Properties

Label 370.2.m.a.249.1
Level 370370
Weight 22
Character 370.249
Analytic conductor 2.9542.954
Analytic rank 11
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [370,2,Mod(159,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) 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("370.159"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 370=2537 370 = 2 \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 370.m (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.954464874792.95446487479
Analytic rank: 11
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(3,11)\Q(\sqrt{-3}, \sqrt{-11})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x32x23x+9 x^{4} - x^{3} - 2x^{2} - 3x + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 249.1
Root 1.18614+1.26217i-1.18614 + 1.26217i of defining polynomial
Character χ\chi == 370.249
Dual form 370.2.m.a.159.1

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+(0.500000+0.866025i)q2+(2.18614+1.26217i)q3+(0.5000000.866025i)q4+(1.50000+1.65831i)q52.52434iq6+(3.00000+1.73205i)q7+1.00000q8+(1.686142.92048i)q9+(0.6861412.12819i)q10+(2.18614+1.26217i)q12+(0.186141+0.322405i)q133.46410iq14+(1.186145.51856i)q15+(0.500000+0.866025i)q16+(0.6861411.18843i)q17+(1.68614+2.92048i)q18+(2.18614+0.469882i)q20+(4.372287.57301i)q21+2.74456q23+(2.18614+1.26217i)q24+(0.5000004.97494i)q250.372281q26+0.939764iq27+(3.00000+1.73205i)q287.72049iq29+(4.18614+3.78651i)q30+11.0371iq31+(0.5000000.866025i)q32+(0.686141+1.18843i)q34+(1.627727.57301i)q353.37228q36+(0.5000006.06218i)q37+(0.8138590.469882i)q39+(1.50000+1.65831i)q40+(2.87228+4.97494i)q41+(4.37228+7.57301i)q429.11684q43+(2.31386+7.17687i)q45+(1.37228+2.37686i)q465.04868iq472.52434iq48+(2.500004.33013i)q49+(4.55842+2.05446i)q50+3.46410iq51+(0.1861410.322405i)q52+(0.813859+0.469882i)q53+(0.8138590.469882i)q54+(3.00000+1.73205i)q56+(6.68614+3.86025i)q58+(10.37235.98844i)q59+(5.37228+1.73205i)q60+(2.058421.18843i)q61+(9.558425.51856i)q62+11.6819iq63+1.00000q64+(0.8138590.174928i)q65+(7.11684+4.10891i)q671.37228q68+(6.00000+3.46410i)q69+(5.74456+5.19615i)q70+(1.372282.37686i)q71+(1.686142.92048i)q72+6.92820iq73+(5.00000+3.46410i)q74+(7.37228+10.2448i)q75+(0.8138590.469882i)q78+(7.11684+4.10891i)q79+(0.6861412.12819i)q80+(3.87228+6.70699i)q815.74456q82+(11.74466.78073i)q838.74456q84+(0.941578+2.92048i)q85+(4.558427.89542i)q86+(9.74456+16.8781i)q87+(8.313864.80001i)q89+(7.372281.58457i)q90+(1.116840.644810i)q91+(1.372282.37686i)q92+(13.930724.1287i)q93+(4.37228+2.52434i)q94+(2.18614+1.26217i)q9612.1168q97+(2.50000+4.33013i)q98+O(q100)q+(-0.500000 + 0.866025i) q^{2} +(-2.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} -2.52434i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.68614 - 2.92048i) q^{9} +(-0.686141 - 2.12819i) q^{10} +(2.18614 + 1.26217i) q^{12} +(0.186141 + 0.322405i) q^{13} -3.46410i q^{14} +(1.18614 - 5.51856i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.686141 - 1.18843i) q^{17} +(1.68614 + 2.92048i) q^{18} +(2.18614 + 0.469882i) q^{20} +(4.37228 - 7.57301i) q^{21} +2.74456 q^{23} +(-2.18614 + 1.26217i) q^{24} +(-0.500000 - 4.97494i) q^{25} -0.372281 q^{26} +0.939764i q^{27} +(3.00000 + 1.73205i) q^{28} -7.72049i q^{29} +(4.18614 + 3.78651i) q^{30} +11.0371i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.686141 + 1.18843i) q^{34} +(1.62772 - 7.57301i) q^{35} -3.37228 q^{36} +(0.500000 - 6.06218i) q^{37} +(-0.813859 - 0.469882i) q^{39} +(-1.50000 + 1.65831i) q^{40} +(2.87228 + 4.97494i) q^{41} +(4.37228 + 7.57301i) q^{42} -9.11684 q^{43} +(2.31386 + 7.17687i) q^{45} +(-1.37228 + 2.37686i) q^{46} -5.04868i q^{47} -2.52434i q^{48} +(2.50000 - 4.33013i) q^{49} +(4.55842 + 2.05446i) q^{50} +3.46410i q^{51} +(0.186141 - 0.322405i) q^{52} +(0.813859 + 0.469882i) q^{53} +(-0.813859 - 0.469882i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(6.68614 + 3.86025i) q^{58} +(-10.3723 - 5.98844i) q^{59} +(-5.37228 + 1.73205i) q^{60} +(2.05842 - 1.18843i) q^{61} +(-9.55842 - 5.51856i) q^{62} +11.6819i q^{63} +1.00000 q^{64} +(-0.813859 - 0.174928i) q^{65} +(-7.11684 + 4.10891i) q^{67} -1.37228 q^{68} +(-6.00000 + 3.46410i) q^{69} +(5.74456 + 5.19615i) q^{70} +(-1.37228 - 2.37686i) q^{71} +(1.68614 - 2.92048i) q^{72} +6.92820i q^{73} +(5.00000 + 3.46410i) q^{74} +(7.37228 + 10.2448i) q^{75} +(0.813859 - 0.469882i) q^{78} +(-7.11684 + 4.10891i) q^{79} +(-0.686141 - 2.12819i) q^{80} +(3.87228 + 6.70699i) q^{81} -5.74456 q^{82} +(-11.7446 - 6.78073i) q^{83} -8.74456 q^{84} +(0.941578 + 2.92048i) q^{85} +(4.55842 - 7.89542i) q^{86} +(9.74456 + 16.8781i) q^{87} +(-8.31386 - 4.80001i) q^{89} +(-7.37228 - 1.58457i) q^{90} +(-1.11684 - 0.644810i) q^{91} +(-1.37228 - 2.37686i) q^{92} +(-13.9307 - 24.1287i) q^{93} +(4.37228 + 2.52434i) q^{94} +(2.18614 + 1.26217i) q^{96} -12.1168 q^{97} +(2.50000 + 4.33013i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q23q32q46q512q7+4q8+q9+3q10+3q125q13q152q163q17+q18+3q20+6q2112q233q242q25++10q98+O(q100) 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9} + 3 q^{10} + 3 q^{12} - 5 q^{13} - q^{15} - 2 q^{16} - 3 q^{17} + q^{18} + 3 q^{20} + 6 q^{21} - 12 q^{23} - 3 q^{24} - 2 q^{25}+ \cdots + 10 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/370Z)×\left(\mathbb{Z}/370\mathbb{Z}\right)^\times.

nn 261261 297297
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.500000 + 0.866025i −0.353553 + 0.612372i
33 −2.18614 + 1.26217i −1.26217 + 0.728714i −0.973494 0.228714i 0.926548π-0.926548\pi
−0.288675 + 0.957427i 0.593215π0.593215\pi
44 −0.500000 0.866025i −0.250000 0.433013i
55 −1.50000 + 1.65831i −0.670820 + 0.741620i
66 2.52434i 1.03056i
77 −3.00000 + 1.73205i −1.13389 + 0.654654i −0.944911 0.327327i 0.893852π-0.893852\pi
−0.188982 + 0.981981i 0.560519π0.560519\pi
88 1.00000 0.353553
99 1.68614 2.92048i 0.562047 0.973494i
1010 −0.686141 2.12819i −0.216977 0.672994i
1111 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1212 2.18614 + 1.26217i 0.631084 + 0.364357i
1313 0.186141 + 0.322405i 0.0516261 + 0.0894191i 0.890684 0.454624i 0.150226π-0.150226\pi
−0.839057 + 0.544043i 0.816893π0.816893\pi
1414 3.46410i 0.925820i
1515 1.18614 5.51856i 0.306260 1.42489i
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 0.686141 1.18843i 0.166414 0.288237i −0.770743 0.637146i 0.780115π-0.780115\pi
0.937156 + 0.348910i 0.113448π0.113448\pi
1818 1.68614 + 2.92048i 0.397427 + 0.688364i
1919 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
2020 2.18614 + 0.469882i 0.488836 + 0.105069i
2121 4.37228 7.57301i 0.954110 1.65257i
2222 0 0
2323 2.74456 0.572281 0.286140 0.958188i 0.407628π-0.407628\pi
0.286140 + 0.958188i 0.407628π0.407628\pi
2424 −2.18614 + 1.26217i −0.446244 + 0.257639i
2525 −0.500000 4.97494i −0.100000 0.994987i
2626 −0.372281 −0.0730104
2727 0.939764i 0.180858i
2828 3.00000 + 1.73205i 0.566947 + 0.327327i
2929 7.72049i 1.43366i −0.697248 0.716830i 0.745593π-0.745593\pi
0.697248 0.716830i 0.254407π-0.254407\pi
3030 4.18614 + 3.78651i 0.764281 + 0.691318i
3131 11.0371i 1.98232i 0.132656 + 0.991162i 0.457650π0.457650\pi
