Properties

Label 175.2.x.a.17.12
Level 175175
Weight 22
Character 175.17
Analytic conductor 1.3971.397
Analytic rank 00
Dimension 288288
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(3,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([21, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 175=527 175 = 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 175.x (of order 6060, degree 1616, 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: 1.397382035371.39738203537
Analytic rank: 00
Dimension: 288288
Relative dimension: 1818 over Q(ζ60)\Q(\zeta_{60})
Twist minimal: yes
Sato-Tate group: SU(2)[C60]\mathrm{SU}(2)[C_{60}]

Embedding invariants

Embedding label 17.12
Character χ\chi == 175.17
Dual form 175.2.x.a.103.12

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+(0.7761820.0406780i)q2+(0.706831+0.872864i)q3+(1.38824+0.145910i)q4+(2.15686+0.589873i)q5+(0.513123+0.706254i)q6+(2.33503+1.24404i)q7+(2.60695+0.412900i)q8+(0.361454+1.70051i)q9+(1.69811+0.370112i)q10+(1.29854+0.276014i)q11+(0.8538911.31488i)q12+(1.79077+0.912442i)q13+(1.86302+0.870614i)q14+(2.03941+1.46571i)q15+(0.7240940.153911i)q16+(0.3332240.868077i)q17+(0.349728+1.30520i)q18+(0.5508845.24131i)q19+(3.080310.504177i)q20+(2.73635+1.15884i)q21+(1.01913+0.161415i)q22+(0.05994821.14388i)q23+(1.482272.56736i)q24+(4.30410+2.54455i)q25+(1.35285+0.781066i)q26+(4.742042.41619i)q27+(3.423101.38631i)q28+(4.040605.56140i)q29+(1.52334+1.22061i)q30+(3.985458.95147i)q31+(5.654781.51519i)q32+(1.15877+0.938356i)q33+(0.2233310.687341i)q34+(4.30252+4.06058i)q35+(0.7499062.30797i)q36+(6.42719+4.17386i)q37+(0.2143814.09062i)q38+(0.4693332.20804i)q39+(5.866380.647200i)q40+(0.06226530.0202312i)q41+(2.07676+1.01078i)q42+(3.34331+3.34331i)q43+(1.842960.193703i)q44+(0.223477+3.88097i)q45+(0.09306140.885420i)q46+(0.174263+0.0668935i)q47+(0.377469+0.740824i)q48+(3.90475+5.80972i)q49+(3.44427+1.79995i)q50+(0.522180+0.904443i)q51+(2.352881.52798i)q52+(8.68044+7.02928i)q53+(3.778981.68251i)q54+(2.63796+1.36130i)q55+(6.600972.27900i)q56+(4.18557+4.18557i)q57+(3.362474.15230i)q58+(3.228603.58572i)q59+(2.617342.33232i)q60+(3.399283.06073i)q61+(3.457566.78585i)q62+(1.27148+4.42040i)q63+(2.919430.948580i)q64+(4.40066+0.911685i)q65+(0.861248+0.775472i)q66+(7.930203.04412i)q67+(0.335933+1.25372i)q68+(1.04082+0.756203i)q69+(3.50472+2.97673i)q70+(8.724916.33902i)q71+(1.644434.28389i)q72+(0.896926+1.38114i)q73+(5.15845+2.97823i)q74+(5.26331+1.95833i)q75+7.35658iq76+(2.68877+2.25993i)q77+(0.2744691.73293i)q78+(4.24463+9.53360i)q79+(1.65256+0.0951587i)q80+(0.6962360.309984i)q81+(0.04915220.0131703i)q82+(0.9785996.17863i)q83+(3.629622.00801i)q84+(1.230771.67576i)q85+(2.45902+2.73102i)q86+(7.71037+0.404083i)q87+(3.499200.183385i)q88+(10.501911.6635i)q89+(0.0155886+3.02143i)q90+(5.316610.0971966i)q91+(0.250126+1.57923i)q92+(10.6304+2.84842i)q93+(0.132539+0.0590102i)q94+(4.2798910.9798i)q95+(2.67442+6.00684i)q96+(2.72136+17.1820i)q97+(3.26713+4.35057i)q98+2.30795iq99+O(q100)q+(0.776182 - 0.0406780i) q^{2} +(-0.706831 + 0.872864i) q^{3} +(-1.38824 + 0.145910i) q^{4} +(2.15686 + 0.589873i) q^{5} +(-0.513123 + 0.706254i) q^{6} +(2.33503 + 1.24404i) q^{7} +(-2.60695 + 0.412900i) q^{8} +(0.361454 + 1.70051i) q^{9} +(1.69811 + 0.370112i) q^{10} +(1.29854 + 0.276014i) q^{11} +(0.853891 - 1.31488i) q^{12} +(-1.79077 + 0.912442i) q^{13} +(1.86302 + 0.870614i) q^{14} +(-2.03941 + 1.46571i) q^{15} +(0.724094 - 0.153911i) q^{16} +(0.333224 - 0.868077i) q^{17} +(0.349728 + 1.30520i) q^{18} +(0.550884 - 5.24131i) q^{19} +(-3.08031 - 0.504177i) q^{20} +(-2.73635 + 1.15884i) q^{21} +(1.01913 + 0.161415i) q^{22} +(-0.0599482 - 1.14388i) q^{23} +(1.48227 - 2.56736i) q^{24} +(4.30410 + 2.54455i) q^{25} +(-1.35285 + 0.781066i) q^{26} +(-4.74204 - 2.41619i) q^{27} +(-3.42310 - 1.38631i) q^{28} +(-4.04060 - 5.56140i) q^{29} +(-1.52334 + 1.22061i) q^{30} +(-3.98545 - 8.95147i) q^{31} +(5.65478 - 1.51519i) q^{32} +(-1.15877 + 0.938356i) q^{33} +(0.223331 - 0.687341i) q^{34} +(4.30252 + 4.06058i) q^{35} +(-0.749906 - 2.30797i) q^{36} +(6.42719 + 4.17386i) q^{37} +(0.214381 - 4.09062i) q^{38} +(0.469333 - 2.20804i) q^{39} +(-5.86638 - 0.647200i) q^{40} +(-0.0622653 - 0.0202312i) q^{41} +(-2.07676 + 1.01078i) q^{42} +(-3.34331 + 3.34331i) q^{43} +(-1.84296 - 0.193703i) q^{44} +(-0.223477 + 3.88097i) q^{45} +(-0.0930614 - 0.885420i) q^{46} +(-0.174263 + 0.0668935i) q^{47} +(-0.377469 + 0.740824i) q^{48} +(3.90475 + 5.80972i) q^{49} +(3.44427 + 1.79995i) q^{50} +(0.522180 + 0.904443i) q^{51} +(2.35288 - 1.52798i) q^{52} +(8.68044 + 7.02928i) q^{53} +(-3.77898 - 1.68251i) q^{54} +(2.63796 + 1.36130i) q^{55} +(-6.60097 - 2.27900i) q^{56} +(4.18557 + 4.18557i) q^{57} +(-3.36247 - 4.15230i) q^{58} +(-3.22860 - 3.58572i) q^{59} +(2.61734 - 2.33232i) q^{60} +(-3.39928 - 3.06073i) q^{61} +(-3.45756 - 6.78585i) q^{62} +(-1.27148 + 4.42040i) q^{63} +(2.91943 - 0.948580i) q^{64} +(-4.40066 + 0.911685i) q^{65} +(-0.861248 + 0.775472i) q^{66} +(-7.93020 - 3.04412i) q^{67} +(-0.335933 + 1.25372i) q^{68} +(1.04082 + 0.756203i) q^{69} +(3.50472 + 2.97673i) q^{70} +(8.72491 - 6.33902i) q^{71} +(-1.64443 - 4.28389i) q^{72} +(0.896926 + 1.38114i) q^{73} +(5.15845 + 2.97823i) q^{74} +(-5.26331 + 1.95833i) q^{75} +7.35658i q^{76} +(2.68877 + 2.25993i) q^{77} +(0.274469 - 1.73293i) q^{78} +(-4.24463 + 9.53360i) q^{79} +(1.65256 + 0.0951587i) q^{80} +(0.696236 - 0.309984i) q^{81} +(-0.0491522 - 0.0131703i) q^{82} +(-0.978599 - 6.17863i) q^{83} +(3.62962 - 2.00801i) q^{84} +(1.23077 - 1.67576i) q^{85} +(-2.45902 + 2.73102i) q^{86} +(7.71037 + 0.404083i) q^{87} +(-3.49920 - 0.183385i) q^{88} +(10.5019 - 11.6635i) q^{89} +(-0.0155886 + 3.02143i) q^{90} +(-5.31661 - 0.0971966i) q^{91} +(0.250126 + 1.57923i) q^{92} +(10.6304 + 2.84842i) q^{93} +(-0.132539 + 0.0590102i) q^{94} +(4.27989 - 10.9798i) q^{95} +(-2.67442 + 6.00684i) q^{96} +(-2.72136 + 17.1820i) q^{97} +(3.26713 + 4.35057i) q^{98} +2.30795i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 288q8q224q310q430q510q736q810q936q106q1136q1220q1428q1530q1642q1714q1830q1912q21+32q22++222q98+O(q100) 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/175Z)×\left(\mathbb{Z}/175\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(1320)e\left(\frac{13}{20}\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 0.776182 0.0406780i 0.548844 0.0287637i 0.224101 0.974566i 0.428056π-0.428056\pi
0.324743 + 0.945802i 0.394722π0.394722\pi
33 −0.706831 + 0.872864i −0.408089 + 0.503948i −0.939208 0.343349i 0.888439π-0.888439\pi
0.531119 + 0.847297i 0.321772π0.321772\pi
44 −1.38824 + 0.145910i −0.694120 + 0.0729549i
55 2.15686 + 0.589873i 0.964578 + 0.263799i
66 −0.513123 + 0.706254i −0.209482 + 0.288327i
77 2.33503 + 1.24404i 0.882559 + 0.470201i
88 −2.60695 + 0.412900i −0.921695 + 0.145982i
99 0.361454 + 1.70051i 0.120485 + 0.566836i
1010 1.69811 + 0.370112i 0.536990 + 0.117040i
1111 1.29854 + 0.276014i 0.391525 + 0.0832213i 0.399468 0.916747i 0.369195π-0.369195\pi
−0.00794259 + 0.999968i 0.502528π0.502528\pi
1212 0.853891 1.31488i 0.246497 0.379572i
1313 −1.79077 + 0.912442i −0.496670 + 0.253066i −0.684336 0.729167i 0.739908π-0.739908\pi
0.187666 + 0.982233i 0.439908π0.439908\pi
1414 1.86302 + 0.870614i 0.497912 + 0.232681i
1515 −2.03941 + 1.46571i −0.526575 + 0.378444i
1616 0.724094 0.153911i 0.181023 0.0384777i
1717 0.333224 0.868077i 0.0808186 0.210540i −0.887217 0.461352i 0.847364π-0.847364\pi
0.968036 + 0.250813i 0.0806978π0.0806978\pi
1818 0.349728 + 1.30520i 0.0824316 + 0.307639i
1919 0.550884 5.24131i 0.126382 1.20244i −0.729027 0.684485i 0.760027π-0.760027\pi
0.855408 0.517954i 0.173306π-0.173306\pi
2020 −3.08031 0.504177i −0.688778 0.112737i
2121 −2.73635 + 1.15884i −0.597120 + 0.252880i
2222 1.01913 + 0.161415i 0.217280 + 0.0344138i
2323 −0.0599482 1.14388i −0.0125001 0.238515i −0.997733 0.0672962i 0.978563π-0.978563\pi
0.985233 0.171219i 0.0547706π-0.0547706\pi
2424 1.48227 2.56736i 0.302566 0.524060i
2525 4.30410 + 2.54455i 0.860820 + 0.508909i
2626 −1.35285 + 0.781066i −0.265315 + 0.153180i
2727 −4.74204 2.41619i −0.912607 0.464996i
2828 −3.42310 1.38631i −0.646905 0.261989i
2929 −4.04060 5.56140i −0.750320 1.03273i −0.997958 0.0638742i 0.979654π-0.979654\pi
0.247638 0.968853i 0.420346π-0.420346\pi
3030 −1.52334 + 1.22061i −0.278122 + 0.222853i
3131 −3.98545 8.95147i −0.715808 1.60773i −0.791915 0.610631i 0.790916π-0.790916\pi
0.0761073 0.997100i 0.475751π-0.475751\pi
3232 5.65478 1.51519i 0.999634 0.267851i
3333 −1.15877 + 0.938356i −0.201716 + 0.163347i
