Properties

Label 325.2.x.b.93.5
Level 325325
Weight 22
Character 325.93
Analytic conductor 2.5952.595
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [325,2,Mod(7,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 325.x (of order 1212, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.595138065692.59513806569
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6++1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 93.5
Root 2.64975i-2.64975i of defining polynomial
Character χ\chi == 325.93
Dual form 325.2.x.b.7.5

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(2.294751.32488i)q2+(0.335680+1.25278i)q3+(2.510604.34849i)q4+(0.889471+3.31955i)q6+(0.0561740+0.0972962i)q78.00544iq8+(1.14131+0.658935i)q9+(0.4795641.78976i)q11+(4.60492+4.60492i)q12+(2.96279+2.05471i)q13+0.297695iq14+(5.585029.67354i)q16+(2.636690.706500i)q17+3.49203q18+(6.72284+1.80138i)q19+(0.1030340.103034i)q21+(1.270734.74241i)q22+(3.10327+0.831519i)q23+(10.0290+2.68727i)q24+(4.07664+8.64040i)q26+(3.95990+3.95990i)q27+(0.282061+0.488544i)q28+(4.03134+2.32749i)q29+(0.624367+0.624367i)q31+(11.76676.79350i)q32+(2.08118+1.20157i)q33+(5.114545.11454i)q34+(5.730743.30864i)q36+(0.737435+1.27728i)q37+(13.0407+13.0407i)q38+(1.579554.40145i)q39+(5.240691.40424i)q41+(0.3729450.0999302i)q42+(1.008603.76415i)q43+(6.578746.57874i)q44+(8.222912.20332i)q46+0.345095q47+(13.99363.74956i)q48+(3.49369+6.05125i)q49+3.54034iq51+(1.49651+18.0422i)q52+(3.59144+3.59144i)q53+(3.84062+14.3334i)q54+(0.778898+0.449697i)q569.02691iq57+(6.16729+10.6821i)q58+(0.332494+1.24088i)q59+(1.391512.41016i)q61+(0.605559+2.25998i)q62+(0.128224+0.0740300i)q6313.6621q64+6.36774q66+(0.124992+0.0721643i)q67+(3.5474713.2394i)q68+(2.08342+3.60858i)q69+(1.416685.28713i)q71+(5.275069.13667i)q729.06221iq73+(3.38447+1.95402i)q74+(9.04509+33.7567i)q76+(0.147197+0.147197i)q77+(9.456058.00753i)q7815.1689iq79+(1.654802.86620i)q81+(13.8865+3.72089i)q828.53853q83+(0.706718+0.189365i)q84+(7.301527.30152i)q86+(1.562595.83166i)q87+(14.32783.83912i)q88+(0.549735+0.147301i)q89+(0.03348400.403690i)q91+(11.406911.4069i)q92+(0.5726040.991779i)q93+(0.7919080.457208i)q94+(12.460612.4606i)q96+(12.9596+7.48223i)q97+(16.0343+9.25742i)q98+(1.726661.72666i)q99+O(q100)q+(2.29475 - 1.32488i) q^{2} +(-0.335680 + 1.25278i) q^{3} +(2.51060 - 4.34849i) q^{4} +(0.889471 + 3.31955i) q^{6} +(-0.0561740 + 0.0972962i) q^{7} -8.00544i q^{8} +(1.14131 + 0.658935i) q^{9} +(0.479564 - 1.78976i) q^{11} +(4.60492 + 4.60492i) q^{12} +(-2.96279 + 2.05471i) q^{13} +0.297695i q^{14} +(-5.58502 - 9.67354i) q^{16} +(2.63669 - 0.706500i) q^{17} +3.49203 q^{18} +(-6.72284 + 1.80138i) q^{19} +(-0.103034 - 0.103034i) q^{21} +(-1.27073 - 4.74241i) q^{22} +(3.10327 + 0.831519i) q^{23} +(10.0290 + 2.68727i) q^{24} +(-4.07664 + 8.64040i) q^{26} +(-3.95990 + 3.95990i) q^{27} +(0.282061 + 0.488544i) q^{28} +(-4.03134 + 2.32749i) q^{29} +(-0.624367 + 0.624367i) q^{31} +(-11.7667 - 6.79350i) q^{32} +(2.08118 + 1.20157i) q^{33} +(5.11454 - 5.11454i) q^{34} +(5.73074 - 3.30864i) q^{36} +(0.737435 + 1.27728i) q^{37} +(-13.0407 + 13.0407i) q^{38} +(-1.57955 - 4.40145i) q^{39} +(-5.24069 - 1.40424i) q^{41} +(-0.372945 - 0.0999302i) q^{42} +(-1.00860 - 3.76415i) q^{43} +(-6.57874 - 6.57874i) q^{44} +(8.22291 - 2.20332i) q^{46} +0.345095 q^{47} +(13.9936 - 3.74956i) q^{48} +(3.49369 + 6.05125i) q^{49} +3.54034i q^{51} +(1.49651 + 18.0422i) q^{52} +(3.59144 + 3.59144i) q^{53} +(-3.84062 + 14.3334i) q^{54} +(0.778898 + 0.449697i) q^{56} -9.02691i q^{57} +(-6.16729 + 10.6821i) q^{58} +(0.332494 + 1.24088i) q^{59} +(1.39151 - 2.41016i) q^{61} +(-0.605559 + 2.25998i) q^{62} +(-0.128224 + 0.0740300i) q^{63} -13.6621 q^{64} +6.36774 q^{66} +(-0.124992 + 0.0721643i) q^{67} +(3.54747 - 13.2394i) q^{68} +(-2.08342 + 3.60858i) q^{69} +(-1.41668 - 5.28713i) q^{71} +(5.27506 - 9.13667i) q^{72} -9.06221i q^{73} +(3.38447 + 1.95402i) q^{74} +(-9.04509 + 33.7567i) q^{76} +(0.147197 + 0.147197i) q^{77} +(-9.45605 - 8.00753i) q^{78} -15.1689i q^{79} +(-1.65480 - 2.86620i) q^{81} +(-13.8865 + 3.72089i) q^{82} -8.53853 q^{83} +(-0.706718 + 0.189365i) q^{84} +(-7.30152 - 7.30152i) q^{86} +(-1.56259 - 5.83166i) q^{87} +(-14.3278 - 3.83912i) q^{88} +(0.549735 + 0.147301i) q^{89} +(-0.0334840 - 0.403690i) q^{91} +(11.4069 - 11.4069i) q^{92} +(-0.572604 - 0.991779i) q^{93} +(0.791908 - 0.457208i) q^{94} +(12.4606 - 12.4606i) q^{96} +(12.9596 + 7.48223i) q^{97} +(16.0343 + 9.25742i) q^{98} +(1.72666 - 1.72666i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+6q2+2q3+6q48q6+2q7+12q916q11+24q12+4q132q164q1720q19+4q2116q22+10q23+32q2424q264q27++60q99+O(q100) 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27}+ \cdots + 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/325Z)×\left(\mathbb{Z}/325\mathbb{Z}\right)^\times.

nn 2727 301301
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(112)e\left(\frac{1}{12}\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 2.29475 1.32488i 1.62264 0.936830i 0.636425 0.771338i 0.280412π-0.280412\pi
0.986211 0.165491i 0.0529210π-0.0529210\pi
33 −0.335680 + 1.25278i −0.193805 + 0.723291i 0.798768 + 0.601640i 0.205486π0.205486\pi
−0.992573 + 0.121651i 0.961181π0.961181\pi
44 2.51060 4.34849i 1.25530 2.17424i
55 0 0
66 0.889471 + 3.31955i 0.363125 + 1.35520i
77 −0.0561740 + 0.0972962i −0.0212318 + 0.0367745i −0.876446 0.481500i 0.840092π-0.840092\pi
0.855214 + 0.518275i 0.173425π0.173425\pi
88 8.00544i 2.83035i
99 1.14131 + 0.658935i 0.380436 + 0.219645i
1010 0 0
1111 0.479564 1.78976i 0.144594 0.539632i −0.855179 0.518332i 0.826553π-0.826553\pi
0.999773 0.0212994i 0.00678031π-0.00678031\pi
1212 4.60492 + 4.60492i 1.32933 + 1.32933i
1313 −2.96279 + 2.05471i −0.821731 + 0.569875i
1414 0.297695i 0.0795622i
1515 0 0
1616 −5.58502 9.67354i −1.39626 2.41838i
1717 2.63669 0.706500i 0.639492 0.171351i 0.0755186 0.997144i 0.475939π-0.475939\pi
0.563973 + 0.825793i 0.309272π0.309272\pi
1818 3.49203 0.823080
1919 −6.72284 + 1.80138i −1.54233 + 0.413265i −0.927016 0.375021i 0.877636π-0.877636\pi
−0.615309 + 0.788286i 0.710969π0.710969\pi
2020 0 0
2121 −0.103034 0.103034i −0.0224838 0.0224838i
2222 −1.27073 4.74241i −0.270920 1.01109i
2323 3.10327 + 0.831519i 0.647077 + 0.173384i 0.567407 0.823438i 0.307947π-0.307947\pi
0.0796701 + 0.996821i 0.474613π0.474613\pi
2424 10.0290 + 2.68727i 2.04717 + 0.548536i
2525 0 0
2626 −4.07664 + 8.64040i −0.799495 + 1.69452i
2727 −3.95990 + 3.95990i −0.762083 + 0.762083i
2828 0.282061 + 0.488544i 0.0533045 + 0.0923261i
2929 −4.03134 + 2.32749i −0.748601 + 0.432205i −0.825188 0.564858i 0.808931π-0.808931\pi
0.0765874 + 0.997063i 0.475598π0.475598\pi
3030 0 0
3131 −0.624367 + 0.624367i −0.112140 + 0.112140i −0.760950 0.648810i 0.775267π-0.775267\pi
0.648810 + 0.760950i 0.275267π0.275267\pi
3232 −11.7667 6.79350i −2.08008 1.20093i
3333 2.08118 + 1.20157i 0.362288 + 0.209167i
3434 5.11454 5.11454i 0.877136 0.877136i
3535 0 0
3636 5.73074 3.30864i 0.955123 0.551441i
3737 0.737435 + 1.27728i 0.121234 + 0.209983i 0.920254 0.391321i 0.127982π-0.127982\pi
−0.799021 + 0.601303i 0.794648π0.794648\pi
3838 −13.0407 + 13.0407i −2.11548 + 2.11548i
3939 −1.57955 4.40145i −0.252930 0.704795i
4040 0 0
4141 −5.24069 1.40424i −0.818458 0.219305i −0.174786 0.984606i 0.555923π-0.555923\pi
