Properties

Label 85.2.l.a.26.6
Level 8585
Weight 22
Character 85.26
Analytic conductor 0.6790.679
Analytic rank 00
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [85,2,Mod(26,85)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(85, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("85.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 85=517 85 = 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 85.l (of order 88, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.6787284171810.678728417181
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 26.6
Character χ\chi == 85.26
Dual form 85.2.l.a.36.6

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.663051.66305i)q2+(1.449890.600564i)q33.53144iq4+(0.382683+0.923880i)q5+(3.41000+1.41247i)q6+(1.37082+3.30945i)q7+(2.546862.54686i)q8+(0.3798150.379815i)q9+(0.900034+2.17287i)q10+(2.293620.950048i)q11+(2.12086+5.12021i)q121.25948iq13+(7.78350+3.22403i)q14+(1.109701.10970i)q151.40821q16+(3.84535+1.48772i)q171.26330q18+(2.56985+2.56985i)q19+(3.26263+1.35142i)q205.62161iq21+(2.234425.39437i)q22+(8.16056+3.38021i)q23+(2.16312+5.22222i)q24+(0.7071070.707107i)q25+(2.094582.09458i)q26+(2.12428+5.12847i)q27+(11.68714.84097i)q28+(3.352008.09244i)q293.69096iq30+(2.25799+0.935290i)q31+(2.751812.75181i)q323.89606q33+(3.92084+8.86913i)q343.58212q35+(1.34129+1.34129i)q36+(4.251281.76094i)q37+8.54755iq38+(0.756400+1.82611i)q39+(3.327631.37835i)q40+(1.655103.99575i)q41+(9.348999.34899i)q42+(5.33668+5.33668i)q43+(3.355048.09978i)q44+(0.4962520.205554i)q45+(7.94993+19.1928i)q4611.3322iq47+(2.04175+0.845719i)q48+(4.12357+4.12357i)q492.35190q50+(6.46880+0.152348i)q514.44779q52+(4.024424.02442i)q53+(12.0616+4.99610i)q54+2.48259iq55+(4.9374211.9200i)q56+(5.269362.18264i)q57+(7.8835719.0326i)q58+(3.16077+3.16077i)q59+(3.918843.91884i)q60+(0.0929426+0.224383i)q61+(5.310572.19971i)q62+(0.7363211.77764i)q6311.9692iq64+(1.16361+0.481983i)q65+(6.47933+6.47933i)q66+7.23278q67+(5.25380+13.5796i)q68+13.8620q69+(5.95724+5.95724i)q70+(1.697890.703290i)q71+1.93467iq72+(2.09426+5.05599i)q73+(9.99859+4.14155i)q74+(0.600564+1.44989i)q75+(9.07527+9.07527i)q76+(6.28827+6.28827i)q77+(1.77898+4.29484i)q78+(8.34789+3.45781i)q79+(0.5388971.30101i)q807.10006iq81+(9.397623.89262i)q82+(5.17302+5.17302i)q8319.8524q84+(0.09707714.12196i)q85+17.7503q86+(9.72006+9.72006i)q87+(8.261173.42189i)q88+2.19350iq89+(0.4834431.16714i)q90+(4.168191.72652i)q91+(11.9370+28.8186i)q92+(2.712142.71214i)q93+(18.845918.8459i)q94+(1.390793.35767i)q95+(5.64246+2.33718i)q96+(3.75810+9.07286i)q97+13.7154iq98+(1.231990.510308i)q99+O(q100)q+(1.66305 - 1.66305i) q^{2} +(-1.44989 - 0.600564i) q^{3} -3.53144i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-3.41000 + 1.41247i) q^{6} +(1.37082 + 3.30945i) q^{7} +(-2.54686 - 2.54686i) q^{8} +(-0.379815 - 0.379815i) q^{9} +(0.900034 + 2.17287i) q^{10} +(2.29362 - 0.950048i) q^{11} +(-2.12086 + 5.12021i) q^{12} -1.25948i q^{13} +(7.78350 + 3.22403i) q^{14} +(1.10970 - 1.10970i) q^{15} -1.40821 q^{16} +(-3.84535 + 1.48772i) q^{17} -1.26330 q^{18} +(-2.56985 + 2.56985i) q^{19} +(3.26263 + 1.35142i) q^{20} -5.62161i q^{21} +(2.23442 - 5.39437i) q^{22} +(-8.16056 + 3.38021i) q^{23} +(2.16312 + 5.22222i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-2.09458 - 2.09458i) q^{26} +(2.12428 + 5.12847i) q^{27} +(11.6871 - 4.84097i) q^{28} +(3.35200 - 8.09244i) q^{29} -3.69096i q^{30} +(2.25799 + 0.935290i) q^{31} +(2.75181 - 2.75181i) q^{32} -3.89606 q^{33} +(-3.92084 + 8.86913i) q^{34} -3.58212 q^{35} +(-1.34129 + 1.34129i) q^{36} +(-4.25128 - 1.76094i) q^{37} +8.54755i q^{38} +(-0.756400 + 1.82611i) q^{39} +(3.32763 - 1.37835i) q^{40} +(-1.65510 - 3.99575i) q^{41} +(-9.34899 - 9.34899i) q^{42} +(5.33668 + 5.33668i) q^{43} +(-3.35504 - 8.09978i) q^{44} +(0.496252 - 0.205554i) q^{45} +(-7.94993 + 19.1928i) q^{46} -11.3322i q^{47} +(2.04175 + 0.845719i) q^{48} +(-4.12357 + 4.12357i) q^{49} -2.35190 q^{50} +(6.46880 + 0.152348i) q^{51} -4.44779 q^{52} +(4.02442 - 4.02442i) q^{53} +(12.0616 + 4.99610i) q^{54} +2.48259i q^{55} +(4.93742 - 11.9200i) q^{56} +(5.26936 - 2.18264i) q^{57} +(-7.88357 - 19.0326i) q^{58} +(3.16077 + 3.16077i) q^{59} +(-3.91884 - 3.91884i) q^{60} +(0.0929426 + 0.224383i) q^{61} +(5.31057 - 2.19971i) q^{62} +(0.736321 - 1.77764i) q^{63} -11.9692i q^{64} +(1.16361 + 0.481983i) q^{65} +(-6.47933 + 6.47933i) q^{66} +7.23278 q^{67} +(5.25380 + 13.5796i) q^{68} +13.8620 q^{69} +(-5.95724 + 5.95724i) q^{70} +(-1.69789 - 0.703290i) q^{71} +1.93467i q^{72} +(-2.09426 + 5.05599i) q^{73} +(-9.99859 + 4.14155i) q^{74} +(0.600564 + 1.44989i) q^{75} +(9.07527 + 9.07527i) q^{76} +(6.28827 + 6.28827i) q^{77} +(1.77898 + 4.29484i) q^{78} +(-8.34789 + 3.45781i) q^{79} +(0.538897 - 1.30101i) q^{80} -7.10006i q^{81} +(-9.39762 - 3.89262i) q^{82} +(-5.17302 + 5.17302i) q^{83} -19.8524 q^{84} +(0.0970771 - 4.12196i) q^{85} +17.7503 q^{86} +(-9.72006 + 9.72006i) q^{87} +(-8.26117 - 3.42189i) q^{88} +2.19350i q^{89} +(0.483443 - 1.16714i) q^{90} +(4.16819 - 1.72652i) q^{91} +(11.9370 + 28.8186i) q^{92} +(-2.71214 - 2.71214i) q^{93} +(-18.8459 - 18.8459i) q^{94} +(-1.39079 - 3.35767i) q^{95} +(-5.64246 + 2.33718i) q^{96} +(-3.75810 + 9.07286i) q^{97} +13.7154i q^{98} +(-1.23199 - 0.510308i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q8q624q98q11+24q128q1524q168q17+8q188q1932q2216q238q24+16q26+24q27+48q288q29+16q3432q35+8q99+O(q100) 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/85Z)×\left(\mathbb{Z}/85\mathbb{Z}\right)^\times.

nn 5252 7171
χ(n)\chi(n) 11 e(18)e\left(\frac{1}{8}\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 1.66305 1.66305i 1.17595 1.17595i 0.195185 0.980767i 0.437469π-0.437469\pi
0.980767 0.195185i 0.0625306π-0.0625306\pi
33 −1.44989 0.600564i −0.837095 0.346736i −0.0773874 0.997001i 0.524658π-0.524658\pi
−0.759707 + 0.650265i 0.774658π0.774658\pi
44 3.53144i 1.76572i
55 −0.382683 + 0.923880i −0.171141 + 0.413171i
66 −3.41000 + 1.41247i −1.39213 + 0.576638i
77 1.37082 + 3.30945i 0.518121 + 1.25085i 0.939056 + 0.343764i 0.111702π0.111702\pi
−0.420935 + 0.907091i 0.638298π0.638298\pi
88 −2.54686 2.54686i −0.900451 0.900451i
99 −0.379815 0.379815i −0.126605 0.126605i
1010 0.900034 + 2.17287i 0.284616 + 0.687123i
1111 2.29362 0.950048i 0.691552 0.286450i −0.00909468 0.999959i 0.502895π-0.502895\pi
0.700647 + 0.713508i 0.252895π0.252895\pi
1212 −2.12086 + 5.12021i −0.612239 + 1.47808i
1313 1.25948i 0.349317i −0.984629 0.174659i 0.944118π-0.944118\pi
0.984629 0.174659i 0.0558822π-0.0558822\pi
1414 7.78350 + 3.22403i 2.08023 + 0.861659i
1515 1.10970 1.10970i 0.286523 0.286523i
1616 −1.40821 −0.352052
1717 −3.84535 + 1.48772i −0.932634 + 0.360825i
1818 −1.26330 −0.297762
1919 −2.56985 + 2.56985i −0.589563 + 0.589563i −0.937513 0.347950i 0.886878π-0.886878\pi
0.347950 + 0.937513i 0.386878π0.386878\pi
2020 3.26263 + 1.35142i 0.729546 + 0.302188i
2121 5.62161i 1.22674i
2222 2.23442 5.39437i 0.476380 1.15008i
2323 −8.16056 + 3.38021i −1.70159 + 0.704823i −0.999970 0.00772401i 0.997541π-0.997541\pi
−0.701624 + 0.712547i 0.747541π0.747541\pi
2424 2.16312 + 5.22222i 0.441544 + 1.06598i
2525 −0.707107 0.707107i −0.141421 0.141421i
2626 −2.09458 2.09458i −0.410780 0.410780i
2727 2.12428 + 5.12847i 0.408818 + 0.986974i
2828 11.6871 4.84097i 2.20866 0.914857i
2929 3.35200 8.09244i 0.622451 1.50273i −0.226367 0.974042i 0.572685π-0.572685\pi
0.848817 0.528686i 0.177315π-0.177315\pi
3030 3.69096i 0.673874i
3131 2.25799 + 0.935290i 0.405547 + 0.167983i 0.576126 0.817361i 0.304564π-0.304564\pi
−0.170579 + 0.985344i 0.554564π0.554564\pi
3232 2.75181 2.75181i 0.486456 0.486456i
3333 −3.89606 −0.678217
3434 −3.92084 + 8.86913i −0.672419 + 1.52104i
3535 −3.58212 −0.605489
3636 −1.34129 + 1.34129i −0.223549 + 0.223549i
