Properties

Label 441.3.l.b.391.12
Level 441441
Weight 33
Character 441.391
Analytic conductor 12.01612.016
Analytic rank 00
Dimension 2828
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [441,3,Mod(97,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.97"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 441=3272 441 = 3^{2} \cdot 7^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 441.l (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [28,1,0,-23,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 12.016379658312.0163796583
Analytic rank: 00
Dimension: 2828
Relative dimension: 1414 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 391.12
Character χ\chi == 441.391
Dual form 441.3.l.b.97.12

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+(1.41697+2.45427i)q2+(2.702161.30320i)q3+(2.01561+3.49114i)q4+(2.07720+1.19927i)q5+(7.02729+4.78521i)q60.0884848q8+(5.603327.04292i)q9+6.79734iq10+(5.695289.86452i)q11+(0.896835+12.0604i)q12+(13.4628+7.77278i)q13+(7.17583+0.533610i)q15+(7.93707+13.7474i)q16+12.1021iq17+(25.2249+3.77242i)q18+16.0014iq19+(8.37367+4.83454i)q20+(16.140127.9555i)q22+(8.0283113.9054i)q23+(0.239100+0.115314i)q24+(9.6234916.6684i)q25+44.0552iq26+(5.9627026.3334i)q27+(16.2339+28.1180i)q29+(8.85832+18.3675i)q30+(36.719421.1999i)q31+(22.6701+39.2658i)q32+(28.245019.2334i)q33+(29.7018+17.1483i)q34+(13.2937+33.7578i)q36+7.22811q37+(39.2718+22.6736i)q38+(46.5083+3.45845i)q39+(0.1838010.106117i)q40+(7.55990+4.36471i)q41+(22.211338.4711i)q43+45.9179q44+(20.08567.90966i)q45+45.5035q46+(22.8382+13.1856i)q47+(39.3629+26.8040i)q48+(27.272447.2372i)q50+(15.7715+32.7018i)q51+(54.2717+31.3338i)q5268.1249q53+(73.078022.6795i)q5427.3208iq55+(20.8531+43.2384i)q57+(46.0060+79.6847i)q58+(82.4104+47.5797i)q59+(16.3266+23.9763i)q60+(42.8184+24.7212i)q61120.159iq6264.9952q64+(18.6434+32.2913i)q65+(7.1814596.5740i)q66+(40.935070.9015i)q67+(42.250224.3931i)q68+(3.5721548.0372i)q69112.881q71+(0.495809+0.623192i)q72+67.9029iq73+(10.2420+17.7397i)q74+(47.726532.4992i)q75+(55.863332.2527i)q76+(57.4129+119.044i)q78+(68.4439118.548i)q79+38.0748iq80+(18.205678.9275i)q81+24.7387iq82+(18.8674+10.8931i)q83+(14.5137+25.1385i)q85+(62.9455109.025i)q86+(80.5101+54.8232i)q87+(0.503946+0.872861i)q88108.432iq89+(47.8732+38.0877i)q90+(32.3639+56.0559i)q92+(126.8499.43279i)q93+(64.722037.3673i)q94+(19.1901+33.2382i)q95+(10.0870+135.646i)q96+(96.5982+55.7710i)q97+(101.38815.1626i)q99+O(q100)q+(1.41697 + 2.45427i) q^{2} +(2.70216 - 1.30320i) q^{3} +(-2.01561 + 3.49114i) q^{4} +(2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} -0.0884848 q^{8} +(5.60332 - 7.04292i) q^{9} +6.79734i q^{10} +(-5.69528 - 9.86452i) q^{11} +(-0.896835 + 12.0604i) q^{12} +(13.4628 + 7.77278i) q^{13} +(7.17583 + 0.533610i) q^{15} +(7.93707 + 13.7474i) q^{16} +12.1021i q^{17} +(25.2249 + 3.77242i) q^{18} +16.0014i q^{19} +(-8.37367 + 4.83454i) q^{20} +(16.1401 - 27.9555i) q^{22} +(8.02831 - 13.9054i) q^{23} +(-0.239100 + 0.115314i) q^{24} +(-9.62349 - 16.6684i) q^{25} +44.0552i q^{26} +(5.96270 - 26.3334i) q^{27} +(16.2339 + 28.1180i) q^{29} +(8.85832 + 18.3675i) q^{30} +(-36.7194 - 21.1999i) q^{31} +(-22.6701 + 39.2658i) q^{32} +(-28.2450 - 19.2334i) q^{33} +(-29.7018 + 17.1483i) q^{34} +(13.2937 + 33.7578i) q^{36} +7.22811 q^{37} +(-39.2718 + 22.6736i) q^{38} +(46.5083 + 3.45845i) q^{39} +(-0.183801 - 0.106117i) q^{40} +(7.55990 + 4.36471i) q^{41} +(-22.2113 - 38.4711i) q^{43} +45.9179 q^{44} +(20.0856 - 7.90966i) q^{45} +45.5035 q^{46} +(-22.8382 + 13.1856i) q^{47} +(39.3629 + 26.8040i) q^{48} +(27.2724 - 47.2372i) q^{50} +(15.7715 + 32.7018i) q^{51} +(-54.2717 + 31.3338i) q^{52} -68.1249 q^{53} +(73.0780 - 22.6795i) q^{54} -27.3208i q^{55} +(20.8531 + 43.2384i) q^{57} +(-46.0060 + 79.6847i) q^{58} +(82.4104 + 47.5797i) q^{59} +(-16.3266 + 23.9763i) q^{60} +(-42.8184 + 24.7212i) q^{61} -120.159i q^{62} -64.9952 q^{64} +(18.6434 + 32.2913i) q^{65} +(7.18145 - 96.5740i) q^{66} +(40.9350 - 70.9015i) q^{67} +(-42.2502 - 24.3931i) q^{68} +(3.57215 - 48.0372i) q^{69} -112.881 q^{71} +(-0.495809 + 0.623192i) q^{72} +67.9029i q^{73} +(10.2420 + 17.7397i) q^{74} +(-47.7265 - 32.4992i) q^{75} +(-55.8633 - 32.2527i) q^{76} +(57.4129 + 119.044i) q^{78} +(-68.4439 - 118.548i) q^{79} +38.0748i q^{80} +(-18.2056 - 78.9275i) q^{81} +24.7387i q^{82} +(-18.8674 + 10.8931i) q^{83} +(-14.5137 + 25.1385i) q^{85} +(62.9455 - 109.025i) q^{86} +(80.5101 + 54.8232i) q^{87} +(0.503946 + 0.872861i) q^{88} -108.432i q^{89} +(47.8732 + 38.0877i) q^{90} +(32.3639 + 56.0559i) q^{92} +(-126.849 - 9.43279i) q^{93} +(-64.7220 - 37.3673i) q^{94} +(-19.1901 + 33.2382i) q^{95} +(-10.0870 + 135.646i) q^{96} +(-96.5982 + 55.7710i) q^{97} +(-101.388 - 15.1626i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q+q223q4+3q512q616q8+6q9+7q11+27q1215q1318q1527q16+9q18108q2010q22+34q23+120q24+31q25+81q27+162q99+O(q100) 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27}+ \cdots - 162 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/441Z)×\left(\mathbb{Z}/441\mathbb{Z}\right)^\times.

nn 199199 344344
χ(n)\chi(n) 1-1 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 1.41697 + 2.45427i 0.708485 + 1.22713i 0.965419 + 0.260704i 0.0839545π0.0839545\pi
−0.256934 + 0.966429i 0.582712π0.582712\pi
33 2.70216 1.30320i 0.900720 0.434401i
44 −2.01561 + 3.49114i −0.503903 + 0.872785i
55 2.07720 + 1.19927i 0.415440 + 0.239855i 0.693125 0.720818i 0.256234π-0.256234\pi
−0.277684 + 0.960672i 0.589567π0.589567\pi
66 7.02729 + 4.78521i 1.17121 + 0.797535i
77 0 0
88 −0.0884848 −0.0110606
99 5.60332 7.04292i 0.622591 0.782547i
1010 6.79734i 0.679734i
1111 −5.69528 9.86452i −0.517753 0.896775i −0.999787 0.0206223i 0.993435π-0.993435\pi
0.482034 0.876152i 0.339898π-0.339898\pi
1212 −0.896835 + 12.0604i −0.0747362 + 1.00503i
1313 13.4628 + 7.77278i 1.03560 + 0.597906i 0.918585 0.395224i 0.129333π-0.129333\pi
0.117019 + 0.993130i 0.462666π0.462666\pi
1414 0 0
1515 7.17583 + 0.533610i 0.478388 + 0.0355740i
1616 7.93707 + 13.7474i 0.496067 + 0.859213i
1717 12.1021i 0.711888i 0.934507 + 0.355944i 0.115841π0.115841\pi
−0.934507 + 0.355944i 0.884159π0.884159\pi
1818 25.2249 + 3.77242i 1.40139 + 0.209579i
1919 16.0014i 0.842181i 0.907019 + 0.421090i 0.138352π0.138352\pi
−0.907019 + 0.421090i 0.861648π0.861648\pi
2020 −8.37367 + 4.83454i −0.418683 + 0.241727i
2121 0 0
2222 16.1401 27.9555i 0.733641 1.27070i
2323 8.02831 13.9054i 0.349057 0.604584i −0.637025 0.770843i 0.719835π-0.719835\pi
0.986082 + 0.166259i 0.0531686π0.0531686\pi
2424 −0.239100 + 0.115314i −0.00996250 + 0.00480474i
2525 −9.62349 16.6684i −0.384939 0.666735i
2626 44.0552i 1.69443i
2727 5.96270 26.3334i 0.220841 0.975310i
2828 0 0
2929 16.2339 + 28.1180i 0.559791 + 0.969586i 0.997513 + 0.0704760i 0.0224518π0.0224518\pi
−0.437723 + 0.899110i 0.644215π0.644215\pi
3030 8.85832 + 18.3675i 0.295277 + 0.612250i
3131 −36.7194 21.1999i −1.18450 0.683869i −0.227445 0.973791i 0.573037π-0.573037\pi
−0.957050 + 0.289922i 0.906371π0.906371\pi
3232 −22.6701 + 39.2658i −0.708442 + 1.22706i
3333 −28.2450 19.2334i −0.855910 0.582830i
3434 −29.7018 + 17.1483i −0.873581 + 0.504362i
3535 0 0
3636 13.2937 + 33.7578i 0.369270 + 0.937716i
3737 7.22811 0.195354 0.0976772 0.995218i 0.468859π-0.468859\pi
