Properties

Label 507.2.e.l.484.3
Level 507507
Weight 22
Character 507.484
Analytic conductor 4.0484.048
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(22,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 507=3132 507 = 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 507.e (of order 33, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.048415382484.04841538248
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x5+3x4+5x22x+1 x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 484.3
Root 0.6234901.07992i-0.623490 - 1.07992i of defining polynomial
Character χ\chi == 507.484
Dual form 507.2.e.l.22.3

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+(1.34601+2.33136i)q2+(0.500000+0.866025i)q3+(2.62349+4.54402i)q4+1.04892q5+(1.34601+2.33136i)q6+(0.2774790.480608i)q78.74094q8+(0.500000+0.866025i)q9+(1.41185+2.44540i)q10+(1.45593+2.52174i)q115.24698q12+1.49396q14+(0.524459+0.908389i)q15+(6.5184211.2902i)q16+(2.425434.20096i)q172.69202q18+(0.376510+0.652135i)q19+(2.75182+4.76630i)q20+0.554958q21+(3.91939+6.78858i)q22+(2.881354.99065i)q23+(4.370477.56988i)q243.89977q251.00000q27+(1.45593+2.52174i)q28+(0.955927+1.65571i)q29+(1.41185+2.44540i)q30+9.51573q31+(8.8067815.2538i)q32+(1.45593+2.52174i)q33+13.0586q34+(0.2910530.504118i)q35+(2.623494.54402i)q36+(2.87651+4.98226i)q372.02715q389.16852q40+(2.45593+4.25379i)q41+(0.746980+1.29381i)q42+(5.548929.61101i)q4315.2784q44+(0.524459+0.908389i)q45+(7.7566713.4349i)q460.753020q47+(6.5184211.2902i)q48+(3.34601+5.79546i)q49+(5.249149.09177i)q50+4.85086q517.58211q53+(1.346012.33136i)q54+(1.52715+2.64510i)q55+(2.42543+4.20096i)q560.753020q57+(2.57338+4.45722i)q58+(2.048923.54883i)q595.50365q60+(1.711642.96464i)q61+(12.8083+22.1846i)q62+(0.277479+0.480608i)q63+21.3424q647.83877q66+(0.9363131.62174i)q67+(12.7262+22.0424i)q68+(2.881354.99065i)q69+1.56704q70+(5.25182+9.09643i)q71+(4.370477.56988i)q7210.4765q73+(7.74363+13.4124i)q74+(1.949893.37730i)q75+(1.975543.42174i)q76+1.61596q77+1.33513q79+(6.8372811.8425i)q80+(0.5000000.866025i)q81+(6.61141+11.4513i)q822.64310q83+(1.45593+2.52174i)q84+(2.544074.40646i)q85+29.8756q86+(0.955927+1.65571i)q87+(12.726222.0424i)q88+(4.96346+8.59696i)q892.82371q90+30.2368q92+(4.75786+8.24086i)q93+(1.013571.75556i)q94+(0.394928+0.684035i)q95+17.6136q96+(8.5368414.7862i)q97+(9.00753+15.6015i)q982.91185q99+O(q100)q+(1.34601 + 2.33136i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62349 + 4.54402i) q^{4} +1.04892 q^{5} +(-1.34601 + 2.33136i) q^{6} +(0.277479 - 0.480608i) q^{7} -8.74094 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.41185 + 2.44540i) q^{10} +(1.45593 + 2.52174i) q^{11} -5.24698 q^{12} +1.49396 q^{14} +(0.524459 + 0.908389i) q^{15} +(-6.51842 - 11.2902i) q^{16} +(2.42543 - 4.20096i) q^{17} -2.69202 q^{18} +(-0.376510 + 0.652135i) q^{19} +(-2.75182 + 4.76630i) q^{20} +0.554958 q^{21} +(-3.91939 + 6.78858i) q^{22} +(-2.88135 - 4.99065i) q^{23} +(-4.37047 - 7.56988i) q^{24} -3.89977 q^{25} -1.00000 q^{27} +(1.45593 + 2.52174i) q^{28} +(0.955927 + 1.65571i) q^{29} +(-1.41185 + 2.44540i) q^{30} +9.51573 q^{31} +(8.80678 - 15.2538i) q^{32} +(-1.45593 + 2.52174i) q^{33} +13.0586 q^{34} +(0.291053 - 0.504118i) q^{35} +(-2.62349 - 4.54402i) q^{36} +(2.87651 + 4.98226i) q^{37} -2.02715 q^{38} -9.16852 q^{40} +(2.45593 + 4.25379i) q^{41} +(0.746980 + 1.29381i) q^{42} +(5.54892 - 9.61101i) q^{43} -15.2784 q^{44} +(-0.524459 + 0.908389i) q^{45} +(7.75667 - 13.4349i) q^{46} -0.753020 q^{47} +(6.51842 - 11.2902i) q^{48} +(3.34601 + 5.79546i) q^{49} +(-5.24914 - 9.09177i) q^{50} +4.85086 q^{51} -7.58211 q^{53} +(-1.34601 - 2.33136i) q^{54} +(1.52715 + 2.64510i) q^{55} +(-2.42543 + 4.20096i) q^{56} -0.753020 q^{57} +(-2.57338 + 4.45722i) q^{58} +(2.04892 - 3.54883i) q^{59} -5.50365 q^{60} +(1.71164 - 2.96464i) q^{61} +(12.8083 + 22.1846i) q^{62} +(0.277479 + 0.480608i) q^{63} +21.3424 q^{64} -7.83877 q^{66} +(-0.936313 - 1.62174i) q^{67} +(12.7262 + 22.0424i) q^{68} +(2.88135 - 4.99065i) q^{69} +1.56704 q^{70} +(-5.25182 + 9.09643i) q^{71} +(4.37047 - 7.56988i) q^{72} -10.4765 q^{73} +(-7.74363 + 13.4124i) q^{74} +(-1.94989 - 3.37730i) q^{75} +(-1.97554 - 3.42174i) q^{76} +1.61596 q^{77} +1.33513 q^{79} +(-6.83728 - 11.8425i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.61141 + 11.4513i) q^{82} -2.64310 q^{83} +(-1.45593 + 2.52174i) q^{84} +(2.54407 - 4.40646i) q^{85} +29.8756 q^{86} +(-0.955927 + 1.65571i) q^{87} +(-12.7262 - 22.0424i) q^{88} +(4.96346 + 8.59696i) q^{89} -2.82371 q^{90} +30.2368 q^{92} +(4.75786 + 8.24086i) q^{93} +(-1.01357 - 1.75556i) q^{94} +(-0.394928 + 0.684035i) q^{95} +17.6136 q^{96} +(8.53684 - 14.7862i) q^{97} +(-9.00753 + 15.6015i) q^{98} -2.91185 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+3q2+3q311q412q53q6+2q724q83q9+q10+5q1122q1210q146q1511q16+q176q187q19+15q20+4q21+10q99+O(q100) 6 q + 3 q^{2} + 3 q^{3} - 11 q^{4} - 12 q^{5} - 3 q^{6} + 2 q^{7} - 24 q^{8} - 3 q^{9} + q^{10} + 5 q^{11} - 22 q^{12} - 10 q^{14} - 6 q^{15} - 11 q^{16} + q^{17} - 6 q^{18} - 7 q^{19} + 15 q^{20} + 4 q^{21}+ \cdots - 10 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/507Z)×\left(\mathbb{Z}/507\mathbb{Z}\right)^\times.

nn 170170 340340
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.34601 + 2.33136i 0.951773 + 1.64852i 0.741585 + 0.670859i 0.234074π0.234074\pi
0.210188 + 0.977661i 0.432592π0.432592\pi
33 0.500000 + 0.866025i 0.288675 + 0.500000i
44 −2.62349 + 4.54402i −1.31174 + 2.27201i
55 1.04892 0.469090 0.234545 0.972105i 0.424640π-0.424640\pi
0.234545 + 0.972105i 0.424640π0.424640\pi
66 −1.34601 + 2.33136i −0.549507 + 0.951773i
77 0.277479 0.480608i 0.104877 0.181653i −0.808811 0.588069i 0.799888π-0.799888\pi
0.913688 + 0.406416i 0.133222π0.133222\pi
88 −8.74094 −3.09039
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 1.41185 + 2.44540i 0.446467 + 0.773304i
1111 1.45593 + 2.52174i 0.438979 + 0.760333i 0.997611 0.0690822i 0.0220071π-0.0220071\pi
−0.558632 + 0.829415i 0.688674π0.688674\pi
1212 −5.24698 −1.51467
1313 0 0
1414 1.49396 0.399277
1515 0.524459 + 0.908389i 0.135415 + 0.234545i
1616 −6.51842 11.2902i −1.62960 2.82256i
1717 2.42543 4.20096i 0.588253 1.01888i −0.406209 0.913780i 0.633149π-0.633149\pi
0.994461 0.105103i 0.0335172π-0.0335172\pi
1818 −2.69202 −0.634516
1919 −0.376510 + 0.652135i −0.0863774 + 0.149610i −0.905977 0.423326i 0.860862π-0.860862\pi
0.819600 + 0.572936i 0.194196π0.194196\pi
2020 −2.75182 + 4.76630i −0.615327 + 1.06578i
2121 0.554958 0.121102
2222 −3.91939 + 6.78858i −0.835616 + 1.44733i
2323 −2.88135 4.99065i −0.600804 1.04062i −0.992700 0.120613i 0.961514π-0.961514\pi
0.391896 0.920010i 0.371819π-0.371819\pi
2424 −4.37047 7.56988i −0.892118 1.54519i
2525 −3.89977 −0.779954
2626 0 0
2727 −1.00000 −0.192450
2828 1.45593 + 2.52174i 0.275144 + 0.476564i
2929 0.955927 + 1.65571i 0.177511 + 0.307458i 0.941027 0.338330i 0.109862π-0.109862\pi
−0.763516 + 0.645789i 0.776529π0.776529\pi
3030 −1.41185 + 2.44540i −0.257768 + 0.446467i
3131 9.51573 1.70908 0.854538 0.519389i 0.173841π-0.173841\pi
0.854538 + 0.519389i 0.173841π0.173841\pi
3232 8.80678 15.2538i 1.55683 2.69652i
3333 −1.45593 + 2.52174i −0.253444 + 0.438979i
3434 13.0586 2.23953