−0.132656 + 0.991162i 0.542350π0.542350\pi
3232 −0.500000 0.866025i −0.0883883 0.153093i
3333 0 0
3434 0.686141 + 1.18843i 0.117672 + 0.203814i
3535 1.62772 7.57301i 0.275135 1.28007i
3636 −3.37228 −0.562047
3737 0.500000 6.06218i 0.0821995 0.996616i
3838 0 0
3939 −0.813859 0.469882i −0.130322 0.0752413i
4040 −1.50000 + 1.65831i −0.237171 + 0.262202i
4141 2.87228 + 4.97494i 0.448575 + 0.776955i 0.998294 0.0583953i 0.0185984π-0.0185984\pi
−0.549719 + 0.835350i 0.685265π0.685265\pi
4242 4.37228 + 7.57301i 0.674658 + 1.16854i
4343 −9.11684 −1.39031 −0.695153 0.718862i 0.744663π-0.744663\pi
−0.695153 + 0.718862i 0.744663π0.744663\pi
4444 0 0
4545 2.31386 + 7.17687i 0.344930 + 1.06986i
4646 −1.37228 + 2.37686i −0.202332 + 0.350449i
4747 5.04868i 0.736425i −0.929742 0.368213i 0.879970π-0.879970\pi
0.929742 0.368213i 0.120030π-0.120030\pi
4848 2.52434i 0.364357i
4949 2.50000 4.33013i 0.357143 0.618590i
5050 4.55842 + 2.05446i 0.644658 + 0.290544i
5151 3.46410i 0.485071i
5252 0.186141 0.322405i 0.0258131 0.0447095i
5353 0.813859 + 0.469882i 0.111792 + 0.0645432i 0.554854 0.831948i 0.312774π-0.312774\pi
−0.443061 + 0.896491i 0.646108π0.646108\pi
5454 −0.813859 0.469882i −0.110752 0.0639428i
5555 0 0
5656 −3.00000 + 1.73205i −0.400892 + 0.231455i
5757 0 0
5858 6.68614 + 3.86025i 0.877933 + 0.506875i
5959 −10.3723 5.98844i −1.35036 0.779628i −0.362057 0.932156i 0.617925π-0.617925\pi
−0.988299 + 0.152528i 0.951259π0.951259\pi
6060 −5.37228 + 1.73205i −0.693559 + 0.223607i
6161 2.05842 1.18843i 0.263554 0.152163i −0.362401 0.932022i 0.618043π-0.618043\pi
0.625955 + 0.779859i 0.284709π0.284709\pi
6262 −9.55842 5.51856i −1.21392 0.700858i
6363 11.6819i 1.47178i
6464 1.00000 0.125000
6565 −0.813859 0.174928i −0.100947 0.0216972i
6666 0 0
6767 −7.11684 + 4.10891i −0.869461 + 0.501983i −0.867169 0.498014i 0.834063π-0.834063\pi
−0.00229183 + 0.999997i 0.500730π0.500730\pi
6868 −1.37228 −0.166414
6969 −6.00000 + 3.46410i −0.722315 + 0.417029i
7070 5.74456 + 5.19615i 0.686607 + 0.621059i
7171 −1.37228 2.37686i −0.162860 0.282082i 0.773033 0.634365i 0.218739π-0.218739\pi
−0.935893 + 0.352284i 0.885405π0.885405\pi
7272 1.68614 2.92048i 0.198714 0.344182i
7373 6.92820i 0.810885i 0.914121 + 0.405442i 0.132883π0.132883\pi
−0.914121 + 0.405442i 0.867117π0.867117\pi
7474 5.00000 + 3.46410i 0.581238 + 0.402694i
7575 7.37228 + 10.2448i 0.851278 + 1.18297i
7676 0 0
7777 0 0
7878 0.813859 0.469882i 0.0921514 0.0532036i
7979 −7.11684 + 4.10891i −0.800708 + 0.462289i −0.843718 0.536786i 0.819638π-0.819638\pi
0.0430110 + 0.999075i 0.486305π0.486305\pi
8080 −0.686141 2.12819i −0.0767129 0.237939i
8181 3.87228 + 6.70699i 0.430253 + 0.745221i
8282 −5.74456 −0.634381
8383 −11.7446 6.78073i −1.28913 0.744281i −0.310634 0.950530i 0.600541π-0.600541\pi
−0.978500 + 0.206248i 0.933875π0.933875\pi
8484 −8.74456 −0.954110
8585 0.941578 + 2.92048i 0.102128 + 0.316771i
8686 4.55842 7.89542i 0.491547 0.851385i
8787 9.74456 + 16.8781i 1.04473 + 1.80952i
8888 0 0
8989 −8.31386 4.80001i −0.881267 0.508800i −0.0101913 0.999948i 0.503244π-0.503244\pi
−0.871076 + 0.491148i 0.836577π0.836577\pi
9090 −7.37228 1.58457i −0.777107 0.167029i
9191 −1.11684 0.644810i −0.117077 0.0675945i
9292 −1.37228 2.37686i −0.143070 0.247805i
9393 −13.9307 24.1287i −1.44455 2.50203i
9494 4.37228 + 2.52434i 0.450966 + 0.260366i
9595 0 0
9696 2.18614 + 1.26217i 0.223122 + 0.128820i
9797 −12.1168 −1.23028 −0.615140 0.788418i 0.710900π-0.710900\pi
−0.615140 + 0.788418i 0.710900π0.710900\pi
9898 2.50000 + 4.33013i 0.252538 + 0.437409i
9999 0 0
100100 −4.05842 + 2.92048i −0.405842 + 0.292048i
101101 1.37228 0.136547 0.0682735 0.997667i 0.478251π-0.478251\pi
0.0682735 + 0.997667i 0.478251π0.478251\pi
102102 −3.00000 1.73205i −0.297044 0.171499i
103103 15.4891 1.52619 0.763094 0.646287i 0.223679π-0.223679\pi
0.763094 + 0.646287i 0.223679π0.223679\pi
104104 0.186141 + 0.322405i 0.0182526 + 0.0316144i
105105 6.00000 + 18.6101i 0.585540 + 1.81616i
106106 −0.813859 + 0.469882i −0.0790490 + 0.0456390i
107107 3.30298 1.90698i 0.319312 0.184355i −0.331774 0.943359i 0.607647π-0.607647\pi
0.651086 + 0.759004i 0.274314π0.274314\pi
108108 0.813859 0.469882i 0.0783137 0.0452144i
109109 −2.05842 1.18843i −0.197161 0.113831i 0.398170 0.917312i 0.369646π-0.369646\pi
−0.595331 + 0.803481i 0.702979π0.702979\pi
110110 0 0
111111 6.55842 + 13.8839i 0.622498 + 1.31780i
112112 3.46410i 0.327327i
113113 10.1168 17.5229i 0.951713 1.64841i 0.209995 0.977702i 0.432655π-0.432655\pi
0.741718 0.670712i 0.234011π-0.234011\pi
114114 0 0
115115 −4.11684 + 4.55134i −0.383898 + 0.424415i
116116 −6.68614 + 3.86025i −0.620793 + 0.358415i
117117 1.25544 0.116065
118118 10.3723 5.98844i 0.954846 0.551281i
119119 4.75372i 0.435773i
120120 1.18614 5.51856i 0.108279 0.503773i
121121 −11.0000 −1.00000
122122 2.37686i 0.215191i
123123 −12.5584 7.25061i −1.13235 0.653765i
124124 9.55842 5.51856i 0.858372 0.495581i
125125 9.00000 + 6.63325i 0.804984 + 0.593296i
126126 −10.1168 5.84096i −0.901280 0.520354i
127127 15.0000 + 8.66025i 1.33103 + 0.768473i 0.985458 0.169917i 0.0543501π-0.0543501\pi
0.345576 + 0.938391i 0.387683π0.387683\pi
128128 −0.500000 + 0.866025i −0.0441942 + 0.0765466i
129129 19.9307 11.5070i 1.75480 1.01313i
130130 0.558422 0.617359i 0.0489768 0.0541459i
131131 5.74456 + 3.31662i 0.501905 + 0.289775i 0.729500 0.683981i 0.239753π-0.239753\pi
−0.227595 + 0.973756i 0.573086π0.573086\pi
132132 0 0
133133 0 0
134134 8.21782i 0.709912i
135135 −1.55842 1.40965i −0.134128 0.121323i
136136 0.686141 1.18843i 0.0588361 0.101907i
137137 2.67181i 0.228269i −0.993465 0.114134i 0.963591π-0.963591\pi
0.993465 0.114134i 0.0364094π-0.0364094\pi
138138 6.92820i 0.589768i
139139 9.37228 16.2333i 0.794947 1.37689i −0.127927 0.991784i 0.540832π-0.540832\pi
0.922873 0.385104i 0.125834π-0.125834\pi
140140 −7.37228 + 2.37686i −0.623071 + 0.200881i
141141 6.37228 + 11.0371i 0.536643 + 0.929493i
142142 2.74456 0.230319
143143 0 0
144144 1.68614 + 2.92048i 0.140512 + 0.243373i
145145 12.8030 + 11.5807i 1.06323 + 0.961728i
146146 −6.00000 3.46410i −0.496564 0.286691i
147147 12.6217i 1.04102i
148148 −5.50000 + 2.59808i −0.452097 + 0.213561i
149149 −10.6277 −0.870657 −0.435328 0.900272i 0.643368π-0.643368\pi
−0.435328 + 0.900272i 0.643368π0.643368\pi
150150 −12.5584 + 1.26217i −1.02539 + 0.103056i
151151 −8.93070 15.4684i −0.726770 1.25880i −0.958241 0.285961i 0.907687π-0.907687\pi
0.231471 0.972842i 0.425646π-0.425646\pi
152152 0 0
153153 −2.31386 4.00772i −0.187064 0.324005i
154154 0 0
155155 −18.3030 16.5557i −1.47013 1.32978i
156156 0.939764i 0.0752413i
157157 5.61684 + 3.24289i 0.448273 + 0.258811i 0.707101 0.707113i 0.250003π-0.250003\pi
−0.258828 + 0.965924i 0.583336π0.583336\pi
158158 8.21782i 0.653775i
159159 −2.37228 −0.188134
160160 2.18614 + 0.469882i 0.172830 + 0.0371474i
161161 −8.23369 + 4.75372i −0.648906 + 0.374646i
162162 −7.74456 −0.608470
163163 −8.55842 + 14.8236i −0.670347 + 1.16108i 0.307458 + 0.951562i 0.400522π0.400522\pi
−0.977806 + 0.209514i 0.932812π0.932812\pi
164164 2.87228 4.97494i 0.224287 0.388477i
165165 0 0