3737 −4.25128 1.76094i −0.698906 0.289496i 0.00479925 0.999988i 0.498472π-0.498472\pi
−0.703705 + 0.710492i 0.748472π0.748472\pi
3838 8.54755i 1.38660i
3939 −0.756400 + 1.82611i −0.121121 + 0.292412i
4040 3.32763 1.37835i 0.526145 0.217936i
4141 −1.65510 3.99575i −0.258483 0.624032i 0.740356 0.672215i 0.234657π-0.234657\pi
−0.998839 + 0.0481830i 0.984657π0.984657\pi
4242 −9.34899 9.34899i −1.44258 1.44258i
4343 5.33668 + 5.33668i 0.813836 + 0.813836i 0.985207 0.171371i 0.0548196π-0.0548196\pi
−0.171371 + 0.985207i 0.554820π0.554820\pi
4444 −3.35504 8.09978i −0.505791 1.22109i
4545 0.496252 0.205554i 0.0739769 0.0306422i
4646 −7.94993 + 19.1928i −1.17215 + 2.82983i
4747 11.3322i 1.65297i −0.562961 0.826484i 0.690338π-0.690338\pi
0.562961 0.826484i 0.309662π-0.309662\pi
4848 2.04175 + 0.845719i 0.294701 + 0.122069i
4949 −4.12357 + 4.12357i −0.589081 + 0.589081i
5050 −2.35190 −0.332609
5151 6.46880 + 0.152348i 0.905814 + 0.0213330i
5252 −4.44779 −0.616797
5353 4.02442 4.02442i 0.552797 0.552797i −0.374450 0.927247i 0.622169π-0.622169\pi
0.927247 + 0.374450i 0.122169π0.122169\pi
5454 12.0616 + 4.99610i 1.64138 + 0.679883i
5555 2.48259i 0.334753i
5656 4.93742 11.9200i 0.659791 1.59288i
5757 5.26936 2.18264i 0.697943 0.289098i
5858 −7.88357 19.0326i −1.03516 2.49911i
5959 3.16077 + 3.16077i 0.411497 + 0.411497i 0.882260 0.470763i 0.156021π-0.156021\pi
−0.470763 + 0.882260i 0.656021π0.656021\pi
6060 −3.91884 3.91884i −0.505920 0.505920i
6161 0.0929426 + 0.224383i 0.0119001 + 0.0287293i 0.929718 0.368273i 0.120051π-0.120051\pi
−0.917818 + 0.397002i 0.870051π0.870051\pi
6262 5.31057 2.19971i 0.674443 0.279364i
6363 0.736321 1.77764i 0.0927677 0.223961i
6464 11.9692i 1.49615i
6565 1.16361 + 0.481983i 0.144328 + 0.0597826i
6666 −6.47933 + 6.47933i −0.797550 + 0.797550i
6767 7.23278 0.883625 0.441812 0.897108i 0.354336π-0.354336\pi
0.441812 + 0.897108i 0.354336π0.354336\pi
6868 5.25380 + 13.5796i 0.637116 + 1.64677i
6969 13.8620 1.66878
7070 −5.95724 + 5.95724i −0.712026 + 0.712026i
7171 −1.69789 0.703290i −0.201503 0.0834651i 0.279650 0.960102i 0.409782π-0.409782\pi
−0.481152 + 0.876637i 0.659782π0.659782\pi
7272 1.93467i 0.228003i
7373 −2.09426 + 5.05599i −0.245114 + 0.591758i −0.997777 0.0666485i 0.978769π-0.978769\pi
0.752662 + 0.658407i 0.228769π0.228769\pi
7474 −9.99859 + 4.14155i −1.16231 + 0.481446i
7575 0.600564 + 1.44989i 0.0693472 + 0.167419i
7676 9.07527 + 9.07527i 1.04100 + 1.04100i
7777 6.28827 + 6.28827i 0.716615 + 0.716615i
7878 1.77898 + 4.29484i 0.201430 + 0.486294i
7979 −8.34789 + 3.45781i −0.939211 + 0.389034i −0.799166 0.601111i 0.794725π-0.794725\pi
−0.140046 + 0.990145i 0.544725π0.544725\pi
8080 0.538897 1.30101i 0.0602505 0.145458i
8181 7.10006i 0.788896i
8282 −9.39762 3.89262i −1.03779 0.429868i
8383 −5.17302 + 5.17302i −0.567812 + 0.567812i −0.931515 0.363703i 0.881512π-0.881512\pi
0.363703 + 0.931515i 0.381512π0.381512\pi
8484 −19.8524 −2.16607
8585 0.0970771 4.12196i 0.0105295 0.447090i
8686 17.7503 1.91406
8787 −9.72006 + 9.72006i −1.04210 + 1.04210i
8888 −8.26117 3.42189i −0.880643 0.364774i
8989 2.19350i 0.232510i 0.993219 + 0.116255i 0.0370890π0.0370890\pi
−0.993219 + 0.116255i 0.962911π0.962911\pi
9090 0.483443 1.16714i 0.0509594 0.123027i
9191 4.16819 1.72652i 0.436945 0.180989i
9292 11.9370 + 28.8186i 1.24452 + 3.00454i
9393 −2.71214 2.71214i −0.281235 0.281235i
9494 −18.8459 18.8459i −1.94381 1.94381i
9595 −1.39079 3.35767i −0.142692 0.344489i
9696 −5.64246 + 2.33718i −0.575882 + 0.238538i
9797 −3.75810 + 9.07286i −0.381577 + 0.921209i 0.610084 + 0.792337i 0.291136π0.291136\pi
−0.991661 + 0.128872i 0.958864π0.958864\pi
9898 13.7154i 1.38546i
9999 −1.23199 0.510308i −0.123820 0.0512879i
100100 −2.49711 + 2.49711i −0.249711 + 0.249711i
101101 5.46415 0.543704 0.271852 0.962339i 0.412364π-0.412364\pi
0.271852 + 0.962339i 0.412364π0.412364\pi
102102 11.0113 10.5046i 1.09028 1.04011i
103103 7.16074 0.705568 0.352784 0.935705i 0.385235π-0.385235\pi
0.352784 + 0.935705i 0.385235π0.385235\pi
104104 −3.20773 + 3.20773i −0.314543 + 0.314543i
105105 5.19369 + 2.15130i 0.506852 + 0.209945i
106106 13.3856i 1.30012i
107107 −0.238471 + 0.575721i −0.0230539 + 0.0556570i −0.934987 0.354681i 0.884589π-0.884589\pi
0.911933 + 0.410338i 0.134589π0.134589\pi
108108 18.1109 7.50177i 1.74272 0.721859i
109109 2.36863 + 5.71837i 0.226873 + 0.547720i 0.995794 0.0916242i 0.0292058π-0.0292058\pi
−0.768921 + 0.639344i 0.779206π0.779206\pi
110110 4.12867 + 4.12867i 0.393653 + 0.393653i
111111 5.10633 + 5.10633i 0.484672 + 0.484672i
112112 −1.93040 4.66039i −0.182405 0.440365i
113113 14.8371 6.14574i 1.39576 0.578143i 0.447113 0.894478i 0.352452π-0.352452\pi
0.948648 + 0.316335i 0.102452π0.102452\pi
114114 5.13335 12.3930i 0.480782 1.16071i
115115 8.83293i 0.823675i
116116 −28.5780 11.8374i −2.65340 1.09907i
117117 −0.478370 + 0.478370i −0.0442253 + 0.0442253i
118118 10.5130 0.967801
119119 −10.1948 10.6866i −0.934557 0.979638i
120120 −5.65249 −0.516000
121121 −3.42008 + 3.42008i −0.310916 + 0.310916i
122122 0.527727 + 0.218592i 0.0477782 + 0.0197904i
123123 6.78740i 0.611999i
124124 3.30292 7.97396i 0.296611 0.716083i
125125 0.923880 0.382683i 0.0826343 0.0342282i
126126 −1.73175 4.18082i −0.154277 0.372457i
127127 4.18456 + 4.18456i 0.371320 + 0.371320i 0.867958 0.496638i 0.165432π-0.165432\pi
−0.496638 + 0.867958i 0.665432π0.665432\pi
128128 −14.4017 14.4017i −1.27294 1.27294i
129129 −4.53258 10.9426i −0.399072 0.963444i
130130 2.73670 1.13358i 0.240024 0.0994213i
131131 6.16914 14.8936i 0.539000 1.30126i −0.386421 0.922322i 0.626289π-0.626289\pi
0.925422 0.378939i 0.123711π-0.123711\pi
132132 13.7587i 1.19754i
133133 −12.0276 4.98198i −1.04292 0.431993i
134134 12.0284 12.0284i 1.03910 1.03910i
135135 −5.55101 −0.477755
136136 13.5826 + 6.00455i 1.16470 + 0.514886i
137137 −17.1320 −1.46369 −0.731843 0.681473i 0.761339π-0.761339\pi
−0.731843 + 0.681473i 0.761339π0.761339\pi
138138 23.0531 23.0531i 1.96241 1.96241i
139139 1.97070 + 0.816292i 0.167153 + 0.0692369i 0.464691 0.885473i 0.346165π-0.346165\pi
−0.297538 + 0.954710i 0.596165π0.596165\pi
140140 12.6501i 1.06913i
141141 −6.80570 + 16.4304i −0.573143 + 1.38369i
142142 −3.99327 + 1.65407i −0.335108 + 0.138806i
143143 −1.19657 2.88877i −0.100062 0.241571i
144144 0.534857 + 0.534857i 0.0445715 + 0.0445715i
145145 6.19369 + 6.19369i 0.514358 + 0.514358i
146146 4.92549 + 11.8912i 0.407636 + 0.984121i
147147 8.45519 3.50226i 0.697373 0.288861i
148148 −6.21865 + 15.0131i −0.511170 + 1.23407i
149149 18.5384i 1.51872i 0.650669 + 0.759362i 0.274489π0.274489\pi
−0.650669 + 0.759362i 0.725511π0.725511\pi
150150 3.41000 + 1.41247i 0.278425 + 0.115328i
151151 −6.30217 + 6.30217i −0.512863 + 0.512863i −0.915403 0.402539i 0.868128π-0.868128\pi
0.402539 + 0.915403i 0.368128π0.368128\pi
152152 13.0901 1.06175
153153 2.02558 + 0.895462i 0.163758 + 0.0723938i
154154 20.9154 1.68541
155155 −1.72819 + 1.72819i −0.138812 + 0.138812i
156156 6.44881 + 2.67118i 0.516318 + 0.213866i
157157 18.2426i 1.45592i −0.685620 0.727960i 0.740469π-0.740469\pi
0.685620 0.727960i 0.259531π-0.259531\pi
158158 −8.13243 + 19.6334i −0.646982 + 1.56195i
159159 −8.25189 + 3.41805i −0.654418 + 0.271069i
160160 1.48927 + 3.59541i 0.117737 + 0.284242i
161161 −22.3733 22.3733i −1.76326 1.76326i
162162 −11.8077 11.8077i −0.927703 0.927703i
163163 −3.58387 8.65222i −0.280710 0.677694i 0.719142 0.694863i 0.244535π-0.244535\pi
−0.999853 + 0.0171684i 0.994535π0.994535\pi
164164 −14.1108 + 5.84488i −1.10187 + 0.456408i
165165 1.49096 3.59949i 0.116071 0.280220i
166166 17.2059i 1.33544i
167167 −8.57484 3.55181i −0.663541 0.274848i 0.0253869 0.999678i 0.491918π-0.491918\pi
−0.688928 + 0.724830i 0.741918π0.741918\pi
168168 −14.3175 + 14.3175i −1.10462 + 1.10462i