3434 0.223331 0.687341i 0.0383009 0.117878i
3535 4.30252 + 4.06058i 0.727258 + 0.686364i
3636 −0.749906 2.30797i −0.124984 0.384662i
3737 6.42719 + 4.17386i 1.05662 + 0.686179i 0.951302 0.308259i 0.0997464π-0.0997464\pi
0.105321 + 0.994438i 0.466413π0.466413\pi
3838 0.214381 4.09062i 0.0347771 0.663587i
3939 0.469333 2.20804i 0.0751534 0.353569i
4040 −5.86638 0.647200i −0.927557 0.102331i
4141 −0.0622653 0.0202312i −0.00972421 0.00315959i 0.304151 0.952624i 0.401627π-0.401627\pi
−0.313875 + 0.949464i 0.601627π0.601627\pi
4242 −2.07676 + 1.01078i −0.320452 + 0.155967i
4343 −3.34331 + 3.34331i −0.509850 + 0.509850i −0.914480 0.404630i 0.867400π-0.867400\pi
0.404630 + 0.914480i 0.367400π0.367400\pi
4444 −1.84296 0.193703i −0.277837 0.0292018i
4545 −0.223477 + 3.88097i −0.0333140 + 0.578541i
4646 −0.0930614 0.885420i −0.0137212 0.130548i
4747 −0.174263 + 0.0668935i −0.0254189 + 0.00975741i −0.371044 0.928615i 0.621000π-0.621000\pi
0.345625 + 0.938373i 0.387667π0.387667\pi
4848 −0.377469 + 0.740824i −0.0544829 + 0.106929i
4949 3.90475 + 5.80972i 0.557822 + 0.829961i
5050 3.44427 + 1.79995i 0.487094 + 0.254551i
5151 0.522180 + 0.904443i 0.0731199 + 0.126647i
5252 2.35288 1.52798i 0.326286 0.211892i
5353 8.68044 + 7.02928i 1.19235 + 0.965546i 0.999876 0.0157564i 0.00501564π-0.00501564\pi
0.192474 + 0.981302i 0.438349π0.438349\pi
5454 −3.77898 1.68251i −0.514254 0.228960i
5555 2.63796 + 1.36130i 0.355703 + 0.183557i
5656 −6.60097 2.27900i −0.882092 0.304544i
5757 4.18557 + 4.18557i 0.554392 + 0.554392i
5858 −3.36247 4.15230i −0.441514 0.545224i
5959 −3.22860 3.58572i −0.420327 0.466821i 0.495374 0.868680i 0.335031π-0.335031\pi
−0.915702 + 0.401859i 0.868364π0.868364\pi
6060 2.61734 2.33232i 0.337897 0.301101i
6161 −3.39928 3.06073i −0.435233 0.391886i 0.422182 0.906511i 0.361264π-0.361264\pi
−0.857415 + 0.514625i 0.827931π0.827931\pi
6262 −3.45756 6.78585i −0.439111 0.861804i
6363 −1.27148 + 4.42040i −0.160192 + 0.556919i
6464 2.91943 0.948580i 0.364929 0.118573i
6565 −4.40066 + 0.911685i −0.545835 + 0.113081i
6666 −0.861248 + 0.775472i −0.106012 + 0.0954540i
6767 −7.93020 3.04412i −0.968829 0.371899i −0.178064 0.984019i 0.556983π-0.556983\pi
−0.790765 + 0.612120i 0.790317π0.790317\pi
6868 −0.335933 + 1.25372i −0.0407379 + 0.152036i
6969 1.04082 + 0.756203i 0.125300 + 0.0910361i
7070 3.50472 + 2.97673i 0.418894 + 0.355788i
7171 8.72491 6.33902i 1.03546 0.752303i 0.0660625 0.997815i 0.478956π-0.478956\pi
0.969393 + 0.245513i 0.0789563π0.0789563\pi
7272 −1.64443 4.28389i −0.193798 0.504862i
7373 0.896926 + 1.38114i 0.104977 + 0.161651i 0.887255 0.461279i 0.152609π-0.152609\pi
−0.782278 + 0.622929i 0.785942π0.785942\pi
7474 5.15845 + 2.97823i 0.599658 + 0.346213i
7575 −5.26331 + 1.95833i −0.607755 + 0.226128i
7676 7.35658i 0.843857i
7777 2.68877 + 2.25993i 0.306414 + 0.257543i
7878 0.274469 1.73293i 0.0310775 0.196216i
7979 −4.24463 + 9.53360i −0.477558 + 1.07261i 0.500775 + 0.865577i 0.333048π0.333048\pi
−0.978333 + 0.207036i 0.933618π0.933618\pi
8080 1.65256 + 0.0951587i 0.184762 + 0.0106391i
8181 0.696236 0.309984i 0.0773596 0.0344427i
8282 −0.0491522 0.0131703i −0.00542796 0.00145442i
8383 −0.978599 6.17863i −0.107415 0.678193i −0.981362 0.192170i 0.938447π-0.938447\pi
0.873946 0.486022i 0.161553π-0.161553\pi
8484 3.62962 2.00801i 0.396024 0.219092i
8585 1.23077 1.67576i 0.133496 0.181762i
8686 −2.45902 + 2.73102i −0.265163 + 0.294493i
8787 7.71037 + 0.404083i 0.826638 + 0.0433223i
8888 −3.49920 0.183385i −0.373016 0.0195489i
8989 10.5019 11.6635i 1.11320 1.23633i 0.144125 0.989559i 0.453963π-0.453963\pi
0.969073 0.246773i 0.0793701π-0.0793701\pi
9090 −0.0155886 + 3.02143i −0.00164319 + 0.318487i
9191 −5.31661 0.0971966i −0.557332 0.0101890i
9292 0.250126 + 1.57923i 0.0260774 + 0.164646i
9393 10.6304 + 2.84842i 1.10233 + 0.295367i
9494 −0.132539 + 0.0590102i −0.0136704 + 0.00608644i
9595 4.27989 10.9798i 0.439107 1.12651i
9696 −2.67442 + 6.00684i −0.272957 + 0.613071i
9797 −2.72136 + 17.1820i −0.276312 + 1.74457i 0.325149 + 0.945663i 0.394586π0.394586\pi
−0.601461 + 0.798902i 0.705414π0.705414\pi
9898 3.26713 + 4.35057i 0.330030 + 0.439474i
9999 2.30795i 0.231958i
100100 −6.34640 2.90443i −0.634640 0.290443i
101101 −3.07011 1.77253i −0.305487 0.176373i 0.339418 0.940636i 0.389770π-0.389770\pi
−0.644905 + 0.764262i 0.723103π0.723103\pi
102102 0.442098 + 0.680771i 0.0437742 + 0.0674064i
103103 2.28092 + 5.94199i 0.224745 + 0.585482i 0.998869 0.0475531i 0.0151423π-0.0151423\pi
−0.774123 + 0.633035i 0.781809π0.781809\pi
104104 4.29169 3.11810i 0.420835 0.305755i
105105 −6.58549 + 0.885366i −0.642678 + 0.0864029i
106106 7.02354 + 5.10290i 0.682186 + 0.495637i
107107 2.55108 9.52075i 0.246622 0.920406i −0.725939 0.687759i 0.758595π-0.758595\pi
0.972561 0.232647i 0.0747386π-0.0747386\pi
108108 6.93564 + 2.66234i 0.667382 + 0.256184i
109109 −8.04882 + 7.24719i −0.770937 + 0.694155i −0.957546 0.288279i 0.906917π-0.906917\pi
0.186609 + 0.982434i 0.440250π0.440250\pi
110110 2.10292 + 0.949309i 0.200505 + 0.0905130i
111111 −8.18615 + 2.65984i −0.776995 + 0.252461i
112112 1.88225 + 0.541411i 0.177856 + 0.0511586i
113113 −3.00115 5.89008i −0.282324 0.554092i 0.705678 0.708533i 0.250643π-0.250643\pi
−0.988002 + 0.154440i 0.950643π0.950643\pi
114114 3.41903 + 3.07851i 0.320221 + 0.288328i
115115 0.545443 2.50255i 0.0508628 0.233364i
116116 6.42078 + 7.13100i 0.596154 + 0.662096i
117117 −2.19890 2.71541i −0.203288 0.251040i
118118 −2.65184 2.65184i −0.244122 0.244122i
119119 1.85801 1.61245i 0.170323 0.147813i
120120 4.71146 4.66309i 0.430095 0.425680i
121121 −8.43897 3.75727i −0.767179 0.341570i
122122 −2.76297 2.23741i −0.250147 0.202565i
123123 0.0616702 0.0400491i 0.00556061 0.00361110i
124124 6.83886 + 11.8453i 0.614148 + 1.06374i
125125 7.78239 + 8.02711i 0.696078 + 0.717966i
126126 −0.807091 + 3.48276i −0.0719014 + 0.310269i
127127 −8.39463 + 16.4754i −0.744903 + 1.46195i 0.137023 + 0.990568i 0.456246π0.456246\pi
−0.881927 + 0.471387i 0.843754π0.843754\pi
128128 −8.70343 + 3.34093i −0.769281 + 0.295299i
129129 −0.555099 5.28141i −0.0488737 0.465003i
130130 −3.37863 + 0.886644i −0.296325 + 0.0777638i
131131 16.6657 + 1.75164i 1.45609 + 0.153041i 0.799255 0.600992i 0.205228π-0.205228\pi
0.656836 + 0.754033i 0.271894π0.271894\pi
132132 1.47174 1.47174i 0.128098 0.128098i
133133 7.80671 11.5533i 0.676928 1.00180i
134134 −6.27911 2.04021i −0.542433 0.176247i
135135 −8.80268 8.00859i −0.757614 0.689270i
136136 −0.510268 + 2.40062i −0.0437551 + 0.205852i
137137 −0.172842 + 3.29801i −0.0147669 + 0.281768i 0.981258 + 0.192697i 0.0617234π0.0617234\pi
−0.996025 + 0.0890717i 0.971610π0.971610\pi
138138 0.838630 + 0.544613i 0.0713889 + 0.0463605i
139139 −2.66592 8.20486i −0.226120 0.695927i −0.998176 0.0603721i 0.980771π-0.980771\pi
0.772055 0.635555i 0.219229π-0.219229\pi
140140 −6.56540 5.00928i −0.554878 0.423362i
141141 0.0647859 0.199391i 0.00545596 0.0167917i
142142 6.51426 5.27514i 0.546665 0.442680i
143143 −2.57723 + 0.690568i −0.215519 + 0.0577482i
144144 0.523454 + 1.17570i 0.0436211 + 0.0979747i
145145 −5.43449 14.3786i −0.451309 1.19408i
146146 0.752360 + 1.03553i 0.0622658 + 0.0857015i
147147 −7.83110 0.698176i −0.645898 0.0575846i
148148 −9.53148 4.85653i −0.783483 0.399205i
149149 −0.0342344 + 0.0197652i −0.00280459 + 0.00161923i −0.501402 0.865215i 0.667182π-0.667182\pi
0.498597 + 0.866834i 0.333849π0.333849\pi
150150 −4.00563 + 1.73412i −0.327058 + 0.141590i
151151 4.89690 8.48169i 0.398504 0.690230i −0.595037 0.803698i 0.702863π-0.702863\pi
0.993542 + 0.113468i 0.0361960π0.0361960\pi
152152 0.728012 + 13.8913i 0.0590496 + 1.12673i
153153 1.59662 + 0.252879i 0.129079 + 0.0204441i
154154 2.17890 + 1.64475i 0.175581 + 0.132537i
155155 −3.31584 21.6580i −0.266334 1.73961i
156156 −0.329372 + 3.13377i −0.0263709 + 0.250902i
157157 −3.40702 12.7152i −0.271910 1.01478i −0.957884 0.287156i 0.907290π-0.907290\pi
0.685974 0.727626i 0.259376π-0.259376\pi
158158 −2.90680 + 7.57247i −0.231253 + 0.602434i
159159 −12.2712 + 2.60832i −0.973170 + 0.206854i
160160 13.0904 + 0.0675377i 1.03488 + 0.00533933i
161161 1.28304 2.74557i 0.101118 0.216381i
162162 0.527797 0.268926i 0.0414676 0.0211288i
163163 1.90187 2.92862i 0.148966 0.229387i −0.756308 0.654216i 0.772999π-0.772999\pi
0.905274 + 0.424828i 0.139666π0.139666\pi
164164 0.0893911 + 0.0190007i 0.00698027 + 0.00148370i
165165 −3.05282 + 1.34037i −0.237662 + 0.104348i
166166 −1.01091 4.75594i −0.0784615 0.369132i
167167 −18.9176 + 2.99626i −1.46389 + 0.231857i −0.836979 0.547235i 0.815681π-0.815681\pi
