Properties

Label 304.2.m.a.227.20
Level 304304
Weight 22
Character 304.227
Analytic conductor 2.4272.427
Analytic rank 00
Dimension 7676
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [304,2,Mod(75,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.75");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 304=2419 304 = 2^{4} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 304.m (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.427452221452.42745222145
Analytic rank: 00
Dimension: 7676
Relative dimension: 3838 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 227.20
Character χ\chi == 304.227
Dual form 304.2.m.a.75.20

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+(0.0324855+1.41384i)q2+(0.5497280.549728i)q3+(1.99789+0.0918587i)q4+(1.499991.49999i)q5+(0.7593690.795085i)q63.48044q7+(0.1947762.82171i)q82.39560iq9+(2.16948+2.07202i)q10+(3.684593.68459i)q11+(1.14879+1.04780i)q12+(3.73303+3.73303i)q13+(0.1130644.92078i)q141.64918q15+(3.983120.367047i)q16+1.51477q17+(3.386990.0778223i)q18+(1.279374.16692i)q19+(2.85904+3.13461i)q20+(1.91329+1.91329i)q21+(5.089725.32911i)q220.482269q23+(1.44410+1.65825i)q24+0.500032iq25+(5.399185.15664i)q26+(2.96611+2.96611i)q27+(6.953530.319708i)q28+(7.267307.26730i)q29+(0.05357442.33167i)q30+2.39300q31+(0.648339+5.61958i)q32+4.05104iq33+(0.0492080+2.14164i)q34+(5.22064+5.22064i)q35+(0.220057+4.78614i)q36+(3.145373.14537i)q37+(5.93292+1.67346i)q38+4.10430q39+(4.524723.94039i)q407.94060q41+(2.64294+2.76724i)q42+(3.02093+3.02093i)q43+(7.69986+7.02293i)q44+(3.593393.59339i)q45+(0.01566670.681851i)q46+3.58534iq47+(2.391411.98786i)q48+5.11344q49+(0.706966+0.0162438i)q50+(0.8327090.832709i)q51+(7.115277.80109i)q52+(3.55950+3.55950i)q53+(4.289964.09725i)q5411.0537q55+(0.677905+9.82079i)q56+(2.99397+1.58737i)q57+(10.5109+10.0387i)q58+(0.408827+0.408827i)q59+(3.294870.151491i)q60+(2.47804+2.47804i)q61+(0.0777377+3.38332i)q62+8.33773iq63+(7.92412+1.09920i)q64+11.1991iq65+(5.72752+0.131600i)q66+(10.669110.6691i)q67+(3.02634+0.139144i)q68+(0.265116+0.265116i)q69+(7.550747.21155i)q70+5.59302iq71+(6.75969+0.466605i)q7213.6019iq73+(4.344874.54923i)q74+(0.2748810.274881i)q75+(2.17327+8.44256i)q76+(12.8240+12.8240i)q77+(0.133330+5.80283i)q785.02027q79+(5.424106.52523i)q803.92569q81+(0.25795511.2267i)q82+(10.349710.3497i)q83+(3.998303.64679i)q84+(2.272142.27214i)q85+(4.17297+4.36925i)q867.99007q87+(9.67917+11.1145i)q887.42593q89+(4.963745.19721i)q90+(12.992612.9926i)q91+(0.9635190.0443005i)q92+(1.315501.31550i)q93+(5.06909+0.116471i)q94+(4.331318.16940i)q95+(2.732833.44565i)q963.70124iq97+(0.166113+7.22959i)q98+(8.82679+8.82679i)q99+O(q100)q+(0.0324855 + 1.41384i) q^{2} +(-0.549728 - 0.549728i) q^{3} +(-1.99789 + 0.0918587i) q^{4} +(1.49999 - 1.49999i) q^{5} +(0.759369 - 0.795085i) q^{6} -3.48044 q^{7} +(-0.194776 - 2.82171i) q^{8} -2.39560i q^{9} +(2.16948 + 2.07202i) q^{10} +(-3.68459 - 3.68459i) q^{11} +(1.14879 + 1.04780i) q^{12} +(-3.73303 + 3.73303i) q^{13} +(-0.113064 - 4.92078i) q^{14} -1.64918 q^{15} +(3.98312 - 0.367047i) q^{16} +1.51477 q^{17} +(3.38699 - 0.0778223i) q^{18} +(1.27937 - 4.16692i) q^{19} +(-2.85904 + 3.13461i) q^{20} +(1.91329 + 1.91329i) q^{21} +(5.08972 - 5.32911i) q^{22} -0.482269 q^{23} +(-1.44410 + 1.65825i) q^{24} +0.500032i q^{25} +(-5.39918 - 5.15664i) q^{26} +(-2.96611 + 2.96611i) q^{27} +(6.95353 - 0.319708i) q^{28} +(7.26730 - 7.26730i) q^{29} +(-0.0535744 - 2.33167i) q^{30} +2.39300 q^{31} +(0.648339 + 5.61958i) q^{32} +4.05104i q^{33} +(0.0492080 + 2.14164i) q^{34} +(-5.22064 + 5.22064i) q^{35} +(0.220057 + 4.78614i) q^{36} +(-3.14537 - 3.14537i) q^{37} +(5.93292 + 1.67346i) q^{38} +4.10430 q^{39} +(-4.52472 - 3.94039i) q^{40} -7.94060 q^{41} +(-2.64294 + 2.76724i) q^{42} +(3.02093 + 3.02093i) q^{43} +(7.69986 + 7.02293i) q^{44} +(-3.59339 - 3.59339i) q^{45} +(-0.0156667 - 0.681851i) q^{46} +3.58534i q^{47} +(-2.39141 - 1.98786i) q^{48} +5.11344 q^{49} +(-0.706966 + 0.0162438i) q^{50} +(-0.832709 - 0.832709i) q^{51} +(7.11527 - 7.80109i) q^{52} +(3.55950 + 3.55950i) q^{53} +(-4.28996 - 4.09725i) q^{54} -11.0537 q^{55} +(0.677905 + 9.82079i) q^{56} +(-2.99397 + 1.58737i) q^{57} +(10.5109 + 10.0387i) q^{58} +(-0.408827 + 0.408827i) q^{59} +(3.29487 - 0.151491i) q^{60} +(2.47804 + 2.47804i) q^{61} +(0.0777377 + 3.38332i) q^{62} +8.33773i q^{63} +(-7.92412 + 1.09920i) q^{64} +11.1991i q^{65} +(-5.72752 + 0.131600i) q^{66} +(-10.6691 - 10.6691i) q^{67} +(-3.02634 + 0.139144i) q^{68} +(0.265116 + 0.265116i) q^{69} +(-7.55074 - 7.21155i) q^{70} +5.59302i q^{71} +(-6.75969 + 0.466605i) q^{72} -13.6019i q^{73} +(4.34487 - 4.54923i) q^{74} +(0.274881 - 0.274881i) q^{75} +(-2.17327 + 8.44256i) q^{76} +(12.8240 + 12.8240i) q^{77} +(0.133330 + 5.80283i) q^{78} -5.02027 q^{79} +(5.42410 - 6.52523i) q^{80} -3.92569 q^{81} +(-0.257955 - 11.2267i) q^{82} +(10.3497 - 10.3497i) q^{83} +(-3.99830 - 3.64679i) q^{84} +(2.27214 - 2.27214i) q^{85} +(-4.17297 + 4.36925i) q^{86} -7.99007 q^{87} +(-9.67917 + 11.1145i) q^{88} -7.42593 q^{89} +(4.96374 - 5.19721i) q^{90} +(12.9926 - 12.9926i) q^{91} +(0.963519 - 0.0443005i) q^{92} +(-1.31550 - 1.31550i) q^{93} +(-5.06909 + 0.116471i) q^{94} +(-4.33131 - 8.16940i) q^{95} +(2.73283 - 3.44565i) q^{96} -3.70124i q^{97} +(0.166113 + 7.22959i) q^{98} +(-8.82679 + 8.82679i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 76q4q44q54q68q74q11+4q168q17+6q1932q208q2312q248q2640q30+44q3612q388q39+12q424q43++76q99+O(q100) 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43}+ \cdots + 76 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/304Z)×\left(\mathbb{Z}/304\mathbb{Z}\right)^\times.