169169 11.4137 0.877977
170170 −6.69357 7.01646i −0.513373 0.538138i
171171 1.95213 0.149283
172172 18.8462 18.8462i 1.43701 1.43701i
173173 −3.97248 1.64545i −0.302022 0.125102i 0.226526 0.974005i 0.427263π-0.427263\pi
−0.528548 + 0.848904i 0.677263π0.677263\pi
174174 32.3298i 2.45092i
175175 1.37082 3.30945i 0.103624 0.250171i
176176 −3.22989 + 1.33786i −0.243462 + 0.100845i
177177 −2.68453 6.48102i −0.201781 0.487143i
178178 3.64789 + 3.64789i 0.273421 + 0.273421i
179179 −0.0832109 0.0832109i −0.00621948 0.00621948i 0.703990 0.710210i 0.251400π-0.251400\pi
−0.710210 + 0.703990i 0.751400π0.751400\pi
180180 −0.725903 1.75249i −0.0541056 0.130623i
181181 −2.14676 + 0.889218i −0.159568 + 0.0660951i −0.461038 0.887381i 0.652523π-0.652523\pi
0.301470 + 0.953476i 0.402523π0.402523\pi
182182 4.06061 9.80318i 0.300993 0.726660i
183183 0.381149i 0.0281754i
184184 29.3927 + 12.1749i 2.16686 + 0.897544i
185185 3.25379 3.25379i 0.239223 0.239223i
186186 −9.02082 −0.661438
187187 −7.40635 + 7.06552i −0.541606 + 0.516682i
188188 −40.0189 −2.91868
189189 −14.0604 + 14.0604i −1.02274 + 1.02274i
190190 −7.89690 3.27100i −0.572902 0.237304i
191191 14.6622i 1.06092i 0.847710 + 0.530461i 0.177981π0.177981\pi
−0.847710 + 0.530461i 0.822019π0.822019\pi
192192 −7.18827 + 17.3540i −0.518768 + 1.25242i
193193 7.75695 3.21303i 0.558357 0.231279i −0.0856146 0.996328i 0.527285π-0.527285\pi
0.643972 + 0.765049i 0.277285π0.277285\pi
194194 8.83869 + 21.3385i 0.634581 + 1.53201i
195195 −1.39765 1.39765i −0.100087 0.100087i
196196 14.5622 + 14.5622i 1.04015 + 1.04015i
197197 −2.55690 6.17290i −0.182171 0.439801i 0.806242 0.591586i 0.201498π-0.201498\pi
−0.988414 + 0.151785i 0.951498π0.951498\pi
198198 −2.89752 + 1.20019i −0.205918 + 0.0852941i
199199 7.22192 17.4353i 0.511949 1.23595i −0.430800 0.902448i 0.641768π-0.641768\pi
0.942748 0.333506i 0.108232π-0.108232\pi
200200 3.60181i 0.254686i
201201 −10.4867 4.34375i −0.739678 0.306384i
202202 9.08714 9.08714i 0.639369 0.639369i
203203 31.3765 2.20220
204204 0.538009 22.8442i 0.0376681 1.59942i
205205 4.32497 0.302069
206206 11.9086 11.9086i 0.829714 0.829714i
207207 4.38336 + 1.81565i 0.304664 + 0.126196i
208208 1.77361i 0.122978i
209209 −3.45277 + 8.33572i −0.238833 + 0.576594i
210210 12.2150 5.05964i 0.842918 0.349148i
211211 2.53326 + 6.11583i 0.174397 + 0.421031i 0.986774 0.162101i 0.0518270π-0.0518270\pi
−0.812377 + 0.583132i 0.801827π0.801827\pi
212212 −14.2120 14.2120i −0.976085 0.976085i
213213 2.03939 + 2.03939i 0.139736 + 0.139736i
214214 0.560861 + 1.35404i 0.0383397 + 0.0925602i
215215 −6.97271 + 2.88819i −0.475535 + 0.196973i
216216 7.65124 18.4717i 0.520601 1.25684i
217217 8.75482i 0.594316i
218218 13.4490 + 5.57077i 0.910884 + 0.377300i
219219 6.07289 6.07289i 0.410368 0.410368i
220220 8.76714 0.591081
221221 1.87376 + 4.84315i 0.126042 + 0.325785i
222222 16.9841 1.13990
223223 2.08077 2.08077i 0.139339 0.139339i −0.633997 0.773336i 0.718587π-0.718587\pi
0.773336 + 0.633997i 0.218587π0.218587\pi
224224 12.8792 + 5.33474i 0.860529 + 0.356443i
225225 0.537139i 0.0358093i
226226 14.4542 34.8955i 0.961478 2.32121i
227227 −19.8871 + 8.23750i −1.31995 + 0.546742i −0.927772 0.373147i 0.878279π-0.878279\pi
−0.392180 + 0.919889i 0.628279π0.628279\pi
228228 −7.70786 18.6084i −0.510466 1.23237i
229229 8.44347 + 8.44347i 0.557960 + 0.557960i 0.928726 0.370766i 0.120905π-0.120905\pi
−0.370766 + 0.928726i 0.620905π0.620905\pi
230230 −14.6896 14.6896i −0.968601 0.968601i
231231 −5.34080 12.8938i −0.351399 0.848351i
232232 −29.1474 + 12.0732i −1.91362 + 0.792647i
233233 −3.85313 + 9.30228i −0.252427 + 0.609412i −0.998399 0.0565648i 0.981985π-0.981985\pi
0.745972 + 0.665977i 0.231985π0.231985\pi
234234 1.59110i 0.104014i
235235 10.4696 + 4.33664i 0.682959 + 0.282891i
236236 11.1621 11.1621i 0.726590 0.726590i
237237 14.1802 0.921101
238238 −34.7267 0.817856i −2.25100 0.0530137i
239239 −16.6253 −1.07540 −0.537701 0.843135i 0.680707π-0.680707\pi
−0.537701 + 0.843135i 0.680707π0.680707\pi
240240 −1.56268 + 1.56268i −0.100871 + 0.100871i
241241 5.47122 + 2.26625i 0.352432 + 0.145982i 0.551874 0.833928i 0.313913π-0.313913\pi
−0.199442 + 0.979910i 0.563913π0.563913\pi
242242 11.3755i 0.731245i
243243 2.10879 5.09108i 0.135279 0.326593i
244244 0.792397 0.328221i 0.0507280 0.0210122i
245245 −2.23166 5.38770i −0.142575 0.344208i
246246 11.2878 + 11.2878i 0.719681 + 0.719681i
247247 3.23668 + 3.23668i 0.205945 + 0.205945i
248248 −3.36873 8.13284i −0.213915 0.516436i
249249 10.6070 4.39358i 0.672194 0.278432i
250250 0.900034 2.17287i 0.0569231 0.137425i
251251 7.77270i 0.490608i 0.969446 + 0.245304i 0.0788878π0.0788878\pi
−0.969446 + 0.245304i 0.921112π0.921112\pi
252252 −6.27762 2.60027i −0.395453 0.163802i
253253 −15.5058 + 15.5058i −0.974844 + 0.974844i
254254 13.9182 0.873307
255255 −2.61626 + 5.91809i −0.163836 + 0.370605i
256256 −23.9630 −1.49768
257257 −5.70344 + 5.70344i −0.355771 + 0.355771i −0.862251 0.506481i 0.830946π-0.830946\pi
0.506481 + 0.862251i 0.330946π0.330946\pi
258258 −25.7360 10.6602i −1.60225 0.663674i
259259 16.4833i 1.02422i
260260 1.70210 4.10922i 0.105559 0.254843i
261261 −4.34677 + 1.80049i −0.269058 + 0.111448i
262262 −14.5092 35.0283i −0.896382 2.16406i
263263 15.0792 + 15.0792i 0.929822 + 0.929822i 0.997694 0.0678724i 0.0216211π-0.0216211\pi
−0.0678724 + 0.997694i 0.521621π0.521621\pi
264264 9.92273 + 9.92273i 0.610702 + 0.610702i
265265 2.17800 + 5.25816i 0.133794 + 0.323006i
266266 −28.2877 + 11.7171i −1.73443 + 0.718424i
267267 1.31734 3.18033i 0.0806197 0.194633i
268268 25.5422i 1.56024i
269269 3.88200 + 1.60798i 0.236690 + 0.0980401i 0.497876 0.867248i 0.334114π-0.334114\pi
−0.261186 + 0.965289i 0.584114π0.584114\pi
270270 −9.23159 + 9.23159i −0.561816 + 0.561816i
271271 −24.7136 −1.50124 −0.750621 0.660733i 0.770245π-0.770245\pi
−0.750621 + 0.660733i 0.770245π0.770245\pi
272272 5.41504 2.09502i 0.328335 0.127029i
273273 −7.08031 −0.428520
274274 −28.4913 + 28.4913i −1.72122 + 1.72122i
275275 −2.29362 0.950048i −0.138310 0.0572900i
276276 48.9527i 2.94661i
277277 7.67765 18.5355i 0.461305 1.11369i −0.506556 0.862207i 0.669082π-0.669082\pi
0.967862 0.251483i 0.0809182π-0.0809182\pi
278278 4.63490 1.91984i 0.277983 0.115144i
279279 −0.502381 1.21285i −0.0300768 0.0726117i
280280 9.12317 + 9.12317i 0.545214 + 0.545214i
281281 17.8053 + 17.8053i 1.06218 + 1.06218i 0.997934 + 0.0642430i 0.0204633π0.0204633\pi
0.0642430 + 0.997934i 0.479537π0.479537\pi
282282 16.0063 + 38.6427i 0.953164 + 2.30114i
283283 7.84059 3.24768i 0.466075 0.193054i −0.137272 0.990533i 0.543833π-0.543833\pi
0.603347 + 0.797479i 0.293833π0.293833\pi
284284 −2.48363 + 5.99601i −0.147376 + 0.355798i
285285 5.70351i 0.337847i
286286 −6.79411 2.81421i −0.401744 0.166408i
287287 10.9549 10.9549i 0.646648 0.646648i
288288 −2.09036 −0.123175
289289 12.5734 11.4416i 0.739611 0.673035i
290290 20.6008 1.20972
291291 10.8977 10.8977i 0.638833 0.638833i
292292 17.8549 + 7.39575i 1.04488 + 0.432804i
293293 25.9873i 1.51820i −0.650977 0.759098i 0.725640π-0.725640\pi
0.650977 0.759098i 0.274360π-0.274360\pi
294294 8.23696 19.8858i 0.480389 1.15976i
295295 −4.12975 + 1.71060i −0.240443 + 0.0995948i
296296 6.34255 + 15.3123i 0.368653 + 0.890008i
297297 9.74457 + 9.74457i 0.565438 + 0.565438i
298298 30.8302 + 30.8302i 1.78594 + 1.78594i
299299 4.25732 + 10.2781i 0.246207 + 0.594397i
300300 5.12021 2.12086i 0.295615 0.122448i
301301 −10.3458 + 24.9771i −0.596325 + 1.43966i
302302 20.9616i 1.20620i
303303 −7.92243 3.28158i −0.455132 0.188522i
304304 3.61887 3.61887i 0.207557 0.207557i
305305 −0.242871 −0.0139067
306306 4.85782 1.87943i 0.277703 0.107440i
307307 16.9475 0.967245 0.483622 0.875277i 0.339321π-0.339321\pi
0.483622 + 0.875277i 0.339321π0.339321\pi
