Properties

Label 510.2.w.b.383.1
Level 510510
Weight 22
Character 510.383
Analytic conductor 4.0724.072
Analytic rank 11
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [510,2,Mod(257,510)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(510, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 2, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("510.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 510=23517 510 = 2 \cdot 3 \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 510.w (of order 88, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.072370503094.07237050309
Analytic rank: 11
Dimension: 44
Coefficient field: Q(ζ8)\Q(\zeta_{8})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+1 x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 383.1
Root 0.707107+0.707107i0.707107 + 0.707107i of defining polynomial
Character χ\chi == 510.383
Dual form 510.2.w.b.257.1

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+1.00000q2+(0.292893+1.70711i)q3+1.00000q4+(2.000001.00000i)q5+(0.292893+1.70711i)q6+(4.121321.70711i)q7+1.00000q8+(2.828431.00000i)q9+(2.000001.00000i)q10+(0.8786802.12132i)q11+(0.292893+1.70711i)q12+(4.41421+4.41421i)q13+(4.121321.70711i)q14+(2.292893.12132i)q15+1.00000q16+(3.000002.82843i)q17+(2.828431.00000i)q18+(3.24264+3.24264i)q19+(2.000001.00000i)q20+(4.121326.53553i)q21+(0.8786802.12132i)q22+(1.29289+3.12132i)q23+(0.292893+1.70711i)q24+(3.00000+4.00000i)q25+(4.41421+4.41421i)q26+(2.535534.53553i)q27+(4.121321.70711i)q28+(0.1213200.292893i)q29+(2.292893.12132i)q30+(0.7071070.292893i)q31+1.00000q32+(3.878680.878680i)q33+(3.000002.82843i)q34+(6.53553+7.53553i)q35+(2.828431.00000i)q36+(2.707111.12132i)q37+(3.24264+3.24264i)q38+(6.242648.82843i)q39+(2.000001.00000i)q40+(1.121320.464466i)q41+(4.121326.53553i)q4211.6569iq43+(0.8786802.12132i)q44+(4.65685+4.82843i)q45+(1.29289+3.12132i)q46+(5.82843+5.82843i)q47+(0.292893+1.70711i)q48+(9.12132+9.12132i)q49+(3.00000+4.00000i)q50+(5.707114.29289i)q51+(4.41421+4.41421i)q52+1.17157iq53+(2.535534.53553i)q54+(0.363961+5.12132i)q55+(4.121321.70711i)q56+(6.48528+4.58579i)q57+(0.1213200.292893i)q58+(6.414216.41421i)q59+(2.292893.12132i)q60+(1.05025+2.53553i)q61+(0.7071070.292893i)q62+(9.94975+8.94975i)q63+1.00000q64+(13.24264.41421i)q65+(3.878680.878680i)q66+(4.41421+4.41421i)q67+(3.000002.82843i)q68+(4.949753.12132i)q69+(6.53553+7.53553i)q70+(2.36396+5.70711i)q71+(2.828431.00000i)q72+(9.36396+3.87868i)q73+(2.707111.12132i)q74+(7.70711+3.94975i)q75+(3.24264+3.24264i)q76+10.2426iq77+(6.242648.82843i)q78+(5.8786814.1924i)q79+(2.000001.00000i)q80+(7.00000+5.65685i)q81+(1.121320.464466i)q8211.6569iq83+(4.121326.53553i)q84+(3.17157+8.65685i)q8511.6569iq86+(0.464466+0.292893i)q87+(0.8786802.12132i)q88+14.1421iq89+(4.65685+4.82843i)q90+(25.727910.6569i)q91+(1.29289+3.12132i)q92+(0.7071071.12132i)q93+(5.82843+5.82843i)q94+(3.242649.72792i)q95+(0.292893+1.70711i)q96+(1.464473.53553i)q97+(9.12132+9.12132i)q98+(0.363961+6.87868i)q99+O(q100)q+1.00000 q^{2} +(-0.292893 + 1.70711i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-4.12132 - 1.70711i) q^{7} +1.00000 q^{8} +(-2.82843 - 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} +(-0.878680 - 2.12132i) q^{11} +(-0.292893 + 1.70711i) q^{12} +(-4.41421 + 4.41421i) q^{13} +(-4.12132 - 1.70711i) q^{14} +(2.29289 - 3.12132i) q^{15} +1.00000 q^{16} +(-3.00000 - 2.82843i) q^{17} +(-2.82843 - 1.00000i) q^{18} +(3.24264 + 3.24264i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(4.12132 - 6.53553i) q^{21} +(-0.878680 - 2.12132i) q^{22} +(-1.29289 + 3.12132i) q^{23} +(-0.292893 + 1.70711i) q^{24} +(3.00000 + 4.00000i) q^{25} +(-4.41421 + 4.41421i) q^{26} +(2.53553 - 4.53553i) q^{27} +(-4.12132 - 1.70711i) q^{28} +(0.121320 - 0.292893i) q^{29} +(2.29289 - 3.12132i) q^{30} +(-0.707107 - 0.292893i) q^{31} +1.00000 q^{32} +(3.87868 - 0.878680i) q^{33} +(-3.00000 - 2.82843i) q^{34} +(6.53553 + 7.53553i) q^{35} +(-2.82843 - 1.00000i) q^{36} +(2.70711 - 1.12132i) q^{37} +(3.24264 + 3.24264i) q^{38} +(-6.24264 - 8.82843i) q^{39} +(-2.00000 - 1.00000i) q^{40} +(1.12132 - 0.464466i) q^{41} +(4.12132 - 6.53553i) q^{42} -11.6569i q^{43} +(-0.878680 - 2.12132i) q^{44} +(4.65685 + 4.82843i) q^{45} +(-1.29289 + 3.12132i) q^{46} +(-5.82843 + 5.82843i) q^{47} +(-0.292893 + 1.70711i) q^{48} +(9.12132 + 9.12132i) q^{49} +(3.00000 + 4.00000i) q^{50} +(5.70711 - 4.29289i) q^{51} +(-4.41421 + 4.41421i) q^{52} +1.17157i q^{53} +(2.53553 - 4.53553i) q^{54} +(-0.363961 + 5.12132i) q^{55} +(-4.12132 - 1.70711i) q^{56} +(-6.48528 + 4.58579i) q^{57} +(0.121320 - 0.292893i) q^{58} +(-6.41421 - 6.41421i) q^{59} +(2.29289 - 3.12132i) q^{60} +(1.05025 + 2.53553i) q^{61} +(-0.707107 - 0.292893i) q^{62} +(9.94975 + 8.94975i) q^{63} +1.00000 q^{64} +(13.2426 - 4.41421i) q^{65} +(3.87868 - 0.878680i) q^{66} +(-4.41421 + 4.41421i) q^{67} +(-3.00000 - 2.82843i) q^{68} +(-4.94975 - 3.12132i) q^{69} +(6.53553 + 7.53553i) q^{70} +(-2.36396 + 5.70711i) q^{71} +(-2.82843 - 1.00000i) q^{72} +(-9.36396 + 3.87868i) q^{73} +(2.70711 - 1.12132i) q^{74} +(-7.70711 + 3.94975i) q^{75} +(3.24264 + 3.24264i) q^{76} +10.2426i q^{77} +(-6.24264 - 8.82843i) q^{78} +(-5.87868 - 14.1924i) q^{79} +(-2.00000 - 1.00000i) q^{80} +(7.00000 + 5.65685i) q^{81} +(1.12132 - 0.464466i) q^{82} -11.6569i q^{83} +(4.12132 - 6.53553i) q^{84} +(3.17157 + 8.65685i) q^{85} -11.6569i q^{86} +(0.464466 + 0.292893i) q^{87} +(-0.878680 - 2.12132i) q^{88} +14.1421i q^{89} +(4.65685 + 4.82843i) q^{90} +(25.7279 - 10.6569i) q^{91} +(-1.29289 + 3.12132i) q^{92} +(0.707107 - 1.12132i) q^{93} +(-5.82843 + 5.82843i) q^{94} +(-3.24264 - 9.72792i) q^{95} +(-0.292893 + 1.70711i) q^{96} +(-1.46447 - 3.53553i) q^{97} +(9.12132 + 9.12132i) q^{98} +(0.363961 + 6.87868i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q24q3+4q48q54q68q7+4q88q1012q114q1212q138q14+12q15+4q1612q174q198q20+8q2112q22+24q99+O(q100) 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 8 q^{7} + 4 q^{8} - 8 q^{10} - 12 q^{11} - 4 q^{12} - 12 q^{13} - 8 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{19} - 8 q^{20} + 8 q^{21} - 12 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/510Z)×\left(\mathbb{Z}/510\mathbb{Z}\right)^\times.