166166 11.7446 6.78073i 0.911555 0.526286i
167167 −2.74456 4.75372i −0.212381 0.367854i 0.740078 0.672521i 0.234788π-0.234788\pi
−0.952459 + 0.304666i 0.901455π0.901455\pi
168168 4.37228 7.57301i 0.337329 0.584271i
169169 6.43070 11.1383i 0.494669 0.856793i
170170 −3.00000 0.644810i −0.230089 0.0494547i
171171 0 0
172172 4.55842 + 7.89542i 0.347576 + 0.602020i
173173 10.5475 + 6.08963i 0.801915 + 0.462986i 0.844140 0.536122i 0.180111π-0.180111\pi
−0.0422252 + 0.999108i 0.513445π0.513445\pi
174174 −19.4891 −1.47747
175175 10.1168 + 14.0588i 0.764762 + 1.06274i
176176 0 0
177177 30.2337 2.27250
178178 8.31386 4.80001i 0.623150 0.359776i
179179 20.1947i 1.50942i 0.656057 + 0.754711i 0.272223π0.272223\pi
−0.656057 + 0.754711i 0.727777π0.727777\pi
180180 5.05842 5.59230i 0.377033 0.416825i
181181 2.43070 + 4.21010i 0.180673 + 0.312934i 0.942110 0.335304i 0.108839π-0.108839\pi
−0.761437 + 0.648239i 0.775506π0.775506\pi
182182 1.11684 0.644810i 0.0827860 0.0477965i
183183 −3.00000 + 5.19615i −0.221766 + 0.384111i
184184 2.74456 0.202332
185185 9.30298 + 9.92242i 0.683969 + 0.729511i
186186 27.8614 2.04290
187187 0 0
188188 −4.37228 + 2.52434i −0.318881 + 0.184106i
189189 −1.62772 2.81929i −0.118399 0.205073i
190190 0 0
191191 24.5986i 1.77989i −0.456068 0.889945i 0.650743π-0.650743\pi
0.456068 0.889945i 0.349257π-0.349257\pi
192192 −2.18614 + 1.26217i −0.157771 + 0.0910892i
193193 −6.62772 −0.477074 −0.238537 0.971133i 0.576668π-0.576668\pi
−0.238537 + 0.971133i 0.576668π0.576668\pi
194194 6.05842 10.4935i 0.434969 0.753389i
195195 2.00000 0.644810i 0.143223 0.0461758i
196196 −5.00000 −0.357143
197197 −6.12772 3.53784i −0.436582 0.252061i 0.265565 0.964093i 0.414442π-0.414442\pi
−0.702147 + 0.712032i 0.747775π0.747775\pi
198198 0 0
199199 8.86263i 0.628255i 0.949381 + 0.314128i 0.101712π0.101712\pi
−0.949381 + 0.314128i 0.898288π0.898288\pi
200200 −0.500000 4.97494i −0.0353553 0.351781i
201201 10.3723 17.9653i 0.731604 1.26718i
202202 −0.686141 + 1.18843i −0.0482767 + 0.0836177i
203203 13.3723 + 23.1615i 0.938550 + 1.62562i
204204 3.00000 1.73205i 0.210042 0.121268i
205205 −12.5584 2.69927i −0.877118 0.188525i
206206 −7.74456 + 13.4140i −0.539589 + 0.934596i
207207 4.62772 8.01544i 0.321649 0.557112i
208208 −0.372281 −0.0258131
209209 0 0
210210 −19.1168 4.10891i −1.31919 0.283542i
211211 −15.4891 −1.06632 −0.533158 0.846016i 0.678995π-0.678995\pi
−0.533158 + 0.846016i 0.678995π0.678995\pi
212212 0.939764i 0.0645432i
213213 6.00000 + 3.46410i 0.411113 + 0.237356i
214214 3.81396i 0.260717i
215215 13.6753 15.1186i 0.932645 1.03108i
216216 0.939764i 0.0639428i
217217 −19.1168 33.1113i −1.29774 2.24774i
218218 2.05842 1.18843i 0.139414 0.0804907i
219219 −8.74456 15.1460i −0.590903 1.02347i
220220 0 0
221221 0.510875 0.0343652
222222 −15.3030 1.26217i −1.02707 0.0847112i
223223 18.6101i 1.24623i −0.782132 0.623113i 0.785868π-0.785868\pi
0.782132 0.623113i 0.214132π-0.214132\pi
224224 3.00000 + 1.73205i 0.200446 + 0.115728i
225225 −15.3723 6.92820i −1.02482 0.461880i
226226 10.1168 + 17.5229i 0.672962 + 1.16561i
227227 5.18614 + 8.98266i 0.344216 + 0.596200i 0.985211 0.171345i 0.0548113π-0.0548113\pi
−0.640995 + 0.767545i 0.721478π0.721478\pi
228228 0 0
229229 −4.43070 7.67420i −0.292789 0.507126i 0.681679 0.731651i 0.261250π-0.261250\pi
−0.974468 + 0.224526i 0.927917π0.927917\pi
230230 −1.88316 5.84096i −0.124172 0.385142i
231231 0 0
232232 7.72049i 0.506875i
233233 14.6487i 0.959668i 0.877359 + 0.479834i 0.159303π0.159303\pi
−0.877359 + 0.479834i 0.840697π0.840697\pi
234234 −0.627719 + 1.08724i −0.0410353 + 0.0710751i
235235 8.37228 + 7.57301i 0.546147 + 0.494009i
236236 11.9769i 0.779628i
237237 10.3723 17.9653i 0.673752 1.16697i
238238 −4.11684 2.37686i −0.266855 0.154069i
239239 −8.48913 4.90120i −0.549116 0.317032i 0.199649 0.979867i 0.436020π-0.436020\pi
−0.748765 + 0.662835i 0.769353π0.769353\pi
240240 4.18614 + 3.78651i 0.270214 + 0.244418i
241241 −18.0000 + 10.3923i −1.15948 + 0.669427i −0.951180 0.308637i 0.900127π-0.900127\pi
−0.208302 + 0.978065i 0.566794π0.566794\pi
242242 5.50000 9.52628i 0.353553 0.612372i
243243 −19.3723 11.1846i −1.24273 0.717492i
244244 −2.05842 1.18843i −0.131777 0.0760815i
245245 3.43070 + 10.6410i 0.219180 + 0.679827i
246246 12.5584 7.25061i 0.800696 0.462282i
247247 0 0
248248 11.0371i 0.700858i
249249 34.2337 2.16947
250250 −10.2446 + 4.47760i −0.647923 + 0.283189i
251251 21.7793i 1.37470i −0.726328 0.687348i 0.758775π-0.758775\pi
0.726328 0.687348i 0.241225π-0.241225\pi
252252 10.1168 5.84096i 0.637301 0.367946i
253253 0 0
254254 −15.0000 + 8.66025i −0.941184 + 0.543393i
255255 −5.74456 5.19615i −0.359738 0.325396i
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 −0.430703 + 0.746000i −0.0268665 + 0.0465342i −0.879146 0.476552i 0.841886π-0.841886\pi
0.852280 + 0.523087i 0.175220π0.175220\pi
258258 23.0140i 1.43279i
259259 9.00000 + 19.0526i 0.559233 + 1.18387i
260260 0.255437 + 0.792287i 0.0158416 + 0.0491356i
261261 −22.5475 13.0178i −1.39566 0.805784i
262262 −5.74456 + 3.31662i −0.354900 + 0.204902i
263263 2.74456 1.58457i 0.169237 0.0977090i −0.412989 0.910736i 0.635515π-0.635515\pi
0.582226 + 0.813027i 0.302182π0.302182\pi
264264 0 0
265265 −2.00000 + 0.644810i −0.122859 + 0.0396104i
266266 0 0
267267 24.2337 1.48308
268268 7.11684 + 4.10891i 0.434730 + 0.250992i
269269 −23.4891 −1.43216 −0.716079 0.698020i 0.754065π-0.754065\pi
−0.716079 + 0.698020i 0.754065π0.754065\pi
270270 2.00000 0.644810i 0.121716 0.0392419i
271271 −9.18614 + 15.9109i −0.558018 + 0.966516i 0.439644 + 0.898172i 0.355105π0.355105\pi
−0.997662 + 0.0683437i 0.978229π0.978229\pi
272272 0.686141 + 1.18843i 0.0416034 + 0.0720592i
273273 3.25544 0.197028
274274 2.31386 + 1.33591i 0.139785 + 0.0807051i
275275 0 0
276276 6.00000 + 3.46410i 0.361158 + 0.208514i
277277 −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i 0.234109π-0.234109\pi
−0.951807 + 0.306699i 0.900776π0.900776\pi
278278 9.37228 + 16.2333i 0.562112 + 0.973607i
279279 32.2337 + 18.6101i 1.92978 + 1.11416i
280280 1.62772 7.57301i 0.0972748 0.452574i
281281 6.12772 + 3.53784i 0.365549 + 0.211050i 0.671512 0.740994i 0.265645π-0.265645\pi
−0.305963 + 0.952043i 0.598978π0.598978\pi
282282 −12.7446 −0.758928
283283 −1.44158 2.49689i −0.0856929 0.148424i 0.819993 0.572373i 0.193977π-0.193977\pi
−0.905686 + 0.423949i 0.860644π0.860644\pi
284284 −1.37228 + 2.37686i −0.0814299 + 0.141041i
285285 0 0
286286 0 0
287287 −17.2337 9.94987i −1.01727 0.587323i
288288 −3.37228 −0.198714
289289 7.55842 + 13.0916i 0.444613 + 0.770092i
290290 −16.4307 + 5.29734i −0.964844 + 0.311071i
291291 26.4891 15.2935i 1.55282 0.896521i
292292 6.00000 3.46410i 0.351123 0.202721i
293293 −24.9891 + 14.4275i −1.45988 + 0.842862i −0.999005 0.0446025i 0.985798π-0.985798\pi
−0.460875 + 0.887465i 0.652465π0.652465\pi
294294 −10.9307 6.31084i −0.637492 0.368056i
295295 25.4891 8.21782i 1.48403 0.478460i
296296 0.500000 6.06218i 0.0290619 0.352357i
297297 0 0
298298 5.31386 9.20387i 0.307824 0.533166i
299299 0.510875 + 0.884861i 0.0295446 + 0.0511728i
