Properties

Label 63.2.g.b.4.4
Level 6363
Weight 22
Character 63.4
Analytic conductor 0.5030.503
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,2,Mod(4,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 63=327 63 = 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 63.g (of order 33, degree 22, 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: 0.5030575327340.503057532734
Analytic rank: 00
Dimension: 1010
Relative dimension: 55 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x102x9+9x88x7+40x636x5+90x43x3+36x29x+9 x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 3 3
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 4.4
Root 0.9206201.59456i0.920620 - 1.59456i of defining polynomial
Character χ\chi == 63.4
Dual form 63.2.g.b.16.4

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+(0.9206201.59456i)q2+(1.588000.691567i)q3+(0.6950841.20392i)q4+1.33475q5+(2.56469+1.89549i)q6+(2.54347+0.728536i)q7+1.12285q8+(2.04347+2.19641i)q9+(1.228802.12835i)q10+1.51302q11+(0.271199+2.39252i)q12+(2.58800+4.48254i)q13+(1.17987+4.72642i)q14+(2.119580.923072i)q15+(2.423884.19829i)q16+(0.7744631.34141i)q17+(5.383581.23637i)q18+(1.252112.16872i)q19+(0.9277651.60694i)q20+(4.54285+0.602068i)q21+(1.392912.41260i)q227.36079q23+(1.783080.776526i)q243.21843q25+(4.76513+8.25344i)q26+(1.726054.90110i)q27+(2.64502+2.55574i)q28+(0.03097130.0536439i)q29+(3.42323+2.53001i)q30+(1.92388+3.33227i)q31+(3.340115.78523i)q32+(2.402671.04635i)q33+(1.425972.46986i)q34+(3.39490+0.972416i)q35+(1.223923.98687i)q36+(0.2816080.487760i)q374.61087q38+(7.209715.32849i)q39+1.49873q40+(4.511887.81481i)q41+(5.142286.68958i)q42+(5.09988+8.83325i)q43+(1.051671.82155i)q44+(2.72753+2.93167i)q45+(6.77649+11.7372i)q46+(4.759258.24327i)q47+(6.75252+4.99060i)q48+(5.938473.70602i)q49+(2.96296+5.13199i)q50+(2.15752+1.59456i)q51+7.19550q52+(0.7553741.30835i)q53+(9.404141.75975i)q54+2.01950q55+(2.85593+0.818036i)q56+(0.488532+4.30983i)q570.114051q58+(4.22166+7.31212i)q59+(0.361984+3.19342i)q60+(1.61958+2.80520i)q61+7.08467q62+(6.797674.09777i)q632.60434q64+(3.45434+5.98309i)q65+(3.88042+2.86790i)q66+(3.466706.00449i)q672.15327q68+(11.6889+5.09048i)q69+(1.57484+6.30861i)q7012.3304q71+(2.29451+2.46624i)q72+(1.37936+2.38912i)q731.03702q74+(5.11086+2.22576i)q75+(1.74064+3.01488i)q76+(3.84831+1.10229i)q77+(1.8592016.4018i)q78+(2.959695.12633i)q79+(3.235295.60368i)q80+(0.648467+8.97661i)q81+(8.3074614.3889i)q82+(2.80111+4.85167i)q83+(2.432825.88772i)q84+(1.033721.79045i)q85+18.7802q86+(0.0120840+0.106605i)q87+1.69889q88+(0.703287+1.21813i)q89+(7.185751.65025i)q90+(3.3168013.2867i)q91+(5.11636+8.86180i)q92+(0.7506376.62212i)q93+(8.7629315.1778i)q94+(1.671262.89470i)q95+(1.30320+11.4968i)q96+(6.0971310.5605i)q97+(0.44239312.8811i)q98+(3.09180+3.32321i)q99+O(q100)q+(0.920620 - 1.59456i) q^{2} +(-1.58800 - 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} +(-2.56469 + 1.89549i) q^{6} +(-2.54347 + 0.728536i) q^{7} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(1.22880 - 2.12835i) q^{10} +1.51302 q^{11} +(0.271199 + 2.39252i) q^{12} +(-2.58800 + 4.48254i) q^{13} +(-1.17987 + 4.72642i) q^{14} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(-1.25211 - 2.16872i) q^{19} +(-0.927765 - 1.60694i) q^{20} +(4.54285 + 0.602068i) q^{21} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(-1.78308 - 0.776526i) q^{24} -3.21843 q^{25} +(4.76513 + 8.25344i) q^{26} +(-1.72605 - 4.90110i) q^{27} +(2.64502 + 2.55574i) q^{28} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(1.92388 + 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(-2.40267 - 1.04635i) q^{33} +(-1.42597 - 2.46986i) q^{34} +(-3.39490 + 0.972416i) q^{35} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} -4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} +1.49873 q^{40} +(4.51188 - 7.81481i) q^{41} +(5.14228 - 6.68958i) q^{42} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(2.72753 + 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(4.75925 - 8.24327i) q^{47} +(-6.75252 + 4.99060i) q^{48} +(5.93847 - 3.70602i) q^{49} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} +7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(-9.40414 - 1.75975i) q^{54} +2.01950 q^{55} +(-2.85593 + 0.818036i) q^{56} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(4.22166 + 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(-1.61958 + 2.80520i) q^{61} +7.08467 q^{62} +(-6.79767 - 4.09777i) q^{63} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(-3.88042 + 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} -2.15327 q^{68} +(11.6889 + 5.09048i) q^{69} +(-1.57484 + 6.30861i) q^{70} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(-1.37936 + 2.38912i) q^{73} -1.03702 q^{74} +(5.11086 + 2.22576i) q^{75} +(-1.74064 + 3.01488i) q^{76} +(-3.84831 + 1.10229i) q^{77} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(-8.30746 - 14.3889i) q^{82} +(2.80111 + 4.85167i) q^{83} +(-2.43282 - 5.88772i) q^{84} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(0.0120840 + 0.106605i) q^{87} +1.69889 q^{88} +(0.703287 + 1.21813i) q^{89} +(7.18575 - 1.65025i) q^{90} +(3.31680 - 13.2867i) q^{91} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(-8.76293 - 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(1.30320 + 11.4968i) q^{96} +(-6.09713 - 10.5605i) q^{97} +(-0.442393 - 12.8811i) q^{98} +(3.09180 + 3.32321i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+2q2+2q34q48q52q6q76q84q97q108q11+22q128q13+16q1419q15+2q16+12q172q18+q19+5q20++35q99+O(q100) 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 7 q^{10} - 8 q^{11} + 22 q^{12} - 8 q^{13} + 16 q^{14} - 19 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + q^{19} + 5 q^{20}+ \cdots + 35 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/63Z)×\left(\mathbb{Z}/63\mathbb{Z}\right)^\times.

nn 1010 2929
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.920620 1.59456i 0.650977 1.12753i −0.331909 0.943311i 0.607693π-0.607693\pi
0.982886 0.184214i 0.0589739π-0.0589739\pi
33 −1.58800 0.691567i −0.916831 0.399277i
44 −0.695084 1.20392i −0.347542 0.601960i
55 1.33475 0.596920 0.298460 0.954422i 0.403527π-0.403527\pi
0.298460 + 0.954422i 0.403527π0.403527\pi
66 −2.56469 + 1.89549i −1.04703 + 0.773830i
77 −2.54347 + 0.728536i −0.961341 + 0.275361i
88 1.12285 0.396987
99 2.04347 + 2.19641i 0.681156 + 0.732138i
1010 1.22880 2.12835i 0.388581 0.673042i
1111 1.51302 0.456192 0.228096 0.973639i 0.426750π-0.426750\pi
0.228096 + 0.973639i 0.426750π0.426750\pi
1212 0.271199 + 2.39252i 0.0782884 + 0.690661i
1313 −2.58800 + 4.48254i −0.717781 + 1.24323i 0.244096 + 0.969751i 0.421509π0.421509\pi
−0.961877 + 0.273482i 0.911824π0.911824\pi
1414 −1.17987 + 4.72642i −0.315335 + 1.26319i
1515 −2.11958 0.923072i −0.547274 0.238336i
1616 2.42388 4.19829i 0.605971 1.04957i
1717 0.774463 1.34141i 0.187835 0.325340i −0.756693 0.653770i 0.773186π-0.773186\pi
0.944528 + 0.328430i 0.106520π0.106520\pi
1818 5.38358 1.23637i 1.26892 0.291416i
1919 −1.25211 2.16872i −0.287254 0.497538i 0.685900 0.727696i 0.259409π-0.259409\pi
−0.973153 + 0.230158i 0.926076π0.926076\pi
2020 −0.927765 1.60694i −0.207455 0.359322i
2121 4.54285 + 0.602068i 0.991332 + 0.131382i
2222 1.39291 2.41260i 0.296970 0.514367i
2323 −7.36079 −1.53483 −0.767415 0.641151i 0.778457π-0.778457\pi
−0.767415 + 0.641151i 0.778457π0.778457\pi
2424 −1.78308 0.776526i −0.363970 0.158508i
2525 −3.21843 −0.643687
2626 4.76513 + 8.25344i 0.934518 + 1.61863i
2727 −1.72605 4.90110i −0.332179 0.943216i
2828 2.64502 + 2.55574i 0.499862 + 0.482990i
2929 −0.0309713 0.0536439i −0.00575123 0.00996143i 0.863135 0.504972i 0.168497π-0.168497\pi
−0.868887 + 0.495011i 0.835164π0.835164\pi
3030 −3.42323 + 2.53001i −0.624993 + 0.461914i
3131 1.92388 + 3.33227i 0.345540 + 0.598493i 0.985452 0.169956i 0.0543625π-0.0543625\pi
−0.639912 + 0.768448i 0.721029π0.721029\pi
3232 −3.34011 5.78523i −0.590453 1.02269i
3333 −2.40267 1.04635i −0.418250 0.182147i
3434 −1.42597 2.46986i −0.244552 0.423577i
3535 −3.39490 + 0.972416i −0.573844 + 0.164368i
3636 1.22392 3.98687i 0.203987 0.664478i
