 4.35926i −0.207143 0.150498i 0.479377 0.877609i 0.340863π-0.340863\pi
−0.686520 + 0.727111i 0.740863π0.740863\pi
840840 −0.787354 7.49117i −0.0271663 0.258470i
841841 −4.72542 14.5434i −0.162946 0.501495i
842842 0.0795268 + 0.137745i 0.00274068 + 0.00474699i
843843 −35.8805 + 62.1468i −1.23579 + 2.14045i
844844 −9.06793 1.92745i −0.312131 0.0663455i
845845 −23.5795 + 72.5703i −0.811160 + 2.49649i
846846 −3.09797 + 0.658495i −0.106511 + 0.0226395i
847847 0.731699 6.96165i 0.0251415 0.239205i
848848 −11.0391 + 12.2602i −0.379085 + 0.421016i
849849 −50.1700 + 22.3371i −1.72183 + 0.766608i
850850 0 0
851851 19.4882 + 21.6438i 0.668046 + 0.741940i
852852 −25.6471 + 18.6337i −0.878656 + 0.638381i
853853 36.9787 26.8666i 1.26613 0.919895i 0.267086 0.963673i 0.413939π-0.413939\pi
0.999041 + 0.0437776i 0.0139393π0.0139393\pi
854854 1.13709 + 1.26287i 0.0389105 + 0.0432144i
855855 −4.56773 2.03368i −0.156213 0.0695505i
856856 10.0490 4.47410i 0.343468 0.152922i
857857 −4.01478 + 4.45887i −0.137142 + 0.152312i −0.807804 0.589452i 0.799344π-0.799344\pi
0.670661 + 0.741764i 0.266010π0.266010\pi
858858 2.66086 25.3164i 0.0908403 0.864287i
859859 −3.57391 + 0.759658i −0.121940 + 0.0259192i −0.268477 0.963286i 0.586520π-0.586520\pi
0.146537 + 0.989205i 0.453187π0.453187\pi
860860 0.264342 0.813560i 0.00901397 0.0277422i
861861 −16.7244 3.55489i −0.569968 0.121150i
862862 0.0212862 0.0368688i 0.000725012 0.00125576i
863863 17.6626 + 30.5926i 0.601243 + 1.04138i 0.992633 + 0.121158i 0.0386608π0.0386608\pi
−0.391391 + 0.920225i 0.628006π0.628006\pi
864864 2.23954 + 6.89259i 0.0761906 + 0.234491i
865865 4.20719 + 40.0287i 0.143049 + 1.36102i
866866 6.67346 + 4.84855i 0.226773 + 0.164760i
867867 38.2325 1.29844
868868 0 0
869869 −47.1246 −1.59859
870870 −5.85410 4.25325i −0.198473 0.144199i
871871 4.30536 + 40.9628i 0.145882 + 1.38797i
872872 6.69098 + 20.5927i 0.226585 + 0.697358i
873873 7.82624 + 13.5554i 0.264878 + 0.458782i
874874 1.31105 2.27080i 0.0443469 0.0768110i
875875 10.9360 + 2.32452i 0.369705 + 0.0785832i
876876 −5.56231 + 17.1190i −0.187933 + 0.578398i
877877 14.9576 3.17934i 0.505083 0.107359i 0.0516791 0.998664i 0.483543π-0.483543\pi
0.453404 + 0.891305i 0.350209π0.350209\pi
878878 0.998158 9.49684i 0.0336862 0.320503i
879879 24.0514 26.7118i 0.811233 0.900966i
880880 27.2644 12.1389i 0.919083 0.409202i
881881 45.3792 + 20.2041i 1.52886 + 0.680694i 0.987139 0.159862i 0.0511050π-0.0511050\pi
0.541724 + 0.840556i 0.317772π0.317772\pi
882882 −3.42903 3.80833i −0.115462 0.128233i
883883 −27.4589 + 19.9501i −0.924067 + 0.671374i −0.944533 0.328416i 0.893485π-0.893485\pi
0.0204659 + 0.999791i 0.493485π0.493485\pi
884884 5.56231 4.04125i 0.187081 0.135922i
885885 −20.3515 22.6027i −0.684109 0.759780i
886886 8.35519 + 3.71997i 0.280698 + 0.124975i
