Properties

Label 538.3.c.b.187.2
Level 538538
Weight 33
Character 538.187
Analytic conductor 14.65914.659
Analytic rank 00
Dimension 4646
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] = [538,3,Mod(187,538)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(538, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) 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("538.187"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 538=2269 538 = 2 \cdot 269
Weight: k k == 3 3
Character orbit: [χ][\chi] == 538.c (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 14.659438222614.6594382226
Analytic rank: 00
Dimension: 4646
Relative dimension: 2323 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 187.2
Character χ\chi == 538.187
Dual form 538.3.c.b.351.2

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+(1.000001.00000i)q2+(3.737583.73758i)q3+2.00000iq4+3.56643q5+7.47516iq6+(0.8913810.891381i)q7+(2.000002.00000i)q8+18.9390iq9+(3.566433.56643i)q102.56603iq11+(7.475167.47516i)q126.86363iq131.78276q14+(13.329813.3298i)q154.00000q16+(18.2796+18.2796i)q17+(18.939018.9390i)q18+(19.226419.2264i)q19+7.13285iq206.66321q21+(2.56603+2.56603i)q22+20.7058q2314.9503q2412.2806q25+(6.86363+6.86363i)q26+(37.147837.1478i)q27+(1.78276+1.78276i)q28+(33.160933.1609i)q29+26.6596iq30+(31.144331.1443i)q31+(4.00000+4.00000i)q32+(9.59075+9.59075i)q3336.5592iq34+(3.179043.17904i)q3537.8780q36+9.51182q3738.4528q38+(25.6534+25.6534i)q39+(7.132857.13285i)q4047.9831q41+(6.66321+6.66321i)q42+27.6003iq43+5.13207q44+67.5445iq45+(20.705820.7058i)q4683.5411q47+(14.9503+14.9503i)q48+47.4109iq49+(12.2806+12.2806i)q50136.643iq51+13.7273q52+7.49037q5374.2956q549.15157iq553.56552iq56143.720q5766.3218q58+(46.045346.0453i)q59+(26.659626.6596i)q6082.0535q6162.2886q62+(16.8819+16.8819i)q638.00000iq6424.4786iq65+19.1815q66+21.7311q67+(36.5592+36.5592i)q68+(77.389677.3896i)q696.35809q70+(10.9828+10.9828i)q71+(37.8780+37.8780i)q72+41.5713iq73+(9.511829.51182i)q74+(45.8997+45.8997i)q75+(38.4528+38.4528i)q76+(2.287312.28731i)q77+51.3067q7861.7849iq7914.2657q80107.235q81+(47.9831+47.9831i)q82+(29.423629.4236i)q8313.3264iq84+(65.1928+65.1928i)q85+(27.600327.6003i)q86247.883q87+(5.132075.13207i)q88137.457iq89+(67.544567.5445i)q90+(6.118116.11811i)q91+41.4116iq92232.808q93+(83.5411+83.5411i)q94+(68.569568.5695i)q9529.9006iq96+97.9964iq97+(47.410947.4109i)q98+48.5981q99+O(q100)q+(-1.00000 - 1.00000i) q^{2} +(-3.73758 - 3.73758i) q^{3} +2.00000i q^{4} +3.56643 q^{5} +7.47516i q^{6} +(0.891381 - 0.891381i) q^{7} +(2.00000 - 2.00000i) q^{8} +18.9390i q^{9} +(-3.56643 - 3.56643i) q^{10} -2.56603i q^{11} +(7.47516 - 7.47516i) q^{12} -6.86363i q^{13} -1.78276 q^{14} +(-13.3298 - 13.3298i) q^{15} -4.00000 q^{16} +(18.2796 + 18.2796i) q^{17} +(18.9390 - 18.9390i) q^{18} +(19.2264 - 19.2264i) q^{19} +7.13285i q^{20} -6.66321 q^{21} +(-2.56603 + 2.56603i) q^{22} +20.7058 q^{23} -14.9503 q^{24} -12.2806 q^{25} +(-6.86363 + 6.86363i) q^{26} +(37.1478 - 37.1478i) q^{27} +(1.78276 + 1.78276i) q^{28} +(33.1609 - 33.1609i) q^{29} +26.6596i q^{30} +(31.1443 - 31.1443i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-9.59075 + 9.59075i) q^{33} -36.5592i q^{34} +(3.17904 - 3.17904i) q^{35} -37.8780 q^{36} +9.51182 q^{37} -38.4528 q^{38} +(-25.6534 + 25.6534i) q^{39} +(7.13285 - 7.13285i) q^{40} -47.9831 q^{41} +(6.66321 + 6.66321i) q^{42} +27.6003i q^{43} +5.13207 q^{44} +67.5445i q^{45} +(-20.7058 - 20.7058i) q^{46} -83.5411 q^{47} +(14.9503 + 14.9503i) q^{48} +47.4109i q^{49} +(12.2806 + 12.2806i) q^{50} -136.643i q^{51} +13.7273 q^{52} +7.49037 q^{53} -74.2956 q^{54} -9.15157i q^{55} -3.56552i q^{56} -143.720 q^{57} -66.3218 q^{58} +(46.0453 - 46.0453i) q^{59} +(26.6596 - 26.6596i) q^{60} -82.0535 q^{61} -62.2886 q^{62} +(16.8819 + 16.8819i) q^{63} -8.00000i q^{64} -24.4786i q^{65} +19.1815 q^{66} +21.7311 q^{67} +(-36.5592 + 36.5592i) q^{68} +(-77.3896 - 77.3896i) q^{69} -6.35809 q^{70} +(-10.9828 + 10.9828i) q^{71} +(37.8780 + 37.8780i) q^{72} +41.5713i q^{73} +(-9.51182 - 9.51182i) q^{74} +(45.8997 + 45.8997i) q^{75} +(38.4528 + 38.4528i) q^{76} +(-2.28731 - 2.28731i) q^{77} +51.3067 q^{78} -61.7849i q^{79} -14.2657 q^{80} -107.235 q^{81} +(47.9831 + 47.9831i) q^{82} +(29.4236 - 29.4236i) q^{83} -13.3264i q^{84} +(65.1928 + 65.1928i) q^{85} +(27.6003 - 27.6003i) q^{86} -247.883 q^{87} +(-5.13207 - 5.13207i) q^{88} -137.457i q^{89} +(67.5445 - 67.5445i) q^{90} +(-6.11811 - 6.11811i) q^{91} +41.4116i q^{92} -232.808 q^{93} +(83.5411 + 83.5411i) q^{94} +(68.5695 - 68.5695i) q^{95} -29.9006i q^{96} +97.9964i q^{97} +(47.4109 - 47.4109i) q^{98} +48.5981 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 46q46q26q332q5+4q7+92q8+32q10+12q128q1410q15184q1650q17+118q18+10q19+16q21+8q22124q2324q24++508q99+O(q100) 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/538Z)×\left(\mathbb{Z}/538\mathbb{Z}\right)^\times.