308308 22.2067 22.2067i 1.26534 1.26534i
309309 −10.3823 4.30048i −0.590628 0.244646i
310310 5.74812i 0.326471i
311311 −6.57851 + 15.8819i −0.373033 + 0.900581i 0.620200 + 0.784444i 0.287051π0.287051\pi
−0.993233 + 0.116138i 0.962949π0.962949\pi
312312 6.57730 2.72441i 0.372366 0.154239i
313313 −2.26352 5.46463i −0.127942 0.308879i 0.846909 0.531738i 0.178461π-0.178461\pi
−0.974851 + 0.222859i 0.928461π0.928461\pi
314314 −30.3383 30.3383i −1.71209 1.71209i
315315 1.36054 + 1.36054i 0.0766579 + 0.0766579i
316316 12.2111 + 29.4801i 0.686926 + 1.65839i
317317 −0.591813 + 0.245137i −0.0332395 + 0.0137683i −0.399241 0.916846i 0.630726π-0.630726\pi
0.366002 + 0.930614i 0.380726π0.380726\pi
318318 −8.03891 + 19.4076i −0.450800 + 1.08833i
319319 21.7455i 1.21752i
320320 11.0581 + 4.58041i 0.618166 + 0.256053i
321321 0.691515 0.691515i 0.0385966 0.0385966i
322322 −74.4157 −4.14702
323323 6.05874 13.7052i 0.337117 0.762576i
324324 −25.0735 −1.39297
325325 −0.890588 + 0.890588i −0.0494010 + 0.0494010i
326326 −20.3492 8.42891i −1.12704 0.466834i
327327 9.71352i 0.537159i
328328 −5.96133 + 14.3919i −0.329160 + 0.794661i
329329 37.5033 15.5344i 2.06762 0.856437i
330330 −3.50659 8.46565i −0.193031 0.466019i
331331 −8.24547 8.24547i −0.453212 0.453212i 0.443207 0.896419i 0.353841π-0.353841\pi
−0.896419 + 0.443207i 0.853841π0.853841\pi
332332 18.2682 + 18.2682i 1.00260 + 1.00260i
333333 0.945868 + 2.28353i 0.0518333 + 0.125137i
334334 −20.1672 + 8.35352i −1.10350 + 0.457084i
335335 −2.76786 + 6.68222i −0.151225 + 0.365088i
336336 7.91638i 0.431874i
337337 28.5300 + 11.8175i 1.55413 + 0.643740i 0.984056 0.177856i 0.0569162π-0.0569162\pi
0.570070 + 0.821596i 0.306916π0.306916\pi
338338 18.9815 18.9815i 1.03246 1.03246i
339339 −25.2031 −1.36885
340340 −14.5565 0.342822i −0.789436 0.0185922i
341341 6.06754 0.328576
342342 3.24648 3.24648i 0.175550 0.175550i
343343 3.86674 + 1.60166i 0.208784 + 0.0864813i
344344 27.1836i 1.46564i
345345 −5.30474 + 12.8068i −0.285598 + 0.689494i
346346 −9.34288 + 3.86995i −0.502276 + 0.208050i
347347 −0.00573993 0.0138574i −0.000308135 0.000743905i 0.923725 0.383055i 0.125128π-0.125128\pi
−0.924034 + 0.382311i 0.875128π0.875128\pi
348348 34.3259 + 34.3259i 1.84006 + 1.84006i
349349 −2.58441 2.58441i −0.138340 0.138340i 0.634545 0.772886i 0.281187π-0.281187\pi
−0.772886 + 0.634545i 0.781187π0.781187\pi
350350 −3.22403 7.78350i −0.172332 0.416046i
351351 6.45921 2.67549i 0.344767 0.142807i
352352 3.69725 8.92595i 0.197064 0.475755i
353353 3.82333i 0.203495i 0.994810 + 0.101748i 0.0324434π0.0324434\pi
−0.994810 + 0.101748i 0.967557π0.967557\pi
354354 −15.2427 6.31374i −0.810141 0.335572i
355355 1.29951 1.29951i 0.0689708 0.0689708i
356356 7.74622 0.410549
357357 8.36337 + 21.6170i 0.442637 + 1.14409i
358358 −0.276767 −0.0146276
359359 −4.73532 + 4.73532i −0.249921 + 0.249921i −0.820938 0.571017i 0.806549π-0.806549\pi
0.571017 + 0.820938i 0.306549π0.306549\pi
360360 −1.78740 0.740366i −0.0942044 0.0390207i
361361 5.79178i 0.304830i
362362 −2.09135 + 5.04897i −0.109919 + 0.265368i
363363 7.01272 2.90476i 0.368072 0.152461i
364364 −6.09712 14.7197i −0.319576 0.771524i
365365 −3.86968 3.86968i −0.202549 0.202549i
366366 −0.633869 0.633869i −0.0331328 0.0331328i
367367 −8.81227 21.2747i −0.459997 1.11053i −0.968398 0.249410i 0.919763π-0.919763\pi
0.508401 0.861120i 0.330237π-0.330237\pi
368368 11.4917 4.76004i 0.599049 0.248134i
369369 −0.889017 + 2.14628i −0.0462804 + 0.111731i
370370 10.8224i 0.562630i
371371 18.8354 + 7.80187i 0.977884 + 0.405053i
372372 −9.57776 + 9.57776i −0.496584 + 0.496584i
373373 −23.7303 −1.22871 −0.614355 0.789030i 0.710584π-0.710584\pi
−0.614355 + 0.789030i 0.710584π0.710584\pi
374374 −0.566816 + 24.0674i −0.0293094 + 1.24450i
375375 −1.56935 −0.0810409
376376 −28.8615 + 28.8615i −1.48842 + 1.48842i
377377 −10.1923 4.22178i −0.524929 0.217433i
378378 46.7662i 2.40539i
379379 1.13970 2.75149i 0.0585427 0.141335i −0.891902 0.452230i 0.850629π-0.850629\pi
0.950444 + 0.310895i 0.100629π0.100629\pi
380380 −11.8574 + 4.91150i −0.608272 + 0.251955i
381381 −3.55406 8.58025i −0.182080 0.439580i
382382 24.3839 + 24.3839i 1.24759 + 1.24759i
383383 −17.2691 17.2691i −0.882408 0.882408i 0.111371 0.993779i 0.464476π-0.464476\pi
−0.993779 + 0.111371i 0.964476π0.964476\pi
384384 12.2317 + 29.5300i 0.624198 + 1.50695i
385385 −8.21602 + 3.40319i −0.418727 + 0.173443i
386386 7.55674 18.2436i 0.384628 0.928574i
387387 4.05390i 0.206071i
388388 32.0403 + 13.2715i 1.62660 + 0.673759i
389389 −1.19407 + 1.19407i −0.0605418 + 0.0605418i −0.736729 0.676188i 0.763631π-0.763631\pi
0.676188 + 0.736729i 0.263631π0.263631\pi
390390 −4.64870 −0.235396
391391 26.3514 25.1387i 1.33265 1.27132i
392392 21.0043 1.06088
393393 −17.8892 + 17.8892i −0.902389 + 0.902389i
394394 −14.5181 6.01357i −0.731409 0.302960i
395395 9.03570i 0.454635i
396396 −1.80212 + 4.35071i −0.0905601 + 0.218631i
397397 −29.1259 + 12.0643i −1.46178 + 0.605491i −0.964969 0.262365i 0.915498π-0.915498\pi
−0.496816 + 0.867856i 0.665498π0.665498\pi
398398 −16.9853 41.0060i −0.851394 2.05545i
399399 14.4467 + 14.4467i 0.723238 + 0.723238i
400400 0.995752 + 0.995752i 0.0497876 + 0.0497876i
401401 1.93870 + 4.68044i 0.0968141 + 0.233730i 0.964865 0.262745i 0.0846276π-0.0846276\pi
−0.868051 + 0.496474i 0.834628π0.834628\pi
402402 −24.6638 + 10.2161i −1.23012 + 0.509531i
403403 1.17798 2.84390i 0.0586794 0.141665i
404404 19.2964i 0.960029i
405405 6.55960 + 2.71708i 0.325949 + 0.135013i
406406 52.1806 52.1806i 2.58968 2.58968i
407407 −11.4238 −0.566256
408408 −16.0871 16.8632i −0.796432 0.834850i
409409 −26.1178 −1.29144 −0.645722 0.763573i 0.723443π-0.723443\pi
−0.645722 + 0.763573i 0.723443π0.723443\pi
410410 7.19263 7.19263i 0.355219 0.355219i
411411 24.8395 + 10.2889i 1.22524 + 0.507513i
412412 25.2877i 1.24584i
413413 −6.12757 + 14.7933i −0.301518 + 0.727929i
414414 10.3092 4.27022i 0.506671 0.209870i
415415 −2.79962 6.75887i −0.137428 0.331780i
416416 −3.46586 3.46586i −0.169928 0.169928i
417417 −2.36707 2.36707i −0.115916 0.115916i
418418 8.12058 + 19.6048i 0.397190 + 0.958903i
419419 6.74298 2.79303i 0.329416 0.136449i −0.211845 0.977303i 0.567947π-0.567947\pi
0.541261 + 0.840855i 0.317947π0.317947\pi
420420 7.59718 18.3412i 0.370704 0.894960i
421421 21.0644i 1.02662i −0.858204 0.513309i 0.828420π-0.828420\pi
0.858204 0.513309i 0.171580π-0.171580\pi
422422 14.3838 + 5.95798i 0.700194 + 0.290030i
423423 −4.30413 + 4.30413i −0.209274 + 0.209274i
424424 −20.4993 −0.995533
425425 3.77105 + 1.66709i 0.182923 + 0.0808660i
426426 6.78319 0.328646
427427 −0.615178 + 0.615178i −0.0297705 + 0.0297705i
428428 2.03313 + 0.842148i 0.0982749 + 0.0407068i
429429 4.90702i 0.236913i
430430 −6.79274 + 16.3991i −0.327575 + 0.790836i
431431 −19.4414 + 8.05290i −0.936460 + 0.387894i −0.798126 0.602491i 0.794175π-0.794175\pi
−0.138334 + 0.990386i 0.544175π0.544175\pi
432432 −2.99142 7.22194i −0.143925 0.347466i
433433 −26.2522 26.2522i −1.26160 1.26160i −0.950318 0.311280i 0.899242π-0.899242\pi
−0.311280 0.950318i 0.600758π-0.600758\pi
434434 14.5597 + 14.5597i 0.698886 + 0.698886i
435435 −5.26046 12.6999i −0.252220 0.608912i
436436 20.1941 8.36467i 0.967121 0.400595i
437437 12.2848 29.6580i 0.587659 1.41874i
438438 20.1990i 0.965145i
439439 0.435448 + 0.180369i 0.0207828 + 0.00860852i 0.393051 0.919517i 0.371420π-0.371420\pi
−0.372268 + 0.928125i 0.621420π0.621420\pi
440440 6.32282 6.32282i 0.301429 0.301429i
441441 3.13238 0.149161
442442 11.1705 + 4.93823i 0.531327 + 0.234888i
443443 −11.0249 −0.523808 −0.261904 0.965094i 0.584350π-0.584350\pi
−0.261904 + 0.965094i 0.584350π0.584350\pi
444444 18.0327 18.0327i 0.855795 0.855795i
445445 −2.02653 0.839416i −0.0960667 0.0397921i
446446 6.92084i 0.327711i
