Properties

Label 368.2.j.d.277.6
Level 368368
Weight 22
Character 368.277
Analytic conductor 2.9382.938
Analytic rank 00
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [368,2,Mod(93,368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(368, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("368.93");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 368=2423 368 = 2^{4} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 368.j (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: 2.938494794382.93849479438
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 277.6
Character χ\chi == 368.277
Dual form 368.2.j.d.93.6

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+(0.408999+1.35378i)q2+(1.35709+1.35709i)q3+(1.665441.10739i)q4+(0.9447810.944781i)q5+(1.282152.39224i)q61.03914iq7+(2.180321.80172i)q80.683369iq9+(1.665440.892612i)q10+(2.320832.32083i)q11+(3.762970.757325i)q12+(3.045663.04566i)q13+(1.40676+0.425006i)q14+2.56430q15+(1.54738+3.68858i)q16+2.64059q17+(0.925131+0.279497i)q18+(0.723364+0.723364i)q19+(0.527237+2.61972i)q20+(1.41020+1.41020i)q21+(4.091112.19268i)q22+1.00000iq23+(0.513797+5.40398i)q243.21478iq25+(2.87749+5.36883i)q26+(3.143873.14387i)q27+(1.15073+1.73062i)q28+(2.382582.38258i)q29+(1.04880+3.47150i)q30+4.88133q31+(5.62640+0.586193i)q32+6.29914q33+(1.08000+3.57478i)q34+(0.981759+0.981759i)q35+(0.756755+1.13811i)q36+(1.04169+1.04169i)q37+(0.6834211.27513i)q38+8.26646iq39+(3.762160.357697i)q402.62724iq41+(2.48587+1.33233i)q42+(2.556532.55653i)q43+(1.29514+6.43527i)q44+(0.645634+0.645634i)q45+(1.353780.408999i)q460.736160q47+(7.105652.90579i)q48+5.92019q49+(4.35210+1.31484i)q50+(3.58351+3.58351i)q51+(8.44511+1.69964i)q52+(6.955366.95536i)q53+(5.541952.97027i)q54+4.38536iq55+(1.872242.26566i)q561.96334iq57+(2.25101+4.19995i)q58+(7.673797.67379i)q59+(4.270692.83968i)q60+(6.856116.85611i)q61+(1.99646+6.60824i)q620.710115q63+(1.507617.85666i)q645.75497q65+(2.57634+8.52765i)q66+(5.257145.25714i)q67+(4.397752.92416i)q68+(1.357091.35709i)q69+(0.9275471.73062i)q70+1.12865iq71+(1.231241.48997i)q7214.8204iq73+(1.83627+0.984169i)q74+(4.36273+4.36273i)q75+(2.005760.403675i)q76+(2.41166+2.41166i)q77+(11.19103.38097i)q78+6.88664q79+(2.022964.94684i)q80+10.5831q81+(3.55671+1.07454i)q82+(7.58934+7.58934i)q83+(0.7869663.91025i)q84+(2.494782.49478i)q85+(4.506592.41536i)q86+6.46672iq87+(9.241650.878674i)q88+7.82916iq89+(0.6099831.13811i)q90+(3.164873.16487i)q91+(1.107391.66544i)q92+(6.62438+6.62438i)q93+(0.3010890.996599i)q94+1.36684q95+(6.840008.43103i)q9614.5175q97+(2.42135+8.01464i)q98+(1.58598+1.58598i)q99+O(q100)q+(-0.408999 + 1.35378i) q^{2} +(-1.35709 + 1.35709i) q^{3} +(-1.66544 - 1.10739i) q^{4} +(-0.944781 - 0.944781i) q^{5} +(-1.28215 - 2.39224i) q^{6} -1.03914i q^{7} +(2.18032 - 1.80172i) q^{8} -0.683369i q^{9} +(1.66544 - 0.892612i) q^{10} +(-2.32083 - 2.32083i) q^{11} +(3.76297 - 0.757325i) q^{12} +(3.04566 - 3.04566i) q^{13} +(1.40676 + 0.425006i) q^{14} +2.56430 q^{15} +(1.54738 + 3.68858i) q^{16} +2.64059 q^{17} +(0.925131 + 0.279497i) q^{18} +(-0.723364 + 0.723364i) q^{19} +(0.527237 + 2.61972i) q^{20} +(1.41020 + 1.41020i) q^{21} +(4.09111 - 2.19268i) q^{22} +1.00000i q^{23} +(-0.513797 + 5.40398i) q^{24} -3.21478i q^{25} +(2.87749 + 5.36883i) q^{26} +(-3.14387 - 3.14387i) q^{27} +(-1.15073 + 1.73062i) q^{28} +(2.38258 - 2.38258i) q^{29} +(-1.04880 + 3.47150i) q^{30} +4.88133 q^{31} +(-5.62640 + 0.586193i) q^{32} +6.29914 q^{33} +(-1.08000 + 3.57478i) q^{34} +(-0.981759 + 0.981759i) q^{35} +(-0.756755 + 1.13811i) q^{36} +(1.04169 + 1.04169i) q^{37} +(-0.683421 - 1.27513i) q^{38} +8.26646i q^{39} +(-3.76216 - 0.357697i) q^{40} -2.62724i q^{41} +(-2.48587 + 1.33233i) q^{42} +(-2.55653 - 2.55653i) q^{43} +(1.29514 + 6.43527i) q^{44} +(-0.645634 + 0.645634i) q^{45} +(-1.35378 - 0.408999i) q^{46} -0.736160 q^{47} +(-7.10565 - 2.90579i) q^{48} +5.92019 q^{49} +(4.35210 + 1.31484i) q^{50} +(-3.58351 + 3.58351i) q^{51} +(-8.44511 + 1.69964i) q^{52} +(-6.95536 - 6.95536i) q^{53} +(5.54195 - 2.97027i) q^{54} +4.38536i q^{55} +(-1.87224 - 2.26566i) q^{56} -1.96334i q^{57} +(2.25101 + 4.19995i) q^{58} +(-7.67379 - 7.67379i) q^{59} +(-4.27069 - 2.83968i) q^{60} +(6.85611 - 6.85611i) q^{61} +(-1.99646 + 6.60824i) q^{62} -0.710115 q^{63} +(1.50761 - 7.85666i) q^{64} -5.75497 q^{65} +(-2.57634 + 8.52765i) q^{66} +(5.25714 - 5.25714i) q^{67} +(-4.39775 - 2.92416i) q^{68} +(-1.35709 - 1.35709i) q^{69} +(-0.927547 - 1.73062i) q^{70} +1.12865i q^{71} +(-1.23124 - 1.48997i) q^{72} -14.8204i q^{73} +(-1.83627 + 0.984169i) q^{74} +(4.36273 + 4.36273i) q^{75} +(2.00576 - 0.403675i) q^{76} +(-2.41166 + 2.41166i) q^{77} +(-11.1910 - 3.38097i) q^{78} +6.88664 q^{79} +(2.02296 - 4.94684i) q^{80} +10.5831 q^{81} +(3.55671 + 1.07454i) q^{82} +(-7.58934 + 7.58934i) q^{83} +(-0.786966 - 3.91025i) q^{84} +(-2.49478 - 2.49478i) q^{85} +(4.50659 - 2.41536i) q^{86} +6.46672i q^{87} +(-9.24165 - 0.878674i) q^{88} +7.82916i q^{89} +(-0.609983 - 1.13811i) q^{90} +(-3.16487 - 3.16487i) q^{91} +(1.10739 - 1.66544i) q^{92} +(-6.62438 + 6.62438i) q^{93} +(0.301089 - 0.996599i) q^{94} +1.36684 q^{95} +(6.84000 - 8.43103i) q^{96} -14.5175 q^{97} +(-2.42135 + 8.01464i) q^{98} +(-1.58598 + 1.58598i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q4q24q3+4q5+2q84q11+38q1212q136q14+40q178q18+8q192q20+34q2210q242q2628q27+10q2816q29++4q99+O(q100) 24 q - 4 q^{2} - 4 q^{3} + 4 q^{5} + 2 q^{8} - 4 q^{11} + 38 q^{12} - 12 q^{13} - 6 q^{14} + 40 q^{17} - 8 q^{18} + 8 q^{19} - 2 q^{20} + 34 q^{22} - 10 q^{24} - 2 q^{26} - 28 q^{27} + 10 q^{28} - 16 q^{29}+ \cdots + 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/368Z)×\left(\mathbb{Z}/368\mathbb{Z}\right)^\times.

