Properties

Label 91.2.e.c.53.2
Level 9191
Weight 22
Character 91.53
Analytic conductor 0.7270.727
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(53,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 91=713 91 = 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 91.e (of order 33, degree 22, 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: 0.7266386583940.726638658394
Analytic rank: 00
Dimension: 1010
Relative dimension: 55 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x10x9+8x8+7x7+41x6+18x5+58x4+28x3+64x2+16x+4 x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 3 3
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 53.2
Root 0.6066611.05077i-0.606661 - 1.05077i of defining polynomial
Character χ\chi == 91.53
Dual form 91.2.e.c.79.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.106661.91679i)q2+(1.23721+2.14292i)q3+(1.44940+2.51043i)q4+(1.06140+1.83839i)q5+5.47671q6+(2.63169+0.272389i)q7+1.98932q8+(1.561402.70442i)q9+(2.349214.06896i)q10+(2.39448+4.14736i)q11+(3.586436.21188i)q12+1.00000q13+(2.390285.34585i)q145.25271q15+(0.697291+1.20774i)q16+(1.889143.27208i)q17+(3.45588+5.98575i)q18+(1.78362+3.08931i)q196.15355q20+(3.83967+5.30250i)q21+10.5995q22+(2.237213.87497i)q23+(2.46122+4.26295i)q24+(0.2468700.427591i)q25+(1.106661.91679i)q26+0.303848q27+(4.49818+6.21188i)q285.90107q29+(5.81296+10.0683i)q30+(1.885583.26592i)q31+(3.532656.11873i)q32+(5.9249610.2623i)q338.36254q34+(2.29251+5.12720i)q35+9.05234q36+(2.812854.87200i)q37+(3.947726.83765i)q38+(1.23721+2.14292i)q39+(2.11146+3.65716i)q40+10.3948q41+(14.4130+1.49180i)q42+3.40733q43+(6.9411012.0223i)q44+(3.314535.74093i)q45+(4.95168+8.57655i)q46+(3.55438+6.15636i)q473.45079q48+(6.85161+1.43369i)q491.09280q50+(4.67454+8.09654i)q51+(1.44940+2.51043i)q52+(6.1900310.7214i)q53+(0.3362570.582415i)q5410.1660q55+(5.23528+0.541869i)q568.82686q57+(6.53049+11.3111i)q58+(2.39448+4.14736i)q59+(7.6132613.1865i)q60+(1.603482.77732i)q618.34680q62+(3.372467.54251i)q6312.8486q64+(1.06140+1.83839i)q65+(13.1139+22.7139i)q66+(1.449782.51109i)q67+(5.47622+9.48510i)q68+11.0717q69+(7.2907510.0683i)q702.53876q71+(3.106125.37996i)q72+(3.85035+6.66901i)q73+(6.22574+10.7833i)q74+(0.610862+1.05804i)q7510.3407q76+(7.43122+10.2623i)q77+5.47671q78+(2.58925+4.48471i)q79+(1.48021+2.56379i)q80+(4.308277.46214i)q81+(11.503519.9247i)q82+3.46731q83+(7.7463317.3247i)q84+8.02051q85+(3.770766.53115i)q86+(7.3008912.6455i)q87+(4.76338+8.25042i)q88+(1.832163.17339i)q8914.6722q90+(2.63169+0.272389i)q91+12.9704q92+(4.66574+8.08129i)q93+(7.8669813.6260i)q94+(3.78625+6.55798i)q95+(8.74129+15.1404i)q965.40733q97+(4.8343214.7197i)q98+14.9549q99+O(q100)q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +(2.34921 - 4.06896i) q^{10} +(-2.39448 + 4.14736i) q^{11} +(-3.58643 - 6.21188i) q^{12} +1.00000 q^{13} +(-2.39028 - 5.34585i) q^{14} -5.25271 q^{15} +(0.697291 + 1.20774i) q^{16} +(1.88914 - 3.27208i) q^{17} +(-3.45588 + 5.98575i) q^{18} +(1.78362 + 3.08931i) q^{19} -6.15355 q^{20} +(-3.83967 + 5.30250i) q^{21} +10.5995 q^{22} +(-2.23721 - 3.87497i) q^{23} +(-2.46122 + 4.26295i) q^{24} +(0.246870 - 0.427591i) q^{25} +(-1.10666 - 1.91679i) q^{26} +0.303848 q^{27} +(-4.49818 + 6.21188i) q^{28} -5.90107 q^{29} +(5.81296 + 10.0683i) q^{30} +(1.88558 - 3.26592i) q^{31} +(3.53265 - 6.11873i) q^{32} +(-5.92496 - 10.2623i) q^{33} -8.36254 q^{34} +(2.29251 + 5.12720i) q^{35} +9.05234 q^{36} +(-2.81285 - 4.87200i) q^{37} +(3.94772 - 6.83765i) q^{38} +(-1.23721 + 2.14292i) q^{39} +(2.11146 + 3.65716i) q^{40} +10.3948 q^{41} +(14.4130 + 1.49180i) q^{42} +3.40733 q^{43} +(-6.94110 - 12.0223i) q^{44} +(3.31453 - 5.74093i) q^{45} +(-4.95168 + 8.57655i) q^{46} +(3.55438 + 6.15636i) q^{47} -3.45079 q^{48} +(6.85161 + 1.43369i) q^{49} -1.09280 q^{50} +(4.67454 + 8.09654i) q^{51} +(-1.44940 + 2.51043i) q^{52} +(6.19003 - 10.7214i) q^{53} +(-0.336257 - 0.582415i) q^{54} -10.1660 q^{55} +(5.23528 + 0.541869i) q^{56} -8.82686 q^{57} +(6.53049 + 11.3111i) q^{58} +(-2.39448 + 4.14736i) q^{59} +(7.61326 - 13.1865i) q^{60} +(-1.60348 - 2.77732i) q^{61} -8.34680 q^{62} +(-3.37246 - 7.54251i) q^{63} -12.8486 q^{64} +(1.06140 + 1.83839i) q^{65} +(-13.1139 + 22.7139i) q^{66} +(1.44978 - 2.51109i) q^{67} +(5.47622 + 9.48510i) q^{68} +11.0717 q^{69} +(7.29075 - 10.0683i) q^{70} -2.53876 q^{71} +(-3.10612 - 5.37996i) q^{72} +(-3.85035 + 6.66901i) q^{73} +(-6.22574 + 10.7833i) q^{74} +(0.610862 + 1.05804i) q^{75} -10.3407 q^{76} +(-7.43122 + 10.2623i) q^{77} +5.47671 q^{78} +(2.58925 + 4.48471i) q^{79} +(-1.48021 + 2.56379i) q^{80} +(4.30827 - 7.46214i) q^{81} +(-11.5035 - 19.9247i) q^{82} +3.46731 q^{83} +(-7.74633 - 17.3247i) q^{84} +8.02051 q^{85} +(-3.77076 - 6.53115i) q^{86} +(7.30089 - 12.6455i) q^{87} +(-4.76338 + 8.25042i) q^{88} +(-1.83216 - 3.17339i) q^{89} -14.6722 q^{90} +(2.63169 + 0.272389i) q^{91} +12.9704 q^{92} +(4.66574 + 8.08129i) q^{93} +(7.86698 - 13.6260i) q^{94} +(-3.78625 + 6.55798i) q^{95} +(8.74129 + 15.1404i) q^{96} -5.40733 q^{97} +(-4.83432 - 14.7197i) q^{98} +14.9549 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q4q28q42q510q6+q7+18q83q9+5q1011q115q12+10q13+10q1410q16+5q179q189q19+2q20+2q21+16q22++22q99+O(q100) 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22}+ \cdots + 22 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/91Z)×\left(\mathbb{Z}/91\mathbb{Z}\right)^\times.

nn 1515 6666
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.10666 1.91679i −0.782527 1.35538i −0.930465 0.366381i 0.880597π-0.880597\pi
0.147938 0.988997i 0.452737π-0.452737\pi
33 −1.23721 + 2.14292i −0.714306 + 1.23721i 0.248921 + 0.968524i 0.419924π0.419924\pi
−0.963227 + 0.268690i 0.913409π0.913409\pi
44 −1.44940 + 2.51043i −0.724699 + 1.25521i
55 1.06140 + 1.83839i 0.474671 + 0.822155i 0.999579 0.0290040i 0.00923354π-0.00923354\pi
−0.524908 + 0.851159i 0.675900π0.675900\pi
66 5.47671 2.23586
77 2.63169 + 0.272389i 0.994686 + 0.102953i
88 1.98932 0.703331
99 −1.56140 2.70442i −0.520466 0.901473i
1010 2.34921 4.06896i 0.742887 1.28672i
1111 −2.39448 + 4.14736i −0.721962 + 1.25048i 0.238250 + 0.971204i 0.423426π0.423426\pi
−0.960212 + 0.279272i 0.909907π0.909907\pi
1212 −3.58643 6.21188i −1.03531 1.79321i
1313 1.00000 0.277350
1414 −2.39028 5.34585i −0.638829 1.42874i
1515 −5.25271 −1.35624
1616 0.697291 + 1.20774i 0.174323 + 0.301936i
1717 1.88914 3.27208i 0.458183 0.793597i −0.540682 0.841227i 0.681834π-0.681834\pi
0.998865 + 0.0476304i 0.0151670π0.0151670\pi
1818 −3.45588 + 5.98575i −0.814558 + 1.41086i
1919 1.78362 + 3.08931i 0.409190 + 0.708737i 0.994799 0.101856i 0.0324781π-0.0324781\pi
−0.585609 + 0.810593i 0.699145π0.699145\pi
2020 −6.15355 −1.37597
2121 −3.83967 + 5.30250i −0.837886 + 1.15710i
2222 10.5995 2.25982
2323 −2.23721 3.87497i −0.466491 0.807987i 0.532776 0.846256i 0.321149π-0.321149\pi
−0.999267 + 0.0382695i 0.987815π0.987815\pi
2424 −2.46122 + 4.26295i −0.502394 + 0.870171i
2525 0.246870 0.427591i 0.0493740 0.0855182i
2626 −1.10666 1.91679i −0.217034 0.375914i
2727 0.303848 0.0584757
2828 −4.49818 + 6.21188i −0.850076 + 1.17393i
2929 −5.90107 −1.09580 −0.547901 0.836543i 0.684573π-0.684573\pi
−0.547901 + 0.836543i 0.684573π0.684573\pi
3030 5.81296 + 10.0683i 1.06130 + 1.83822i
3131 1.88558 3.26592i 0.338660 0.586577i −0.645521 0.763743i 0.723360π-0.723360\pi
0.984181 + 0.177166i 0.0566929π0.0566929\pi
3232 3.53265 6.11873i 0.624490 1.08165i
3333 −5.92496 10.2623i −1.03140 1.78644i
3434 −8.36254 −1.43416
3535 2.29251 + 5.12720i 0.387505 + 0.866655i
3636 9.05234 1.50872