3535 0.291053 0.504118i 0.0491969 0.0852115i
3636 −2.62349 4.54402i −0.437248 0.757336i
3737 2.87651 + 4.98226i 0.472895 + 0.819079i 0.999519 0.0310199i 0.00987552π-0.00987552\pi
−0.526623 + 0.850099i 0.676542π0.676542\pi
3838 −2.02715 −0.328847
3939 0 0
4040 −9.16852 −1.44967
4141 2.45593 + 4.25379i 0.383551 + 0.664330i 0.991567 0.129595i 0.0413676π-0.0413676\pi
−0.608016 + 0.793925i 0.708034π0.708034\pi
4242 0.746980 + 1.29381i 0.115261 + 0.199639i
4343 5.54892 9.61101i 0.846202 1.46566i −0.0383713 0.999264i 0.512217π-0.512217\pi
0.884573 0.466401i 0.154450π-0.154450\pi
4444 −15.2784 −2.30331
4545 −0.524459 + 0.908389i −0.0781817 + 0.135415i
4646 7.75667 13.4349i 1.14366 1.98087i
4747 −0.753020 −0.109839 −0.0549197 0.998491i 0.517490π-0.517490\pi
−0.0549197 + 0.998491i 0.517490π0.517490\pi
4848 6.51842 11.2902i 0.940853 1.62960i
4949 3.34601 + 5.79546i 0.478002 + 0.827923i
5050 −5.24914 9.09177i −0.742340 1.28577i
5151 4.85086 0.679256
5252 0 0
5353 −7.58211 −1.04148 −0.520741 0.853715i 0.674344π-0.674344\pi
−0.520741 + 0.853715i 0.674344π0.674344\pi
5454 −1.34601 2.33136i −0.183169 0.317258i
5555 1.52715 + 2.64510i 0.205920 + 0.356665i
5656 −2.42543 + 4.20096i −0.324111 + 0.561377i
5757 −0.753020 −0.0997400
5858 −2.57338 + 4.45722i −0.337901 + 0.585261i
5959 2.04892 3.54883i 0.266746 0.462018i −0.701273 0.712892i 0.747385π-0.747385\pi
0.968020 + 0.250874i 0.0807181π0.0807181\pi
6060 −5.50365 −0.710518
6161 1.71164 2.96464i 0.219153 0.379583i −0.735397 0.677637i 0.763004π-0.763004\pi
0.954549 + 0.298054i 0.0963374π0.0963374\pi
6262 12.8083 + 22.1846i 1.62665 + 2.81744i
6363 0.277479 + 0.480608i 0.0349591 + 0.0605509i
6464 21.3424 2.66780
6565 0 0
6666 −7.83877 −0.964886
6767 −0.936313 1.62174i −0.114389 0.198127i 0.803146 0.595782i 0.203158π-0.203158\pi
−0.917535 + 0.397654i 0.869824π0.869824\pi
6868 12.7262 + 22.0424i 1.54327 + 2.67303i
6969 2.88135 4.99065i 0.346874 0.600804i
7070 1.56704 0.187297
7171 −5.25182 + 9.09643i −0.623277 + 1.07955i 0.365595 + 0.930774i 0.380866π0.380866\pi
−0.988871 + 0.148773i 0.952468π0.952468\pi
7272 4.37047 7.56988i 0.515065 0.892118i
7373 −10.4765 −1.22618 −0.613091 0.790012i 0.710074π-0.710074\pi
−0.613091 + 0.790012i 0.710074π0.710074\pi
7474 −7.74363 + 13.4124i −0.900178 + 1.55915i
7575 −1.94989 3.37730i −0.225153 0.389977i
7676 −1.97554 3.42174i −0.226610 0.392500i
7777 1.61596 0.184155
7878 0 0
7979 1.33513 0.150213 0.0751067 0.997176i 0.476070π-0.476070\pi
0.0751067 + 0.997176i 0.476070π0.476070\pi
8080 −6.83728 11.8425i −0.764431 1.32403i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 −6.61141 + 11.4513i −0.730108 + 1.26458i
8383 −2.64310 −0.290118 −0.145059 0.989423i 0.546337π-0.546337\pi
−0.145059 + 0.989423i 0.546337π0.546337\pi
8484 −1.45593 + 2.52174i −0.158855 + 0.275144i
8585 2.54407 4.40646i 0.275943 0.477948i
8686 29.8756 3.22157
8787 −0.955927 + 1.65571i −0.102486 + 0.177511i
8888 −12.7262 22.0424i −1.35661 2.34972i
8989 4.96346 + 8.59696i 0.526126 + 0.911276i 0.999537 + 0.0304348i 0.00968919π0.00968919\pi
−0.473411 + 0.880842i 0.656977π0.656977\pi
9090 −2.82371 −0.297645
9191 0 0
9292 30.2368 3.15241
9393 4.75786 + 8.24086i 0.493368 + 0.854538i
9494 −1.01357 1.75556i −0.104542 0.181072i
9595 −0.394928 + 0.684035i −0.0405188 + 0.0701806i
9696 17.6136 1.79768
9797 8.53684 14.7862i 0.866784 1.50131i 0.00151988 0.999999i 0.499516π-0.499516\pi
0.865264 0.501316i 0.167150π-0.167150\pi
9898 −9.00753 + 15.6015i −0.909898 + 1.57599i
9999 −2.91185 −0.292652
100100 10.2310 17.7206i 1.02310 1.77206i
101101 −3.66152 6.34194i −0.364335 0.631047i 0.624334 0.781157i 0.285370π-0.285370\pi
−0.988669 + 0.150111i 0.952037π0.952037\pi
102102 6.52930 + 11.3091i 0.646497 + 1.11977i
103103 −4.21983 −0.415792 −0.207896 0.978151i 0.566662π-0.566662\pi
−0.207896 + 0.978151i 0.566662π0.566662\pi
104104 0 0
105105 0.582105 0.0568077
106106 −10.2056 17.6766i −0.991255 1.71690i
107107 −3.19687 5.53713i −0.309053 0.535295i 0.669103 0.743170i 0.266679π-0.266679\pi
−0.978155 + 0.207875i 0.933345π0.933345\pi
108108 2.62349 4.54402i 0.252445 0.437248i
109109 3.46011 0.331418 0.165709 0.986175i 0.447009π-0.447009\pi
0.165709 + 0.986175i 0.447009π0.447009\pi
110110 −4.11111 + 7.12066i −0.391979 + 0.678928i
111111 −2.87651 + 4.98226i −0.273026 + 0.472895i
112112 −7.23490 −0.683634
113113 −4.67845 + 8.10331i −0.440111 + 0.762295i −0.997697 0.0678240i 0.978394π-0.978394\pi
0.557586 + 0.830119i 0.311728π0.311728\pi
114114 −1.01357 1.75556i −0.0949299 0.164423i
115115 −3.02230 5.23478i −0.281831 0.488146i
116116 −10.0315 −0.931398
117117 0 0
118118 11.0315 1.01553
119119 −1.34601 2.33136i −0.123389 0.213715i
120120 −4.58426 7.94017i −0.418484 0.724835i
121121 1.26055 2.18334i 0.114596 0.198486i
122122 9.21552 0.834334
123123 −2.45593 + 4.25379i −0.221443 + 0.383551i
124124 −24.9644 + 43.2396i −2.24187 + 3.88303i
125125 −9.33513 −0.834959
126126 −0.746980 + 1.29381i −0.0665462 + 0.115261i
127127 2.24094 + 3.88142i 0.198851 + 0.344420i 0.948156 0.317805i 0.102946π-0.102946\pi
−0.749305 + 0.662225i 0.769612π0.769612\pi
128128 11.1136 + 19.2493i 0.982310 + 1.70141i
129129 11.0978 0.977110
130130 0 0
131131 −9.21744 −0.805331 −0.402666 0.915347i 0.631916π-0.631916\pi
−0.402666 + 0.915347i 0.631916π0.631916\pi
132132 −7.63922 13.2315i −0.664909 1.15166i
133133 0.208947 + 0.361908i 0.0181180 + 0.0313814i
134134 2.52057 4.36576i 0.217744 0.377144i
135135 −1.04892 −0.0902764
136136 −21.2005 + 36.7204i −1.81793 + 3.14875i
137137 −3.73490 + 6.46903i −0.319094 + 0.552687i −0.980299 0.197518i 0.936712π-0.936712\pi
0.661205 + 0.750205i 0.270045π0.270045\pi
138138 15.5133 1.32058
139139 8.99880 15.5864i 0.763269 1.32202i −0.177889 0.984051i 0.556927π-0.556927\pi
0.941157 0.337969i 0.109740π-0.109740\pi
140140 1.52715 + 2.64510i 0.129067 + 0.223551i
141141 −0.376510 0.652135i −0.0317079 0.0549197i
142142 −28.2760 −2.37287
143143 0 0
144144 13.0368 1.08640
145145 1.00269 + 1.73671i 0.0832687 + 0.144226i
146146 −14.1015 24.4245i −1.16705 2.02138i
147147 −3.34601 + 5.79546i −0.275974 + 0.478002i
148148 −30.1860 −2.48127
149149 7.66756 13.2806i 0.628151 1.08799i −0.359771 0.933041i 0.617145π-0.617145\pi
0.987922 0.154949i 0.0495214π-0.0495214\pi
150150 5.24914 9.09177i 0.428590 0.742340i
151151 −2.53079 −0.205953 −0.102977 0.994684i 0.532837π-0.532837\pi
−0.102977 + 0.994684i 0.532837π0.532837\pi
152152 3.29105 5.70027i 0.266940 0.462353i
153153 2.42543 + 4.20096i 0.196084 + 0.339628i
154154 2.17510 + 3.76738i 0.175274 + 0.303584i
155155 9.98121 0.801710
156156 0 0
157157 17.2392 1.37584 0.687919 0.725787i 0.258524π-0.258524\pi
0.687919 + 0.725787i 0.258524π0.258524\pi
158158 1.79709 + 3.11266i 0.142969 + 0.247630i
159159 −3.79105 6.56630i −0.300650 0.520741i
160160 9.23759 16.0000i 0.730295 1.26491i
161161 −3.19806 −0.252043
162162 1.34601 2.33136i 0.105753 0.183169i
163163 7.85354 13.6027i 0.615137 1.06545i −0.375223 0.926934i 0.622434π-0.622434\pi
0.990360 0.138514i 0.0442326π-0.0442326\pi
164164 −25.7724 −2.01249
165165 −1.52715 + 2.64510i −0.118888 + 0.205920i
166166 −3.55765 6.16202i −0.276127 0.478266i
167167 2.69806 + 4.67318i 0.208782 + 0.361622i 0.951331 0.308170i 0.0997166π-0.0997166\pi
