Properties

Label 819.2.fm.g.496.4
Level 819819
Weight 22
Character 819.496
Analytic conductor 6.5406.540
Analytic rank 00
Dimension 3232
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [819,2,Mod(370,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 5])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.370"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 819=32713 819 = 3^{2} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 819.fm (of order 1212, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32,8,0,-12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.539747925546.53974792554
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 496.4
Character χ\chi == 819.496
Dual form 819.2.fm.g.748.4

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.112775+0.0302180i)q2+(1.720250.993184i)q4+(1.24841+1.24841i)q5+(2.18126+1.49736i)q7+(0.3291030.329103i)q8+(0.103066+0.178515i)q10+(0.5066991.89103i)q11+(1.857493.09026i)q13+(0.291240+0.102952i)q14+(1.95920+3.39343i)q16+(2.139073.70498i)q17+(4.122481.10462i)q19+(0.9076743.38749i)q20+(0.1142860.197949i)q22+(5.539273.19810i)q231.88292iq25+(0.1160970.404635i)q26+(5.239460.409435i)q28+(3.57954+6.19995i)q29+(3.026283.02628i)q31+(0.359327+1.34103i)q32+(0.3531910.353191i)q34+(4.592450.853791i)q35+(0.732202+2.73261i)q37+0.498293q380.821715iq40+(2.9490111.0059i)q41+(1.552340.896243i)q43+(2.74978+2.74978i)q44+(0.7213330.193281i)q46+(4.686654.68665i)q47+(2.515816.53228i)q49+(0.05689820.212347i)q50+(0.126138+7.16084i)q524.27793q53+(2.993351.72821i)q55+(1.21065+0.225074i)q56+(0.216333+0.807367i)q58+(0.436704+1.62980i)q59+(2.66960+1.54129i)q61+(0.2498410.432737i)q627.67470iq64+(1.539016.17685i)q65+(0.01903800.00510122i)q67+(7.35945+4.24898i)q68+(0.4921150.235061i)q70+(1.231094.59449i)q71+(0.6984920.698492i)q73+(0.165148+0.286046i)q74+(8.188772.19417i)q76+(1.72631+4.88353i)q775.93719q79+(1.79052+6.68230i)q80+(0.6651511.15208i)q82+(9.876839.87683i)q83+(7.295801.95490i)q85+(0.1479830.147983i)q86+(0.789099+0.455587i)q88+(7.76240+2.07993i)q89+(8.67892+3.95934i)q9112.7052q92+(0.6701590.386917i)q94+(6.52558+3.76755i)q95+(14.26763.82300i)q97+(0.4811140.660657i)q98+O(q100)q+(0.112775 + 0.0302180i) q^{2} +(-1.72025 - 0.993184i) q^{4} +(1.24841 + 1.24841i) q^{5} +(-2.18126 + 1.49736i) q^{7} +(-0.329103 - 0.329103i) q^{8} +(0.103066 + 0.178515i) q^{10} +(0.506699 - 1.89103i) q^{11} +(-1.85749 - 3.09026i) q^{13} +(-0.291240 + 0.102952i) q^{14} +(1.95920 + 3.39343i) q^{16} +(2.13907 - 3.70498i) q^{17} +(4.12248 - 1.10462i) q^{19} +(-0.907674 - 3.38749i) q^{20} +(0.114286 - 0.197949i) q^{22} +(5.53927 - 3.19810i) q^{23} -1.88292i q^{25} +(-0.116097 - 0.404635i) q^{26} +(5.23946 - 0.409435i) q^{28} +(3.57954 + 6.19995i) q^{29} +(-3.02628 - 3.02628i) q^{31} +(0.359327 + 1.34103i) q^{32} +(0.353191 - 0.353191i) q^{34} +(-4.59245 - 0.853791i) q^{35} +(-0.732202 + 2.73261i) q^{37} +0.498293 q^{38} -0.821715i q^{40} +(2.94901 - 11.0059i) q^{41} +(-1.55234 - 0.896243i) q^{43} +(-2.74978 + 2.74978i) q^{44} +(0.721333 - 0.193281i) q^{46} +(4.68665 - 4.68665i) q^{47} +(2.51581 - 6.53228i) q^{49} +(0.0568982 - 0.212347i) q^{50} +(0.126138 + 7.16084i) q^{52} -4.27793 q^{53} +(2.99335 - 1.72821i) q^{55} +(1.21065 + 0.225074i) q^{56} +(0.216333 + 0.807367i) q^{58} +(0.436704 + 1.62980i) q^{59} +(2.66960 + 1.54129i) q^{61} +(-0.249841 - 0.432737i) q^{62} -7.67470i q^{64} +(1.53901 - 6.17685i) q^{65} +(-0.0190380 - 0.00510122i) q^{67} +(-7.35945 + 4.24898i) q^{68} +(-0.492115 - 0.235061i) q^{70} +(-1.23109 - 4.59449i) q^{71} +(0.698492 - 0.698492i) q^{73} +(-0.165148 + 0.286046i) q^{74} +(-8.18877 - 2.19417i) q^{76} +(1.72631 + 4.88353i) q^{77} -5.93719 q^{79} +(-1.79052 + 6.68230i) q^{80} +(0.665151 - 1.15208i) q^{82} +(-9.87683 - 9.87683i) q^{83} +(7.29580 - 1.95490i) q^{85} +(-0.147983 - 0.147983i) q^{86} +(-0.789099 + 0.455587i) q^{88} +(7.76240 + 2.07993i) q^{89} +(8.67892 + 3.95934i) q^{91} -12.7052 q^{92} +(0.670159 - 0.386917i) q^{94} +(6.52558 + 3.76755i) q^{95} +(14.2676 - 3.82300i) q^{97} +(0.481114 - 0.660657i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+8q212q4+16q8+4q11+32q14+12q16+4q22+12q23+24q284q294q32+20q35+4q3748q4324q44+84q46+24q49+44q50++32q98+O(q100) 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50}+ \cdots + 32 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/819Z)×\left(\mathbb{Z}/819\mathbb{Z}\right)^\times.

nn 9292 379379 703703
χ(n)\chi(n) 11 e(112)e\left(\frac{1}{12}\right) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.112775 + 0.0302180i 0.0797441 + 0.0213674i 0.298471 0.954419i 0.403524π-0.403524\pi
−0.218726 + 0.975786i 0.570190π0.570190\pi
33 0 0
44 −1.72025 0.993184i −0.860123 0.496592i
55 1.24841 + 1.24841i 0.558308 + 0.558308i 0.928825 0.370518i 0.120820π-0.120820\pi
−0.370518 + 0.928825i 0.620820π0.620820\pi
66 0 0
77 −2.18126 + 1.49736i −0.824440 + 0.565950i
88 −0.329103 0.329103i −0.116356 0.116356i
99 0 0
1010 0.103066 + 0.178515i 0.0325922 + 0.0564514i
1111 0.506699 1.89103i 0.152775 0.570166i −0.846510 0.532373i 0.821301π-0.821301\pi
0.999286 0.0377930i 0.0120328π-0.0120328\pi
1212 0 0
1313 −1.85749 3.09026i −0.515175 0.857085i
1414 −0.291240 + 0.102952i −0.0778371 + 0.0275151i
1515 0 0
1616 1.95920 + 3.39343i 0.489800 + 0.848358i
1717 2.13907 3.70498i 0.518801 0.898589i −0.480960 0.876742i 0.659712π-0.659712\pi
0.999761 0.0218471i 0.00695471π-0.00695471\pi
1818 0 0
1919 4.12248 1.10462i 0.945762 0.253416i 0.247199 0.968965i 0.420490π-0.420490\pi
0.698563 + 0.715549i 0.253823π0.253823\pi
2020 −0.907674 3.38749i −0.202962 0.757465i
2121 0 0
2222 0.114286 0.197949i 0.0243659 0.0422030i
2323 5.53927 3.19810i 1.15502 0.666850i 0.204913 0.978780i 0.434309π-0.434309\pi
0.950105 + 0.311930i 0.100976π0.100976\pi
2424 0 0
2525 1.88292i 0.376585i
2626 −0.116097 0.404635i −0.0227685 0.0793554i
2727 0 0
2828 5.23946 0.409435i 0.990166 0.0773760i
2929 3.57954 + 6.19995i 0.664704 + 1.15130i 0.979365 + 0.202097i 0.0647758π0.0647758\pi
−0.314661 + 0.949204i 0.601891π0.601891\pi
3030 0 0
3131 −3.02628 3.02628i −0.543535 0.543535i 0.381028 0.924563i 0.375570π-0.375570\pi
−0.924563 + 0.381028i 0.875570π0.875570\pi
3232 0.359327 + 1.34103i 0.0635206 + 0.237062i
3333 0 0
3434 0.353191 0.353191i 0.0605718 0.0605718i
3535 −4.59245 0.853791i −0.776265 0.144317i
3636 0 0
3737 −0.732202 + 2.73261i −0.120373 + 0.449239i −0.999633 0.0271042i 0.991371π-0.991371\pi
0.879259 + 0.476343i 0.158038π0.158038\pi
3838 0.498293 0.0808338
3939 0 0
4040 0.821715i 0.129925i
4141 2.94901 11.0059i 0.460558 1.71883i −0.210654 0.977561i 0.567559π-0.567559\pi
0.671212 0.741266i 0.265774π-0.265774\pi
4242 0 0
