Properties

Label 819.2.s.d.289.1
Level 819819
Weight 22
Character 819.289
Analytic conductor 6.5406.540
Analytic rank 00
Dimension 1212
Inner twists 22

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) 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("819.289"); 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.s (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,4,0,8,-1,0,-3,6,0,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x12x11+7x102x9+33x811x7+55x6+17x5+47x4+x3+8x2+x+1 x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 289.1
Root 0.2179530.377506i0.217953 - 0.377506i of defining polynomial
Character χ\chi == 819.289
Dual form 819.2.s.d.802.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q1.85816q2+1.45276q4+(0.0986811+0.170921i)q5+(1.038262.43352i)q7+1.01686q8+(0.1833650.317598i)q10+(2.09137+3.62236i)q11+(2.72221+2.36423i)q13+(1.92926+4.52187i)q144.79501q160.841305q17+(0.6758761.17065i)q19+(0.143360+0.248307i)q20+(3.886106.73092i)q22+4.11519q23+(2.48052+4.29639i)q25+(5.058304.39312i)q26+(1.508353.53532i)q28+(4.119317.13485i)q29+(0.640350+1.10912i)q31+6.87618q32+1.56328q34+(0.313482+0.417603i)q35+3.04485q37+(1.25589+2.17526i)q38+(0.100344+0.173802i)q40+(2.69848+4.67390i)q41+(2.66389+4.61399i)q43+(3.03826+5.26242i)q447.64669q46+(5.83204+10.1014i)q47+(4.844035.05326i)q49+(4.609217.98339i)q50+(3.95472+3.43466i)q52+(2.32398+4.02525i)q53+(0.4127570.714916i)q55+(1.055762.47454i)q56+(7.65434+13.2577i)q586.05811q59+(5.68285+9.84298i)q61+(1.189872.06092i)q623.18704q64+(0.1354650.698587i)q65+(6.69851+11.6022i)q671.22222q68+(0.5825000.775973i)q70+(2.98520+5.17051i)q71+(1.942733.36491i)q735.65782q74+(0.9818871.70068i)q76+(6.64368+8.85034i)q77+(5.366699.29537i)q79+(0.4731770.819566i)q80+(5.014218.68486i)q823.07390q83+(0.08302100.143797i)q85+(4.949948.57354i)q86+(2.12662+3.68341i)q88+11.9841q89+(2.92702+9.07924i)q91+5.97840q92+(10.836918.7700i)q94+0.266785q95+(9.73637+16.8639i)q97+(9.00098+9.38977i)q98+O(q100)q-1.85816 q^{2} +1.45276 q^{4} +(-0.0986811 + 0.170921i) q^{5} +(1.03826 - 2.43352i) q^{7} +1.01686 q^{8} +(0.183365 - 0.317598i) q^{10} +(-2.09137 + 3.62236i) q^{11} +(-2.72221 + 2.36423i) q^{13} +(-1.92926 + 4.52187i) q^{14} -4.79501 q^{16} -0.841305 q^{17} +(-0.675876 - 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +4.11519 q^{23} +(2.48052 + 4.29639i) q^{25} +(5.05830 - 4.39312i) q^{26} +(1.50835 - 3.53532i) q^{28} +(-4.11931 - 7.13485i) q^{29} +(0.640350 + 1.10912i) q^{31} +6.87618 q^{32} +1.56328 q^{34} +(0.313482 + 0.417603i) q^{35} +3.04485 q^{37} +(1.25589 + 2.17526i) q^{38} +(-0.100344 + 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(-3.03826 + 5.26242i) q^{44} -7.64669 q^{46} +(-5.83204 + 10.1014i) q^{47} +(-4.84403 - 5.05326i) q^{49} +(-4.60921 - 7.98339i) q^{50} +(-3.95472 + 3.43466i) q^{52} +(2.32398 + 4.02525i) q^{53} +(-0.412757 - 0.714916i) q^{55} +(1.05576 - 2.47454i) q^{56} +(7.65434 + 13.2577i) q^{58} -6.05811 q^{59} +(5.68285 + 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(-0.135465 - 0.698587i) q^{65} +(-6.69851 + 11.6022i) q^{67} -1.22222 q^{68} +(-0.582500 - 0.775973i) q^{70} +(-2.98520 + 5.17051i) q^{71} +(-1.94273 - 3.36491i) q^{73} -5.65782 q^{74} +(-0.981887 - 1.70068i) q^{76} +(6.64368 + 8.85034i) q^{77} +(5.36669 - 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(-5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(4.94994 - 8.57354i) q^{86} +(-2.12662 + 3.68341i) q^{88} +11.9841 q^{89} +(2.92702 + 9.07924i) q^{91} +5.97840 q^{92} +(10.8369 - 18.7700i) q^{94} +0.266785 q^{95} +(-9.73637 + 16.8639i) q^{97} +(9.00098 + 9.38977i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+4q2+8q4q53q7+6q8+4q104q112q13+2q1416q16+10q17q19+q205q222q23+7q25+16q26q283q29+20q98+O(q100) 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29}+ \cdots - 20 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(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\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 −1.85816 −1.31392 −0.656959 0.753926i 0.728158π-0.728158\pi
−0.656959 + 0.753926i 0.728158π0.728158\pi
33 0 0
44 1.45276 0.726381
55 −0.0986811 + 0.170921i −0.0441315 + 0.0764381i −0.887247 0.461294i 0.847385π-0.847385\pi
0.843116 + 0.537732i 0.180719π0.180719\pi
66 0 0
77 1.03826 2.43352i 0.392426 0.919784i
88 1.01686 0.359513
99 0 0
1010 0.183365 0.317598i 0.0579852 0.100433i
1111 −2.09137 + 3.62236i −0.630571 + 1.09218i 0.356864 + 0.934156i 0.383846π0.383846\pi
−0.987435 + 0.158025i 0.949487π0.949487\pi
1212 0 0
1313 −2.72221 + 2.36423i −0.755005 + 0.655719i
1414 −1.92926 + 4.52187i −0.515616 + 1.20852i
1515 0 0
1616 −4.79501 −1.19875
1717 −0.841305 −0.204047 −0.102023 0.994782i 0.532532π-0.532532\pi
−0.102023 + 0.994782i 0.532532π0.532532\pi
1818 0 0
1919 −0.675876 1.17065i −0.155057 0.268566i 0.778023 0.628236i 0.216223π-0.216223\pi
−0.933080 + 0.359670i 0.882889π0.882889\pi
2020 −0.143360 + 0.248307i −0.0320563 + 0.0555232i
2121 0 0
2222 3.88610 6.73092i 0.828519 1.43504i
2323 4.11519 0.858077 0.429038 0.903286i 0.358853π-0.358853\pi
0.429038 + 0.903286i 0.358853π0.358853\pi
2424 0 0
2525 2.48052 + 4.29639i 0.496105 + 0.859279i
2626 5.05830 4.39312i 0.992015 0.861561i
2727 0 0
2828 1.50835 3.53532i 0.285051 0.668113i
2929 −4.11931 7.13485i −0.764936 1.32491i −0.940280 0.340401i 0.889437π-0.889437\pi
0.175344 0.984507i 0.443896π-0.443896\pi
3030 0 0
3131 0.640350 + 1.10912i 0.115010 + 0.199203i 0.917784 0.397080i 0.129977π-0.129977\pi
−0.802774 + 0.596284i 0.796643π0.796643\pi
3232 6.87618 1.21555
3333 0 0
3434 1.56328 0.268100
3535 0.313482 + 0.417603i 0.0529881 + 0.0705878i
3636 0 0
3737 3.04485 0.500570 0.250285 0.968172i 0.419476π-0.419476\pi
0.250285 + 0.968172i 0.419476π0.419476\pi
3838 1.25589 + 2.17526i 0.203732 + 0.352874i
3939 0 0
4040 −0.100344 + 0.173802i −0.0158659 + 0.0274805i
4141 2.69848 + 4.67390i 0.421431 + 0.729941i 0.996080 0.0884599i 0.0281945π-0.0281945\pi
−0.574648 + 0.818400i 0.694861π0.694861\pi
4242 0 0
4343 −2.66389 + 4.61399i −0.406239 + 0.703627i −0.994465 0.105070i 0.966493π-0.966493\pi
0.588226 + 0.808697i 0.299827π0.299827\pi
4444 −3.03826 + 5.26242i −0.458035 + 0.793340i
4545 0 0
4646 −7.64669 −1.12744
4747 −5.83204 + 10.1014i −0.850690 + 1.47344i 0.0298969 + 0.999553i 0.490482π0.490482\pi
−0.880587 + 0.473885i 0.842851π0.842851\pi
4848 0 0