3737 −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i 0.181408π-0.181408\pi
−0.888245 + 0.459370i 0.848075π0.848075\pi
3838 −4.61087 −0.747982
3939 7.20971 5.32849i 1.15448 0.853241i
4040 1.49873 0.236969
4141 4.51188 7.81481i 0.704638 1.22047i −0.262185 0.965018i 0.584443π-0.584443\pi
0.966822 0.255450i 0.0822237π-0.0822237\pi
4242 5.14228 6.68958i 0.793471 1.03222i
4343 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i 0.116959π0.116959\pi
−0.155526 + 0.987832i 0.549707π0.549707\pi
4444 −1.05167 1.82155i −0.158546 0.274609i
4545 2.72753 + 2.93167i 0.406596 + 0.437028i
4646 −6.77649 + 11.7372i −0.999139 + 1.73056i
4747 4.75925 8.24327i 0.694209 1.20240i −0.276238 0.961089i 0.589088π-0.589088\pi
0.970447 0.241315i 0.0775788π-0.0775788\pi
4848 −6.75252 + 4.99060i −0.974643 + 0.720330i
4949 5.93847 3.70602i 0.848353 0.529431i
5050 −2.96296 + 5.13199i −0.419025 + 0.725773i
5151 −2.15752 + 1.59456i −0.302113 + 0.223283i
5252 7.19550 0.997836
5353 0.755374 1.30835i 0.103759 0.179715i −0.809472 0.587159i 0.800246π-0.800246\pi
0.913230 + 0.407444i 0.133580π0.133580\pi
5454 −9.40414 1.75975i −1.27974 0.239471i
5555 2.01950 0.272310
5656 −2.85593 + 0.818036i −0.381640 + 0.109315i
5757 0.488532 + 4.30983i 0.0647077 + 0.570851i
5858 −0.114051 −0.0149757
5959 4.22166 + 7.31212i 0.549613 + 0.951957i 0.998301 + 0.0582689i 0.0185581π0.0185581\pi
−0.448688 + 0.893688i 0.648109π0.648109\pi
6060 0.361984 + 3.19342i 0.0467319 + 0.412269i
6161 −1.61958 + 2.80520i −0.207367 + 0.359169i −0.950884 0.309547i 0.899823π-0.899823\pi
0.743518 + 0.668716i 0.233156π0.233156\pi
6262 7.08467 0.899754
6363 −6.79767 4.09777i −0.856426 0.516271i
6464 −2.60434 −0.325543
6565 −3.45434 + 5.98309i −0.428458 + 0.742111i
6666 −3.88042 + 2.86790i −0.477646 + 0.353014i
6767 −3.46670 6.00449i −0.423524 0.733566i 0.572757 0.819725i 0.305874π-0.305874\pi
−0.996281 + 0.0861595i 0.972541π0.972541\pi
6868 −2.15327 −0.261122
6969 11.6889 + 5.09048i 1.40718 + 0.612822i
7070 −1.57484 + 6.30861i −0.188230 + 0.754023i
7171 −12.3304 −1.46335 −0.731673 0.681656i 0.761260π-0.761260\pi
−0.731673 + 0.681656i 0.761260π0.761260\pi
7272 2.29451 + 2.46624i 0.270410 + 0.290649i
7373 −1.37936 + 2.38912i −0.161442 + 0.279625i −0.935386 0.353629i 0.884948π-0.884948\pi
0.773944 + 0.633254i 0.218281π0.218281\pi
7474 −1.03702 −0.120551
7575 5.11086 + 2.22576i 0.590152 + 0.257009i
7676 −1.74064 + 3.01488i −0.199665 + 0.345830i
7777 −3.84831 + 1.10229i −0.438556 + 0.125617i
7878 −1.85920 16.4018i −0.210512 1.85714i
7979 2.95969 5.12633i 0.332991 0.576758i −0.650106 0.759844i 0.725275π-0.725275\pi
0.983097 + 0.183086i 0.0586087π0.0586087\pi
8080 3.23529 5.60368i 0.361716 0.626511i
8181 −0.648467 + 8.97661i −0.0720519 + 0.997401i
8282 −8.30746 14.3889i −0.917406 1.58899i
8383 2.80111 + 4.85167i 0.307462 + 0.532540i 0.977806 0.209510i 0.0671870π-0.0671870\pi
−0.670344 + 0.742050i 0.733854π0.733854\pi
8484 −2.43282 5.88772i −0.265443 0.642403i
8585 1.03372 1.79045i 0.112122 0.194202i
8686 18.7802 2.02512
8787 0.0120840 + 0.106605i 0.00129554 + 0.0114293i
8888 1.69889 0.181102
8989 0.703287 + 1.21813i 0.0745483 + 0.129121i 0.900890 0.434048i 0.142915π-0.142915\pi
−0.826341 + 0.563169i 0.809582π0.809582\pi
9090 7.18575 1.65025i 0.757444 0.173952i
9191 3.31680 13.2867i 0.347695 1.39282i
9292 5.11636 + 8.86180i 0.533418 + 0.923906i
9393 −0.750637 6.62212i −0.0778374 0.686682i
9494 −8.76293 15.1778i −0.903827 1.56548i
9595 −1.67126 2.89470i −0.171467 0.296990i
9696 1.30320 + 11.4968i 0.133007 + 1.17339i
9797 −6.09713 10.5605i −0.619070 1.07226i −0.989656 0.143462i 0.954176π-0.954176\pi
0.370586 0.928798i 0.379157π-0.379157\pi
9898 −0.442393 12.8811i −0.0446885 1.30119i
9999 3.09180 + 3.32321i 0.310738 + 0.333995i
100100 2.23708 + 3.87474i 0.223708 + 0.387474i
101101 1.11867 0.111312 0.0556560 0.998450i 0.482275π-0.482275\pi
0.0556560 + 0.998450i 0.482275π0.482275\pi
102102 0.556368 + 4.90828i 0.0550886 + 0.485993i
103103 1.93045 0.190213 0.0951063 0.995467i 0.469681π-0.469681\pi
0.0951063 + 0.995467i 0.469681π0.469681\pi
104104 −2.90593 + 5.03322i −0.284950 + 0.493548i
105105 6.06359 + 0.803612i 0.591746 + 0.0784245i
106106 −1.39082 2.40898i −0.135089 0.233981i
107107 2.88969 + 5.00509i 0.279357 + 0.483860i 0.971225 0.238163i 0.0765454π-0.0765454\pi
−0.691868 + 0.722024i 0.743212π0.743212\pi
108108 −4.70077 + 5.48470i −0.452332 + 0.527766i
109109 −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i 0.962494π-0.962494\pi
0.598340 + 0.801242i 0.295827π0.295827\pi
110110 1.85920 3.22022i 0.177267 0.307036i
111111 0.109874 + 0.969312i 0.0104288 + 0.0920030i
112112 −3.10647 + 12.4441i −0.293534 + 1.17586i
113113 7.25105 12.5592i 0.682121 1.18147i −0.292211 0.956354i 0.594391π-0.594391\pi
0.974332 0.225115i 0.0722758π-0.0722758\pi
114114 7.32205 + 3.18873i 0.685773 + 0.298652i
115115 −9.82483 −0.916170
116116 −0.0430553 + 0.0745740i −0.00399759 + 0.00692403i
117117 −15.1340 + 3.47562i −1.39914 + 0.321322i
118118 15.5462 1.43114
119119 −0.992558 + 3.97606i −0.0909877 + 0.364485i
120120 −2.37997 1.03647i −0.217261 0.0946164i
121121 −8.71078 −0.791889
122122 2.98204 + 5.16505i 0.269982 + 0.467622i
123123 −12.5693 + 9.28962i −1.13334 + 0.837617i
124124 2.67452 4.63241i 0.240179 0.416002i
125125 −10.9696 −0.981149
126126 −12.7922 + 7.06681i −1.13962 + 0.629561i
127127 8.50004 0.754257 0.377128 0.926161i 0.376912π-0.376912\pi
0.377128 + 0.926161i 0.376912π0.376912\pi
128128 4.28260 7.41769i 0.378532 0.655637i
129129 −1.98981 17.5541i −0.175193 1.54555i
130130 6.36027 + 11.0163i 0.557832 + 0.966194i
131131 −2.01346 −0.175917 −0.0879585 0.996124i 0.528034π-0.528034\pi
−0.0879585 + 0.996124i 0.528034π0.528034\pi
132132 0.410328 + 3.61992i 0.0357145 + 0.315074i
133133 4.76469 + 4.60386i 0.413151 + 0.399205i
134134 −12.7660 −1.10282
135135 −2.30386 6.54175i −0.198285 0.563024i
136136 0.869605 1.50620i 0.0745680 0.129156i
137137 2.21740 0.189445 0.0947225 0.995504i 0.469804π-0.469804\pi
0.0947225 + 0.995504i 0.469804π0.469804\pi
138138 18.8781 13.9523i 1.60701 1.18770i
139139 0.377669 0.654143i 0.0320335 0.0554836i −0.849564 0.527485i 0.823135π-0.823135\pi
0.881598 + 0.472002i 0.156468π0.156468\pi
140140 3.53045 + 3.41128i 0.298378 + 0.288306i
141141 −13.2585 + 9.79894i −1.11656 + 0.825220i
142142 −11.3516 + 19.6615i −0.952604 + 1.64996i
143143 −3.91568 + 6.78216i −0.327446 + 0.567153i
144144 14.1743 3.25523i 1.18119 0.271269i
145145 −0.0413391 0.0716014i −0.00343303 0.00594618i
146146 2.53973 + 4.39894i 0.210189 + 0.364059i
147147 −11.9932 + 1.77829i −0.989185 + 0.146671i
148148 −0.391482 + 0.678068i −0.0321797 + 0.0557368i
149149 6.58499 0.539463 0.269732 0.962936i 0.413065π-0.413065\pi
0.269732 + 0.962936i 0.413065π0.413065\pi
150150 8.25428 6.10050i 0.673959 0.498104i
151151 12.6671 1.03083 0.515417 0.856939i 0.327637π-0.327637\pi
0.515417 + 0.856939i 0.327637π0.327637\pi
152152 −1.40593 2.43514i −0.114036 0.197516i
153153 4.52888 1.04009i 0.366138 0.0840861i
154154 −1.78517 + 7.15115i −0.143853 + 0.576256i
155155 2.56791 + 4.44775i 0.206260 + 0.357252i
156156 −11.4264 4.97617i −0.914846 0.398413i
157157 8.65372 + 14.9887i 0.690642 + 1.19623i 0.971628 + 0.236515i 0.0760052π0.0760052\pi
−0.280986 + 0.959712i 0.590662π0.590662\pi
158158 −5.44950 9.43882i −0.433539 0.750912i
159159 −2.10434 + 1.55526i −0.166885 + 0.123340i
160160 −4.45822 7.72186i −0.352453 0.610467i
161161 18.7219 5.36260i 1.47549 0.422632i
162162 13.7168 + 9.29807i 1.07769 + 0.730525i
163163 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i 0.00783167π-0.00783167\pi
−0.521154 + 0.853463i 0.674498π0.674498\pi
164164 −12.5445 −0.979564
165165 −3.20697 1.39662i −0.249662 0.108727i
166166 10.3150 0.800602
167167 1.76248 3.05270i 0.136385 0.236225i −0.789741 0.613440i 0.789785π-0.789785\pi
0.926126 + 0.377215i 0.123118π0.123118\pi
168168 5.10094 + 0.676031i 0.393546 + 0.0521569i
169169 −6.89546 11.9433i −0.530420 0.918714i
170170 −1.90332 3.29665i −0.145978 0.252842i
171171 2.20475 7.18186i 0.168602 0.549210i
172172 7.08968 12.2797i 0.540583 0.936318i
173173 −5.07046 + 8.78229i −0.385500 + 0.667705i −0.991838 0.127502i 0.959304π-0.959304\pi