−0.742549 + 0.669792i 0.766383π0.766383\pi
168168 −4.85086 −0.374252
169169 0 0
170170 13.6974 1.05054
171171 −0.376510 0.652135i −0.0287925 0.0498700i
172172 29.1151 + 50.4288i 2.22000 + 3.84516i
173173 −11.9710 + 20.7344i −0.910138 + 1.57640i −0.0962694 + 0.995355i 0.530691π0.530691\pi
−0.813868 + 0.581049i 0.802642π0.802642\pi
174174 −5.14675 −0.390174
175175 −1.08211 + 1.87426i −0.0817995 + 0.141681i
176176 18.9807 32.8755i 1.43072 2.47808i
177177 4.09783 0.308012
178178 −13.3617 + 23.1432i −1.00150 + 1.73466i
179179 −9.20440 15.9425i −0.687969 1.19160i −0.972494 0.232929i 0.925169π-0.925169\pi
0.284525 0.958669i 0.408164π-0.408164\pi
180180 −2.75182 4.76630i −0.205109 0.355259i
181181 −3.63342 −0.270070 −0.135035 0.990841i 0.543115π-0.543115\pi
−0.135035 + 0.990841i 0.543115π0.543115\pi
182182 0 0
183183 3.42327 0.253056
184184 25.1857 + 43.6230i 1.85672 + 3.21593i
185185 3.01722 + 5.22598i 0.221831 + 0.384222i
186186 −12.8083 + 22.1846i −0.939148 + 1.62665i
187187 14.1250 1.03292
188188 1.97554 3.42174i 0.144081 0.249556i
189189 −0.277479 + 0.480608i −0.0201836 + 0.0349591i
190190 −2.12631 −0.154259
191191 10.5891 18.3409i 0.766201 1.32710i −0.173409 0.984850i 0.555478π-0.555478\pi
0.939609 0.342249i 0.111189π-0.111189\pi
192192 10.6712 + 18.4831i 0.770128 + 1.33390i
193193 −8.80559 15.2517i −0.633840 1.09784i −0.986760 0.162189i 0.948144π-0.948144\pi
0.352920 0.935654i 0.385189π-0.385189\pi
194194 45.9627 3.29993
195195 0 0
196196 −35.1129 −2.50806
197197 −2.33124 4.03783i −0.166094 0.287683i 0.770949 0.636897i 0.219782π-0.219782\pi
−0.937043 + 0.349213i 0.886449π0.886449\pi
198198 −3.91939 6.78858i −0.278539 0.482443i
199199 −7.51842 + 13.0223i −0.532967 + 0.923125i 0.466292 + 0.884631i 0.345590π0.345590\pi
−0.999259 + 0.0384944i 0.987744π0.987744\pi
200200 34.0877 2.41036
201201 0.936313 1.62174i 0.0660424 0.114389i
202202 9.85690 17.0726i 0.693529 1.20123i
203203 1.06100 0.0744675
204204 −12.7262 + 22.0424i −0.891010 + 1.54327i
205205 2.57606 + 4.46187i 0.179920 + 0.311631i
206206 −5.67994 9.83794i −0.395740 0.685442i
207207 5.76271 0.400536
208208 0 0
209209 −2.19269 −0.151671
210210 0.783520 + 1.35710i 0.0540680 + 0.0936485i
211211 0.230054 + 0.398465i 0.0158375 + 0.0274314i 0.873836 0.486222i 0.161625π-0.161625\pi
−0.857998 + 0.513653i 0.828292π0.828292\pi
212212 19.8916 34.4532i 1.36616 2.36626i
213213 −10.5036 −0.719698
214214 8.60603 14.9061i 0.588296 1.01896i
215215 5.82036 10.0812i 0.396945 0.687529i
216216 8.74094 0.594746
217217 2.64042 4.57333i 0.179243 0.310458i
218218 4.65734 + 8.06675i 0.315435 + 0.546349i
219219 −5.23825 9.07292i −0.353968 0.613091i
220220 −16.0258 −1.08046
221221 0 0
222222 −15.4873 −1.03944
223223 −8.17510 14.1597i −0.547445 0.948202i −0.998449 0.0556803i 0.982267π-0.982267\pi
0.451004 0.892522i 0.351066π-0.351066\pi
224224 −4.88740 8.46522i −0.326553 0.565606i
225225 1.94989 3.37730i 0.129992 0.225153i
226226 −25.1890 −1.67555
227227 3.28017 5.68142i 0.217712 0.377089i −0.736396 0.676551i 0.763474π-0.763474\pi
0.954108 + 0.299462i 0.0968072π0.0968072\pi
228228 1.97554 3.42174i 0.130833 0.226610i
229229 3.95539 0.261380 0.130690 0.991423i 0.458281π-0.458281\pi
0.130690 + 0.991423i 0.458281π0.458281\pi
230230 8.13610 14.0921i 0.536479 0.929209i
231231 0.807979 + 1.39946i 0.0531611 + 0.0920777i
232232 −8.35570 14.4725i −0.548579 0.950166i
233233 8.35690 0.547478 0.273739 0.961804i 0.411739π-0.411739\pi
0.273739 + 0.961804i 0.411739π0.411739\pi
234234 0 0
235235 −0.789856 −0.0515245
236236 10.7506 + 18.6206i 0.699806 + 1.21210i
237237 0.667563 + 1.15625i 0.0433629 + 0.0751067i
238238 3.62349 6.27607i 0.234876 0.406817i
239239 −20.1008 −1.30021 −0.650107 0.759843i 0.725276π-0.725276\pi
−0.650107 + 0.759843i 0.725276π0.725276\pi
240240 6.83728 11.8425i 0.441345 0.764431i
241241 −9.50634 + 16.4655i −0.612357 + 1.06063i 0.378485 + 0.925607i 0.376445π0.376445\pi
−0.990842 + 0.135026i 0.956888π0.956888\pi
242242 6.78687 0.436277
243243 0.500000 0.866025i 0.0320750 0.0555556i
244244 8.98092 + 15.5554i 0.574944 + 0.995833i
245245 3.50969 + 6.07896i 0.224226 + 0.388370i
246246 −13.2228 −0.843056
247247 0 0
248248 −83.1764 −5.28171
249249 −1.32155 2.28900i −0.0837500 0.145059i
250250 −12.5652 21.7635i −0.794692 1.37645i
251251 0.381887 0.661448i 0.0241045 0.0417502i −0.853722 0.520730i 0.825660π-0.825660\pi
0.877826 + 0.478980i 0.158993π0.158993\pi
252252 −2.91185 −0.183430
253253 8.39008 14.5321i 0.527480 0.913622i
254254 −6.03266 + 10.4489i −0.378522 + 0.655620i
255255 5.08815 0.318632
256256 −8.57553 + 14.8533i −0.535971 + 0.928329i
257257 6.54556 + 11.3373i 0.408301 + 0.707198i 0.994700 0.102825i 0.0327880π-0.0327880\pi
−0.586398 + 0.810023i 0.699455π0.699455\pi
258258 14.9378 + 25.8730i 0.929987 + 1.61078i
259259 3.19269 0.198384
260260 0 0
261261 −1.91185 −0.118341
262262 −12.4068 21.4892i −0.766493 1.32760i
263263 −9.18867 15.9152i −0.566598 0.981376i −0.996899 0.0786906i 0.974926π-0.974926\pi
0.430301 0.902685i 0.358407π-0.358407\pi
264264 12.7262 22.0424i 0.783242 1.35661i
265265 −7.95300 −0.488549
266266 −0.562491 + 0.974263i −0.0344885 + 0.0597359i
267267 −4.96346 + 8.59696i −0.303759 + 0.526126i
268268 9.82563 0.600196
269269 −11.8312 + 20.4923i −0.721363 + 1.24944i 0.239090 + 0.970997i 0.423151π0.423151\pi
−0.960453 + 0.278441i 0.910182π0.910182\pi
270270 −1.41185 2.44540i −0.0859227 0.148822i
271271 −9.87651 17.1066i −0.599955 1.03915i −0.992827 0.119560i 0.961852π-0.961852\pi
0.392872 0.919593i 0.371482π-0.371482\pi
272272 −63.2398 −3.83448
273273 0 0
274274 −20.1089 −1.21482
275275 −5.67778 9.83421i −0.342383 0.593025i
276276 15.1184 + 26.1859i 0.910021 + 1.57620i
277277 −0.888887 + 1.53960i −0.0534081 + 0.0925055i −0.891493 0.453034i 0.850342π-0.850342\pi
0.838085 + 0.545539i 0.183675π0.183675\pi
278278 48.4499 2.90583
279279 −4.75786 + 8.24086i −0.284846 + 0.493368i
280280 −2.54407 + 4.40646i −0.152037 + 0.263337i
281281 −1.62133 −0.0967207 −0.0483603 0.998830i 0.515400π-0.515400\pi
−0.0483603 + 0.998830i 0.515400π0.515400\pi
282282 1.01357 1.75556i 0.0603574 0.104542i
283283 −2.49180 4.31593i −0.148122 0.256555i 0.782411 0.622762i 0.213990π-0.213990\pi
−0.930533 + 0.366207i 0.880656π0.880656\pi
284284 −27.5562 47.7288i −1.63516 2.83218i
285285 −0.789856 −0.0467870
286286 0 0
287287 2.72587 0.160903
288288 8.80678 + 15.2538i 0.518945 + 0.898838i
289289 −3.26540 5.65583i −0.192082 0.332696i
290290 −2.69926 + 4.67525i −0.158506 + 0.274540i
291291 17.0737 1.00088
292292 27.4850 47.6054i 1.60844 2.78590i
293293 −0.0358763 + 0.0621395i −0.00209591 + 0.00363023i −0.867071 0.498184i 0.834000π-0.834000\pi
0.864976 + 0.501814i 0.167334π0.167334\pi
294294 −18.0151 −1.05066
295295 2.14914 3.72243i 0.125128 0.216728i
296296 −25.1434 43.5496i −1.46143 2.53127i
297297 −1.45593 2.52174i −0.0844815 0.146326i
298298 41.2825 2.39143
299299 0 0
300300 20.4620 1.18138
301301 −3.07942 5.33371i −0.177495 0.307430i
302302 −3.40648 5.90019i −0.196021 0.339518i
303303 3.66152 6.34194i 0.210349 0.364335i
304304 9.81700 0.563044
305305 1.79536 3.10966i 0.102802 0.178059i
306306 −6.52930 + 11.3091i −0.373255 + 0.646497i
307307 5.19806 0.296669 0.148335 0.988937i 0.452609π-0.452609\pi