−0.643672 + 0.765301i 0.722590π0.722590\pi
4242 −0.372945 0.0999302i −0.0575466 0.0154196i
4343 −1.00860 3.76415i −0.153810 0.574027i −0.999204 0.0398840i 0.987301π-0.987301\pi
0.845394 0.534143i 0.179366π-0.179366\pi
4444 −6.57874 6.57874i −0.991782 0.991782i
4545 0 0
4646 8.22291 2.20332i 1.21240 0.324862i
4747 0.345095 0.0503372 0.0251686 0.999683i 0.491988π-0.491988\pi
0.0251686 + 0.999683i 0.491988π0.491988\pi
4848 13.9936 3.74956i 2.01980 0.541203i
4949 3.49369 + 6.05125i 0.499098 + 0.864464i
5050 0 0
5151 3.54034i 0.495747i
5252 1.49651 + 18.0422i 0.207528 + 2.50201i
5353 3.59144 + 3.59144i 0.493322 + 0.493322i 0.909351 0.416029i 0.136579π-0.136579\pi
−0.416029 + 0.909351i 0.636579π0.636579\pi
5454 −3.84062 + 14.3334i −0.522642 + 1.95053i
5555 0 0
5656 0.778898 + 0.449697i 0.104085 + 0.0600933i
5757 9.02691i 1.19564i
5858 −6.16729 + 10.6821i −0.809805 + 1.40262i
5959 0.332494 + 1.24088i 0.0432870 + 0.161549i 0.984186 0.177138i 0.0566839π-0.0566839\pi
−0.940899 + 0.338687i 0.890017π0.890017\pi
6060 0 0
6161 1.39151 2.41016i 0.178164 0.308589i −0.763088 0.646295i 0.776318π-0.776318\pi
0.941252 + 0.337706i 0.109651π0.109651\pi
6262 −0.605559 + 2.25998i −0.0769061 + 0.287017i
6363 −0.128224 + 0.0740300i −0.0161547 + 0.00932691i
6464 −13.6621 −1.70776
6565 0 0
6666 6.36774 0.783815
6767 −0.124992 + 0.0721643i −0.0152702 + 0.00881627i −0.507616 0.861584i 0.669473π-0.669473\pi
0.492345 + 0.870400i 0.336140π0.336140\pi
6868 3.54747 13.2394i 0.430194 1.60551i
6969 −2.08342 + 3.60858i −0.250814 + 0.434422i
7070 0 0
7171 −1.41668 5.28713i −0.168129 0.627467i −0.997620 0.0689472i 0.978036π-0.978036\pi
0.829491 0.558520i 0.188631π-0.188631\pi
7272 5.27506 9.13667i 0.621672 1.07677i
7373 9.06221i 1.06065i −0.847794 0.530326i 0.822070π-0.822070\pi
0.847794 0.530326i 0.177930π-0.177930\pi
7474 3.38447 + 1.95402i 0.393436 + 0.227151i
7575 0 0
7676 −9.04509 + 33.7567i −1.03754 + 3.87216i
7777 0.147197 + 0.147197i 0.0167747 + 0.0167747i
7878 −9.45605 8.00753i −1.07069 0.906675i
7979 15.1689i 1.70664i −0.521388 0.853320i 0.674586π-0.674586\pi
0.521388 0.853320i 0.325414π-0.325414\pi
8080 0 0
8181 −1.65480 2.86620i −0.183867 0.318467i
8282 −13.8865 + 3.72089i −1.53351 + 0.410903i
8383 −8.53853 −0.937226 −0.468613 0.883404i 0.655246π-0.655246\pi
−0.468613 + 0.883404i 0.655246π0.655246\pi
8484 −0.706718 + 0.189365i −0.0771093 + 0.0206614i
8585 0 0
8686 −7.30152 7.30152i −0.787343 0.787343i
8787 −1.56259 5.83166i −0.167527 0.625219i
8888 −14.3278 3.83912i −1.52735 0.409251i
8989 0.549735 + 0.147301i 0.0582718 + 0.0156139i 0.287837 0.957679i 0.407064π-0.407064\pi
−0.229565 + 0.973293i 0.573730π0.573730\pi
9090 0 0
9191 −0.0334840 0.403690i −0.00351007 0.0423182i
9292 11.4069 11.4069i 1.18925 1.18925i
9393 −0.572604 0.991779i −0.0593763 0.102843i
9494 0.791908 0.457208i 0.0816791 0.0471574i
9595 0 0
9696 12.4606 12.4606i 1.27175 1.27175i
9797 12.9596 + 7.48223i 1.31585 + 0.759705i 0.983058 0.183296i 0.0586766π-0.0586766\pi
0.332790 + 0.943001i 0.392010π0.392010\pi
9898 16.0343 + 9.25742i 1.61971 + 0.935140i
9999 1.72666 1.72666i 0.173536 0.173536i
100100 0 0
101101 7.19717 4.15529i 0.716146 0.413467i −0.0971867 0.995266i 0.530984π-0.530984\pi
0.813332 + 0.581799i 0.197651π0.197651\pi
102102 4.69052 + 8.12422i 0.464431 + 0.804418i
103103 7.72940 7.72940i 0.761600 0.761600i −0.215011 0.976612i 0.568979π-0.568979\pi
0.976612 + 0.215011i 0.0689789π0.0689789\pi
104104 16.4489 + 23.7185i 1.61295 + 2.32579i
105105 0 0
106106 12.9997 + 3.48325i 1.26264 + 0.338324i
107107 −7.15177 1.91631i −0.691388 0.185257i −0.104018 0.994575i 0.533170π-0.533170\pi
−0.587370 + 0.809318i 0.699837π0.699837\pi
108108 7.27785 + 27.1613i 0.700311 + 2.61360i
109109 3.34544 + 3.34544i 0.320435 + 0.320435i 0.848934 0.528499i 0.177245π-0.177245\pi
−0.528499 + 0.848934i 0.677245π0.677245\pi
110110 0 0
111111 −1.84768 + 0.495085i −0.175374 + 0.0469914i
112112 1.25493 0.118580
113113 5.90688 1.58274i 0.555672 0.148892i 0.0299550 0.999551i 0.490464π-0.490464\pi
0.525717 + 0.850659i 0.323797π0.323797\pi
114114 −11.9595 20.7145i −1.12011 1.94009i
115115 0 0
116116 23.3736i 2.17019i
117117 −4.73539 + 0.392775i −0.437787 + 0.0363121i
118118 2.40701 + 2.40701i 0.221583 + 0.221583i
119119 −0.0793738 + 0.296227i −0.00727618 + 0.0271551i
120120 0 0
121121 6.55303 + 3.78340i 0.595730 + 0.343945i
122122 7.37430i 0.667638i
123123 3.51839 6.09404i 0.317243 0.549481i
124124 1.14751 + 4.28258i 0.103050 + 0.384587i
125125 0 0
126126 −0.196161 + 0.339761i −0.0174754 + 0.0302684i
127127 3.01994 11.2706i 0.267976 1.00010i −0.692427 0.721488i 0.743459π-0.743459\pi
0.960403 0.278613i 0.0898747π-0.0898747\pi
128128 −7.81784 + 4.51363i −0.691006 + 0.398953i
129129 5.05420 0.444997
130130 0 0
131131 7.46380 0.652115 0.326058 0.945350i 0.394280π-0.394280\pi
0.326058 + 0.945350i 0.394280π0.394280\pi
132132 10.4500 6.03333i 0.909559 0.525134i
133133 0.202381 0.755298i 0.0175487 0.0654926i
134134 −0.191218 + 0.331199i −0.0165187 + 0.0286112i
135135 0 0
136136 −5.65584 21.1079i −0.484984 1.80998i
137137 −9.24213 + 16.0078i −0.789608 + 1.36764i 0.136599 + 0.990626i 0.456383π0.456383\pi
−0.926207 + 0.377015i 0.876950π0.876950\pi
138138 11.0411i 0.939879i
139139 −9.44862 5.45516i −0.801421 0.462701i 0.0425466 0.999094i 0.486453π-0.486453\pi
−0.843968 + 0.536394i 0.819786π0.819786\pi
140140 0 0
141141 −0.115842 + 0.432327i −0.00975562 + 0.0364085i
142142 −10.2557 10.2557i −0.860643 0.860643i
143143 2.25659 + 6.28804i 0.188705 + 0.525833i
144144 14.7207i 1.22672i
145145 0 0
146146 −12.0063 20.7955i −0.993650 1.72105i
147147 −8.75362 + 2.34553i −0.721987 + 0.193456i
148148 7.40562 0.608738
149149 13.4468 3.60307i 1.10161 0.295175i 0.338189 0.941078i 0.390186π-0.390186\pi
0.763419 + 0.645903i 0.223519π0.223519\pi
150150 0 0
151151 −8.49593 8.49593i −0.691389 0.691389i 0.271149 0.962537i 0.412596π-0.412596\pi
−0.962537 + 0.271149i 0.912596π0.912596\pi
152152 14.4208 + 53.8193i 1.16968 + 4.36532i
153153 3.47482 + 0.931075i 0.280922 + 0.0752729i
154154 0.532801 + 0.142763i 0.0429343 + 0.0115042i
155155 0 0
156156 −23.1052 4.18163i −1.84990 0.334799i
157157 5.14491 5.14491i 0.410609 0.410609i −0.471342 0.881951i 0.656230π-0.656230\pi
0.881951 + 0.471342i 0.156230π0.156230\pi
158158 −20.0970 34.8090i −1.59883 2.76926i
159159 −5.70484 + 3.29369i −0.452423 + 0.261207i
160160 0 0
161161 −0.255227 + 0.255227i −0.0201147 + 0.0201147i
162162 −7.59474 4.38482i −0.596699 0.344504i
163163 −17.7686 10.2587i −1.39175 0.803526i −0.398239 0.917282i 0.630379π-0.630379\pi
−0.993509 + 0.113756i 0.963712π0.963712\pi
164164 −19.2636 + 19.2636i −1.50423 + 1.50423i
165165 0 0
166166 −19.5938 + 11.3125i −1.52078 + 0.878021i
167167 −1.27050 2.20058i −0.0983146 0.170286i 0.812673 0.582721i 0.198012π-0.198012\pi
−0.910987 + 0.412435i 0.864678π0.864678\pi
168168 −0.824831 + 0.824831i −0.0636371 + 0.0636371i
169169 4.55630 12.1754i 0.350484 0.936569i
170170 0 0
171171 −8.85983 2.37398i −0.677528 0.181543i
172172 −18.9005 5.06438i −1.44115 0.386155i
173173 −0.0204199 0.0762079i −0.00155249 0.00579398i 0.965145 0.261715i 0.0842880π-0.0842880\pi
−0.966698 + 0.255921i 0.917621π0.917621\pi
174174 −11.3120 11.3120i −0.857560 0.857560i
175175 0 0
176176 −19.9916 + 5.35675i −1.50693 + 0.403780i