0.606339 + 0.795206i 0.292638π0.292638\pi
174174 0.181113 + 0.0788742i 0.0137302 + 0.00597944i
175175 8.18599 2.34474i 0.618802 0.177246i
176176 3.66738 6.35208i 0.276439 0.478806i
177177 −1.64715 14.5312i −0.123808 1.09223i
178178 2.58984 0.194117
179179 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i 0.813083π-0.813083\pi
0.896061 + 0.443931i 0.146416π0.146416\pi
180180 1.63364 5.32148i 0.121764 0.396640i
181181 −16.9941 −1.26316 −0.631581 0.775310i 0.717594π-0.717594\pi
−0.631581 + 0.775310i 0.717594π0.717594\pi
182182 −18.1329 17.5208i −1.34410 1.29873i
183183 4.51188 3.33460i 0.333528 0.246501i
184184 −8.26505 −0.609308
185185 −0.375877 0.651039i −0.0276351 0.0478653i
186186 −11.2504 4.89953i −0.824922 0.359251i
187187 1.17178 2.02957i 0.0856887 0.148417i
188188 −13.2323 −0.965066
189189 7.96079 + 11.2083i 0.579062 + 0.815283i
190190 −6.15437 −0.446485
191191 −11.3470 + 19.6535i −0.821038 + 1.42208i 0.0838717 + 0.996477i 0.473271π0.473271\pi
−0.904910 + 0.425603i 0.860062π0.860062\pi
192192 4.13568 + 1.80108i 0.298467 + 0.129982i
193193 −3.09349 5.35808i −0.222674 0.385683i 0.732945 0.680288i 0.238145π-0.238145\pi
−0.955619 + 0.294605i 0.904812π0.904812\pi
194194 −22.4526 −1.61200
195195 9.62319 7.11222i 0.689131 0.509317i
196196 −8.58948 4.57345i −0.613534 0.326675i
197197 9.77010 0.696091 0.348045 0.937478i 0.386846π-0.386846\pi
0.348045 + 0.937478i 0.386846π0.386846\pi
198198 8.14544 1.87065i 0.578871 0.132942i
199199 −4.33973 + 7.51664i −0.307636 + 0.532840i −0.977845 0.209332i 0.932871π-0.932871\pi
0.670209 + 0.742172i 0.266204π0.266204\pi
200200 −3.61381 −0.255535
201201 1.35259 + 11.9326i 0.0954044 + 0.841659i
202202 1.02987 1.78379i 0.0724615 0.125507i
203203 0.117856 + 0.113878i 0.00827188 + 0.00799267i
204204 3.41938 + 1.48913i 0.239405 + 0.104260i
205205 6.02225 10.4308i 0.420612 0.728522i
206206 1.77721 3.07822i 0.123824 0.214470i
207207 −15.0415 16.1673i −1.04546 1.12371i
208208 12.5460 + 21.7303i 0.869909 + 1.50673i
209209 −1.89446 3.28130i −0.131043 0.226973i
210210 6.86367 8.92894i 0.473638 0.616156i
211211 −2.84219 + 4.92283i −0.195665 + 0.338901i −0.947118 0.320885i 0.896020π-0.896020\pi
0.751453 + 0.659786i 0.229353π0.229353\pi
212212 −2.10019 −0.144242
213213 19.5806 + 8.52728i 1.34164 + 0.584280i
214214 10.6412 0.727420
215215 6.80708 + 11.7902i 0.464239 + 0.804086i
216216 −1.93810 5.50319i −0.131871 0.374445i
217217 −7.32102 7.07390i −0.496983 0.480207i
218218 7.58786 + 13.1426i 0.513915 + 0.890126i
219219 3.84265 2.83999i 0.259662 0.191909i
220220 −1.40372 2.43132i −0.0946390 0.163920i
221221 4.00862 + 6.94313i 0.269649 + 0.467045i
222222 1.64678 + 0.717167i 0.110525 + 0.0481331i
223223 5.86133 + 10.1521i 0.392503 + 0.679836i 0.992779 0.119957i 0.0382758π-0.0382758\pi
−0.600276 + 0.799793i 0.704942π0.704942\pi
224224 12.7102 + 12.2812i 0.849236 + 0.820571i
225225 −6.57677 7.06901i −0.438451 0.471267i
226226 −13.3509 23.1245i −0.888091 1.53822i
227227 11.1831 0.742247 0.371123 0.928584i 0.378973π-0.378973\pi
0.371123 + 0.928584i 0.378973π0.378973\pi
228228 4.84913 3.58385i 0.321141 0.237346i
229229 −9.65647 −0.638118 −0.319059 0.947735i 0.603367π-0.603367\pi
−0.319059 + 0.947735i 0.603367π0.603367\pi
230230 −9.04494 + 15.6663i −0.596406 + 1.03301i
231231 6.87341 + 0.910938i 0.452237 + 0.0599353i
232232 −0.0347761 0.0602340i −0.00228317 0.00395456i
233233 −9.64492 16.7055i −0.631860 1.09441i −0.987171 0.159666i 0.948958π-0.948958\pi
0.355311 0.934748i 0.384375π-0.384375\pi
234234 −8.39058 + 27.3318i −0.548509 + 1.78674i
235235 6.35243 11.0027i 0.414387 0.717739i
236236 5.86881 10.1651i 0.382027 0.661690i
237237 −8.24519 + 6.09378i −0.535582 + 0.395833i
238238 5.42630 + 5.24314i 0.351735 + 0.339862i
239239 −0.194641 + 0.337128i −0.0125903 + 0.0218070i −0.872252 0.489057i 0.837341π-0.837341\pi
0.859662 + 0.510864i 0.170674π0.170674\pi
240240 −9.01295 + 6.66121i −0.581784 + 0.429979i
241241 10.6361 0.685134 0.342567 0.939493i 0.388704π-0.388704\pi
0.342567 + 0.939493i 0.388704π0.388704\pi
242242 −8.01932 + 13.8899i −0.515502 + 0.892875i
243243 7.23769 13.8064i 0.464298 0.885679i
244244 4.50299 0.288274
245245 7.92639 4.94662i 0.506399 0.316028i
246246 3.24130 + 28.5948i 0.206658 + 1.82314i
247247 12.9618 0.824741
248248 2.16023 + 3.74163i 0.137175 + 0.237594i
249249 −1.09290 9.64159i −0.0692599 0.611011i
250250 −10.0988 + 17.4917i −0.638705 + 1.10627i
251251 −3.26628 −0.206166 −0.103083 0.994673i 0.532871π-0.532871\pi
−0.103083 + 0.994673i 0.532871π0.532871\pi
252252 −0.208441 + 11.0321i −0.0131306 + 0.694960i
253253 −11.1370 −0.700176
254254 7.82531 13.5538i 0.491004 0.850443i
255255 −2.87976 + 2.12835i −0.180337 + 0.133282i
256256 −10.4896 18.1686i −0.655603 1.13554i
257257 −4.69573 −0.292912 −0.146456 0.989217i 0.546787π-0.546787\pi
−0.146456 + 0.989217i 0.546787π0.546787\pi
258258 −29.8229 12.9878i −1.85669 0.808584i
259259 1.07161 + 1.03544i 0.0665867 + 0.0643391i
260260 9.60421 0.595628
261261 0.0545353 0.177646i 0.00337565 0.0109960i
262262 −1.85363 + 3.21059i −0.114518 + 0.198351i
263263 19.5498 1.20549 0.602747 0.797932i 0.294073π-0.294073\pi
0.602747 + 0.797932i 0.294073π0.294073\pi
264264 −2.69783 1.17490i −0.166040 0.0723098i
265265 1.00824 1.74632i 0.0619355 0.107276i
266266 11.7276 3.35918i 0.719066 0.205965i
267267 −0.274400 2.42076i −0.0167930 0.148148i
268268 −4.81929 + 8.34725i −0.294385 + 0.509890i
269269 7.88365 13.6549i 0.480675 0.832553i −0.519079 0.854726i 0.673725π-0.673725\pi
0.999754 + 0.0221730i 0.00705846π0.00705846\pi
270270 −12.5522 2.34883i −0.763903 0.142945i
271271 7.39882 + 12.8151i 0.449446 + 0.778464i 0.998350 0.0574218i 0.0182880π-0.0182880\pi
−0.548904 + 0.835886i 0.684955π0.684955\pi
272272 −3.75442 6.50285i −0.227645 0.394293i
273273 −14.4557 + 18.8054i −0.874898 + 1.13815i
274274 2.04138 3.53578i 0.123324 0.213604i
275275 −4.86954 −0.293644
276276 −1.99624 17.6108i −0.120159 1.06005i
277277 −7.45122 −0.447701 −0.223850 0.974624i 0.571863π-0.571863\pi
−0.223850 + 0.974624i 0.571863π0.571863\pi
278278 −0.695380 1.20443i −0.0417061 0.0722371i
279279 −3.38764 + 11.0350i −0.202812 + 0.660650i
280280 −3.81196 + 1.09188i −0.227808 + 0.0652521i
281281 −12.9938 22.5060i −0.775146 1.34259i −0.934712 0.355406i 0.884343π-0.884343\pi
0.159566 0.987187i 0.448991π-0.448991\pi
282282 3.41901 + 30.1625i 0.203599 + 1.79615i
283283 −9.37768 16.2426i −0.557445 0.965524i −0.997709 0.0676550i 0.978448π-0.978448\pi
0.440263 0.897869i 0.354885π-0.354885\pi
284284 8.57064 + 14.8448i 0.508574 + 0.880876i
285285 0.652070 + 5.75257i 0.0386253 + 0.340753i
286286 7.20971 + 12.4876i 0.426319 + 0.738406i
287287 −5.78246 + 23.1638i −0.341328 + 1.36732i
288288 5.88136 19.1582i 0.346563 1.12891i
289289 7.30041 + 12.6447i 0.429436 + 0.743805i
290290 −0.152230 −0.00893928
291291 2.37890 + 20.9867i 0.139454 + 1.23026i
292292 3.83507 0.224431
293293 −1.23089 + 2.13196i −0.0719093 + 0.124551i −0.899738 0.436430i 0.856243π-0.856243\pi
0.827829 + 0.560981i 0.189576π0.189576\pi
294294 −8.20562 + 20.7611i −0.478562 + 1.21081i
295295 5.63487 + 9.75988i 0.328075 + 0.568242i
296296 −0.316203 0.547680i −0.0183790 0.0318333i
297297 −2.61155 7.41544i −0.151537 0.430287i
298298 6.06227 10.5002i 0.351178 0.608258i
299299 19.0497 32.9950i 1.10167 1.90815i
300300 −0.872835 7.70016i −0.0503932 0.444569i
301301 −19.4067 18.7517i −1.11858 1.08083i
302302 11.6616 20.1985i 0.671050 1.16229i
303303 −1.77645 0.773637i −0.102054 0.0444443i
304304 −12.1399 −0.696270
305305 −2.16175 + 3.74425i −0.123781 + 0.214395i
306306 2.51090 8.17911i 0.143538 0.467568i
307307 −4.66277 −0.266118 −0.133059 0.991108i 0.542480π-0.542480\pi
−0.133059 + 0.991108i 0.542480π0.542480\pi
308308 4.00196 + 3.86688i 0.228033 + 0.220336i
309309 −3.06555 1.33503i −0.174393 0.0759475i
310310 9.45629 0.537081
311311 −13.7410 23.8002i −0.779183 1.34958i −0.932413 0.361393i 0.882301π-0.882301\pi
0.153231 0.988190i 0.451032π-0.451032\pi
312312 8.09542 5.98309i 0.458313 0.338726i
313313 −2.74666 + 4.75735i −0.155250 + 0.268901i −0.933150 0.359487i 0.882952π-0.882952\pi
0.777900 + 0.628388i 0.216285π0.216285\pi
314314 31.8671 1.79837