0.0976772 + 0.995218i 0.468859π0.468859\pi
3838 −39.2718 + 22.6736i −1.03347 + 0.596673i
3939 46.5083 + 3.45845i 1.19252 + 0.0886783i
4040 −0.183801 0.106117i −0.00459502 0.00265294i
4141 7.55990 + 4.36471i 0.184388 + 0.106456i 0.589353 0.807876i 0.299383π-0.299383\pi
−0.404965 + 0.914332i 0.632716π0.632716\pi
4242 0 0
4343 −22.2113 38.4711i −0.516542 0.894676i −0.999816 0.0192072i 0.993886π-0.993886\pi
0.483274 0.875469i 0.339448π-0.339448\pi
4444 45.9179 1.04359
4545 20.0856 7.90966i 0.446347 0.175770i
4646 45.5035 0.989207
4747 −22.8382 + 13.1856i −0.485919 + 0.280545i −0.722880 0.690974i 0.757182π-0.757182\pi
0.236961 + 0.971519i 0.423849π0.423849\pi
4848 39.3629 + 26.8040i 0.820060 + 0.558418i
4949 0 0
5050 27.2724 47.2372i 0.545448 0.944744i
5151 15.7715 + 32.7018i 0.309245 + 0.641212i
5252 −54.2717 + 31.3338i −1.04369 + 0.602573i
5353 −68.1249 −1.28538 −0.642688 0.766128i 0.722181π-0.722181\pi
−0.642688 + 0.766128i 0.722181π0.722181\pi
5454 73.0780 22.6795i 1.35330 0.419992i
5555 27.3208i 0.496742i
5656 0 0
5757 20.8531 + 43.2384i 0.365844 + 0.758568i
5858 −46.0060 + 79.6847i −0.793207 + 1.37387i
5959 82.4104 + 47.5797i 1.39679 + 0.806435i 0.994055 0.108883i 0.0347274π-0.0347274\pi
0.402732 + 0.915318i 0.368061π0.368061\pi
6060 −16.3266 + 23.9763i −0.272110 + 0.399605i
6161 −42.8184 + 24.7212i −0.701941 + 0.405266i −0.808070 0.589087i 0.799488π-0.799488\pi
0.106129 + 0.994352i 0.466154π0.466154\pi
6262 120.159i 1.93804i
6363 0 0
6464 −64.9952 −1.01555
6565 18.6434 + 32.2913i 0.286821 + 0.496789i
6666 7.18145 96.5740i 0.108810 1.46324i
6767 40.9350 70.9015i 0.610971 1.05823i −0.380107 0.924943i 0.624113π-0.624113\pi
0.991077 0.133289i 0.0425539π-0.0425539\pi
6868 −42.2502 24.3931i −0.621326 0.358723i
6969 3.57215 48.0372i 0.0517703 0.696192i
7070 0 0
7171 −112.881 −1.58987 −0.794936 0.606694i 0.792496π-0.792496\pi
−0.794936 + 0.606694i 0.792496π0.792496\pi
7272 −0.495809 + 0.623192i −0.00688624 + 0.00865544i
7373 67.9029i 0.930176i 0.885264 + 0.465088i 0.153977π0.153977\pi
−0.885264 + 0.465088i 0.846023π0.846023\pi
7474 10.2420 + 17.7397i 0.138406 + 0.239726i
7575 −47.7265 32.4992i −0.636353 0.433323i
7676 −55.8633 32.2527i −0.735043 0.424377i
7777 0 0
7878 57.4129 + 119.044i 0.736063 + 1.52621i
7979 −68.4439 118.548i −0.866379 1.50061i −0.865671 0.500613i 0.833108π-0.833108\pi
−0.000707812 1.00000i 0.500225π-0.500225\pi
8080 38.0748i 0.475936i
8181 −18.2056 78.9275i −0.224760 0.974414i
8282 24.7387i 0.301691i
8383 −18.8674 + 10.8931i −0.227318 + 0.131242i −0.609334 0.792913i 0.708563π-0.708563\pi
0.382016 + 0.924156i 0.375230π0.375230\pi
8484 0 0
8585 −14.5137 + 25.1385i −0.170750 + 0.295747i
8686 62.9455 109.025i 0.731924 1.26773i
8787 80.5101 + 54.8232i 0.925404 + 0.630151i
8888 0.503946 + 0.872861i 0.00572666 + 0.00991887i
8989 108.432i 1.21834i −0.793040 0.609169i 0.791503π-0.791503\pi
0.793040 0.609169i 0.208497π-0.208497\pi
9090 47.8732 + 38.0877i 0.531924 + 0.423197i
9191 0 0
9292 32.3639 + 56.0559i 0.351782 + 0.609304i
9393 −126.849 9.43279i −1.36397 0.101428i
9494 −64.7220 37.3673i −0.688532 0.397524i
9595 −19.1901 + 33.2382i −0.202001 + 0.349876i
9696 −10.0870 + 135.646i −0.105072 + 1.41298i
9797 −96.5982 + 55.7710i −0.995857 + 0.574959i −0.907020 0.421088i 0.861649π-0.861649\pi
−0.0888375 + 0.996046i 0.528315π0.528315\pi
9898 0 0
9999 −101.388 15.1626i −1.02412 0.153158i
100100 77.5888 0.775888
101101 66.5650 38.4313i 0.659059 0.380508i −0.132859 0.991135i 0.542416π-0.542416\pi
0.791919 + 0.610627i 0.209082π0.209082\pi
102102 −57.9111 + 85.0449i −0.567756 + 0.833774i
103103 −130.580 75.3905i −1.26777 0.731946i −0.293203 0.956050i 0.594721π-0.594721\pi
−0.974565 + 0.224104i 0.928054π0.928054\pi
104104 −1.19126 0.687773i −0.0114544 0.00661320i
105105 0 0
106106 −96.5310 167.197i −0.910669 1.57733i
107107 76.6044 0.715929 0.357964 0.933735i 0.383471π-0.383471\pi
0.357964 + 0.933735i 0.383471π0.383471\pi
108108 79.9150 + 73.8945i 0.739954 + 0.684208i
109109 −25.1970 −0.231165 −0.115582 0.993298i 0.536873π-0.536873\pi
−0.115582 + 0.993298i 0.536873π0.536873\pi
110110 67.0525 38.7128i 0.609568 0.351934i
111111 19.5315 9.41970i 0.175960 0.0848622i
112112 0 0
113113 37.0748 64.2154i 0.328095 0.568277i −0.654039 0.756461i 0.726927π-0.726927\pi
0.982134 + 0.188184i 0.0602600π0.0602600\pi
114114 −76.5702 + 112.447i −0.671669 + 0.986374i
115115 33.3528 19.2563i 0.290025 0.167446i
116116 −130.885 −1.12832
117117 130.180 51.2644i 1.11265 0.438157i
118118 269.676i 2.28539i
119119 0 0
120120 −0.634952 0.0472164i −0.00529127 0.000393470i
121121 −4.37253 + 7.57345i −0.0361366 + 0.0625905i
122122 −121.345 70.0585i −0.994629 0.574250i
123123 26.1162 + 1.94205i 0.212327 + 0.0157891i
124124 148.024 85.4617i 1.19374 0.689207i
125125 106.128i 0.849027i
126126 0 0
127127 52.2864 0.411704 0.205852 0.978583i 0.434003π-0.434003\pi
0.205852 + 0.978583i 0.434003π0.434003\pi
128128 −1.41571 2.45209i −0.0110603 0.0191569i
129129 −110.154 75.0092i −0.853908 0.581466i
130130 −52.8342 + 91.5116i −0.406417 + 0.703935i
131131 161.548 + 93.2696i 1.23319 + 0.711982i 0.967693 0.252131i 0.0811313π-0.0811313\pi
0.265495 + 0.964112i 0.414465π0.414465\pi
132132 124.078 59.8404i 0.939981 0.453336i
133133 0 0
134134 232.015 1.73145
135135 43.9666 47.5488i 0.325679 0.352213i
136136 1.07085i 0.00787392i
137137 76.6871 + 132.826i 0.559760 + 0.969533i 0.997516 + 0.0704389i 0.0224400π0.0224400\pi
−0.437756 + 0.899094i 0.644227π0.644227\pi
138138 122.958 59.3003i 0.890998 0.429713i
139139 79.0232 + 45.6241i 0.568513 + 0.328231i 0.756555 0.653930i 0.226881π-0.226881\pi
−0.188043 + 0.982161i 0.560214π0.560214\pi
140140 0 0
141141 −44.5288 + 65.3924i −0.315807 + 0.463776i
142142 −159.949 277.040i −1.12640 1.95098i
143143 177.073i 1.23827i
144144 141.296 + 21.1310i 0.981221 + 0.146743i
145145 77.8757i 0.537074i
146146 −166.652 + 96.2164i −1.14145 + 0.659016i
147147 0 0
148148 −14.5691 + 25.2344i −0.0984396 + 0.170502i
149149 −56.2062 + 97.3519i −0.377223 + 0.653369i −0.990657 0.136377i 0.956454π-0.956454\pi
0.613434 + 0.789746i 0.289787π0.289787\pi
150150 12.1347 163.184i 0.0808980 1.08789i
151151 −14.0984 24.4192i −0.0933671 0.161717i 0.815559 0.578674i 0.196430π-0.196430\pi
−0.908926 + 0.416958i 0.863096π0.863096\pi
152152 1.41588i 0.00931503i
153153 85.2342 + 67.8120i 0.557086 + 0.443216i
154154 0 0
155155 −50.8490 88.0731i −0.328058 0.568214i
156156 −105.817 + 155.396i −0.678311 + 0.996128i
157157 −8.87726 5.12529i −0.0565431 0.0326452i 0.471462 0.881886i 0.343726π-0.343726\pi
−0.528005 + 0.849241i 0.677060π0.677060\pi
158158 193.966 335.959i 1.22763 2.12632i
159159 −184.084 + 88.7806i −1.15776 + 0.558368i
160160 −94.1810 + 54.3754i −0.588631 + 0.339846i
161161 0 0
162162 167.912 156.519i 1.03650 0.966168i
163163 −177.682 −1.09007 −0.545037 0.838412i 0.683485π-0.683485\pi
−0.545037 + 0.838412i 0.683485π0.683485\pi
164164 −30.4757 + 17.5951i −0.185827 + 0.107287i
165165 −35.6046 73.8252i −0.215785 0.447425i
166166 −53.4692 30.8705i −0.322104 0.185967i
167167 −53.9725 31.1611i −0.323189 0.186593i 0.329624 0.944112i 0.393078π-0.393078\pi
−0.652813 + 0.757519i 0.726411π0.726411\pi
168168 0 0
169169 36.3322 + 62.9292i 0.214983 + 0.372362i