0.148335 + 0.988937i 0.452609π0.452609\pi
308308 −4.23945 + 7.34294i −0.241565 + 0.418403i
309309 −2.10992 3.65448i −0.120029 0.207896i
310310 13.4348 + 23.2698i 0.763047 + 1.32164i
311311 −22.5429 −1.27829 −0.639145 0.769087i 0.720711π-0.720711\pi
−0.639145 + 0.769087i 0.720711π0.720711\pi
312312 0 0
313313 22.6612 1.28088 0.640442 0.768006i 0.278751π-0.278751\pi
0.640442 + 0.768006i 0.278751π0.278751\pi
314314 23.2042 + 40.1908i 1.30949 + 2.26810i
315315 0.291053 + 0.504118i 0.0163990 + 0.0284038i
316316 −3.50269 + 6.06683i −0.197042 + 0.341286i
317317 −26.3424 −1.47954 −0.739769 0.672861i 0.765065π-0.765065\pi
−0.739769 + 0.672861i 0.765065π0.765065\pi
318318 10.2056 17.6766i 0.572301 0.991255i
319319 −2.78352 + 4.82120i −0.155847 + 0.269935i
320320 22.3864 1.25144
321321 3.19687 5.53713i 0.178432 0.309053i
322322 −4.30463 7.45583i −0.239887 0.415497i
323323 1.82640 + 3.16341i 0.101623 + 0.176017i
324324 5.24698 0.291499
325325 0 0
326326 42.2838 2.34188
327327 1.73005 + 2.99654i 0.0956722 + 0.165709i
328328 −21.4671 37.1821i −1.18532 2.05304i
329329 −0.208947 + 0.361908i −0.0115196 + 0.0199526i
330330 −8.22223 −0.452619
331331 −5.61476 + 9.72505i −0.308615 + 0.534537i −0.978060 0.208325i 0.933199π-0.933199\pi
0.669445 + 0.742862i 0.266532π0.266532\pi
332332 6.93416 12.0103i 0.380561 0.659151i
333333 −5.75302 −0.315264
334334 −7.26324 + 12.5803i −0.397427 + 0.688364i
335335 −0.982115 1.70107i −0.0536587 0.0929395i
336336 −3.61745 6.26561i −0.197348 0.341817i
337337 2.30798 0.125724 0.0628618 0.998022i 0.479977π-0.479977\pi
0.0628618 + 0.998022i 0.479977π0.479977\pi
338338 0 0
339339 −9.35690 −0.508197
340340 13.3487 + 23.1206i 0.723935 + 1.25389i
341341 13.8542 + 23.9962i 0.750247 + 1.29947i
342342 1.01357 1.75556i 0.0548078 0.0949299i
343343 7.59850 0.410280
344344 −48.5027 + 84.0092i −2.61509 + 4.52947i
345345 3.02230 5.23478i 0.162715 0.281831i
346346 −64.4523 −3.46498
347347 4.56853 7.91293i 0.245252 0.424788i −0.716951 0.697124i 0.754463π-0.754463\pi
0.962202 + 0.272336i 0.0877961π0.0877961\pi
348348 −5.01573 8.68750i −0.268871 0.465699i
349349 11.9879 + 20.7637i 0.641699 + 1.11145i 0.985053 + 0.172249i 0.0551033π0.0551033\pi
−0.343355 + 0.939206i 0.611563π0.611563\pi
350350 −5.82610 −0.311418
351351 0 0
352352 51.2881 2.73367
353353 −13.5620 23.4900i −0.721830 1.25025i −0.960265 0.279088i 0.909968π-0.909968\pi
0.238435 0.971158i 0.423366π-0.423366\pi
354354 5.51573 + 9.55352i 0.293158 + 0.507764i
355355 −5.50873 + 9.54140i −0.292373 + 0.506405i
356356 −52.0863 −2.76057
357357 1.34601 2.33136i 0.0712384 0.123389i
358358 24.7784 42.9175i 1.30958 2.26826i
359359 26.0790 1.37640 0.688200 0.725521i 0.258401π-0.258401\pi
0.688200 + 0.725521i 0.258401π0.258401\pi
360360 4.58426 7.94017i 0.241612 0.418484i
361361 9.21648 + 15.9634i 0.485078 + 0.840180i
362362 −4.89062 8.47080i −0.257045 0.445215i
363363 2.52111 0.132324
364364 0 0
365365 −10.9890 −0.575190
366366 4.60776 + 7.98088i 0.240851 + 0.417167i
367367 −4.78717 8.29162i −0.249888 0.432819i 0.713606 0.700547i 0.247061π-0.247061\pi
−0.963495 + 0.267728i 0.913727π0.913727\pi
368368 −37.5637 + 65.0623i −1.95815 + 3.39161i
369369 −4.91185 −0.255701
370370 −8.12242 + 14.0685i −0.422265 + 0.731384i
371371 −2.10388 + 3.64402i −0.109228 + 0.189188i
372372 −49.9288 −2.58869
373373 −14.0749 + 24.3784i −0.728769 + 1.26227i 0.228635 + 0.973512i 0.426574π0.426574\pi
−0.957404 + 0.288753i 0.906759π0.906759\pi
374374 19.0124 + 32.9304i 0.983107 + 1.70279i
375375 −4.66756 8.08446i −0.241032 0.417480i
376376 6.58211 0.339446
377377 0 0
378378 −1.49396 −0.0768410
379379 8.02326 + 13.8967i 0.412127 + 0.713825i 0.995122 0.0986504i 0.0314526π-0.0314526\pi
−0.582995 + 0.812476i 0.698119π0.698119\pi
380380 −2.07218 3.58912i −0.106301 0.184118i
381381 −2.24094 + 3.88142i −0.114807 + 0.198851i
382382 57.0122 2.91700
383383 −12.3083 + 21.3186i −0.628923 + 1.08933i 0.358845 + 0.933397i 0.383171π0.383171\pi
−0.987768 + 0.155930i 0.950163π0.950163\pi
384384 −11.1136 + 19.2493i −0.567137 + 0.982310i
385385 1.69501 0.0863855
386386 23.7048 41.0580i 1.20654 2.08980i
387387 5.54892 + 9.61101i 0.282067 + 0.488555i
388388 44.7926 + 77.5831i 2.27400 + 3.93868i
389389 −17.2198 −0.873080 −0.436540 0.899685i 0.643796π-0.643796\pi
−0.436540 + 0.899685i 0.643796π0.643796\pi
390390 0 0
391391 −27.9541 −1.41370
392392 −29.2473 50.6578i −1.47721 2.55860i
393393 −4.60872 7.98254i −0.232479 0.402666i
394394 6.27575 10.8699i 0.316168 0.547619i
395395 1.40044 0.0704636
396396 7.63922 13.2315i 0.383885 0.664909i
397397 −1.01961 + 1.76602i −0.0511730 + 0.0886342i −0.890477 0.455028i 0.849629π-0.849629\pi
0.839304 + 0.543662i 0.182963π0.182963\pi
398398 −40.4795 −2.02905
399399 −0.208947 + 0.361908i −0.0104605 + 0.0181180i
400400 25.4203 + 44.0293i 1.27102 + 2.20147i
401401 −0.730718 1.26564i −0.0364903 0.0632031i 0.847203 0.531269i 0.178284π-0.178284\pi
−0.883694 + 0.468065i 0.844951π0.844951\pi
402402 5.04115 0.251430
403403 0 0
404404 38.4239 1.91166
405405 −0.524459 0.908389i −0.0260606 0.0451382i
406406 1.42812 + 2.47357i 0.0708762 + 0.122761i
407407 −8.37598 + 14.5076i −0.415182 + 0.719116i
408408 −42.4010 −2.09916
409409 −14.9695 + 25.9279i −0.740194 + 1.28205i 0.212213 + 0.977224i 0.431933π0.431933\pi
−0.952407 + 0.304830i 0.901400π0.901400\pi
410410 −6.93482 + 12.0115i −0.342486 + 0.593204i
411411 −7.46980 −0.368458
412412 11.0707 19.1750i 0.545414 0.944684i
413413 −1.13706 1.96945i −0.0559512 0.0969104i
414414 7.75667 + 13.4349i 0.381219 + 0.660291i
415415 −2.77240 −0.136092
416416 0 0
417417 17.9976 0.881347
418418 −2.95138 5.11194i −0.144357 0.250033i
419419 −3.32371 5.75683i −0.162374 0.281240i 0.773346 0.633984i 0.218582π-0.218582\pi
−0.935720 + 0.352745i 0.885248π0.885248\pi
420420 −1.52715 + 2.64510i −0.0745171 + 0.129067i
421421 −13.5646 −0.661100 −0.330550 0.943788i 0.607234π-0.607234\pi
−0.330550 + 0.943788i 0.607234π0.607234\pi
422422 −0.619309 + 1.07268i −0.0301475 + 0.0522170i
423423 0.376510 0.652135i 0.0183066 0.0317079i
424424 66.2747 3.21858
425425 −9.45862 + 16.3828i −0.458810 + 0.794683i
426426 −14.1380 24.4878i −0.684989 1.18644i
427427 −0.949886 1.64525i −0.0459682 0.0796193i
428428 33.5478 1.62159
429429 0 0
430430 31.3370 1.51121
431431 17.9731 + 31.1304i 0.865736 + 1.49950i 0.866314 + 0.499499i 0.166483π0.166483\pi
−0.000578325 1.00000i 0.500184π0.500184\pi
432432 6.51842 + 11.2902i 0.313618 + 0.543201i
433433 16.2371 28.1234i 0.780303 1.35152i −0.151462 0.988463i 0.548398π-0.548398\pi
0.931765 0.363061i 0.118268π-0.118268\pi
434434 14.2161 0.682395
435435 −1.00269 + 1.73671i −0.0480752 + 0.0832687i
436436 −9.07756 + 15.7228i −0.434736 + 0.752985i
437437 4.33944 0.207583
438438 14.1015 24.4245i 0.673795 1.16705i
439439 −6.41603 11.1129i −0.306221 0.530390i 0.671312 0.741175i 0.265731π-0.265731\pi
−0.977532 + 0.210785i 0.932398π0.932398\pi
440440 −13.3487 23.1206i −0.636374 1.10223i
441441 −6.69202 −0.318668
442442 0 0
443443 11.9608 0.568273 0.284137 0.958784i 0.408293π-0.408293\pi
0.284137 + 0.958784i 0.408293π0.408293\pi
444444 −15.0930 26.1418i −0.716282 1.24064i
445445 5.20626 + 9.01751i 0.246800 + 0.427471i