4343 −1.55234 0.896243i −0.236730 0.136676i 0.376943 0.926236i 0.376975π-0.376975\pi
−0.613673 + 0.789561i 0.710309π0.710309\pi
4444 −2.74978 + 2.74978i −0.414545 + 0.414545i
4545 0 0
4646 0.721333 0.193281i 0.106355 0.0284977i
4747 4.68665 4.68665i 0.683618 0.683618i −0.277196 0.960814i 0.589405π-0.589405\pi
0.960814 + 0.277196i 0.0894050π0.0894050\pi
4848 0 0
4949 2.51581 6.53228i 0.359402 0.933183i
5050 0.0568982 0.212347i 0.00804663 0.0300304i
5151 0 0
5252 0.126138 + 7.16084i 0.0174922 + 0.993030i
5353 −4.27793 −0.587619 −0.293809 0.955864i 0.594923π-0.594923\pi
−0.293809 + 0.955864i 0.594923π0.594923\pi
5454 0 0
5555 2.99335 1.72821i 0.403624 0.233032i
5656 1.21065 + 0.225074i 0.161780 + 0.0300768i
5757 0 0
5858 0.216333 + 0.807367i 0.0284060 + 0.106013i
5959 0.436704 + 1.62980i 0.0568541 + 0.212182i 0.988509 0.151162i 0.0483015π-0.0483015\pi
−0.931655 + 0.363344i 0.881635π0.881635\pi
6060 0 0
6161 2.66960 + 1.54129i 0.341807 + 0.197342i 0.661071 0.750323i 0.270102π-0.270102\pi
−0.319264 + 0.947666i 0.603436π0.603436\pi
6262 −0.249841 0.432737i −0.0317298 0.0549577i
6363 0 0
6464 7.67470i 0.959338i
6565 1.53901 6.17685i 0.190891 0.766144i
6666 0 0
6767 −0.0190380 0.00510122i −0.00232586 0.000623213i 0.257656 0.966237i 0.417050π-0.417050\pi
−0.259982 + 0.965614i 0.583717π0.583717\pi
6868 −7.35945 + 4.24898i −0.892465 + 0.515265i
6969 0 0
7070 −0.492115 0.235061i −0.0588189 0.0280952i
7171 −1.23109 4.59449i −0.146104 0.545266i −0.999704 0.0243373i 0.992252π-0.992252\pi
0.853600 0.520929i 0.174414π-0.174414\pi
7272 0 0
7373 0.698492 0.698492i 0.0817523 0.0817523i −0.665048 0.746800i 0.731589π-0.731589\pi
0.746800 + 0.665048i 0.231589π0.231589\pi
7474 −0.165148 + 0.286046i −0.0191981 + 0.0332521i
7575 0 0
7676 −8.18877 2.19417i −0.939316 0.251689i
7777 1.72631 + 4.88353i 0.196731 + 0.556530i
7878 0 0
7979 −5.93719 −0.667987 −0.333993 0.942575i 0.608396π-0.608396\pi
−0.333993 + 0.942575i 0.608396π0.608396\pi
8080 −1.79052 + 6.68230i −0.200186 + 0.747104i
8181 0 0
8282 0.665151 1.15208i 0.0734536 0.127225i
8383 −9.87683 9.87683i −1.08412 1.08412i −0.996120 0.0880033i 0.971951π-0.971951\pi
−0.0880033 0.996120i 0.528049π-0.528049\pi
8484 0 0
8585 7.29580 1.95490i 0.791340 0.212039i
8686 −0.147983 0.147983i −0.0159574 0.0159574i
8787 0 0
8888 −0.789099 + 0.455587i −0.0841183 + 0.0485657i
8989 7.76240 + 2.07993i 0.822813 + 0.220472i 0.645576 0.763696i 0.276617π-0.276617\pi
0.177237 + 0.984168i 0.443284π0.443284\pi
9090 0 0
9191 8.67892 + 3.95934i 0.909798 + 0.415052i
9292 −12.7052 −1.32461
9393 0 0
9494 0.670159 0.386917i 0.0691216 0.0399074i
9595 6.52558 + 3.76755i 0.669511 + 0.386542i
9696 0 0
9797 14.2676 3.82300i 1.44866 0.388167i 0.553102 0.833113i 0.313444π-0.313444\pi
0.895557 + 0.444946i 0.146777π0.146777\pi
9898 0.481114 0.660657i 0.0485999 0.0667364i
9999 0 0
100100 −1.87009 + 3.23909i −0.187009 + 0.323909i
101101 8.00479 + 13.8647i 0.796506 + 1.37959i 0.921878 + 0.387480i 0.126654π0.126654\pi
−0.125372 + 0.992110i 0.540012π0.540012\pi
102102 0 0
103103 −11.8151 −1.16418 −0.582088 0.813126i 0.697764π-0.697764\pi
−0.582088 + 0.813126i 0.697764π0.697764\pi
104104 −0.405710 + 1.62832i −0.0397831 + 0.159670i
105105 0 0
106106 −0.482444 0.129271i −0.0468591 0.0125559i
107107 3.99556 + 6.92051i 0.386265 + 0.669031i 0.991944 0.126678i 0.0404316π-0.0404316\pi
−0.605679 + 0.795709i 0.707098π0.707098\pi
108108 0 0
109109 −8.75647 + 8.75647i −0.838718 + 0.838718i −0.988690 0.149972i 0.952082π-0.952082\pi
0.149972 + 0.988690i 0.452082π0.452082\pi
110110 0.389799 0.104446i 0.0371659 0.00995857i
111111 0 0
112112 −9.35472 4.46833i −0.883938 0.422218i
113113 −4.27217 + 7.39961i −0.401892 + 0.696097i −0.993954 0.109795i 0.964981π-0.964981\pi
0.592063 + 0.805892i 0.298314π0.298314\pi
114114 0 0
115115 10.9079 + 2.92275i 1.01716 + 0.272548i
116116 14.2206i 1.32035i
117117 0 0
118118 0.196998i 0.0181351i
119119 0.881822 + 11.2845i 0.0808365 + 1.03445i
120120 0 0
121121 6.20705 + 3.58364i 0.564277 + 0.325785i
122122 0.254490 + 0.254490i 0.0230404 + 0.0230404i
123123 0 0
124124 2.20029 + 8.21159i 0.197592 + 0.737422i
125125 8.59274 8.59274i 0.768558 0.768558i
126126 0 0
127127 −5.29483 + 3.05697i −0.469840 + 0.271262i −0.716173 0.697923i 0.754108π-0.754108\pi
0.246333 + 0.969185i 0.420774π0.420774\pi
128128 0.950568 3.54757i 0.0840191 0.313564i
129129 0 0
130130 0.360215 0.650090i 0.0315929 0.0570166i
131131 5.76435i 0.503634i 0.967775 + 0.251817i 0.0810280π0.0810280\pi
−0.967775 + 0.251817i 0.918972π0.918972\pi
132132 0 0
133133 −7.33820 + 8.58230i −0.636303 + 0.744180i
134134 −0.00199287 0.00115058i −0.000172157 9.93951e-5i
135135 0 0
136136 −1.92330 + 0.515346i −0.164921 + 0.0441905i
137137 6.06188 1.62427i 0.517901 0.138771i 0.00960548 0.999954i 0.496942π-0.496942\pi
0.508296 + 0.861183i 0.330276π0.330276\pi
138138 0 0
139139 −18.1314 10.4682i −1.53789 0.887900i −0.998962 0.0455477i 0.985497π-0.985497\pi
−0.538927 0.842353i 0.681170π-0.681170\pi
140140 7.05217 + 6.02988i 0.596017 + 0.509618i
141141 0 0
142142 0.555346i 0.0466036i
143143 −6.78495 + 1.94673i −0.567386 + 0.162794i
144144 0 0
145145 −3.27135 + 12.2089i −0.271671 + 1.01389i
146146 0.0998797 0.0576656i 0.00826610 0.00477244i
147147 0 0
148148 3.97356 3.97356i 0.326624 0.326624i
149149 −4.00070 14.9308i −0.327750 1.22318i −0.911518 0.411260i 0.865089π-0.865089\pi
0.583768 0.811921i 0.301578π-0.301578\pi
150150 0 0
151151 3.12599 + 3.12599i 0.254390 + 0.254390i 0.822768 0.568378i 0.192429π-0.192429\pi
−0.568378 + 0.822768i 0.692429π0.692429\pi
152152 −1.72026 0.993190i −0.139531 0.0805583i
153153 0 0
154154 0.0471139 + 0.602907i 0.00379655 + 0.0485837i
155155 7.55609i 0.606920i
156156 0 0
157157 6.93064i 0.553125i −0.960996 0.276563i 0.910805π-0.910805\pi
0.960996 0.276563i 0.0891953π-0.0891953\pi
158158 −0.669569 0.179410i −0.0532680 0.0142731i
159159 0 0
160160 −1.22557 + 2.12274i −0.0968896 + 0.167818i
161161 −7.29389 + 15.2702i −0.574839 + 1.20346i
162162 0 0
163163 −12.4944 + 3.34785i −0.978634 + 0.262224i −0.712469 0.701703i 0.752423π-0.752423\pi
−0.266165 + 0.963928i 0.585757π0.585757\pi
164164 −16.0039 + 16.0039i −1.24969 + 1.24969i
165165 0 0
166166 −0.815404 1.41232i −0.0632876 0.109617i
167167 0.900490 + 0.241286i 0.0696820 + 0.0186712i 0.293492 0.955962i 0.405183π-0.405183\pi
−0.223810 + 0.974633i 0.571849π0.571849\pi
168168 0 0
169169 −6.09946 + 11.4803i −0.469189 + 0.883098i
170170 0.881858 0.0676355
171171 0 0
172172 1.78027 + 3.08352i 0.135744 + 0.235116i
173173 0.263780 0.456880i 0.0200548 0.0347360i −0.855824 0.517267i 0.826949π-0.826949\pi
0.875879 + 0.482531i 0.160283π0.160283\pi
174174 0 0