3737 −2.81285 4.87200i −0.462429 0.800951i 0.536652 0.843804i 0.319689π-0.319689\pi
−0.999081 + 0.0428524i 0.986355π0.986355\pi
3838 3.94772 6.83765i 0.640404 1.10921i
3939 −1.23721 + 2.14292i −0.198113 + 0.343141i
4040 2.11146 + 3.65716i 0.333851 + 0.578247i
4141 10.3948 1.62340 0.811698 0.584077i 0.198543π-0.198543\pi
0.811698 + 0.584077i 0.198543π0.198543\pi
4242 14.4130 + 1.49180i 2.22398 + 0.230189i
4343 3.40733 0.519613 0.259807 0.965661i 0.416341π-0.416341\pi
0.259807 + 0.965661i 0.416341π0.416341\pi
4444 −6.94110 12.0223i −1.04641 1.81244i
4545 3.31453 5.74093i 0.494101 0.855807i
4646 −4.95168 + 8.57655i −0.730085 + 1.26454i
4747 3.55438 + 6.15636i 0.518459 + 0.897998i 0.999770 + 0.0214479i 0.00682759π0.00682759\pi
−0.481311 + 0.876550i 0.659839π0.659839\pi
4848 −3.45079 −0.498079
4949 6.85161 + 1.43369i 0.978801 + 0.204813i
5050 −1.09280 −0.154546
5151 4.67454 + 8.09654i 0.654566 + 1.13374i
5252 −1.44940 + 2.51043i −0.200995 + 0.348134i
5353 6.19003 10.7214i 0.850266 1.47270i −0.0307027 0.999529i 0.509774π-0.509774\pi
0.880968 0.473175i 0.156892π-0.156892\pi
5454 −0.336257 0.582415i −0.0457588 0.0792566i
5555 −10.1660 −1.37078
5656 5.23528 + 0.541869i 0.699594 + 0.0724103i
5757 −8.82686 −1.16915
5858 6.53049 + 11.3111i 0.857495 + 1.48522i
5959 −2.39448 + 4.14736i −0.311734 + 0.539940i −0.978738 0.205115i 0.934243π-0.934243\pi
0.667003 + 0.745055i 0.267577π0.267577\pi
6060 7.61326 13.1865i 0.982867 1.70238i
6161 −1.60348 2.77732i −0.205305 0.355599i 0.744925 0.667148i 0.232485π-0.232485\pi
−0.950230 + 0.311550i 0.899152π0.899152\pi
6262 −8.34680 −1.06004
6363 −3.37246 7.54251i −0.424890 0.950267i
6464 −12.8486 −1.60608
6565 1.06140 + 1.83839i 0.131650 + 0.228025i
6666 −13.1139 + 22.7139i −1.61420 + 2.79588i
6767 1.44978 2.51109i 0.177118 0.306778i −0.763774 0.645484i 0.776656π-0.776656\pi
0.940892 + 0.338706i 0.109989π0.109989\pi
6868 5.47622 + 9.48510i 0.664090 + 1.15024i
6969 11.0717 1.33287
7070 7.29075 10.0683i 0.871411 1.20340i
7171 −2.53876 −0.301295 −0.150648 0.988588i 0.548136π-0.548136\pi
−0.150648 + 0.988588i 0.548136π0.548136\pi
7272 −3.10612 5.37996i −0.366060 0.634034i
7373 −3.85035 + 6.66901i −0.450650 + 0.780548i −0.998426 0.0560762i 0.982141π-0.982141\pi
0.547777 + 0.836625i 0.315474π0.315474\pi
7474 −6.22574 + 10.7833i −0.723727 + 1.25353i
7575 0.610862 + 1.05804i 0.0705362 + 0.122172i
7676 −10.3407 −1.18616
7777 −7.43122 + 10.2623i −0.846867 + 1.16950i
7878 5.47671 0.620115
7979 2.58925 + 4.48471i 0.291313 + 0.504569i 0.974120 0.226029i 0.0725745π-0.0725745\pi
−0.682807 + 0.730598i 0.739241π0.739241\pi
8080 −1.48021 + 2.56379i −0.165492 + 0.286641i
8181 4.30827 7.46214i 0.478696 0.829126i
8282 −11.5035 19.9247i −1.27035 2.20032i
8383 3.46731 0.380587 0.190294 0.981727i 0.439056π-0.439056\pi
0.190294 + 0.981727i 0.439056π0.439056\pi
8484 −7.74633 17.3247i −0.845194 1.89027i
8585 8.02051 0.869946
8686 −3.77076 6.53115i −0.406612 0.704272i
8787 7.30089 12.6455i 0.782738 1.35574i
8888 −4.76338 + 8.25042i −0.507778 + 0.879498i
8989 −1.83216 3.17339i −0.194209 0.336379i 0.752432 0.658670i 0.228881π-0.228881\pi
−0.946641 + 0.322291i 0.895547π0.895547\pi
9090 −14.6722 −1.54659
9191 2.63169 + 0.272389i 0.275876 + 0.0285541i
9292 12.9704 1.35226
9393 4.66574 + 8.08129i 0.483814 + 0.837991i
9494 7.86698 13.6260i 0.811417 1.40542i
9595 −3.78625 + 6.55798i −0.388461 + 0.672835i
9696 8.74129 + 15.1404i 0.892154 + 1.54526i
9797 −5.40733 −0.549031 −0.274516 0.961583i 0.588518π-0.588518\pi
−0.274516 + 0.961583i 0.588518π0.588518\pi
9898 −4.83432 14.7197i −0.488340 1.48692i
9999 14.9549 1.50303
100100 0.715625 + 1.23950i 0.0715625 + 0.123950i
101101 −4.65862 + 8.06897i −0.463550 + 0.802892i −0.999135 0.0415891i 0.986758π-0.986758\pi
0.535585 + 0.844482i 0.320091π0.320091\pi
102102 10.3463 17.9202i 1.02443 1.77437i
103103 −3.65318 6.32749i −0.359958 0.623466i 0.627995 0.778217i 0.283876π-0.283876\pi
−0.987953 + 0.154751i 0.950542π0.950542\pi
104104 1.98932 0.195069
105105 −13.8235 1.43078i −1.34904 0.139630i
106106 −27.4011 −2.66143
107107 −3.37365 5.84333i −0.326143 0.564896i 0.655600 0.755108i 0.272416π-0.272416\pi
−0.981743 + 0.190212i 0.939082π0.939082\pi
108108 −0.440397 + 0.762790i −0.0423772 + 0.0733995i
109109 −2.08822 + 3.61691i −0.200016 + 0.346437i −0.948533 0.316678i 0.897433π-0.897433\pi
0.748518 + 0.663115i 0.230766π0.230766\pi
110110 11.2503 + 19.4861i 1.07267 + 1.85792i
111111 13.9204 1.32126
112112 1.50608 + 3.36834i 0.142311 + 0.318278i
113113 5.90107 0.555126 0.277563 0.960707i 0.410473π-0.410473\pi
0.277563 + 0.960707i 0.410473π0.410473\pi
114114 9.76834 + 16.9193i 0.914889 + 1.58463i
115115 4.74915 8.22577i 0.442860 0.767057i
116116 8.55300 14.8142i 0.794126 1.37547i
117117 −1.56140 2.70442i −0.144351 0.250024i
118118 10.5995 0.975763
119119 5.86291 8.09654i 0.537452 0.742208i
120120 −10.4493 −0.953888
121121 −5.96705 10.3352i −0.542459 0.939567i
122122 −3.54903 + 6.14709i −0.321314 + 0.556532i
123123 −12.8606 + 22.2752i −1.15960 + 2.00849i
124124 5.46591 + 9.46724i 0.490853 + 0.850183i
125125 11.6621 1.04309
126126 −10.7253 + 14.8113i −0.955482 + 1.31950i
127127 −10.5268 −0.934100 −0.467050 0.884231i 0.654683π-0.654683\pi
−0.467050 + 0.884231i 0.654683π0.654683\pi
128128 7.15377 + 12.3907i 0.632309 + 1.09519i
129129 −4.21560 + 7.30163i −0.371163 + 0.642873i
130130 2.34921 4.06896i 0.206040 0.356871i
131131 −2.71204 4.69740i −0.236952 0.410413i 0.722886 0.690967i 0.242815π-0.242815\pi
−0.959838 + 0.280554i 0.909482π0.909482\pi
132132 34.3505 2.98983
133133 3.85243 + 8.61596i 0.334048 + 0.747099i
134134 −6.41765 −0.554400
135135 0.322504 + 0.558593i 0.0277567 + 0.0480761i
136136 3.75810 6.50922i 0.322255 0.558161i
137137 −11.1224 + 19.2645i −0.950248 + 1.64588i −0.205363 + 0.978686i 0.565837π0.565837\pi
−0.744886 + 0.667192i 0.767496π0.767496\pi
138138 −12.2526 21.2221i −1.04301 1.80654i
139139 −4.00000 −0.339276 −0.169638 0.985506i 0.554260π-0.554260\pi
−0.169638 + 0.985506i 0.554260π0.554260\pi
140140 −16.1942 1.67616i −1.36866 0.141661i
141141 −17.5901 −1.48135
142142 2.80955 + 4.86628i 0.235772 + 0.408369i
143143 −2.39448 + 4.14736i −0.200236 + 0.346819i
144144 2.17750 3.77153i 0.181458 0.314294i
145145 −6.26338 10.8485i −0.520146 0.900919i
146146 17.0441 1.41058
147147 −11.5492 + 12.9087i −0.952561 + 1.06469i
148148 16.3077 1.34049
149149 −1.47736 2.55887i −0.121030 0.209630i 0.799144 0.601140i 0.205286π-0.205286\pi
−0.920174 + 0.391509i 0.871953π0.871953\pi
150150 1.35203 2.34179i 0.110393 0.191206i
151151 9.27736 16.0689i 0.754981 1.30766i −0.190403 0.981706i 0.560980π-0.560980\pi
0.945384 0.325959i 0.105687π-0.105687\pi
152152 3.54818 + 6.14564i 0.287796 + 0.498477i
153153 −11.7988 −0.953875
154154 27.8946 + 2.88719i 2.24781 + 0.232656i
155155 8.00541 0.643010
156156 −3.58643 6.21188i −0.287144 0.497348i
157157 4.89982 8.48673i 0.391048 0.677315i −0.601540 0.798843i 0.705446π-0.705446\pi
0.992588 + 0.121528i 0.0387793π0.0387793\pi
158158 5.73084 9.92610i 0.455921 0.789678i
159159 15.3168 + 26.5294i 1.21470 + 2.10392i
160160 14.9982 1.18571
161161 −4.83216 10.8071i −0.380828 0.851720i
162162 −19.0712 −1.49837
163163 −6.91709 11.9808i −0.541788 0.938405i −0.998801 0.0489451i 0.984414π-0.984414\pi
0.457013 0.889460i 0.348919π-0.348919\pi
164164 −15.0662 + 26.0954i −1.17647 + 2.03771i
165165 12.5775 21.7848i 0.979156 1.69595i
166166 −3.83714 6.64612i −0.297820 0.515839i
167167 17.3534 1.34285 0.671424 0.741073i 0.265683π-0.265683\pi
0.671424 + 0.741073i 0.265683π0.265683\pi
168168 −7.63834 + 10.5484i −0.589311 + 0.813824i
169169 1.00000 0.0769231
