Properties

Label 630.2.l.i.571.7
Level 630630
Weight 22
Character 630.571
Analytic conductor 5.0315.031
Analytic rank 00
Dimension 1616
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [630,2,Mod(331,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 2])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.331"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 630=23257 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 630.l (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,8,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.030575327345.03057532734
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x16x15+2x144x13+5x12+2x1135x10+81x966x8++6561 x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 3 3
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 571.7
Root 1.525360.820531i1.52536 - 0.820531i of defining polynomial
Character χ\chi == 630.571
Dual form 630.2.l.i.331.7

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5000000.866025i)q2+(1.473280.910737i)q3+(0.5000000.866025i)q41.00000q5+(0.05208081.73127i)q6+(2.16962+1.51418i)q71.00000q8+(1.341122.68354i)q9+(0.500000+0.866025i)q10+5.14142q11+(1.525360.820531i)q12+(1.623662.81226i)q13+(2.396131.12185i)q14+(1.47328+0.910737i)q15+(0.500000+0.866025i)q16+(2.89695+5.01766i)q17+(1.653462.50321i)q18+(2.349804.06997i)q19+(0.500000+0.866025i)q20+(4.57548+0.254868i)q21+(2.570714.45260i)q222.66925q23+(1.47328+0.910737i)q24+1.00000q25+(1.623662.81226i)q26+(0.4681625.17502i)q27+(0.2265132.63604i)q28+(0.227646+0.394295i)q29+(0.0520808+1.73127i)q30+(3.570716.18465i)q31+(0.500000+0.866025i)q32+(7.574754.68248i)q33+(2.89695+5.01766i)q34+(2.169621.51418i)q35+(2.99458+0.180332i)q36+(2.00070+3.46531i)q374.69959q38+(0.1691235.62199i)q39+1.00000q40+(3.71105+6.42773i)q41+(2.508463.83505i)q42+(1.804973.12631i)q43+(2.570714.45260i)q44+(1.34112+2.68354i)q45+(1.33463+2.31164i)q46+(1.579212.73527i)q47+(0.0520808+1.73127i)q48+(2.41449+6.57041i)q49+(0.5000000.866025i)q50+(0.301751+10.0308i)q513.24732q52+(1.63008+2.82338i)q53+(4.715782.18207i)q545.14142q55+(2.169621.51418i)q56+(7.168583.85616i)q57+0.455293q58+(5.56657+9.64157i)q59+(1.52536+0.820531i)q60+(2.99783+5.19239i)q617.14142q62+(6.973093.79157i)q63+1.00000q64+(1.62366+2.81226i)q65+(0.2677698.90117i)q66+(5.88868+10.1995i)q67+5.79389q68+(3.93256+2.43099i)q69+(2.39613+1.12185i)q704.38588q71+(1.34112+2.68354i)q72+(6.9414312.0229i)q73+4.00140q74+(1.473280.910737i)q75+(2.34980+4.06997i)q76+(11.1549+7.78505i)q77+(4.953342.66453i)q78+(1.47595+2.55642i)q79+(0.5000000.866025i)q80+(5.402827.19789i)q81+(3.71105+6.42773i)q82+(6.13291+10.6225i)q83+(2.067024.08992i)q84+(2.896955.01766i)q853.60995q86+(0.694486+0.373581i)q875.14142q88+(4.832148.36951i)q89+(1.65346+2.50321i)q90+(7.781023.64302i)q91+(1.33463+2.31164i)q92+(10.89325.85975i)q93+(1.579212.73527i)q94+(2.34980+4.06997i)q95+(1.52536+0.820531i)q96+(3.91728+6.78493i)q97+(6.89738+1.19419i)q98+(6.8952313.7972i)q99+O(q100)q+(0.500000 - 0.866025i) q^{2} +(1.47328 - 0.910737i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.0520808 - 1.73127i) q^{6} +(2.16962 + 1.51418i) q^{7} -1.00000 q^{8} +(1.34112 - 2.68354i) q^{9} +(-0.500000 + 0.866025i) q^{10} +5.14142 q^{11} +(-1.52536 - 0.820531i) q^{12} +(1.62366 - 2.81226i) q^{13} +(2.39613 - 1.12185i) q^{14} +(-1.47328 + 0.910737i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.89695 + 5.01766i) q^{17} +(-1.65346 - 2.50321i) q^{18} +(-2.34980 - 4.06997i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.57548 + 0.254868i) q^{21} +(2.57071 - 4.45260i) q^{22} -2.66925 q^{23} +(-1.47328 + 0.910737i) q^{24} +1.00000 q^{25} +(-1.62366 - 2.81226i) q^{26} +(-0.468162 - 5.17502i) q^{27} +(0.226513 - 2.63604i) q^{28} +(0.227646 + 0.394295i) q^{29} +(0.0520808 + 1.73127i) q^{30} +(-3.57071 - 6.18465i) q^{31} +(0.500000 + 0.866025i) q^{32} +(7.57475 - 4.68248i) q^{33} +(2.89695 + 5.01766i) q^{34} +(-2.16962 - 1.51418i) q^{35} +(-2.99458 + 0.180332i) q^{36} +(2.00070 + 3.46531i) q^{37} -4.69959 q^{38} +(-0.169123 - 5.62199i) q^{39} +1.00000 q^{40} +(-3.71105 + 6.42773i) q^{41} +(2.50846 - 3.83505i) q^{42} +(-1.80497 - 3.12631i) q^{43} +(-2.57071 - 4.45260i) q^{44} +(-1.34112 + 2.68354i) q^{45} +(-1.33463 + 2.31164i) q^{46} +(1.57921 - 2.73527i) q^{47} +(0.0520808 + 1.73127i) q^{48} +(2.41449 + 6.57041i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.301751 + 10.0308i) q^{51} -3.24732 q^{52} +(-1.63008 + 2.82338i) q^{53} +(-4.71578 - 2.18207i) q^{54} -5.14142 q^{55} +(-2.16962 - 1.51418i) q^{56} +(-7.16858 - 3.85616i) q^{57} +0.455293 q^{58} +(5.56657 + 9.64157i) q^{59} +(1.52536 + 0.820531i) q^{60} +(-2.99783 + 5.19239i) q^{61} -7.14142 q^{62} +(6.97309 - 3.79157i) q^{63} +1.00000 q^{64} +(-1.62366 + 2.81226i) q^{65} +(-0.267769 - 8.90117i) q^{66} +(5.88868 + 10.1995i) q^{67} +5.79389 q^{68} +(-3.93256 + 2.43099i) q^{69} +(-2.39613 + 1.12185i) q^{70} -4.38588 q^{71} +(-1.34112 + 2.68354i) q^{72} +(6.94143 - 12.0229i) q^{73} +4.00140 q^{74} +(1.47328 - 0.910737i) q^{75} +(-2.34980 + 4.06997i) q^{76} +(11.1549 + 7.78505i) q^{77} +(-4.95334 - 2.66453i) q^{78} +(-1.47595 + 2.55642i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.40282 - 7.19789i) q^{81} +(3.71105 + 6.42773i) q^{82} +(6.13291 + 10.6225i) q^{83} +(-2.06702 - 4.08992i) q^{84} +(2.89695 - 5.01766i) q^{85} -3.60995 q^{86} +(0.694486 + 0.373581i) q^{87} -5.14142 q^{88} +(-4.83214 - 8.36951i) q^{89} +(1.65346 + 2.50321i) q^{90} +(7.78102 - 3.64302i) q^{91} +(1.33463 + 2.31164i) q^{92} +(-10.8932 - 5.85975i) q^{93} +(-1.57921 - 2.73527i) q^{94} +(2.34980 + 4.06997i) q^{95} +(1.52536 + 0.820531i) q^{96} +(3.91728 + 6.78493i) q^{97} +(6.89738 + 1.19419i) q^{98} +(6.89523 - 13.7972i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+8q2q38q416q52q6+4q716q8+9q98q102q11q12+2q13+8q14+q158q16+11q17+3q182q19+8q20+5q99+O(q100) 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9} - 8 q^{10} - 2 q^{11} - q^{12} + 2 q^{13} + 8 q^{14} + q^{15} - 8 q^{16} + 11 q^{17} + 3 q^{18} - 2 q^{19} + 8 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/630Z)×\left(\mathbb{Z}/630\mathbb{Z}\right)^\times.