446446 22.0075 38.1182i 1.04209 1.80495i
447447 15.3351 0.725327
448448 5.92208 10.2573i 0.279792 0.484614i
449449 −6.23945 + 10.8070i −0.294458 + 0.510016i −0.974859 0.222824i 0.928472π-0.928472\pi
0.680401 + 0.732840i 0.261806π0.261806\pi
450450 10.4983 0.494893
451451 −7.15130 + 12.3864i −0.336742 + 0.583254i
452452 −24.5477 42.5179i −1.15463 1.99987i
453453 −1.26540 2.19173i −0.0594536 0.102977i
454454 17.6606 0.828851
455455 0 0
456456 6.58211 0.308235
457457 16.2262 + 28.1045i 0.759028 + 1.31468i 0.943347 + 0.331809i 0.107659π0.107659\pi
−0.184319 + 0.982867i 0.559008π0.559008\pi
458458 5.32400 + 9.22144i 0.248774 + 0.430890i
459459 −2.42543 + 4.20096i −0.113209 + 0.196084i
460460 31.7159 1.47876
461461 12.2017 21.1340i 0.568290 0.984308i −0.428445 0.903568i 0.640938π-0.640938\pi
0.996735 0.0807398i 0.0257283π-0.0257283\pi
462462 −2.17510 + 3.76738i −0.101195 + 0.175274i
463463 33.1836 1.54217 0.771086 0.636731i 0.219714π-0.219714\pi
0.771086 + 0.636731i 0.219714π0.219714\pi
464464 12.4623 21.5853i 0.578546 1.00207i
465465 4.99061 + 8.64398i 0.231434 + 0.400855i
466466 11.2485 + 19.4829i 0.521075 + 0.902529i
467467 −38.5206 −1.78252 −0.891261 0.453490i 0.850179π-0.850179\pi
−0.891261 + 0.453490i 0.850179π0.850179\pi
468468 0 0
469469 −1.03923 −0.0479871
470470 −1.06315 1.84144i −0.0490397 0.0849392i
471471 8.61960 + 14.9296i 0.397170 + 0.687919i
472472 −17.9095 + 31.0201i −0.824350 + 1.42782i
473473 32.3153 1.48586
474474 −1.79709 + 3.11266i −0.0825432 + 0.142969i
475475 1.46830 2.54318i 0.0673704 0.116689i
476476 14.1250 0.647417
477477 3.79105 6.56630i 0.173580 0.300650i
478478 −27.0559 46.8622i −1.23751 2.14343i
479479 −4.17241 7.22682i −0.190642 0.330202i 0.754821 0.655931i 0.227724π-0.227724\pi
−0.945463 + 0.325729i 0.894390π0.894390\pi
480480 18.4752 0.843272
481481 0 0
482482 −51.1825 −2.33130
483483 −1.59903 2.76960i −0.0727584 0.126021i
484484 6.61410 + 11.4560i 0.300641 + 0.520725i
485485 8.95444 15.5095i 0.406600 0.704252i
486486 2.69202 0.122113
487487 −7.42931 + 12.8679i −0.336654 + 0.583102i −0.983801 0.179263i 0.942629π-0.942629\pi
0.647147 + 0.762365i 0.275962π0.275962\pi
488488 −14.9613 + 25.9137i −0.677266 + 1.17306i
489489 15.7071 0.710299
490490 −9.44816 + 16.3647i −0.426824 + 0.739281i
491491 −2.49947 4.32920i −0.112799 0.195374i 0.804099 0.594496i 0.202648π-0.202648\pi
−0.916898 + 0.399122i 0.869315π0.869315\pi
492492 −12.8862 22.3196i −0.580955 1.00624i
493493 9.27413 0.417686
494494 0 0
495495 −3.05429 −0.137280
496496 −62.0275 107.435i −2.78512 4.82396i
497497 2.91454 + 5.04814i 0.130735 + 0.226440i
498498 3.55765 6.16202i 0.159422 0.276127i
499499 0.385371 0.0172516 0.00862579 0.999963i 0.497254π-0.497254\pi
0.00862579 + 0.999963i 0.497254π0.497254\pi
500500 24.4906 42.4190i 1.09525 1.89703i
501501 −2.69806 + 4.67318i −0.120541 + 0.208782i
502502 2.05610 0.0917681
503503 −11.3089 + 19.5877i −0.504241 + 0.873370i 0.495747 + 0.868467i 0.334894π0.334894\pi
−0.999988 + 0.00490359i 0.998439π0.998439\pi
504504 −2.42543 4.20096i −0.108037 0.187126i
505505 −3.84063 6.65217i −0.170906 0.296018i
506506 45.1726 2.00817
507507 0 0
508508 −23.5163 −1.04337
509509 −5.80194 10.0493i −0.257166 0.445425i 0.708315 0.705896i 0.249456π-0.249456\pi
−0.965482 + 0.260471i 0.916122π0.916122\pi
510510 6.84870 + 11.8623i 0.303265 + 0.525271i
511511 −2.90701 + 5.03509i −0.128599 + 0.222739i
512512 −1.71678 −0.0758715
513513 0.376510 0.652135i 0.0166233 0.0287925i
514514 −17.6208 + 30.5201i −0.777220 + 1.34618i
515515 −4.42626 −0.195044
516516 −29.1151 + 50.4288i −1.28172 + 2.22000i
517517 −1.09634 1.89892i −0.0482171 0.0835145i
518518 4.29739 + 7.44330i 0.188816 + 0.327040i
519519 −23.9420 −1.05094
520520 0 0
521521 −1.62671 −0.0712675 −0.0356337 0.999365i 0.511345π-0.511345\pi
−0.0356337 + 0.999365i 0.511345π0.511345\pi
522522 −2.57338 4.45722i −0.112634 0.195087i
523523 −5.03588 8.72239i −0.220203 0.381404i 0.734666 0.678429i 0.237339π-0.237339\pi
−0.954870 + 0.297025i 0.904005π0.904005\pi
524524 24.1819 41.8842i 1.05639 1.82972i
525525 −2.16421 −0.0944539
526526 24.7361 42.8442i 1.07854 1.86809i
527527 23.0797 39.9752i 1.00537 1.74135i
528528 37.9614 1.65206
529529 −5.10441 + 8.84109i −0.221931 + 0.384395i
530530 −10.7048 18.5413i −0.464988 0.805383i
531531 2.04892 + 3.54883i 0.0889154 + 0.154006i
532532 −2.19269 −0.0950650
533533 0 0
534534 −26.7235 −1.15644
535535 −3.35325 5.80800i −0.144974 0.251102i
536536 8.18425 + 14.1755i 0.353506 + 0.612290i
537537 9.20440 15.9425i 0.397199 0.687969i
538538 −63.6999 −2.74630
539539 −9.74309 + 16.8755i −0.419665 + 0.726881i
540540 2.75182 4.76630i 0.118420 0.205109i
541541 20.4674 0.879962 0.439981 0.898007i 0.354985π-0.354985\pi
0.439981 + 0.898007i 0.354985π0.354985\pi
542542 26.5878 46.0514i 1.14204 1.97808i
543543 −1.81671 3.14663i −0.0779624 0.135035i
544544 −42.7204 73.9939i −1.83162 3.17246i
545545 3.62937 0.155465
546546 0 0
547547 −27.5478 −1.17786 −0.588929 0.808185i 0.700450π-0.700450\pi
−0.588929 + 0.808185i 0.700450π0.700450\pi
548548 −19.5969 33.9429i −0.837140 1.44997i
549549 1.71164 + 2.96464i 0.0730508 + 0.126528i
550550 15.2847 26.4739i 0.651742 1.12885i
551551 −1.43967 −0.0613318
552552 −25.1857 + 43.6230i −1.07198 + 1.85672i
553553 0.370469 0.641672i 0.0157540 0.0272867i
554554 −4.78581 −0.203329
555555 −3.01722 + 5.22598i −0.128074 + 0.221831i
556556 47.2165 + 81.7814i 2.00243 + 3.46831i
557557 18.9928 + 32.8964i 0.804749 + 1.39387i 0.916460 + 0.400126i 0.131034π0.131034\pi
−0.111711 + 0.993741i 0.535633π0.535633\pi
558558 −25.6165 −1.08443
559559 0 0
560560 −7.58881 −0.320686
561561 7.06249 + 12.2326i 0.298179 + 0.516460i
562562 −2.18233 3.77991i −0.0920562 0.159446i
563563 14.8862 25.7837i 0.627378 1.08665i −0.360697 0.932683i 0.617461π-0.617461\pi
0.988076 0.153968i 0.0492054π-0.0492054\pi
564564 3.95108 0.166371
565565 −4.90731 + 8.49970i −0.206452 + 0.357585i
566566 6.70799 11.6186i 0.281958 0.488365i
567567 −0.554958 −0.0233061
568568 45.9059 79.5113i 1.92617 3.33622i
569569 10.9770 + 19.0128i 0.460181 + 0.797057i 0.998970 0.0453839i 0.0144511π-0.0144511\pi
−0.538788 + 0.842441i 0.681118π0.681118\pi
570570 −1.06315 1.84144i −0.0445307 0.0771294i
571571 2.46575 0.103188 0.0515942 0.998668i 0.483570π-0.483570\pi
0.0515942 + 0.998668i 0.483570π0.483570\pi
572572 0 0
573573 21.1782 0.884732
574574 3.66905 + 6.35499i 0.153143 + 0.265252i
575575 11.2366 + 19.4624i 0.468600 + 0.811639i
576576 −10.6712 + 18.4831i −0.444634 + 0.770128i
577577 −17.4547 −0.726650 −0.363325 0.931662i 0.618359π-0.618359\pi
−0.363325 + 0.931662i 0.618359π0.618359\pi
578578 8.79052 15.2256i 0.365637 0.633303i
579579 8.80559 15.2517i 0.365948 0.633840i
580580 −10.5222 −0.436909
581581 −0.733406 + 1.27030i −0.0304268 + 0.0527008i
582582 22.9813 + 39.8049i 0.952607 + 1.64996i
583583 −11.0390 19.1201i −0.457188 0.791873i
584584 91.5745 3.78938
585585 0 0
586586 −0.193159 −0.00797934
587587 3.13169 + 5.42424i 0.129259 + 0.223882i 0.923390 0.383864i 0.125407π-0.125407\pi
−0.794131 + 0.607747i 0.792074π0.792074\pi
588588 −17.5565 30.4087i −0.724016 1.25403i
589589 −3.58277 + 6.20554i −0.147625 + 0.255695i
590590 11.5711 0.476374
591591 2.33124 4.03783i 0.0958944 0.166094i