nn 271271
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.00000 1.00000i −0.500000 0.500000i
33 −3.73758 3.73758i −1.24586 1.24586i −0.957532 0.288328i 0.906901π-0.906901\pi
−0.288328 0.957532i 0.593099π-0.593099\pi
44 2.00000i 0.500000i
55 3.56643 0.713285 0.356643 0.934241i 0.383921π-0.383921\pi
0.356643 + 0.934241i 0.383921π0.383921\pi
66 7.47516i 1.24586i
77 0.891381 0.891381i 0.127340 0.127340i −0.640564 0.767904i 0.721300π-0.721300\pi
0.767904 + 0.640564i 0.221300π0.221300\pi
88 2.00000 2.00000i 0.250000 0.250000i
99 18.9390i 2.10433i
1010 −3.56643 3.56643i −0.356643 0.356643i
1111 2.56603i 0.233276i −0.993175 0.116638i 0.962788π-0.962788\pi
0.993175 0.116638i 0.0372117π-0.0372117\pi
1212 7.47516 7.47516i 0.622930 0.622930i
1313 6.86363i 0.527971i −0.964527 0.263986i 0.914963π-0.914963\pi
0.964527 0.263986i 0.0850372π-0.0850372\pi
1414 −1.78276 −0.127340
1515 −13.3298 13.3298i −0.888654 0.888654i
1616 −4.00000 −0.250000
1717 18.2796 + 18.2796i 1.07527 + 1.07527i 0.996926 + 0.0783435i 0.0249631π0.0249631\pi
0.0783435 + 0.996926i 0.475037π0.475037\pi
1818 18.9390 18.9390i 1.05217 1.05217i
1919 19.2264 19.2264i 1.01191 1.01191i 0.0119866 0.999928i 0.496184π-0.496184\pi
0.999928 0.0119866i 0.00381555π-0.00381555\pi
2020 7.13285i 0.356643i
2121 −6.66321 −0.317296
2222 −2.56603 + 2.56603i −0.116638 + 0.116638i
2323 20.7058 0.900252 0.450126 0.892965i 0.351379π-0.351379\pi
0.450126 + 0.892965i 0.351379π0.351379\pi
2424 −14.9503 −0.622930
2525 −12.2806 −0.491224
2626 −6.86363 + 6.86363i −0.263986 + 0.263986i
2727 37.1478 37.1478i 1.37584 1.37584i
2828 1.78276 + 1.78276i 0.0636700 + 0.0636700i
2929 33.1609 33.1609i 1.14348 1.14348i 0.155670 0.987809i 0.450246π-0.450246\pi
0.987809 0.155670i 0.0497535π-0.0497535\pi
3030 26.6596i 0.888654i
3131 31.1443 31.1443i 1.00465 1.00465i 0.00466538 0.999989i 0.498515π-0.498515\pi
0.999989 0.00466538i 0.00148504π-0.00148504\pi
3232 4.00000 + 4.00000i 0.125000 + 0.125000i
3333 −9.59075 + 9.59075i −0.290629 + 0.290629i
3434 36.5592i 1.07527i
3535 3.17904 3.17904i 0.0908298 0.0908298i
3636 −37.8780 −1.05217
3737 9.51182 0.257076 0.128538 0.991705i 0.458972π-0.458972\pi
0.128538 + 0.991705i 0.458972π0.458972\pi
3838 −38.4528 −1.01191
3939 −25.6534 + 25.6534i −0.657778 + 0.657778i
4040 7.13285 7.13285i 0.178321 0.178321i
4141 −47.9831 −1.17032 −0.585159 0.810918i 0.698968π-0.698968\pi
−0.585159 + 0.810918i 0.698968π0.698968\pi
4242 6.66321 + 6.66321i 0.158648 + 0.158648i
4343 27.6003i 0.641867i 0.947102 + 0.320933i 0.103997π0.103997\pi
−0.947102 + 0.320933i 0.896003π0.896003\pi
4444 5.13207 0.116638
4545 67.5445i 1.50099i
4646 −20.7058 20.7058i −0.450126 0.450126i
4747 −83.5411 −1.77747 −0.888735 0.458421i 0.848415π-0.848415\pi
−0.888735 + 0.458421i 0.848415π0.848415\pi
4848 14.9503 + 14.9503i 0.311465 + 0.311465i
4949 47.4109i 0.967569i
5050 12.2806 + 12.2806i 0.245612 + 0.245612i
5151 136.643i 2.67927i
5252 13.7273 0.263986
5353 7.49037 0.141328 0.0706638 0.997500i 0.477488π-0.477488\pi
0.0706638 + 0.997500i 0.477488π0.477488\pi
5454 −74.2956 −1.37584
5555 9.15157i 0.166392i
5656 3.56552i 0.0636700i
5757 −143.720 −2.52141
5858 −66.3218 −1.14348
5959 46.0453 46.0453i 0.780430 0.780430i −0.199474 0.979903i 0.563923π-0.563923\pi
0.979903 + 0.199474i 0.0639232π0.0639232\pi
6060 26.6596 26.6596i 0.444327 0.444327i
6161 −82.0535 −1.34514 −0.672570 0.740034i 0.734810π-0.734810\pi
−0.672570 + 0.740034i 0.734810π0.734810\pi
6262 −62.2886 −1.00465
6363 16.8819 + 16.8819i 0.267966 + 0.267966i
6464 8.00000i 0.125000i
6565 24.4786i 0.376594i
6666 19.1815 0.290629
6767 21.7311 0.324345 0.162173 0.986762i 0.448150π-0.448150\pi
0.162173 + 0.986762i 0.448150π0.448150\pi
6868 −36.5592 + 36.5592i −0.537635 + 0.537635i
6969 −77.3896 77.3896i −1.12159 1.12159i
7070 −6.35809 −0.0908298
7171 −10.9828 + 10.9828i −0.154688 + 0.154688i −0.780208 0.625520i 0.784887π-0.784887\pi
0.625520 + 0.780208i 0.284887π0.284887\pi
7272 37.8780 + 37.8780i 0.526083 + 0.526083i
7373 41.5713i 0.569469i 0.958606 + 0.284735i 0.0919055π0.0919055\pi
−0.958606 + 0.284735i 0.908095π0.908095\pi
7474 −9.51182 9.51182i −0.128538 0.128538i
7575 45.8997 + 45.8997i 0.611996 + 0.611996i
7676 38.4528 + 38.4528i 0.505957 + 0.505957i
7777 −2.28731 2.28731i −0.0297053 0.0297053i
7878 51.3067 0.657778
7979 61.7849i 0.782087i −0.920372 0.391043i 0.872114π-0.872114\pi
0.920372 0.391043i 0.127886π-0.127886\pi
8080 −14.2657 −0.178321
8181 −107.235 −1.32388
8282 47.9831 + 47.9831i 0.585159 + 0.585159i
8383 29.4236 29.4236i 0.354501 0.354501i −0.507280 0.861781i 0.669349π-0.669349\pi
0.861781 + 0.507280i 0.169349π0.169349\pi
8484 13.3264i 0.158648i
8585 65.1928 + 65.1928i 0.766974 + 0.766974i
8686 27.6003 27.6003i 0.320933 0.320933i
8787 −247.883 −2.84923
8888 −5.13207 5.13207i −0.0583189 0.0583189i
8989 137.457i 1.54447i −0.635340 0.772233i 0.719140π-0.719140\pi
0.635340 0.772233i 0.280860π-0.280860\pi
9090 67.5445 67.5445i 0.750495 0.750495i
9191 −6.11811 6.11811i −0.0672319 0.0672319i
9292 41.4116i 0.450126i
9393 −232.808 −2.50332
9494 83.5411 + 83.5411i 0.888735 + 0.888735i
9595 68.5695 68.5695i 0.721784 0.721784i
9696 29.9006i 0.311465i
9797 97.9964i 1.01027i 0.863040 + 0.505136i 0.168558π0.168558\pi
−0.863040 + 0.505136i 0.831442π0.831442\pi
9898 47.4109 47.4109i 0.483785 0.483785i
9999 48.5981 0.490890
100100 24.5612i 0.245612i
101101 −30.4105 30.4105i −0.301094 0.301094i 0.540348 0.841442i 0.318293π-0.318293\pi
−0.841442 + 0.540348i 0.818293π0.818293\pi
102102 −136.643 + 136.643i −1.33964 + 1.33964i
103103 53.4784i 0.519208i −0.965715 0.259604i 0.916408π-0.916408\pi
0.965715 0.259604i 0.0835920π-0.0835920\pi
104104 −13.7273 13.7273i −0.131993 0.131993i
105105 −23.7639 −0.226322
106106 −7.49037 7.49037i −0.0706638 0.0706638i
107107 −60.7293 + 60.7293i −0.567563 + 0.567563i −0.931445 0.363882i 0.881451π-0.881451\pi
0.363882 + 0.931445i 0.381451π0.381451\pi
108108 74.2956 + 74.2956i 0.687922 + 0.687922i
109109 42.2357 42.2357i 0.387484 0.387484i −0.486305 0.873789i 0.661656π-0.661656\pi
0.873789 + 0.486305i 0.161656π0.161656\pi
110110 −9.15157 + 9.15157i −0.0831961 + 0.0831961i
111111 −35.5512 35.5512i −0.320281 0.320281i
112112 −3.56552 + 3.56552i −0.0318350 + 0.0318350i
113113 152.587 152.587i 1.35033 1.35033i 0.465037 0.885291i 0.346041π-0.346041\pi
0.885291 0.465037i 0.153959π-0.153959\pi