nn 9797 191191 229229
χ(n)\chi(n) 1-1 1-1 e(34)e\left(\frac{3}{4}\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 0.0324855 + 1.41384i 0.0229707 + 0.999736i
33 −0.549728 0.549728i −0.317385 0.317385i 0.530377 0.847762i 0.322050π-0.322050\pi
−0.847762 + 0.530377i 0.822050π0.822050\pi
44 −1.99789 + 0.0918587i −0.998945 + 0.0459293i
55 1.49999 1.49999i 0.670818 0.670818i −0.287087 0.957905i 0.592687π-0.592687\pi
0.957905 + 0.287087i 0.0926868π0.0926868\pi
66 0.759369 0.795085i 0.310011 0.324592i
77 −3.48044 −1.31548 −0.657741 0.753244i 0.728488π-0.728488\pi
−0.657741 + 0.753244i 0.728488π0.728488\pi
88 −0.194776 2.82171i −0.0688637 0.997626i
99 2.39560i 0.798533i
1010 2.16948 + 2.07202i 0.686050 + 0.655232i
1111 −3.68459 3.68459i −1.11094 1.11094i −0.993023 0.117921i 0.962377π-0.962377\pi
−0.117921 0.993023i 0.537623π-0.537623\pi
1212 1.14879 + 1.04780i 0.331628 + 0.302473i
1313 −3.73303 + 3.73303i −1.03536 + 1.03536i −0.0360050 + 0.999352i 0.511463π0.511463\pi
−0.999352 + 0.0360050i 0.988537π0.988537\pi
1414 −0.113064 4.92078i −0.0302176 1.31513i
1515 −1.64918 −0.425816
1616 3.98312 0.367047i 0.995781 0.0917617i
1717 1.51477 0.367385 0.183693 0.982984i 0.441195π-0.441195\pi
0.183693 + 0.982984i 0.441195π0.441195\pi
1818 3.38699 0.0778223i 0.798322 0.0183429i
1919 1.27937 4.16692i 0.293507 0.955957i
2020 −2.85904 + 3.13461i −0.639300 + 0.700920i
2121 1.91329 + 1.91329i 0.417515 + 0.417515i
2222 5.08972 5.32911i 1.08513 1.13617i
2323 −0.482269 −0.100560 −0.0502800 0.998735i 0.516011π-0.516011\pi
−0.0502800 + 0.998735i 0.516011π0.516011\pi
2424 −1.44410 + 1.65825i −0.294776 + 0.338488i
2525 0.500032i 0.100006i
2626 −5.39918 5.15664i −1.05887 1.01130i
2727 −2.96611 + 2.96611i −0.570828 + 0.570828i
2828 6.95353 0.319708i 1.31409 0.0604192i
2929 7.26730 7.26730i 1.34950 1.34950i 0.463303 0.886200i 0.346664π-0.346664\pi
0.886200 0.463303i 0.153336π-0.153336\pi
3030 −0.0535744 2.33167i −0.00978129 0.425703i
3131 2.39300 0.429795 0.214897 0.976637i 0.431058π-0.431058\pi
0.214897 + 0.976637i 0.431058π0.431058\pi
3232 0.648339 + 5.61958i 0.114611 + 0.993410i
3333 4.05104i 0.705195i
3434 0.0492080 + 2.14164i 0.00843910 + 0.367288i
3535 −5.22064 + 5.22064i −0.882449 + 0.882449i
3636 0.220057 + 4.78614i 0.0366761 + 0.797690i
3737 −3.14537 3.14537i −0.517096 0.517096i 0.399596 0.916691i 0.369150π-0.369150\pi
−0.916691 + 0.399596i 0.869150π0.869150\pi
3838 5.93292 + 1.67346i 0.962447 + 0.271471i
3939 4.10430 0.657214
4040 −4.52472 3.94039i −0.715421 0.623031i
4141 −7.94060 −1.24011 −0.620057 0.784557i 0.712890π-0.712890\pi
−0.620057 + 0.784557i 0.712890π0.712890\pi
4242 −2.64294 + 2.76724i −0.407814 + 0.426995i
4343 3.02093 + 3.02093i 0.460687 + 0.460687i 0.898881 0.438193i 0.144382π-0.144382\pi
−0.438193 + 0.898881i 0.644382π0.644382\pi
4444 7.69986 + 7.02293i 1.16080 + 1.05875i
4545 −3.59339 3.59339i −0.535670 0.535670i
4646 −0.0156667 0.681851i −0.00230993 0.100533i
4747 3.58534i 0.522975i 0.965207 + 0.261488i 0.0842130π0.0842130\pi
−0.965207 + 0.261488i 0.915787π0.915787\pi
4848 −2.39141 1.98786i −0.345170 0.286922i
4949 5.11344 0.730492
5050 −0.706966 + 0.0162438i −0.0999800 + 0.00229722i
5151 −0.832709 0.832709i −0.116603 0.116603i
5252 7.11527 7.80109i 0.986711 1.08182i
5353 3.55950 + 3.55950i 0.488935 + 0.488935i 0.907970 0.419035i 0.137631π-0.137631\pi
−0.419035 + 0.907970i 0.637631π0.637631\pi
5454 −4.28996 4.09725i −0.583790 0.557565i
5555 −11.0537 −1.49048
5656 0.677905 + 9.82079i 0.0905889 + 1.31236i
5757 −2.99397 + 1.58737i −0.396562 + 0.210252i
5858 10.5109 + 10.0387i 1.38015 + 1.31815i
5959 −0.408827 + 0.408827i −0.0532248 + 0.0532248i −0.733218 0.679993i 0.761983π-0.761983\pi
0.679993 + 0.733218i 0.261983π0.261983\pi
6060 3.29487 0.151491i 0.425366 0.0195574i
6161 2.47804 + 2.47804i 0.317281 + 0.317281i 0.847722 0.530441i 0.177974π-0.177974\pi
−0.530441 + 0.847722i 0.677974π0.677974\pi
6262 0.0777377 + 3.38332i 0.00987270 + 0.429682i
6363 8.33773i 1.05046i
6464 −7.92412 + 1.09920i −0.990516 + 0.137400i
6565 11.1991i 1.38907i
6666 −5.72752 + 0.131600i −0.705009 + 0.0161988i
6767 −10.6691 10.6691i −1.30344 1.30344i −0.926056 0.377387i 0.876823π-0.876823\pi
−0.377387 0.926056i 0.623177π-0.623177\pi
6868 −3.02634 + 0.139144i −0.366997 + 0.0168737i
6969 0.265116 + 0.265116i 0.0319163 + 0.0319163i
7070 −7.55074 7.21155i −0.902486 0.861945i
7171 5.59302i 0.663769i 0.943320 + 0.331885i 0.107684π0.107684\pi
−0.943320 + 0.331885i 0.892316π0.892316\pi
7272 −6.75969 + 0.466605i −0.796637 + 0.0549899i
7373 13.6019i 1.59198i −0.605311 0.795989i 0.706951π-0.706951\pi
0.605311 0.795989i 0.293049π-0.293049\pi
7474 4.34487 4.54923i 0.505081 0.528837i
7575 0.274881 0.274881i 0.0317406 0.0317406i
7676 −2.17327 + 8.44256i −0.249291 + 0.968429i
7777 12.8240 + 12.8240i 1.46143 + 1.46143i
7878 0.133330 + 5.80283i 0.0150967 + 0.657041i
7979 −5.02027 −0.564825 −0.282412 0.959293i 0.591135π-0.591135\pi
−0.282412 + 0.959293i 0.591135π0.591135\pi
8080 5.42410 6.52523i 0.606432 0.729543i
8181 −3.92569 −0.436188
8282 −0.257955 11.2267i −0.0284863 1.23979i
8383 10.3497 10.3497i 1.13603 1.13603i 0.146870 0.989156i 0.453080π-0.453080\pi
0.989156 0.146870i 0.0469198π-0.0469198\pi
8484 −3.99830 3.64679i −0.436250 0.397898i
8585 2.27214 2.27214i 0.246448 0.246448i
8686 −4.17297 + 4.36925i −0.449983 + 0.471148i
8787 −7.99007 −0.856625
8888 −9.67917 + 11.1145i −1.03180 + 1.18481i
8989 −7.42593 −0.787147 −0.393573 0.919293i 0.628761π-0.628761\pi
−0.393573 + 0.919293i 0.628761π0.628761\pi
9090 4.96374 5.19721i 0.523224 0.547834i
9191 12.9926 12.9926i 1.36199 1.36199i
9292 0.963519 0.0443005i 0.100454 0.00461865i
9393 −1.31550 1.31550i −0.136411 0.136411i
9494 −5.06909 + 0.116471i −0.522837 + 0.0120131i
9595 −4.33131 8.16940i −0.444383 0.838163i
9696 2.73283 3.44565i 0.278918 0.351670i
9797 3.70124i 0.375804i −0.982188 0.187902i 0.939831π-0.939831\pi
0.982188 0.187902i 0.0601688π-0.0601688\pi
9898 0.166113 + 7.22959i 0.0167799 + 0.730299i
9999 −8.82679 + 8.82679i −0.887126 + 0.887126i
100100 −0.0459323 0.999009i −0.00459323 0.0999009i
101101 4.78718 4.78718i 0.476342 0.476342i −0.427618 0.903960i 0.640647π-0.640647\pi
0.903960 + 0.427618i 0.140647π0.140647\pi
102102 1.15027 1.20437i 0.113893 0.119250i
103103 11.4253i 1.12577i 0.826536 + 0.562885i 0.190308π0.190308\pi
−0.826536 + 0.562885i 0.809692π0.809692\pi
104104 11.2606 + 9.80644i 1.10420 + 0.961600i
105105 5.73986 0.560153
106106 −4.91694 + 5.14820i −0.477575 + 0.500037i
107107 11.7874 11.7874i 1.13953 1.13953i 0.150999 0.988534i 0.451751π-0.451751\pi
0.988534 0.150999i 0.0482490π-0.0482490\pi
108108 5.65350 6.19842i 0.544008 0.596443i
109109 10.3205 10.3205i 0.988523 0.988523i −0.0114120 0.999935i 0.503633π-0.503633\pi
0.999935 + 0.0114120i 0.00363264π0.00363264\pi
110110 −0.359086 15.6282i −0.0342375 1.49009i
111111 3.45819i 0.328237i
112112 −13.8630 + 1.27748i −1.30993 + 0.120711i
113113 14.0443i 1.32118i 0.750747 + 0.660590i 0.229694π0.229694\pi
−0.750747 + 0.660590i 0.770306π0.770306\pi
114114 −2.34154 4.18144i −0.219306 0.391627i
115115 −0.723400 + 0.723400i −0.0674574 + 0.0674574i
116116 −13.8517 + 15.1868i −1.28610 + 1.41006i
117117 8.94285 + 8.94285i 0.826766 + 0.826766i
118118 −0.591297 0.564735i −0.0544333 0.0519881i
119119 −5.27205 −0.483288
120120 0.321220 + 4.65350i 0.0293232 + 0.424805i
121121 16.1523i 1.46839i
122122 −3.42306 + 3.58406i −0.309909 + 0.324485i
123123 4.36517 + 4.36517i 0.393594 + 0.393594i
124124 −4.78094 + 0.219817i −0.429341 + 0.0197402i
125125 8.25002 + 8.25002i 0.737904 + 0.737904i
126126 −11.7882 + 0.270856i −1.05018 + 0.0241297i
127127 5.68283 0.504269 0.252135 0.967692i 0.418867π-0.418867\pi
0.252135 + 0.967692i 0.418867π0.418867\pi
128128 −1.81152 11.1677i −0.160117 0.987098i
129129 3.32138i 0.292431i
130130 −15.8337 + 0.363807i −1.38871 + 0.0319080i
131131 0.994673 0.994673i 0.0869050 0.0869050i −0.662318 0.749223i 0.730427π-0.730427\pi
0.749223 + 0.662318i 0.230427π0.230427\pi
132132 −0.372123 8.09352i −0.0323891 0.704451i
133133 −4.45276 + 14.5027i −0.386104 + 1.25754i
134134 14.7379 15.4311i 1.27316 1.33304i