175175 2.81942 + 4.10715i 0.213128 + 0.310471i
176176 7.40979 1.98545i 0.558534 0.149659i
177177 0 0
178178 0.812555 + 0.469129i 0.0609036 + 0.0351627i
179179 −7.16206 + 4.13502i −0.535317 + 0.309066i −0.743179 0.669093i 0.766683π-0.766683\pi
0.207862 + 0.978158i 0.433350π0.433350\pi
180180 0 0
181181 14.9785 1.11334 0.556672 0.830732i 0.312078π-0.312078\pi
0.556672 + 0.830732i 0.312078π0.312078\pi
182182 0.859124 + 0.708775i 0.0636825 + 0.0525379i
183183 0 0
184184 −2.87550 0.770488i −0.211985 0.0568011i
185185 −4.32553 + 2.49734i −0.318019 + 0.183608i
186186 0 0
187187 −5.92234 5.92234i −0.433085 0.433085i
188188 −12.7169 + 3.40748i −0.927475 + 0.248516i
189189 0 0
190190 0.622076 + 0.622076i 0.0451301 + 0.0451301i
191191 −7.26461 + 12.5827i −0.525649 + 0.910450i 0.473905 + 0.880576i 0.342844π0.342844\pi
−0.999554 + 0.0298741i 0.990489π0.990489\pi
192192 0 0
193193 5.06711 18.9107i 0.364738 1.36122i −0.503037 0.864265i 0.667784π-0.667784\pi
0.867775 0.496957i 0.165549π-0.165549\pi
194194 1.72456 0.123816
195195 0 0
196196 −10.8156 + 8.73846i −0.772541 + 0.624176i
197197 21.0175 + 5.63163i 1.49744 + 0.401237i 0.912240 0.409655i 0.134351π-0.134351\pi
0.585196 + 0.810892i 0.301018π0.301018\pi
198198 0 0
199199 −9.64065 + 16.6981i −0.683408 + 1.18370i 0.290527 + 0.956867i 0.406170π0.406170\pi
−0.973934 + 0.226830i 0.927164π0.927164\pi
200200 −0.619676 + 0.619676i −0.0438177 + 0.0438177i
201201 0 0
202202 0.483778 + 1.80548i 0.0340385 + 0.127033i
203203 −17.0915 8.16384i −1.19959 0.572989i
204204 0 0
205205 17.4215 10.0583i 1.21677 0.702501i
206206 −1.33245 0.357029i −0.0928363 0.0248754i
207207 0 0
208208 6.84741 12.3577i 0.474782 0.856853i
209209 8.35542i 0.577957i
210210 0 0
211211 1.51130 + 2.61764i 0.104042 + 0.180206i 0.913346 0.407184i 0.133489π-0.133489\pi
−0.809304 + 0.587389i 0.800156π0.800156\pi
212212 7.35909 + 4.24877i 0.505424 + 0.291807i
213213 0 0
214214 0.241476 + 0.901200i 0.0165070 + 0.0616048i
215215 −0.819079 3.05685i −0.0558607 0.208475i
216216 0 0
217217 11.1325 + 2.06967i 0.755726 + 0.140498i
218218 −1.25212 + 0.722910i −0.0848040 + 0.0489616i
219219 0 0
220220 −6.86574 −0.462888
221221 −15.4227 + 0.271670i −1.03744 + 0.0182745i
222222 0 0
223223 1.13865 4.24949i 0.0762495 0.284567i −0.917264 0.398279i 0.869608π-0.869608\pi
0.993514 + 0.113712i 0.0362742π0.0362742\pi
224224 −2.79179 2.38709i −0.186534 0.159494i
225225 0 0
226226 −0.705396 + 0.705396i −0.0469223 + 0.0469223i
227227 3.95917 1.06086i 0.262780 0.0704116i −0.125024 0.992154i 0.539901π-0.539901\pi
0.387803 + 0.921742i 0.373234π0.373234\pi
228228 0 0
229229 9.60039 9.60039i 0.634412 0.634412i −0.314760 0.949171i 0.601924π-0.601924\pi
0.949171 + 0.314760i 0.101924π0.101924\pi
230230 1.14182 + 0.659228i 0.0752892 + 0.0434682i
231231 0 0
232232 0.862385 3.21846i 0.0566183 0.211303i
233233 16.3500i 1.07113i −0.844495 0.535563i 0.820100π-0.820100\pi
0.844495 0.535563i 0.179900π-0.179900\pi
234234 0 0
235235 11.7018 0.763339
236236 0.867456 3.23739i 0.0564666 0.210736i
237237 0 0
238238 −0.241548 + 1.29926i −0.0156572 + 0.0842184i
239239 −6.11495 + 6.11495i −0.395543 + 0.395543i −0.876658 0.481115i 0.840232π-0.840232\pi
0.481115 + 0.876658i 0.340232π0.340232\pi
240240 0 0
241241 3.47625 + 12.9736i 0.223925 + 0.835700i 0.982832 + 0.184501i 0.0590670π0.0590670\pi
−0.758907 + 0.651199i 0.774266π0.774266\pi
242242 0.591711 + 0.591711i 0.0380366 + 0.0380366i
243243 0 0
244244 −3.06158 5.30281i −0.195997 0.339478i
245245 11.2958 5.01422i 0.721660 0.320347i
246246 0 0
247247 −11.0710 10.6877i −0.704432 0.680045i
248248 1.99192i 0.126487i
249249 0 0
250250 1.22870 0.709393i 0.0777101 0.0448659i
251251 1.74301 3.01899i 0.110018 0.190557i −0.805759 0.592243i 0.798242π-0.798242\pi
0.915777 + 0.401686i 0.131576π0.131576\pi
252252 0 0
253253 −3.24095 12.0954i −0.203756 0.760430i
254254 −0.689501 + 0.184751i −0.0432631 + 0.0115923i
255255 0 0
256256 −7.46030 + 12.9216i −0.466269 + 0.807601i
257257 −6.72396 11.6462i −0.419429 0.726472i 0.576453 0.817130i 0.304436π-0.304436\pi
−0.995882 + 0.0906578i 0.971103π0.971103\pi
258258 0 0
259259 −2.49459 7.05692i −0.155006 0.438496i
260260 −8.78223 + 9.09717i −0.544651 + 0.564183i
261261 0 0
262262 −0.174187 + 0.650076i −0.0107613 + 0.0401618i
263263 10.2679 + 17.7846i 0.633147 + 1.09664i 0.986904 + 0.161306i 0.0515705π0.0515705\pi
−0.353757 + 0.935337i 0.615096π0.615096\pi
264264 0 0
265265 −5.34063 5.34063i −0.328072 0.328072i
266266 −1.08691 + 0.746125i −0.0666426 + 0.0457479i
267267 0 0
268268 0.0276836 + 0.0276836i 0.00169104 + 0.00169104i
269269 9.29875 + 5.36864i 0.566955 + 0.327332i 0.755932 0.654650i 0.227184π-0.227184\pi
−0.188977 + 0.981981i 0.560517π0.560517\pi
270270 0 0
271271 −1.44767 0.387901i −0.0879396 0.0235633i 0.214581 0.976706i 0.431161π-0.431161\pi
−0.302521 + 0.953143i 0.597828π0.597828\pi
272272 16.7635 1.01643
273273 0 0
274274 0.732712 0.0442647
275275 −3.56065 0.954075i −0.214716 0.0575329i
276276 0 0
277277 4.07919 + 2.35512i 0.245095 + 0.141506i 0.617516 0.786558i 0.288139π-0.288139\pi
−0.372421 + 0.928064i 0.621472π0.621472\pi
278278 −1.72845 1.72845i −0.103666 0.103666i
279279 0 0
280280 1.23041 + 1.79238i 0.0735308 + 0.107115i
281281 −8.01227 8.01227i −0.477972 0.477972i 0.426511 0.904483i 0.359743π-0.359743\pi
−0.904483 + 0.426511i 0.859743π0.859743\pi
282282 0 0
283283 −3.93934 6.82313i −0.234169 0.405593i 0.724862 0.688894i 0.241904π-0.241904\pi
−0.959031 + 0.283301i 0.908570π0.908570\pi
284284 −2.44540 + 9.12636i −0.145108 + 0.541550i
285285 0 0
286286 −0.824001 + 0.0145147i −0.0487242 + 0.000858275i
287287 10.0472 + 28.4224i 0.593067 + 1.67772i
288288 0 0
289289 −0.651246 1.12799i −0.0383086 0.0663525i
290290 −0.737855 + 1.27800i −0.0433284 + 0.0750469i
291291 0 0
292292 −1.89531 + 0.507847i −0.110915 + 0.0297195i
293293 −3.16216 11.8013i −0.184735 0.689442i −0.994687 0.102945i 0.967173π-0.967173\pi
0.809952 0.586497i 0.199493π-0.199493\pi
294294 0 0
295295 −1.48948 + 2.57986i −0.0867210 + 0.150205i
296296 1.14028 0.658343i 0.0662776 0.0382654i
297297 0 0
298298 1.80472i 0.104545i
299299 −20.1721 11.1774i −1.16658 0.646404i
300300 0 0
301301 4.72806 0.369472i 0.272521 0.0212960i
302302 0.258073 + 0.446996i 0.0148504 + 0.0257217i
303303 0 0
304304 11.8252 + 11.8252i 0.678221 + 0.678221i
305305 1.40859 + 5.25694i 0.0806558 + 0.301011i
306306 0 0
307307 −7.97207 + 7.97207i −0.454990 + 0.454990i −0.897007 0.442017i 0.854263π-0.854263\pi
0.442017 + 0.897007i 0.354263π0.354263\pi
308308 1.88058 10.1154i 0.107156 0.576380i
309309 0 0
310310 0.228330 0.852140i 0.0129683 0.0483983i
311311 13.0428 0.739588 0.369794 0.929114i 0.379428π-0.379428\pi