−0.626910 + 0.779092i 0.715681π0.715681\pi
168168 6.65503 4.15088i 0.513447 0.320247i
169169 −5.26691 + 7.24928i −0.405147 + 0.557637i
170170 0.887137 1.35076i 0.0680403 0.103599i
171171 9.11202 0.957712i 0.696813 0.0732380i
172172 4.15350 5.12914i 0.316701 0.391093i
173173 −4.95159 + 0.259502i −0.376462 + 0.0197296i −0.239629 0.970865i 0.577026π-0.577026\pi
−0.136833 + 0.990594i 0.543692π0.543692\pi
174174 6.00109 0.454941
175175 6.88471 + 11.2961i 0.520435 + 0.853901i
176176 0.982748 0.0740774
177177 5.41192 0.283626i 0.406785 0.0213187i
178178 7.67694 9.48023i 0.575411 0.710573i
179179 −20.1419 + 2.11700i −1.50548 + 0.158232i −0.821052 0.570853i 0.806613π-0.806613\pi
−0.684424 + 0.729085i 0.739946π0.739946\pi
180180 −0.256033 5.42033i −0.0190835 0.404007i
181181 2.67679 3.68429i 0.198965 0.273851i −0.697863 0.716231i 0.745866π-0.745866\pi
0.896828 + 0.442380i 0.145866π0.145866\pi
182182 −4.13061 + 0.140827i −0.306181 + 0.0104388i
183183 5.07431 0.803693i 0.375104 0.0594107i
184184 0.628589 + 2.95728i 0.0463402 + 0.218014i
185185 11.4005 + 12.7937i 0.838182 + 0.940609i
186186 8.36704 + 1.77847i 0.613501 + 0.130404i
187187 0.672306 1.03526i 0.0491639 0.0757058i
188188 0.232159 0.118291i 0.0169319 0.00862725i
189189 −8.06700 11.5412i −0.586788 0.839495i
190190 2.87534 8.69645i 0.208599 0.630907i
191191 15.1405 3.21821i 1.09553 0.232861i 0.375510 0.926818i 0.377468π-0.377468\pi
0.720016 + 0.693957i 0.244134π0.244134\pi
192192 −1.23556 + 3.21875i −0.0891690 + 0.232293i
193193 −2.02940 7.57383i −0.146080 0.545176i −0.999705 0.0242890i 0.992268π-0.992268\pi
0.853625 0.520887i 0.174399π-0.174399\pi
194194 −1.41334 + 13.4470i −0.101472 + 0.965442i
195195 2.31475 4.48558i 0.165763 0.321219i
196196 −6.26843 7.49555i −0.447745 0.535396i
197197 −16.1577 2.55912i −1.15119 0.182330i −0.448469 0.893799i 0.648030π-0.648030\pi
−0.702718 + 0.711469i 0.748030π0.748030\pi
198198 0.0938827 + 1.79139i 0.00667196 + 0.127308i
199199 −13.6561 + 23.6530i −0.968053 + 1.67672i −0.266874 + 0.963731i 0.585991π0.585991\pi
−0.701179 + 0.712985i 0.747343π0.747343\pi
200200 −12.2712 4.85634i −0.867706 0.343395i
201201 8.26242 4.77031i 0.582786 0.336472i
202202 −2.45507 1.25092i −0.172738 0.0880144i
203203 −2.51634 18.0127i −0.176613 1.26424i
204204 −0.856878 1.17939i −0.0599935 0.0825739i
205205 −0.122364 0.0803646i −0.00854626 0.00561291i
206206 2.01212 + 4.51928i 0.140191 + 0.314873i
207207 1.92351 0.515402i 0.133693 0.0358229i
208208 −1.15625 + 0.936312i −0.0801715 + 0.0649216i
209209 2.16202 6.65402i 0.149550 0.460268i
210210 −5.07553 + 0.955090i −0.350245 + 0.0659075i
211211 4.53761 + 13.9653i 0.312382 + 0.961413i 0.976819 + 0.214068i 0.0686715π0.0686715\pi
−0.664437 + 0.747345i 0.731328π0.731328\pi
212212 −13.0762 8.49176i −0.898075 0.583216i
213213 −0.633938 + 12.0963i −0.0434367 + 0.828823i
214214 1.59282 7.49361i 0.108883 0.512253i
215215 −9.18319 + 5.23893i −0.626288 + 0.357292i
216216 13.3599 + 4.34090i 0.909027 + 0.295361i
217217 1.82978 25.8600i 0.124214 1.75549i
218218 −5.95255 + 5.95255i −0.403158 + 0.403158i
219219 −1.83953 0.193342i −0.124304 0.0130648i
220220 −3.86075 1.50490i −0.260292 0.101461i
221221 0.195344 + 1.85857i 0.0131402 + 0.125021i
222222 −6.24575 + 2.39752i −0.419187 + 0.160911i
223223 9.81559 19.2642i 0.657301 1.29003i −0.286046 0.958216i 0.592341π-0.592341\pi
0.943346 0.331809i 0.107659π-0.107659\pi
224224 15.0891 + 3.49672i 1.00818 + 0.233634i
225225 −2.77129 + 8.23890i −0.184753 + 0.549260i
226226 −2.56903 4.44970i −0.170890 0.295989i
227227 −7.88440 + 5.12019i −0.523306 + 0.339839i −0.779107 0.626891i 0.784327π-0.784327\pi
0.255801 + 0.966729i 0.417661π0.417661\pi
228228 −6.42129 5.19986i −0.425260 0.344369i
229229 −2.84380 1.26614i −0.187923 0.0836689i 0.310618 0.950535i 0.399464π-0.399464\pi
−0.498541 + 0.866866i 0.666131π0.666131\pi
230230 0.321565 1.96462i 0.0212033 0.129543i
231231 −3.87312 + 0.749537i −0.254833 + 0.0493159i
232232 12.8299 + 12.8299i 0.842326 + 0.842326i
233233 18.3487 + 22.6587i 1.20206 + 1.48442i 0.831420 + 0.555644i 0.187528π0.187528\pi
0.370640 + 0.928777i 0.379138π0.379138\pi
234234 −1.81720 2.01821i −0.118794 0.131934i
235235 −0.415321 + 0.0414867i −0.0270925 + 0.00270629i
236236 5.00526 + 4.50675i 0.325814 + 0.293365i
237237 −5.32129 10.4436i −0.345655 0.678386i
238238 1.37656 1.32713i 0.0892292 0.0860252i
239239 3.05660 0.993150i 0.197715 0.0642416i −0.208485 0.978025i 0.566853π-0.566853\pi
0.406201 + 0.913784i 0.366853π0.366853\pi
240240 −1.25114 + 1.37520i −0.0807607 + 0.0887686i
241241 −19.9300 + 17.9451i −1.28381 + 1.15594i −0.304733 + 0.952438i 0.598567π0.598567\pi
−0.979074 + 0.203506i 0.934766π0.934766\pi
242242 −6.70302 2.57305i −0.430886 0.165402i
243243 3.91085 14.5955i 0.250881 0.936301i
244244 5.16561 + 3.75303i 0.330694 + 0.240263i
245245 4.99501 + 14.8341i 0.319120 + 0.947714i
246246 0.0462382 0.0335940i 0.00294804 0.00214188i
247247 3.79589 + 9.88862i 0.241527 + 0.629198i
248248 14.0859 + 21.6904i 0.894457 + 1.37734i
249249 6.08480 + 3.51306i 0.385609 + 0.222631i
250250 6.36708 + 5.91393i 0.402689 + 0.374030i
251251 13.7541i 0.868150i 0.900877 + 0.434075i 0.142925π0.142925\pi
−0.900877 + 0.434075i 0.857075π0.857075\pi
252252 1.12014 6.32210i 0.0705625 0.398255i
253253 0.237881 1.50192i 0.0149555 0.0944250i
254254 −5.84558 + 13.1294i −0.366784 + 0.823811i
255255 0.592764 + 2.25878i 0.0371203 + 0.141450i
256256 −12.2281 + 5.44431i −0.764257 + 0.340269i
257257 8.92621 + 2.39177i 0.556802 + 0.149195i 0.526237 0.850338i 0.323603π-0.323603\pi
0.0305651 + 0.999533i 0.490269π0.490269\pi
258258 −0.645695 4.07676i −0.0401992 0.253808i
259259 9.81526 + 17.7418i 0.609890 + 1.10242i
260260 5.97615 1.90774i 0.370625 0.118313i
261261 7.99672 8.88126i 0.494985 0.549736i
262262 13.0069 + 0.681663i 0.803569 + 0.0421133i
263263 8.38032 + 0.439194i 0.516752 + 0.0270819i 0.308930 0.951085i 0.400029π-0.400029\pi
0.207822 + 0.978167i 0.433362π0.433362\pi
264264 2.63341 2.92470i 0.162075 0.180003i
265265 14.5761 + 20.2815i 0.895404 + 1.24588i
266266 5.58947 9.28504i 0.342712 0.569303i
267267 2.75761 + 17.4109i 0.168763 + 1.06553i
268268 11.4532 + 3.06887i 0.699615 + 0.187461i
269269 4.02317 1.79123i 0.245297 0.109213i −0.280406 0.959882i 0.590469π-0.590469\pi
0.525703 + 0.850668i 0.323802π0.323802\pi
270270 −7.15826 5.85805i −0.435638 0.356510i
271271 −1.39604 + 3.13556i −0.0848035 + 0.190472i −0.950970 0.309285i 0.899910π-0.899910\pi
0.866166 + 0.499756i 0.166577π0.166577\pi
272272 0.107679 0.679856i 0.00652898 0.0412223i
273273 3.84278 4.57197i 0.232576 0.276708i
274274 2.56689i 0.155072i
275275 4.88673 + 4.49219i 0.294681 + 0.270889i
276276 −1.55525 0.897924i −0.0936150 0.0540487i
277277 4.19321 + 6.45697i 0.251945 + 0.387962i 0.941901 0.335889i 0.109037π-0.109037\pi
−0.689956 + 0.723851i 0.742370π0.742370\pi
278278 −2.40300 6.26003i −0.144122 0.375451i
279279 13.7815 10.0128i 0.825076 0.599453i
280280 −12.8931 8.80922i −0.770508 0.526452i
281281 19.6291 + 14.2614i 1.17097 + 0.850761i 0.991125 0.132934i 0.0424398π-0.0424398\pi
0.179847 + 0.983695i 0.442440π0.442440\pi
282282 0.0421749 0.157399i 0.00251148 0.00937296i
283283 −6.76781 2.59792i −0.402304 0.154430i 0.148798 0.988868i 0.452459π-0.452459\pi
−0.551103 + 0.834437i 0.685793π0.685793\pi
284284 −11.1873 + 10.0731i −0.663846 + 0.597730i
285285 6.55874 + 11.4966i 0.388506 + 0.681003i
286286 −1.97231 + 0.640843i −0.116625 + 0.0378939i
287287 −0.120223 0.124701i −0.00709655 0.00736086i
288288 4.62055 + 9.06833i 0.272268 + 0.534357i
289289 11.9909 + 10.7967i 0.705350 + 0.635100i
290290 −4.80305 10.9394i −0.282045 0.642382i
291291 −13.0740 14.5201i −0.766410 0.851185i
292292 −1.44667 1.78649i −0.0846599 0.104546i
293293 −22.0206 22.0206i −1.28645 1.28645i −0.936925 0.349529i 0.886342π-0.886342\pi
−0.349529 0.936925i 0.613658π-0.613658\pi
294294 −6.10676 0.223359i −0.356154 0.0130265i
295295 −4.84852 9.63836i −0.282291 0.561167i
296296 −18.4787 8.22726i −1.07405 0.478200i
297297 −5.49084 4.44640i −0.318611 0.258006i
298298 −0.0257681 + 0.0167340i −0.00149271 + 0.000969375i
299299 1.15108 + 1.99372i 0.0665684 + 0.115300i
300300 7.02100 3.48660i 0.405358 0.201299i
301301 −11.9659 + 3.64755i −0.689705 + 0.210241i
302302 3.45587 6.78253i 0.198863 0.390291i
303303 3.71722 1.42691i 0.213549 0.0819738i
304304 −0.407803 3.87999i −0.0233891 0.222533i
305305 −5.52634 8.60671i −0.316437 0.492819i
306306 1.24955 + 0.131333i 0.0714322 + 0.00750783i