300300 5.18614 11.5070i 0.299422 0.664357i
301301 27.3505 15.7908i 1.57646 0.910169i
302302 17.8614 1.02781
303303 −3.00000 + 1.73205i −0.172345 + 0.0995037i
304304 0 0
305305 −1.11684 + 5.19615i −0.0639503 + 0.297531i
306306 4.62772 0.264549
307307 20.1398i 1.14944i 0.818350 + 0.574720i 0.194889π0.194889\pi
−0.818350 + 0.574720i 0.805111π0.805111\pi
308308 0 0
309309 −33.8614 + 19.5499i −1.92631 + 1.11215i
310310 23.4891 7.57301i 1.33409 0.430118i
311311 16.4198 + 9.47999i 0.931083 + 0.537561i 0.887154 0.461474i 0.152679π-0.152679\pi
0.0439291 + 0.999035i 0.486012π0.486012\pi
312312 −0.813859 0.469882i −0.0460757 0.0266018i
313313 −14.1753 + 24.5523i −0.801233 + 1.38778i 0.117571 + 0.993064i 0.462489π0.462489\pi
−0.918805 + 0.394713i 0.870844π0.870844\pi
314314 −5.61684 + 3.24289i −0.316977 + 0.183007i
315315 −19.3723 17.5229i −1.09150 0.987303i
316316 7.11684 + 4.10891i 0.400354 + 0.231144i
317317 −11.3614 6.55951i −0.638120 0.368419i 0.145770 0.989319i 0.453434π-0.453434\pi
−0.783890 + 0.620900i 0.786767π0.786767\pi
318318 1.18614 2.05446i 0.0665155 0.115208i
319319 0 0
320320 −1.50000 + 1.65831i −0.0838525 + 0.0927025i
321321 −4.81386 + 8.33785i −0.268683 + 0.465373i
322322 9.50744i 0.529829i
323323 0 0
324324 3.87228 6.70699i 0.215127 0.372610i
325325 1.51087 1.08724i 0.0838082 0.0603093i
326326 −8.55842 14.8236i −0.474007 0.821004i
327327 6.00000 0.331801
328328 2.87228 + 4.97494i 0.158595 + 0.274695i
329329 8.74456 + 15.1460i 0.482103 + 0.835027i
330330 0 0
331331 −24.0000 13.8564i −1.31916 0.761617i −0.335566 0.942017i 0.608928π-0.608928\pi
−0.983593 + 0.180400i 0.942261π0.942261\pi
332332 13.5615i 0.744281i
333333 −16.8614 11.6819i −0.923999 0.640166i
334334 5.48913 0.300352
335335 3.86141 17.9653i 0.210971 0.981550i
336336 4.37228 + 7.57301i 0.238528 + 0.413142i
337337 −0.941578 + 0.543620i −0.0512910 + 0.0296129i −0.525426 0.850839i 0.676094π-0.676094\pi
0.474135 + 0.880452i 0.342761π0.342761\pi
338338 6.43070 + 11.1383i 0.349784 + 0.605844i
339339 51.0767i 2.77410i
340340 2.05842 2.27567i 0.111634 0.123416i
341341 0 0
342342 0 0
343343 6.92820i 0.374088i
344344 −9.11684 −0.491547
345345 3.25544 15.1460i 0.175267 0.815435i
346346 −10.5475 + 6.08963i −0.567040 + 0.327380i
347347 −2.74456 −0.147336 −0.0736679 0.997283i 0.523470π-0.523470\pi
−0.0736679 + 0.997283i 0.523470π0.523470\pi
348348 9.74456 16.8781i 0.522363 0.904760i
349349 −0.313859 + 0.543620i −0.0168005 + 0.0290993i −0.874303 0.485380i 0.838681π-0.838681\pi
0.857503 + 0.514479i 0.172015π0.172015\pi
350350 −17.2337 + 1.73205i −0.921179 + 0.0925820i
351351 −0.302985 + 0.174928i −0.0161721 + 0.00933698i
352352 0 0
353353 −12.1753 + 21.0882i −0.648024 + 1.12241i 0.335570 + 0.942015i 0.391071π0.391071\pi
−0.983594 + 0.180395i 0.942262π0.942262\pi
354354 −15.1168 + 26.1831i −0.803451 + 1.39162i
355355 6.00000 + 1.28962i 0.318447 + 0.0684459i
356356 9.60002i 0.508800i
357357 −6.00000 10.3923i −0.317554 0.550019i
358358 −17.4891 10.0974i −0.924329 0.533662i
359359 −10.3723 −0.547428 −0.273714 0.961811i 0.588252π-0.588252\pi
−0.273714 + 0.961811i 0.588252π0.588252\pi
360360 2.31386 + 7.17687i 0.121951 + 0.378254i
361361 −9.50000 + 16.4545i −0.500000 + 0.866025i
362362 −4.86141 −0.255510
363363 24.0475 13.8839i 1.26217 0.728714i
364364 1.28962i 0.0675945i
365365 −11.4891 10.3923i −0.601368 0.543958i
366366 −3.00000 5.19615i −0.156813 0.271607i
367367 −19.1168 + 11.0371i −0.997891 + 0.576133i −0.907624 0.419785i 0.862106π-0.862106\pi
−0.0902675 + 0.995918i 0.528772π0.528772\pi
368368 −1.37228 + 2.37686i −0.0715351 + 0.123902i
369369 19.3723 1.00848
370370 −13.2446 + 3.09541i −0.688552 + 0.160923i
371371 −3.25544 −0.169014
372372 −13.9307 + 24.1287i −0.722273 + 1.25101i
373373 −10.5000 + 6.06218i −0.543669 + 0.313888i −0.746565 0.665313i 0.768298π-0.768298\pi
0.202895 + 0.979200i 0.434965π0.434965\pi
374374 0 0
375375 −28.0475 3.14170i −1.44837 0.162237i
376376 5.04868i 0.260366i
377377 2.48913 1.43710i 0.128196 0.0740143i
378378 3.25544 0.167442
379379 −5.37228 + 9.30506i −0.275956 + 0.477969i −0.970376 0.241601i 0.922328π-0.922328\pi
0.694420 + 0.719570i 0.255661π0.255661\pi
380380 0 0
381381 −43.7228 −2.23999
382382 21.3030 + 12.2993i 1.08996 + 0.629286i
383383 6.25544 + 10.8347i 0.319638 + 0.553629i 0.980412 0.196955i 0.0631054π-0.0631054\pi
−0.660775 + 0.750584i 0.729772π0.729772\pi
384384 2.52434i 0.128820i
385385 0 0
386386 3.31386 5.73977i 0.168671 0.292147i
387387 −15.3723 + 26.6256i −0.781417 + 1.35345i
388388 6.05842 + 10.4935i 0.307570 + 0.532726i
389389 7.54755 4.35758i 0.382676 0.220938i −0.296306 0.955093i 0.595755π-0.595755\pi
0.678982 + 0.734155i 0.262421π0.262421\pi
390390 −0.441578 + 2.05446i −0.0223602 + 0.104031i
391391 1.88316 3.26172i 0.0952353 0.164952i
392392 2.50000 4.33013i 0.126269 0.218704i
393393 −16.7446 −0.844651
394394 6.12772 3.53784i 0.308710 0.178234i
395395 3.86141 17.9653i 0.194288 0.903933i
396396 0 0
397397 16.8781i 0.847086i −0.905876 0.423543i 0.860786π-0.860786\pi
0.905876 0.423543i 0.139214π-0.139214\pi
398398 −7.67527 4.43132i −0.384726 0.222122i
399399 0 0
400400 4.55842 + 2.05446i 0.227921 + 0.102723i
401401 13.2665i 0.662497i 0.943543 + 0.331249i 0.107470π0.107470\pi
−0.943543 + 0.331249i 0.892530π0.892530\pi
402402 10.3723 + 17.9653i 0.517322 + 0.896029i
403403 −3.55842 + 2.05446i −0.177258 + 0.102340i
404404 −0.686141 1.18843i −0.0341368 0.0591266i
405405 −16.9307 3.63903i −0.841293 0.180825i
406406 −26.7446 −1.32731
407407 0 0
408408 3.46410i 0.171499i
409409 25.5000 + 14.7224i 1.26089 + 0.727977i 0.973247 0.229759i 0.0737939π-0.0737939\pi
0.287646 + 0.957737i 0.407127π0.407127\pi
410410 8.61684 9.52628i 0.425556 0.470469i
411411 3.37228 + 5.84096i 0.166342 + 0.288113i
412412 −7.74456 13.4140i −0.381547 0.660859i
413413 41.4891 2.04155
414414 4.62772 + 8.01544i 0.227440 + 0.393938i
415415 28.8614 9.30506i 1.41675 0.456768i
416416 0.186141 0.322405i 0.00912630 0.0158072i
417417 47.3176i 2.31715i
418418 0 0
419419 8.48913 14.7036i 0.414721 0.718318i −0.580678 0.814133i 0.697213π-0.697213\pi
0.995399 + 0.0958155i 0.0305459π0.0305459\pi
420420 13.1168 14.5012i 0.640036 0.707587i
421421 10.5947i 0.516353i 0.966098 + 0.258177i 0.0831217π0.0831217\pi
−0.966098 + 0.258177i 0.916878π0.916878\pi
422422 7.74456 13.4140i 0.376999 0.652982i
423423 −14.7446 8.51278i −0.716905 0.413905i
424424 0.813859 + 0.469882i 0.0395245 + 0.0228195i
425425 −6.25544 2.81929i −0.303433 0.136756i
426426 −6.00000 + 3.46410i −0.290701 + 0.167836i
427427 −4.11684 + 7.13058i −0.199228 + 0.345073i
428428 −3.30298 1.90698i −0.159656 0.0921773i
429429 0 0
430430 6.25544 + 19.4024i 0.301664 + 0.935668i
431431 27.0475 15.6159i 1.30283 0.752192i 0.321945 0.946758i 0.395663π-0.395663\pi
0.980889 + 0.194566i 0.0623300π0.0623300\pi
432432 −0.813859 0.469882i −0.0391568 0.0226072i
433433 20.9870i 1.00857i −0.863537 0.504285i 0.831756π-0.831756\pi
0.863537 0.504285i 0.168244π-0.168244\pi
434434 38.2337 1.83528
435435 −42.6060 9.15759i −2.04280 0.439073i
436436 2.37686i 0.113831i
437437 0 0
438438 17.4891 0.835663