315315 −9.07321 5.46951i −0.511217 0.308172i
316316 −8.22893 −0.462914
317317 −4.93879 + 8.55424i −0.277390 + 0.480454i −0.970735 0.240152i 0.922803π-0.922803\pi
0.693345 + 0.720606i 0.256136π0.256136\pi
318318 0.542654 + 4.78730i 0.0304305 + 0.268459i
319319 −0.0468601 0.0811641i −0.00262366 0.00454432i
320320 −3.47615 −0.194323
321321 −1.12746 9.94649i −0.0629288 0.555159i
322322 8.68480 34.7902i 0.483985 1.93878i
323323 −3.87885 −0.215825
324324 11.2579 5.45879i 0.625437 0.303266i
325325 8.32930 14.4268i 0.462026 0.800253i
326326 22.4986 1.24608
327327 11.4806 8.48494i 0.634876 0.469218i
328328 5.06616 8.77485i 0.279732 0.484510i
329329 −6.09950 + 24.4338i −0.336276 + 1.34708i
330330 −5.17940 + 3.82794i −0.285116 + 0.210721i
331331 10.3471 17.9217i 0.568729 0.985067i −0.427963 0.903796i 0.640769π-0.640769\pi
0.996692 0.0812710i 0.0258979π-0.0258979\pi
332332 3.89401 6.74463i 0.213712 0.370160i
333333 0.495864 1.61525i 0.0271732 0.0885152i
334334 −3.24514 5.62076i −0.177566 0.307554i
335335 −4.62718 8.01452i −0.252810 0.437880i
336336 13.5390 17.6129i 0.738613 0.960861i
337337 0.748747 1.29687i 0.0407869 0.0706449i −0.844911 0.534906i 0.820347π-0.820347\pi
0.885698 + 0.464261i 0.153680π0.153680\pi
338338 −25.3924 −1.38116
339339 −20.2002 + 14.9294i −1.09712 + 0.810852i
340340 −2.87408 −0.155869
341341 2.91087 + 5.04177i 0.157632 + 0.273027i
342342 −9.42217 10.1274i −0.509493 0.547626i
343343 −12.4044 + 13.7525i −0.669772 + 0.742567i
344344 5.72639 + 9.91840i 0.308746 + 0.534764i
345345 15.6018 + 6.79453i 0.839973 + 0.365805i
346346 9.33593 + 16.1703i 0.501903 + 0.869321i
347347 14.7694 + 25.5813i 0.792862 + 1.37328i 0.924188 + 0.381938i 0.124743π0.124743\pi
−0.131326 + 0.991339i 0.541923π0.541923\pi
348348 0.119945 0.0886477i 0.00642971 0.00475202i
349349 18.0006 + 31.1780i 0.963551 + 1.66892i 0.713458 + 0.700698i 0.247128π0.247128\pi
0.250094 + 0.968222i 0.419539π0.419539\pi
350350 3.79735 15.2117i 0.202977 0.813098i
351351 26.4364 + 4.94691i 1.41107 + 0.264046i
352352 −5.05363 8.75315i −0.269360 0.466545i
353353 −29.4930 −1.56975 −0.784877 0.619652i 0.787274π-0.787274\pi
−0.784877 + 0.619652i 0.787274π0.787274\pi
354354 −24.6873 10.7512i −1.31211 0.571421i
355355 −16.4580 −0.873500
356356 0.977687 1.69340i 0.0518173 0.0897502i
357357 4.32589 5.62755i 0.228950 0.297841i
358358 −1.56612 2.71260i −0.0827720 0.143365i
359359 2.70535 + 4.68580i 0.142783 + 0.247307i 0.928544 0.371224i 0.121062π-0.121062\pi
−0.785761 + 0.618531i 0.787728π0.787728\pi
360360 3.06260 + 3.29182i 0.161413 + 0.173494i
361361 6.36444 11.0235i 0.334971 0.580186i
362362 −15.6451 + 27.0981i −0.822289 + 1.42425i
363363 13.8327 + 6.02409i 0.726028 + 0.316183i
364364 −18.3015 + 5.24218i −0.959261 + 0.274765i
365365 −1.84110 + 3.18888i −0.0963676 + 0.166914i
366366 −1.16350 10.2644i −0.0608169 0.536527i
367367 −23.0843 −1.20499 −0.602496 0.798122i 0.705827π-0.705827\pi
−0.602496 + 0.798122i 0.705827π0.705827\pi
368368 −17.8417 + 30.9027i −0.930063 + 1.61092i
369369 26.3844 6.05936i 1.37352 0.315438i
370370 −1.38416 −0.0719591
371371 −0.968093 + 3.87805i −0.0502609 + 0.201339i
372372 −7.45075 + 5.50664i −0.386304 + 0.285506i
373373 21.5030 1.11338 0.556692 0.830719i 0.312070π-0.312070\pi
0.556692 + 0.830719i 0.312070π0.312070\pi
374374 −2.15752 3.73694i −0.111563 0.193232i
375375 17.4197 + 7.58620i 0.899548 + 0.391750i
376376 5.34392 9.25595i 0.275592 0.477339i
377377 0.320615 0.0165125
378378 25.2012 2.37539i 1.29621 0.122177i
379379 5.72168 0.293903 0.146952 0.989144i 0.453054π-0.453054\pi
0.146952 + 0.989144i 0.453054π0.453054\pi
380380 −2.32333 + 4.02412i −0.119184 + 0.206433i
381381 −13.4980 5.87835i −0.691526 0.301157i
382382 20.8925 + 36.1869i 1.06895 + 1.85148i
383383 −34.9209 −1.78437 −0.892187 0.451666i 0.850830π-0.850830\pi
−0.892187 + 0.451666i 0.850830π0.850830\pi
384384 −11.9306 + 8.81756i −0.608831 + 0.449969i
385385 −5.13654 + 1.47128i −0.261783 + 0.0749834i
386386 −11.3917 −0.579823
387387 −8.98003 + 29.2519i −0.456480 + 1.48696i
388388 −8.47603 + 14.6809i −0.430305 + 0.745311i
389389 −28.8822 −1.46438 −0.732192 0.681098i 0.761503π-0.761503\pi
−0.732192 + 0.681098i 0.761503π0.761503\pi
390390 −2.48157 21.8924i −0.125659 1.10857i
391391 −5.70066 + 9.87383i −0.288295 + 0.499341i
392392 6.66801 4.16130i 0.336785 0.210177i
393393 3.19737 + 1.39244i 0.161286 + 0.0702395i
394394 8.99455 15.5790i 0.453139 0.784860i
395395 3.95046 6.84239i 0.198769 0.344278i
396396 1.85182 6.03219i 0.0930574 0.303129i
397397 5.59226 + 9.68607i 0.280667 + 0.486130i 0.971549 0.236838i 0.0761109π-0.0761109\pi
−0.690882 + 0.722968i 0.742778π0.742778\pi
398398 7.99049 + 13.8399i 0.400527 + 0.693734i
399399 −4.38243 10.6060i −0.219396 0.530965i
400400 −7.80111 + 13.5119i −0.390056 + 0.675596i
401401 −1.08212 −0.0540386 −0.0270193 0.999635i 0.508602π-0.508602\pi
−0.0270193 + 0.999635i 0.508602π0.508602\pi
402402 20.2724 + 8.82858i 1.01110 + 0.440330i
403403 −19.9160 −0.992088
404404 −0.777570 1.34679i −0.0386856 0.0670054i
405405 −0.865544 + 11.9816i −0.0430092 + 0.595368i
406406 0.290086 0.0830905i 0.0143967 0.00412371i
407407 −0.426078 0.737988i −0.0211199 0.0365807i
408408 −2.42257 + 1.79045i −0.119935 + 0.0886405i
409409 10.8674 + 18.8229i 0.537360 + 0.930735i 0.999045 + 0.0436908i 0.0139116π0.0139116\pi
−0.461685 + 0.887044i 0.652755π0.652755\pi
410410 −11.0884 19.2057i −0.547618 0.948501i
411411 −3.52122 1.53348i −0.173689 0.0756410i
412412 −1.34182 2.32410i −0.0661069 0.114500i
413413 −16.0648 15.5225i −0.790497 0.763814i
414414 −39.6273 + 9.10068i −1.94758 + 0.447274i
415415 3.73879 + 6.47578i 0.183530 + 0.317884i
416416 34.5767 1.69526
417417 −1.05212 + 0.777593i −0.0515226 + 0.0380789i
418418 −6.97632 −0.341223
419419 12.5906 21.8075i 0.615090 1.06537i −0.375279 0.926912i 0.622453π-0.622453\pi
0.990369 0.138455i 0.0442135π-0.0442135\pi
420420 −3.24722 7.85865i −0.158448 0.383463i
421421 −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i 0.909527π-0.909527\pi
0.237090 0.971488i 0.423806π-0.423806\pi
422422 5.23316 + 9.06411i 0.254746 + 0.441234i
423423 27.8310 6.39158i 1.35319 0.310769i
424424 0.848171 1.46907i 0.0411908 0.0713446i
425425 −2.49256 + 4.31724i −0.120907 + 0.209417i
426426 31.6236 23.3721i 1.53217 1.13238i
427427 2.07567 8.31487i 0.100449 0.402385i
428428 4.01715 6.95791i 0.194176 0.336323i
429429 10.9084 8.06209i 0.526663 0.389241i
430430 25.0669 1.20884
431431 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i 0.795756π-0.795756\pi
0.918887 + 0.394520i 0.129089π0.129089\pi
432432 −24.7600 4.63321i −1.19127 0.222915i
433433 9.71430 0.466839 0.233420 0.972376i 0.425008π-0.425008\pi
0.233420 + 0.972376i 0.425008π0.425008\pi
434434 −18.0196 + 5.16144i −0.864970 + 0.247757i
435435 0.0161292 + 0.142292i 0.000773334 + 0.00682236i
436436 11.4579 0.548735
437437 9.21651 + 15.9635i 0.440885 + 0.763636i
438438 −0.990919 8.74189i −0.0473479 0.417704i
439439 7.41176 12.8375i 0.353744 0.612703i −0.633158 0.774022i 0.718242π-0.718242\pi
0.986902 + 0.161320i 0.0515751π0.0515751\pi
440440 2.26760 0.108103
441441 20.2750 + 5.47021i 0.965478 + 0.260486i
442442 14.7617 0.702141
443443 10.9510 18.9676i 0.520297 0.901180i −0.479425 0.877583i 0.659155π-0.659155\pi
0.999722 0.0235972i 0.00751192π-0.00751192\pi
444444 1.09060 0.806033i 0.0517577 0.0382526i
445445 0.938715 + 1.62590i 0.0444994 + 0.0770751i
446446 21.5842 1.02204
447447 −10.4569 4.55396i −0.494596 0.215395i
448448 6.62406 1.89736i 0.312957 0.0896416i
449449 21.4952 1.01442 0.507212 0.861822i 0.330676π-0.330676\pi
0.507212 + 0.861822i 0.330676π0.330676\pi
450450 −17.3267 + 3.97919i −0.816787 + 0.187581i
451451 6.82655 11.8239i 0.321450 0.556767i
452452 −20.1603 −0.948263
453453 −20.1153 8.76016i −0.945101 0.411588i
454454 10.2954 17.8321i 0.483185 0.836902i
455455 4.42711 17.7344i 0.207546 0.831402i
456456 0.548548 + 4.83929i 0.0256881 + 0.226621i
457457 −20.3128 + 35.1827i −0.950190 + 1.64578i −0.205181 + 0.978724i 0.565778π0.565778\pi
−0.745009 + 0.667054i 0.767555π0.767555\pi
458458 −8.88995 + 15.3978i −0.415400 + 0.719494i
459459 −7.91114 1.48037i −0.369261 0.0690978i