4949 −4.84403 5.05326i −0.692004 0.721894i
5050 −4.60921 7.98339i −0.651841 1.12902i
5151 0 0
5252 −3.95472 + 3.43466i −0.548422 + 0.476302i
5353 2.32398 + 4.02525i 0.319223 + 0.552911i 0.980326 0.197384i 0.0632446π-0.0632446\pi
−0.661103 + 0.750295i 0.729911π0.729911\pi
5454 0 0
5555 −0.412757 0.714916i −0.0556562 0.0963993i
5656 1.05576 2.47454i 0.141082 0.330674i
5757 0 0
5858 7.65434 + 13.2577i 1.00506 + 1.74082i
5959 −6.05811 −0.788698 −0.394349 0.918961i 0.629030π-0.629030\pi
−0.394349 + 0.918961i 0.629030π0.629030\pi
6060 0 0
6161 5.68285 + 9.84298i 0.727614 + 1.26026i 0.957889 + 0.287139i 0.0927042π0.0927042\pi
−0.230275 + 0.973126i 0.573962π0.573962\pi
6262 −1.18987 2.06092i −0.151114 0.261737i
6363 0 0
6464 −3.18704 −0.398380
6565 −0.135465 0.698587i −0.0168023 0.0866490i
6666 0 0
6767 −6.69851 + 11.6022i −0.818354 + 1.41743i 0.0885411 + 0.996073i 0.471780π0.471780\pi
−0.906895 + 0.421357i 0.861554π0.861554\pi
6868 −1.22222 −0.148216
6969 0 0
7070 −0.582500 0.775973i −0.0696221 0.0927465i
7171 −2.98520 + 5.17051i −0.354278 + 0.613627i −0.986994 0.160757i 0.948607π-0.948607\pi
0.632716 + 0.774384i 0.281940π0.281940\pi
7272 0 0
7373 −1.94273 3.36491i −0.227380 0.393833i 0.729651 0.683820i 0.239683π-0.239683\pi
−0.957031 + 0.289986i 0.906349π0.906349\pi
7474 −5.65782 −0.657708
7575 0 0
7676 −0.981887 1.70068i −0.112630 0.195081i
7777 6.64368 + 8.85034i 0.757118 + 1.00859i
7878 0 0
7979 5.36669 9.29537i 0.603799 1.04581i −0.388441 0.921474i 0.626986π-0.626986\pi
0.992240 0.124337i 0.0396805π-0.0396805\pi
8080 0.473177 0.819566i 0.0529028 0.0916303i
8181 0 0
8282 −5.01421 8.68486i −0.553726 0.959082i
8383 −3.07390 −0.337404 −0.168702 0.985667i 0.553958π-0.553958\pi
−0.168702 + 0.985667i 0.553958π0.553958\pi
8484 0 0
8585 0.0830210 0.143797i 0.00900489 0.0155969i
8686 4.94994 8.57354i 0.533765 0.924509i
8787 0 0
8888 −2.12662 + 3.68341i −0.226698 + 0.392653i
8989 11.9841 1.27032 0.635159 0.772382i 0.280935π-0.280935\pi
0.635159 + 0.772382i 0.280935π0.280935\pi
9090 0 0
9191 2.92702 + 9.07924i 0.306836 + 0.951763i
9292 5.97840 0.623291
9393 0 0
9494 10.8369 18.7700i 1.11774 1.93598i
9595 0.266785 0.0273715
9696 0 0
9797 −9.73637 + 16.8639i −0.988578 + 1.71227i −0.363771 + 0.931488i 0.618511π0.618511\pi
−0.624807 + 0.780779i 0.714822π0.714822\pi
9898 9.00098 + 9.38977i 0.909236 + 0.948510i
9999 0 0
100100 3.60361 + 6.24164i 0.360361 + 0.624164i
101101 −8.46697 + 14.6652i −0.842495 + 1.45924i 0.0452843 + 0.998974i 0.485581π0.485581\pi
−0.887779 + 0.460270i 0.847753π0.847753\pi
102102 0 0
103103 3.61712 6.26504i 0.356406 0.617313i −0.630952 0.775822i 0.717335π-0.717335\pi
0.987357 + 0.158509i 0.0506688π0.0506688\pi
104104 −2.76809 + 2.40408i −0.271434 + 0.235739i
105105 0 0
106106 −4.31833 7.47957i −0.419434 0.726480i
107107 9.85249 0.952477 0.476238 0.879316i 0.342000π-0.342000\pi
0.476238 + 0.879316i 0.342000π0.342000\pi
108108 0 0
109109 6.90796 + 11.9649i 0.661662 + 1.14603i 0.980179 + 0.198115i 0.0634821π0.0634821\pi
−0.318516 + 0.947917i 0.603185π0.603185\pi
110110 0.766969 + 1.32843i 0.0731277 + 0.126661i
111111 0 0
112112 −4.97847 + 11.6687i −0.470421 + 1.10259i
113113 −2.13432 + 3.69675i −0.200780 + 0.347761i −0.948780 0.315938i 0.897681π-0.897681\pi
0.748000 + 0.663699i 0.231014π0.231014\pi
114114 0 0
115115 −0.406092 + 0.703371i −0.0378682 + 0.0655897i
116116 −5.98437 10.3652i −0.555635 0.962388i
117117 0 0
118118 11.2569 1.03629
119119 −0.873495 + 2.04733i −0.0800732 + 0.187679i
120120 0 0
121121 −3.24765 5.62509i −0.295240 0.511372i
122122 −10.5596 18.2898i −0.956026 1.65589i
123123 0 0
124124 0.930276 + 1.61129i 0.0835412 + 0.144698i
125125 −1.96593 −0.175839
126126 0 0
127127 1.09512 + 1.89680i 0.0971761 + 0.168314i 0.910515 0.413477i 0.135686π-0.135686\pi
−0.813339 + 0.581791i 0.802352π0.802352\pi
128128 −7.83033 −0.692110
129129 0 0
130130 0.251715 + 1.29809i 0.0220769 + 0.113850i
131131 1.13806 1.97117i 0.0994326 0.172222i −0.812017 0.583633i 0.801631π-0.801631\pi
0.911450 + 0.411411i 0.134964π0.134964\pi
132132 0 0
133133 −3.55054 + 0.429314i −0.307871 + 0.0372262i
134134 12.4469 21.5587i 1.07525 1.86239i
135135 0 0
136136 −0.855486 −0.0733573
137137 −13.4480 −1.14894 −0.574469 0.818526i 0.694791π-0.694791\pi
−0.574469 + 0.818526i 0.694791π0.694791\pi
138138 0 0
139139 −2.02270 + 3.50342i −0.171563 + 0.297156i −0.938966 0.344009i 0.888215π-0.888215\pi
0.767403 + 0.641165i 0.221548π0.221548\pi
140140 0.455415 + 0.606678i 0.0384896 + 0.0512736i
141141 0 0
142142 5.54698 9.60765i 0.465492 0.806256i
143143 −2.87093 14.8053i −0.240079 1.23808i
144144 0 0
145145 1.62599 0.135031
146146 3.60991 + 6.25255i 0.298758 + 0.517465i
147147 0 0
148148 4.42344 0.363605
149149 7.67596 + 13.2952i 0.628840 + 1.08918i 0.987785 + 0.155823i 0.0498031π0.0498031\pi
−0.358945 + 0.933359i 0.616864π0.616864\pi
150150 0 0
151151 −3.06054 5.30101i −0.249063 0.431390i 0.714203 0.699939i 0.246789π-0.246789\pi
−0.963266 + 0.268548i 0.913456π0.913456\pi
152152 −0.687268 1.19038i −0.0557448 0.0965528i
153153 0 0
154154 −12.3450 16.4454i −0.994791 1.32520i
155155 −0.252762 −0.0203023
156156 0 0
157157 −2.26834 3.92888i −0.181033 0.313559i 0.761199 0.648518i 0.224611π-0.224611\pi
−0.942233 + 0.334959i 0.891278π0.891278\pi
158158 −9.97217 + 17.2723i −0.793343 + 1.37411i
159159 0 0
160160 −0.678549 + 1.17528i −0.0536440 + 0.0929142i
161161 4.27265 10.0144i 0.336732 0.789245i
162162 0 0
163163 −0.911271 1.57837i −0.0713762 0.123627i 0.828128 0.560538i 0.189406π-0.189406\pi
−0.899505 + 0.436911i 0.856072π0.856072\pi
164164 3.92025 + 6.79007i 0.306120 + 0.530215i
165165 0 0
166166 5.71180 0.443322
167167 −5.35397 9.27336i −0.414303 0.717594i 0.581052 0.813866i 0.302641π-0.302641\pi
−0.995355 + 0.0962726i 0.969308π0.969308\pi
168168 0 0
169169 1.82086 12.8718i 0.140066 0.990142i
170170 −0.154266 + 0.267197i −0.0118317 + 0.0204931i
171171 0 0
172172 −3.87000 + 6.70303i −0.295085 + 0.511102i
173173 −6.74634 11.6850i −0.512915 0.888395i −0.999888 0.0149778i 0.995232π-0.995232\pi
0.486973 0.873417i 0.338101π-0.338101\pi
174174 0 0
175175 13.0308 1.57562i 0.985035 0.119106i
176176 10.0281 17.3692i 0.755898 1.30925i
177177 0 0
178178 −22.2685 −1.66909
179179 5.23458 9.06657i 0.391251 0.677667i −0.601364 0.798975i 0.705376π-0.705376\pi
0.992615 + 0.121309i 0.0387090π0.0387090\pi