887887 −17.6869 + 7.87470i −0.593867 + 0.264406i −0.681585 0.731739i 0.738709π-0.738709\pi
0.0877185 + 0.996145i 0.472042π0.472042\pi
888888 −9.56308 + 10.6209i −0.320916 + 0.356413i
889889 −0.991644 + 9.43486i −0.0332587 + 0.316435i
890890 4.89833 1.04117i 0.164192 0.0349001i
891891 14.0390 43.2075i 0.470323 1.44751i
892892 39.5400 + 8.40448i 1.32390 + 0.281403i
893893 −1.85410 + 3.21140i −0.0620452 + 0.107465i
894894 5.86319 + 10.1553i 0.196094 + 0.339645i
895895 11.3531 + 34.9413i 0.379493 + 1.16796i
896896 −1.05471 10.0349i −0.0352354 0.335242i
897897 87.2385 + 63.3825i 2.91281 + 2.11628i
898898 16.1151 0.537769
899899 0 0
900900 0 0
901901 −2.29180 1.66509i −0.0763508 0.0554721i
902902 1.26573 + 12.0426i 0.0421441 + 0.400975i
903903 0.145898 + 0.449028i 0.00485518 + 0.0149427i
904904 −10.4787 18.1497i −0.348517 0.603649i
905905 −20.3241 + 35.2024i −0.675597 + 1.17017i
906906 −2.59451 0.551481i −0.0861969 0.0183217i
907907 −17.1631 + 52.8226i −0.569892 + 1.75395i 0.0830564 + 0.996545i 0.473532π0.473532\pi
−0.652948 + 0.757402i 0.726468π0.726468\pi
908908 28.4882 6.05535i 0.945413 0.200954i
909909 0.522642 4.97261i 0.0173350 0.164931i
910910 −3.92324 + 4.35720i −0.130054 + 0.144440i
911911 −12.9640 + 5.77194i −0.429516 + 0.191233i −0.610096 0.792327i 0.708869π-0.708869\pi
0.180580 + 0.983560i 0.442202π0.442202\pi
912912 −6.57624 2.92793i −0.217761 0.0969534i
913913 8.97733 + 9.97033i 0.297106 + 0.329970i
914914 3.49613 2.54009i 0.115642 0.0840186i
915915 18.4164 13.3803i 0.608828 0.442339i
916916 5.26357 + 5.84579i 0.173913 + 0.193150i
917917 17.7378 + 7.89736i 0.585753 + 0.260794i
918918 −0.329497 + 0.146702i −0.0108750 + 0.00484188i
919919 16.4211 18.2375i 0.541684 0.601601i −0.408705 0.912667i 0.634019π-0.634019\pi
0.950388 + 0.311066i 0.100686π0.100686\pi
920920 2.36206 22.4735i 0.0778749 0.740930i
921921 −36.0908 + 7.67133i −1.18923 + 0.252779i
922922 4.61590 14.2063i 0.152016 0.467859i
923923 50.1733 + 10.6647i 1.65148 + 0.351032i
924924 −9.00000 + 15.5885i −0.296078 + 0.512823i
925925 0 0
926926 −1.78747 5.50127i −0.0587399 0.180783i
927927 0.632996 + 6.02255i 0.0207903 + 0.197807i
928928 −12.4184 9.02251i −0.407655 0.296179i
929929 −23.2951 −0.764288 −0.382144 0.924103i 0.624814π-0.624814\pi
−0.382144 + 0.924103i 0.624814π0.624814\pi
930930 0 0
931931 −6.00000 −0.196642
932932 −6.79180 4.93453i −0.222473 0.161636i
933933 3.95325 + 37.6126i 0.129423 + 1.23138i
934934 1.84752 + 5.68609i 0.0604528 + 0.186055i
935935 2.56231 + 4.43804i 0.0837964 + 0.145140i
936936 −11.2987 + 19.5698i −0.369308 + 0.639660i
937937 55.0200 + 11.6949i 1.79743 + 0.382055i 0.980785 0.195091i 0.0625002π-0.0625002\pi
0.816641 + 0.577146i 0.195833π0.195833\pi
938938 −0.708204 + 2.17963i −0.0231237 + 0.0711674i
