Properties

Label 825.2.cb.a.169.16
Level 825825
Weight 22
Character 825.169
Analytic conductor 6.5886.588
Analytic rank 00
Dimension 240240
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(169,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 825=35211 825 = 3 \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 825.cb (of order 1010, 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: 6.587658166766.58765816676
Analytic rank: 00
Dimension: 240240
Relative dimension: 6060 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 169.16
Character χ\chi == 825.169
Dual form 825.2.cb.a.454.16

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+(1.413040.459125i)q2+(0.9510570.309017i)q3+(0.167853+0.121952i)q4+(1.85059+1.25512i)q51.48576q6+(1.083030.351897i)q7+(1.56542+2.15462i)q8+(0.8090170.587785i)q9+(2.038702.62318i)q10+(2.385142.30458i)q11+(0.197323+0.0641141i)q12+(0.944395+1.29985i)q131.69193q14+(2.14787+0.621823i)q15+(1.350994.15793i)q16+0.334780iq17+(1.41304+0.459125i)q18+(1.89006+1.37321i)q19+(0.157563+0.436359i)q20+(0.9212790.669348i)q21+(4.42839+2.16139i)q22+(0.809321+0.262964i)q23+(2.15462+1.56542i)q24+(1.84937+4.64541i)q25+(0.7376762.27033i)q26+(0.5877850.809017i)q27+(0.224704+0.0730108i)q28+(4.38760+3.18778i)q29+(2.749531.86480i)q30+(1.10692+3.40675i)q31+1.16909iq32+(1.556252.92884i)q33+(0.1537060.473057i)q34+(2.44591+0.708109i)q35+0.207478q363.52650iq37+(3.301201.07263i)q38+(1.29985+0.944395i)q39+(0.192658+5.95210i)q40+(3.128772.27318i)q41+(1.60912+0.522834i)q42+10.1739iq43+(0.6814020.0959571i)q44+(2.234900.0723392i)q45+1.26434q46+(12.85984.17842i)q47+(2.569743.53695i)q48+(4.61400+3.35227i)q49+(0.4804077.41324i)q50+(0.103453+0.318395i)q51+0.333354iq527.48023iq53+(1.20200+0.873307i)q54+(7.306441.27120i)q55+(2.45360+1.78264i)q56+(1.37321+1.89006i)q57+(4.736276.51892i)q58+1.60356q59+(0.284693+0.366312i)q60+(10.82377.86389i)q615.32208iq62+(0.6693480.921279i)q63+(2.16523+6.66389i)q64+(0.116227+3.59081i)q65+(3.54375+3.42405i)q66+(4.823556.63904i)q67+(0.0408272+0.0561938i)q68+(0.688449+0.500188i)q69+(3.131062.12356i)q70+(3.000019.23308i)q71+(2.53291+0.822991i)q72+(9.41599+12.9600i)q73+(1.61910+4.98309i)q74+(3.19436+3.84656i)q750.484718q76+(1.772203.33525i)q77+(1.403141.93126i)q783.20383q79+(2.718559.39028i)q80+(0.3090170.951057i)q81+(3.37740+4.64859i)q827.65826iq83+0.236268q84+(0.420188+0.619540i)q85+(4.6710814.3761i)q86+(5.15794+1.67592i)q87+(8.69925+1.53143i)q88+(0.6416281.97473i)q89+(3.191210.923878i)q90+(1.48022+1.07544i)q91+(0.1679160.0545592i)q92+(2.10548+2.89795i)q9320.0899q94+(5.22126+0.169002i)q95+(0.361268+1.11187i)q968.64882iq97+(8.058882.61849i)q98+(0.5750223.26640i)q99+O(q100)q+(-1.41304 - 0.459125i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.167853 + 0.121952i) q^{4} +(1.85059 + 1.25512i) q^{5} -1.48576 q^{6} +(1.08303 - 0.351897i) q^{7} +(1.56542 + 2.15462i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.03870 - 2.62318i) q^{10} +(2.38514 - 2.30458i) q^{11} +(0.197323 + 0.0641141i) q^{12} +(0.944395 + 1.29985i) q^{13} -1.69193 q^{14} +(2.14787 + 0.621823i) q^{15} +(-1.35099 - 4.15793i) q^{16} +0.334780i q^{17} +(-1.41304 + 0.459125i) q^{18} +(-1.89006 + 1.37321i) q^{19} +(0.157563 + 0.436359i) q^{20} +(0.921279 - 0.669348i) q^{21} +(-4.42839 + 2.16139i) q^{22} +(-0.809321 + 0.262964i) q^{23} +(2.15462 + 1.56542i) q^{24} +(1.84937 + 4.64541i) q^{25} +(-0.737676 - 2.27033i) q^{26} +(0.587785 - 0.809017i) q^{27} +(0.224704 + 0.0730108i) q^{28} +(4.38760 + 3.18778i) q^{29} +(-2.74953 - 1.86480i) q^{30} +(1.10692 + 3.40675i) q^{31} +1.16909i q^{32} +(1.55625 - 2.92884i) q^{33} +(0.153706 - 0.473057i) q^{34} +(2.44591 + 0.708109i) q^{35} +0.207478 q^{36} -3.52650i q^{37} +(3.30120 - 1.07263i) q^{38} +(1.29985 + 0.944395i) q^{39} +(0.192658 + 5.95210i) q^{40} +(-3.12877 - 2.27318i) q^{41} +(-1.60912 + 0.522834i) q^{42} +10.1739i q^{43} +(0.681402 - 0.0959571i) q^{44} +(2.23490 - 0.0723392i) q^{45} +1.26434 q^{46} +(12.8598 - 4.17842i) q^{47} +(-2.56974 - 3.53695i) q^{48} +(-4.61400 + 3.35227i) q^{49} +(-0.480407 - 7.41324i) q^{50} +(0.103453 + 0.318395i) q^{51} +0.333354i q^{52} -7.48023i q^{53} +(-1.20200 + 0.873307i) q^{54} +(7.30644 - 1.27120i) q^{55} +(2.45360 + 1.78264i) q^{56} +(-1.37321 + 1.89006i) q^{57} +(-4.73627 - 6.51892i) q^{58} +1.60356 q^{59} +(0.284693 + 0.366312i) q^{60} +(-10.8237 - 7.86389i) q^{61} -5.32208i q^{62} +(0.669348 - 0.921279i) q^{63} +(-2.16523 + 6.66389i) q^{64} +(0.116227 + 3.59081i) q^{65} +(-3.54375 + 3.42405i) q^{66} +(4.82355 - 6.63904i) q^{67} +(-0.0408272 + 0.0561938i) q^{68} +(-0.688449 + 0.500188i) q^{69} +(-3.13106 - 2.12356i) q^{70} +(3.00001 - 9.23308i) q^{71} +(2.53291 + 0.822991i) q^{72} +(9.41599 + 12.9600i) q^{73} +(-1.61910 + 4.98309i) q^{74} +(3.19436 + 3.84656i) q^{75} -0.484718 q^{76} +(1.77220 - 3.33525i) q^{77} +(-1.40314 - 1.93126i) q^{78} -3.20383 q^{79} +(2.71855 - 9.39028i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.37740 + 4.64859i) q^{82} -7.65826i q^{83} +0.236268 q^{84} +(-0.420188 + 0.619540i) q^{85} +(4.67108 - 14.3761i) q^{86} +(5.15794 + 1.67592i) q^{87} +(8.69925 + 1.53143i) q^{88} +(-0.641628 - 1.97473i) q^{89} +(-3.19121 - 0.923878i) q^{90} +(1.48022 + 1.07544i) q^{91} +(-0.167916 - 0.0545592i) q^{92} +(2.10548 + 2.89795i) q^{93} -20.0899 q^{94} +(-5.22126 + 0.169002i) q^{95} +(0.361268 + 1.11187i) q^{96} -8.64882i q^{97} +(8.05888 - 2.61849i) q^{98} +(0.575022 - 3.26640i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q+60q4+6q516q6+10q7+60q9+8q10+4q1120q1264q1624q1944q20+8q2140q22+40q2312q24+4q25+40q26+30q28+4q99+O(q100) 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/825Z)×\left(\mathbb{Z}/825\mathbb{Z}\right)^\times.

nn 376376 551551 727727
χ(n)\chi(n) e(15)e\left(\frac{1}{5}\right) 11 e(910)e\left(\frac{9}{10}\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 −1.41304 0.459125i −0.999170 0.324650i −0.236636 0.971598i 0.576045π-0.576045\pi
−0.762534 + 0.646948i 0.776045π0.776045\pi
33 0.951057 0.309017i 0.549093 0.178411i
44 0.167853 + 0.121952i 0.0839265 + 0.0609762i
55 1.85059 + 1.25512i 0.827609 + 0.561305i
66 −1.48576 −0.606558
77 1.08303 0.351897i 0.409346 0.133005i −0.0971033 0.995274i 0.530958π-0.530958\pi
0.506449 + 0.862270i 0.330958π0.330958\pi
88 1.56542 + 2.15462i 0.553460 + 0.761773i
99 0.809017 0.587785i 0.269672 0.195928i
1010 −2.03870 2.62318i −0.644695 0.829523i
1111 2.38514 2.30458i 0.719148 0.694857i
1212 0.197323 + 0.0641141i 0.0569622 + 0.0185082i
1313 0.944395 + 1.29985i 0.261928 + 0.360513i 0.919644 0.392753i 0.128477π-0.128477\pi
−0.657716 + 0.753266i 0.728477π0.728477\pi
1414 −1.69193 −0.452186
1515 2.14787 + 0.621823i 0.554577 + 0.160554i
1616 −1.35099 4.15793i −0.337748 1.03948i
1717 0.334780i 0.0811960i 0.999176 + 0.0405980i 0.0129263π0.0129263\pi
−0.999176 + 0.0405980i 0.987074π0.987074\pi
1818 −1.41304 + 0.459125i −0.333057 + 0.108217i
1919 −1.89006 + 1.37321i −0.433609 + 0.315035i −0.783090 0.621908i 0.786358π-0.786358\pi
0.349481 + 0.936943i 0.386358π0.386358\pi
2020 0.157563 + 0.436359i 0.0352321 + 0.0975728i
2121 0.921279 0.669348i 0.201039 0.146064i
2222 −4.42839 + 2.16139i −0.944136 + 0.460809i
2323 −0.809321 + 0.262964i −0.168755 + 0.0548318i −0.392176 0.919890i 0.628278π-0.628278\pi
0.223421 + 0.974722i 0.428278π0.428278\pi
2424 2.15462 + 1.56542i 0.439810 + 0.319540i
2525 1.84937 + 4.64541i 0.369873 + 0.929082i
2626 −0.737676 2.27033i −0.144670 0.445249i
2727 0.587785 0.809017i 0.113119 0.155695i
2828 0.224704 + 0.0730108i 0.0424651 + 0.0137977i
2929 4.38760 + 3.18778i 0.814758 + 0.591956i 0.915206 0.402986i 0.132028π-0.132028\pi
−0.100448 + 0.994942i 0.532028π0.532028\pi
3030 −2.74953 1.86480i −0.501993 0.340464i
3131 1.10692 + 3.40675i 0.198808 + 0.611870i 0.999911 + 0.0133424i 0.00424714π0.00424714\pi
−0.801103 + 0.598527i 0.795753π0.795753\pi
3232 1.16909i 0.206668i
3333 1.55625 2.92884i 0.270909 0.509845i
3434 0.153706 0.473057i 0.0263603 0.0811287i
3535 2.44591 + 0.708109i 0.413435 + 0.119692i
3636 0.207478 0.0345796
3737 3.52650i 0.579754i −0.957064 0.289877i 0.906386π-0.906386\pi