177177 −1.66616 −0.125236
178178 1.45666 0.390312i 0.109182 0.0292551i
179179 10.6120 + 18.3806i 0.793181 + 1.37383i 0.923988 + 0.382421i 0.124910π0.124910\pi
−0.130808 + 0.991408i 0.541757π0.541757\pi
180180 0 0
181181 22.5267i 1.67440i −0.546899 0.837198i 0.684192π-0.684192\pi
0.546899 0.837198i 0.315808π-0.315808\pi
182182 −0.611677 0.882008i −0.0453405 0.0653788i
183183 2.55229 + 2.55229i 0.188671 + 0.188671i
184184 6.65667 24.8430i 0.490737 1.83145i
185185 0 0
186186 −2.62797 1.51726i −0.192692 0.111251i
187187 5.05785i 0.369866i
188188 0.866395 1.50064i 0.0631883 0.109445i
189189 −0.162840 0.607727i −0.0118449 0.0442056i
190190 0 0
191191 −9.80326 + 16.9797i −0.709339 + 1.22861i 0.255764 + 0.966739i 0.417673π0.417673\pi
−0.965103 + 0.261872i 0.915660π0.915660\pi
192192 4.58610 17.1156i 0.330974 1.23521i
193193 −14.4730 + 8.35601i −1.04179 + 0.601479i −0.920340 0.391119i 0.872088π-0.872088\pi
−0.121451 + 0.992597i 0.538755π0.538755\pi
194194 39.6521 2.84686
195195 0 0
196196 35.0850 2.50607
197197 −13.1517 + 7.59315i −0.937021 + 0.540990i −0.889025 0.457858i 0.848617π-0.848617\pi
−0.0479960 + 0.998848i 0.515283π0.515283\pi
198198 1.67465 6.24989i 0.119012 0.444160i
199199 −6.97357 + 12.0786i −0.494343 + 0.856228i −0.999979 0.00651960i 0.997925π-0.997925\pi
0.505636 + 0.862747i 0.331258π0.331258\pi
200200 0 0
201201 −0.0484483 0.180811i −0.00341728 0.0127535i
202202 11.0105 19.0707i 0.774696 1.34181i
203203 0.522979i 0.0367059i
204204 15.3951 + 8.88838i 1.07787 + 0.622311i
205205 0 0
206206 7.49657 27.9776i 0.522311 1.94929i
207207 2.99388 + 2.99388i 0.208089 + 0.208089i
208208 36.4236 + 17.1851i 2.52552 + 1.19157i
209209 12.8961i 0.892044i
210210 0 0
211211 11.8091 + 20.4539i 0.812969 + 1.40810i 0.910777 + 0.412898i 0.135483π0.135483\pi
−0.0978083 + 0.995205i 0.531183π0.531183\pi
212212 24.6340 6.60065i 1.69187 0.453335i
213213 7.09915 0.486426
214214 −18.9504 + 5.07776i −1.29543 + 0.347108i
215215 0 0
216216 31.7007 + 31.7007i 2.15696 + 2.15696i
217217 −0.0256753 0.0958217i −0.00174296 0.00650480i
218218 12.1093 + 3.24467i 0.820143 + 0.219757i
219219 11.3529 + 3.04201i 0.767159 + 0.205560i
220220 0 0
221221 −6.36032 + 7.51086i −0.427841 + 0.505235i
222222 −3.58405 + 3.58405i −0.240546 + 0.240546i
223223 4.86319 + 8.42330i 0.325664 + 0.564066i 0.981646 0.190710i 0.0610790π-0.0610790\pi
−0.655983 + 0.754776i 0.727746π0.727746\pi
224224 1.32196 0.763236i 0.0883274 0.0509958i
225225 0 0
226226 11.4579 11.4579i 0.762168 0.762168i
227227 −7.94647 4.58790i −0.527426 0.304510i 0.212542 0.977152i 0.431826π-0.431826\pi
−0.739968 + 0.672642i 0.765159π0.765159\pi
228228 −39.2534 22.6629i −2.59962 1.50089i
229229 12.5270 12.5270i 0.827811 0.827811i −0.159403 0.987214i 0.550957π-0.550957\pi
0.987214 + 0.159403i 0.0509569π0.0509569\pi
230230 0 0
231231 −0.233817 + 0.134994i −0.0153840 + 0.00888197i
232232 18.6326 + 32.2726i 1.22329 + 2.11880i
233233 11.8637 11.8637i 0.777214 0.777214i −0.202142 0.979356i 0.564790π-0.564790\pi
0.979356 + 0.202142i 0.0647903π0.0647903\pi
234234 −10.3462 + 7.17513i −0.676350 + 0.469053i
235235 0 0
236236 6.23072 + 1.66952i 0.405585 + 0.108676i
237237 19.0033 + 5.09192i 1.23440 + 0.330756i
238238 0.210321 + 0.784929i 0.0136331 + 0.0508794i
239239 −18.2161 18.2161i −1.17830 1.17830i −0.980177 0.198124i 0.936515π-0.936515\pi
−0.198124 0.980177i 0.563485π-0.563485\pi
240240 0 0
241241 −5.28403 + 1.41585i −0.340374 + 0.0912030i −0.424957 0.905213i 0.639711π-0.639711\pi
0.0845830 + 0.996416i 0.473044π0.473044\pi
242242 20.0501 1.28887
243243 −12.0818 + 3.23730i −0.775046 + 0.207673i
244244 −6.98703 12.1019i −0.447299 0.774744i
245245 0 0
246246 18.6458i 1.18881i
247247 16.2171 19.1506i 1.03187 1.21853i
248248 4.99833 + 4.99833i 0.317394 + 0.317394i
249249 2.86622 10.6969i 0.181639 0.677887i
250250 0 0
251251 11.3169 + 6.53384i 0.714319 + 0.412412i 0.812658 0.582741i 0.198020π-0.198020\pi
−0.0983394 + 0.995153i 0.531353π0.531353\pi
252252 0.743439i 0.0468322i
253253 2.97643 5.15533i 0.187127 0.324113i
254254 −8.00209 29.8642i −0.502096 1.87385i
255255 0 0
256256 1.70209 2.94811i 0.106381 0.184257i
257257 −4.51603 + 16.8541i −0.281702 + 1.05133i 0.669513 + 0.742800i 0.266503π0.266503\pi
−0.951215 + 0.308528i 0.900164π0.900164\pi
258258 11.5981 6.69619i 0.722069 0.416887i
259259 −0.165699 −0.0102960
260260 0 0
261261 −6.13467 −0.379727
262262 17.1276 9.88862i 1.05815 0.610921i
263263 −5.39593 + 20.1379i −0.332727 + 1.24175i 0.573585 + 0.819146i 0.305552π0.305552\pi
−0.906312 + 0.422608i 0.861115π0.861115\pi
264264 9.61911 16.6608i 0.592015 1.02540i
265265 0 0
266266 −0.536261 2.00135i −0.0328803 0.122711i
267267 −0.369071 + 0.639249i −0.0225868 + 0.0391214i
268268 0.724703i 0.0442683i
269269 −9.15088 5.28326i −0.557939 0.322126i 0.194379 0.980927i 0.437731π-0.437731\pi
−0.752318 + 0.658800i 0.771064π0.771064\pi
270270 0 0
271271 −2.04739 + 7.64095i −0.124370 + 0.464155i −0.999816 0.0191601i 0.993901π-0.993901\pi
0.875446 + 0.483315i 0.160567π0.160567\pi
272272 −21.5603 21.5603i −1.30729 1.30729i
273273 0.516973 + 0.0935629i 0.0312887 + 0.00566269i
274274 48.9787i 2.95891i
275275 0 0
276276 10.4612 + 18.1194i 0.629693 + 1.09066i
277277 −9.86609 + 2.64361i −0.592796 + 0.158839i −0.542731 0.839907i 0.682610π-0.682610\pi
−0.0500653 + 0.998746i 0.515943π0.515943\pi
278278 −28.9097 −1.73389
279279 −1.12401 + 0.301178i −0.0672929 + 0.0180311i
280280 0 0
281281 12.4763 + 12.4763i 0.744271 + 0.744271i 0.973397 0.229126i 0.0735867π-0.0735867\pi
−0.229126 + 0.973397i 0.573587π0.573587\pi
282282 0.306952 + 1.14556i 0.0182787 + 0.0682171i
283283 7.98478 + 2.13952i 0.474646 + 0.127181i 0.488208 0.872727i 0.337651π-0.337651\pi
−0.0135626 + 0.999908i 0.504317π0.504317\pi
284284 −26.5478 7.11345i −1.57532 0.422105i
285285 0 0
286286 13.5092 + 11.4398i 0.798816 + 0.676451i
287287 0.431018 0.431018i 0.0254422 0.0254422i
288288 −8.95295 15.5070i −0.527557 0.913756i
289289 −8.26943 + 4.77436i −0.486437 + 0.280844i
290290 0 0
291291 −13.7238 + 13.7238i −0.804506 + 0.804506i
292292 −39.4069 22.7516i −2.30611 1.33144i
293293 5.52378 + 3.18916i 0.322703 + 0.186313i 0.652597 0.757705i 0.273680π-0.273680\pi
−0.329894 + 0.944018i 0.607013π0.607013\pi
294294 −16.9799 + 16.9799i −0.990287 + 0.990287i
295295 0 0
296296 10.2251 5.90349i 0.594325 0.343133i
297297 5.18823 + 8.98628i 0.301052 + 0.521437i
298298 26.0836 26.0836i 1.51098 1.51098i
299299 −10.9029 + 3.91272i −0.630531 + 0.226278i
300300 0 0
301301 0.422894 + 0.113314i 0.0243752 + 0.00653132i
302302 −30.7521 8.24001i −1.76959 0.474159i
303303 2.78970 + 10.4113i 0.160264 + 0.598114i
304304 54.9729 + 54.9729i 3.15291 + 3.15291i
305305 0 0
306306 9.20741 2.46712i 0.526353 0.141036i
307307 26.5460 1.51506 0.757530 0.652801i 0.226406π-0.226406\pi
0.757530 + 0.652801i 0.226406π0.226406\pi
308308 1.00964 0.270532i 0.0575296 0.0154150i
309309 7.08860 + 12.2778i 0.403256 + 0.698460i
310310 0 0
311311 3.54417i 0.200972i −0.994938 0.100486i 0.967960π-0.967960\pi
0.994938 0.100486i 0.0320397π-0.0320397\pi
312312 −35.2355 + 12.6450i −1.99482 + 0.715879i
313313 6.21088 + 6.21088i 0.351060 + 0.351060i 0.860504 0.509444i 0.170149π-0.170149\pi
−0.509444 + 0.860504i 0.670149π0.670149\pi
314314 4.98993 18.6227i 0.281598 1.05094i
315315 0 0