180180 0 0
181181 12.5209 0.930674 0.465337 0.885133i 0.345933π-0.345933\pi
0.465337 + 0.885133i 0.345933π0.345933\pi
182182 −5.43888 16.8707i −0.403157 1.25054i
183183 0 0
184184 4.18455 0.308489
185185 −0.300469 + 0.520428i −0.0220909 + 0.0382626i
186186 0 0
187187 1.75948 3.04751i 0.128666 0.222856i
188188 −8.47256 + 14.6749i −0.617925 + 1.07028i
189189 0 0
190190 −0.495729 −0.0359640
191191 6.55685 + 11.3568i 0.474437 + 0.821749i 0.999572 0.0292704i 0.00931840π-0.00931840\pi
−0.525135 + 0.851019i 0.675985π0.675985\pi
192192 0 0
193193 −0.520786 + 0.902028i −0.0374870 + 0.0649294i −0.884160 0.467184i 0.845269π-0.845269\pi
0.846673 + 0.532113i 0.178602π0.178602\pi
194194 18.0917 31.3358i 1.29891 2.24978i
195195 0 0
196196 −7.03722 7.34118i −0.502658 0.524370i
197197 0.739167 + 1.28027i 0.0526635 + 0.0912158i 0.891155 0.453698i 0.149896π-0.149896\pi
−0.838492 + 0.544914i 0.816562π0.816562\pi
198198 0 0
199199 14.0999 0.999512 0.499756 0.866166i 0.333423π-0.333423\pi
0.499756 + 0.866166i 0.333423π0.333423\pi
200200 2.52233 + 4.36881i 0.178356 + 0.308922i
201201 0 0
202202 15.7330 27.2503i 1.10697 1.91733i
203203 −21.6397 + 2.61657i −1.51881 + 0.183647i
204204 0 0
205205 −1.06516 −0.0743937
206206 −6.72120 + 11.6415i −0.468288 + 0.811099i
207207 0 0
208208 13.0530 11.3365i 0.905064 0.786044i
209209 5.65402 0.391097
210210 0 0
211211 −13.2346 22.9230i −0.911108 1.57809i −0.812501 0.582959i 0.801895π-0.801895\pi
−0.0986067 0.995126i 0.531439π-0.531439\pi
212212 3.37619 + 5.84774i 0.231878 + 0.401624i
213213 0 0
214214 −18.3075 −1.25148
215215 −0.525751 0.910628i −0.0358559 0.0621043i
216216 0 0
217217 3.36391 0.406748i 0.228357 0.0276118i
218218 −12.8361 22.2328i −0.869370 1.50579i
219219 0 0
220220 −0.599638 1.03860i −0.0404276 0.0700227i
221221 2.29021 1.98904i 0.154056 0.133797i
222222 0 0
223223 0.364024 + 0.630508i 0.0243769 + 0.0422219i 0.877956 0.478740i 0.158907π-0.158907\pi
−0.853580 + 0.520962i 0.825573π0.825573\pi
224224 7.13928 16.7333i 0.477013 1.11804i
225225 0 0
226226 3.96591 6.86916i 0.263808 0.456929i
227227 2.85195 0.189291 0.0946454 0.995511i 0.469828π-0.469828\pi
0.0946454 + 0.995511i 0.469828π0.469828\pi
228228 0 0
229229 −1.58676 + 2.74835i −0.104856 + 0.181616i −0.913679 0.406436i 0.866772π-0.866772\pi
0.808823 + 0.588052i 0.200105π0.200105\pi
230230 0.754584 1.30698i 0.0497558 0.0861795i
231231 0 0
232232 −4.18874 7.25511i −0.275004 0.476321i
233233 6.70354 11.6109i 0.439163 0.760653i −0.558462 0.829530i 0.688608π-0.688608\pi
0.997625 + 0.0688769i 0.0219416π0.0219416\pi
234234 0 0
235235 −1.15102 1.99363i −0.0750845 0.130050i
236236 −8.80099 −0.572896
237237 0 0
238238 1.62309 3.80427i 0.105210 0.246594i
239239 15.5538 1.00609 0.503046 0.864259i 0.332212π-0.332212\pi
0.503046 + 0.864259i 0.332212π0.332212\pi
240240 0 0
241241 −7.57574 −0.487996 −0.243998 0.969776i 0.578459π-0.578459\pi
−0.243998 + 0.969776i 0.578459π0.578459\pi
242242 6.03465 + 10.4523i 0.387922 + 0.671900i
243243 0 0
244244 8.25583 + 14.2995i 0.528525 + 0.915433i
245245 1.34172 0.329283i 0.0857194 0.0210371i
246246 0 0
247247 4.60756 + 1.58883i 0.293172 + 0.101095i
248248 0.651143 + 1.12781i 0.0413476 + 0.0716162i
249249 0 0
250250 3.65302 0.231038
251251 0.637382 1.10398i 0.0402312 0.0696825i −0.845209 0.534436i 0.820524π-0.820524\pi
0.885440 + 0.464754i 0.153857π0.153857\pi
252252 0 0
253253 −8.60638 + 14.9067i −0.541079 + 0.937176i
254254 −2.03491 3.52456i −0.127682 0.221151i
255255 0 0
256256 20.9241 1.30776
257257 8.48019 0.528980 0.264490 0.964388i 0.414796π-0.414796\pi
0.264490 + 0.964388i 0.414796π0.414796\pi
258258 0 0
259259 3.16135 7.40970i 0.196437 0.460416i
260260 −0.196798 1.01488i −0.0122049 0.0629402i
261261 0 0
262262 −2.11470 + 3.66276i −0.130646 + 0.226286i
263263 6.39415 11.0750i 0.394280 0.682913i −0.598729 0.800952i 0.704327π-0.704327\pi
0.993009 + 0.118038i 0.0376606π0.0376606\pi
264264 0 0
265265 −0.917333 −0.0563513
266266 6.59747 0.797735i 0.404517 0.0489122i
267267 0 0
268268 −9.73135 + 16.8552i −0.594437 + 1.02959i
269269 4.71172 0.287278 0.143639 0.989630i 0.454120π-0.454120\pi
0.143639 + 0.989630i 0.454120π0.454120\pi
270270 0 0
271271 −18.0112 −1.09410 −0.547052 0.837098i 0.684250π-0.684250\pi
−0.547052 + 0.837098i 0.684250π0.684250\pi
272272 4.03407 0.244601
273273 0 0
274274 24.9885 1.50961
275275 −20.7508 −1.25132
276276 0 0
277277 −26.1209 −1.56945 −0.784725 0.619844i 0.787196π-0.787196\pi
−0.784725 + 0.619844i 0.787196π0.787196\pi
278278 3.75850 6.50991i 0.225420 0.390439i
279279 0 0
280280 0.318766 + 0.424642i 0.0190499 + 0.0253772i
281281 3.66197 0.218455 0.109227 0.994017i 0.465162π-0.465162\pi
0.109227 + 0.994017i 0.465162π0.465162\pi
282282 0 0
283283 −3.82263 + 6.62099i −0.227232 + 0.393577i −0.956987 0.290132i 0.906301π-0.906301\pi
0.729755 + 0.683709i 0.239634π0.239634\pi
284284 −4.33678 + 7.51153i −0.257341 + 0.445727i
285285 0 0
286286 5.33465 + 27.5106i 0.315445 + 1.62674i
287287 14.1757 1.71406i 0.836768 0.101178i
288288 0 0
289289 −16.2922 −0.958365
290290 −3.02135 −0.177420
291291 0 0
292292 −2.82233 4.88842i −0.165164 0.286073i
293293 −8.57670 + 14.8553i −0.501056 + 0.867855i 0.498943 + 0.866635i 0.333722π0.333722\pi
−0.999999 + 0.00122001i 0.999612π0.999612\pi
294294 0 0
295295 0.597821 1.03546i 0.0348065 0.0602866i
296296 3.09617 0.179961
297297 0 0
298298 −14.2632 24.7045i −0.826244 1.43110i
299299 −11.2024 + 9.72925i −0.647852 + 0.562657i
300300 0 0
301301 8.46242 + 11.2732i 0.487766 + 0.649774i
302302 5.68698 + 9.85014i 0.327249 + 0.566812i
303303 0 0
304304 3.24083 + 5.61328i 0.185874 + 0.321944i
305305 −2.24316 −0.128443
306306 0 0
307307 −28.0696 −1.60201 −0.801007 0.598655i 0.795702π-0.795702\pi
−0.801007 + 0.598655i 0.795702π0.795702\pi
308308 9.65169 + 12.8574i 0.549956 + 0.732621i
309309 0 0
310310 0.469672 0.0266756
311311 −11.7670 20.3811i −0.667248 1.15571i −0.978671 0.205436i 0.934139π-0.934139\pi
0.311423 0.950271i 0.399194π-0.399194\pi
312312 0 0
313313 1.67430 2.89997i 0.0946370 0.163916i −0.814820 0.579714i 0.803164π-0.803164\pi
0.909457 + 0.415798i 0.136498π0.136498\pi
314314 4.21494 + 7.30050i 0.237863 + 0.411991i
315315 0 0
316316 7.79652 13.5040i 0.438588 0.759658i
317317 −3.63917 + 6.30323i −0.204396 + 0.354025i −0.949940 0.312432i 0.898856π-0.898856\pi
0.745544 + 0.666456i 0.232190π0.232190\pi