592592 37.5006 64.9529i 1.54126 2.66955i
593593 −22.8745 −0.939345 −0.469672 0.882841i 0.655628π-0.655628\pi
−0.469672 + 0.882841i 0.655628π0.655628\pi
594594 3.91939 6.78858i 0.160814 0.278539i
595595 −1.41185 2.44540i −0.0578804 0.100252i
596596 40.2315 + 69.6831i 1.64795 + 2.85433i
597597 −15.0368 −0.615417
598598 0 0
599599 −1.05621 −0.0431557 −0.0215778 0.999767i 0.506869π-0.506869\pi
−0.0215778 + 0.999767i 0.506869π0.506869\pi
600600 17.0438 + 29.5208i 0.695812 + 1.20518i
601601 16.6618 + 28.8591i 0.679650 + 1.17719i 0.975086 + 0.221826i 0.0712015π0.0712015\pi
−0.295437 + 0.955362i 0.595465π0.595465\pi
602602 8.28986 14.3585i 0.337869 0.585207i
603603 1.87263 0.0762592
604604 6.63951 11.5000i 0.270158 0.467927i
605605 1.32222 2.29015i 0.0537557 0.0931076i
606606 19.7138 0.800818
607607 −8.12014 + 14.0645i −0.329586 + 0.570860i −0.982430 0.186633i 0.940243π-0.940243\pi
0.652844 + 0.757493i 0.273576π0.273576\pi
608608 6.63169 + 11.4864i 0.268950 + 0.465836i
609609 0.530499 + 0.918852i 0.0214969 + 0.0372338i
610610 9.66632 0.391378
611611 0 0
612612 −25.4523 −1.02885
613613 5.52393 + 9.56772i 0.223109 + 0.386437i 0.955751 0.294178i 0.0950460π-0.0950460\pi
−0.732641 + 0.680615i 0.761713π0.761713\pi
614614 6.99665 + 12.1185i 0.282362 + 0.489065i
615615 −2.57606 + 4.46187i −0.103877 + 0.179920i
616616 −14.1250 −0.569112
617617 −2.32975 + 4.03524i −0.0937922 + 0.162453i −0.909104 0.416570i 0.863232π-0.863232\pi
0.815312 + 0.579022i 0.196566π0.196566\pi
618618 5.67994 9.83794i 0.228481 0.395740i
619619 −31.9259 −1.28321 −0.641604 0.767036i 0.721731π-0.721731\pi
−0.641604 + 0.767036i 0.721731π0.721731\pi
620620 −26.1856 + 45.3548i −1.05164 + 1.82149i
621621 2.88135 + 4.99065i 0.115625 + 0.200268i
622622 −30.3430 52.5555i −1.21664 2.10729i
623623 5.50902 0.220714
624624 0 0
625625 9.70709 0.388283
626626 30.5022 + 52.8313i 1.21911 + 2.11156i
627627 −1.09634 1.89892i −0.0437837 0.0758356i
628628 −45.2269 + 78.3353i −1.80475 + 3.12592i
629629 27.9071 1.11273
630630 −0.783520 + 1.35710i −0.0312162 + 0.0540680i
631631 −19.7207 + 34.1572i −0.785067 + 1.35978i 0.143892 + 0.989593i 0.454038π0.454038\pi
−0.928959 + 0.370183i 0.879295π0.879295\pi
632632 −11.6703 −0.464218
633633 −0.230054 + 0.398465i −0.00914381 + 0.0158375i
634634 −35.4572 61.4136i −1.40818 2.43905i
635635 2.35056 + 4.07129i 0.0932791 + 0.161564i
636636 39.7832 1.57750
637637 0 0
638638 −14.9866 −0.593325
639639 −5.25182 9.09643i −0.207759 0.359849i
640640 11.6572 + 20.1909i 0.460792 + 0.798115i
641641 −22.7255 + 39.3617i −0.897603 + 1.55469i −0.0670544 + 0.997749i 0.521360π0.521360\pi
−0.830549 + 0.556946i 0.811973π0.811973\pi
642642 17.2121 0.679306
643643 −14.8735 + 25.7616i −0.586552 + 1.01594i 0.408128 + 0.912925i 0.366182π0.366182\pi
−0.994680 + 0.103013i 0.967152π0.967152\pi
644644 8.39008 14.5321i 0.330616 0.572643i
645645 11.6407 0.458353
646646 −4.91670 + 8.51597i −0.193445 + 0.335056i
647647 8.46562 + 14.6629i 0.332818 + 0.576457i 0.983063 0.183267i 0.0586673π-0.0586673\pi
−0.650245 + 0.759724i 0.725334π0.725334\pi
648648 4.37047 + 7.56988i 0.171688 + 0.297373i
649649 11.9323 0.468384
650650 0 0
651651 5.28083 0.206972
652652 41.2074 + 71.3733i 1.61381 + 2.79519i
653653 16.5988 + 28.7500i 0.649561 + 1.12507i 0.983228 + 0.182382i 0.0583806π0.0583806\pi
−0.333667 + 0.942691i 0.608286π0.608286\pi
654654 −4.65734 + 8.06675i −0.182116 + 0.315435i
655655 −9.66833 −0.377773
656656 32.0175 55.4560i 1.25007 2.16519i
657657 5.23825 9.07292i 0.204364 0.353968i
658658 −1.12498 −0.0438564
659659 21.3286 36.9421i 0.830842 1.43906i −0.0665286 0.997785i 0.521192π-0.521192\pi
0.897371 0.441277i 0.145474π-0.145474\pi
660660 −8.01291 13.8788i −0.311902 0.540230i
661661 19.3451 + 33.5067i 0.752438 + 1.30326i 0.946638 + 0.322298i 0.104455π0.104455\pi
−0.194201 + 0.980962i 0.562211π0.562211\pi
662662 −30.2301 −1.17493
663663 0 0
664664 23.1032 0.896578
665665 0.219169 + 0.379611i 0.00849899 + 0.0147207i
666666 −7.74363 13.4124i −0.300059 0.519718i
667667 5.50873 9.54140i 0.213299 0.369444i
668668 −28.3134 −1.09548
669669 8.17510 14.1597i 0.316067 0.547445i
670670 2.64387 4.57932i 0.102142 0.176915i
671671 9.96807 0.384813
672672 4.88740 8.46522i 0.188535 0.326553i
673673 1.29709 + 2.24663i 0.0499993 + 0.0866013i 0.889942 0.456074i 0.150745π-0.150745\pi
−0.839943 + 0.542675i 0.817411π0.817411\pi
674674 3.10656 + 5.38073i 0.119660 + 0.207258i
675675 3.89977 0.150102
676676 0 0
677677 1.75302 0.0673740 0.0336870 0.999432i 0.489275π-0.489275\pi
0.0336870 + 0.999432i 0.489275π0.489275\pi
678678 −12.5945 21.8143i −0.483688 0.837773i
679679 −4.73759 8.20574i −0.181812 0.314907i
680680 −22.2376 + 38.5166i −0.852773 + 1.47705i
681681 6.56033 0.251393
682682 −37.2958 + 64.5983i −1.42813 + 2.47360i
683683 8.16756 14.1466i 0.312523 0.541306i −0.666385 0.745608i 0.732159π-0.732159\pi
0.978908 + 0.204302i 0.0654925π0.0654925\pi
684684 3.95108 0.151073
685685 −3.91760 + 6.78548i −0.149684 + 0.259260i
686686 10.2277 + 17.7148i 0.390494 + 0.676355i
687687 1.97770 + 3.42547i 0.0754539 + 0.130690i
688688 −144.681 −5.51590
689689 0 0
690690 16.2722 0.619472
691691 7.95526 + 13.7789i 0.302632 + 0.524175i 0.976731 0.214466i 0.0688012π-0.0688012\pi
−0.674099 + 0.738641i 0.735468π0.735468\pi
692692 −62.8116 108.793i −2.38774 4.13568i
693693 −0.807979 + 1.39946i −0.0306926 + 0.0531611i
694694 24.5972 0.933696
695695 9.43900 16.3488i 0.358042 0.620146i
696696 8.35570 14.4725i 0.316722 0.548579i
697697 23.8267 0.902500
698698 −32.2717 + 55.8963i −1.22150 + 2.11571i
699699 4.17845 + 7.23728i 0.158043 + 0.273739i
700700 −5.67778 9.83421i −0.214600 0.371698i
701701 −20.8635 −0.788005 −0.394002 0.919109i 0.628910π-0.628910\pi
−0.394002 + 0.919109i 0.628910π0.628910\pi
702702 0 0
703703 −4.33214 −0.163390
704704 31.0730 + 53.8200i 1.17111 + 2.02842i
705705 −0.394928 0.684035i −0.0148739 0.0257623i
706706 36.5091 63.2356i 1.37404 2.37990i
707707 −4.06398 −0.152842
708708 −10.7506 + 18.6206i −0.404033 + 0.699806i
709709 7.82424 13.5520i 0.293846 0.508955i −0.680870 0.732404i 0.738398π-0.738398\pi
0.974716 + 0.223449i 0.0717315π0.0717315\pi
710710 −29.6592 −1.11309
711711 −0.667563 + 1.15625i −0.0250356 + 0.0433629i
712712 −43.3853 75.1455i −1.62593 2.81620i
713713 −27.4182 47.4897i −1.02682 1.77850i
714714 7.24698 0.271211
715715 0 0
716716 96.5906 3.60976
717717 −10.0504 17.4078i −0.375339 0.650107i
718718 35.1027 + 60.7996i 1.31002 + 2.26902i
719719 13.5797 23.5208i 0.506438 0.877176i −0.493534 0.869726i 0.664295π-0.664295\pi
0.999972 0.00744977i 0.00237136π-0.00237136\pi
720720 13.6746 0.509621
721721 −1.17092 + 2.02808i −0.0436072 + 0.0755298i
722722 −24.8110 + 42.9738i −0.923368 + 1.59932i
723723 −19.0127 −0.707089
724724 9.53223 16.5103i 0.354262 0.613601i
725725 −3.72790 6.45691i −0.138451 0.239804i
726726 3.39344 + 5.87760i 0.125942 + 0.218138i
727727 31.7784 1.17859 0.589297 0.807916i 0.299405π-0.299405\pi
0.589297 + 0.807916i 0.299405π0.299405\pi
728728 0 0
729729 1.00000 0.0370370
730730 −14.7913 25.6193i −0.547450 0.948212i
731731 −26.9170 46.6216i −0.995561 1.72436i
732732 −8.98092 + 15.5554i −0.331944 + 0.574944i
733733 −46.8907 −1.73195 −0.865973 0.500090i 0.833300π-0.833300\pi