nn 241241 307307 341341
χ(n)\chi(n) e(18)e\left(\frac{1}{8}\right) e(34)e\left(\frac{3}{4}\right) 1-1

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 1.00000 0.707107
33 −0.292893 + 1.70711i −0.169102 + 0.985599i
44 1.00000 0.500000
55 −2.00000 1.00000i −0.894427 0.447214i
66 −0.292893 + 1.70711i −0.119573 + 0.696923i
77 −4.12132 1.70711i −1.55771 0.645226i −0.573023 0.819540i 0.694229π-0.694229\pi
−0.984690 + 0.174314i 0.944229π0.944229\pi
88 1.00000 0.353553
99 −2.82843 1.00000i −0.942809 0.333333i
1010 −2.00000 1.00000i −0.632456 0.316228i
1111 −0.878680 2.12132i −0.264932 0.639602i 0.734299 0.678827i 0.237511π-0.237511\pi
−0.999230 + 0.0392245i 0.987511π0.987511\pi
1212 −0.292893 + 1.70711i −0.0845510 + 0.492799i
1313 −4.41421 + 4.41421i −1.22428 + 1.22428i −0.258188 + 0.966095i 0.583125π0.583125\pi
−0.966095 + 0.258188i 0.916875π0.916875\pi
1414 −4.12132 1.70711i −1.10147 0.456243i
1515 2.29289 3.12132i 0.592022 0.805921i
1616 1.00000 0.250000
1717 −3.00000 2.82843i −0.727607 0.685994i
1818 −2.82843 1.00000i −0.666667 0.235702i
1919 3.24264 + 3.24264i 0.743913 + 0.743913i 0.973329 0.229416i 0.0736815π-0.0736815\pi
−0.229416 + 0.973329i 0.573682π0.573682\pi
2020 −2.00000 1.00000i −0.447214 0.223607i
2121 4.12132 6.53553i 0.899346 1.42617i
2222 −0.878680 2.12132i −0.187335 0.452267i
2323 −1.29289 + 3.12132i −0.269587 + 0.650840i −0.999464 0.0327381i 0.989577π-0.989577\pi
0.729877 + 0.683578i 0.239577π0.239577\pi
2424 −0.292893 + 1.70711i −0.0597866 + 0.348462i
2525 3.00000 + 4.00000i 0.600000 + 0.800000i
2626 −4.41421 + 4.41421i −0.865699 + 0.865699i
2727 2.53553 4.53553i 0.487964 0.872864i
2828 −4.12132 1.70711i −0.778856 0.322613i
2929 0.121320 0.292893i 0.0225286 0.0543889i −0.912215 0.409712i 0.865629π-0.865629\pi
0.934744 + 0.355323i 0.115629π0.115629\pi
3030 2.29289 3.12132i 0.418623 0.569873i
3131 −0.707107 0.292893i −0.127000 0.0526052i 0.318278 0.947997i 0.396895π-0.396895\pi
−0.445279 + 0.895392i 0.646895π0.646895\pi
3232 1.00000 0.176777
3333 3.87868 0.878680i 0.675191 0.152958i
3434 −3.00000 2.82843i −0.514496 0.485071i
3535 6.53553 + 7.53553i 1.10471 + 1.27374i
3636 −2.82843 1.00000i −0.471405 0.166667i
3737 2.70711 1.12132i 0.445046 0.184344i −0.148895 0.988853i 0.547572π-0.547572\pi
0.593940 + 0.804509i 0.297572π0.297572\pi
3838 3.24264 + 3.24264i 0.526026 + 0.526026i
3939 −6.24264 8.82843i −0.999623 1.41368i
4040 −2.00000 1.00000i −0.316228 0.158114i
4141 1.12132 0.464466i 0.175121 0.0725374i −0.293400 0.955990i 0.594787π-0.594787\pi
0.468521 + 0.883452i 0.344787π0.344787\pi
4242 4.12132 6.53553i 0.635934 1.00845i
4343 11.6569i 1.77765i −0.458243 0.888827i 0.651521π-0.651521\pi
0.458243 0.888827i 0.348479π-0.348479\pi
4444 −0.878680 2.12132i −0.132466 0.319801i
4545 4.65685 + 4.82843i 0.694203 + 0.719779i
4646 −1.29289 + 3.12132i −0.190627 + 0.460214i
4747 −5.82843 + 5.82843i −0.850163 + 0.850163i −0.990153 0.139990i 0.955293π-0.955293\pi
0.139990 + 0.990153i 0.455293π0.455293\pi
4848 −0.292893 + 1.70711i −0.0422755 + 0.246400i
4949 9.12132 + 9.12132i 1.30305 + 1.30305i
5050 3.00000 + 4.00000i 0.424264 + 0.565685i
5151 5.70711 4.29289i 0.799155 0.601125i
5252 −4.41421 + 4.41421i −0.612141 + 0.612141i
5353 1.17157i 0.160928i 0.996758 + 0.0804640i 0.0256402π0.0256402\pi
−0.996758 + 0.0804640i 0.974360π0.974360\pi
5454 2.53553 4.53553i 0.345042 0.617208i
5555 −0.363961 + 5.12132i −0.0490765 + 0.690559i
5656 −4.12132 1.70711i −0.550735 0.228122i
5757 −6.48528 + 4.58579i −0.858997 + 0.607402i
5858 0.121320 0.292893i 0.0159301 0.0384588i
5959 −6.41421 6.41421i −0.835059 0.835059i 0.153144 0.988204i 0.451060π-0.451060\pi
−0.988204 + 0.153144i 0.951060π0.951060\pi
6060 2.29289 3.12132i 0.296011 0.402961i
6161 1.05025 + 2.53553i 0.134471 + 0.324642i 0.976744 0.214410i 0.0687828π-0.0687828\pi
−0.842273 + 0.539052i 0.818783π0.818783\pi
6262 −0.707107 0.292893i −0.0898027 0.0371975i
6363 9.94975 + 8.94975i 1.25355 + 1.12756i
6464 1.00000 0.125000
6565 13.2426 4.41421i 1.64255 0.547516i
6666 3.87868 0.878680i 0.477432 0.108158i
6767 −4.41421 + 4.41421i −0.539282 + 0.539282i −0.923318 0.384036i 0.874534π-0.874534\pi
0.384036 + 0.923318i 0.374534π0.374534\pi
6868 −3.00000 2.82843i −0.363803 0.342997i
6969 −4.94975 3.12132i −0.595880 0.375763i
7070 6.53553 + 7.53553i 0.781146 + 0.900669i
7171 −2.36396 + 5.70711i −0.280551 + 0.677309i −0.999849 0.0173925i 0.994464π-0.994464\pi
0.719298 + 0.694701i 0.244464π0.244464\pi
7272 −2.82843 1.00000i −0.333333 0.117851i
7373 −9.36396 + 3.87868i −1.09597 + 0.453965i −0.856084 0.516836i 0.827110π-0.827110\pi
−0.239885 + 0.970801i 0.577110π0.577110\pi
7474 2.70711 1.12132i 0.314695 0.130351i
7575 −7.70711 + 3.94975i −0.889940 + 0.456078i
7676 3.24264 + 3.24264i 0.371956 + 0.371956i
7777 10.2426i 1.16726i
7878 −6.24264 8.82843i −0.706840 0.999623i
7979 −5.87868 14.1924i −0.661403 1.59677i −0.795606 0.605815i 0.792847π-0.792847\pi
0.134203 0.990954i 0.457153π-0.457153\pi
8080 −2.00000 1.00000i −0.223607 0.111803i
8181 7.00000 + 5.65685i 0.777778 + 0.628539i
8282 1.12132 0.464466i 0.123829 0.0512917i
8383 11.6569i 1.27951i −0.768581 0.639753i 0.779037π-0.779037\pi
0.768581 0.639753i 0.220963π-0.220963\pi
8484 4.12132 6.53553i 0.449673 0.713085i
8585 3.17157 + 8.65685i 0.344005 + 0.938968i
8686 11.6569i 1.25699i
8787 0.464466 + 0.292893i 0.0497960 + 0.0314014i
8888 −0.878680 2.12132i −0.0936676 0.226134i
8989 14.1421i 1.49906i 0.661968 + 0.749532i 0.269721π0.269721\pi
−0.661968 + 0.749532i 0.730279π0.730279\pi
9090 4.65685 + 4.82843i 0.490876 + 0.508961i
9191 25.7279 10.6569i 2.69702 1.11714i
9292 −1.29289 + 3.12132i −0.134793 + 0.325420i
9393 0.707107 1.12132i 0.0733236 0.116276i
9494 −5.82843 + 5.82843i −0.601156 + 0.601156i
9595 −3.24264 9.72792i −0.332688 0.998064i
9696 −0.292893 + 1.70711i −0.0298933 + 0.174231i
9797 −1.46447 3.53553i −0.148694 0.358979i 0.831929 0.554882i 0.187236π-0.187236\pi
−0.980623 + 0.195902i 0.937236π0.937236\pi
9898 9.12132 + 9.12132i 0.921392 + 0.921392i
9999 0.363961 + 6.87868i 0.0365795 + 0.691333i
100100 3.00000 + 4.00000i 0.300000 + 0.400000i
101101 10.8284i 1.07747i 0.842476 + 0.538734i 0.181097π0.181097\pi
−0.842476 + 0.538734i 0.818903π0.818903\pi
102102 5.70711 4.29289i 0.565088 0.425060i
103103 −1.34315 1.34315i −0.132344 0.132344i 0.637832 0.770176i 0.279832π-0.279832\pi
−0.770176 + 0.637832i 0.779832π0.779832\pi
104104 −4.41421 + 4.41421i −0.432849 + 0.432849i
105105 −14.7782 + 8.94975i −1.44220 + 0.873406i
106106 1.17157i 0.113793i
107107 −6.53553 + 2.70711i −0.631814 + 0.261706i −0.675524 0.737338i 0.736082π-0.736082\pi
0.0437097 + 0.999044i 0.486082π0.486082\pi
108108 2.53553 4.53553i 0.243982 0.436432i
109109 −6.70711 + 2.77817i −0.642424 + 0.266101i −0.680022 0.733192i 0.738030π-0.738030\pi
0.0375973 + 0.999293i 0.488030π0.488030\pi
110110 −0.363961 + 5.12132i −0.0347023 + 0.488299i
111111 1.12132 + 4.94975i 0.106431 + 0.469809i
112112 −4.12132 1.70711i −0.389428 0.161306i
113113 −1.36396 + 3.29289i −0.128311 + 0.309769i −0.974959 0.222383i 0.928617π-0.928617\pi
0.846649 + 0.532152i 0.178617π0.178617\pi
114114 −6.48528 + 4.58579i −0.607402 + 0.429498i
115115 5.70711 4.94975i 0.532190 0.461566i
116116 0.121320 0.292893i 0.0112643 0.0271945i
117117 16.8995 8.07107i 1.56236 0.746170i
118118 −6.41421 6.41421i −0.590476 0.590476i
119119 7.53553 + 16.7782i 0.690781 + 1.53805i
120120 2.29289 3.12132i 0.209312 0.284936i
121121 4.05025 4.05025i 0.368205 0.368205i
122122 1.05025 + 2.53553i 0.0950854 + 0.229556i
123123 0.464466 + 2.05025i 0.0418795 + 0.184865i
124124 −0.707107 0.292893i −0.0635001 0.0263026i
125125 −2.00000 11.0000i −0.178885 0.983870i
126126 9.94975 + 8.94975i 0.886394 + 0.797307i
127127 −1.65685 −0.147022 −0.0735110 0.997294i 0.523420π-0.523420\pi
−0.0735110 + 0.997294i 0.523420π0.523420\pi
128128 1.00000 0.0883883
129129 19.8995 + 3.41421i 1.75205 + 0.300605i
130130 13.2426 4.41421i 1.16146 0.387152i
131131 −8.53553 3.53553i −0.745753 0.308901i −0.0227456 0.999741i 0.507241π-0.507241\pi
−0.723007 + 0.690840i 0.757241π0.757241\pi
132132 3.87868 0.878680i 0.337596 0.0764792i
133133 −7.82843 18.8995i −0.678811 1.63879i
134134 −4.41421 + 4.41421i −0.381330 + 0.381330i
135135 −9.60660 + 6.53553i −0.826805 + 0.562489i
136136 −3.00000 2.82843i −0.257248 0.242536i
137137 7.48528 + 7.48528i 0.639511 + 0.639511i 0.950435 0.310924i 0.100638π-0.100638\pi