439439 −14.4416 + 8.33785i −0.689259 + 0.397944i −0.803334 0.595528i 0.796943π-0.796943\pi
0.114075 + 0.993472i 0.463609π0.463609\pi
440440 0 0
441441 −8.43070 14.6024i −0.401462 0.695353i
442442 −0.255437 + 0.442430i −0.0121499 + 0.0210443i
443443 28.6526i 1.36133i −0.732597 0.680663i 0.761692π-0.761692\pi
0.732597 0.680663i 0.238308π-0.238308\pi
444444 8.74456 12.6217i 0.414999 0.598999i
445445 20.4307 6.58696i 0.968508 0.312252i
446446 16.1168 + 9.30506i 0.763155 + 0.440608i
447447 23.2337 13.4140i 1.09892 0.634459i
448448 −3.00000 + 1.73205i −0.141737 + 0.0818317i
449449 5.69702 3.28917i 0.268859 0.155226i −0.359510 0.933141i 0.617056π-0.617056\pi
0.628369 + 0.777915i 0.283723π0.283723\pi
450450 13.6861 9.84868i 0.645171 0.464271i
451451 0 0
452452 −20.2337 −0.951713
453453 39.0475 + 22.5441i 1.83461 + 1.05921i
454454 −10.3723 −0.486795
455455 2.74456 0.884861i 0.128667 0.0414829i
456456 0 0
457457 −9.80298 16.9793i −0.458564 0.794257i 0.540321 0.841459i 0.318303π-0.318303\pi
−0.998885 + 0.0472023i 0.984969π0.984969\pi
458458 8.86141 0.414066
459459 1.11684 + 0.644810i 0.0521298 + 0.0300972i
460460 6.00000 + 1.28962i 0.279751 + 0.0601289i
461461 27.8614 + 16.0858i 1.29764 + 0.749190i 0.979995 0.199021i 0.0637763π-0.0637763\pi
0.317640 + 0.948211i 0.397110π0.397110\pi
462462 0 0
463463 −2.25544 3.90653i −0.104819 0.181552i 0.808845 0.588022i 0.200093π-0.200093\pi
−0.913664 + 0.406470i 0.866760π0.866760\pi
464464 6.68614 + 3.86025i 0.310396 + 0.179207i
465465 60.9090 + 13.0916i 2.82459 + 0.607107i
466466 −12.6861 7.32435i −0.587674 0.339294i
467467 −22.3723 −1.03527 −0.517633 0.855603i 0.673187π-0.673187\pi
−0.517633 + 0.855603i 0.673187π0.673187\pi
468468 −0.627719 1.08724i −0.0290163 0.0502577i
469469 14.2337 24.6535i 0.657251 1.13839i
470470 −10.7446 + 3.46410i −0.495610 + 0.159787i
471471 −16.3723 −0.754395
472472 −10.3723 5.98844i −0.477423 0.275640i
473473 0 0
474474 10.3723 + 17.9653i 0.476415 + 0.825174i
475475 0 0
476476 4.11684 2.37686i 0.188695 0.108943i
477477 2.74456 1.58457i 0.125665 0.0725527i
478478 8.48913 4.90120i 0.388284 0.224176i
479479 31.4198 + 18.1402i 1.43561 + 0.828849i 0.997540 0.0700928i 0.0223295π-0.0223295\pi
0.438068 + 0.898942i 0.355663π0.355663\pi
480480 −5.37228 + 1.73205i −0.245210 + 0.0790569i
481481 2.04755 0.967215i 0.0933601 0.0441012i
482482 20.7846i 0.946713i
483483 12.0000 20.7846i 0.546019 0.945732i
484484 5.50000 + 9.52628i 0.250000 + 0.433013i
485485 18.1753 20.0935i 0.825296 0.912399i
486486 19.3723 11.1846i 0.878745 0.507343i
487487 −2.00000 −0.0906287 −0.0453143 0.998973i 0.514429π-0.514429\pi
−0.0453143 + 0.998973i 0.514429π0.514429\pi
488488 2.05842 1.18843i 0.0931804 0.0537977i
489489 43.2087i 1.95396i
490490 −10.9307 2.34941i −0.493799 0.106136i
491491 −19.7228 −0.890078 −0.445039 0.895511i 0.646810π-0.646810\pi
−0.445039 + 0.895511i 0.646810π0.646810\pi
492492 14.5012i 0.653765i
493493 −9.17527 5.29734i −0.413233 0.238580i
494494 0 0
495495 0 0
496496 −9.55842 5.51856i −0.429186 0.247791i
497497 8.23369 + 4.75372i 0.369331 + 0.213234i
498498 −17.1168 + 29.6472i −0.767024 + 1.32852i
499499 12.0000 6.92820i 0.537194 0.310149i −0.206747 0.978394i 0.566288π-0.566288\pi
0.743941 + 0.668245i 0.232954π0.232954\pi
500500 1.24456 11.1109i 0.0556585 0.496892i
501501 12.0000 + 6.92820i 0.536120 + 0.309529i
502502 18.8614 + 10.8896i 0.841826 + 0.486028i
503503 11.4891 19.8997i 0.512275 0.887286i −0.487624 0.873054i 0.662136π-0.662136\pi
0.999899 0.0142322i 0.00453039π-0.00453039\pi
504504 11.6819i 0.520354i
505505 −2.05842 + 2.27567i −0.0915986 + 0.101266i
506506 0 0
507507 32.4665i 1.44189i
508508 17.3205i 0.768473i
509509 −10.8030 + 18.7113i −0.478834 + 0.829365i −0.999705 0.0242705i 0.992274π-0.992274\pi
0.520872 + 0.853635i 0.325607π0.325607\pi
510510 7.37228 2.37686i 0.326450 0.105249i
511511 −12.0000 20.7846i −0.530849 0.919457i
512512 1.00000 0.0441942
513513 0 0
514514 −0.430703 0.746000i −0.0189975 0.0329046i
515515 −23.2337 + 25.6858i −1.02380 + 1.13185i
516516 −19.9307 11.5070i −0.877400 0.506567i
517517 0 0
518518 −21.0000 1.73205i −0.922687 0.0761019i
519519 −30.7446 −1.34954
520520 −0.813859 0.174928i −0.0356901 0.00767111i
521521 −2.18614 3.78651i −0.0957766 0.165890i 0.814156 0.580646i 0.197200π-0.197200\pi
−0.909932 + 0.414756i 0.863867π0.863867\pi
522522 22.5475 13.0178i 0.986879 0.569775i
523523 −8.55842 14.8236i −0.374234 0.648192i 0.615978 0.787763i 0.288761π-0.288761\pi
−0.990212 + 0.139571i 0.955428π0.955428\pi
524524 6.63325i 0.289775i
525525 −39.8614 17.9653i −1.73969 0.784071i
526526 3.16915i 0.138181i
527527 13.1168 + 7.57301i 0.571379 + 0.329886i
528528 0 0
529529 −15.4674 −0.672495
530530 0.441578 2.05446i 0.0191809 0.0892399i
531531 −34.9783 + 20.1947i −1.51793 + 0.876375i
532532 0 0
533533 −1.06930 + 1.85208i −0.0463164 + 0.0802223i
534534 −12.1168 + 20.9870i −0.524347 + 0.908196i
535535 −1.79211 + 8.33785i −0.0774797 + 0.360477i
536536 −7.11684 + 4.10891i −0.307401 + 0.177478i
537537 −25.4891 44.1485i −1.09994 1.90515i
538538 11.7446 20.3422i 0.506344 0.877014i
539539 0 0
540540 −0.441578 + 2.05446i −0.0190025 + 0.0884097i
541541 44.3508i 1.90679i −0.301723 0.953396i 0.597562π-0.597562\pi
0.301723 0.953396i 0.402438π-0.402438\pi
542542 −9.18614 15.9109i −0.394579 0.683430i
543543 −10.6277 6.13592i −0.456079 0.263317i
544544 −1.37228 −0.0588361
545545 5.05842 1.63086i 0.216679 0.0698584i
546546 −1.62772 + 2.81929i −0.0696599 + 0.120655i
547547 46.0951 1.97088 0.985442 0.170012i 0.0543807π-0.0543807\pi
0.985442 + 0.170012i 0.0543807π0.0543807\pi
548548 −2.31386 + 1.33591i −0.0988432 + 0.0570671i
549549 8.01544i 0.342091i
550550 0 0
551551 0 0
552552 −6.00000 + 3.46410i −0.255377 + 0.147442i
553553 14.2337 24.6535i 0.605278 1.04837i
554554 7.00000 0.297402
555555 −32.8614 9.94987i −1.39489 0.422349i
556556 −18.7446 −0.794947
557557 −22.2446 + 38.5287i −0.942532 + 1.63251i −0.181914 + 0.983314i 0.558229π0.558229\pi
−0.760618 + 0.649200i 0.775104π0.775104\pi
558558 −32.2337 + 18.6101i −1.36456 + 0.787830i
559559 −1.69702 2.93932i −0.0717761 0.124320i
560560 5.74456 + 5.19615i 0.242752 + 0.219578i
561561 0 0
562562 −6.12772 + 3.53784i −0.258482 + 0.149235i
563563 −8.23369 −0.347009 −0.173504 0.984833i 0.555509π-0.555509\pi
−0.173504 + 0.984833i 0.555509π0.555509\pi
564564 6.37228 11.0371i 0.268321 0.464746i
565565 13.8832 + 43.0612i 0.584069 + 1.81160i
566566 2.88316 0.121188
567567 −23.2337 13.4140i −0.975723 0.563334i
568568 −1.37228 2.37686i −0.0575796 0.0997309i
569569 6.19082i 0.259533i −0.991545 0.129766i 0.958577π-0.958577\pi
0.991545 0.129766i 0.0414227π-0.0414227\pi
570570 0 0
571571 19.2337 33.3137i 0.804905 1.39414i −0.111451 0.993770i 0.535550π-0.535550\pi
0.916355 0.400366i 0.131117π-0.131117\pi
572572 0 0
573573 31.0475 + 53.7759i 1.29703 + 2.24652i
574574 17.2337 9.94987i 0.719320 0.415300i
575575 −1.37228 13.6540i −0.0572281 0.569412i
576576 1.68614 2.92048i 0.0702559 0.121687i
577577 −13.2337 + 22.9214i −0.550926 + 0.954231i 0.447282 + 0.894393i 0.352392π0.352392\pi
−0.998208 + 0.0598384i 0.980941π0.980941\pi
578578 −15.1168 −0.628778