nn 127127 281281 451451
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{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 0.500000 0.866025i 0.353553 0.612372i
33 1.47328 0.910737i 0.850599 0.525814i
44 −0.500000 0.866025i −0.250000 0.433013i
55 −1.00000 −0.447214
66 −0.0520808 1.73127i −0.0212619 0.706787i
77 2.16962 + 1.51418i 0.820039 + 0.572308i
88 −1.00000 −0.353553
99 1.34112 2.68354i 0.447039 0.894515i
1010 −0.500000 + 0.866025i −0.158114 + 0.273861i
1111 5.14142 1.55019 0.775097 0.631842i 0.217701π-0.217701\pi
0.775097 + 0.631842i 0.217701π0.217701\pi
1212 −1.52536 0.820531i −0.440334 0.236867i
1313 1.62366 2.81226i 0.450323 0.779982i −0.548083 0.836424i 0.684642π-0.684642\pi
0.998406 + 0.0564419i 0.0179756π0.0179756\pi
1414 2.39613 1.12185i 0.640393 0.299828i
1515 −1.47328 + 0.910737i −0.380400 + 0.235151i
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 −2.89695 + 5.01766i −0.702613 + 1.21696i 0.264933 + 0.964267i 0.414650π0.414650\pi
−0.967546 + 0.252694i 0.918683π0.918683\pi
1818 −1.65346 2.50321i −0.389724 0.590013i
1919 −2.34980 4.06997i −0.539080 0.933715i −0.998954 0.0457301i 0.985439π-0.985439\pi
0.459873 0.887984i 0.347895π-0.347895\pi
2020 0.500000 + 0.866025i 0.111803 + 0.193649i
2121 4.57548 + 0.254868i 0.998452 + 0.0556167i
2222 2.57071 4.45260i 0.548077 0.949297i
2323 −2.66925 −0.556578 −0.278289 0.960497i 0.589767π-0.589767\pi
−0.278289 + 0.960497i 0.589767π0.589767\pi
2424 −1.47328 + 0.910737i −0.300732 + 0.185903i
2525 1.00000 0.200000
2626 −1.62366 2.81226i −0.318426 0.551531i
2727 −0.468162 5.17502i −0.0900979 0.995933i
2828 0.226513 2.63604i 0.0428069 0.498164i
2929 0.227646 + 0.394295i 0.0422728 + 0.0732187i 0.886388 0.462944i 0.153207π-0.153207\pi
−0.844115 + 0.536162i 0.819873π0.819873\pi
3030 0.0520808 + 1.73127i 0.00950861 + 0.316085i
3131 −3.57071 6.18465i −0.641318 1.11080i −0.985139 0.171760i 0.945055π-0.945055\pi
0.343821 0.939035i 0.388279π-0.388279\pi
3232 0.500000 + 0.866025i 0.0883883 + 0.153093i
3333 7.57475 4.68248i 1.31859 0.815115i
3434 2.89695 + 5.01766i 0.496822 + 0.860521i
3535 −2.16962 1.51418i −0.366732 0.255944i
3636 −2.99458 + 0.180332i −0.499096 + 0.0300553i
3737 2.00070 + 3.46531i 0.328913 + 0.569694i 0.982296 0.187333i 0.0599844π-0.0599844\pi
−0.653384 + 0.757027i 0.726651π0.726651\pi
3838 −4.69959 −0.762375
3939 −0.169123 5.62199i −0.0270814 0.900238i
4040 1.00000 0.158114
4141 −3.71105 + 6.42773i −0.579569 + 1.00384i 0.415960 + 0.909383i 0.363446π0.363446\pi
−0.995529 + 0.0944596i 0.969888π0.969888\pi
4242 2.50846 3.83505i 0.387064 0.591761i
4343 −1.80497 3.12631i −0.275256 0.476757i 0.694944 0.719064i 0.255429π-0.255429\pi
−0.970200 + 0.242307i 0.922096π0.922096\pi
4444 −2.57071 4.45260i −0.387549 0.671254i
4545 −1.34112 + 2.68354i −0.199922 + 0.400039i
4646 −1.33463 + 2.31164i −0.196780 + 0.340833i
4747 1.57921 2.73527i 0.230352 0.398981i −0.727560 0.686044i 0.759346π-0.759346\pi
0.957912 + 0.287063i 0.0926790π0.0926790\pi
4848 0.0520808 + 1.73127i 0.00751722 + 0.249887i
4949 2.41449 + 6.57041i 0.344927 + 0.938629i
5050 0.500000 0.866025i 0.0707107 0.122474i
5151 0.301751 + 10.0308i 0.0422535 + 1.40459i
5252 −3.24732 −0.450323
5353 −1.63008 + 2.82338i −0.223909 + 0.387821i −0.955991 0.293395i 0.905215π-0.905215\pi
0.732083 + 0.681216i 0.238548π0.238548\pi
5454 −4.71578 2.18207i −0.641736 0.296942i
5555 −5.14142 −0.693268
5656 −2.16962 1.51418i −0.289927 0.202341i
5757 −7.16858 3.85616i −0.949502 0.510761i
5858 0.455293 0.0597828
5959 5.56657 + 9.64157i 0.724705 + 1.25523i 0.959095 + 0.283083i 0.0913573π0.0913573\pi
−0.234390 + 0.972143i 0.575309π0.575309\pi
6060 1.52536 + 0.820531i 0.196923 + 0.105930i
6161 −2.99783 + 5.19239i −0.383833 + 0.664818i −0.991606 0.129293i 0.958729π-0.958729\pi
0.607774 + 0.794110i 0.292063π0.292063\pi
6262 −7.14142 −0.906961
6363 6.97309 3.79157i 0.878527 0.477693i
6464 1.00000 0.125000
6565 −1.62366 + 2.81226i −0.201390 + 0.348819i
6666 −0.267769 8.90117i −0.0329601 1.09566i
6767 5.88868 + 10.1995i 0.719417 + 1.24607i 0.961231 + 0.275744i 0.0889241π0.0889241\pi
−0.241815 + 0.970322i 0.577743π0.577743\pi
6868 5.79389 0.702613
6969 −3.93256 + 2.43099i −0.473425 + 0.292657i
7070 −2.39613 + 1.12185i −0.286393 + 0.134087i
7171 −4.38588 −0.520508 −0.260254 0.965540i 0.583806π-0.583806\pi
−0.260254 + 0.965540i 0.583806π0.583806\pi
7272 −1.34112 + 2.68354i −0.158052 + 0.316259i
7373 6.94143 12.0229i 0.812433 1.40718i −0.0987235 0.995115i 0.531476π-0.531476\pi
0.911157 0.412060i 0.135191π-0.135191\pi
7474 4.00140 0.465153
7575 1.47328 0.910737i 0.170120 0.105163i
7676 −2.34980 + 4.06997i −0.269540 + 0.466857i
7777 11.1549 + 7.78505i 1.27122 + 0.887189i
7878 −4.95334 2.66453i −0.560856 0.301698i
7979 −1.47595 + 2.55642i −0.166057 + 0.287619i −0.937030 0.349248i 0.886437π-0.886437\pi
0.770973 + 0.636868i 0.219770π0.219770\pi
8080 0.500000 0.866025i 0.0559017 0.0968246i
8181 −5.40282 7.19789i −0.600313 0.799765i
8282 3.71105 + 6.42773i 0.409817 + 0.709824i
8383 6.13291 + 10.6225i 0.673174 + 1.16597i 0.976999 + 0.213244i 0.0684030π0.0684030\pi
−0.303824 + 0.952728i 0.598264π0.598264\pi
8484 −2.06702 4.08992i −0.225530 0.446247i
8585 2.89695 5.01766i 0.314218 0.544242i
8686 −3.60995 −0.389271
8787 0.694486 + 0.373581i 0.0744567 + 0.0400521i
8888 −5.14142 −0.548077
8989 −4.83214 8.36951i −0.512206 0.887166i −0.999900 0.0141515i 0.995495π-0.995495\pi
0.487694 0.873014i 0.337838π-0.337838\pi
9090 1.65346 + 2.50321i 0.174290 + 0.263862i
9191 7.78102 3.64302i 0.815672 0.381892i
9292 1.33463 + 2.31164i 0.139144 + 0.241005i
9393 −10.8932 5.85975i −1.12958 0.607628i
9494 −1.57921 2.73527i −0.162883 0.282122i
9595 2.34980 + 4.06997i 0.241084 + 0.417570i
9696 1.52536 + 0.820531i 0.155682 + 0.0837450i
9797 3.91728 + 6.78493i 0.397740 + 0.688905i 0.993447 0.114296i 0.0364614π-0.0364614\pi
−0.595707 + 0.803202i 0.703128π0.703128\pi
9898 6.89738 + 1.19419i 0.696741 + 0.120632i
9999 6.89523 13.7972i 0.692997 1.38667i
100100 −0.500000 0.866025i −0.0500000 0.0866025i
101101 −5.72942 −0.570099 −0.285049 0.958513i 0.592010π-0.592010\pi
−0.285049 + 0.958513i 0.592010π0.592010\pi
102102 8.83779 + 4.75407i 0.875071 + 0.470723i
103103 −14.0309 −1.38250 −0.691252 0.722614i 0.742941π-0.742941\pi
−0.691252 + 0.722614i 0.742941π0.742941\pi
104104 −1.62366 + 2.81226i −0.159213 + 0.275765i
105105 −4.57548 0.254868i −0.446521 0.0248725i
106106 1.63008 + 2.82338i 0.158327 + 0.274231i
107107 7.30355 + 12.6501i 0.706061 + 1.22293i 0.966307 + 0.257391i 0.0828627π0.0828627\pi
−0.260247 + 0.965542i 0.583804π0.583804\pi
108108 −4.24762 + 2.99295i −0.408727 + 0.287997i
109109 1.60392 2.77806i 0.153627 0.266090i −0.778931 0.627110i 0.784238π-0.784238\pi
0.932558 + 0.361019i 0.117571π0.117571\pi
110110 −2.57071 + 4.45260i −0.245107 + 0.424538i
111111 6.10358 + 3.28327i 0.579326 + 0.311634i
112112 −2.39613 + 1.12185i −0.226413 + 0.106005i
113113 1.14968 1.99131i 0.108153 0.187327i −0.806869 0.590731i 0.798840π-0.798840\pi
0.915022 + 0.403404i 0.132173π0.132173\pi
114114 −6.92382 + 4.28009i −0.648475 + 0.400868i
115115 2.66925 0.248909
116116 0.227646 0.394295i 0.0211364 0.0366094i
117117 −5.36932 8.12874i −0.496394 0.751502i
118118 11.1331 1.02489
119119 −13.8829 + 6.49989i −1.27265 + 0.595844i
120120 1.47328 0.910737i 0.134492 0.0831385i
121121 15.4341 1.40310
122122 2.99783 + 5.19239i 0.271411 + 0.470097i
123123 0.386549 + 12.8496i 0.0348540 + 1.15861i
124124 −3.57071 + 6.18465i −0.320659 + 0.555398i
125125 −1.00000 −0.0894427
126126 0.202949 7.93466i 0.0180801 0.706876i
127127 −2.31880 −0.205760 −0.102880 0.994694i 0.532806π-0.532806\pi
−0.102880 + 0.994694i 0.532806π0.532806\pi
128128 0.500000 0.866025i 0.0441942 0.0765466i
129129 −5.50648 2.96207i −0.484818 0.260796i
130130 1.62366 + 2.81226i 0.142405 + 0.246652i
131131 −18.7621 −1.63925 −0.819626 0.572899i 0.805819π-0.805819\pi
−0.819626 + 0.572899i 0.805819π0.805819\pi
132132 −7.84252 4.21869i −0.682604 0.367190i
133133 1.06452 12.3883i 0.0923055 1.07420i
134134 11.7774 1.01741
135135 0.468162 + 5.17502i 0.0402930 + 0.445395i
136136 2.89695 5.01766i 0.248411 0.430261i
137137 −6.39791 −0.546610 −0.273305 0.961927i 0.588117π-0.588117\pi