0.369794 + 0.929114i 0.379428π0.379428\pi
312312 0 0
313313 3.57391i 0.202009i 0.994886 + 0.101005i 0.0322057π0.0322057\pi
−0.994886 + 0.101005i 0.967794π0.967794\pi
314314 0.209430 0.781604i 0.0118188 0.0441085i
315315 0 0
316316 10.2134 + 5.89673i 0.574551 + 0.331717i
317317 −23.4565 + 23.4565i −1.31745 + 1.31745i −0.401662 + 0.915788i 0.631567π0.631567\pi
−0.915788 + 0.401662i 0.868433π0.868433\pi
318318 0 0
319319 13.5380 3.62750i 0.757983 0.203101i
320320 9.58121 9.58121i 0.535606 0.535606i
321321 0 0
322322 −1.28401 + 1.50169i −0.0715548 + 0.0836860i
323323 4.72570 17.6366i 0.262945 0.981324i
324324 0 0
325325 −5.81873 + 3.49751i −0.322765 + 0.194007i
326326 −1.51022 −0.0836434
327327 0 0
328328 −4.59260 + 2.65154i −0.253584 + 0.146407i
329329 −3.20520 + 17.2404i −0.176708 + 0.950495i
330330 0 0
331331 −0.245395 0.915826i −0.0134881 0.0503383i 0.958854 0.283900i 0.0916285π-0.0916285\pi
−0.972342 + 0.233562i 0.924962π0.924962\pi
332332 7.18106 + 26.8001i 0.394112 + 1.47085i
333333 0 0
334334 0.0942618 + 0.0544221i 0.00515778 + 0.00297784i
335335 −0.0173989 0.0301357i −0.000950602 0.00164649i
336336 0 0
337337 14.1901i 0.772982i 0.922293 + 0.386491i 0.126313π0.126313\pi
−0.922293 + 0.386491i 0.873687π0.873687\pi
338338 −1.03478 + 1.11038i −0.0562846 + 0.0603965i
339339 0 0
340340 −14.4921 3.88316i −0.785947 0.210594i
341341 −7.25617 + 4.18935i −0.392944 + 0.226866i
342342 0 0
343343 4.29355 + 18.0157i 0.231830 + 0.972756i
344344 0.215923 + 0.805837i 0.0116418 + 0.0434478i
345345 0 0
346346 0.0435539 0.0435539i 0.00234147 0.00234147i
347347 6.92103 11.9876i 0.371540 0.643527i −0.618262 0.785972i 0.712163π-0.712163\pi
0.989803 + 0.142445i 0.0454965π0.0454965\pi
348348 0 0
349349 14.7875 + 3.96231i 0.791559 + 0.212098i 0.631875 0.775071i 0.282286π-0.282286\pi
0.159684 + 0.987168i 0.448952π0.448952\pi
350350 0.193851 + 0.548382i 0.0103617 + 0.0293123i
351351 0 0
352352 2.71798 0.144869
353353 4.07649 15.2137i 0.216970 0.809742i −0.768494 0.639857i 0.778994π-0.778994\pi
0.985464 0.169885i 0.0543398π-0.0543398\pi
354354 0 0
355355 4.19892 7.27274i 0.222856 0.385997i
356356 −11.2875 11.2875i −0.598235 0.598235i
357357 0 0
358358 −0.932655 + 0.249904i −0.0492924 + 0.0132078i
359359 4.68787 + 4.68787i 0.247416 + 0.247416i 0.819910 0.572493i 0.194024π-0.194024\pi
−0.572493 + 0.819910i 0.694024π0.694024\pi
360360 0 0
361361 −0.679814 + 0.392491i −0.0357797 + 0.0206574i
362362 1.68920 + 0.452621i 0.0887826 + 0.0237892i
363363 0 0
364364 −10.9975 15.4308i −0.576427 0.808794i
365365 1.74402 0.0912859
366366 0 0
367367 28.4547 16.4284i 1.48533 0.857553i 0.485465 0.874256i 0.338650π-0.338650\pi
0.999860 + 0.0167033i 0.00531706π0.00531706\pi
368368 21.7051 + 12.5314i 1.13145 + 0.653246i
369369 0 0
370370 −0.563277 + 0.150930i −0.0292834 + 0.00784646i
371371 9.33128 6.40561i 0.484456 0.332563i
372372 0 0
373373 −3.93986 + 6.82405i −0.203998 + 0.353336i −0.949813 0.312818i 0.898727π-0.898727\pi
0.745815 + 0.666153i 0.232060π0.232060\pi
374374 −0.488932 0.846855i −0.0252821 0.0437899i
375375 0 0
376376 −3.08478 −0.159086
377377 12.5105 22.5781i 0.644324 1.16283i
378378 0 0
379379 10.8095 + 2.89639i 0.555245 + 0.148778i 0.525521 0.850781i 0.323870π-0.323870\pi
0.0297243 + 0.999558i 0.490537π0.490537\pi
380380 −7.48374 12.9622i −0.383908 0.664947i
381381 0 0
382382 −1.19949 + 1.19949i −0.0613713 + 0.0613713i
383383 −2.32841 + 0.623897i −0.118976 + 0.0318796i −0.317816 0.948152i 0.602949π-0.602949\pi
0.198840 + 0.980032i 0.436283π0.436283\pi
384384 0 0
385385 −3.94153 + 8.25182i −0.200879 + 0.420552i
386386 1.14289 1.97954i 0.0581715 0.100756i
387387 0 0
388388 −28.3408 7.59389i −1.43879 0.385522i
389389 16.8210i 0.852858i −0.904521 0.426429i 0.859771π-0.859771\pi
0.904521 0.426429i 0.140229π-0.140229\pi
390390 0 0
391391 27.3638i 1.38385i
392392 −2.97776 + 1.32183i −0.150400 + 0.0667627i
393393 0 0
394394 2.20008 + 1.27022i 0.110838 + 0.0639926i
395395 −7.41208 7.41208i −0.372942 0.372942i
396396 0 0
397397 −6.08873 22.7234i −0.305585 1.14046i −0.932441 0.361322i 0.882325π-0.882325\pi
0.626856 0.779135i 0.284341π-0.284341\pi
398398 −1.59181 + 1.59181i −0.0797903 + 0.0797903i
399399 0 0
400400 6.38957 3.68902i 0.319479 0.184451i
401401 −2.23318 + 8.33434i −0.111520 + 0.416197i −0.999003 0.0446427i 0.985785π-0.985785\pi
0.887483 + 0.460840i 0.152452π0.152452\pi
402402 0 0
403403 −3.73071 + 14.9733i −0.185840 + 0.745872i
404404 31.8009i 1.58216i
405405 0 0
406406 −1.68080 1.43715i −0.0834168 0.0713246i
407407 4.79644 + 2.76922i 0.237751 + 0.137265i
408408 0 0
409409 −12.9780 + 3.47744i −0.641720 + 0.171948i −0.564982 0.825103i 0.691117π-0.691117\pi
−0.0767375 + 0.997051i 0.524450π0.524450\pi
410410 2.26865 0.607883i 0.112041 0.0300212i
411411 0 0
412412 20.3249 + 11.7346i 1.00133 + 0.578121i
413413 −3.39297 2.90112i −0.166957 0.142755i
414414 0 0
415415 24.6608i 1.21055i
416416 3.47668 3.60136i 0.170458 0.176571i
417417 0 0
418418 0.252484 0.942285i 0.0123494 0.0460886i
419419 15.0514 8.68991i 0.735308 0.424530i −0.0850532 0.996376i 0.527106π-0.527106\pi
0.820361 + 0.571846i 0.193773π0.193773\pi
420420 0 0
421421 −21.2490 + 21.2490i −1.03561 + 1.03561i −0.0362722 + 0.999342i 0.511548π0.511548\pi
−0.999342 + 0.0362722i 0.988452π0.988452\pi
422422 0.0913368 + 0.340874i 0.00444621 + 0.0165935i
423423 0 0
424424 1.40788 + 1.40788i 0.0683727 + 0.0683727i
425425 −6.97619 4.02771i −0.338395 0.195372i
426426 0 0
427427 −8.13097 + 0.635391i −0.393485 + 0.0307487i
428428 15.8733i 0.767265i
429429 0 0
430430 0.369487i 0.0178183i
431431 −23.3087 6.24554i −1.12274 0.300837i −0.350748 0.936470i 0.614073π-0.614073\pi
−0.771991 + 0.635633i 0.780739π0.780739\pi
432432 0 0
433433 −2.27124 + 3.93391i −0.109149 + 0.189051i −0.915426 0.402487i 0.868146π-0.868146\pi
0.806277 + 0.591538i 0.201479π0.201479\pi
434434 1.19293 + 0.569811i 0.0572626 + 0.0273518i
435435 0 0
436436 23.7601 6.36649i 1.13790 0.304900i
437437 19.3029 19.3029i 0.923381 0.923381i
438438 0 0
439439 8.50036 + 14.7231i 0.405700 + 0.702693i 0.994403 0.105657i 0.0336944π-0.0336944\pi
−0.588703 + 0.808350i 0.700361π0.700361\pi
440440 −1.55388 0.416362i −0.0740785 0.0198493i
441441 0 0
442442 −1.74750 0.435405i −0.0831203 0.0207101i
443443 36.6165 1.73970 0.869851 0.493315i 0.164215π-0.164215\pi
0.869851 + 0.493315i 0.164215π0.164215\pi
444444 0 0
445445 7.09408 + 12.2873i 0.336292 + 0.582474i
446446 0.256823 0.444830i 0.0121609 0.0210633i
447447 0 0
448448 11.4918 + 16.7405i 0.542937 + 0.790916i
449449 32.7480 8.77481i 1.54547 0.414109i 0.617445 0.786614i 0.288168π-0.288168\pi
0.928030 + 0.372505i 0.121501π0.121501\pi