939939 47.0185 9.99408i 1.53439 0.326145i
940940 −1.60700 + 15.2896i −0.0524147 + 0.498692i
941941 −34.0138 + 37.7762i −1.10882 + 1.23147i −0.138314 + 0.990388i 0.544168π0.544168\pi
−0.970505 + 0.241080i 0.922498π0.922498\pi
942942 3.75935 1.67377i 0.122486 0.0545344i
943943 −46.8596 20.8632i −1.52596 0.679401i
944944 −12.5128 13.8969i −0.407257 0.452304i
945945 −3.16228 + 2.29753i −0.102869 + 0.0747386i
946946 0.270510 0.196537i 0.00879503 0.00638997i
947947 −1.49854 1.66430i −0.0486961 0.0540825i 0.718305 0.695729i 0.244918π-0.244918\pi
−0.767001 + 0.641646i 0.778252π0.778252\pi
948948 43.0505 + 19.1673i 1.39821 + 0.622525i
949949 26.6067 11.8460i 0.863689 0.384539i
950950 0 0
951951 5.20565 49.5284i 0.168805 1.60607i
952952 0.777843 0.165336i 0.0252100 0.00535856i
953953 −16.5185 + 50.8387i −0.535087 + 1.64683i 0.208375 + 0.978049i 0.433182π0.433182\pi
−0.743462 + 0.668778i 0.766818π0.766818\pi
954954 4.38120 + 0.931252i 0.141846 + 0.0301504i
955955 15.9164 27.5680i 0.515043 0.892080i
956956 15.1587 + 26.2557i 0.490269 + 0.849170i
957957 11.1074 + 34.1850i 0.359051 + 1.10504i
958958 −1.01701 9.67619i −0.0328581 0.312624i
959959 −5.55369 4.03499i −0.179338 0.130297i
960960 −24.0903 −0.777512
961961 0 0
962962 11.1246 0.358672
963963 13.5172 + 9.82084i 0.435586 + 0.316472i
964964 −2.85497 27.1632i −0.0919523 0.874868i
965965 5.03851 + 15.5069i 0.162195 + 0.499186i
966966 3.00000 + 5.19615i 0.0965234 + 0.167183i
967967 −6.45207 + 11.1753i −0.207485 + 0.359374i −0.950922 0.309432i 0.899861π-0.899861\pi
0.743437 + 0.668806i 0.233194π0.233194\pi
968968 10.0798 + 2.14252i 0.323976 + 0.0688632i
969969 0.381966 1.17557i 0.0122705 0.0377648i
970970 −5.84806 + 1.24304i −0.187770 + 0.0399118i
971971 −1.89316 + 18.0122i −0.0607545 + 0.578040i 0.921222 + 0.389037i 0.127192π0.127192\pi
−0.981977 + 0.189003i 0.939474π0.939474\pi
972972 −23.8932 + 26.5361i −0.766374 + 0.851145i
973973 0.914963 0.407368i 0.0293324 0.0130596i
974974 −6.48724 2.88831i −0.207865 0.0925473i
975975 0 0
976976 11.3230 8.22665i 0.362441 0.263329i
977977 −34.3713 + 24.9722i −1.09964 + 0.798932i −0.981000 0.194006i 0.937852π-0.937852\pi
−0.118636 + 0.992938i 0.537852π0.537852\pi
978978 7.26163 + 8.06486i 0.232201 + 0.257886i
979979 −22.7248 10.1177i −0.726288 0.323364i
980980 −22.7248 + 10.1177i −0.725917 + 0.323199i
981981 −22.0067 + 24.4410i −0.702621 + 0.780340i
982982 −0.381921 + 3.63374i −0.0121876 + 0.115957i
983983 −2.93900 + 0.624703i −0.0937394 + 0.0199249i −0.254543 0.967062i 0.581925π-0.581925\pi
0.160803 + 0.986986i 0.448592π0.448592\pi
984984 7.77817 23.9388i 0.247959 0.763140i
985985 16.1961 + 3.44258i 0.516050 + 0.109690i
986986 0.381966 0.661585i 0.0121643 0.0210691i
987987 −4.24264 7.34847i −0.135045 0.233904i
988988 3.93314 + 12.1050i 0.125130 + 0.385111i