−0.310924 + 0.950435i 0.600638π0.600638\pi
138138 −4.94975 3.12132i −0.421350 0.265704i
139139 3.12132 7.53553i 0.264747 0.639156i −0.734473 0.678638i 0.762571π-0.762571\pi
0.999220 + 0.0394819i 0.0125707π0.0125707\pi
140140 6.53553 + 7.53553i 0.552353 + 0.636869i
141141 −8.24264 11.6569i −0.694156 0.981684i
142142 −2.36396 + 5.70711i −0.198379 + 0.478930i
143143 13.2426 + 5.48528i 1.10741 + 0.458702i
144144 −2.82843 1.00000i −0.235702 0.0833333i
145145 −0.535534 + 0.464466i −0.0444737 + 0.0385718i
146146 −9.36396 + 3.87868i −0.774967 + 0.321002i
147147 −18.2426 + 12.8995i −1.50463 + 1.06393i
148148 2.70711 1.12132i 0.222523 0.0921720i
149149 22.1421i 1.81395i −0.421180 0.906977i 0.638384π-0.638384\pi
0.421180 0.906977i 0.361616π-0.361616\pi
150150 −7.70711 + 3.94975i −0.629283 + 0.322496i
151151 6.65685 6.65685i 0.541727 0.541727i −0.382308 0.924035i 0.624871π-0.624871\pi
0.924035 + 0.382308i 0.124871π0.124871\pi
152152 3.24264 + 3.24264i 0.263013 + 0.263013i
153153 5.65685 + 11.0000i 0.457330 + 0.889297i
154154 10.2426i 0.825376i
155155 1.12132 + 1.29289i 0.0900666 + 0.103848i
156156 −6.24264 8.82843i −0.499811 0.706840i
157157 16.0711 + 16.0711i 1.28261 + 1.28261i 0.939177 + 0.343434i 0.111590π0.111590\pi
0.343434 + 0.939177i 0.388410π0.388410\pi
158158 −5.87868 14.1924i −0.467683 1.12909i
159159 −2.00000 0.343146i −0.158610 0.0272132i
160160 −2.00000 1.00000i −0.158114 0.0790569i
161161 10.6569 10.6569i 0.839878 0.839878i
162162 7.00000 + 5.65685i 0.549972 + 0.444444i
163163 3.36396 8.12132i 0.263486 0.636111i −0.735664 0.677347i 0.763130π-0.763130\pi
0.999149 + 0.0412361i 0.0131296π0.0131296\pi
164164 1.12132 0.464466i 0.0875604 0.0362687i
165165 −8.63604 2.12132i −0.672315 0.165145i
166166 11.6569i 0.904747i
167167 −1.39340 3.36396i −0.107824 0.260311i 0.860753 0.509022i 0.169993π-0.169993\pi
−0.968578 + 0.248711i 0.919993π0.919993\pi
168168 4.12132 6.53553i 0.317967 0.504227i
169169 25.9706i 1.99774i
170170 3.17157 + 8.65685i 0.243249 + 0.663950i
171171 −5.92893 12.4142i −0.453397 0.949339i
172172 11.6569i 0.888827i
173173 −15.1924 + 6.29289i −1.15506 + 0.478440i −0.876226 0.481901i 0.839947π-0.839947\pi
−0.278830 + 0.960340i 0.589947π0.589947\pi
174174 0.464466 + 0.292893i 0.0352111 + 0.0222042i
175175 −5.53553 21.6066i −0.418447 1.63331i
176176 −0.878680 2.12132i −0.0662330 0.159901i
177177 12.8284 9.07107i 0.964244 0.681823i
178178 14.1421i 1.06000i
179179 1.24264 + 1.24264i 0.0928793 + 0.0928793i 0.752020 0.659140i 0.229080π-0.229080\pi
−0.659140 + 0.752020i 0.729080π0.729080\pi
180180 4.65685 + 4.82843i 0.347101 + 0.359890i
181181 −3.87868 + 1.60660i −0.288300 + 0.119418i −0.522147 0.852856i 0.674869π-0.674869\pi
0.233847 + 0.972273i 0.424869π0.424869\pi
182182 25.7279 10.6569i 1.90708 0.789939i
183183 −4.63604 + 1.05025i −0.342706 + 0.0776369i
184184 −1.29289 + 3.12132i −0.0953134 + 0.230107i
185185 −6.53553 0.464466i −0.480502 0.0341482i
186186 0.707107 1.12132i 0.0518476 0.0822192i
187187 −3.36396 + 8.84924i −0.245997 + 0.647121i
188188 −5.82843 + 5.82843i −0.425082 + 0.425082i
189189 −18.1924 + 14.3640i −1.32330 + 1.04482i
190190 −3.24264 9.72792i −0.235246 0.705738i
191191 −17.6569 −1.27761 −0.638803 0.769371i 0.720570π-0.720570\pi
−0.638803 + 0.769371i 0.720570π0.720570\pi
192192 −0.292893 + 1.70711i −0.0211377 + 0.123200i
193193 8.29289 + 3.43503i 0.596936 + 0.247259i 0.660631 0.750711i 0.270289π-0.270289\pi
−0.0636957 + 0.997969i 0.520289π0.520289\pi
194194 −1.46447 3.53553i −0.105143 0.253837i
195195 3.65685 + 23.8995i 0.261873 + 1.71148i
196196 9.12132 + 9.12132i 0.651523 + 0.651523i
197197 1.05025 2.53553i 0.0748274 0.180649i −0.882040 0.471175i 0.843830π-0.843830\pi
0.956867 + 0.290525i 0.0938301π0.0938301\pi
198198 0.363961 + 6.87868i 0.0258656 + 0.488846i
199199 7.77817 + 3.22183i 0.551380 + 0.228389i 0.640938 0.767592i 0.278545π-0.278545\pi
−0.0895581 + 0.995982i 0.528545π0.528545\pi
200200 3.00000 + 4.00000i 0.212132 + 0.282843i
201201 −6.24264 8.82843i −0.440322 0.622709i
202202 10.8284i 0.761885i
203203 −1.00000 + 1.00000i −0.0701862 + 0.0701862i
204204 5.70711 4.29289i 0.399577 0.300563i
205205 −2.70711 0.192388i −0.189073 0.0134370i
206206 −1.34315 1.34315i −0.0935814 0.0935814i
207207 6.77817 7.53553i 0.471116 0.523756i
208208 −4.41421 + 4.41421i −0.306071 + 0.306071i
209209 4.02944 9.72792i 0.278722 0.672894i
210210 −14.7782 + 8.94975i −1.01979 + 0.617591i
211211 −1.60660 3.87868i −0.110603 0.267019i 0.858880 0.512176i 0.171161π-0.171161\pi
−0.969483 + 0.245157i 0.921161π0.921161\pi
212212 1.17157i 0.0804640i
213213 −9.05025 5.70711i −0.620113 0.391045i
214214 −6.53553 + 2.70711i −0.446760 + 0.185054i
215215 −11.6569 + 23.3137i −0.794991 + 1.58998i
216216 2.53553 4.53553i 0.172521 0.308604i
217217 2.41421 + 2.41421i 0.163887 + 0.163887i
218218 −6.70711 + 2.77817i −0.454263 + 0.188162i
219219 −3.87868 17.1213i −0.262097 1.15695i
220220 −0.363961 + 5.12132i −0.0245382 + 0.345279i
221221 25.7279 0.757359i 1.73065 0.0509455i
222222 1.12132 + 4.94975i 0.0752581 + 0.332205i
223223 −23.3137 −1.56120 −0.780601 0.625030i 0.785087π-0.785087\pi
−0.780601 + 0.625030i 0.785087π0.785087\pi
224224 −4.12132 1.70711i −0.275367 0.114061i
225225 −4.48528 14.3137i −0.299019 0.954247i
226226 −1.36396 + 3.29289i −0.0907293 + 0.219040i
227227 4.53553 + 1.87868i 0.301034 + 0.124692i 0.528088 0.849190i 0.322909π-0.322909\pi
−0.227054 + 0.973882i 0.572909π0.572909\pi
228228 −6.48528 + 4.58579i −0.429498 + 0.303701i
229229 −11.5858 + 11.5858i −0.765610 + 0.765610i −0.977330 0.211720i 0.932094π-0.932094\pi
0.211720 + 0.977330i 0.432094π0.432094\pi
230230 5.70711 4.94975i 0.376315 0.326377i
231231 −17.4853 3.00000i −1.15045 0.197386i
232232 0.121320 0.292893i 0.00796507 0.0192294i
233233 3.12132 + 7.53553i 0.204484 + 0.493669i 0.992538 0.121938i 0.0389109π-0.0389109\pi
−0.788053 + 0.615607i 0.788911π0.788911\pi
234234 16.8995 8.07107i 1.10475 0.527622i
235235 17.4853 5.82843i 1.14061 0.380205i
236236 −6.41421 6.41421i −0.417530 0.417530i
237237 25.9497 5.87868i 1.68562 0.381861i
238238 7.53553 + 16.7782i 0.488456 + 1.08757i
239239 −12.0000 −0.776215 −0.388108 0.921614i 0.626871π-0.626871\pi
−0.388108 + 0.921614i 0.626871π0.626871\pi
240240 2.29289 3.12132i 0.148006 0.201480i
241241 1.36396 + 0.564971i 0.0878605 + 0.0363930i 0.426181 0.904638i 0.359859π-0.359859\pi
−0.338320 + 0.941031i 0.609859π0.609859\pi
242242 4.05025 4.05025i 0.260360 0.260360i
243243 −11.7071 + 10.2929i −0.751011 + 0.660289i
244244 1.05025 + 2.53553i 0.0672355 + 0.162321i
245245 −9.12132 27.3640i −0.582740 1.74822i
246246 0.464466 + 2.05025i 0.0296133 + 0.130719i
247247 −28.6274 −1.82152
248248 −0.707107 0.292893i −0.0449013 0.0185987i
249249 19.8995 + 3.41421i 1.26108 + 0.216367i
250250 −2.00000 11.0000i −0.126491 0.695701i
251251 9.17157 0.578905 0.289452 0.957192i 0.406527π-0.406527\pi
0.289452 + 0.957192i 0.406527π0.406527\pi
252252 9.94975 + 8.94975i 0.626775 + 0.563781i
253253 7.75736 0.487701
254254 −1.65685 −0.103960
255255 −15.7071 + 2.87868i −0.983617 + 0.180270i
256256 1.00000 0.0625000
257257 3.17157 0.197837 0.0989186 0.995096i 0.468462π-0.468462\pi
0.0989186 + 0.995096i 0.468462π0.468462\pi
258258 19.8995 + 3.41421i 1.23889 + 0.212560i
259259 −13.0711 −0.812197
260260 13.2426 4.41421i 0.821274 0.273758i
261261 −0.636039 + 0.707107i −0.0393698 + 0.0437688i
262262 −8.53553 3.53553i −0.527327 0.218426i
263263 −8.00000 −0.493301 −0.246651 0.969104i 0.579330π-0.579330\pi
−0.246651 + 0.969104i 0.579330π0.579330\pi
264264 3.87868 0.878680i 0.238716 0.0540790i
265265 1.17157 2.34315i 0.0719691 0.143938i
266266 −7.82843 18.8995i −0.479992 1.15880i
267267 −24.1421 4.14214i −1.47747 0.253495i
268268 −4.41421 + 4.41421i −0.269641 + 0.269641i
269269 −29.0919 12.0503i −1.77376 0.734717i −0.994094 0.108526i 0.965387π-0.965387\pi
−0.779670 0.626191i 0.784613π-0.784613\pi
270270 −9.60660 + 6.53553i −0.584639 + 0.397740i
271271 −0.686292 −0.0416892 −0.0208446 0.999783i 0.506636π-0.506636\pi
−0.0208446 + 0.999783i 0.506636π0.506636\pi
272272 −3.00000 2.82843i −0.181902 0.171499i
273273 10.6569 + 47.0416i 0.644982 + 2.84709i
274274 7.48528 + 7.48528i 0.452202 + 0.452202i
275275 5.84924 9.87868i 0.352723 0.595707i
276276 −4.94975 3.12132i −0.297940 0.187881i
277277 11.0919 + 26.7782i 0.666447 + 1.60894i 0.787511 + 0.616300i 0.211369π0.211369\pi
−0.121065 + 0.992645i 0.538631π0.538631\pi