318318 0 0
319319 34.4600 1.92939
320320 0.314501 0.544732i 0.0175811 0.0304514i
321321 0 0
322322 −7.93926 + 18.6084i −0.442438 + 1.03700i
323323 0.568618 + 0.984875i 0.0316388 + 0.0547999i
324324 0 0
325325 −16.9102 5.83116i −0.938007 0.323455i
326326 1.69329 + 2.93286i 0.0937826 + 0.162436i
327327 0 0
328328 2.74396 + 4.75268i 0.151510 + 0.262423i
329329 18.5267 + 24.6802i 1.02141 + 1.36067i
330330 0 0
331331 7.16168 + 12.4044i 0.393642 + 0.681807i 0.992927 0.118728i 0.0378818π-0.0378818\pi
−0.599285 + 0.800536i 0.704548π0.704548\pi
332332 −4.46564 −0.245084
333333 0 0
334334 9.94855 + 17.2314i 0.544360 + 0.942860i
335335 −1.32203 2.28983i −0.0722304 0.125107i
336336 0 0
337337 17.1802 0.935868 0.467934 0.883764i 0.344999π-0.344999\pi
0.467934 + 0.883764i 0.344999π0.344999\pi
338338 −3.38344 + 23.9180i −0.184035 + 1.30097i
339339 0 0
340340 0.120610 0.208902i 0.00654098 0.0113293i
341341 −5.35683 −0.290089
342342 0 0
343343 −17.3266 + 6.54142i −0.935547 + 0.353203i
344344 −2.70879 + 4.69176i −0.146048 + 0.252963i
345345 0 0
346346 12.5358 + 21.7126i 0.673928 + 1.16728i
347347 7.70278 0.413507 0.206753 0.978393i 0.433710π-0.433710\pi
0.206753 + 0.978393i 0.433710π0.433710\pi
348348 0 0
349349 −11.1850 19.3730i −0.598721 1.03702i −0.993010 0.118029i 0.962343π-0.962343\pi
0.394289 0.918986i 0.370991π-0.370991\pi
350350 −24.2133 + 2.92776i −1.29426 + 0.156495i
351351 0 0
352352 −14.3806 + 24.9080i −0.766490 + 1.32760i
353353 −11.1311 + 19.2797i −0.592451 + 1.02616i 0.401450 + 0.915881i 0.368506π0.368506\pi
−0.993901 + 0.110275i 0.964827π0.964827\pi
354354 0 0
355355 −0.589165 1.02046i −0.0312697 0.0541606i
356356 17.4101 0.922735
357357 0 0
358358 −9.72670 + 16.8471i −0.514072 + 0.890399i
359359 −1.37921 + 2.38887i −0.0727920 + 0.126079i −0.900124 0.435634i 0.856524π-0.856524\pi
0.827332 + 0.561713i 0.189858π0.189858\pi
360360 0 0
361361 8.58638 14.8721i 0.451915 0.782740i
362362 −23.2659 −1.22283
363363 0 0
364364 4.25227 + 13.1900i 0.222880 + 0.691342i
365365 0.766844 0.0401385
366366 0 0
367367 7.07485 12.2540i 0.369304 0.639654i −0.620153 0.784481i 0.712929π-0.712929\pi
0.989457 + 0.144827i 0.0462626π0.0462626\pi
368368 −19.7324 −1.02862
369369 0 0
370370 0.558320 0.967039i 0.0290257 0.0502740i
371371 12.2084 1.47619i 0.633830 0.0766397i
372372 0 0
373373 2.52142 + 4.36723i 0.130554 + 0.226127i 0.923890 0.382657i 0.124991π-0.124991\pi
−0.793336 + 0.608784i 0.791658π0.791658\pi
374374 −3.26940 + 5.66276i −0.169056 + 0.292814i
375375 0 0
376376 −5.93034 + 10.2716i −0.305834 + 0.529720i
377377 28.0820 + 9.68358i 1.44630 + 0.498730i
378378 0 0
379379 3.02982 + 5.24780i 0.155631 + 0.269561i 0.933289 0.359127i 0.116925π-0.116925\pi
−0.777657 + 0.628688i 0.783592π0.783592\pi
380380 0.387575 0.0198822
381381 0 0
382382 −12.1837 21.1028i −0.623371 1.07971i
383383 −2.27052 3.93266i −0.116018 0.200950i 0.802168 0.597098i 0.203680π-0.203680\pi
−0.918186 + 0.396149i 0.870346π0.870346\pi
384384 0 0
385385 −2.16831 + 0.262182i −0.110507 + 0.0133620i
386386 0.967705 1.67611i 0.0492549 0.0853120i
387387 0 0
388388 −14.1446 + 24.4992i −0.718085 + 1.24376i
389389 2.25383 + 3.90374i 0.114273 + 0.197927i 0.917489 0.397761i 0.130213π-0.130213\pi
−0.803216 + 0.595688i 0.796879π0.796879\pi
390390 0 0
391391 −3.46213 −0.175088
392392 −4.92567 5.13843i −0.248784 0.259530i
393393 0 0
394394 −1.37349 2.37896i −0.0691955 0.119850i
395395 1.05918 + 1.83456i 0.0532932 + 0.0923065i
396396 0 0
397397 −2.00174 3.46712i −0.100465 0.174010i 0.811412 0.584475i 0.198700π-0.198700\pi
−0.911876 + 0.410465i 0.865366π0.865366\pi
398398 −26.1998 −1.31328
399399 0 0
400400 −11.8941 20.6012i −0.594706 1.03006i
401401 −12.6135 −0.629887 −0.314944 0.949110i 0.601986π-0.601986\pi
−0.314944 + 0.949110i 0.601986π0.601986\pi
402402 0 0
403403 −4.36537 1.50532i −0.217455 0.0749853i
404404 −12.3005 + 21.3051i −0.611972 + 1.05997i
405405 0 0
406406 40.2101 4.86201i 1.99559 0.241297i
407407 −6.36790 + 11.0295i −0.315645 + 0.546713i
408408 0 0
409409 20.6952 1.02331 0.511657 0.859190i 0.329032π-0.329032\pi
0.511657 + 0.859190i 0.329032π0.329032\pi
410410 1.97923 0.0977472
411411 0 0
412412 5.25482 9.10162i 0.258886 0.448404i
413413 −6.28990 + 14.7425i −0.309506 + 0.725432i
414414 0 0
415415 0.303336 0.525393i 0.0148902 0.0257905i
416416 −18.7184 + 16.2569i −0.917746 + 0.797058i
417417 0 0
418418 −10.5061 −0.513869
419419 −10.9088 18.8945i −0.532928 0.923058i −0.999261 0.0384484i 0.987758π-0.987758\pi
0.466333 0.884609i 0.345575π-0.345575\pi
420420 0 0
421421 9.42727 0.459457 0.229728 0.973255i 0.426216π-0.426216\pi
0.229728 + 0.973255i 0.426216π0.426216\pi
422422 24.5920 + 42.5947i 1.19712 + 2.07348i
423423 0 0
424424 2.36315 + 4.09310i 0.114765 + 0.198779i
425425 −2.08688 3.61458i −0.101228 0.175333i
426426 0 0
427427 29.8534 3.60973i 1.44471 0.174687i
428428 14.3133 0.691861
429429 0 0
430430 0.976930 + 1.69209i 0.0471118 + 0.0816000i
431431 10.2138 17.6908i 0.491980 0.852134i −0.507977 0.861370i 0.669607π-0.669607\pi
0.999957 + 0.00923613i 0.00293999π0.00293999\pi
432432 0 0
433433 −13.1743 + 22.8186i −0.633117 + 1.09659i 0.353794 + 0.935323i 0.384891π0.384891\pi
−0.986911 + 0.161267i 0.948442π0.948442\pi
434434 −6.25069 + 0.755803i −0.300043 + 0.0362797i
435435 0 0
436436 10.0356 + 17.3822i 0.480619 + 0.832457i
437437 −2.78136 4.81745i −0.133050 0.230450i
438438 0 0
439439 25.1310 1.19944 0.599720 0.800210i 0.295279π-0.295279\pi
0.599720 + 0.800210i 0.295279π0.295279\pi
440440 −0.419714 0.726967i −0.0200091 0.0346568i
441441 0 0
442442 −4.25558 + 3.69595i −0.202417 + 0.175799i
443443 9.25995 16.0387i 0.439953 0.762022i −0.557732 0.830021i 0.688328π-0.688328\pi
0.997685 + 0.0679994i 0.0216616π0.0216616\pi
444444 0 0
445445 −1.18261 + 2.04834i −0.0560611 + 0.0971006i
446446 −0.676415 1.17159i −0.0320292 0.0554762i
447447 0 0
448448 −3.30898 + 7.75573i −0.156335 + 0.366424i
449449 5.82155 10.0832i 0.274736 0.475856i −0.695333 0.718688i 0.744743π-0.744743\pi
0.970068 + 0.242832i 0.0780763π0.0780763\pi
450450 0 0
451451 −22.5740 −1.06297
452452 −3.10066 + 5.37050i −0.145843 + 0.252607i
453453 0 0
454454 −5.29939 −0.248713
455455 −1.84067 0.395660i −0.0862920 0.0185488i
456456 0 0
457457 20.5184 0.959812 0.479906 0.877320i 0.340671π-0.340671\pi
0.479906 + 0.877320i 0.340671π0.340671\pi
458458 2.94845 5.10687i 0.137772 0.238629i