135135 8.89830i 0.765844i
136136 −0.295040 4.27424i −0.0252995 0.366513i
137137 10.6023i 0.905817i −0.891557 0.452909i 0.850386π-0.850386\pi
0.891557 0.452909i 0.149614π-0.149614\pi
138138 −0.366220 + 0.383445i −0.0311747 + 0.0326410i
139139 9.25182 + 9.25182i 0.784729 + 0.784729i 0.980625 0.195895i 0.0627613π-0.0627613\pi
−0.195895 + 0.980625i 0.562761π0.562761\pi
140140 9.95070 10.9098i 0.840987 0.922048i
141141 1.97096 1.97096i 0.165985 0.165985i
142142 −7.90764 + 0.181692i −0.663594 + 0.0152473i
143143 27.5093 2.30045
144144 −0.879297 9.54197i −0.0732748 0.795164i
145145 21.8018i 1.81054i
146146 19.2309 0.441864i 1.59156 0.0365689i
147147 −2.81100 2.81100i −0.231847 0.231847i
148148 6.57303 + 5.99517i 0.540300 + 0.492800i
149149 0.265791 0.265791i 0.0217745 0.0217745i −0.696136 0.717910i 0.745099π-0.745099\pi
0.717910 + 0.696136i 0.245099π0.245099\pi
150150 0.397568 + 0.379709i 0.0324613 + 0.0310031i
151151 8.26373i 0.672493i −0.941774 0.336246i 0.890843π-0.890843\pi
0.941774 0.336246i 0.109157π-0.109157\pi
152152 −12.0070 2.79840i −0.973899 0.226980i
153153 3.62878i 0.293369i
154154 −17.7145 + 18.5476i −1.42747 + 1.49461i
155155 3.58948 3.58948i 0.288314 0.288314i
156156 −8.19994 + 0.377016i −0.656521 + 0.0301854i
157157 −11.1943 11.1943i −0.893405 0.893405i 0.101437 0.994842i 0.467656π-0.467656\pi
−0.994842 + 0.101437i 0.967656π0.967656\pi
158158 −0.163086 7.09786i −0.0129744 0.564676i
159159 3.91351i 0.310362i
160160 9.40184 + 7.45683i 0.743281 + 0.589514i
161161 1.67851 0.132285
162162 −0.127528 5.55030i −0.0100196 0.436073i
163163 5.31053 5.31053i 0.415953 0.415953i −0.467853 0.883806i 0.654972π-0.654972\pi
0.883806 + 0.467853i 0.154972π0.154972\pi
164164 15.8644 0.729413i 1.23881 0.0569576i
165165 6.07653 + 6.07653i 0.473058 + 0.473058i
166166 14.9690 + 14.2966i 1.16182 + 1.10963i
167167 9.02701i 0.698531i 0.937024 + 0.349266i 0.113569π0.113569\pi
−0.937024 + 0.349266i 0.886431π0.886431\pi
168168 5.02610 5.77142i 0.387772 0.445275i
169169 14.8710i 1.14393i
170170 3.28626 + 3.13864i 0.252045 + 0.240722i
171171 −9.98227 3.06486i −0.763363 0.234375i
172172 −6.31298 5.75798i −0.481360 0.439042i
173173 7.82463 7.82463i 0.594895 0.594895i −0.344054 0.938950i 0.611800π-0.611800\pi
0.938950 + 0.344054i 0.111800π0.111800\pi
174174 −0.259561 11.2967i −0.0196773 0.856399i
175175 1.74033i 0.131557i
176176 −16.0286 13.3237i −1.20820 1.00432i
177177 0.449487 0.0337855
178178 −0.241235 10.4991i −0.0180813 0.786939i
179179 2.95338 + 2.95338i 0.220746 + 0.220746i 0.808813 0.588067i 0.200111π-0.200111\pi
−0.588067 + 0.808813i 0.700111π0.700111\pi
180180 7.50927 + 6.84910i 0.559708 + 0.510502i
181181 −6.95777 6.95777i −0.517167 0.517167i 0.399546 0.916713i 0.369168π-0.369168\pi
−0.916713 + 0.399546i 0.869168π0.869168\pi
182182 18.7915 + 17.9474i 1.39292 + 1.33035i
183183 2.72450i 0.201401i
184184 0.0939343 + 1.36082i 0.00692493 + 0.100321i
185185 −9.43607 −0.693754
186186 1.81717 1.90264i 0.133241 0.139508i
187187 −5.58129 5.58129i −0.408144 0.408144i
188188 −0.329344 7.16311i −0.0240199 0.522423i
189189 10.3234 10.3234i 0.750914 0.750914i
190190 11.4095 6.38917i 0.827734 0.463519i
191191 3.91455i 0.283247i −0.989921 0.141624i 0.954768π-0.954768\pi
0.989921 0.141624i 0.0452322π-0.0452322\pi
192192 4.96037 + 3.75185i 0.357984 + 0.270766i
193193 17.5680i 1.26457i −0.774736 0.632285i 0.782117π-0.782117\pi
0.774736 0.632285i 0.217883π-0.217883\pi
194194 5.23297 0.120237i 0.375705 0.00863249i
195195 6.15643 6.15643i 0.440871 0.440871i
196196 −10.2161 + 0.469714i −0.729721 + 0.0335510i
197197 −16.2889 + 16.2889i −1.16053 + 1.16053i −0.176176 + 0.984359i 0.556373π0.556373\pi
−0.984359 + 0.176176i 0.943627π0.943627\pi
198198 −12.7664 12.1929i −0.907270 0.866514i
199199 21.6100 1.53189 0.765945 0.642906i 0.222272π-0.222272\pi
0.765945 + 0.642906i 0.222272π0.222272\pi
200200 1.41095 0.0973942i 0.0997690 0.00688681i
201201 11.7302i 0.827387i
202202 6.92382 + 6.61279i 0.487158 + 0.465274i
203203 −25.2934 + 25.2934i −1.77525 + 1.77525i
204204 1.74015 + 1.58717i 0.121835 + 0.111124i
205205 −11.9109 + 11.9109i −0.831891 + 0.831891i
206206 −16.1536 + 0.371157i −1.12547 + 0.0258597i
207207 1.15532i 0.0803004i
208208 −13.4989 + 16.2393i −0.935982 + 1.12599i
209209 −20.0673 + 10.6394i −1.38809 + 0.735944i
210210 0.186462 + 8.11524i 0.0128671 + 0.560005i
211211 −16.6981 16.6981i −1.14954 1.14954i −0.986642 0.162901i 0.947915π-0.947915\pi
−0.162901 0.986642i 0.552085π-0.552085\pi
212212 −7.43846 6.78452i −0.510876 0.465963i
213213 3.07464 3.07464i 0.210671 0.210671i
214214 17.0485 + 16.2826i 1.16541 + 1.11306i
215215 9.06275 0.618075
216216 8.94724 + 7.79178i 0.608782 + 0.530164i
217217 −8.32868 −0.565387
218218 14.9268 + 14.2562i 1.01097 + 0.965555i
219219 −7.47732 + 7.47732i −0.505271 + 0.505271i
220220 22.0841 1.01538i 1.48891 0.0684569i
221221 −5.65467 + 5.65467i −0.380374 + 0.380374i
222222 −4.88933 + 0.112341i −0.328151 + 0.00753984i
223223 −1.63480 −0.109474 −0.0547372 0.998501i 0.517432π-0.517432\pi
−0.0547372 + 0.998501i 0.517432π0.517432\pi
224224 −2.25650 19.5586i −0.150769 1.30681i
225225 1.19788 0.0798584
226226 −19.8565 + 0.456238i −1.32083 + 0.0303485i
227227 0.463368 + 0.463368i 0.0307548 + 0.0307548i 0.722317 0.691562i 0.243077π-0.243077\pi
−0.691562 + 0.722317i 0.743077π0.743077\pi
228228 5.83582 3.44640i 0.386486 0.228244i
229229 −8.36381 + 8.36381i −0.552696 + 0.552696i −0.927218 0.374522i 0.877807π-0.877807\pi
0.374522 + 0.927218i 0.377807π0.377807\pi
230230 −1.04627 0.999273i −0.0689892 0.0658901i
231231 14.0994i 0.927671i
232232 −21.9217 19.0907i −1.43923 1.25337i
233233 9.02414i 0.591191i 0.955313 + 0.295596i 0.0955181π0.0955181\pi
−0.955313 + 0.295596i 0.904482π0.904482\pi
234234 −12.3532 + 12.9343i −0.807557 + 0.845540i
235235 5.37799 + 5.37799i 0.350821 + 0.350821i
236236 0.779237 0.854346i 0.0507240 0.0556132i
237237 2.75978 + 2.75978i 0.179267 + 0.179267i
238238 −0.171265 7.45384i −0.0111015 0.483161i
239239 0.575236i 0.0372089i 0.999827 + 0.0186045i 0.00592233π0.00592233\pi
−0.999827 + 0.0186045i 0.994078π0.994078\pi
240240 −6.56888 + 0.605325i −0.424019 + 0.0390736i
241241 10.2254i 0.658678i −0.944212 0.329339i 0.893174π-0.893174\pi
0.944212 0.329339i 0.106826π-0.106826\pi
242242 −22.8368 + 0.524717i −1.46801 + 0.0337301i
243243 11.0564 + 11.0564i 0.709268 + 0.709268i
244244 −5.17849 4.72323i −0.331519 0.302374i
245245 7.67014 7.67014i 0.490027 0.490027i
246246 −6.02985 + 6.31346i −0.384449 + 0.402531i
247247 10.7793 + 20.3312i 0.685871 + 1.29364i
248248 −0.466098 6.75235i −0.0295973 0.428775i
249249 −11.3790 −0.721116
250250 −11.3962 + 11.9322i −0.720759 + 0.754660i
251251 −9.67088 9.67088i −0.610421 0.610421i 0.332635 0.943056i 0.392062π-0.392062\pi
−0.943056 + 0.332635i 0.892062π0.892062\pi
252252 −0.765893 16.6579i −0.0482467 1.04935i
253253 1.77696 + 1.77696i 0.111717 + 0.111717i
254254 0.184610 + 8.03461i 0.0115834 + 0.504136i
255255 −2.49812 −0.156438
256256 15.7306 2.92399i 0.983160 0.182749i
257257 18.8850i 1.17802i 0.808127 + 0.589008i 0.200481π0.200481\pi
−0.808127 + 0.589008i 0.799519π0.799519\pi
258258 4.69589 0.107897i 0.292354 0.00671735i
259259 10.9473 + 10.9473i 0.680230 + 0.680230i
260260 −1.02873 22.3745i −0.0637991 1.38761i
261261 −17.4095 17.4095i −1.07762 1.07762i
262262 1.43862 + 1.37400i 0.0888783 + 0.0848858i
263263 −12.0775 −0.744732 −0.372366 0.928086i 0.621453π-0.621453\pi
−0.372366 + 0.928086i 0.621453π0.621453\pi
264264 11.4309 0.789045i 0.703521 0.0485623i
265265 10.6785 0.655973
266266 −20.6492 5.82437i −1.26608 0.357115i
267267 4.08224 + 4.08224i 0.249829 + 0.249829i
268268 22.2958 + 20.3357i 1.36193 + 1.24220i
269269 8.54359 8.54359i 0.520912 0.520912i −0.396935 0.917847i 0.629926π-0.629926\pi
0.917847 + 0.396935i 0.129926π0.129926\pi
270270 −12.5808 + 0.289066i −0.765641 + 0.0175920i
271271 8.30882i 0.504725i 0.967633 + 0.252362i 0.0812075π0.0812075\pi
−0.967633 + 0.252362i 0.918793π0.918793\pi
272272 6.03351 0.555991i 0.365835 0.0337119i
273273 −14.2848 −0.864553
274274 14.9900 0.344422i 0.905578 0.0208073i