−0.273305 + 0.961927i 0.588117π0.588117\pi
138138 0.139017 + 4.62119i 0.0118339 + 0.393382i
139139 10.4744 18.1422i 0.888429 1.53880i 0.0466966 0.998909i 0.485131π-0.485131\pi
0.841732 0.539895i 0.181536π-0.181536\pi
140140 −0.226513 + 2.63604i −0.0191438 + 0.222786i
141141 −0.164493 5.46807i −0.0138528 0.460495i
142142 −2.19294 + 3.79828i −0.184027 + 0.318745i
143143 8.34792 14.4590i 0.698088 1.20912i
144144 1.65346 + 2.50321i 0.137788 + 0.208601i
145145 −0.227646 0.394295i −0.0189050 0.0327444i
146146 −6.94143 12.0229i −0.574477 0.995023i
147147 9.54114 + 7.48109i 0.786940 + 0.617030i
148148 2.00070 3.46531i 0.164456 0.284847i
149149 −12.3598 −1.01255 −0.506276 0.862372i 0.668978π-0.668978\pi
−0.506276 + 0.862372i 0.668978π0.668978\pi
150150 −0.0520808 1.73127i −0.00425238 0.141357i
151151 19.4157 1.58002 0.790012 0.613091i 0.210074π-0.210074\pi
0.790012 + 0.613091i 0.210074π0.210074\pi
152152 2.34980 + 4.06997i 0.190594 + 0.330118i
153153 9.57997 + 14.5033i 0.774494 + 1.17253i
154154 12.3195 5.76791i 0.992734 0.464791i
155155 3.57071 + 6.18465i 0.286806 + 0.496763i
156156 −4.78422 + 2.95746i −0.383044 + 0.236786i
157157 1.23050 + 2.13128i 0.0982043 + 0.170095i 0.910941 0.412536i 0.135357π-0.135357\pi
−0.812737 + 0.582631i 0.802023π0.802023\pi
158158 1.47595 + 2.55642i 0.117420 + 0.203378i
159159 0.169792 + 5.64421i 0.0134654 + 0.447615i
160160 −0.500000 0.866025i −0.0395285 0.0684653i
161161 −5.79126 4.04174i −0.456415 0.318534i
162162 −8.93496 + 1.08003i −0.701997 + 0.0848554i
163163 4.96118 + 8.59301i 0.388589 + 0.673057i 0.992260 0.124177i 0.0396291π-0.0396291\pi
−0.603671 + 0.797234i 0.706296π0.706296\pi
164164 7.42210 0.579569
165165 −7.57475 + 4.68248i −0.589694 + 0.364530i
166166 12.2658 0.952012
167167 −3.26841 + 5.66106i −0.252917 + 0.438066i −0.964328 0.264711i 0.914723π-0.914723\pi
0.711410 + 0.702777i 0.248057π0.248057\pi
168168 −4.57548 0.254868i −0.353006 0.0196635i
169169 1.22744 + 2.12600i 0.0944188 + 0.163538i
170170 −2.89695 5.01766i −0.222186 0.384837i
171171 −14.0733 + 0.847485i −1.07621 + 0.0648088i
172172 −1.80497 + 3.12631i −0.137628 + 0.238379i
173173 −6.36448 + 11.0236i −0.483883 + 0.838109i −0.999829 0.0185118i 0.994107π-0.994107\pi
0.515946 + 0.856621i 0.327441π0.327441\pi
174174 0.670774 0.414652i 0.0508512 0.0314347i
175175 2.16962 + 1.51418i 0.164008 + 0.114462i
176176 −2.57071 + 4.45260i −0.193774 + 0.335627i
177177 16.9821 + 9.13507i 1.27645 + 0.686634i
178178 −9.66427 −0.724368
179179 11.6182 20.1233i 0.868386 1.50409i 0.00474023 0.999989i 0.498491π-0.498491\pi
0.863646 0.504100i 0.168176π-0.168176\pi
180180 2.99458 0.180332i 0.223202 0.0134411i
181181 −19.0687 −1.41737 −0.708683 0.705527i 0.750710π-0.750710\pi
−0.708683 + 0.705527i 0.750710π0.750710\pi
182182 0.735561 8.56007i 0.0545234 0.634514i
183183 0.312259 + 10.3801i 0.0230828 + 0.767318i
184184 2.66925 0.196780
185185 −2.00070 3.46531i −0.147094 0.254775i
186186 −10.5213 + 6.50395i −0.771460 + 0.476893i
187187 −14.8944 + 25.7979i −1.08919 + 1.88653i
188188 −3.15842 −0.230352
189189 6.82020 11.9367i 0.496097 0.868267i
190190 4.69959 0.340944
191191 −13.1495 + 22.7755i −0.951462 + 1.64798i −0.209197 + 0.977874i 0.567085π0.567085\pi
−0.742265 + 0.670107i 0.766248π0.766248\pi
192192 1.47328 0.910737i 0.106325 0.0657268i
193193 −2.34431 4.06047i −0.168747 0.292279i 0.769232 0.638969i 0.220639π-0.220639\pi
−0.937980 + 0.346690i 0.887305π0.887305\pi
194194 7.83456 0.562489
195195 0.169123 + 5.62199i 0.0121112 + 0.402599i
196196 4.48289 5.37621i 0.320207 0.384015i
197197 10.4576 0.745076 0.372538 0.928017i 0.378488π-0.378488\pi
0.372538 + 0.928017i 0.378488π0.378488\pi
198198 −8.50112 12.8701i −0.604148 0.914635i
199199 −8.16053 + 14.1345i −0.578485 + 1.00197i 0.417168 + 0.908829i 0.363023π0.363023\pi
−0.995653 + 0.0931362i 0.970311π0.970311\pi
200200 −1.00000 −0.0707107
201201 17.9647 + 9.66368i 1.26713 + 0.681624i
202202 −2.86471 + 4.96182i −0.201560 + 0.349113i
203203 −0.103130 + 1.20017i −0.00723828 + 0.0842353i
204204 8.53604 5.27671i 0.597642 0.369444i
205205 3.71105 6.42773i 0.259191 0.448932i
206206 −7.01544 + 12.1511i −0.488789 + 0.846608i
207207 −3.57978 + 7.16306i −0.248812 + 0.497867i
208208 1.62366 + 2.81226i 0.112581 + 0.194995i
209209 −12.0813 20.9254i −0.835680 1.44744i
210210 −2.50846 + 3.83505i −0.173100 + 0.264644i
211211 −2.17495 + 3.76713i −0.149730 + 0.259340i −0.931128 0.364693i 0.881174π-0.881174\pi
0.781398 + 0.624033i 0.214507π0.214507\pi
212212 3.26016 0.223909
213213 −6.46164 + 3.99438i −0.442744 + 0.273691i
214214 14.6071 0.998520
215215 1.80497 + 3.12631i 0.123098 + 0.213212i
216216 0.468162 + 5.17502i 0.0318544 + 0.352115i
217217 1.61762 18.8250i 0.109811 1.27793i
218218 −1.60392 2.77806i −0.108631 0.188154i
219219 −0.723031 24.0349i −0.0488579 1.62413i
220220 2.57071 + 4.45260i 0.173317 + 0.300194i
221221 9.40732 + 16.2940i 0.632805 + 1.09605i
222222 5.89519 3.64422i 0.395659 0.244584i
223223 1.72717 + 2.99154i 0.115660 + 0.200328i 0.918043 0.396480i 0.129768π-0.129768\pi
−0.802384 + 0.596809i 0.796435π0.796435\pi
224224 −0.226513 + 2.63604i −0.0151345 + 0.176128i
225225 1.34112 2.68354i 0.0894077 0.178903i
226226 −1.14968 1.99131i −0.0764758 0.132460i
227227 −19.2095 −1.27498 −0.637491 0.770458i 0.720028π-0.720028\pi
−0.637491 + 0.770458i 0.720028π0.720028\pi
228228 0.244759 + 8.13625i 0.0162095 + 0.538837i
229229 −21.6622 −1.43148 −0.715739 0.698368i 0.753910π-0.753910\pi
−0.715739 + 0.698368i 0.753910π0.753910\pi
230230 1.33463 2.31164i 0.0880027 0.152425i
231231 23.5245 + 1.31038i 1.54780 + 0.0862167i
232232 −0.227646 0.394295i −0.0149457 0.0258867i
233233 −1.36959 2.37220i −0.0897248 0.155408i 0.817670 0.575687i 0.195265π-0.195265\pi
−0.907395 + 0.420279i 0.861932π0.861932\pi
234234 −9.72436 + 0.585595i −0.635701 + 0.0382816i
235235 −1.57921 + 2.73527i −0.103016 + 0.178430i
236236 5.56657 9.64157i 0.362353 0.627613i
237237 0.153737 + 5.11052i 0.00998630 + 0.331964i
238238 −1.31239 + 15.2729i −0.0850697 + 0.989996i
239239 11.2181 19.4304i 0.725641 1.25685i −0.233068 0.972460i 0.574877π-0.574877\pi
0.958710 0.284387i 0.0917901π-0.0917901\pi
240240 −0.0520808 1.73127i −0.00336180 0.111753i
241241 21.8355 1.40655 0.703273 0.710920i 0.251721π-0.251721\pi
0.703273 + 0.710920i 0.251721π0.251721\pi
242242 7.71707 13.3664i 0.496072 0.859222i
243243 −14.5153 5.68397i −0.931154 0.364627i
244244 5.99566 0.383833
245245 −2.41449 6.57041i −0.154256 0.419768i
246246 11.3214 + 6.09006i 0.721826 + 0.388288i
247247 −15.2611 −0.971041
248248 3.57071 + 6.18465i 0.226740 + 0.392725i
249249 18.7098 + 10.0645i 1.18569 + 0.637811i
250250 −0.500000 + 0.866025i −0.0316228 + 0.0547723i
251251 −5.65826 −0.357146 −0.178573 0.983927i 0.557148π-0.557148\pi
−0.178573 + 0.983927i 0.557148π0.557148\pi
252252 −6.77014 4.14309i −0.426479 0.260990i
253253 −13.7237 −0.862804
254254 −1.15940 + 2.00814i −0.0727471 + 0.126002i
255255 −0.301751 10.0308i −0.0188964 0.628152i
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 7.76277 0.484228 0.242114 0.970248i 0.422159π-0.422159\pi
0.242114 + 0.970248i 0.422159π0.422159\pi
258258 −5.31847 + 3.28771i −0.331113 + 0.204684i
259259 −0.906368 + 10.5478i −0.0563190 + 0.655411i
260260 3.24732 0.201390
261261 1.36341 0.0821036i 0.0843928 0.00508209i
262262 −9.38105 + 16.2485i −0.579563 + 1.00383i
263263 9.18265 0.566227 0.283113 0.959086i 0.408633π-0.408633\pi
0.283113 + 0.959086i 0.408633π0.408633\pi
264264 −7.57475 + 4.68248i −0.466194 + 0.288187i
265265 1.63008 2.82338i 0.100135 0.173439i
266266 −10.1963 7.11605i −0.625177 0.436313i
267267 −14.7415 7.92983i −0.902166 0.485298i
268268 5.88868 10.1995i 0.359708 0.623033i
269269 9.03012 15.6406i 0.550576 0.953626i −0.447657 0.894205i 0.647741π-0.647741\pi
0.998233 0.0594206i 0.0189253π-0.0189253\pi
270270 4.71578 + 2.18207i 0.286993 + 0.132797i
271271 −12.2464 21.2114i −0.743917 1.28850i −0.950699 0.310115i 0.899632π-0.899632\pi
0.206782 0.978387i 0.433701π-0.433701\pi
272272 −2.89695 5.01766i −0.175653 0.304240i
273273 8.14579 12.4537i 0.493006 0.753729i
274274 −3.19895 + 5.54075i −0.193256 + 0.334729i
275275 5.14142 0.310039
276276 4.07158 + 2.19020i 0.245080 + 0.131835i