459459 0 0
460460 −0.589955 + 1.02183i −0.0275068 + 0.0476431i
461461 1.02038 1.76734i 0.0475236 0.0823134i −0.841285 0.540592i 0.818200π-0.818200\pi
0.888809 + 0.458278i 0.151534π0.151534\pi
462462 0 0
463463 3.03155 0.140888 0.0704441 0.997516i 0.477558π-0.477558\pi
0.0704441 + 0.997516i 0.477558π0.477558\pi
464464 19.7521 + 34.2116i 0.916968 + 1.58824i
465465 0 0
466466 −12.4563 + 21.5749i −0.577025 + 0.999436i
467467 −6.46371 + 11.1955i −0.299105 + 0.518065i −0.975931 0.218078i 0.930021π-0.930021\pi
0.676827 + 0.736142i 0.263355π0.263355\pi
468468 0 0
469469 21.2793 + 28.3470i 0.982585 + 1.30894i
470470 2.13879 + 3.70449i 0.0986549 + 0.170875i
471471 0 0
472472 −6.16022 −0.283547
473473 −11.1423 19.2991i −0.512326 0.887374i
474474 0 0
475475 3.35305 5.80766i 0.153849 0.266474i
476476 −1.26898 + 2.97429i −0.0581637 + 0.136326i
477477 0 0
478478 −28.9015 −1.32192
479479 18.2911 31.6810i 0.835740 1.44754i −0.0576873 0.998335i 0.518373π-0.518373\pi
0.893427 0.449209i 0.148294π-0.148294\pi
480480 0 0
481481 −8.28872 + 7.19872i −0.377933 + 0.328233i
482482 14.0769 0.641187
483483 0 0
484484 −4.71806 8.17191i −0.214457 0.371451i
485485 −1.92159 3.32829i −0.0872550 0.151130i
486486 0 0
487487 36.7496 1.66528 0.832642 0.553812i 0.186827π-0.186827\pi
0.832642 + 0.553812i 0.186827π0.186827\pi
488488 5.77864 + 10.0089i 0.261587 + 0.453081i
489489 0 0
490490 −2.49313 + 0.611861i −0.112628 + 0.0276411i
491491 −4.09899 7.09965i −0.184985 0.320403i 0.758587 0.651572i 0.225890π-0.225890\pi
−0.943571 + 0.331169i 0.892557π0.892557\pi
492492 0 0
493493 3.46560 + 6.00259i 0.156083 + 0.270343i
494494 −8.56159 2.95231i −0.385204 0.132831i
495495 0 0
496496 −3.07048 5.31823i −0.137869 0.238795i
497497 9.48313 + 12.6329i 0.425376 + 0.566662i
498498 0 0
499499 21.6266 37.4584i 0.968141 1.67687i 0.267211 0.963638i 0.413898π-0.413898\pi
0.700929 0.713231i 0.252769π-0.252769\pi
500500 −2.85604 −0.127726
501501 0 0
502502 −1.18436 + 2.05137i −0.0528605 + 0.0915571i
503503 0.00909609 0.0157549i 0.000405575 0.000702476i −0.865823 0.500351i 0.833204π-0.833204\pi
0.866228 + 0.499649i 0.166538π0.166538\pi
504504 0 0
505505 −1.67106 2.89436i −0.0743612 0.128797i
506506 15.9920 27.6990i 0.710933 1.23137i
507507 0 0
508508 1.59095 + 2.75560i 0.0705869 + 0.122260i
509509 −43.1006 −1.91040 −0.955200 0.295960i 0.904361π-0.904361\pi
−0.955200 + 0.295960i 0.904361π0.904361\pi
510510 0 0
511511 −10.2056 + 1.23402i −0.451471 + 0.0545897i
512512 −23.2197 −1.02617
513513 0 0
514514 −15.7576 −0.695036
515515 0.713884 + 1.23648i 0.0314575 + 0.0544859i
516516 0 0
517517 −24.3939 42.2514i −1.07284 1.85822i
518518 −5.87430 + 13.7684i −0.258102 + 0.604949i
519519 0 0
520520 −0.137748 0.710362i −0.00604065 0.0311514i
521521 10.4770 + 18.1467i 0.459006 + 0.795022i 0.998909 0.0467056i 0.0148723π-0.0148723\pi
−0.539903 + 0.841727i 0.681539π0.681539\pi
522522 0 0
523523 −34.7403 −1.51909 −0.759543 0.650457i 0.774577π-0.774577\pi
−0.759543 + 0.650457i 0.774577π0.774577\pi
524524 1.65333 2.86365i 0.0722260 0.125099i
525525 0 0
526526 −11.8814 + 20.5791i −0.518052 + 0.897292i
527527 −0.538730 0.933107i −0.0234674 0.0406468i
528528 0 0
529529 −6.06520 −0.263704
530530 1.70455 0.0740410
531531 0 0
532532 −5.15809 + 0.623691i −0.223631 + 0.0270404i
533533 −18.3960 6.34352i −0.796819 0.274769i
534534 0 0
535535 −0.972255 + 1.68400i −0.0420343 + 0.0728055i
536536 −6.81142 + 11.7977i −0.294209 + 0.509584i
537537 0 0
538538 −8.75513 −0.377460
539539 28.4353 6.97856i 1.22480 0.300588i
540540 0 0
541541 1.64923 2.85655i 0.0709059 0.122813i −0.828393 0.560148i 0.810744π-0.810744\pi
0.899299 + 0.437335i 0.144078π0.144078\pi
542542 33.4678 1.43756
543543 0 0
544544 −5.78497 −0.248029
545545 −2.72674 −0.116801
546546 0 0
547547 21.9417 0.938161 0.469080 0.883155i 0.344585π-0.344585\pi
0.469080 + 0.883155i 0.344585π0.344585\pi
548548 −19.5367 −0.834567
549549 0 0
550550 38.5583 1.64413
551551 −5.56828 + 9.64455i −0.237217 + 0.410871i
552552 0 0
553553 −17.0484 22.7110i −0.724973 0.965768i
554554 48.5368 2.06213
555555 0 0
556556 −2.93850 + 5.08963i −0.124620 + 0.215848i
557557 −7.14329 + 12.3725i −0.302671 + 0.524241i −0.976740 0.214427i 0.931212π-0.931212\pi
0.674069 + 0.738668i 0.264545π0.264545\pi
558558 0 0
559559 −3.65686 18.8583i −0.154669 0.797621i
560560 −1.50315 2.00241i −0.0635196 0.0846172i
561561 0 0
562562 −6.80453 −0.287032
563563 −6.78784 −0.286073 −0.143037 0.989717i 0.545687π-0.545687\pi
−0.143037 + 0.989717i 0.545687π0.545687\pi
564564 0 0
565565 −0.421234 0.729599i −0.0177215 0.0306945i
566566 7.10307 12.3029i 0.298564 0.517128i
567567 0 0
568568 −3.03552 + 5.25767i −0.127367 + 0.220607i
569569 17.3212 0.726143 0.363072 0.931761i 0.381728π-0.381728\pi
0.363072 + 0.931761i 0.381728π0.381728\pi
570570 0 0
571571 6.50581 + 11.2684i 0.272260 + 0.471568i 0.969440 0.245328i 0.0788957π-0.0788957\pi
−0.697180 + 0.716896i 0.745562π0.745562\pi
572572 −4.17078 21.5086i −0.174389 0.899318i
573573 0 0
574574 −26.3408 + 3.18501i −1.09944 + 0.132940i
575575 10.2078 + 17.6805i 0.425696 + 0.737327i
576576 0 0
577577 0.365767 + 0.633528i 0.0152271 + 0.0263741i 0.873539 0.486755i 0.161820π-0.161820\pi
−0.858311 + 0.513129i 0.828486π0.828486\pi
578578 30.2735 1.25921
579579 0 0
580580 2.36218 0.0980842
581581 −3.19151 + 7.48039i −0.132406 + 0.310339i
582582 0 0
583583 −19.4412 −0.805173
584584 −1.97548 3.42163i −0.0817459 0.141588i
585585 0 0
586586 15.9369 27.6035i 0.658347 1.14029i
587587 −4.26142 7.38099i −0.175888 0.304646i 0.764581 0.644528i 0.222946π-0.222946\pi
−0.940468 + 0.339882i 0.889613π0.889613\pi
588588 0 0
589589 0.865594 1.49925i 0.0356662 0.0617756i
590590 −1.11085 + 1.92404i −0.0457329 + 0.0792117i
591591 0 0
592592 −14.6001 −0.600059
593593 −15.6547 + 27.1147i −0.642860 + 1.11347i 0.341932 + 0.939725i 0.388919π0.388919\pi
−0.984791 + 0.173741i 0.944415π0.944415\pi
594594 0 0
595595 −0.263734 0.351332i −0.0108120 0.0144032i
596596 11.1514 + 19.3147i 0.456777 + 0.791161i
597597 0 0
598598 20.8159 18.0785i 0.851225 0.739285i
599599 −0.375116 0.649720i −0.0153268 0.0265468i 0.858260 0.513215i 0.171546π-0.171546\pi
−0.873587 + 0.486668i 0.838212π0.838212\pi
600600 0 0
601601 4.77652 + 8.27318i 0.194838 + 0.337470i 0.946848 0.321683i 0.104248π-0.104248\pi
−0.752009 + 0.659153i 0.770915π0.770915\pi