170170 −82.2621 −0.483895
171171 112.697 + 89.6612i 0.659046 + 0.524334i
172172 179.077 1.04115
173173 76.2216 44.0066i 0.440587 0.254373i −0.263259 0.964725i 0.584797π-0.584797\pi
0.703847 + 0.710352i 0.251464π0.251464\pi
174174 −20.4701 + 275.276i −0.117644 + 1.58205i
175175 0 0
176176 90.4077 156.591i 0.513680 0.889720i
177177 284.692 + 21.1703i 1.60843 + 0.119606i
178178 266.121 153.645i 1.49506 0.863175i
179179 12.9521 0.0723579 0.0361789 0.999345i 0.488481π-0.488481\pi
0.0361789 + 0.999345i 0.488481π0.488481\pi
180180 −12.8711 + 86.0646i −0.0715059 + 0.478137i
181181 225.852i 1.24780i −0.781503 0.623901i 0.785547π-0.785547\pi
0.781503 0.623901i 0.214453π-0.214453\pi
182182 0 0
183183 −83.4853 + 122.602i −0.456204 + 0.669955i
184184 −0.710384 + 1.23042i −0.00386078 + 0.00668707i
185185 15.0143 + 8.66848i 0.0811581 + 0.0468567i
186186 −156.591 324.688i −0.841889 1.74563i
187187 119.381 68.9249i 0.638404 0.368582i
188188 106.308i 0.565470i
189189 0 0
190190 −108.767 −0.572459
191191 −51.9453 89.9718i −0.271965 0.471057i 0.697400 0.716682i 0.254340π-0.254340\pi
−0.969365 + 0.245625i 0.921007π0.921007\pi
192192 −175.627 + 84.7020i −0.914726 + 0.441156i
193193 −81.1711 + 140.592i −0.420575 + 0.728458i −0.995996 0.0893998i 0.971505π-0.971505\pi
0.575420 + 0.817858i 0.304838π0.304838\pi
194194 −273.754 158.052i −1.41110 0.814699i
195195 92.4594 + 62.9600i 0.474151 + 0.322872i
196196 0 0
197197 301.595 1.53094 0.765470 0.643472i 0.222507π-0.222507\pi
0.765470 + 0.643472i 0.222507π0.222507\pi
198198 −106.450 270.317i −0.537627 1.36524i
199199 57.8010i 0.290457i 0.989398 + 0.145229i 0.0463917π0.0463917\pi
−0.989398 + 0.145229i 0.953608π0.953608\pi
200200 0.851533 + 1.47490i 0.00425766 + 0.00737449i
201201 18.2138 244.934i 0.0906160 1.21858i
202202 188.641 + 108.912i 0.933868 + 0.539169i
203203 0 0
204204 −145.956 10.8536i −0.715470 0.0532039i
205205 10.4690 + 18.1328i 0.0510681 + 0.0884526i
206206 427.304i 2.07429i
207207 −52.9497 134.459i −0.255796 0.649562i
208208 246.772i 1.18640i
209209 157.846 91.1327i 0.755246 0.436042i
210210 0 0
211211 −21.2197 + 36.7535i −0.100567 + 0.174187i −0.911918 0.410371i 0.865399π-0.865399\pi
0.811351 + 0.584559i 0.198732π0.198732\pi
212212 137.313 237.834i 0.647704 1.12186i
213213 −305.022 + 147.107i −1.43203 + 0.690642i
214214 108.546 + 188.007i 0.507225 + 0.878540i
215215 106.550i 0.495580i
216216 −0.527609 + 2.33010i −0.00244263 + 0.0107875i
217217 0 0
218218 −35.7034 61.8400i −0.163777 0.283670i
219219 88.4912 + 183.484i 0.404070 + 0.837828i
220220 95.3808 + 55.0681i 0.433549 + 0.250310i
221221 −94.0670 + 162.929i −0.425642 + 0.737234i
222222 50.7940 + 34.5881i 0.228802 + 0.155802i
223223 −166.212 + 95.9625i −0.745345 + 0.430325i −0.824009 0.566576i 0.808268π-0.808268\pi
0.0786645 + 0.996901i 0.474934π0.474934\pi
224224 0 0
225225 −171.318 25.6208i −0.761411 0.113870i
226226 210.135 0.929802
227227 −194.664 + 112.390i −0.857552 + 0.495108i −0.863192 0.504876i 0.831538π-0.831538\pi
0.00563942 + 0.999984i 0.498205π0.498205\pi
228228 −192.983 14.3506i −0.846417 0.0629414i
229229 138.693 + 80.0742i 0.605644 + 0.349669i 0.771259 0.636522i 0.219627π-0.219627\pi
−0.165614 + 0.986191i 0.552961π0.552961\pi
230230 94.5200 + 54.5712i 0.410957 + 0.237266i
231231 0 0
232232 −1.43646 2.48802i −0.00619162 0.0107242i
233233 −246.598 −1.05836 −0.529180 0.848510i 0.677500π-0.677500\pi
−0.529180 + 0.848510i 0.677500π0.677500\pi
234234 310.277 + 246.855i 1.32597 + 1.05494i
235235 −63.2527 −0.269160
236236 −332.215 + 191.804i −1.40769 + 0.812730i
237237 −339.439 231.140i −1.43223 0.975275i
238238 0 0
239239 −110.141 + 190.769i −0.460839 + 0.798197i −0.999003 0.0446434i 0.985785π-0.985785\pi
0.538164 + 0.842840i 0.319118π0.319118\pi
240240 49.6193 + 102.884i 0.206747 + 0.428684i
241241 228.282 131.799i 0.947230 0.546883i 0.0550106 0.998486i 0.482481π-0.482481\pi
0.892219 + 0.451602i 0.149147π0.149147\pi
242242 −24.7830 −0.102409
243243 −152.053 189.549i −0.625732 0.780038i
244244 199.313i 0.816858i
245245 0 0
246246 32.2395 + 66.8478i 0.131055 + 0.271739i
247247 −124.376 + 215.425i −0.503545 + 0.872165i
248248 3.24911 + 1.87587i 0.0131012 + 0.00756400i
249249 −36.7868 + 54.0230i −0.147738 + 0.216960i
250250 260.467 150.381i 1.04187 0.601523i
251251 23.0003i 0.0916348i −0.998950 0.0458174i 0.985411π-0.985411\pi
0.998950 0.0458174i 0.0145892π-0.0145892\pi
252252 0 0
253253 −182.894 −0.722901
254254 74.0883 + 128.325i 0.291686 + 0.505215i
255255 −6.45780 + 86.8426i −0.0253247 + 0.340559i
256256 −125.978 + 218.201i −0.492103 + 0.852347i
257257 15.4300 + 8.90852i 0.0600389 + 0.0346635i 0.529719 0.848173i 0.322297π-0.322297\pi
−0.469680 + 0.882837i 0.655631π0.655631\pi
258258 28.0072 376.633i 0.108555 1.45982i
259259 0 0
260260 −150.311 −0.578120
261261 288.997 + 43.2198i 1.10727 + 0.165593i
262262 528.641i 2.01771i
263263 181.504 + 314.375i 0.690130 + 1.19534i 0.971795 + 0.235828i 0.0757801π0.0757801\pi
−0.281665 + 0.959513i 0.590887π0.590887\pi
264264 2.49926 + 1.70186i 0.00946688 + 0.00644645i
265265 −141.509 81.7004i −0.533997 0.308303i
266266 0 0
267267 −141.309 293.001i −0.529248 1.09738i
268268 165.018 + 285.820i 0.615740 + 1.06649i
269269 196.159i 0.729215i 0.931161 + 0.364607i 0.118797π0.118797\pi
−0.931161 + 0.364607i 0.881203π0.881203\pi
270270 178.997 + 40.5305i 0.662951 + 0.150113i
271271 95.2916i 0.351629i 0.984423 + 0.175815i 0.0562560π0.0562560\pi
−0.984423 + 0.175815i 0.943744π0.943744\pi
272272 −166.372 + 96.0552i −0.611663 + 0.353144i
273273 0 0
274274 −217.327 + 376.421i −0.793163 + 1.37380i
275275 −109.617 + 189.862i −0.398607 + 0.690408i
276276 160.505 + 109.295i 0.581539 + 0.395997i
277277 107.725 + 186.586i 0.388901 + 0.673596i 0.992302 0.123842i 0.0395216π-0.0395216\pi
−0.603401 + 0.797438i 0.706188π0.706188\pi
278278 258.592i 0.930187i
279279 −355.060 + 139.822i −1.27262 + 0.501153i
280280 0 0
281281 101.916 + 176.523i 0.362689 + 0.628196i 0.988402 0.151857i 0.0485254π-0.0485254\pi
−0.625713 + 0.780053i 0.715192π0.715192\pi
282282 −223.586 16.6264i −0.792860 0.0589587i
283283 −104.320 60.2294i −0.368624 0.212825i 0.304233 0.952598i 0.401600π-0.401600\pi
−0.672857 + 0.739773i 0.734933π0.734933\pi
284284 227.524 394.083i 0.801141 1.38762i
285285 −8.53852 + 114.823i −0.0299597 + 0.402889i
286286 434.583 250.907i 1.51952 0.877297i
287287 0 0
288288 149.518 + 379.683i 0.519161 + 1.31834i
289289 142.539 0.493215
290290 −191.128 + 110.348i −0.659061 + 0.380509i
291291 −188.343 + 276.589i −0.647226 + 0.950478i
292292 −237.059 136.866i −0.811844 0.468719i
293293 −151.688 87.5769i −0.517705 0.298897i 0.218290 0.975884i 0.429952π-0.429952\pi
−0.735995 + 0.676987i 0.763285π0.763285\pi
294294 0 0
295295 114.122 + 197.665i 0.386854 + 0.670051i
296296 −0.639578 −0.00216074
297297 −293.725 + 91.1568i −0.988974 + 0.306925i
298298 −318.570 −1.06903
299299 216.168 124.805i 0.722969 0.417406i
300300 209.657 101.114i 0.698858 0.337047i
301301 0 0
302302 39.9541 69.2026i 0.132298 0.229148i
303303 129.785 190.595i 0.428335 0.629027i
304304 −219.978 + 127.004i −0.723612 + 0.417778i
305305 −118.590 −0.388819
306306 −45.6542 + 305.275i −0.149197 + 0.997630i
307307 18.3665i 0.0598259i 0.999553 + 0.0299129i 0.00952300π0.00952300\pi