307307 −2.33566 + 2.33566i −0.133303 + 0.133303i −0.770610 0.637307i 0.780048π-0.780048\pi
0.637307 + 0.770610i 0.280048π0.280048\pi
308308 −4.06240 2.74501i −0.231477 0.156412i
309309 −6.79877 2.20905i −0.386768 0.125669i
310310 −3.45470 16.6757i −0.196214 0.947114i
311311 1.28441 6.04267i 0.0728321 0.342648i −0.926611 0.376022i 0.877292π-0.877292\pi
0.999443 + 0.0333736i 0.0106251π0.0106251\pi
312312 −0.311828 + 5.95003i −0.0176538 + 0.336854i
313313 9.39345 + 6.10018i 0.530949 + 0.344802i 0.782107 0.623144i 0.214145π-0.214145\pi
−0.251158 + 0.967946i 0.580811π0.580811\pi
314314 −3.16170 9.73071i −0.178425 0.549136i
315315 −5.34989 + 8.78418i −0.301432 + 0.494933i
316316 4.50152 13.8542i 0.253230 0.779362i
317317 6.98886 5.65947i 0.392534 0.317867i −0.412654 0.910888i 0.635398π-0.635398\pi
0.805187 + 0.593021i 0.202065π0.202065\pi
318318 −9.41859 + 2.52370i −0.528168 + 0.141522i
319319 −3.71186 8.33698i −0.207824 0.466781i
320320 6.85635 0.323864i 0.383281 0.0181045i
321321 6.50714 + 8.95630i 0.363193 + 0.499892i
322322 0.884192 2.18326i 0.0492741 0.121668i
323323 −4.36630 2.22474i −0.242947 0.123788i
324324 −0.921313 + 0.531920i −0.0511840 + 0.0295511i
325325 −10.0294 0.629452i −0.556331 0.0349157i
326326 1.35707 2.35051i 0.0751610 0.130183i
327327 −0.636653 12.1481i −0.0352070 0.671790i
328328 0.170676 + 0.0270324i 0.00942401 + 0.00149262i
329329 −0.490129 0.0605914i −0.0270217 0.00334051i
330330 −2.31502 + 1.16456i −0.127438 + 0.0641068i
331331 0.755353 7.18671i 0.0415180 0.395017i −0.953953 0.299955i 0.903028π-0.903028\pi
0.995471 0.0950622i 0.0303050π-0.0303050\pi
332332 2.26005 + 8.43463i 0.124036 + 0.462910i
333333 −4.77456 + 12.4381i −0.261644 + 0.681606i
334334 −14.5616 + 3.09517i −0.796777 + 0.169360i
335335 −15.3087 11.2436i −0.836404 0.614301i
336336 −1.80301 + 1.26026i −0.0983624 + 0.0687531i
337337 9.03950 4.60585i 0.492413 0.250897i −0.190108 0.981763i 0.560884π-0.560884\pi
0.682521 + 0.730866i 0.260884π0.260884\pi
338338 −3.79320 + 5.84101i −0.206323 + 0.317709i
339339 7.26254 + 1.54370i 0.394447 + 0.0838423i
340340 −1.46410 + 2.50594i −0.0794018 + 0.135904i
341341 −2.70455 12.7239i −0.146459 0.689038i
342342 7.03363 1.11402i 0.380335 0.0602392i
343343 1.89023 + 18.4235i 0.102063 + 0.994778i
344344 7.33539 10.0963i 0.395498 0.544356i
345345 1.79885 + 2.24498i 0.0968468 + 0.120866i
346346 −3.83278 + 0.402841i −0.206051 + 0.0216569i
347347 −5.04462 + 6.22958i −0.270809 + 0.334422i −0.894349 0.447370i 0.852361π-0.852361\pi
0.623540 + 0.781792i 0.285694π0.285694\pi
348348 −10.7628 + 0.564054i −0.576946 + 0.0302365i
349349 8.82065 0.472158 0.236079 0.971734i 0.424138π-0.424138\pi
0.236079 + 0.971734i 0.424138π0.424138\pi
350350 5.80329 + 8.48774i 0.310199 + 0.453689i
351351 10.6965 0.570939
352352 7.76119 0.406747i 0.413673 0.0216797i
353353 −10.5951 + 13.0839i −0.563923 + 0.696387i −0.976740 0.214427i 0.931211π-0.931211\pi
0.412817 + 0.910814i 0.364545π0.364545\pi
354354 4.18910 0.440292i 0.222648 0.0234012i
355355 22.5576 8.52579i 1.19723 0.452502i
356356 −12.8773 + 17.7241i −0.682497 + 0.939376i
357357 0.0941494 + 2.76151i 0.00498292 + 0.146155i
358358 −15.5477 + 2.46251i −0.821720 + 0.130148i
359359 −2.87394 13.5208i −0.151681 0.713602i −0.986590 0.163215i 0.947813π-0.947813\pi
0.834910 0.550387i 0.185520π-0.185520\pi
360360 −1.01986 10.2098i −0.0537514 0.538102i
361361 −8.58309 1.82439i −0.451742 0.0960206i
362362 1.92781 2.96857i 0.101323 0.156024i
363363 9.24451 4.71031i 0.485211 0.247227i
364364 7.39491 0.640814i 0.387599 0.0335878i
365365 1.11984 + 3.50801i 0.0586153 + 0.183618i
366366 3.90590 0.830225i 0.204165 0.0433966i
367367 −0.372403 + 0.970143i −0.0194393 + 0.0506410i −0.942957 0.332916i 0.891968π-0.891968\pi
0.923517 + 0.383557i 0.125301π0.125301\pi
368368 −0.219464 0.819049i −0.0114403 0.0426959i
369369 0.0118973 0.113195i 0.000619350 0.00589272i
370370 9.36929 + 9.46647i 0.487086 + 0.492138i
371371 11.5244 + 27.2124i 0.598319 + 1.41280i
372372 −15.1732 2.40320i −0.786695 0.124600i
373373 −1.15167 21.9752i −0.0596314 1.13783i −0.850544 0.525904i 0.823727π-0.823727\pi
0.790912 0.611930i 0.209606π-0.209606\pi
374374 0.479720 0.830899i 0.0248057 0.0429648i
375375 −12.5074 + 1.11916i −0.645880 + 0.0577930i
376376 0.426675 0.246341i 0.0220041 0.0127041i
377377 12.3102 + 6.27237i 0.634009 + 0.323044i
378378 −6.73093 8.62989i −0.346202 0.443874i
379379 −17.8299 24.5408i −0.915862 1.26058i −0.965125 0.261790i 0.915687π-0.915687\pi
0.0492625 0.998786i 0.484313π-0.484313\pi
380380 −4.33944 + 15.8671i −0.222609 + 0.813966i
381381 −8.44719 18.9727i −0.432762 0.972000i
382382 11.6209 3.11380i 0.594575 0.159316i
383383 −16.6188 + 13.4576i −0.849179 + 0.687652i −0.951683 0.307081i 0.900648π-0.900648\pi
0.102504 + 0.994733i 0.467315π0.467315\pi
384384 3.23567 9.95838i 0.165120 0.508186i
385385 4.46623 + 6.46039i 0.227620 + 0.329252i
386386 −1.88327 5.79612i −0.0958562 0.295015i
387387 −6.89379 4.47688i −0.350431 0.227572i
388388 1.27088 24.2498i 0.0645190 1.23110i
389389 4.37542 20.5847i 0.221842 1.04369i −0.716395 0.697695i 0.754209π-0.754209\pi
0.938238 0.345992i 0.112457π-0.112457\pi
390390 1.61420 3.57579i 0.0817383 0.181067i
391391 −1.01295 0.329128i −0.0512271 0.0166447i
392392 −12.5783 13.5334i −0.635301 0.683539i
393393 −13.3088 + 13.3088i −0.671340 + 0.671340i
394394 −12.6454 1.32909i −0.637066 0.0669583i
395395 −14.7787 + 18.0589i −0.743596 + 0.908639i
396396 −0.336752 3.20399i −0.0169224 0.161006i
397397 4.78454 1.83661i 0.240129 0.0921770i −0.235327 0.971916i 0.575616π-0.575616\pi
0.475457 + 0.879739i 0.342283π0.342283\pi
398398 −9.63744 + 18.9145i −0.483081 + 0.948100i
399399 4.56645 + 14.9804i 0.228608 + 0.749960i
400400 3.50821 + 1.18004i 0.175410 + 0.0590022i
401401 −17.1661 29.7326i −0.857235 1.48477i −0.874556 0.484924i 0.838847π-0.838847\pi
0.0173216 0.999850i 0.494486π-0.494486\pi
402402 6.21910 4.03873i 0.310180 0.201433i
403403 15.3047 + 12.3935i 0.762382 + 0.617364i
404404 4.52068 + 2.01273i 0.224912 + 0.100137i
405405 1.68454 0.257902i 0.0837053 0.0128153i
406406 −2.68586 13.8788i −0.133297 0.688792i
407407 7.19393 + 7.19393i 0.356590 + 0.356590i
408408 −1.73474 2.14223i −0.0858825 0.106056i
409409 17.5576 + 19.4997i 0.868168 + 0.964198i 0.999632 0.0271225i 0.00863443π-0.00863443\pi
−0.131464 + 0.991321i 0.541968π0.541968\pi
410410 −0.0982457 0.0574001i −0.00485201 0.00283479i
411411 −2.75655 2.48201i −0.135970 0.122428i
412412 −4.03345 7.91610i −0.198714 0.389998i
413413 −3.07812 12.3893i −0.151464 0.609635i
414414 1.47203 0.478291i 0.0723462 0.0235067i
415415 1.53390 13.9037i 0.0752963 0.682505i
416416 −8.74388 + 7.87302i −0.428704 + 0.386007i
417417 9.04608 + 3.47247i 0.442989 + 0.170047i
418418 1.40745 5.25268i 0.0688407 0.256917i
419419 20.8379 + 15.1396i 1.01800 + 0.739617i 0.965871 0.259023i 0.0834006π-0.0834006\pi
0.0521248 + 0.998641i 0.483401π0.483401\pi
420420 9.01305 2.18999i 0.439792 0.106860i
421421 −9.53283 + 6.92601i −0.464602 + 0.337553i −0.795334 0.606172i 0.792704π-0.792704\pi
0.330732 + 0.943725i 0.392704π0.392704\pi
422422 4.09009 + 10.6551i 0.199103 + 0.518680i
423423 −0.176741 0.272158i −0.00859345 0.0132328i
424424 −25.5318 14.7408i −1.23994 0.715877i
425425 3.64309 2.88839i 0.176716 0.140107i
426426 9.41470i 0.456144i
427427 −4.12978 11.3757i −0.199854 0.550510i
428428 −2.15233 + 13.5893i −0.104037 + 0.656864i
429429 1.21890 2.73769i 0.0588489 0.132177i
430430 −6.91472 + 4.43992i −0.333457 + 0.214112i
431431 −14.2385 + 6.33937i −0.685842 + 0.305357i −0.719914 0.694063i 0.755819π-0.755819\pi
0.0340723 + 0.999419i 0.489152π0.489152\pi
432432 −3.80556 1.01970i −0.183095 0.0490602i
433433 0.121416 + 0.766591i 0.00583489 + 0.0368400i 0.990434 0.137987i 0.0440633π-0.0440633\pi
−0.984599 + 0.174827i 0.944063π0.944063\pi
434434 0.368312 20.1465i 0.0176796 0.967063i
435435 16.3918 + 5.41969i 0.785928 + 0.259854i
436436 10.1163 11.2352i 0.484481 0.538070i
437437 −6.02845 0.315938i −0.288380 0.0151134i
438438 −1.43567 0.0752404i −0.0685991 0.00359512i
439439 7.06803 7.84984i 0.337339 0.374653i −0.550478 0.834850i 0.685555π-0.685555\pi
0.887817 + 0.460197i 0.152221π0.152221\pi
440440 −7.43911 2.45962i −0.354646 0.117258i
441441 −8.46810 + 8.74002i −0.403243 + 0.416191i
442442 0.227225 + 1.43464i 0.0108080 + 0.0682391i
443443 26.2546 + 7.03490i 1.24739 + 0.334238i 0.821329 0.570455i 0.193233π-0.193233\pi
0.426064 + 0.904693i 0.359900π0.359900\pi
444444 10.9762 4.88694i 0.520909 0.231924i
445445 29.5311 18.9618i 1.39991 0.898878i
446446 6.83506 15.3518i 0.323650 0.726929i