277277 −13.1167 −0.788104 −0.394052 0.919088i 0.628927π-0.628927\pi
−0.394052 + 0.919088i 0.628927π0.628927\pi
278278 −10.4744 18.1422i −0.628214 1.08810i
279279 −21.3855 + 1.28782i −1.28032 + 0.0770999i
280280 2.16962 + 1.51418i 0.129660 + 0.0904898i
281281 1.06057 + 1.83696i 0.0632684 + 0.109584i 0.895925 0.444206i 0.146514π-0.146514\pi
−0.832656 + 0.553790i 0.813181π0.813181\pi
282282 −4.81774 2.59158i −0.286892 0.154326i
283283 5.62680 + 9.74590i 0.334478 + 0.579334i 0.983385 0.181535i 0.0581065π-0.0581065\pi
−0.648906 + 0.760869i 0.724773π0.724773\pi
284284 2.19294 + 3.79828i 0.130127 + 0.225387i
285285 7.16858 + 3.85616i 0.424630 + 0.228419i
286286 −8.34792 14.4590i −0.493623 0.854980i
287287 −17.7843 + 8.32650i −1.04978 + 0.491498i
288288 2.99458 0.180332i 0.176457 0.0106261i
289289 −8.28460 14.3493i −0.487329 0.844079i
290290 −0.455293 −0.0267357
291291 11.9505 + 6.42850i 0.700553 + 0.376845i
292292 −13.8829 −0.812433
293293 4.80935 8.33003i 0.280965 0.486646i −0.690658 0.723182i 0.742679π-0.742679\pi
0.971623 + 0.236536i 0.0760121π0.0760121\pi
294294 11.2494 4.52232i 0.656077 0.263747i
295295 −5.56657 9.64157i −0.324098 0.561354i
296296 −2.00070 3.46531i −0.116288 0.201417i
297297 −2.40702 26.6069i −0.139669 1.54389i
298298 −6.17989 + 10.7039i −0.357991 + 0.620059i
299299 −4.33397 + 7.50665i −0.250640 + 0.434121i
300300 −1.52536 0.820531i −0.0880668 0.0473734i
301301 0.817700 9.51595i 0.0471314 0.548490i
302302 9.70783 16.8145i 0.558623 0.967563i
303303 −8.44105 + 5.21800i −0.484925 + 0.299766i
304304 4.69959 0.269540
305305 2.99783 5.19239i 0.171655 0.297315i
306306 17.3502 1.04482i 0.991848 0.0597285i
307307 −9.13535 −0.521382 −0.260691 0.965422i 0.583950π-0.583950\pi
−0.260691 + 0.965422i 0.583950π0.583950\pi
308308 1.16460 13.5530i 0.0663591 0.772252i
309309 −20.6714 + 12.7784i −1.17596 + 0.726941i
310310 7.14142 0.405605
311311 −10.2974 17.8356i −0.583911 1.01136i −0.995010 0.0997726i 0.968188π-0.968188\pi
0.411100 0.911590i 0.365145π-0.365145\pi
312312 0.169123 + 5.62199i 0.00957472 + 0.318282i
313313 0.275427 0.477053i 0.0155680 0.0269646i −0.858136 0.513422i 0.828378π-0.828378\pi
0.873704 + 0.486457i 0.161711π0.161711\pi
314314 2.46099 0.138882
315315 −6.97309 + 3.79157i −0.392889 + 0.213631i
316316 2.95190 0.166057
317317 13.4872 23.3605i 0.757517 1.31206i −0.186596 0.982437i 0.559746π-0.559746\pi
0.944113 0.329621i 0.106921π-0.106921\pi
318318 4.97292 + 2.67506i 0.278868 + 0.150010i
319319 1.17042 + 2.02723i 0.0655312 + 0.113503i
320320 −1.00000 −0.0559017
321321 22.2811 + 11.9856i 1.24361 + 0.668969i
322322 −6.39588 + 2.99451i −0.356429 + 0.166877i
323323 27.2289 1.51506
324324 −3.53214 + 8.27792i −0.196230 + 0.459884i
325325 1.62366 2.81226i 0.0900646 0.155996i
326326 9.92235 0.549548
327327 −0.167066 5.55361i −0.00923879 0.307115i
328328 3.71105 6.42773i 0.204908 0.354912i
329329 7.56800 3.54328i 0.417237 0.195348i
330330 0.267769 + 8.90117i 0.0147402 + 0.489993i
331331 8.44384 14.6252i 0.464115 0.803871i −0.535046 0.844823i 0.679706π-0.679706\pi
0.999161 + 0.0409516i 0.0130390π0.0130390\pi
332332 6.13291 10.6225i 0.336587 0.582986i
333333 11.9825 0.721579i 0.656636 0.0395423i
334334 3.26841 + 5.66106i 0.178840 + 0.309759i
335335 −5.88868 10.1995i −0.321733 0.557258i
336336 −2.50846 + 3.83505i −0.136848 + 0.209219i
337337 12.8294 22.2212i 0.698863 1.21047i −0.269998 0.962861i 0.587023π-0.587023\pi
0.968861 0.247606i 0.0796437π-0.0796437\pi
338338 2.45489 0.133528
339339 −0.119753 3.98082i −0.00650409 0.216209i
340340 −5.79389 −0.314218
341341 −18.3585 31.7978i −0.994168 1.72195i
342342 −6.30270 + 12.6116i −0.340811 + 0.681955i
343343 −4.71028 + 17.9113i −0.254331 + 0.967117i
344344 1.80497 + 3.12631i 0.0973176 + 0.168559i
345345 3.93256 2.43099i 0.211722 0.130880i
346346 6.36448 + 11.0236i 0.342157 + 0.592633i
347347 8.51177 + 14.7428i 0.456936 + 0.791436i 0.998797 0.0490321i 0.0156137π-0.0156137\pi
−0.541862 + 0.840468i 0.682280π0.682280\pi
348348 −0.0237120 0.788233i −0.00127110 0.0422537i
349349 −11.3156 19.5992i −0.605709 1.04912i −0.991939 0.126716i 0.959556π-0.959556\pi
0.386230 0.922403i 0.373777π-0.373777\pi
350350 2.39613 1.12185i 0.128079 0.0599655i
351351 −15.3137 7.08589i −0.817383 0.378217i
352352 2.57071 + 4.45260i 0.137019 + 0.237324i
353353 −8.74841 −0.465631 −0.232815 0.972521i 0.574794π-0.574794\pi
−0.232815 + 0.972521i 0.574794π0.574794\pi
354354 16.4022 10.1394i 0.871769 0.538901i
355355 4.38588 0.232778
356356 −4.83214 + 8.36951i −0.256103 + 0.443583i
357357 −14.5338 + 22.2199i −0.769209 + 1.17600i
358358 −11.6182 20.1233i −0.614041 1.06355i
359359 13.0119 + 22.5373i 0.686741 + 1.18947i 0.972886 + 0.231284i 0.0742928π0.0742928\pi
−0.286145 + 0.958186i 0.592374π0.592374\pi
360360 1.34112 2.68354i 0.0706830 0.141435i
361361 −1.54309 + 2.67271i −0.0812152 + 0.140669i
362362 −9.53436 + 16.5140i −0.501115 + 0.867956i
363363 22.7388 14.0565i 1.19348 0.737772i
364364 −7.04545 4.91705i −0.369282 0.257723i
365365 −6.94143 + 12.0229i −0.363331 + 0.629308i
366366 9.14555 + 4.91962i 0.478045 + 0.257153i
367367 34.5588 1.80395 0.901976 0.431786i 0.142116π-0.142116\pi
0.901976 + 0.431786i 0.142116π0.142116\pi
368368 1.33463 2.31164i 0.0695722 0.120503i
369369 12.2721 + 18.5791i 0.638862 + 0.967189i
370370 −4.00140 −0.208023
371371 −7.81177 + 3.65742i −0.405567 + 0.189884i
372372 0.371931 + 12.3637i 0.0192837 + 0.641028i
373373 8.97898 0.464914 0.232457 0.972607i 0.425324π-0.425324\pi
0.232457 + 0.972607i 0.425324π0.425324\pi
374374 14.8944 + 25.7979i 0.770171 + 1.33398i
375375 −1.47328 + 0.910737i −0.0760799 + 0.0470303i
376376 −1.57921 + 2.73527i −0.0814416 + 0.141061i
377377 1.47848 0.0761457
378378 −6.92739 11.8748i −0.356306 0.610775i
379379 −21.2288 −1.09045 −0.545225 0.838290i 0.683556π-0.683556\pi
−0.545225 + 0.838290i 0.683556π0.683556\pi
380380 2.34980 4.06997i 0.120542 0.208785i
381381 −3.41624 + 2.11181i −0.175019 + 0.108192i
382382 13.1495 + 22.7755i 0.672785 + 1.16530i
383383 0.216305 0.0110527 0.00552634 0.999985i 0.498241π-0.498241\pi
0.00552634 + 0.999985i 0.498241π0.498241\pi
384384 −0.0520808 1.73127i −0.00265774 0.0883484i
385385 −11.1549 7.78505i −0.568507 0.396763i
386386 −4.68862 −0.238645
387387 −10.8103 + 0.650988i −0.549516 + 0.0330916i
388388 3.91728 6.78493i 0.198870 0.344453i
389389 −11.6262 −0.589474 −0.294737 0.955578i 0.595232π-0.595232\pi
−0.294737 + 0.955578i 0.595232π0.595232\pi
390390 4.95334 + 2.66453i 0.250822 + 0.134924i
391391 7.73269 13.3934i 0.391059 0.677334i
392392 −2.41449 6.57041i −0.121950 0.331856i
393393 −27.6419 + 17.0873i −1.39435 + 0.861942i
394394 5.22882 9.05658i 0.263424 0.456264i
395395 1.47595 2.55642i 0.0742630 0.128627i
396396 −15.3964 + 0.927160i −0.773696 + 0.0465915i
397397 −14.1667 24.5375i −0.711007 1.23150i −0.964479 0.264158i 0.914906π-0.914906\pi
0.253472 0.967343i 0.418427π-0.418427\pi
398398 8.16053 + 14.1345i 0.409051 + 0.708496i
399399 −9.71415 19.2210i −0.486316 0.962251i
400400 −0.500000 + 0.866025i −0.0250000 + 0.0433013i
401401 −6.82249 −0.340699 −0.170349 0.985384i 0.554490π-0.554490\pi
−0.170349 + 0.985384i 0.554490π0.554490\pi
402402 17.3514 10.7261i 0.865407 0.534968i
403403 −23.1905 −1.15520
404404 2.86471 + 4.96182i 0.142525 + 0.246860i
405405 5.40282 + 7.19789i 0.268468 + 0.357666i
406406 0.987811 + 0.689397i 0.0490242 + 0.0342142i
407407 10.2864 + 17.8166i 0.509879 + 0.883137i
408408 −0.301751 10.0308i −0.0149389 0.496598i
409409 −5.58692 9.67683i −0.276255 0.478489i 0.694196 0.719786i 0.255760π-0.255760\pi
−0.970451 + 0.241298i 0.922427π0.922427\pi
410410 −3.71105 6.42773i −0.183276 0.317443i
411411 −9.42592 + 5.82681i −0.464946 + 0.287415i
412412 7.01544 + 12.1511i 0.345626 + 0.598642i
413413 −2.52180 + 29.3473i −0.124090 + 1.44409i
414414 4.41350 + 6.68171i 0.216912 + 0.328388i
415415 −6.13291 10.6225i −0.301053 0.521439i
416416 3.24732 0.159213
417417 −1.09103 36.2681i −0.0534281 1.77605i
418418 −24.1626 −1.18183
419419 −2.78160 + 4.81787i −0.135890 + 0.235368i −0.925937 0.377678i 0.876723π-0.876723\pi
0.790047 + 0.613046i 0.210056π0.210056\pi
420420 2.06702 + 4.08992i 0.100860 + 0.199568i
421421 −17.2899 29.9470i −0.842658 1.45953i −0.887640 0.460539i 0.847656π-0.847656\pi