278278 3.12132 7.53553i 0.187204 0.451951i
279279 1.70711 + 1.53553i 0.102202 + 0.0919300i
280280 6.53553 + 7.53553i 0.390573 + 0.450334i
281281 −2.51472 + 2.51472i −0.150016 + 0.150016i −0.778125 0.628109i 0.783829π-0.783829\pi
0.628109 + 0.778125i 0.283829π0.283829\pi
282282 −8.24264 11.6569i −0.490842 0.694156i
283283 16.7782 + 6.94975i 0.997359 + 0.413120i 0.820828 0.571175i 0.193512π-0.193512\pi
0.176531 + 0.984295i 0.443512π0.443512\pi
284284 −2.36396 + 5.70711i −0.140275 + 0.338654i
285285 17.5563 2.68629i 1.03995 0.159122i
286286 13.2426 + 5.48528i 0.783054 + 0.324351i
287287 −5.41421 −0.319591
288288 −2.82843 1.00000i −0.166667 0.0589256i
289289 1.00000 + 16.9706i 0.0588235 + 0.998268i
290290 −0.535534 + 0.464466i −0.0314476 + 0.0272744i
291291 6.46447 1.46447i 0.378954 0.0858485i
292292 −9.36396 + 3.87868i −0.547984 + 0.226983i
293293 5.58579 + 5.58579i 0.326325 + 0.326325i 0.851187 0.524862i 0.175883π-0.175883\pi
−0.524862 + 0.851187i 0.675883π0.675883\pi
294294 −18.2426 + 12.8995i −1.06393 + 0.752314i
295295 6.41421 + 19.2426i 0.373450 + 1.12035i
296296 2.70711 1.12132i 0.157347 0.0651754i
297297 −11.8492 1.39340i −0.687563 0.0808532i
298298 22.1421i 1.28266i
299299 −8.07107 19.4853i −0.466762 1.12686i
300300 −7.70711 + 3.94975i −0.444970 + 0.228039i
301301 −19.8995 + 48.0416i −1.14699 + 2.76907i
302302 6.65685 6.65685i 0.383059 0.383059i
303303 −18.4853 3.17157i −1.06195 0.182202i
304304 3.24264 + 3.24264i 0.185978 + 0.185978i
305305 0.435029 6.12132i 0.0249097 0.350506i
306306 5.65685 + 11.0000i 0.323381 + 0.628828i
307307 3.72792 3.72792i 0.212764 0.212764i −0.592677 0.805440i 0.701929π-0.701929\pi
0.805440 + 0.592677i 0.201929π0.201929\pi
308308 10.2426i 0.583629i
309309 2.68629 1.89949i 0.152818 0.108058i
310310 1.12132 + 1.29289i 0.0636867 + 0.0734314i
311311 25.1924 + 10.4350i 1.42853 + 0.591716i 0.956988 0.290128i 0.0936978π-0.0936978\pi
0.471541 + 0.881844i 0.343698π0.343698\pi
312312 −6.24264 8.82843i −0.353420 0.499811i
313313 7.70711 18.6066i 0.435631 1.05171i −0.541810 0.840501i 0.682261π-0.682261\pi
0.977441 0.211206i 0.0677392π-0.0677392\pi
314314 16.0711 + 16.0711i 0.906943 + 0.906943i
315315 −10.9497 27.8492i −0.616948 1.56913i
316316 −5.87868 14.1924i −0.330702 0.798384i
317317 −19.5355 8.09188i −1.09722 0.454485i −0.240704 0.970598i 0.577378π-0.577378\pi
−0.856520 + 0.516113i 0.827378π0.827378\pi
318318 −2.00000 0.343146i −0.112154 0.0192427i
319319 −0.727922 −0.0407558
320320 −2.00000 1.00000i −0.111803 0.0559017i
321321 −2.70711 11.9497i −0.151096 0.666970i
322322 10.6569 10.6569i 0.593883 0.593883i
323323 −0.556349 18.8995i −0.0309561 1.05160i
324324 7.00000 + 5.65685i 0.388889 + 0.314270i
325325 −30.8995 4.41421i −1.71400 0.244857i
326326 3.36396 8.12132i 0.186313 0.449798i
327327 −2.77817 12.2635i −0.153633 0.678171i
328328 1.12132 0.464466i 0.0619146 0.0256458i
329329 33.9706 14.0711i 1.87286 0.775763i
330330 −8.63604 2.12132i −0.475398 0.116775i
331331 −4.41421 4.41421i −0.242627 0.242627i 0.575309 0.817936i 0.304882π-0.304882\pi
−0.817936 + 0.575309i 0.804882π0.804882\pi
332332 11.6569i 0.639753i
333333 −8.77817 + 0.464466i −0.481041 + 0.0254526i
334334 −1.39340 3.36396i −0.0762434 0.184068i
335335 13.2426 4.41421i 0.723523 0.241174i
336336 4.12132 6.53553i 0.224836 0.356543i
337337 6.77817 2.80761i 0.369231 0.152940i −0.190350 0.981716i 0.560962π-0.560962\pi
0.559581 + 0.828776i 0.310962π0.310962\pi
338338 25.9706i 1.41261i
339339 −5.22183 3.29289i −0.283611 0.178845i
340340 3.17157 + 8.65685i 0.172003 + 0.469484i
341341 1.75736i 0.0951663i
342342 −5.92893 12.4142i −0.320600 0.671284i
343343 −10.0711 24.3137i −0.543787 1.31282i
344344 11.6569i 0.628495i
345345 6.77817 + 11.1924i 0.364925 + 0.602578i
346346 −15.1924 + 6.29289i −0.816748 + 0.338308i
347347 −7.84924 + 18.9497i −0.421369 + 1.01728i 0.560575 + 0.828104i 0.310580π0.310580\pi
−0.981944 + 0.189172i 0.939420π0.939420\pi
348348 0.464466 + 0.292893i 0.0248980 + 0.0157007i
349349 −0.757359 + 0.757359i −0.0405405 + 0.0405405i −0.727086 0.686546i 0.759126π-0.759126\pi
0.686546 + 0.727086i 0.259126π0.259126\pi
350350 −5.53553 21.6066i −0.295887 1.15492i
351351 8.82843 + 31.2132i 0.471227 + 1.66604i
352352 −0.878680 2.12132i −0.0468338 0.113067i
353353 −16.6569 16.6569i −0.886555 0.886555i 0.107636 0.994190i 0.465672π-0.465672\pi
−0.994190 + 0.107636i 0.965672π0.965672\pi
354354 12.8284 9.07107i 0.681823 0.482122i
355355 10.4350 9.05025i 0.553834 0.480338i
356356 14.1421i 0.749532i
357357 −30.8492 + 7.94975i −1.63272 + 0.420745i
358358 1.24264 + 1.24264i 0.0656756 + 0.0656756i
359359 8.65685 8.65685i 0.456891 0.456891i −0.440742 0.897634i 0.645285π-0.645285\pi
0.897634 + 0.440742i 0.145285π0.145285\pi
360360 4.65685 + 4.82843i 0.245438 + 0.254480i
361361 2.02944i 0.106812i
362362 −3.87868 + 1.60660i −0.203859 + 0.0844411i
363363 5.72792 + 8.10051i 0.300638 + 0.425166i
364364 25.7279 10.6569i 1.34851 0.558571i
365365 22.6066 + 1.60660i 1.18328 + 0.0840934i
366366 −4.63604 + 1.05025i −0.242330 + 0.0548976i
367367 −4.12132 1.70711i −0.215131 0.0891102i 0.272515 0.962151i 0.412144π-0.412144\pi
−0.487646 + 0.873041i 0.662144π0.662144\pi
368368 −1.29289 + 3.12132i −0.0673967 + 0.162710i
369369 −3.63604 + 0.192388i −0.189285 + 0.0100153i
370370 −6.53553 0.464466i −0.339766 0.0241464i
371371 2.00000 4.82843i 0.103835 0.250679i
372372 0.707107 1.12132i 0.0366618 0.0581378i
373373 −11.2426 11.2426i −0.582122 0.582122i 0.353364 0.935486i 0.385038π-0.385038\pi
−0.935486 + 0.353364i 0.885038π0.885038\pi
374374 −3.36396 + 8.84924i −0.173946 + 0.457583i
375375 19.3640 0.192388i 0.999951 0.00993488i
376376 −5.82843 + 5.82843i −0.300578 + 0.300578i
377377 0.757359 + 1.82843i 0.0390060 + 0.0941688i
378378 −18.1924 + 14.3640i −0.935715 + 0.738802i
379379 −34.0919 14.1213i −1.75118 0.725364i −0.997692 0.0679048i 0.978369π-0.978369\pi
−0.753491 0.657459i 0.771631π-0.771631\pi
380380 −3.24264 9.72792i −0.166344 0.499032i
381381 0.485281 2.82843i 0.0248617 0.144905i
382382 −17.6569 −0.903403
383383 27.3137 1.39567 0.697833 0.716261i 0.254148π-0.254148\pi
0.697833 + 0.716261i 0.254148π0.254148\pi
384384 −0.292893 + 1.70711i −0.0149466 + 0.0871154i
385385 10.2426 20.4853i 0.522013 1.04403i
386386 8.29289 + 3.43503i 0.422097 + 0.174838i
387387 −11.6569 + 32.9706i −0.592551 + 1.67599i
388388 −1.46447 3.53553i −0.0743470 0.179490i
389389 2.41421 2.41421i 0.122405 0.122405i −0.643250 0.765656i 0.722415π-0.722415\pi
0.765656 + 0.643250i 0.222415π0.222415\pi
390390 3.65685 + 23.8995i 0.185172 + 1.21020i
391391 12.7071 5.70711i 0.642626 0.288621i
392392 9.12132 + 9.12132i 0.460696 + 0.460696i
393393 8.53553 13.5355i 0.430561 0.682777i
394394 1.05025 2.53553i 0.0529110 0.127738i
395395 −2.43503 + 34.2635i −0.122520 + 1.72398i
396396 0.363961 + 6.87868i 0.0182897 + 0.345667i
397397 4.26346 10.2929i 0.213977 0.516586i −0.780051 0.625716i 0.784807π-0.784807\pi
0.994027 + 0.109131i 0.0348068π0.0348068\pi
398398 7.77817 + 3.22183i 0.389885 + 0.161496i
399399 34.5563 7.82843i 1.72998 0.391912i
400400 3.00000 + 4.00000i 0.150000 + 0.200000i
401401 1.94975 0.807612i 0.0973657 0.0403302i −0.333469 0.942761i 0.608219π-0.608219\pi
0.430835 + 0.902431i 0.358219π0.358219\pi
402402 −6.24264 8.82843i −0.311355 0.440322i
403403 4.41421 1.82843i 0.219888 0.0910804i
404404 10.8284i 0.538734i
405405 −8.34315 18.3137i −0.414574 0.910015i
406406 −1.00000 + 1.00000i −0.0496292 + 0.0496292i
407407 −4.75736 4.75736i −0.235814 0.235814i
408408 5.70711 4.29289i 0.282544 0.212530i
409409 10.8284i 0.535431i 0.963498 + 0.267716i 0.0862688π0.0862688\pi
−0.963498 + 0.267716i 0.913731π0.913731\pi
410410 −2.70711 0.192388i −0.133694 0.00950137i
411411 −14.9706 + 10.5858i −0.738443 + 0.522158i
412412 −1.34315 1.34315i −0.0661720 0.0661720i
413413 15.4853 + 37.3848i 0.761981 + 1.83958i
414414 6.77817 7.53553i 0.333129 0.370351i
415415 −11.6569 + 23.3137i −0.572212 + 1.14442i
416416 −4.41421 + 4.41421i −0.216425 + 0.216425i
417417 11.9497 + 7.53553i 0.585182 + 0.369017i
418418 4.02944 9.72792i 0.197086 0.475808i
419419 −13.6066 + 5.63604i −0.664726 + 0.275339i −0.689426 0.724356i 0.742137π-0.742137\pi
0.0246997 + 0.999695i 0.492137π0.492137\pi
420420 −14.7782 + 8.94975i −0.721101 + 0.436703i
421421 38.1421i 1.85893i −0.368905 0.929467i 0.620267π-0.620267\pi
0.368905 0.929467i 0.379733π-0.379733\pi