114114 143.720 + 143.720i 1.26070 + 1.26070i
115115 73.8457 0.642137
116116 66.3218 + 66.3218i 0.571739 + 0.571739i
117117 129.990 1.11103
118118 −92.0907 −0.780430
119119 32.5881 0.273850
120120 −53.3192 −0.444327
121121 114.415 0.945582
122122 82.0535 + 82.0535i 0.672570 + 0.672570i
123123 179.340 + 179.340i 1.45805 + 1.45805i
124124 62.2886 + 62.2886i 0.502327 + 0.502327i
125125 −132.959 −1.06367
126126 33.7637i 0.267966i
127127 73.7961i 0.581072i 0.956864 + 0.290536i 0.0938336π0.0938336\pi
−0.956864 + 0.290536i 0.906166π0.906166\pi
128128 −8.00000 + 8.00000i −0.0625000 + 0.0625000i
129129 103.158 103.158i 0.799676 0.799676i
130130 −24.4786 + 24.4786i −0.188297 + 0.188297i
131131 42.9213 0.327644 0.163822 0.986490i 0.447618π-0.447618\pi
0.163822 + 0.986490i 0.447618π0.447618\pi
132132 −19.1815 19.1815i −0.145314 0.145314i
133133 34.2760i 0.257715i
134134 −21.7311 21.7311i −0.162173 0.162173i
135135 132.485 132.485i 0.981369 0.981369i
136136 73.1184 0.537635
137137 −78.8845 + 78.8845i −0.575799 + 0.575799i −0.933743 0.357944i 0.883478π-0.883478\pi
0.357944 + 0.933743i 0.383478π0.383478\pi
138138 154.779i 1.12159i
139139 −81.8983 81.8983i −0.589196 0.589196i 0.348218 0.937414i 0.386787π-0.386787\pi
−0.937414 + 0.348218i 0.886787π0.886787\pi
140140 6.35809 + 6.35809i 0.0454149 + 0.0454149i
141141 312.241 + 312.241i 2.21448 + 2.21448i
142142 21.9657 0.154688
143143 −17.6123 −0.123163
144144 75.7560i 0.526083i
145145 118.266 118.266i 0.815627 0.815627i
146146 41.5713 41.5713i 0.284735 0.284735i
147147 177.202 177.202i 1.20546 1.20546i
148148 19.0236i 0.128538i
149149 135.917i 0.912192i −0.889931 0.456096i 0.849247π-0.849247\pi
0.889931 0.456096i 0.150753π-0.150753\pi
150150 91.7994i 0.611996i
151151 249.028i 1.64919i −0.565724 0.824595i 0.691403π-0.691403\pi
0.565724 0.824595i 0.308597π-0.308597\pi
152152 76.9055i 0.505957i
153153 −346.197 + 346.197i −2.26273 + 2.26273i
154154 4.57462i 0.0297053i
155155 111.074 111.074i 0.716605 0.716605i
156156 −51.3067 51.3067i −0.328889 0.328889i
157157 −46.5704 46.5704i −0.296627 0.296627i 0.543064 0.839691i 0.317264π-0.317264\pi
−0.839691 + 0.543064i 0.817264π0.817264\pi
158158 −61.7849 + 61.7849i −0.391043 + 0.391043i
159159 −27.9958 27.9958i −0.176074 0.176074i
160160 14.2657 + 14.2657i 0.0891607 + 0.0891607i
161161 18.4568 18.4568i 0.114638 0.114638i
162162 107.235 + 107.235i 0.661942 + 0.661942i
163163 156.419 156.419i 0.959628 0.959628i −0.0395881 0.999216i 0.512605π-0.512605\pi
0.999216 + 0.0395881i 0.0126046π0.0126046\pi
164164 95.9661i 0.585159i
165165 −34.2047 + 34.2047i −0.207301 + 0.207301i
166166 −58.8472 −0.354501
167167 −100.759 100.759i −0.603349 0.603349i 0.337850 0.941200i 0.390300π-0.390300\pi
−0.941200 + 0.337850i 0.890300π0.890300\pi
168168 −13.3264 + 13.3264i −0.0793239 + 0.0793239i
169169 121.891 0.721246
170170 130.386i 0.766974i
171171 364.128 + 364.128i 2.12941 + 2.12941i
172172 −55.2006 −0.320933
173173 −74.9613 −0.433303 −0.216651 0.976249i 0.569513π-0.569513\pi
−0.216651 + 0.976249i 0.569513π0.569513\pi
174174 247.883 + 247.883i 1.42461 + 1.42461i
175175 −10.9467 + 10.9467i −0.0625525 + 0.0625525i
176176 10.2641i 0.0583189i
177177 −344.196 −1.94461
178178 −137.457 + 137.457i −0.772233 + 0.772233i
179179 11.6583 + 11.6583i 0.0651301 + 0.0651301i 0.738922 0.673791i 0.235335π-0.235335\pi
−0.673791 + 0.738922i 0.735335π0.735335\pi
180180 −135.089 −0.750495
181181 −192.374 + 192.374i −1.06284 + 1.06284i −0.0649502 + 0.997889i 0.520689π0.520689\pi
−0.997889 + 0.0649502i 0.979311π0.979311\pi
182182 12.2362i 0.0672319i
183183 306.682 + 306.682i 1.67586 + 1.67586i
184184 41.4116 41.4116i 0.225063 0.225063i
185185 33.9232 0.183369
186186 232.808 + 232.808i 1.25166 + 1.25166i
187187 46.9060 46.9060i 0.250834 0.250834i
188188 167.082i 0.888735i
189189 66.2256i 0.350400i
190190 −137.139 −0.721784
191191 42.8213i 0.224195i −0.993697 0.112098i 0.964243π-0.964243\pi
0.993697 0.112098i 0.0357570π-0.0357570\pi
192192 −29.9006 + 29.9006i −0.155732 + 0.155732i
193193 −224.710 + 224.710i −1.16430 + 1.16430i −0.180775 + 0.983524i 0.557861π0.557861\pi
−0.983524 + 0.180775i 0.942139π0.942139\pi
194194 97.9964 97.9964i 0.505136 0.505136i
195195 −91.4908 + 91.4908i −0.469184 + 0.469184i
196196 −94.8218 −0.483785
197197 40.5886 40.5886i 0.206034 0.206034i −0.596546 0.802579i 0.703460π-0.703460\pi
0.802579 + 0.596546i 0.203460π0.203460\pi
198198 −48.5981 48.5981i −0.245445 0.245445i
199199 81.1621i 0.407850i −0.978987 0.203925i 0.934630π-0.934630\pi
0.978987 0.203925i 0.0653698π-0.0653698\pi
200200 −24.5612 + 24.5612i −0.122806 + 0.122806i
201201 −81.2218 81.2218i −0.404089 0.404089i
202202 60.8210i 0.301094i
203203 59.1179i 0.291221i
204204 273.286 1.33964
205205 −171.128 −0.834771
206206 −53.4784 + 53.4784i −0.259604 + 0.259604i
207207 392.147i 1.89443i
208208 27.4545i 0.131993i
209209 −49.3355 49.3355i −0.236055 0.236055i
210210 23.7639 + 23.7639i 0.113161 + 0.113161i
211211 221.892i 1.05162i 0.850602 + 0.525810i 0.176238π0.176238\pi
−0.850602 + 0.525810i 0.823762π0.823762\pi
212212 14.9807i 0.0706638i
213213 82.0984 0.385438
214214 121.459 0.567563
215215 98.4344i 0.457834i
216216 148.591i 0.687922i
217217 55.5228i 0.255866i
218218 −84.4714 −0.387484
219219 155.376 155.376i 0.709479 0.709479i
220220 18.3031 0.0831961
221221 125.464 125.464i 0.567712 0.567712i
222222 71.1023i 0.320281i
223223 −236.861 + 236.861i −1.06216 + 1.06216i −0.0642236 + 0.997936i 0.520457π0.520457\pi
−0.997936 + 0.0642236i 0.979543π0.979543\pi
224224 7.13104 0.0318350
225225 232.582i 1.03370i
226226 −305.174 −1.35033
227227 237.886 237.886i 1.04796 1.04796i 0.0491659 0.998791i 0.484344π-0.484344\pi
0.998791 0.0491659i 0.0156563π-0.0156563\pi
228228 287.440i 1.26070i
229229 106.805 + 106.805i 0.466399 + 0.466399i 0.900746 0.434347i 0.143021π-0.143021\pi
−0.434347 + 0.900746i 0.643021π0.643021\pi
230230 −73.8457 73.8457i −0.321068 0.321068i
231231 17.0980i 0.0740174i
232232 132.644i 0.571739i
233233 27.8816i 0.119663i 0.998208 + 0.0598317i 0.0190564π0.0190564\pi
−0.998208 + 0.0598317i 0.980944π0.980944\pi
234234 −129.990 129.990i −0.555514 0.555514i
235235 −297.943 −1.26784
236236 92.0907 + 92.0907i 0.390215 + 0.390215i
237237 −230.926 + 230.926i −0.974370 + 0.974370i
238238 −32.5881 32.5881i −0.136925 0.136925i
239239 366.238 1.53237 0.766187 0.642617i 0.222151π-0.222151\pi