−0.999553 + 0.0299129i 0.990477π0.990477\pi
308308 0 0
309309 −451.097 33.5446i −1.45986 0.108558i
310310 144.103 249.594i 0.464849 0.805142i
311311 353.193 + 203.916i 1.13567 + 0.655679i 0.945355 0.326044i 0.105716π-0.105716\pi
0.190315 + 0.981723i 0.439049π0.439049\pi
312312 −4.11528 0.306021i −0.0131900 0.000980836i
313313 −348.791 + 201.374i −1.11435 + 0.643369i −0.939952 0.341307i 0.889130π-0.889130\pi
−0.174396 + 0.984676i 0.555797π0.555797\pi
314314 29.0495i 0.0925145i
315315 0 0
316316 551.826 1.74628
317317 148.273 + 256.817i 0.467739 + 0.810149i 0.999320 0.0368589i 0.0117352π-0.0117352\pi
−0.531581 + 0.847007i 0.678402π0.678402\pi
318318 −478.733 325.992i −1.50545 1.02513i
319319 184.914 320.280i 0.579667 1.00401i
320320 −135.008 77.9470i −0.421901 0.243584i
321321 206.997 99.8311i 0.644851 0.311000i
322322 0 0
323323 −193.651 −0.599539
324324 312.243 + 95.5291i 0.963712 + 0.294843i
325325 299.205i 0.920631i
326326 −251.770 436.079i −0.772302 1.33767i
327327 −68.0862 + 32.8368i −0.208215 + 0.100418i
328328 −0.668937 0.386211i −0.00203944 0.00117747i
329329 0 0
330330 130.736 191.991i 0.396169 0.581791i
331331 −266.479 461.556i −0.805074 1.39443i −0.916241 0.400627i 0.868792π-0.868792\pi
0.111167 0.993802i 0.464541π-0.464541\pi
332332 87.8252i 0.264534i
333333 40.5014 50.9070i 0.121626 0.152874i
334334 176.617i 0.528794i
335335 170.061 98.1846i 0.507644 0.293088i
336336 0 0
337337 149.044 258.152i 0.442267 0.766029i −0.555590 0.831456i 0.687508π-0.687508\pi
0.997857 + 0.0654274i 0.0208411π0.0208411\pi
338338 −102.963 + 178.338i −0.304625 + 0.527626i
339339 16.4962 221.836i 0.0486614 0.654384i
340340 −58.5081 101.339i −0.172083 0.298056i
341341 482.959i 1.41630i
342342 −60.3642 + 403.635i −0.176503 + 1.18022i
343343 0 0
344344 1.96536 + 3.40411i 0.00571326 + 0.00989566i
345345 65.0298 95.4990i 0.188492 0.276809i
346346 216.008 + 124.712i 0.624300 + 0.360439i
347347 90.4019 156.581i 0.260524 0.451241i −0.705857 0.708354i 0.749438π-0.749438\pi
0.966381 + 0.257113i 0.0827712π0.0827712\pi
348348 −353.673 + 170.570i −1.01630 + 0.490144i
349349 −151.888 + 87.6925i −0.435209 + 0.251268i −0.701563 0.712607i 0.747514π-0.747514\pi
0.266354 + 0.963875i 0.414181π0.414181\pi
350350 0 0
351351 284.958 308.175i 0.811847 0.877992i
352352 516.452 1.46719
353353 −34.0434 + 19.6549i −0.0964401 + 0.0556797i −0.547444 0.836842i 0.684399π-0.684399\pi
0.451004 + 0.892522i 0.351066π0.351066\pi
354354 351.443 + 728.707i 0.992776 + 2.05849i
355355 −234.476 135.375i −0.660497 0.381338i
356356 378.552 + 218.557i 1.06335 + 0.613924i
357357 0 0
358358 18.3527 + 31.7878i 0.0512645 + 0.0887927i
359359 247.647 0.689824 0.344912 0.938635i 0.387909π-0.387909\pi
0.344912 + 0.938635i 0.387909π0.387909\pi
360360 −1.77727 + 0.699885i −0.00493687 + 0.00194413i
361361 104.954 0.290732
362362 554.302 320.026i 1.53122 0.884050i
363363 −1.94553 + 26.1630i −0.00535959 + 0.0720742i
364364 0 0
365365 −81.4341 + 141.048i −0.223107 + 0.386433i
366366 −419.193 31.1721i −1.14534 0.0851697i
367367 −343.635 + 198.398i −0.936334 + 0.540593i −0.888809 0.458277i 0.848467π-0.848467\pi
−0.0475248 + 0.998870i 0.515133π0.515133\pi
368368 254.885 0.692622
369369 73.1009 28.7869i 0.198105 0.0780134i
370370 49.1319i 0.132789i
371371 0 0
372372 288.610 423.836i 0.775834 1.13935i
373373 −186.570 + 323.149i −0.500189 + 0.866352i 0.499811 + 0.866134i 0.333403π0.333403\pi
−1.00000 0.000217836i 0.999931π0.999931\pi
374374 338.320 + 195.329i 0.904599 + 0.522271i
375375 −138.307 286.776i −0.368818 0.764736i
376376 2.02083 1.16673i 0.00537455 0.00310300i
377377 504.731i 1.33881i
378378 0 0
379379 548.285 1.44666 0.723331 0.690502i 0.242610π-0.242610\pi
0.723331 + 0.690502i 0.242610π0.242610\pi
380380 −77.3595 133.991i −0.203578 0.352607i
381381 141.286 68.1398i 0.370830 0.178845i
382382 147.210 254.975i 0.385366 0.667474i
383383 −4.04111 2.33314i −0.0105512 0.00609174i 0.494715 0.869055i 0.335272π-0.335272\pi
−0.505266 + 0.862963i 0.668606π0.668606\pi
384384 −7.02105 4.78097i −0.0182840 0.0124504i
385385 0 0
386386 −460.068 −1.19189
387387 −395.406 59.1335i −1.02172 0.152800i
388388 449.651i 1.15889i
389389 336.313 + 582.511i 0.864558 + 1.49746i 0.867486 + 0.497462i 0.165735π0.165735\pi
−0.00292782 + 0.999996i 0.500932π0.500932\pi
390390 −23.5083 + 316.132i −0.0602777 + 0.810596i
391391 168.285 + 97.1594i 0.430397 + 0.248490i
392392 0 0
393393 558.077 + 41.4998i 1.42004 + 0.105597i
394394 427.351 + 740.194i 1.08465 + 1.87867i
395395 328.332i 0.831220i
396396 257.293 323.396i 0.649730 0.816658i
397397 106.271i 0.267684i −0.991003 0.133842i 0.957268π-0.957268\pi
0.991003 0.133842i 0.0427315π-0.0427315\pi
398398 −141.859 + 81.9023i −0.356429 + 0.205785i
399399 0 0
400400 152.765 264.596i 0.381911 0.661490i
401401 149.197 258.416i 0.372061 0.644429i −0.617821 0.786319i 0.711985π-0.711985\pi
0.989882 + 0.141890i 0.0453178π0.0453178\pi
402402 626.941 302.363i 1.55955 0.752146i
403403 −329.565 570.823i −0.817779 1.41643i
404404 309.850i 0.766957i
405405 56.8391 185.782i 0.140343 0.458721i
406406 0 0
407407 −41.1662 71.3019i −0.101145 0.175189i
408408 −1.39554 2.89361i −0.00342044 0.00709219i
409409 −570.795 329.549i −1.39559 0.805743i −0.401661 0.915789i 0.631567π-0.631567\pi
−0.993927 + 0.110046i 0.964900π0.964900\pi
410410 −29.6684 + 51.3872i −0.0723620 + 0.125335i
411411 380.320 + 258.978i 0.925353 + 0.630117i
412412 526.398 303.916i 1.27766 0.737660i
413413 0 0
414414 254.971 320.478i 0.615872 0.774101i
415415 −52.2553 −0.125916
416416 −610.409 + 352.420i −1.46733 + 0.847164i
417417 272.991 + 20.3002i 0.654654 + 0.0486815i
418418 447.328 + 258.265i 1.07016 + 0.617858i
419419 485.296 + 280.186i 1.15822 + 0.668701i 0.950878 0.309566i 0.100184π-0.100184\pi
0.207346 + 0.978268i 0.433517π0.433517\pi
420420 0 0
421421 57.9969 + 100.454i 0.137760 + 0.238607i 0.926648 0.375929i 0.122676π-0.122676\pi
−0.788889 + 0.614536i 0.789343π0.789343\pi
422422 −120.271 −0.285001
423423 −35.1043 + 234.731i −0.0829889 + 0.554919i
424424 6.02802 0.0142170
425425 201.722 116.464i 0.474641 0.274034i
426426 −793.246 540.159i −1.86208 1.26798i
427427 0 0
428428 −154.405 + 267.437i −0.360759 + 0.624852i
429429 −230.762 478.479i −0.537906 1.11533i
430430 261.501 150.978i 0.608142 0.351111i
431431 −322.507 −0.748277 −0.374138 0.927373i 0.622061π-0.622061\pi
−0.374138 + 0.927373i 0.622061π0.622061\pi
432432 409.342 127.038i 0.947550 0.294069i
433433 117.316i 0.270937i 0.990782 + 0.135468i 0.0432539π0.0432539\pi
−0.990782 + 0.135468i 0.956746π0.956746\pi
434434 0 0
435435 101.488 + 210.432i 0.233305 + 0.483753i
436436 50.7873 87.9662i 0.116485 0.201757i
437437 222.507 + 128.464i 0.509169 + 0.293969i
438438 −324.930 + 477.173i −0.741849 + 1.08944i
439439 −187.788 + 108.419i −0.427763 + 0.246969i −0.698393 0.715714i 0.746101π-0.746101\pi
0.270630 + 0.962683i 0.412768π0.412768\pi
440440 2.41748i 0.00549427i
441441 0 0
442442 −533.160 −1.20625
443443 74.8709 + 129.680i 0.169009 + 0.292732i 0.938072 0.346441i 0.112610π-0.112610\pi
−0.769063 + 0.639173i 0.779277π0.779277\pi
444444 −6.48242 + 87.1737i −0.0146001 + 0.196337i
445445 130.040 225.235i 0.292224 0.506147i
446446 −471.035 271.952i −1.05613 0.609758i
447447 −25.0086 + 336.308i −0.0559477 + 0.752368i