422422 −1.60660 3.87868i −0.0782081 0.188811i
423423 22.3137 10.6569i 1.08493 0.518154i
424424 1.17157i 0.0568966i
425425 2.31371 20.4853i 0.112231 0.993682i
426426 −9.05025 5.70711i −0.438486 0.276510i
427427 12.2426i 0.592463i
428428 −6.53553 + 2.70711i −0.315907 + 0.130853i
429429 −13.2426 + 21.0000i −0.639361 + 1.01389i
430430 −11.6569 + 23.3137i −0.562143 + 1.12429i
431431 13.3934 + 32.3345i 0.645137 + 1.55750i 0.819663 + 0.572847i 0.194161π0.194161\pi
−0.174525 + 0.984653i 0.555839π0.555839\pi
432432 2.53553 4.53553i 0.121991 0.218216i
433433 28.9706i 1.39224i 0.717927 + 0.696118i 0.245091π0.245091\pi
−0.717927 + 0.696118i 0.754909π0.754909\pi
434434 2.41421 + 2.41421i 0.115886 + 0.115886i
435435 −0.636039 1.05025i −0.0304957 0.0503558i
436436 −6.70711 + 2.77817i −0.321212 + 0.133050i
437437 −14.3137 + 5.92893i −0.684718 + 0.283619i
438438 −3.87868 17.1213i −0.185330 0.818088i
439439 −9.77817 + 23.6066i −0.466687 + 1.12668i 0.498914 + 0.866652i 0.333732π0.333732\pi
−0.965601 + 0.260030i 0.916268π0.916268\pi
440440 −0.363961 + 5.12132i −0.0173512 + 0.244149i
441441 −16.6777 34.9203i −0.794175 1.66287i
442442 25.7279 0.757359i 1.22375 0.0360239i
443443 22.0711 22.0711i 1.04863 1.04863i 0.0498725 0.998756i 0.484119π-0.484119\pi
0.998756 0.0498725i 0.0158815π-0.0158815\pi
444444 1.12132 + 4.94975i 0.0532155 + 0.234905i
445445 14.1421 28.2843i 0.670402 1.34080i
446446 −23.3137 −1.10394
447447 37.7990 + 6.48528i 1.78783 + 0.306743i
448448 −4.12132 1.70711i −0.194714 0.0806532i
449449 4.19239 + 10.1213i 0.197851 + 0.477655i 0.991402 0.130849i 0.0417702π-0.0417702\pi
−0.793551 + 0.608503i 0.791770π0.791770\pi
450450 −4.48528 14.3137i −0.211438 0.674755i
451451 −1.97056 1.97056i −0.0927902 0.0927902i
452452 −1.36396 + 3.29289i −0.0641553 + 0.154885i
453453 9.41421 + 13.3137i 0.442318 + 0.625533i
454454 4.53553 + 1.87868i 0.212863 + 0.0881708i
455455 −62.1127 4.41421i −2.91189 0.206942i
456456 −6.48528 + 4.58579i −0.303701 + 0.214749i
457457 9.65685i 0.451729i 0.974159 + 0.225864i 0.0725206π0.0725206\pi
−0.974159 + 0.225864i 0.927479π0.927479\pi
458458 −11.5858 + 11.5858i −0.541368 + 0.541368i
459459 −20.4350 + 6.43503i −0.953825 + 0.300361i
460460 5.70711 4.94975i 0.266095 0.230783i
461461 −19.7279 19.7279i −0.918821 0.918821i 0.0781228 0.996944i 0.475107π-0.475107\pi
−0.996944 + 0.0781228i 0.975107π0.975107\pi
462462 −17.4853 3.00000i −0.813489 0.139573i
463463 8.17157 8.17157i 0.379765 0.379765i −0.491252 0.871017i 0.663461π-0.663461\pi
0.871017 + 0.491252i 0.163461π0.163461\pi
464464 0.121320 0.292893i 0.00563216 0.0135972i
465465 −2.53553 + 1.53553i −0.117583 + 0.0712087i
466466 3.12132 + 7.53553i 0.144592 + 0.349077i
467467 26.4853i 1.22559i −0.790241 0.612796i 0.790045π-0.790045\pi
0.790241 0.612796i 0.209955π-0.209955\pi
468468 16.8995 8.07107i 0.781179 0.373085i
469469 25.7279 10.6569i 1.18801 0.492088i
470470 17.4853 5.82843i 0.806536 0.268845i
471471 −32.1421 + 22.7279i −1.48103 + 1.04725i
472472 −6.41421 6.41421i −0.295238 0.295238i
473473 −24.7279 + 10.2426i −1.13699 + 0.470957i
474474 25.9497 5.87868i 1.19191 0.270017i
475475 −3.24264 + 22.6985i −0.148783 + 1.04148i
476476 7.53553 + 16.7782i 0.345391 + 0.769026i
477477 1.17157 3.31371i 0.0536426 0.151724i
478478 −12.0000 −0.548867
479479 20.3640 + 8.43503i 0.930453 + 0.385406i 0.795850 0.605493i 0.207024π-0.207024\pi
0.134603 + 0.990900i 0.457024π0.457024\pi
480480 2.29289 3.12132i 0.104656 0.142468i
481481 −7.00000 + 16.8995i −0.319173 + 0.770551i
482482 1.36396 + 0.564971i 0.0621267 + 0.0257337i
483483 15.0711 + 21.3137i 0.685757 + 0.969807i
484484 4.05025 4.05025i 0.184102 0.184102i
485485 −0.606602 + 8.53553i −0.0275444 + 0.387579i
486486 −11.7071 + 10.2929i −0.531045 + 0.466895i
487487 −3.53553 + 8.53553i −0.160210 + 0.386782i −0.983517 0.180815i 0.942127π-0.942127\pi
0.823307 + 0.567597i 0.192127π0.192127\pi
488488 1.05025 + 2.53553i 0.0475427 + 0.114778i
489489 12.8787 + 8.12132i 0.582394 + 0.367259i
490490 −9.12132 27.3640i −0.412059 1.23618i
491491 18.4142 + 18.4142i 0.831022 + 0.831022i 0.987657 0.156635i 0.0500646π-0.0500646\pi
−0.156635 + 0.987657i 0.550065π0.550065\pi
492492 0.464466 + 2.05025i 0.0209397 + 0.0924325i
493493 −1.19239 + 0.535534i −0.0537025 + 0.0241192i
494494 −28.6274 −1.28801
495495 6.15076 14.1213i 0.276456 0.634706i
496496 −0.707107 0.292893i −0.0317500 0.0131513i
497497 19.4853 19.4853i 0.874034 0.874034i
498498 19.8995 + 3.41421i 0.891718 + 0.152995i
499499 13.0208 + 31.4350i 0.582892 + 1.40723i 0.890180 + 0.455609i 0.150578π0.150578\pi
−0.307288 + 0.951616i 0.599422π0.599422\pi
500500 −2.00000 11.0000i −0.0894427 0.491935i
501501 6.15076 1.39340i 0.274796 0.0622524i
502502 9.17157 0.409347
503503 22.6066 + 9.36396i 1.00798 + 0.417518i 0.824717 0.565546i 0.191334π-0.191334\pi
0.183262 + 0.983064i 0.441334π0.441334\pi
504504 9.94975 + 8.94975i 0.443197 + 0.398653i
505505 10.8284 21.6569i 0.481859 0.963717i
506506 7.75736 0.344857
507507 44.3345 + 7.60660i 1.96897 + 0.337821i
508508 −1.65685 −0.0735110
509509 35.6569 1.58046 0.790231 0.612809i 0.209960π-0.209960\pi
0.790231 + 0.612809i 0.209960π0.209960\pi
510510 −15.7071 + 2.87868i −0.695522 + 0.127470i
511511 45.2132 2.00011
512512 1.00000 0.0441942
513513 22.9289 6.48528i 1.01234 0.286332i
514514 3.17157 0.139892
515515 1.34315 + 4.02944i 0.0591861 + 0.177558i
516516 19.8995 + 3.41421i 0.876026 + 0.150302i
517517 17.4853 + 7.24264i 0.769002 + 0.318531i
518518 −13.0711 −0.574310
519519 −6.29289 27.7782i −0.276227 1.21933i
520520 13.2426 4.41421i 0.580728 0.193576i
521521 9.70711 + 23.4350i 0.425276 + 1.02671i 0.980767 + 0.195184i 0.0625305π0.0625305\pi
−0.555490 + 0.831523i 0.687469π0.687469\pi
522522 −0.636039 + 0.707107i −0.0278387 + 0.0309492i
523523 −8.41421 + 8.41421i −0.367928 + 0.367928i −0.866721 0.498793i 0.833777π-0.833777\pi
0.498793 + 0.866721i 0.333777π0.333777\pi
524524 −8.53553 3.53553i −0.372877 0.154451i
525525 38.5061 3.12132i 1.68054 0.136226i
526526 −8.00000 −0.348817
527527 1.29289 + 2.87868i 0.0563193 + 0.125397i
528528 3.87868 0.878680i 0.168798 0.0382396i
529529 8.19239 + 8.19239i 0.356191 + 0.356191i
530530 1.17157 2.34315i 0.0508899 0.101780i
531531 11.7279 + 24.5563i 0.508948 + 1.06565i
532532 −7.82843 18.8995i −0.339405 0.819397i
533533 −2.89949 + 7.00000i −0.125591 + 0.303204i
534534 −24.1421 4.14214i −1.04473 0.179248i
535535 15.7782 + 1.12132i 0.682150 + 0.0484789i
536536 −4.41421 + 4.41421i −0.190665 + 0.190665i
537537 −2.48528 + 1.75736i −0.107248 + 0.0758357i
538538 −29.0919 12.0503i −1.25424 0.519523i
539539 11.3345 27.3640i 0.488213 1.17865i
540540 −9.60660 + 6.53553i −0.413402 + 0.281245i
541541 −36.5061 15.1213i −1.56952 0.650116i −0.582810 0.812609i 0.698047π-0.698047\pi
−0.986710 + 0.162492i 0.948047π0.948047\pi
542542 −0.686292 −0.0294787
543543 −1.60660 7.09188i −0.0689459 0.304342i
544544 −3.00000 2.82843i −0.128624 0.121268i
545545 16.1924 + 1.15076i 0.693606 + 0.0492930i
546546 10.6569 + 47.0416i 0.456071 + 2.01320i
547547 27.3640 11.3345i 1.17000 0.484629i 0.288806 0.957388i 0.406742π-0.406742\pi
0.881192 + 0.472758i 0.156742π0.156742\pi
548548 7.48528 + 7.48528i 0.319755 + 0.319755i
549549 −0.435029 8.22183i −0.0185666 0.350899i
550550 5.84924 9.87868i 0.249413 0.421228i
551551 1.34315 0.556349i 0.0572199 0.0237013i
552552 −4.94975 3.12132i −0.210675 0.132852i
553553 68.5269i 2.91406i
554554 11.0919 + 26.7782i 0.471249 + 1.13770i
555555 2.70711 11.0208i 0.114910 0.467808i
556556 3.12132 7.53553i 0.132373 0.319578i
557557 −10.8995 + 10.8995i −0.461826 + 0.461826i −0.899254 0.437427i 0.855890π-0.855890\pi
0.437427 + 0.899254i 0.355890π0.355890\pi
558558 1.70711 + 1.53553i 0.0722676 + 0.0650043i
559559 51.4558 + 51.4558i 2.17635 + 2.17635i
560560 6.53553 + 7.53553i 0.276177 + 0.318434i
561561 −14.1213 8.33452i −0.596203 0.351884i
562562 −2.51472 + 2.51472i −0.106077 + 0.106077i
563563 5.02944i 0.211966i −0.994368 0.105983i 0.966201π-0.966201\pi
0.994368 0.105983i 0.0337988π-0.0337988\pi
564564 −8.24264 11.6569i −0.347078 0.490842i
565565 6.02082 5.22183i 0.253298 0.219684i
566566 16.7782 + 6.94975i 0.705239 + 0.292120i
567567 −19.1924 35.2635i −0.806005 1.48093i
568568 −2.36396 + 5.70711i −0.0991896 + 0.239465i
569569 8.65685 + 8.65685i 0.362914 + 0.362914i 0.864885 0.501971i 0.167391π-0.167391\pi
−0.501971 + 0.864885i 0.667391π0.667391\pi