0.766187 + 0.642617i 0.222151π0.222151\pi
240240 53.3192 + 53.3192i 0.222163 + 0.222163i
241241 −20.8243 + 20.8243i −0.0864077 + 0.0864077i −0.748990 0.662582i 0.769461π-0.769461\pi
0.662582 + 0.748990i 0.269461π0.269461\pi
242242 −114.415 114.415i −0.472791 0.472791i
243243 66.4678 + 66.4678i 0.273530 + 0.273530i
244244 164.107i 0.672570i
245245 169.087i 0.690153i
246246 358.681i 1.45805i
247247 −131.963 131.963i −0.534262 0.534262i
248248 124.577i 0.502327i
249249 −219.946 −0.883318
250250 132.959 + 132.959i 0.531834 + 0.531834i
251251 −169.149 169.149i −0.673902 0.673902i 0.284711 0.958613i 0.408102π-0.408102\pi
−0.958613 + 0.284711i 0.908102π0.908102\pi
252252 −33.7637 + 33.7637i −0.133983 + 0.133983i
253253 53.1318i 0.210007i
254254 73.7961 73.7961i 0.290536 0.290536i
255255 487.327i 1.91108i
256256 16.0000 0.0625000
257257 −53.7468 53.7468i −0.209132 0.209132i 0.594767 0.803898i 0.297244π-0.297244\pi
−0.803898 + 0.594767i 0.797244π0.797244\pi
258258 −206.316 −0.799676
259259 8.47865 8.47865i 0.0327361 0.0327361i
260260 48.9573 0.188297
261261 628.034 + 628.034i 2.40626 + 2.40626i
262262 −42.9213 42.9213i −0.163822 0.163822i
263263 −44.7508 −0.170155 −0.0850776 0.996374i 0.527114π-0.527114\pi
−0.0850776 + 0.996374i 0.527114π0.527114\pi
264264 38.3630i 0.145314i
265265 26.7138 0.100807
266266 −34.2760 + 34.2760i −0.128857 + 0.128857i
267267 −513.758 + 513.758i −1.92419 + 1.92419i
268268 43.4623i 0.162173i
269269 240.734 + 120.034i 0.894921 + 0.446225i
270270 −264.970 −0.981369
271271 168.597 + 168.597i 0.622131 + 0.622131i 0.946076 0.323945i 0.105009π-0.105009\pi
−0.323945 + 0.946076i 0.605009π0.605009\pi
272272 −73.1184 73.1184i −0.268817 0.268817i
273273 45.7338i 0.167523i
274274 157.769 0.575799
275275 31.5124i 0.114591i
276276 154.779 154.779i 0.560794 0.560794i
277277 137.561 137.561i 0.496609 0.496609i −0.413771 0.910381i 0.635789π-0.635789\pi
0.910381 + 0.413771i 0.135789π0.135789\pi
278278 163.797i 0.589196i
279279 589.842 + 589.842i 2.11413 + 2.11413i
280280 12.7162i 0.0454149i
281281 229.073 229.073i 0.815205 0.815205i −0.170204 0.985409i 0.554443π-0.554443\pi
0.985409 + 0.170204i 0.0544427π0.0544427\pi
282282 624.483i 2.21448i
283283 11.2423 0.0397254 0.0198627 0.999803i 0.493677π-0.493677\pi
0.0198627 + 0.999803i 0.493677π0.493677\pi
284284 −21.9657 21.9657i −0.0773439 0.0773439i
285285 −512.568 −1.79848
286286 17.6123 + 17.6123i 0.0615815 + 0.0615815i
287287 −42.7712 + 42.7712i −0.149028 + 0.149028i
288288 −75.7560 + 75.7560i −0.263042 + 0.263042i
289289 379.287i 1.31241i
290290 −236.532 −0.815627
291291 366.269 366.269i 1.25866 1.25866i
292292 −83.1425 −0.284735
293293 480.569 1.64017 0.820083 0.572244i 0.193927π-0.193927\pi
0.820083 + 0.572244i 0.193927π0.193927\pi
294294 −354.404 −1.20546
295295 164.217 164.217i 0.556669 0.556669i
296296 19.0236 19.0236i 0.0642690 0.0642690i
297297 −95.3224 95.3224i −0.320951 0.320951i
298298 −135.917 + 135.917i −0.456096 + 0.456096i
299299 142.117i 0.475308i
300300 −91.7994 + 91.7994i −0.305998 + 0.305998i
301301 24.6023 + 24.6023i 0.0817354 + 0.0817354i
302302 −249.028 + 249.028i −0.824595 + 0.824595i
303303 227.323i 0.750242i
304304 −76.9055 + 76.9055i −0.252979 + 0.252979i
305305 −292.638 −0.959469
306306 692.394 2.26273
307307 572.021 1.86326 0.931630 0.363408i 0.118387π-0.118387\pi
0.931630 + 0.363408i 0.118387π0.118387\pi
308308 4.57462 4.57462i 0.0148527 0.0148527i
309309 −199.880 + 199.880i −0.646860 + 0.646860i
310310 −222.148 −0.716605
311311 −364.716 364.716i −1.17272 1.17272i −0.981558 0.191163i 0.938774π-0.938774\pi
−0.191163 0.981558i 0.561226π-0.561226\pi
312312 102.613i 0.328889i
313313 354.557 1.13277 0.566385 0.824141i 0.308341π-0.308341\pi
0.566385 + 0.824141i 0.308341π0.308341\pi
314314 93.1408i 0.296627i
315315 60.2079 + 60.2079i 0.191136 + 0.191136i
316316 123.570 0.391043
317317 −239.526 239.526i −0.755603 0.755603i 0.219916 0.975519i 0.429422π-0.429422\pi
−0.975519 + 0.219916i 0.929422π0.929422\pi
318318 55.9917i 0.176074i
319319 −85.0919 85.0919i −0.266746 0.266746i
320320 28.5314i 0.0891607i
321321 453.961 1.41421
322322 −36.9135 −0.114638
323323 702.901 2.17616
324324 214.469i 0.661942i
325325 84.2895i 0.259352i
326326 −312.839 −0.959628
327327 −315.719 −0.965500
328328 −95.9661 + 95.9661i −0.292580 + 0.292580i
329329 −74.4669 + 74.4669i −0.226343 + 0.226343i
330330 68.4094 0.207301
331331 −521.688 −1.57610 −0.788048 0.615614i 0.788908π-0.788908\pi
−0.788048 + 0.615614i 0.788908π0.788908\pi
332332 58.8472 + 58.8472i 0.177251 + 0.177251i
333333 180.144i 0.540974i
334334 201.519i 0.603349i
335335 77.5025 0.231351
336336 26.6528 0.0793239
337337 −285.098 + 285.098i −0.845988 + 0.845988i −0.989630 0.143641i 0.954119π-0.954119\pi
0.143641 + 0.989630i 0.454119π0.454119\pi
338338 −121.891 121.891i −0.360623 0.360623i
339339 −1140.61 −3.36464
340340 −130.386 + 130.386i −0.383487 + 0.383487i
341341 −79.9173 79.9173i −0.234361 0.234361i
342342 728.257i 2.12941i
343343 85.9388 + 85.9388i 0.250550 + 0.250550i
344344 55.2006 + 55.2006i 0.160467 + 0.160467i
345345 −276.004 276.004i −0.800012 0.800012i
346346 74.9613 + 74.9613i 0.216651 + 0.216651i
347347 −126.473 −0.364475 −0.182238 0.983255i 0.558334π-0.558334\pi
−0.182238 + 0.983255i 0.558334π0.558334\pi
348348 495.766i 1.42461i
349349 −120.593 −0.345538 −0.172769 0.984962i 0.555271π-0.555271\pi
−0.172769 + 0.984962i 0.555271π0.555271\pi
350350 21.8934 0.0625525
351351 −254.969 254.969i −0.726406 0.726406i
352352 10.2641 10.2641i 0.0291595 0.0291595i
353353 362.527i 1.02699i −0.858093 0.513494i 0.828351π-0.828351\pi
0.858093 0.513494i 0.171649π-0.171649\pi
354354 344.196 + 344.196i 0.972306 + 0.972306i
355355 −39.1694 + 39.1694i −0.110336 + 0.110336i
356356 274.915 0.772233
357357 −121.801 121.801i −0.341179 0.341179i
358358 23.3166i 0.0651301i
359359 −129.816 + 129.816i −0.361606 + 0.361606i −0.864404 0.502798i 0.832304π-0.832304\pi
0.502798 + 0.864404i 0.332304π0.332304\pi
360360 135.089 + 135.089i 0.375247 + 0.375247i
361361 378.307i 1.04794i
362362 384.748 1.06284
363363 −427.637 427.637i −1.17806 1.17806i
364364 12.2362 12.2362i 0.0336160 0.0336160i
365365 148.261i 0.406194i
366366 613.363i 1.67586i
367367 −446.162 + 446.162i −1.21570 + 1.21570i −0.246578 + 0.969123i 0.579306π0.579306\pi
−0.969123 + 0.246578i 0.920694π0.920694\pi
368368 −82.8232 −0.225063