−0.865973 + 0.500090i 0.833300π0.833300\pi
734734 12.8872 22.3212i 0.475674 0.823891i
735735 −3.50969 + 6.07896i −0.129457 + 0.224226i
736736 −101.502 −3.74141
737737 2.72641 4.72227i 0.100428 0.173947i
738738 −6.61141 11.4513i −0.243369 0.421528i
739739 8.52393 + 14.7639i 0.313558 + 0.543098i 0.979130 0.203236i 0.0651457π-0.0651457\pi
−0.665572 + 0.746334i 0.731812π0.731812\pi
740740 −31.6626 −1.16394
741741 0 0
742742 −11.3274 −0.415840
743743 −5.81618 10.0739i −0.213375 0.369576i 0.739394 0.673273i 0.235112π-0.235112\pi
−0.952769 + 0.303697i 0.901779π0.901779\pi
744744 −41.5882 72.0329i −1.52470 2.64085i
745745 8.04264 13.9303i 0.294660 0.510365i
746746 −75.7797 −2.77449
747747 1.32155 2.28900i 0.0483531 0.0837500i
748748 −37.0567 + 64.1842i −1.35493 + 2.34681i
749749 −3.54825 −0.129650
750750 12.5652 21.7635i 0.458815 0.794692i
751751 6.51477 + 11.2839i 0.237727 + 0.411756i 0.960062 0.279788i 0.0902642π-0.0902642\pi
−0.722334 + 0.691544i 0.756931π0.756931\pi
752752 4.90850 + 8.50177i 0.178995 + 0.310028i
753753 0.763774 0.0278335
754754 0 0
755755 −2.65459 −0.0966106
756756 −1.45593 2.52174i −0.0529516 0.0917148i
757757 −11.3949 19.7366i −0.414156 0.717339i 0.581184 0.813772i 0.302590π-0.302590\pi
−0.995339 + 0.0964337i 0.969256π0.969256\pi
758758 −21.5988 + 37.4102i −0.784504 + 1.35880i
759759 16.7802 0.609081
760760 3.45204 5.97911i 0.125219 0.216885i
761761 −19.1712 + 33.2055i −0.694956 + 1.20370i 0.275240 + 0.961376i 0.411243π0.411243\pi
−0.970196 + 0.242323i 0.922091π0.922091\pi
762762 −12.0653 −0.437080
763763 0.960107 1.66295i 0.0347582 0.0602030i
764764 55.5608 + 96.2342i 2.01012 + 3.48163i
765765 2.54407 + 4.40646i 0.0919812 + 0.159316i
766766 −66.2683 −2.39437
767767 0 0
768768 −17.1511 −0.618886
769769 −1.81940 3.15129i −0.0656091 0.113638i 0.831355 0.555742i 0.187566π-0.187566\pi
−0.896964 + 0.442104i 0.854232π0.854232\pi
770770 2.28150 + 3.95167i 0.0822194 + 0.142408i
771771 −6.54556 + 11.3373i −0.235733 + 0.408301i
772772 92.4055 3.32575
773773 −19.6712 + 34.0715i −0.707524 + 1.22547i 0.258249 + 0.966079i 0.416855π0.416855\pi
−0.965773 + 0.259389i 0.916479π0.916479\pi
774774 −14.9378 + 25.8730i −0.536928 + 0.929987i
775775 −37.1092 −1.33300
776776 −74.6200 + 129.246i −2.67870 + 4.63965i
777777 1.59634 + 2.76495i 0.0572685 + 0.0991919i
778778 −23.1781 40.1456i −0.830974 1.43929i
779779 −3.69873 −0.132521
780780 0 0
781781 −30.5851 −1.09442
782782 −37.6265 65.1710i −1.34552 2.33051i
783783 −0.955927 1.65571i −0.0341620 0.0591704i
784784 43.6214 75.5545i 1.55791 2.69837i
785785 18.0825 0.645392
786786 12.4068 21.4892i 0.442535 0.766493i
787787 −12.7126 + 22.0189i −0.453155 + 0.784888i −0.998580 0.0532720i 0.983035π-0.983035\pi
0.545425 + 0.838160i 0.316368π0.316368\pi
788788 24.4639 0.871492
789789 9.18867 15.9152i 0.327125 0.566598i
790790 1.88500 + 3.26492i 0.0670654 + 0.116161i
791791 2.59634 + 4.49700i 0.0923153 + 0.159895i
792792 25.4523 0.904409
793793 0 0
794794 −5.48965 −0.194820
795795 −3.97650 6.88750i −0.141032 0.244275i
796796 −39.4490 68.3276i −1.39823 2.42181i
797797 −10.3569 + 17.9387i −0.366860 + 0.635420i −0.989073 0.147428i 0.952901π-0.952901\pi
0.622213 + 0.782848i 0.286234π0.286234\pi
798798 −1.12498 −0.0398239
799799 −1.82640 + 3.16341i −0.0646133 + 0.111913i
800800 −34.3444 + 59.4863i −1.21426 + 2.10316i
801801 −9.92692 −0.350750
802802 1.96711 3.40713i 0.0694610 0.120310i
803803 −15.2530 26.4190i −0.538267 0.932306i
804804 4.91281 + 8.50924i 0.173262 + 0.300098i
805805 −3.35450 −0.118231
806806 0 0
807807 −23.6625 −0.832959
808808 32.0051 + 55.4345i 1.12594 + 1.95018i
809809 −5.54892 9.61101i −0.195090 0.337905i 0.751840 0.659345i 0.229166π-0.229166\pi
−0.946930 + 0.321440i 0.895833π0.895833\pi
810810 1.41185 2.44540i 0.0496075 0.0859227i
811811 4.84223 0.170034 0.0850169 0.996380i 0.472906π-0.472906\pi
0.0850169 + 0.996380i 0.472906π0.472906\pi
812812 −2.78352 + 4.82120i −0.0976824 + 0.169191i
813813 9.87651 17.1066i 0.346384 0.599955i
814814 −45.0966 −1.58064
815815 8.23772 14.2681i 0.288555 0.499791i
816816 −31.6199 54.7673i −1.10692 1.91724i
817817 4.17845 + 7.23728i 0.146185 + 0.253201i
818818 −80.5964 −2.81799
819819 0 0
820820 −27.0331 −0.944037
821821 −21.8690 37.8783i −0.763235 1.32196i −0.941175 0.337920i 0.890277π-0.890277\pi
0.177940 0.984041i 0.443057π-0.443057\pi
822822 −10.0544 17.4148i −0.350688 0.607410i
823823 −6.04988 + 10.4787i −0.210885 + 0.365264i −0.951992 0.306123i 0.900968π-0.900968\pi
0.741106 + 0.671388i 0.234301π0.234301\pi
824824 36.8853 1.28496
825825 5.67778 9.83421i 0.197675 0.342383i
826826 3.06100 5.30181i 0.106506 0.184473i
827827 35.3212 1.22824 0.614120 0.789213i 0.289511π-0.289511\pi
0.614120 + 0.789213i 0.289511π0.289511\pi
828828 −15.1184 + 26.1859i −0.525401 + 0.910021i
829829 −26.7473 46.3276i −0.928971 1.60903i −0.785047 0.619437i 0.787361π-0.787361\pi
−0.143925 0.989589i 0.545972π-0.545972\pi
830830 −3.73168 6.46345i −0.129528 0.224350i
831831 −1.77777 −0.0616703
832832 0 0
833833 32.4620 1.12474
834834 24.2250 + 41.9589i 0.838842 + 1.45292i
835835 2.83004 + 4.90178i 0.0979377 + 0.169633i
836836 5.75249 9.96360i 0.198954 0.344598i
837837 −9.51573 −0.328912
838838 8.94749 15.4975i 0.309086 0.535353i
839839 11.5761 20.0503i 0.399650 0.692214i −0.594033 0.804441i 0.702465π-0.702465\pi
0.993683 + 0.112227i 0.0357983π0.0357983\pi
840840 −5.08815 −0.175558
841841 12.6724 21.9493i 0.436980 0.756871i
842842 −18.2582 31.6241i −0.629218 1.08984i
843843 −0.810667 1.40412i −0.0279209 0.0483603i
844844 −2.41417 −0.0830993
845845 0 0
846846 2.02715 0.0696948
847847 −0.699554 1.21166i −0.0240370 0.0416332i
848848 49.4233 + 85.6037i 1.69720 + 2.93964i
849849 2.49180 4.31593i 0.0855185 0.148122i
850850 −50.9256 −1.74673
851851 16.5765 28.7113i 0.568235 0.984212i
852852 27.5562 47.7288i 0.944060 1.63516i
853853 −26.7265 −0.915097 −0.457548 0.889185i 0.651272π-0.651272\pi
−0.457548 + 0.889185i 0.651272π0.651272\pi
854854 2.55711 4.42905i 0.0875026 0.151559i
855855 −0.394928 0.684035i −0.0135063 0.0233935i
856856 27.9436 + 48.3997i 0.955093 + 1.65427i
857857 42.6064 1.45541 0.727703 0.685892i 0.240588π-0.240588\pi
0.727703 + 0.685892i 0.240588π0.240588\pi
858858 0 0
859859 33.6079 1.14669 0.573344 0.819315i 0.305646π-0.305646\pi
0.573344 + 0.819315i 0.305646π0.305646\pi
860860 30.5393 + 52.8956i 1.04138 + 1.80372i
861861 1.36294 + 2.36068i 0.0464488 + 0.0804516i
862862 −48.3841 + 83.8037i −1.64797 + 2.85437i
863863 −18.7047 −0.636715 −0.318358 0.947971i 0.603131π-0.603131\pi
−0.318358 + 0.947971i 0.603131π0.603131\pi
864864 −8.80678 + 15.2538i −0.299613 + 0.518945i
865865 −12.5566 + 21.7486i −0.426937 + 0.739476i
866866 87.4210 2.97069
867867 3.26540 5.65583i 0.110899 0.192082i
868868 13.8542 + 23.9962i 0.470242 + 0.814484i
869869 1.94385 + 3.36684i 0.0659404 + 0.114212i
870870 −5.39852 −0.183027
871871 0 0
872872 −30.2446 −1.02421
873873 8.53684 + 14.7862i 0.288928 + 0.500438i
874874 5.84093 + 10.1168i 0.197572 + 0.342205i
875875 −2.59030 + 4.48653i −0.0875682 + 0.151673i
876876 54.9700 1.85726
877877 18.4119 31.8903i 0.621724 1.07686i −0.367440 0.930047i 0.619766π-0.619766\pi
0.989165 0.146811i 0.0469008π-0.0469008\pi