450450 0 0
451451 −19.3181 11.1533i −0.909654 0.525189i
452452 14.6984 8.48610i 0.691353 0.399153i
453453 0 0
454454 0.478554 0.0224596
455455 5.89199 + 15.7778i 0.276221 + 0.739674i
456456 0 0
457457 −2.18565 0.585644i −0.102241 0.0273953i 0.207336 0.978270i 0.433521π-0.433521\pi
−0.309577 + 0.950874i 0.600187π0.600187\pi
458458 1.37279 0.792582i 0.0641463 0.0370349i
459459 0 0
460460 −15.8614 15.8614i −0.739540 0.739540i
461461 24.5455 6.57694i 1.14320 0.306319i 0.362961 0.931804i 0.381766π-0.381766\pi
0.780235 + 0.625486i 0.215099π0.215099\pi
462462 0 0
463463 −22.6265 22.6265i −1.05154 1.05154i −0.998597 0.0529442i 0.983139π-0.983139\pi
−0.0529442 0.998597i 0.516861π-0.516861\pi
464464 −14.0261 + 24.2939i −0.651144 + 1.12781i
465465 0 0
466466 0.494066 1.84388i 0.0228871 0.0854160i
467467 11.2941 0.522627 0.261314 0.965254i 0.415844π-0.415844\pi
0.261314 + 0.965254i 0.415844π0.415844\pi
468468 0 0
469469 0.0491652 0.0173797i 0.00227024 0.000802520i
470470 1.31967 + 0.353604i 0.0608718 + 0.0163105i
471471 0 0
472472 0.392653 0.680095i 0.0180733 0.0313039i
473473 −2.48139 + 2.48139i −0.114094 + 0.114094i
474474 0 0
475475 −2.07991 7.76231i −0.0954326 0.356159i
476476 9.69063 20.2879i 0.444169 0.929895i
477477 0 0
478478 −0.874396 + 0.504833i −0.0399939 + 0.0230905i
479479 −19.3716 5.19059i −0.885109 0.237164i −0.212499 0.977161i 0.568160π-0.568160\pi
−0.672610 + 0.739997i 0.734827π0.734827\pi
480480 0 0
481481 9.80456 2.81311i 0.447049 0.128267i
482482 1.56814i 0.0714269i
483483 0 0
484484 −7.11843 12.3295i −0.323565 0.560431i
485485 22.5846 + 13.0392i 1.02551 + 0.592081i
486486 0 0
487487 −8.13109 30.3456i −0.368455 1.37509i −0.862676 0.505756i 0.831213π-0.831213\pi
0.494221 0.869336i 0.335453π-0.335453\pi
488488 −0.371329 1.38582i −0.0168093 0.0627331i
489489 0 0
490490 1.42540 0.224144i 0.0643931 0.0101258i
491491 16.8341 9.71919i 0.759714 0.438621i −0.0694792 0.997583i 0.522134π-0.522134\pi
0.829193 + 0.558962i 0.188800π0.188800\pi
492492 0 0
493493 30.6276 1.37940
494494 −0.925574 1.53986i −0.0416436 0.0692814i
495495 0 0
496496 4.34038 16.1985i 0.194889 0.727336i
497497 9.56495 + 8.17841i 0.429047 + 0.366852i
498498 0 0
499499 11.8051 11.8051i 0.528471 0.528471i −0.391645 0.920116i 0.628094π-0.628094\pi
0.920116 + 0.391645i 0.128094π0.128094\pi
500500 −23.3158 + 6.24745i −1.04271 + 0.279394i
501501 0 0
502502 0.287797 0.287797i 0.0128450 0.0128450i
503503 −25.9585 14.9871i −1.15743 0.668243i −0.206743 0.978395i 0.566287π-0.566287\pi
−0.950687 + 0.310153i 0.899620π0.899620\pi
504504 0 0
505505 −7.31560 + 27.3022i −0.325540 + 1.21493i
506506 1.46199i 0.0649935i
507507 0 0
508508 12.1445 0.538827
509509 3.62928 13.5446i 0.160865 0.600356i −0.837667 0.546182i 0.816081π-0.816081\pi
0.998532 0.0541739i 0.0172525π-0.0172525\pi
510510 0 0
511511 −0.477699 + 2.56949i −0.0211322 + 0.113668i
512512 −6.42580 + 6.42580i −0.283983 + 0.283983i
513513 0 0
514514 −0.406370 1.51659i −0.0179242 0.0668940i
515515 −14.7501 14.7501i −0.649969 0.649969i
516516 0 0
517517 −6.48785 11.2373i −0.285335 0.494215i
518518 −0.0680817 0.871228i −0.00299134 0.0382795i
519519 0 0
520520 −2.53932 + 1.52633i −0.111356 + 0.0669339i
521521 0.875247i 0.0383452i 0.999816 + 0.0191726i 0.00610321π0.00610321\pi
−0.999816 + 0.0191726i 0.993897π0.993897\pi
522522 0 0
523523 −11.7198 + 6.76640i −0.512469 + 0.295874i −0.733848 0.679314i 0.762278π-0.762278\pi
0.221379 + 0.975188i 0.428944π0.428944\pi
524524 5.72506 9.91610i 0.250100 0.433187i
525525 0 0
526526 0.620553 + 2.31593i 0.0270574 + 0.100980i
527527 −17.6857 + 4.73887i −0.770401 + 0.206428i
528528 0 0
529529 8.95568 15.5117i 0.389377 0.674421i
530530 −0.440907 0.763674i −0.0191518 0.0331719i
531531 0 0
532532 21.1473 7.47548i 0.916853 0.324103i
533533 −39.4888 + 11.3301i −1.71045 + 0.490759i
534534 0 0
535535 −3.65155 + 13.6278i −0.157870 + 0.589180i
536536 0.00458664 + 0.00794430i 0.000198113 + 0.000343141i
537537 0 0
538538 0.886440 + 0.886440i 0.0382171 + 0.0382171i
539539 −11.0779 8.06736i −0.477161 0.347486i
540540 0 0
541541 8.68791 + 8.68791i 0.373522 + 0.373522i 0.868758 0.495236i 0.164918π-0.164918\pi
−0.495236 + 0.868758i 0.664918π0.664918\pi
542542 −0.151539 0.0874914i −0.00650918 0.00375808i
543543 0 0
544544 5.73710 + 1.53725i 0.245976 + 0.0659091i
545545 −21.8634 −0.936526
546546 0 0
547547 16.2786 0.696022 0.348011 0.937490i 0.386857π-0.386857\pi
0.348011 + 0.937490i 0.386857π0.386857\pi
548548 −12.0411 3.22641i −0.514371 0.137825i
549549 0 0
550550 −0.372723 0.215192i −0.0158930 0.00917582i
551551 21.6051 + 21.6051i 0.920410 + 0.920410i
552552 0 0
553553 12.9506 8.89013i 0.550715 0.378047i
554554 0.388865 + 0.388865i 0.0165213 + 0.0165213i
555555 0 0
556556 20.7937 + 36.0157i 0.881849 + 1.52741i
557557 −2.13873 + 7.98185i −0.0906210 + 0.338202i −0.996319 0.0857210i 0.972681π-0.972681\pi
0.905698 + 0.423923i 0.139347π0.139347\pi
558558 0 0
559559 0.113826 + 6.46190i 0.00481433 + 0.273309i
560560 −6.10024 17.2569i −0.257782 0.729237i
561561 0 0
562562 −0.661470 1.14570i −0.0279024 0.0483285i
563563 −14.0767 + 24.3815i −0.593261 + 1.02756i 0.400528 + 0.916284i 0.368827π0.368827\pi
−0.993790 + 0.111274i 0.964507π0.964507\pi
564564 0 0
565565 −14.5712 + 3.90435i −0.613016 + 0.164257i
566566 −0.238078 0.888519i −0.0100072 0.0373472i
567567 0 0
568568 −1.10691 + 1.91722i −0.0464448 + 0.0804447i
569569 8.62645 4.98048i 0.361640 0.208793i −0.308160 0.951335i 0.599713π-0.599713\pi
0.669800 + 0.742542i 0.266380π0.266380\pi
570570 0 0
571571 5.15214i 0.215610i 0.994172 + 0.107805i 0.0343823π0.0343823\pi
−0.994172 + 0.107805i 0.965618π0.965618\pi
572572 13.6052 + 3.38986i 0.568864 + 0.141737i
573573 0 0
574574 0.274205 + 3.50895i 0.0114451 + 0.146461i
575575 −6.02177 10.4300i −0.251125 0.434962i
576576 0 0
577577 −9.50342 9.50342i −0.395633 0.395633i 0.481057 0.876689i 0.340253π-0.340253\pi
−0.876689 + 0.481057i 0.840253π0.840253\pi
578578 −0.0393588 0.146889i −0.00163711 0.00610978i
579579 0 0
580580 17.7532 17.7532i 0.737161 0.737161i
581581 36.3332 + 6.75477i 1.50735 + 0.280235i
582582 0 0
583583 −2.16762 + 8.08967i −0.0897737 + 0.335040i
584584 −0.459752 −0.0190247
585585 0 0
586586 1.42645i 0.0589263i
587587 −9.73498 + 36.3314i −0.401806 + 1.49956i 0.408066 + 0.912952i 0.366203π0.366203\pi
−0.809872 + 0.586607i 0.800463π0.800463\pi
588588 0 0
589589 −15.8186 9.13289i −0.651795 0.376314i
590590 −0.245935 + 0.245935i −0.0101250 + 0.0101250i
591591 0 0
592592 −10.7075 + 2.86906i −0.440074 + 0.117918i
593593 −25.8396 + 25.8396i −1.06110 + 1.06110i −0.0630974 + 0.998007i 0.520098π0.520098\pi
−0.998007 + 0.0630974i 0.979902π0.979902\pi