0.0449814 0.998988i 0.485677π-0.485677\pi
422422 2.17495 + 3.76713i 0.105875 + 0.183381i
423423 −5.22232 7.90620i −0.253918 0.384413i
424424 1.63008 2.82338i 0.0791636 0.137115i
425425 −2.89695 + 5.01766i −0.140523 + 0.243392i
426426 0.228420 + 7.59313i 0.0110670 + 0.367889i
427427 −14.3664 + 6.72624i −0.695238 + 0.325506i
428428 7.30355 12.6501i 0.353030 0.611466i
429429 −0.869533 28.9050i −0.0419814 1.39554i
430430 3.60995 0.174087
431431 19.2277 33.3034i 0.926167 1.60417i 0.136495 0.990641i 0.456416π-0.456416\pi
0.789673 0.613528i 0.210250π-0.210250\pi
432432 4.71578 + 2.18207i 0.226888 + 0.104985i
433433 30.9550 1.48760 0.743800 0.668402i 0.233021π-0.233021\pi
0.743800 + 0.668402i 0.233021π0.233021\pi
434434 −15.4941 10.8134i −0.743743 0.519061i
435435 −0.694486 0.373581i −0.0332981 0.0179119i
436436 −3.20783 −0.153627
437437 6.27220 + 10.8638i 0.300040 + 0.519685i
438438 −21.1764 11.3913i −1.01185 0.544298i
439439 −13.4194 + 23.2431i −0.640474 + 1.10933i 0.344853 + 0.938657i 0.387929π0.387929\pi
−0.985327 + 0.170676i 0.945405π0.945405\pi
440440 5.14142 0.245107
441441 20.8701 + 2.33228i 0.993814 + 0.111061i
442442 18.8146 0.894922
443443 16.1258 27.9308i 0.766162 1.32703i −0.173468 0.984840i 0.555497π-0.555497\pi
0.939630 0.342192i 0.111169π-0.111169\pi
444444 −0.208396 6.92749i −0.00989004 0.328764i
445445 4.83214 + 8.36951i 0.229065 + 0.396753i
446446 3.45434 0.163568
447447 −18.2094 + 11.2565i −0.861276 + 0.532414i
448448 2.16962 + 1.51418i 0.102505 + 0.0715385i
449449 −9.45029 −0.445987 −0.222993 0.974820i 0.571583π-0.571583\pi
−0.222993 + 0.974820i 0.571583π0.571583\pi
450450 −1.65346 2.50321i −0.0779448 0.118003i
451451 −19.0801 + 33.0476i −0.898445 + 1.55615i
452452 −2.29937 −0.108153
453453 28.6047 17.6826i 1.34397 0.830799i
454454 −9.60477 + 16.6359i −0.450774 + 0.780764i
455455 −7.78102 + 3.64302i −0.364780 + 0.170787i
456456 7.16858 + 3.85616i 0.335700 + 0.180581i
457457 −12.6657 + 21.9376i −0.592474 + 1.02620i 0.401424 + 0.915892i 0.368516π0.368516\pi
−0.993898 + 0.110303i 0.964818π0.964818\pi
458458 −10.8311 + 18.7600i −0.506104 + 0.876598i
459459 27.3227 + 12.6427i 1.27532 + 0.590110i
460460 −1.33463 2.31164i −0.0622273 0.107781i
461461 0.0688453 + 0.119244i 0.00320645 + 0.00555373i 0.867624 0.497221i 0.165646π-0.165646\pi
−0.864418 + 0.502774i 0.832313π0.832313\pi
462462 12.8971 19.7176i 0.600025 0.917345i
463463 −8.01422 + 13.8810i −0.372452 + 0.645106i −0.989942 0.141473i 0.954816π-0.954816\pi
0.617490 + 0.786579i 0.288150π0.288150\pi
464464 −0.455293 −0.0211364
465465 10.8932 + 5.85975i 0.505162 + 0.271739i
466466 −2.73918 −0.126890
467467 10.9032 + 18.8849i 0.504540 + 0.873888i 0.999986 + 0.00524984i 0.00167108π0.00167108\pi
−0.495447 + 0.868638i 0.664996π0.664996\pi
468468 −4.35504 + 8.71434i −0.201312 + 0.402820i
469469 −2.66772 + 31.0456i −0.123184 + 1.43355i
470470 1.57921 + 2.73527i 0.0728436 + 0.126169i
471471 3.75391 + 2.01932i 0.172971 + 0.0930453i
472472 −5.56657 9.64157i −0.256222 0.443789i
473473 −9.28012 16.0736i −0.426700 0.739066i
474474 4.50271 + 2.42212i 0.206816 + 0.111252i
475475 −2.34980 4.06997i −0.107816 0.186743i
476476 12.5705 + 8.77302i 0.576170 + 0.402111i
477477 5.39054 + 8.16087i 0.246816 + 0.373661i
478478 −11.2181 19.4304i −0.513106 0.888725i
479479 −16.2660 −0.743213 −0.371606 0.928390i 0.621193π-0.621193\pi
−0.371606 + 0.928390i 0.621193π0.621193\pi
480480 −1.52536 0.820531i −0.0696229 0.0374519i
481481 12.9938 0.592468
482482 10.9177 18.9101i 0.497289 0.861330i
483483 −12.2131 0.680306i −0.555716 0.0309550i
484484 −7.71707 13.3664i −0.350776 0.607562i
485485 −3.91728 6.78493i −0.177875 0.308088i
486486 −12.1801 + 9.72859i −0.552500 + 0.441298i
487487 −17.0685 + 29.5636i −0.773449 + 1.33965i 0.162213 + 0.986756i 0.448137π0.448137\pi
−0.935662 + 0.352897i 0.885196π0.885196\pi
488488 2.99783 5.19239i 0.135705 0.235048i
489489 15.1352 + 8.14159i 0.684437 + 0.368176i
490490 −6.89738 1.19419i −0.311592 0.0539481i
491491 21.6539 37.5057i 0.977228 1.69261i 0.304849 0.952401i 0.401394π-0.401394\pi
0.672379 0.740207i 0.265273π-0.265273\pi
492492 10.9348 6.75958i 0.492981 0.304746i
493493 −2.63792 −0.118806
494494 −7.63055 + 13.2165i −0.343315 + 0.594639i
495495 −6.89523 + 13.7972i −0.309918 + 0.620139i
496496 7.14142 0.320659
497497 −9.51569 6.64103i −0.426837 0.297891i
498498 18.0710 11.1709i 0.809781 0.500582i
499499 6.64628 0.297528 0.148764 0.988873i 0.452470π-0.452470\pi
0.148764 + 0.988873i 0.452470π0.452470\pi
500500 0.500000 + 0.866025i 0.0223607 + 0.0387298i
501501 0.340443 + 11.3170i 0.0152099 + 0.505606i
502502 −2.82913 + 4.90019i −0.126270 + 0.218706i
503503 35.8333 1.59773 0.798865 0.601510i 0.205434π-0.205434\pi
0.798865 + 0.601510i 0.205434π0.205434\pi
504504 −6.97309 + 3.79157i −0.310606 + 0.168890i
505505 5.72942 0.254956
506506 −6.86187 + 11.8851i −0.305047 + 0.528358i
507507 3.74459 + 2.01431i 0.166303 + 0.0894587i
508508 1.15940 + 2.00814i 0.0514400 + 0.0890967i
509509 13.8746 0.614981 0.307490 0.951551i 0.400511π-0.400511\pi
0.307490 + 0.951551i 0.400511π0.400511\pi
510510 −8.83779 4.75407i −0.391344 0.210514i
511511 33.2652 15.5745i 1.47156 0.688976i
512512 −1.00000 −0.0441942
513513 −19.9621 + 14.0656i −0.881347 + 0.621014i
514514 3.88139 6.72276i 0.171201 0.296528i
515515 14.0309 0.618275
516516 0.188009 + 6.24978i 0.00827663 + 0.275131i
517517 8.11938 14.0632i 0.357090 0.618498i
518518 8.68151 + 6.05886i 0.381444 + 0.266211i
519519 0.662935 + 22.0372i 0.0290996 + 0.967328i
520520 1.62366 2.81226i 0.0712023 0.123326i
521521 −5.15160 + 8.92284i −0.225696 + 0.390917i −0.956528 0.291641i 0.905799π-0.905799\pi
0.730832 + 0.682557i 0.239132π0.239132\pi
522522 0.610600 1.22180i 0.0267252 0.0534766i
523523 6.16132 + 10.6717i 0.269416 + 0.466642i 0.968711 0.248191i 0.0798360π-0.0798360\pi
−0.699295 + 0.714833i 0.746503π0.746503\pi
524524 9.38105 + 16.2485i 0.409813 + 0.709817i
525525 4.57548 + 0.254868i 0.199690 + 0.0111233i
526526 4.59133 7.95241i 0.200191 0.346742i
527527 41.3766 1.80239
528528 0.267769 + 8.90117i 0.0116532 + 0.387374i
529529 −15.8751 −0.690221
530530 −1.63008 2.82338i −0.0708061 0.122640i
531531 33.3390 2.00766i 1.44679 0.0871248i
532532 −11.2608 + 5.27225i −0.488220 + 0.228581i
533533 12.0510 + 20.8729i 0.521986 + 0.904106i
534534 −14.2382 + 8.80161i −0.616147 + 0.380883i
535535 −7.30355 12.6501i −0.315760 0.546912i
536536 −5.88868 10.1995i −0.254352 0.440551i
537537 −1.21017 40.2285i −0.0522228 1.73599i
538538 −9.03012 15.6406i −0.389316 0.674315i
539539 12.4139 + 33.7812i 0.534704 + 1.45506i
540540 4.24762 2.99295i 0.182788 0.128796i
541541 13.9275 + 24.1231i 0.598789 + 1.03713i 0.993000 + 0.118113i 0.0376847π0.0376847\pi
−0.394211 + 0.919020i 0.628982π0.628982\pi
542542 −24.4928 −1.05206
543543 −28.0936 + 17.3666i −1.20561 + 0.745272i
544544 −5.79389 −0.248411
545545 −1.60392 + 2.77806i −0.0687042 + 0.118999i
546546 −6.71228 13.2813i −0.287259 0.568387i
547547 4.11573 + 7.12866i 0.175976 + 0.304799i 0.940499 0.339798i 0.110359π-0.110359\pi
−0.764523 + 0.644597i 0.777025π0.777025\pi
548548 3.19895 + 5.54075i 0.136653 + 0.236689i
549549 9.91357 + 15.0084i 0.423101 + 0.640543i
550550 2.57071 4.45260i 0.109615 0.189859i
551551 1.06984 1.85303i 0.0455769 0.0789415i
552552 3.93256 2.43099i 0.167381 0.103470i
553553 −7.07313 + 3.31159i −0.300780 + 0.140823i
554554 −6.55834 + 11.3594i −0.278637 + 0.482613i
555555 −6.10358 3.28327i −0.259083 0.139367i
556556 −20.9488 −0.888429
557557 12.5376 21.7157i 0.531234 0.920125i −0.468101 0.883675i 0.655062π-0.655062\pi
0.999335 0.0364501i 0.0116050π-0.0116050\pi
558558 −9.57746 + 19.1643i −0.405446 + 0.811290i
559559 −11.7227 −0.495816
560560 2.39613 1.12185i 0.101255 0.0474069i
561561 1.55143 + 51.5724i 0.0655012 + 2.17739i
562562 2.12114 0.0894751
563563 −8.20455 14.2107i −0.345780 0.598909i 0.639715 0.768612i 0.279052π-0.279052\pi
−0.985495 + 0.169703i 0.945719π0.945719\pi
564564 −4.65324 + 2.87649i −0.195937 + 0.121122i
565565 −1.14968 + 1.99131i −0.0483676 + 0.0837751i
566566 11.2536 0.473024
567567 −0.823124 23.7975i −0.0345679 0.999402i
568568 4.38588 0.184027
569569 15.8903 27.5227i 0.666154 1.15381i −0.312817 0.949813i 0.601273π-0.601273\pi