602602 −15.7245 20.9473i −0.640884 0.853750i
603603 0 0
604604 −4.44624 7.70111i −0.180915 0.313354i
605605 1.28193 0.0521177
606606 0 0
607607 −11.1197 19.2599i −0.451336 0.781737i 0.547133 0.837045i 0.315719π-0.315719\pi
−0.998469 + 0.0553087i 0.982386π0.982386\pi
608608 −4.64745 8.04961i −0.188479 0.326455i
609609 0 0
610610 4.16815 0.168764
611611 −8.00594 41.2863i −0.323886 1.67027i
612612 0 0
613613 4.13993 7.17057i 0.167210 0.289617i −0.770228 0.637769i 0.779857π-0.779857\pi
0.937438 + 0.348152i 0.113191π0.113191\pi
614614 52.1578 2.10492
615615 0 0
616616 6.75567 + 8.99952i 0.272194 + 0.362601i
617617 10.1656 17.6073i 0.409252 0.708845i −0.585554 0.810633i 0.699123π-0.699123\pi
0.994806 + 0.101789i 0.0324565π0.0324565\pi
618618 0 0
619619 −2.67049 4.62542i −0.107336 0.185911i 0.807354 0.590067i 0.200899π-0.200899\pi
−0.914690 + 0.404156i 0.867565π0.867565\pi
620620 −0.367203 −0.0147472
621621 0 0
622622 21.8651 + 37.8714i 0.876709 + 1.51850i
623623 12.4427 29.1636i 0.498506 1.16842i
624624 0 0
625625 −12.2086 + 21.1459i −0.488345 + 0.845838i
626626 −3.11112 + 5.38862i −0.124345 + 0.215372i
627627 0 0
628628 −3.29536 5.70773i −0.131499 0.227763i
629629 −2.56165 −0.102140
630630 0 0
631631 −3.23331 + 5.60026i −0.128716 + 0.222943i −0.923179 0.384369i 0.874419π-0.874419\pi
0.794463 + 0.607312i 0.207752π0.207752\pi
632632 5.45714 9.45205i 0.217074 0.375982i
633633 0 0
634634 6.76217 11.7124i 0.268560 0.465160i
635635 −0.432271 −0.0171541
636636 0 0
637637 25.1335 + 2.30365i 0.995826 + 0.0912741i
638638 −64.0322 −2.53506
639639 0 0
640640 0.772706 1.33837i 0.0305439 0.0529035i
641641 −23.3289 −0.921434 −0.460717 0.887547i 0.652408π-0.652408\pi
−0.460717 + 0.887547i 0.652408π0.652408\pi
642642 0 0
643643 1.79439 3.10797i 0.0707637 0.122566i −0.828472 0.560030i 0.810790π-0.810790\pi
0.899236 + 0.437463i 0.144123π0.144123\pi
644644 6.20714 14.5485i 0.244596 0.573293i
645645 0 0
646646 −1.05658 1.83006i −0.0415707 0.0720026i
647647 −19.8262 + 34.3400i −0.779448 + 1.35004i 0.152812 + 0.988255i 0.451167π0.451167\pi
−0.932260 + 0.361788i 0.882166π0.882166\pi
648648 0 0
649649 12.6697 21.9446i 0.497331 0.861402i
650650 31.4218 + 10.8352i 1.23246 + 0.424993i
651651 0 0
652652 −1.32386 2.29299i −0.0518464 0.0898005i
653653 −18.1355 −0.709699 −0.354849 0.934923i 0.615468π-0.615468\pi
−0.354849 + 0.934923i 0.615468π0.615468\pi
654654 0 0
655655 0.224610 + 0.389035i 0.00877623 + 0.0152009i
656656 −12.9392 22.4114i −0.505192 0.875017i
657657 0 0
658658 −34.4256 45.8599i −1.34205 1.78780i
659659 6.74052 11.6749i 0.262573 0.454791i −0.704352 0.709851i 0.748762π-0.748762\pi
0.966925 + 0.255061i 0.0820955π0.0820955\pi
660660 0 0
661661 −5.15611 + 8.93064i −0.200549 + 0.347362i −0.948706 0.316161i 0.897606π-0.897606\pi
0.748156 + 0.663523i 0.230939π0.230939\pi
662662 −13.3076 23.0494i −0.517213 0.895839i
663663 0 0
664664 −3.12571 −0.121301
665665 0.276992 0.649226i 0.0107413 0.0251759i
666666 0 0
667667 −16.9517 29.3613i −0.656374 1.13687i
668668 −7.77805 13.4720i −0.300942 0.521247i
669669 0 0
670670 2.45655 + 4.25487i 0.0949049 + 0.164380i
671671 −47.5397 −1.83525
672672 0 0
673673 4.61528 + 7.99390i 0.177906 + 0.308142i 0.941163 0.337953i 0.109734π-0.109734\pi
−0.763257 + 0.646095i 0.776401π0.776401\pi
674674 −31.9237 −1.22965
675675 0 0
676676 2.64527 18.6997i 0.101741 0.719221i
677677 −10.5467 + 18.2674i −0.405343 + 0.702075i −0.994361 0.106045i 0.966181π-0.966181\pi
0.589018 + 0.808120i 0.299515π0.299515\pi
678678 0 0
679679 30.9297 + 41.2027i 1.18697 + 1.58122i
680680 0.0844203 0.146220i 0.00323737 0.00560729i
681681 0 0
682682 9.95385 0.381153
683683 38.2212 1.46249 0.731246 0.682113i 0.238939π-0.238939\pi
0.731246 + 0.682113i 0.238939π0.238939\pi
684684 0 0
685685 1.32706 2.29854i 0.0507044 0.0878226i
686686 32.1955 12.1550i 1.22923 0.464081i
687687 0 0
688688 12.7734 22.1241i 0.486980 0.843474i
689689 −15.8430 5.46317i −0.603570 0.208130i
690690 0 0
691691 −26.2322 −0.997920 −0.498960 0.866625i 0.666285π-0.666285\pi
−0.498960 + 0.866625i 0.666285π0.666285\pi
692692 −9.80084 16.9755i −0.372572 0.645313i
693693 0 0
694694 −14.3130 −0.543314
695695 −0.399204 0.691442i −0.0151427 0.0262279i
696696 0 0
697697 −2.27024 3.93218i −0.0859916 0.148942i
698698 20.7836 + 35.9982i 0.786670 + 1.36255i
699699 0 0
700700 18.9306 2.28900i 0.715511 0.0865161i
701701 46.7346 1.76514 0.882570 0.470180i 0.155811π-0.155811\pi
0.882570 + 0.470180i 0.155811π0.155811\pi
702702 0 0
703703 −2.05794 3.56446i −0.0776167 0.134436i
704704 6.66528 11.5446i 0.251207 0.435104i
705705 0 0
706706 20.6835 35.8248i 0.778433 1.34828i
707707 26.8972 + 35.8309i 1.01157 + 1.34756i
708708 0 0
709709 23.7232 + 41.0898i 0.890944 + 1.54316i 0.838745 + 0.544524i 0.183290π0.183290\pi
0.0521988 + 0.998637i 0.483377π0.483377\pi
710710 1.09476 + 1.89619i 0.0410858 + 0.0711626i
711711 0 0
712712 12.1861 0.456695
713713 2.63516 + 4.56423i 0.0986876 + 0.170932i
714714 0 0
715715 2.81384 + 0.970301i 0.105232 + 0.0362872i
716716 7.60461 13.1716i 0.284197 0.492244i
717717 0 0
718718 2.56280 4.43890i 0.0956428 0.165658i
719719 −24.6190 42.6413i −0.918133 1.59025i −0.802249 0.596990i 0.796363π-0.796363\pi
−0.115884 0.993263i 0.536970π-0.536970\pi
720720 0 0
721721 −11.4906 15.3071i −0.427931 0.570066i
722722 −15.9549 + 27.6347i −0.593779 + 1.02846i
723723 0 0
724724 18.1900 0.676024
725725 20.4361 35.3963i 0.758977 1.31459i
726726 0 0
727727 −32.0495 −1.18865 −0.594325 0.804225i 0.702581π-0.702581\pi
−0.594325 + 0.804225i 0.702581π0.702581\pi
728728 2.97636 + 9.23227i 0.110311 + 0.342171i
729729 0 0
730730 −1.42492 −0.0527387
731731 2.24114 3.88178i 0.0828917 0.143573i
732732 0 0
733733 −14.1005 + 24.4228i −0.520813 + 0.902075i 0.478894 + 0.877873i 0.341038π0.341038\pi
−0.999707 + 0.0242025i 0.992295π0.992295\pi
734734 −13.1462 + 22.7699i −0.485236 + 0.840453i
735735 0 0
736736 28.2968 1.04303
737737 −28.0181 48.5288i −1.03206 1.78758i
738738 0 0
739739 21.2685 36.8381i 0.782375 1.35511i −0.148180 0.988960i 0.547342π-0.547342\pi
0.930555 0.366153i 0.119325π-0.119325\pi
740740 −0.436510 + 0.756058i −0.0160464 + 0.0277932i
741741 0 0
742742 −22.6852 + 2.74299i −0.832801 + 0.100698i
743743 7.95711 + 13.7821i 0.291918 + 0.505617i 0.974263 0.225413i 0.0723732π-0.0723732\pi
−0.682345 + 0.731030i 0.739040π0.739040\pi
744744 0 0