447447 0.00694557 0.0438526i 0.000328514 0.00207416i
448448 7.99703 + 1.41691i 0.377824 + 0.0669426i
449449 39.0168i 1.84131i −0.390372 0.920657i 0.627654π-0.627654\pi
0.390372 0.920657i 0.372346π-0.372346\pi
450450 −1.81588 + 6.50762i −0.0856016 + 0.306772i
451451 −0.0752701 0.0434572i −0.00354433 0.00204632i
452452 5.02573 + 7.73894i 0.236390 + 0.364009i
453453 3.94207 + 10.2694i 0.185215 + 0.482501i
454454 −5.91145 + 4.29492i −0.277438 + 0.201571i
455455 −11.4099 3.34576i −0.534902 0.156852i
456456 −12.6398 9.18334i −0.591912 0.430049i
457457 −5.95677 + 22.2310i −0.278646 + 1.03992i 0.674713 + 0.738080i 0.264268π0.264268\pi
−0.953359 + 0.301840i 0.902399π0.902399\pi
458458 −2.25881 0.867075i −0.105547 0.0405158i
459459 −3.67760 + 3.31133i −0.171656 + 0.154560i
460460 −0.392059 + 3.55372i −0.0182798 + 0.165693i
461461 −23.0880 + 7.50175i −1.07532 + 0.349391i −0.792556 0.609799i 0.791250π-0.791250\pi
−0.282760 + 0.959191i 0.591250π0.591250\pi
462462 −2.97576 + 0.739328i −0.138445 + 0.0343967i
463463 2.79874 + 5.49284i 0.130069 + 0.255274i 0.946851 0.321671i 0.104245π-0.104245\pi
−0.816783 + 0.576945i 0.804245π0.804245\pi
464464 −3.78173 3.40509i −0.175563 0.158077i
465465 21.2482 + 12.4143i 0.985362 + 0.575697i
466466 15.1636 + 16.8409i 0.702441 + 0.780140i
467467 18.4601 + 22.7963i 0.854231 + 1.05489i 0.997868 + 0.0652571i 0.0207868π0.0207868\pi
−0.143637 + 0.989630i 0.545880π0.545880\pi
468468 3.44880 + 3.44880i 0.159421 + 0.159421i
469469 −14.7303 16.9736i −0.680182 0.783767i
470470 −0.320677 + 0.0490956i −0.0147917 + 0.00226461i
471471 13.5068 + 6.01362i 0.622361 + 0.277093i
472472 9.89733 + 8.01470i 0.455561 + 0.368906i
473473 −5.26423 + 3.41863i −0.242050 + 0.157189i
474474 −4.55512 7.88970i −0.209224 0.362386i
475475 15.7078 21.1574i 0.720725 0.970768i
476476 −2.34409 + 2.50956i −0.107441 + 0.115026i
477477 −8.81577 + 17.3019i −0.403646 + 0.792200i
478478 2.33208 0.895202i 0.106667 0.0409456i
479479 0.950688 + 9.04519i 0.0434380 + 0.413285i 0.994536 + 0.104395i 0.0332908π0.0332908\pi
−0.951098 + 0.308890i 0.900043π0.900043\pi
480480 −9.31162 + 11.3784i −0.425015 + 0.519349i
481481 −15.3180 1.60999i −0.698441 0.0734091i
482482 −14.7394 + 14.7394i −0.671360 + 0.671360i
483483 1.48961 + 3.06058i 0.0677798 + 0.139261i
484484 12.2635 + 3.98466i 0.557433 + 0.181121i
485485 −16.0048 + 35.4539i −0.726739 + 1.60988i
486486 2.44182 11.4878i 0.110763 0.521099i
487487 −0.0277991 + 0.530438i −0.00125970 + 0.0240364i −0.999187 0.0403139i 0.987164π-0.987164\pi
0.997927 + 0.0643504i 0.0204975π0.0204975\pi
488488 10.1255 + 6.57559i 0.458361 + 0.297663i
489489 1.21199 + 3.73011i 0.0548080 + 0.168682i
490490 4.48046 + 11.3108i 0.202407 + 0.510968i
491491 1.98288 6.10267i 0.0894861 0.275410i −0.896291 0.443466i 0.853749π-0.853749\pi
0.985777 + 0.168056i 0.0537489π0.0537489\pi
492492 −0.0797694 + 0.0645960i −0.00359628 + 0.00291221i
493493 −6.17415 + 1.65436i −0.278070 + 0.0745086i
494494 3.34855 + 7.52097i 0.150658 + 0.338384i
495495 −1.36140 + 4.97793i −0.0611902 + 0.223741i
496496 −4.26357 5.86830i −0.191440 0.263494i
497497 28.2589 3.94772i 1.26758 0.177079i
498498 4.86582 + 2.47926i 0.218043 + 0.111098i
499499 5.43364 3.13711i 0.243243 0.140437i −0.373423 0.927661i 0.621816π-0.621816\pi
0.616666 + 0.787225i 0.288483π0.288483\pi
500500 −11.9751 10.0080i −0.535541 0.447572i
501501 10.7562 18.6303i 0.480553 0.832343i
502502 0.559489 + 10.6757i 0.0249712 + 0.476479i
503503 −4.92568 0.780151i −0.219625 0.0347852i 0.0456521 0.998957i 0.485463π-0.485463\pi
−0.265277 + 0.964172i 0.585463π0.585463\pi
504504 1.48951 12.0488i 0.0663480 0.536695i
505505 −5.57623 5.63407i −0.248139 0.250713i
506506 0.123544 1.17544i 0.00549220 0.0522548i
507507 −2.60482 9.72131i −0.115684 0.431739i
508508 9.24984 24.0966i 0.410395 1.06912i
509509 −22.1320 + 4.70429i −0.980982 + 0.208514i −0.670374 0.742024i 0.733866π-0.733866\pi
−0.310609 + 0.950538i 0.600533π0.600533\pi
510510 0.551976 + 1.72911i 0.0244419 + 0.0765663i
511511 0.376159 + 4.34082i 0.0166403 + 0.192027i
512512 7.34327 3.74158i 0.324530 0.165356i
513513 −15.2763 + 23.5235i −0.674467 + 1.03859i
514514 7.02566 + 1.49335i 0.309889 + 0.0658688i
515515 1.41460 + 14.1615i 0.0623348 + 0.624030i
516516 1.54122 + 7.25087i 0.0678484 + 0.319202i
517517 −0.244752 + 0.0387649i −0.0107642 + 0.00170488i
518518 8.34013 + 13.3716i 0.366444 + 0.587513i
519519 3.27343 4.50548i 0.143687 0.197769i
520520 11.0959 4.19375i 0.486586 0.183908i
521521 30.6917 3.22582i 1.34463 0.141326i 0.595287 0.803513i 0.297038π-0.297038\pi
0.749339 + 0.662187i 0.230372π0.230372\pi
522522 5.84564 7.21877i 0.255857 0.315957i
523523 −30.5923 + 1.60327i −1.33771 + 0.0701062i −0.707716 0.706497i 0.750274π-0.750274\pi
−0.629990 + 0.776603i 0.716941π0.716941\pi
524524 −23.3916 −1.02187
525525 −14.7262 1.97499i −0.642706 0.0861955i
526526 6.52252 0.284395
527527 −9.09861 + 0.476838i −0.396342 + 0.0207714i
528528 −0.694637 + 0.857805i −0.0302302 + 0.0373312i
529529 21.5691 2.26701i 0.937789 0.0985656i
530530 12.1387 + 15.1492i 0.527273 + 0.658041i
531531 4.93056 6.78633i 0.213968 0.294502i
532532 −9.15184 + 17.1778i −0.396783 + 0.744754i
533533 0.129963 0.0205840i 0.00562930 0.000891594i
534534 2.84865 + 13.4018i 0.123273 + 0.579954i
535535 11.1183 19.0301i 0.480688 0.822744i
536536 21.9306 + 4.66148i 0.947256 + 0.201345i
537537 12.3891 19.0775i 0.534628 0.823254i
538538 3.04985 1.55398i 0.131488 0.0669966i
539539 3.46693 + 8.62194i 0.149331 + 0.371373i
540540 13.3888 + 9.83344i 0.576161 + 0.423164i
541541 −38.7310 + 8.23253i −1.66518 + 0.353944i −0.941712 0.336419i 0.890784π-0.890784\pi
−0.723463 + 0.690363i 0.757451π0.757451\pi
542542 −0.956035 + 2.49056i −0.0410652 + 0.106979i
543543 1.32384 + 4.94065i 0.0568115 + 0.212023i
544544 0.569001 5.41369i 0.0243957 0.232110i
545545 −21.6351 + 10.8834i −0.926747 + 0.466194i
546546 2.79672 3.70500i 0.119689 0.158559i
547547 37.0235 + 5.86395i 1.58301 + 0.250724i 0.885079 0.465440i 0.154104π-0.154104\pi
0.697932 + 0.716164i 0.254104π0.254104\pi
548548 −0.241267 4.60365i −0.0103064 0.196658i
549549 3.97611 6.88682i 0.169696 0.293922i
550550 3.97573 + 3.28798i 0.169525 + 0.140200i
551551 −31.3750 + 18.1143i −1.33662 + 0.771697i
552552 −3.02561 1.54162i −0.128778 0.0656159i
553553 −21.7715 + 16.9808i −0.925817 + 0.722097i
554554 3.51735 + 4.84122i 0.149438 + 0.205684i
555555 −19.2254 + 0.908122i −0.816071 + 0.0385476i
556556 4.89811 + 11.0013i 0.207726 + 0.466560i
557557 5.81572 1.55832i 0.246420 0.0660280i −0.133495 0.991050i 0.542620π-0.542620\pi
0.379915 + 0.925021i 0.375953π0.375953\pi
558558 10.2896 8.33239i 0.435595 0.352738i
559559 2.93652 9.03767i 0.124201 0.382253i
560560 3.74040 + 2.27804i 0.158061 + 0.0962647i
561561 0.428435 + 1.31859i 0.0180885 + 0.0556708i
562562 15.8159 + 10.2709i 0.667152 + 0.433253i
563563 1.58169 30.1805i 0.0666604 1.27196i −0.736600 0.676329i 0.763570π-0.763570\pi
0.803260 0.595628i 0.203097π-0.203097\pi
564564 −0.0608453 + 0.286255i −0.00256205 + 0.0120535i
565565 −2.99866 14.4744i −0.126154 0.608942i
566566 −5.35873 1.74116i −0.225244 0.0731863i
567567 2.01137 + 0.142319i 0.0844694 + 0.00597682i
568568 −20.1280 + 20.1280i −0.844552 + 0.844552i
569569 −4.95634 0.520932i −0.207781 0.0218386i 6.62580e−5 1.00000i 0.499979π-0.499979\pi
−0.207847 + 0.978161i 0.566646π0.566646\pi
570570 5.55844 + 8.65670i 0.232817 + 0.362589i
571571 0.255295 + 2.42897i 0.0106837 + 0.101649i 0.998564 0.0535674i 0.0170592π-0.0170592\pi
−0.987880 + 0.155216i 0.950393π0.950393\pi
572572 3.47706 1.33472i 0.145383 0.0558073i
573573 −7.89270 + 15.4903i −0.329722 + 0.647117i
574574 −0.0983877 0.0919002i −0.00410662 0.00383584i
575575 2.65263 5.07591i 0.110622 0.211680i
576576 2.66831 + 4.62165i 0.111180 + 0.192569i
577577 20.3829 13.2368i 0.848553 0.551057i −0.0455274 0.998963i 0.514497π-0.514497\pi
0.894081 + 0.447906i 0.147830π0.147830\pi
578578 9.74635 + 7.89244i 0.405395 + 0.328282i
579579 8.04537 + 3.58203i 0.334354 + 0.148864i
580580 9.64235 + 19.1680i 0.400377 + 0.795908i
581581 5.40137 15.6447i 0.224087 0.649052i
582582 −10.7384 10.7384i −0.445123 0.445123i
583583 9.33174 + 11.5237i 0.386481 + 0.477264i
584584 −2.90851 3.23023i −0.120355 0.133668i
585585 −3.14097 7.15383i −0.129863 0.295774i
586586 −17.9877 16.1962i −0.743066 0.669060i
587587 −4.09368 8.03430i −0.168964 0.331611i 0.790961 0.611866i 0.209581π-0.209581\pi
−0.959926 + 0.280255i 0.909581π0.909581\pi
588588 10.9733 0.173399i 0.452532 0.00715085i
589589 −49.1130 + 15.9578i −2.02366 + 0.657528i