369369 908.751i 2.46274i
370370 −33.9232 33.9232i −0.0916843 0.0916843i
371371 6.67677 6.67677i 0.0179967 0.0179967i
372372 465.617i 1.25166i
373373 239.176 + 239.176i 0.641223 + 0.641223i 0.950856 0.309633i 0.100206π-0.100206\pi
−0.309633 + 0.950856i 0.600206π0.600206\pi
374374 −93.8120 −0.250834
375375 496.943 + 496.943i 1.32518 + 1.32518i
376376 −167.082 + 167.082i −0.444368 + 0.444368i
377377 −227.604 227.604i −0.603724 0.603724i
378378 −66.2256 + 66.2256i −0.175200 + 0.175200i
379379 127.534 127.534i 0.336502 0.336502i −0.518547 0.855049i 0.673527π-0.673527\pi
0.855049 + 0.518547i 0.173527π0.173527\pi
380380 137.139 + 137.139i 0.360892 + 0.360892i
381381 275.819 275.819i 0.723934 0.723934i
382382 −42.8213 + 42.8213i −0.112098 + 0.112098i
383383 1.83699 + 1.83699i 0.00479631 + 0.00479631i 0.709501 0.704705i 0.248920π-0.248920\pi
−0.704705 + 0.709501i 0.748920π0.748920\pi
384384 59.8013 0.155732
385385 −8.15753 8.15753i −0.0211884 0.0211884i
386386 449.420 1.16430
387387 −522.722 −1.35070
388388 −195.993 −0.505136
389389 185.801 0.477637 0.238819 0.971064i 0.423240π-0.423240\pi
0.238819 + 0.971064i 0.423240π0.423240\pi
390390 182.982 0.469184
391391 378.494 + 378.494i 0.968014 + 0.968014i
392392 94.8218 + 94.8218i 0.241892 + 0.241892i
393393 −160.422 160.422i −0.408198 0.408198i
394394 −81.1773 −0.206034
395395 220.351i 0.557851i
396396 97.1962i 0.245445i
397397 96.1820 96.1820i 0.242272 0.242272i −0.575517 0.817789i 0.695199π-0.695199\pi
0.817789 + 0.575517i 0.195199π0.195199\pi
398398 −81.1621 + 81.1621i −0.203925 + 0.203925i
399399 −128.109 + 128.109i −0.321076 + 0.321076i
400400 49.1224 0.122806
401401 78.5972 + 78.5972i 0.196003 + 0.196003i 0.798284 0.602281i 0.205741π-0.205741\pi
−0.602281 + 0.798284i 0.705741π0.705741\pi
402402 162.444i 0.404089i
403403 −213.763 213.763i −0.530429 0.530429i
404404 60.8210 60.8210i 0.150547 0.150547i
405405 −382.444 −0.944307
406406 −59.1179 + 59.1179i −0.145611 + 0.145611i
407407 24.4076i 0.0599696i
408408 −273.286 273.286i −0.669818 0.669818i
409409 97.1382 + 97.1382i 0.237502 + 0.237502i 0.815815 0.578313i 0.196289π-0.196289\pi
−0.578313 + 0.815815i 0.696289π0.696289\pi
410410 171.128 + 171.128i 0.417386 + 0.417386i
411411 589.674 1.43473
412412 106.957 0.259604
413413 82.0879i 0.198760i
414414 392.147 392.147i 0.947215 0.947215i
415415 104.937 104.937i 0.252861 0.252861i
416416 27.4545 27.4545i 0.0659964 0.0659964i
417417 612.203i 1.46811i
418418 98.6710i 0.236055i
419419 63.9019i 0.152511i −0.997088 0.0762553i 0.975704π-0.975704\pi
0.997088 0.0762553i 0.0242964π-0.0242964\pi
420420 47.5277i 0.113161i
421421 524.780i 1.24651i 0.782019 + 0.623254i 0.214190π0.214190\pi
−0.782019 + 0.623254i 0.785810π0.785810\pi
422422 221.892 221.892i 0.525810 0.525810i
423423 1582.18i 3.74039i
424424 14.9807 14.9807i 0.0353319 0.0353319i
425425 −224.484 224.484i −0.528198 0.528198i
426426 −82.0984 82.0984i −0.192719 0.192719i
427427 −73.1409 + 73.1409i −0.171290 + 0.171290i
428428 −121.459 121.459i −0.283782 0.283782i
429429 65.8273 + 65.8273i 0.153444 + 0.153444i
430430 98.4344 98.4344i 0.228917 0.228917i
431431 −82.8266 82.8266i −0.192173 0.192173i 0.604461 0.796634i 0.293388π-0.293388\pi
−0.796634 + 0.604461i 0.793388π0.793388\pi
432432 −148.591 + 148.591i −0.343961 + 0.343961i
433433 200.557i 0.463180i −0.972813 0.231590i 0.925607π-0.925607\pi
0.972813 0.231590i 0.0743928π-0.0743928\pi
434434 −55.5228 + 55.5228i −0.127933 + 0.127933i
435435 −884.056 −2.03231
436436 84.4714 + 84.4714i 0.193742 + 0.193742i
437437 398.098 398.098i 0.910979 0.910979i
438438 −310.752 −0.709479
439439 51.1340i 0.116478i 0.998303 + 0.0582392i 0.0185486π0.0185486\pi
−0.998303 + 0.0582392i 0.981451π0.981451\pi
440440 −18.3031 18.3031i −0.0415980 0.0415980i
441441 −897.915 −2.03609
442442 −250.929 −0.567712
443443 307.613 + 307.613i 0.694386 + 0.694386i 0.963194 0.268807i 0.0866295π-0.0866295\pi
−0.268807 + 0.963194i 0.586630π0.586630\pi
444444 71.1023 71.1023i 0.160140 0.160140i
445445 490.232i 1.10164i
446446 473.723 1.06216
447447 −507.999 + 507.999i −1.13646 + 1.13646i
448448 −7.13104 7.13104i −0.0159175 0.0159175i
449449 −41.1705 −0.0916937 −0.0458468 0.998948i 0.514599π-0.514599\pi
−0.0458468 + 0.998948i 0.514599π0.514599\pi
450450 −232.582 + 232.582i −0.516849 + 0.516849i
451451 123.126i 0.273007i
452452 305.174 + 305.174i 0.675164 + 0.675164i
453453 −930.760 + 930.760i −2.05466 + 2.05466i
454454 −475.772 −1.04796
455455 −21.8198 21.8198i −0.0479556 0.0479556i
456456 −287.440 + 287.440i −0.630352 + 0.630352i
457457 339.800i 0.743545i 0.928324 + 0.371772i 0.121250π0.121250\pi
−0.928324 + 0.371772i 0.878750π0.878750\pi
458458 213.611i 0.466399i
459459 1358.09 2.95881
460460 147.691i 0.321068i
461461 −214.144 + 214.144i −0.464520 + 0.464520i −0.900134 0.435614i 0.856531π-0.856531\pi
0.435614 + 0.900134i 0.356531π0.356531\pi
462462 17.0980 17.0980i 0.0370087 0.0370087i
463463 274.915 274.915i 0.593769 0.593769i −0.344878 0.938647i 0.612080π-0.612080\pi
0.938647 + 0.344878i 0.112080π0.112080\pi
464464 −132.644 + 132.644i −0.285870 + 0.285870i
465465 −830.294 −1.78558
466466 27.8816 27.8816i 0.0598317 0.0598317i
467467 −74.6671 74.6671i −0.159887 0.159887i 0.622630 0.782517i 0.286064π-0.286064\pi
−0.782517 + 0.622630i 0.786064π0.786064\pi
468468 259.980i 0.555514i
469469 19.3707 19.3707i 0.0413022 0.0413022i
470470 297.943 + 297.943i 0.633922 + 0.633922i
471471 348.121i 0.739111i
472472 184.181i 0.390215i
473473 70.8232 0.149732
474474 461.852 0.974370
475475 −236.111 + 236.111i −0.497077 + 0.497077i
476476 65.1763i 0.136925i
477477 141.860i 0.297400i
478478 −366.238 366.238i −0.766187 0.766187i
479479 −240.022 240.022i −0.501089 0.501089i 0.410687 0.911776i 0.365289π-0.365289\pi
−0.911776 + 0.410687i 0.865289π0.865289\pi
480480 106.638i 0.222163i
481481 65.2856i 0.135729i
482482 41.6485 0.0864077
483483 −137.967 −0.285646
484484 228.831i 0.472791i
485485 349.497i 0.720613i
486486 132.936i 0.273530i
487487 −421.501 −0.865506 −0.432753 0.901513i 0.642458π-0.642458\pi
−0.432753 + 0.901513i 0.642458π0.642458\pi
488488 −164.107 + 164.107i −0.336285 + 0.336285i
489489 −1169.26 −2.39112
490490 169.087 169.087i 0.345076 0.345076i
491491 960.328i 1.95586i 0.208931 + 0.977930i 0.433002π0.433002\pi
−0.208931 + 0.977930i 0.566998π0.566998\pi
492492 −358.681 + 358.681i −0.729026 + 0.729026i