447447 11.1335 26.8786i 0.526596 1.27132i
448448 39.6114 16.4076i 1.87146 0.775186i
449449 6.60636 + 15.9492i 0.311773 + 0.752688i 0.999639 + 0.0268500i 0.00854766π0.00854766\pi
−0.687866 + 0.725838i 0.741452π0.741452\pi
450450 0.893287 + 0.893287i 0.0421100 + 0.0421100i
451451 −7.59232 7.59232i −0.357508 0.357508i
452452 −21.7033 52.3965i −1.02084 2.46452i
453453 12.9223 5.35260i 0.607143 0.251487i
454454 −19.3738 + 46.7725i −0.909257 + 2.19514i
455455 4.51162i 0.211508i
456456 −18.9792 7.86144i −0.888782 0.368146i
457457 −7.96742 + 7.96742i −0.372700 + 0.372700i −0.868460 0.495760i 0.834890π-0.834890\pi
0.495760 + 0.868460i 0.334890π0.334890\pi
458458 28.0837 1.31227
459459 −15.7983 16.5604i −0.737402 0.772973i
460460 −31.1930 −1.45438
461461 21.2185 21.2185i 0.988244 0.988244i −0.0116873 0.999932i 0.503720π-0.503720\pi
0.999932 + 0.0116873i 0.00372025π0.00372025\pi
462462 −30.3250 12.5610i −1.41085 0.584392i
463463 17.1592i 0.797457i 0.917069 + 0.398728i 0.130548π0.130548\pi
−0.917069 + 0.398728i 0.869452π0.869452\pi
464464 −4.72031 + 11.3958i −0.219135 + 0.529038i
465465 3.54358 1.46780i 0.164329 0.0680675i
466466 9.06218 + 21.8780i 0.419798 + 1.01348i
467467 18.8030 + 18.8030i 0.870099 + 0.870099i 0.992483 0.122384i 0.0390540π-0.0390540\pi
−0.122384 + 0.992483i 0.539054π0.539054\pi
468468 1.68934 + 1.68934i 0.0780896 + 0.0780896i
469469 9.91483 + 23.9365i 0.457824 + 1.10529i
470470 24.6234 10.1993i 1.13579 0.470461i
471471 −10.9559 + 26.4498i −0.504820 + 1.21874i
472472 16.1001i 0.741066i
473473 17.3104 + 7.17020i 0.795933 + 0.329686i
474474 23.5823 23.5823i 1.08317 1.08317i
475475 3.63431 0.166754
476476 −37.7391 + 36.0024i −1.72977 + 1.65017i
477477 −3.05707 −0.139974
478478 −27.6487 + 27.6487i −1.26462 + 1.26462i
479479 −21.1662 8.76732i −0.967107 0.400589i −0.157473 0.987523i 0.550335π-0.550335\pi
−0.809635 + 0.586934i 0.800335π0.800335\pi
480480 6.10736i 0.278761i
481481 −2.21787 + 5.35441i −0.101126 + 0.244140i
482482 12.8678 5.33000i 0.586111 0.242775i
483483 19.0022 + 45.8755i 0.864632 + 2.08741i
484484 12.0778 + 12.0778i 0.548992 + 0.548992i
485485 −6.94407 6.94407i −0.315314 0.315314i
486486 −4.95968 11.9737i −0.224975 0.543139i
487487 14.5174 6.01330i 0.657846 0.272489i −0.0286857 0.999588i 0.509132π-0.509132\pi
0.686532 + 0.727100i 0.259132π0.259132\pi
488488 0.334761 0.808185i 0.0151539 0.0365848i
489489 14.6971i 0.664627i
490490 −12.6713 5.24864i −0.572433 0.237110i
491491 0.607534 0.607534i 0.0274176 0.0274176i −0.693265 0.720683i 0.743828π-0.743828\pi
0.720683 + 0.693265i 0.243828π0.243828\pi
492492 23.9693 1.08062
493493 −0.850318 + 36.1051i −0.0382964 + 1.62609i
494494 10.7655 0.484362
495495 0.942926 0.942926i 0.0423814 0.0423814i
496496 −3.17972 1.31708i −0.142773 0.0591387i
497497 6.58317i 0.295296i
498498 10.3333 24.9467i 0.463045 1.11789i
499499 −20.9163 + 8.66380i −0.936340 + 0.387845i −0.798080 0.602551i 0.794151π-0.794151\pi
−0.138260 + 0.990396i 0.544151π0.544151\pi
500500 −1.35142 3.26263i −0.0604376 0.145909i
501501 10.2995 + 10.2995i 0.460147 + 0.460147i
502502 12.9264 + 12.9264i 0.576931 + 0.576931i
503503 6.54963 + 15.8122i 0.292034 + 0.705032i 0.999999 0.00121517i 0.000386801π-0.000386801\pi
−0.707966 + 0.706247i 0.750387π0.750387\pi
504504 −6.40270 + 2.65208i −0.285199 + 0.118133i
505505 −2.09104 + 5.04822i −0.0930501 + 0.224643i
506506 51.5739i 2.29274i
507507 −16.5486 6.85467i −0.734950 0.304426i
508508 14.7775 14.7775i 0.655647 0.655647i
509509 29.7081 1.31679 0.658393 0.752674i 0.271236π-0.271236\pi
0.658393 + 0.752674i 0.271236π0.271236\pi
510510 5.49111 + 14.1930i 0.243150 + 0.628477i
511511 −19.6034 −0.867203
512512 −11.0481 + 11.0481i −0.488263 + 0.488263i
513513 −18.6384 7.72030i −0.822907 0.340859i
514514 18.9701i 0.836737i
515515 −2.74030 + 6.61566i −0.120752 + 0.291521i
516516 −38.6432 + 16.0066i −1.70117 + 0.704649i
517517 −10.7661 25.9917i −0.473493 1.14311i
518518 −27.4125 27.4125i −1.20444 1.20444i
519519 4.77146 + 4.77146i 0.209444 + 0.209444i
520520 −1.73601 4.19110i −0.0761290 0.183792i
521521 −35.7139 + 14.7932i −1.56465 + 0.648101i −0.985890 0.167395i 0.946465π-0.946465\pi
−0.578764 + 0.815495i 0.696465π0.696465\pi
522522 −4.23458 + 10.2232i −0.185342 + 0.447456i
523523 0.599508i 0.0262147i 0.999914 + 0.0131073i 0.00417231π0.00417231\pi
−0.999914 + 0.0131073i 0.995828π0.995828\pi
524524 −52.5960 21.7860i −2.29767 0.951724i
525525 −3.97508 + 3.97508i −0.173487 + 0.173487i
526526 50.1547 2.18685
527527 −10.0742 0.237259i −0.438839 0.0103352i
528528 5.48646 0.238767
529529 38.9054 38.9054i 1.69154 1.69154i
530530 12.3667 + 5.12244i 0.537174 + 0.222505i
531531 2.40101i 0.104195i
532532 −17.5936 + 42.4747i −0.762779 + 1.84151i
533533 −5.03258 + 2.08456i −0.217985 + 0.0902925i
534534 −3.09825 7.47983i −0.134074 0.323684i
535535 −0.440638 0.440638i −0.0190504 0.0190504i
536536 −18.4209 18.4209i −0.795661 0.795661i
537537 0.0706732 + 0.170620i 0.00304977 + 0.00736281i
538538 9.13009 3.78181i 0.393626 0.163045i
539539 −5.54031 + 13.3755i −0.238638 + 0.576123i
540540 19.6031i 0.843582i
541541 36.6847 + 15.1953i 1.57720 + 0.653297i 0.987966 0.154668i 0.0494308π-0.0494308\pi
0.589231 + 0.807965i 0.299431π0.299431\pi
542542 −41.0998 + 41.0998i −1.76539 + 1.76539i
543543 3.64660 0.156491
544544 −6.48774 + 14.6756i −0.278160 + 0.629211i
545545 −6.18952 −0.265130
546546 −11.7749 + 11.7749i −0.503919 + 0.503919i
547547 −3.73035 1.54516i −0.159498 0.0660663i 0.301506 0.953464i 0.402511π-0.402511\pi
−0.461004 + 0.887398i 0.652511π0.652511\pi
548548 60.5007i 2.58446i
549549 0.0499231 0.120525i 0.00213067 0.00514388i
550550 −5.39437 + 2.23442i −0.230017 + 0.0952760i
551551 12.1822 + 29.4105i 0.518980 + 1.25293i
552552 −35.3045 35.3045i −1.50266 1.50266i
553553 −22.8869 22.8869i −0.973250 0.973250i
554554 −18.0571 43.5937i −0.767172 1.85212i
555555 −6.67175 + 2.76353i −0.283200 + 0.117305i
556556 2.88269 6.95942i 0.122253 0.295145i
557557 5.42781i 0.229984i 0.993366 + 0.114992i 0.0366842π0.0366842\pi
−0.993366 + 0.114992i 0.963316π0.963316\pi
558558 −2.85252 1.18155i −0.120757 0.0500190i
559559 6.72145 6.72145i 0.284287 0.284287i
560560 5.04437 0.213163
561561 14.9817 5.79624i 0.632528 0.244718i
562562 59.2222 2.49814
563563 −3.66888 + 3.66888i −0.154625 + 0.154625i −0.780180 0.625555i 0.784873π-0.784873\pi
0.625555 + 0.780180i 0.284873π0.284873\pi
564564 58.0231 + 24.0339i 2.44321 + 1.01201i
565565 16.0596i 0.675632i
566566 7.63822 18.4403i 0.321058 0.775104i
567567 23.4973 9.73290i 0.986794 0.408744i
568568 2.53311 + 6.11547i 0.106287 + 0.256600i
569569 8.48266 + 8.48266i 0.355611 + 0.355611i 0.862192 0.506581i 0.169091π-0.169091\pi
−0.506581 + 0.862192i 0.669091π0.669091\pi
570570 9.48520 + 9.48520i 0.397291 + 0.397291i
571571 −16.6512 40.1996i −0.696833 1.68230i −0.730539 0.682871i 0.760731π-0.760731\pi
0.0337061 0.999432i 0.489269π-0.489269\pi
572572 −10.2015 + 4.22561i −0.426548 + 0.176682i
573573 8.80561 21.2586i 0.367860 0.888092i
574574 36.4371i 1.52085i
575575 8.16056 + 3.38021i 0.340319 + 0.140965i
576576 −4.54607 + 4.54607i −0.189420 + 0.189420i
577577 27.7097 1.15357 0.576784 0.816897i 0.304307π-0.304307\pi
0.576784 + 0.816897i 0.304307π0.304307\pi
578578 1.88222 39.9380i 0.0782900 1.66120i
579579 −13.1764 −0.547591
580580 21.8727 21.8727i 0.908212 0.908212i
581581 −24.2111 10.0286i −1.00445 0.416055i
582582 36.2467i 1.50247i
583583 5.40709 13.0539i 0.223939 0.540636i
584584 18.2107 7.54311i 0.753563 0.312136i
585585 −0.258892 0.625020i −0.0107039 0.0258414i
586586 −43.2181 43.2181i −1.78532 1.78532i
587587 3.09653 + 3.09653i 0.127808 + 0.127808i 0.768117 0.640309i 0.221194π-0.221194\pi
−0.640309 + 0.768117i 0.721194π0.721194\pi
588588 −12.3680 29.8590i −0.510048 1.23137i
589589 −8.20624 + 3.39914i −0.338132 + 0.140059i