590590 −4.15540 7.28390i −0.171075 0.299873i
591591 13.6545 12.2946i 0.561671 0.505731i
592592 5.29629 + 2.03306i 0.217676 + 0.0835581i
593593 6.63849 24.7752i 0.272610 1.01740i −0.684816 0.728716i 0.740117π-0.740117\pi
0.957426 0.288679i 0.0932160π-0.0932160\pi
594594 −4.44277 3.22786i −0.182289 0.132441i
595595 4.95860 2.38184i 0.203283 0.0976458i
596596 0.0446416 0.0324340i 0.00182859 0.00132855i
597597 −10.9933 28.6386i −0.449926 1.17210i
598598 0.974545 + 1.50067i 0.0398521 + 0.0613669i
599599 23.1803 + 13.3832i 0.947123 + 0.546822i 0.892186 0.451668i 0.149171π-0.149171\pi
0.0549370 + 0.998490i 0.482504π0.482504\pi
600600 12.9126 7.27848i 0.527155 0.297143i
601601 3.83116i 0.156276i −0.996943 0.0781382i 0.975102π-0.975102\pi
0.996943 0.0781382i 0.0248975π-0.0248975\pi
602602 −9.13938 + 3.31791i −0.372493 + 0.135228i
603603 2.31015 14.5857i 0.0940764 0.593975i
604604 −5.56051 + 12.4891i −0.226254 + 0.508175i
605605 −15.9854 13.0818i −0.649898 0.531852i
606606 2.82720 1.25875i 0.114847 0.0511332i
607607 −32.5210 8.71399i −1.31999 0.353690i −0.471015 0.882125i 0.656112π-0.656112\pi
−0.848974 + 0.528435i 0.822779π0.822779\pi
608608 −4.82648 30.4732i −0.195740 1.23585i
609609 17.5013 + 10.5355i 0.709187 + 0.426921i
610610 −4.63955 6.45557i −0.187850 0.261379i
611611 0.251029 0.278796i 0.0101555 0.0112789i
612612 −2.25339 0.118095i −0.0910877 0.00477370i
613613 −44.3520 2.32439i −1.79136 0.0938813i −0.872537 0.488547i 0.837527π-0.837527\pi
−0.918825 + 0.394666i 0.870860π0.870860\pi
614614 −1.71789 + 1.90791i −0.0693284 + 0.0769970i
615615 0.156638 0.0500028i 0.00631625 0.00201631i
616616 −7.94261 4.78134i −0.320017 0.192646i
617617 −5.46815 34.5246i −0.220140 1.38991i −0.811902 0.583794i 0.801568π-0.801568\pi
0.591762 0.806112i 0.298432π-0.298432\pi
618618 −5.36695 1.43807i −0.215890 0.0578476i
619619 12.2138 5.43792i 0.490913 0.218568i −0.146324 0.989237i 0.546744π-0.546744\pi
0.637237 + 0.770668i 0.280077π0.280077\pi
620620 7.76329 + 29.5826i 0.311781 + 1.18807i
621621 −2.47955 + 5.56917i −0.0995011 + 0.223483i
622622 0.751132 4.74246i 0.0301176 0.190155i
623623 39.0321 14.1700i 1.56379 0.567709i
624624 1.67106i 0.0668960i
625625 12.0506 + 21.9040i 0.482022 + 0.876159i
626626 7.53917 + 4.35274i 0.301326 + 0.173971i
627627 4.27987 + 6.59042i 0.170921 + 0.263196i
628628 6.58503 + 17.1546i 0.262771 + 0.684543i
629629 5.76493 4.18846i 0.229863 0.167005i
630630 −3.79517 + 7.03575i −0.151203 + 0.280311i
631631 11.1996 + 8.13699i 0.445849 + 0.323928i 0.787955 0.615733i 0.211140π-0.211140\pi
−0.342106 + 0.939662i 0.611140π0.611140\pi
632632 7.12911 26.6062i 0.283581 1.05834i
633633 −15.3972 5.91041i −0.611982 0.234918i
634634 5.19442 4.67707i 0.206297 0.185750i
635635 −27.8244 + 30.5834i −1.10418 + 1.21366i
636636 16.6548 5.41147i 0.660405 0.214579i
637637 −12.2935 6.84101i −0.487088 0.271051i
638638 −3.22021 6.32003i −0.127489 0.250212i
639639 13.9332 + 12.5455i 0.551189 + 0.496293i
640640 −20.7428 + 2.07201i −0.819931 + 0.0819035i
641641 −1.56927 1.74285i −0.0619824 0.0688384i 0.711356 0.702832i 0.248081π-0.248081\pi
−0.773339 + 0.633993i 0.781415π0.781415\pi
642642 5.41505 + 6.68703i 0.213715 + 0.263916i
643643 −16.5284 16.5284i −0.651816 0.651816i 0.301614 0.953430i 0.402475π-0.402475\pi
−0.953430 + 0.301614i 0.902475π0.902475\pi
644644 −1.38057 + 3.99872i −0.0544020 + 0.157572i
645645 1.91809 11.7187i 0.0755247 0.461424i
646646 −3.47954 1.54919i −0.136901 0.0609521i
647647 −9.11290 7.37948i −0.358265 0.290117i 0.433242 0.901278i 0.357370π-0.357370\pi
−0.791507 + 0.611161i 0.790703π0.790703\pi
648648 −1.68706 + 1.09559i −0.0662739 + 0.0430388i
649649 −3.20276 5.54735i −0.125719 0.217752i
650650 −7.81024 0.0805937i −0.306343 0.00316115i
651651 21.2789 + 19.8758i 0.833986 + 0.778994i
652652 −2.21293 + 4.34313i −0.0866652 + 0.170090i
653653 −19.4319 + 7.45920i −0.760429 + 0.291901i −0.707515 0.706698i 0.750184π-0.750184\pi
−0.0529133 + 0.998599i 0.516851π0.516851\pi
654654 −0.988318 9.40322i −0.0386463 0.367695i
655655 34.9124 + 13.6087i 1.36414 + 0.531736i
656656 −0.0481998 0.00506600i −0.00188188 0.000197794i
657657 −2.02445 + 2.02445i −0.0789813 + 0.0789813i
658658 −0.382894 0.0270925i −0.0149268 0.00105618i
659659 30.5370 + 9.92209i 1.18955 + 0.386510i 0.835908 0.548870i 0.184942π-0.184942\pi
0.353646 + 0.935379i 0.384942π0.384942\pi
660660 4.04247 2.30620i 0.157353 0.0897686i
661661 2.10304 9.89402i 0.0817988 0.384833i −0.918136 0.396266i 0.870306π-0.870306\pi
0.999935 + 0.0114328i 0.00363925π0.00363925\pi
662662 0.293951 5.60892i 0.0114247 0.217997i
663663 −1.76035 1.14319i −0.0683665 0.0443977i
664664 5.10231 + 15.7033i 0.198008 + 0.609406i
665665 23.6530 20.3139i 0.917223 0.787741i
666666 −3.19997 + 9.84849i −0.123996 + 0.381621i
667667 −6.11935 + 4.95535i −0.236942 + 0.191872i
668668 25.8250 6.91979i 0.999199 0.267735i
669669 9.87704 + 22.1842i 0.381868 + 0.857691i
670670 −12.3397 8.10432i −0.476725 0.313097i
671671 −3.56931 4.91273i −0.137792 0.189654i
672672 −13.7176 + 10.6991i −0.529167 + 0.412727i
673673 10.0639 + 5.12781i 0.387935 + 0.197663i 0.637070 0.770806i 0.280146π-0.280146\pi
−0.249135 + 0.968469i 0.580146π0.580146\pi
674674 6.82894 3.94269i 0.263041 0.151867i
675675 −14.2621 22.4659i −0.548949 0.864712i
676676 6.25399 10.8322i 0.240538 0.416624i
677677 −1.27981 24.4201i −0.0491869 0.938542i −0.906095 0.423074i 0.860951π-0.860951\pi
0.856908 0.515469i 0.172382π-0.172382\pi
678678 5.69985 + 0.902768i 0.218901 + 0.0346706i
679679 −27.7294 + 36.7350i −1.06416 + 1.40976i
680680 −2.51664 + 4.87681i −0.0965086 + 0.187017i
681681 1.10371 10.5011i 0.0422943 0.402404i
682682 −2.61681 9.76605i −0.100203 0.373961i
683683 −5.90842 + 15.3920i −0.226079 + 0.588957i −0.998960 0.0455944i 0.985482π-0.985482\pi
0.772881 + 0.634552i 0.218815π0.218815\pi
684684 −12.5099 + 2.65907i −0.478329 + 0.101672i
685685 −2.31820 + 7.01141i −0.0885740 + 0.267892i
686686 2.21659 + 14.2231i 0.0846299 + 0.543042i
687687 3.11525 1.58730i 0.118854 0.0605593i
688688 −1.90630 + 2.93544i −0.0726770 + 0.111913i
689689 −21.9585 4.66741i −0.836550 0.177814i
690690 1.48756 + 1.66934i 0.0566303 + 0.0635506i
691691 5.84621 + 27.5043i 0.222400 + 1.04631i 0.937687 + 0.347480i 0.112963π0.112963\pi
−0.715287 + 0.698831i 0.753704π0.753704\pi
692692 6.83613 1.08274i 0.259870 0.0411594i
693693 −2.87117 + 5.38914i −0.109067 + 0.204716i
694694 −3.66214 + 5.04050i −0.139013 + 0.191335i
695695 −0.910198 19.2693i −0.0345258 0.730926i
696696 −20.2674 + 2.13019i −0.768233 + 0.0807445i
697697 −0.0383106 + 0.0473096i −0.00145112 + 0.00179198i
698698 6.84643 0.358806i 0.259141 0.0135810i
699699 −32.7474 −1.23862
700700 −11.2058 14.6771i −0.423541 0.554741i
701701 −35.1051 −1.32590 −0.662951 0.748663i 0.730696π-0.730696\pi
−0.662951 + 0.748663i 0.730696π0.730696\pi
702702 8.30246 0.435113i 0.313356 0.0164223i
703703 25.4172 31.3876i 0.958627 1.18381i
704704 4.05282 0.425969i 0.152747 0.0160543i
705705 0.257349 0.391842i 0.00969234 0.0147576i
706706 −7.69154 + 10.5865i −0.289475 + 0.398428i
707707 −4.96372 7.95823i −0.186680 0.299300i
708708 −7.47165 + 1.18339i −0.280802 + 0.0444746i
709709 −10.9224 51.3859i −0.410200 1.92984i −0.365421 0.930842i 0.619075π-0.619075\pi
−0.0447789 0.998997i 0.514258π-0.514258\pi
710710 17.1620 7.53517i 0.644079 0.282790i
711711 −17.7462 3.77207i −0.665534 0.141464i
712712 −22.5620 + 34.7425i −0.845548 + 1.30203i
713713 −10.0005 + 5.09550i −0.374521 + 0.190828i
714714 0.185410 + 2.13961i 0.00693879 + 0.0800728i
715715 −5.96608 0.0307811i −0.223119 0.00115115i
716716 27.6529 5.87780i 1.03344 0.219664i
717717 −1.29362 + 3.36999i −0.0483110 + 0.125854i
718718 −2.78070 10.3777i −0.103775 0.387293i
719719 −0.289532 + 2.75471i −0.0107977 + 0.102733i −0.998593 0.0530223i 0.983115π-0.983115\pi
0.987796 + 0.155756i 0.0497812π0.0497812\pi
720720 0.435506 + 2.84458i 0.0162303 + 0.106011i
721721 −2.06603 + 16.7123i −0.0769430 + 0.622398i
722722 −6.73625 1.06692i −0.250697 0.0397066i
723723 −1.57644 30.0803i −0.0586286 1.11870i
724724 −3.17846 + 5.50525i −0.118126 + 0.204601i
725725 −3.23988 34.2183i −0.120326 1.27084i
726726 6.98382 4.03211i 0.259194 0.149646i
727727 5.31536 + 2.70831i 0.197136 + 0.100446i 0.549772 0.835315i 0.314715π-0.314715\pi
−0.352636 + 0.935761i 0.614715π0.614715\pi
728728 13.9003 1.94184i 0.515178 0.0719695i
729729 11.3195 + 15.5799i 0.419239 + 0.577033i
730730 1.01190 + 2.67730i 0.0374522 + 0.0990914i
731731 1.78818 + 4.01632i 0.0661383 + 0.148549i
732732 −6.92710 + 1.85611i −0.256033 + 0.0686038i