493493 1212.33 2.45910
494494 263.925i 0.534262i
495495 173.322 0.350144
496496 −124.577 + 124.577i −0.251164 + 0.251164i
497497 19.5798i 0.0393959i
498498 219.946 + 219.946i 0.441659 + 0.441659i
499499 −144.355 144.355i −0.289289 0.289289i 0.547510 0.836799i 0.315576π-0.315576\pi
−0.836799 + 0.547510i 0.815576π0.815576\pi
500500 265.917i 0.531834i
501501 753.192i 1.50338i
502502 338.299i 0.673902i
503503 443.700 + 443.700i 0.882107 + 0.882107i 0.993749 0.111642i 0.0356108π-0.0356108\pi
−0.111642 + 0.993749i 0.535611π0.535611\pi
504504 67.5274 0.133983
505505 −108.457 108.457i −0.214766 0.214766i
506506 −53.1318 + 53.1318i −0.105003 + 0.105003i
507507 −455.576 455.576i −0.898572 0.898572i
508508 −147.592 −0.290536
509509 308.901 + 308.901i 0.606879 + 0.606879i 0.942129 0.335250i 0.108821π-0.108821\pi
−0.335250 + 0.942129i 0.608821π0.608821\pi
510510 −487.327 + 487.327i −0.955542 + 0.955542i
511511 37.0558 + 37.0558i 0.0725163 + 0.0725163i
512512 −16.0000 16.0000i −0.0312500 0.0312500i
513513 1428.43i 2.78447i
514514 107.494i 0.209132i
515515 190.727i 0.370343i
516516 206.316 + 206.316i 0.399838 + 0.399838i
517517 214.369i 0.414641i
518518 −16.9573 −0.0327361
519519 280.174 + 280.174i 0.539834 + 0.539834i
520520 −48.9573 48.9573i −0.0941486 0.0941486i
521521 306.825 306.825i 0.588916 0.588916i −0.348422 0.937338i 0.613282π-0.613282\pi
0.937338 + 0.348422i 0.113282π0.113282\pi
522522 1256.07i 2.40626i
523523 −430.202 + 430.202i −0.822567 + 0.822567i −0.986475 0.163909i 0.947590π-0.947590\pi
0.163909 + 0.986475i 0.447590π0.447590\pi
524524 85.8426i 0.163822i
525525 81.8282 0.155863
526526 44.7508 + 44.7508i 0.0850776 + 0.0850776i
527527 1138.61 2.16055
528528 38.3630 38.3630i 0.0726572 0.0726572i
529529 −100.270 −0.189546
530530 −26.7138 26.7138i −0.0504035 0.0504035i
531531 872.053 + 872.053i 1.64228 + 1.64228i
532532 68.5521 0.128857
533533 329.338i 0.617895i
534534 1027.52 1.92419
535535 −216.586 + 216.586i −0.404835 + 0.404835i
536536 43.4623 43.4623i 0.0810863 0.0810863i
537537 87.1476i 0.162286i
538538 −120.699 360.768i −0.224348 0.670573i
539539 121.658 0.225710
540540 264.970 + 264.970i 0.490685 + 0.490685i
541541 −136.419 136.419i −0.252161 0.252161i 0.569695 0.821856i 0.307061π-0.307061\pi
−0.821856 + 0.569695i 0.807061π0.807061\pi
542542 337.195i 0.622131i
543543 1438.02 2.64830
544544 146.237i 0.268817i
545545 150.631 150.631i 0.276386 0.276386i
546546 45.7338 45.7338i 0.0837616 0.0837616i
547547 814.963i 1.48988i 0.667133 + 0.744939i 0.267521π0.267521\pi
−0.667133 + 0.744939i 0.732479π0.732479\pi
548548 −157.769 157.769i −0.287900 0.287900i
549549 1554.01i 2.83062i
550550 31.5124 31.5124i 0.0572953 0.0572953i
551551 1275.13i 2.31421i
552552 −309.558 −0.560794
553553 −55.0738 55.0738i −0.0995910 0.0995910i
554554 −275.122 −0.496609
555555 −126.791 126.791i −0.228452 0.228452i
556556 163.797 163.797i 0.294598 0.294598i
557557 473.160 473.160i 0.849479 0.849479i −0.140589 0.990068i 0.544900π-0.544900\pi
0.990068 + 0.140589i 0.0448996π0.0448996\pi
558558 1179.68i 2.11413i
559559 189.438 0.338887
560560 −12.7162 + 12.7162i −0.0227075 + 0.0227075i
561561 −350.630 −0.625009
562562 −458.145 −0.815205
563563 103.066 0.183065 0.0915327 0.995802i 0.470823π-0.470823\pi
0.0915327 + 0.995802i 0.470823π0.470823\pi
564564 −624.483 + 624.483i −1.10724 + 1.10724i
565565 544.191 544.191i 0.963169 0.963169i
566566 −11.2423 11.2423i −0.0198627 0.0198627i
567567 −95.5869 + 95.5869i −0.168584 + 0.168584i
568568 43.9313i 0.0773439i
569569 −403.594 + 403.594i −0.709304 + 0.709304i −0.966389 0.257084i 0.917238π-0.917238\pi
0.257084 + 0.966389i 0.417238π0.417238\pi
570570 512.568 + 512.568i 0.899242 + 0.899242i
571571 208.349 208.349i 0.364885 0.364885i −0.500723 0.865608i 0.666932π-0.666932\pi
0.865608 + 0.500723i 0.166932π0.166932\pi
572572 35.2246i 0.0615815i
573573 −160.048 + 160.048i −0.279316 + 0.279316i
574574 85.5423 0.149028
575575 −254.280 −0.442226
576576 151.512 0.263042
577577 710.572 710.572i 1.23149 1.23149i 0.268104 0.963390i 0.413603π-0.413603\pi
0.963390 0.268104i 0.0863972π-0.0863972\pi
578578 379.287 379.287i 0.656205 0.656205i
579579 1679.74 2.90111
580580 236.532 + 236.532i 0.407813 + 0.407813i
581581 52.4553i 0.0902845i
582582 −732.539 −1.25866
583583 19.2205i 0.0329683i
584584 83.1425 + 83.1425i 0.142367 + 0.142367i
585585 463.601 0.792480
586586 −480.569 480.569i −0.820083 0.820083i
587587 745.134i 1.26939i 0.772761 + 0.634697i 0.218875π0.218875\pi
−0.772761 + 0.634697i 0.781125π0.781125\pi
588588 354.404 + 354.404i 0.602728 + 0.602728i
589589 1197.58i 2.03325i
590590 −328.435 −0.556669
591591 −303.406 −0.513378
592592 −38.0473 −0.0642690
593593 166.041i 0.280002i −0.990151 0.140001i 0.955289π-0.955289\pi
0.990151 0.140001i 0.0447106π-0.0447106\pi
594594 190.645i 0.320951i
595595 116.223 0.195333
596596 271.833 0.456096
597597 −303.350 + 303.350i −0.508124 + 0.508124i
598598 −142.117 + 142.117i −0.237654 + 0.237654i
599599 −487.490 −0.813839 −0.406919 0.913464i 0.633397π-0.633397\pi
−0.406919 + 0.913464i 0.633397π0.633397\pi
600600 183.599 0.305998
601601 556.414 + 556.414i 0.925813 + 0.925813i 0.997432 0.0716191i 0.0228166π-0.0228166\pi
−0.0716191 + 0.997432i 0.522817π0.522817\pi
602602 49.2047i 0.0817354i
603603 411.566i 0.682530i
604604 498.055 0.824595
605605 408.054 0.674470
606606 227.323 227.323i 0.375121 0.375121i
607607 617.124 + 617.124i 1.01668 + 1.01668i 0.999859 + 0.0168196i 0.00535409π0.00535409\pi
0.0168196 + 0.999859i 0.494646π0.494646\pi
608608 153.811 0.252979
609609 −220.958 + 220.958i −0.362821 + 0.362821i
610610 292.638 + 292.638i 0.479734 + 0.479734i
611611 573.395i 0.938453i
612612 −692.394 692.394i −1.13136 1.13136i
613613 586.008 + 586.008i 0.955967 + 0.955967i 0.999071 0.0431036i 0.0137246π-0.0137246\pi
−0.0431036 + 0.999071i 0.513725π0.513725\pi
614614 −572.021 572.021i −0.931630 0.931630i
615615 639.605 + 639.605i 1.04001 + 1.04001i
616616 −9.14925 −0.0148527
617617 381.746i 0.618714i 0.950946 + 0.309357i 0.100114π0.100114\pi
−0.950946 + 0.309357i 0.899886π0.899886\pi
618618 399.760 0.646860
619619 −819.066 −1.32321 −0.661604 0.749853i 0.730124π-0.730124\pi
−0.661604 + 0.749853i 0.730124π0.730124\pi
620620 222.148 + 222.148i 0.358303 + 0.358303i
621621 769.175 769.175i 1.23861 1.23861i
622622 729.433i 1.17272i
623623 −122.527 122.527i −0.196672 0.196672i