nn 4747 9797 277277
χ(n)\chi(n) 11 11 e(14)e\left(\frac{1}{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 −0.408999 + 1.35378i −0.289206 + 0.957267i
33 −1.35709 + 1.35709i −0.783514 + 0.783514i −0.980422 0.196908i 0.936910π-0.936910\pi
0.196908 + 0.980422i 0.436910π0.436910\pi
44 −1.66544 1.10739i −0.832720 0.553694i
55 −0.944781 0.944781i −0.422519 0.422519i 0.463551 0.886070i 0.346575π-0.346575\pi
−0.886070 + 0.463551i 0.846575π0.846575\pi
66 −1.28215 2.39224i −0.523436 0.976629i
77 1.03914i 0.392757i −0.980528 0.196379i 0.937082π-0.937082\pi
0.980528 0.196379i 0.0629182π-0.0629182\pi
88 2.18032 1.80172i 0.770860 0.637004i
99 0.683369i 0.227790i
1010 1.66544 0.892612i 0.526658 0.282269i
1111 −2.32083 2.32083i −0.699757 0.699757i 0.264601 0.964358i 0.414760π-0.414760\pi
−0.964358 + 0.264601i 0.914760π0.914760\pi
1212 3.76297 0.757325i 1.08628 0.218621i
1313 3.04566 3.04566i 0.844715 0.844715i −0.144753 0.989468i 0.546239π-0.546239\pi
0.989468 + 0.144753i 0.0462386π0.0462386\pi
1414 1.40676 + 0.425006i 0.375974 + 0.113588i
1515 2.56430 0.662100
1616 1.54738 + 3.68858i 0.386846 + 0.922144i
1717 2.64059 0.640438 0.320219 0.947344i 0.396244π-0.396244\pi
0.320219 + 0.947344i 0.396244π0.396244\pi
1818 0.925131 + 0.279497i 0.218056 + 0.0658781i
1919 −0.723364 + 0.723364i −0.165951 + 0.165951i −0.785197 0.619246i 0.787438π-0.787438\pi
0.619246 + 0.785197i 0.287438π0.287438\pi
2020 0.527237 + 2.61972i 0.117894 + 0.585786i
2121 1.41020 + 1.41020i 0.307731 + 0.307731i
2222 4.09111 2.19268i 0.872228 0.467480i
2323 1.00000i 0.208514i
2424 −0.513797 + 5.40398i −0.104878 + 1.10308i
2525 3.21478i 0.642955i
2626 2.87749 + 5.36883i 0.564322 + 1.05291i
2727 −3.14387 3.14387i −0.605038 0.605038i
2828 −1.15073 + 1.73062i −0.217467 + 0.327057i
2929 2.38258 2.38258i 0.442433 0.442433i −0.450396 0.892829i 0.648717π-0.648717\pi
0.892829 + 0.450396i 0.148717π0.148717\pi
3030 −1.04880 + 3.47150i −0.191483 + 0.633806i
3131 4.88133 0.876712 0.438356 0.898801i 0.355561π-0.355561\pi
0.438356 + 0.898801i 0.355561π0.355561\pi
3232 −5.62640 + 0.586193i −0.994616 + 0.103625i
3333 6.29914 1.09654
3434 −1.08000 + 3.57478i −0.185218 + 0.613070i
3535 −0.981759 + 0.981759i −0.165947 + 0.165947i
3636 −0.756755 + 1.13811i −0.126126 + 0.189685i
3737 1.04169 + 1.04169i 0.171253 + 0.171253i 0.787530 0.616277i 0.211360π-0.211360\pi
−0.616277 + 0.787530i 0.711360π0.711360\pi
3838 −0.683421 1.27513i −0.110865 0.206853i
3939 8.26646i 1.32369i
4040 −3.76216 0.357697i −0.594850 0.0565569i
4141 2.62724i 0.410306i −0.978730 0.205153i 0.934231π-0.934231\pi
0.978730 0.205153i 0.0657693π-0.0657693\pi
4242 −2.48587 + 1.33233i −0.383578 + 0.205583i
4343 −2.55653 2.55653i −0.389867 0.389867i 0.484773 0.874640i 0.338902π-0.338902\pi
−0.874640 + 0.484773i 0.838902π0.838902\pi
4444 1.29514 + 6.43527i 0.195250 + 0.970153i
4545 −0.645634 + 0.645634i −0.0962455 + 0.0962455i
4646 −1.35378 0.408999i −0.199604 0.0603036i
4747 −0.736160 −0.107380 −0.0536900 0.998558i 0.517098π-0.517098\pi
−0.0536900 + 0.998558i 0.517098π0.517098\pi
4848 −7.10565 2.90579i −1.02561 0.419414i
4949 5.92019 0.845742
5050 4.35210 + 1.31484i 0.615480 + 0.185946i
5151 −3.58351 + 3.58351i −0.501792 + 0.501792i
5252 −8.44511 + 1.69964i −1.17113 + 0.235698i
5353 −6.95536 6.95536i −0.955392 0.955392i 0.0436542 0.999047i 0.486100π-0.486100\pi
−0.999047 + 0.0436542i 0.986100π0.986100\pi
5454 5.54195 2.97027i 0.754163 0.404202i
5555 4.38536i 0.591321i
5656 −1.87224 2.26566i −0.250188 0.302761i
5757 1.96334i 0.260050i
5858 2.25101 + 4.19995i 0.295572 + 0.551481i
5959 −7.67379 7.67379i −0.999043 0.999043i 0.000956675 1.00000i 0.499695π-0.499695\pi
−1.00000 0.000956675i 0.999695π0.999695\pi
6060 −4.27069 2.83968i −0.551344 0.366601i
6161 6.85611 6.85611i 0.877834 0.877834i −0.115476 0.993310i 0.536839π-0.536839\pi
0.993310 + 0.115476i 0.0368393π0.0368393\pi
6262 −1.99646 + 6.60824i −0.253550 + 0.839248i
6363 −0.710115 −0.0894661
6464 1.50761 7.85666i 0.188452 0.982082i
6565 −5.75497 −0.713817
6666 −2.57634 + 8.52765i −0.317125 + 1.04968i
6767 5.25714 5.25714i 0.642261 0.642261i −0.308850 0.951111i 0.599944π-0.599944\pi
0.951111 + 0.308850i 0.0999439π0.0999439\pi
6868 −4.39775 2.92416i −0.533305 0.354607i
6969 −1.35709 1.35709i −0.163374 0.163374i
7070 −0.927547 1.73062i −0.110863 0.206849i
7171 1.12865i 0.133946i 0.997755 + 0.0669728i 0.0213341π0.0213341\pi
−0.997755 + 0.0669728i 0.978666π0.978666\pi
7272 −1.23124 1.48997i −0.145103 0.175594i
7373 14.8204i 1.73459i −0.497791 0.867297i 0.665855π-0.665855\pi
0.497791 0.867297i 0.334145π-0.334145\pi
7474 −1.83627 + 0.984169i −0.213462 + 0.114407i
7575 4.36273 + 4.36273i 0.503765 + 0.503765i
7676 2.00576 0.403675i 0.230077 0.0463047i
7777 −2.41166 + 2.41166i −0.274835 + 0.274835i
7878 −11.1910 3.38097i −1.26713 0.382820i
7979 6.88664 0.774807 0.387403 0.921910i 0.373372π-0.373372\pi
0.387403 + 0.921910i 0.373372π0.373372\pi
8080 2.02296 4.94684i 0.226174 0.553073i
8181 10.5831 1.17590
8282 3.55671 + 1.07454i 0.392773 + 0.118663i
8383 −7.58934 + 7.58934i −0.833039 + 0.833039i −0.987931 0.154893i 0.950497π-0.950497\pi
0.154893 + 0.987931i 0.450497π0.450497\pi
8484 −0.786966 3.91025i −0.0858650 0.426643i
8585 −2.49478 2.49478i −0.270597 0.270597i
8686 4.50659 2.41536i 0.485958 0.260455i
8787 6.46672i 0.693306i
8888 −9.24165 0.878674i −0.985163 0.0936669i
8989 7.82916i 0.829889i 0.909847 + 0.414944i 0.136199π0.136199\pi
−0.909847 + 0.414944i 0.863801π0.863801\pi
9090 −0.609983 1.13811i −0.0642979 0.119967i
9191 −3.16487 3.16487i −0.331768 0.331768i
9292 1.10739 1.66544i 0.115453 0.173634i
9393 −6.62438 + 6.62438i −0.686917 + 0.686917i
9494 0.301089 0.996599i 0.0310549 0.102791i
9595 1.36684 0.140235
9696 6.84000 8.43103i 0.698104 0.860488i
9797 −14.5175 −1.47403 −0.737013 0.675878i 0.763765π-0.763765\pi
−0.737013 + 0.675878i 0.763765π0.763765\pi
9898 −2.42135 + 8.01464i −0.244593 + 0.809601i
9999 −1.58598 + 1.58598i −0.159397 + 0.159397i
100100 −3.56001 + 5.35402i −0.356001 + 0.535402i
101101 −2.65938 2.65938i −0.264619 0.264619i 0.562309 0.826927i 0.309913π-0.309913\pi
−0.826927 + 0.562309i 0.809913π0.809913\pi
102102 −3.38564 6.31694i −0.335228 0.625470i
103103 5.78991i 0.570497i 0.958454 + 0.285248i 0.0920761π0.0920761\pi
−0.958454 + 0.285248i 0.907924π0.907924\pi
104104 1.15310 12.1280i 0.113071 1.18924i
105105 2.66466i 0.260044i
106106 12.2608 6.57130i 1.19087 0.638261i
107107 −2.22067 2.22067i −0.214680 0.214680i 0.591572 0.806252i 0.298508π-0.298508\pi
−0.806252 + 0.591572i 0.798508π0.798508\pi
108108 1.75444 + 8.71741i 0.168821 + 0.838833i
109109 −9.38645 + 9.38645i −0.899059 + 0.899059i −0.995353 0.0962942i 0.969301π-0.969301\pi
0.0962942 + 0.995353i 0.469301π0.469301\pi
110110 −5.93681 1.79360i −0.566052 0.171013i
111111 −2.82733 −0.268358
112112 3.83294 1.60794i 0.362179 0.151937i
113113 1.89466 0.178234 0.0891172 0.996021i 0.471595π-0.471595\pi
0.0891172 + 0.996021i 0.471595π0.471595\pi
114114 2.65792 + 0.803001i 0.248937 + 0.0752080i
115115 0.944781 0.944781i 0.0881013 0.0881013i
116116 −6.60647 + 1.32960i −0.613396 + 0.123450i
117117 −2.08131 2.08131i −0.192417 0.192417i
118118 13.5272 7.25006i 1.24528 0.667422i
119119 2.74394i 0.251537i
120120 5.59100 4.62015i 0.510386 0.421760i
121121 0.227490i 0.0206809i
122122 6.47752 + 12.0858i 0.586447 + 1.09420i
123123 3.56540 + 3.56540i 0.321481 + 0.321481i
124124 −8.12956 5.40552i −0.730056 0.485430i
125125 −7.76117 + 7.76117i −0.694180 + 0.694180i
126126 0.290436 0.961340i 0.0258741 0.0856429i
127127 1.62302 0.144019 0.0720096 0.997404i 0.477059π-0.477059\pi
0.0720096 + 0.997404i 0.477059π0.477059\pi
128128 10.0196 + 5.25434i 0.885614 + 0.464422i
129129 6.93886 0.610933
130130 2.35378 7.79097i 0.206440 0.683313i
131131 0.00207687 0.00207687i 0.000181457 0.000181457i −0.707016 0.707198i 0.749959π-0.749959\pi
0.707198 + 0.707016i 0.249959π0.249959\pi
132132 −10.4908 6.97559i −0.913110 0.607147i
133133 0.751675 + 0.751675i 0.0651785 + 0.0651785i
134134 4.96684 + 9.26717i 0.429070 + 0.800561i