590590 −4.02316 + 9.71276i −0.165631 + 0.399868i
591591 10.4856i 0.431320i
592592 5.98668 + 2.47976i 0.246051 + 0.101918i
593593 25.3698 25.3698i 1.04181 1.04181i 0.0427255 0.999087i 0.486396π-0.486396\pi
0.999087 0.0427255i 0.0136041π-0.0136041\pi
594594 32.4114 1.32985
595595 13.7745 5.32919i 0.564700 0.218476i
596596 65.4673 2.68164
597597 −20.9420 + 20.9420i −0.857099 + 0.857099i
598598 24.1730 + 10.0128i 0.988509 + 0.409454i
599599 11.1415i 0.455230i −0.973751 0.227615i 0.926907π-0.926907\pi
0.973751 0.227615i 0.0730928π-0.0730928\pi
600600 2.16312 5.22222i 0.0883088 0.213196i
601601 18.8938 7.82606i 0.770693 0.319232i 0.0375402 0.999295i 0.488048π-0.488048\pi
0.733153 + 0.680063i 0.238048π0.238048\pi
602602 24.3324 + 58.7437i 0.991716 + 2.39421i
603603 −2.74712 2.74712i −0.111871 0.111871i
604604 22.2558 + 22.2558i 0.905574 + 0.905574i
605605 −1.85093 4.46855i −0.0752512 0.181672i
606606 −18.6328 + 7.71795i −0.756905 + 0.313520i
607607 0.602934 1.45561i 0.0244723 0.0590814i −0.911171 0.412028i 0.864820π-0.864820\pi
0.935643 + 0.352947i 0.114820π0.114820\pi
608608 14.1435i 0.573593i
609609 −45.4925 18.8436i −1.84345 0.763582i
610610 −0.403905 + 0.403905i −0.0163536 + 0.0163536i
611611 −14.2727 −0.577410
612612 3.16227 7.15321i 0.127827 0.289151i
613613 −22.4800 −0.907959 −0.453980 0.891012i 0.649996π-0.649996\pi
−0.453980 + 0.891012i 0.649996π0.649996\pi
614614 28.1845 28.1845i 1.13743 1.13743i
615615 −6.27074 2.59743i −0.252861 0.104738i
616616 32.0307i 1.29055i
617617 10.4081 25.1273i 0.419013 1.01159i −0.563621 0.826034i 0.690592π-0.690592\pi
0.982634 0.185554i 0.0594079π-0.0594079\pi
618618 −24.4181 + 10.1143i −0.982241 + 0.406858i
619619 5.49924 + 13.2763i 0.221033 + 0.533621i 0.995031 0.0995671i 0.0317458π-0.0317458\pi
−0.773998 + 0.633188i 0.781746π0.781746\pi
620620 6.10301 + 6.10301i 0.245103 + 0.245103i
621621 −34.6706 34.6706i −1.39128 1.39128i
622622 15.4720 + 37.3527i 0.620371 + 1.49771i
623623 −7.25927 + 3.00689i −0.290837 + 0.120469i
624624 1.06517 2.57154i 0.0426408 0.102944i
625625 1.00000i 0.0400000i
626626 −12.8523 5.32358i −0.513680 0.212773i
627627 10.0123 10.0123i 0.399852 0.399852i
628628 −64.4228 −2.57075
629629 18.9674 + 0.446705i 0.756280 + 0.0178113i
630630 4.52529 0.180292
631631 −16.4538 + 16.4538i −0.655014 + 0.655014i −0.954196 0.299182i 0.903286π-0.903286\pi
0.299182 + 0.954196i 0.403286π0.403286\pi
632632 30.0675 + 12.4544i 1.19602 + 0.495408i
633633 10.3887i 0.412913i
634634 −0.576538 + 1.39189i −0.0228972 + 0.0552788i
635635 −5.46739 + 2.26467i −0.216967 + 0.0898706i
636636 12.0706 + 29.1411i 0.478632 + 1.15552i
637637 5.19356 + 5.19356i 0.205776 + 0.205776i
638638 −36.1638 36.1638i −1.43174 1.43174i
639639 0.377764 + 0.912004i 0.0149441 + 0.0360783i
640640 18.8167 7.79414i 0.743796 0.308090i
641641 −2.06038 + 4.97419i −0.0813800 + 0.196469i −0.959332 0.282280i 0.908909π-0.908909\pi
0.877952 + 0.478748i 0.158909π0.158909\pi
642642 2.30004i 0.0907754i
643643 14.9568 + 6.19532i 0.589839 + 0.244319i 0.657582 0.753383i 0.271580π-0.271580\pi
−0.0677421 + 0.997703i 0.521580π0.521580\pi
644644 −79.0101 + 79.0101i −3.11343 + 3.11343i
645645 11.8442 0.466365
646646 −12.7163 32.8683i −0.500318 1.29319i
647647 −25.8383 −1.01581 −0.507904 0.861413i 0.669580π-0.669580\pi
−0.507904 + 0.861413i 0.669580π0.669580\pi
648648 −18.0829 + 18.0829i −0.710362 + 0.710362i
649649 10.2525 + 4.24672i 0.402445 + 0.166698i
650650 2.96218i 0.116186i
651651 5.25783 12.6935i 0.206071 0.497499i
652652 −30.5548 + 12.6562i −1.19662 + 0.495656i
653653 −4.77529 11.5286i −0.186872 0.451148i 0.802483 0.596675i 0.203512π-0.203512\pi
−0.989354 + 0.145528i 0.953512π0.953512\pi
654654 −16.1540 16.1540i −0.631672 0.631672i
655655 11.3991 + 11.3991i 0.445399 + 0.445399i
656656 2.33072 + 5.62685i 0.0909992 + 0.219691i
657657 2.71577 1.12491i 0.105952 0.0438868i
658658 36.5353 88.2040i 1.42429 3.43855i
659659 41.7109i 1.62483i 0.583082 + 0.812413i 0.301847π0.301847\pi
−0.583082 + 0.812413i 0.698153π0.698153\pi
660660 −12.7114 5.26523i −0.494791 0.204949i
661661 −12.8495 + 12.8495i −0.499789 + 0.499789i −0.911372 0.411583i 0.864976π-0.864976\pi
0.411583 + 0.911372i 0.364976π0.364976\pi
662662 −27.4252 −1.06591
663663 0.191880 8.14734i 0.00745199 0.316417i
664664 26.3499 1.02257
665665 9.20551 9.20551i 0.356974 0.356974i
666666 5.37063 + 2.22459i 0.208108 + 0.0862011i
667667 77.3693i 2.99575i
668668 −12.5430 + 30.2815i −0.485304 + 1.17163i
669669 −4.26653 + 1.76726i −0.164954 + 0.0683260i
670670 6.50975 + 15.7159i 0.251493 + 0.607159i
671671 0.426350 + 0.426350i 0.0164590 + 0.0164590i
672672 −15.4696 15.4696i −0.596753 0.596753i
673673 2.44794 + 5.90984i 0.0943610 + 0.227808i 0.964012 0.265860i 0.0856559π-0.0856559\pi
−0.869651 + 0.493668i 0.835656π0.835656\pi
674674 67.0997 27.7936i 2.58458 1.07057i
675675 2.12428 5.12847i 0.0817636 0.197395i
676676 40.3069i 1.55026i
677677 −38.7001 16.0301i −1.48737 0.616087i −0.516624 0.856212i 0.672811π-0.672811\pi
−0.970742 + 0.240125i 0.922811π0.922811\pi
678678 −41.9140 + 41.9140i −1.60970 + 1.60970i
679679 −35.1779 −1.35000
680680 −10.7453 + 10.2508i −0.412064 + 0.393101i
681681 33.7812 1.29450
682682 10.0906 10.0906i 0.386389 0.386389i
683683 27.9994 + 11.5977i 1.07137 + 0.443775i 0.847473 0.530838i 0.178123π-0.178123\pi
0.223895 + 0.974613i 0.428123π0.428123\pi
684684 6.89384i 0.263593i
685685 6.55613 15.8279i 0.250497 0.604753i
686686 9.09419 3.76694i 0.347218 0.143822i
687687 −7.17126 17.3130i −0.273601 0.660530i
688688 −7.51514 7.51514i −0.286512 0.286512i
689689 −5.06869 5.06869i −0.193102 0.193102i
690690 12.4762 + 30.1203i 0.474962 + 1.14666i
691691 5.35185 2.21681i 0.203594 0.0843314i −0.278556 0.960420i 0.589856π-0.589856\pi
0.482150 + 0.876088i 0.339856π0.339856\pi
692692 −5.81083 + 14.0286i −0.220895 + 0.533287i
693693 4.77676i 0.181454i
694694 −0.0325913 0.0134997i −0.00123715 0.000512443i
695695 −1.50831 + 1.50831i −0.0572135 + 0.0572135i
696696 49.5113 1.87672
697697 12.3090 + 12.9027i 0.466236 + 0.488726i
698698 −8.59600 −0.325363
699699 11.1732 11.1732i 0.422611 0.422611i
700700 −11.6871 4.84097i −0.441732 0.182971i
701701 5.24783i 0.198208i −0.995077 0.0991039i 0.968402π-0.968402\pi
0.995077 0.0991039i 0.0315976π-0.0315976\pi
702702 6.29250 15.1914i 0.237495 0.573364i
703703 15.4505 6.39979i 0.582726 0.241373i
704704 −11.3713 27.4527i −0.428572 1.03466i
705705 −12.5753 12.5753i −0.473613 0.473613i
706706 6.35837 + 6.35837i 0.239300 + 0.239300i
707707 7.49037 + 18.0833i 0.281704 + 0.680094i
708708 −22.8873 + 9.48025i −0.860159 + 0.356290i
709709 15.9798 38.5786i 0.600134 1.44885i −0.273310 0.961926i 0.588118π-0.588118\pi
0.873444 0.486925i 0.161882π-0.161882\pi
710710 4.32229i 0.162213i
711711 4.48398 + 1.85733i 0.168162 + 0.0696551i
712712 5.58654 5.58654i 0.209364 0.209364i
713713 −21.5879 −0.808475
714714 49.8588 + 22.0414i 1.86592 + 0.824880i
715715 3.12678 0.116935
716716 −0.293855 + 0.293855i −0.0109819 + 0.0109819i
717717 24.1049 + 9.98458i 0.900214 + 0.372881i
718718 15.7501i 0.587789i
719719 3.89643 9.40681i 0.145312 0.350815i −0.834419 0.551130i 0.814197π-0.814197\pi
0.979731 + 0.200316i 0.0641967π0.0641967\pi
720720 −0.698825 + 0.289463i −0.0260437 + 0.0107876i
721721 9.81608 + 23.6981i 0.365570 + 0.882564i
722722 9.63199 + 9.63199i 0.358465 + 0.358465i
723723 −6.57164 6.57164i −0.244402 0.244402i
724724 3.14022 + 7.58117i 0.116705 + 0.281752i
725725 −8.09244 + 3.35200i −0.300546 + 0.124490i
726726 6.83172 16.4932i 0.253549 0.612121i
727727 46.0182i 1.70672i 0.521321 + 0.853361i 0.325439π0.325439\pi
−0.521321 + 0.853361i 0.674561π0.674561\pi
728728 −15.0130 6.21860i −0.556420 0.230477i
729729 −21.1766 + 21.1766i −0.784317 + 0.784317i
730730 −12.8709 −0.476374
731731 −28.4609 12.5819i −1.05266 0.465358i