624624 102.613 102.613i 0.164445 0.164445i
625625 −167.172 −0.267475
626626 −354.557 354.557i −0.566385 0.566385i
627627 368.791i 0.588183i
628628 93.1408 93.1408i 0.148313 0.148313i
629629 173.872 + 173.872i 0.276426 + 0.276426i
630630 120.416i 0.191136i
631631 917.988 1.45481 0.727407 0.686206i 0.240725π-0.240725\pi
0.727407 + 0.686206i 0.240725π0.240725\pi
632632 −123.570 123.570i −0.195522 0.195522i
633633 829.338 829.338i 1.31017 1.31017i
634634 479.052i 0.755603i
635635 263.189i 0.414470i
636636 55.9917 55.9917i 0.0880372 0.0880372i
637637 325.411 0.510849
638638 170.184i 0.266746i
639639 −208.004 208.004i −0.325514 0.325514i
640640 −28.5314 + 28.5314i −0.0445803 + 0.0445803i
641641 1021.28i 1.59326i 0.604467 + 0.796630i 0.293386π0.293386\pi
−0.604467 + 0.796630i 0.706614π0.706614\pi
642642 −453.961 453.961i −0.707104 0.707104i
643643 −671.534 −1.04438 −0.522188 0.852830i 0.674884π-0.674884\pi
−0.522188 + 0.852830i 0.674884π0.674884\pi
644644 36.9135 + 36.9135i 0.0573191 + 0.0573191i
645645 367.906 367.906i 0.570397 0.570397i
646646 −702.901 702.901i −1.08808 1.08808i
647647 407.848 407.848i 0.630368 0.630368i −0.317792 0.948160i 0.602941π-0.602941\pi
0.948160 + 0.317792i 0.102941π0.102941\pi
648648 −214.469 + 214.469i −0.330971 + 0.330971i
649649 −118.154 118.154i −0.182055 0.182055i
650650 84.2895 84.2895i 0.129676 0.129676i
651651 −207.521 + 207.521i −0.318773 + 0.318773i
652652 312.839 + 312.839i 0.479814 + 0.479814i
653653 395.816 0.606150 0.303075 0.952967i 0.401987π-0.401987\pi
0.303075 + 0.952967i 0.401987π0.401987\pi
654654 315.719 + 315.719i 0.482750 + 0.482750i
655655 153.076 0.233703
656656 191.932 0.292580
657657 −787.318 −1.19835
658658 148.934 0.226343
659659 −981.691 −1.48967 −0.744834 0.667250i 0.767471π-0.767471\pi
−0.744834 + 0.667250i 0.767471π0.767471\pi
660660 −68.4094 68.4094i −0.103651 0.103651i
661661 32.1231 + 32.1231i 0.0485978 + 0.0485978i 0.730988 0.682390i 0.239060π-0.239060\pi
−0.682390 + 0.730988i 0.739060π0.739060\pi
662662 521.688 + 521.688i 0.788048 + 0.788048i
663663 −937.866 −1.41458
664664 117.694i 0.177251i
665665 122.243i 0.183824i
666666 180.144 180.144i 0.270487 0.270487i
667667 686.623 686.623i 1.02942 1.02942i
668668 201.519 201.519i 0.301675 0.301675i
669669 1770.58 2.64660
670670 −77.5025 77.5025i −0.115675 0.115675i
671671 210.552i 0.313788i
672672 −26.6528 26.6528i −0.0396620 0.0396620i
673673 −777.793 + 777.793i −1.15571 + 1.15571i −0.170321 + 0.985389i 0.554481π0.554481\pi
−0.985389 + 0.170321i 0.945519π0.945519\pi
674674 570.196 0.845988
675675 −456.197 + 456.197i −0.675847 + 0.675847i
676676 243.781i 0.360623i
677677 −903.696 903.696i −1.33485 1.33485i −0.900968 0.433886i 0.857142π-0.857142\pi
−0.433886 0.900968i 0.642858π-0.642858\pi
678678 1140.61 + 1140.61i 1.68232 + 1.68232i
679679 87.3521 + 87.3521i 0.128648 + 0.128648i
680680 260.771 0.383487
681681 −1778.24 −2.61121
682682 159.835i 0.234361i
683683 −628.247 + 628.247i −0.919835 + 0.919835i −0.997017 0.0771823i 0.975408π-0.975408\pi
0.0771823 + 0.997017i 0.475408π0.475408\pi
684684 −728.257 + 728.257i −1.06470 + 1.06470i
685685 −281.336 + 281.336i −0.410709 + 0.410709i
686686 171.878i 0.250550i
687687 798.388i 1.16214i
688688 110.401i 0.160467i
689689 51.4111i 0.0746170i
690690 552.009i 0.800012i
691691 467.326 467.326i 0.676304 0.676304i −0.282858 0.959162i 0.591282π-0.591282\pi
0.959162 + 0.282858i 0.0912825π0.0912825\pi
692692 149.923i 0.216651i
693693 43.3194 43.3194i 0.0625099 0.0625099i
694694 126.473 + 126.473i 0.182238 + 0.182238i
695695 −292.084 292.084i −0.420265 0.420265i
696696 −495.766 + 495.766i −0.712307 + 0.712307i
697697 −877.110 877.110i −1.25841 1.25841i
698698 120.593 + 120.593i 0.172769 + 0.172769i
699699 104.210 104.210i 0.149084 0.149084i
700700 −21.8934 21.8934i −0.0312763 0.0312763i
701701 −713.369 + 713.369i −1.01764 + 1.01764i −0.0178035 + 0.999842i 0.505667π0.505667\pi
−0.999842 + 0.0178035i 0.994333π0.994333\pi
702702 509.937i 0.726406i
703703 182.878 182.878i 0.260139 0.260139i
704704 −20.5283 −0.0291595
705705 1113.59 + 1113.59i 1.57956 + 1.57956i
706706 −362.527 + 362.527i −0.513494 + 0.513494i
707707 −54.2146 −0.0766827
708708 688.393i 0.972306i
709709 417.364 + 417.364i 0.588665 + 0.588665i 0.937270 0.348605i 0.113344π-0.113344\pi
−0.348605 + 0.937270i 0.613344π0.613344\pi
710710 78.3389 0.110336
711711 1170.14 1.64577
712712 −274.915 274.915i −0.386116 0.386116i
713713 644.868 644.868i 0.904443 0.904443i
714714 243.602i 0.341179i
715715 −62.8130 −0.0878503
716716 −23.3166 + 23.3166i −0.0325651 + 0.0325651i
717717 −1368.84 1368.84i −1.90912 1.90912i
718718 259.633 0.361606
719719 −308.569 + 308.569i −0.429164 + 0.429164i −0.888343 0.459180i 0.848143π-0.848143\pi
0.459180 + 0.888343i 0.348143π0.348143\pi
720720 270.178i 0.375247i
721721 −47.6696 47.6696i −0.0661160 0.0661160i
722722 −378.307 + 378.307i −0.523972 + 0.523972i
723723 155.665 0.215304
724724 −384.748 384.748i −0.531419 0.531419i
725725 −407.236 + 407.236i −0.561704 + 0.561704i
726726 855.274i 1.17806i
727727 230.505i 0.317063i 0.987354 + 0.158532i 0.0506760π0.0506760\pi
−0.987354 + 0.158532i 0.949324π0.949324\pi
728728 −24.4724 −0.0336160
729729 468.254i 0.642324i
730730 148.261 148.261i 0.203097 0.203097i
731731 −504.522 + 504.522i −0.690180 + 0.690180i
732732 −613.363 + 613.363i −0.837928 + 0.837928i
733733 −715.564 + 715.564i −0.976213 + 0.976213i −0.999724 0.0235111i 0.992516π-0.992516\pi
0.0235111 + 0.999724i 0.492516π0.492516\pi
734734 892.325 1.21570
735735 631.978 631.978i 0.859834 0.859834i
736736 82.8232 + 82.8232i 0.112532 + 0.112532i
737737 55.7628i 0.0756619i
738738 −908.751 + 908.751i −1.23137 + 1.23137i
739739 −195.309 195.309i −0.264288 0.264288i 0.562505 0.826794i 0.309838π-0.309838\pi
−0.826794 + 0.562505i 0.809838π0.809838\pi
740740 67.8464i 0.0916843i
741741 986.442i 1.33123i
742742 −13.3535 −0.0179967
743743 149.544 0.201271 0.100635 0.994923i 0.467912π-0.467912\pi
0.100635 + 0.994923i 0.467912π0.467912\pi
744744 −465.617 + 465.617i −0.625829 + 0.625829i
745745 484.737i 0.650653i
746746 478.352i 0.641223i
747747 557.254 + 557.254i 0.745989 + 0.745989i
748748 93.8120 + 93.8120i 0.125417 + 0.125417i
749749 108.266i 0.144547i
750750 993.886i 1.32518i
751751 1082.37 1.44124 0.720622 0.693328i 0.243856π-0.243856\pi
0.720622 + 0.693328i 0.243856π0.243856\pi