0.957064 0.289877i 0.0936143π-0.0936143\pi
3838 3.30120 1.07263i 0.535526 0.174003i
3939 1.29985 + 0.944395i 0.208142 + 0.151224i
4040 0.192658 + 5.95210i 0.0304619 + 0.941110i
4141 −3.12877 2.27318i −0.488632 0.355012i 0.316026 0.948750i 0.397651π-0.397651\pi
−0.804658 + 0.593739i 0.797651π0.797651\pi
4242 −1.60912 + 0.522834i −0.248292 + 0.0806750i
4343 10.1739i 1.55150i 0.631039 + 0.775751i 0.282629π0.282629\pi
−0.631039 + 0.775751i 0.717371π0.717371\pi
4444 0.681402 0.0959571i 0.102725 0.0144661i
4545 2.23490 0.0723392i 0.333159 0.0107837i
4646 1.26434 0.186416
4747 12.8598 4.17842i 1.87580 0.609485i 0.886680 0.462384i 0.153006π-0.153006\pi
0.989122 0.147101i 0.0469942π-0.0469942\pi
4848 −2.56974 3.53695i −0.370910 0.510514i
4949 −4.61400 + 3.35227i −0.659143 + 0.478895i
5050 −0.480407 7.41324i −0.0679399 1.04839i
5151 0.103453 + 0.318395i 0.0144863 + 0.0445842i
5252 0.333354i 0.0462279i
5353 7.48023i 1.02749i −0.857943 0.513744i 0.828258π-0.828258\pi
0.857943 0.513744i 0.171742π-0.171742\pi
5454 −1.20200 + 0.873307i −0.163572 + 0.118842i
5555 7.30644 1.27120i 0.985200 0.171409i
5656 2.45360 + 1.78264i 0.327876 + 0.238216i
5757 −1.37321 + 1.89006i −0.181886 + 0.250344i
5858 −4.73627 6.51892i −0.621903 0.855976i
5959 1.60356 0.208766 0.104383 0.994537i 0.466713π-0.466713\pi
0.104383 + 0.994537i 0.466713π0.466713\pi
6060 0.284693 + 0.366312i 0.0367537 + 0.0472907i
6161 −10.8237 7.86389i −1.38583 1.00687i −0.996308 0.0858520i 0.972639π-0.972639\pi
−0.389526 0.921015i 0.627361π-0.627361\pi
6262 5.32208i 0.675905i
6363 0.669348 0.921279i 0.0843299 0.116070i
6464 −2.16523 + 6.66389i −0.270654 + 0.832987i
6565 0.116227 + 3.59081i 0.0144162 + 0.445385i
6666 −3.54375 + 3.42405i −0.436205 + 0.421471i
6767 4.82355 6.63904i 0.589290 0.811088i −0.405385 0.914146i 0.632863π-0.632863\pi
0.994675 + 0.103058i 0.0328627π0.0328627\pi
6868 −0.0408272 + 0.0561938i −0.00495102 + 0.00681450i
6969 −0.688449 + 0.500188i −0.0828796 + 0.0602155i
7070 −3.13106 2.12356i −0.374234 0.253814i
7171 3.00001 9.23308i 0.356036 1.09576i −0.599371 0.800471i 0.704583π-0.704583\pi
0.955407 0.295293i 0.0954174π-0.0954174\pi
7272 2.53291 + 0.822991i 0.298506 + 0.0969904i
7373 9.41599 + 12.9600i 1.10206 + 1.51685i 0.832627 + 0.553834i 0.186836π0.186836\pi
0.269432 + 0.963019i 0.413164π0.413164\pi
7474 −1.61910 + 4.98309i −0.188217 + 0.579273i
7575 3.19436 + 3.84656i 0.368853 + 0.444163i
7676 −0.484718 −0.0556009
7777 1.77220 3.33525i 0.201961 0.380087i
7878 −1.40314 1.93126i −0.158875 0.218672i
7979 −3.20383 −0.360459 −0.180229 0.983625i 0.557684π-0.557684\pi
−0.180229 + 0.983625i 0.557684π0.557684\pi
8080 2.71855 9.39028i 0.303943 1.04987i
8181 0.309017 0.951057i 0.0343352 0.105673i
8282 3.37740 + 4.64859i 0.372972 + 0.513351i
8383 7.65826i 0.840604i −0.907384 0.420302i 0.861924π-0.861924\pi
0.907384 0.420302i 0.138076π-0.138076\pi
8484 0.236268 0.0257789
8585 −0.420188 + 0.619540i −0.0455757 + 0.0671986i
8686 4.67108 14.3761i 0.503695 1.55022i
8787 5.15794 + 1.67592i 0.552989 + 0.179677i
8888 8.69925 + 1.53143i 0.927343 + 0.163251i
8989 −0.641628 1.97473i −0.0680124 0.209321i 0.911274 0.411801i 0.135100π-0.135100\pi
−0.979286 + 0.202480i 0.935100π0.935100\pi
9090 −3.19121 0.923878i −0.336383 0.0973853i
9191 1.48022 + 1.07544i 0.155169 + 0.112737i
9292 −0.167916 0.0545592i −0.0175065 0.00568819i
9393 2.10548 + 2.89795i 0.218329 + 0.300503i
9494 −20.0899 −2.07211
9595 −5.22126 + 0.169002i −0.535690 + 0.0173392i
9696 0.361268 + 1.11187i 0.0368718 + 0.113480i
9797 8.64882i 0.878155i −0.898449 0.439077i 0.855305π-0.855305\pi
0.898449 0.439077i 0.144695π-0.144695\pi
9898 8.05888 2.61849i 0.814070 0.264507i
9999 0.575022 3.26640i 0.0577919 0.328285i
100100 −0.256097 + 1.00528i −0.0256097 + 0.100528i
101101 5.16305 + 3.75118i 0.513743 + 0.373256i 0.814242 0.580526i 0.197153π-0.197153\pi
−0.300499 + 0.953782i 0.597153π0.597153\pi
102102 0.497402i 0.0492501i
103103 3.47870 4.78801i 0.342766 0.471777i −0.602481 0.798133i 0.705821π-0.705821\pi
0.945247 + 0.326356i 0.105821π0.105821\pi
104104 −1.32230 + 4.06962i −0.129662 + 0.399059i
105105 2.54502 0.0823772i 0.248368 0.00803920i
106106 −3.43436 + 10.5699i −0.333574 + 1.02664i
107107 11.7035 + 3.80271i 1.13142 + 0.367622i 0.814117 0.580701i 0.197222π-0.197222\pi
0.317307 + 0.948323i 0.397222π0.397222\pi
108108 0.197323 0.0641141i 0.0189874 0.00616939i
109109 −2.05837 + 6.33502i −0.197156 + 0.606785i 0.802788 + 0.596264i 0.203349π0.203349\pi
−0.999945 + 0.0105207i 0.996651π0.996651\pi
110110 −10.9079 1.55830i −1.04003 0.148578i
111111 −1.08975 3.35390i −0.103434 0.318338i
112112 −2.92633 4.02775i −0.276512 0.380586i
113113 3.60880 4.96709i 0.339487 0.467264i −0.604804 0.796374i 0.706749π-0.706749\pi
0.944292 + 0.329110i 0.106749π0.106749\pi
114114 2.80817 2.04025i 0.263009 0.191087i
115115 −1.82777 0.529152i −0.170441 0.0493437i
116116 0.347715 + 1.07016i 0.0322845 + 0.0993616i
117117 1.52806 + 0.496498i 0.141269 + 0.0459012i
118118 −2.26590 0.736236i −0.208593 0.0677760i
119119 0.117808 + 0.362576i 0.0107994 + 0.0332373i
120120 2.02253 + 5.60125i 0.184631 + 0.511322i
121121 0.377813 10.9935i 0.0343466 0.999410i
122122 11.6838 + 16.0814i 1.05780 + 1.45594i
123123 −3.67809 1.19508i −0.331642 0.107757i
124124 −0.229661 + 0.706824i −0.0206242 + 0.0634746i
125125 −2.40811 + 10.9179i −0.215388 + 0.976529i
126126 −1.36880 + 0.994489i −0.121942 + 0.0885962i
127127 −8.37340 + 11.5250i −0.743019 + 1.02268i 0.255420 + 0.966830i 0.417786π0.417786\pi
−0.998439 + 0.0558481i 0.982214π0.982214\pi
128128 7.49346 10.3139i 0.662335 0.911625i
129129 3.14390 + 9.67594i 0.276805 + 0.851919i
130130 1.48440 5.12732i 0.130190 0.449696i
131131 −7.08937 5.15073i −0.619402 0.450022i 0.233311 0.972402i 0.425044π-0.425044\pi
−0.852712 + 0.522381i 0.825044π0.825044\pi
132132 0.618400 0.301825i 0.0538248 0.0262705i
133133 −1.56376 + 2.15233i −0.135595 + 0.186631i
134134 −9.86401 + 7.16662i −0.852121 + 0.619102i
135135 2.10316 0.759420i 0.181011 0.0653605i
136136 −0.721323 + 0.524072i −0.0618529 + 0.0449388i
137137 −6.84710 + 2.22476i −0.584987 + 0.190074i −0.586534 0.809925i 0.699508π-0.699508\pi
0.00154619 + 0.999999i 0.499508π0.499508\pi
138138 1.20245 0.390701i 0.102360 0.0332587i
139139 5.03733 3.65983i 0.427260 0.310423i −0.353292 0.935513i 0.614938π-0.614938\pi
0.780552 + 0.625090i 0.214938π0.214938\pi
140140 0.324198 + 0.417143i 0.0273997 + 0.0352550i
141141 10.9392 7.94782i 0.921250 0.669327i
142142 −8.47827 + 11.6693i −0.711480 + 0.979269i
143143 5.24812 + 0.923889i 0.438870 + 0.0772594i
144144 −3.53695 2.56974i −0.294746 0.214145i
145145 4.11862 + 11.4062i 0.342033 + 0.947236i
146146 −7.35492 22.6361i −0.608698 1.87338i
147147 −3.35227 + 4.61400i −0.276490 + 0.380556i
148148 0.430065 0.591934i 0.0353512 0.0486567i
149149 −9.56831 + 6.95178i −0.783867 + 0.569512i −0.906137 0.422984i 0.860982π-0.860982\pi
0.122270 + 0.992497i 0.460982π0.460982\pi
150150 −2.74771 6.90196i −0.224350 0.563542i
151151 0.561166 1.72709i 0.0456670 0.140549i −0.925623 0.378447i 0.876458π-0.876458\pi
0.971290 + 0.237898i 0.0764584π0.0764584\pi
152152 −5.91748 1.92270i −0.479971 0.155952i
153153 0.196779 + 0.270843i 0.0159086 + 0.0218963i
154154 −4.03549 + 3.89918i −0.325189 + 0.314205i
155155 −2.22741 + 7.69380i −0.178910 + 0.617981i
156156 0.103012 + 0.317039i 0.00824758 + 0.0253834i
157157 3.13986 + 1.02020i 0.250588 + 0.0814210i 0.431618 0.902057i 0.357943π-0.357943\pi
−0.181030 + 0.983478i 0.557943π0.557943\pi
158158 4.52714 + 1.47096i 0.360160 + 0.117023i
159159 −2.31152 7.11412i −0.183315 0.564186i
160160 −1.46734 + 2.16351i −0.116004 + 0.171040i
161161 −0.783981 + 0.569595i −0.0617863 + 0.0448904i
162162 −0.873307 + 1.20200i −0.0686135 + 0.0944383i
163163 −0.343477 0.472756i −0.0269032 0.0370291i 0.795353 0.606146i 0.207285π-0.207285\pi
−0.822257 + 0.569117i 0.807285π0.807285\pi
164164 −0.247953 0.763121i −0.0193619 0.0595898i
165165 6.55601 3.46680i 0.510385 0.269890i
166166 −3.51610 + 10.8214i −0.272902 + 0.839906i