579579 14.4891 8.36530i 0.602147 0.347650i
580580 3.62772 16.8781i 0.150633 0.700824i
581581 46.9783 1.94899
582582 30.5870i 1.26787i
583583 0 0
584584 6.92820i 0.286691i
585585 −1.88316 + 2.08191i −0.0778589 + 0.0860763i
586586 28.8550i 1.19199i
587587 −15.3030 26.5055i −0.631622 1.09400i −0.987220 0.159362i 0.949056π-0.949056\pi
0.355598 0.934639i 0.384277π-0.384277\pi
588588 10.9307 6.31084i 0.450775 0.260255i
589589 0 0
590590 −5.62772 + 26.1831i −0.231690 + 1.07794i
591591 17.8614 0.734720
592592 5.00000 + 3.46410i 0.205499 + 0.142374i
593593 10.8896i 0.447184i −0.974683 0.223592i 0.928222π-0.928222\pi
0.974683 0.223592i 0.0717783π-0.0717783\pi
594594 0 0
595595 −7.88316 7.13058i −0.323178 0.292325i
596596 5.31386 + 9.20387i 0.217664 + 0.377005i
597597 −11.1861 19.3750i −0.457818 0.792964i
598598 −1.02175 −0.0417824
599599 6.81386 + 11.8020i 0.278407 + 0.482215i 0.970989 0.239124i 0.0768603π-0.0768603\pi
−0.692582 + 0.721339i 0.743527π0.743527\pi
600600 7.37228 + 10.2448i 0.300972 + 0.418243i
601601 −12.8723 + 22.2954i −0.525071 + 0.909450i 0.474502 + 0.880254i 0.342628π0.342628\pi
−0.999574 + 0.0291960i 0.990705π0.990705\pi
602602 31.5817i 1.28717i
603603 27.7128i 1.12855i
604604 −8.93070 + 15.4684i −0.363385 + 0.629402i
605605 16.5000 18.2414i 0.670820 0.741620i
606606 3.46410i 0.140720i
607607 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i 0.781424π-0.781424\pi
0.935713 + 0.352763i 0.114758π0.114758\pi
608608 0 0
609609 −58.4674 33.7562i −2.36922 1.36787i
610610 −3.94158 3.56529i −0.159590 0.144354i
611611 1.62772 0.939764i 0.0658504 0.0380188i
612612 −2.31386 + 4.00772i −0.0935322 + 0.162003i
613613 −30.9416 17.8641i −1.24972 0.721525i −0.278665 0.960388i 0.589892π-0.589892\pi
−0.971053 + 0.238863i 0.923225π0.923225\pi
614614 −17.4416 10.0699i −0.703885 0.406388i
615615 30.8614 9.94987i 1.24445 0.401218i
616616 0 0
617617 11.4891 + 6.63325i 0.462535 + 0.267045i 0.713109 0.701053i 0.247286π-0.247286\pi
−0.250575 + 0.968097i 0.580620π0.580620\pi
618618 39.0998i 1.57282i
619619 −38.4674 −1.54613 −0.773067 0.634324i 0.781278π-0.781278\pi
−0.773067 + 0.634324i 0.781278π0.781278\pi
620620 −5.18614 + 24.1287i −0.208280 + 0.969031i
621621 2.57924i 0.103501i
622622 −16.4198 + 9.47999i −0.658375 + 0.380113i
623623 33.2554 1.33235
624624 0.813859 0.469882i 0.0325804 0.0188103i
625625 −24.5000 + 4.97494i −0.980000 + 0.198997i
626626 −14.1753 24.5523i −0.566558 0.981307i
627627 0 0
628628 6.48577i 0.258811i
629629 −6.86141 4.75372i −0.273582 0.189543i
630630 24.8614 8.01544i 0.990502 0.319343i
631631 −10.3247 5.96099i −0.411021 0.237303i 0.280207 0.959940i 0.409597π-0.409597\pi
−0.691228 + 0.722636i 0.742930π0.742930\pi
632632 −7.11684 + 4.10891i −0.283093 + 0.163444i
633633 33.8614 19.5499i 1.34587 0.777038i
634634 11.3614 6.55951i 0.451219 0.260511i
635635 −36.8614 + 11.8843i −1.46280 + 0.471614i
636636 1.18614 + 2.05446i 0.0470335 + 0.0814645i
637637 1.86141 0.0737516
638638 0 0
639639 −9.25544 −0.366139
640640 −0.686141 2.12819i −0.0271221 0.0841243i
641641 13.5000 23.3827i 0.533218 0.923561i −0.466029 0.884769i 0.654316π-0.654316\pi
0.999247 0.0387913i 0.0123508π-0.0123508\pi
642642 −4.81386 8.33785i −0.189988 0.329069i
643643 7.86141 0.310024 0.155012 0.987913i 0.450458π-0.450458\pi
0.155012 + 0.987913i 0.450458π0.450458\pi
644644 8.23369 + 4.75372i 0.324453 + 0.187323i
645645 −10.8139 + 50.3118i −0.425795 + 1.98103i
646646 0 0
647647 11.7446 + 20.3422i 0.461726 + 0.799734i 0.999047 0.0436444i 0.0138969π-0.0138969\pi
−0.537321 + 0.843378i 0.680564π0.680564\pi
648648 3.87228 + 6.70699i 0.152118 + 0.263475i
649649 0 0
650650 0.186141 + 1.85208i 0.00730104 + 0.0726444i
651651 83.5842 + 48.2574i 3.27592 + 1.89136i
652652 17.1168 0.670347
653653 13.5000 + 23.3827i 0.528296 + 0.915035i 0.999456 + 0.0329874i 0.0105021π0.0105021\pi
−0.471160 + 0.882048i 0.656165π0.656165\pi
654654 −3.00000 + 5.19615i −0.117309 + 0.203186i
655655 −14.1168 + 4.55134i −0.551591 + 0.177836i
656656 −5.74456 −0.224287
657657 20.2337 + 11.6819i 0.789391 + 0.455755i
658658 −17.4891 −0.681797
659659 −0.510875 0.884861i −0.0199009 0.0344693i 0.855903 0.517136i 0.173002π-0.173002\pi
−0.875804 + 0.482666i 0.839668π0.839668\pi
660660 0 0
661661 43.2921 24.9947i 1.68387 0.972182i 0.724820 0.688939i 0.241923π-0.241923\pi
0.959048 0.283243i 0.0914103π-0.0914103\pi
662662 24.0000 13.8564i 0.932786 0.538545i
663663 −1.11684 + 0.644810i −0.0433746 + 0.0250424i
664664 −11.7446 6.78073i −0.455777 0.263143i
665665 0 0
666666 18.5475 8.76144i 0.718703 0.339499i
667667 21.1894i 0.820456i
668668 −2.74456 + 4.75372i −0.106190 + 0.183927i
669669 23.4891 + 40.6844i 0.908142 + 1.57295i
670670 13.6277 + 12.3267i 0.526485 + 0.476223i
671671 0 0
672672 −8.74456 −0.337329
673673 6.00000 3.46410i 0.231283 0.133531i −0.379881 0.925035i 0.624035π-0.624035\pi
0.611164 + 0.791504i 0.290702π0.290702\pi
674674 1.08724i 0.0418789i
675675 4.67527 0.469882i 0.179951 0.0180858i
676676 −12.8614 −0.494669
677677 4.84630i 0.186258i −0.995654 0.0931291i 0.970313π-0.970313\pi
0.995654 0.0931291i 0.0296869π-0.0296869\pi
678678 −44.2337 25.5383i −1.69878 0.980794i
679679 36.3505 20.9870i 1.39501 0.805407i
680680 0.941578 + 2.92048i 0.0361079 + 0.111995i
681681 −22.6753 13.0916i −0.868918 0.501670i
682682 0 0
683683 5.44158 9.42509i 0.208216 0.360641i −0.742936 0.669362i 0.766568π-0.766568\pi
0.951153 + 0.308721i 0.0999009π0.0999009\pi
684684 0 0
685685 4.43070 + 4.00772i 0.169288 + 0.153127i
686686 6.00000 + 3.46410i 0.229081 + 0.132260i
687687 19.3723 + 11.1846i 0.739099 + 0.426719i
688688 4.55842 7.89542i 0.173788 0.301010i
689689 0.349857i 0.0133285i
690690 11.4891 + 10.3923i 0.437384 + 0.395628i
691691 −6.74456 + 11.6819i −0.256575 + 0.444401i −0.965322 0.261061i 0.915927π-0.915927\pi
0.708747 + 0.705463i 0.249261π0.249261\pi
692692 12.1793i 0.462986i
693693 0 0
694694 1.37228 2.37686i 0.0520911 0.0902244i
695695 12.8614 + 39.8921i 0.487861 + 1.51319i
696696 9.74456 + 16.8781i 0.369367 + 0.639762i
697697 7.88316 0.298596
698698 −0.313859 0.543620i −0.0118798 0.0205763i
699699 −18.4891 32.0241i −0.699323 1.21126i
700700 7.11684 15.7908i 0.268991 0.596838i
701701 32.7446 + 18.9051i 1.23675 + 0.714035i 0.968427 0.249295i 0.0801990π-0.0801990\pi
0.268318 + 0.963331i 0.413532π0.413532\pi
702702 0.349857i 0.0132045i
703703 0 0
704704 0 0
705705 −27.8614 5.98844i −1.04932 0.225538i
706706 −12.1753 21.0882i −0.458222 0.793664i
707707 −4.11684 + 2.37686i −0.154830 + 0.0893911i
708708 −15.1168 26.1831i −0.568126 0.984023i
709709 22.0742i 0.829015i 0.910046 + 0.414508i 0.136046π0.136046\pi
−0.910046 + 0.414508i 0.863954π0.863954\pi
710710 −4.11684 + 4.55134i −0.154502 + 0.170809i
711711 27.7128i 1.03931i
712712 −8.31386 4.80001i −0.311575 0.179888i
713713 30.2921i 1.13445i
714714 12.0000 0.449089
715715 0 0
716716 17.4891 10.0974i 0.653599 0.377356i
717717 24.7446 0.924103
718718 5.18614 8.98266i 0.193545 0.335230i
719719 −19.6753 + 34.0786i −0.733764 + 1.27092i 0.221500 + 0.975160i 0.428905π0.428905\pi
−0.955264 + 0.295755i 0.904429π0.904429\pi
720720 −7.37228 1.58457i −0.274749 0.0590536i