594594 0 0
595595 −12.9868 + 15.1886i −0.532409 + 0.622672i
596596 −7.94687 + 29.6581i −0.325517 + 1.21484i
597597 0 0
598598 −1.93716 1.87009i −0.0792162 0.0764738i
599599 −5.32027 −0.217381 −0.108690 0.994076i 0.534666π-0.534666\pi
−0.108690 + 0.994076i 0.534666π0.534666\pi
600600 0 0
601601 −21.4564 + 12.3879i −0.875225 + 0.505312i −0.869081 0.494669i 0.835289π-0.835289\pi
−0.00614424 + 0.999981i 0.501956π0.501956\pi
602602 0.544373 + 0.101205i 0.0221870 + 0.00412482i
603603 0 0
604604 −2.27279 8.48216i −0.0924785 0.345134i
605605 3.27510 + 12.2228i 0.133152 + 0.496929i
606606 0 0
607607 19.5367 + 11.2795i 0.792971 + 0.457822i 0.841007 0.541024i 0.181963π-0.181963\pi
−0.0480365 + 0.998846i 0.515296π0.515296\pi
608608 2.96263 + 5.13143i 0.120151 + 0.208107i
609609 0 0
610610 0.635418i 0.0257273i
611611 −23.1884 5.77758i −0.938102 0.233736i
612612 0 0
613613 −22.2201 5.95385i −0.897459 0.240474i −0.219535 0.975605i 0.570454π-0.570454\pi
−0.677925 + 0.735131i 0.737121π0.737121\pi
614614 −1.13995 + 0.658151i −0.0460047 + 0.0265608i
615615 0 0
616616 1.03905 2.17532i 0.0418647 0.0876462i
617617 −7.79350 29.0858i −0.313755 1.17095i −0.925143 0.379618i 0.876055π-0.876055\pi
0.611389 0.791330i 0.290611π-0.290611\pi
618618 0 0
619619 7.55579 7.55579i 0.303693 0.303693i −0.538764 0.842457i 0.681109π-0.681109\pi
0.842457 + 0.538764i 0.181109π0.181109\pi
620620 −7.50459 + 12.9983i −0.301392 + 0.522026i
621621 0 0
622622 1.47090 + 0.394127i 0.0589778 + 0.0158031i
623623 −20.0462 + 7.08625i −0.803135 + 0.283905i
624624 0 0
625625 12.0400 0.481599
626626 −0.107997 + 0.403049i −0.00431641 + 0.0161091i
627627 0 0
628628 −6.88340 + 11.9224i −0.274678 + 0.475755i
629629 8.55805 + 8.55805i 0.341232 + 0.341232i
630630 0 0
631631 13.6759 3.66444i 0.544428 0.145879i 0.0238855 0.999715i 0.492396π-0.492396\pi
0.520543 + 0.853836i 0.325730π0.325730\pi
632632 1.95395 + 1.95395i 0.0777240 + 0.0777240i
633633 0 0
634634 −3.35413 + 1.93651i −0.133209 + 0.0769085i
635635 −10.4265 2.79377i −0.413763 0.110867i
636636 0 0
637637 −24.8596 + 4.35912i −0.984972 + 0.172715i
638638 1.63637 0.0647844
639639 0 0
640640 5.61554 3.24213i 0.221974 0.128157i
641641 32.0667 + 18.5137i 1.26656 + 0.731248i 0.974335 0.225102i 0.0722714π-0.0722714\pi
0.292224 + 0.956350i 0.405605π0.405605\pi
642642 0 0
643643 −33.2886 + 8.91965i −1.31277 + 0.351757i −0.846266 0.532761i 0.821155π-0.821155\pi
−0.466507 + 0.884517i 0.654488π0.654488\pi
644644 27.7134 19.0243i 1.09206 0.749662i
645645 0 0
646646 1.06588 1.84617i 0.0419366 0.0726364i
647647 −3.03363 5.25440i −0.119264 0.206572i 0.800212 0.599717i 0.204720π-0.204720\pi
−0.919476 + 0.393145i 0.871387π0.871387\pi
648648 0 0
649649 3.30328 0.129665
650650 −0.761896 + 0.218602i −0.0298840 + 0.00857428i
651651 0 0
652652 24.8184 + 6.65007i 0.971964 + 0.260437i
653653 15.1009 + 26.1555i 0.590943 + 1.02354i 0.994106 + 0.108416i 0.0345777π0.0345777\pi
−0.403162 + 0.915129i 0.632089π0.632089\pi
654654 0 0
655655 −7.19630 + 7.19630i −0.281183 + 0.281183i
656656 43.1253 11.5554i 1.68376 0.451162i
657657 0 0
658658 −0.882439 + 1.84744i −0.0344010 + 0.0720206i
659659 −4.37179 + 7.57216i −0.170301 + 0.294969i −0.938525 0.345211i 0.887807π-0.887807\pi
0.768224 + 0.640181i 0.221141π0.221141\pi
660660 0 0
661661 17.3494 + 4.64874i 0.674812 + 0.180815i 0.579921 0.814673i 0.303083π-0.303083\pi
0.0948903 + 0.995488i 0.469750π0.469750\pi
662662 0.110698i 0.00430239i
663663 0 0
664664 6.50100i 0.252288i
665665 −19.8754 + 1.55315i −0.770734 + 0.0602287i
666666 0 0
667667 39.6561 + 22.8955i 1.53549 + 0.886516i
668668 −1.30942 1.30942i −0.0506631 0.0506631i
669669 0 0
670670 −0.00105152 0.00392433i −4.06238e−5 0.000151610i
671671 4.26731 4.26731i 0.164738 0.164738i
672672 0 0
673673 22.0524 12.7319i 0.850057 0.490780i −0.0106133 0.999944i 0.503378π-0.503378\pi
0.860670 + 0.509163i 0.170045π0.170045\pi
674674 −0.428796 + 1.60029i −0.0165166 + 0.0616408i
675675 0 0
676676 21.8946 13.6910i 0.842100 0.526577i
677677 21.8547i 0.839946i 0.907537 + 0.419973i 0.137961π0.137961\pi
−0.907537 + 0.419973i 0.862039π0.862039\pi
678678 0 0
679679 −25.3970 + 29.7028i −0.974649 + 1.13989i
680680 −3.04444 1.75771i −0.116749 0.0674050i
681681 0 0
682682 −0.944911 + 0.253188i −0.0361825 + 0.00969507i
683683 −30.9579 + 8.29515i −1.18457 + 0.317405i −0.796738 0.604324i 0.793443π-0.793443\pi
−0.387833 + 0.921729i 0.626776π0.626776\pi
684684 0 0
685685 9.59550 + 5.53997i 0.366625 + 0.211671i
686686 −0.0601935 + 2.16147i −0.00229820 + 0.0825252i
687687 0 0
688688 7.02368i 0.267775i
689689 7.94621 + 13.2199i 0.302726 + 0.503639i
690690 0 0
691691 −7.27863 + 27.1642i −0.276892 + 1.03337i 0.677671 + 0.735365i 0.262989π0.262989\pi
−0.954563 + 0.298010i 0.903677π0.903677\pi
692692 −0.907533 + 0.523964i −0.0344992 + 0.0199181i
693693 0 0
694694 1.14276 1.14276i 0.0433786 0.0433786i
695695 −9.56691 35.7042i −0.362894 1.35434i
696696 0 0
697697 −34.4683 34.4683i −1.30558 1.30558i
698698 1.54794 + 0.893701i 0.0585902 + 0.0338271i
699699 0 0
700700 −0.770936 9.86551i −0.0291386 0.372881i
701701 41.8411i 1.58032i 0.612904 + 0.790158i 0.290001π0.290001\pi
−0.612904 + 0.790158i 0.709999π0.709999\pi
702702 0 0
703703 12.0740i 0.455378i
704704 −14.5131 3.88876i −0.546981 0.146563i
705705 0 0
706706 0.919455 1.59254i 0.0346041 0.0599361i
707707 −38.2210 18.2565i −1.43745 0.686606i
708708 0 0
709709 −36.1012 + 9.67328i −1.35581 + 0.363288i −0.862275 0.506440i 0.830961π-0.830961\pi
−0.493532 + 0.869727i 0.664295π0.664295\pi
710710 0.693302 0.693302i 0.0260192 0.0260192i
711711 0 0
712712 −1.87012 3.23914i −0.0700857 0.121392i
713713 −26.4417 7.08503i −0.990249 0.265336i
714714 0 0
715715 −10.9008 6.04011i −0.407665 0.225887i
716716 16.4273 0.613918
717717 0 0
718718 0.387018 + 0.670334i 0.0144434 + 0.0250166i
719719 −14.7469 + 25.5425i −0.549968 + 0.952573i 0.448308 + 0.893879i 0.352027π0.352027\pi
−0.998276 + 0.0586936i 0.981307π0.981307\pi
720720 0 0
721721 25.7718 17.6915i 0.959794 0.658866i
722722 −0.0885265 + 0.0237206i −0.00329461 + 0.000882789i
723723 0 0
724724 −25.7667 14.8764i −0.957612 0.552878i
725725 11.6740 6.74000i 0.433562 0.250317i
726726 0 0
727727 −3.04387 −0.112891 −0.0564455 0.998406i 0.517977π-0.517977\pi
−0.0564455 + 0.998406i 0.517977π0.517977\pi
728728 −1.55323 4.15929i −0.0575665 0.154154i
729729 0 0
730730 0.196682 + 0.0527007i 0.00727952 + 0.00195054i
731731 −6.64113 + 3.83426i −0.245631 + 0.141815i
732732 0 0
733733 0.928339 + 0.928339i 0.0342890 + 0.0342890i 0.724043 0.689754i 0.242282π-0.242282\pi
−0.689754 + 0.724043i 0.742282π0.742282\pi
734734 3.70542 0.992865i 0.136770 0.0366473i