316316 −65.9619 38.0831i −3.71065 2.14234i
317317 8.52812i 0.478987i −0.970898 0.239494i 0.923019π-0.923019\pi
0.970898 0.239494i 0.0769814π-0.0769814\pi
318318 −8.72748 + 15.1164i −0.489413 + 0.847688i
319319 2.23236 + 8.33129i 0.124988 + 0.466463i
320320 0 0
321321 4.80142 8.31631i 0.267989 0.464171i
322322 −0.247539 + 0.923827i −0.0137948 + 0.0514829i
323323 −16.4534 + 9.49937i −0.915491 + 0.528559i
324324 −16.6182 −0.923233
325325 0 0
326326 −54.3663 −3.01107
327327 −5.31409 + 3.06809i −0.293870 + 0.169666i
328328 −11.2415 + 41.9540i −0.620710 + 2.31652i
329329 −0.0193853 + 0.0335764i −0.00106875 + 0.00185113i
330330 0 0
331331 4.66054 + 17.3934i 0.256166 + 0.956026i 0.967438 + 0.253109i 0.0814530π0.0814530\pi
−0.711271 + 0.702917i 0.751880π0.751880\pi
332332 −21.4368 + 37.1297i −1.17650 + 2.03776i
333333 1.94369i 0.106513i
334334 −5.83099 3.36652i −0.319058 0.184208i
335335 0 0
336336 −0.421256 + 1.57215i −0.0229814 + 0.0857677i
337337 20.0865 + 20.0865i 1.09418 + 1.09418i 0.995077 + 0.0991030i 0.0315973π0.0315973\pi
0.0991030 + 0.995077i 0.468403π0.468403\pi
338338 −5.67532 33.9761i −0.308697 1.84805i
339339 7.93129i 0.430769i
340340 0 0
341341 0.818040 + 1.41689i 0.0442994 + 0.0767288i
342342 −23.4764 + 6.29048i −1.26946 + 0.340150i
343343 −1.57145 −0.0848505
344344 −30.1336 + 8.07428i −1.62470 + 0.435336i
345345 0 0
346346 −0.147825 0.147825i −0.00794710 0.00794710i
347347 1.85743 + 6.93201i 0.0997119 + 0.372130i 0.997692 0.0679068i 0.0216321π-0.0216321\pi
−0.897980 + 0.440037i 0.854965π0.854965\pi
348348 −29.2819 7.84607i −1.56968 0.420593i
349349 3.52885 + 0.945552i 0.188895 + 0.0506143i 0.352026 0.935990i 0.385493π-0.385493\pi
−0.163131 + 0.986604i 0.552159π0.552159\pi
350350 0 0
351351 3.59590 19.8688i 0.191935 1.06052i
352352 −17.8016 + 17.8016i −0.948827 + 0.948827i
353353 0.881628 + 1.52702i 0.0469243 + 0.0812753i 0.888534 0.458812i 0.151725π-0.151725\pi
−0.841609 + 0.540087i 0.818391π0.818391\pi
354354 −3.82343 + 2.20746i −0.203213 + 0.117325i
355355 0 0
356356 2.02070 2.02070i 0.107097 0.107097i
357357 −0.344462 0.198875i −0.0182309 0.0105256i
358358 48.7040 + 28.1193i 2.57409 + 1.48615i
359359 8.58021 8.58021i 0.452846 0.452846i −0.443452 0.896298i 0.646246π-0.646246\pi
0.896298 + 0.443452i 0.146246π0.146246\pi
360360 0 0
361361 25.4972 14.7208i 1.34196 0.774778i
362362 −29.8451 51.6933i −1.56862 2.71694i
363363 −6.93947 + 6.93947i −0.364228 + 0.364228i
364364 −1.83951 0.867900i −0.0964163 0.0454903i
365365 0 0
366366 9.23835 + 2.47541i 0.482896 + 0.129392i
367367 −13.5337 3.62635i −0.706454 0.189294i −0.112334 0.993670i 0.535833π-0.535833\pi
−0.594120 + 0.804377i 0.702499π0.702499\pi
368368 −9.28811 34.6637i −0.484176 1.80697i
369369 −5.05594 5.05594i −0.263202 0.263202i
370370 0 0
371371 −0.551179 + 0.147688i −0.0286158 + 0.00766757i
372372 −5.75032 −0.298140
373373 −27.9078 + 7.47789i −1.44501 + 0.387190i −0.894286 0.447495i 0.852316π-0.852316\pi
−0.550727 + 0.834685i 0.685650π0.685650\pi
374374 −6.70103 11.6065i −0.346502 0.600159i
375375 0 0
376376 2.76263i 0.142472i
377377 7.16169 15.1791i 0.368846 0.781765i
378378 −1.17884 1.17884i −0.0606330 0.0606330i
379379 2.45278 9.15390i 0.125991 0.470204i −0.873882 0.486138i 0.838405π-0.838405\pi
0.999873 + 0.0159336i 0.00507204π0.00507204\pi
380380 0 0
381381 13.1058 + 7.56661i 0.671428 + 0.387649i
382382 51.9525i 2.65812i
383383 −10.5361 + 18.2490i −0.538369 + 0.932483i 0.460623 + 0.887596i 0.347626π0.347626\pi
−0.998992 + 0.0448868i 0.985707π0.985707\pi
384384 −3.03028 11.3091i −0.154638 0.577118i
385385 0 0
386386 −22.1414 + 38.3500i −1.12697 + 1.95196i
387387 1.32920 4.96065i 0.0675672 0.252164i
388388 65.0727 37.5698i 3.30357 1.90732i
389389 0.0604806 0.00306649 0.00153324 0.999999i 0.499512π-0.499512\pi
0.00153324 + 0.999999i 0.499512π0.499512\pi
390390 0 0
391391 8.76984 0.443510
392392 48.4429 27.9685i 2.44673 1.41262i
393393 −2.50545 + 9.35047i −0.126383 + 0.471669i
394394 −20.1200 + 34.8488i −1.01363 + 1.75566i
395395 0 0
396396 −3.17341 11.8433i −0.159470 0.595150i
397397 4.10812 7.11548i 0.206181 0.357116i −0.744327 0.667815i 0.767230π-0.767230\pi
0.950508 + 0.310699i 0.100563π0.100563\pi
398398 36.9565i 1.85246i
399399 0.878284 + 0.507077i 0.0439692 + 0.0253856i
400400 0 0
401401 −2.32904 + 8.69210i −0.116307 + 0.434063i −0.999381 0.0351698i 0.988803π-0.988803\pi
0.883075 + 0.469233i 0.155469π0.155469\pi
402402 −0.350730 0.350730i −0.0174928 0.0174928i
403403 0.566974 3.13276i 0.0282430 0.156054i
404404 41.7291i 2.07610i
405405 0 0
406406 −0.692882 1.20011i −0.0343872 0.0595603i
407407 2.63966 0.707294i 0.130843 0.0350593i
408408 28.3420 1.40314
409409 34.6013 9.27138i 1.71092 0.458440i 0.735272 0.677772i 0.237054π-0.237054\pi
0.975650 + 0.219332i 0.0703877π0.0703877\pi
410410 0 0
411411 −16.9518 16.9518i −0.836173 0.836173i
412412 −14.2058 53.0166i −0.699867 2.61194i
413413 −0.139411 0.0373550i −0.00685995 0.00183812i
414414 10.8367 + 2.90369i 0.532596 + 0.142709i
415415 0 0
416416 48.8209 4.04944i 2.39364 0.198540i
417417 10.0058 10.0058i 0.489987 0.489987i
418418 17.0858 + 29.5934i 0.835693 + 1.44746i
419419 −11.3282 + 6.54037i −0.553421 + 0.319518i −0.750501 0.660870i 0.770188π-0.770188\pi
0.197080 + 0.980387i 0.436854π0.436854\pi
420420 0 0
421421 −13.7924 + 13.7924i −0.672203 + 0.672203i −0.958223 0.286021i 0.907667π-0.907667\pi
0.286021 + 0.958223i 0.407667π0.407667\pi
422422 54.1978 + 31.2911i 2.63831 + 1.52323i
423423 0.393860 + 0.227395i 0.0191501 + 0.0110563i
424424 28.7510 28.7510i 1.39627 1.39627i
425425 0 0
426426 16.2908 9.40550i 0.789292 0.455698i
427427 0.156333 + 0.270777i 0.00756548 + 0.0131038i
428428 −26.2883 + 26.2883i −1.27069 + 1.27069i
429429 −8.63501 + 0.716228i −0.416902 + 0.0345798i
430430 0 0
431431 21.4619 + 5.75070i 1.03378 + 0.277002i 0.735535 0.677487i 0.236931π-0.236931\pi
0.298249 + 0.954488i 0.403597π0.403597\pi
432432 60.4224 + 16.1901i 2.90707 + 0.778948i
433433 −0.0475058 0.177294i −0.00228298 0.00852021i 0.964775 0.263077i 0.0847372π-0.0847372\pi
−0.967058 + 0.254556i 0.918071π0.918071\pi
434434 −0.185871 0.185871i −0.00892207 0.00892207i
435435 0 0
436436 22.9467 6.14854i 1.09895 0.294462i
437437 −22.3607 −1.06966
438438 30.0825 8.06057i 1.43740 0.385149i
439439 −8.64682 14.9767i −0.412690 0.714800i 0.582493 0.812836i 0.302077π-0.302077\pi
−0.995183 + 0.0980356i 0.968744π0.968744\pi
440440 0 0
441441 9.20846i 0.438498i
442442 −4.64440 + 25.6622i −0.220912 + 1.22063i
443443 −24.4472 24.4472i −1.16152 1.16152i −0.984143 0.177377i 0.943239π-0.943239\pi
−0.177377 0.984143i 0.556761π-0.556761\pi
444444 −2.48592 + 9.27758i −0.117977 + 0.440295i
445445 0 0
446446 22.3197 + 12.8863i 1.05687 + 0.610183i
447447 18.0554i 0.853989i
448448 0.767456 1.32927i 0.0362589 0.0628022i
449449 9.62407 + 35.9175i 0.454188 + 1.69505i 0.690465 + 0.723366i 0.257406π0.257406\pi
−0.236277 + 0.971686i 0.575927π0.575927\pi
450450 0 0
451451 −5.02649 + 8.70613i −0.236688 + 0.409956i
452452 7.94727 29.6596i 0.373808 1.39507i
453453 13.4954 7.79158i 0.634070 0.366080i
454454 −24.3136 −1.14109
455455 0 0
456456 −72.2643 −3.38409
457457 8.16394 4.71345i 0.381893 0.220486i −0.296749 0.954956i 0.595902π-0.595902\pi
0.678642 + 0.734470i 0.262569π0.262569\pi
458458 12.1497 45.3433i 0.567718 2.11875i