570570 17.5563 2.68629i 0.735355 0.112516i
571571 −4.29289 10.3640i −0.179652 0.433718i 0.808242 0.588851i 0.200419π-0.200419\pi
−0.987894 + 0.155133i 0.950419π0.950419\pi
572572 13.2426 + 5.48528i 0.553703 + 0.229351i
573573 5.17157 30.1421i 0.216046 1.25921i
574574 −5.41421 −0.225985
575575 −16.3640 + 4.19239i −0.682424 + 0.174835i
576576 −2.82843 1.00000i −0.117851 0.0416667i
577577 −11.9706 + 11.9706i −0.498341 + 0.498341i −0.910921 0.412580i 0.864628π-0.864628\pi
0.412580 + 0.910921i 0.364628π0.364628\pi
578578 1.00000 + 16.9706i 0.0415945 + 0.705882i
579579 −8.29289 + 13.1508i −0.344641 + 0.546527i
580580 −0.535534 + 0.464466i −0.0222368 + 0.0192859i
581581 −19.8995 + 48.0416i −0.825570 + 1.99310i
582582 6.46447 1.46447i 0.267961 0.0607041i
583583 2.48528 1.02944i 0.102930 0.0426349i
584584 −9.36396 + 3.87868i −0.387483 + 0.160501i
585585 −41.8701 0.757359i −1.73111 0.0313130i
586586 5.58579 + 5.58579i 0.230747 + 0.230747i
587587 36.8284i 1.52007i −0.649881 0.760036i 0.725181π-0.725181\pi
0.649881 0.760036i 0.274819π-0.274819\pi
588588 −18.2426 + 12.8995i −0.752314 + 0.531966i
589589 −1.34315 3.24264i −0.0553434 0.133611i
590590 6.41421 + 19.2426i 0.264069 + 0.792207i
591591 4.02082 + 2.53553i 0.165394 + 0.104298i
592592 2.70711 1.12132i 0.111261 0.0460860i
593593 22.1421i 0.909269i −0.890678 0.454634i 0.849770π-0.849770\pi
0.890678 0.454634i 0.150230π-0.150230\pi
594594 −11.8492 1.39340i −0.486180 0.0571718i
595595 1.70711 41.0919i 0.0699846 1.68460i
596596 22.1421i 0.906977i
597597 −7.77817 + 12.3345i −0.318339 + 0.504818i
598598 −8.07107 19.4853i −0.330051 0.796812i
599599 14.9706i 0.611681i −0.952083 0.305840i 0.901063π-0.901063\pi
0.952083 0.305840i 0.0989374π-0.0989374\pi
600600 −7.70711 + 3.94975i −0.314641 + 0.161248i
601601 −0.778175 + 0.322330i −0.0317424 + 0.0131481i −0.398498 0.917169i 0.630468π-0.630468\pi
0.366756 + 0.930317i 0.380468π0.380468\pi
602602 −19.8995 + 48.0416i −0.811043 + 1.95803i
603603 16.8995 8.07107i 0.688201 0.328679i
604604 6.65685 6.65685i 0.270864 0.270864i
605605 −12.1508 + 4.05025i −0.493999 + 0.164666i
606606 −18.4853 3.17157i −0.750913 0.128836i
607607 1.19239 + 2.87868i 0.0483975 + 0.116842i 0.946229 0.323497i 0.104858π-0.104858\pi
−0.897832 + 0.440339i 0.854858π0.854858\pi
608608 3.24264 + 3.24264i 0.131506 + 0.131506i
609609 −1.41421 2.00000i −0.0573068 0.0810441i
610610 0.435029 6.12132i 0.0176138 0.247845i
611611 51.4558i 2.08168i
612612 5.65685 + 11.0000i 0.228665 + 0.444649i
613613 −14.0711 14.0711i −0.568325 0.568325i 0.363334 0.931659i 0.381638π-0.381638\pi
−0.931659 + 0.363334i 0.881638π0.881638\pi
614614 3.72792 3.72792i 0.150447 0.150447i
615615 1.12132 4.56497i 0.0452160 0.184077i
616616 10.2426i 0.412688i
617617 −40.4350 + 16.7487i −1.62785 + 0.674279i −0.994989 0.0999842i 0.968121π-0.968121\pi
−0.632864 + 0.774263i 0.718121π0.718121\pi
618618 2.68629 1.89949i 0.108058 0.0764089i
619619 −20.6777 + 8.56497i −0.831106 + 0.344255i −0.757340 0.653020i 0.773502π-0.773502\pi
−0.0737654 + 0.997276i 0.523502π0.523502\pi
620620 1.12132 + 1.29289i 0.0450333 + 0.0519238i
621621 10.8787 + 13.7782i 0.436546 + 0.552899i
622622 25.1924 + 10.4350i 1.01012 + 0.418407i
623623 24.1421 58.2843i 0.967234 2.33511i
624624 −6.24264 8.82843i −0.249906 0.353420i
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 7.70711 18.6066i 0.308038 0.743669i
627627 15.4264 + 9.72792i 0.616071 + 0.388496i
628628 16.0711 + 16.0711i 0.641305 + 0.641305i
629629 −11.2929 4.29289i −0.450277 0.171169i
630630 −10.9497 27.8492i −0.436248 1.10954i
631631 −20.1716 + 20.1716i −0.803018 + 0.803018i −0.983566 0.180548i 0.942213π-0.942213\pi
0.180548 + 0.983566i 0.442213π0.442213\pi
632632 −5.87868 14.1924i −0.233841 0.564543i
633633 7.09188 1.60660i 0.281877 0.0638567i
634634 −19.5355 8.09188i −0.775855 0.321370i
635635 3.31371 + 1.65685i 0.131501 + 0.0657503i
636636 −2.00000 0.343146i −0.0793052 0.0136066i
637637 −80.5269 −3.19059
638638 −0.727922 −0.0288187
639639 12.3934 13.7782i 0.490275 0.545056i
640640 −2.00000 1.00000i −0.0790569 0.0395285i
641641 3.94975 + 1.63604i 0.156006 + 0.0646197i 0.459320 0.888271i 0.348093π-0.348093\pi
−0.303314 + 0.952891i 0.598093π0.598093\pi
642642 −2.70711 11.9497i −0.106841 0.471619i
643643 −10.3345 24.9497i −0.407554 0.983922i −0.985779 0.168045i 0.946255π-0.946255\pi
0.578225 0.815877i 0.303745π-0.303745\pi
644644 10.6569 10.6569i 0.419939 0.419939i
645645 −36.3848 26.7279i −1.43265 1.05241i
646646 −0.556349 18.8995i −0.0218893 0.743591i
647647 −15.3431 15.3431i −0.603201 0.603201i 0.337959 0.941161i 0.390263π-0.390263\pi
−0.941161 + 0.337959i 0.890263π0.890263\pi
648648 7.00000 + 5.65685i 0.274986 + 0.222222i
649649 −7.97056 + 19.2426i −0.312872 + 0.755340i
650650 −30.8995 4.41421i −1.21198 0.173140i
651651 −4.82843 + 3.41421i −0.189241 + 0.133814i
652652 3.36396 8.12132i 0.131743 0.318055i
653653 25.7782 + 10.6777i 1.00878 + 0.417849i 0.825009 0.565120i 0.191170π-0.191170\pi
0.183769 + 0.982969i 0.441170π0.441170\pi
654654 −2.77817 12.2635i −0.108635 0.479539i
655655 13.5355 + 15.6066i 0.528877 + 0.609800i
656656 1.12132 0.464466i 0.0437802 0.0181344i
657657 30.3640 1.60660i 1.18461 0.0626795i
658658 33.9706 14.0711i 1.32431 0.548547i
659659 17.5147i 0.682277i 0.940013 + 0.341138i 0.110812π0.110812\pi
−0.940013 + 0.341138i 0.889188π0.889188\pi
660660 −8.63604 2.12132i −0.336157 0.0825723i
661661 −6.41421 + 6.41421i −0.249484 + 0.249484i −0.820759 0.571275i 0.806449π-0.806449\pi
0.571275 + 0.820759i 0.306449π0.306449\pi
662662 −4.41421 4.41421i −0.171563 0.171563i
663663 −6.24264 + 44.1421i −0.242444 + 1.71434i
664664 11.6569i 0.452374i
665665 −3.24264 + 45.6274i −0.125744 + 1.76936i
666666 −8.77817 + 0.464466i −0.340147 + 0.0179977i
667667 0.757359 + 0.757359i 0.0293251 + 0.0293251i
668668 −1.39340 3.36396i −0.0539122 0.130156i
669669 6.82843 39.7990i 0.264002 1.53872i
670670 13.2426 4.41421i 0.511608 0.170536i
671671 4.45584 4.45584i 0.172016 0.172016i
672672 4.12132 6.53553i 0.158983 0.252114i
673673 −0.636039 + 1.53553i −0.0245175 + 0.0591905i −0.935664 0.352892i 0.885198π-0.885198\pi
0.911147 + 0.412082i 0.135198π0.135198\pi
674674 6.77817 2.80761i 0.261086 0.108145i
675675 25.7487 3.46447i 0.991069 0.133347i
676676 25.9706i 0.998868i
677677 1.19239 + 2.87868i 0.0458272 + 0.110637i 0.945136 0.326679i 0.105929π-0.105929\pi
−0.899308 + 0.437315i 0.855929π0.855929\pi
678678 −5.22183 3.29289i −0.200543 0.126463i
679679 17.0711i 0.655127i
680680 3.17157 + 8.65685i 0.121624 + 0.331975i
681681 −4.53553 + 7.19239i −0.173802 + 0.275613i
682682 1.75736i 0.0672928i
683683 −41.8492 + 17.3345i −1.60132 + 0.663287i −0.991601 0.129333i 0.958716π-0.958716\pi
−0.609716 + 0.792620i 0.708716π0.708716\pi
684684 −5.92893 12.4142i −0.226698 0.474669i
685685 −7.48528 22.4558i −0.285998 0.857994i
686686 −10.0711 24.3137i −0.384515 0.928302i
687687 −16.3848 23.1716i −0.625118 0.884051i
688688 11.6569i 0.444413i
689689 −5.17157 5.17157i −0.197021 0.197021i
690690 6.77817 + 11.1924i 0.258041 + 0.426087i
691691 −15.7071 + 6.50610i −0.597527 + 0.247504i −0.660885 0.750487i 0.729819π-0.729819\pi
0.0633584 + 0.997991i 0.479819π0.479819\pi
692692 −15.1924 + 6.29289i −0.577528 + 0.239220i
693693 10.2426 28.9706i 0.389086 1.10050i
694694 −7.84924 + 18.9497i −0.297953 + 0.719323i
695695 −13.7782 + 11.9497i −0.522636 + 0.453280i
696696 0.464466 + 0.292893i 0.0176055 + 0.0111021i
697697 −4.67767 1.77817i −0.177179 0.0673532i
698698 −0.757359 + 0.757359i −0.0286665 + 0.0286665i
699699 −13.7782 + 3.12132i −0.521138 + 0.118059i
700700 −5.53553 21.6066i −0.209224 0.816653i
701701 −12.3431 −0.466194 −0.233097 0.972453i 0.574886π-0.574886\pi
−0.233097 + 0.972453i 0.574886π0.574886\pi
702702 8.82843 + 31.2132i 0.333208 + 1.17807i
703703 12.4142 + 5.14214i 0.468211 + 0.193939i
704704 −0.878680 2.12132i −0.0331165 0.0799503i
705705 4.82843 + 31.5563i 0.181849 + 1.18848i
706706 −16.6569 16.6569i −0.626889 0.626889i
707707 18.4853 44.6274i 0.695211 1.67839i
708708 12.8284 9.07107i 0.482122 0.340912i
709709 −10.3640 4.29289i −0.389227 0.161223i 0.179483 0.983761i 0.442557π-0.442557\pi
−0.568710 + 0.822538i 0.692557π0.692557\pi
710710 10.4350 9.05025i 0.391620 0.339650i
711711 2.43503 + 46.0208i 0.0913207 + 1.72592i
712712 14.1421i 0.529999i
713713 1.82843 1.82843i 0.0684751 0.0684751i
714714 −30.8492 + 7.94975i −1.15450 + 0.297512i