989989 0.148055 + 1.40865i 0.00470787 + 0.0447924i
990990 −6.55524 4.76266i −0.208339 0.151367i
991991 4.44897 0.141326 0.0706631 0.997500i 0.477488π-0.477488\pi
0.0706631 + 0.997500i 0.477488π0.477488\pi
992992 0 0
993993 −58.6525 −1.86128
994994 2.30902 + 1.67760i 0.0732376 + 0.0532102i
995995 3.44312 + 32.7591i 0.109154 + 1.03853i
996996 −4.14590 12.7598i −0.131368 0.404309i
997997 −24.3328 42.1457i −0.770628 1.33477i −0.937219 0.348741i 0.886609π-0.886609\pi
0.166591 0.986026i 0.446724π-0.446724\pi
998998 3.51118 6.08154i 0.111144 0.192508i
999999 7.25434 + 1.54196i 0.229517 + 0.0487854i
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 961.2.g.p.816.2 16
31.2 even 5 961.2.g.i.846.2 16
31.3 odd 30 inner 961.2.g.p.338.1 16
31.4 even 5 961.2.c.h.439.2 8
31.5 even 3 961.2.d.j.374.2 8
31.6 odd 6 inner 961.2.g.p.732.2 16
31.7 even 15 961.2.c.h.521.2 8
31.8 even 5 961.2.g.i.547.1 16
31.9 even 15 961.2.d.h.531.1 8
31.10 even 15 961.2.d.h.628.1 8
31.11 odd 30 961.2.a.h.1.2 yes 4
31.12 odd 30 961.2.g.i.448.2 16
31.13 odd 30 961.2.d.j.388.1 8
31.14 even 15 961.2.g.i.844.2 16
31.15 odd 10 inner 961.2.g.p.235.2 16
31.16 even 5 inner 961.2.g.p.235.1 16
31.17 odd 30 961.2.g.i.844.1 16
31.18 even 15 961.2.d.j.388.2 8
31.19 even 15 961.2.g.i.448.1 16
31.20 even 15 961.2.a.h.1.1 4
31.21 odd 30 961.2.d.h.628.2 8
31.22 odd 30 961.2.d.h.531.2 8
31.23 odd 10 961.2.g.i.547.2 16
31.24 odd 30 961.2.c.h.521.1 8
31.25 even 3 inner 961.2.g.p.732.1 16
31.26 odd 6 961.2.d.j.374.1 8
31.27 odd 10 961.2.c.h.439.1 8
31.28 even 15 inner 961.2.g.p.338.2 16
31.29 odd 10 961.2.g.i.846.1 16
31.30 odd 2 inner 961.2.g.p.816.1 16
93.11 even 30 8649.2.a.r.1.3 4
93.20 odd 30 8649.2.a.r.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
961.2.a.h.1.1 4 31.20 even 15
961.2.a.h.1.2 yes 4 31.11 odd 30
961.2.c.h.439.1 8 31.27 odd 10
961.2.c.h.439.2 8 31.4 even 5
961.2.c.h.521.1 8 31.24 odd 30
961.2.c.h.521.2 8 31.7 even 15
961.2.d.h.531.1 8 31.9 even 15
961.2.d.h.531.2 8 31.22 odd 30
961.2.d.h.628.1 8 31.10 even 15
961.2.d.h.628.2 8 31.21 odd 30
961.2.d.j.374.1 8 31.26 odd 6
961.2.d.j.374.2 8 31.5 even 3
961.2.d.j.388.1 8 31.13 odd 30
961.2.d.j.388.2 8 31.18 even 15
961.2.g.i.448.1 16 31.19 even 15
961.2.g.i.448.2 16 31.12 odd 30
961.2.g.i.547.1 16 31.8 even 5
961.2.g.i.547.2 16 31.23 odd 10
961.2.g.i.844.1 16 31.17 odd 30
961.2.g.i.844.2 16 31.14 even 15
961.2.g.i.846.1 16 31.29 odd 10
961.2.g.i.846.2 16 31.2 even 5
961.2.g.p.235.1 16 31.16 even 5 inner
961.2.g.p.235.2 16 31.15 odd 10 inner
961.2.g.p.338.1 16 31.3 odd 30 inner
961.2.g.p.338.2 16 31.28 even 15 inner
961.2.g.p.732.1 16 31.25 even 3 inner
961.2.g.p.732.2 16 31.6 odd 6 inner
961.2.g.p.816.1 16 31.30 odd 2 inner
961.2.g.p.816.2 16 1.1 even 1 trivial
8649.2.a.r.1.3 4 93.11 even 30
8649.2.a.r.1.4 4 93.20 odd 30