167167 −6.15976 + 2.00143i −0.476656 + 0.154875i −0.537485 0.843273i 0.680626π-0.680626\pi
0.0608289 + 0.998148i 0.480626π0.480626\pi
168168 2.88438 + 0.937192i 0.222535 + 0.0723059i
169169 3.21950 9.90860i 0.247654 0.762200i
170170 0.878188 0.682517i 0.0673539 0.0523466i
171171 −0.721938 + 2.22190i −0.0552080 + 0.169913i
172172 −1.24073 + 1.70772i −0.0946047 + 0.130212i
173173 9.90987i 0.753434i 0.926328 + 0.376717i 0.122947π0.122947\pi
−0.926328 + 0.376717i 0.877053π0.877053\pi
174174 −6.51892 4.73627i −0.494198 0.359056i
175175 3.63762 + 4.38032i 0.274978 + 0.331121i
176176 −12.8046 6.80379i −0.965183 0.512855i
177177 1.52508 0.495529i 0.114632 0.0372462i
178178 3.08496i 0.231227i
179179 6.74480 + 20.7583i 0.504130 + 1.55155i 0.802229 + 0.597017i 0.203647π0.203647\pi
−0.298099 + 0.954535i 0.596353π0.596353\pi
180180 0.383956 + 0.260409i 0.0286184 + 0.0194097i
181181 −18.0079 −1.33851 −0.669257 0.743031i 0.733388π-0.733388\pi
−0.669257 + 0.743031i 0.733388π0.733388\pi
182182 −1.59785 2.19925i −0.118440 0.163019i
183183 −12.7240 4.13429i −0.940588 0.305615i
184184 −1.83352 1.33213i −0.135169 0.0982057i
185185 4.42617 6.52611i 0.325419 0.479809i
186186 −1.64461 5.06160i −0.120589 0.371135i
187187 0.771527 + 0.798498i 0.0564197 + 0.0583919i
188188 2.66813 + 0.866928i 0.194593 + 0.0632272i
189189 0.351897 1.08303i 0.0255967 0.0787787i
190190 7.45544 + 2.15840i 0.540874 + 0.156587i
191191 −9.65493 −0.698607 −0.349303 0.937010i 0.613582π-0.613582\pi
−0.349303 + 0.937010i 0.613582π0.613582\pi
192192 7.00683i 0.505675i
193193 −13.5014 18.5831i −0.971855 1.33764i −0.941104 0.338117i 0.890210π-0.890210\pi
−0.0307508 0.999527i 0.509790π-0.509790\pi
194194 −3.97089 + 12.2211i −0.285093 + 0.877426i
195195 1.22016 + 3.37915i 0.0873775 + 0.241986i
196196 −1.18329 −0.0845208
197197 −0.215950 0.297229i −0.0153858 0.0211767i 0.801255 0.598323i 0.204166π-0.204166\pi
−0.816641 + 0.577147i 0.804166π0.804166\pi
198198 −2.31221 + 4.35154i −0.164322 + 0.309251i
199199 −22.7175 −1.61040 −0.805199 0.593004i 0.797942π-0.797942\pi
−0.805199 + 0.593004i 0.797942π0.797942\pi
200200 −7.11405 + 11.2567i −0.503039 + 0.795969i
201201 2.53589 7.80466i 0.178868 0.550498i
202202 −5.57334 7.67105i −0.392139 0.539733i
203203 5.87367 + 1.90847i 0.412251 + 0.133948i
204204 −0.0214641 + 0.0660598i −0.00150279 + 0.00462511i
205205 −2.93696 8.13370i −0.205126 0.568082i
206206 −7.11383 + 5.16850i −0.495644 + 0.360107i
207207 −0.500188 + 0.688449i −0.0347654 + 0.0478505i
208208 4.12881 5.68282i 0.286281 0.394032i
209209 −1.34339 + 7.63109i −0.0929243 + 0.527853i
210210 −3.63403 1.05208i −0.250772 0.0726003i
211211 0.731974 2.25278i 0.0503911 0.155088i −0.922694 0.385532i 0.874018π-0.874018\pi
0.973086 + 0.230444i 0.0740179π0.0740179\pi
212212 0.912231 1.25558i 0.0626523 0.0862335i
213213 9.70823i 0.665197i
214214 −14.7916 10.7468i −1.01114 0.734633i
215215 −12.7694 + 18.8277i −0.870866 + 1.28404i
216216 2.66325 0.181212
217217 2.39765 + 3.30008i 0.162763 + 0.224024i
218218 5.81713 8.00659i 0.393985 0.542274i
219219 12.9600 + 9.41599i 0.875756 + 0.636274i
220220 1.38143 + 0.677662i 0.0931362 + 0.0456880i
221221 −0.435163 + 0.316164i −0.0292722 + 0.0212675i
222222 5.23953i 0.351654i
223223 17.1956i 1.15150i 0.817625 + 0.575751i 0.195290π0.195290\pi
−0.817625 + 0.575751i 0.804710π0.804710\pi
224224 0.411399 + 1.26616i 0.0274878 + 0.0845986i
225225 4.22667 + 2.67119i 0.281778 + 0.178079i
226226 −7.37989 + 5.36181i −0.490903 + 0.356662i
227227 7.93701 + 10.9244i 0.526798 + 0.725075i 0.986638 0.162927i 0.0520934π-0.0520934\pi
−0.459840 + 0.888002i 0.652093π0.652093\pi
228228 −0.460994 + 0.149786i −0.0305301 + 0.00991982i
229229 −26.5252 −1.75283 −0.876416 0.481554i 0.840073π-0.840073\pi
−0.876416 + 0.481554i 0.840073π0.840073\pi
230230 2.33977 + 1.58689i 0.154280 + 0.104636i
231231 0.654814 3.71965i 0.0430836 0.244735i
232232 14.4438i 0.948284i
233233 −11.2407 + 3.65234i −0.736405 + 0.239273i −0.653121 0.757253i 0.726541π-0.726541\pi
−0.0832840 + 0.996526i 0.526541π0.526541\pi
234234 −1.93126 1.40314i −0.126250 0.0917263i
235235 29.0427 + 8.40806i 1.89454 + 0.548482i
236236 0.269163 + 0.195558i 0.0175210 + 0.0127298i
237237 −3.04702 + 0.990037i −0.197925 + 0.0643098i
238238 0.566423i 0.0367157i
239239 −3.25985 −0.210862 −0.105431 0.994427i 0.533622π-0.533622\pi
−0.105431 + 0.994427i 0.533622π0.533622\pi
240240 −0.316261 9.77077i −0.0204145 0.630700i
241241 −7.45439 + 22.9423i −0.480180 + 1.47784i 0.358663 + 0.933467i 0.383233π0.383233\pi
−0.838843 + 0.544374i 0.816767π0.816767\pi
242242 −5.58126 + 15.3608i −0.358777 + 0.987430i
243243 1.00000i 0.0641500i
244244 −0.857773 2.63995i −0.0549133 0.169006i
245245 −12.7461 + 0.412567i −0.814319 + 0.0263579i
246246 4.64859 + 3.37740i 0.296384 + 0.215335i
247247 −3.56992 1.15994i −0.227149 0.0738051i
248248 −5.60744 + 7.71798i −0.356073 + 0.490092i
249249 −2.36653 7.28344i −0.149973 0.461569i
250250 8.41544 14.3218i 0.532239 0.905793i
251251 −11.8220 8.58921i −0.746200 0.542146i 0.148447 0.988920i 0.452573π-0.452573\pi
−0.894647 + 0.446774i 0.852573π0.852573\pi
252252 0.224704 0.0730108i 0.0141550 0.00459925i
253253 −1.32432 + 2.49235i −0.0832595 + 0.156693i
254254 17.1234 12.4409i 1.07442 0.780608i
255255 −0.208174 + 0.719063i −0.0130363 + 0.0450295i
256256 −3.98662 + 2.89645i −0.249164 + 0.181028i
257257 1.12199 0.364556i 0.0699877 0.0227404i −0.273814 0.961783i 0.588285π-0.588285\pi
0.343802 + 0.939042i 0.388285π0.388285\pi
258258 15.1159i 0.941077i
259259 −1.24097 3.81930i −0.0771099 0.237320i
260260 −0.418399 + 0.616902i −0.0259480 + 0.0382587i
261261 5.42338 0.335699
262262 7.65274 + 10.5331i 0.472788 + 0.650737i
263263 16.4735 + 5.35256i 1.01580 + 0.330053i 0.769161 0.639055i 0.220674π-0.220674\pi
0.246637 + 0.969108i 0.420674π0.420674\pi
264264 8.74671 1.23174i 0.538323 0.0758082i
265265 9.38855 13.8428i 0.576734 0.850358i
266266 3.19784 2.32337i 0.196072 0.142455i
267267 −1.22045 1.67980i −0.0746903 0.102802i
268268 1.61929 0.526140i 0.0989141 0.0321391i
269269 −20.4757 −1.24842 −0.624212 0.781255i 0.714580π-0.714580\pi
−0.624212 + 0.781255i 0.714580π0.714580\pi
270270 −3.32052 + 0.107479i −0.202080 + 0.00654094i
271271 −7.33051 5.32593i −0.445297 0.323527i 0.342439 0.939540i 0.388747π-0.388747\pi
−0.787736 + 0.616013i 0.788747π0.788747\pi
272272 1.39199 0.452286i 0.0844019 0.0274238i
273273 1.74010 + 0.565393i 0.105316 + 0.0342192i
274274 10.6967 0.646210
275275 15.1167 + 6.81795i 0.911573 + 0.411138i
276276 −0.176557 −0.0106275
277277 −17.6687 5.74092i −1.06161 0.344939i −0.274397 0.961617i 0.588478π-0.588478\pi
−0.787216 + 0.616678i 0.788478π0.788478\pi
278278 −8.79826 + 2.85873i −0.527685 + 0.171455i
279279 2.89795 + 2.10548i 0.173496 + 0.126052i
280280 2.30318 + 6.37850i 0.137641 + 0.381188i
281281 −25.5737 −1.52560 −0.762800 0.646635i 0.776176π-0.776176\pi
−0.762800 + 0.646635i 0.776176π0.776176\pi
282282 −19.1066 + 6.20812i −1.13778 + 0.369688i
283283 −7.08969 9.75812i −0.421438 0.580060i 0.544523 0.838746i 0.316711π-0.316711\pi
−0.965962 + 0.258686i 0.916711π0.916711\pi
284284 1.62956 1.18394i 0.0966964 0.0702540i
285285 −4.91349 + 1.77419i −0.291050 + 0.105094i
286286 −6.99163 3.71503i −0.413423 0.219674i
287287 −4.18847 1.36092i −0.247238 0.0803324i
288288 0.687173 + 0.945813i 0.0404921 + 0.0557326i
289289 16.8879 0.993407
290290 −0.582897 18.0084i −0.0342289 1.05749i
291291 −2.67263 8.22552i −0.156672 0.482188i
292292 3.32368i 0.194504i
293293 −11.8281 + 3.84318i −0.691005 + 0.224521i −0.633407 0.773819i 0.718344π-0.718344\pi
−0.0575979 + 0.998340i 0.518344π0.518344\pi
294294 6.85529 4.98066i 0.399809 0.290478i
295295 2.96754 + 2.01266i 0.172777 + 0.117182i
296296 7.59827 5.52047i 0.441640 0.320871i
297297 −0.462493 3.28422i −0.0268366 0.190570i
298298 16.7121 5.43010i 0.968108 0.314557i
299299 −1.10613 0.803652i −0.0639692 0.0464764i
300300 0.0670862 + 1.03522i 0.00387322 + 0.0597683i
301301 3.58016 + 11.0186i 0.206357 + 0.635101i
302302 −1.58590 + 2.18280i −0.0912582 + 0.125606i
303303 6.06953 + 1.97211i 0.348685 + 0.113295i
304304 8.26316 + 6.00354i 0.473925 + 0.344326i