745745 −3.02989 −0.111007
746746 −4.68521 8.11502i −0.171538 0.297112i
747747 0 0
748748 2.55611 4.42731i 0.0934605 0.161878i
749749 10.2295 23.9762i 0.373777 0.876072i
750750 0 0
751751 18.1996 0.664114 0.332057 0.943259i 0.392257π-0.392257\pi
0.332057 + 0.943259i 0.392257π0.392257\pi
752752 27.9646 48.4362i 1.01977 1.76629i
753753 0 0
754754 −52.1809 17.9937i −1.90032 0.655290i
755755 1.20807 0.0439662
756756 0 0
757757 22.4502 + 38.8849i 0.815967 + 1.41330i 0.908632 + 0.417598i 0.137128π0.137128\pi
−0.0926649 + 0.995697i 0.529539π0.529539\pi
758758 −5.62989 9.75126i −0.204487 0.354182i
759759 0 0
760760 0.271282 0.00984042
761761 −13.2444 22.9399i −0.480108 0.831572i 0.519631 0.854391i 0.326069π-0.326069\pi
−0.999740 + 0.0228184i 0.992736π0.992736\pi
762762 0 0
763763 36.2892 4.38791i 1.31376 0.158853i
764764 9.52554 + 16.4987i 0.344622 + 0.596903i
765765 0 0
766766 4.21900 + 7.30752i 0.152439 + 0.264031i
767767 16.4914 14.3227i 0.595471 0.517164i
768768 0 0
769769 −6.98127 12.0919i −0.251751 0.436045i 0.712257 0.701919i 0.247673π-0.247673\pi
−0.964008 + 0.265873i 0.914340π0.914340\pi
770770 4.02907 0.487176i 0.145198 0.0175566i
771771 0 0
772772 −0.756579 + 1.31043i −0.0272299 + 0.0471635i
773773 −12.8113 −0.460790 −0.230395 0.973097i 0.574002π-0.574002\pi
−0.230395 + 0.973097i 0.574002π0.574002\pi
774774 0 0
775775 −3.17681 + 5.50239i −0.114114 + 0.197652i
776776 −9.90048 + 17.1481i −0.355406 + 0.615582i
777777 0 0
778778 −4.18797 7.25378i −0.150146 0.260061i
779779 3.64767 6.31795i 0.130691 0.226364i
780780 0 0
781781 −12.4863 21.6269i −0.446795 0.773871i
782782 6.43320 0.230051
783783 0 0
784784 23.2271 + 24.2304i 0.829540 + 0.865372i
785785 0.895370 0.0319571
786786 0 0
787787 −27.3199 −0.973848 −0.486924 0.873444i 0.661881π-0.661881\pi
−0.486924 + 0.873444i 0.661881π0.661881\pi
788788 1.07383 + 1.85993i 0.0382537 + 0.0662574i
789789 0 0
790790 −1.96813 3.40890i −0.0700229 0.121283i
791791 6.78013 + 9.03210i 0.241074 + 0.321145i
792792 0 0
793793 −38.7410 13.3591i −1.37573 0.474396i
794794 3.71956 + 6.44247i 0.132002 + 0.228635i
795795 0 0
796796 20.4837 0.726027
797797 −14.7002 + 25.4614i −0.520707 + 0.901891i 0.479003 + 0.877813i 0.340998π0.340998\pi
−0.999710 + 0.0240775i 0.992335π0.992335\pi
798798 0 0
799799 4.90652 8.49835i 0.173580 0.300650i
800800 17.0565 + 29.5428i 0.603040 + 1.04450i
801801 0 0
802802 23.4379 0.827621
803803 16.2519 0.573517
804804 0 0
805805 1.29004 + 1.71852i 0.0454679 + 0.0605697i
806806 8.11157 + 2.79713i 0.285718 + 0.0985246i
807807 0 0
808808 −8.60968 + 14.9124i −0.302888 + 0.524617i
809809 −3.00617 + 5.20683i −0.105691 + 0.183063i −0.914020 0.405668i 0.867039π-0.867039\pi
0.808329 + 0.588731i 0.200372π0.200372\pi
810810 0 0
811811 8.44807 0.296652 0.148326 0.988939i 0.452612π-0.452612\pi
0.148326 + 0.988939i 0.452612π0.452612\pi
812812 −31.4374 + 3.80125i −1.10323 + 0.133398i
813813 0 0
814814 11.8326 20.4946i 0.414732 0.718337i
815815 0.359701 0.0125998
816816 0 0
817817 7.20184 0.251960
818818 −38.4551 −1.34455
819819 0 0
820820 −1.54742 −0.0540382
821821 34.2635 1.19581 0.597903 0.801569i 0.296001π-0.296001\pi
0.597903 + 0.801569i 0.296001π0.296001\pi
822822 0 0
823823 −6.23732 −0.217419 −0.108710 0.994074i 0.534672π-0.534672\pi
−0.108710 + 0.994074i 0.534672π0.534672\pi
824824 3.67809 6.37064i 0.128132 0.221932i
825825 0 0
826826 11.6876 27.3940i 0.406665 0.953158i
827827 −19.5232 −0.678889 −0.339445 0.940626i 0.610239π-0.610239\pi
−0.339445 + 0.940626i 0.610239π0.610239\pi
828828 0 0
829829 −16.3383 + 28.2988i −0.567453 + 0.982857i 0.429364 + 0.903131i 0.358738π0.358738\pi
−0.996817 + 0.0797254i 0.974596π0.974596\pi
830830 −0.563647 + 0.976265i −0.0195645 + 0.0338866i
831831 0 0
832832 8.67580 7.53489i 0.300779 0.261225i
833833 4.07530 + 4.25133i 0.141201 + 0.147300i
834834 0 0
835835 2.11334 0.0731353
836836 8.21395 0.284085
837837 0 0
838838 20.2702 + 35.1091i 0.700223 + 1.21282i
839839 12.3713 21.4278i 0.427106 0.739769i −0.569508 0.821985i 0.692866π-0.692866\pi
0.996615 + 0.0822161i 0.0261998π0.0261998\pi
840840 0 0
841841 −19.4374 + 33.6665i −0.670255 + 1.16092i
842842 −17.5174 −0.603689
843843 0 0
844844 −19.2267 33.3017i −0.661812 1.14629i
845845 2.02038 + 1.58143i 0.0695032 + 0.0544029i
846846 0 0
847847 −17.0607 + 2.06289i −0.586211 + 0.0708818i
848848 −11.1435 19.3011i −0.382670 0.662803i
849849 0 0
850850 3.87776 + 6.71647i 0.133006 + 0.230373i
851851 12.5301 0.429528
852852 0 0
853853 18.2245 0.623994 0.311997 0.950083i 0.399002π-0.399002\pi
0.311997 + 0.950083i 0.399002π0.399002\pi
854854 −55.4724 + 6.70745i −1.89823 + 0.229524i
855855 0 0
856856 10.0186 0.342427
857857 1.27340 + 2.20559i 0.0434984 + 0.0753414i 0.886955 0.461856i 0.152816π-0.152816\pi
−0.843457 + 0.537197i 0.819483π0.819483\pi
858858 0 0
859859 −27.0045 + 46.7732i −0.921382 + 1.59588i −0.124104 + 0.992269i 0.539606π0.539606\pi
−0.797278 + 0.603612i 0.793728π0.793728\pi
860860 −0.763792 1.32293i −0.0260451 0.0451114i
861861 0 0
862862 −18.9788 + 32.8723i −0.646421 + 1.11963i
863863 0.621545 1.07655i 0.0211576 0.0366461i −0.855253 0.518211i 0.826598π-0.826598\pi
0.876410 + 0.481565i 0.159931π0.159931\pi
864864 0 0
865865 2.66295 0.0905429
866866 24.4800 42.4006i 0.831864 1.44083i
867867 0 0
868868 4.88696 0.590908i 0.165874 0.0200567i
869869 22.4474 + 38.8801i 0.761477 + 1.31892i
870870 0 0
871871 −9.19540 47.4203i −0.311574 1.60678i
872872 7.02440 + 12.1666i 0.237876 + 0.412013i
873873 0 0
874874 5.16821 + 8.95161i 0.174817 + 0.302793i
875875 −2.04116 + 4.78414i −0.0690036 + 0.161733i
876876 0 0
877877 −0.401330 0.695125i −0.0135520 0.0234727i 0.859170 0.511690i 0.170981π-0.170981\pi
−0.872722 + 0.488218i 0.837647π0.837647\pi
878878 −46.6975 −1.57597
879879 0 0
880880 1.97917 + 3.42803i 0.0667179 + 0.115559i
881881 −18.5318 32.0980i −0.624352 1.08141i −0.988666 0.150133i 0.952030π-0.952030\pi
0.364314 0.931276i 0.381304π-0.381304\pi
882882 0 0
883883 −22.8671 −0.769539 −0.384770 0.923013i 0.625719π-0.625719\pi
−0.384770 + 0.923013i 0.625719π0.625719\pi
884884 3.32713 2.88960i 0.111904 0.0971877i
885885 0 0
886886 −17.2065 + 29.8025i −0.578063 + 1.00123i
887887 49.2573 1.65390 0.826950 0.562276i 0.190074π-0.190074\pi
0.826950 + 0.562276i 0.190074π0.190074\pi
888888 0 0
889889 5.75292 0.695616i 0.192947 0.0233302i
890890 2.19748 3.80614i 0.0736597 0.127582i