275275 1.84241 1.84241i 0.111102 0.111102i
276276 −0.554026 0.505320i −0.0333485 0.0304167i
277277 9.55608 9.55608i 0.574169 0.574169i −0.359122 0.933291i 0.616924π-0.616924\pi
0.933291 + 0.359122i 0.116924π0.116924\pi
278278 −12.7801 + 13.3812i −0.766497 + 0.802548i
279279 5.73266i 0.343205i
280280 15.7480 + 13.7143i 0.941123 + 0.819585i
281281 9.32142 0.556069 0.278035 0.960571i 0.410317π-0.410317\pi
0.278035 + 0.960571i 0.410317π0.410317\pi
282282 2.85065 + 2.72259i 0.169754 + 0.162128i
283283 4.19436 + 4.19436i 0.249329 + 0.249329i 0.820695 0.571366i 0.193586π-0.193586\pi
−0.571366 + 0.820695i 0.693586π0.693586\pi
284284 −0.513767 11.1742i −0.0304865 0.663069i
285285 −2.10991 + 6.87199i −0.124980 + 0.407061i
286286 0.893655 + 38.8938i 0.0528429 + 2.29984i
287287 27.6368 1.63135
288288 13.4623 1.55316i 0.793271 0.0915209i
289289 −14.7055 −0.865028
290290 30.8243 0.708243i 1.81006 0.0415895i
291291 −2.03467 + 2.03467i −0.119275 + 0.119275i
292292 1.24945 + 27.1750i 0.0731185 + 1.59030i
293293 −13.7219 13.7219i −0.801640 0.801640i 0.181712 0.983352i 0.441836π-0.441836\pi
−0.983352 + 0.181712i 0.941836π0.941836\pi
294294 3.88299 4.06562i 0.226461 0.237112i
295295 1.22648i 0.0714083i
296296 −8.26269 + 9.48797i −0.480259 + 0.551477i
297297 21.8578 1.26832
298298 0.384421 + 0.367152i 0.0222689 + 0.0212686i
299299 1.80032 1.80032i 0.104115 0.104115i
300300 −0.523932 + 0.574433i −0.0302493 + 0.0331649i
301301 −10.5142 10.5142i −0.606026 0.606026i
302302 11.6836 0.268451i 0.672315 0.0154476i
303303 −5.26329 −0.302368
304304 3.56643 17.0669i 0.204549 0.978856i
305305 7.43410 0.425675
306306 5.13051 0.117883i 0.293292 0.00673890i
307307 9.90107 + 9.90107i 0.565084 + 0.565084i 0.930747 0.365663i 0.119158π-0.119158\pi
−0.365663 + 0.930747i 0.619158π0.619158\pi
308308 −26.7989 24.4429i −1.52701 1.39276i
309309 6.28081 6.28081i 0.357303 0.357303i
310310 5.19156 + 4.95835i 0.294861 + 0.281615i
311311 17.4462 0.989283 0.494642 0.869097i 0.335299π-0.335299\pi
0.494642 + 0.869097i 0.335299π0.335299\pi
312312 −0.799419 11.5812i −0.0452582 0.655654i
313313 9.14849i 0.517103i 0.965997 + 0.258552i 0.0832452π0.0832452\pi
−0.965997 + 0.258552i 0.916755π0.916755\pi
314314 15.4633 16.1906i 0.872647 0.913691i
315315 12.5066 + 12.5066i 0.704665 + 0.704665i
316316 10.0299 0.461155i 0.564229 0.0259420i
317317 −19.0979 + 19.0979i −1.07264 + 1.07264i −0.0754990 + 0.997146i 0.524055π0.524055\pi
−0.997146 + 0.0754990i 0.975945π0.975945\pi
318318 5.53308 0.127132i 0.310280 0.00712924i
319319 −53.5539 −2.99845
320320 −10.2373 + 13.5349i −0.572285 + 0.756626i
321321 −12.9597 −0.723342
322322 0.0545271 + 2.37314i 0.00303868 + 0.132250i
323323 1.93795 6.31191i 0.107830 0.351204i
324324 7.84310 0.360609i 0.435728 0.0200338i
325325 −1.86664 1.86664i −0.103542 0.103542i
326326 7.68076 + 7.33573i 0.425398 + 0.406289i
327327 −11.3469 −0.627485
328328 1.54664 + 22.4061i 0.0853988 + 1.23717i
329329 12.4785i 0.687964i
330330 −8.39385 + 8.78865i −0.462066 + 0.483799i
331331 −3.09582 + 3.09582i −0.170162 + 0.170162i −0.787050 0.616889i 0.788393π-0.788393\pi
0.616889 + 0.787050i 0.288393π0.288393\pi
332332 −19.7268 + 21.6282i −1.08265 + 1.18700i
333333 −7.53504 + 7.53504i −0.412918 + 0.412918i
334334 −12.7628 + 0.293247i −0.698347 + 0.0160458i
335335 −32.0073 −1.74875
336336 8.32315 + 6.91861i 0.454065 + 0.377441i
337337 12.1693i 0.662903i 0.943472 + 0.331452i 0.107538π0.107538\pi
−0.943472 + 0.331452i 0.892462π0.892462\pi
338338 21.0253 0.483093i 1.14362 0.0262768i
339339 7.72056 7.72056i 0.419323 0.419323i
340340 −4.33077 + 4.74821i −0.234869 + 0.257508i
341341 −8.81720 8.81720i −0.477478 0.477478i
342342 4.00894 14.2129i 0.216779 0.768545i
343343 6.56604 0.354533
344344 7.93579 9.11260i 0.427869 0.491318i
345345 0.795346 0.0428200
346346 11.3170 + 10.8086i 0.608403 + 0.581073i
347347 −8.14038 8.14038i −0.436999 0.436999i 0.454002 0.891001i 0.349996π-0.349996\pi
−0.891001 + 0.454002i 0.849996π0.849996\pi
348348 15.9633 0.733957i 0.855721 0.0393442i
349349 11.7882 + 11.7882i 0.631010 + 0.631010i 0.948321 0.317311i 0.102780π-0.102780\pi
−0.317311 + 0.948321i 0.602780π0.602780\pi
350350 2.46055 0.0565355i 0.131522 0.00302195i
351351 22.1452i 1.18202i
352352 18.3170 23.0947i 0.976297 1.23095i
353353 4.06776 0.216505 0.108253 0.994123i 0.465474π-0.465474\pi
0.108253 + 0.994123i 0.465474π0.465474\pi
354354 0.0146018 + 0.635503i 0.000776078 + 0.0337766i
355355 8.38950 + 8.38950i 0.445268 + 0.445268i
356356 14.8362 0.682136i 0.786316 0.0361531i
357357 2.89819 + 2.89819i 0.153389 + 0.153389i
358358 −4.07966 + 4.27155i −0.215617 + 0.225758i
359359 −7.30143 −0.385355 −0.192677 0.981262i 0.561717π-0.561717\pi
−0.192677 + 0.981262i 0.561717π0.561717\pi
360360 −9.43960 + 10.8394i −0.497510 + 0.571287i
361361 −15.7264 10.6621i −0.827707 0.561161i
362362 9.61114 10.0632i 0.505150 0.528910i
363363 8.87939 8.87939i 0.466047 0.466047i
364364 −24.7643 + 27.1512i −1.29800 + 1.42311i
365365 −20.4027 20.4027i −1.06793 1.06793i
366366 3.85200 0.0885067i 0.201347 0.00462632i
367367 8.15940i 0.425917i 0.977061 + 0.212959i 0.0683100π0.0683100\pi
−0.977061 + 0.212959i 0.931690π0.931690\pi
368368 −1.92094 + 0.177015i −0.100136 + 0.00922755i
369369 19.0225i 0.990272i
370370 −0.306536 13.3411i −0.0159360 0.693571i
371371 −12.3886 12.3886i −0.643185 0.643185i
372372 2.74906 + 2.50738i 0.142532 + 0.130001i
373373 −7.35016 7.35016i −0.380577 0.380577i 0.490733 0.871310i 0.336729π-0.336729\pi
−0.871310 + 0.490733i 0.836729π0.836729\pi
374374 7.70974 8.07236i 0.398661 0.417412i
375375 9.07053i 0.468400i
376376 10.1168 0.698337i 0.521734 0.0360140i
377377 54.2581i 2.79443i
378378 14.9309 + 14.2602i 0.767965 + 0.733467i
379379 20.2426 20.2426i 1.03979 1.03979i 0.0406169 0.999175i 0.487068π-0.487068\pi
0.999175 0.0406169i 0.0129323π-0.0129323\pi
380380 9.40391 + 15.9237i 0.482410 + 0.816868i
381381 −3.12401 3.12401i −0.160048 0.160048i
382382 5.53455 0.127166i 0.283172 0.00650639i
383383 18.4669 0.943615 0.471807 0.881702i 0.343602π-0.343602\pi
0.471807 + 0.881702i 0.343602π0.343602\pi
384384 −5.14337 + 7.13506i −0.262472 + 0.364109i
385385 38.4718 1.96070
386386 24.8383 0.570704i 1.26424 0.0290481i
387387 7.23693 7.23693i 0.367874 0.367874i
388388 0.339991 + 7.39467i 0.0172604 + 0.375408i
389389 −16.3368 + 16.3368i −0.828309 + 0.828309i −0.987283 0.158974i 0.949181π-0.949181\pi
0.158974 + 0.987283i 0.449181π0.449181\pi
390390 8.90420 + 8.50421i 0.450882 + 0.430628i
391391 −0.730525 −0.0369442
392392 −0.995976 14.4287i −0.0503044 0.728758i
393393 −1.09360 −0.0551648
394394 −23.5590 22.5007i −1.18689 1.13357i
395395 −7.53038 + 7.53038i −0.378895 + 0.378895i
396396 16.8241 18.4458i 0.845445 0.926935i
397397 −13.0533 13.0533i −0.655126 0.655126i 0.299097 0.954223i 0.403315π-0.403315\pi
−0.954223 + 0.299097i 0.903315π0.903315\pi
398398 0.702011 + 30.5530i 0.0351886 + 1.53149i
399399 10.4203 5.52473i 0.521670 0.276582i
400400 0.183535 + 1.99169i 0.00917676 + 0.0995845i
401401 26.3416i 1.31544i −0.753263 0.657719i 0.771521π-0.771521\pi
0.753263 0.657719i 0.228479π-0.228479\pi
402402 −16.5847 + 0.381063i −0.827169 + 0.0190057i
403403 −8.93313 + 8.93313i −0.444991 + 0.444991i
404404 −9.12451 + 10.0040i −0.453961 + 0.497717i
405405 −5.88852 + 5.88852i −0.292603 + 0.292603i
406406 −36.5825 34.9391i −1.81556 1.73400i
407407 23.1788i 1.14893i
408408 −2.18747 + 2.51186i −0.108296 + 0.124356i
409409 −0.821310 −0.0406112 −0.0203056 0.999794i 0.506464π-0.506464\pi
−0.0203056 + 0.999794i 0.506464π0.506464\pi
410410 −17.2270 16.4531i −0.850780 0.812562i
411411 −5.82839 + 5.82839i −0.287493 + 0.287493i
412412 −1.04951 22.8265i −0.0517058 1.12458i
413413 1.42290 1.42290i 0.0700162 0.0700162i
414414 −1.63344 + 0.0375312i −0.0802793 + 0.00184456i
415415 31.0489i 1.52413i
416416 −23.3983 18.5578i −1.14720 0.909870i
417417 10.1720i 0.498123i
418418 −15.6943 28.0264i −0.767636 1.37081i
419419 2.51426 2.51426i 0.122830 0.122830i −0.643020 0.765849i 0.722319π-0.722319\pi
0.765849 + 0.643020i 0.222319π0.222319\pi
420420 −11.4676 + 0.527256i −0.559562 + 0.0257274i