721721 −46.4674 + 26.8280i −1.73054 + 0.999125i
722722 −9.50000 16.4545i −0.353553 0.612372i
723723 26.2337 45.4381i 0.975641 1.68986i
724724 2.43070 4.21010i 0.0903364 0.156467i
725725 −38.4090 + 3.86025i −1.42647 + 0.143366i
726726 27.7677i 1.03056i
727727 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i 0.119270π-0.119270\pi
−0.782267 + 0.622944i 0.785937π0.785937\pi
728728 −1.11684 0.644810i −0.0413930 0.0238983i
729729 33.2337 1.23088
730730 14.7446 4.75372i 0.545721 0.175943i
731731 −6.25544 + 10.8347i −0.231366 + 0.400737i
732732 6.00000 0.221766
733733 −2.23369 + 1.28962i −0.0825031 + 0.0476332i −0.540684 0.841226i 0.681835π-0.681835\pi
0.458181 + 0.888859i 0.348501π0.348501\pi
734734 22.0742i 0.814775i
735735 −20.9307 18.9325i −0.772041 0.698337i
736736 −1.37228 2.37686i −0.0505830 0.0876123i
737737 0 0
738738 −9.68614 + 16.7769i −0.356552 + 0.617566i
739739 −20.9783 −0.771697 −0.385849 0.922562i 0.626091π-0.626091\pi
−0.385849 + 0.922562i 0.626091π0.626091\pi
740740 3.94158 13.0178i 0.144895 0.478545i
741741 0 0
742742 1.62772 2.81929i 0.0597554 0.103499i
743743 −24.6060 + 14.2063i −0.902705 + 0.521177i −0.878077 0.478519i 0.841174π-0.841174\pi
−0.0246285 + 0.999697i 0.507840π0.507840\pi
744744 −13.9307 24.1287i −0.510724 0.884601i
745745 15.9416 17.6241i 0.584054 0.645696i
746746 12.1244i 0.443904i
747747 −39.6060 + 22.8665i −1.44911 + 0.836642i
748748 0 0
749749 −6.60597 + 11.4419i −0.241377 + 0.418077i
750750 16.7446 22.7190i 0.611425 0.829582i
751751 −19.3505 −0.706111 −0.353055 0.935602i 0.614857π-0.614857\pi
−0.353055 + 0.935602i 0.614857π0.614857\pi
752752 4.37228 + 2.52434i 0.159441 + 0.0920531i
753753 27.4891 + 47.6126i 1.00176 + 1.73510i
754754 2.87419i 0.104672i
755755 39.0475 + 8.39275i 1.42109 + 0.305444i
756756 −1.62772 + 2.81929i −0.0591996 + 0.102537i
757757 −13.6168 + 23.5851i −0.494913 + 0.857214i −0.999983 0.00586448i 0.998133π-0.998133\pi
0.505070 + 0.863078i 0.331467π0.331467\pi
758758 −5.37228 9.30506i −0.195130 0.337975i
759759 0 0
760760 0 0
761761 −24.1753 + 41.8728i −0.876353 + 1.51789i −0.0210379 + 0.999779i 0.506697π0.506697\pi
−0.855315 + 0.518109i 0.826636π0.826636\pi
762762 21.8614 37.8651i 0.791955 1.37171i
763763 8.23369 0.298080
764764 −21.3030 + 12.2993i −0.770715 + 0.444972i
765765 10.1168 + 2.17448i 0.365775 + 0.0786185i
766766 −12.5109 −0.452036
767767 4.45877i 0.160997i
768768 2.18614 + 1.26217i 0.0788856 + 0.0455446i
769769 39.7995i 1.43521i 0.696452 + 0.717603i 0.254761π0.254761\pi
−0.696452 + 0.717603i 0.745239π0.745239\pi
770770 0 0
771771 2.17448i 0.0783120i
772772 3.31386 + 5.73977i 0.119268 + 0.206579i
773773 6.89403 3.98027i 0.247961 0.143160i −0.370869 0.928685i 0.620940π-0.620940\pi
0.618830 + 0.785525i 0.287607π0.287607\pi
774774 −15.3723 26.6256i −0.552545 0.957036i
775775 54.9090 5.51856i 1.97239 0.198232i
776776 −12.1168 −0.434969
777777 −43.7228 30.2921i −1.56855 1.08672i
778778 8.71516i 0.312454i
779779 0 0
780780 −1.55842 1.40965i −0.0558005 0.0504734i
781781 0 0
782782 1.88316 + 3.26172i 0.0673415 + 0.116639i
783783 7.25544 0.259288
784784 2.50000 + 4.33013i 0.0892857 + 0.154647i
785785 −13.8030 + 4.45015i −0.492650 + 0.158833i
786786 8.37228 14.5012i 0.298629 0.517241i
787787 20.5446i 0.732334i −0.930549 0.366167i 0.880670π-0.880670\pi
0.930549 0.366167i 0.119330π-0.119330\pi
788788 7.07568i 0.252061i
789789 −4.00000 + 6.92820i −0.142404 + 0.246651i
790790 13.6277 + 12.3267i 0.484852 + 0.438566i
791791 70.0916i 2.49217i
792792 0 0
793793 0.766312 + 0.442430i 0.0272125 + 0.0157112i
794794 14.6168 + 8.43904i 0.518732 + 0.299490i
795795 3.55842 3.93398i 0.126204 0.139524i
796796 7.67527 4.43132i 0.272043 0.157064i
797797 −3.81386 + 6.60580i −0.135094 + 0.233989i −0.925633 0.378422i 0.876467π-0.876467\pi
0.790539 + 0.612411i 0.209800π0.209800\pi
798798 0 0
799799 −6.00000 3.46410i −0.212265 0.122551i
800800 −4.05842 + 2.92048i −0.143487 + 0.103255i
801801 −28.0367 + 16.1870i −0.990627 + 0.571939i
802802 −11.4891 6.63325i −0.405695 0.234228i
803803 0 0
804804 −20.7446 −0.731604
805805 4.46738 20.7846i 0.157454 0.732561i
806806 4.10891i 0.144730i
807807 51.3505 29.6472i 1.80762 1.04363i
808808 1.37228 0.0482767
809809 −16.0693 + 9.27761i −0.564966 + 0.326183i −0.755136 0.655568i 0.772429π-0.772429\pi
0.190170 + 0.981751i 0.439096π0.439096\pi
810810 11.6168 12.8429i 0.408174 0.451254i
811811 −5.11684 8.86263i −0.179677 0.311209i 0.762093 0.647467i 0.224172π-0.224172\pi
−0.941770 + 0.336258i 0.890838π0.890838\pi
812812 13.3723 23.1615i 0.469275 0.812808i
813813 46.3778i 1.62654i
814814 0 0
815815 −11.7446 36.4280i −0.411394 1.27602i
816816 −3.00000 1.73205i −0.105021 0.0606339i
817817 0 0
818818 −25.5000 + 14.7224i −0.891587 + 0.514758i
819819 −3.76631 + 2.17448i −0.131606 + 0.0759825i
820820 3.94158 + 12.2255i 0.137646 + 0.426935i
821821 16.1168 + 27.9152i 0.562482 + 0.974247i 0.997279 + 0.0737186i 0.0234867π0.0234867\pi
−0.434797 + 0.900528i 0.643180π0.643180\pi
822822 −6.74456 −0.235244
823823 −4.11684 2.37686i −0.143504 0.0828522i 0.426529 0.904474i 0.359736π-0.359736\pi
−0.570033 + 0.821622i 0.693070π0.693070\pi
824824 15.4891 0.539589
825825 0 0
826826 −20.7446 + 35.9306i −0.721796 + 1.25019i
827827 14.2337 + 24.6535i 0.494954 + 0.857285i 0.999983 0.00581705i 0.00185164π-0.00185164\pi
−0.505029 + 0.863102i 0.668518π0.668518\pi
828828 −9.25544 −0.321649
829829 −2.23369 1.28962i −0.0775792 0.0447904i 0.460709 0.887551i 0.347595π-0.347595\pi
−0.538288 + 0.842761i 0.680929π0.680929\pi
830830 −6.37228 + 29.6472i −0.221185 + 1.02907i
831831 15.3030 + 8.83518i 0.530855 + 0.306489i
832832 0.186141 + 0.322405i 0.00645327 + 0.0111774i
833833 −3.43070 5.94215i −0.118867 0.205883i
834834 −40.9783 23.6588i −1.41896 0.819237i
835835 12.0000 + 2.57924i 0.415277 + 0.0892583i
836836 0 0
837837 −10.3723 −0.358518
838838 8.48913 + 14.7036i 0.293252 + 0.507927i
839839 27.3030 47.2902i 0.942604 1.63264i 0.182124 0.983276i 0.441703π-0.441703\pi
0.760479 0.649362i 0.224964π-0.224964\pi
840840 6.00000 + 18.6101i 0.207020 + 0.642110i
841841 −30.6060 −1.05538
842842 −9.17527 5.29734i −0.316201 0.182558i
843843 −17.8614 −0.615180
844844 7.74456 + 13.4140i 0.266579 + 0.461728i
845845 8.82473 + 27.3716i 0.303580 + 0.941611i
846846 14.7446 8.51278i 0.506929 0.292675i
847847 33.0000 19.0526i 1.13389 0.654654i
848848 −0.813859 + 0.469882i −0.0279480 + 0.0161358i
849849 6.30298 + 3.63903i 0.216318 + 0.124891i
850850 5.56930 4.00772i 0.191025 0.137464i
851851 1.37228 16.6380i 0.0470412 0.570344i
852852 6.92820i 0.237356i
853853 0.616844 1.06841i 0.0211203 0.0365815i −0.855272 0.518179i 0.826610π-0.826610\pi
0.876392 + 0.481598i 0.159943π0.159943\pi
854854 −4.11684 7.13058i −0.140876 0.244004i
855855 0 0
856856 3.30298 1.90698i 0.112894 0.0651792i
857857 18.8614 0.644293 0.322147 0.946690i 0.395596π-0.395596\pi
0.322147 + 0.946690i 0.395596π0.395596\pi
858858 0 0
859859 3.46410i 0.118194i −0.998252 0.0590968i 0.981178π-0.981178\pi
0.998252 0.0590968i 0.0188221π-0.0188221\pi
860860 −19.9307 4.28384i −0.679631 0.146078i
861861 50.2337 1.71196
862862 31.2318i 1.06376i