733733 23.4127 18.9592i 0.864768 0.700275i −0.0905384 0.995893i 0.528859π-0.528859\pi
0.955306 + 0.295618i 0.0955255π0.0955255\pi
734734 −0.249589 + 0.768156i −0.00921250 + 0.0283532i
735735 −16.4788 6.12522i −0.607828 0.225932i
736736 −2.07219 6.37755i −0.0763820 0.235080i
737737 −9.45749 6.14177i −0.348371 0.226235i
738738 0.00462993 0.0883442i 0.000170430 0.00325200i
739739 −9.39272 + 44.1893i −0.345517 + 1.62553i 0.371472 + 0.928444i 0.378853π0.378853\pi
−0.716989 + 0.697084i 0.754480π0.754480\pi
740740 −17.6933 16.0972i −0.650420 0.591746i
741741 −11.3145 3.67629i −0.415648 0.135052i
742742 10.0520 + 20.6530i 0.369021 + 0.758194i
743743 23.4363 23.4363i 0.859793 0.859793i −0.131520 0.991313i 0.541986π-0.541986\pi
0.991313 + 0.131520i 0.0419858π0.0419858\pi
744744 −28.8891 3.03637i −1.05913 0.111319i
745745 −0.0854978 + 0.0224369i −0.00313240 + 0.000822026i
746746 −1.78782 17.0099i −0.0654566 0.622778i
747747 10.1531 3.89741i 0.371482 0.142599i
748748 −0.782267 + 1.53529i −0.0286025 + 0.0561356i
749749 17.8010 19.0576i 0.650434 0.696351i
750750 −9.66250 + 1.37745i −0.352825 + 0.0502972i
751751 19.3994 + 33.6008i 0.707894 + 1.22611i 0.965637 + 0.259895i 0.0836881π0.0836881\pi
−0.257742 + 0.966214i 0.582979π0.582979\pi
752752 −0.115887 + 0.0752582i −0.00422598 + 0.00274438i
753753 −12.0054 9.72182i −0.437503 0.354283i
754754 9.81013 + 4.36775i 0.357264 + 0.159064i
755755 15.5651 15.4053i 0.566470 0.560655i
756756 12.8829 + 14.8448i 0.468546 + 0.539901i
757757 2.63808 + 2.63808i 0.0958825 + 0.0958825i 0.753421 0.657538i 0.228402π-0.228402\pi
−0.657538 + 0.753421i 0.728402π0.728402\pi
758758 −14.8376 18.3229i −0.538924 0.665516i
759759 1.14283 + 1.26924i 0.0414821 + 0.0460706i
760760 −6.62387 + 30.3910i −0.240273 + 1.10240i
761761 29.5054 + 26.5668i 1.06957 + 0.963044i 0.999405 0.0344912i 0.0109811π-0.0109811\pi
0.0701640 + 0.997535i 0.477648π0.477648\pi
762762 −7.32833 14.3827i −0.265477 0.521029i
763763 −27.8100 + 6.90941i −1.00679 + 0.250138i
764764 −20.5490 + 6.67679i −0.743438 + 0.241558i
765765 3.29452 + 1.48723i 0.119113 + 0.0537708i
766766 −12.3518 + 11.1216i −0.446287 + 0.401839i
767767 9.05342 + 3.47528i 0.326900 + 0.125485i
768768 3.89107 14.5217i 0.140407 0.524006i
769769 −0.563611 0.409487i −0.0203243 0.0147665i 0.577577 0.816336i 0.303998π-0.303998\pi
−0.597901 + 0.801570i 0.703998π0.703998\pi
770770 3.72940 + 4.83277i 0.134398 + 0.174161i
771771 −8.39701 + 6.10079i −0.302411 + 0.219714i
772772 3.92239 + 10.2182i 0.141170 + 0.367760i
773773 17.8463 + 27.4809i 0.641888 + 0.988421i 0.998531 + 0.0541802i 0.0172546π0.0172546\pi
−0.356643 + 0.934241i 0.616079π0.616079\pi
774774 −5.53295 3.19445i −0.198878 0.114822i
775775 5.62365 48.6692i 0.202008 1.74825i
776776 45.9162i 1.64829i
777777 −22.4239 3.97304i −0.804452 0.142532i
778778 2.55878 16.1555i 0.0917365 0.579202i
779779 −0.140339 + 0.315207i −0.00502817 + 0.0112935i
780780 −2.55893 + 6.56481i −0.0916245 + 0.235058i
781781 13.0793 5.82329i 0.468015 0.208374i
782782 −0.799623 0.214258i −0.0285945 0.00766186i
783783 5.72327 + 36.1353i 0.204533 + 1.29137i
784784 3.72159 + 3.60580i 0.132914 + 0.128779i
785785 0.151863 29.4346i 0.00542024 1.05057i
786786 −9.78868 + 10.8714i −0.349151 + 0.387771i
787787 −26.6351 1.39588i −0.949438 0.0497579i −0.428674 0.903459i 0.641019π-0.641019\pi
−0.520763 + 0.853701i 0.674353π0.674353\pi
788788 22.8041 + 1.19511i 0.812363 + 0.0425741i
789789 −6.30682 + 7.00444i −0.224529 + 0.249365i
790790 −10.7364 + 14.6181i −0.381982 + 0.520090i
791791 0.319693 17.4871i 0.0113670 0.621768i
792792 −0.952952 6.01670i −0.0338617 0.213794i
793793 8.88006 + 2.37940i 0.315340 + 0.0844951i
794794 3.63897 1.62017i 0.129142 0.0574978i
795795 −28.0059 1.61265i −0.993266 0.0571949i
796796 15.5067 34.8286i 0.549620 1.23447i
797797 −2.59453 + 16.3812i −0.0919030 + 0.580252i 0.898165 + 0.439660i 0.144901π0.144901\pi
−0.990067 + 0.140593i 0.955099π0.955099\pi
798798 4.15377 + 11.4418i 0.147042 + 0.405035i
799799 0.173565i 0.00614027i
800800 28.1942 + 7.86731i 0.996817 + 0.278151i
801801 23.6299 + 13.6427i 0.834921 + 0.482042i
802802 −14.5335 22.3796i −0.513196 0.790252i
803803 0.783481 + 2.04104i 0.0276484 + 0.0720267i
804804 −10.7742 + 7.82790i −0.379976 + 0.276069i
805805 4.38689 5.16498i 0.154617 0.182042i
806806 12.3834 + 8.99706i 0.436186 + 0.316908i
807807 −1.28020 + 4.77777i −0.0450652 + 0.168186i
808808 8.73549 + 3.35324i 0.307314 + 0.117967i
809809 32.1490 28.9471i 1.13030 1.01773i 0.130645 0.991429i 0.458295π-0.458295\pi
0.999654 0.0262968i 0.00837151π-0.00837151\pi
810810 1.29702 0.268703i 0.0455725 0.00944126i
811811 24.7816 8.05202i 0.870198 0.282745i 0.160317 0.987066i 0.448748π-0.448748\pi
0.709881 + 0.704321i 0.248748π0.248748\pi
812812 6.12152 + 24.6388i 0.214823 + 0.864652i
813813 −1.75015 3.43487i −0.0613805 0.120466i
814814 5.87644 + 5.29117i 0.205969 + 0.185455i
815815 5.82958 5.19477i 0.204201 0.181965i
816816 0.517311 + 0.574532i 0.0181095 + 0.0201127i
817817 15.6816 + 19.3651i 0.548629 + 0.677500i
818818 14.4211 + 14.4211i 0.504223 + 0.504223i
819819 −1.75643 9.07607i −0.0613745 0.317144i
820820 0.181596 + 0.0937112i 0.00634162 + 0.00327254i
821821 24.2885 + 10.8140i 0.847676 + 0.377410i 0.784151 0.620571i 0.213099π-0.213099\pi
0.0635253 + 0.997980i 0.479766π0.479766\pi
822822 −2.24055 1.81436i −0.0781480 0.0632830i
823823 2.03336 1.32048i 0.0708785 0.0460290i −0.508713 0.860936i 0.669879π-0.669879\pi
0.579592 + 0.814907i 0.303212π0.303212\pi
824824 −8.39968 14.5487i −0.292617 0.506827i
825825 −7.37516 + 1.09023i −0.256770 + 0.0379568i
826826 −2.89315 9.49111i −0.100666 0.330238i
827827 2.88877 5.66953i 0.100452 0.197149i −0.835311 0.549778i 0.814712π-0.814712\pi
0.935763 + 0.352629i 0.114712π0.114712\pi
828828 −2.59509 + 0.996160i −0.0901855 + 0.0346190i
829829 −1.85268 17.6271i −0.0643462 0.612213i −0.978414 0.206653i 0.933743π-0.933743\pi
0.914068 0.405561i 0.132924π-0.132924\pi
830830 0.625014 10.8542i 0.0216946 0.376755i
831831 −8.59994 0.903890i −0.298329 0.0313556i
832832 −4.36250 + 4.36250i −0.151242 + 0.151242i
833833 6.34445 1.45369i 0.219822 0.0503674i
834834 7.16266 + 2.32729i 0.248023 + 0.0805875i
835835 −42.5701 4.69648i −1.47320 0.162528i
836836 −2.03052 + 9.55283i −0.0702269 + 0.330391i
837837 −2.72928 + 52.0778i −0.0943379 + 1.80007i
838838 16.7898 + 10.9034i 0.579995 + 0.376653i
839839 7.84911 + 24.1571i 0.270981 + 0.833995i 0.990255 + 0.139268i 0.0444749π0.0444749\pi
−0.719273 + 0.694727i 0.755525π0.755525\pi
840840 16.8025 5.02725i 0.579740 0.173457i
841841 −5.64130 + 17.3621i −0.194528 + 0.598695i
842842 −7.11748 + 5.76362i −0.245284 + 0.198627i
843843 −26.3226 + 7.05313i −0.906600 + 0.242923i
844844 −8.33697 18.7251i −0.286970 0.644546i
845845 −15.6361 + 12.5289i −0.537900 + 0.431007i
846846 −0.148254 0.204054i −0.00509708 0.00701553i
847847 −15.0311 19.2717i −0.516474 0.662184i
848848 7.36733 + 3.75384i 0.252995 + 0.128908i
849849 7.05132 4.07108i 0.242001 0.139719i
850850 2.71021 2.39011i 0.0929594 0.0819801i
851851 4.38910 7.60214i 0.150456 0.260598i
852852 −0.884906 16.8850i −0.0303164 0.578471i
853853 19.9447 + 3.15894i 0.682895 + 0.108160i 0.488237 0.872711i 0.337640π-0.337640\pi
0.194658 + 0.980871i 0.437640π0.437640\pi
854854 −3.66821 8.66164i −0.125523 0.296395i
855855 20.2183 + 3.30928i 0.691451 + 0.113175i
856856 −2.71941 + 25.8734i −0.0929475 + 0.884336i
857857 0.962594 + 3.59245i 0.0328816 + 0.122716i 0.980416 0.196938i 0.0630999π-0.0630999\pi
−0.947534 + 0.319654i 0.896433π0.896433\pi
858858 0.834723 2.17453i 0.0284970 0.0742372i
859859 21.6111 4.59358i 0.737361 0.156731i 0.176103 0.984372i 0.443651π-0.443651\pi
0.561258 + 0.827641i 0.310318π0.310318\pi
860860 11.9841 8.61281i 0.408653 0.293694i
861861 0.193824 0.0167960i 0.00660552 0.000572408i
862862 −10.7938 + 5.49970i −0.367637 + 0.187320i
863863 −21.4531 + 33.0348i −0.730270 + 1.12452i 0.257146 + 0.966373i 0.417218π0.417218\pi
−0.987416 + 0.158145i 0.949449π0.949449\pi
864864 −30.4762 6.47792i −1.03682 0.220383i
865865 −10.8330 2.36110i −0.368332 0.0802797i
866866 0.125424 + 0.590076i 0.00426210 + 0.0200516i
867867 −17.8996 + 2.83502i −0.607903 + 0.0962823i
868868 1.23305 + 36.1669i 0.0418525 + 1.22758i
869869 −8.14324 + 11.2082i −0.276240 + 0.380212i
870870 12.9435 + 3.53988i 0.438826 + 0.120013i
871871 16.9787 1.78454i 0.575303 0.0604667i
872872 17.9905 22.2164i 0.609235 0.752343i
873873 −30.2017 + 1.58281i −1.02217 + 0.0535699i
874874 −4.69203 −0.158710
875875 8.18613 + 28.4251i 0.276742 + 0.960944i
876876 2.58191 0.0872347