421421 9.64923 + 9.64923i 0.470275 + 0.470275i 0.902003 0.431729i 0.142096π-0.142096\pi
−0.431729 + 0.902003i 0.642096π0.642096\pi
422422 23.0660 24.1509i 1.12283 1.17565i
423423 8.58903 0.417613
424424 9.35059 10.7372i 0.454105 0.521444i
425425 0.757432i 0.0367409i
426426 4.44693 + 4.24717i 0.215454 + 0.205776i
427427 −8.62467 8.62467i −0.417377 0.417377i
428428 −22.4672 + 24.6327i −1.08599 + 1.19067i
429429 −15.1226 15.1226i −0.730128 0.730128i
430430 0.294408 + 12.8133i 0.0141976 + 0.617911i
431431 5.87725 0.283097 0.141549 0.989931i 0.454792π-0.454792\pi
0.141549 + 0.989931i 0.454792π0.454792\pi
432432 −10.7257 + 12.9031i −0.516040 + 0.620800i
433433 2.62302i 0.126054i −0.998012 0.0630271i 0.979925π-0.979925\pi
0.998012 0.0630271i 0.0200754π-0.0200754\pi
434434 −0.270561 11.7754i −0.0129874 0.565238i
435435 −11.9851 + 11.9851i −0.574639 + 0.574639i
436436 −19.6712 + 21.5672i −0.942077 + 1.03288i
437437 −0.617000 + 2.00957i −0.0295151 + 0.0961310i
438438 −10.8146 10.3288i −0.516744 0.493531i
439439 34.6282i 1.65272i −0.563146 0.826358i 0.690409π-0.690409\pi
0.563146 0.826358i 0.309591π-0.309591\pi
440440 2.15300 + 31.1904i 0.102640 + 1.48694i
441441 12.2498i 0.583322i
442442 −8.17850 7.81111i −0.389012 0.371537i
443443 3.58478 + 3.58478i 0.170318 + 0.170318i 0.787119 0.616801i 0.211572π-0.211572\pi
−0.616801 + 0.787119i 0.711572π0.711572\pi
444444 −0.317665 6.90909i −0.0150757 0.327891i
445445 −11.1389 + 11.1389i −0.528032 + 0.528032i
446446 −0.0531074 2.31135i −0.00251471 0.109446i
447447 −0.292226 −0.0138218
448448 27.5794 3.82571i 1.30301 0.180748i
449449 6.98073i 0.329441i −0.986340 0.164721i 0.947328π-0.947328\pi
0.986340 0.164721i 0.0526722π-0.0526722\pi
450450 0.0389136 + 1.69361i 0.00183441 + 0.0798374i
451451 29.2578 + 29.2578i 1.37770 + 1.37770i
452452 −1.29009 28.0590i −0.0606809 1.31979i
453453 −4.54280 + 4.54280i −0.213439 + 0.213439i
454454 −0.640076 + 0.670181i −0.0300402 + 0.0314532i
455455 38.9776i 1.82730i
456456 5.06224 + 8.13896i 0.237061 + 0.381142i
457457 1.61947i 0.0757556i −0.999282 0.0378778i 0.987940π-0.987940\pi
0.999282 0.0378778i 0.0120598π-0.0120598\pi
458458 −12.0968 11.5534i −0.565246 0.539854i
459459 −4.49297 + 4.49297i −0.209714 + 0.209714i
460460 1.37882 1.51172i 0.0642880 0.0704845i
461461 11.2678 + 11.2678i 0.524792 + 0.524792i 0.919015 0.394223i 0.128986π-0.128986\pi
−0.394223 + 0.919015i 0.628986π0.628986\pi
462462 19.9343 0.458026i 0.927426 0.0213093i
463463 26.2153i 1.21833i −0.793043 0.609165i 0.791505π-0.791505\pi
0.793043 0.609165i 0.208495π-0.208495\pi
464464 26.2791 31.6140i 1.21998 1.46764i
465465 −3.94648 −0.183013
466466 −12.7587 + 0.293154i −0.591035 + 0.0135801i
467467 7.45814 7.45814i 0.345121 0.345121i −0.513167 0.858289i 0.671528π-0.671528\pi
0.858289 + 0.513167i 0.171528π0.171528\pi
468468 −18.6883 17.0453i −0.863867 0.787921i
469469 37.1333 + 37.1333i 1.71465 + 1.71465i
470470 −7.42891 + 7.77832i −0.342670 + 0.358787i
471471 12.3077i 0.567107i
472472 1.23322 + 1.07396i 0.0567637 + 0.0494332i
473473 22.2617i 1.02360i
474474 −3.81224 + 3.99154i −0.175102 + 0.183338i
475475 2.08359 + 0.639726i 0.0956018 + 0.0293526i
476476 10.5330 0.484284i 0.482778 0.0221971i
477477 8.52714 8.52714i 0.390431 0.390431i
478478 −0.813292 + 0.0186868i −0.0371991 + 0.000854716i
479479 22.0408i 1.00707i 0.863975 + 0.503534i 0.167967π0.167967\pi
−0.863975 + 0.503534i 0.832033π0.832033\pi
480480 −1.06923 9.26768i −0.0488033 0.423010i
481481 23.4835 1.07076
482482 14.4571 0.332178i 0.658504 0.0151303i
483483 −0.922721 0.922721i −0.0419853 0.0419853i
484484 −1.48373 32.2706i −0.0674424 1.46685i
485485 −5.55184 5.55184i −0.252096 0.252096i
486486 −15.2728 + 15.9911i −0.692788 + 0.725373i
487487 21.9766i 0.995856i 0.867218 + 0.497928i 0.165906π0.165906\pi
−0.867218 + 0.497928i 0.834094π0.834094\pi
488488 6.50966 7.47499i 0.294679 0.338377i
489489 −5.83869 −0.264035
490490 11.0935 + 10.5952i 0.501154 + 0.478642i
491491 −17.7224 17.7224i −0.799803 0.799803i 0.183261 0.983064i 0.441335π-0.441335\pi
−0.983064 + 0.183261i 0.941335π0.941335\pi
492492 −9.12210 8.32014i −0.411256 0.375101i
493493 11.0083 11.0083i 0.495787 0.495787i
494494 −28.3948 + 15.9007i −1.27754 + 0.715406i
495495 26.4803i 1.19020i
496496 9.53160 0.878342i 0.427982 0.0394387i
497497 19.4662i 0.873176i
498498 −0.369653 16.0881i −0.0165646 0.720925i
499499 −30.3549 + 30.3549i −1.35887 + 1.35887i −0.483562 + 0.875310i 0.660657π0.660657\pi
−0.875310 + 0.483562i 0.839343π0.839343\pi
500500 −17.2405 15.7248i −0.771017 0.703234i
501501 4.96240 4.96240i 0.221704 0.221704i
502502 13.3589 13.9872i 0.596238 0.624281i
503503 7.49320 0.334105 0.167053 0.985948i 0.446575π-0.446575\pi
0.167053 + 0.985948i 0.446575π0.446575\pi
504504 23.5267 1.62399i 1.04796 0.0723382i
505505 14.3615i 0.639077i
506506 −2.45461 + 2.57006i −0.109121 + 0.114253i
507507 −8.17502 + 8.17502i −0.363066 + 0.363066i
508508 −11.3537 + 0.522017i −0.503737 + 0.0231608i
509509 −21.4192 + 21.4192i −0.949391 + 0.949391i −0.998780 0.0493888i 0.984273π-0.984273\pi
0.0493888 + 0.998780i 0.484273π0.484273\pi
510510 −0.0811527 3.53194i −0.00359350 0.156397i
511511 47.3405i 2.09422i
512512 4.64507 + 22.1455i 0.205285 + 0.978702i
513513 8.56479 + 16.1543i 0.378145 + 0.713229i
514514 −26.7004 + 0.613490i −1.17771 + 0.0270599i
515515 17.1379 + 17.1379i 0.755186 + 0.755186i
516516 0.305097 + 6.63574i 0.0134311 + 0.292122i
517517 13.2105 13.2105i 0.580996 0.580996i
518518 −15.1221 + 15.8333i −0.664425 + 0.695676i
519519 −8.60283 −0.377622
520520 31.6005 2.18131i 1.38577 0.0956566i
521521 28.5238 1.24965 0.624824 0.780765i 0.285171π-0.285171\pi
0.624824 + 0.780765i 0.285171π0.285171\pi
522522 24.0487 25.1798i 1.05258 1.10209i
523523 2.87573 2.87573i 0.125747 0.125747i −0.641433 0.767179i 0.721660π-0.721660\pi
0.767179 + 0.641433i 0.221660π0.221660\pi
524524 −1.89588 + 2.07862i −0.0828218 + 0.0908048i
525525 −0.956708 + 0.956708i −0.0417541 + 0.0417541i
526526 −0.392344 17.0757i −0.0171070 0.744535i
527527 3.62483 0.157900
528528 1.48692 + 16.1358i 0.0647099 + 0.702220i
529529 −22.7674 −0.989888
530530 0.346896 + 15.0977i 0.0150682 + 0.655800i
531531 0.979386 + 0.979386i 0.0425017 + 0.0425017i
532532 7.56393 29.3838i 0.327938 1.27395i
533533 29.6425 29.6425i 1.28396 1.28396i
534534 −5.63902 + 5.90425i −0.244024 + 0.255502i
535535 35.3621i 1.52884i
536536 −28.0271 + 32.1833i −1.21059 + 1.39011i
537537 3.24711i 0.140123i
538538 12.3568 + 11.8017i 0.532740 + 0.508809i
539539 −18.8409 18.8409i −0.811536 0.811536i
540540 −0.817386 17.7778i −0.0351747 0.765035i
541541 1.13344 + 1.13344i 0.0487304 + 0.0487304i 0.731052 0.682322i 0.239030π-0.239030\pi
−0.682322 + 0.731052i 0.739030π0.739030\pi
542542 −11.7473 + 0.269916i −0.504591 + 0.0115939i
543543 7.64975i 0.328282i
544544 0.982083 + 8.51235i 0.0421065 + 0.364964i
545545 30.9613i 1.32624i
546546 −0.464048 20.1964i −0.0198594 0.864325i
547547 −13.4249 13.4249i −0.574008 0.574008i 0.359238 0.933246i 0.383037π-0.383037\pi
−0.933246 + 0.359238i 0.883037π0.883037\pi
548548 0.973915 + 21.1823i 0.0416036 + 0.904861i
549549 5.93640 5.93640i 0.253359 0.253359i
550550 2.66473 + 2.54502i 0.113624 + 0.108520i
551551 −20.9847 39.5798i −0.893977 1.68616i
552552 0.696444 0.799720i 0.0296426 0.0340384i
553553 17.4727 0.743017
554554 13.8212 + 13.2003i 0.587207 + 0.560828i
555555 5.18727 + 5.18727i 0.220187 + 0.220187i
556556 −19.3340 17.6343i −0.819943 0.747859i
557557 7.79578 + 7.79578i 0.330318 + 0.330318i 0.852707 0.522389i 0.174959π-0.174959\pi
−0.522389 + 0.852707i 0.674959π0.674959\pi
558558 8.10507 0.186228i 0.343115 0.00788368i
559559 −22.5544 −0.953951
560560 −18.8782 + 22.7107i −0.797751 + 0.959701i
561561 6.13638i 0.259078i
562562 0.302811 + 13.1790i 0.0127733 + 0.555922i
563563 −4.84245 4.84245i −0.204085 0.204085i 0.597663 0.801748i 0.296096π-0.296096\pi
−0.801748 + 0.597663i 0.796096π0.796096\pi
564564 −3.75671 + 4.11881i −0.158186 + 0.173433i
565565 21.0664 + 21.0664i 0.886272 + 0.886272i
566566 −5.79390 + 6.06641i −0.243536 + 0.254990i
567567 13.6631 0.573797
568568 15.7819 1.08939i 0.662194 0.0457096i