715715 −21.0000 24.2132i −0.785355 0.905522i
716716 1.24264 + 1.24264i 0.0464397 + 0.0464397i
717717 3.51472 20.4853i 0.131260 0.765037i
718718 8.65685 8.65685i 0.323071 0.323071i
719719 −15.3345 + 37.0208i −0.571881 + 1.38064i 0.328070 + 0.944653i 0.393602π0.393602\pi
−0.899951 + 0.435990i 0.856398π0.856398\pi
720720 4.65685 + 4.82843i 0.173551 + 0.179945i
721721 3.24264 + 7.82843i 0.120762 + 0.291546i
722722 2.02944i 0.0755278i
723723 −1.36396 + 2.16295i −0.0507263 + 0.0804410i
724724 −3.87868 + 1.60660i −0.144150 + 0.0597089i
725725 1.53553 0.393398i 0.0570283 0.0146104i
726726 5.72792 + 8.10051i 0.212583 + 0.300638i
727727 −20.6569 20.6569i −0.766120 0.766120i 0.211301 0.977421i 0.432230π-0.432230\pi
−0.977421 + 0.211301i 0.932230π0.932230\pi
728728 25.7279 10.6569i 0.953540 0.394969i
729729 −14.1421 23.0000i −0.523783 0.851852i
730730 22.6066 + 1.60660i 0.836708 + 0.0594630i
731731 −32.9706 + 34.9706i −1.21946 + 1.29343i
732732 −4.63604 + 1.05025i −0.171353 + 0.0388185i
733733 47.2548 1.74540 0.872699 0.488259i 0.162368π-0.162368\pi
0.872699 + 0.488259i 0.162368π0.162368\pi
734734 −4.12132 1.70711i −0.152121 0.0630105i
735735 49.3848 7.55635i 1.82158 0.278720i
736736 −1.29289 + 3.12132i −0.0476567 + 0.115053i
737737 13.2426 + 5.48528i 0.487799 + 0.202053i
738738 −3.63604 + 0.192388i −0.133844 + 0.00708191i
739739 13.9289 13.9289i 0.512384 0.512384i −0.402872 0.915256i 0.631988π-0.631988\pi
0.915256 + 0.402872i 0.131988π0.131988\pi
740740 −6.53553 0.464466i −0.240251 0.0170741i
741741 8.38478 48.8701i 0.308022 1.79529i
742742 2.00000 4.82843i 0.0734223 0.177257i
743743 −13.1924 31.8492i −0.483982 1.16844i −0.957702 0.287760i 0.907089π-0.907089\pi
0.473721 0.880675i 0.342911π-0.342911\pi
744744 0.707107 1.12132i 0.0259238 0.0411096i
745745 −22.1421 + 44.2843i −0.811225 + 1.62245i
746746 −11.2426 11.2426i −0.411622 0.411622i
747747 −11.6569 + 32.9706i −0.426502 + 1.20633i
748748 −3.36396 + 8.84924i −0.122999 + 0.323560i
749749 31.5563 1.15304
750750 19.3640 0.192388i 0.707072 0.00702502i
751751 −5.05025 2.09188i −0.184286 0.0763339i 0.288632 0.957440i 0.406800π-0.406800\pi
−0.472919 + 0.881106i 0.656800π0.656800\pi
752752 −5.82843 + 5.82843i −0.212541 + 0.212541i
753753 −2.68629 + 15.6569i −0.0978939 + 0.570567i
754754 0.757359 + 1.82843i 0.0275814 + 0.0665874i
755755 −19.9706 + 6.65685i −0.726803 + 0.242268i
756756 −18.1924 + 14.3640i −0.661651 + 0.522412i
757757 13.3137 0.483895 0.241947 0.970289i 0.422214π-0.422214\pi
0.241947 + 0.970289i 0.422214π0.422214\pi
758758 −34.0919 14.1213i −1.23827 0.512909i
759759 −2.27208 + 13.2426i −0.0824712 + 0.480677i
760760 −3.24264 9.72792i −0.117623 0.352869i
761761 −26.9706 −0.977682 −0.488841 0.872373i 0.662580π-0.662580\pi
−0.488841 + 0.872373i 0.662580π0.662580\pi
762762 0.485281 2.82843i 0.0175799 0.102463i
763763 32.3848 1.17241
764764 −17.6569 −0.638803
765765 −0.313708 27.6569i −0.0113422 0.999936i
766766 27.3137 0.986884
767767 56.6274 2.04470
768768 −0.292893 + 1.70711i −0.0105689 + 0.0615999i
769769 −48.6274 −1.75355 −0.876775 0.480901i 0.840310π-0.840310\pi
−0.876775 + 0.480901i 0.840310π0.840310\pi
770770 10.2426 20.4853i 0.369119 0.738238i
771771 −0.928932 + 5.41421i −0.0334547 + 0.194988i
772772 8.29289 + 3.43503i 0.298468 + 0.123629i
773773 −46.0000 −1.65451 −0.827253 0.561830i 0.810097π-0.810097\pi
−0.827253 + 0.561830i 0.810097π0.810097\pi
774774 −11.6569 + 32.9706i −0.418997 + 1.18510i
775775 −0.949747 3.70711i −0.0341159 0.133163i
776776 −1.46447 3.53553i −0.0525713 0.126918i
777777 3.82843 22.3137i 0.137344 0.800500i
778778 2.41421 2.41421i 0.0865537 0.0865537i
779779 5.14214 + 2.12994i 0.184236 + 0.0763131i
780780 3.65685 + 23.8995i 0.130936 + 0.855739i
781781 14.1838 0.507535
782782 12.7071 5.70711i 0.454405 0.204086i
783783 −1.02082 1.29289i −0.0364810 0.0462042i
784784 9.12132 + 9.12132i 0.325761 + 0.325761i
785785 −16.0711 48.2132i −0.573601 1.72080i
786786 8.53553 13.5355i 0.304452 0.482797i
787787 −8.67767 20.9497i −0.309326 0.746778i −0.999727 0.0233517i 0.992566π-0.992566\pi
0.690402 0.723426i 0.257434π-0.257434\pi
788788 1.05025 2.53553i 0.0374137 0.0903247i
789789 2.34315 13.6569i 0.0834182 0.486197i
790790 −2.43503 + 34.2635i −0.0866344 + 1.21904i
791791 11.2426 11.2426i 0.399742 0.399742i
792792 0.363961 + 6.87868i 0.0129328 + 0.244423i
793793 −15.8284 6.55635i −0.562084 0.232823i
794794 4.26346 10.2929i 0.151304 0.365281i
795795 3.65685 + 2.68629i 0.129695 + 0.0952729i
796796 7.77817 + 3.22183i 0.275690 + 0.114195i
797797 −8.34315 −0.295529 −0.147765 0.989023i 0.547208π-0.547208\pi
−0.147765 + 0.989023i 0.547208π0.547208\pi
798798 34.5563 7.82843i 1.22328 0.277123i
799799 33.9706 1.00000i 1.20179 0.0353775i
800800 3.00000 + 4.00000i 0.106066 + 0.141421i
801801 14.1421 40.0000i 0.499688 1.41333i
802802 1.94975 0.807612i 0.0688480 0.0285178i
803803 16.4558 + 16.4558i 0.580714 + 0.580714i
804804 −6.24264 8.82843i −0.220161 0.311355i
805805 −31.9706 + 10.6569i −1.12681 + 0.375605i
806806 4.41421 1.82843i 0.155484 0.0644036i
807807 29.0919 46.1335i 1.02408 1.62398i
808808 10.8284i 0.380943i
809809 11.7071 + 28.2635i 0.411600 + 0.993690i 0.984708 + 0.174211i 0.0557374π0.0557374\pi
−0.573108 + 0.819480i 0.694263π0.694263\pi
810810 −8.34315 18.3137i −0.293148 0.643478i
811811 1.80761 4.36396i 0.0634738 0.153239i −0.888960 0.457985i 0.848571π-0.848571\pi
0.952434 + 0.304745i 0.0985714π0.0985714\pi
812812 −1.00000 + 1.00000i −0.0350931 + 0.0350931i
813813 0.201010 1.17157i 0.00704973 0.0410889i
814814 −4.75736 4.75736i −0.166745 0.166745i
815815 −14.8492 + 12.8787i −0.520146 + 0.451120i
816816 5.70711 4.29289i 0.199789 0.150281i
817817 37.7990 37.7990i 1.32242 1.32242i
818818 10.8284i 0.378607i
819819 −83.4264 + 4.41421i −2.91515 + 0.154245i
820820 −2.70711 0.192388i −0.0945363 0.00671849i
821821 31.3345 + 12.9792i 1.09358 + 0.452977i 0.855255 0.518208i 0.173401π-0.173401\pi
0.238328 + 0.971185i 0.423401π0.423401\pi
822822 −14.9706 + 10.5858i −0.522158 + 0.369222i
823823 17.7782 42.9203i 0.619708 1.49611i −0.232335 0.972636i 0.574636π-0.574636\pi
0.852043 0.523472i 0.175364π-0.175364\pi
824824 −1.34315 1.34315i −0.0467907 0.0467907i
825825 15.1508 + 12.8787i 0.527482 + 0.448378i
826826 15.4853 + 37.3848i 0.538802 + 1.30078i
827827 20.1924 + 8.36396i 0.702158 + 0.290843i 0.705055 0.709152i 0.250922π-0.250922\pi
−0.00289711 + 0.999996i 0.500922π0.500922\pi
828828 6.77817 7.53553i 0.235558 0.261878i
829829 −20.3431 −0.706547 −0.353273 0.935520i 0.614931π-0.614931\pi
−0.353273 + 0.935520i 0.614931π0.614931\pi
830830 −11.6569 + 23.3137i −0.404615 + 0.809231i
831831 −48.9619 + 11.0919i −1.69847 + 0.384773i
832832 −4.41421 + 4.41421i −0.153035 + 0.153035i
833833 −1.56497 53.1630i −0.0542230 1.84199i
834834 11.9497 + 7.53553i 0.413786 + 0.260934i
835835 −0.577164 + 8.12132i −0.0199736 + 0.281050i
836836 4.02944 9.72792i 0.139361 0.336447i
837837 −3.12132 + 2.46447i −0.107889 + 0.0851844i
838838 −13.6066 + 5.63604i −0.470032 + 0.194694i
839839 −38.0208 + 15.7487i −1.31262 + 0.543707i −0.925649 0.378383i 0.876480π-0.876480\pi
−0.386975 + 0.922090i 0.626480π0.626480\pi
840840 −14.7782 + 8.94975i −0.509895 + 0.308796i
841841 20.4350 + 20.4350i 0.704656 + 0.704656i
842842 38.1421i 1.31446i
843843 −3.55635 5.02944i −0.122487 0.173223i
844844 −1.60660 3.87868i −0.0553015 0.133510i
845845 −25.9706 + 51.9411i −0.893415 + 1.78683i
846846 22.3137 10.6569i 0.767161 0.366390i
847847 −23.6066 + 9.77817i −0.811132 + 0.335982i
848848 1.17157i 0.0402320i
849849 −16.7782 + 26.6066i −0.575825 + 0.913136i
850850 2.31371 20.4853i 0.0793595 0.702639i
851851 9.89949i 0.339350i
852852 −9.05025 5.70711i −0.310057 0.195522i
853853 3.92031 + 9.46447i 0.134229 + 0.324057i 0.976675 0.214724i 0.0688851π-0.0688851\pi
−0.842446 + 0.538781i 0.818885π0.818885\pi
854854 12.2426i 0.418935i
855855 −0.556349 + 30.7574i −0.0190267 + 1.05188i
856856 −6.53553 + 2.70711i −0.223380 + 0.0925270i
857857 −18.3345 + 44.2635i −0.626295 + 1.51201i 0.217898 + 0.975972i 0.430080π0.430080\pi
−0.844193 + 0.536039i 0.819920π0.819920\pi
858858 −13.2426 + 21.0000i −0.452096 + 0.716928i
859859 −17.7279 + 17.7279i −0.604869 + 0.604869i −0.941601 0.336732i 0.890678π-0.890678\pi
0.336732 + 0.941601i 0.390678π0.390678\pi
860860 −11.6569 + 23.3137i −0.397495 + 0.794991i
861861 1.58579 9.24264i 0.0540435 0.314988i
862862 13.3934 + 32.3345i 0.456181 + 1.10132i