459459 −7.64337 + 13.2387i −0.356762 + 0.617930i
460460 0 0
461461 −8.51149 31.7653i −0.396419 1.47946i −0.819349 0.573295i 0.805665π-0.805665\pi
0.422930 0.906162i 0.361002π-0.361002\pi
462462 −0.357701 + 0.619557i −0.0166418 + 0.0288244i
463463 18.6729i 0.867805i −0.900960 0.433903i 0.857136π-0.857136\pi
0.900960 0.433903i 0.142864π-0.142864\pi
464464 45.0302 + 25.9982i 2.09047 + 1.20694i
465465 0 0
466466 11.5063 42.9421i 0.533019 1.98925i
467467 12.1678 + 12.1678i 0.563057 + 0.563057i 0.930175 0.367118i 0.119655π-0.119655\pi
−0.367118 + 0.930175i 0.619655π0.619655\pi
468468 −10.1807 + 21.5779i −0.470602 + 0.997437i
469469 0.0162150i 0.000748740i
470470 0 0
471471 4.71838 + 8.17247i 0.217411 + 0.376568i
472472 9.93381 2.66176i 0.457241 0.122517i
473473 −7.22059 −0.332003
474474 50.3541 13.4923i 2.31284 0.619723i
475475 0 0
476476 1.08886 + 1.08886i 0.0499080 + 0.0499080i
477477 1.73242 + 6.46546i 0.0793219 + 0.296033i
478478 −65.9355 17.6674i −3.01582 0.808087i
479479 −31.8403 8.53158i −1.45482 0.389818i −0.557123 0.830430i 0.688095π-0.688095\pi
−0.897697 + 0.440612i 0.854761π0.854761\pi
480480 0 0
481481 −4.80931 2.26908i −0.219285 0.103461i
482482 −10.2497 + 10.2497i −0.466862 + 0.466862i
483483 −0.234068 0.405417i −0.0106504 0.0184471i
484484 32.9041 18.9972i 1.49564 0.863508i
485485 0 0
486486 −23.4357 + 23.4357i −1.06306 + 1.06306i
487487 −28.5670 16.4931i −1.29449 0.747376i −0.315045 0.949077i 0.602020π-0.602020\pi
−0.979447 + 0.201701i 0.935353π0.935353\pi
488488 −19.2944 11.1396i −0.873415 0.504267i
489489 18.8165 18.8165i 0.850911 0.850911i
490490 0 0
491491 −18.4427 + 10.6479i −0.832307 + 0.480533i −0.854642 0.519218i 0.826223π-0.826223\pi
0.0223350 + 0.999751i 0.492890π0.492890\pi
492492 −17.6666 30.5994i −0.796470 1.37953i
493493 −8.98502 + 8.98502i −0.404665 + 0.404665i
494494 11.8420 65.4317i 0.532795 2.94391i
495495 0 0
496496 9.52693 + 2.55273i 0.427772 + 0.114621i
497497 0.593999 + 0.159161i 0.0266445 + 0.00713937i
498498 −7.59477 28.3441i −0.340330 1.27013i
499499 −14.9199 14.9199i −0.667904 0.667904i 0.289326 0.957231i 0.406569π-0.406569\pi
−0.957231 + 0.289326i 0.906569π0.906569\pi
500500 0 0
501501 3.18332 0.852967i 0.142220 0.0381077i
502502 34.6261 1.54544
503503 42.1943 11.3059i 1.88135 0.504106i 0.881881 0.471471i 0.156277π-0.156277\pi
0.999467 0.0326345i 0.0103897π-0.0103897\pi
504504 0.592643 + 1.02649i 0.0263984 + 0.0457234i
505505 0 0
506506 15.7736i 0.701224i
507507 13.7236 + 9.79506i 0.609486 + 0.435014i
508508 −41.4280 41.4280i −1.83807 1.83807i
509509 −9.67023 + 36.0898i −0.428626 + 1.59965i 0.327250 + 0.944938i 0.393878π0.393878\pi
−0.755876 + 0.654715i 0.772789π0.772789\pi
510510 0 0
511511 0.881719 + 0.509060i 0.0390049 + 0.0225195i
512512 27.0748i 1.19655i
513513 19.4885 33.7551i 0.860438 1.49032i
514514 11.9664 + 44.6591i 0.527814 + 1.96983i
515515 0 0
516516 12.6891 21.9781i 0.558605 0.967533i
517517 0.165495 0.617635i 0.00727846 0.0271636i
518518 −0.380238 + 0.219530i −0.0167067 + 0.00964562i
519519 0.102326 0.00449161
520520 0 0
521521 −35.6853 −1.56340 −0.781701 0.623653i 0.785648π-0.785648\pi
−0.781701 + 0.623653i 0.785648π0.785648\pi
522522 −14.0776 + 8.12768i −0.616158 + 0.355739i
523523 1.11694 4.16849i 0.0488406 0.182275i −0.937196 0.348802i 0.886589π-0.886589\pi
0.986037 + 0.166527i 0.0532552π0.0532552\pi
524524 18.7386 32.4562i 0.818600 1.41786i
525525 0 0
526526 14.2979 + 53.3604i 0.623417 + 2.32662i
527527 −1.20515 + 2.08738i −0.0524971 + 0.0909276i
528528 26.8432i 1.16820i
529529 −10.9797 6.33914i −0.477379 0.275615i
530530 0 0
531531 −0.438183 + 1.63532i −0.0190155 + 0.0709670i
532532 −2.77630 2.77630i −0.120368 0.120368i
533533 18.4124 6.60765i 0.797529 0.286209i
534534 1.95589i 0.0846398i
535535 0 0
536536 0.577707 + 1.00062i 0.0249531 + 0.0432201i
537537 −26.5890 + 7.12450i −1.14740 + 0.307445i
538538 −27.9987 −1.20711
539539 12.5057 3.35089i 0.538659 0.144333i
540540 0 0
541541 −5.42748 5.42748i −0.233345 0.233345i 0.580742 0.814088i 0.302762π-0.302762\pi
−0.814088 + 0.580742i 0.802762π0.802762\pi
542542 5.42507 + 20.2467i 0.233027 + 0.869668i
543543 28.2209 + 7.56177i 1.21108 + 0.324507i
544544 −35.8247 9.59920i −1.53597 0.411563i
545545 0 0
546546 1.31029 0.470222i 0.0560751 0.0201237i
547547 −11.6940 + 11.6940i −0.500000 + 0.500000i −0.911438 0.411438i 0.865027π-0.865027\pi
0.411438 + 0.911438i 0.365027π0.365027\pi
548548 46.4066 + 80.3785i 1.98239 + 3.43360i
549549 3.17628 1.83382i 0.135560 0.0782657i
550550 0 0
551551 22.9093 22.9093i 0.975971 0.975971i
552552 28.8883 + 16.6786i 1.22957 + 0.709890i
553553 1.47588 + 0.852100i 0.0627608 + 0.0362350i
554554 −19.1378 + 19.1378i −0.813087 + 0.813087i
555555 0 0
556556 −47.4434 + 27.3915i −2.01205 + 1.16166i
557557 −2.43751 4.22190i −0.103281 0.178888i 0.809754 0.586770i 0.199601π-0.199601\pi
−0.913034 + 0.407882i 0.866267π0.866267\pi
558558 −2.18031 + 2.18031i −0.0922998 + 0.0922998i
559559 10.7225 + 9.08000i 0.453514 + 0.384043i
560560 0 0
561561 6.33635 + 1.69782i 0.267521 + 0.0716820i
562562 45.1595 + 12.1004i 1.90494 + 0.510426i
563563 10.0853 + 37.6390i 0.425047 + 1.58630i 0.763821 + 0.645428i 0.223321π0.223321\pi
−0.338774 + 0.940868i 0.610012π0.610012\pi
564564 1.58913 + 1.58913i 0.0669146 + 0.0669146i
565565 0 0
566566 21.1577 5.66919i 0.889325 0.238294i
567567 0.371828 0.0156153
568568 −42.3258 + 11.3412i −1.77595 + 0.475865i
569569 1.84104 + 3.18877i 0.0771804 + 0.133680i 0.902032 0.431668i 0.142075π-0.142075\pi
−0.824852 + 0.565349i 0.808742π0.808742\pi
570570 0 0
571571 2.96698i 0.124164i −0.998071 0.0620821i 0.980226π-0.980226\pi
0.998071 0.0620821i 0.0197741π-0.0197741\pi
572572 33.0089 + 5.97401i 1.38017 + 0.249786i
573573 −17.9811 17.9811i −0.751170 0.751170i
574574 0.418034 1.56012i 0.0174484 0.0651184i
575575 0 0
576576 −15.5927 9.00245i −0.649696 0.375102i
577577 35.0533i 1.45929i −0.683827 0.729644i 0.739686π-0.739686\pi
0.683827 0.729644i 0.260314π-0.260314\pi
578578 −12.6509 + 21.9120i −0.526207 + 0.911417i
579579 −5.60990 20.9364i −0.233139 0.870088i
580580 0 0
581581 0.479643 0.830767i 0.0198990 0.0344660i
582582 −13.3104 + 49.6753i −0.551736 + 2.05911i
583583 8.15012 4.70547i 0.337543 0.194881i
584584 −72.5469 −3.00201
585585 0 0
586586 16.9010 0.698173
587587 6.10926 3.52719i 0.252156 0.145583i −0.368595 0.929590i 0.620161π-0.620161\pi
0.620751 + 0.784008i 0.286828π0.286828\pi
588588 −11.7774 + 43.9537i −0.485690 + 1.81262i
589589 3.07280 5.32224i 0.126612 0.219299i
590590 0 0
591591 −5.09774 19.0250i −0.209693 0.782585i
592592 8.23718 14.2672i 0.338546 0.586379i
593593 40.0169i 1.64330i −0.569993 0.821649i 0.693054π-0.693054\pi
0.569993 0.821649i 0.306946π-0.306946\pi
594594 23.8114 + 13.7475i 0.976995 + 0.564068i
595595 0 0
596596 18.0917 67.5192i 0.741066 2.76570i
597597 −12.7909 12.7909i −0.523495 0.523495i
598598 −19.8356 + 23.4237i −0.811138 + 0.957867i
599599 13.9207i 0.568784i −0.958708 0.284392i 0.908208π-0.908208\pi
0.958708 0.284392i 0.0917918π-0.0917918\pi
600600 0 0
601601 1.15689 + 2.00379i 0.0471906 + 0.0817365i 0.888656 0.458575i 0.151640π-0.151640\pi
−0.841465 + 0.540311i 0.818307π0.818307\pi
602602 1.12057 0.300255i 0.0456708 0.0122375i
603603 −0.190206 −0.00774580
604604 −58.2743 + 15.6145i −2.37115 + 0.635347i