135135 5.94054i 0.511280i
136136 5.75734 4.75761i 0.493688 0.407961i
137137 9.54941i 0.815861i 0.913013 + 0.407931i 0.133749π0.133749\pi
−0.913013 + 0.407931i 0.866251π0.866251\pi
138138 2.39224 1.28215i 0.203641 0.109144i
139139 9.01775 + 9.01775i 0.764876 + 0.764876i 0.977199 0.212324i 0.0681031π-0.0681031\pi
−0.212324 + 0.977199i 0.568103π0.568103\pi
140140 2.72225 0.547872i 0.230072 0.0463037i
141141 0.999033 0.999033i 0.0841338 0.0841338i
142142 −1.52794 0.461615i −0.128222 0.0387378i
143143 −14.1369 −1.18219
144144 2.52066 1.05743i 0.210055 0.0881195i
145145 −4.50203 −0.373873
146146 20.0635 + 6.06151i 1.66047 + 0.501654i
147147 −8.03421 + 8.03421i −0.662651 + 0.662651i
148148 −0.581317 2.88843i −0.0477840 0.237427i
149149 11.5838 + 11.5838i 0.948985 + 0.948985i 0.998760 0.0497750i 0.0158504π-0.0158504\pi
−0.0497750 + 0.998760i 0.515850π0.515850\pi
150150 −7.69053 + 4.12183i −0.627929 + 0.336546i
151151 22.2288i 1.80895i −0.426522 0.904477i 0.640261π-0.640261\pi
0.426522 0.904477i 0.359739π-0.359739\pi
152152 −0.273868 + 2.88047i −0.0222136 + 0.233637i
153153 1.80450i 0.145885i
154154 −2.27850 4.25123i −0.183606 0.342574i
155155 −4.61179 4.61179i −0.370428 0.370428i
156156 9.15418 13.7673i 0.732921 1.10227i
157157 −11.9676 + 11.9676i −0.955119 + 0.955119i −0.999035 0.0439160i 0.986017π-0.986017\pi
0.0439160 + 0.999035i 0.486017π0.486017\pi
158158 −2.81662 + 9.32299i −0.224079 + 0.741697i
159159 18.8781 1.49713
160160 5.86954 + 4.76189i 0.464028 + 0.376461i
161161 1.03914 0.0818956
162162 −4.32848 + 14.3272i −0.340077 + 1.12565i
163163 6.67263 6.67263i 0.522641 0.522641i −0.395727 0.918368i 0.629507π-0.629507\pi
0.918368 + 0.395727i 0.129507π0.129507\pi
164164 −2.90938 + 4.37552i −0.227184 + 0.341670i
165165 −5.95131 5.95131i −0.463309 0.463309i
166166 −7.17027 13.3783i −0.556521 1.03836i
167167 16.4261i 1.27109i 0.772062 + 0.635547i 0.219225π0.219225\pi
−0.772062 + 0.635547i 0.780775π0.780775\pi
168168 5.61548 + 0.533907i 0.433244 + 0.0411918i
169169 5.55215i 0.427088i
170170 4.39775 2.35702i 0.337292 0.180775i
171171 0.494325 + 0.494325i 0.0378019 + 0.0378019i
172172 1.42668 + 7.08881i 0.108783 + 0.540517i
173173 0.408306 0.408306i 0.0310429 0.0310429i −0.691415 0.722458i 0.743012π-0.743012\pi
0.722458 + 0.691415i 0.243012π0.243012\pi
174174 −8.75452 2.64488i −0.663679 0.200508i
175175 −3.34060 −0.252525
176176 4.96935 12.1518i 0.374579 0.915975i
177177 20.8280 1.56553
178178 −10.5990 3.20211i −0.794425 0.240009i
179179 0.793254 0.793254i 0.0592906 0.0592906i −0.676840 0.736130i 0.736651π-0.736651\pi
0.736130 + 0.676840i 0.236651π0.236651\pi
180180 1.79023 0.360298i 0.133436 0.0268550i
181181 4.26161 + 4.26161i 0.316763 + 0.316763i 0.847522 0.530760i 0.178093π-0.178093\pi
−0.530760 + 0.847522i 0.678093π0.678093\pi
182182 5.57896 2.99011i 0.413540 0.221641i
183183 18.6087i 1.37559i
184184 1.80172 + 2.18032i 0.132825 + 0.160736i
185185 1.96834i 0.144715i
186186 −6.25859 11.6773i −0.458902 0.856223i
187187 −6.12837 6.12837i −0.448151 0.448151i
188188 1.22603 + 0.815215i 0.0894175 + 0.0594557i
189189 −3.26691 + 3.26691i −0.237633 + 0.237633i
190190 −0.559036 + 1.85040i −0.0405568 + 0.134242i
191191 −17.9897 −1.30169 −0.650846 0.759210i 0.725586π-0.725586\pi
−0.650846 + 0.759210i 0.725586π0.725586\pi
192192 8.61621 + 12.7081i 0.621821 + 0.917130i
193193 6.61497 0.476156 0.238078 0.971246i 0.423483π-0.423483\pi
0.238078 + 0.971246i 0.423483π0.423483\pi
194194 5.93763 19.6535i 0.426297 1.41104i
195195 7.81000 7.81000i 0.559286 0.559286i
196196 −9.85973 6.55595i −0.704266 0.468282i
197197 10.7577 + 10.7577i 0.766455 + 0.766455i 0.977480 0.211026i 0.0676804π-0.0676804\pi
−0.211026 + 0.977480i 0.567680π0.567680\pi
198198 −1.49841 2.79574i −0.106487 0.198685i
199199 9.31387i 0.660242i 0.943939 + 0.330121i 0.107090π0.107090\pi
−0.943939 + 0.330121i 0.892910π0.892910\pi
200200 −5.79213 7.00925i −0.409565 0.495629i
201201 14.2688i 1.00644i
202202 4.68791 2.51254i 0.329840 0.176781i
203203 −2.47583 2.47583i −0.173769 0.173769i
204204 9.93647 1.99979i 0.695692 0.140013i
205205 −2.48217 + 2.48217i −0.173362 + 0.173362i
206206 −7.83826 2.36806i −0.546118 0.164991i
207207 0.683369 0.0474974
208208 15.9470 + 6.52136i 1.10572 + 0.452175i
209209 3.35761 0.232251
210210 3.60737 + 1.08984i 0.248932 + 0.0752063i
211211 18.8579 18.8579i 1.29823 1.29823i 0.368669 0.929561i 0.379814π-0.379814\pi
0.929561 0.368669i 0.120186π-0.120186\pi
212212 3.88145 + 19.2860i 0.266579 + 1.32457i
213213 −1.53167 1.53167i −0.104948 0.104948i
214214 3.91455 2.09805i 0.267593 0.143420i
215215 4.83072i 0.329452i
216216 −12.5190 1.19028i −0.851811 0.0809882i
217217 5.07237i 0.344335i
218218 −8.86814 16.5462i −0.600626 1.12065i
219219 20.1125 + 20.1125i 1.35908 + 1.35908i
220220 4.85629 7.30355i 0.327411 0.492405i
221221 8.04236 8.04236i 0.540988 0.540988i
222222 1.15637 3.82758i 0.0776107 0.256890i
223223 −13.8120 −0.924923 −0.462461 0.886639i 0.653034π-0.653034\pi
−0.462461 + 0.886639i 0.653034π0.653034\pi
224224 0.609135 + 5.84661i 0.0406996 + 0.390643i
225225 −2.19688 −0.146459
226226 −0.774913 + 2.56495i −0.0515464 + 0.170618i
227227 1.69489 1.69489i 0.112494 0.112494i −0.648619 0.761113i 0.724653π-0.724653\pi
0.761113 + 0.648619i 0.224653π0.224653\pi
228228 −2.17417 + 3.26982i −0.143988 + 0.216549i
229229 12.9935 + 12.9935i 0.858636 + 0.858636i 0.991177 0.132542i 0.0423138π-0.0423138\pi
−0.132542 + 0.991177i 0.542314π0.542314\pi
230230 0.892612 + 1.66544i 0.0588571 + 0.109816i
231231 6.54568i 0.430674i
232232 0.902051 9.48752i 0.0592225 0.622886i
233233 20.6606i 1.35352i −0.736202 0.676762i 0.763383π-0.763383\pi
0.736202 0.676762i 0.236617π-0.236617\pi
234234 3.66889 1.96639i 0.239843 0.128547i
235235 0.695511 + 0.695511i 0.0453701 + 0.0453701i
236236 4.28238 + 21.2781i 0.278759 + 1.38509i
237237 −9.34576 + 9.34576i −0.607072 + 0.607072i
238238 3.71469 + 1.12227i 0.240788 + 0.0727458i
239239 23.3888 1.51290 0.756448 0.654054i 0.226933π-0.226933\pi
0.756448 + 0.654054i 0.226933π0.226933\pi
240240 3.96795 + 9.45862i 0.256130 + 0.610551i
241241 3.48282 0.224348 0.112174 0.993689i 0.464219π-0.464219\pi
0.112174 + 0.993689i 0.464219π0.464219\pi
242242 0.307972 + 0.0930431i 0.0197972 + 0.00598104i
243243 −4.93060 + 4.93060i −0.316298 + 0.316298i
244244 −19.0108 + 3.82606i −1.21704 + 0.244939i
245245 −5.59329 5.59329i −0.357342 0.357342i
246246 −6.28501 + 3.36852i −0.400717 + 0.214769i
247247 4.40625i 0.280363i
248248 10.6429 8.79478i 0.675823 0.558469i
249249 20.5988i 1.30540i
250250 −7.33261 13.6812i −0.463755 0.865276i
251251 −20.7487 20.7487i −1.30964 1.30964i −0.921670 0.387974i 0.873175π-0.873175\pi
−0.387974 0.921670i 0.626825π-0.626825\pi
252252 1.18265 + 0.786373i 0.0745002 + 0.0495368i
253253 2.32083 2.32083i 0.145909 0.145909i
254254 −0.663811 + 2.19721i −0.0416512 + 0.137865i
255255 6.77127 0.424034
256256 −11.2112 + 11.4153i −0.700701 + 0.713455i
257257 −2.99626 −0.186901 −0.0934507 0.995624i 0.529790π-0.529790\pi
−0.0934507 + 0.995624i 0.529790π0.529790\pi
258258 −2.83798 + 9.39369i −0.176685 + 0.584826i
259259 1.08246 1.08246i 0.0672608 0.0672608i
260260 9.58457 + 6.37299i 0.594410 + 0.395236i
261261 −1.62818 1.62818i −0.100782 0.100782i
262262 0.00196218 + 0.00366105i 0.000121224 + 0.000226181i
263263 12.6198i 0.778170i −0.921202 0.389085i 0.872791π-0.872791\pi
0.921202 0.389085i 0.127209π-0.127209\pi
264264 13.7342 11.3493i 0.845279 0.698500i
265265 13.1426i 0.807343i
266266 −1.32504 + 0.710169i −0.0812432 + 0.0435432i
267267 −10.6248 10.6248i −0.650230 0.650230i
268268 −14.5771 + 2.93376i −0.890440 + 0.179208i
269269 −7.66183 + 7.66183i −0.467150 + 0.467150i −0.900990 0.433840i 0.857158π-0.857158\pi
0.433840 + 0.900990i 0.357158π0.357158\pi
270270 −8.04218 2.42967i −0.489432 0.147865i
271271 14.6836 0.891965 0.445982 0.895042i 0.352854π-0.352854\pi
0.445982 + 0.895042i 0.352854π0.352854\pi
272272 4.08601 + 9.74003i 0.247751 + 0.590576i
273273 8.59000 0.519890