305305 −10.1602 28.1378i −0.581769 1.61117i
306306 −0.153706 0.473057i −0.00878677 0.0270429i
307307 14.7273i 0.840533i −0.907401 0.420266i 0.861937π-0.861937\pi
0.907401 0.420266i 0.138063π-0.138063\pi
308308 0.704211 0.343708i 0.0401261 0.0195846i
309309 1.82886 5.62865i 0.104040 0.320203i
310310 6.67983 9.84899i 0.379389 0.559385i
311311 14.6914 0.833075 0.416538 0.909119i 0.363243π-0.363243\pi
0.416538 + 0.909119i 0.363243π0.363243\pi
312312 4.27905i 0.242254i
313313 18.3410 5.95934i 1.03669 0.336842i 0.259259 0.965808i 0.416522π-0.416522\pi
0.777433 + 0.628966i 0.216522π0.216522\pi
314314 −3.96835 2.88317i −0.223947 0.162707i
315315 2.39500 0.864799i 0.134943 0.0487259i
316316 −0.537772 0.390714i −0.0302520 0.0219794i
317317 26.6977 8.67462i 1.49949 0.487215i 0.559624 0.828747i 0.310946π-0.310946\pi
0.939870 + 0.341532i 0.110946π0.110946\pi
318318 11.1138i 0.623231i
319319 17.8116 2.50828i 0.997256 0.140436i
320320 −12.3709 + 9.61452i −0.691555 + 0.537468i
321321 12.3058 0.686844
322322 1.36931 0.444916i 0.0763087 0.0247942i
323323 −0.459722 0.632753i −0.0255796 0.0352073i
324324 0.167853 0.121952i 0.00932517 0.00677513i
325325 −4.29179 + 6.79100i −0.238066 + 0.376697i
326326 0.268293 + 0.825722i 0.0148594 + 0.0457325i
327327 6.66103i 0.368356i
328328 10.2998i 0.568711i
329329 12.4572 9.05068i 0.686788 0.498980i
330330 −10.8556 + 1.88870i −0.597581 + 0.103970i
331331 8.11726 + 5.89754i 0.446165 + 0.324158i 0.788080 0.615573i 0.211075π-0.211075\pi
−0.341915 + 0.939731i 0.611075π0.611075\pi
332332 0.933943 1.28546i 0.0512568 0.0705489i
333333 −2.07283 2.85300i −0.113590 0.156344i
334334 9.62289 0.526541
335335 17.2592 6.23203i 0.942969 0.340492i
336336 −4.02775 2.92633i −0.219732 0.159644i
337337 8.50999i 0.463569i −0.972767 0.231784i 0.925544π-0.925544\pi
0.972767 0.231784i 0.0744564π-0.0744564\pi
338338 −9.09856 + 12.5231i −0.494896 + 0.681166i
339339 1.89726 5.83916i 0.103045 0.317140i
340340 −0.146084 + 0.0527488i −0.00792252 + 0.00286071i
341341 10.4913 + 5.57459i 0.568135 + 0.301881i
342342 2.04025 2.80817i 0.110324 0.151848i
343343 −8.50287 + 11.7032i −0.459112 + 0.631914i
344344 −21.9208 + 15.9264i −1.18189 + 0.858695i
345345 −1.90183 + 0.0615585i −0.102391 + 0.00331420i
346346 4.54987 14.0030i 0.244602 0.752808i
347347 −10.5614 3.43162i −0.566968 0.184219i 0.0114862 0.999934i 0.496344π-0.496344\pi
−0.578454 + 0.815715i 0.696344π0.696344\pi
348348 0.661393 + 0.910330i 0.0354544 + 0.0487988i
349349 10.2585 31.5725i 0.549126 1.69004i −0.161845 0.986816i 0.551744π-0.551744\pi
0.710971 0.703221i 0.248256π-0.248256\pi
350350 −3.12899 7.85969i −0.167252 0.420118i
351351 1.60670 0.0857593
352352 2.69426 + 2.78845i 0.143605 + 0.148625i
353353 −10.4098 14.3278i −0.554056 0.762592i 0.436500 0.899704i 0.356218π-0.356218\pi
−0.990556 + 0.137112i 0.956218π0.956218\pi
354354 −2.38251 −0.126629
355355 17.1404 13.3213i 0.909717 0.707020i
356356 0.133123 0.409712i 0.00705553 0.0217147i
357357 0.224084 + 0.308425i 0.0118598 + 0.0163236i
358358 32.4291i 1.71393i
359359 −5.63206 −0.297249 −0.148624 0.988894i 0.547485π-0.547485\pi
−0.148624 + 0.988894i 0.547485π0.547485\pi
360360 3.65442 + 4.70211i 0.192605 + 0.247823i
361361 −4.18470 + 12.8792i −0.220248 + 0.677852i
362362 25.4458 + 8.26786i 1.33740 + 0.434549i
363363 −3.03786 10.5722i −0.159446 0.554897i
364364 0.117306 + 0.361032i 0.00614853 + 0.0189232i
365365 1.15883 + 35.8018i 0.0606562 + 1.87395i
366366 16.0814 + 11.6838i 0.840589 + 0.610724i
367367 1.76001 + 0.571863i 0.0918719 + 0.0298510i 0.354592 0.935021i 0.384620π-0.384620\pi
−0.262720 + 0.964872i 0.584620π0.584620\pi
368368 2.18677 + 3.00984i 0.113994 + 0.156899i
369369 −3.86737 −0.201327
370370 −9.25066 + 7.18949i −0.480919 + 0.373764i
371371 −2.63227 8.10129i −0.136661 0.420598i
372372 0.743198i 0.0385330i
373373 13.4960 4.38512i 0.698798 0.227053i 0.0619910 0.998077i 0.480255π-0.480255\pi
0.636807 + 0.771024i 0.280255π0.280255\pi
374374 −0.723589 1.48254i −0.0374159 0.0766601i
375375 1.08357 + 11.1277i 0.0559555 + 0.574632i
376376 29.1340 + 21.1671i 1.50247 + 1.09161i
377377 8.71374i 0.448780i
378378 −0.994489 + 1.36880i −0.0511510 + 0.0704033i
379379 −3.51892 + 10.8301i −0.180755 + 0.556306i −0.999849 0.0173523i 0.994476π-0.994476\pi
0.819095 + 0.573658i 0.194476π0.194476\pi
380380 −0.897014 0.608377i −0.0460158 0.0312091i
381381 −4.40216 + 13.5484i −0.225529 + 0.694108i
382382 13.6428 + 4.43282i 0.698027 + 0.226803i
383383 −13.4176 + 4.35964i −0.685608 + 0.222767i −0.631049 0.775743i 0.717375π-0.717375\pi
−0.0545588 + 0.998511i 0.517375π0.517375\pi
384384 3.93955 12.1247i 0.201039 0.618735i
385385 7.46574 3.94786i 0.380490 0.201202i
386386 10.5461 + 32.4576i 0.536782 + 1.65205i
387387 5.98006 + 8.23084i 0.303983 + 0.418397i
388388 1.05474 1.45173i 0.0535465 0.0737004i
389389 12.0646 8.76541i 0.611697 0.444424i −0.238314 0.971188i 0.576595π-0.576595\pi
0.850012 + 0.526764i 0.176595π0.176595\pi
390390 −0.172686 5.33508i −0.00874429 0.270152i
391391 −0.0880351 0.270944i −0.00445213 0.0137022i
392392 −14.4457 4.69370i −0.729619 0.237068i
393393 −8.33406 2.70790i −0.420398 0.136595i
394394 0.168680 + 0.519144i 0.00849799 + 0.0261541i
395395 −5.92897 4.02117i −0.298319 0.202327i
396396 0.494864 0.478149i 0.0248678 0.0240279i
397397 5.16665 + 7.11129i 0.259307 + 0.356905i 0.918744 0.394855i 0.129205π-0.129205\pi
−0.659437 + 0.751760i 0.729205π0.729205\pi
398398 32.1007 + 10.4301i 1.60906 + 0.522816i
399399 −0.822116 + 2.53021i −0.0411573 + 0.126669i
400400 16.8168 13.9655i 0.840841 0.698273i
401401 14.3838 10.4504i 0.718291 0.521869i −0.167547 0.985864i 0.553584π-0.553584\pi
0.885838 + 0.463995i 0.153584π0.153584\pi
402402 −7.16662 + 9.86401i −0.357439 + 0.491972i
403403 −3.38288 + 4.65614i −0.168513 + 0.231939i
404404 0.409169 + 1.25929i 0.0203569 + 0.0626521i
405405 1.76555 1.37216i 0.0877309 0.0681834i
406406 −7.42350 5.39349i −0.368422 0.267674i
407407 −8.12711 8.41121i −0.402846 0.416928i
408408 −0.524072 + 0.721323i −0.0259454 + 0.0357108i
409409 8.65156 6.28573i 0.427792 0.310809i −0.352973 0.935633i 0.614829π-0.614829\pi
0.780766 + 0.624824i 0.214829π0.214829\pi
410410 0.415660 + 12.8417i 0.0205280 + 0.634205i
411411 −5.82449 + 4.23174i −0.287301 + 0.208736i
412412 1.16782 0.379447i 0.0575343 0.0186940i
413413 1.73670 0.564290i 0.0854576 0.0277669i
414414 1.02287 0.743158i 0.0502713 0.0365242i
415415 9.61201 14.1723i 0.471835 0.695691i
416416 −1.51964 + 1.10408i −0.0745064 + 0.0541321i
417417 3.65983 5.03733i 0.179223 0.246679i
418418 5.40188 10.1662i 0.264215 0.497248i
419419 7.73548 + 5.62016i 0.377903 + 0.274563i 0.760480 0.649361i 0.224963π-0.224963\pi
−0.382577 + 0.923923i 0.624963π0.624963\pi
420420 0.437235 + 0.296544i 0.0213349 + 0.0144698i
421421 7.69125 + 23.6712i 0.374849 + 1.15367i 0.943581 + 0.331143i 0.107434π0.107434\pi
−0.568732 + 0.822523i 0.692566π0.692566\pi
422422 −2.06862 + 2.84721i −0.100699 + 0.138600i
423423 7.94782 10.9392i 0.386436 0.531884i
424424 16.1170 11.7097i 0.782712 0.568674i
425425 −1.55519 + 0.619131i −0.0754378 + 0.0300323i
426426 −4.45729 + 13.7181i −0.215956 + 0.664645i
427427 −14.4897 4.70798i −0.701204 0.227835i
428428 1.50072 + 2.06557i 0.0725402 + 0.0998431i
429429 5.27676 0.743088i 0.254764 0.0358766i
430430 26.6879 20.7415i 1.28701 1.00025i
431431 −1.26233 3.88505i −0.0608043 0.187136i 0.916040 0.401086i 0.131367π-0.131367\pi
−0.976845 + 0.213950i 0.931367π0.931367\pi
432432 −4.15793 1.35099i −0.200049 0.0649997i
433433 −26.9318 8.75066i −1.29426 0.420530i −0.420678 0.907210i 0.638208π-0.638208\pi
−0.873580 + 0.486680i 0.838208π0.838208\pi
434434 −1.87282 5.76396i −0.0898985 0.276679i
435435 7.44176 + 9.57524i 0.356805 + 0.459098i
436436 −1.11807 + 0.812329i −0.0535460 + 0.0389035i
437437 1.16856 1.60838i 0.0558997 0.0769394i
438438 −13.9899 19.2554i −0.668463 0.920060i
439439 7.67554 + 23.6229i 0.366334 + 1.12746i 0.949142 + 0.314849i 0.101954π0.101954\pi
−0.582808 + 0.812610i 0.698046π0.698046\pi
440440 14.1766 + 13.7526i 0.675844 + 0.655630i