170170 −8.87598 15.3737i −0.680757 1.17911i
171171 5.56987 9.64730i 0.425939 0.737747i
172172 −4.93858 + 8.55387i −0.376563 + 0.652226i
173173 1.48069 + 2.56463i 0.112575 + 0.194985i 0.916808 0.399329i 0.130757π-0.130757\pi
−0.804233 + 0.594314i 0.797424π0.797424\pi
174174 −32.3184 −2.45005
175175 0.766156 1.05804i 0.0579160 0.0799806i
176176 −6.67859 −0.503418
177177 −5.92496 10.2623i −0.445348 0.771365i
178178 −4.05516 + 7.02374i −0.303947 + 0.526452i
179179 2.83444 4.90939i 0.211856 0.366945i −0.740440 0.672123i 0.765383π-0.765383\pi
0.952295 + 0.305178i 0.0987159π0.0987159\pi
180180 9.60813 + 16.6418i 0.716148 + 1.24040i
181181 7.17645 0.533421 0.266711 0.963777i 0.414063π-0.414063\pi
0.266711 + 0.963777i 0.414063π0.414063\pi
182182 −2.39028 5.34585i −0.177179 0.396261i
183183 7.93541 0.586603
184184 −4.45054 7.70855i −0.328098 0.568282i
185185 5.97110 10.3423i 0.439004 0.760377i
186186 10.3268 17.8865i 0.757196 1.31150i
187187 9.04700 + 15.6699i 0.661582 + 1.14589i
188188 −20.6068 −1.50291
189189 0.799636 + 0.0827650i 0.0581649 + 0.00602027i
190190 16.7604 1.21593
191191 −5.94088 10.2899i −0.429867 0.744552i 0.566994 0.823722i 0.308106π-0.308106\pi
−0.996861 + 0.0791703i 0.974773π0.974773\pi
192192 15.8965 27.5335i 1.14723 1.98706i
193193 −11.4851 + 19.8927i −0.826714 + 1.43191i 0.0738876 + 0.997267i 0.476459π0.476459\pi
−0.900602 + 0.434645i 0.856874π0.856874\pi
194194 5.98408 + 10.3647i 0.429632 + 0.744145i
195195 −5.25271 −0.376154
196196 −13.5299 + 15.1225i −0.966420 + 1.08018i
197197 16.9216 1.20561 0.602806 0.797888i 0.294049π-0.294049\pi
0.602806 + 0.797888i 0.294049π0.294049\pi
198198 −16.5500 28.6655i −1.17616 2.03717i
199199 −5.02953 + 8.71140i −0.356534 + 0.617535i −0.987379 0.158374i 0.949375π-0.949375\pi
0.630845 + 0.775909i 0.282708π0.282708\pi
200200 0.491103 0.850616i 0.0347262 0.0601476i
201201 3.58737 + 6.21351i 0.253034 + 0.438267i
202202 20.6221 1.45096
203203 −15.5298 1.60739i −1.08998 0.112817i
204204 −27.1010 −1.89745
205205 11.0330 + 19.1098i 0.770580 + 1.33468i
206206 −8.08566 + 14.0048i −0.563355 + 0.975759i
207207 −6.98636 + 12.1007i −0.485586 + 0.841059i
208208 0.697291 + 1.20774i 0.0483484 + 0.0837419i
209209 −17.0833 −1.18168
210210 12.5554 + 28.0802i 0.866406 + 1.93772i
211211 −24.4609 −1.68396 −0.841978 0.539512i 0.818609π-0.818609\pi
−0.841978 + 0.539512i 0.818609π0.818609\pi
212212 17.9436 + 31.0793i 1.23237 + 2.13453i
213213 3.14099 5.44035i 0.215217 0.372767i
214214 −7.46697 + 12.9332i −0.510431 + 0.884093i
215215 3.61654 + 6.26402i 0.246646 + 0.427203i
216216 0.604452 0.0411277
217217 5.85187 8.08129i 0.397251 0.548594i
218218 9.24382 0.626071
219219 −9.52742 16.5020i −0.643804 1.11510i
220220 14.7345 25.5210i 0.993402 1.72062i
221221 1.88914 3.27208i 0.127077 0.220104i
222222 −15.4051 26.6825i −1.03393 1.79081i
223223 −29.2625 −1.95956 −0.979780 0.200076i 0.935881π-0.935881\pi
−0.979780 + 0.200076i 0.935881π0.935881\pi
224224 10.9635 15.1404i 0.732531 1.01161i
225225 −1.54185 −0.102790
226226 −6.53049 11.3111i −0.434401 0.752405i
227227 5.03685 8.72408i 0.334307 0.579038i −0.649044 0.760751i 0.724831π-0.724831\pi
0.983352 + 0.181713i 0.0581643π0.0581643\pi
228228 12.7936 22.1592i 0.847279 1.46753i
229229 5.56997 + 9.64748i 0.368074 + 0.637523i 0.989264 0.146137i 0.0466839π-0.0466839\pi
−0.621190 + 0.783660i 0.713351π0.713351\pi
230230 −21.0228 −1.38620
231231 −12.7973 28.6212i −0.842003 1.88314i
232232 −11.7391 −0.770711
233233 8.54166 + 14.7946i 0.559583 + 0.969226i 0.997531 + 0.0702257i 0.0223720π0.0223720\pi
−0.437948 + 0.899000i 0.644295π0.644295\pi
234234 −3.45588 + 5.98575i −0.225918 + 0.391301i
235235 −7.54522 + 13.0687i −0.492196 + 0.852508i
236236 −6.94110 12.0223i −0.451827 0.782587i
237237 −12.8138 −0.832347
238238 −22.0076 2.27787i −1.42654 0.147652i
239239 6.92142 0.447710 0.223855 0.974622i 0.428136π-0.428136\pi
0.223855 + 0.974622i 0.428136π0.428136\pi
240240 −3.66266 6.34392i −0.236424 0.409498i
241241 −3.24812 + 5.62592i −0.209230 + 0.362397i −0.951472 0.307735i 0.900429π-0.900429\pi
0.742242 + 0.670132i 0.233762π0.233762\pi
242242 −13.2070 + 22.8752i −0.848978 + 1.47047i
243243 11.1163 + 19.2539i 0.713109 + 1.23514i
244244 9.29634 0.595137
245245 4.63660 + 14.1177i 0.296221 + 0.901945i
246246 56.9293 3.62968
247247 1.78362 + 3.08931i 0.113489 + 0.196568i
248248 3.75103 6.49697i 0.238190 0.412558i
249249 −4.28981 + 7.43017i −0.271856 + 0.470868i
250250 −12.9060 22.3538i −0.816246 1.41378i
251251 −9.86804 −0.622865 −0.311433 0.950268i 0.600809π-0.600809\pi
−0.311433 + 0.950268i 0.600809π0.600809\pi
252252 23.8230 + 2.46576i 1.50071 + 0.155328i
253253 21.4278 1.34716
254254 11.6496 + 20.1776i 0.730959 + 1.26606i
255255 −9.92309 + 17.1873i −0.621408 + 1.07631i
256256 2.98497 5.17012i 0.186560 0.323132i
257257 −3.43234 5.94499i −0.214104 0.370838i 0.738891 0.673825i 0.235350π-0.235350\pi
−0.952995 + 0.302986i 0.902016π0.902016\pi
258258 18.6610 1.16178
259259 −6.07547 13.5878i −0.377511 0.844304i
260260 −6.15355 −0.381627
261261 9.21392 + 15.9590i 0.570327 + 0.987836i
262262 −6.00262 + 10.3969i −0.370843 + 0.642320i
263263 0.0632753 0.109596i 0.00390172 0.00675798i −0.864068 0.503375i 0.832091π-0.832091\pi
0.867970 + 0.496617i 0.165425π0.165425\pi
264264 −11.7867 20.4151i −0.725418 1.25646i
265265 26.2803 1.61439
266266 12.2517 16.9193i 0.751199 1.03739i
267267 9.06710 0.554897
268268 4.20261 + 7.27913i 0.256715 + 0.444643i
269269 2.12154 3.67462i 0.129353 0.224045i −0.794073 0.607822i 0.792043π-0.792043\pi
0.923426 + 0.383777i 0.125377π0.125377\pi
270270 0.713805 1.23635i 0.0434408 0.0752417i
271271 −0.783616 1.35726i −0.0476013 0.0824479i 0.841243 0.540657i 0.181824π-0.181824\pi
−0.888844 + 0.458209i 0.848491π0.848491\pi
272272 5.26911 0.319487
273273 −3.83967 + 5.30250i −0.232388 + 0.320922i
274274 49.2348 2.97438
275275 1.18225 + 2.04771i 0.0712923 + 0.123482i
276276 −16.0472 + 27.7946i −0.965929 + 1.67304i
277277 6.37260 11.0377i 0.382892 0.663189i −0.608582 0.793491i 0.708261π-0.708261\pi
0.991474 + 0.130302i 0.0415947π0.0415947\pi
278278 4.42664 + 7.66717i 0.265492 + 0.459846i
279279 −11.7766 −0.705045
280280 4.56054 + 10.1996i 0.272545 + 0.609546i
281281 4.62986 0.276194 0.138097 0.990419i 0.455901π-0.455901\pi
0.138097 + 0.990419i 0.455901π0.455901\pi
282282 19.4663 + 33.7166i 1.15920 + 2.00779i
283283 −1.82416 + 3.15954i −0.108435 + 0.187815i −0.915136 0.403144i 0.867917π-0.867917\pi
0.806701 + 0.590959i 0.201251π0.201251\pi
284284 3.67967 6.37338i 0.218348 0.378190i
285285 −9.36881 16.2273i −0.554960 0.961220i
286286 10.5995 0.626762
287287 27.3559 + 2.83143i 1.61477 + 0.167134i
288288 −22.0635 −1.30010
289289 1.36231 + 2.35959i 0.0801360 + 0.138800i
290290 −13.8629 + 24.0112i −0.814057 + 1.40999i
291291 6.69003 11.5875i 0.392176 0.679269i
292292 −11.1614 19.3321i −0.653171 1.13132i
293293 −21.0415 −1.22926 −0.614630 0.788816i 0.710695π-0.710695\pi
−0.614630 + 0.788816i 0.710695π0.710695\pi
294294 37.5242 + 7.85189i 2.18846 + 0.457932i
295295 −10.1660 −0.591886
296296 −5.59566 9.69196i −0.325241 0.563334i
297297 −0.727559 + 1.26017i −0.0422172 + 0.0731224i
298298 −3.26988 + 5.66359i −0.189419 + 0.328083i
299299 −2.23721 3.87497i −0.129381 0.224095i
300300 −3.54152 −0.204470
301301 8.96705 + 0.928120i 0.516852 + 0.0534960i
302302 −41.0676 −2.36317
303303 −11.5274 19.9661i −0.662233 1.14702i
304304 −2.48740 + 4.30830i −0.142662 + 0.247098i
305305 3.40387 5.89567i 0.194905 0.337585i
306306 13.0573 + 22.6158i 0.746434 + 1.29286i
307307 −4.95861 −0.283003 −0.141502 0.989938i 0.545193π-0.545193\pi