877877 22.4814 1.17820i 0.759145 0.0397851i 0.331164 0.943573i 0.392559π-0.392559\pi
0.427980 + 0.903788i 0.359225π0.359225\pi
878878 5.16677 6.38042i 0.174370 0.215329i
879879 34.7858 3.65613i 1.17329 0.123318i
880880 2.11965 + 0.579696i 0.0714534 + 0.0195416i
881881 1.48864 2.04893i 0.0501535 0.0690304i −0.783204 0.621765i 0.786416π-0.786416\pi
0.833357 + 0.552735i 0.186416π0.186416\pi
882882 −6.21726 + 7.12831i −0.209346 + 0.240023i
883883 41.9699 6.64738i 1.41240 0.223702i 0.596833 0.802366i 0.296426π-0.296426\pi
0.815566 + 0.578664i 0.196426π0.196426\pi
884884 −0.542368 2.55164i −0.0182418 0.0858209i
885885 11.8401 + 2.58060i 0.397999 + 0.0867459i
886886 20.6645 + 4.39238i 0.694238 + 0.147565i
887887 −17.3204 + 26.6711i −0.581563 + 0.895528i −0.999919 0.0127551i 0.995940π-0.995940\pi
0.418356 + 0.908283i 0.362606π0.362606\pi
888888 20.2426 10.3141i 0.679298 0.346120i
889889 −40.0977 + 28.0274i −1.34483 + 0.940008i
890890 22.1502 15.9191i 0.742477 0.533610i
891891 0.989652 0.210357i 0.0331546 0.00704723i
892892 −10.8156 + 28.1755i −0.362132 + 0.943385i
893893 0.254611 + 0.950220i 0.00852022 + 0.0317979i
894894 0.00360720 0.0343202i 0.000120643 0.00114784i
895895 −44.6920 7.31508i −1.49389 0.244516i
896896 −24.4790 3.02618i −0.817787 0.101098i
897897 −2.55386 0.404492i −0.0852710 0.0135056i
898898 −1.58712 30.2841i −0.0529630 1.01059i
899899 −33.6791 + 58.3340i −1.12326 + 1.94555i
900900 2.64508 11.8419i 0.0881692 0.394731i
901901 8.99448 5.19297i 0.299650 0.173003i
902902 −0.0601911 0.0306689i −0.00200414 0.00102116i
903903 5.27409 13.0228i 0.175511 0.433373i
904904 10.2558 + 14.1160i 0.341104 + 0.469490i
905905 7.94674 6.36754i 0.264158 0.211664i
906906 3.47751 + 7.81061i 0.115532 + 0.259490i
907907 −21.0096 + 5.62950i −0.697611 + 0.186924i −0.590160 0.807286i 0.700936π-0.700936\pi
−0.107451 + 0.994210i 0.534269π0.534269\pi
908908 10.1983 8.25846i 0.338444 0.274067i
909909 1.90450 5.86143i 0.0631681 0.194411i
910910 −8.99223 2.13279i −0.298089 0.0707014i
911911 1.19819 + 3.68765i 0.0396978 + 0.122177i 0.968941 0.247290i 0.0795401π-0.0795401\pi
−0.929244 + 0.369468i 0.879540π0.879540\pi
912912 3.67495 + 2.38654i 0.121690 + 0.0790263i
913913 0.434634 8.29332i 0.0143843 0.274469i
914914 −3.71923 + 17.4976i −0.123021 + 0.578769i
915915 11.4187 + 1.25975i 0.377490 + 0.0416459i
916916 4.13261 + 1.34277i 0.136545 + 0.0443663i
917917 36.7359 + 24.8229i 1.21313 + 0.819724i
918918 −2.71979 + 2.71979i −0.0897665 + 0.0897665i
919919 −7.89240 0.829525i −0.260346 0.0273635i −0.0265440 0.999648i 0.508450π-0.508450\pi
−0.233802 + 0.972284i 0.575117π0.575117\pi
920920 −0.388639 + 6.74923i −0.0128130 + 0.222516i
921921 −0.387796 3.68963i −0.0127783 0.121578i
922922 −17.6154 + 6.76190i −0.580131 + 0.222691i
923923 −9.84030 + 19.3127i −0.323897 + 0.635684i
924924 5.26745 1.60566i 0.173286 0.0528224i
925925 17.0427 + 34.3190i 0.560359 + 1.12840i
926926 2.39577 + 4.14960i 0.0787299 + 0.136364i
927927 −9.27996 + 6.02647i −0.304794 + 0.197935i
928928 −31.2753 25.3262i −1.02666 0.831375i
929929 44.5122 + 19.8181i 1.46040 + 0.650211i 0.974619 0.223870i 0.0718693π-0.0718693\pi
0.485779 + 0.874082i 0.338536π0.338536\pi
930930 16.9975 + 8.77140i 0.557369 + 0.287625i
931931 32.6017 17.2656i 1.06848 0.565856i
932932 −28.7785 28.7785i −0.942670 0.942670i
933933 4.36656 + 5.39226i 0.142955 + 0.176535i
934934 15.2557 + 16.9432i 0.499182 + 0.554398i
935935 2.06074 1.83634i 0.0673935 0.0600547i
936936 6.85360 + 6.17101i 0.224017 + 0.201706i
937937 18.7668 + 36.8319i 0.613085 + 1.20325i 0.963765 + 0.266752i 0.0859503π0.0859503\pi
−0.350680 + 0.936495i 0.614050π0.614050\pi
938938 −12.1238 12.5754i −0.395858 0.410601i
939939 −11.9642 + 3.88740i −0.390437 + 0.126861i
940940 0.570511 0.118193i 0.0186080 0.00385502i
941941 33.6343 30.2845i 1.09645 0.987246i 0.0964808 0.995335i 0.469241π-0.469241\pi
0.999967 + 0.00808856i 0.00257470π0.00257470\pi
942942 10.7284 + 4.11824i 0.349549 + 0.134179i
943943 −0.0194094 + 0.0724368i −0.000632057 + 0.00235887i
944944 −2.88969 2.09948i −0.0940513 0.0683323i
945945 −10.5916 29.6512i −0.344544 0.964553i
946946 −3.94694 + 2.86762i −0.128326 + 0.0932344i
947947 2.86529 + 7.46435i 0.0931095 + 0.242559i 0.972224 0.234052i 0.0751985π-0.0751985\pi
−0.879115 + 0.476611i 0.841865π0.841865\pi
948948 8.91106 + 13.7218i 0.289418 + 0.445664i
949949 −2.86640 1.65492i −0.0930472 0.0537208i
950950 11.3315 17.0610i 0.367642 0.553530i
951951 10.1006i 0.327535i
952952 −4.17795 + 4.97074i −0.135408 + 0.161102i
953953 0.239793 1.51399i 0.00776765 0.0490430i −0.983500 0.180908i 0.942096π-0.942096\pi
0.991268 + 0.131865i 0.0420965π0.0420965\pi
954954 −6.13884 + 13.7881i −0.198752 + 0.446405i
955955 34.5542 + 1.98973i 1.11815 + 0.0643860i
956956 −4.09839 + 1.82472i −0.132551 + 0.0590156i
957957 9.90071 + 2.65289i 0.320044 + 0.0857556i
958958 1.10585 + 6.98204i 0.0357283 + 0.225580i
959959 −4.50644 + 7.48595i −0.145520 + 0.241734i
960960 −4.56359 + 6.21357i −0.147289 + 0.200542i
961961 −43.5019 + 48.3137i −1.40329 + 1.55851i
962962 −11.9551 0.626538i −0.385447 0.0202004i
963963 17.1122 + 0.896813i 0.551433 + 0.0288994i
964964 25.0493 27.8201i 0.806783 0.896024i
965965 0.0904578 17.5328i 0.00291194 0.564401i
966966 1.28071 + 2.31497i 0.0412062 + 0.0744830i
967967 −3.11543 19.6701i −0.100186 0.632547i −0.985774 0.168076i 0.946245π-0.946245\pi
0.885588 0.464471i 0.153755π-0.153755\pi
968968 23.5513 + 6.31056i 0.756969 + 0.202829i
969969 5.02813 2.23867i 0.161527 0.0719163i
970970 −10.9804 + 28.1697i −0.352560 + 0.904475i
971971 −12.0980 + 27.1725i −0.388242 + 0.872007i 0.608665 + 0.793427i 0.291705π0.291705\pi
−0.996908 + 0.0785798i 0.974961π0.974961\pi
972972 −3.29957 + 20.8327i −0.105834 + 0.668208i
973973 3.98212 22.4751i 0.127661 0.720519i
974974 0.412847i 0.0132285i
975975 7.63851 8.30938i 0.244628 0.266113i
976976 −2.93248 1.69307i −0.0938663 0.0541938i
977977 −17.4584 26.8835i −0.558542 0.860080i 0.440752 0.897629i 0.354712π-0.354712\pi
−0.999295 + 0.0375488i 0.988045π0.988045\pi
978978 1.09246 + 2.84595i 0.0349329 + 0.0910033i
979979 16.8565 12.2469i 0.538735 0.391414i
980980 −9.09871 19.8644i −0.290648 0.634546i
981981 −15.2332 11.0676i −0.486358 0.353360i
982982 1.29083 4.81745i 0.0411921 0.153731i
983983 −36.0017 13.8198i −1.14828 0.440782i −0.291550 0.956555i 0.594171π-0.594171\pi
−0.856725 + 0.515774i 0.827504π0.827504\pi
984984 −0.144235 + 0.129870i −0.00459803 + 0.00414009i
985985 −33.3403 15.0506i −1.06231 0.479553i
986986 −4.72497 + 1.53524i −0.150474 + 0.0488919i
987987 0.399326 0.384988i 0.0127107 0.0122543i
988988 −6.71245 13.1739i −0.213551 0.419118i
989989 4.02477 + 3.62392i 0.127980 + 0.115234i
990990 −0.854200 + 3.91916i −0.0271482 + 0.124559i
991991 3.12017 + 3.46530i 0.0991154 + 0.110079i 0.790662 0.612253i 0.209737π-0.209737\pi
−0.691546 + 0.722332i 0.743070π0.743070\pi
992992 −36.1001 44.5799i −1.14618 1.41541i
993993 5.73911 + 5.73911i 0.182125 + 0.182125i
994994 21.7735 4.21366i 0.690613 0.133649i
995995 −43.4065 + 42.9609i −1.37608 + 1.36195i
996996 −8.95976 3.98914i −0.283901 0.126401i
997997 −12.6622 10.2537i −0.401017 0.324737i 0.407505 0.913203i 0.366399π-0.366399\pi
−0.808522 + 0.588466i 0.799732π0.799732\pi
998998 4.08988 2.65600i 0.129463 0.0840743i
999999 −20.3931 35.3220i −0.645210 1.11754i
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 175.2.x.a.17.12 yes 288
5.2 odd 4 875.2.bb.a.143.12 288
5.3 odd 4 875.2.bb.b.143.7 288
5.4 even 2 875.2.bb.c.857.7 288
7.5 odd 6 inner 175.2.x.a.117.7 yes 288
25.3 odd 20 inner 175.2.x.a.3.7 288
25.4 even 10 875.2.bb.a.507.12 288
25.21 even 5 875.2.bb.b.507.7 288
25.22 odd 20 875.2.bb.c.493.12 288
35.12 even 12 875.2.bb.a.768.12 288
35.19 odd 6 875.2.bb.c.607.12 288
35.33 even 12 875.2.bb.b.768.7 288
175.47 even 60 875.2.bb.c.243.7 288
175.54 odd 30 875.2.bb.a.257.12 288
175.96 odd 30 875.2.bb.b.257.7 288
175.103 even 60 inner 175.2.x.a.103.12 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.3.7 288 25.3 odd 20 inner
175.2.x.a.17.12 yes 288 1.1 even 1 trivial
175.2.x.a.103.12 yes 288 175.103 even 60 inner
175.2.x.a.117.7 yes 288 7.5 odd 6 inner
875.2.bb.a.143.12 288 5.2 odd 4
875.2.bb.a.257.12 288 175.54 odd 30
875.2.bb.a.507.12 288 25.4 even 10
875.2.bb.a.768.12 288 35.12 even 12
875.2.bb.b.143.7 288 5.3 odd 4
875.2.bb.b.257.7 288 175.96 odd 30
875.2.bb.b.507.7 288 25.21 even 5
875.2.bb.b.768.7 288 35.33 even 12
875.2.bb.c.243.7 288 175.47 even 60
875.2.bb.c.493.12 288 25.22 odd 20
875.2.bb.c.607.12 288 35.19 odd 6
875.2.bb.c.857.7 288 5.4 even 2