0.978971 0.203999i 0.0653940π-0.0653940\pi
570570 6.92382 4.28009i 0.290007 0.179273i
571571 −13.0878 22.6687i −0.547708 0.948657i −0.998431 0.0559938i 0.982167π-0.982167\pi
0.450723 0.892664i 0.351166π-0.351166\pi
572572 −16.6958 −0.698088
573573 1.36967 + 45.5305i 0.0572188 + 1.90206i
574574 −1.68120 + 19.5649i −0.0701720 + 0.816625i
575575 −2.66925 −0.111316
576576 1.34112 2.68354i 0.0558798 0.111814i
577577 21.3065 36.9039i 0.887000 1.53633i 0.0435950 0.999049i 0.486119π-0.486119\pi
0.843405 0.537279i 0.180548π-0.180548\pi
578578 −16.5692 −0.689188
579579 −7.15185 3.84716i −0.297221 0.159882i
580580 −0.227646 + 0.394295i −0.00945250 + 0.0163722i
581581 −2.77837 + 32.3332i −0.115266 + 1.34141i
582582 11.5425 7.13523i 0.478453 0.295765i
583583 −8.38091 + 14.5162i −0.347102 + 0.601198i
584584 −6.94143 + 12.0229i −0.287238 + 0.497512i
585585 5.36932 + 8.12874i 0.221994 + 0.336082i
586586 −4.80935 8.33003i −0.198672 0.344111i
587587 9.85073 + 17.0620i 0.406583 + 0.704223i 0.994504 0.104695i 0.0333868π-0.0333868\pi
−0.587921 + 0.808918i 0.700053π0.700053\pi
588588 1.70825 12.0034i 0.0704469 0.495012i
589589 −16.7809 + 29.0653i −0.691444 + 1.19762i
590590 −11.1331 −0.458344
591591 15.4071 9.52416i 0.633761 0.391772i
592592 −4.00140 −0.164456
593593 −11.4796 19.8832i −0.471411 0.816507i 0.528055 0.849210i 0.322922π-0.322922\pi
−0.999465 + 0.0327034i 0.989588π0.989588\pi
594594 −24.2458 11.2189i −0.994816 0.460318i
595595 13.8829 6.49989i 0.569145 0.266470i
596596 6.17989 + 10.7039i 0.253138 + 0.438448i
597597 0.850014 + 28.2561i 0.0347888 + 1.15645i
598598 4.33397 + 7.50665i 0.177229 + 0.306970i
599599 4.31627 + 7.47600i 0.176358 + 0.305461i 0.940630 0.339432i 0.110235π-0.110235\pi
−0.764272 + 0.644894i 0.776902π0.776902\pi
600600 −1.47328 + 0.910737i −0.0601465 + 0.0371807i
601601 10.2828 + 17.8104i 0.419445 + 0.726500i 0.995884 0.0906402i 0.0288913π-0.0288913\pi
−0.576439 + 0.817140i 0.695558π0.695558\pi
602602 −7.83221 5.46613i −0.319217 0.222783i
603603 35.2682 2.12383i 1.43623 0.0864890i
604604 −9.70783 16.8145i −0.395006 0.684171i
605605 −15.4341 −0.627487
606606 0.298393 + 9.91916i 0.0121214 + 0.402938i
607607 −15.4125 −0.625573 −0.312786 0.949823i 0.601262π-0.601262\pi
−0.312786 + 0.949823i 0.601262π0.601262\pi
608608 2.34980 4.06997i 0.0952968 0.165059i
609609 0.941099 + 1.86211i 0.0381352 + 0.0754565i
610610 −2.99783 5.19239i −0.121379 0.210234i
611611 −5.12821 8.88232i −0.207465 0.359340i
612612 7.77028 15.5482i 0.314095 0.628497i
613613 −3.08756 + 5.34781i −0.124705 + 0.215996i −0.921618 0.388099i 0.873132π-0.873132\pi
0.796912 + 0.604095i 0.206465π0.206465\pi
614614 −4.56767 + 7.91144i −0.184336 + 0.319280i
615615 −0.386549 12.8496i −0.0155872 0.518148i
616616 −11.1549 7.78505i −0.449444 0.313669i
617617 6.63619 11.4942i 0.267163 0.462740i −0.700965 0.713196i 0.747247π-0.747247\pi
0.968128 + 0.250456i 0.0805804π0.0805804\pi
618618 0.730740 + 24.2912i 0.0293947 + 0.977136i
619619 25.1378 1.01037 0.505187 0.863010i 0.331423π-0.331423\pi
0.505187 + 0.863010i 0.331423π0.331423\pi
620620 3.57071 6.18465i 0.143403 0.248381i
621621 1.24964 + 13.8134i 0.0501465 + 0.554314i
622622 −20.5948 −0.825775
623623 2.18908 25.4754i 0.0877038 1.02065i
624624 4.95334 + 2.66453i 0.198292 + 0.106666i
625625 1.00000 0.0400000
626626 −0.275427 0.477053i −0.0110083 0.0190669i
627627 −36.8567 19.8261i −1.47191 0.791779i
628628 1.23050 2.13128i 0.0491021 0.0850474i
629629 −23.1837 −0.924394
630630 −0.202949 + 7.93466i −0.00808569 + 0.316124i
631631 −22.4313 −0.892978 −0.446489 0.894789i 0.647326π-0.647326\pi
−0.446489 + 0.894789i 0.647326π0.647326\pi
632632 1.47595 2.55642i 0.0587101 0.101689i
633633 0.226547 + 7.53086i 0.00900442 + 0.299325i
634634 −13.4872 23.3605i −0.535645 0.927765i
635635 2.31880 0.0920187
636636 4.80313 2.96915i 0.190457 0.117734i
637637 22.3980 + 3.87793i 0.887443 + 0.153649i
638638 2.34085 0.0926750
639639 −5.88197 + 11.7697i −0.232687 + 0.465602i
640640 −0.500000 + 0.866025i −0.0197642 + 0.0342327i
641641 −39.1457 −1.54616 −0.773082 0.634306i 0.781286π-0.781286\pi
−0.773082 + 0.634306i 0.781286π0.781286\pi
642642 21.5204 13.3032i 0.849341 0.525036i
643643 −17.4010 + 30.1395i −0.686230 + 1.18859i 0.286818 + 0.957985i 0.407402π0.407402\pi
−0.973048 + 0.230601i 0.925931π0.925931\pi
644644 −0.604620 + 7.03625i −0.0238254 + 0.277267i
645645 5.50648 + 2.96207i 0.216817 + 0.116631i
646646 13.6145 23.5810i 0.535654 0.927780i
647647 15.2199 26.3617i 0.598357 1.03638i −0.394707 0.918807i 0.629154π-0.629154\pi
0.993064 0.117578i 0.0375129π-0.0375129\pi
648648 5.40282 + 7.19789i 0.212243 + 0.282760i
649649 28.6200 + 49.5713i 1.12343 + 1.94585i
650650 −1.62366 2.81226i −0.0636853 0.110306i
651651 −14.7614 29.2078i −0.578547 1.14474i
652652 4.96118 8.59301i 0.194295 0.336528i
653653 −13.5323 −0.529559 −0.264779 0.964309i 0.585299π-0.585299\pi
−0.264779 + 0.964309i 0.585299π0.585299\pi
654654 −4.89310 2.63212i −0.191335 0.102924i
655655 18.7621 0.733096
656656 −3.71105 6.42773i −0.144892 0.250961i
657657 −22.9547 34.7518i −0.895550 1.35579i
658658 0.715423 8.32572i 0.0278901 0.324570i
659659 4.39992 + 7.62088i 0.171397 + 0.296867i 0.938908 0.344167i 0.111839π-0.111839\pi
−0.767512 + 0.641035i 0.778505π0.778505\pi
660660 7.84252 + 4.21869i 0.305270 + 0.164212i
661661 17.9543 + 31.0978i 0.698342 + 1.20956i 0.969041 + 0.246900i 0.0794119π0.0794119\pi
−0.270699 + 0.962664i 0.587255π0.587255\pi
662662 −8.44384 14.6252i −0.328179 0.568423i
663663 28.6992 + 15.4380i 1.11458 + 0.599562i
664664 −6.13291 10.6225i −0.238003 0.412234i
665665 −1.06452 + 12.3883i −0.0412803 + 0.480398i
666666 5.36634 10.7379i 0.207941 0.416086i
667667 −0.607646 1.05247i −0.0235281 0.0407519i
668668 6.53683 0.252917
669669 5.26911 + 2.83439i 0.203716 + 0.109584i
670670 −11.7774 −0.454999
671671 −15.4131 + 26.6962i −0.595015 + 1.03060i
672672 2.06702 + 4.08992i 0.0797370 + 0.157772i
673673 −11.4811 19.8858i −0.442563 0.766541i 0.555316 0.831639i 0.312597π-0.312597\pi
−0.997879 + 0.0650982i 0.979264π0.979264\pi
674674 −12.8294 22.2212i −0.494171 0.855929i
675675 −0.468162 5.17502i −0.0180196 0.199187i
676676 1.22744 2.12600i 0.0472094 0.0817691i
677677 16.2831 28.2031i 0.625810 1.08393i −0.362574 0.931955i 0.618102π-0.618102\pi
0.988384 0.151980i 0.0485648π-0.0485648\pi
678678 −3.50737 1.88670i −0.134700 0.0724583i
679679 −1.77463 + 20.6522i −0.0681040 + 0.792559i
680680 −2.89695 + 5.01766i −0.111093 + 0.192418i
681681 −28.3011 + 17.4948i −1.08450 + 0.670404i
682682 −36.7170 −1.40597
683683 −25.6672 + 44.4569i −0.982128 + 1.70110i −0.328066 + 0.944655i 0.606397π0.606397\pi
−0.654062 + 0.756441i 0.726936π0.726936\pi
684684 7.77059 + 11.7641i 0.297116 + 0.449811i
685685 6.39791 0.244452
686686 13.1565 + 13.0349i 0.502316 + 0.497673i
687687 −31.9145 + 19.7286i −1.21761 + 0.752692i
688688 3.60995 0.137628
689689 5.29339 + 9.16843i 0.201662 + 0.349289i
690690 −0.139017 4.62119i −0.00529228 0.175926i
691691 −19.6397 + 34.0170i −0.747130 + 1.29407i 0.202064 + 0.979372i 0.435235π0.435235\pi
−0.949193 + 0.314694i 0.898098π0.898098\pi
692692 12.7290 0.483883
693693 35.8516 19.4940i 1.36189 0.740517i
694694 17.0235 0.646204
695695 −10.4744 + 18.1422i −0.397318 + 0.688174i
696696 −0.694486 0.373581i −0.0263244 0.0141606i
697697 −21.5014 37.2416i −0.814425 1.41063i
698698 −22.6312 −0.856602
699699 −4.17824 2.24758i −0.158036 0.0850113i
700700 0.226513 2.63604i 0.00856138 0.0996328i
701701 −40.2576 −1.52051 −0.760254 0.649626i 0.774926π-0.774926\pi
−0.760254 + 0.649626i 0.774926π0.774926\pi
702702 −13.7934 + 9.71908i −0.520598 + 0.366823i
703703 9.40247 16.2856i 0.354621 0.614222i
704704 5.14142 0.193774
705705 0.164493 + 5.46807i 0.00619517 + 0.205940i
706706 −4.37421 + 7.57635i −0.164625 + 0.285140i
707707 −12.4307 8.67540i −0.467503 0.326272i
708708 −0.579822 19.2744i −0.0217911 0.724377i
709709 −6.62156 + 11.4689i −0.248678 + 0.430722i −0.963159 0.268932i 0.913329π-0.913329\pi
0.714481 + 0.699654i 0.246663π0.246663\pi
710710 2.19294 3.79828i 0.0822996 0.142547i
711711 4.88084 + 7.38922i 0.183046 + 0.277118i
712712 4.83214 + 8.36951i 0.181092 + 0.313661i
713713 9.53112 + 16.5084i 0.356943 + 0.618244i