−0.141502 + 0.989938i 0.545193π0.545193\pi
308308 −14.9921 33.5298i −0.854253 1.91054i
309309 18.0791 1.02848
310310 −8.85927 15.3447i −0.503173 0.871521i
311311 1.21079 2.09715i 0.0686575 0.118918i −0.829653 0.558279i 0.811462π-0.811462\pi
0.898311 + 0.439361i 0.144795π0.144795\pi
312312 −2.46122 + 4.26295i −0.139339 + 0.241342i
313313 −6.98026 12.0902i −0.394548 0.683377i 0.598496 0.801126i 0.295765π-0.295765\pi
−0.993043 + 0.117749i 0.962432π0.962432\pi
314314 −21.6897 −1.22402
315315 10.2866 14.2055i 0.579583 0.800390i
316316 −15.0114 −0.844457
317317 −1.53431 2.65750i −0.0861753 0.149260i 0.819716 0.572770i 0.194131π-0.194131\pi
−0.905891 + 0.423510i 0.860798π0.860798\pi
318318 33.9010 58.7182i 1.90107 3.29275i
319319 14.1300 24.4739i 0.791127 1.37027i
320320 −13.6375 23.6208i −0.762359 1.32044i
321321 16.6957 0.931863
322322 −15.3674 + 21.2221i −0.856394 + 1.18266i
323323 13.4780 0.749936
324324 12.4888 + 21.6312i 0.693821 + 1.20173i
325325 0.246870 0.427591i 0.0136939 0.0237185i
326326 −15.3098 + 26.5173i −0.847929 + 1.46866i
327327 −5.16716 8.94978i −0.285745 0.494924i
328328 20.6786 1.14179
329329 7.67710 + 17.1698i 0.423252 + 0.946603i
330330 −55.6761 −3.06487
331331 −6.80261 11.7825i −0.373905 0.647623i 0.616257 0.787545i 0.288648π-0.288648\pi
−0.990162 + 0.139922i 0.955315π0.955315\pi
332332 −5.02551 + 8.70445i −0.275811 + 0.477719i
333333 −8.78395 + 15.2142i −0.481358 + 0.833736i
334334 −19.2044 33.2629i −1.05082 1.82007i
335335 6.15516 0.336292
336336 −9.08142 0.939958i −0.495432 0.0512789i
337337 −35.1646 −1.91554 −0.957769 0.287538i 0.907163π-0.907163\pi
−0.957769 + 0.287538i 0.907163π0.907163\pi
338338 −1.10666 1.91679i −0.0601944 0.104260i
339339 −7.30089 + 12.6455i −0.396530 + 0.686810i
340340 −11.6249 + 20.1349i −0.630449 + 1.09197i
341341 9.02997 + 15.6404i 0.489000 + 0.846973i
342342 −24.6558 −1.33323
343343 17.6408 + 5.63933i 0.952514 + 0.304495i
344344 6.77828 0.365460
345345 11.7514 + 20.3541i 0.632676 + 1.09583i
346346 3.27724 5.67635i 0.176186 0.305162i
347347 2.73551 4.73804i 0.146850 0.254351i −0.783212 0.621755i 0.786420π-0.786420\pi
0.930062 + 0.367404i 0.119753π0.119753\pi
348348 21.1638 + 36.6567i 1.13450 + 1.96501i
349349 4.34196 0.232420 0.116210 0.993225i 0.462925π-0.462925\pi
0.116210 + 0.993225i 0.462925π0.462925\pi
350350 −2.87593 0.297668i −0.153725 0.0159110i
351351 0.303848 0.0162182
352352 16.9177 + 29.3023i 0.901717 + 1.56182i
353353 −13.7996 + 23.9016i −0.734479 + 1.27216i 0.220472 + 0.975393i 0.429240π0.429240\pi
−0.954951 + 0.296762i 0.904093π0.904093\pi
354354 −13.1139 + 22.7139i −0.696993 + 1.20723i
355355 −2.69463 4.66724i −0.143016 0.247712i
356356 10.6221 0.562971
357357 10.0965 + 22.5809i 0.534365 + 1.19511i
358358 −12.5470 −0.663132
359359 −3.31427 5.74049i −0.174921 0.302971i 0.765213 0.643777i 0.222634π-0.222634\pi
−0.940134 + 0.340806i 0.889300π0.889300\pi
360360 6.59366 11.4206i 0.347516 0.601916i
361361 3.13742 5.43418i 0.165128 0.286009i
362362 −7.94189 13.7558i −0.417417 0.722987i
363363 29.5301 1.54993
364364 −4.49818 + 6.21188i −0.235769 + 0.325591i
365365 −16.3470 −0.855643
366366 −8.78181 15.2105i −0.459033 0.795068i
367367 −15.6037 + 27.0264i −0.814506 + 1.41077i 0.0951768 + 0.995460i 0.469658π0.469658\pi
−0.909682 + 0.415305i 0.863675π0.863675\pi
368368 3.11998 5.40396i 0.162640 0.281701i
369369 −16.2304 28.1119i −0.844923 1.46345i
370370 −26.4319 −1.37413
371371 19.2107 26.5294i 0.997368 1.37734i
372372 −27.0500 −1.40248
373373 7.88730 + 13.6612i 0.408389 + 0.707350i 0.994709 0.102729i 0.0327574π-0.0327574\pi
−0.586321 + 0.810079i 0.699424π0.699424\pi
374374 20.0239 34.6825i 1.03541 1.79339i
375375 −14.4285 + 24.9909i −0.745084 + 1.29052i
376376 7.07080 + 12.2470i 0.364649 + 0.631590i
377377 −5.90107 −0.303921
378378 −0.726282 1.62433i −0.0373559 0.0835465i
379379 31.6512 1.62581 0.812907 0.582393i 0.197884π-0.197884\pi
0.812907 + 0.582393i 0.197884π0.197884\pi
380380 −10.9756 19.0102i −0.563035 0.975205i
381381 13.0239 22.5580i 0.667233 1.15568i
382382 −13.1491 + 22.7749i −0.672766 + 1.16526i
383383 −6.19675 10.7331i −0.316639 0.548435i 0.663145 0.748491i 0.269221π-0.269221\pi
−0.979785 + 0.200055i 0.935888π0.935888\pi
384384 −35.4030 −1.80665
385385 −26.7537 2.76910i −1.36350 0.141126i
386386 50.8404 2.58771
387387 −5.32020 9.21486i −0.270441 0.468418i
388388 7.83737 13.5747i 0.397882 0.689152i
389389 7.03705 12.1885i 0.356792 0.617983i −0.630631 0.776083i 0.717204π-0.717204\pi
0.987423 + 0.158100i 0.0505370π0.0505370\pi
390390 5.81296 + 10.0683i 0.294351 + 0.509831i
391391 −16.9056 −0.854954
392392 13.6300 + 2.85207i 0.688421 + 0.144051i
393393 13.4215 0.677026
394394 −18.7265 32.4352i −0.943425 1.63406i
395395 −5.49644 + 9.52012i −0.276556 + 0.479009i
396396 −21.6756 + 37.5433i −1.08924 + 1.88662i
397397 3.48652 + 6.03884i 0.174984 + 0.303081i 0.940156 0.340745i 0.110679π-0.110679\pi
−0.765172 + 0.643826i 0.777346π0.777346\pi
398398 22.2639 1.11599
399399 −23.2296 2.40434i −1.16293 0.120368i
400400 0.688560 0.0344280
401401 −1.36841 2.37016i −0.0683352 0.118360i 0.829833 0.558011i 0.188435π-0.188435\pi
−0.898169 + 0.439651i 0.855102π0.855102\pi
402402 7.94000 13.7525i 0.396011 0.685912i
403403 1.88558 3.26592i 0.0939275 0.162687i
404404 −13.5044 23.3903i −0.671868 1.16371i
405405 18.2911 0.908894
406406 14.1052 + 31.5463i 0.700029 + 1.56561i
407407 26.9412 1.33543
408408 9.29915 + 16.1066i 0.460377 + 0.797396i
409409 12.2577 21.2309i 0.606104 1.04980i −0.385772 0.922594i 0.626065π-0.626065\pi
0.991876 0.127208i 0.0406017π-0.0406017\pi
410410 24.4196 42.2961i 1.20600 2.08885i
411411 −27.5215 47.6686i −1.35754 2.35132i
412412 21.1796 1.04345
413413 −7.43122 + 10.2623i −0.365667 + 0.504977i
414414 30.9261 1.51994
415415 3.68020 + 6.37429i 0.180654 + 0.312902i
416416 3.53265 6.11873i 0.173202 0.299995i
417417 4.94886 8.57167i 0.242347 0.419757i
418418 18.9054 + 32.7452i 0.924696 + 1.60162i
419419 −3.01252 −0.147171 −0.0735856 0.997289i 0.523444π-0.523444\pi
−0.0735856 + 0.997289i 0.523444π0.523444\pi
420420 23.6276 32.6292i 1.15291 1.59214i
421421 −10.0000 −0.487370 −0.243685 0.969854i 0.578356π-0.578356\pi
−0.243685 + 0.969854i 0.578356π0.578356\pi
422422 27.0699 + 46.8864i 1.31774 + 2.28240i
423423 11.0996 19.2251i 0.539681 0.934755i
424424 12.3140 21.3284i 0.598018 1.03580i
425425 −0.932742 1.61556i −0.0452447 0.0783660i
426426 −13.9040 −0.673653
427427 −3.46337 7.74581i −0.167604 0.374846i
428428 19.5590 0.945421
429429 −5.92496 10.2623i −0.286060 0.495470i
430430 8.00456 13.8643i 0.386014 0.668596i
431431 9.39711 16.2763i 0.452643 0.784001i −0.545906 0.837846i 0.683815π-0.683815\pi
0.998549 + 0.0538455i 0.0171478π0.0171478\pi
432432 0.211871 + 0.366971i 0.0101936 + 0.0176559i
433433 −7.76911 −0.373360 −0.186680 0.982421i 0.559773π-0.559773\pi
−0.186680 + 0.982421i 0.559773π0.559773\pi
434434 −21.9662 2.27358i −1.05441 0.109135i
435435 30.9966 1.48617
436436 −6.05333 10.4847i −0.289902 0.502125i
437437 7.98066 13.8229i 0.381767 0.661240i
438438 −21.0873 + 36.5242i −1.00759 + 1.74519i
439439 18.9841 + 32.8814i 0.906060 + 1.56934i 0.819488 + 0.573096i 0.194258π0.194258\pi
0.0865713 + 0.996246i 0.472409π0.472409\pi
440440 −20.2234 −0.964112
441441 −6.82079 20.7682i −0.324799 0.988961i
442442 −8.36254 −0.397766
443443 −17.8135 30.8539i −0.846344 1.46591i −0.884449 0.466637i 0.845465π-0.845465\pi
0.0381050 0.999274i 0.487868π-0.487868\pi
444444 −20.1762 + 34.9461i −0.957518 + 1.65847i
445445 3.88930 6.73647i 0.184371 0.319339i
446446 32.3837 + 56.0901i 1.53341 + 2.65594i
447447 7.31125 0.345810