274274 −12.9278 3.90570i −0.780997 0.235952i
275275 −7.46095 + 7.46095i −0.449912 + 0.449912i
276276 0.757325 + 3.76297i 0.0455856 + 0.226504i
277277 −1.64422 1.64422i −0.0987914 0.0987914i 0.655984 0.754775i 0.272254π-0.272254\pi
−0.754775 + 0.655984i 0.772254π0.772254\pi
278278 −15.8963 + 8.51980i −0.953397 + 0.510984i
279279 3.33575i 0.199706i
280280 −0.371697 + 3.90940i −0.0222131 + 0.233632i
281281 0.247492i 0.0147641i 0.999973 + 0.00738207i 0.00234981π0.00234981\pi
−0.999973 + 0.00738207i 0.997650π0.997650\pi
282282 0.943868 + 1.76107i 0.0562065 + 0.104870i
283283 −17.4833 17.4833i −1.03927 1.03927i −0.999197 0.0400784i 0.987239π-0.987239\pi
−0.0400784 0.999197i 0.512761π-0.512761\pi
284284 1.24985 1.87969i 0.0741649 0.111539i
285285 −1.85492 + 1.85492i −0.109876 + 0.109876i
286286 5.78199 19.1383i 0.341896 1.13167i
287287 −2.73007 −0.161151
288288 0.400586 + 3.84491i 0.0236048 + 0.226563i
289289 −10.0273 −0.589840
290290 1.84132 6.09475i 0.108126 0.357896i
291291 19.7015 19.7015i 1.15492 1.15492i
292292 −16.4119 + 24.6825i −0.960435 + 1.44443i
293293 22.8784 + 22.8784i 1.33657 + 1.33657i 0.899358 + 0.437214i 0.144035π0.144035\pi
0.437214 + 0.899358i 0.355965π0.355965\pi
294294 −7.59058 14.1625i −0.442691 0.825976i
295295 14.5001i 0.844229i
296296 4.14805 + 0.394387i 0.241101 + 0.0229233i
297297 14.5928i 0.846759i
298298 −20.4198 + 10.9442i −1.18288 + 0.633980i
299299 3.04566 + 3.04566i 0.176135 + 0.176135i
300300 −2.43463 12.0971i −0.140563 0.698427i
301301 −2.65659 + 2.65659i −0.153123 + 0.153123i
302302 30.0929 + 9.09155i 1.73165 + 0.523160i
303303 7.21803 0.414665
304304 −3.78751 1.54886i −0.217228 0.0888334i
305305 −12.9550 −0.741804
306306 2.44290 + 0.738038i 0.139651 + 0.0421908i
307307 −13.2707 + 13.2707i −0.757399 + 0.757399i −0.975848 0.218449i 0.929900π-0.929900\pi
0.218449 + 0.975848i 0.429900π0.429900\pi
308308 6.68713 1.34583i 0.381035 0.0766860i
309309 −7.85741 7.85741i −0.446992 0.446992i
310310 8.12956 4.35713i 0.461728 0.247468i
311311 25.7509i 1.46020i −0.683339 0.730101i 0.739473π-0.739473\pi
0.683339 0.730101i 0.260527π-0.260527\pi
312312 14.8938 + 18.0236i 0.843198 + 1.02038i
313313 23.6082i 1.33441i −0.744873 0.667206i 0.767490π-0.767490\pi
0.744873 0.667206i 0.232510π-0.232510\pi
314314 −11.3068 21.0962i −0.638078 1.19053i
315315 0.670904 + 0.670904i 0.0378011 + 0.0378011i
316316 −11.4693 7.62618i −0.645197 0.429006i
317317 0.887639 0.887639i 0.0498548 0.0498548i −0.681740 0.731595i 0.738776π-0.738776\pi
0.731595 + 0.681740i 0.238776π0.238776\pi
318318 −7.72110 + 25.5567i −0.432978 + 1.43315i
319319 −11.0591 −0.619191
320320 −8.84719 + 5.99846i −0.494573 + 0.335324i
321321 6.02729 0.336410
322322 −0.425006 + 1.40676i −0.0236847 + 0.0783959i
323323 −1.91011 + 1.91011i −0.106281 + 0.106281i
324324 −17.6255 11.7196i −0.979197 0.651090i
325325 −9.79113 9.79113i −0.543114 0.543114i
326326 6.30418 + 11.7624i 0.349156 + 0.651458i
327327 25.4765i 1.40885i
328328 −4.73356 5.72824i −0.261367 0.316289i
329329 0.764972i 0.0421743i
330330 10.4908 5.62268i 0.577502 0.309519i
331331 22.2908 + 22.2908i 1.22521 + 1.22521i 0.965755 + 0.259456i 0.0835433π0.0835433\pi
0.259456 + 0.965755i 0.416457π0.416457\pi
332332 21.0439 4.23525i 1.15494 0.232439i
333333 0.711859 0.711859i 0.0390096 0.0390096i
334334 −22.2374 6.71827i −1.21678 0.367607i
335335 −9.93369 −0.542735
336336 −3.01952 + 7.38376i −0.164728 + 0.402817i
337337 −15.3503 −0.836183 −0.418091 0.908405i 0.637301π-0.637301\pi
−0.418091 + 0.908405i 0.637301π0.637301\pi
338338 7.51638 + 2.27082i 0.408837 + 0.123516i
339339 −2.57122 + 2.57122i −0.139649 + 0.139649i
340340 1.39222 + 6.91760i 0.0755037 + 0.375160i
341341 −11.3287 11.3287i −0.613485 0.613485i
342342 −0.871385 + 0.467029i −0.0471191 + 0.0252540i
343343 13.4259i 0.724929i
344344 −10.1802 0.967910i −0.548880 0.0521862i
345345 2.56430i 0.138057i
346346 0.385760 + 0.719753i 0.0207386 + 0.0386942i
347347 −8.55518 8.55518i −0.459266 0.459266i 0.439148 0.898415i 0.355280π-0.355280\pi
−0.898415 + 0.439148i 0.855280π0.855280\pi
348348 7.16117 10.7699i 0.383879 0.577330i
349349 6.27907 6.27907i 0.336111 0.336111i −0.518791 0.854901i 0.673618π-0.673618\pi
0.854901 + 0.518791i 0.173618π0.173618\pi
350350 1.36630 4.52243i 0.0730318 0.241734i
351351 −19.1503 −1.02217
352352 14.4184 + 11.6975i 0.768502 + 0.623477i
353353 −30.2465 −1.60986 −0.804930 0.593370i 0.797797π-0.797797\pi
−0.804930 + 0.593370i 0.797797π0.797797\pi
354354 −8.51863 + 28.1965i −0.452760 + 1.49863i
355355 1.06632 1.06632i 0.0565946 0.0565946i
356356 8.66991 13.0390i 0.459505 0.691065i
357357 3.72377 + 3.72377i 0.197083 + 0.197083i
358358 0.749452 + 1.39833i 0.0396098 + 0.0739041i
359359 6.80471i 0.359139i −0.983745 0.179569i 0.942530π-0.942530\pi
0.983745 0.179569i 0.0574704π-0.0574704\pi
360360 −0.244439 + 2.57094i −0.0128831 + 0.135501i
361361 17.9535i 0.944920i
362362 −7.51227 + 4.02629i −0.394836 + 0.211617i
363363 0.308724 + 0.308724i 0.0162038 + 0.0162038i
364364 1.76616 + 8.77563i 0.0925720 + 0.459968i
365365 −14.0020 + 14.0020i −0.732899 + 0.732899i
366366 −25.1920 7.61092i −1.31681 0.397829i
367367 17.0408 0.889523 0.444761 0.895649i 0.353288π-0.353288\pi
0.444761 + 0.895649i 0.353288π0.353288\pi
368368 −3.68858 + 1.54738i −0.192280 + 0.0806629i
369369 −1.79538 −0.0934636
370370 2.66470 + 0.805048i 0.138531 + 0.0418524i
371371 −7.22758 + 7.22758i −0.375237 + 0.375237i
372372 18.3683 3.69675i 0.952351 0.191668i
373373 −9.22733 9.22733i −0.477773 0.477773i 0.426646 0.904419i 0.359695π-0.359695\pi
−0.904419 + 0.426646i 0.859695π0.859695\pi
374374 10.8030 5.78997i 0.558607 0.299392i
375375 21.0652i 1.08780i
376376 −1.60507 + 1.32635i −0.0827750 + 0.0684015i
377377 14.5131i 0.747460i
378378 −3.08652 5.75885i −0.158753 0.296203i
379379 22.6596 + 22.6596i 1.16395 + 1.16395i 0.983604 + 0.180342i 0.0577205π0.0577205\pi
0.180342 + 0.983604i 0.442280π0.442280\pi
380380 −2.27639 1.51362i −0.116776 0.0776473i
381381 −2.20257 + 2.20257i −0.112841 + 0.112841i
382382 7.35777 24.3541i 0.376457 1.24607i
383383 −12.2027 −0.623531 −0.311766 0.950159i 0.600920π-0.600920\pi
−0.311766 + 0.950159i 0.600920π0.600920\pi
384384 −20.7280 + 6.46684i −1.05777 + 0.330010i
385385 4.55699 0.232246
386386 −2.70552 + 8.95522i −0.137707 + 0.455809i
387387 −1.74705 + 1.74705i −0.0888077 + 0.0888077i
388388 24.1780 + 16.0765i 1.22745 + 0.816160i
389389 13.4433 + 13.4433i 0.681601 + 0.681601i 0.960361 0.278760i 0.0899234π-0.0899234\pi
−0.278760 + 0.960361i 0.589923π0.589923\pi
390390 7.37874 + 13.7673i 0.373637 + 0.697134i
391391 2.64059i 0.133540i
392392 12.9079 10.6665i 0.651949 0.538741i
393393 0.00563697i 0.000284348i
394394 −18.9634 + 10.1637i −0.955365 + 0.512039i
395395 −6.50636 6.50636i −0.327371 0.327371i
396396 4.39766 0.885062i 0.220991 0.0444760i
397397 5.80463 5.80463i 0.291326 0.291326i −0.546278 0.837604i 0.683956π-0.683956\pi
0.837604 + 0.546278i 0.183956π0.183956\pi
398398 −12.6089 3.80936i −0.632028 0.190946i
399399 −2.04018 −0.102137
400400 11.8580 4.97449i 0.592898 0.248724i
401401 29.9626 1.49626 0.748132 0.663550i 0.230951π-0.230951\pi
0.748132 + 0.663550i 0.230951π0.230951\pi
402402 −19.3168 5.83591i −0.963434 0.291069i
403403 14.8669 14.8669i 0.740572 0.740572i
404404 1.48408 + 7.37402i 0.0738355 + 0.366871i
405405 −9.99873 9.99873i −0.496841 0.496841i
406406 4.36433 2.33911i 0.216598 0.116088i
407407 4.83517i 0.239671i
408408 −1.35673 + 14.2697i −0.0671681 + 0.706455i
409409 32.7649i 1.62012i 0.586348 + 0.810059i 0.300565π0.300565\pi
−0.586348 + 0.810059i 0.699435π0.699435\pi
410410 −2.34511 4.37552i −0.115817 0.216091i
411411 −12.9594 12.9594i −0.639239 0.639239i
412412 6.41168 9.64275i 0.315881 0.475064i
413413 −7.97413 + 7.97413i −0.392381 + 0.392381i
414414 −0.279497 + 0.925131i −0.0137365 + 0.0454677i
415415 14.3405 0.703949
416416 −15.3508 + 18.9215i −0.752634 + 0.927702i
417417 −24.4757 −1.19858
418418 −1.37326 + 4.54547i −0.0671682 + 0.222326i
419419 7.29280 7.29280i 0.356277 0.356277i −0.506162 0.862439i 0.668936π-0.668936\pi