714714 11.9761 + 23.6965i 0.448194 + 0.886821i
715715 −8.34792 + 14.4590i −0.312194 + 0.540737i
716716 −23.2364 −0.868386
717717 −1.16850 38.8432i −0.0436384 1.45063i
718718 26.0238 0.971199
719719 −22.7520 39.4076i −0.848507 1.46966i −0.882541 0.470236i 0.844169π-0.844169\pi
0.0340340 0.999421i 0.489165π-0.489165\pi
720720 −1.65346 2.50321i −0.0616208 0.0932892i
721721 −30.4417 21.2454i −1.13371 0.791218i
722722 1.54309 + 2.67271i 0.0574278 + 0.0994679i
723723 32.1698 19.8864i 1.19641 0.739582i
724724 9.53436 + 16.5140i 0.354342 + 0.613738i
725725 0.227646 + 0.394295i 0.00845457 + 0.0146437i
726726 −0.803823 26.7206i −0.0298327 0.991696i
727727 0.0908081 + 0.157284i 0.00336789 + 0.00583335i 0.867704 0.497080i 0.165595π-0.165595\pi
−0.864337 + 0.502914i 0.832261π0.832261\pi
728728 −7.78102 + 3.64302i −0.288384 + 0.135019i
729729 −26.5616 + 4.84550i −0.983765 + 0.179463i
730730 6.94143 + 12.0229i 0.256914 + 0.444988i
731731 20.9156 0.773593
732732 8.83329 5.46047i 0.326488 0.201825i
733733 46.1227 1.70358 0.851790 0.523883i 0.175517π-0.175517\pi
0.851790 + 0.523883i 0.175517π0.175517\pi
734734 17.2794 29.9288i 0.637794 1.10469i
735735 −9.54114 7.48109i −0.351930 0.275944i
736736 −1.33463 2.31164i −0.0491950 0.0852082i
737737 30.2761 + 52.4398i 1.11524 + 1.93165i
738738 22.2260 1.33844i 0.818152 0.0492686i
739739 −8.94515 + 15.4935i −0.329053 + 0.569936i −0.982324 0.187188i 0.940063π-0.940063\pi
0.653271 + 0.757124i 0.273396π0.273396\pi
740740 −2.00070 + 3.46531i −0.0735472 + 0.127387i
741741 −22.4839 + 13.8989i −0.825967 + 0.510587i
742742 −0.738468 + 8.59390i −0.0271100 + 0.315492i
743743 −8.34901 + 14.4609i −0.306295 + 0.530519i −0.977549 0.210709i 0.932423π-0.932423\pi
0.671253 + 0.741228i 0.265756π0.265756\pi
744744 10.8932 + 5.85975i 0.399366 + 0.214829i
745745 12.3598 0.452827
746746 4.48949 7.77603i 0.164372 0.284701i
747747 36.7309 2.21192i 1.34391 0.0809298i
748748 29.7888 1.08919
749749 −3.30870 + 38.5048i −0.120897 + 1.40694i
750750 0.0520808 + 1.73127i 0.00190172 + 0.0632170i
751751 31.2552 1.14052 0.570260 0.821464i 0.306843π-0.306843\pi
0.570260 + 0.821464i 0.306843π0.306843\pi
752752 1.57921 + 2.73527i 0.0575879 + 0.0997452i
753753 −8.33620 + 5.15318i −0.303788 + 0.187792i
754754 0.739241 1.28040i 0.0269216 0.0466295i
755755 −19.4157 −0.706608
756756 −13.7476 + 0.0618842i −0.499995 + 0.00225071i
757757 23.1959 0.843069 0.421534 0.906812i 0.361492π-0.361492\pi
0.421534 + 0.906812i 0.361492π0.361492\pi
758758 −10.6144 + 18.3847i −0.385532 + 0.667761i
759759 −20.2189 + 12.4987i −0.733901 + 0.453675i
760760 −2.34980 4.06997i −0.0852361 0.147633i
761761 26.4849 0.960077 0.480039 0.877247i 0.340623π-0.340623\pi
0.480039 + 0.877247i 0.340623π0.340623\pi
762762 0.120765 + 4.01446i 0.00437485 + 0.145428i
763763 7.68638 3.59871i 0.278266 0.130282i
764764 26.2989 0.951462
765765 −9.57997 14.5033i −0.346364 0.524370i
766766 0.108153 0.187326i 0.00390771 0.00676835i
767767 36.1529 1.30540
768768 −1.52536 0.820531i −0.0550418 0.0296083i
769769 20.5798 35.6452i 0.742126 1.28540i −0.209399 0.977830i 0.567151π-0.567151\pi
0.951525 0.307570i 0.0995159π-0.0995159\pi
770770 −12.3195 + 5.76791i −0.443964 + 0.207861i
771771 11.4367 7.06985i 0.411884 0.254614i
772772 −2.34431 + 4.06047i −0.0843736 + 0.146139i
773773 −13.2736 + 22.9905i −0.477418 + 0.826912i −0.999665 0.0258823i 0.991761π-0.991761\pi
0.522247 + 0.852794i 0.325094π0.325094\pi
774774 −4.84136 + 9.68745i −0.174019 + 0.348208i
775775 −3.57071 6.18465i −0.128264 0.222159i
776776 −3.91728 6.78493i −0.140622 0.243565i
777777 8.27097 + 16.3654i 0.296719 + 0.587105i
778778 −5.81312 + 10.0686i −0.208410 + 0.360977i
779779 34.8809 1.24974
780780 4.78422 2.95746i 0.171303 0.105894i
781781 −22.5496 −0.806889
782782 −7.73269 13.3934i −0.276520 0.478947i
783783 1.93391 1.36267i 0.0691122 0.0486978i
784784 −6.89738 1.19419i −0.246335 0.0426497i
785785 −1.23050 2.13128i −0.0439183 0.0760687i
786786 0.977145 + 32.4822i 0.0348536 + 1.15860i
787787 −12.1086 20.9727i −0.431624 0.747595i 0.565389 0.824824i 0.308726π-0.308726\pi
−0.997013 + 0.0772296i 0.975393π0.975393\pi
788788 −5.22882 9.05658i −0.186269 0.322627i
789789 13.5286 8.36298i 0.481632 0.297730i
790790 −1.47595 2.55642i −0.0525119 0.0909533i
791791 5.50959 2.57955i 0.195898 0.0917183i
792792 −6.89523 + 13.7972i −0.245011 + 0.490263i
793793 9.73492 + 16.8614i 0.345697 + 0.598765i
794794 −28.3334 −1.00552
795795 −0.169792 5.64421i −0.00602189 0.200179i
796796 16.3211 0.578485
797797 3.05746 5.29567i 0.108301 0.187582i −0.806781 0.590850i 0.798792π-0.798792\pi
0.915082 + 0.403268i 0.132126π0.132126\pi
798798 −21.5029 1.19777i −0.761195 0.0424007i
799799 9.14978 + 15.8479i 0.323696 + 0.560658i
800800 0.500000 + 0.866025i 0.0176777 + 0.0306186i
801801 −28.9404 + 1.74277i −1.02256 + 0.0615779i
802802 −3.41125 + 5.90845i −0.120455 + 0.208635i
803803 35.6888 61.8148i 1.25943 2.18140i
804804 −0.613374 20.3898i −0.0216320 0.719091i
805805 5.79126 + 4.04174i 0.204115 + 0.142453i
806806 −11.5952 + 20.0836i −0.408425 + 0.707413i
807807 −0.940592 31.2671i −0.0331104 1.10065i
808808 5.72942 0.201560
809809 10.3380 17.9059i 0.363464 0.629538i −0.625065 0.780573i 0.714927π-0.714927\pi
0.988528 + 0.151035i 0.0482607π0.0482607\pi
810810 8.93496 1.08003i 0.313943 0.0379485i
811811 15.2973 0.537160 0.268580 0.963257i 0.413446π-0.413446\pi
0.268580 + 0.963257i 0.413446π0.413446\pi
812812 1.09094 0.510771i 0.0382845 0.0179246i
813813 −37.3605 20.0971i −1.31029 0.704837i
814814 20.5729 0.721078
815815 −4.96118 8.59301i −0.173782 0.301000i
816816 −8.83779 4.75407i −0.309384 0.166426i
817817 −8.48264 + 14.6924i −0.296770 + 0.514021i
818818 −11.1738 −0.390684
819819 0.659041 25.7664i 0.0230288 0.900351i
820820 −7.42210 −0.259191
821821 −3.37590 + 5.84724i −0.117820 + 0.204070i −0.918903 0.394482i 0.870924π-0.870924\pi
0.801084 + 0.598552i 0.204257π0.204257\pi
822822 0.333208 + 11.0765i 0.0116220 + 0.386337i
823823 −11.3370 19.6362i −0.395183 0.684476i 0.597942 0.801540i 0.295985π-0.295985\pi
−0.993124 + 0.117063i 0.962652π0.962652\pi
824824 14.0309 0.488789
825825 7.57475 4.68248i 0.263719 0.163023i
826826 24.1546 + 16.8576i 0.840448 + 0.586551i
827827 −26.0867 −0.907122 −0.453561 0.891225i 0.649847π-0.649847\pi
−0.453561 + 0.891225i 0.649847π0.649847\pi
828828 7.99328 0.481351i 0.277786 0.0167281i
829829 −1.68725 + 2.92240i −0.0586005 + 0.101499i −0.893837 0.448391i 0.851997π-0.851997\pi
0.835237 + 0.549890i 0.185330π0.185330\pi
830830 −12.2658 −0.425753
831831 −19.3245 + 11.9458i −0.670361 + 0.414397i
832832 1.62366 2.81226i 0.0562903 0.0974977i
833833 −39.9627 6.91903i −1.38463 0.239730i
834834 −31.9546 17.1892i −1.10650 0.595212i
835835 3.26841 5.66106i 0.113108 0.195909i
836836 −12.0813 + 20.9254i −0.417840 + 0.723720i
837837 −30.3340 + 21.3739i −1.04850 + 0.738790i
838838 2.78160 + 4.81787i 0.0960887 + 0.166430i
839839 −11.2557 19.4955i −0.388590 0.673058i 0.603670 0.797234i 0.293704π-0.293704\pi
−0.992260 + 0.124176i 0.960371π0.960371\pi
840840 4.57548 + 0.254868i 0.157869 + 0.00879377i
841841 14.3964 24.9352i 0.496426 0.859835i
842842 −34.5798 −1.19170
843843 3.23551 + 1.74046i 0.111437 + 0.0599447i
844844 4.34991 0.149730
845845 −1.22744 2.12600i −0.0422254 0.0731365i
846846 −9.45813 + 0.569563i −0.325177 + 0.0195820i
847847 33.4862 + 23.3701i 1.15060 + 0.803008i
848848 −1.63008 2.82338i −0.0559771 0.0969553i
849849 17.1658 + 9.23392i 0.589129 + 0.316907i
850850 2.89695 + 5.01766i 0.0993645 + 0.172104i
851851 −5.34037 9.24980i −0.183066 0.317079i
852852 6.69006 + 3.59875i 0.229198 + 0.123291i
853853 12.9138 + 22.3673i 0.442159 + 0.765842i 0.997849 0.0655473i 0.0208793π-0.0208793\pi
−0.555690 + 0.831389i 0.687546π0.687546\pi
854854 −1.35809 + 15.8048i −0.0464730 + 0.540828i
855855 14.0733 0.847485i 0.481296 0.0289834i
856856 −7.30355 12.6501i −0.249630 0.432372i
857857 24.4314 0.834562 0.417281 0.908777i 0.362983π-0.362983\pi
0.417281 + 0.908777i 0.362983π0.362983\pi
858858 −25.4672 13.6994i −0.869436 0.467691i
859859 18.9041 0.644999 0.322500 0.946570i 0.395477π-0.395477\pi
0.322500 + 0.946570i 0.395477π0.395477\pi
860860 1.80497 3.12631i 0.0615491 0.106606i