735735 0 0
736736 6.27914 + 6.27914i 0.231452 + 0.231452i
737737 −0.0192931 + 0.0334166i −0.000710669 + 0.00123091i
738738 0 0
739739 −7.76649 + 28.9849i −0.285695 + 1.06623i 0.662635 + 0.748942i 0.269438π0.269438\pi
−0.948330 + 0.317285i 0.897229π0.897229\pi
740740 9.92129 0.364714
741741 0 0
742742 1.24590 0.440421i 0.0457385 0.0161684i
743743 39.4397 + 10.5678i 1.44690 + 0.387697i 0.894946 0.446175i 0.147214π-0.147214\pi
0.551958 + 0.833872i 0.313881π0.313881\pi
744744 0 0
745745 13.6453 23.6344i 0.499926 0.865897i
746746 −0.650528 + 0.650528i −0.0238175 + 0.0238175i
747747 0 0
748748 4.30591 + 16.0699i 0.157440 + 0.587573i
749749 −19.0779 9.11265i −0.697090 0.332969i
750750 0 0
751751 −31.0690 + 17.9377i −1.13372 + 0.654556i −0.944869 0.327448i 0.893811π-0.893811\pi
−0.188856 + 0.982005i 0.560478π0.560478\pi
752752 25.0859 + 6.72175i 0.914789 + 0.245117i
753753 0 0
754754 2.09314 2.16820i 0.0762277 0.0789614i
755755 7.80507i 0.284056i
756756 0 0
757757 −0.439138 0.760610i −0.0159607 0.0276448i 0.857935 0.513759i 0.171747π-0.171747\pi
−0.873895 + 0.486114i 0.838414π0.838414\pi
758758 1.13152 + 0.653282i 0.0410986 + 0.0237283i
759759 0 0
760760 −0.907679 3.38750i −0.0329250 0.122878i
761761 9.46773 + 35.3341i 0.343205 + 1.28086i 0.894695 + 0.446677i 0.147393π0.147393\pi
−0.551490 + 0.834181i 0.685941π0.685941\pi
762762 0 0
763763 5.98855 32.2118i 0.216800 1.16614i
764764 24.9938 14.4302i 0.904245 0.522066i
765765 0 0
766766 −0.281440 −0.0101689
767767 4.22535 4.37687i 0.152568 0.158040i
768768 0 0
769769 7.85943 29.3318i 0.283418 1.05773i −0.666569 0.745443i 0.732238π-0.732238\pi
0.949987 0.312288i 0.101096π-0.101096\pi
770770 −0.693860 + 0.811496i −0.0250050 + 0.0292443i
771771 0 0
772772 −27.4985 + 27.4985i −0.989692 + 0.989692i
773773 19.1599 5.13389i 0.689134 0.184653i 0.102776 0.994705i 0.467228π-0.467228\pi
0.586359 + 0.810052i 0.300561π0.300561\pi
774774 0 0
775775 −5.69824 + 5.69824i −0.204687 + 0.204687i
776776 −5.95369 3.43737i −0.213725 0.123394i
777777 0 0
778778 0.508297 1.89699i 0.0182233 0.0680104i
779779 48.6290i 1.74231i
780780 0 0
781781 −9.31209 −0.333213
782782 0.826882 3.08596i 0.0295692 0.110354i
783783 0 0
784784 27.0958 4.26080i 0.967708 0.152171i
785785 8.65231 8.65231i 0.308814 0.308814i
786786 0 0
787787 2.27486 + 8.48989i 0.0810900 + 0.302632i 0.994545 0.104308i 0.0332626π-0.0332626\pi
−0.913455 + 0.406940i 0.866596π0.866596\pi
788788 −30.5620 30.5620i −1.08873 1.08873i
789789 0 0
790790 −0.611921 1.05988i −0.0217712 0.0377087i
791791 −1.76118 22.5375i −0.0626204 0.801340i
792792 0 0
793793 −0.195750 11.1127i −0.00695128 0.394624i
794794 2.74663i 0.0974743i
795795 0 0
796796 33.1686 19.1499i 1.17563 0.678750i
797797 −12.3887 + 21.4579i −0.438832 + 0.760079i −0.997600 0.0692450i 0.977941π-0.977941\pi
0.558768 + 0.829324i 0.311274π0.311274\pi
798798 0 0
799799 −7.33886 27.3890i −0.259630 0.968953i
800800 2.52505 0.676585i 0.0892739 0.0239209i
801801 0 0
802802 −0.503695 + 0.872425i −0.0177861 + 0.0308064i
803803 −0.966941 1.67479i −0.0341226 0.0591021i
804804 0 0
805805 −28.1693 + 9.95773i −0.992838 + 0.350964i
806806 −0.873195 + 1.57588i −0.0307570 + 0.0555080i
807807 0 0
808808 1.92852 7.19733i 0.0678450 0.253201i
809809 3.75373 + 6.50166i 0.131974 + 0.228586i 0.924438 0.381334i 0.124535π-0.124535\pi
−0.792463 + 0.609920i 0.791202π0.791202\pi
810810 0 0
811811 32.4572 + 32.4572i 1.13973 + 1.13973i 0.988499 + 0.151229i 0.0483229π0.0483229\pi
0.151229 + 0.988499i 0.451677π0.451677\pi
812812 21.2934 + 31.0188i 0.747250 + 1.08855i
813813 0 0
814814 0.457239 + 0.457239i 0.0160262 + 0.0160262i
815815 −19.7777 11.4186i −0.692781 0.399977i
816816 0 0
817817 −7.38949 1.98001i −0.258526 0.0692717i
818818 −1.56868 −0.0548475
819819 0 0
820820 −39.9589 −1.39543
821821 −30.4367 8.15549i −1.06225 0.284629i −0.314944 0.949110i 0.601986π-0.601986\pi
−0.747305 + 0.664482i 0.768652π0.768652\pi
822822 0 0
823823 27.4139 + 15.8274i 0.955590 + 0.551710i 0.894813 0.446442i 0.147309π-0.147309\pi
0.0607767 + 0.998151i 0.480642π0.480642\pi
824824 3.88839 + 3.88839i 0.135459 + 0.135459i
825825 0 0
826826 −0.294977 0.429704i −0.0102636 0.0149513i
827827 −25.1824 25.1824i −0.875678 0.875678i 0.117406 0.993084i 0.462542π-0.462542\pi
−0.993084 + 0.117406i 0.962542π0.962542\pi
828828 0 0
829829 1.05432 + 1.82614i 0.0366182 + 0.0634246i 0.883754 0.467952i 0.155008π-0.155008\pi
−0.847135 + 0.531377i 0.821675π0.821675\pi
830830 0.745200 2.78112i 0.0258663 0.0965342i
831831 0 0
832832 −23.7169 + 14.2557i −0.822234 + 0.494227i
833833 −18.8205 23.2940i −0.652090 0.807091i
834834 0 0
835835 0.822960 + 1.42541i 0.0284797 + 0.0493283i
836836 −8.29847 + 14.3734i −0.287009 + 0.497114i
837837 0 0
838838 1.96001 0.525184i 0.0677076 0.0181422i
839839 6.14897 + 22.9483i 0.212286 + 0.792262i 0.987104 + 0.160078i 0.0511746π0.0511746\pi
−0.774818 + 0.632184i 0.782159π0.782159\pi
840840 0 0
841841 −11.1262 + 19.2712i −0.383663 + 0.664525i
842842 −3.03847 + 1.75426i −0.104713 + 0.0604558i
843843 0 0
844844 6.00398i 0.206666i
845845 −21.9468 + 6.71748i −0.754992 + 0.231088i
846846 0 0
847847 −18.9052 + 1.47734i −0.649591 + 0.0507620i
848848 −8.38131 14.5169i −0.287815 0.498511i
849849 0 0
850850 −0.665032 0.665032i −0.0228104 0.0228104i
851851 4.68331 + 17.4783i 0.160542 + 0.599150i
852852 0 0
853853 −4.73993 + 4.73993i −0.162292 + 0.162292i −0.783581 0.621289i 0.786609π-0.786609\pi
0.621289 + 0.783581i 0.286609π0.286609\pi
854854 −0.936173 0.174046i −0.0320352 0.00595572i
855855 0 0
856856 0.962612 3.59252i 0.0329014 0.122790i
857857 11.3220 0.386751 0.193376 0.981125i 0.438056π-0.438056\pi
0.193376 + 0.981125i 0.438056π0.438056\pi
858858 0 0
859859 48.4452i 1.65293i 0.562988 + 0.826465i 0.309652π0.309652\pi
−0.562988 + 0.826465i 0.690348π0.690348\pi
860860 −1.62699 + 6.07202i −0.0554800 + 0.207054i
861861 0 0
862862 −2.43991 1.40868i −0.0831038 0.0479800i
863863 13.2582 13.2582i 0.451313 0.451313i −0.444477 0.895790i 0.646610π-0.646610\pi
0.895790 + 0.444477i 0.146610π0.146610\pi
864864 0 0
865865 0.899682 0.241069i 0.0305901 0.00819660i
866866 −0.375015 + 0.375015i −0.0127435 + 0.0127435i
867867 0 0
868868 −17.0951 14.6170i −0.580246 0.496133i
869869 −3.00837 + 11.2274i −0.102052 + 0.380863i
870870 0 0
871871 0.0195988 + 0.0683079i 0.000664080 + 0.00231452i
872872 5.76357 0.195179
873873 0 0
874874 2.76018 1.59359i 0.0933645 0.0539040i
875875 −5.87658 + 31.6095i −0.198665 + 1.06860i
876876 0 0
877877 1.83431 + 6.84575i 0.0619403 + 0.231164i 0.989956 0.141377i 0.0451530π-0.0451530\pi
−0.928015 + 0.372542i 0.878486π0.878486\pi
878878 0.513728 + 1.91726i 0.0173375 + 0.0647044i
879879 0 0