891891 0 0
892892 0.528840 + 0.915978i 0.0177069 + 0.0306692i
893893 15.7669 0.527620
894894 0 0
895895 1.03311 + 1.78940i 0.0345330 + 0.0598130i
896896 −8.12993 + 19.0552i −0.271602 + 0.636591i
897897 0 0
898898 −10.8174 + 18.7362i −0.360980 + 0.625236i
899899 5.27559 9.13760i 0.175951 0.304756i
900900 0 0
901901 −1.95518 3.38647i −0.0651365 0.112820i
902902 41.9462 1.39666
903903 0 0
904904 −2.17029 + 3.75906i −0.0721829 + 0.125024i
905905 −1.23558 + 2.14009i −0.0410721 + 0.0711390i
906906 0 0
907907 2.50228 4.33407i 0.0830867 0.143910i −0.821488 0.570226i 0.806855π-0.806855\pi
0.904574 + 0.426316i 0.140189π0.140189\pi
908908 4.14321 0.137497
909909 0 0
910910 3.42026 + 0.735200i 0.113381 + 0.0243716i
911911 −49.0582 −1.62537 −0.812685 0.582703i 0.801995π-0.801995\pi
−0.812685 + 0.582703i 0.801995π0.801995\pi
912912 0 0
913913 6.42866 11.1348i 0.212757 0.368507i
914914 −38.1266 −1.26111
915915 0 0
916916 −2.30518 + 3.99270i −0.0761654 + 0.131922i
917917 −3.61529 4.81608i −0.119387 0.159041i
918918 0 0
919919 −14.8028 25.6392i −0.488299 0.845758i 0.511611 0.859217i 0.329049π-0.329049\pi
−0.999909 + 0.0134590i 0.995716π0.995716\pi
920920 −0.412937 + 0.715227i −0.0136141 + 0.0235803i
921921 0 0
922922 −1.89602 + 3.28401i −0.0624422 + 0.108153i
923923 −4.09794 21.1329i −0.134885 0.695598i
924924 0 0
925925 7.55282 + 13.0819i 0.248335 + 0.430129i
926926 −5.63311 −0.185116
927927 0 0
928928 −28.3251 49.0605i −0.929817 1.61049i
929929 8.41525 + 14.5756i 0.276095 + 0.478211i 0.970411 0.241460i 0.0776261π-0.0776261\pi
−0.694316 + 0.719671i 0.744293π0.744293\pi
930930 0 0
931931 −2.64164 + 9.08604i −0.0865764 + 0.297783i
932932 9.73865 16.8678i 0.319000 0.552524i
933933 0 0
934934 12.0106 20.8030i 0.392999 0.680695i
935935 0.347255 + 0.601463i 0.0113565 + 0.0196699i
936936 0 0
937937 44.0131 1.43784 0.718922 0.695091i 0.244636π-0.244636\pi
0.718922 + 0.695091i 0.244636π0.244636\pi
938938 −39.5403 52.6734i −1.29104 1.71985i
939939 0 0
940940 −1.67216 2.89627i −0.0545400 0.0944660i
941941 26.5338 + 45.9578i 0.864976 + 1.49818i 0.867071 + 0.498184i 0.166000π0.166000\pi
−0.00209573 + 0.999998i 0.500667π0.500667\pi
942942 0 0
943943 11.1048 + 19.2340i 0.361620 + 0.626345i
944944 29.0487 0.945453
945945 0 0
946946 20.7043 + 35.8609i 0.673154 + 1.16594i
947947 27.8817 0.906034 0.453017 0.891502i 0.350348π-0.350348\pi
0.453017 + 0.891502i 0.350348π0.350348\pi
948948 0 0
949949 13.2439 + 4.56694i 0.429917 + 0.148249i
950950 −6.23051 + 10.7916i −0.202145 + 0.350125i
951951 0 0
952952 −0.888219 + 2.08184i −0.0287873 + 0.0674729i
953953 −18.1784 + 31.4859i −0.588856 + 1.01993i 0.405527 + 0.914083i 0.367088π0.367088\pi
−0.994383 + 0.105845i 0.966245π0.966245\pi
954954 0 0
955955 −2.58815 −0.0837505
956956 22.5960 0.730807
957957 0 0
958958 −33.9877 + 58.8685i −1.09809 + 1.90195i
959959 −13.9625 + 32.7259i −0.450873 + 1.05677i
960960 0 0
961961 14.6799 25.4263i 0.473545 0.820205i
962962 15.4018 13.3764i 0.496573 0.431272i
963963 0 0
964964 −11.0057 −0.354471
965965 −0.102784 0.178026i −0.00330872 0.00573087i
966966 0 0
967967 −15.2681 −0.490988 −0.245494 0.969398i 0.578950π-0.578950\pi
−0.245494 + 0.969398i 0.578950π0.578950\pi
968968 −3.30239 5.71990i −0.106143 0.183845i
969969 0 0
970970 3.57063 + 6.18450i 0.114646 + 0.198572i
971971 −18.4460 31.9494i −0.591961 1.02531i −0.993968 0.109669i 0.965021π-0.965021\pi
0.402008 0.915636i 0.368313π-0.368313\pi
972972 0 0
973973 6.42554 + 8.55974i 0.205993 + 0.274413i
974974 −68.2867 −2.18805
975975 0 0
976976 −27.2493 47.1972i −0.872229 1.51074i
977977 −0.221957 + 0.384441i −0.00710104 + 0.0122994i −0.869554 0.493838i 0.835594π-0.835594\pi
0.862453 + 0.506137i 0.168927π0.168927\pi
978978 0 0
979979 −25.0633 + 43.4109i −0.801026 + 1.38742i
980980 1.94920 0.478370i 0.0622649 0.0152810i
981981 0 0
982982 7.61658 + 13.1923i 0.243055 + 0.420983i
983983 22.7802 + 39.4564i 0.726575 + 1.25846i 0.958323 + 0.285688i 0.0922222π0.0922222\pi
−0.231748 + 0.972776i 0.574444π0.574444\pi
984984 0 0
985985 −0.291767 −0.00929648
986986 −6.43964 11.1538i −0.205080 0.355209i
987987 0 0
988988 6.69369 + 2.30820i 0.212955 + 0.0734336i
989989 −10.9624 + 18.9875i −0.348585 + 0.603766i
990990 0 0
991991 −26.8148 + 46.4445i −0.851799 + 1.47536i 0.0277842 + 0.999614i 0.491155π0.491155\pi
−0.879583 + 0.475745i 0.842178π0.842178\pi
992992 4.40316 + 7.62650i 0.139801 + 0.242142i
993993 0 0
994994 −17.6212 23.4739i −0.558910 0.744548i
995995 −1.39139 + 2.40996i −0.0441100 + 0.0764008i
996996 0 0
997997 29.0852 0.921139 0.460569 0.887624i 0.347645π-0.347645\pi
0.460569 + 0.887624i 0.347645π0.347645\pi
998998 −40.1857 + 69.6038i −1.27206 + 2.20327i
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.s.d.289.1 12
3.2 odd 2 91.2.h.b.16.6 yes 12
7.4 even 3 819.2.n.d.172.6 12
13.9 even 3 819.2.n.d.100.6 12
21.2 odd 6 637.2.f.k.393.1 12
21.5 even 6 637.2.f.j.393.1 12
21.11 odd 6 91.2.g.b.81.1 yes 12
21.17 even 6 637.2.g.l.263.1 12
21.20 even 2 637.2.h.l.471.6 12
39.23 odd 6 1183.2.e.g.170.6 12
39.29 odd 6 1183.2.e.h.170.1 12
39.35 odd 6 91.2.g.b.9.1 12
91.74 even 3 inner 819.2.s.d.802.1 12
273.23 odd 6 8281.2.a.ce.1.1 6
273.68 even 6 8281.2.a.ca.1.6 6
273.74 odd 6 91.2.h.b.74.6 yes 12
273.107 odd 6 8281.2.a.bz.1.6 6
273.152 even 6 637.2.f.j.295.1 12
273.179 odd 6 1183.2.e.g.508.6 12
273.191 odd 6 637.2.f.k.295.1 12
273.230 even 6 637.2.g.l.373.1 12
273.257 even 6 8281.2.a.cf.1.1 6
273.263 odd 6 1183.2.e.h.508.1 12
273.269 even 6 637.2.h.l.165.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.1 12 39.35 odd 6
91.2.g.b.81.1 yes 12 21.11 odd 6
91.2.h.b.16.6 yes 12 3.2 odd 2
91.2.h.b.74.6 yes 12 273.74 odd 6
637.2.f.j.295.1 12 273.152 even 6
637.2.f.j.393.1 12 21.5 even 6
637.2.f.k.295.1 12 273.191 odd 6
637.2.f.k.393.1 12 21.2 odd 6
637.2.g.l.263.1 12 21.17 even 6
637.2.g.l.373.1 12 273.230 even 6
637.2.h.l.165.6 12 273.269 even 6
637.2.h.l.471.6 12 21.20 even 2
819.2.n.d.100.6 12 13.9 even 3
819.2.n.d.172.6 12 7.4 even 3
819.2.s.d.289.1 12 1.1 even 1 trivial
819.2.s.d.802.1 12 91.74 even 3 inner
1183.2.e.g.170.6 12 39.23 odd 6
1183.2.e.g.508.6 12 273.179 odd 6
1183.2.e.h.170.1 12 39.29 odd 6
1183.2.e.h.508.1 12 273.263 odd 6
8281.2.a.bz.1.6 6 273.107 odd 6
8281.2.a.ca.1.6 6 273.68 even 6
8281.2.a.ce.1.1 6 273.23 odd 6
8281.2.a.cf.1.1 6 273.257 even 6