0.862439 + 0.506162i 0.168936π0.168936\pi
420420 −2.95082 + 4.43784i −0.143985 + 0.216544i
421421 −28.3286 28.3286i −1.38065 1.38065i −0.843465 0.537184i 0.819488π-0.819488\pi
−0.537184 0.843465i 0.680512π-0.680512\pi
422422 17.8166 + 33.2423i 0.867297 + 1.61821i
423423 0.503069i 0.0244601i
424424 −27.6965 2.63332i −1.34506 0.127885i
425425 8.48891i 0.411773i
426426 2.70000 1.44709i 0.130815 0.0701119i
427427 −7.12444 7.12444i −0.344776 0.344776i
428428 1.23925 + 6.15754i 0.0599014 + 0.297636i
429429 19.1851 19.1851i 0.926263 0.926263i
430430 −6.53973 1.97576i −0.315374 0.0952795i
431431 28.6230 1.37872 0.689360 0.724419i 0.257892π-0.257892\pi
0.689360 + 0.724419i 0.257892π0.257892\pi
432432 6.73164 16.4612i 0.323876 0.791989i
433433 −20.1257 −0.967182 −0.483591 0.875294i 0.660668π-0.660668\pi
−0.483591 + 0.875294i 0.660668π0.660668\pi
434434 6.86688 + 2.07459i 0.329621 + 0.0995837i
435435 6.10964 6.10964i 0.292935 0.292935i
436436 26.0270 5.23813i 1.24647 0.250861i
437437 −0.723364 0.723364i −0.0346032 0.0346032i
438438 −35.4540 + 19.0020i −1.69406 + 0.907948i
439439 29.2451i 1.39579i 0.716198 + 0.697897i 0.245881π0.245881\pi
−0.716198 + 0.697897i 0.754119π0.754119\pi
440440 7.90118 + 9.56149i 0.376674 + 0.455826i
441441 4.04568i 0.192651i
442442 7.59827 + 14.1769i 0.361413 + 0.674326i
443443 22.0509 + 22.0509i 1.04767 + 1.04767i 0.998805 + 0.0488650i 0.0155604π0.0155604\pi
0.0488650 + 0.998805i 0.484440π0.484440\pi
444444 4.70875 + 3.13095i 0.223467 + 0.148588i
445445 7.39684 7.39684i 0.350644 0.350644i
446446 5.64911 18.6985i 0.267493 0.885398i
447447 −31.4406 −1.48709
448448 −8.16416 1.56662i −0.385720 0.0740158i
449449 −14.7479 −0.695994 −0.347997 0.937496i 0.613138π-0.613138\pi
−0.347997 + 0.937496i 0.613138π0.613138\pi
450450 0.898520 2.97409i 0.0423567 0.140200i
451451 −6.09739 + 6.09739i −0.287115 + 0.287115i
452452 −3.15544 2.09812i −0.148419 0.0986874i
453453 30.1664 + 30.1664i 1.41734 + 1.41734i
454454 1.60130 + 2.98771i 0.0751526 + 0.140220i
455455 5.98021i 0.280357i
456456 −3.53738 4.28070i −0.165653 0.200462i
457457 38.4217i 1.79729i 0.438675 + 0.898646i 0.355448π0.355448\pi
−0.438675 + 0.898646i 0.644552π0.644552\pi
458458 −22.9047 + 12.2760i −1.07027 + 0.573621i
459459 −8.30168 8.30168i −0.387489 0.387489i
460460 −2.61972 + 0.527237i −0.122145 + 0.0245826i
461461 −13.6064 + 13.6064i −0.633711 + 0.633711i −0.948997 0.315286i 0.897900π-0.897900\pi
0.315286 + 0.948997i 0.397900π0.397900\pi
462462 8.86140 + 2.67717i 0.412270 + 0.124553i
463463 26.3626 1.22517 0.612586 0.790404i 0.290129π-0.290129\pi
0.612586 + 0.790404i 0.290129π0.290129\pi
464464 12.4751 + 5.10156i 0.579141 + 0.236834i
465465 12.5172 0.580471
466466 27.9700 + 8.45017i 1.29568 + 0.391447i
467467 7.32038 7.32038i 0.338747 0.338747i −0.517149 0.855896i 0.673007π-0.673007\pi
0.855896 + 0.517149i 0.173007π0.173007\pi
468468 1.16148 + 5.77112i 0.0536895 + 0.266770i
469469 −5.46289 5.46289i −0.252253 0.252253i
470470 −1.22603 + 0.657105i −0.0565526 + 0.0303100i
471471 32.4822i 1.49670i
472472 −30.5574 2.90532i −1.40652 0.133728i
473473 11.8665i 0.545624i
474474 −8.82970 16.4745i −0.405562 0.756699i
475475 2.32545 + 2.32545i 0.106699 + 0.106699i
476476 −3.03861 + 4.56987i −0.139274 + 0.209460i
477477 −4.75308 + 4.75308i −0.217629 + 0.217629i
478478 −9.56599 + 31.6633i −0.437538 + 1.44825i
479479 37.5883 1.71745 0.858727 0.512433i 0.171256π-0.171256\pi
0.858727 + 0.512433i 0.171256π0.171256\pi
480480 −14.4278 + 1.50317i −0.658535 + 0.0686102i
481481 6.34528 0.289320
482482 −1.42447 + 4.71498i −0.0648828 + 0.214761i
483483 −1.41020 + 1.41020i −0.0641664 + 0.0641664i
484484 −0.251920 + 0.378871i −0.0114509 + 0.0172214i
485485 13.7158 + 13.7158i 0.622804 + 0.622804i
486486 −4.65834 8.69155i −0.211306 0.394257i
487487 0.799551i 0.0362311i −0.999836 0.0181156i 0.994233π-0.994233\pi
0.999836 0.0181156i 0.00576667π-0.00576667\pi
488488 2.59574 27.3013i 0.117504 1.23587i
489489 18.1107i 0.818993i
490490 9.85973 5.28443i 0.445417 0.238726i
491491 −6.00074 6.00074i −0.270809 0.270809i 0.558617 0.829426i 0.311332π-0.311332\pi
−0.829426 + 0.558617i 0.811332π0.811332\pi
492492 −1.98968 9.88623i −0.0897016 0.445706i
493493 6.29141 6.29141i 0.283351 0.283351i
494494 −5.96509 1.80215i −0.268382 0.0810825i
495495 2.99682 0.134697
496496 7.55328 + 18.0052i 0.339152 + 0.808455i
497497 1.17282 0.0526081
498498 27.8862 + 8.42488i 1.24961 + 0.377528i
499499 11.7126 11.7126i 0.524326 0.524326i −0.394549 0.918875i 0.629099π-0.629099\pi
0.918875 + 0.394549i 0.129099π0.129099\pi
500500 21.5204 4.33114i 0.962421 0.193694i
501501 −22.2917 22.2917i −0.995920 0.995920i
502502 36.5753 19.6030i 1.63244 0.874923i
503503 34.7455i 1.54922i −0.632436 0.774612i 0.717945π-0.717945\pi
0.632436 0.774612i 0.282055π-0.282055\pi
504504 −1.54828 + 1.27943i −0.0689659 + 0.0569903i
505505 5.02507i 0.223613i
506506 2.19268 + 4.09111i 0.0974764 + 0.181872i
507507 7.53474 + 7.53474i 0.334630 + 0.334630i
508508 −2.70303 1.79731i −0.119928 0.0797426i
509509 17.9923 17.9923i 0.797494 0.797494i −0.185206 0.982700i 0.559295π-0.559295\pi
0.982700 + 0.185206i 0.0592951π0.0592951\pi
510510 −2.76944 + 9.16681i −0.122633 + 0.405913i
511511 −15.4004 −0.681275
512512 −10.8684 19.8464i −0.480320 0.877093i
513513 4.54832 0.200813
514514 1.22547 4.05627i 0.0540530 0.178915i
515515 5.47020 5.47020i 0.241046 0.241046i
516516 −11.5563 7.68401i −0.508736 0.338270i
517517 1.70850 + 1.70850i 0.0751399 + 0.0751399i
518518 1.02269 + 1.90814i 0.0449343 + 0.0838388i
519519 1.10821i 0.0486452i
520520 −12.5477 + 10.3688i −0.550253 + 0.454704i
521521 29.4574i 1.29055i 0.763950 + 0.645275i 0.223257π0.223257\pi
−0.763950 + 0.645275i 0.776743π0.776743\pi
522522 2.87012 1.53827i 0.125622 0.0673284i
523523 17.8554 + 17.8554i 0.780762 + 0.780762i 0.979959 0.199197i 0.0638334π-0.0638334\pi
−0.199197 + 0.979959i 0.563833π0.563833\pi
524524 −0.00575879 + 0.00115900i −0.000251574 + 5.06311e-5i
525525 4.53348 4.53348i 0.197857 0.197857i
526526 17.0844 + 5.16148i 0.744917 + 0.225051i
527527 12.8896 0.561479
528528 9.74718 + 23.2349i 0.424191 + 1.01117i
529529 −1.00000 −0.0434783
530530 −17.7922 5.37530i −0.772843 0.233488i
531531 −5.24403 + 5.24403i −0.227572 + 0.227572i
532532 −0.419474 2.08427i −0.0181865 0.0903644i
533533 −8.00170 8.00170i −0.346592 0.346592i
534534 18.7292 10.0382i 0.810494 0.434393i
535535 4.19610i 0.181413i
536536 1.99037 20.9341i 0.0859708 0.904217i
537537 2.15303i 0.0929101i
538538 −7.23875 13.5061i −0.312085 0.582289i
539539 −13.7398 13.7398i −0.591813 0.591813i
540540 6.57848 9.89361i 0.283093 0.425753i
541541 27.0332 27.0332i 1.16225 1.16225i 0.178265 0.983982i 0.442951π-0.442951\pi
0.983982 0.178265i 0.0570485π-0.0570485\pi
542542 −6.00557 + 19.8784i −0.257961 + 0.853848i
543543 −11.5667 −0.496377
544544 −14.8570 + 1.54790i −0.636990 + 0.0663655i
545545 17.7363 0.759739
546546 −3.51330 + 11.6290i −0.150355 + 0.497674i
547547 10.7547 10.7547i 0.459837 0.459837i −0.438765 0.898602i 0.644584π-0.644584\pi
0.898602 + 0.438765i 0.144584π0.144584\pi
548548 10.5749 15.9040i 0.451738 0.679384i
549549 −4.68525 4.68525i −0.199962 0.199962i
550550 −7.04897 13.1520i −0.300569 0.560803i
551551 3.44694i 0.146845i
552552 −5.40398 0.513797i −0.230009 0.0218687i
553553 7.15617i 0.304311i
554554 2.89839 1.55342i 0.123141 0.0659987i
555555 2.67121 + 2.67121i 0.113386 + 0.113386i
556556 −5.03238 25.0047i −0.213420 1.06043i
557557 20.3767 20.3767i 0.863388 0.863388i −0.128342 0.991730i 0.540966π-0.540966\pi
0.991730 + 0.128342i 0.0409656π0.0409656\pi
558558 4.51587 + 1.36432i 0.191172 + 0.0577561i
559559 −15.5727 −0.658653
560560 −5.14045 2.10214i −0.217224 0.0888315i
561561 16.6335 0.702265
562562 −0.335050 0.101224i −0.0141332 0.00426987i
563563 0.0151291 0.0151291i 0.000637614 0.000637614i −0.706788 0.707426i 0.749856π-0.749856\pi
0.707426 + 0.706788i 0.249856π0.249856\pi
564564 −2.77015 + 0.557513i −0.116644 + 0.0234755i
565565 −1.79004 1.79004i −0.0753075 0.0753075i