863863 6.51472 + 6.51472i 0.221764 + 0.221764i 0.809241 0.587477i 0.199879π-0.199879\pi
−0.587477 + 0.809241i 0.699879π0.699879\pi
864864 2.53553 4.53553i 0.0862606 0.154302i
865865 36.6777 + 2.60660i 1.24708 + 0.0886271i
866866 28.9706i 0.984460i
867867 −29.2635 3.26346i −0.993839 0.110833i
868868 2.41421 + 2.41421i 0.0819437 + 0.0819437i
869869 −24.9411 + 24.9411i −0.846070 + 0.846070i
870870 −0.636039 1.05025i −0.0215637 0.0356069i
871871 38.9706i 1.32047i
872872 −6.70711 + 2.77817i −0.227131 + 0.0940809i
873873 0.606602 + 11.4645i 0.0205304 + 0.388013i
874874 −14.3137 + 5.92893i −0.484168 + 0.200549i
875875 −10.5355 + 48.7487i −0.356166 + 1.64801i
876876 −3.87868 17.1213i −0.131048 0.578476i
877877 −40.7487 16.8787i −1.37599 0.569953i −0.432582 0.901595i 0.642397π-0.642397\pi
−0.943405 + 0.331642i 0.892397π0.892397\pi
878878 −9.77817 + 23.6066i −0.329997 + 0.796684i
879879 −11.1716 + 7.89949i −0.376808 + 0.266443i
880880 −0.363961 + 5.12132i −0.0122691 + 0.172640i
881881 2.73654 6.60660i 0.0921965 0.222582i −0.871054 0.491188i 0.836563π-0.836563\pi
0.963250 + 0.268606i 0.0865629π0.0865629\pi
882882 −16.6777 34.9203i −0.561566 1.17583i
883883 −18.8995 18.8995i −0.636019 0.636019i 0.313552 0.949571i 0.398481π-0.398481\pi
−0.949571 + 0.313552i 0.898481π0.898481\pi
884884 25.7279 0.757359i 0.865324 0.0254728i
885885 −34.7279 + 5.31371i −1.16737 + 0.178618i
886886 22.0711 22.0711i 0.741492 0.741492i
887887 1.92031 + 4.63604i 0.0644777 + 0.155663i 0.952834 0.303492i 0.0981524π-0.0981524\pi
−0.888356 + 0.459155i 0.848152π0.848152\pi
888888 1.12132 + 4.94975i 0.0376290 + 0.166103i
889889 6.82843 + 2.82843i 0.229018 + 0.0948624i
890890 14.1421 28.2843i 0.474045 0.948091i
891891 5.84924 19.8198i 0.195957 0.663988i
892892 −23.3137 −0.780601
893893 −37.7990 −1.26489
894894 37.7990 + 6.48528i 1.26419 + 0.216900i
895895 −1.24264 3.72792i −0.0415369 0.124611i
896896 −4.12132 1.70711i −0.137684 0.0570304i
897897 35.6274 8.07107i 1.18956 0.269485i
898898 4.19239 + 10.1213i 0.139902 + 0.337753i
899899 −0.171573 + 0.171573i −0.00572228 + 0.00572228i
900900 −4.48528 14.3137i −0.149509 0.477124i
901901 3.31371 3.51472i 0.110396 0.117092i
902902 −1.97056 1.97056i −0.0656126 0.0656126i
903903 −76.1838 48.0416i −2.53524 1.59873i
904904 −1.36396 + 3.29289i −0.0453647 + 0.109520i
905905 9.36396 + 0.665476i 0.311269 + 0.0221212i
906906 9.41421 + 13.3137i 0.312766 + 0.442318i
907907 −17.3223 + 41.8198i −0.575179 + 1.38860i 0.321917 + 0.946768i 0.395673π0.395673\pi
−0.897096 + 0.441836i 0.854327π0.854327\pi
908908 4.53553 + 1.87868i 0.150517 + 0.0623462i
909909 10.8284 30.6274i 0.359156 1.01585i
910910 −62.1127 4.41421i −2.05902 0.146330i
911911 −5.87868 + 2.43503i −0.194769 + 0.0806761i −0.477936 0.878395i 0.658615π-0.658615\pi
0.283167 + 0.959071i 0.408615π0.408615\pi
912912 −6.48528 + 4.58579i −0.214749 + 0.151851i
913913 −24.7279 + 10.2426i −0.818375 + 0.338982i
914914 9.65685i 0.319420i
915915 10.3223 + 2.53553i 0.341246 + 0.0838222i
916916 −11.5858 + 11.5858i −0.382805 + 0.382805i
917917 29.1421 + 29.1421i 0.962358 + 0.962358i
918918 −20.4350 + 6.43503i −0.674456 + 0.212388i
919919 18.6863i 0.616404i −0.951321 0.308202i 0.900273π-0.900273\pi
0.951321 0.308202i 0.0997272π-0.0997272\pi
920920 5.70711 4.94975i 0.188158 0.163188i
921921 5.27208 + 7.45584i 0.173721 + 0.245678i
922922 −19.7279 19.7279i −0.649705 0.649705i
923923 −14.7574 35.6274i −0.485744 1.17269i
924924 −17.4853 3.00000i −0.575224 0.0986928i
925925 12.6066 + 7.46447i 0.414503 + 0.245430i
926926 8.17157 8.17157i 0.268535 0.268535i
927927 2.45584 + 5.14214i 0.0806605 + 0.168890i
928928 0.121320 0.292893i 0.00398254 0.00961469i
929929 −23.0208 + 9.53553i −0.755288 + 0.312851i −0.726897 0.686746i 0.759038π-0.759038\pi
−0.0283911 + 0.999597i 0.509038π0.509038\pi
930930 −2.53553 + 1.53553i −0.0831434 + 0.0503521i
931931 59.1543i 1.93870i
932932 3.12132 + 7.53553i 0.102242 + 0.246835i
933933 −25.1924 + 39.9497i −0.824762 + 1.30790i
934934 26.4853i 0.866625i
935935 15.5772 14.3345i 0.509428 0.468789i
936936 16.8995 8.07107i 0.552377 0.263811i
937937 17.6569i 0.576824i −0.957506 0.288412i 0.906873π-0.906873\pi
0.957506 0.288412i 0.0931273π-0.0931273\pi
938938 25.7279 10.6569i 0.840046 0.347959i
939939 29.5061 + 18.6066i 0.962895 + 0.607203i
940940 17.4853 5.82843i 0.570307 0.190102i
941941 3.29289 + 7.94975i 0.107345 + 0.259154i 0.968420 0.249324i 0.0802083π-0.0802083\pi
−0.861075 + 0.508478i 0.830208π0.830208\pi
942942 −32.1421 + 22.7279i −1.04725 + 0.740516i
943943 4.10051i 0.133531i
944944 −6.41421 6.41421i −0.208765 0.208765i
945945 50.7487 10.5355i 1.65086 0.342721i
946946 −24.7279 + 10.2426i −0.803974 + 0.333017i
947947 4.29289 1.77817i 0.139500 0.0577829i −0.311841 0.950134i 0.600946π-0.600946\pi
0.451341 + 0.892351i 0.350946π0.350946\pi
948948 25.9497 5.87868i 0.842809 0.190931i
949949 24.2132 58.4558i 0.785994 1.89756i
950950 −3.24264 + 22.6985i −0.105205 + 0.736436i
951951 19.5355 30.9792i 0.633483 1.00457i
952952 7.53553 + 16.7782i 0.244228 + 0.543784i
953953 29.2843 29.2843i 0.948611 0.948611i −0.0501320 0.998743i 0.515964π-0.515964\pi
0.998743 + 0.0501320i 0.0159642π0.0159642\pi
954954 1.17157 3.31371i 0.0379311 0.107285i
955955 35.3137 + 17.6569i 1.14272 + 0.571362i
956956 −12.0000 −0.388108
957957 0.213203 1.24264i 0.00689189 0.0401689i
958958 20.3640 + 8.43503i 0.657930 + 0.272523i
959959 −18.0711 43.6274i −0.583545 1.40880i
960960 2.29289 3.12132i 0.0740028 0.100740i
961961 −21.5061 21.5061i −0.693745 0.693745i
962962 −7.00000 + 16.8995i −0.225689 + 0.544862i
963963 21.1924 1.12132i 0.682915 0.0361340i
964964 1.36396 + 0.564971i 0.0439302 + 0.0181965i
965965 −13.1508 15.1630i −0.423338 0.488113i
966966 15.0711 + 21.3137i 0.484904 + 0.685757i
967967 23.9411i 0.769895i −0.922939 0.384947i 0.874220π-0.874220\pi
0.922939 0.384947i 0.125780π-0.125780\pi
968968 4.05025 4.05025i 0.130180 0.130180i
969969 32.4264 + 4.58579i 1.04169 + 0.147317i
970970 −0.606602 + 8.53553i −0.0194768 + 0.274059i
971971 7.72792 + 7.72792i 0.248001 + 0.248001i 0.820150 0.572149i 0.193890π-0.193890\pi
−0.572149 + 0.820150i 0.693890π0.693890\pi
972972 −11.7071 + 10.2929i −0.375506 + 0.330145i
973973 −25.7279 + 25.7279i −0.824799 + 0.824799i
974974 −3.53553 + 8.53553i −0.113286 + 0.273496i
975975 16.5858 51.4558i 0.531170 1.64791i
976976 1.05025 + 2.53553i 0.0336178 + 0.0811605i
977977 6.54416i 0.209366i −0.994506 0.104683i 0.966617π-0.966617\pi
0.994506 0.104683i 0.0333828π-0.0333828\pi
978978 12.8787 + 8.12132i 0.411815 + 0.259691i
979979 30.0000 12.4264i 0.958804 0.397150i
980980 −9.12132 27.3640i −0.291370 0.874110i
981981 21.7487 1.15076i 0.694384 0.0367409i
982982 18.4142 + 18.4142i 0.587621 + 0.587621i
983983 37.6777 15.6066i 1.20173 0.497773i 0.310173 0.950680i 0.399613π-0.399613\pi
0.891558 + 0.452907i 0.149613π0.149613\pi
984984 0.464466 + 2.05025i 0.0148066 + 0.0653597i
985985 −4.63604 + 4.02082i −0.147716 + 0.128114i
986986 −1.19239 + 0.535534i −0.0379734 + 0.0170549i
987987 14.0711 + 62.1127i 0.447887 + 1.97707i
988988 −28.6274 −0.910759
989989 36.3848 + 15.0711i 1.15697 + 0.479232i
990990 6.15076 14.1213i 0.195484 0.448805i
991991 −5.77817 + 13.9497i −0.183550 + 0.443128i −0.988693 0.149952i 0.952088π-0.952088\pi
0.805144 + 0.593080i 0.202088π0.202088\pi
992992 −0.707107 0.292893i −0.0224507 0.00929937i
993993 8.82843 6.24264i 0.280162 0.198104i
994994 19.4853 19.4853i 0.618036 0.618036i
995995 −12.3345 14.2218i −0.391031 0.450862i
996996 19.8995 + 3.41421i 0.630540 + 0.108183i
997997 23.0919 55.7487i 0.731327 1.76558i 0.0932026 0.995647i 0.470290π-0.470290\pi
0.638125 0.769933i 0.279710π-0.279710\pi
998998 13.0208 + 31.4350i 0.412167 + 0.995058i
999999 1.77817 15.1213i 0.0562590 0.478417i
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 510.2.w.b.383.1 yes 4
3.2 odd 2 510.2.w.a.383.1 yes 4
5.2 odd 4 510.2.z.a.77.1 yes 4
15.2 even 4 510.2.z.b.77.1 yes 4
17.2 even 8 510.2.z.b.53.1 yes 4
51.2 odd 8 510.2.z.a.53.1 yes 4
85.2 odd 8 510.2.w.a.257.1 4
255.2 even 8 inner 510.2.w.b.257.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
510.2.w.a.257.1 4 85.2 odd 8
510.2.w.a.383.1 yes 4 3.2 odd 2
510.2.w.b.257.1 yes 4 255.2 even 8 inner
510.2.w.b.383.1 yes 4 1.1 even 1 trivial
510.2.z.a.53.1 yes 4 51.2 odd 8
510.2.z.a.77.1 yes 4 5.2 odd 4
510.2.z.b.53.1 yes 4 17.2 even 8
510.2.z.b.77.1 yes 4 15.2 even 4