441441 −1.76239 + 5.42408i −0.0839234 + 0.258290i
442442 0.760061 0.246959i 0.0361524 0.0117466i
443443 −18.8108 6.11200i −0.893727 0.290390i −0.174082 0.984731i 0.555696π-0.555696\pi
−0.719646 + 0.694342i 0.755696π0.755696\pi
444444 0.226099 0.695860i 0.0107302 0.0330241i
445445 1.29112 4.45973i 0.0612051 0.211411i
446446 7.89492 24.2981i 0.373835 1.15055i
447447 −6.95178 + 9.56831i −0.328808 + 0.452566i
448448 7.97912i 0.376978i
449449 10.4666 + 7.60441i 0.493948 + 0.358874i 0.806701 0.590960i 0.201251π-0.201251\pi
−0.312752 + 0.949835i 0.601251π0.601251\pi
450450 −4.74605 5.71506i −0.223731 0.269411i
451451 −12.7013 + 1.78863i −0.598081 + 0.0842235i
452452 1.21150 0.393639i 0.0569840 0.0185152i
453453 1.81597i 0.0853217i
454454 −6.19967 19.0806i −0.290965 0.895498i
455455 1.38947 + 3.84805i 0.0651395 + 0.180399i
456456 −6.22200 −0.291372
457457 −22.3917 30.8195i −1.04744 1.44167i −0.891009 0.453986i 0.850002π-0.850002\pi
−0.156429 0.987689i 0.549998π-0.549998\pi
458458 37.4811 + 12.1784i 1.75138 + 0.569057i
459459 0.270843 + 0.196779i 0.0126418 + 0.00918484i
460460 −0.242265 0.311721i −0.0112957 0.0145341i
461461 −3.22683 9.93117i −0.150289 0.462541i 0.847365 0.531012i 0.178188π-0.178188\pi
−0.997653 + 0.0684710i 0.978188π0.978188\pi
462462 −2.63306 + 4.95538i −0.122501 + 0.230545i
463463 −13.0716 4.24723i −0.607490 0.197386i −0.0109121 0.999940i 0.503473π-0.503473\pi
−0.596578 + 0.802555i 0.703473π0.703473\pi
464464 7.32695 22.5500i 0.340145 1.04686i
465465 0.259124 + 8.00555i 0.0120166 + 0.371248i
466466 17.5605 0.813474
467467 19.6140i 0.907626i 0.891097 + 0.453813i 0.149937π0.149937\pi
−0.891097 + 0.453813i 0.850063π0.850063\pi
468468 0.195941 + 0.269689i 0.00905737 + 0.0124664i
469469 2.88778 8.88766i 0.133345 0.410394i
470470 −37.1782 25.2151i −1.71490 1.16309i
471471 3.30144 0.152123
472472 2.51025 + 3.45507i 0.115544 + 0.159032i
473473 23.4465 + 24.2662i 1.07807 + 1.11576i
474474 4.76011 0.218639
475475 −9.87452 6.24053i −0.453074 0.286335i
476476 −0.0244425 + 0.0752264i −0.00112032 + 0.00344800i
477477 −4.39677 6.05163i −0.201314 0.277085i
478478 4.60630 + 1.49668i 0.210687 + 0.0684564i
479479 8.31169 25.5807i 0.379771 1.16881i −0.560433 0.828200i 0.689365π-0.689365\pi
0.940203 0.340614i 0.110635π-0.110635\pi
480480 −0.726966 + 2.51105i −0.0331813 + 0.114613i
481481 4.58392 3.33041i 0.209009 0.151854i
482482 21.0667 28.9958i 0.959562 1.32072i
483483 −0.569595 + 0.783981i −0.0259175 + 0.0356723i
484484 1.40410 1.79922i 0.0638228 0.0817826i
485485 10.8553 16.0054i 0.492913 0.726769i
486486 −0.459125 + 1.41304i −0.0208263 + 0.0640968i
487487 −10.6228 + 14.6210i −0.481364 + 0.662541i −0.978766 0.204979i 0.934287π-0.934287\pi
0.497402 + 0.867520i 0.334287π0.334287\pi
488488 35.6313i 1.61295i
489489 −0.472756 0.343477i −0.0213788 0.0155326i
490490 18.2002 + 5.26908i 0.822201 + 0.238033i
491491 24.4711 1.10437 0.552184 0.833722i 0.313795π-0.313795\pi
0.552184 + 0.833722i 0.313795π0.313795\pi
492492 −0.471635 0.649150i −0.0212629 0.0292659i
493493 −1.06720 + 1.46888i −0.0480645 + 0.0661551i
494494 4.51189 + 3.27808i 0.202999 + 0.147488i
495495 5.16384 5.32304i 0.232097 0.239253i
496496 12.6696 9.20498i 0.568881 0.413316i
497497 11.0554i 0.495901i
498498 11.3783i 0.509875i
499499 −9.77256 30.0768i −0.437480 1.34642i −0.890524 0.454936i 0.849662π-0.849662\pi
0.453044 0.891488i 0.350338π-0.350338\pi
500500 −1.73567 + 1.53893i −0.0776217 + 0.0688231i
501501 −5.23980 + 3.80694i −0.234097 + 0.170082i
502502 12.7615 + 17.5647i 0.569573 + 0.783950i
503503 21.1073 6.85817i 0.941128 0.305791i 0.202022 0.979381i 0.435249π-0.435249\pi
0.739105 + 0.673590i 0.235249π0.235249\pi
504504 3.03282 0.135092
505505 4.84653 + 13.4221i 0.215668 + 0.597276i
506506 3.01562 2.91376i 0.134061 0.129533i
507507 10.4185i 0.462702i
508508 −2.81100 + 0.913350i −0.124718 + 0.0405233i
509509 −26.6172 19.3385i −1.17979 0.857165i −0.187639 0.982238i 0.560084π-0.560084\pi
−0.992148 + 0.125072i 0.960084π0.960084\pi
510510 0.624297 0.920487i 0.0276443 0.0407598i
511511 14.7584 + 10.7226i 0.652872 + 0.474339i
512512 −17.2863 + 5.61665i −0.763952 + 0.248223i
513513 2.33624i 0.103148i
514514 −1.75279 −0.0773123
515515 12.4472 4.49448i 0.548487 0.198051i
516516 −0.652290 + 2.00754i −0.0287154 + 0.0883771i
517517 21.0431 39.6027i 0.925473 1.74172i
518518 5.96658i 0.262157i
519519 3.06232 + 9.42485i 0.134421 + 0.413705i
520520 −7.55488 + 5.87156i −0.331303 + 0.257485i
521521 −8.78134 6.38002i −0.384718 0.279514i 0.378570 0.925573i 0.376416π-0.376416\pi
−0.763287 + 0.646059i 0.776416π0.776416\pi
522522 −7.66345 2.49001i −0.335420 0.108985i
523523 −23.2819 + 32.0448i −1.01805 + 1.40122i −0.104485 + 0.994527i 0.533319π0.533319\pi
−0.913563 + 0.406696i 0.866681π0.866681\pi
524524 −0.561829 1.72913i −0.0245436 0.0755375i
525525 4.81318 + 3.04185i 0.210064 + 0.132757i
526526 −20.8202 15.1268i −0.907803 0.659558i
527527 −1.14051 + 0.370574i −0.0496814 + 0.0161425i
528528 −14.2804 2.51395i −0.621474 0.109405i
529529 −18.0215 + 13.0934i −0.783545 + 0.569279i
530530 −19.6220 + 15.2500i −0.852325 + 0.662416i
531531 1.29731 0.942551i 0.0562985 0.0409032i
532532 −0.524963 + 0.170571i −0.0227600 + 0.00739518i
533533 6.21371i 0.269146i
534534 0.953304 + 2.93397i 0.0412535 + 0.126965i
535535 16.8856 + 21.7266i 0.730028 + 0.939321i
536536 21.8555 0.944013
537537 12.8294 + 17.6581i 0.553628 + 0.762004i
538538 28.9330 + 9.40089i 1.24739 + 0.405301i
539539 −3.27948 + 18.6290i −0.141257 + 0.802407i
540540 0.445635 + 0.129014i 0.0191771 + 0.00555189i
541541 −2.58758 + 1.87999i −0.111249 + 0.0808269i −0.642019 0.766689i 0.721903π-0.721903\pi
0.530770 + 0.847516i 0.321903π0.321903\pi
542542 7.91304 + 10.8914i 0.339894 + 0.467824i
543543 −17.1265 + 5.56474i −0.734969 + 0.238806i
544544 −0.391388 −0.0167806
545545 −11.7604 + 9.14003i −0.503760 + 0.391516i
546546 −2.19925 1.59785i −0.0941191 0.0683815i
547547 14.1673 4.60325i 0.605752 0.196821i 0.00994761 0.999951i 0.496834π-0.496834\pi
0.595804 + 0.803130i 0.296834π0.296834\pi
548548 −1.42062 0.461588i −0.0606859 0.0197181i
549549 −13.3788 −0.570995
550550 −18.2303 16.5745i −0.777341 0.706739i
551551 −12.6703 −0.539773
552552 −2.15543 0.700341i −0.0917411 0.0298085i
553553 −3.46983 + 1.12742i −0.147552 + 0.0479427i
554554 22.3308 + 16.2243i 0.948747 + 0.689305i
555555 2.19286 7.57446i 0.0930817 0.321518i
556556 1.29185 0.0547869
557557 15.3542 4.98887i 0.650577 0.211385i 0.0349082 0.999391i 0.488886π-0.488886\pi
0.615668 + 0.788005i 0.288886π0.288886\pi
558558 −3.12824 4.30565i −0.132429 0.182273i
559559 −13.2245 + 9.60816i −0.559337 + 0.406382i
560560 −0.360146 11.1266i −0.0152189 0.470184i
561561 0.980515 + 0.521001i 0.0413974 + 0.0219967i
562562 36.1367 + 11.7415i 1.52433 + 0.495286i
563563 −5.59789 7.70483i −0.235923 0.324720i 0.674596 0.738187i 0.264318π-0.264318\pi
−0.910519 + 0.413467i 0.864318π0.864318\pi
564564 2.80544 0.118130
565565 12.9127 4.66258i 0.543241 0.196156i
566566 5.53782 + 17.0437i 0.232772 + 0.716399i
567567 1.13876i 0.0478235i
568568 24.5900 7.98979i 1.03178 0.335244i
569569 −14.6199 + 10.6220i −0.612899 + 0.445297i −0.850434 0.526082i 0.823661π-0.823661\pi
0.237535 + 0.971379i 0.423661π0.423661\pi
570570 7.75753 0.251096i 0.324927 0.0105172i
571571 −4.25376 + 3.09053i −0.178014 + 0.129335i −0.673224 0.739438i 0.735091π-0.735091\pi
0.495210 + 0.868773i 0.335091π0.335091\pi
572572 0.768242 + 0.795098i 0.0321218 + 0.0332447i
573573 −9.18239 + 2.98354i −0.383600 + 0.124639i
574574 5.29365 + 3.84606i 0.220953 + 0.160531i
575575 −2.71831 3.27331i −0.113361 0.136506i
576576 2.16523 + 6.66389i 0.0902179 + 0.277662i
577577 −4.56807 + 6.28741i −0.190171 + 0.261748i −0.893447 0.449169i 0.851720π-0.851720\pi
0.703275 + 0.710918i 0.251720π0.251720\pi
578578 −23.8633 7.75366i −0.992583 0.322510i
579579 −18.5831 13.5014i −0.772289 0.561101i
580580 −0.699693 + 2.41684i −0.0290532 + 0.100354i
581581 −2.69492 8.29411i −0.111804 0.344098i
582582 12.8501i 0.532652i
583583 −17.2388 17.8414i −0.713958 0.738916i
584584 −13.1839 + 40.5757i −0.545552 + 1.67904i