448448 0 0
449449 −263.767 −0.587455 −0.293727 0.955889i 0.594896π-0.594896\pi
−0.293727 + 0.955889i 0.594896π0.594896\pi
450450 −179.872 456.763i −0.399715 1.01503i
451451 99.4331i 0.220473i
452452 149.457 + 258.866i 0.330656 + 0.572713i
453453 −69.9194 47.6114i −0.154347 0.105102i
454454 −551.668 318.505i −1.21513 0.701554i
455455 0 0
456456 −1.84518 3.82594i −0.00404646 0.00839023i
457457 109.396 + 189.480i 0.239379 + 0.414617i 0.960536 0.278154i 0.0897227π-0.0897227\pi
−0.721157 + 0.692772i 0.756389π0.756389\pi
458458 453.851i 0.990941i
459459 318.689 + 72.1613i 0.694312 + 0.157214i
460460 155.253i 0.337506i
461461 −334.892 + 193.350i −0.726446 + 0.419414i −0.817121 0.576467i 0.804431π-0.804431\pi
0.0906743 + 0.995881i 0.471098π0.471098\pi
462462 0 0
463463 241.881 418.950i 0.522421 0.904860i −0.477238 0.878774i 0.658362π-0.658362\pi
0.999660 0.0260863i 0.00830447π-0.00830447\pi
464464 −257.700 + 446.349i −0.555387 + 0.961959i
465465 −252.179 171.721i −0.542321 0.369292i
466466 −349.422 605.216i −0.749832 1.29875i
467467 115.519i 0.247363i 0.992322 + 0.123682i 0.0394702π0.0394702\pi
−0.992322 + 0.123682i 0.960530π0.960530\pi
468468 −83.4205 + 557.805i −0.178249 + 1.19189i
469469 0 0
470470 −89.6272 155.239i −0.190696 0.330295i
471471 −30.6671 2.28047i −0.0651106 0.00484176i
472472 −7.29207 4.21008i −0.0154493 0.00891966i
473473 −252.999 + 438.208i −0.534882 + 0.926443i
474474 86.3041 1160.59i 0.182076 2.44851i
475475 266.718 153.990i 0.561511 0.324189i
476476 0 0
477477 −381.726 + 479.798i −0.800264 + 1.00587i
478478 −624.264 −1.30599
479479 394.602 227.823i 0.823803 0.475623i −0.0279230 0.999610i 0.508889π-0.508889\pi
0.851726 + 0.523987i 0.175556π0.175556\pi
480480 −183.630 + 269.668i −0.382562 + 0.561808i
481481 97.3110 + 56.1825i 0.202310 + 0.116804i
482482 646.939 + 373.510i 1.34220 + 0.774918i
483483 0 0
484484 −17.6267 30.5303i −0.0364187 0.0630790i
485485 −267.539 −0.551626
486486 249.749 641.764i 0.513888 1.32050i
487487 324.669 0.666671 0.333335 0.942808i 0.391826π-0.391826\pi
0.333335 + 0.942808i 0.391826π0.391826\pi
488488 3.78878 2.18745i 0.00776389 0.00448248i
489489 −480.126 + 231.556i −0.981852 + 0.473530i
490490 0 0
491491 −155.221 + 268.850i −0.316132 + 0.547557i −0.979678 0.200579i 0.935718π-0.935718\pi
0.663545 + 0.748136i 0.269051π0.269051\pi
492492 −59.4200 + 87.2608i −0.120772 + 0.177359i
493493 −340.287 + 196.465i −0.690237 + 0.398509i
494494 −704.946 −1.42702
495495 −192.418 153.087i −0.388724 0.309267i
496496 673.061i 1.35698i
497497 0 0
498498 −184.713 13.7356i −0.370909 0.0275816i
499499 387.110 670.494i 0.775771 1.34368i −0.158589 0.987345i 0.550694π-0.550694\pi
0.934360 0.356331i 0.115972π-0.115972\pi
500500 370.509 + 213.914i 0.741019 + 0.427827i
501501 −186.452 13.8649i −0.372159 0.0276745i
502502 56.4489 32.5908i 0.112448 0.0649219i
503503 106.472i 0.211674i −0.994384 0.105837i 0.966248π-0.966248\pi
0.994384 0.105837i 0.0337521π-0.0337521\pi
504504 0 0
505505 184.359 0.365067
506506 −259.155 448.870i −0.512165 0.887096i
507507 180.185 + 122.696i 0.355394 + 0.242005i
508508 −105.389 + 182.539i −0.207459 + 0.359329i
509509 293.258 + 169.313i 0.576146 + 0.332638i 0.759600 0.650390i 0.225395π-0.225395\pi
−0.183454 + 0.983028i 0.558728π0.558728\pi
510510 −222.285 + 107.204i −0.435853 + 0.210204i
511511 0 0
512512 −725.356 −1.41671
513513 421.372 + 95.4118i 0.821387 + 0.185988i
514514 50.4924i 0.0982343i
515515 −180.828 313.202i −0.351121 0.608160i
516516 483.895 233.374i 0.937782 0.452276i
517517 260.140 + 150.192i 0.503172 + 0.290506i
518518 0 0
519519 148.613 218.245i 0.286346 0.420511i
520520 −1.64966 2.85729i −0.00317241 0.00549478i
521521 97.1593i 0.186486i −0.995643 0.0932431i 0.970277π-0.970277\pi
0.995643 0.0932431i 0.0297234π-0.0297234\pi
522522 303.427 + 770.516i 0.581278 + 1.47608i
523523 593.254i 1.13433i −0.823605 0.567164i 0.808041π-0.808041\pi
0.823605 0.567164i 0.191959π-0.191959\pi
524524 −651.235 + 375.990i −1.24281 + 0.717539i
525525 0 0
526526 −514.372 + 890.919i −0.977894 + 1.69376i
527527 256.564 444.382i 0.486838 0.843229i
528528 40.2264 540.953i 0.0761863 1.02453i
529529 135.592 + 234.853i 0.256319 + 0.443957i
530530 463.068i 0.873713i
531531 796.872 313.806i 1.50070 0.590972i
532532 0 0
533533 67.8519 + 117.523i 0.127302 + 0.220493i
534534 518.871 761.984i 0.971668 1.42694i
535535 159.123 + 91.8696i 0.297426 + 0.171719i
536536 −3.62213 + 6.27371i −0.00675770 + 0.0117047i
537537 34.9985 16.8792i 0.0651742 0.0314323i
538538 −481.426 + 277.951i −0.894843 + 0.516638i
539539 0 0
540540 77.3800 + 249.334i 0.143296 + 0.461729i
541541 −578.154 −1.06868 −0.534338 0.845271i 0.679439π-0.679439\pi
−0.534338 + 0.845271i 0.679439π0.679439\pi
542542 −233.871 + 135.025i −0.431496 + 0.249124i
543543 −294.332 610.289i −0.542047 1.12392i
544544 −475.199 274.356i −0.873528 0.504332i
545545 −52.3392 30.2181i −0.0960352 0.0554460i
546546 0 0
547547 110.283 + 191.016i 0.201615 + 0.349207i 0.949049 0.315129i 0.102048π-0.102048\pi
−0.747434 + 0.664336i 0.768714π0.768714\pi
548548 −618.286 −1.12826
549549 −65.8156 + 440.088i −0.119883 + 0.801617i
550550 −621.296 −1.12963
551551 −449.928 + 259.766i −0.816566 + 0.471445i
552552 −0.316081 + 4.25057i −0.000572611 + 0.00770030i
553553 0 0
554554 −305.288 + 528.774i −0.551061 + 0.954465i
555555 51.8677 + 3.85699i 0.0934553 + 0.00694954i
556556 −318.560 + 183.921i −0.572950 + 0.330793i
557557 −359.594 −0.645590 −0.322795 0.946469i 0.604622π-0.604622\pi
−0.322795 + 0.946469i 0.604622π0.604622\pi
558558 −846.269 673.288i −1.51661 1.20661i
559559 690.574i 1.23537i
560560 0 0
561561 232.764 341.824i 0.414910 0.609313i
562562 −288.823 + 500.256i −0.513920 + 0.890135i
563563 854.592 + 493.399i 1.51792 + 0.876374i 0.999778 + 0.0210827i 0.00671133π0.00671133\pi
0.518147 + 0.855292i 0.326622π0.326622\pi
564564 −138.541 287.262i −0.245641 0.509330i
565565 154.024 88.9255i 0.272608 0.157390i
566566 341.373i 0.603133i
567567 0 0
568568 9.98825 0.0175849
569569 −41.8937 72.5620i −0.0736269 0.127525i 0.826861 0.562406i 0.190124π-0.190124\pi
−0.900488 + 0.434880i 0.856791π0.856791\pi
570570 −293.906 + 141.746i −0.515625 + 0.248677i
571571 175.350 303.715i 0.307093 0.531901i −0.670632 0.741790i 0.733977π-0.733977\pi
0.977725 + 0.209889i 0.0673103π0.0673103\pi
572572 618.186 + 356.910i 1.08074 + 0.623968i
573573 −257.616 175.423i −0.449592 0.306148i
574574 0 0
575575 −309.041 −0.537463
576576 −364.189 + 457.756i −0.632273 + 0.794716i
577577 753.475i 1.30585i −0.757423 0.652925i 0.773542π-0.773542\pi
0.757423 0.652925i 0.226458π-0.226458\pi
578578 201.974 + 349.829i 0.349436 + 0.605240i
579579 −36.1166 + 485.685i −0.0623775 + 0.838835i
580580 −271.875 156.967i −0.468750 0.270633i
581581 0 0
582582 −945.699 70.3242i −1.62491 0.120832i
583583 387.991 + 672.019i 0.665507 + 1.15269i
584584 6.00837i 0.0102883i
585585 331.890 + 49.6345i 0.567333 + 0.0848453i
586586 496.375i 0.847057i
587587 112.348 64.8642i 0.191394 0.110501i −0.401241 0.915972i 0.631421π-0.631421\pi
0.592635 + 0.805471i 0.298088π0.298088\pi
588588 0 0
589589 339.229 587.562i 0.575941 0.997559i
590590 −323.415 + 560.172i −0.548161 + 0.949443i
591591 814.958 393.040i 1.37895 0.665042i