605605 0 0
606606 20.1954 + 20.1954i 0.820381 + 0.820381i
607607 −6.10830 22.7965i −0.247928 0.925282i −0.971889 0.235440i 0.924347π-0.924347\pi
0.723960 0.689842i 0.242320π-0.242320\pi
608608 91.3432 + 24.4753i 3.70446 + 0.992606i
609609 0.655175 + 0.175554i 0.0265490 + 0.00711379i
610610 0 0
611611 −1.02244 + 0.709071i −0.0413637 + 0.0286860i
612612 12.7726 12.7726i 0.516303 0.516303i
613613 −5.32964 9.23121i −0.215262 0.372845i 0.738091 0.674701i 0.235727π-0.235727\pi
−0.953354 + 0.301856i 0.902394π0.902394\pi
614614 60.9165 35.1702i 2.45839 1.41935i
615615 0 0
616616 1.17838 1.17838i 0.0474783 0.0474783i
617617 11.8892 + 6.86421i 0.478639 + 0.276343i 0.719849 0.694130i 0.244211π-0.244211\pi
−0.241210 + 0.970473i 0.577544π0.577544\pi
618618 32.5332 + 18.7830i 1.30868 + 0.755565i
619619 16.8604 16.8604i 0.677679 0.677679i −0.281796 0.959474i 0.590930π-0.590930\pi
0.959474 + 0.281796i 0.0909301π0.0909301\pi
620620 0 0
621621 −15.5814 + 8.99592i −0.625260 + 0.360994i
622622 −4.69560 8.13301i −0.188276 0.326104i
623623 −0.0452127 + 0.0452127i −0.00181141 + 0.00181141i
624624 −33.7558 + 39.8620i −1.35131 + 1.59576i
625625 0 0
626626 22.4811 + 6.02379i 0.898526 + 0.240759i
627627 −16.1560 4.32898i −0.645207 0.172883i
628628 −9.45576 35.2894i −0.377326 1.40820i
629629 2.84678 + 2.84678i 0.113509 + 0.113509i
630630 0 0
631631 29.5533 7.91879i 1.17650 0.315242i 0.382962 0.923764i 0.374904π-0.374904\pi
0.793537 + 0.608522i 0.208237π0.208237\pi
632632 −121.434 −4.83038
633633 −29.5882 + 7.92814i −1.17603 + 0.315115i
634634 −11.2987 19.5700i −0.448729 0.777222i
635635 0 0
636636 33.0766i 1.31157i
637637 −22.7847 10.7501i −0.902761 0.425933i
638638 16.1607 + 16.1607i 0.639807 + 0.639807i
639639 1.86700 6.96776i 0.0738576 0.275640i
640640 0 0
641641 −13.2495 7.64957i −0.523322 0.302140i 0.214971 0.976620i 0.431034π-0.431034\pi
−0.738293 + 0.674480i 0.764368π0.764368\pi
642642 25.4452i 1.00424i
643643 11.1740 19.3539i 0.440660 0.763245i −0.557079 0.830460i 0.688078π-0.688078\pi
0.997739 + 0.0672147i 0.0214113π0.0214113\pi
644644 0.469078 + 1.75062i 0.0184843 + 0.0689842i
645645 0 0
646646 −25.1710 + 43.5974i −0.990340 + 1.71532i
647647 −1.21024 + 4.51668i −0.0475795 + 0.177569i −0.985627 0.168939i 0.945966π-0.945966\pi
0.938047 + 0.346508i 0.112633π0.112633\pi
648648 −22.9452 + 13.2474i −0.901373 + 0.520408i
649649 2.38033 0.0934361
650650 0 0
651651 0.128662 0.00504265
652652 −89.2199 + 51.5111i −3.49412 + 2.01733i
653653 −6.34274 + 23.6714i −0.248211 + 0.926335i 0.723532 + 0.690291i 0.242518π0.242518\pi
−0.971742 + 0.236044i 0.924149π0.924149\pi
654654 −8.12969 + 14.0810i −0.317896 + 0.550612i
655655 0 0
656656 15.6854 + 58.5387i 0.612412 + 2.28555i
657657 5.97141 10.3428i 0.232967 0.403510i
658658 0.102733i 0.00400494i
659659 35.2803 + 20.3691i 1.37433 + 0.793467i 0.991469 0.130341i 0.0416072π-0.0416072\pi
0.382856 + 0.923808i 0.374941π0.374941\pi
660660 0 0
661661 4.42523 16.5152i 0.172122 0.642367i −0.824902 0.565275i 0.808770π-0.808770\pi
0.997024 0.0770916i 0.0245634π-0.0245634\pi
662662 33.7389 + 33.7389i 1.31130 + 1.31130i
663663 −7.27440 10.4893i −0.282514 0.407371i
664664 68.3547i 2.65268i
665665 0 0
666666 2.57515 + 4.46029i 0.0997850 + 0.172833i
667667 −14.4457 + 3.87071i −0.559340 + 0.149875i
668668 −12.7589 −0.493657
669669 −12.1850 + 3.26496i −0.471099 + 0.126231i
670670 0 0
671671 −3.64628 3.64628i −0.140763 0.140763i
672672 0.512407 + 1.91233i 0.0197665 + 0.0737696i
673673 23.0041 + 6.16392i 0.886742 + 0.237602i 0.673314 0.739357i 0.264870π-0.264870\pi
0.213428 + 0.976959i 0.431537π0.431537\pi
674674 72.7057 + 19.4814i 2.80052 + 0.750396i
675675 0 0
676676 −41.5055 50.3805i −1.59636 1.93771i
677677 −26.1344 + 26.1344i −1.00443 + 1.00443i −0.00443504 + 0.999990i 0.501412π0.501412\pi
−0.999990 + 0.00443504i 0.998588π0.998588\pi
678678 10.5080 + 18.2004i 0.403557 + 0.698981i
679679 −1.45598 + 0.840613i −0.0558756 + 0.0322598i
680680 0 0
681681 8.41509 8.41509i 0.322467 0.322467i
682682 3.75440 + 2.16761i 0.143764 + 0.0830019i
683683 23.1988 + 13.3938i 0.887676 + 0.512500i 0.873181 0.487395i 0.162053π-0.162053\pi
0.0144941 + 0.999895i 0.495386π0.495386\pi
684684 −32.5667 + 32.5667i −1.24522 + 1.24522i
685685 0 0
686686 −3.60610 + 2.08198i −0.137682 + 0.0794905i
687687 11.4885 + 19.8987i 0.438314 + 0.759182i
688688 −30.7796 + 30.7796i −1.17346 + 1.17346i
689689 −18.0201 3.26131i −0.686510 0.124246i
690690 0 0
691691 −38.9899 10.4473i −1.48325 0.397435i −0.575796 0.817593i 0.695308π-0.695308\pi
−0.907451 + 0.420158i 0.861975π0.861975\pi
692692 −0.382655 0.102532i −0.0145464 0.00389769i
693693 0.0710042 + 0.264991i 0.00269723 + 0.0100662i
694694 13.4464 + 13.4464i 0.510419 + 0.510419i
695695 0 0
696696 −46.6850 + 12.5092i −1.76959 + 0.474160i
697697 −14.8102 −0.560976
698698 9.35058 2.50548i 0.353925 0.0948339i
699699 10.8801 + 18.8449i 0.411524 + 0.712780i
700700 0 0
701701 24.9781i 0.943410i −0.881756 0.471705i 0.843639π-0.843639\pi
0.881756 0.471705i 0.156361π-0.156361\pi
702702 −18.0721 50.3582i −0.682086 1.90065i
703703 −7.25852 7.25852i −0.273760 0.273760i
704704 −6.55185 + 24.4519i −0.246932 + 0.921564i
705705 0 0
706706 4.04624 + 2.33610i 0.152282 + 0.0879202i
707707 0.933677i 0.0351145i
708708 −4.18306 + 7.24528i −0.157209 + 0.272294i
709709 −2.64139 9.85779i −0.0991993 0.370217i 0.898423 0.439130i 0.144713π-0.144713\pi
−0.997623 + 0.0689135i 0.978047π0.978047\pi
710710 0 0
711711 9.99535 17.3124i 0.374855 0.649268i
712712 1.17921 4.40087i 0.0441927 0.164930i
713713 −2.45675 + 1.41841i −0.0920061 + 0.0531198i
714714 −1.05394 −0.0394428
715715 0 0
716716 106.570 3.98272
717717 28.9355 16.7059i 1.08061 0.623893i
718718 8.32175 31.0572i 0.310565 1.15904i
719719 −14.2117 + 24.6153i −0.530005 + 0.917996i 0.469382 + 0.882995i 0.344477π0.344477\pi
−0.999387 + 0.0350008i 0.988857π0.988857\pi
720720 0 0
721721 0.317850 + 1.18623i 0.0118373 + 0.0441776i
722722 39.0065 67.5612i 1.45167 2.51437i
723723 7.09498i 0.263865i
724724 −97.9570 56.5555i −3.64054 2.10187i
725725 0 0
726726 −6.73044 + 25.1183i −0.249790 + 0.932229i
727727 8.56116 + 8.56116i 0.317516 + 0.317516i 0.847812 0.530296i 0.177919π-0.177919\pi
−0.530296 + 0.847812i 0.677919π0.677919\pi
728728 −3.23172 + 0.268054i −0.119775 + 0.00993473i
729729 26.1513i 0.968566i
730730 0 0
731731 −5.31873 9.21232i −0.196720 0.340730i
732732 17.5064 4.69082i 0.647054 0.173378i
733733 17.2200 0.636036 0.318018 0.948085i 0.396983π-0.396983\pi
0.318018 + 0.948085i 0.396983π0.396983\pi
734734 −35.8610 + 9.60893i −1.32365 + 0.354672i
735735 0 0
736736 −30.8663 30.8663i −1.13775 1.13775i
737737 0.0692148 + 0.258313i 0.00254956 + 0.00951508i
738738 −18.3007 4.90365i −0.673656 0.180506i
739739 −15.7497 4.22013i −0.579364 0.155240i −0.0427762 0.999085i 0.513620π-0.513620\pi
−0.536588 + 0.843845i 0.680287π0.680287\pi
740740 0 0
741741 18.5477 + 26.7449i 0.681367 + 0.982497i
742742 −1.06915 + 1.06915i −0.0392498 + 0.0392498i
743743 −16.5599 28.6826i −0.607525 1.05226i −0.991647 0.128982i 0.958829π-0.958829\pi
0.384122 0.923282i 0.374504π-0.374504\pi
744744 −7.93963 + 4.58395i −0.291081 + 0.168056i
745745 0 0
746746 −54.1344 + 54.1344i −1.98200 + 1.98200i
747747 −9.74510 5.62634i −0.356555 0.205857i
748748 −21.9940 12.6982i −0.804179 0.464293i