569569 20.2563 0.849190 0.424595 0.905383i 0.360417π-0.360417\pi
0.424595 + 0.905383i 0.360417π0.360417\pi
570570 −9.78443 2.75983i −0.409825 0.115597i
571571 18.3379 + 18.3379i 0.767419 + 0.767419i 0.977651 0.210233i 0.0674222π-0.0674222\pi
−0.210233 + 0.977651i 0.567422π0.567422\pi
572572 −54.9606 + 2.52697i −2.29802 + 0.105658i
573573 −2.15194 + 2.15194i −0.0898985 + 0.0898985i
574574 0.897795 + 39.0740i 0.0374732 + 1.63092i
575575 0.241150i 0.0100566i
576576 2.63325 + 18.9830i 0.109719 + 0.790959i
577577 −5.18354 −0.215793 −0.107897 0.994162i 0.534412π-0.534412\pi
−0.107897 + 0.994162i 0.534412π0.534412\pi
578578 −0.477715 20.7912i −0.0198703 0.864800i
579579 −9.65759 + 9.65759i −0.401356 + 0.401356i
580580 2.00268 + 43.5576i 0.0831570 + 1.80863i
581581 −36.0214 + 36.0214i −1.49442 + 1.49442i
582582 −2.94280 2.81061i −0.121983 0.116503i
583583 26.2306i 1.08636i
584584 −38.3806 + 2.64932i −1.58820 + 0.109630i
585585 26.8284 1.10922
586586 18.9548 19.8463i 0.783014 0.819842i
587587 −1.88371 1.88371i −0.0777491 0.0777491i 0.667163 0.744912i 0.267509π-0.267509\pi
−0.744912 + 0.667163i 0.767509π0.767509\pi
588588 5.87428 + 5.35785i 0.242251 + 0.220954i
589589 3.06153 9.97142i 0.126148 0.410865i
590590 −1.73404 + 0.0398427i −0.0713894 + 0.00164030i
591591 17.9089 0.736673
592592 −13.6829 11.3739i −0.562363 0.467464i
593593 44.2304 1.81632 0.908162 0.418619i 0.137486π-0.137486\pi
0.908162 + 0.418619i 0.137486π0.137486\pi
594594 0.710061 + 30.9034i 0.0291342 + 1.26798i
595595 −7.90805 + 7.90805i −0.324198 + 0.324198i
596596 −0.506607 + 0.555437i −0.0207514 + 0.0227516i
597597 −11.8796 11.8796i −0.486199 0.486199i
598598 2.60385 + 2.48689i 0.106480 + 0.101696i
599599 25.1207i 1.02640i 0.858268 + 0.513202i 0.171541π0.171541\pi
−0.858268 + 0.513202i 0.828459π0.828459\pi
600600 −0.829177 0.722096i −0.0338510 0.0294795i
601601 21.0826 0.859976 0.429988 0.902835i 0.358518π-0.358518\pi
0.429988 + 0.902835i 0.358518π0.358518\pi
602602 14.5238 15.2069i 0.591945 0.619787i
603603 −25.5590 + 25.5590i −1.04084 + 1.04084i
604604 0.759095 + 16.5100i 0.0308871 + 0.671783i
605605 24.2284 + 24.2284i 0.985026 + 0.985026i
606606 −0.170981 7.44145i −0.00694561 0.302288i
607607 −15.2446 −0.618759 −0.309379 0.950939i 0.600121π-0.600121\pi
−0.309379 + 0.950939i 0.600121π0.600121\pi
608608 24.2458 + 4.48794i 0.983297 + 0.182010i
609609 27.8089 1.12687
610610 0.241501 + 10.5106i 0.00977807 + 0.425563i
611611 −13.3842 13.3842i −0.541466 0.541466i
612612 0.333334 + 7.24989i 0.0134742 + 0.293059i
613613 21.4123 21.4123i 0.864833 0.864833i −0.127062 0.991895i 0.540555π-0.540555\pi
0.991895 + 0.127062i 0.0405546π0.0405546\pi
614614 −13.6769 + 14.3202i −0.551954 + 0.577915i
615615 13.0955 0.528060
616616 33.6878 38.6834i 1.35732 1.55860i
617617 47.5231i 1.91321i 0.291390 + 0.956604i 0.405882π0.405882\pi
−0.291390 + 0.956604i 0.594118π0.594118\pi
618618 9.08409 + 8.67602i 0.365416 + 0.349001i
619619 −1.43559 1.43559i −0.0577014 0.0577014i 0.677667 0.735369i 0.262991π-0.262991\pi
−0.735369 + 0.677667i 0.762991π0.762991\pi
620620 −6.84166 + 7.50111i −0.274768 + 0.301252i
621621 1.43046 1.43046i 0.0574024 0.0574024i
622622 0.566749 + 24.6661i 0.0227246 + 0.989022i
623623 25.8455 1.03548
624624 16.3479 1.50647i 0.654441 0.0603071i
625625 22.2498 0.889992
626626 −12.9345 + 0.297193i −0.516967 + 0.0118782i
627627 16.8803 + 5.18277i 0.674136 + 0.206980i
628628 23.3933 + 21.3367i 0.933495 + 0.851428i
629629 −4.76450 4.76450i −0.189973 0.189973i
630630 −17.2760 + 18.0886i −0.688292 + 0.720665i
631631 −0.490988 −0.0195459 −0.00977296 0.999952i 0.503111π-0.503111\pi
−0.00977296 + 0.999952i 0.503111π0.503111\pi
632632 0.977828 + 14.1658i 0.0388959 + 0.563484i
633633 18.3588i 0.729696i
634634 −27.6218 26.3810i −1.09700 1.04772i
635635 8.52421 8.52421i 0.338273 0.338273i
636636 0.359490 + 7.81877i 0.0142547 + 0.310034i
637637 −19.0886 + 19.0886i −0.756320 + 0.756320i
638638 −1.73973 75.7167i −0.0688765 2.99765i
639639 13.3986 0.530042
640640 −19.4688 14.0343i −0.769573 0.554754i
641641 16.9893i 0.671039i 0.942033 + 0.335519i 0.108912π0.108912\pi
−0.942033 + 0.335519i 0.891088π0.891088\pi
642642 −0.421004 18.3230i −0.0166157 0.723151i
643643 12.5699 12.5699i 0.495709 0.495709i −0.414390 0.910099i 0.636005π-0.636005\pi
0.910099 + 0.414390i 0.136005π0.136005\pi
644644 −3.35347 + 0.154185i −0.132145 + 0.00607575i
645645 −4.98204 4.98204i −0.196168 0.196168i
646646 8.98699 + 2.53490i 0.353588 + 0.0997344i
647647 −37.3005 −1.46643 −0.733217 0.679995i 0.761982π-0.761982\pi
−0.733217 + 0.679995i 0.761982π0.761982\pi
648648 0.764630 + 11.0772i 0.0300375 + 0.435153i
649649 3.01272 0.118260
650650 2.57849 2.69976i 0.101137 0.105893i
651651 4.57850 + 4.57850i 0.179446 + 0.179446i
652652 −10.1220 + 11.0977i −0.396410 + 0.434619i
653653 −19.3569 19.3569i −0.757496 0.757496i 0.218370 0.975866i 0.429926π-0.429926\pi
−0.975866 + 0.218370i 0.929926π0.929926\pi
654654 −0.368610 16.0427i −0.0144138 0.627320i
655655 2.98401i 0.116595i
656656 −31.6284 + 2.91457i −1.23488 + 0.113795i
657657 −32.5846 −1.27125
658658 17.6427 0.405372i 0.687783 0.0158030i
659659 27.9807 + 27.9807i 1.08997 + 1.08997i 0.995530 + 0.0944429i 0.0301070π0.0301070\pi
0.0944429 + 0.995530i 0.469893π0.469893\pi
660660 −12.6984 11.5821i −0.494286 0.450831i
661661 −27.6554 27.6554i −1.07567 1.07567i −0.996892 0.0787770i 0.974898π-0.974898\pi
−0.0787770 0.996892i 0.525102π-0.525102\pi
662662 −4.47756 4.27642i −0.174025 0.166208i
663663 6.21706 0.241451
664664 −31.2197 27.1880i −1.21156 1.05510i
665665 15.0749 + 28.4331i 0.584578 + 1.10259i
666666 −10.8981 10.4086i −0.422294 0.403324i
667667 −3.50479 + 3.50479i −0.135706 + 0.135706i
668668 −0.829209 18.0350i −0.0320831 0.697794i
669669 0.898696 + 0.898696i 0.0347456 + 0.0347456i
670670 −1.03977 45.2532i −0.0401700 1.74828i
671671 18.2611i 0.704963i
672672 −9.51143 + 11.9924i −0.366911 + 0.462615i
673673 10.1211i 0.390141i 0.980789 + 0.195070i 0.0624935π0.0624935\pi
−0.980789 + 0.195070i 0.937506π0.937506\pi
674674 −17.2054 + 0.395326i −0.662728 + 0.0152274i
675675 −1.48315 1.48315i −0.0570865 0.0570865i
676676 1.36603 + 29.7107i 0.0525398 + 1.14272i
677677 −22.3139 22.3139i −0.857593 0.857593i 0.133461 0.991054i 0.457391π-0.457391\pi
−0.991054 + 0.133461i 0.957391π0.957391\pi
678678 11.1664 + 10.6648i 0.428845 + 0.409581i
679679 12.8819i 0.494363i
680680 −6.85389 5.96878i −0.262835 0.228892i
681681 0.509452i 0.0195223i
682682 12.1797 12.7525i 0.466384 0.488320i
683683 14.4876 14.4876i 0.554354 0.554354i −0.373340 0.927695i 0.621788π-0.621788\pi
0.927695 + 0.373340i 0.121788π0.121788\pi
684684 20.2250 + 5.20628i 0.773322 + 0.199067i
685685 −15.9034 15.9034i −0.607638 0.607638i
686686 0.213301 + 9.28333i 0.00814388 + 0.354439i
687687 9.19563 0.350835
688688 13.1416 + 10.9239i 0.501017 + 0.416470i
689689 −26.5755 −1.01244
690690 0.0258372 + 1.12449i 0.000983606 + 0.0428087i
691691 −24.4373 + 24.4373i −0.929638 + 0.929638i −0.997682 0.0680444i 0.978324π-0.978324\pi
0.0680444 + 0.997682i 0.478324π0.478324\pi
692692 −14.9140 + 16.3515i −0.566944 + 0.621591i
693693 30.7211 30.7211i 1.16700 1.16700i
694694 11.2448 11.7736i 0.426845 0.446922i
695695 27.7554 1.05282
696696 1.55627 + 22.5457i 0.0589904 + 0.854591i
697697 −12.0282 −0.455599
698698 −16.2838 + 17.0496i −0.616349 + 0.645339i
699699 4.96082 4.96082i 0.187635 0.187635i
700700 0.159864 + 3.47699i 0.00604231 + 0.131418i
701701 16.1800 + 16.1800i 0.611110 + 0.611110i 0.943235 0.332125i 0.107766π-0.107766\pi
−0.332125 + 0.943235i 0.607766π0.607766\pi
702702 31.3097 0.719397i 1.18171 0.0271519i
703703 −17.1306 + 9.08241i −0.646092 + 0.342550i
704704 33.2472 + 25.1470i 1.25305 + 0.947764i
705705 5.91285i 0.222691i
706706 0.132143 + 5.75117i 0.00497328 + 0.216448i
707707 −16.6615 + 16.6615i −0.626619 + 0.626619i
708708 −0.898026 + 0.0412893i −0.0337499 + 0.00155175i
709709 11.6536 11.6536i 0.437660 0.437660i −0.453563 0.891224i 0.649847π-0.649847\pi
0.891224 + 0.453563i 0.149847π0.149847\pi
710710 −11.5889 + 12.1340i −0.434923 + 0.455379i
711711 12.0266i 0.451031i