448448 −33.8136 3.49982i −1.59754 0.165351i
449449 −8.05285 −0.380038 −0.190019 0.981780i 0.560855π-0.560855\pi
−0.190019 + 0.981780i 0.560855π0.560855\pi
450450 1.70630 + 2.95540i 0.0804359 + 0.139319i
451451 −24.8901 + 43.1110i −1.17203 + 2.03002i
452452 −8.55300 + 14.8142i −0.402299 + 0.696803i
453453 22.9562 + 39.7612i 1.07857 + 1.86815i
454454 −22.2963 −1.04642
455455 2.29251 + 5.12720i 0.107475 + 0.240367i
456456 −17.5595 −0.822297
457457 −7.79881 13.5079i −0.364813 0.631875i 0.623933 0.781478i 0.285534π-0.285534\pi
−0.988746 + 0.149603i 0.952200π0.952200\pi
458458 12.3281 21.3530i 0.576056 0.997759i
459459 0.574012 0.994218i 0.0267926 0.0464061i
460460 13.7668 + 23.8448i 0.641880 + 1.11177i
461461 −25.6991 −1.19692 −0.598462 0.801151i 0.704221π-0.704221\pi
−0.598462 + 0.801151i 0.704221π0.704221\pi
462462 −40.6986 + 56.2038i −1.89347 + 2.61484i
463463 −20.5209 −0.953685 −0.476842 0.878989i 0.658219π-0.658219\pi
−0.476842 + 0.878989i 0.658219π0.658219\pi
464464 −4.11476 7.12698i −0.191023 0.330862i
465465 −9.90440 + 17.1549i −0.459306 + 0.795541i
466466 18.9054 32.7452i 0.875778 1.51689i
467467 −5.91241 10.2406i −0.273594 0.473878i 0.696186 0.717862i 0.254879π-0.254879\pi
−0.969779 + 0.243984i 0.921546π0.921546\pi
468468 9.05234 0.418445
469469 4.49936 6.21351i 0.207761 0.286913i
470470 33.4000 1.54063
471471 12.1242 + 20.9998i 0.558656 + 0.967620i
472472 −4.76338 + 8.25042i −0.219253 + 0.379757i
473473 −8.15878 + 14.1314i −0.375141 + 0.649764i
474474 14.1805 + 24.5614i 0.651334 + 1.12814i
475475 1.76128 0.0808133
476476 11.8281 + 26.4535i 0.542140 + 1.21250i
477477 −38.6604 −1.77014
478478 −7.65967 13.2669i −0.350345 0.606816i
479479 −11.3276 + 19.6200i −0.517571 + 0.896459i 0.482221 + 0.876050i 0.339830π0.339830\pi
−0.999792 + 0.0204092i 0.993503π0.993503\pi
480480 −18.5560 + 32.1399i −0.846960 + 1.46698i
481481 −2.81285 4.87200i −0.128255 0.222144i
482482 14.3783 0.654913
483483 29.1372 + 3.01580i 1.32579 + 0.137224i
484484 34.5945 1.57248
485485 −5.73933 9.94081i −0.260610 0.451389i
486486 24.6039 42.6152i 1.11606 1.93306i
487487 16.3584 28.3335i 0.741268 1.28391i −0.210650 0.977562i 0.567558π-0.567558\pi
0.951918 0.306353i 0.0991087π-0.0991087\pi
488488 −3.18984 5.52497i −0.144397 0.250104i
489489 34.2317 1.54801
490490 21.9295 24.5109i 0.990675 1.10729i
491491 6.17281 0.278575 0.139288 0.990252i 0.455519π-0.455519\pi
0.139288 + 0.990252i 0.455519π0.455519\pi
492492 −37.2803 64.5713i −1.68072 2.91110i
493493 −11.1479 + 19.3088i −0.502078 + 0.869625i
494494 3.94772 6.83765i 0.177616 0.307640i
495495 15.8731 + 27.4931i 0.713444 + 1.23572i
496496 5.25919 0.236145
497497 −6.68123 0.691531i −0.299694 0.0310194i
498498 18.9895 0.850938
499499 7.31934 + 12.6775i 0.327659 + 0.567521i 0.982047 0.188637i 0.0604071π-0.0604071\pi
−0.654388 + 0.756159i 0.727074π0.727074\pi
500500 −16.9030 + 29.2768i −0.755925 + 1.30930i
501501 −21.4699 + 37.1870i −0.959205 + 1.66139i
502502 10.9206 + 18.9150i 0.487409 + 0.844218i
503503 12.7787 0.569774 0.284887 0.958561i 0.408044π-0.408044\pi
0.284887 + 0.958561i 0.408044π0.408044\pi
504504 −6.70891 15.0045i −0.298839 0.668352i
505505 −19.7786 −0.880136
506506 −23.7134 41.0727i −1.05419 1.82591i
507507 −1.23721 + 2.14292i −0.0549466 + 0.0951703i
508508 15.2575 26.4267i 0.676941 1.17250i
509509 −5.84263 10.1197i −0.258970 0.448549i 0.706996 0.707217i 0.250050π-0.250050\pi
−0.965966 + 0.258668i 0.916716π0.916716\pi
510510 43.9260 1.94507
511511 −11.9495 + 16.5020i −0.528615 + 0.730005i
512512 15.4017 0.680664
513513 0.541949 + 0.938683i 0.0239276 + 0.0414439i
514514 −7.59688 + 13.1582i −0.335084 + 0.580382i
515515 7.75495 13.4320i 0.341724 0.591883i
516516 −12.2202 21.1659i −0.537962 0.931778i
517517 −34.0435 −1.49723
518518 −19.3215 + 26.6825i −0.848937 + 1.17236i
519519 −7.32772 −0.321651
520520 2.11146 + 3.65716i 0.0925937 + 0.160377i
521521 −4.23838 + 7.34108i −0.185687 + 0.321619i −0.943808 0.330495i 0.892784π-0.892784\pi
0.758121 + 0.652114i 0.226118π0.226118\pi
522522 20.3934 35.3224i 0.892594 1.54602i
523523 −16.3554 28.3284i −0.715172 1.23871i −0.962893 0.269883i 0.913015π-0.913015\pi
0.247721 0.968831i 0.420318π-0.420318\pi
524524 15.7233 0.686876
525525 1.31940 + 2.95084i 0.0575833 + 0.128785i
526526 −0.280097 −0.0122128
527527 −7.12425 12.3396i −0.310337 0.537520i
528528 8.26284 14.3117i 0.359594 0.622835i
529529 1.48975 2.58032i 0.0647716 0.112188i
530530 −29.0834 50.3739i −1.26330 2.18810i
531531 14.9549 0.648989
532532 −27.2135 2.81669i −1.17985 0.122119i
533533 10.3948 0.450249
534534 −10.0342 17.3797i −0.434222 0.752095i
535535 7.16156 12.4042i 0.309621 0.536280i
536536 2.88407 4.99536i 0.124573 0.215767i
537537 7.01361 + 12.1479i 0.302660 + 0.524222i
538538 −9.39131 −0.404888
539539 −22.3520 + 24.9831i −0.962771 + 1.07610i
540540 −1.86975 −0.0804610
541541 14.0853 + 24.3964i 0.605573 + 1.04888i 0.991961 + 0.126547i 0.0403893π0.0403893\pi
−0.386388 + 0.922336i 0.626277π0.626277\pi
542542 −1.73440 + 3.00406i −0.0744987 + 0.129035i
543543 −8.87880 + 15.3785i −0.381026 + 0.659956i
544544 −13.3473 23.1182i −0.572262 0.991187i
545545 −8.86574 −0.379767
546546 14.4130 + 1.49180i 0.616820 + 0.0638430i
547547 −18.5377 −0.792615 −0.396307 0.918118i 0.629709π-0.629709\pi
−0.396307 + 0.918118i 0.629709π0.629709\pi
548548 −32.2415 55.8438i −1.37729 2.38553i
549549 −5.00735 + 8.67299i −0.213709 + 0.370154i
550550 2.61670 4.53225i 0.111576 0.193256i
551551 −10.5252 18.2303i −0.448391 0.776635i
552552 22.0251 0.937449
553553 5.59252 + 12.5077i 0.237818 + 0.531880i
554554 −28.2092 −1.19850
555555 14.7751 + 25.5912i 0.627167 + 1.08628i
556556 5.79759 10.0417i 0.245873 0.425864i
557557 −2.00142 + 3.46655i −0.0848027 + 0.146883i −0.905307 0.424758i 0.860359π-0.860359\pi
0.820504 + 0.571640i 0.193693π0.193693\pi
558558 13.0327 + 22.5732i 0.551717 + 0.955602i
559559 3.40733 0.144115
560560 −4.59379 + 6.34392i −0.194123 + 0.268079i
561561 −44.7723 −1.89029
562562 −5.12368 8.87448i −0.216129 0.374347i
563563 8.93100 15.4689i 0.376397 0.651938i −0.614138 0.789199i 0.710496π-0.710496\pi
0.990535 + 0.137260i 0.0438296π0.0438296\pi
564564 25.4951 44.1587i 1.07354 1.85942i
565565 6.26338 + 10.8485i 0.263503 + 0.456400i
566566 8.07490 0.339413
567567 13.3706 18.4645i 0.561514 0.775437i
568568 −5.05041 −0.211910
569569 18.7336 + 32.4475i 0.785353 + 1.36027i 0.928788 + 0.370612i 0.120852π0.120852\pi
−0.143434 + 0.989660i 0.545815π0.545815\pi
570570 −20.7362 + 35.9161i −0.868544 + 1.50436i
571571 −8.78514 + 15.2163i −0.367646 + 0.636782i −0.989197 0.146592i 0.953170π-0.953170\pi
0.621551 + 0.783374i 0.286503π0.286503\pi
572572 −6.94110 12.0223i −0.290222 0.502679i
573573 29.4006 1.22823
574574 −24.8465 55.5691i −1.03707 2.31941i
575575 −2.20920 −0.0921301
576576 20.0618 + 34.7481i 0.835908 + 1.44784i
577577 17.1247 29.6608i 0.712910 1.23480i −0.250850 0.968026i 0.580710π-0.580710\pi
0.963760 0.266770i 0.0859565π-0.0859565\pi
578578 3.01524 5.22254i 0.125417 0.217229i
579579 −28.4190 49.2232i −1.18105 2.04565i
580580 36.3125 1.50780
581581 9.12490 + 0.944459i 0.378565 + 0.0391828i
582582 −29.6144 −1.22756
583583 29.6438 + 51.3445i 1.22772 + 2.12647i
584584 −7.65959 + 13.2668i −0.316956 + 0.548984i
585585 3.31453 5.74093i 0.137039 0.237358i
586586 23.2859 + 40.3323i 0.961930 + 1.66611i
587587 −29.4494 −1.21551 −0.607754 0.794126i 0.707929π-0.707929\pi
−0.607754 + 0.794126i 0.707929π0.707929\pi
588588 −15.6669 47.7032i −0.646092 1.96725i
589589 13.4526 0.554305
590590 11.2503 + 19.4861i 0.463167 + 0.802229i
591591 −20.9356 + 36.2616i −0.861176 + 1.49160i