585585 2.20466 + 2.83671i 0.0911513 + 0.117284i
586586 18.4781 0.763323
587587 7.22521i 0.298216i −0.988821 0.149108i 0.952360π-0.952360\pi
0.988821 0.149108i 0.0476403π-0.0476403\pi
588588 −1.12538 + 0.365657i −0.0464097 + 0.0150794i
589589 −6.77031 4.91892i −0.278966 0.202680i
590590 −3.26919 4.20644i −0.134590 0.173176i
591591 −0.297229 0.215950i −0.0122264 0.00888298i
592592 −14.6630 + 4.76428i −0.602644 + 0.195811i
593593 15.1769i 0.623239i −0.950207 0.311619i 0.899129π-0.899129\pi
0.950207 0.311619i 0.100871π-0.100871\pi
594594 −0.854344 + 4.85308i −0.0350542 + 0.199124i
595595 −0.237060 + 0.818842i −0.00971853 + 0.0335693i
596596 −2.45386 −0.100514
597597 −21.6056 + 7.02008i −0.884258 + 0.287313i
598598 1.19403 + 1.64344i 0.0488276 + 0.0672054i
599599 16.6965 12.1307i 0.682199 0.495647i −0.191887 0.981417i 0.561461π-0.561461\pi
0.874087 + 0.485770i 0.161461π0.161461\pi
600600 −3.28735 + 12.9041i −0.134205 + 0.526809i
601601 −3.85300 11.8583i −0.157167 0.483711i 0.841207 0.540714i 0.181846π-0.181846\pi
−0.998374 + 0.0570024i 0.981846π0.981846\pi
602602 17.2135i 0.701568i
603603 8.20631i 0.334187i
604604 0.304816 0.221462i 0.0124028 0.00901115i
605605 14.4973 19.8703i 0.589399 0.807842i
606606 −7.67105 5.57334i −0.311615 0.226401i
607607 −12.1196 + 16.6813i −0.491921 + 0.677072i −0.980741 0.195313i 0.937428π-0.937428\pi
0.488820 + 0.872385i 0.337428π0.337428\pi
608608 −1.60540 2.20965i −0.0651077 0.0896130i
609609 6.17594 0.250262
610610 1.43794 + 44.4247i 0.0582205 + 1.79870i
611611 17.5761 + 12.7698i 0.711052 + 0.516609i
612612 0.0694593i 0.00280773i
613613 −21.4925 + 29.5818i −0.868073 + 1.19480i 0.111511 + 0.993763i 0.464431π0.464431\pi
−0.979584 + 0.201036i 0.935569π0.935569\pi
614614 −6.76168 + 20.8103i −0.272879 + 0.839835i
615615 −5.30667 6.82804i −0.213985 0.275333i
616616 9.96043 1.40266i 0.401317 0.0565147i
617617 −21.5935 + 29.7209i −0.869323 + 1.19652i 0.109942 + 0.993938i 0.464933π0.464933\pi
−0.979265 + 0.202582i 0.935067π0.935067\pi
618618 −5.16850 + 7.11383i −0.207908 + 0.286160i
619619 −5.48353 + 3.98402i −0.220402 + 0.160131i −0.692507 0.721411i 0.743494π-0.743494\pi
0.472106 + 0.881542i 0.343494π0.343494\pi
620620 −1.31215 + 1.01979i −0.0526974 + 0.0409557i
621621 −0.262964 + 0.809321i −0.0105524 + 0.0324769i
622622 −20.7596 6.74520i −0.832384 0.270458i
623623 −1.38980 1.91290i −0.0556812 0.0766387i
624624 2.17064 6.68055i 0.0868952 0.267436i
625625 −18.1597 + 17.1821i −0.726387 + 0.687286i
626626 −28.6526 −1.14519
627627 1.08050 + 7.67273i 0.0431508 + 0.306419i
628628 0.402619 + 0.554157i 0.0160662 + 0.0221133i
629629 1.18060 0.0470737
630630 −3.78128 + 0.122393i −0.150650 + 0.00487624i
631631 −11.1154 + 34.2096i −0.442496 + 1.36186i 0.442710 + 0.896665i 0.354017π0.354017\pi
−0.885206 + 0.465199i 0.845983π0.845983\pi
632632 −5.01534 6.90302i −0.199500 0.274588i
633633 2.36872i 0.0941480i
634634 −41.7077 −1.65642
635635 −29.9609 + 10.8185i −1.18896 + 0.429317i
636636 0.479588 1.47602i 0.0190169 0.0585280i
637637 −8.71488 2.83163i −0.345296 0.112193i
638638 −26.3201 4.63343i −1.04202 0.183439i
639639 −3.00001 9.23308i −0.118679 0.365255i
640640 26.8124 9.68157i 1.05985 0.382698i
641641 −36.6321 26.6148i −1.44688 1.05122i −0.986547 0.163476i 0.947729π-0.947729\pi
−0.460335 0.887745i 0.652271π-0.652271\pi
642642 −17.3886 5.64991i −0.686274 0.222984i
643643 17.8552 + 24.5756i 0.704140 + 0.969166i 0.999903 + 0.0139045i 0.00442609π0.00442609\pi
−0.295763 + 0.955261i 0.595574π0.595574\pi
644644 −0.201057 −0.00792275
645645 −6.32635 + 21.8522i −0.249100 + 0.860428i
646646 0.359093 + 1.10518i 0.0141283 + 0.0434825i
647647 0.461196i 0.0181315i 0.999959 + 0.00906574i 0.00288576π0.00288576\pi
−0.999959 + 0.00906574i 0.997114π0.997114\pi
648648 2.53291 0.822991i 0.0995019 0.0323301i
649649 3.82473 3.69554i 0.150134 0.145063i
650650 9.18239 7.62548i 0.360163 0.299096i
651651 3.30008 + 2.39765i 0.129340 + 0.0939712i
652652 0.121241i 0.00474818i
653653 −4.74471 + 6.53053i −0.185675 + 0.255560i −0.891700 0.452628i 0.850487π-0.850487\pi
0.706025 + 0.708187i 0.250487π0.250487\pi
654654 3.05824 9.41231i 0.119587 0.368050i
655655 −6.65476 18.4299i −0.260023 0.720115i
656656 −5.22480 + 16.0803i −0.203994 + 0.627829i
657657 15.2354 + 4.95028i 0.594389 + 0.193129i
658658 −21.7579 + 7.06957i −0.848212 + 0.275601i
659659 −1.70781 + 5.25610i −0.0665269 + 0.204749i −0.978794 0.204847i 0.934330π-0.934330\pi
0.912267 + 0.409596i 0.134330π0.134330\pi
660660 1.52323 + 0.217608i 0.0592917 + 0.00847039i
661661 4.67077 + 14.3752i 0.181672 + 0.559129i 0.999875 0.0158003i 0.00502959π-0.00502959\pi
−0.818203 + 0.574929i 0.805030π0.805030\pi
662662 −8.76231 12.0603i −0.340557 0.468736i
663663 −0.316164 + 0.435163i −0.0122788 + 0.0169003i
664664 16.5006 11.9884i 0.640349 0.465241i
665665 −5.59530 + 2.02038i −0.216976 + 0.0783469i
666666 1.61910 + 4.98309i 0.0627390 + 0.193091i
667667 −4.38925 1.42615i −0.169952 0.0552209i
668668 −1.27801 0.415251i −0.0494478 0.0160666i
669669 5.31373 + 16.3540i 0.205441 + 0.632281i
670670 −27.2492 + 0.882003i −1.05273 + 0.0340747i
671671 −43.9391 + 6.18763i −1.69625 + 0.238871i
672672 0.782528 + 1.07706i 0.0301867 + 0.0415484i
673673 −36.5783 11.8850i −1.40999 0.458133i −0.497582 0.867417i 0.665779π-0.665779\pi
−0.912407 + 0.409284i 0.865779π0.865779\pi
674674 −3.90715 + 12.0250i −0.150498 + 0.463184i
675675 4.84525 + 1.23433i 0.186494 + 0.0475096i
676676 1.74878 1.27056i 0.0672607 0.0488678i
677677 7.19047 9.89683i 0.276352 0.380366i −0.648169 0.761496i 0.724465π-0.724465\pi
0.924521 + 0.381130i 0.124465π0.124465\pi
678678 −5.36181 + 7.37989i −0.205919 + 0.283423i
679679 −3.04349 9.36691i −0.116799 0.359469i
680680 −1.99264 + 0.0644980i −0.0764144 + 0.00247338i
681681 10.9244 + 7.93701i 0.418622 + 0.304147i
682682 −12.2652 12.6939i −0.469658 0.486075i
683683 −5.82242 + 8.01388i −0.222789 + 0.306642i −0.905750 0.423812i 0.860692π-0.860692\pi
0.682961 + 0.730454i 0.260692π0.260692\pi
684684 −0.392145 + 0.284910i −0.0149940 + 0.0108938i
685685 −15.4635 4.47679i −0.590830 0.171049i
686686 17.3881 12.6332i 0.663882 0.482338i
687687 −25.2269 + 8.19673i −0.962468 + 0.312725i
688688 42.3023 13.7449i 1.61276 0.524018i
689689 9.72316 7.06429i 0.370423 0.269128i
690690 2.71563 + 0.786193i 0.103382 + 0.0299298i
691691 15.3657 11.1638i 0.584537 0.424691i −0.255820 0.966724i 0.582345π-0.582345\pi
0.840357 + 0.542033i 0.182345π0.182345\pi
692692 −1.20853 + 1.66340i −0.0459415 + 0.0632330i
693693 −0.526670 3.73995i −0.0200066 0.142069i
694694 13.3482 + 9.69803i 0.506691 + 0.368132i
695695 13.9155 0.450419i 0.527846 0.0170854i
696696 4.46339 + 13.7369i 0.169184 + 0.520696i
697697 0.761016 1.04745i 0.0288255 0.0396750i
698698 −28.9914 + 39.9033i −1.09734 + 1.51036i
699699 −9.56194 + 6.94716i −0.361666 + 0.262766i
700700 0.0763952 + 1.17887i 0.00288747 + 0.0445570i
701701 −8.29230 + 25.5211i −0.313196 + 0.963918i 0.663295 + 0.748358i 0.269158π0.269158\pi
−0.976491 + 0.215560i 0.930842π0.930842\pi
702702 −2.27033 0.737676i −0.0856882 0.0278418i
703703 4.84262 + 6.66530i 0.182643 + 0.251386i
704704 10.1931 + 20.8843i 0.384167 + 0.787106i
705705 30.2195 0.978145i 1.13813 0.0368391i
706706 8.13116 + 25.0252i 0.306020 + 0.941834i
707707 6.91176 + 2.24577i 0.259943 + 0.0844607i
708708 0.316420 + 0.102811i 0.0118918 + 0.00386388i
709709 −5.26535 16.2051i −0.197744 0.608594i −0.999934 0.0115245i 0.996332π-0.996332\pi
0.802189 0.597070i 0.203668π-0.203668\pi
710710 −30.3362 + 10.9539i −1.13850 + 0.411094i
711711 −2.59195 + 1.88316i −0.0972057 + 0.0706241i
712712 3.25037 4.47375i 0.121813 0.167661i
713713 −1.79170 2.46607i −0.0670998 0.0923550i
714714 −0.175034 0.538700i −0.00655049 0.0201603i
715715 8.55253 + 8.29674i 0.319847 + 0.310280i
716716 −1.39939 + 4.30689i −0.0522978 + 0.160956i
717717 −3.10030 + 1.00735i −0.115783 + 0.0376201i
718718 7.95832 + 2.58582i 0.297002 + 0.0965018i
719719 7.13894 21.9714i 0.266238 0.819395i −0.725168 0.688572i 0.758238π-0.758238\pi
0.991406 0.130823i 0.0417621π-0.0417621\pi
720720 −3.32011 9.19482i −0.123733 0.342671i