592592 57.3700 + 99.3678i 0.0969088 + 0.167851i
593593 503.348i 0.848815i −0.905471 0.424408i 0.860482π-0.860482\pi
0.905471 0.424408i 0.139518π-0.139518\pi
594594 −639.923 591.713i −1.07731 0.996151i
595595 0 0
596596 −226.580 392.447i −0.380167 0.658469i
597597 75.3264 + 156.187i 0.126175 + 0.261620i
598598 612.607 + 353.689i 1.02443 + 0.591453i
599599 141.278 244.701i 0.235857 0.408516i −0.723664 0.690152i 0.757544π-0.757544\pi
0.959521 + 0.281636i 0.0908770π0.0908770\pi
600600 4.22307 + 2.87569i 0.00703845 + 0.00479281i
601601 159.905 92.3214i 0.266065 0.153613i −0.361033 0.932553i 0.617576π-0.617576\pi
0.627098 + 0.778940i 0.284242π0.284242\pi
602602 0 0
603603 −269.982 685.586i −0.447731 1.13696i
604604 113.668 0.188192
605605 −18.1653 + 10.4877i −0.0300252 + 0.0173351i
606606 651.673 + 48.4598i 1.07537 + 0.0799667i
607607 905.567 + 522.829i 1.49187 + 0.861333i 0.999957 0.00930928i 0.00296328π-0.00296328\pi
0.491916 + 0.870643i 0.336297π0.336297\pi
608608 −628.310 362.755i −1.03340 0.596636i
609609 0 0
610610 −168.038 291.051i −0.275473 0.477133i
611611 −409.956 −0.670959
612612 −408.540 + 160.882i −0.667549 + 0.262879i
613613 105.329 0.171826 0.0859131 0.996303i 0.472619π-0.472619\pi
0.0859131 + 0.996303i 0.472619π0.472619\pi
614614 −45.0764 + 26.0248i −0.0734143 + 0.0423857i
615615 51.9195 + 35.3545i 0.0844220 + 0.0574869i
616616 0 0
617617 269.908 467.495i 0.437452 0.757690i −0.560040 0.828466i 0.689214π-0.689214\pi
0.997492 + 0.0707759i 0.0225475π0.0225475\pi
618618 −556.864 1154.64i −0.901075 1.86836i
619619 968.123 558.946i 1.56401 0.902982i 0.567166 0.823603i 0.308040π-0.308040\pi
0.996845 0.0793787i 0.0252936π-0.0252936\pi
620620 409.968 0.661238
621621 −318.307 294.326i −0.512571 0.473956i
622622 1155.77i 1.85816i
623623 0 0
624624 321.594 + 666.818i 0.515376 + 1.06862i
625625 −113.310 + 196.259i −0.181296 + 0.314014i
626626 −988.452 570.683i −1.57900 0.911635i
627627 307.762 451.961i 0.490848 0.720831i
628628 35.7862 20.6612i 0.0569845 0.0329000i
629629 87.4754i 0.139071i
630630 0 0
631631 −710.879 −1.12659 −0.563296 0.826255i 0.690467π-0.690467\pi
−0.563296 + 0.826255i 0.690467π0.690467\pi
632632 6.05625 + 10.4897i 0.00958268 + 0.0165977i
633633 −9.44156 + 126.967i −0.0149156 + 0.200580i
634634 −420.198 + 727.805i −0.662773 + 1.14796i
635635 108.609 + 62.7057i 0.171038 + 0.0987491i
636636 61.0968 821.611i 0.0960641 1.29184i
637637 0 0
638638 1048.07 1.64274
639639 −632.508 + 795.011i −0.989840 + 1.24415i
640640 6.79131i 0.0106114i
641641 −535.389 927.321i −0.835240 1.44668i −0.893835 0.448397i 0.851995π-0.851995\pi
0.0585942 0.998282i 0.481338π-0.481338\pi
642642 538.321 + 366.568i 0.838506 + 0.570979i
643643 664.371 + 383.575i 1.03324 + 0.596539i 0.917910 0.396788i 0.129875π-0.129875\pi
0.115326 + 0.993328i 0.463209π0.463209\pi
644644 0 0
645645 −138.856 287.914i −0.215280 0.446378i
646646 −274.398 475.271i −0.424764 0.735713i
647647 17.1084i 0.0264427i 0.999913 + 0.0132214i 0.00420861π0.00420861\pi
−0.999913 + 0.0132214i 0.995791π0.995791\pi
648648 1.61092 + 6.98389i 0.00248598 + 0.0107776i
649649 1083.92i 1.67014i
650650 734.328 423.965i 1.12974 0.652253i
651651 0 0
652652 358.138 620.314i 0.549292 0.951402i
653653 484.144 838.561i 0.741414 1.28417i −0.210437 0.977607i 0.567489π-0.567489\pi
0.951851 0.306560i 0.0991779π-0.0991779\pi
654654 −177.066 120.573i −0.270744 0.184362i
655655 223.711 + 387.480i 0.341544 + 0.591572i
656656 138.572i 0.211238i
657657 478.235 + 380.482i 0.727907 + 0.579120i
658658 0 0
659659 470.849 + 815.535i 0.714490 + 1.23753i 0.963156 + 0.268944i 0.0866747π0.0866747\pi
−0.248665 + 0.968589i 0.579992π0.579992\pi
660660 329.499 + 24.5023i 0.499241 + 0.0371246i
661661 4.75875 + 2.74747i 0.00719933 + 0.00415653i 0.503595 0.863940i 0.332010π-0.332010\pi
−0.496396 + 0.868096i 0.665344π0.665344\pi
662662 755.187 1308.02i 1.14077 1.97586i
663663 −41.8546 + 562.848i −0.0631290 + 0.848941i
664664 1.66948 0.963876i 0.00251428 0.00145162i
665665 0 0
666666 182.329 + 27.2675i 0.273767 + 0.0409422i
667667 521.324 0.781595
668668 217.575 125.617i 0.325712 0.188050i
669669 −324.072 + 475.914i −0.484413 + 0.711381i
670670 481.942 + 278.249i 0.719316 + 0.415297i
671671 487.726 + 281.589i 0.726864 + 0.419655i
672672 0 0
673673 329.366 + 570.479i 0.489400 + 0.847666i 0.999926 0.0121964i 0.00388233π-0.00388233\pi
−0.510525 + 0.859863i 0.670549π0.670549\pi
674674 844.764 1.25336
675675 −496.316 + 154.030i −0.735283 + 0.228193i
676676 −292.926 −0.433323
677677 −730.516 + 421.763i −1.07905 + 0.622989i −0.930639 0.365937i 0.880748π-0.880748\pi
−0.148409 + 0.988926i 0.547415π0.547415\pi
678678 567.819 273.849i 0.837491 0.403907i
679679 0 0
680680 1.28424 2.22438i 0.00188860 0.00327114i
681681 −379.548 + 557.382i −0.557339 + 0.818475i
682682 −1185.31 + 684.338i −1.73799 + 1.00343i
683683 580.828 0.850407 0.425203 0.905098i 0.360203π-0.360203\pi
0.425203 + 0.905098i 0.360203π0.360203\pi
684684 −540.173 + 212.719i −0.789727 + 0.310992i
685685 367.875i 0.537044i
686686 0 0
687687 479.122 + 35.6286i 0.697412 + 0.0518611i
688688 352.585 610.695i 0.512478 0.887638i
689689 −917.155 529.520i −1.33114 0.768534i
690690 326.525 + 24.2811i 0.473225 + 0.0351900i
691691 −976.744 + 563.924i −1.41352 + 0.816098i −0.995718 0.0924390i 0.970534π-0.970534\pi
−0.417805 + 0.908537i 0.637200π0.637200\pi
692692 354.801i 0.512718i
693693 0 0
694694 512.388 0.738311
695695 109.432 + 189.541i 0.157455 + 0.272721i
696696 −7.12392 4.85102i −0.0102355 0.00696985i
697697 −52.8222 + 91.4907i −0.0757851 + 0.131264i
698698 −430.441 248.515i −0.616678 0.356039i
699699 −666.346 + 321.367i −0.953285 + 0.459752i
700700 0 0
701701 352.754 0.503216 0.251608 0.967829i 0.419041π-0.419041\pi
0.251608 + 0.967829i 0.419041π0.419041\pi
702702 1160.12 + 262.688i 1.65259 + 0.374200i
703703 115.660i 0.164524i
704704 370.166 + 641.147i 0.525804 + 0.910720i
705705 −170.919 + 82.4311i −0.242438 + 0.116924i
706706 −96.4769 55.7009i −0.136653 0.0788965i
707707 0 0
708708 −647.737 + 951.229i −0.914883 + 1.34354i
709709 396.038 + 685.959i 0.558587 + 0.967502i 0.997615 + 0.0690279i 0.0219898π0.0219898\pi
−0.439027 + 0.898474i 0.644677π0.644677\pi
710710 767.290i 1.08069i
711711 −1218.44 182.219i −1.71370 0.256286i
712712 9.59460i 0.0134756i
713713 −589.589 + 340.399i −0.826913 + 0.477418i
714714 0 0
715715 212.359 367.816i 0.297005 0.514428i
716716 −26.1063 + 45.2175i −0.0364613 + 0.0631529i
717717 −49.0064 + 659.024i −0.0683493 + 0.919141i
718718 350.908 + 607.791i 0.488730 + 0.846505i
719719 546.494i 0.760075i −0.924971 0.380037i 0.875911π-0.875911\pi
0.924971 0.380037i 0.124089π-0.124089\pi
720720 268.158 + 213.346i 0.372442 + 0.296313i
721721 0 0
722722 148.717 + 257.586i 0.205979 + 0.356767i
723723 445.094 653.640i 0.615622 0.904066i
724724 788.483 + 455.231i 1.08906 + 0.628772i
725725 312.454 541.186i 0.430971 0.746464i
726726 −66.9676 + 32.2973i −0.0922418 + 0.0444866i
727727 113.839 65.7248i 0.156587 0.0904055i −0.419659 0.907682i 0.637850π-0.637850\pi
0.576246 + 0.817276i 0.304517π0.304517\pi
728728 0 0
729729 −657.892 314.036i −0.902459 0.430777i
730730 −461.559 −0.632272
731731 465.581 268.803i 0.636910 0.367720i
732732 −259.746 538.576i −0.354844 0.735760i