592592 3.92275 6.79439i 0.161224 0.279248i
593593 17.0001 + 29.4450i 0.698109 + 1.20916i 0.969121 + 0.246584i 0.0793081π0.0793081\pi
−0.271013 + 0.962576i 0.587359π0.587359\pi
594594 3.22064 0.132145
595595 21.1075 + 2.18470i 0.865324 + 0.0895640i
596596 8.56514 0.350842
597597 −12.4452 21.5557i −0.509349 0.882218i
598598 −4.95168 + 8.57655i −0.202489 + 0.350721i
599599 −10.7209 + 18.5691i −0.438043 + 0.758713i −0.997539 0.0701203i 0.977662π-0.977662\pi
0.559495 + 0.828834i 0.310995π0.310995\pi
600600 1.21520 + 2.10479i 0.0496103 + 0.0859276i
601601 40.4039 1.64811 0.824054 0.566511i 0.191707π-0.191707\pi
0.824054 + 0.566511i 0.191707π0.191707\pi
602602 −8.14447 18.2151i −0.331944 0.742392i
603603 −9.05472 −0.368737
604604 26.8931 + 46.5803i 1.09427 + 1.89533i
605605 12.6668 21.9396i 0.514980 0.891971i
606606 −25.5139 + 44.1914i −1.03643 + 1.79515i
607607 21.9456 + 38.0110i 0.890746 + 1.54282i 0.838983 + 0.544158i 0.183151π0.183151\pi
0.0517636 + 0.998659i 0.483516π0.483516\pi
608608 25.2036 1.02214
609609 22.6582 31.2904i 0.918156 1.26795i
610610 −15.0677 −0.610074
611611 3.55438 + 6.15636i 0.143795 + 0.249060i
612612 17.1011 29.6200i 0.691272 1.19732i
613613 7.15777 12.3976i 0.289100 0.500735i −0.684496 0.729017i 0.739977π-0.739977\pi
0.973595 + 0.228282i 0.0733108π0.0733108\pi
614614 5.48750 + 9.50464i 0.221458 + 0.383576i
615615 −54.6009 −2.20172
616616 −14.7831 + 20.4151i −0.595628 + 0.822547i
617617 −36.9097 −1.48593 −0.742965 0.669330i 0.766581π-0.766581\pi
−0.742965 + 0.669330i 0.766581π0.766581\pi
618618 −20.0074 34.6538i −0.804815 1.39398i
619619 −7.14646 + 12.3780i −0.287240 + 0.497515i −0.973150 0.230172i 0.926071π-0.926071\pi
0.685910 + 0.727687i 0.259405π0.259405\pi
620620 −11.6030 + 20.0970i −0.465988 + 0.807115i
621621 −0.679774 1.17740i −0.0272784 0.0472476i
622622 −5.35973 −0.214906
623623 −3.95728 8.85046i −0.158545 0.354586i
624624 −3.45079 −0.138142
625625 11.1438 + 19.3016i 0.445750 + 0.772062i
626626 −15.4496 + 26.7594i −0.617489 + 1.06952i
627627 21.1357 36.6082i 0.844080 1.46199i
628628 14.2036 + 24.6013i 0.566784 + 0.981698i
629629 −21.2554 −0.847510
630630 −38.6128 3.99656i −1.53837 0.159227i
631631 −0.0431064 −0.00171604 −0.000858019 1.00000i 0.500273π-0.500273\pi
−0.000858019 1.00000i 0.500273π0.500273\pi
632632 5.15084 + 8.92152i 0.204890 + 0.354879i
633633 30.2633 52.4176i 1.20286 2.08341i
634634 −3.39592 + 5.88190i −0.134869 + 0.233600i
635635 −11.1731 19.3524i −0.443390 0.767975i
636636 −88.8004 −3.52116
637637 6.85161 + 1.43369i 0.271471 + 0.0568048i
638638 −62.5484 −2.47632
639639 3.96401 + 6.86587i 0.156814 + 0.271610i
640640 −15.1860 + 26.3029i −0.600279 + 1.03971i
641641 −21.3328 + 36.9494i −0.842594 + 1.45942i 0.0451008 + 0.998982i 0.485639π0.485639\pi
−0.887695 + 0.460433i 0.847694π0.847694\pi
642642 −18.4765 32.0022i −0.729208 1.26303i
643643 −5.49737 −0.216795 −0.108398 0.994108i 0.534572π-0.534572\pi
−0.108398 + 0.994108i 0.534572π0.534572\pi
644644 34.1342 + 3.53301i 1.34508 + 0.139220i
645645 −17.8977 −0.704722
646646 −14.9156 25.8345i −0.586845 1.01645i
647647 19.0933 33.0706i 0.750637 1.30014i −0.196877 0.980428i 0.563080π-0.563080\pi
0.947514 0.319713i 0.103587π-0.103587\pi
648648 8.57053 14.8446i 0.336682 0.583150i
649649 −11.4671 19.8615i −0.450121 0.779633i
650650 −1.09280 −0.0428633
651651 10.0775 + 22.5384i 0.394969 + 0.883348i
652652 40.1024 1.57053
653653 −19.2510 33.3437i −0.753349 1.30484i −0.946191 0.323608i 0.895104π-0.895104\pi
0.192843 0.981230i 0.438229π-0.438229\pi
654654 −11.4366 + 19.8088i −0.447206 + 0.774584i
655655 5.75711 9.97161i 0.224949 0.389623i
656656 7.24820 + 12.5543i 0.282995 + 0.490161i
657657 24.0477 0.938192
658658 24.4151 33.7166i 0.951798 1.31441i
659659 19.4843 0.759002 0.379501 0.925191i 0.376096π-0.376096\pi
0.379501 + 0.925191i 0.376096π0.376096\pi
660660 36.4595 + 63.1498i 1.41919 + 2.45810i
661661 20.8334 36.0844i 0.810324 1.40352i −0.102314 0.994752i 0.532625π-0.532625\pi
0.912638 0.408770i 0.134042π-0.134042\pi
662662 −15.0564 + 26.0784i −0.585182 + 1.01356i
663663 4.67454 + 8.09654i 0.181544 + 0.314443i
664664 6.89760 0.267679
665665 −11.7506 + 16.2273i −0.455668 + 0.629266i
666666 38.8834 1.50670
667667 13.2020 + 22.8665i 0.511182 + 0.885393i
668668 −25.1520 + 43.5645i −0.973160 + 1.68556i
669669 36.2040 62.7071i 1.39973 2.42440i
670670 −6.81168 11.7982i −0.263158 0.455803i
671671 15.3580 0.592890
672672 18.8803 + 42.2258i 0.728324 + 1.62889i
673673 −14.3157 −0.551830 −0.275915 0.961182i 0.588981π-0.588981\pi
−0.275915 + 0.961182i 0.588981π0.588981\pi
674674 38.9153 + 67.4033i 1.49896 + 2.59628i
675675 0.0750110 0.129923i 0.00288718 0.00500073i
676676 −1.44940 + 2.51043i −0.0557460 + 0.0965550i
677677 14.7641 + 25.5721i 0.567429 + 0.982815i 0.996819 + 0.0796963i 0.0253950π0.0253950\pi
−0.429391 + 0.903119i 0.641272π0.641272\pi
678678 32.3184 1.24118
679679 −14.2304 1.47290i −0.546114 0.0565247i
680680 15.9554 0.611860
681681 12.4633 + 21.5871i 0.477596 + 0.827220i
682682 19.9862 34.6172i 0.765312 1.32556i
683683 −23.5349 + 40.7637i −0.900539 + 1.55978i −0.0737441 + 0.997277i 0.523495π0.523495\pi
−0.826795 + 0.562503i 0.809839π0.809839\pi
684684 16.1459 + 27.9655i 0.617354 + 1.06929i
685685 −47.2210 −1.80422
686686 −8.71296 40.0546i −0.332662 1.52929i
687687 −27.5650 −1.05167
688688 2.37590 + 4.11518i 0.0905804 + 0.156890i
689689 6.19003 10.7214i 0.235821 0.408454i
690690 26.0097 45.0501i 0.990172 1.71503i
691691 15.4334 + 26.7314i 0.587113 + 1.01691i 0.994608 + 0.103703i 0.0330690π0.0330690\pi
−0.407495 + 0.913207i 0.633598π0.633598\pi
692692 −8.58442 −0.326331
693693 39.3568 + 4.07356i 1.49504 + 0.154742i
694694 −12.1091 −0.459656
695695 −4.24559 7.35358i −0.161044 0.278937i
696696 14.5238 25.1560i 0.550524 0.953535i
697697 19.6372 34.0127i 0.743813 1.28832i
698698 −4.80508 8.32264i −0.181875 0.315017i
699699 −42.2715 −1.59885
700700 1.54568 + 3.45691i 0.0584211 + 0.130659i
701701 6.48958 0.245108 0.122554 0.992462i 0.460892π-0.460892\pi
0.122554 + 0.992462i 0.460892π0.460892\pi
702702 −0.336257 0.582415i −0.0126912 0.0219818i
703703 10.0341 17.3795i 0.378443 0.655482i
704704 30.7657 53.2878i 1.15953 2.00836i
705705 −18.6701 32.3376i −0.703157 1.21790i
706706 61.0860 2.29900
707707 −14.4580 + 19.9661i −0.543747 + 0.750902i
708708 34.3505 1.29097
709709 6.68689 + 11.5820i 0.251131 + 0.434972i 0.963838 0.266490i 0.0858641π-0.0858641\pi
−0.712706 + 0.701463i 0.752531π0.752531\pi
710710 −5.96409 + 10.3301i −0.223828 + 0.387682i
711711 8.08569 14.0048i 0.303237 0.525222i
712712 −3.64475 6.31290i −0.136593 0.236586i
713713 −16.8738 −0.631929
714714 32.1094 44.3424i 1.20167 1.65947i
715715 −10.1660 −0.380186
716716 8.21645 + 14.2313i 0.307063 + 0.531849i
717717 −8.56328 + 14.8320i −0.319802 + 0.553913i
718718 −7.33555 + 12.7055i −0.273760 + 0.474167i
719719 8.37048 + 14.4981i 0.312166 + 0.540688i 0.978831 0.204670i 0.0656120π-0.0656120\pi
−0.666665 + 0.745358i 0.732279π0.732279\pi
720720 9.24476 0.344532
721721 −7.89050 17.6471i −0.293858 0.657212i
722722 −13.8883 −0.516868
723723 −8.03725 13.9209i −0.298909 0.517725i
724724 −10.4015 + 18.0160i −0.386570 + 0.669558i
725725 −1.45680 + 2.52325i −0.0541041 + 0.0937110i
726726 −32.6798 56.6030i −1.21286 2.10074i
727727 38.8138 1.43952 0.719761 0.694221i 0.244251π-0.244251\pi
0.719761 + 0.694221i 0.244251π0.244251\pi
728728 5.23528 + 0.541869i 0.194032 + 0.0200830i
729729 −29.1632 −1.08012
730730 18.0906 + 31.3339i 0.669564 + 1.15972i
731731 6.43692 11.1491i 0.238078 0.412364i
732732 −11.5016 + 19.9213i −0.425110 + 0.736312i