878878 17.2721 29.9162i 0.582905 1.00962i
879879 −0.0717525 −0.00242015
880880 19.9092 34.4837i 0.671138 1.16244i
881881 20.5625 + 35.6153i 0.692768 + 1.19991i 0.970927 + 0.239374i 0.0769423π0.0769423\pi
−0.278159 + 0.960535i 0.589724π0.589724\pi
882882 −9.00753 15.6015i −0.303299 0.525330i
883883 30.7482 1.03476 0.517380 0.855756i 0.326907π-0.326907\pi
0.517380 + 0.855756i 0.326907π0.326907\pi
884884 0 0
885885 4.29829 0.144485
886886 16.0993 + 27.8849i 0.540867 + 0.936810i
887887 −3.79470 6.57261i −0.127414 0.220687i 0.795260 0.606268i 0.207334π-0.207334\pi
−0.922674 + 0.385581i 0.874001π0.874001\pi
888888 25.1434 43.5496i 0.843757 1.46143i
889889 2.48725 0.0834198
890890 −14.0154 + 24.2753i −0.469796 + 0.813710i
891891 1.45593 2.52174i 0.0487754 0.0844815i
892892 85.7891 2.87243
893893 0.283520 0.491071i 0.00948763 0.0164331i
894894 20.6412 + 35.7517i 0.690346 + 1.19572i
895895 −9.65465 16.7223i −0.322719 0.558967i
896896 12.3351 0.412088
897897 0 0
898898 −33.5934 −1.12103
899899 9.09634 + 15.7553i 0.303380 + 0.525470i
900900 10.2310 + 17.7206i 0.341034 + 0.590688i
901901 −18.3898 + 31.8521i −0.612655 + 1.06115i
902902 −38.5029 −1.28201
903903 3.07942 5.33371i 0.102477 0.177495i
904904 40.8940 70.8305i 1.36012 2.35579i
905905 −3.81115 −0.126687
906906 3.40648 5.90019i 0.113173 0.196021i
907907 −9.66666 16.7431i −0.320976 0.555947i 0.659713 0.751517i 0.270678π-0.270678\pi
−0.980690 + 0.195570i 0.937344π0.937344\pi
908908 17.2110 + 29.8103i 0.571166 + 0.989289i
909909 7.32304 0.242890
910910 0 0
911911 22.7149 0.752577 0.376288 0.926503i 0.377200π-0.377200\pi
0.376288 + 0.926503i 0.377200π0.377200\pi
912912 4.90850 + 8.50177i 0.162537 + 0.281522i
913913 −3.84817 6.66522i −0.127356 0.220587i
914914 −43.6812 + 75.6580i −1.44485 + 2.50255i
915915 3.59073 0.118706
916916 −10.3769 + 17.9734i −0.342864 + 0.593857i
917917 −2.55765 + 4.42997i −0.0844609 + 0.146291i
918918 −13.0586 −0.430998
919919 −7.14556 + 12.3765i −0.235710 + 0.408262i −0.959479 0.281781i 0.909075π-0.909075\pi
0.723769 + 0.690043i 0.242408π0.242408\pi
920920 26.4178 + 45.7569i 0.870968 + 1.50856i
921921 2.59903 + 4.50165i 0.0856410 + 0.148335i
922922 65.6945 2.16353
923923 0 0
924924 −8.47889 −0.278935
925925 −11.2177 19.4297i −0.368837 0.638844i
926926 44.6655 + 77.3629i 1.46780 + 2.54230i
927927 2.10992 3.65448i 0.0692987 0.120029i
928928 33.6746 1.10542
929929 16.3605 28.3373i 0.536772 0.929716i −0.462303 0.886722i 0.652977π-0.652977\pi
0.999075 0.0429946i 0.0136898π-0.0136898\pi
930930 −13.4348 + 23.2698i −0.440545 + 0.763047i
931931 −5.03923 −0.165154
932932 −21.9242 + 37.9739i −0.718152 + 1.24388i
933933 −11.2714 19.5227i −0.369010 0.639145i
934934 −51.8492 89.8054i −1.69656 2.93852i
935935 14.8159 0.484533
936936 0 0
937937 −4.01400 −0.131132 −0.0655658 0.997848i 0.520885π-0.520885\pi
−0.0655658 + 0.997848i 0.520885π0.520885\pi
938938 −1.39881 2.42282i −0.0456729 0.0791077i
939939 11.3306 + 19.6251i 0.369759 + 0.640442i
940940 2.07218 3.58912i 0.0675870 0.117064i
941941 28.2669 0.921476 0.460738 0.887536i 0.347585π-0.347585\pi
0.460738 + 0.887536i 0.347585π0.347585\pi
942942 −23.2042 + 40.1908i −0.756032 + 1.30949i
943943 14.1528 24.5134i 0.460878 0.798265i
944944 −53.4228 −1.73876
945945 −0.291053 + 0.504118i −0.00946794 + 0.0163990i
946946 43.4967 + 75.3385i 1.41420 + 2.44947i
947947 −18.9227 32.7751i −0.614906 1.06505i −0.990401 0.138225i 0.955860π-0.955860\pi
0.375495 0.926825i 0.377473π-0.377473\pi
948948 −7.00538 −0.227524
949949 0 0
950950 7.90541 0.256485
951951 −13.1712 22.8132i −0.427106 0.739769i
952952 11.7654 + 20.3783i 0.381319 + 0.660463i
953953 20.4128 35.3560i 0.661236 1.14529i −0.319055 0.947736i 0.603366π-0.603366\pi
0.980291 0.197558i 0.0633011π-0.0633011\pi
954954 20.4112 0.660837
955955 11.1071 19.2381i 0.359417 0.622529i
956956 52.7343 91.3385i 1.70555 2.95410i
957957 −5.56704 −0.179957
958958 11.2322 19.4548i 0.362896 0.628555i
959959 2.07271 + 3.59004i 0.0669314 + 0.115929i
960960 11.1932 + 19.3872i 0.361260 + 0.625720i
961961 59.5491 1.92094
962962 0 0
963963 6.39373 0.206035
964964 −49.8796 86.3939i −1.60651 2.78256i
965965 −9.23633 15.9978i −0.297328 0.514987i
966966 4.30463 7.45583i 0.138499 0.239887i
967967 −10.2798 −0.330575 −0.165288 0.986245i 0.552855π-0.552855\pi
−0.165288 + 0.986245i 0.552855π0.552855\pi
968968 −11.0184 + 19.0845i −0.354145 + 0.613398i
969969 −1.82640 + 3.16341i −0.0586723 + 0.101623i
970970 48.2111 1.54796
971971 9.74027 16.8707i 0.312580 0.541405i −0.666340 0.745648i 0.732140π-0.732140\pi
0.978920 + 0.204243i 0.0654733π0.0654733\pi
972972 2.62349 + 4.54402i 0.0841485 + 0.145749i
973973 −4.99396 8.64979i −0.160099 0.277300i
974974 −39.9997 −1.28167
975975 0 0
976976 −44.6286 −1.42853
977977 23.5269 + 40.7498i 0.752693 + 1.30370i 0.946513 + 0.322665i 0.104579π0.104579\pi
−0.193821 + 0.981037i 0.562088π0.562088\pi
978978 21.1419 + 36.6189i 0.676044 + 1.17094i
979979 −14.4529 + 25.0331i −0.461916 + 0.800062i
980980 −36.8305 −1.17651
981981 −1.73005 + 2.99654i −0.0552364 + 0.0956722i
982982 6.72862 11.6543i 0.214719 0.371904i
983983 −34.4295 −1.09813 −0.549065 0.835779i 0.685016π-0.685016\pi
−0.549065 + 0.835779i 0.685016π0.685016\pi
984984 21.4671 37.1821i 0.684346 1.18532i
985985 −2.44528 4.23535i −0.0779131 0.134949i
986986 12.4831 + 21.6213i 0.397542 + 0.688563i
987987 −0.417895 −0.0133017
988988 0 0
989989 −63.9536 −2.03361
990990 −4.11111 7.12066i −0.130660 0.226309i
991991 −3.65399 6.32890i −0.116073 0.201044i 0.802135 0.597142i 0.203697π-0.203697\pi
−0.918208 + 0.396098i 0.870364π0.870364\pi
992992 83.8030 145.151i 2.66075 4.60855i
993993 −11.2295 −0.356358
994994 −7.84601 + 13.5897i −0.248860 + 0.431039i
995995 −7.88620 + 13.6593i −0.250009 + 0.433029i
996996 13.8683 0.439434
997997 17.8458 30.9098i 0.565181 0.978923i −0.431851 0.901945i 0.642140π-0.642140\pi
0.997033 0.0769780i 0.0245271π-0.0245271\pi
998998 0.518713 + 0.898438i 0.0164196 + 0.0284396i
999999 −2.87651 4.98226i −0.0910088 0.157632i
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 507.2.e.l.484.3 6
13.2 odd 12 507.2.b.f.337.6 6
13.3 even 3 507.2.a.i.1.1 3
13.4 even 6 507.2.e.i.22.1 6
13.5 odd 4 507.2.j.i.361.6 12
13.6 odd 12 507.2.j.i.316.1 12
13.7 odd 12 507.2.j.i.316.6 12
13.8 odd 4 507.2.j.i.361.1 12
13.9 even 3 inner 507.2.e.l.22.3 6
13.10 even 6 507.2.a.l.1.3 yes 3
13.11 odd 12 507.2.b.f.337.1 6
13.12 even 2 507.2.e.i.484.1 6
39.2 even 12 1521.2.b.k.1351.1 6
39.11 even 12 1521.2.b.k.1351.6 6
39.23 odd 6 1521.2.a.n.1.1 3
39.29 odd 6 1521.2.a.s.1.3 3
52.3 odd 6 8112.2.a.cg.1.3 3
52.23 odd 6 8112.2.a.cp.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.a.i.1.1 3 13.3 even 3
507.2.a.l.1.3 yes 3 13.10 even 6
507.2.b.f.337.1 6 13.11 odd 12
507.2.b.f.337.6 6 13.2 odd 12
507.2.e.i.22.1 6 13.4 even 6
507.2.e.i.484.1 6 13.12 even 2
507.2.e.l.22.3 6 13.9 even 3 inner
507.2.e.l.484.3 6 1.1 even 1 trivial
507.2.j.i.316.1 12 13.6 odd 12
507.2.j.i.316.6 12 13.7 odd 12
507.2.j.i.361.1 12 13.8 odd 4
507.2.j.i.361.6 12 13.5 odd 4
1521.2.a.n.1.1 3 39.23 odd 6
1521.2.a.s.1.3 3 39.29 odd 6
1521.2.b.k.1351.1 6 39.2 even 12
1521.2.b.k.1351.6 6 39.11 even 12
8112.2.a.cg.1.3 3 52.3 odd 6
8112.2.a.cp.1.1 3 52.23 odd 6