733733 1107.87 + 639.630i 1.51142 + 0.872620i 0.999911 + 0.0133434i 0.00424746π0.00424746\pi
0.511511 + 0.859277i 0.329086π0.329086\pi
734734 −973.840 562.247i −1.32676 0.766004i
735735 0 0
736736 364.006 + 630.477i 0.494573 + 0.856626i
737737 −932.546 −1.26533
738738 174.233 + 138.619i 0.236088 + 0.187830i
739739 −19.8731 −0.0268919 −0.0134460 0.999910i 0.504280π-0.504280\pi
−0.0134460 + 0.999910i 0.504280π0.504280\pi
740740 −60.5258 + 34.9446i −0.0817916 + 0.0472224i
741741 −55.3402 + 744.199i −0.0746831 + 1.00432i
742742 0 0
743743 729.663 1263.81i 0.982050 1.70096i 0.327677 0.944790i 0.393734π-0.393734\pi
0.654374 0.756171i 0.272932π-0.272932\pi
744744 11.2242 + 0.834659i 0.0150864 + 0.00112185i
745745 −233.503 + 134.813i −0.313427 + 0.180957i
746746 −1057.46 −1.41751
747747 −29.0009 + 193.920i −0.0388232 + 0.259598i
748748 555.703i 0.742919i
749749 0 0
750750 507.847 745.795i 0.677130 0.994393i
751751 494.911 857.211i 0.659003 1.14143i −0.321871 0.946784i 0.604312π-0.604312\pi
0.980874 0.194643i 0.0623549π-0.0623549\pi
752752 −362.536 209.310i −0.482096 0.278338i
753753 −29.9741 62.1505i −0.0398062 0.0825372i
754754 −1238.74 + 715.189i −1.64290 + 0.948527i
755755 67.6315i 0.0895781i
756756 0 0
757757 −499.688 −0.660089 −0.330045 0.943965i 0.607064π-0.607064\pi
−0.330045 + 0.943965i 0.607064π0.607064\pi
758758 776.903 + 1345.64i 1.02494 + 1.77525i
759759 −494.209 + 238.348i −0.651131 + 0.314029i
760760 1.69803 2.94108i 0.00223425 0.00386984i
761761 594.048 + 342.974i 0.780614 + 0.450688i 0.836648 0.547741i 0.184512π-0.184512\pi
−0.0560336 + 0.998429i 0.517845π0.517845\pi
762762 367.431 + 250.201i 0.482193 + 0.328348i
763763 0 0
764764 418.806 0.548175
765765 95.7236 + 243.078i 0.125129 + 0.317749i
766766 13.2239i 0.0172636i
767767 739.652 + 1281.12i 0.964345 + 1.67029i
768768 −56.0534 + 753.789i −0.0729861 + 0.981496i
769769 −586.160 338.420i −0.762237 0.440078i 0.0678613 0.997695i 0.478382π-0.478382\pi
−0.830098 + 0.557617i 0.811716π0.811716\pi
770770 0 0
771771 53.3039 + 3.96379i 0.0691361 + 0.00514111i
772772 −327.219 566.759i −0.423858 0.734144i
773773 505.019i 0.653323i 0.945141 + 0.326661i 0.105924π0.105924\pi
−0.945141 + 0.326661i 0.894076π0.894076\pi
774774 −415.149 1054.22i −0.536369 1.36204i
775775 816.069i 1.05299i
776776 8.54747 4.93489i 0.0110148 0.00635939i
777777 0 0
778778 −953.091 + 1650.80i −1.22505 + 2.12185i
779779 −69.8416 + 120.969i −0.0896555 + 0.155288i
780780 −406.165 + 195.886i −0.520724 + 0.251136i
781781 642.889 + 1113.52i 0.823161 + 1.42576i
782782 550.688i 0.704205i
783783 837.240 259.835i 1.06927 0.331845i
784784 0 0
785785 −12.2932 21.2925i −0.0156602 0.0271242i
786786 688.927 + 1428.47i 0.876497 + 1.81739i
787787 −16.0382 9.25964i −0.0203789 0.0117657i 0.489776 0.871848i 0.337079π-0.337079\pi
−0.510155 + 0.860083i 0.670412π0.670412\pi
788788 −607.898 + 1052.91i −0.771445 + 1.33618i
789789 900.147 + 612.953i 1.14087 + 0.776873i
790790 805.814 465.237i 1.02002 0.588907i
791791 0 0
792792 8.97126 + 1.34166i 0.0113274 + 0.00169402i
793793 −768.610 −0.969243
794794 260.817 150.583i 0.328484 0.189651i
795795 −488.852 36.3521i −0.614909 0.0457259i
796796 −201.791 116.504i −0.253507 0.146362i
797797 615.232 + 355.205i 0.771935 + 0.445677i 0.833565 0.552422i 0.186296π-0.186296\pi
−0.0616293 + 0.998099i 0.519630π0.519630\pi
798798 0 0
799799 −159.574 276.390i −0.199717 0.345920i
800800 872.664 1.09083
801801 −763.679 607.580i −0.953407 0.758527i
802802 845.628 1.05440
803803 669.829 386.726i 0.834159 0.481602i
804804 818.387 + 557.279i 1.01789 + 0.693133i
805805 0 0
806806 933.967 1617.68i 1.15877 2.00705i
807807 255.635 + 530.052i 0.316772 + 0.656818i
808808 −5.88999 + 3.40059i −0.00728960 + 0.00420865i
809809 1131.54 1.39869 0.699344 0.714786i 0.253476π-0.253476\pi
0.699344 + 0.714786i 0.253476π0.253476\pi
810810 536.497 123.749i 0.662342 0.152777i
811811 199.736i 0.246283i 0.992389 + 0.123142i 0.0392970π0.0392970\pi
−0.992389 + 0.123142i 0.960703π0.960703\pi
812812 0 0
813813 124.184 + 257.493i 0.152748 + 0.316720i
814814 116.662 202.065i 0.143320 0.248238i
815815 −369.082 213.090i −0.452861 0.261460i
816816 −324.385 + 476.373i −0.397531 + 0.583791i
817817 615.592 355.412i 0.753479 0.435021i
818818 1867.84i 2.28343i
819819 0 0
820820 −84.4055 −0.102934
821821 −196.680 340.660i −0.239562 0.414933i 0.721027 0.692907i 0.243670π-0.243670\pi
−0.960589 + 0.277974i 0.910337π0.910337\pi
822822 −96.6983 + 1300.37i −0.117638 + 1.58196i
823823 424.378 735.045i 0.515648 0.893128i −0.484187 0.874965i 0.660885π-0.660885\pi
0.999835 0.0181639i 0.00578208π-0.00578208\pi
824824 11.5544 + 6.67091i 0.0140223 + 0.00809577i
825825 −48.7735 + 655.891i −0.0591193 + 0.795019i
826826 0 0
827827 495.009 0.598559 0.299280 0.954165i 0.403254π-0.403254\pi
0.299280 + 0.954165i 0.403254π0.403254\pi
828828 576.143 + 86.1629i 0.695825 + 0.104061i
829829 947.240i 1.14263i 0.820731 + 0.571315i 0.193566π0.193566\pi
−0.820731 + 0.571315i 0.806434π0.806434\pi
830830 −74.0442 128.248i −0.0892099 0.154516i
831831 534.251 + 363.797i 0.642901 + 0.437782i
832832 −875.021 505.193i −1.05171 0.607204i
833833 0 0
834834 336.998 + 698.757i 0.404074 + 0.837838i
835835 −74.7412 129.456i −0.0895105 0.155037i
836836 734.752i 0.878891i
837837 −777.212 + 840.536i −0.928569 + 1.00422i
838838 1588.06i 1.89506i
839839 787.270 454.531i 0.938343 0.541753i 0.0489028 0.998804i 0.484428π-0.484428\pi
0.889441 + 0.457051i 0.151094π0.151094\pi
840840 0 0
841841 −106.581 + 184.604i −0.126731 + 0.219505i
842842 −164.360 + 284.680i −0.195202 + 0.338099i
843843 505.438 + 344.177i 0.599570 + 0.408276i
844844 −85.5412 148.162i −0.101352 0.175547i
845845 174.289i 0.206259i
846846 −625.833 + 246.451i −0.739756 + 0.291314i
847847 0 0
848848 −540.712 936.540i −0.637632 1.10441i
849849 −360.382 26.7987i −0.424478 0.0315651i
850850 571.669 + 330.053i 0.672552 + 0.388298i
851851 58.0295 100.510i 0.0681898 0.118108i
852852 101.236 1361.39i 0.118821 1.59787i
853853 −768.763 + 443.845i −0.901246 + 0.520335i −0.877604 0.479386i 0.840859π-0.840859\pi
−0.0236417 + 0.999720i 0.507526π0.507526\pi
854854 0 0
855855 126.566 + 321.399i 0.148030 + 0.375905i
856856 −6.77833 −0.00791861
857857 −151.668 + 87.5656i −0.176976 + 0.102177i −0.585871 0.810404i 0.699247π-0.699247\pi
0.408895 + 0.912581i 0.365914π0.365914\pi
858858 847.331 1244.34i 0.987565 1.45028i
859859 −1192.54 688.515i −1.38829 0.801531i −0.395170 0.918608i 0.629314π-0.629314\pi
−0.993123 + 0.117077i 0.962648π0.962648\pi
860860 371.980 + 214.763i 0.432535 + 0.249724i
861861 0 0
862862 −456.983 791.518i −0.530143 0.918235i
863863 1522.75 1.76448 0.882241 0.470799i 0.156034π-0.156034\pi
0.882241 + 0.470799i 0.156034π0.156034\pi
864864 898.827 + 831.112i 1.04031 + 0.961935i
865865 211.104 0.244050
866866 −287.924 + 166.233i −0.332475 + 0.191955i
867867 385.163 185.757i 0.444248 0.214253i
868868 0 0
869869 −779.616 + 1350.33i −0.897141 + 1.55389i
870870 −372.652 + 547.255i −0.428335 + 0.629028i
871871 1102.20 636.358i 1.26545 0.730606i
872872 2.22955 0.00255682
873873 −148.480 + 992.836i −0.170080 + 1.13727i
874874 728.121i 0.833091i
875875 0 0
876876 −818.934 60.8977i −0.934856 0.0695179i
877877 359.527 622.719i 0.409951 0.710056i −0.584933 0.811082i 0.698879π-0.698879\pi