460460 6.82908 + 11.8283i 0.318408 + 0.551498i
461461 1.41541 + 2.45155i 0.0659220 + 0.114180i 0.897103 0.441822i 0.145668π-0.145668\pi
−0.831181 + 0.556003i 0.812334π0.812334\pi
462462 7.78035 10.1214i 0.361975 0.470892i
463463 −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i 0.390850π0.390850\pi
−0.983719 + 0.179711i 0.942484π0.942484\pi
464464 −0.300284 −0.0139403
465465 −1.00192 8.83890i −0.0464627 0.409894i
466466 −35.5173 −1.64531
467467 −13.3219 23.0742i −0.616464 1.06775i −0.990126 0.140182i 0.955231π-0.955231\pi
0.373661 0.927565i 0.378102π-0.378102\pi
468468 14.7038 + 15.8043i 0.679682 + 0.730554i
469469 13.1919 + 12.7466i 0.609146 + 0.588585i
470470 −11.6964 20.2587i −0.539513 0.934463i
471471 −3.37640 29.7866i −0.155576 1.37249i
472472 4.74028 + 8.21041i 0.218189 + 0.377915i
473473 7.71620 + 13.3648i 0.354791 + 0.614516i
474474 2.12622 + 18.7575i 0.0976604 + 0.861561i
475475 4.02983 + 6.97987i 0.184901 + 0.320258i
476476 5.47677 1.56873i 0.251027 0.0719027i
477477 4.41725 1.01445i 0.202252 0.0464485i
478478 0.358381 + 0.620734i 0.0163920 + 0.0283917i
479479 −31.5791 −1.44289 −0.721443 0.692474i 0.756521π-0.756521\pi
−0.721443 + 0.692474i 0.756521π0.756521\pi
480480 1.73945 + 15.3455i 0.0793947 + 0.700421i
481481 2.91520 0.132922
482482 9.79185 16.9600i 0.446007 0.772506i
483483 −33.4390 4.43169i −1.52153 0.201649i
484484 6.05472 + 10.4871i 0.275215 + 0.476686i
485485 −8.13817 14.0957i −0.369535 0.640054i
486486 −15.3519 24.2514i −0.696378 1.10006i
487487 −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i 0.835541π-0.835541\pi
0.862536 + 0.505996i 0.168875π0.168875\pi
488488 −1.81855 + 3.14982i −0.0823218 + 0.142586i
489489 −2.38378 21.0297i −0.107798 0.950996i
490490 −0.590486 17.1931i −0.0266754 0.776704i
491491 −9.06981 + 15.7094i −0.409315 + 0.708954i −0.994813 0.101720i 0.967566π-0.967566\pi
0.585498 + 0.810674i 0.300899π0.300899\pi
492492 19.9207 + 8.67539i 0.898094 + 0.391117i
493493 −0.0959447 −0.00432113
494494 11.9329 20.6684i 0.536887 0.929916i
495495 4.12679 + 4.43567i 0.185486 + 0.199368i
496496 18.6531 0.837549
497497 31.3619 8.98311i 1.40677 0.402948i
498498 −16.3803 7.13355i −0.734017 0.319662i
499499 −21.3091 −0.953928 −0.476964 0.878923i 0.658263π-0.658263\pi
−0.476964 + 0.878923i 0.658263π0.658263\pi
500500 7.62478 + 13.2065i 0.340990 + 0.590613i
501501 −4.90996 + 3.62881i −0.219361 + 0.162123i
502502 −3.00701 + 5.20829i −0.134209 + 0.232457i
503503 −17.0738 −0.761285 −0.380642 0.924722i 0.624297π-0.624297\pi
−0.380642 + 0.924722i 0.624297π0.624297\pi
504504 −7.63275 4.60118i −0.339990 0.204953i
505505 1.49315 0.0664443
506506 −10.2529 + 17.7586i −0.455799 + 0.789466i
507507 2.69038 + 23.7346i 0.119484 + 1.05409i
508508 −5.90824 10.2334i −0.262136 0.454032i
509509 36.7735 1.62996 0.814979 0.579490i 0.196748π-0.196748\pi
0.814979 + 0.579490i 0.196748π0.196748\pi
510510 0.742614 + 6.55135i 0.0328835 + 0.290099i
511511 1.76780 7.08155i 0.0782027 0.313270i
512512 −21.4975 −0.950065
513513 −8.46788 + 9.88003i −0.373866 + 0.436214i
514514 −4.32299 + 7.48764i −0.190679 + 0.330265i
515515 2.57667 0.113542
516516 −19.7506 + 14.5971i −0.869473 + 0.642603i
517517 7.20083 12.4722i 0.316692 0.548527i
518518 2.63762 0.755504i 0.115890 0.0331949i
519519 14.1254 10.4397i 0.620037 0.458251i
520520 −3.87870 + 6.71810i −0.170092 + 0.294608i
521521 −9.57535 + 16.5850i −0.419504 + 0.726602i −0.995890 0.0905758i 0.971129π-0.971129\pi
0.576386 + 0.817178i 0.304463π0.304463\pi
522522 −0.233061 0.250504i −0.0102008 0.0109643i
523523 −20.9715 36.3236i −0.917018 1.58832i −0.803920 0.594737i 0.797256π-0.797256\pi
−0.113097 0.993584i 0.536077π-0.536077\pi
524524 1.39952 + 2.42405i 0.0611385 + 0.105895i
525525 −14.6209 1.93771i −0.638107 0.0845688i
526526 17.9980 31.1734i 0.784749 1.35922i
527527 5.95991 0.259618
528528 −10.2167 + 7.55085i −0.444624 + 0.328609i
529529 31.1812 1.35570
530530 −1.85641 3.21539i −0.0806372 0.139668i
531531 −7.43362 + 24.2146i −0.322592 + 1.05082i
532532 2.23082 8.93637i 0.0967183 0.387441i
533533 23.3535 + 40.4494i 1.01155 + 1.75206i
534534 −4.11266 1.79105i −0.177972 0.0775063i
535535 3.85702 + 6.68056i 0.166754 + 0.288826i
536536 −3.89258 6.74214i −0.168134 0.291216i
537537 −2.36956 + 1.75128i −0.102254 + 0.0755732i
538538 −14.5157 25.1419i −0.625816 1.08395i
539539 8.98500 5.60726i 0.387011 0.241522i
540540 −6.27438 + 7.32073i −0.270006 + 0.315034i
541541 −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i 0.186423π-0.186423\pi
−0.895371 + 0.445320i 0.853090π0.853090\pi
542542 27.2460 1.17032
543543 26.9866 + 11.7526i 1.15811 + 0.504351i
544544 −10.3472 −0.443631
545545 −5.50059 + 9.52731i −0.235620 + 0.408105i
546546 16.6781 + 40.3631i 0.713758 + 1.72738i
547547 1.38738 + 2.40301i 0.0593201 + 0.102745i 0.894160 0.447747i 0.147773π-0.147773\pi
−0.834840 + 0.550492i 0.814440π0.814440\pi
548548 −1.54128 2.66957i −0.0658401 0.114038i
549549 −9.47096 + 2.17507i −0.404211 + 0.0928296i
550550 −4.48300 + 7.76478i −0.191156 + 0.331091i
551551 −0.0775590 + 0.134336i −0.00330413 + 0.00572291i
552552 13.1249 + 5.71584i 0.558632 + 0.243282i
553553 −3.79316 + 15.1949i −0.161302 + 0.646154i
554554 −6.85975 + 11.8814i −0.291443 + 0.504794i
555555 0.146655 + 1.29379i 0.00622516 + 0.0549184i
556556 −1.05005 −0.0445319
557557 15.5344 26.9064i 0.658214 1.14006i −0.322864 0.946445i 0.604646π-0.604646\pi
0.981078 0.193614i 0.0620211π-0.0620211\pi
558558 14.4773 + 15.5609i 0.612873 + 0.658744i
559559 −52.7939 −2.23294
560560 −4.14637 + 16.6098i −0.175216 + 0.701893i
561561 −3.26436 + 2.41260i −0.137822 + 0.101860i
562562 −47.8495 −2.01841
563563 −0.144020 0.249451i −0.00606973 0.0105131i 0.862975 0.505247i 0.168599π-0.168599\pi
−0.869044 + 0.494734i 0.835265π0.835265\pi
564564 21.0129 + 9.15104i 0.884802 + 0.385328i
565565 9.67836 16.7634i 0.407172 0.705242i
566566 −34.5331 −1.45154
567567 −4.89042 23.3042i −0.205378 0.978683i
568568 −13.8451 −0.580929
569569 8.04004 13.9258i 0.337056 0.583798i −0.646821 0.762641i 0.723902π-0.723902\pi
0.983878 + 0.178843i 0.0572354π0.0572354\pi
570570 9.77313 + 4.25616i 0.409351 + 0.178271i
571571 7.64289 + 13.2379i 0.319845 + 0.553988i 0.980456 0.196741i 0.0630358π-0.0630358\pi
−0.660610 + 0.750729i 0.729702π0.729702\pi
572572 10.8869 0.455204
573573 31.6107 23.3626i 1.32056 0.975985i
574574 31.6126 + 30.5456i 1.31949 + 1.27495i
575575 23.6902 0.987950
576576 −5.32189 5.72021i −0.221745 0.238342i
577577 12.0812 20.9253i 0.502949 0.871133i −0.497045 0.867725i 0.665582π-0.665582\pi
0.999994 0.00340833i 0.00108491π-0.00108491\pi
578578 26.8836 1.11821
579579 1.20698 + 10.6480i 0.0501603 + 0.442515i
580580 −0.0574683 + 0.0995380i −0.00238624 + 0.00413309i
581581 −10.6592 10.2994i −0.442216 0.427289i
582582 35.6546 + 15.5275i 1.47793 + 0.643634i
583583 1.14289 1.97955i 0.0473338 0.0819845i
584584 −1.54881 + 2.68262i −0.0640902 + 0.111007i
585585 −20.2002 + 4.63910i −0.835174 + 0.191803i
586586 2.26636 + 3.92546i 0.0936226 + 0.162159i
587587 18.0145 + 31.2020i 0.743537 + 1.28784i 0.950875 + 0.309574i 0.100186π0.100186\pi
−0.207339 + 0.978269i 0.566480π0.566480\pi
588588 10.4772 + 13.2028i 0.432073 + 0.544476i
589589 4.81783 8.34472i 0.198515 0.343838i
590590 20.7503 0.854276
591591 −15.5149 6.75668i −0.638197 0.277933i
592592 −2.73034 −0.112216
593593 12.4668 + 21.5932i 0.511951 + 0.886726i 0.999904 + 0.0138558i 0.00441057π0.00441057\pi
−0.487953 + 0.872870i 0.662256π0.662256\pi
594594 −14.2286 2.66253i −0.583807 0.109245i
595595 −1.32482 + 5.30706i −0.0543124 + 0.217568i
596596 −4.57712 7.92780i −0.187486 0.324735i
597597 12.0897 8.93518i 0.494800 0.365693i
598598 −35.0751 60.7518i −1.43433 2.48433i
599599 −19.7642 34.2325i −0.807542 1.39870i −0.914561 0.404447i 0.867464π-0.867464\pi
0.107019 0.994257i 0.465869π-0.465869\pi
600600 5.73873 + 2.49920i 0.234283 + 0.102029i
601601 1.86447 + 3.22936i 0.0760534 + 0.131728i 0.901544 0.432688i 0.142435π-0.142435\pi
−0.825490 + 0.564416i 0.809101π0.809101\pi
602602 −47.7669 + 13.6821i −1.94683 + 0.557639i
603603 6.10427 19.8843i 0.248585 0.809751i
604604 −8.80470 15.2502i −0.358258 0.620521i
605605 −11.6267 −0.472694