749749 0.588194 0.588194i 0.0214921 0.0214921i
750750 0 0
751751 18.9961 10.9674i 0.693176 0.400205i −0.111625 0.993750i 0.535605π-0.535605\pi
0.804801 + 0.593545i 0.202272π0.202272\pi
752752 −1.92736 3.33829i −0.0702836 0.121735i
753753 −11.9843 + 11.9843i −0.436732 + 0.436732i
754754 −3.67617 44.3207i −0.133878 1.61407i
755755 0 0
756756 −3.05152 0.817652i −0.110983 0.0297377i
757757 2.84678 + 0.762791i 0.103468 + 0.0277241i 0.310181 0.950677i 0.399610π-0.399610\pi
−0.206714 + 0.978401i 0.566277π0.566277\pi
758758 −6.49926 24.2556i −0.236064 0.881002i
759759 5.45935 + 5.45935i 0.198162 + 0.198162i
760760 0 0
761761 −21.2875 + 5.70396i −0.771670 + 0.206768i −0.623109 0.782135i 0.714131π-0.714131\pi
−0.148561 + 0.988903i 0.547464π0.547464\pi
762762 40.0993 1.45265
763763 −0.513426 + 0.137572i −0.0185873 + 0.00498044i
764764 49.2241 + 85.2587i 1.78087 + 3.08455i
765765 0 0
766766 55.8361i 2.01744i
767767 −3.53477 2.99330i −0.127633 0.108082i
768768 3.12197 + 3.12197i 0.112654 + 0.112654i
769769 −5.46718 + 20.4038i −0.197152 + 0.735780i 0.794548 + 0.607202i 0.207708π0.207708\pi
−0.991699 + 0.128578i 0.958959π0.958959\pi
770770 0 0
771771 −19.5984 11.3152i −0.705820 0.407506i
772772 83.9143i 3.02014i
773773 9.34781 16.1909i 0.336217 0.582346i −0.647500 0.762065i 0.724186π-0.724186\pi
0.983718 + 0.179719i 0.0575189π0.0575189\pi
774774 −3.52206 13.1445i −0.126598 0.472470i
775775 0 0
776776 59.8985 103.747i 2.15023 3.72431i
777777 0.0556218 0.207583i 0.00199542 0.00744702i
778778 0.138788 0.0801293i 0.00497579 0.00287278i
779779 37.7619 1.35296
780780 0 0
781781 −10.1421 −0.362912
782782 20.1246 11.6190i 0.719656 0.415493i
783783 6.74705 25.1803i 0.241120 0.899872i
784784 39.0246 67.5927i 1.39374 2.41402i
785785 0 0
786786 6.63883 + 24.7764i 0.236799 + 0.883747i
787787 −21.6615 + 37.5189i −0.772150 + 1.33740i 0.164232 + 0.986422i 0.447485π0.447485\pi
−0.936382 + 0.350981i 0.885848π0.885848\pi
788788 76.2534i 2.71642i
789789 −23.4169 13.5198i −0.833665 0.481317i
790790 0 0
791791 −0.177818 + 0.663626i −0.00632248 + 0.0235958i
792792 −13.8227 13.8227i −0.491168 0.491168i
793793 0.829444 + 9.99995i 0.0294544 + 0.355109i
794794 21.7710i 0.772625i
795795 0 0
796796 35.0157 + 60.6489i 1.24110 + 2.14964i
797797 33.9650 9.10089i 1.20310 0.322370i 0.399050 0.916929i 0.369340π-0.369340\pi
0.804052 + 0.594559i 0.202673π0.202673\pi
798798 2.68726 0.0951280
799799 0.909909 0.243809i 0.0321903 0.00862535i
800800 0 0
801801 0.530356 + 0.530356i 0.0187392 + 0.0187392i
802802 6.17139 + 23.0319i 0.217919 + 0.813286i
803803 −16.2191 4.34591i −0.572361 0.153364i
804804 −0.907890 0.243268i −0.0320188 0.00857942i
805805 0 0
806806 −2.84946 7.94010i −0.100368 0.279678i
807807 9.69052 9.69052i 0.341122 0.341122i
808808 −33.2649 57.6165i −1.17026 2.02694i
809809 −17.8779 + 10.3218i −0.628554 + 0.362896i −0.780192 0.625540i 0.784879π-0.784879\pi
0.151638 + 0.988436i 0.451545π0.451545\pi
810810 0 0
811811 −22.0471 + 22.0471i −0.774178 + 0.774178i −0.978834 0.204656i 0.934392π-0.934392\pi
0.204656 + 0.978834i 0.434392π0.434392\pi
812812 −2.27416 1.31299i −0.0798075 0.0460769i
813813 −8.88514 5.12984i −0.311615 0.179911i
814814 5.12029 5.12029i 0.179466 0.179466i
815815 0 0
816816 34.2477 19.7729i 1.19891 0.692190i
817817 13.5613 + 23.4889i 0.474450 + 0.821772i
818818 67.1180 67.1180i 2.34672 2.34672i
819819 0.227790 0.482799i 0.00795963 0.0168704i
820820 0 0
821821 35.4477 + 9.49818i 1.23713 + 0.331489i 0.817353 0.576137i 0.195441π-0.195441\pi
0.419780 + 0.907626i 0.362107π0.362107\pi
822822 −61.3594 16.4412i −2.14016 0.573453i
823823 −6.11025 22.8038i −0.212990 0.794889i −0.986865 0.161550i 0.948351π-0.948351\pi
0.773875 0.633339i 0.218316π-0.218316\pi
824824 −61.8772 61.8772i −2.15559 2.15559i
825825 0 0
826826 −0.369404 + 0.0989816i −0.0128532 + 0.00344401i
827827 4.44429 0.154543 0.0772716 0.997010i 0.475379π-0.475379\pi
0.0772716 + 0.997010i 0.475379π0.475379\pi
828828 20.5352 5.50240i 0.713649 0.191222i
829829 −14.6685 25.4065i −0.509457 0.882406i −0.999940 0.0109548i 0.996513π-0.996513\pi
0.490483 0.871451i 0.336820π-0.336820\pi
830830 0 0
831831 13.2474i 0.459548i
832832 40.4780 28.0718i 1.40332 0.973213i
833833 13.4870 + 13.4870i 0.467296 + 0.467296i
834834 9.70441 36.2174i 0.336036 1.25410i
835835 0 0
836836 56.0786 + 32.3770i 1.93952 + 1.11978i
837837 4.94486i 0.170919i
838838 −17.3304 + 30.0171i −0.598668 + 1.03692i
839839 −2.19656 8.19766i −0.0758336 0.283015i 0.917587 0.397534i 0.130134π-0.130134\pi
−0.993421 + 0.114519i 0.963467π0.963467\pi
840840 0 0
841841 −3.66554 + 6.34891i −0.126398 + 0.218928i
842842 −13.3770 + 49.9236i −0.461001 + 1.72048i
843843 −19.8180 + 11.4419i −0.682568 + 0.394081i
844844 118.591 4.08208
845845 0 0
846846 1.20508 0.0414316
847847 −0.736220 + 0.425057i −0.0252968 + 0.0146051i
848848 14.6837 54.8002i 0.504239 1.88185i
849849 −5.36067 + 9.28495i −0.183978 + 0.318659i
850850 0 0
851851 1.22638 + 4.57693i 0.0420399 + 0.156895i
852852 17.8231 30.8705i 0.610610 1.05761i
853853 34.3415i 1.17583i 0.808923 + 0.587915i 0.200051π0.200051\pi
−0.808923 + 0.587915i 0.799949π0.799949\pi
854854 0.717491 + 0.414244i 0.0245521 + 0.0141751i
855855 0 0
856856 −15.3409 + 57.2531i −0.524342 + 1.95687i
857857 −24.6090 24.6090i −0.840626 0.840626i 0.148314 0.988940i 0.452615π-0.452615\pi
−0.988940 + 0.148314i 0.952615π0.952615\pi
858858 −18.8663 + 13.0839i −0.644085 + 0.446677i
859859 12.8606i 0.438798i 0.975635 + 0.219399i 0.0704097π0.0704097\pi
−0.975635 + 0.219399i 0.929590π0.929590\pi
860860 0 0
861861 0.395284 + 0.684653i 0.0134713 + 0.0233329i
862862 56.8688 15.2379i 1.93696 0.519007i
863863 2.75373 0.0937379 0.0468690 0.998901i 0.485076π-0.485076\pi
0.0468690 + 0.998901i 0.485076π0.485076\pi
864864 73.4965 19.6933i 2.50040 0.669980i
865865 0 0
866866 −0.343907 0.343907i −0.0116864 0.0116864i
867867 −3.20532 11.9624i −0.108858 0.406264i
868868 −0.481140 0.128921i −0.0163309 0.00437586i
869869 −27.1487 7.27447i −0.920957 0.246770i
870870 0 0
871871 0.222049 0.470631i 0.00752385 0.0159467i
872872 26.7817 26.7817i 0.906944 0.906944i
873873 9.86060 + 17.0791i 0.333731 + 0.578039i
874874 −51.3123 + 29.6252i −1.73566 + 1.00209i
875875 0 0
876876 41.7308 41.7308i 1.40995 1.40995i
877877 40.9311 + 23.6316i 1.38214 + 0.797981i 0.992413 0.122948i 0.0392349π-0.0392349\pi
0.389730 + 0.920929i 0.372568π0.372568\pi
878878 −39.6847 22.9119i −1.33929 0.773241i
879879 −5.84953 + 5.84953i −0.197300 + 0.197300i
880880 0 0
881881 35.7854 20.6607i 1.20564 0.696077i 0.243837 0.969816i 0.421594π-0.421594\pi
0.961804 + 0.273739i 0.0882605π0.0882605\pi
882882 12.2001 + 21.1311i 0.410798 + 0.711523i
883883 −13.4808 + 13.4808i −0.453666 + 0.453666i −0.896569 0.442903i 0.853949π-0.853949\pi
0.442903 + 0.896569i 0.353949π0.353949\pi
884884 16.6927 + 46.5145i 0.561435 + 1.56445i
885885 0 0
886886 −88.4897 23.7108i −2.97287 0.796578i
887887 22.1438 + 5.93341i 0.743516 + 0.199225i 0.610640 0.791908i 0.290912π-0.290912\pi
0.132876 + 0.991133i 0.457579π0.457579\pi
888888 3.96337 + 14.7915i 0.133002 + 0.496371i
889889 0.926941 + 0.926941i 0.0310886 + 0.0310886i
890890 0 0
891891 −5.92339 + 1.58717i −0.198441 + 0.0531721i
892892 48.8381 1.63522
893893 −2.32002 + 0.621647i −0.0776364 + 0.0208026i