0.994884 + 0.101026i 0.0322124π0.0322124\pi
878878 −532.180 307.254i −0.606128 0.349948i
879879 −524.014 38.9668i −0.596148 0.0443309i
880880 375.590 216.847i 0.426807 0.246417i
881881 1065.56i 1.20949i −0.796418 0.604747i 0.793274π-0.793274\pi
0.796418 0.604747i 0.206726π-0.206726\pi
882882 0 0
883883 −378.403 −0.428543 −0.214271 0.976774i 0.568738π-0.568738\pi
−0.214271 + 0.976774i 0.568738π0.568738\pi
884884 −379.205 656.802i −0.428965 0.742989i
885885 565.974 + 385.398i 0.639518 + 0.435478i
886886 −212.180 + 367.506i −0.239481 + 0.414793i
887887 −1522.62 879.087i −1.71660 0.991079i −0.924938 0.380118i 0.875883π-0.875883\pi
−0.791661 0.610960i 0.790783π-0.790783\pi
888888 −1.72824 + 0.833501i −0.00194622 + 0.000938627i
889889 0 0
890890 737.050 0.828146
891891 −674.897 + 629.104i −0.757460 + 0.706065i
892892 773.693i 0.867368i
893893 −210.989 365.443i −0.236270 0.409231i
894894 −860.826 + 415.161i −0.962893 + 0.464386i
895895 26.9040 + 15.5331i 0.0300604 + 0.0173554i
896896 0 0
897897 421.474 618.952i 0.469871 0.690025i
898898 −373.750 647.355i −0.416203 0.720885i
899899 1376.63i 1.53129i
900900 434.755 546.452i 0.483061 0.607169i
901901 824.454i 0.915044i
902902 244.035 140.894i 0.270549 0.156202i
903903 0 0
904904 −3.28055 + 5.68209i −0.00362893 + 0.00628549i
905905 270.859 469.141i 0.299291 0.518388i
906906 17.7774 239.065i 0.0196218 0.263868i
907907 −371.175 642.893i −0.409233 0.708813i 0.585571 0.810621i 0.300870π-0.300870\pi
−0.994804 + 0.101808i 0.967537π0.967537\pi
908908 906.135i 0.997946i
909909 102.316 684.155i 0.112559 0.752646i
910910 0 0
911911 394.703 + 683.645i 0.433263 + 0.750434i 0.997152 0.0754169i 0.0240288π-0.0240288\pi
−0.563889 + 0.825851i 0.690695π0.690695\pi
912912 −428.903 + 629.862i −0.470288 + 0.690638i
913913 214.911 + 124.079i 0.235390 + 0.135902i
914914 −310.023 + 536.975i −0.339193 + 0.587500i
915915 −320.449 + 154.547i −0.350217 + 0.168904i
916916 −559.101 + 322.797i −0.610372 + 0.352398i
917917 0 0
918918 274.470 + 884.398i 0.298987 + 0.963396i
919919 −427.558 −0.465243 −0.232621 0.972567i 0.574730π-0.574730\pi
−0.232621 + 0.972567i 0.574730π0.574730\pi
920920 −2.95122 + 1.70389i −0.00320785 + 0.00185205i
921921 23.9353 + 49.6293i 0.0259884 + 0.0538863i
922922 −949.064 547.942i −1.02935 0.594297i
923923 −1519.70 877.398i −1.64648 0.950594i
924924 0 0
925925 −69.5596 120.481i −0.0751996 0.130250i
926926 1370.95 1.48051
927927 −1262.65 + 497.229i −1.36208 + 0.536385i
928928 −1472.10 −1.58632
929929 −978.107 + 564.711i −1.05286 + 0.607869i −0.923449 0.383722i 0.874642π-0.874642\pi
−0.129412 + 0.991591i 0.541309π0.541309\pi
930930 64.1179 862.238i 0.0689440 0.927138i
931931 0 0
932932 497.045 860.908i 0.533310 0.923721i
933933 1220.13 + 90.7313i 1.30775 + 0.0972469i
934934 −283.514 + 163.687i −0.303548 + 0.175253i
935935 330.639 0.353625
936936 −11.5189 + 4.53612i −0.0123066 + 0.00484629i
937937 736.130i 0.785625i −0.919619 0.392812i 0.871502π-0.871502\pi
0.919619 0.392812i 0.128498π-0.128498\pi
938938 0 0
939939 −680.056 + 998.691i −0.724234 + 1.06357i
940940 127.493 220.824i 0.135631 0.234919i
941941 75.0157 + 43.3103i 0.0797191 + 0.0460259i 0.539330 0.842095i 0.318678π-0.318678\pi
−0.459611 + 0.888121i 0.652011π0.652011\pi
942942 −37.8575 78.4965i −0.0401884 0.0833296i
943943 121.386 70.0825i 0.128724 0.0743187i
944944 1510.57i 1.60018i
945945 0 0
946946 −1433.97 −1.51582
947947 −293.684 508.676i −0.310121 0.537145i 0.668268 0.743921i 0.267036π-0.267036\pi
−0.978388 + 0.206776i 0.933703π0.933703\pi
948948 1491.12 719.141i 1.57291 0.758588i
949949 −527.794 + 914.166i −0.556158 + 0.963294i
950950 755.862 + 436.397i 0.795645 + 0.459366i
951951 735.343 + 500.730i 0.773232 + 0.526530i
952952 0 0
953953 −396.549 −0.416106 −0.208053 0.978118i 0.566713π-0.566713\pi
−0.208053 + 0.978118i 0.566713π0.566713\pi
954954 −1718.45 256.996i −1.80131 0.269388i
955955 249.186i 0.260928i
956956 −444.001 769.033i −0.464436 0.804427i
957957 82.2763 1106.43i 0.0859732 1.15614i
958958 1118.28 + 645.638i 1.16730 + 0.673944i
959959 0 0
960960 −466.394 34.6821i −0.485828 0.0361272i
961961 418.375 + 724.646i 0.435353 + 0.754054i
962962 318.436i 0.331014i
963963 429.239 539.519i 0.445731 0.560248i
964964 1062.62i 1.10230i
965965 −337.217 + 194.693i −0.349448 + 0.201754i
966966 0 0
967967 −163.959 + 283.985i −0.169554 + 0.293676i −0.938263 0.345922i 0.887566π-0.887566\pi
0.768709 + 0.639598i 0.220899π0.220899\pi
968968 0.386903 0.670135i 0.000399693 0.000692288i
969969 −523.276 + 252.367i −0.540016 + 0.260440i
970970 −379.094 656.611i −0.390819 0.676918i
971971 1039.52i 1.07057i −0.844673 0.535283i 0.820205π-0.820205\pi
0.844673 0.535283i 0.179795π-0.179795\pi
972972 968.223 148.781i 0.996114 0.153067i
973973 0 0
974974 460.046 + 796.823i 0.472326 + 0.818093i
975975 −389.925 808.499i −0.399923 0.829230i
976976 −679.705 392.428i −0.696419 0.402078i
977977 −743.417 + 1287.64i −0.760918 + 1.31795i 0.181460 + 0.983398i 0.441918π0.441918\pi
−0.942378 + 0.334550i 0.891416π0.891416\pi
978978 −1248.62 850.247i −1.27671 0.869373i
979979 −1069.63 + 617.552i −1.09258 + 0.630799i
980980 0 0
981981 −141.187 + 177.460i −0.143921 + 0.180897i
982982 −879.774 −0.895900
983983 −958.645 + 553.474i −0.975223 + 0.563045i −0.900825 0.434183i 0.857037π-0.857037\pi
−0.0743987 + 0.997229i 0.523704π0.523704\pi
984984 −2.31088 0.171842i −0.00234846 0.000174637i
985985 626.474 + 361.695i 0.636014 + 0.367203i
986986 −964.353 556.769i −0.978046 0.564675i
987987 0 0
988988 −501.386 868.425i −0.507475 0.878973i
989989 −713.277 −0.721210
990990 103.066 689.166i 0.104107 0.696127i
991991 1087.01 1.09688 0.548439 0.836191i 0.315222π-0.315222\pi
0.548439 + 0.836191i 0.315222π0.315222\pi
992992 1664.87 961.211i 1.67829 0.968963i
993993 −1321.57 899.920i −1.33089 0.906264i
994994 0 0
995995 −69.3191 + 120.064i −0.0696675 + 0.120668i
996996 −114.454 237.318i −0.114914 0.238271i
997997 −716.543 + 413.696i −0.718699 + 0.414941i −0.814274 0.580481i 0.802864π-0.802864\pi
0.0955746 + 0.995422i 0.469531π0.469531\pi
998998 2194.09 2.19849
999999 43.0991 190.341i 0.0431422 0.190531i
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 441.3.l.b.391.12 28
7.2 even 3 441.3.k.b.31.12 28
7.3 odd 6 441.3.t.a.166.3 28
7.4 even 3 63.3.t.a.40.3 yes 28
7.5 odd 6 63.3.k.a.31.12 28
7.6 odd 2 441.3.l.a.391.12 28
9.7 even 3 441.3.l.a.97.12 28
21.5 even 6 189.3.k.a.10.3 28
21.11 odd 6 189.3.t.a.145.12 28
63.11 odd 6 189.3.k.a.19.3 28
63.16 even 3 441.3.t.a.178.3 28
63.25 even 3 63.3.k.a.61.12 yes 28
63.34 odd 6 inner 441.3.l.b.97.12 28
63.47 even 6 189.3.t.a.73.12 28
63.52 odd 6 441.3.k.b.313.12 28
63.61 odd 6 63.3.t.a.52.3 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.3.k.a.31.12 28 7.5 odd 6
63.3.k.a.61.12 yes 28 63.25 even 3
63.3.t.a.40.3 yes 28 7.4 even 3
63.3.t.a.52.3 yes 28 63.61 odd 6
189.3.k.a.10.3 28 21.5 even 6
189.3.k.a.19.3 28 63.11 odd 6
189.3.t.a.73.12 28 63.47 even 6
189.3.t.a.145.12 28 21.11 odd 6
441.3.k.b.31.12 28 7.2 even 3
441.3.k.b.313.12 28 63.52 odd 6
441.3.l.a.97.12 28 9.7 even 3
441.3.l.a.391.12 28 7.6 odd 2
441.3.l.b.97.12 28 63.34 odd 6 inner
441.3.l.b.391.12 28 1.1 even 1 trivial
441.3.t.a.166.3 28 7.3 odd 6
441.3.t.a.178.3 28 63.16 even 3