566566 30.8192 16.5179i 1.29543 0.694299i
567567 10.9973i 0.461844i
568568 2.03350 + 2.46081i 0.0853239 + 0.103253i
569569 28.2556i 1.18453i −0.805742 0.592267i 0.798233π-0.798233\pi
0.805742 0.592267i 0.201767π-0.201767\pi
570570 −1.75250 3.26982i −0.0734040 0.136958i
571571 20.3606 + 20.3606i 0.852064 + 0.852064i 0.990387 0.138323i 0.0441712π-0.0441712\pi
−0.138323 + 0.990387i 0.544171π0.544171\pi
572572 23.5442 + 15.6551i 0.984434 + 0.654572i
573573 24.4136 24.4136i 1.01989 1.01989i
574574 1.11659 3.69591i 0.0466058 0.154264i
575575 3.21478 0.134065
576576 −5.36900 1.03026i −0.223708 0.0429274i
577577 −12.2293 −0.509111 −0.254555 0.967058i 0.581929π-0.581929\pi
−0.254555 + 0.967058i 0.581929π0.581929\pi
578578 4.10114 13.5747i 0.170585 0.564634i
579579 −8.97709 + 8.97709i −0.373075 + 0.373075i
580580 7.49786 + 4.98549i 0.311332 + 0.207011i
581581 7.88638 + 7.88638i 0.327182 + 0.327182i
582582 18.6136 + 34.7293i 0.771558 + 1.43958i
583583 32.2844i 1.33708i
584584 −26.7022 32.3132i −1.10494 1.33713i
585585 3.93277i 0.162600i
586586 −40.3296 + 21.6151i −1.66600 + 0.892912i
587587 −0.477560 0.477560i −0.0197110 0.0197110i 0.697183 0.716894i 0.254437π-0.254437\pi
−0.716894 + 0.697183i 0.754437π0.754437\pi
588588 22.2775 4.48351i 0.918708 0.184897i
589589 −3.53098 + 3.53098i −0.145491 + 0.145491i
590590 −19.6300 5.93053i −0.808153 0.244156i
591591 −29.1983 −1.20106
592592 −2.23046 + 5.45425i −0.0916714 + 0.224168i
593593 −44.7662 −1.83833 −0.919164 0.393874i 0.871135π-0.871135\pi
−0.919164 + 0.393874i 0.871135π0.871135\pi
594594 −19.7554 5.96842i −0.810574 0.244887i
595595 −2.59242 + 2.59242i −0.106279 + 0.106279i
596596 −6.46439 32.1200i −0.264792 1.31569i
597597 −12.6397 12.6397i −0.517309 0.517309i
598598 −5.36883 + 2.87749i −0.219548 + 0.117669i
599599 0.331335i 0.0135380i −0.999977 0.00676899i 0.997845π-0.997845\pi
0.999977 0.00676899i 0.00215465π-0.00215465\pi
600600 17.3726 + 1.65174i 0.709232 + 0.0674322i
601601 15.2465i 0.621918i −0.950423 0.310959i 0.899350π-0.899350\pi
0.950423 0.310959i 0.100650π-0.100650\pi
602602 −2.50989 4.68297i −0.102296 0.190864i
603603 −3.59256 3.59256i −0.146301 0.146301i
604604 −24.6159 + 37.0207i −1.00161 + 1.50635i
605605 −0.214928 + 0.214928i −0.00873808 + 0.00873808i
606606 −2.95216 + 9.77163i −0.119924 + 0.396945i
607607 3.73658 0.151663 0.0758315 0.997121i 0.475839π-0.475839\pi
0.0758315 + 0.997121i 0.475839π0.475839\pi
608608 3.64590 4.49397i 0.147861 0.182254i
609609 6.71982 0.272301
610610 5.29859 17.5383i 0.214534 0.710104i
611611 −2.24210 + 2.24210i −0.0907055 + 0.0907055i
612612 −1.99828 + 3.00529i −0.0807757 + 0.121481i
613613 −2.71214 2.71214i −0.109542 0.109542i 0.650211 0.759753i 0.274680π-0.274680\pi
−0.759753 + 0.650211i 0.774680π0.774680\pi
614614 −12.5379 23.3933i −0.505989 0.944077i
615615 6.73704i 0.271664i
616616 −0.913064 + 9.60335i −0.0367884 + 0.386930i
617617 35.3903i 1.42476i −0.701795 0.712379i 0.747618π-0.747618\pi
0.701795 0.712379i 0.252382π-0.252382\pi
618618 13.8509 7.42353i 0.557164 0.298618i
619619 −2.08383 2.08383i −0.0837563 0.0837563i 0.663987 0.747744i 0.268863π-0.268863\pi
−0.747744 + 0.663987i 0.768863π0.768863\pi
620620 2.57362 + 12.7877i 0.103359 + 0.513566i
621621 3.14387 3.14387i 0.126159 0.126159i
622622 34.8611 + 10.5321i 1.39780 + 0.422299i
623623 8.13558 0.325945
624624 −30.4915 + 12.7914i −1.22064 + 0.512065i
625625 −1.40867 −0.0563468
626626 31.9603 + 9.65571i 1.27739 + 0.385920i
627627 −4.55657 + 4.55657i −0.181972 + 0.181972i
628628 33.1841 6.67855i 1.32419 0.266503i
629629 2.75068 + 2.75068i 0.109677 + 0.109677i
630630 −1.18265 + 0.633857i −0.0471181 + 0.0252535i
631631 9.64495i 0.383960i 0.981399 + 0.191980i 0.0614908π0.0614908\pi
−0.981399 + 0.191980i 0.938509π0.938509\pi
632632 15.0151 12.4078i 0.597268 0.493555i
633633 51.1835i 2.03436i
634634 0.838624 + 1.56471i 0.0333060 + 0.0621426i
635635 −1.53339 1.53339i −0.0608509 0.0608509i
636636 −31.4403 20.9053i −1.24669 0.828951i
637637 18.0309 18.0309i 0.714411 0.714411i
638638 4.52316 14.9716i 0.179074 0.592731i
639639 0.771282 0.0305114
640640 −4.50211 14.4305i −0.177961 0.570416i
641641 −12.4528 −0.491854 −0.245927 0.969288i 0.579092π-0.579092\pi
−0.245927 + 0.969288i 0.579092π0.579092\pi
642642 −2.46515 + 8.15962i −0.0972918 + 0.322034i
643643 −29.4591 + 29.4591i −1.16175 + 1.16175i −0.177660 + 0.984092i 0.556853π0.556853\pi
−0.984092 + 0.177660i 0.943147π0.943147\pi
644644 −1.73062 1.15073i −0.0681961 0.0453451i
645645 −6.55571 6.55571i −0.258131 0.258131i
646646 −1.80464 3.36710i −0.0710024 0.132477i
647647 20.4981i 0.805864i 0.915230 + 0.402932i 0.132009π0.132009\pi
−0.915230 + 0.402932i 0.867991π0.867991\pi
648648 23.0746 19.0678i 0.906456 0.749054i
649649 35.6192i 1.39817i
650650 17.2596 9.25048i 0.676977 0.362834i
651651 6.88365 + 6.88365i 0.269792 + 0.269792i
652652 −18.5021 + 3.72368i −0.724597 + 0.145830i
653653 20.5538 20.5538i 0.804331 0.804331i −0.179439 0.983769i 0.557428π-0.557428\pi
0.983769 + 0.179439i 0.0574281π0.0574281\pi
654654 34.4895 + 10.4198i 1.34865 + 0.407448i
655655 −0.00392437 −0.000153338
656656 9.69079 4.06535i 0.378362 0.158725i
657657 −10.1278 −0.395123
658658 −1.03560 0.312873i −0.0403721 0.0121970i
659659 −22.8047 + 22.8047i −0.888345 + 0.888345i −0.994364 0.106019i 0.966190π-0.966190\pi
0.106019 + 0.994364i 0.466190π0.466190\pi
660660 3.32114 + 16.5020i 0.129275 + 0.642338i
661661 26.5982 + 26.5982i 1.03455 + 1.03455i 0.999381 + 0.0351672i 0.0111964π0.0111964\pi
0.0351672 + 0.999381i 0.488804π0.488804\pi
662662 −39.2937 + 21.0599i −1.52719 + 0.818516i
663663 21.8284i 0.847743i
664664 −2.87335 + 30.2211i −0.111508 + 1.17281i
665665 1.42034i 0.0550783i
666666 0.672551 + 1.25485i 0.0260608 + 0.0486244i
667667 2.38258 + 2.38258i 0.0922537 + 0.0922537i
668668 18.1901 27.3568i 0.703797 1.05847i
669669 18.7441 18.7441i 0.724690 0.724690i
670670 4.06286 13.4480i 0.156962 0.519543i
671671 −31.8237 −1.22854
672672 −8.76100 7.10771i −0.337963 0.274186i
673673 −3.50318 −0.135038 −0.0675188 0.997718i 0.521508π-0.521508\pi
−0.0675188 + 0.997718i 0.521508π0.521508\pi
674674 6.27824 20.7809i 0.241829 0.800450i
675675 −10.1068 + 10.1068i −0.389012 + 0.389012i
676676 −6.14838 + 9.24677i −0.236476 + 0.355645i
677677 19.1608 + 19.1608i 0.736411 + 0.736411i 0.971881 0.235471i 0.0756632π-0.0756632\pi
−0.235471 + 0.971881i 0.575663π0.575663\pi
678678 −2.42924 4.53248i −0.0932943 0.174069i
679679 15.0857i 0.578935i
680680 −9.93433 0.944533i −0.380964 0.0362212i
681681 4.60022i 0.176281i
682682 19.9700 10.7032i 0.764693 0.409846i
683683 25.0664 + 25.0664i 0.959141 + 0.959141i 0.999197 0.0400569i 0.0127539π-0.0127539\pi
−0.0400569 + 0.999197i 0.512754π0.512754\pi
684684 −0.275859 1.37068i −0.0105477 0.0524092i
685685 9.02211 9.02211i 0.344717 0.344717i
686686 18.1757 + 5.49116i 0.693950 + 0.209653i
687687 −35.2667 −1.34551
688688 5.47403 13.3859i 0.208695 0.510332i
689689 −42.3674 −1.61407
690690 −3.47150 1.04880i −0.132158 0.0399270i
691691 −17.8490 + 17.8490i −0.679006 + 0.679006i −0.959775 0.280769i 0.909411π-0.909411\pi
0.280769 + 0.959775i 0.409411π0.409411\pi
692692 −1.13216 + 0.227856i −0.0430384 + 0.00866179i
693693 1.64806 + 1.64806i 0.0626045 + 0.0626045i
694694 15.0809 8.08278i 0.572463 0.306818i
695695 17.0396i 0.646349i
696696 11.6512 + 14.0995i 0.441638 + 0.534442i
697697 6.93748i 0.262776i
698698 5.93235 + 11.0686i 0.224543 + 0.418953i
699699 28.0383 + 28.0383i 1.06050 + 1.06050i
700700 5.56357 + 3.69934i 0.210283 + 0.139822i
701701 −17.2434 + 17.2434i −0.651275 + 0.651275i −0.953300 0.302025i 0.902337π-0.902337\pi
0.302025 + 0.953300i 0.402337π0.402337\pi
702702 7.83246 25.9253i 0.295617 0.978489i
703703 −1.50704 −0.0568392
704704 −21.7329 + 14.7351i −0.819089 + 0.555348i
705705 −1.88774 −0.0710963
706706 12.3708 40.9471i 0.465580 1.54107i
707707 −2.76347 + 2.76347i −0.103931 + 0.103931i
708708 −34.6878 23.0647i −1.30365 0.866824i
709709 −22.7158 22.7158i −0.853109 0.853109i 0.137406 0.990515i 0.456123π-0.456123\pi