733733 −18.8639 32.6733i −0.696756 1.20682i −0.969585 0.244754i 0.921293π-0.921293\pi
0.272830 0.962062i 0.412040π-0.412040\pi
734734 69.0719 2.54949
735735 −35.9895 7.53074i −1.32749 0.277776i
736736 −31.6132 −1.16528
737737 6.94292 + 12.0255i 0.255746 + 0.442965i
738738 −35.9232 + 62.2208i −1.32235 + 2.29038i
739739 4.61476 7.99300i 0.169757 0.294027i −0.768578 0.639757i 0.779035π-0.779035\pi
0.938334 + 0.345729i 0.112368π0.112368\pi
740740 17.3090 + 29.9801i 0.636291 + 1.10209i
741741 −8.82686 −0.324263
742742 −72.1111 7.46375i −2.64728 0.274003i
743743 −3.56327 −0.130724 −0.0653619 0.997862i 0.520820π-0.520820\pi
−0.0653619 + 0.997862i 0.520820π0.520820\pi
744744 9.28164 + 16.0763i 0.340282 + 0.589385i
745745 3.13614 5.43195i 0.114899 0.199011i
746746 17.4571 30.2366i 0.639151 1.10704i
747747 −5.41386 9.37707i −0.198083 0.343089i
748748 −52.4508 −1.91779
749749 −7.28674 16.2968i −0.266252 0.595472i
750750 63.8698 2.33220
751751 −25.6053 44.3496i −0.934350 1.61834i −0.775789 0.630992i 0.782648π-0.782648\pi
−0.158561 0.987349i 0.550685π-0.550685\pi
752752 −4.95687 + 8.58555i −0.180758 + 0.313083i
753753 12.2089 21.1464i 0.444916 0.770618i
754754 6.53049 + 11.3111i 0.237826 + 0.411927i
755755 39.3879 1.43347
756756 −1.36677 + 1.88747i −0.0497088 + 0.0686466i
757757 25.2305 0.917019 0.458509 0.888690i 0.348384π-0.348384\pi
0.458509 + 0.888690i 0.348384π0.348384\pi
758758 −35.0272 60.6688i −1.27224 2.20359i
759759 −26.5108 + 45.9181i −0.962282 + 1.66672i
760760 −7.53207 + 13.0459i −0.273217 + 0.473226i
761761 −1.82372 3.15878i −0.0661099 0.114506i 0.831076 0.556159i 0.187725π-0.187725\pi
−0.897186 + 0.441653i 0.854392π0.854392\pi
762762 −57.6520 −2.08851
763763 −6.48077 + 8.94978i −0.234620 + 0.324004i
764764 34.4428 1.24610
765765 −12.5232 21.6908i −0.452777 0.784233i
766766 −13.7154 + 23.7558i −0.495558 + 0.858331i
767767 −2.39448 + 4.14736i −0.0864596 + 0.149752i
768768 7.38609 + 12.7931i 0.266523 + 0.461631i
769769 21.9882 0.792914 0.396457 0.918053i 0.370240π-0.370240\pi
0.396457 + 0.918053i 0.370240π0.370240\pi
770770 24.2995 + 54.3458i 0.875693 + 1.95849i
771771 16.9862 0.611742
772772 −33.2929 57.6650i −1.19824 2.07541i
773773 −10.9295 + 18.9305i −0.393108 + 0.680882i −0.992858 0.119305i 0.961933π-0.961933\pi
0.599750 + 0.800187i 0.295267π0.295267\pi
774774 −11.7753 + 20.3954i −0.423255 + 0.733099i
775775 −0.930986 1.61252i −0.0334420 0.0579233i
776776 −10.7569 −0.386151
777777 36.6342 + 3.79176i 1.31424 + 0.136029i
778778 −31.1505 −1.11680
779779 18.5404 + 32.1128i 0.664277 + 1.15056i
780780 7.61326 13.1865i 0.272598 0.472154i
781781 6.07900 10.5291i 0.217524 0.376762i
782782 18.7088 + 32.4046i 0.669025 + 1.15879i
783783 −1.79303 −0.0640777
784784 3.04603 + 9.27468i 0.108787 + 0.331239i
785785 20.8026 0.742477
786786 −14.8531 25.7263i −0.529791 0.917625i
787787 −19.9336 + 34.5261i −0.710557 + 1.23072i 0.254091 + 0.967180i 0.418224π0.418224\pi
−0.964648 + 0.263541i 0.915109π0.915109\pi
788788 −24.5261 + 42.4804i −0.873706 + 1.51330i
789789 0.156570 + 0.271188i 0.00557405 + 0.00965454i
790790 24.3308 0.865651
791791 15.5298 + 1.60739i 0.552176 + 0.0571521i
792792 29.7502 1.05713
793793 −1.60348 2.77732i −0.0569414 0.0986254i
794794 7.71680 13.3659i 0.273859 0.474338i
795795 −32.5144 + 56.3166i −1.15317 + 1.99734i
796796 −14.5796 25.2526i −0.516759 0.895053i
797797 −40.1971 −1.42385 −0.711927 0.702253i 0.752178π-0.752178\pi
−0.711927 + 0.702253i 0.752178π0.752178\pi
798798 21.0986 + 47.1871i 0.746884 + 1.67041i
799799 26.8589 0.950198
800800 −1.74421 3.02106i −0.0616671 0.106811i
801801 −5.72146 + 9.90986i −0.202158 + 0.350148i
802802 −3.02873 + 5.24592i −0.106948 + 0.185240i
803803 −18.4392 31.9376i −0.650704 1.12705i
804804 −20.7981 −0.733492
805805 14.7389 20.3541i 0.519478 0.717387i
806806 −8.34680 −0.294003
807807 5.24960 + 9.09258i 0.184795 + 0.320074i
808808 −9.26749 + 16.0518i −0.326029 + 0.564699i
809809 −1.26924 + 2.19840i −0.0446243 + 0.0772915i −0.887475 0.460856i 0.847542π-0.847542\pi
0.842851 + 0.538148i 0.180876π0.180876\pi
810810 −20.2421 35.0603i −0.711235 1.23189i
811811 −41.7062 −1.46450 −0.732251 0.681035i 0.761530π-0.761530\pi
−0.732251 + 0.681035i 0.761530π0.761530\pi
812812 26.5441 36.6567i 0.931515 1.28640i
813813 3.87801 0.136008
814814 −29.8148 51.6407i −1.04501 1.81001i
815815 14.6836 25.4327i 0.514343 0.890868i
816816 −6.51902 + 11.2913i −0.228211 + 0.395274i
817817 6.07737 + 10.5263i 0.212620 + 0.368269i
818818 −54.2604 −1.89717
819819 −3.37246 7.54251i −0.117843 0.263557i
820820 −63.9650 −2.23375
821821 −15.9652 27.6525i −0.557189 0.965079i −0.997730 0.0673467i 0.978547π-0.978547\pi
0.440541 0.897733i 0.354787π-0.354787\pi
822822 −60.9140 + 105.506i −2.12462 + 3.67995i
823823 17.1266 29.6641i 0.596995 1.03402i −0.396267 0.918135i 0.629695π-0.629695\pi
0.993262 0.115890i 0.0369720π-0.0369720\pi
824824 −7.26734 12.5874i −0.253170 0.438503i
825825 −5.85078 −0.203698
826826 27.8946 + 2.88719i 0.970578 + 0.100458i
827827 36.9755 1.28576 0.642882 0.765965i 0.277739π-0.277739\pi
0.642882 + 0.765965i 0.277739π0.277739\pi
828828 −20.2520 35.0775i −0.703807 1.21903i
829829 9.99473 17.3114i 0.347131 0.601249i −0.638607 0.769533i 0.720489π-0.720489\pi
0.985739 + 0.168284i 0.0538225π0.0538225\pi
830830 8.14547 14.1084i 0.282733 0.489708i
831831 15.7685 + 27.3119i 0.547005 + 0.947440i
832832 −12.8486 −0.445446
833833 17.6348 19.7106i 0.611009 0.682932i
834834 −21.9068 −0.758571
835835 18.4189 + 31.9024i 0.637412 + 1.10403i
836836 24.7605 42.8865i 0.856360 1.48326i
837837 0.572931 0.992346i 0.0198034 0.0343005i
838838 3.33384 + 5.77438i 0.115166 + 0.199473i
839839 12.8147 0.442411 0.221206 0.975227i 0.429001π-0.429001\pi
0.221206 + 0.975227i 0.429001π0.429001\pi
840840 −27.4994 2.84628i −0.948819 0.0982060i
841841 5.82265 0.200781
842842 11.0666 + 19.1679i 0.381381 + 0.660571i
843843 −5.72812 + 9.92140i −0.197287 + 0.341711i
844844 35.4535 61.4073i 1.22036 2.11373i
845845 1.06140 + 1.83839i 0.0365132 + 0.0632427i
846846 −49.1340 −1.68926
847847 −12.8882 28.8245i −0.442845 0.990422i
848848 17.2650 0.592882
849849 −4.51375 7.81805i −0.154912 0.268315i
850850 −2.06446 + 3.57575i −0.0708104 + 0.122647i
851851 −12.5859 + 21.7994i −0.431439 + 0.747274i
852852 9.10508 + 15.7705i 0.311935 + 0.540287i
853853 −30.1839 −1.03348 −0.516739 0.856143i 0.672854π-0.672854\pi
−0.516739 + 0.856143i 0.672854π0.672854\pi
854854 −11.0143 + 15.2105i −0.376903 + 0.520494i
855855 23.6474 0.808724
856856 −6.71127 11.6243i −0.229386 0.397309i
857857 26.6164 46.1009i 0.909197 1.57478i 0.0940154 0.995571i 0.470030π-0.470030\pi
0.815182 0.579205i 0.196637π-0.196637\pi
858858 −13.1139 + 22.7139i −0.447700 + 0.775438i
859859 6.13597 + 10.6278i 0.209357 + 0.362616i 0.951512 0.307611i 0.0995297π-0.0995297\pi
−0.742155 + 0.670228i 0.766196π0.766196\pi
860860 −20.9672 −0.714975
861861 −39.9127 + 55.1185i −1.36022 + 1.87843i
862862 −41.5977 −1.41682
863863 −12.2226 21.1702i −0.416064 0.720643i 0.579476 0.814989i 0.303257π-0.303257\pi
−0.995539 + 0.0943460i 0.969924π0.969924\pi
864864 1.07339 1.85917i 0.0365175 0.0632501i
865865 −3.14320 + 5.44418i −0.106872 + 0.185108i
866866 8.59778 + 14.8918i 0.292164 + 0.506043i
867867 −6.74189 −0.228967
868868 11.8058 + 26.4037i 0.400716 + 0.896200i
869869 −24.7996 −0.841268
870870 −34.3027 59.4141i −1.16297 2.01432i
871871 1.44978 2.51109i 0.0491238 0.0850850i
872872 −4.15415 + 7.19519i −0.140677 + 0.243660i
873873 8.44300 + 14.6237i 0.285752 + 0.494937i
874874 −35.3276 −1.19497
875875 30.6910 + 3.17663i 1.03755 + 0.107390i