712712 1.44639 + 20.9538i 0.0542058 + 0.785278i
713713 −1.15407 −0.0432202
714714 −4.00343 + 4.19173i −0.149825 + 0.156872i
715715 41.2639 41.2639i 1.54318 1.54318i
716716 −6.17182 5.62923i −0.230652 0.210374i
717717 0.316223 0.316223i 0.0118096 0.0118096i
718718 −0.237191 10.3231i −0.00885188 0.385253i
719719 49.0662i 1.82986i −0.403611 0.914931i 0.632245π-0.632245\pi
0.403611 0.914931i 0.367755π-0.367755\pi
720720 −15.6318 12.9940i −0.582564 0.484256i
721721 39.7651i 1.48093i
722722 14.5636 22.5810i 0.542000 0.840379i
723723 −5.62120 + 5.62120i −0.209055 + 0.209055i
724724 14.5400 + 13.2617i 0.540374 + 0.492868i
725725 3.63388 + 3.63388i 0.134959 + 0.134959i
726726 12.8425 + 12.2656i 0.476630 + 0.455219i
727727 −10.6283 −0.394182 −0.197091 0.980385i 0.563149π-0.563149\pi
−0.197091 + 0.980385i 0.563149π0.563149\pi
728728 −39.1920 34.1307i −1.45255 1.26497i
729729 0.378928i 0.0140344i
730730 28.1834 29.5090i 1.04311 1.09218i
731731 4.57600 + 4.57600i 0.169250 + 0.169250i
732732 0.250269 + 5.44324i 0.00925020 + 0.201188i
733733 36.3785 + 36.3785i 1.34367 + 1.34367i 0.892375 + 0.451295i 0.149038π0.149038\pi
0.451295 + 0.892375i 0.350962π0.350962\pi
734734 −11.5361 + 0.265062i −0.425805 + 0.00978363i
735735 −8.43297 −0.311055
736736 −0.312674 2.71015i −0.0115253 0.0998973i
737737 78.6227i 2.89610i
738738 −26.8948 + 0.617956i −0.990010 + 0.0227473i
739739 −9.52584 + 9.52584i −0.350414 + 0.350414i −0.860263 0.509850i 0.829701π-0.829701\pi
0.509850 + 0.860263i 0.329701π0.329701\pi
740740 18.8522 0.866785i 0.693022 0.0318637i
741741 5.25092 17.1023i 0.192897 0.628268i
742742 17.1131 17.9180i 0.628241 0.657790i
743743 15.1555i 0.556001i −0.960581 0.278000i 0.910328π-0.910328\pi
0.960581 0.278000i 0.0896716π-0.0896716\pi
744744 −3.45573 + 3.96818i −0.126693 + 0.145481i
745745 0.797372i 0.0292134i
746746 10.1532 10.6307i 0.371734 0.389219i
747747 −24.7937 24.7937i −0.907154 0.907154i
748748 11.6635 + 10.6381i 0.426459 + 0.388968i
749749 −41.0254 + 41.0254i −1.49903 + 1.49903i
750750 12.8243 0.294661i 0.468276 0.0107595i
751751 −40.2293 −1.46799 −0.733994 0.679156i 0.762346π-0.762346\pi
−0.733994 + 0.679156i 0.762346π0.762346\pi
752752 1.31599 + 14.2808i 0.0479891 + 0.520769i
753753 10.6327i 0.387477i
754754 −76.7123 + 1.76260i −2.79370 + 0.0641902i
755755 −12.3955 12.3955i −0.451120 0.451120i
756756 −19.6766 + 21.5732i −0.715632 + 0.784610i
757757 −35.3310 + 35.3310i −1.28413 + 1.28413i −0.345827 + 0.938298i 0.612402π0.612402\pi
−0.938298 + 0.345827i 0.887598π0.887598\pi
758758 29.2774 + 27.9622i 1.06340 + 1.01563i
759759 1.95369i 0.0709144i
760760 −22.2081 + 13.8129i −0.805572 + 0.501047i
761761 5.10254i 0.184967i 0.995714 + 0.0924834i 0.0294805π0.0294805\pi
−0.995714 + 0.0924834i 0.970519π0.970519\pi
762762 4.31536 4.51833i 0.156329 0.163682i
763763 −35.9198 + 35.9198i −1.30038 + 1.30038i
764764 0.359585 + 7.82084i 0.0130093 + 0.282948i
765765 −5.44314 5.44314i −0.196797 0.196797i
766766 0.599907 + 26.1093i 0.0216755 + 0.943366i
767767 3.05233i 0.110213i
768768 −10.2549 7.04012i −0.370042 0.254039i
769769 35.3943 1.27635 0.638175 0.769891i 0.279690π-0.279690\pi
0.638175 + 0.769891i 0.279690π0.279690\pi
770770 1.24978 + 54.3929i 0.0450388 + 1.96019i
771771 10.3816 10.3816i 0.373885 0.373885i
772772 1.61377 + 35.0988i 0.0580808 + 1.26323i
773773 12.5110 + 12.5110i 0.449991 + 0.449991i 0.895351 0.445360i 0.146924π-0.146924\pi
−0.445360 + 0.895351i 0.646924π0.646924\pi
774774 10.4670 + 9.99677i 0.376227 + 0.359327i
775775 1.19658i 0.0429823i
776776 −10.4438 + 0.720913i −0.374912 + 0.0258793i
777777 12.0360i 0.431790i
778778 −23.6283 22.5669i −0.847117 0.809063i
779779 −10.1590 + 33.0878i −0.363983 + 1.18550i
780780 −11.7343 + 12.8654i −0.420157 + 0.460655i
781781 20.6080 20.6080i 0.737411 0.737411i
782782 −0.0237315 1.03285i −0.000848635 0.0369345i
783783 43.1112i 1.54067i
784784 20.3675 1.87687i 0.727410 0.0670312i
785785 −33.5829 −1.19862
786786 −0.0355261 1.54617i −0.00126717 0.0551502i
787787 0.304154 + 0.304154i 0.0108419 + 0.0108419i 0.712507 0.701665i 0.247560π-0.247560\pi
−0.701665 + 0.712507i 0.747560π0.747560\pi
788788 31.0471 34.0397i 1.10601 1.21261i
789789 6.63935 + 6.63935i 0.236367 + 0.236367i
790790 −10.8914 10.4021i −0.387498 0.370091i
791791 48.8805i 1.73799i
792792 26.6259 + 23.1874i 0.946111 + 0.823929i
793793 −18.5012 −0.656998
794794 18.0312 18.8793i 0.639905 0.670002i
795795 −5.87025 5.87025i −0.208196 0.208196i
796796 −43.1743 + 1.98506i −1.53027 + 0.0703587i
797797 −10.6768 + 10.6768i −0.378190 + 0.378190i −0.870449 0.492259i 0.836171π-0.836171\pi
0.492259 + 0.870449i 0.336171π0.336171\pi
798798 8.14959 + 14.5532i 0.288492 + 0.515179i
799799 5.43095i 0.192133i
800800 −2.80997 + 0.324191i −0.0993474 + 0.0114619i
801801 17.7895i 0.628563i
802802 37.2429 0.855721i 1.31509 0.0302166i
803803 −50.1173 + 50.1173i −1.76860 + 1.76860i
804804 −1.07752 23.4357i −0.0380013 0.826514i
805805 2.51775 2.51775i 0.0887390 0.0887390i
806806 −12.9202 12.3398i −0.455095 0.434652i
807807 −9.39329 −0.330660
808808 −14.4405 12.5756i −0.508014 0.442408i
809809 9.58027i 0.336824i −0.985717 0.168412i 0.946136π-0.946136\pi
0.985717 0.168412i 0.0538640π-0.0538640\pi
810810 −8.51672 8.13413i −0.299247 0.285804i
811811 −22.4309 + 22.4309i −0.787654 + 0.787654i −0.981109 0.193455i 0.938031π-0.938031\pi
0.193455 + 0.981109i 0.438031π0.438031\pi
812812 48.2099 52.8568i 1.69184 1.85491i
813813 4.56759 4.56759i 0.160192 0.160192i
814814 −32.7711 + 0.752974i −1.14863 + 0.0263917i
815815 15.9315i 0.558058i
816816 −3.62243 3.01114i −0.126810 0.105411i
817817 16.4528 8.72308i 0.575612 0.305182i
818818 −0.0266807 1.16120i −0.000932868 0.0406005i
819819 −31.1250 31.1250i −1.08760 1.08760i
820820 22.7025 24.8907i 0.792805 0.869221i
821821 24.5153 24.5153i 0.855590 0.855590i −0.135225 0.990815i 0.543176π-0.543176\pi
0.990815 + 0.135225i 0.0431756π0.0431756\pi
822822 −8.42975 8.05107i −0.294021 0.280813i
823823 −23.3599 −0.814274 −0.407137 0.913367i 0.633473π-0.633473\pi
−0.407137 + 0.913367i 0.633473π0.633473\pi
824824 32.2389 2.22538i 1.12310 0.0775246i
825825 −2.02565 −0.0705240
826826 2.05797 + 1.96553i 0.0716061 + 0.0683894i
827827 24.9222 24.9222i 0.866631 0.866631i −0.125467 0.992098i 0.540043π-0.540043\pi
0.992098 + 0.125467i 0.0400428π0.0400428\pi
828828 −0.106126 2.30821i −0.00368815 0.0802157i
829829 8.85684 8.85684i 0.307611 0.307611i −0.536371 0.843982i 0.680205π-0.680205\pi
0.843982 + 0.536371i 0.180205π0.180205\pi
830830 43.8983 1.00864i 1.52373 0.0350104i
831831 −10.5065 −0.364466
832832 25.4776 33.6844i 0.883278 1.16780i
833833 7.74568 0.268372
834834 14.3815 0.330441i 0.497992 0.0114423i
835835 13.5405 + 13.5405i 0.468587 + 0.468587i
836836 39.1150 23.0998i 1.35282 0.798922i
837837 −7.09789 + 7.09789i −0.245339 + 0.245339i
838838 3.63644 + 3.47309i 0.125619 + 0.119976i
839839 23.5109i 0.811686i 0.913943 + 0.405843i 0.133022π0.133022\pi
−0.913943 + 0.405843i 0.866978π0.866978\pi
840840 −1.11799 16.1962i −0.0385742 0.558823i
841841 76.6272i 2.64232i
842842 −13.3290 + 13.9559i −0.459348 + 0.480953i
843843 −5.12424 5.12424i −0.176488 0.176488i
844844 34.8948 + 31.8271i 1.20113 + 1.09553i
845845 −22.3065 22.3065i −0.767366 0.767366i
846846 0.279019 + 12.1435i 0.00959287 + 0.417503i
847847 56.2172i 1.93165i
848848 15.4844 + 12.8714i 0.531738 + 0.442007i
849849 4.61151i 0.158267i
850850 −1.07089 + 0.0246056i −0.0367312 + 0.000843964i
851851 1.51691 + 1.51691i 0.0519991 + 0.0519991i
852852 −5.86035 + 6.42522i −0.200772 + 0.220124i
853853 −2.97132 + 2.97132i −0.101736 + 0.101736i −0.756143 0.654407i 0.772918π-0.772918\pi
0.654407 + 0.756143i 0.272918π0.272918\pi
854854 11.9137 12.4741i 0.407680 0.426855i
855855 −19.5706 + 10.3761i −0.669301 + 0.354854i
856856 −35.5566 30.9648i −1.21530 1.05836i
857857 35.1401 1.20036 0.600181 0.799864i 0.295095π-0.295095\pi
0.600181 + 0.799864i 0.295095π0.295095\pi
858858 20.8897 21.8723i 0.713164 0.746707i
859859 34.6341 + 34.6341i 1.18170 + 1.18170i 0.979304 + 0.202395i 0.0648725π0.0648725\pi
0.202395 + 0.979304i 0.435128π0.435128\pi