880880 11.7291 + 6.77183i 0.395389 + 0.228278i
881881 12.1808 + 21.0977i 0.410380 + 0.710800i 0.994931 0.100557i 0.0320626π-0.0320626\pi
−0.584551 + 0.811357i 0.698729π0.698729\pi
882882 0 0
883883 4.51673i 0.152000i −0.997108 0.0760000i 0.975785π-0.975785\pi
0.997108 0.0760000i 0.0242149π-0.0242149\pi
884884 26.8006 + 14.8502i 0.901401 + 0.499467i
885885 0 0
886886 4.12943 + 1.10648i 0.138731 + 0.0371729i
887887 −38.3035 + 22.1145i −1.28611 + 0.742533i −0.977957 0.208805i 0.933042π-0.933042\pi
−0.308148 + 0.951338i 0.599709π0.599709\pi
888888 0 0
889889 6.97202 14.5963i 0.233834 0.489545i
890890 0.428738 + 1.60007i 0.0143713 + 0.0536346i
891891 0 0
892892 −6.17928 + 6.17928i −0.206898 + 0.206898i
893893 14.1437 24.4976i 0.473300 0.819780i
894894 0 0
895895 −14.1034 3.77900i −0.471426 0.126318i
896896 3.23856 + 9.16152i 0.108193 + 0.306065i
897897 0 0
898898 3.95832 0.132091
899899 7.93007 29.5954i 0.264483 0.987063i
900900 0 0
901901 −9.15079 + 15.8496i −0.304857 + 0.528028i
902902 −1.84157 1.84157i −0.0613176 0.0613176i
903903 0 0
904904 3.84122 1.02925i 0.127757 0.0342324i
905905 18.6994 + 18.6994i 0.621589 + 0.621589i
906906 0 0
907907 29.3466 16.9433i 0.974439 0.562593i 0.0738526 0.997269i 0.476471π-0.476471\pi
0.900587 + 0.434676i 0.143137π0.143137\pi
908908 −7.86438 2.10725i −0.260989 0.0699317i
909909 0 0
910910 0.187697 + 1.95739i 0.00622209 + 0.0648868i
911911 −4.66390 −0.154522 −0.0772610 0.997011i 0.524617π-0.524617\pi
−0.0772610 + 0.997011i 0.524617π0.524617\pi
912912 0 0
913913 −23.6819 + 13.6728i −0.783757 + 0.452502i
914914 −0.228791 0.132092i −0.00756772 0.00436923i
915915 0 0
916916 −26.0500 + 6.98007i −0.860716 + 0.230628i
917917 −8.63132 12.5736i −0.285031 0.415216i
918918 0 0
919919 −12.0900 + 20.9405i −0.398812 + 0.690763i −0.993580 0.113135i 0.963911π-0.963911\pi
0.594767 + 0.803898i 0.297244π0.297244\pi
920920 −2.62793 4.55170i −0.0866402 0.150065i
921921 0 0
922922 2.96686 0.0977084
923923 −11.9115 + 12.3386i −0.392070 + 0.406131i
924924 0 0
925925 5.14530 + 1.37868i 0.169177 + 0.0453307i
926926 −1.86798 3.23543i −0.0613856 0.106323i
927927 0 0
928928 −7.02806 + 7.02806i −0.230708 + 0.230708i
929929 15.0006 4.01941i 0.492155 0.131872i −0.00420200 0.999991i 0.501338π-0.501338\pi
0.496357 + 0.868119i 0.334671π0.334671\pi
930930 0 0
931931 3.15573 29.7082i 0.103425 0.973647i
932932 −16.2386 + 28.1261i −0.531913 + 0.921300i
933933 0 0
934934 1.27369 + 0.341285i 0.0416765 + 0.0111672i
935935 14.7871i 0.483589i
936936 0 0
937937 25.4720i 0.832134i 0.909334 + 0.416067i 0.136592π0.136592\pi
−0.909334 + 0.416067i 0.863408π0.863408\pi
938938 0.00606980 0.000474322i 0.000198186 1.54872e-5i
939939 0 0
940940 −20.1299 11.6220i −0.656565 0.379068i
941941 12.6726 + 12.6726i 0.413116 + 0.413116i 0.882823 0.469706i 0.155640π-0.155640\pi
−0.469706 + 0.882823i 0.655640π0.655640\pi
942942 0 0
943943 −18.8625 70.3957i −0.614246 2.29240i
944944 −4.67503 + 4.67503i −0.152159 + 0.152159i
945945 0 0
946946 −0.354822 + 0.204856i −0.0115362 + 0.00666046i
947947 −3.21690 + 12.0056i −0.104535 + 0.390130i −0.998292 0.0584214i 0.981393π-0.981393\pi
0.893757 + 0.448552i 0.148060π0.148060\pi
948948 0 0
949949 −3.45597 0.861083i −0.112185 0.0279519i
950950 0.938247i 0.0304408i
951951 0 0
952952 3.42356 4.00398i 0.110958 0.129770i
953953 −25.0716 14.4751i −0.812147 0.468893i 0.0355538 0.999368i 0.488680π-0.488680\pi
−0.847701 + 0.530474i 0.822014π0.822014\pi
954954 0 0
955955 −24.7776 + 6.63914i −0.801785 + 0.214838i
956956 16.5925 4.44594i 0.536639 0.143792i
957957 0 0
958958 −2.02778 1.17074i −0.0655147 0.0378249i
959959 −10.7904 + 12.6198i −0.348441 + 0.407514i
960960 0 0
961961 12.6833i 0.409139i
962962 1.19072 0.0209745i 0.0383903 0.000676243i
963963 0 0
964964 6.90512 25.7703i 0.222399 0.830004i
965965 29.9342 17.2825i 0.963617 0.556344i
966966 0 0
967967 20.8937 20.8937i 0.671895 0.671895i −0.286258 0.958153i 0.592411π-0.592411\pi
0.958153 + 0.286258i 0.0924113π0.0924113\pi
968968 −0.863372 3.22215i −0.0277498 0.103564i
969969 0 0
970970 2.15297 + 2.15297i 0.0691276 + 0.0691276i
971971 35.5507 + 20.5252i 1.14088 + 0.658685i 0.946647 0.322271i 0.104446π-0.104446\pi
0.194229 + 0.980956i 0.437780π0.437780\pi
972972 0 0
973973 55.2241 4.31546i 1.77040 0.138347i
974974 3.66794i 0.117528i
975975 0 0
976976 12.0788i 0.386633i
977977 22.0546 + 5.90951i 0.705589 + 0.189062i 0.593733 0.804662i 0.297654π-0.297654\pi
0.111856 + 0.993724i 0.464320π0.464320\pi
978978 0 0
979979 7.86639 13.6250i 0.251411 0.435457i
980980 −24.4115 2.59309i −0.779798 0.0828334i
981981 0 0
982982 2.19217 0.587390i 0.0699549 0.0187444i
983983 21.0430 21.0430i 0.671167 0.671167i −0.286818 0.957985i 0.592598π-0.592598\pi
0.957985 + 0.286818i 0.0925976π0.0925976\pi
984984 0 0
985985 19.2080 + 33.2692i 0.612017 + 1.06004i
986986 3.45403 + 0.925505i 0.109999 + 0.0294741i
987987 0 0
988988 8.42998 + 29.3811i 0.268193 + 0.934737i
989989 −11.4651 −0.364569
990990 0 0
991991 1.24883 + 2.16303i 0.0396703 + 0.0687110i 0.885179 0.465251i 0.154036π-0.154036\pi
−0.845509 + 0.533962i 0.820703π0.820703\pi
992992 2.97089 5.14574i 0.0943259 0.163377i
993993 0 0
994994 0.831554 + 1.21136i 0.0263753 + 0.0384219i
995995 −32.8817 + 8.81062i −1.04242 + 0.279315i
996996 0 0
997997 −5.16724 2.98331i −0.163648 0.0944823i 0.415939 0.909392i 0.363453π-0.363453\pi
−0.579587 + 0.814910i 0.696786π0.696786\pi
998998 1.68806 0.974599i 0.0534345 0.0308504i
999999 0 0
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 819.2.fm.g.496.4 32
3.2 odd 2 91.2.bc.a.41.5 yes 32
7.6 odd 2 inner 819.2.fm.g.496.3 32
13.7 odd 12 inner 819.2.fm.g.748.3 32
21.2 odd 6 637.2.x.b.80.3 32
21.5 even 6 637.2.x.b.80.4 32
21.11 odd 6 637.2.bb.b.509.4 32
21.17 even 6 637.2.bb.b.509.3 32
21.20 even 2 91.2.bc.a.41.6 yes 32
39.20 even 12 91.2.bc.a.20.6 yes 32
91.20 even 12 inner 819.2.fm.g.748.4 32
273.20 odd 12 91.2.bc.a.20.5 32
273.59 odd 12 637.2.x.b.215.4 32
273.137 even 12 637.2.x.b.215.3 32
273.215 odd 12 637.2.bb.b.423.4 32
273.254 even 12 637.2.bb.b.423.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bc.a.20.5 32 273.20 odd 12
91.2.bc.a.20.6 yes 32 39.20 even 12
91.2.bc.a.41.5 yes 32 3.2 odd 2
91.2.bc.a.41.6 yes 32 21.20 even 2
637.2.x.b.80.3 32 21.2 odd 6
637.2.x.b.80.4 32 21.5 even 6
637.2.x.b.215.3 32 273.137 even 12
637.2.x.b.215.4 32 273.59 odd 12
637.2.bb.b.423.3 32 273.254 even 12
637.2.bb.b.423.4 32 273.215 odd 12
637.2.bb.b.509.3 32 21.17 even 6
637.2.bb.b.509.4 32 21.11 odd 6
819.2.fm.g.496.3 32 7.6 odd 2 inner
819.2.fm.g.496.4 32 1.1 even 1 trivial
819.2.fm.g.748.3 32 13.7 odd 12 inner
819.2.fm.g.748.4 32 91.20 even 12 inner