861861 −18.6181 + 28.4641i −0.634502 + 0.970055i
862862 −19.2277 33.3034i −0.654899 1.13432i
863863 1.64446 + 2.84828i 0.0559779 + 0.0969566i 0.892656 0.450738i 0.148839π-0.148839\pi
−0.836679 + 0.547694i 0.815506π0.815506\pi
864864 4.24762 2.99295i 0.144507 0.101822i
865865 6.36448 11.0236i 0.216399 0.374814i
866866 15.4775 26.8078i 0.525946 0.910965i
867867 −25.2740 13.5955i −0.858351 0.461729i
868868 −17.1118 + 8.01162i −0.580811 + 0.271932i
869869 −7.58846 + 13.1436i −0.257421 + 0.445866i
870870 −0.670774 + 0.414652i −0.0227414 + 0.0140580i
871871 38.2449 1.29588
872872 −1.60392 + 2.77806i −0.0543154 + 0.0940771i
873873 23.4612 1.41282i 0.794041 0.0478167i
874874 12.5444 0.424321
875875 −2.16962 1.51418i −0.0733465 0.0511888i
876876 −20.4534 + 12.6436i −0.691055 + 0.427189i
877877 −26.7992 −0.904946 −0.452473 0.891778i 0.649458π-0.649458\pi
−0.452473 + 0.891778i 0.649458π0.649458\pi
878878 13.4194 + 23.2431i 0.452883 + 0.784417i
879879 −0.500949 16.6525i −0.0168966 0.561676i
880880 2.57071 4.45260i 0.0866585 0.150097i
881881 20.9761 0.706703 0.353352 0.935491i 0.385042π-0.385042\pi
0.353352 + 0.935491i 0.385042π0.385042\pi
882882 12.4549 16.9079i 0.419377 0.569318i
883883 −24.9042 −0.838093 −0.419047 0.907965i 0.637636π-0.637636\pi
−0.419047 + 0.907965i 0.637636π0.637636\pi
884884 9.40732 16.2940i 0.316403 0.548025i
885885 −16.9821 9.13507i −0.570846 0.307072i
886886 −16.1258 27.9308i −0.541758 0.938353i
887887 22.1820 0.744798 0.372399 0.928073i 0.378535π-0.378535\pi
0.372399 + 0.928073i 0.378535π0.378535\pi
888888 −6.10358 3.28327i −0.204823 0.110179i
889889 −5.03091 3.51109i −0.168731 0.117758i
890890 9.66427 0.323947
891891 −27.7781 37.0073i −0.930602 1.23979i
892892 1.72717 2.99154i 0.0578298 0.100164i
893893 −14.8433 −0.496712
894894 0.643707 + 21.3981i 0.0215288 + 0.715659i
895895 −11.6182 + 20.1233i −0.388354 + 0.672649i
896896 2.39613 1.12185i 0.0800491 0.0374785i
897897 0.451433 + 15.0065i 0.0150729 + 0.501053i
898898 −4.72515 + 8.18419i −0.157680 + 0.273110i
899899 1.62572 2.81582i 0.0542207 0.0939130i
900900 −2.99458 + 0.180332i −0.0998192 + 0.00601105i
901901 −9.44451 16.3584i −0.314642 0.544976i
902902 19.0801 + 33.0476i 0.635296 + 1.10037i
903903 −7.46183 14.7644i −0.248314 0.491328i
904904 −1.14968 + 1.99131i −0.0382379 + 0.0662300i
905905 19.0687 0.633866
906906 −1.01118 33.6137i −0.0335943 1.11674i
907907 56.6729 1.88179 0.940897 0.338694i 0.109985π-0.109985\pi
0.940897 + 0.338694i 0.109985π0.109985\pi
908908 9.60477 + 16.6359i 0.318745 + 0.552083i
909909 −7.68382 + 15.3751i −0.254856 + 0.509962i
910910 −0.735561 + 8.56007i −0.0243836 + 0.283763i
911911 22.6917 + 39.3032i 0.751809 + 1.30217i 0.946945 + 0.321396i 0.104152π0.104152\pi
−0.195136 + 0.980776i 0.562515π0.562515\pi
912912 6.92382 4.28009i 0.229271 0.141728i
913913 31.5318 + 54.6148i 1.04355 + 1.80748i
914914 12.6657 + 21.9376i 0.418943 + 0.725630i
915915 −0.312259 10.3801i −0.0103230 0.343155i
916916 10.8311 + 18.7600i 0.357870 + 0.619848i
917917 −40.7066 28.4093i −1.34425 0.938157i
918918 24.6102 17.3408i 0.812259 0.572333i
919919 −5.64196 9.77216i −0.186111 0.322354i 0.757839 0.652441i 0.226255π-0.226255\pi
−0.943950 + 0.330087i 0.892922π0.892922\pi
920920 −2.66925 −0.0880027
921921 −13.4589 + 8.31990i −0.443487 + 0.274150i
922922 0.137691 0.00453460
923923 −7.12119 + 12.3343i −0.234397 + 0.405987i
924924 −10.6274 21.0280i −0.349616 0.691769i
925925 2.00070 + 3.46531i 0.0657826 + 0.113939i
926926 8.01422 + 13.8810i 0.263364 + 0.456159i
927927 −18.8170 + 37.6525i −0.618033 + 1.23667i
928928 −0.227646 + 0.394295i −0.00747285 + 0.0129434i
929929 4.35489 7.54290i 0.142879 0.247474i −0.785700 0.618607i 0.787697π-0.787697\pi
0.928580 + 0.371133i 0.121031π0.121031\pi
930930 10.5213 6.50395i 0.345007 0.213273i
931931 21.0678 25.2660i 0.690468 0.828060i
932932 −1.36959 + 2.37220i −0.0448624 + 0.0777040i
933933 −31.4145 16.8986i −1.02846 0.553236i
934934 21.8064 0.713527
935935 14.8944 25.7979i 0.487099 0.843680i
936936 5.36932 + 8.12874i 0.175502 + 0.265696i
937937 −12.4809 −0.407735 −0.203867 0.978999i 0.565351π-0.565351\pi
−0.203867 + 0.978999i 0.565351π0.565351\pi
938938 25.5524 + 17.8331i 0.834315 + 0.582271i
939939 −0.0286889 0.953675i −0.000936227 0.0311220i
940940 3.15842 0.103016
941941 −11.7985 20.4356i −0.384620 0.666182i 0.607096 0.794629i 0.292334π-0.292334\pi
−0.991716 + 0.128446i 0.959001π0.959001\pi
942942 3.62573 2.24132i 0.118133 0.0730261i
943943 9.90574 17.1572i 0.322575 0.558717i
944944 −11.1331 −0.362353
945945 −6.82020 + 11.9367i −0.221861 + 0.388301i
946946 −18.5602 −0.603445
947947 7.86869 13.6290i 0.255698 0.442882i −0.709387 0.704819i 0.751028π-0.751028\pi
0.965085 + 0.261937i 0.0843614π0.0843614\pi
948948 4.34897 2.68840i 0.141248 0.0873152i
949949 −22.5411 39.0423i −0.731714 1.26737i
950950 −4.69959 −0.152475
951951 −1.40485 46.6999i −0.0455554 1.51435i
952952 13.8829 6.49989i 0.449948 0.210663i
953953 −3.60070 −0.116638 −0.0583191 0.998298i 0.518574π-0.518574\pi
−0.0583191 + 0.998298i 0.518574π0.518574\pi
954954 9.76279 0.587910i 0.316082 0.0190343i
955955 13.1495 22.7755i 0.425507 0.736999i
956956 −22.4363 −0.725641
957957 3.57064 + 1.92074i 0.115422 + 0.0620886i
958958 −8.13300 + 14.0868i −0.262765 + 0.455123i
959959 −13.8810 9.68761i −0.448242 0.312829i
960960 −1.47328 + 0.910737i −0.0475500 + 0.0293939i
961961 −9.99990 + 17.3203i −0.322578 + 0.558721i
962962 6.49692 11.2530i 0.209469 0.362811i
963963 43.7420 2.63412i 1.40957 0.0848834i
964964 −10.9177 18.9101i −0.351636 0.609052i
965965 2.34431 + 4.06047i 0.0754660 + 0.130711i
966966 −6.69572 + 10.2367i −0.215431 + 0.329361i
967967 17.9234 31.0443i 0.576379 0.998317i −0.419511 0.907750i 0.637799π-0.637799\pi
0.995890 0.0905674i 0.0288681π-0.0288681\pi
968968 −15.4341 −0.496072
969969 40.1159 24.7984i 1.28871 0.796640i
970970 −7.83456 −0.251553
971971 −4.25320 7.36675i −0.136492 0.236410i 0.789675 0.613526i 0.210249π-0.210249\pi
−0.926166 + 0.377115i 0.876916π0.876916\pi
972972 2.33517 + 15.4126i 0.0749005 + 0.494358i
973973 50.1962 23.5015i 1.60922 0.753424i
974974 17.0685 + 29.5636i 0.546911 + 0.947278i
975975 −0.169123 5.62199i −0.00541628 0.180048i
976976 −2.99783 5.19239i −0.0959581 0.166204i
977977 −17.7804 30.7965i −0.568845 0.985269i −0.996681 0.0814119i 0.974057π-0.974057\pi
0.427835 0.903857i 0.359276π-0.359276\pi
978978 14.6184 9.03666i 0.467446 0.288960i
979979 −24.8440 43.0311i −0.794018 1.37528i
980980 −4.48289 + 5.37621i −0.143201 + 0.171737i
981981 −5.30402 8.02988i −0.169344 0.256374i
982982 −21.6539 37.5057i −0.691004 1.19685i
983983 −61.4109 −1.95870 −0.979351 0.202167i 0.935202π-0.935202\pi
−0.979351 + 0.202167i 0.935202π0.935202\pi
984984 −0.386549 12.8496i −0.0123227 0.409632i
985985 −10.4576 −0.333208
986986 −1.31896 + 2.28450i −0.0420042 + 0.0727534i
987987 7.92279 12.1127i 0.252185 0.385552i
988988 7.63055 + 13.2165i 0.242760 + 0.420473i
989989 4.81793 + 8.34490i 0.153201 + 0.265352i
990990 8.50112 + 12.8701i 0.270183 + 0.409037i
991991 −12.6801 + 21.9626i −0.402796 + 0.697664i −0.994062 0.108813i 0.965295π-0.965295\pi
0.591266 + 0.806477i 0.298628π0.298628\pi
992992 3.57071 6.18465i 0.113370 0.196363i
993993 −0.879524 29.2371i −0.0279108 0.927811i
994994 −10.5091 + 4.92031i −0.333330 + 0.156063i
995995 8.16053 14.1345i 0.258706 0.448093i
996996 −0.638814 21.2354i −0.0202416 0.672870i
997997 −1.33138 −0.0421652 −0.0210826 0.999778i 0.506711π-0.506711\pi
−0.0210826 + 0.999778i 0.506711π0.506711\pi
998998 3.32314 5.75585i 0.105192 0.182198i
999999 16.9964 11.9760i 0.537743 0.378903i
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 630.2.l.i.571.7 yes 16
3.2 odd 2 1890.2.l.i.361.7 16
7.2 even 3 630.2.i.i.121.4 16
9.2 odd 6 1890.2.i.i.991.4 16
9.7 even 3 630.2.i.i.151.4 yes 16
21.2 odd 6 1890.2.i.i.1171.4 16
63.2 odd 6 1890.2.l.i.1801.7 16
63.16 even 3 inner 630.2.l.i.331.7 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.i.i.121.4 16 7.2 even 3
630.2.i.i.151.4 yes 16 9.7 even 3
630.2.l.i.331.7 yes 16 63.16 even 3 inner
630.2.l.i.571.7 yes 16 1.1 even 1 trivial
1890.2.i.i.991.4 16 9.2 odd 6
1890.2.i.i.1171.4 16 21.2 odd 6
1890.2.l.i.361.7 16 3.2 odd 2
1890.2.l.i.1801.7 16 63.2 odd 6