721721 2.08264 6.40970i 0.0775614 0.238710i
722722 11.8263 16.2775i 0.440129 0.605786i
723723 24.1229i 0.897141i
724724 −3.02268 2.19610i −0.112337 0.0816175i
725725 −6.69426 + 26.2776i −0.248619 + 0.975926i
726726 −0.561339 + 16.3337i −0.0208332 + 0.606200i
727727 11.2608 3.65885i 0.417639 0.135699i −0.0926568 0.995698i 0.529536π-0.529536\pi
0.510296 + 0.859999i 0.329536π0.329536\pi
728728 4.87283i 0.180599i
729729 −0.309017 0.951057i −0.0114451 0.0352243i
730730 14.8000 51.1215i 0.547773 1.89209i
731731 −3.40601 −0.125976
732732 −1.63158 2.24568i −0.0603050 0.0830027i
733733 −35.9672 11.6864i −1.32848 0.431649i −0.443080 0.896482i 0.646114π-0.646114\pi
−0.885398 + 0.464833i 0.846114π0.846114\pi
734734 −2.22441 1.61613i −0.0821046 0.0596525i
735735 −11.9948 + 4.33114i −0.442434 + 0.159756i
736736 −0.307429 0.946168i −0.0113320 0.0348762i
737737 −3.79536 26.9513i −0.139804 0.992764i
738738 5.46475 + 1.77561i 0.201160 + 0.0653609i
739739 9.71365 29.8955i 0.357322 1.09973i −0.597328 0.801997i 0.703771π-0.703771\pi
0.954651 0.297729i 0.0962290π-0.0962290\pi
740740 1.53882 0.555645i 0.0565682 0.0204259i
741741 −3.75364 −0.137893
742742 12.6560i 0.464616i
743743 29.6786 + 40.8491i 1.08880 + 1.49861i 0.849447 + 0.527675i 0.176936π0.176936\pi
0.239355 + 0.970932i 0.423064π0.423064\pi
744744 −2.94801 + 9.07303i −0.108079 + 0.332633i
745745 −26.4323 + 0.855562i −0.968405 + 0.0313454i
746746 −21.0837 −0.771931
747747 −4.50141 6.19567i −0.164698 0.226688i
748748 0.0321245 + 0.228120i 0.00117459 + 0.00834088i
749749 14.0134 0.512039
750750 3.57787 16.2214i 0.130645 0.592321i
751751 8.65908 26.6499i 0.315974 0.972469i −0.659377 0.751812i 0.729180π-0.729180\pi
0.975352 0.220657i 0.0708201π-0.0708201\pi
752752 −34.7471 47.8253i −1.26710 1.74401i
753753 −13.8976 4.51562i −0.506458 0.164558i
754754 4.00069 12.3129i 0.145697 0.448408i
755755 3.20619 2.49181i 0.116685 0.0906862i
756756 0.191145 0.138875i 0.00695187 0.00505083i
757757 5.16566 7.10993i 0.187749 0.258415i −0.704758 0.709448i 0.748944π-0.748944\pi
0.892507 + 0.451033i 0.148944π0.148944\pi
758758 9.94475 13.6878i 0.361210 0.497162i
759759 −0.489327 + 2.77961i −0.0177614 + 0.100893i
760760 −8.53761 10.9853i −0.309691 0.398477i
761761 13.2757 40.8585i 0.481245 1.48112i −0.356101 0.934448i 0.615894π-0.615894\pi
0.837346 0.546673i 0.184106π-0.184106\pi
762762 12.4409 17.1234i 0.450684 0.620314i
763763 7.58534i 0.274608i
764764 −1.62061 1.17744i −0.0586316 0.0425983i
765765 0.0242177 + 0.748199i 0.000875593 + 0.0270512i
766766 20.9612 0.757360
767767 1.51440 + 2.08439i 0.0546817 + 0.0752629i
768768 −2.89645 + 3.98662i −0.104517 + 0.143855i
769769 22.8608 + 16.6093i 0.824381 + 0.598948i 0.917964 0.396664i 0.129832π-0.129832\pi
−0.0935829 + 0.995611i 0.529832π0.529832\pi
770770 −12.3620 + 2.15078i −0.445494 + 0.0775088i
771771 0.954421 0.693427i 0.0343726 0.0249732i
772772 4.76577i 0.171524i
773773 40.9479i 1.47279i 0.676551 + 0.736396i 0.263474π0.263474\pi
−0.676551 + 0.736396i 0.736526π0.736526\pi
774774 −4.67108 14.3761i −0.167898 0.516738i
775775 −13.7786 + 11.4424i −0.494943 + 0.411024i
776776 18.6349 13.5391i 0.668954 0.486024i
777777 −2.36046 3.24889i −0.0846810 0.116553i
778778 −21.0721 + 6.84675i −0.755472 + 0.245468i
779779 9.03511 0.323716
780780 −0.207287 + 0.716001i −0.00742208 + 0.0256370i
781781 −14.1229 28.9360i −0.505358 1.03541i
782782 0.423274i 0.0151363i
783783 5.15794 1.67592i 0.184330 0.0598923i
784784 20.1720 + 14.6558i 0.720428 + 0.523422i
785785 4.53012 + 5.82886i 0.161687 + 0.208041i
786786 10.5331 + 7.65274i 0.375703 + 0.272964i
787787 −6.49565 + 2.11056i −0.231545 + 0.0752335i −0.422491 0.906367i 0.638844π-0.638844\pi
0.190946 + 0.981600i 0.438844π0.438844\pi
788788 0.0762263i 0.00271545i
789789 17.3212 0.616652
790790 6.53165 + 8.40422i 0.232386 + 0.299009i
791791 2.16053 6.64942i 0.0768195 0.236426i
792792 7.93799 3.87434i 0.282064 0.137669i
793793 21.4958i 0.763338i
794794 −4.03572 12.4207i −0.143222 0.440793i
795795 4.65137 16.0665i 0.164967 0.569821i
796796 −3.81319 2.77045i −0.135155 0.0981959i
797797 27.2448 + 8.85238i 0.965061 + 0.313567i 0.748821 0.662773i 0.230620π-0.230620\pi
0.216241 + 0.976340i 0.430620π0.430620\pi
798798 2.32337 3.19784i 0.0822463 0.113202i
799799 1.39885 + 4.30522i 0.0494877 + 0.152308i
800800 −5.43090 + 2.16208i −0.192011 + 0.0764409i
801801 −1.67980 1.22045i −0.0593529 0.0431224i
802802 −25.1229 + 8.16292i −0.887120 + 0.288243i
803803 52.3259 + 9.21154i 1.84654 + 0.325068i
804804 1.37745 1.00078i 0.0485790 0.0352947i
805805 −2.16573 + 0.0701006i −0.0763321 + 0.00247072i
806806 6.91790 5.02615i 0.243672 0.177038i
807807 −19.4735 + 6.32733i −0.685501 + 0.222733i
808808 16.9966i 0.597937i
809809 8.37642 + 25.7800i 0.294499 + 0.906375i 0.983389 + 0.181509i 0.0580983π0.0580983\pi
−0.688890 + 0.724866i 0.741902π0.741902\pi
810810 −3.12479 + 1.12831i −0.109794 + 0.0396449i
811811 40.6518 1.42748 0.713739 0.700411i 0.247000π-0.247000\pi
0.713739 + 0.700411i 0.247000π0.247000\pi
812812 0.753170 + 1.03665i 0.0264311 + 0.0363793i
813813 −8.61753 2.80001i −0.302230 0.0982005i
814814 7.62214 + 15.6167i 0.267156 + 0.547366i
815815 −0.0422721 1.30598i −0.00148073 0.0457465i
816816 1.18410 0.860298i 0.0414518 0.0301165i
817817 −13.9709 19.2292i −0.488778 0.672745i
818818 −15.1109 + 4.90984i −0.528342 + 0.171669i
819819 1.82965 0.0639332
820820 0.498946 1.72343i 0.0174240 0.0601850i
821821 −15.0989 10.9700i −0.526955 0.382855i 0.292263 0.956338i 0.405592π-0.405592\pi
−0.819218 + 0.573483i 0.805592π0.805592\pi
822822 10.1731 3.30545i 0.354829 0.115291i
823823 −8.86937 2.88183i −0.309167 0.100454i 0.150324 0.988637i 0.451968π-0.451968\pi
−0.459491 + 0.888182i 0.651968π0.651968\pi
824824 15.7620 0.549094
825825 16.4837 + 1.81293i 0.573890 + 0.0631182i
826826 −2.71311 −0.0944013
827827 27.1453 + 8.82004i 0.943934 + 0.306703i 0.740249 0.672333i 0.234708π-0.234708\pi
0.203686 + 0.979036i 0.434708π0.434708\pi
828828 −0.167916 + 0.0545592i −0.00583548 + 0.00189606i
829829 19.3361 + 14.0485i 0.671570 + 0.487924i 0.870551 0.492079i 0.163763π-0.163763\pi
−0.198980 + 0.980004i 0.563763π0.563763\pi
830830 −20.0890 + 15.6129i −0.697300 + 0.541933i
831831 −18.5780 −0.644464
832832 −10.7069 + 3.47888i −0.371194 + 0.120608i
833833 −1.12227 1.54467i −0.0388844 0.0535198i
834834 −7.48425 + 5.43762i −0.259158 + 0.188290i
835835 −13.9112 4.02739i −0.481417 0.139374i
836836 −1.15612 + 1.11707i −0.0399853 + 0.0386347i
837837 3.40675 + 1.10692i 0.117754 + 0.0382607i
838838 −8.35019 11.4931i −0.288453 0.397021i
839839 −24.9313 −0.860722 −0.430361 0.902657i 0.641614π-0.641614\pi
−0.430361 + 0.902657i 0.641614π0.641614\pi
840840 4.16152 + 5.35459i 0.143586 + 0.184751i
841841 0.127628 + 0.392800i 0.00440098 + 0.0135448i
842842 36.9797i 1.27440i
843843 −24.3220 + 7.90271i −0.837696 + 0.272184i
844844 0.397596 0.288870i 0.0136858 0.00994333i
845845 18.3944 14.2959i 0.632787 0.491794i
846846 −16.2531 + 11.8085i −0.558792 + 0.405986i
847847 −3.45940 12.0392i −0.118866 0.413673i
848848 −31.1023 + 10.1057i −1.06806 + 0.347033i
849849 −9.75812 7.08969i −0.334898 0.243318i
850850 2.48180 0.160831i 0.0851252 0.00551645i
851851 0.927344 + 2.85407i 0.0317890 + 0.0978363i
852852 1.18394 1.62956i 0.0405612 0.0558277i
853853 −3.66268 1.19008i −0.125408 0.0407475i 0.245641 0.969361i 0.421002π-0.421002\pi
−0.371049 + 0.928613i 0.621002π0.621002\pi
854854 18.3129 + 13.3051i 0.626655 + 0.455292i
855855 −4.12475 + 3.20570i −0.141063 + 0.109633i
856856 10.1276 + 31.1695i 0.346154 + 1.06535i
857857 46.7797i 1.59797i −0.601354 0.798983i 0.705372π-0.705372\pi
0.601354 0.798983i 0.294628π-0.294628\pi
858858 −7.79744 1.37268i −0.266200 0.0468624i
859859 17.2747 53.1662i 0.589407 1.81401i 0.00860323 0.999963i 0.497261π-0.497261\pi
0.580803 0.814044i 0.302739π-0.302739\pi
860860 −4.43946 + 1.60302i −0.151384 + 0.0546627i
861861 −4.40402 −0.150089
862862 6.06930i 0.206721i
863863 30.5781 9.93542i 1.04089 0.338206i 0.261803 0.965121i 0.415683π-0.415683\pi
0.779087 + 0.626916i 0.215683π0.215683\pi