−0.990515 + 0.137406i 0.956123π0.956123\pi
710710 1.00744 + 1.87969i 0.0378087 + 0.0705436i
711711 4.70611i 0.176493i
712712 14.1059 + 17.0701i 0.528643 + 0.639729i
713713 4.88133i 0.182807i
714714 −6.56417 + 3.51814i −0.245658 + 0.131663i
715715 13.3563 + 13.3563i 0.499498 + 0.499498i
716716 −2.19956 + 0.442677i −0.0822013 + 0.0165436i
717717 −31.7406 + 31.7406i −1.18538 + 1.18538i
718718 9.21207 + 2.78312i 0.343792 + 0.103865i
719719 −5.56231 −0.207439 −0.103720 0.994607i 0.533074π-0.533074\pi
−0.103720 + 0.994607i 0.533074π0.533074\pi
720720 −3.38052 1.38243i −0.125984 0.0515201i
721721 6.01652 0.224067
722722 −24.3051 7.34295i −0.904541 0.273276i
723723 −4.72650 + 4.72650i −0.175780 + 0.175780i
724724 −2.37820 11.8167i −0.0883851 0.439165i
725725 −7.65945 7.65945i −0.284465 0.284465i
726726 −0.544212 + 0.291676i −0.0201976 + 0.0108251i
727727 24.9482i 0.925276i 0.886547 + 0.462638i 0.153097π0.153097\pi
−0.886547 + 0.462638i 0.846903π0.846903\pi
728728 −12.6026 1.19823i −0.467085 0.0444093i
729729 18.3668i 0.680254i
730730 −13.2288 24.6825i −0.489622 0.913539i
731731 −6.75075 6.75075i −0.249685 0.249685i
732732 20.6070 30.9916i 0.761657 1.14548i
733733 −4.28174 + 4.28174i −0.158150 + 0.158150i −0.781746 0.623597i 0.785671π-0.785671\pi
0.623597 + 0.781746i 0.285671π0.285671\pi
734734 −6.96967 + 23.0695i −0.257255 + 0.851511i
735735 15.1812 0.559965
736736 −0.586193 5.62640i −0.0216073 0.207392i
737737 −24.4018 −0.898854
738738 0.734307 2.43055i 0.0270302 0.0894696i
739739 −22.1800 + 22.1800i −0.815904 + 0.815904i −0.985512 0.169608i 0.945750π-0.945750\pi
0.169608 + 0.985512i 0.445750π0.445750\pi
740740 −2.17972 + 3.27815i −0.0801279 + 0.120507i
741741 −5.97966 5.97966i −0.219668 0.219668i
742742 −6.82849 12.7406i −0.250682 0.467723i
743743 6.84629i 0.251166i −0.992083 0.125583i 0.959920π-0.959920\pi
0.992083 0.125583i 0.0400801π-0.0400801\pi
744744 −2.50801 + 26.3786i −0.0919482 + 0.967085i
745745 21.8884i 0.801929i
746746 16.2657 8.71781i 0.595531 0.319182i
747747 5.18632 + 5.18632i 0.189758 + 0.189758i
748748 3.41995 + 16.9929i 0.125046 + 0.621322i
749749 −2.30758 + 2.30758i −0.0843173 + 0.0843173i
750750 28.5176 + 8.61562i 1.04132 + 0.314598i
751751 −23.1178 −0.843580 −0.421790 0.906693i 0.638598π-0.638598\pi
−0.421790 + 0.906693i 0.638598π0.638598\pi
752752 −1.13912 2.71538i −0.0415395 0.0990199i
753753 56.3155 2.05225
754754 19.6475 + 5.93582i 0.715519 + 0.216170i
755755 −21.0014 + 21.0014i −0.764318 + 0.764318i
756756 9.05859 1.82311i 0.329458 0.0663058i
757757 21.7823 + 21.7823i 0.791691 + 0.791691i 0.981769 0.190078i 0.0608741π-0.0608741\pi
−0.190078 + 0.981769i 0.560874π0.560874\pi
758758 −39.9439 + 21.4084i −1.45083 + 0.777587i
759759 6.29914i 0.228644i
760760 2.98016 2.46267i 0.108102 0.0893302i
761761 20.6449i 0.748378i 0.927353 + 0.374189i 0.122079π0.122079\pi
−0.927353 + 0.374189i 0.877921π0.877921\pi
762762 −2.08095 3.88265i −0.0753848 0.140653i
763763 9.75382 + 9.75382i 0.353112 + 0.353112i
764764 29.9608 + 19.9216i 1.08394 + 0.720739i
765765 −1.70486 + 1.70486i −0.0616392 + 0.0616392i
766766 4.99090 16.5198i 0.180329 0.596886i
767767 −46.7436 −1.68781
768768 −0.276942 30.7061i −0.00999329 1.10801i
769769 −18.1582 −0.654803 −0.327402 0.944885i 0.606173π-0.606173\pi
−0.327402 + 0.944885i 0.606173π0.606173\pi
770770 −1.86380 + 6.16916i −0.0671668 + 0.222321i
771771 4.06618 4.06618i 0.146440 0.146440i
772772 −11.0168 7.32534i −0.396505 0.263645i
773773 27.1002 + 27.1002i 0.974727 + 0.974727i 0.999688 0.0249615i 0.00794632π-0.00794632\pi
−0.0249615 + 0.999688i 0.507946π0.507946\pi
774774 −1.65058 3.07967i −0.0593290 0.110696i
775775 15.6924i 0.563687i
776776 −31.6528 + 26.1564i −1.13627 + 0.938961i
777777 2.93798i 0.105400i
778778 −23.6975 + 12.7010i −0.849597 + 0.455351i
779779 1.90045 + 1.90045i 0.0680908 + 0.0680908i
780780 −21.6558 + 4.35839i −0.775402 + 0.156055i
781781 2.61940 2.61940i 0.0937294 0.0937294i
782782 −3.57478 1.08000i −0.127834 0.0386207i
783783 −14.9810 −0.535378
784784 9.16080 + 21.8371i 0.327172 + 0.779896i
785785 22.6135 0.807112
786786 −0.00763122 0.00230551i −0.000272197 8.22350e-5i
787787 14.0686 14.0686i 0.501490 0.501490i −0.410411 0.911901i 0.634615π-0.634615\pi
0.911901 + 0.410411i 0.134615π0.134615\pi
788788 −6.00336 29.8293i −0.213861 1.06262i
789789 17.1262 + 17.1262i 0.609708 + 0.609708i
790790 11.4693 6.14709i 0.408059 0.218704i
791791 1.96881i 0.0700029i
792792 −0.600459 + 6.31546i −0.0213364 + 0.224410i
793793 41.7628i 1.48304i
794794 5.48410 + 10.2323i 0.194624 + 0.363130i
795795 −17.8356 17.8356i −0.632565 0.632565i
796796 10.3141 15.5117i 0.365572 0.549797i
797797 34.3747 34.3747i 1.21761 1.21761i 0.249148 0.968465i 0.419849π-0.419849\pi
0.968465 0.249148i 0.0801505π-0.0801505\pi
798798 0.834430 2.76195i 0.0295385 0.0977720i
799799 −1.94390 −0.0687702
800800 1.88448 + 18.0876i 0.0666264 + 0.639494i
801801 5.35020 0.189040
802802 −12.2547 + 40.5628i −0.432728 + 1.43232i
803803 −34.3956 + 34.3956i −1.21379 + 1.21379i
804804 15.8011 23.7638i 0.557261 0.838085i
805805 −0.981759 0.981759i −0.0346024 0.0346024i
806806 14.0460 + 26.2070i 0.494748 + 0.923103i
807807 20.7955i 0.732037i
808808 −10.5898 1.00685i −0.372547 0.0354209i
809809 19.8794i 0.698922i −0.936951 0.349461i 0.886365π-0.886365\pi
0.936951 0.349461i 0.113635π-0.113635\pi
810810 17.6255 9.44661i 0.619299 0.331920i
811811 18.6464 + 18.6464i 0.654763 + 0.654763i 0.954136 0.299373i 0.0967776π-0.0967776\pi
−0.299373 + 0.954136i 0.596778π0.596778\pi
812812 1.38164 + 6.86504i 0.0484861 + 0.240916i
813813 −19.9269 + 19.9269i −0.698867 + 0.698867i
814814 6.54576 + 1.97758i 0.229429 + 0.0693141i
815815 −12.6084 −0.441651
816816 −18.7631 7.67300i −0.656841 0.268609i
817817 3.69860 0.129398
818818 −44.3564 13.4008i −1.55089 0.468547i
819819 −2.16277 + 2.16277i −0.0755734 + 0.0755734i
820820 6.88263 1.38518i 0.240352 0.0483726i
821821 14.7887 + 14.7887i 0.516129 + 0.516129i 0.916398 0.400269i 0.131083π-0.131083\pi
−0.400269 + 0.916398i 0.631083π0.631083\pi
822822 22.8445 12.2438i 0.796794 0.427051i
823823 11.6401i 0.405749i 0.979205 + 0.202875i 0.0650284π0.0650284\pi
−0.979205 + 0.202875i 0.934972π0.934972\pi
824824 10.4318 + 12.6239i 0.363409 + 0.439773i
825825 20.2503i 0.705026i
826826 −7.53381 14.0566i −0.262135 0.489093i
827827 −22.7061 22.7061i −0.789569 0.789569i 0.191855 0.981423i 0.438550π-0.438550\pi
−0.981423 + 0.191855i 0.938550π0.938550\pi
828828 −1.13811 0.756755i −0.0395521 0.0262991i
829829 4.08997 4.08997i 0.142051 0.142051i −0.632505 0.774556i 0.717973π-0.717973\pi
0.774556 + 0.632505i 0.217973π0.217973\pi
830830 −5.86526 + 19.4139i −0.203586 + 0.673868i
831831 4.46269 0.154809
832832 −19.3371 28.5204i −0.670392 0.988768i
833833 15.6328 0.541645
834834 10.0105 33.1348i 0.346637 1.14736i
835835 15.5191 15.5191i 0.537061 0.537061i
836836 −5.59190 3.71818i −0.193400 0.128596i
837837 −15.3463 15.3463i −0.530444 0.530444i
838838 6.89010 + 12.8556i 0.238015 + 0.444089i
839839 1.07505i 0.0371149i −0.999828 0.0185575i 0.994093π-0.994093\pi
0.999828 0.0185575i 0.00590736π-0.00590736\pi
840840 −4.80098 5.80983i −0.165649 0.200458i
841841 17.6467i 0.608506i
842842 49.9370 26.7643i 1.72094 0.922358i
843843 −0.335868 0.335868i −0.0115679 0.0115679i
844844 −52.2896 + 10.5237i −1.79988 + 0.362240i
845845 −5.24556 + 5.24556i −0.180453 + 0.180453i
846846 −0.681045 0.205755i −0.0234148 0.00707399i
847847 −0.236394 −0.00812258
848848 14.8928 36.4180i 0.511420 1.25060i
849849 47.4527 1.62857
850850 11.4921 + 3.47195i 0.394176 + 0.119087i
851851 −1.04169 + 1.04169i −0.0357087 + 0.0357087i
852852 0.854752 + 4.24706i 0.0292833 + 0.145502i
853853 10.5166 + 10.5166i 0.360081 + 0.360081i 0.863843 0.503762i 0.168051π-0.168051\pi
−0.503762 + 0.863843i 0.668051π0.668051\pi
854854 12.5588 6.73104i 0.429754 0.230331i
855855 0.934057i 0.0319441i
856856 −8.84280 0.840753i −0.302241 0.0287363i
857857 9.90117i 0.338218i −0.985597 0.169109i 0.945911π-0.945911\pi