732732 −1.34601 −0.0497498
733733 −1.80962 + 1.80962i −0.0668398 + 0.0668398i −0.739736 0.672897i 0.765050π-0.765050\pi
0.672897 + 0.739736i 0.265050π0.265050\pi
734734 −50.0360 20.7256i −1.84686 0.764996i
735735 9.15184i 0.337571i
736736 −13.1546 + 31.7580i −0.484885 + 1.17062i
737737 16.5892 6.87149i 0.611072 0.253114i
738738 2.09088 + 5.04783i 0.0769664 + 0.185813i
739739 1.75127 + 1.75127i 0.0644215 + 0.0644215i 0.738583 0.674162i 0.235495π-0.235495\pi
−0.674162 + 0.738583i 0.735495π0.735495\pi
740740 −11.4906 11.4906i −0.422402 0.422402i
741741 −2.74899 6.63666i −0.100987 0.243804i
742742 44.2989 18.3492i 1.62627 0.673621i
743743 0.610291 1.47337i 0.0223894 0.0540528i −0.912289 0.409546i 0.865687π-0.865687\pi
0.934679 + 0.355493i 0.115687π0.115687\pi
744744 13.8149i 0.506478i
745745 −17.1272 7.09433i −0.627493 0.259916i
746746 −39.4646 + 39.4646i −1.44490 + 1.44490i
747747 3.92957 0.143776
748748 24.9515 + 26.1551i 0.912317 + 0.956326i
749749 −2.23222 −0.0815636
750750 −2.60990 + 2.60990i −0.0953001 + 0.0953001i
751751 11.7741 + 4.87697i 0.429641 + 0.177963i 0.587015 0.809576i 0.300303π-0.300303\pi
−0.157374 + 0.987539i 0.550303π0.550303\pi
752752 15.9580i 0.581930i
753753 4.66801 11.2696i 0.170112 0.410686i
754754 −23.9713 + 9.92922i −0.872982 + 0.361601i
755755 −3.41071 8.23418i −0.124128 0.299672i
756756 49.6535 + 49.6535i 1.80588 + 1.80588i
757757 −32.5674 32.5674i −1.18368 1.18368i −0.978783 0.204901i 0.934313π-0.934313\pi
−0.204901 0.978783i 0.565687π-0.565687\pi
758758 −2.68047 6.47123i −0.0973592 0.235046i
759759 31.7940 13.1695i 1.15405 0.478023i
760760 −5.00936 + 12.0937i −0.181709 + 0.438683i
761761 29.7003i 1.07664i −0.842742 0.538318i 0.819060π-0.819060\pi
0.842742 0.538318i 0.180940π-0.180940\pi
762762 −20.1799 8.35879i −0.731041 0.302807i
763763 −15.6777 + 15.6777i −0.567571 + 0.567571i
764764 51.7788 1.87329
765765 −1.60245 + 1.52871i −0.0579368 + 0.0552706i
766766 −57.4385 −2.07534
767767 3.98093 3.98093i 0.143743 0.143743i
768768 34.7437 + 14.3913i 1.25370 + 0.519301i
769769 43.8299i 1.58055i −0.612755 0.790273i 0.709939π-0.709939\pi
0.612755 0.790273i 0.290061π-0.290061\pi
770770 −8.00397 + 19.3233i −0.288443 + 0.696363i
771771 11.6946 4.84408i 0.421172 0.174455i
772772 −11.3466 27.3932i −0.408375 0.985904i
773773 19.7369 + 19.7369i 0.709887 + 0.709887i 0.966511 0.256624i 0.0826103π-0.0826103\pi
−0.256624 + 0.966511i 0.582610π0.582610\pi
774774 −6.74182 6.74182i −0.242330 0.242330i
775775 −0.935290 2.25799i −0.0335966 0.0811094i
776776 32.6787 13.5359i 1.17310 0.485912i
777777 −9.89930 + 23.8990i −0.355135 + 0.857372i
778778 3.97159i 0.142388i
779779 14.5218 + 6.01513i 0.520298 + 0.215515i
780780 −4.93571 + 4.93571i −0.176727 + 0.176727i
781781 −4.56247 −0.163258
782782 2.01670 85.6304i 0.0721170 3.06214i
783783 48.6224 1.73762
784784 5.80684 5.80684i 0.207387 0.207387i
785785 16.8540 + 6.98115i 0.601545 + 0.249168i
786786 59.5010i 2.12233i
787787 11.4892 27.7373i 0.409544 0.988728i −0.575713 0.817652i 0.695276π-0.695276\pi
0.985258 0.171076i 0.0547244π-0.0547244\pi
788788 −21.7992 + 9.02954i −0.776566 + 0.321664i
789789 −12.8071 30.9192i −0.455946 1.10075i
790790 −15.0268 15.0268i −0.534629 0.534629i
791791 40.6781 + 40.6781i 1.44635 + 1.44635i
792792 1.83803 + 4.43740i 0.0653115 + 0.157676i
793793 0.282607 0.117060i 0.0100357 0.00415691i
794794 −28.3741 + 68.5012i −1.00696 + 2.43102i
795795 8.93178i 0.316778i
796796 −61.5717 25.5038i −2.18235 0.903959i
797797 3.65013 3.65013i 0.129294 0.129294i −0.639498 0.768793i 0.720858π-0.720858\pi
0.768793 + 0.639498i 0.220858π0.220858\pi
798798 48.0509 1.70099
799799 16.8591 + 43.5761i 0.596432 + 1.54161i
800800 −3.89165 −0.137591
801801 0.833123 0.833123i 0.0294370 0.0294370i
802802 11.0079 + 4.55963i 0.388704 + 0.161006i
803803 13.5861i 0.479445i
804804 −15.3397 + 37.0333i −0.540990 + 1.30606i
805805 29.2321 12.1083i 1.03030 0.426763i
806806 −2.77050 6.68857i −0.0975866 0.235595i
807807 −4.66278 4.66278i −0.164138 0.164138i
808808 −13.9164 13.9164i −0.489579 0.489579i
809809 8.50871 + 20.5418i 0.299150 + 0.722213i 0.999961 + 0.00886509i 0.00282188π0.00282188\pi
−0.700810 + 0.713348i 0.747178π0.747178\pi
810810 15.4275 6.39030i 0.542069 0.224532i
811811 −5.99450 + 14.4720i −0.210495 + 0.508181i −0.993500 0.113836i 0.963686π-0.963686\pi
0.783004 + 0.622016i 0.213686π0.213686\pi
812812 110.804i 3.88847i
813813 35.8320 + 14.8421i 1.25668 + 0.520535i
814814 −18.9983 + 18.9983i −0.665889 + 0.665889i
815815 9.36510 0.328045
816816 −9.10941 0.214537i −0.318893 0.00751031i
817817 −27.4289 −0.959615
818818 −43.4351 + 43.4351i −1.51867 + 1.51867i
819819 −2.23890 0.927383i −0.0782335 0.0324054i
820820 15.2734i 0.533370i
821821 13.3707 32.2797i 0.466640 1.12657i −0.498981 0.866613i 0.666292π-0.666292\pi
0.965621 0.259955i 0.0837077π-0.0837077\pi
822822 58.4201 24.1984i 2.03764 0.844017i
823823 0.935339 + 2.25811i 0.0326039 + 0.0787127i 0.939343 0.342980i 0.111436π-0.111436\pi
−0.906739 + 0.421692i 0.861436π0.861436\pi
824824 −18.2374 18.2374i −0.635330 0.635330i
825825 2.75493 + 2.75493i 0.0959144 + 0.0959144i
826826 14.4114 + 34.7923i 0.501438 + 1.21058i
827827 −46.9533 + 19.4487i −1.63273 + 0.676298i −0.995534 0.0944054i 0.969905π-0.969905\pi
−0.637194 + 0.770703i 0.719905π0.719905\pi
828828 6.41185 15.4796i 0.222827 0.537952i
829829 41.5846i 1.44429i 0.691740 + 0.722147i 0.256844π0.256844\pi
−0.691740 + 0.722147i 0.743156π0.743156\pi
830830 −15.8962 6.58442i −0.551765 0.228549i
831831 −22.2635 + 22.2635i −0.772313 + 0.772313i
832832 −15.0750 −0.522631
833833 9.72184 21.9913i 0.336842 0.761952i
834834 −7.87308 −0.272623
835835 6.56289 6.56289i 0.227118 0.227118i
836836 29.4371 + 12.1933i 1.01810 + 0.421713i
837837 13.5668i 0.468939i
838838 6.56894 15.8588i 0.226920 0.547834i
839839 4.10912 1.70205i 0.141863 0.0587614i −0.310623 0.950533i 0.600538π-0.600538\pi
0.452485 + 0.891772i 0.350538π0.350538\pi
840840 −7.74855 18.7067i −0.267350 0.645441i
841841 −33.7456 33.7456i −1.16364 1.16364i
842842 −35.0311 35.0311i −1.20725 1.20725i
843843 −15.1225 36.5090i −0.520848 1.25744i
844844 21.5977 8.94607i 0.743424 0.307936i
845845 −4.36784 + 10.5449i −0.150258 + 0.362755i
846846 14.3159i 0.492191i
847847 −16.0069 6.63027i −0.550004 0.227819i
848848 −5.66721 + 5.66721i −0.194613 + 0.194613i
849849 −13.3184 −0.457088
850850 9.04388 3.49897i 0.310202 0.120014i
851851 40.6451 1.39330
852852 7.20198 7.20198i 0.246736 0.246736i
853853 16.5251 + 6.84491i 0.565808 + 0.234365i 0.647204 0.762317i 0.275938π-0.275938\pi
−0.0813967 + 0.996682i 0.525938π0.525938\pi
854854 2.04614i 0.0700174i
855855 −0.747048 + 1.80353i −0.0255485 + 0.0616796i
856856 2.07363 0.858928i 0.0708754 0.0293575i
857857 14.7557 + 35.6234i 0.504045 + 1.21687i 0.947263 + 0.320458i 0.103837π0.103837\pi
−0.443218 + 0.896414i 0.646163π0.646163\pi
858858 8.16060 + 8.16060i 0.278598 + 0.278598i
859859 2.48184 + 2.48184i 0.0846792 + 0.0846792i 0.748178 0.663498i 0.230929π-0.230929\pi
−0.663498 + 0.748178i 0.730929π0.730929\pi
860860 10.1995 + 24.6237i 0.347799 + 0.839662i
861861 −22.4626 + 9.30430i −0.765522 + 0.317090i
862862 −18.9396 + 45.7243i −0.645086 + 1.55738i
863863 21.9552i 0.747365i −0.927557 0.373683i 0.878095π-0.878095\pi
0.927557 0.373683i 0.121905π-0.121905\pi
864864 19.9582 + 8.26695i 0.678991 + 0.281247i
865865 3.04040 3.04040i 0.103377 0.103377i
866866 −87.3171 −2.96715
867867 −25.1014 + 9.03793i −0.852490 + 0.306944i
868868 30.9171 1.04940
869869 −15.8618 + 15.8618i −0.538075 + 0.538075i
870870 −29.8689 12.3721i −1.01265 0.419453i
871871 9.10956i 0.308666i
872872 8.53133 20.5964i 0.288907 0.697484i
873873 4.87339 2.01862i 0.164939 0.0683200i
874874 −28.8925 69.7528i −0.977305 2.35942i
875875 2.53294 + 2.53294i 0.0856291 + 0.0856291i