894894 23.9211 + 41.4326i 0.800042 + 1.38571i
895895 0 0
896896 1.01420i 0.0338819i
897897 −1.24187 14.9723i −0.0414650 0.499911i
898898 69.6712 + 69.6712i 2.32496 + 2.32496i
899899 1.06382 3.97024i 0.0354805 0.132415i
900900 0 0
901901 12.0069 + 6.93217i 0.400007 + 0.230944i
902902 26.6379i 0.886946i
903903 −0.283915 + 0.491754i −0.00944808 + 0.0163646i
904904 −12.6705 47.2871i −0.421416 1.57275i
905905 0 0
906906 20.6458 35.7595i 0.685910 1.18803i
907907 6.24222 23.2963i 0.207270 0.773541i −0.781476 0.623935i 0.785533π-0.785533\pi
0.988746 0.149606i 0.0478004π-0.0478004\pi
908908 −39.9008 + 23.0367i −1.32416 + 0.764501i
909909 10.9523 0.363264
910910 0 0
911911 58.5135 1.93864 0.969320 0.245803i 0.0790515π-0.0790515\pi
0.969320 + 0.245803i 0.0790515π0.0790515\pi
912912 −87.3221 + 50.4154i −2.89152 + 1.66942i
913913 −4.09477 + 15.2819i −0.135517 + 0.505757i
914914 12.4895 21.6324i 0.413116 0.715537i
915915 0 0
916916 −23.0233 85.9241i −0.760711 2.83901i
917917 −0.419271 + 0.726199i −0.0138456 + 0.0239812i
918918 40.5061i 1.33690i
919919 38.8451 + 22.4272i 1.28138 + 0.739806i 0.977101 0.212776i 0.0682506π-0.0682506\pi
0.304281 + 0.952582i 0.401584π0.401584\pi
920920 0 0
921921 −8.91097 + 33.2562i −0.293626 + 1.09583i
922922 −61.6169 61.6169i −2.02924 2.02924i
923923 15.0609 + 12.7538i 0.495735 + 0.419797i
924924 1.35567i 0.0445981i
925925 0 0
926926 −24.7394 42.8498i −0.812986 1.40813i
927927 13.9148 3.72846i 0.457022 0.122459i
928928 63.2473 2.07619
929929 −27.1090 + 7.26384i −0.889418 + 0.238319i −0.674466 0.738306i 0.735626π-0.735626\pi
−0.214952 + 0.976625i 0.568960π0.568960\pi
930930 0 0
931931 −34.3881 34.3881i −1.12702 1.12702i
932932 −21.8041 81.3738i −0.714215 2.66549i
933933 4.44006 + 1.18971i 0.145361 + 0.0389493i
934934 44.0428 + 11.8012i 1.44113 + 0.386148i
935935 0 0
936936 3.14434 + 37.9088i 0.102776 + 1.23909i
937937 −20.7545 + 20.7545i −0.678019 + 0.678019i −0.959552 0.281533i 0.909157π-0.909157\pi
0.281533 + 0.959552i 0.409157π0.409157\pi
938938 −0.0214829 0.0372095i −0.000701442 0.00121493i
939939 −9.86572 + 5.69597i −0.321955 + 0.185881i
940940 0 0
941941 −6.70533 + 6.70533i −0.218588 + 0.218588i −0.807903 0.589315i 0.799398π-0.799398\pi
0.589315 + 0.807903i 0.299398π0.299398\pi
942942 21.6550 + 12.5025i 0.705559 + 0.407355i
943943 −15.0956 8.71547i −0.491582 0.283815i
944944 10.1467 10.1467i 0.330249 0.330249i
945945 0 0
946946 −16.5695 + 9.56639i −0.538720 + 0.311030i
947947 2.25542 + 3.90651i 0.0732915 + 0.126945i 0.900342 0.435183i 0.143316π-0.143316\pi
−0.827051 + 0.562128i 0.809983π0.809983\pi
948948 69.8518 69.8518i 2.26868 2.26868i
949949 18.6203 + 26.8495i 0.604439 + 0.871570i
950950 0 0
951951 10.6838 + 2.86272i 0.346447 + 0.0928302i
952952 2.37143 + 0.635422i 0.0768584 + 0.0205941i
953953 1.48646 + 5.54756i 0.0481513 + 0.179703i 0.985813 0.167845i 0.0536809π-0.0536809\pi
−0.937662 + 0.347548i 0.887014π0.887014\pi
954954 12.5414 + 12.5414i 0.406043 + 0.406043i
955955 0 0
956956 −124.946 + 33.4791i −4.04103 + 1.08279i
957957 −11.1866 −0.361612
958958 −84.3690 + 22.6066i −2.72584 + 0.730386i
959959 −1.03833 1.79845i −0.0335296 0.0580749i
960960 0 0
961961 30.2203i 0.974849i
962962 −14.0424 + 1.16475i −0.452746 + 0.0375529i
963963 −6.89966 6.89966i −0.222338 0.222338i
964964 −7.10927 + 26.5322i −0.228974 + 0.854543i
965965 0 0
966966 −1.07426 0.620222i −0.0345636 0.0199553i
967967 17.6414i 0.567310i −0.958926 0.283655i 0.908453π-0.908453\pi
0.958926 0.283655i 0.0915470π-0.0915470\pi
968968 30.2877 52.4599i 0.973485 1.68612i
969969 −6.37750 23.8012i −0.204875 0.764604i
970970 0 0
971971 −16.6987 + 28.9229i −0.535886 + 0.928181i 0.463234 + 0.886236i 0.346689π0.346689\pi
−0.999120 + 0.0419454i 0.986644π0.986644\pi
972972 −16.2551 + 60.6650i −0.521384 + 1.94583i
973973 1.06153 0.612876i 0.0340312 0.0196479i
974974 −87.4056 −2.80065
975975 0 0
976976 −31.0864 −0.995050
977977 −13.2886 + 7.67217i −0.425139 + 0.245454i −0.697274 0.716805i 0.745604π-0.745604\pi
0.272134 + 0.962259i 0.412270π0.412270\pi
978978 18.2497 68.1088i 0.583561 2.17788i
979979 0.527266 0.913252i 0.0168515 0.0291877i
980980 0 0
981981 1.61375 + 6.02261i 0.0515232 + 0.192287i
982982 −28.2143 + 48.8686i −0.900354 + 1.55946i
983983 4.80751i 0.153336i 0.997057 + 0.0766679i 0.0244281π0.0244281\pi
−0.997057 + 0.0766679i 0.975572π0.975572\pi
984984 −48.7854 28.1663i −1.55522 0.897908i
985985 0 0
986986 −8.71437 + 32.5225i −0.277522 + 1.03573i
987987 −0.0355565 0.0355565i −0.00113177 0.00113177i
988988 −42.5617 118.599i −1.35407 3.77315i
989989 12.5198i 0.398108i
990990 0 0
991991 −0.219558 0.380286i −0.00697450 0.0120802i 0.862517 0.506028i 0.168887π-0.168887\pi
−0.869492 + 0.493948i 0.835553π0.835553\pi
992992 11.5884 3.10509i 0.367931 0.0985867i
993993 −23.3545 −0.741131
994994 1.57395 0.421739i 0.0499227 0.0133767i
995995 0 0
996996 −39.3193 39.3193i −1.24588 1.24588i
997997 1.70003 + 6.34461i 0.0538406 + 0.200936i 0.987607 0.156947i 0.0501653π-0.0501653\pi
−0.933766 + 0.357883i 0.883499π0.883499\pi
998998 −54.0044 14.4704i −1.70948 0.458053i
999999 −7.97806 2.13771i −0.252415 0.0676343i
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 325.2.x.b.93.5 20
5.2 odd 4 325.2.s.b.132.5 20
5.3 odd 4 65.2.o.a.2.1 20
5.4 even 2 65.2.t.a.28.1 yes 20
13.7 odd 12 325.2.s.b.293.5 20
15.8 even 4 585.2.cf.a.262.5 20
15.14 odd 2 585.2.dp.a.28.5 20
65.3 odd 12 845.2.k.e.577.10 20
65.4 even 6 845.2.t.e.188.1 20
65.7 even 12 inner 325.2.x.b.7.5 20
65.8 even 4 845.2.t.f.427.5 20
65.9 even 6 845.2.t.f.188.5 20
65.18 even 4 845.2.t.e.427.1 20
65.19 odd 12 845.2.o.g.488.5 20
65.23 odd 12 845.2.k.d.577.1 20
65.24 odd 12 845.2.k.e.268.10 20
65.28 even 12 845.2.f.d.437.1 20
65.29 even 6 845.2.f.e.408.1 20
65.33 even 12 65.2.t.a.7.1 yes 20
65.34 odd 4 845.2.o.e.258.1 20
65.38 odd 4 845.2.o.g.587.5 20
65.43 odd 12 845.2.o.f.357.5 20
65.44 odd 4 845.2.o.f.258.5 20
65.48 odd 12 845.2.o.e.357.1 20
65.49 even 6 845.2.f.d.408.10 20
65.54 odd 12 845.2.k.d.268.1 20
65.58 even 12 845.2.t.g.657.5 20
65.59 odd 12 65.2.o.a.33.1 yes 20
65.63 even 12 845.2.f.e.437.10 20
65.64 even 2 845.2.t.g.418.5 20
195.59 even 12 585.2.cf.a.163.5 20
195.98 odd 12 585.2.dp.a.397.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.2.1 20 5.3 odd 4
65.2.o.a.33.1 yes 20 65.59 odd 12
65.2.t.a.7.1 yes 20 65.33 even 12
65.2.t.a.28.1 yes 20 5.4 even 2
325.2.s.b.132.5 20 5.2 odd 4
325.2.s.b.293.5 20 13.7 odd 12
325.2.x.b.7.5 20 65.7 even 12 inner
325.2.x.b.93.5 20 1.1 even 1 trivial
585.2.cf.a.163.5 20 195.59 even 12
585.2.cf.a.262.5 20 15.8 even 4
585.2.dp.a.28.5 20 15.14 odd 2
585.2.dp.a.397.5 20 195.98 odd 12
845.2.f.d.408.10 20 65.49 even 6
845.2.f.d.437.1 20 65.28 even 12
845.2.f.e.408.1 20 65.29 even 6
845.2.f.e.437.10 20 65.63 even 12
845.2.k.d.268.1 20 65.54 odd 12
845.2.k.d.577.1 20 65.23 odd 12
845.2.k.e.268.10 20 65.24 odd 12
845.2.k.e.577.10 20 65.3 odd 12
845.2.o.e.258.1 20 65.34 odd 4
845.2.o.e.357.1 20 65.48 odd 12
845.2.o.f.258.5 20 65.44 odd 4
845.2.o.f.357.5 20 65.43 odd 12
845.2.o.g.488.5 20 65.19 odd 12
845.2.o.g.587.5 20 65.38 odd 4
845.2.t.e.188.1 20 65.4 even 6
845.2.t.e.427.1 20 65.18 even 4
845.2.t.f.188.5 20 65.9 even 6
845.2.t.f.427.5 20 65.8 even 4
845.2.t.g.418.5 20 65.64 even 2
845.2.t.g.657.5 20 65.58 even 12