864864 0.945813 + 0.687173i 0.0321772 + 0.0233781i
865865 −12.4380 + 18.3391i −0.422906 + 0.623548i
866866 34.0380 + 24.7301i 1.15666 + 0.840362i
867867 16.0614 5.21866i 0.545473 0.177235i
868868 0.846327i 0.0287262i
869869 −7.64158 + 7.38348i −0.259223 + 0.250467i
870870 −6.11928 16.9469i −0.207463 0.574554i
871871 13.1851 0.446759
872872 −16.8718 + 5.48197i −0.571350 + 0.185643i
873873 −5.08365 6.99704i −0.172055 0.236814i
874874 −2.38967 + 1.73620i −0.0808317 + 0.0587277i
875875 1.23393 + 12.6718i 0.0417146 + 0.428386i
876876 1.02707 + 3.16101i 0.0347016 + 0.106800i
877877 25.3900i 0.857359i −0.903457 0.428680i 0.858979π-0.858979\pi
0.903457 0.428680i 0.141021π-0.141021\pi
878878 36.9041i 1.24545i
879879 −10.0616 + 7.31017i −0.339369 + 0.246566i
880880 −15.1565 28.6623i −0.510927 0.966205i
881881 9.78071 + 7.10610i 0.329521 + 0.239411i 0.740227 0.672357i 0.234718π-0.234718\pi
−0.410707 + 0.911768i 0.634718π0.634718\pi
882882 4.98066 6.85529i 0.167708 0.230830i
883883 30.6203 + 42.1452i 1.03046 + 1.41830i 0.904605 + 0.426251i 0.140166π0.140166\pi
0.125851 + 0.992049i 0.459834π0.459834\pi
884884 −0.111600 −0.00375353
885885 3.44424 + 0.997132i 0.115777 + 0.0335182i
886886 23.7742 + 17.2730i 0.798711 + 0.580297i
887887 22.1114i 0.742428i −0.928547 0.371214i 0.878942π-0.878942\pi
0.928547 0.371214i 0.121058π-0.121058\pi
888888 5.52047 7.59827i 0.185255 0.254981i
889889 −5.01301 + 15.4285i −0.168131 + 0.517454i
890890 −3.87198 + 5.70899i −0.129789 + 0.191366i
891891 −1.45474 2.98056i −0.0487355 0.0998525i
892892 −2.09704 + 2.88633i −0.0702142 + 0.0966415i
893893 −18.5680 + 25.5567i −0.621355 + 0.855222i
894894 14.2162 10.3287i 0.475461 0.345442i
895895 −13.5723 + 46.8807i −0.453671 + 1.56705i
896896 4.48621 13.8071i 0.149874 0.461264i
897897 −1.30034 0.422505i −0.0434169 0.0141070i
898898 −11.2983 15.5508i −0.377030 0.518937i
899899 −6.00324 + 18.4761i −0.200219 + 0.616211i
900900 0.383702 + 0.963819i 0.0127901 + 0.0321273i
901901 2.50423 0.0834280
902902 18.7686 + 3.30407i 0.624928 + 0.110013i
903903 6.80987 + 9.37298i 0.226618 + 0.311913i
904904 16.3515 0.543842
905905 −33.3252 22.6020i −1.10777 0.751315i
906906 −0.833757 + 2.56604i −0.0276997 + 0.0852509i
907907 17.6290 + 24.2643i 0.585362 + 0.805681i 0.994270 0.106894i 0.0340905π-0.0340905\pi
−0.408909 + 0.912575i 0.634091π0.634091\pi
908908 2.80162i 0.0929751i
909909 6.38188 0.211674
910910 −0.196648 6.07539i −0.00651883 0.201397i
911911 −13.9466 + 42.9234i −0.462073 + 1.42211i 0.400554 + 0.916273i 0.368818π0.368818\pi
−0.862627 + 0.505841i 0.831182π0.831182\pi
912912 9.71393 + 3.15625i 0.321660 + 0.104514i
913913 −17.6491 18.2661i −0.584100 0.604518i
914914 17.4903 + 53.8297i 0.578529 + 1.78053i
915915 −18.3580 23.6210i −0.606895 0.780887i
916916 −4.45233 3.23481i −0.147109 0.106881i
917917 −9.49052 3.08366i −0.313405 0.101831i
918918 −0.292365 0.402407i −0.00964950 0.0132814i
919919 19.0384 0.628019 0.314009 0.949420i 0.398328π-0.398328\pi
0.314009 + 0.949420i 0.398328π0.398328\pi
920920 −1.72111 4.76650i −0.0567434 0.157147i
921921 −4.55099 14.0065i −0.149960 0.461530i
922922 15.5147i 0.510948i
923923 14.8348 4.82012i 0.488293 0.158656i
924924 0.563533 0.544499i 0.0185389 0.0179127i
925925 16.3821 6.52180i 0.538639 0.214435i
926926 16.5207 + 12.0030i 0.542905 + 0.394444i
927927 5.91831i 0.194383i
928928 −3.72680 + 5.12950i −0.122338 + 0.168384i
929929 4.79898 14.7697i 0.157449 0.484579i −0.840951 0.541111i 0.818004π-0.818004\pi
0.998401 + 0.0565312i 0.0180041π0.0180041\pi
930930 3.30939 11.4311i 0.108519 0.374841i
931931 4.11737 12.6720i 0.134941 0.415307i
932932 −2.33220 0.757779i −0.0763938 0.0248219i
933933 13.9724 4.53990i 0.457436 0.148630i
934934 9.00526 27.7153i 0.294661 0.906873i
935935 0.425573 + 2.44605i 0.0139177 + 0.0799943i
936936 1.32230 + 4.06962i 0.0432207 + 0.133020i
937937 −5.34348 7.35467i −0.174564 0.240267i 0.712766 0.701402i 0.247442π-0.247442\pi
−0.887330 + 0.461135i 0.847442π0.847442\pi
938938 −8.16109 + 11.2328i −0.266469 + 0.366763i
939939 15.6018 11.3353i 0.509144 0.369915i
940940 3.84952 + 4.95314i 0.125558 + 0.161554i
941941 −0.860081 2.64706i −0.0280378 0.0862916i 0.936058 0.351845i 0.114445π-0.114445\pi
−0.964096 + 0.265553i 0.914445π0.914445\pi
942942 −4.66507 1.51577i −0.151996 0.0493866i
943943 3.12994 + 1.01698i 0.101925 + 0.0331174i
944944 −2.16641 6.66751i −0.0705105 0.217009i
945945 2.01054 1.56257i 0.0654030 0.0508304i
946946 −21.9897 45.0539i −0.714947 1.46483i
947947 16.7615 + 23.0702i 0.544674 + 0.749679i 0.989278 0.146048i 0.0466554π-0.0466554\pi
−0.444603 + 0.895727i 0.646655π0.646655\pi
948948 −0.632189 0.205411i −0.0205325 0.00667142i
949949 −7.95362 + 24.4787i −0.258185 + 0.794613i
950950 11.0879 + 13.3518i 0.359740 + 0.433188i
951951 22.7104 16.5001i 0.736437 0.535053i
952952 −0.596793 + 0.821416i −0.0193422 + 0.0266222i
953953 −8.53054 + 11.7413i −0.276331 + 0.380338i −0.924514 0.381147i 0.875529π-0.875529\pi
0.648183 + 0.761485i 0.275529π0.275529\pi
954954 3.43436 + 10.5699i 0.111191 + 0.342212i
955955 −17.8673 12.1181i −0.578173 0.392131i
956956 −0.547176 0.397546i −0.0176969 0.0128576i
957957 16.1647 7.88959i 0.522531 0.255034i
958958 −23.4895 + 32.3305i −0.758911 + 1.04455i
959959 −6.63272 + 4.81895i −0.214182 + 0.155612i
960960 −8.79439 + 12.9668i −0.283838 + 0.418501i
961961 14.6989 10.6794i 0.474157 0.344496i
962962 −8.00633 + 2.60142i −0.258135 + 0.0838730i
963963 11.7035 3.80271i 0.377141 0.122541i
964964 −4.04910 + 2.94185i −0.130413 + 0.0947505i
965965 −1.66163 51.3357i −0.0534899 1.65255i
966966 1.16481 0.846281i 0.0374770 0.0272286i
967967 18.8965 26.0088i 0.607670 0.836386i −0.388714 0.921359i 0.627080π-0.627080\pi
0.996383 + 0.0849731i 0.0270804π0.0270804\pi
968968 24.2783 16.3954i 0.780333 0.526969i
969969 −0.632753 0.459722i −0.0203270 0.0147684i
970970 −22.6874 + 17.6324i −0.728449 + 0.566142i
971971 −16.7009 51.4001i −0.535958 1.64951i −0.741570 0.670876i 0.765918π-0.765918\pi
0.205612 0.978634i 0.434082π-0.434082\pi
972972 0.121952 0.167853i 0.00391162 0.00538389i
973973 4.16768 5.73632i 0.133610 0.183898i
974974 21.7233 15.7829i 0.696059 0.505716i
975975 −1.98321 + 7.78486i −0.0635134 + 0.249315i
976976 −18.0747 + 55.6283i −0.578558 + 1.78062i
977977 54.9031 + 17.8391i 1.75651 + 0.570723i 0.996829 0.0795765i 0.0253568π-0.0253568\pi
0.759677 + 0.650300i 0.225357π0.225357\pi
978978 0.510324 + 0.702401i 0.0163184 + 0.0224603i
979979 −6.08129 3.23132i −0.194359 0.103274i
980980 −2.18979 1.48517i −0.0699501 0.0474419i
981981 2.05837 + 6.33502i 0.0657188 + 0.202262i
982982 −34.5787 11.2353i −1.10345 0.358533i
983983 −6.65373 2.16193i −0.212221 0.0689548i 0.200977 0.979596i 0.435588π-0.435588\pi
−0.413198 + 0.910641i 0.635588π0.635588\pi
984984 −3.18281 9.79569i −0.101464 0.312275i
985985 −0.0265771 0.821091i −0.000846817 0.0261621i
986986 2.18240 1.58561i 0.0695019 0.0504961i
987987 9.05068 12.4572i 0.288086 0.396517i
988988 −0.457765 0.630059i −0.0145634 0.0200449i
989989 −2.67537 8.23393i −0.0850717 0.261824i
990990 −9.74065 + 5.15083i −0.309578 + 0.163704i
991991 −7.38517 + 22.7292i −0.234598 + 0.722018i 0.762577 + 0.646898i 0.223934π0.223934\pi
−0.997175 + 0.0751198i 0.976066π0.976066\pi
992992 −3.98279 + 1.29409i −0.126454 + 0.0410873i
993993 9.54241 + 3.10052i 0.302819 + 0.0983920i
994994 −5.07579 + 15.6217i −0.160994 + 0.495490i
995995 −42.0407 28.5131i −1.33278 0.903925i
996996 0.491003 1.51115i 0.0155580 0.0478827i
997997 −5.40154 + 7.43458i −0.171068 + 0.235455i −0.885940 0.463801i 0.846485π-0.846485\pi
0.714871 + 0.699256i 0.246485π0.246485\pi
998998 46.9866i 1.48733i
999999 −2.85300 2.07283i −0.0902650 0.0655813i
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 825.2.cb.a.169.16 yes 240
11.3 even 5 825.2.by.a.619.16 yes 240
25.4 even 10 825.2.by.a.4.16 240
275.179 even 10 inner 825.2.cb.a.454.16 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.by.a.4.16 240 25.4 even 10
825.2.by.a.619.16 yes 240 11.3 even 5
825.2.cb.a.169.16 yes 240 1.1 even 1 trivial
825.2.cb.a.454.16 yes 240 275.179 even 10 inner