606606 −2.86904 + 2.12043i −0.116547 + 0.0861365i
607607 23.6528 0.960036 0.480018 0.877259i 0.340630π-0.340630\pi
0.480018 + 0.877259i 0.340630π0.340630\pi
608608 −8.36436 + 14.4875i −0.339219 + 0.587545i
609609 −0.108401 0.262343i −0.00439263 0.0106307i
610610 3.98029 + 6.89407i 0.161157 + 0.279133i
611611 24.6339 + 42.6671i 0.996580 + 1.72613i
612612 −4.40013 4.72947i −0.177865 0.191177i
613613 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i 0.808888π-0.808888\pi
0.901833 + 0.432084i 0.142222π0.142222\pi
614614 −4.29264 + 7.43507i −0.173237 + 0.300055i
615615 −16.7769 + 12.3994i −0.676512 + 0.499990i
616616 −4.32107 + 1.23770i −0.174101 + 0.0498684i
617617 −17.5615 + 30.4174i −0.706999 + 1.22456i 0.258966 + 0.965886i 0.416618π0.416618\pi
−0.965965 + 0.258672i 0.916715π0.916715\pi
618618 −4.95100 + 3.65914i −0.199158 + 0.147192i
619619 −21.1632 −0.850622 −0.425311 0.905047i 0.639835π-0.639835\pi
−0.425311 + 0.905047i 0.639835π0.639835\pi
620620 3.56983 6.18312i 0.143368 0.248320i
621621 12.7051 + 36.0759i 0.509839 + 1.44768i
622622 −50.6011 −2.02892
623623 −2.67624 2.58590i −0.107221 0.103602i
624624 −4.89504 43.1841i −0.195959 1.72875i
625625 1.45048 0.0580192
626626 5.05726 + 8.75943i 0.202129 + 0.350097i
627627 0.739157 + 6.52085i 0.0295191 + 0.260418i
628628 12.0301 20.8368i 0.480054 0.831477i
629629 −0.872381 −0.0347841
630630 −17.0745 + 9.43244i −0.680263 + 0.375798i
631631 4.74845 0.189033 0.0945164 0.995523i 0.469870π-0.469870\pi
0.0945164 + 0.995523i 0.469870π0.469870\pi
632632 3.32329 5.75610i 0.132193 0.228965i
633633 7.91786 5.85186i 0.314707 0.232591i
634634 9.09350 + 15.7504i 0.361149 + 0.625529i
635635 11.3455 0.450231
636636 3.33510 + 1.45242i 0.132245 + 0.0575924i
637637 1.24363 + 36.2106i 0.0492745 + 1.43472i
638638 −0.172562 −0.00683178
639639 −25.1967 27.0826i −0.996767 1.07137i
640640 5.71622 9.90078i 0.225953 0.391363i
641641 −9.87469 −0.390027 −0.195013 0.980801i 0.562475π-0.562475\pi
−0.195013 + 0.980801i 0.562475π0.562475\pi
642642 −16.8982 7.35913i −0.666921 0.290442i
643643 21.9748 38.0615i 0.866602 1.50100i 0.00115462 0.999999i 0.499632π-0.499632\pi
0.865448 0.501000i 0.167034π-0.167034\pi
644644 −19.4694 18.8123i −0.767204 0.741307i
645645 −2.65590 23.4304i −0.104576 0.922570i
646646 −3.57095 + 6.18507i −0.140497 + 0.243348i
647647 22.1936 38.4404i 0.872521 1.51125i 0.0131398 0.999914i 0.495817π-0.495817\pi
0.859381 0.511336i 0.170849π-0.170849\pi
648648 −0.728131 + 10.0794i −0.0286037 + 0.395955i
649649 6.38743 + 11.0634i 0.250729 + 0.434275i
650650 −15.3362 26.5631i −0.601537 1.04189i
651651 6.73368 + 16.2963i 0.263914 + 0.638703i
652652 8.49341 14.7110i 0.332628 0.576128i
653653 41.9912 1.64324 0.821622 0.570033i 0.193070π-0.193070\pi
0.821622 + 0.570033i 0.193070π0.193070\pi
654654 −2.96053 26.1179i −0.115766 1.02129i
655655 −2.68748 −0.105008
656656 −21.8726 37.8844i −0.853980 1.47914i
657657 −8.06616 + 1.85245i −0.314691 + 0.0722708i
658658 33.3459 + 32.2203i 1.29996 + 1.25608i
659659 −19.6365 34.0114i −0.764928 1.32489i −0.940284 0.340390i 0.889441π-0.889441\pi
0.175356 0.984505i 0.443892π-0.443892\pi
660660 0.547687 + 4.83170i 0.0213187 + 0.188074i
661661 0.0933694 + 0.161721i 0.00363165 + 0.00629020i 0.867836 0.496852i 0.165511π-0.165511\pi
−0.864204 + 0.503142i 0.832177π0.832177\pi
662662 −19.0515 32.9982i −0.740459 1.28251i
663663 −1.56403 13.7979i −0.0607419 0.535866i
664664 3.14522 + 5.44769i 0.122058 + 0.211411i
665665 6.35969 + 6.14502i 0.246618 + 0.238293i
666666 −2.11911 2.27772i −0.0821139 0.0882598i
667667 0.227973 + 0.394862i 0.00882717 + 0.0152891i
668668 −4.90028 −0.189597
669669 −2.28690 20.1750i −0.0884166 0.780012i
670670 −17.0395 −0.658294
671671 −2.45046 + 4.24432i −0.0945989 + 0.163850i
672672 −11.6905 28.2924i −0.450971 1.09140i
673673 −5.43382 9.41166i −0.209458 0.362793i 0.742086 0.670305i 0.233837π-0.233837\pi
−0.951544 + 0.307512i 0.900503π0.900503\pi
674674 −1.37862 2.38785i −0.0531026 0.0919764i
675675 5.55519 + 15.7738i 0.213819 + 0.607136i
676676 −9.58584 + 16.6032i −0.368686 + 0.638583i
677677 −14.1950 + 24.5865i −0.545560 + 0.944937i 0.453012 + 0.891505i 0.350350π0.350350\pi
−0.998571 + 0.0534326i 0.982984π0.982984\pi
678678 5.20910 + 45.9547i 0.200054 + 1.76488i
679679 23.2016 + 22.4184i 0.890396 + 0.860341i
680680 1.16071 2.01041i 0.0445111 0.0770956i
681681 −17.7587 7.73385i −0.680514 0.296362i
682682 10.7192 0.410460
683683 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i 0.760593π-0.760593\pi
0.956779 + 0.290816i 0.0939267π0.0939267\pi
684684 −10.1789 + 2.33764i −0.389199 + 0.0893821i
685685 2.95968 0.113083
686686 10.5095 + 32.4404i 0.401256 + 1.23858i
687687 15.3345 + 6.67810i 0.585046 + 0.254786i
688688 49.4461 1.88511
689689 3.90981 + 6.77199i 0.148952 + 0.257992i
690690 25.1976 18.6228i 0.959258 0.708960i
691691 −5.95416 + 10.3129i −0.226507 + 0.392321i −0.956770 0.290844i 0.906064π-0.906064\pi
0.730264 + 0.683165i 0.239397π0.239397\pi
692692 14.0976 0.535909
693693 −10.2850 6.19999i −0.390694 0.235518i
694694 54.3880 2.06454
695695 0.504096 0.873119i 0.0191214 0.0331193i
696696 0.0135685 + 0.119702i 0.000514313 + 0.00453727i
697697 −6.98857 12.1046i −0.264711 0.458493i
698698 66.2870 2.50900
699699 3.76313 + 33.1984i 0.142335 + 1.25568i
700700 −8.51283 8.22548i −0.321755 0.310894i
701701 −31.3902 −1.18559 −0.592795 0.805353i 0.701976π-0.701976\pi
−0.592795 + 0.805353i 0.701976π0.701976\pi
702702 32.2260 37.6002i 1.21629 1.41913i
703703 −0.705208 + 1.22146i −0.0265974 + 0.0460681i
704704 −3.94041 −0.148510
705705 −17.6968 + 13.0792i −0.666499 + 0.492590i
706706 −27.1518 + 47.0284i −1.02187 + 1.76994i
707707 −2.84531 + 0.814992i −0.107009 + 0.0306509i
708708 −16.3495 + 12.0834i −0.614451 + 0.454123i
709709 −0.312609 + 0.541455i −0.0117403 + 0.0203348i −0.871836 0.489798i 0.837070π-0.837070\pi
0.860096 + 0.510133i 0.170404π0.170404\pi
710710 −15.1516 + 26.2433i −0.568628 + 0.984893i
711711 17.3076 3.97480i 0.649085 0.149067i
712712 0.789685 + 1.36777i 0.0295947 + 0.0512595i
713713 −14.1613 24.5281i −0.530345 0.918584i
714714 −4.99097 12.0787i −0.186782 0.452035i
715715 −5.22647 + 9.05251i −0.195459 + 0.338545i
716716 −2.36489 −0.0883802
717717 0.542236 0.400751i 0.0202502 0.0149663i
718718 9.96239 0.371793
719719 12.1969 + 21.1257i 0.454869 + 0.787857i 0.998681 0.0513506i 0.0163526π-0.0163526\pi
−0.543811 + 0.839208i 0.683019π0.683019\pi
720720 18.9192 4.34492i 0.705078 0.161926i
721721 −4.91003 + 1.40640i −0.182859 + 0.0523771i
722722 −11.7185 20.2970i −0.436116 0.755376i
723723 −16.8902 7.35561i −0.628152 0.273558i
724724 11.8123 + 20.4595i 0.439002 + 0.760373i
725725 0.0996792 + 0.172649i 0.00370199 + 0.00641204i
726726 22.3404 16.5112i 0.829132 0.612787i
727727 −18.9253 32.7796i −0.701900 1.21573i −0.967799 0.251726i 0.919002π-0.919002\pi
0.265899 0.964001i 0.414331π-0.414331\pi
728728 3.72426 14.9189i 0.138030 0.552932i
729729 −21.0415 + 16.9191i −0.779314 + 0.626634i
730730 3.38991 + 5.87150i 0.125466 + 0.217314i
731731 15.7987 0.584335
732732 −7.15073 3.11412i −0.264299 0.115101i
733733 2.40155 0.0887033 0.0443516 0.999016i 0.485878π-0.485878\pi
0.0443516 + 0.999016i 0.485878π0.485878\pi
734734 −21.2519 + 36.8093i −0.784421 + 1.35866i
735735 −16.0080 + 2.37358i −0.590464 + 0.0875508i
736736 24.5858 + 42.5839i 0.906245 + 1.56966i
737737 −5.24517 9.08490i −0.193208 0.334646i
738738 14.6280 47.6500i 0.538465 1.75402i
739739 −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i 0.355451π0.355451\pi
−0.997587 + 0.0694277i 0.977883π0.977883\pi
740740 −0.522533 + 0.905053i −0.0192087 + 0.0332704i
741741 −20.5833 8.96397i −0.756148 0.329300i
742742 5.29255 + 5.11390i 0.194296 + 0.187737i
743743 −2.54785 + 4.41300i −0.0934715 + 0.161897i −0.908970 0.416862i 0.863130π-0.863130\pi
0.815498 + 0.578760i 0.196463π0.196463\pi
744744 −0.842852 7.43565i −0.0309004 0.272604i
745745 8.78934 0.322016
746746 19.7961 34.2879i 0.724787 1.25537i
747747 −4.93228 + 16.0666i −0.180463 + 0.587847i
748748 −3.25793 −0.119122
749749 −10.9962 10.6251i −0.401793 0.388231i
750750 28.1336 20.7927i 1.02729 0.759242i
751751 −0.975011 −0.0355787 −0.0177893 0.999842i 0.505663π-0.505663\pi