876876 −21.4461 21.4461i −0.724596 0.724596i
877877 2.16444 + 5.22542i 0.0730879 + 0.176450i 0.956201 0.292710i 0.0945569π-0.0945569\pi
−0.883113 + 0.469159i 0.844557π0.844557\pi
878878 1.02413 0.424209i 0.0345628 0.0143164i
879879 −15.6071 + 37.6788i −0.526413 + 1.27087i
880880 3.49601i 0.117850i
881881 31.7736 + 13.1611i 1.07048 + 0.443407i 0.847160 0.531338i 0.178311π-0.178311\pi
0.223320 + 0.974745i 0.428311π0.428311\pi
882882 5.20930 5.20930i 0.175406 0.175406i
883883 −58.3115 −1.96234 −0.981170 0.193148i 0.938130π-0.938130\pi
−0.981170 + 0.193148i 0.938130π0.938130\pi
884884 17.1033 6.61706i 0.575246 0.222556i
885885 7.01500 0.235807
886886 −18.3349 + 18.3349i −0.615973 + 0.615973i
887887 41.1137 + 17.0299i 1.38046 + 0.571807i 0.944605 0.328208i 0.106445π-0.106445\pi
0.435859 + 0.900015i 0.356445π0.356445\pi
888888 26.0102i 0.872846i
889889 −8.11232 + 19.5849i −0.272078 + 0.656855i
890890 −4.76620 + 1.97422i −0.159763 + 0.0661761i
891891 −6.74540 16.2848i −0.225979 0.545563i
892892 −7.34813 7.34813i −0.246034 0.246034i
893893 29.1220 + 29.1220i 0.974529 + 0.974529i
894894 −26.1849 63.2159i −0.875754 2.11426i
895895 0.108720 0.0450334i 0.00363412 0.00150530i
896896 27.9196 67.4038i 0.932727 2.25180i
897897 17.4589i 0.582935i
898898 37.5109 + 15.5375i 1.25175 + 0.518494i
899899 15.1376 15.1376i 0.504866 0.504866i
900900 1.89688 0.0632292
901901 −9.48808 + 21.4625i −0.316094 + 0.715019i
902902 −25.2527 −0.840824
903903 30.0007 30.0007i 0.998361 0.998361i
904904 −53.4405 22.1358i −1.77740 0.736225i
905905 2.32364i 0.0772404i
906906 12.5888 30.3920i 0.418234 1.00971i
907907 −32.6800 + 13.5365i −1.08512 + 0.449472i −0.852303 0.523048i 0.824795π-0.824795\pi
−0.232819 + 0.972520i 0.574795π0.574795\pi
908908 29.0903 + 70.2301i 0.965394 + 2.33067i
909909 −2.07537 2.07537i −0.0688355 0.0688355i
910910 7.50303 + 7.50303i 0.248723 + 0.248723i
911911 −18.8207 45.4373i −0.623559 1.50540i −0.847496 0.530801i 0.821891π-0.821891\pi
0.223937 0.974604i 0.428109π-0.428109\pi
912912 −7.42034 + 3.07361i −0.245712 + 0.101777i
913913 −6.95031 + 16.7795i −0.230022 + 0.555322i
914914 26.5004i 0.876554i
915915 0.352136 + 0.145859i 0.0116413 + 0.00482197i
916916 29.8176 29.8176i 0.985202 0.985202i
917917 57.7465 1.90696
918918 −53.8140 1.26738i −1.77613 0.0418299i
919919 49.6635 1.63825 0.819123 0.573618i 0.194460π-0.194460\pi
0.819123 + 0.573618i 0.194460π0.194460\pi
920920 −22.4962 + 22.4962i −0.741679 + 0.741679i
921921 −24.5720 10.1781i −0.809676 0.335379i
922922 70.5747i 2.32425i
923923 −0.885781 + 2.13846i −0.0291558 + 0.0703884i
924924 −45.5338 + 18.8607i −1.49795 + 0.620472i
925925 1.76094 + 4.25128i 0.0578993 + 0.139781i
926926 28.5366 + 28.5366i 0.937770 + 0.937770i
927927 −2.71975 2.71975i −0.0893284 0.0893284i
928928 −13.0448 31.4929i −0.428216 1.03381i
929929 −31.5196 + 13.0558i −1.03412 + 0.428348i −0.834199 0.551463i 0.814070π-0.814070\pi
−0.199924 + 0.979811i 0.564070π0.564070\pi
930930 3.45212 8.33415i 0.113199 0.273287i
931931 21.1939i 0.694601i
932932 32.8505 + 13.6071i 1.07605 + 0.445716i
933933 19.0762 19.0762i 0.624528 0.624528i
934934 62.5405 2.04639
935935 −3.69340 9.54644i −0.120787 0.312202i
936936 2.43668 0.0796455
937937 −27.2430 + 27.2430i −0.889991 + 0.889991i −0.994522 0.104530i 0.966666π-0.966666\pi
0.104530 + 0.994522i 0.466666π0.466666\pi
938938 56.2964 + 23.3187i 1.83814 + 0.761383i
939939 9.28250i 0.302923i
940940 15.3146 36.9727i 0.499507 1.20592i
941941 34.3095 14.2115i 1.11846 0.463280i 0.254615 0.967043i 0.418051π-0.418051\pi
0.863842 + 0.503762i 0.168051π0.168051\pi
942942 25.7671 + 62.2074i 0.839539 + 2.02683i
943943 27.0130 + 27.0130i 0.879665 + 0.879665i
944944 −4.45102 4.45102i −0.144868 0.144868i
945945 −7.60943 18.3708i −0.247535 0.597602i
946946 40.7124 16.8636i 1.32367 0.548283i
947947 −0.853817 + 2.06130i −0.0277453 + 0.0669832i −0.937145 0.348940i 0.886542π-0.886542\pi
0.909400 + 0.415923i 0.136542π0.136542\pi
948948 50.0765i 1.62641i
949949 6.36792 + 2.63768i 0.206712 + 0.0856227i
950950 6.04403 6.04403i 0.196094 0.196094i
951951 1.00528 0.0325986
952952 −1.25250 + 53.1820i −0.0405938 + 1.72364i
953953 25.8280 0.836651 0.418326 0.908297i 0.362617π-0.362617\pi
0.418326 + 0.908297i 0.362617π0.362617\pi
954954 −5.08404 + 5.08404i −0.164602 + 0.164602i
955955 −13.5461 5.61099i −0.438342 0.181567i
956956 58.7114i 1.89886i
957957 −13.0596 + 31.5286i −0.422157 + 1.01918i
958958 −49.7808 + 20.6199i −1.60834 + 0.666198i
959959 −23.4849 56.6975i −0.758366 1.83086i
960960 −13.2822 13.2822i −0.428681 0.428681i
961961 −17.6966 17.6966i −0.570857 0.570857i
962962 5.21621 + 12.5930i 0.168177 + 0.406016i
963963 0.309242 0.128092i 0.00996519 0.00412772i
964964 8.00314 19.3213i 0.257764 0.622297i
965965 8.39606i 0.270279i
966966 107.895 + 44.6914i 3.47145 + 1.43792i
967967 22.2041 22.2041i 0.714035 0.714035i −0.253341 0.967377i 0.581530π-0.581530\pi
0.967377 + 0.253341i 0.0815296π0.0815296\pi
968968 17.4209 0.559930
969969 −17.0153 + 16.2323i −0.546612 + 0.521457i
970970 −23.0966 −0.741587
971971 29.0808 29.0808i 0.933248 0.933248i −0.0646590 0.997907i 0.520596π-0.520596\pi
0.997907 + 0.0646590i 0.0205960π0.0205960\pi
972972 −17.9789 7.44709i −0.576672 0.238865i
973973 7.64093i 0.244957i
974974 14.1427 34.1435i 0.453161 1.09403i
975975 1.82611 0.756400i 0.0584824 0.0242242i
976976 −0.130882 0.315978i −0.00418944 0.0101142i
977977 −19.7205 19.7205i −0.630916 0.630916i 0.317382 0.948298i 0.397196π-0.397196\pi
−0.948298 + 0.317382i 0.897196π0.897196\pi
978978 24.4420 + 24.4420i 0.781569 + 0.781569i
979979 2.08393 + 5.03105i 0.0666026 + 0.160793i
980980 −19.0264 + 7.88098i −0.607775 + 0.251749i
981981 1.27228 3.07156i 0.0406208 0.0980673i
982982 2.02071i 0.0644836i
983983 −52.3778 21.6956i −1.67059 0.691982i −0.671782 0.740749i 0.734471π-0.734471\pi
−0.998810 + 0.0487673i 0.984471π0.984471\pi
984984 17.2866 17.2866i 0.551075 0.551075i
985985 6.68150 0.212890
986986 58.6303 + 61.4585i 1.86717 + 1.95724i
987987 −63.7050 −2.02775
988988 11.4301 11.4301i 0.363641 0.363641i
989989 −61.5894 25.5112i −1.95843 0.811208i
990990 3.13626i 0.0996768i
991991 −13.7333 + 33.1551i −0.436252 + 1.05321i 0.540980 + 0.841035i 0.318053π0.318053\pi
−0.977233 + 0.212171i 0.931947π0.931947\pi
992992 8.78730 3.63982i 0.278997 0.115564i
993993 7.00310 + 16.9070i 0.222237 + 0.536526i
994994 −10.9481 10.9481i −0.347253 0.347253i
995995 13.3444 + 13.3444i 0.423045 + 0.423045i
996996 −15.5157 37.4581i −0.491633 1.18691i
997997 30.4465 12.6113i 0.964249 0.399405i 0.155681 0.987807i 0.450243π-0.450243\pi
0.808568 + 0.588402i 0.200243π0.200243\pi
998998 −20.3764 + 49.1930i −0.645004 + 1.55718i
999999 25.5433i 0.808153i
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 85.2.l.a.26.6 24
3.2 odd 2 765.2.be.b.451.1 24
5.2 odd 4 425.2.n.f.349.6 24
5.3 odd 4 425.2.n.c.349.1 24
5.4 even 2 425.2.m.b.26.1 24
17.2 even 8 inner 85.2.l.a.36.6 yes 24
17.6 odd 16 1445.2.a.p.1.12 12
17.7 odd 16 1445.2.d.j.866.1 24
17.10 odd 16 1445.2.d.j.866.2 24
17.11 odd 16 1445.2.a.q.1.12 12
51.2 odd 8 765.2.be.b.631.1 24
85.2 odd 8 425.2.n.c.274.1 24
85.19 even 8 425.2.m.b.376.1 24
85.53 odd 8 425.2.n.f.274.6 24
85.74 odd 16 7225.2.a.bs.1.1 12
85.79 odd 16 7225.2.a.bq.1.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.l.a.26.6 24 1.1 even 1 trivial
85.2.l.a.36.6 yes 24 17.2 even 8 inner
425.2.m.b.26.1 24 5.4 even 2
425.2.m.b.376.1 24 85.19 even 8
425.2.n.c.274.1 24 85.2 odd 8
425.2.n.c.349.1 24 5.3 odd 4
425.2.n.f.274.6 24 85.53 odd 8
425.2.n.f.349.6 24 5.2 odd 4
765.2.be.b.451.1 24 3.2 odd 2
765.2.be.b.631.1 24 51.2 odd 8
1445.2.a.p.1.12 12 17.6 odd 16
1445.2.a.q.1.12 12 17.11 odd 16
1445.2.d.j.866.1 24 17.7 odd 16
1445.2.d.j.866.2 24 17.10 odd 16
7225.2.a.bq.1.1 12 85.79 odd 16
7225.2.a.bs.1.1 12 85.74 odd 16