860860 −18.1064 + 0.832492i −0.617422 + 0.0283877i
861861 −15.1927 15.1927i −0.517766 0.517766i
862862 0.190926 + 8.30950i 0.00650295 + 0.283023i
863863 −22.4122 −0.762921 −0.381461 0.924385i 0.624579π-0.624579\pi
−0.381461 + 0.924385i 0.624579π0.624579\pi
864864 −18.5913 14.7452i −0.632490 0.501643i
865865 23.4738i 0.798133i
866866 3.70853 0.0852100i 0.126021 0.00289555i
867867 8.08401 + 8.08401i 0.274547 + 0.274547i
868868 16.6398 0.765061i 0.564791 0.0259679i
869869 18.4976 + 18.4976i 0.627489 + 0.627489i
870870 −17.3343 16.5556i −0.587688 0.561288i
871871 79.6564 2.69906
872872 −31.1316 27.1113i −1.05425 0.918103i
873873 −8.86669 −0.300092
874874 −2.86126 0.807057i −0.0967836 0.0272991i
875875 −28.7137 28.7137i −0.970699 0.970699i
876876 14.2520 15.6257i 0.481531 0.527944i
877877 −19.6785 + 19.6785i −0.664496 + 0.664496i −0.956437 0.291940i 0.905699π-0.905699\pi
0.291940 + 0.956437i 0.405699π0.405699\pi
878878 48.9588 1.12492i 1.65228 0.0379641i
879879 15.0866i 0.508857i
880880 −44.0283 + 4.05723i −1.48419 + 0.136769i
881881 6.88025 0.231801 0.115901 0.993261i 0.463025π-0.463025\pi
0.115901 + 0.993261i 0.463025π0.463025\pi
882882 17.3192 0.397940i 0.583168 0.0133993i
883883 32.4715 32.4715i 1.09275 1.09275i 0.0975191 0.995234i 0.468909π-0.468909\pi
0.995234 0.0975191i 0.0310907π-0.0310907\pi
884884 10.7780 11.8168i 0.362503 0.397443i
885885 0.674228 0.674228i 0.0226639 0.0226639i
886886 −4.95185 + 5.18476i −0.166361 + 0.174185i
887887 11.4832i 0.385567i −0.981241 0.192783i 0.938249π-0.938249\pi
0.981241 0.192783i 0.0617515π-0.0617515\pi
888888 9.75803 0.673573i 0.327458 0.0226036i
889889 −19.7787 −0.663357
890890 −16.1104 15.3867i −0.540022 0.515764i
891891 14.4646 + 14.4646i 0.484581 + 0.484581i
892892 3.26615 0.150171i 0.109359 0.00502809i
893893 14.9398 + 4.58697i 0.499942 + 0.153497i
894894 −0.00949310 0.413161i −0.000317497 0.0138182i
895895 8.86010 0.296161
896896 6.30487 + 38.8686i 0.210631 + 1.29851i
897897 −1.97938 −0.0660894
898898 9.86964 0.226773i 0.329354 0.00756750i
899899 17.3906 17.3906i 0.580010 0.580010i
900900 −2.39322 + 0.110035i −0.0797742 + 0.00366784i
901901 5.39182 + 5.39182i 0.179627 + 0.179627i
902902 −40.4154 + 42.3164i −1.34569 + 1.40898i
903903 11.5598i 0.384687i
904904 39.6291 2.73550i 1.31804 0.0909814i
905905 −20.8732 −0.693849
906906 −6.57037 6.27522i −0.218286 0.208480i
907907 1.11054 1.11054i 0.0368750 0.0368750i −0.688429 0.725304i 0.741699π-0.741699\pi
0.725304 + 0.688429i 0.241699π0.241699\pi
908908 −0.968323 0.883194i −0.0321349 0.0293098i
909909 −11.4682 11.4682i −0.380375 0.380375i
910910 55.1081 1.26621i 1.82682 0.0419744i
911911 4.52560 0.149940 0.0749699 0.997186i 0.476114π-0.476114\pi
0.0749699 + 0.997186i 0.476114π0.476114\pi
912912 −11.3427 + 7.42160i −0.375596 + 0.245754i
913913 −76.2686 −2.52412
914914 2.28967 0.0526093i 0.0757357 0.00174016i
915915 −4.08673 4.08673i −0.135103 0.135103i
916916 15.9417 17.4783i 0.526728 0.577498i
917917 −3.46190 + 3.46190i −0.114322 + 0.114322i
918918 −6.49829 6.20638i −0.214476 0.204841i
919919 −34.2586 −1.13009 −0.565043 0.825062i 0.691140π-0.691140\pi
−0.565043 + 0.825062i 0.691140π0.691140\pi
920920 2.18213 + 1.90033i 0.0719427 + 0.0626519i
921921 10.8858i 0.358699i
922922 −15.5648 + 16.2969i −0.512599 + 0.536709i
923923 −20.8789 20.8789i −0.687238 0.687238i
924924 1.29515 + 28.1690i 0.0426073 + 0.926692i
925925 1.57279 1.57279i 0.0517129 0.0517129i
926926 37.0643 0.851619i 1.21801 0.0279859i
927927 27.3705 0.898964
928928 45.5508 + 36.1275i 1.49528 + 1.18594i
929929 13.5486 0.444516 0.222258 0.974988i 0.428657π-0.428657\pi
0.222258 + 0.974988i 0.428657π0.428657\pi
930930 −0.128203 5.57969i −0.00420395 0.182965i
931931 6.54198 21.3073i 0.214405 0.698319i
932932 −0.828946 18.0292i −0.0271530 0.590567i
933933 −9.59066 9.59066i −0.313984 0.313984i
934934 10.7869 + 10.3023i 0.352958 + 0.337103i
935935 −16.7438 −0.547581
936936 23.4923 26.9760i 0.767870 0.881738i
937937 32.7572i 1.07013i −0.844811 0.535065i 0.820287π-0.820287\pi
0.844811 0.535065i 0.179713π-0.179713\pi
938938 −51.2942 + 53.7068i −1.67482 + 1.75359i
939939 5.02918 5.02918i 0.164121 0.164121i
940940 −11.2386 10.2506i −0.366564 0.334338i
941941 24.7542 24.7542i 0.806965 0.806965i −0.177208 0.984173i 0.556707π-0.556707\pi
0.984173 + 0.177208i 0.0567066π0.0567066\pi
942942 −17.4011 + 0.399821i −0.566957 + 0.0130269i
943943 3.82950 0.124706
944944 −1.47835 + 1.77847i −0.0481162 + 0.0578842i
945945 30.9700i 1.00745i
946946 31.4745 0.723184i 1.02333 0.0235127i
947947 27.4034 27.4034i 0.890491 0.890491i −0.104078 0.994569i 0.533189π-0.533189\pi
0.994569 + 0.104078i 0.0331893π0.0331893\pi
948948 −5.76725 5.26023i −0.187312 0.170844i
949949 50.7762 + 50.7762i 1.64827 + 1.64827i
950950 −0.836783 + 2.96665i −0.0271488 + 0.0962508i
951951 20.9973 0.680884
952952 1.02687 + 14.8762i 0.0332810 + 0.482141i
953953 −35.9912 −1.16587 −0.582935 0.812519i 0.698096π-0.698096\pi
−0.582935 + 0.812519i 0.698096π0.698096\pi
954954 12.3330 + 11.7790i 0.399296 + 0.381359i
955955 −5.87181 5.87181i −0.190007 0.190007i
956956 −0.0528404 1.14926i −0.00170898 0.0371697i
957957 29.4401 + 29.4401i 0.951663 + 0.951663i
958958 −31.1621 + 0.716006i −1.00680 + 0.0231331i
959959 36.9007i 1.19159i
960960 13.0683 1.81278i 0.421777 0.0585073i
961961 −25.2736 −0.815276
962962 0.762874 + 33.2020i 0.0245961 + 1.07047i
963963 −28.2379 28.2379i −0.909955 0.909955i
964964 0.939294 + 20.4293i 0.0302526 + 0.657983i
965965 −26.3518 26.3518i −0.848296 0.848296i
966966 1.27460 1.33456i 0.0410097 0.0429386i
967967 −20.6822 −0.665093 −0.332547 0.943087i 0.607908π-0.607908\pi
−0.332547 + 0.943087i 0.607908π0.607908\pi
968968 45.5773 3.14609i 1.46491 0.101119i
969969 −4.53518 + 2.40449i −0.145691 + 0.0772433i
970970 7.66907 8.02977i 0.246239 0.257821i
971971 5.17002 5.17002i 0.165914 0.165914i −0.619267 0.785181i 0.712570π-0.712570\pi
0.785181 + 0.619267i 0.212570π0.212570\pi
972972 −23.1051 21.0738i −0.741095 0.675943i
973973 −32.2004 32.2004i −1.03230 1.03230i
974974 −31.0714 + 0.713922i −0.995593 + 0.0228755i
975975 2.05228i 0.0657256i
976976 10.7799 + 8.96079i 0.345057 + 0.286828i
977977 25.5684i 0.818006i −0.912533 0.409003i 0.865877π-0.865877\pi
0.912533 0.409003i 0.134123π-0.134123\pi
978978 −0.189673 8.25498i −0.00606507 0.263965i
979979 27.3615 + 27.3615i 0.874476 + 0.874476i
980980 −14.6195 + 16.0287i −0.467003 + 0.512017i
981981 −24.7237 24.7237i −0.789368 0.789368i
982982 24.4810 25.6324i 0.781220 0.817964i
983983 20.9464i 0.668085i −0.942558 0.334042i 0.891587π-0.891587\pi
0.942558 0.334042i 0.108413π-0.108413\pi
984984 11.4670 13.1675i 0.365555 0.419764i
985985 48.8665i 1.55702i
986986 15.9215 + 15.2063i 0.507045 + 0.484268i
987987 −6.85980 + 6.85980i −0.218350 + 0.218350i
988988 −23.4035 39.6292i −0.744564 1.26077i
989989 −1.45690 1.45690i −0.0463267 0.0463267i
990990 −37.4389 + 0.860225i −1.18989 + 0.0273398i
991991 35.4955 1.12755 0.563776 0.825928i 0.309348π-0.309348\pi
0.563776 + 0.825928i 0.309348π0.309348\pi
992992 1.55147 + 13.4476i 0.0492594 + 0.426963i
993993 3.40371 0.108014
994994 27.5220 0.632368i 0.872946 0.0200575i
995995 32.4148 32.4148i 1.02762 1.02762i
996996 22.7340 1.04526i 0.720355 0.0331204i
997997 −33.0690 + 33.0690i −1.04731 + 1.04731i −0.0484820 + 0.998824i 0.515438π0.515438\pi
−0.998824 + 0.0484820i 0.984562π0.984562\pi
998998 −43.9031 41.9309i −1.38973 1.32730i
999999 18.6590 0.590345
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 304.2.m.a.227.20 yes 76
4.3 odd 2 1216.2.m.a.303.23 76
16.5 even 4 1216.2.m.a.911.16 76
16.11 odd 4 inner 304.2.m.a.75.19 76
19.18 odd 2 inner 304.2.m.a.227.19 yes 76
76.75 even 2 1216.2.m.a.303.16 76
304.37 odd 4 1216.2.m.a.911.23 76
304.75 even 4 inner 304.2.m.a.75.20 yes 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.m.a.75.19 76 16.11 odd 4 inner
304.2.m.a.75.20 yes 76 304.75 even 4 inner
304.2.m.a.227.19 yes 76 19.18 odd 2 inner
304.2.m.a.227.20 yes 76 1.1 even 1 trivial
1216.2.m.a.303.16 76 76.75 even 2
1216.2.m.a.303.23 76 4.3 odd 2
1216.2.m.a.911.16 76 16.5 even 4
1216.2.m.a.911.23 76 304.37 odd 4