0.985597 0.169109i 0.0540889π-0.0540889\pi
858858 18.1257 + 33.8190i 0.618801 + 1.15456i
859859 −15.9867 15.9867i −0.545458 0.545458i 0.379666 0.925124i 0.376039π-0.376039\pi
−0.925124 + 0.379666i 0.876039π0.876039\pi
860860 5.34948 8.04528i 0.182416 0.274342i
861861 3.70494 3.70494i 0.126264 0.126264i
862862 −11.7067 + 38.7492i −0.398733 + 1.31980i
863863 −10.6622 −0.362944 −0.181472 0.983396i 0.558086π-0.558086\pi
−0.181472 + 0.983396i 0.558086π0.558086\pi
864864 19.5316 + 15.8458i 0.664478 + 0.539083i
865865 −0.771520 −0.0262325
866866 8.23140 27.2458i 0.279714 0.925851i
867867 13.6079 13.6079i 0.462148 0.462148i
868868 −5.61709 + 8.44773i −0.190656 + 0.286735i
869869 −15.9827 15.9827i −0.542176 0.542176i
870870 5.77227 + 10.7699i 0.195698 + 0.365135i
871871 32.0229i 1.08506i
872872 −3.55374 + 37.3772i −0.120345 + 1.26575i
873873 9.92080i 0.335768i
874874 1.27513 0.683421i 0.0431319 0.0231171i
875875 8.06493 + 8.06493i 0.272644 + 0.272644i
876876 −11.2238 55.7686i −0.379219 1.88425i
877877 −33.6382 + 33.6382i −1.13588 + 1.13588i −0.146702 + 0.989181i 0.546866π0.546866\pi
−0.989181 + 0.146702i 0.953134π0.953134\pi
878878 −39.5915 11.9612i −1.33615 0.403672i
879879 −62.0960 −2.09445
880880 −16.1757 + 6.78582i −0.545284 + 0.228750i
881881 −26.5560 −0.894695 −0.447348 0.894360i 0.647631π-0.647631\pi
−0.447348 + 0.894360i 0.647631π0.647631\pi
882882 5.47696 + 1.65468i 0.184419 + 0.0557158i
883883 13.3950 13.3950i 0.450777 0.450777i −0.444835 0.895612i 0.646738π-0.646738\pi
0.895612 + 0.444835i 0.146738π0.146738\pi
884884 −22.3001 + 4.48806i −0.750033 + 0.150950i
885885 −19.6779 19.6779i −0.661466 0.661466i
886886 −38.8709 + 20.8333i −1.30589 + 0.699908i
887887 21.3699i 0.717532i 0.933428 + 0.358766i 0.116802π0.116802\pi
−0.933428 + 0.358766i 0.883198π0.883198\pi
888888 −6.16449 + 5.09405i −0.206867 + 0.170945i
889889 1.68654i 0.0565646i
890890 6.98840 + 13.0390i 0.234252 + 0.437068i
891891 −24.5616 24.5616i −0.822845 0.822845i
892892 23.0031 + 15.2953i 0.770202 + 0.512124i
893893 0.532512 0.532512i 0.0178198 0.0178198i
894894 12.8591 42.5636i 0.430074 1.42354i
895895 −1.49890 −0.0501028
896896 5.45999 10.4117i 0.182405 0.347831i
897897 −8.26646 −0.276009
898898 6.03185 19.9653i 0.201285 0.666252i
899899 11.6301 11.6301i 0.387887 0.387887i
900900 3.65877 + 2.43280i 0.121959 + 0.0810933i
901901 −18.3663 18.3663i −0.611869 0.611869i
902902 −5.76070 10.7483i −0.191810 0.357881i
903903 7.21044i 0.239948i
904904 4.13097 3.41364i 0.137394 0.113536i
905905 8.05258i 0.267677i
906906 −53.1767 + 28.5007i −1.76668 + 0.946871i
907907 −31.9140 31.9140i −1.05969 1.05969i −0.998102 0.0615842i 0.980385π-0.980385\pi
−0.0615842 0.998102i 0.519615π-0.519615\pi
908908 −4.69963 + 0.945835i −0.155963 + 0.0313886i
909909 −1.81734 + 1.81734i −0.0602774 + 0.0602774i
910910 −8.09589 2.44590i −0.268376 0.0810808i
911911 2.44657 0.0810584 0.0405292 0.999178i 0.487096π-0.487096\pi
0.0405292 + 0.999178i 0.487096π0.487096\pi
912912 7.24192 3.03803i 0.239804 0.100599i
913913 35.2272 1.16585
914914 −52.0145 15.7144i −1.72049 0.519787i
915915 17.5811 17.5811i 0.581214 0.581214i
916916 −7.25106 36.0288i −0.239582 1.19042i
917917 −0.00215815 0.00215815i −7.12684e−5 7.12684e-5i
918918 14.6340 7.84327i 0.482995 0.258866i
919919 3.55117i 0.117142i 0.998283 + 0.0585712i 0.0186545π0.0186545\pi
−0.998283 + 0.0585712i 0.981346π0.981346\pi
920920 0.357697 3.76216i 0.0117929 0.124035i
921921 36.0190i 1.18687i
922922 −12.8550 23.9850i −0.423358 0.789903i
923923 3.43748 + 3.43748i 0.113146 + 0.113146i
924924 −7.24860 + 10.9014i −0.238462 + 0.358631i
925925 3.34880 3.34880i 0.110108 0.110108i
926926 −10.7823 + 35.6891i −0.354327 + 1.17282i
927927 3.95665 0.129953
928928 −12.0087 + 14.8020i −0.394204 + 0.485899i
929929 1.01716 0.0333718 0.0166859 0.999861i 0.494688π-0.494688\pi
0.0166859 + 0.999861i 0.494688π0.494688\pi
930930 −5.11951 + 16.9455i −0.167875 + 0.555665i
931931 −4.28245 + 4.28245i −0.140352 + 0.140352i
932932 −22.8793 + 34.4091i −0.749438 + 1.12711i
933933 34.9463 + 34.9463i 1.14409 + 1.14409i
934934 6.91616 + 12.9042i 0.226304 + 0.422239i
935935 11.5799i 0.378704i
936936 −8.28788 0.787992i −0.270898 0.0257563i
937937 36.5659i 1.19456i −0.802034 0.597278i 0.796249π-0.796249\pi
0.802034 0.597278i 0.203751π-0.203751\pi
938938 9.62987 5.16124i 0.314426 0.168520i
939939 32.0383 + 32.0383i 1.04553 + 1.04553i
940940 −0.388131 1.92853i −0.0126594 0.0629018i
941941 −16.9584 + 16.9584i −0.552827 + 0.552827i −0.927256 0.374429i 0.877839π-0.877839\pi
0.374429 + 0.927256i 0.377839π0.377839\pi
942942 43.9737 + 13.2852i 1.43274 + 0.432854i
943943 2.62724 0.0855548
944944 16.4311 40.1797i 0.534786 1.30774i
945945 6.17304 0.200809
946946 −16.0647 4.85340i −0.522308 0.157798i
947947 −11.7928 + 11.7928i −0.383215 + 0.383215i −0.872259 0.489044i 0.837346π-0.837346\pi
0.489044 + 0.872259i 0.337346π0.337346\pi
948948 25.9142 5.21542i 0.841654 0.169389i
949949 −45.1379 45.1379i −1.46524 1.46524i
950950 −4.09926 + 2.19704i −0.132998 + 0.0712816i
951951 2.40921i 0.0781238i
952952 −4.94381 5.98268i −0.160230 0.193900i
953953 55.4065i 1.79479i −0.441224 0.897397i 0.645456π-0.645456\pi
0.441224 0.897397i 0.354544π-0.354544\pi
954954 −4.49062 8.37863i −0.145389 0.271268i
955955 16.9964 + 16.9964i 0.549989 + 0.549989i
956956 −38.9527 25.9005i −1.25982 0.837682i
957957 15.0082 15.0082i 0.485145 0.485145i
958958 −15.3736 + 50.8863i −0.496698 + 1.64406i
959959 9.92316 0.320436
960960 3.86598 20.1468i 0.124774 0.650236i
961961 −7.17265 −0.231376
962962 −2.59521 + 8.59011i −0.0836729 + 0.276956i
963963 −1.51754 + 1.51754i −0.0489020 + 0.0489020i
964964 −5.80044 3.85684i −0.186819 0.124220i
965965 −6.24970 6.24970i −0.201185 0.201185i
966966 −1.33233 2.48587i −0.0428671 0.0799816i
967967 38.1599i 1.22714i 0.789640 + 0.613570i 0.210267π0.210267\pi
−0.789640 + 0.613570i 0.789733π0.789733\pi
968968 −0.409873 0.496002i −0.0131738 0.0159421i
969969 5.18437i 0.166546i
970970 −24.1780 + 12.9585i −0.776309 + 0.416071i
971971 22.9272 + 22.9272i 0.735768 + 0.735768i 0.971756 0.235988i 0.0758325π-0.0758325\pi
−0.235988 + 0.971756i 0.575832π0.575832\pi
972972 13.6717 2.75153i 0.438520 0.0882554i
973973 9.37069 9.37069i 0.300411 0.300411i
974974 1.08242 + 0.327015i 0.0346828 + 0.0104782i
975975 26.5748 0.851076
976976 35.8983 + 14.6803i 1.14908 + 0.469904i
977977 10.6791 0.341656 0.170828 0.985301i 0.445356π-0.445356\pi
0.170828 + 0.985301i 0.445356π0.445356\pi
978978 −24.5179 7.40724i −0.783995 0.236858i
979979 18.1701 18.1701i 0.580720 0.580720i
980980 3.12135 + 15.5092i 0.0997077 + 0.495424i
981981 6.41441 + 6.41441i 0.204796 + 0.204796i
982982 10.5780 5.66938i 0.337557 0.180917i
983983 48.9907i 1.56256i −0.624180 0.781280i 0.714567π-0.714567\pi
0.624180 0.781280i 0.285433π-0.285433\pi
984984 14.1976 + 1.34987i 0.452602 + 0.0430323i
985985 20.3274i 0.647683i
986986 5.94401 + 11.0904i 0.189296 + 0.353189i
987987 −1.03813 1.03813i −0.0330442 0.0330442i
988988 4.87943 7.33834i 0.155235 0.233464i
989989 2.55653 2.55653i 0.0812929 0.0812929i
990990 −1.22569 + 4.05703i −0.0389551 + 0.128941i
991991 52.6490 1.67245 0.836225 0.548386i 0.184757π-0.184757\pi
0.836225 + 0.548386i 0.184757π0.184757\pi
992992 −27.4643 + 2.86140i −0.871992 + 0.0908495i
993993 −60.5010 −1.91994
994994 −0.479681 + 1.58774i −0.0152146 + 0.0503600i
995995 8.79957 8.79957i 0.278965 0.278965i
996996 −22.8109 + 34.3061i −0.722790 + 1.08703i
997997 −26.0987 26.0987i −0.826554 0.826554i 0.160485 0.987038i 0.448694π-0.448694\pi
−0.987038 + 0.160485i 0.948694π0.948694\pi
998998 11.0658 + 20.6467i 0.350282 + 0.653558i
999999 6.54988i 0.207229i
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 368.2.j.d.277.6 yes 24
4.3 odd 2 1472.2.j.d.369.9 24
16.3 odd 4 1472.2.j.d.1105.9 24
16.13 even 4 inner 368.2.j.d.93.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
368.2.j.d.93.6 24 16.13 even 4 inner
368.2.j.d.277.6 yes 24 1.1 even 1 trivial
1472.2.j.d.369.9 24 4.3 odd 2
1472.2.j.d.1105.9 24 16.3 odd 4