876876 55.2361 1.86625
877877 26.4376 + 45.7913i 0.892736 + 1.54626i 0.836582 + 0.547842i 0.184550π0.184550\pi
0.0561539 + 0.998422i 0.482116π0.482116\pi
878878 42.0178 72.7770i 1.41803 2.45611i
879879 26.0329 45.0903i 0.878068 1.52086i
880880 −7.08864 12.2779i −0.238958 0.413887i
881881 55.0118 1.85339 0.926697 0.375809i 0.122635π-0.122635\pi
0.926697 + 0.375809i 0.122635π0.122635\pi
882882 −32.2600 + 36.0574i −1.08625 + 1.21412i
883883 44.1730 1.48654 0.743269 0.668992i 0.233274π-0.233274\pi
0.743269 + 0.668992i 0.233274π0.233274\pi
884884 5.47622 + 9.48510i 0.184185 + 0.319018i
885885 12.5775 21.7848i 0.422788 0.732290i
886886 −39.4270 + 68.2895i −1.32457 + 2.29423i
887887 2.54330 + 4.40512i 0.0853955 + 0.147909i 0.905560 0.424219i 0.139451π-0.139451\pi
−0.820164 + 0.572128i 0.806118π0.806118\pi
888888 27.6921 0.929286
889889 −27.7032 2.86738i −0.929136 0.0961688i
890890 −17.2165 −0.577100
891891 20.6321 + 35.7359i 0.691202 + 1.19720i
892892 42.4130 73.4614i 1.42009 2.45967i
893893 −12.6793 + 21.9612i −0.424296 + 0.734903i
894894 −8.09108 14.0142i −0.270606 0.468704i
895895 12.0339 0.402248
896896 15.4514 + 34.5571i 0.516196 + 1.15447i
897897 11.0717 0.369672
898898 8.91178 + 15.4356i 0.297390 + 0.515094i
899899 −11.1270 + 19.2724i −0.371105 + 0.642772i
900900 2.23475 3.87070i 0.0744917 0.129023i
901901 −23.3876 40.5086i −0.779155 1.34954i
902902 110.180 3.66859
903903 −13.0830 + 18.0674i −0.435377 + 0.601244i
904904 11.7391 0.390437
905905 7.61706 + 13.1931i 0.253200 + 0.438555i
906906 50.8094 88.0044i 1.68803 2.92375i
907907 9.06264 15.6969i 0.300920 0.521209i −0.675425 0.737429i 0.736040π-0.736040\pi
0.976345 + 0.216220i 0.0693730π0.0693730\pi
908908 14.6008 + 25.2893i 0.484544 + 0.839255i
909909 29.0958 0.965048
910910 7.29075 10.0683i 0.241686 0.333763i
911911 −9.65804 −0.319985 −0.159993 0.987118i 0.551147π-0.551147\pi
−0.159993 + 0.987118i 0.551147π0.551147\pi
912912 −6.15489 10.6606i −0.203809 0.353007i
913913 −8.30241 + 14.3802i −0.274770 + 0.475915i
914914 −17.2613 + 29.8974i −0.570952 + 0.988918i
915915 8.42263 + 14.5884i 0.278444 + 0.482278i
916916 −32.2924 −1.06697
917917 −5.85774 13.1008i −0.193440 0.432628i
918918 −2.54095 −0.0838637
919919 −23.8801 41.3616i −0.787733 1.36439i −0.927353 0.374188i 0.877922π-0.877922\pi
0.139620 0.990205i 0.455412π-0.455412\pi
920920 9.44758 16.3637i 0.311477 0.539495i
921921 6.13487 10.6259i 0.202151 0.350135i
922922 28.4401 + 49.2598i 0.936626 + 1.62228i
923923 −2.53876 −0.0835643
924924 90.4000 + 9.35670i 2.97394 + 0.307813i
925925 −2.77763 −0.0913279
926926 22.7096 + 39.3342i 0.746285 + 1.29260i
927927 −11.4081 + 19.7595i −0.374692 + 0.648986i
928928 −20.8464 + 36.1071i −0.684317 + 1.18527i
929929 −16.9905 29.4285i −0.557442 0.965517i −0.997709 0.0676505i 0.978450π-0.978450\pi
0.440267 0.897867i 0.354884π-0.354884\pi
930930 43.8433 1.43768
931931 7.79153 + 23.7239i 0.255357 + 0.777520i
932932 −49.5210 −1.62212
933933 2.99601 + 5.18924i 0.0980850 + 0.169888i
934934 −13.0861 + 22.6657i −0.428189 + 0.741645i
935935 −19.2049 + 33.2639i −0.628068 + 1.08785i
936936 −3.10612 5.37996i −0.101527 0.175849i
937937 −24.7948 −0.810012 −0.405006 0.914314i 0.632731π-0.632731\pi
−0.405006 + 0.914314i 0.632731π0.632731\pi
938938 −16.8893 1.74810i −0.551454 0.0570774i
939939 34.5443 1.12731
940940 −21.8720 37.8835i −0.713387 1.23562i
941941 4.12098 7.13774i 0.134340 0.232684i −0.791005 0.611810i 0.790442π-0.790442\pi
0.925345 + 0.379126i 0.123775π0.123775\pi
942942 26.8349 46.4793i 0.874327 1.51438i
943943 −23.2554 40.2796i −0.757301 1.31168i
944944 −6.67859 −0.217370
945945 0.696577 + 1.55789i 0.0226596 + 0.0506783i
946946 36.1160 1.17423
947947 −9.98643 17.2970i −0.324515 0.562077i 0.656899 0.753979i 0.271868π-0.271868\pi
−0.981414 + 0.191902i 0.938535π0.938535\pi
948948 18.5723 32.1682i 0.603200 1.04477i
949949 −3.85035 + 6.66901i −0.124988 + 0.216485i
950950 −1.94914 3.37602i −0.0632386 0.109532i
951951 7.59307 0.246222
952952 11.6632 16.1066i 0.378007 0.522018i
953953 −21.5341 −0.697557 −0.348778 0.937205i 0.613403π-0.613403\pi
−0.348778 + 0.937205i 0.613403π0.613403\pi
954954 42.7839 + 74.1040i 1.38518 + 2.39920i
955955 12.6113 21.8434i 0.408091 0.706835i
956956 −10.0319 + 17.3757i −0.324455 + 0.561972i
957957 34.9636 + 60.5588i 1.13021 + 1.95759i
958958 50.1432 1.62005
959959 −34.5181 + 47.6686i −1.11465 + 1.53930i
960960 67.4900 2.17823
961961 8.38917 + 14.5305i 0.270618 + 0.468725i
962962 −6.22574 + 10.7833i −0.200726 + 0.347667i
963963 −10.5352 + 18.2475i −0.339492 + 0.588018i
964964 −9.41564 16.3084i −0.303257 0.525257i
965965 −48.7610 −1.56967
966966 −26.4643 59.1874i −0.851476 1.90432i
967967 43.2887 1.39207 0.696036 0.718007i 0.254945π-0.254945\pi
0.696036 + 0.718007i 0.254945π0.254945\pi
968968 −11.8704 20.5601i −0.381528 0.660827i
969969 −16.6752 + 28.8822i −0.535683 + 0.927831i
970970 −12.7030 + 22.0022i −0.407868 + 0.706449i
971971 26.3356 + 45.6147i 0.845151 + 1.46384i 0.885490 + 0.464658i 0.153823π0.153823\pi
−0.0403390 + 0.999186i 0.512844π0.512844\pi
972972 −64.4476 −2.06716
973973 −10.5268 1.08956i −0.337473 0.0349296i
974974 −72.4127 −2.32025
975975 0.610862 + 1.05804i 0.0195632 + 0.0338845i
976976 2.23619 3.87319i 0.0715787 0.123978i
977977 −7.70305 + 13.3421i −0.246442 + 0.426851i −0.962536 0.271153i 0.912595π-0.912595\pi
0.716094 + 0.698004i 0.245928π0.245928\pi
978978 −37.8829 65.6151i −1.21136 2.09814i
979979 17.5483 0.560845
980980 −42.1617 8.82227i −1.34681 0.281817i
981981 13.0422 0.416405
982982 −6.83121 11.8320i −0.217993 0.377575i
983983 −3.79073 + 6.56574i −0.120906 + 0.209415i −0.920125 0.391625i 0.871913π-0.871913\pi
0.799219 + 0.601039i 0.205246π0.205246\pi
984984 −25.5839 + 44.3126i −0.815584 + 1.41263i
985985 17.9605 + 31.1085i 0.572270 + 0.991201i
986986 49.3480 1.57156
987987 −46.2918 4.79136i −1.47348 0.152511i
988988 −10.3407 −0.328981
989989 −7.62293 13.2033i −0.242395 0.419841i
990990 35.1323 60.8510i 1.11658 1.93397i
991991 9.50923 16.4705i 0.302071 0.523202i −0.674534 0.738244i 0.735655π-0.735655\pi
0.976605 + 0.215042i 0.0689888π0.0689888\pi
992992 −13.3222 23.0747i −0.422980 0.732623i
993993 33.6651 1.06833
994994 6.06834 + 13.5718i 0.192476 + 0.430472i
995995 −21.3533 −0.676946
996996 −12.4353 21.5385i −0.394027 0.682474i
997997 −23.0499 + 39.9236i −0.729998 + 1.26439i 0.226885 + 0.973922i 0.427146π0.427146\pi
−0.956883 + 0.290473i 0.906187π0.906187\pi
998998 16.2001 28.0593i 0.512804 0.888202i
999999 −0.854680 1.48035i −0.0270409 0.0468362i
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 91.2.e.c.53.2 10
3.2 odd 2 819.2.j.h.235.4 10
4.3 odd 2 1456.2.r.p.417.5 10
7.2 even 3 inner 91.2.e.c.79.2 yes 10
7.3 odd 6 637.2.a.k.1.4 5
7.4 even 3 637.2.a.l.1.4 5
7.5 odd 6 637.2.e.m.79.2 10
7.6 odd 2 637.2.e.m.508.2 10
13.12 even 2 1183.2.e.f.508.4 10
21.2 odd 6 819.2.j.h.352.4 10
21.11 odd 6 5733.2.a.bl.1.2 5
21.17 even 6 5733.2.a.bm.1.2 5
28.23 odd 6 1456.2.r.p.625.5 10
91.25 even 6 8281.2.a.bw.1.2 5
91.38 odd 6 8281.2.a.bx.1.2 5
91.51 even 6 1183.2.e.f.170.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.2 10 1.1 even 1 trivial
91.2.e.c.79.2 yes 10 7.2 even 3 inner
637.2.a.k.1.4 5 7.3 odd 6
637.2.a.l.1.4 5 7.4 even 3
637.2.e.m.79.2 10 7.5 odd 6
637.2.e.m.508.2 10 7.6 odd 2
819.2.j.h.235.4 10 3.2 odd 2
819.2.j.h.352.4 10 21.2 odd 6
1183.2.e.f.170.4 10 91.51 even 6
1183.2.e.f.508.4 10 13.12 even 2
1456.2.r.p.417.5 10 4.3 odd 2
1456.2.r.p.625.5 10 28.23 odd 6
5733.2.a.bl.1.2 5 21.11 odd 6
5733.2.a.bm.1.2 5 21.17 even 6
8281.2.a.bw.1.2 5 91.25 even 6
8281.2.a.bx.1.2 5 91.38 odd 6