−0.0177893 + 0.999842i 0.505663π0.505663\pi
752752 −23.0718 39.9615i −0.841341 1.45724i
753753 5.18685 + 2.25885i 0.189019 + 0.0823172i
754754 0.295165 0.511240i 0.0107493 0.0186183i
755755 16.9075 0.615326
756756 7.96047 17.3749i 0.289520 0.631917i
757757 11.6346 0.422865 0.211433 0.977393i 0.432187π-0.432187\pi
0.211433 + 0.977393i 0.432187π0.432187\pi
758758 5.26750 9.12357i 0.191324 0.331383i
759759 17.6855 + 7.70198i 0.641943 + 0.279564i
760760 −1.87657 3.25031i −0.0680703 0.117901i
761761 −54.1749 −1.96384 −0.981920 0.189298i 0.939379π-0.939379\pi
−0.981920 + 0.189298i 0.939379π0.939379\pi
762762 −21.8000 + 16.1117i −0.789729 + 0.583666i
763763 5.28158 21.1573i 0.191206 0.765946i
764764 31.5484 1.14138
765765 6.04494 1.38826i 0.218555 0.0501927i
766766 −32.1489 + 55.6835i −1.16159 + 2.01193i
767767 −43.7025 −1.57801
768768 4.09272 + 36.1060i 0.147683 + 1.30286i
769769 −10.4326 + 18.0698i −0.376208 + 0.651612i −0.990507 0.137462i 0.956106π-0.956106\pi
0.614299 + 0.789074i 0.289439π0.289439\pi
770770 −2.38276 + 9.54503i −0.0858687 + 0.343979i
771771 7.45681 + 3.24742i 0.268551 + 0.116953i
772772 −4.30047 + 7.44863i −0.154777 + 0.268082i
773773 −27.4972 + 47.6266i −0.989007 + 1.71301i −0.366447 + 0.930439i 0.619426π0.619426\pi
−0.622561 + 0.782572i 0.713908π0.713908\pi
774774 38.3768 + 41.2491i 1.37942 + 1.48267i
775775 −6.19189 10.7247i −0.222419 0.385242i
776776 −6.84616 11.8579i −0.245763 0.425674i
777777 −0.985640 2.38537i −0.0353596 0.0855746i
778778 −26.5895 + 46.0544i −0.953281 + 1.65113i
779779 −22.5975 −0.809639
780780 −15.2515 6.64196i −0.546090 0.237820i
781781 −18.6560 −0.667566
782782 10.4963 + 18.1801i 0.375346 + 0.650119i
783783 −0.209456 + 0.244386i −0.00748534 + 0.00873364i
784784 −1.16477 33.9144i −0.0415989 1.21123i
785785 11.5506 + 20.0062i 0.412258 + 0.714051i
786786 5.16390 3.81649i 0.184190 0.136130i
787787 −4.59475 7.95833i −0.163785 0.283684i 0.772438 0.635090i 0.219037π-0.219037\pi
−0.936223 + 0.351406i 0.885704π0.885704\pi
788788 −6.79103 11.7624i −0.241921 0.419019i
789789 −31.0451 13.5200i −1.10523 0.481325i
790790 −7.27374 12.5985i −0.258788 0.448234i
791791 −9.29301 + 37.2266i −0.330421 + 1.32362i
792792 3.47163 + 3.73146i 0.123359 + 0.132592i
793793 −8.38296 14.5197i −0.297688 0.515610i
794794 20.5934 0.730832
795795 −2.80878 + 2.07588i −0.0996170 + 0.0736241i
796796 12.0659 0.427665
797797 3.53774 6.12754i 0.125313 0.217049i −0.796542 0.604583i 0.793340π-0.793340\pi
0.921855 + 0.387534i 0.126673π0.126673\pi
798798 −20.9465 2.77605i −0.741498 0.0982713i
799799 −7.37174 12.7682i −0.260793 0.451707i
800800 10.7499 + 18.6194i 0.380067 + 0.658295i
801801 −1.23837 + 4.03392i −0.0437556 + 0.142532i
802802 −0.996224 + 1.72551i −0.0351779 + 0.0609299i
803803 −2.08699 + 3.61477i −0.0736483 + 0.127563i
804804 13.4257 9.92255i 0.473488 0.349941i
805805 24.9892 7.15774i 0.880752 0.252277i
806806 −18.3351 + 31.7573i −0.645827 + 1.11860i
807807 −21.9625 + 16.2318i −0.773116 + 0.571388i
808808 1.25610 0.0441894
809809 −2.97060 + 5.14522i −0.104441 + 0.180896i −0.913510 0.406817i 0.866639π-0.866639\pi
0.809069 + 0.587714i 0.199972π0.199972\pi
810810 18.3085 + 12.4106i 0.643295 + 0.436065i
811811 44.4139 1.55958 0.779791 0.626039i 0.215325π-0.215325\pi
0.779791 + 0.626039i 0.215325π0.215325\pi
812812 0.0551801 0.221044i 0.00193644 0.00775713i
813813 −2.88678 25.4672i −0.101244 0.893173i
814814 −1.56902 −0.0549942
815815 8.15485 + 14.1246i 0.285652 + 0.494764i
816816 1.46485 + 12.9229i 0.0512801 + 0.452393i
817817 12.7712 22.1204i 0.446808 0.773894i
818818 40.0191 1.39924
819819 35.9608 19.8658i 1.25657 0.694168i
820820 −16.7439 −0.584721
821821 −3.17761 + 5.50378i −0.110899 + 0.192083i −0.916133 0.400874i 0.868706π-0.868706\pi
0.805234 + 0.592958i 0.202040π0.202040\pi
822822 −5.68693 + 4.20305i −0.198355 + 0.146598i
823823 4.73216 + 8.19635i 0.164953 + 0.285707i 0.936639 0.350297i 0.113919π-0.113919\pi
−0.771686 + 0.636004i 0.780586π0.780586\pi
824824 2.16760 0.0755120
825825 7.73282 + 3.36762i 0.269222 + 0.117245i
826826 −39.5412 + 11.3259i −1.37581 + 0.394080i
827827 −4.86261 −0.169090 −0.0845448 0.996420i 0.526944π-0.526944\pi
−0.0845448 + 0.996420i 0.526944π0.526944\pi
828828 −9.00905 + 29.3465i −0.313086 + 1.01986i
829829 20.3926 35.3211i 0.708266 1.22675i −0.257234 0.966349i 0.582811π-0.582811\pi
0.965500 0.260403i 0.0838555π-0.0838555\pi
830830 13.7680 0.477896
831831 11.8325 + 5.15302i 0.410466 + 0.178756i
832832 6.74003 11.6741i 0.233668 0.404725i
833833 −0.372159 10.8361i −0.0128946 0.375449i
834834 0.271315 + 2.39354i 0.00939486 + 0.0828815i
835835 2.35247 4.07460i 0.0814107 0.141007i
836836 −2.63362 + 4.56156i −0.0910856 + 0.157765i
837837 13.0110 15.1808i 0.449727 0.524726i
838838 −23.1823 40.1529i −0.800818 1.38706i
839839 9.60171 + 16.6307i 0.331488 + 0.574154i 0.982804 0.184653i 0.0591161π-0.0591161\pi
−0.651316 + 0.758807i 0.725783π0.725783\pi
840840 6.80849 + 0.902334i 0.234915 + 0.0311335i
841841 14.4981 25.1114i 0.499934 0.865911i
842842 −54.6126 −1.88207
843843 5.06976 + 44.7255i 0.174612 + 1.54043i
844844 7.90225 0.272007
845845 −9.20374 15.9413i −0.316618 0.548399i
846846 15.4300 50.2625i 0.530496 1.72806i
847847 22.1556 6.34612i 0.761276 0.218055i
848848 −3.66188 6.34256i −0.125749 0.217804i
849849 3.65886 + 32.2785i 0.125572 + 1.10780i
850850 4.58940 + 7.94907i 0.157415 + 0.272651i
851851 2.07286 + 3.59029i 0.0710566 + 0.123074i
852852 −3.34398 29.5006i −0.114563 1.01068i
853853 −6.95055 12.0387i −0.237982 0.412198i 0.722153 0.691734i 0.243153π-0.243153\pi
−0.960135 + 0.279536i 0.909819π0.909819\pi
854854 −11.3477 10.9646i −0.388309 0.375202i
855855 2.94280 9.58601i 0.100642 0.327835i
856856 3.24469 + 5.61996i 0.110901 + 0.192086i
857857 56.9838 1.94653 0.973265 0.229686i 0.0737700π-0.0737700\pi
0.973265 + 0.229686i 0.0737700π0.0737700\pi
858858 −2.81299 24.8163i −0.0960340 0.847213i
859859 −20.1002 −0.685810 −0.342905 0.939370i 0.611411π-0.611411\pi
−0.342905 + 0.939370i 0.611411π0.611411\pi
860860 9.46298 16.3904i 0.322685 0.558907i
861861 25.2019 32.7851i 0.858877 1.11731i
862862 −4.50214 7.79794i −0.153344 0.265599i
863863 −3.08893 5.35018i −0.105148 0.182122i 0.808650 0.588289i 0.200198π-0.200198\pi
−0.913799 + 0.406167i 0.866865π0.866865\pi
864864 −22.5888 + 26.3558i −0.768486 + 0.896643i
865865 −6.76781 + 11.7222i −0.230112 + 0.398566i
866866 8.94318 15.4900i 0.303902 0.526373i
867867 −2.84838 25.1285i −0.0967361 0.853407i
868868 −3.42769 + 13.7309i −0.116343 + 0.466056i
869869 4.47806 7.75623i 0.151908 0.263112i
870870 0.241742 + 0.105278i 0.00819581 + 0.00356925i
871871 35.8872 1.21599
872872 −4.62732 + 8.01476i −0.156701 + 0.271414i
873873 10.7360 34.9720i 0.363359 1.18362i
874874 33.9396 1.14802
875875 27.9008 7.99173i 0.943219 0.270170i
876876 −6.09009 2.65221i −0.205765 0.0896099i
877877 −37.2574 −1.25809 −0.629046 0.777368i 0.716554π-0.716554\pi
−0.629046 + 0.777368i 0.716554π0.716554\pi
878878 −13.6468 23.6370i −0.460558 0.797710i
879879 3.42905 2.53431i 0.115659 0.0854801i
880880 4.89504 8.47846i 0.165012 0.285809i
881881 −11.7848 −0.397041 −0.198520 0.980097i 0.563614π-0.563614\pi
−0.198520 + 0.980097i 0.563614π0.563614\pi
882882 27.3882 27.2938i 0.922208 0.919030i
883883 −29.2308 −0.983693 −0.491847 0.870682i 0.663678π-0.663678\pi
−0.491847 + 0.870682i 0.663678π0.663678\pi
884884 5.57265 9.65211i 0.187428 0.324636i
885885 −2.19854 19.3956i −0.0739032 0.651974i
886886 −20.1634 34.9240i −0.677402 1.17329i
887887 28.5161 0.957479 0.478739 0.877957i 0.341094π-0.341094\pi
0.478739 + 0.877957i 0.341094π0.341094\pi
888888 0.123372 + 1.08839i 0.00414010 + 0.0365240i
889889 −21.6196 + 6.19258i −0.725098 + 0.207693i
890890 3.45680 0.115872
891891 −0.981141 + 13.5818i −0.0328695 + 0.455006i
892892 8.14822 14.1131i 0.272823 0.472543i
893893 −23.8364 −0.797656
894894 −16.8884 + 12.4818i −0.564834 + 0.417453i
895895 1.13531 1.96642i 0.0379493 0.0657301i
896896 −5.48862 + 21.9867i −0.183362 + 0.734524i
897897 −53.0691 + 39.2219i −1.77193 + 1.30958i
898898 19.7890 34.2755i 0.660366 1.14379i
899899 0.119171 0.206410i 0.00397456 0.00688414i