863863 6.60597 + 3.81396i 0.224870 + 0.129829i 0.608203 0.793781i 0.291891π-0.291891\pi
−0.383333 + 0.923610i 0.625224π0.625224\pi
864864 0.813859 0.469882i 0.0276881 0.0159857i
865865 −25.9198 + 8.35668i −0.881301 + 0.284136i
866866 18.1753 + 10.4935i 0.617621 + 0.356583i
867867 −33.0475 19.0800i −1.12235 0.647991i
868868 −19.1168 + 33.1113i −0.648868 + 1.12387i
869869 0 0
870870 29.2337 32.3191i 0.991115 1.09572i
871871 −2.64947 1.52967i −0.0897738 0.0518309i
872872 −2.05842 1.18843i −0.0697070 0.0402453i
873873 −20.4307 + 35.3870i −0.691475 + 1.19767i
874874 0 0
875875 −38.4891 4.31129i −1.30117 0.145748i
876876 −8.74456 + 15.1460i −0.295451 + 0.511737i
877877 15.9932i 0.540053i 0.962853 + 0.270026i 0.0870324π0.0870324\pi
−0.962853 + 0.270026i 0.912968π0.912968\pi
878878 16.6757i 0.562778i
879879 36.4198 63.0810i 1.22841 2.12767i
880880 0 0
881881 −8.05842 13.9576i −0.271495 0.470243i 0.697750 0.716342i 0.254185π-0.254185\pi
−0.969245 + 0.246098i 0.920851π0.920851\pi
882882 16.8614 0.567753
883883 29.6753 + 51.3991i 0.998652 + 1.72972i 0.544274 + 0.838907i 0.316805π0.316805\pi
0.454378 + 0.890809i 0.349862π0.349862\pi
884884 −0.255437 0.442430i −0.00859129 0.0148805i
885885 −45.3505 + 50.1369i −1.52444 + 1.68533i
886886 24.8139 + 14.3263i 0.833638 + 0.481301i
887887 21.7793i 0.731277i 0.930757 + 0.365638i 0.119149π0.119149\pi
−0.930757 + 0.365638i 0.880851π0.880851\pi
888888 6.55842 + 13.8839i 0.220086 + 0.465912i
889889 −60.0000 −2.01234
890890 −4.51087 + 20.9870i −0.151205 + 0.703485i
891891 0 0
892892 −16.1168 + 9.30506i −0.539632 + 0.311557i
893893 0 0
894894 26.8280i 0.897261i
895895 −33.4891 30.2921i −1.11942 1.01255i
896896 3.46410i 0.115728i
897897 −2.23369 1.28962i −0.0745807 0.0430592i
898898 6.57835i 0.219522i
899899 85.2119 2.84198
900900 1.68614 + 16.7769i 0.0562047 + 0.559230i
901901 1.11684 0.644810i 0.0372075 0.0214817i
902902 0 0
903903 −39.8614 + 69.0420i −1.32650 + 2.29757i
904904 10.1168 17.5229i 0.336481 0.582803i
905905 −10.6277 2.28429i −0.353277 0.0759323i
906906 −39.0475 + 22.5441i −1.29727 + 0.748978i
907907 13.2554 + 22.9591i 0.440140 + 0.762344i 0.997699 0.0677926i 0.0215956π-0.0215956\pi
−0.557560 + 0.830137i 0.688262π0.688262\pi
908908 5.18614 8.98266i 0.172108 0.298100i
909909 2.31386 4.00772i 0.0767459 0.132928i
910910 −0.605969 + 2.81929i −0.0200877 + 0.0934586i
911911 49.2520i 1.63179i −0.578198 0.815896i 0.696244π-0.696244\pi
0.578198 0.815896i 0.303756π-0.303756\pi
912912 0 0
913913 0 0
914914 19.6060 0.648508
915915 −4.11684 12.7692i −0.136099 0.422136i
916916 −4.43070 + 7.67420i −0.146395 + 0.253563i
917917 −22.9783 −0.758809
918918 −1.11684 + 0.644810i −0.0368613 + 0.0212819i
919919 3.46410i 0.114270i −0.998366 0.0571351i 0.981803π-0.981803\pi
0.998366 0.0571351i 0.0181966π-0.0181966\pi
920920 −4.11684 + 4.55134i −0.135728 + 0.150053i
921921 −25.4198 44.0284i −0.837612 1.45079i
922922 −27.8614 + 16.0858i −0.917567 + 0.529757i
923923 0.510875 0.884861i 0.0168156 0.0291256i
924924 0 0
925925 −30.4090 + 0.543620i −0.999840 + 0.0178741i
926926 4.51087 0.148237
927927 26.1168 45.2357i 0.857790 1.48574i
928928 −6.68614 + 3.86025i −0.219483 + 0.126719i
929929 −18.9891 32.8901i −0.623013 1.07909i −0.988922 0.148439i 0.952575π-0.952575\pi
0.365909 0.930651i 0.380758π-0.380758\pi
930930 −41.7921 + 46.2029i −1.37042 + 1.51505i
931931 0 0
932932 12.6861 7.32435i 0.415548 0.239917i
933933 −47.8614 −1.56691
934934 11.1861 19.3750i 0.366022 0.633968i
935935 0 0
936936 1.25544 0.0410353
937937 −42.9416 24.7923i −1.40284 0.809930i −0.408157 0.912912i 0.633828π-0.633828\pi
−0.994683 + 0.102982i 0.967162π0.967162\pi
938938 14.2337 + 24.6535i 0.464746 + 0.804964i
939939 71.5663i 2.33548i
940940 2.37228 11.0371i 0.0773753 0.359991i
941941 6.43070 11.1383i 0.209635 0.363098i −0.741965 0.670439i 0.766106π-0.766106\pi
0.951600 + 0.307341i 0.0994391π0.0994391\pi
942942 8.18614 14.1788i 0.266719 0.461971i
943943 7.88316 + 13.6540i 0.256711 + 0.444636i
944944 10.3723 5.98844i 0.337589 0.194907i
945945 7.11684 + 1.52967i 0.231511 + 0.0497602i
946946 0 0
947947 −19.9307 + 34.5210i −0.647661 + 1.12178i 0.336019 + 0.941855i 0.390919π0.390919\pi
−0.983680 + 0.179926i 0.942414π0.942414\pi
948948 −20.7446 −0.673752
949949 −2.23369 + 1.28962i −0.0725086 + 0.0418628i
950950 0 0
951951 33.1168 1.07389
952952 4.75372i 0.154069i
953953 11.4891 + 6.63325i 0.372169 + 0.214872i 0.674406 0.738361i 0.264400π-0.264400\pi
−0.302236 + 0.953233i 0.597733π0.597733\pi
954954 3.16915i 0.102605i
955955 40.7921 + 36.8979i 1.32000 + 1.19399i
956956 9.80240i 0.317032i
957957 0 0
958958 −31.4198 + 18.1402i −1.01513 + 0.586085i
959959 4.62772 + 8.01544i 0.149437 + 0.258832i
960960 1.18614 5.51856i 0.0382825 0.178111i
961961 −90.8179 −2.92961
962962 −0.186141 + 2.25684i −0.00600142 + 0.0727633i
963963 12.8617i 0.414464i
964964 18.0000 + 10.3923i 0.579741 + 0.334714i
965965 9.94158 10.9908i 0.320031 0.353807i
966966 12.0000 + 20.7846i 0.386094 + 0.668734i
967967 17.1168 + 29.6472i 0.550441 + 0.953391i 0.998243 + 0.0592584i 0.0188736π0.0188736\pi
−0.447802 + 0.894133i 0.647793π0.647793\pi
968968 −11.0000 −0.353553
969969 0 0
970970 8.31386 + 25.7870i 0.266942 + 0.827971i
971971 8.48913 14.7036i 0.272429 0.471861i −0.697054 0.717018i 0.745506π-0.745506\pi
0.969483 + 0.245158i 0.0788397π0.0788397\pi
972972 22.3692i 0.717492i
973973 64.9331i 2.08166i
974974 1.00000 1.73205i 0.0320421 0.0554985i
975975 −1.93070 + 4.28384i −0.0618320 + 0.137193i
976976 2.37686i 0.0760815i
977977 28.1168 48.6998i 0.899538 1.55804i 0.0714512 0.997444i 0.477237π-0.477237\pi
0.828086 0.560601i 0.189430π-0.189430\pi
978978 37.4198 + 21.6043i 1.19655 + 0.690831i
979979 0 0
980980 7.50000 8.29156i 0.239579 0.264864i
981981 −6.94158 + 4.00772i −0.221628 + 0.127957i
982982 9.86141 17.0805i 0.314690 0.545059i
983983 −37.6277 21.7244i −1.20014 0.692900i −0.239552 0.970884i 0.577001π-0.577001\pi
−0.960586 + 0.277984i 0.910334π0.910334\pi
984984 −12.5584 7.25061i −0.400348 0.231141i
985985 15.0584 4.85491i 0.479801 0.154690i
986986 9.17527 5.29734i 0.292200 0.168702i
987987 −38.2337 22.0742i −1.21699 0.702630i
988988 0 0
989989 −25.0217 −0.795645
990990 0 0
991991 6.28339i 0.199599i −0.995008 0.0997993i 0.968180π-0.968180\pi
0.995008 0.0997993i 0.0318201π-0.0318201\pi
992992 9.55842 5.51856i 0.303480 0.175214i
993993 69.9565 2.22000
994994 −8.23369 + 4.75372i −0.261157 + 0.150779i
995995 −14.6970 13.2940i −0.465927 0.421447i
996996 −17.1168 29.6472i −0.542368 0.939409i
997997 16.5584 28.6800i 0.524410 0.908306i −0.475186 0.879886i 0.657619π-0.657619\pi
0.999596 0.0284200i 0.00904759π-0.00904759\pi
998998 13.8564i 0.438617i
999999 5.69702 + 0.469882i 0.180246 + 0.0148664i
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 370.2.m.a.249.1 yes 4
5.4 even 2 370.2.m.b.249.2 yes 4
37.11 even 6 370.2.m.b.159.2 yes 4
185.159 even 6 inner 370.2.m.a.159.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.m.a.159.1 4 185.159 even 6 inner
370.2.m.a.249.1 yes 4 1.1 even 1 trivial
370.2.m.b.159.2 yes 4 37.11 even 6
370.2.m.b.249.2 yes 4 5.4 even 2