900900 −3.93912 + 12.8315i −0.131304 + 0.427715i
901901 −1.17002 2.02653i −0.0389790 0.0675135i
902902 −12.5693 21.7707i −0.418513 0.724885i
903903 17.8498 + 43.1986i 0.594004 + 1.43756i
904904 8.14183 14.1021i 0.270793 0.469028i
905905 −22.6829 −0.754006
906906 −32.4872 + 24.0104i −1.07931 + 0.797690i
907907 −7.89155 −0.262035 −0.131017 0.991380i 0.541824π-0.541824\pi
−0.131017 + 0.991380i 0.541824π0.541824\pi
908908 −7.77317 13.4635i −0.257962 0.446803i
909909 2.28597 + 2.45707i 0.0758209 + 0.0814957i
910910 −24.2029 23.3860i −0.802319 0.775237i
911911 −14.2206 24.6308i −0.471150 0.816055i 0.528306 0.849054i 0.322827π-0.322827\pi
−0.999455 + 0.0329991i 0.989494π0.989494\pi
912912 19.2781 + 8.39554i 0.638361 + 0.278004i
913913 4.23813 + 7.34065i 0.140262 + 0.242940i
914914 37.4007 + 64.7798i 1.23710 + 2.14273i
915915 6.02225 4.45087i 0.199089 0.147141i
916916 6.71206 + 11.6256i 0.221773 + 0.384121i
917917 5.12118 1.46688i 0.169116 0.0484406i
918918 −9.64370 + 11.2519i −0.318290 + 0.371369i
919919 3.99271 + 6.91558i 0.131707 + 0.228124i 0.924335 0.381582i 0.124621π-0.124621\pi
−0.792627 + 0.609706i 0.791287π0.791287\pi
920920 −11.0318 −0.363708
921921 7.40446 + 3.22462i 0.243985 + 0.106255i
922922 5.21221 0.171655
923923 31.9110 55.2714i 1.05036 1.81928i
924924 −3.68090 8.90821i −0.121093 0.293059i
925925 0.906337 + 1.56982i 0.0298002 + 0.0516154i
926926 25.6529 + 44.4322i 0.843008 + 1.46013i
927927 3.94481 + 4.24006i 0.129565 + 0.139262i
928928 −0.206895 + 0.358353i −0.00679167 + 0.0117635i
929929 −9.40031 + 16.2818i −0.308414 + 0.534189i −0.978016 0.208531i 0.933132π-0.933132\pi
0.669601 + 0.742721i 0.266465π0.266465\pi
930930 −15.0166 6.53966i −0.492412 0.214444i
931931 −15.4729 8.23853i −0.507104 0.270007i
932932 −13.4081 + 23.2234i −0.439196 + 0.760709i
933933 5.36130 + 47.2974i 0.175521 + 1.54845i
934934 −49.0577 −1.60522
935935 1.56403 2.70898i 0.0511493 0.0885932i
936936 −16.9932 + 3.90260i −0.555440 + 0.127561i
937937 48.5788 1.58700 0.793500 0.608570i 0.208256π-0.208256\pi
0.793500 + 0.608570i 0.208256π0.208256\pi
938938 32.4700 9.30052i 1.06018 0.303673i
939939 7.65172 5.65516i 0.249704 0.184549i
940940 −17.6619 −0.576067
941941 −10.2425 17.7406i −0.333898 0.578328i 0.649375 0.760468i 0.275031π-0.275031\pi
−0.983272 + 0.182141i 0.941697π0.941697\pi
942942 −50.6049 22.0383i −1.64880 0.718046i
943943 −33.2110 + 57.5231i −1.08150 + 1.87321i
944944 40.9312 1.33220
945945 10.6257 + 14.9603i 0.345654 + 0.486659i
946946 28.4148 0.923843
947947 7.42524 12.8609i 0.241288 0.417923i −0.719793 0.694188i 0.755764π-0.755764\pi
0.961081 + 0.276265i 0.0890969π0.0890969\pi
948948 13.0675 + 5.69086i 0.424413 + 0.184831i
949949 −7.13954 12.3661i −0.231759 0.401419i
950950 14.8398 0.481466
951951 13.7586 10.1686i 0.446154 0.329739i
952952 −1.11449 + 4.46451i −0.0361209 + 0.144696i
953953 46.4678 1.50524 0.752620 0.658456i 0.228790π-0.228790\pi
0.752620 + 0.658456i 0.228790π0.228790\pi
954954 2.44901 7.97750i 0.0792896 0.258281i
955955 −15.1454 + 26.2326i −0.490094 + 0.848868i
956956 0.541167 0.0175026
957957 0.0182833 + 0.161295i 0.000591015 + 0.00521394i
958958 −29.0724 + 50.3548i −0.939285 + 1.62689i
959959 −5.63988 + 1.61545i −0.182121 + 0.0521657i
960960 5.52012 + 2.40399i 0.178161 + 0.0775886i
961961 8.09733 14.0250i 0.261204 0.452419i
962962 2.68380 4.64847i 0.0865291 0.149873i
963963 −5.08826 + 16.5747i −0.163967 + 0.534112i
964964 −7.39301 12.8051i −0.238113 0.412423i
965965 −4.12905 7.15172i −0.132919 0.230222i
966966 −37.8512 + 49.2406i −1.21784 + 1.58429i
967967 0.863670 1.49592i 0.0277738 0.0481056i −0.851804 0.523860i 0.824492π-0.824492\pi
0.879578 + 0.475754i 0.157825π0.157825\pi
968968 −9.78089 −0.314370
969969 6.15960 + 2.68249i 0.197875 + 0.0861739i
970970 −29.9687 −0.962235
971971 −3.78085 6.54863i −0.121333 0.210156i 0.798960 0.601384i 0.205384π-0.205384\pi
−0.920294 + 0.391228i 0.872050π0.872050\pi
972972 −21.6526 + 0.882976i −0.694506 + 0.0283215i
973973 −0.484024 + 1.93894i −0.0155171 + 0.0621595i
974974 0.281870 + 0.488213i 0.00903169 + 0.0156434i
975975 −23.2040 + 17.1494i −0.743122 + 0.549220i
976976 7.85137 + 13.5990i 0.251316 + 0.435293i
977977 28.3101 + 49.0345i 0.905721 + 1.56875i 0.819947 + 0.572440i 0.194003π0.194003\pi
0.0857737 + 0.996315i 0.472664π0.472664\pi
978978 −35.7277 15.5593i −1.14245 0.497531i
979979 1.06408 + 1.84305i 0.0340083 + 0.0589041i
980980 −11.4648 6.10443i −0.366231 0.194999i
981981 −24.0990 + 5.53449i −0.769422 + 0.176703i
982982 16.6997 + 28.9247i 0.532909 + 0.923025i
983983 32.2972 1.03012 0.515061 0.857154i 0.327769π-0.327769\pi
0.515061 + 0.857154i 0.327769π0.327769\pi
984984 −14.1134 + 10.4308i −0.449920 + 0.332523i
985985 13.0407 0.415510
986986 −0.0883286 + 0.152990i −0.00281296 + 0.00487218i
987987 26.5836 34.5826i 0.846165 1.10078i
988988 −9.00955 15.6050i −0.286632 0.496461i
989989 −37.5391 65.0197i −1.19367 2.06750i
990990 10.8721 2.49686i 0.345540 0.0793554i
991991 −7.15502 + 12.3929i −0.227287 + 0.393672i −0.957003 0.290078i 0.906319π-0.906319\pi
0.729716 + 0.683750i 0.239652π0.239652\pi
992992 12.8520 22.2602i 0.408050 0.706764i
993993 −28.8253 + 21.3039i −0.914742 + 0.676059i
994994 14.5483 58.2785i 0.461444 1.84848i
995995 −5.79247 + 10.0329i −0.183634 + 0.318063i
996996 −10.8480 + 8.01748i −0.343734 + 0.254044i
997997 56.2524 1.78153 0.890765 0.454463i 0.150169π-0.150169\pi
0.890765 + 0.454463i 0.150169π0.150169\pi
998998 −19.6176 + 33.9787i −0.620985 + 1.07558i
999999 −1.90449 + 2.22209i −0.0602553 + 0.0703038i
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 63.2.g.b.4.4 10
3.2 odd 2 189.2.g.b.172.2 10
4.3 odd 2 1008.2.t.i.193.5 10
7.2 even 3 63.2.h.b.58.2 yes 10
7.3 odd 6 441.2.f.f.148.4 10
7.4 even 3 441.2.f.e.148.4 10
7.5 odd 6 441.2.h.f.373.2 10
7.6 odd 2 441.2.g.f.67.4 10
9.2 odd 6 189.2.h.b.46.4 10
9.4 even 3 567.2.e.f.487.4 10
9.5 odd 6 567.2.e.e.487.2 10
9.7 even 3 63.2.h.b.25.2 yes 10
12.11 even 2 3024.2.t.i.1873.2 10
21.2 odd 6 189.2.h.b.37.4 10
21.5 even 6 1323.2.h.f.226.4 10
21.11 odd 6 1323.2.f.e.442.2 10
21.17 even 6 1323.2.f.f.442.2 10
21.20 even 2 1323.2.g.f.361.2 10
28.23 odd 6 1008.2.q.i.625.2 10
36.7 odd 6 1008.2.q.i.529.2 10
36.11 even 6 3024.2.q.i.2881.4 10
63.2 odd 6 189.2.g.b.100.2 10
63.4 even 3 3969.2.a.z.1.2 5
63.11 odd 6 1323.2.f.e.883.2 10
63.16 even 3 inner 63.2.g.b.16.4 yes 10
63.20 even 6 1323.2.h.f.802.4 10
63.23 odd 6 567.2.e.e.163.2 10
63.25 even 3 441.2.f.e.295.4 10
63.31 odd 6 3969.2.a.ba.1.2 5
63.32 odd 6 3969.2.a.bc.1.4 5
63.34 odd 6 441.2.h.f.214.2 10
63.38 even 6 1323.2.f.f.883.2 10
63.47 even 6 1323.2.g.f.667.2 10
63.52 odd 6 441.2.f.f.295.4 10
63.58 even 3 567.2.e.f.163.4 10
63.59 even 6 3969.2.a.bb.1.4 5
63.61 odd 6 441.2.g.f.79.4 10
84.23 even 6 3024.2.q.i.2305.4 10
252.79 odd 6 1008.2.t.i.961.5 10
252.191 even 6 3024.2.t.i.289.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.4 10 1.1 even 1 trivial
63.2.g.b.16.4 yes 10 63.16 even 3 inner
63.2.h.b.25.2 yes 10 9.7 even 3
63.2.h.b.58.2 yes 10 7.2 even 3
189.2.g.b.100.2 10 63.2 odd 6
189.2.g.b.172.2 10 3.2 odd 2
189.2.h.b.37.4 10 21.2 odd 6
189.2.h.b.46.4 10 9.2 odd 6
441.2.f.e.148.4 10 7.4 even 3
441.2.f.e.295.4 10 63.25 even 3
441.2.f.f.148.4 10 7.3 odd 6
441.2.f.f.295.4 10 63.52 odd 6
441.2.g.f.67.4 10 7.6 odd 2
441.2.g.f.79.4 10 63.61 odd 6
441.2.h.f.214.2 10 63.34 odd 6
441.2.h.f.373.2 10 7.5 odd 6
567.2.e.e.163.2 10 63.23 odd 6
567.2.e.e.487.2 10 9.5 odd 6
567.2.e.f.163.4 10 63.58 even 3
567.2.e.f.487.4 10 9.4 even 3
1008.2.q.i.529.2 10 36.7 odd 6
1008.2.q.i.625.2 10 28.23 odd 6
1008.2.t.i.193.5 10 4.3 odd 2
1008.2.t.i.961.5 10 252.79 odd 6
1323.2.f.e.442.2 10 21.11 odd 6
1323.2.f.e.883.2 10 63.11 odd 6
1323.2.f.f.442.2 10 21.17 even 6
1323.2.f.f.883.2 10 63.38 even 6
1323.2.g.f.361.2 10 21.20 even 2
1323.2.g.f.667.2 10 63.47 even 6
1323.2.h.f.226.4 10 21.5 even 6
1323.2.h.f.802.4 10 63.20 even 6
3024.2.q.i.2305.4 10 84.23 even 6
3024.2.q.i.2881.4 10 36.11 even 6
3024.2.t.i.289.2 10 252.191 even 6
3024.2.t.i.1873.2 10 12.11 even 2
3969.2.a.z.1.2 5 63.4 even 3
3969.2.a.ba.1.2 5 63.31 odd 6
3969.2.a.bb.1.4 5 63.59 even 6
3969.2.a.bc.1.4 5 63.32 odd 6