752752 334.164 0.444368
753753 1264.42i 1.67917i
754754 455.208i 0.603724i
755755 888.139i 1.17634i
756756 132.451 0.175200
757757 −662.151 + 662.151i −0.874704 + 0.874704i −0.992981 0.118277i 0.962263π-0.962263\pi
0.118277 + 0.992981i 0.462263π0.462263\pi
758758 −255.069 −0.336502
759759 −198.584 + 198.584i −0.261639 + 0.261639i
760760 274.278i 0.360892i
761761 206.058 206.058i 0.270773 0.270773i −0.558639 0.829411i 0.688676π-0.688676\pi
0.829411 + 0.558639i 0.188676π0.188676\pi
762762 −551.638 −0.723934
763763 75.2962i 0.0986844i
764764 85.6426 0.112098
765765 −1234.69 + 1234.69i −1.61397 + 1.61397i
766766 3.67397i 0.00479631i
767767 −316.038 316.038i −0.412045 0.412045i
768768 −59.8013 59.8013i −0.0778662 0.0778662i
769769 914.612i 1.18935i −0.803965 0.594676i 0.797280π-0.797280\pi
0.803965 0.594676i 0.202720π-0.202720\pi
770770 16.3151i 0.0211884i
771771 401.766i 0.521097i
772772 −449.420 449.420i −0.582150 0.582150i
773773 −854.338 −1.10522 −0.552612 0.833439i 0.686369π-0.686369\pi
−0.552612 + 0.833439i 0.686369π0.686369\pi
774774 522.722 + 522.722i 0.675351 + 0.675351i
775775 −382.471 + 382.471i −0.493510 + 0.493510i
776776 195.993 + 195.993i 0.252568 + 0.252568i
777777 −63.3792 −0.0815692
778778 −185.801 185.801i −0.238819 0.238819i
779779 −922.540 + 922.540i −1.18426 + 1.18426i
780780 −182.982 182.982i −0.234592 0.234592i
781781 28.1823 + 28.1823i 0.0360849 + 0.0360849i
782782 756.987i 0.968014i
783783 2463.71i 3.14650i
784784 189.644i 0.241892i
785785 −166.090 166.090i −0.211580 0.211580i
786786 320.844i 0.408198i
787787 315.408 0.400773 0.200386 0.979717i 0.435780π-0.435780\pi
0.200386 + 0.979717i 0.435780π0.435780\pi
788788 81.1773 + 81.1773i 0.103017 + 0.103017i
789789 167.260 + 167.260i 0.211989 + 0.211989i
790790 −220.351 + 220.351i −0.278926 + 0.278926i
791791 272.026i 0.343902i
792792 97.1962 97.1962i 0.122722 0.122722i
793793 563.185i 0.710195i
794794 −192.364 −0.242272
795795 −99.8451 99.8451i −0.125591 0.125591i
796796 162.324 0.203925
797797 434.738 434.738i 0.545468 0.545468i −0.379658 0.925127i 0.623958π-0.623958\pi
0.925127 + 0.379658i 0.123958π0.123958\pi
798798 256.219 0.321076
799799 −1527.10 1527.10i −1.91126 1.91126i
800800 −49.1224 49.1224i −0.0614030 0.0614030i
801801 2603.31 3.25007
802802 157.194i 0.196003i
803803 106.673 0.132843
804804 162.444 162.444i 0.202044 0.202044i
805805 65.8247 65.8247i 0.0817698 0.0817698i
806806 427.526i 0.530429i
807807 −451.123 1348.40i −0.559012 1.67088i
808808 −121.642 −0.150547
809809 424.674 + 424.674i 0.524937 + 0.524937i 0.919058 0.394121i 0.128951π-0.128951\pi
−0.394121 + 0.919058i 0.628951π0.628951\pi
810810 382.444 + 382.444i 0.472154 + 0.472154i
811811 119.913i 0.147858i −0.997263 0.0739292i 0.976446π-0.976446\pi
0.997263 0.0739292i 0.0235539π-0.0235539\pi
812812 118.236 0.145611
813813 1260.29i 1.55018i
814814 −24.4076 + 24.4076i −0.0299848 + 0.0299848i
815815 557.858 557.858i 0.684489 0.684489i
816816 546.571i 0.669818i
817817 530.653 + 530.653i 0.649515 + 0.649515i
818818 194.276i 0.237502i
819819 115.871 115.871i 0.141478 0.141478i
820820 342.256i 0.417386i
821821 1398.26 1.70311 0.851557 0.524262i 0.175659π-0.175659\pi
0.851557 + 0.524262i 0.175659π0.175659\pi
822822 −589.674 589.674i −0.717365 0.717365i
823823 −278.835 −0.338804 −0.169402 0.985547i 0.554184π-0.554184\pi
−0.169402 + 0.985547i 0.554184π0.554184\pi
824824 −106.957 106.957i −0.129802 0.129802i
825825 117.780 117.780i 0.142764 0.142764i
826826 −82.0879 + 82.0879i −0.0993800 + 0.0993800i
827827 132.422i 0.160124i 0.996790 + 0.0800618i 0.0255118π0.0255118\pi
−0.996790 + 0.0800618i 0.974488π0.974488\pi
828828 −784.294 −0.947215
829829 51.8265 51.8265i 0.0625169 0.0625169i −0.675157 0.737674i 0.735924π-0.735924\pi
0.737674 + 0.675157i 0.235924π0.235924\pi
830830 −209.874 −0.252861
831831 −1028.29 −1.23741
832832 −54.9090 −0.0659964
833833 −866.651 + 866.651i −1.04040 + 1.04040i
834834 612.203 612.203i 0.734056 0.734056i
835835 −359.351 359.351i −0.430360 0.430360i
836836 98.6710 98.6710i 0.118028 0.118028i
837837 2313.88i 2.76450i
838838 −63.9019 + 63.9019i −0.0762553 + 0.0762553i
839839 −326.817 326.817i −0.389531 0.389531i 0.484989 0.874520i 0.338824π-0.338824\pi
−0.874520 + 0.484989i 0.838824π0.838824\pi
840840 −47.5277 + 47.5277i −0.0565806 + 0.0565806i
841841 1358.29i 1.61509i
842842 524.780 524.780i 0.623254 0.623254i
843843 −1712.35 −2.03126
844844 −443.784 −0.525810
845845 434.714 0.514454
846846 −1582.18 + 1582.18i −1.87019 + 1.87019i
847847 101.988 101.988i 0.120411 0.120411i
848848 −29.9615 −0.0353319
849849 −42.0190 42.0190i −0.0494923 0.0494923i
850850 448.969i 0.528198i
851851 196.950 0.231433
852852 164.197i 0.192719i
853853 663.796 + 663.796i 0.778190 + 0.778190i 0.979523 0.201333i 0.0645273π-0.0645273\pi
−0.201333 + 0.979523i 0.564527π0.564527\pi
854854 146.282 0.171290
855855 1298.64 + 1298.64i 1.51887 + 1.51887i
856856 242.917i 0.283782i
857857 176.448 + 176.448i 0.205890 + 0.205890i 0.802518 0.596628i 0.203493π-0.203493\pi
−0.596628 + 0.802518i 0.703493π0.703493\pi
858858 131.655i 0.153444i
859859 1508.88 1.75656 0.878278 0.478151i 0.158693π-0.158693\pi
0.878278 + 0.478151i 0.158693π0.158693\pi
860860 −196.869 −0.228917
861861 319.721 0.371337
862862 165.653i 0.192173i
863863 699.998i 0.811121i −0.914068 0.405561i 0.867076π-0.867076\pi
0.914068 0.405561i 0.132924π-0.132924\pi
864864 297.182 0.343961
865865 −267.344 −0.309068
866866 −200.557 + 200.557i −0.231590 + 0.231590i
867867 1417.61 1417.61i 1.63508 1.63508i
868868 111.046 0.127933
869869 −158.542 −0.182442
870870 884.056 + 884.056i 1.01616 + 1.01616i
871871 149.154i 0.171245i
872872 168.943i 0.193742i
873873 −1855.95 −2.12595
874874 −796.195 −0.910979
875875 −118.517 + 118.517i −0.135448 + 0.135448i
876876 310.752 + 310.752i 0.354739 + 0.354739i
877877 −1280.46 −1.46004 −0.730021 0.683424i 0.760490π-0.760490\pi
−0.730021 + 0.683424i 0.760490π0.760490\pi
878878 51.1340 51.1340i 0.0582392 0.0582392i
879879 −1796.16 1796.16i −2.04342 2.04342i
880880 36.6063i 0.0415980i
881881 1094.10 + 1094.10i 1.24188 + 1.24188i 0.959218 + 0.282667i 0.0912191π0.0912191\pi
0.282667 + 0.959218i 0.408781π0.408781\pi
882882 897.915 + 897.915i 1.01804 + 1.01804i
883883 636.432 + 636.432i 0.720761 + 0.720761i 0.968760 0.247999i 0.0797730π-0.0797730\pi
−0.247999 + 0.968760i 0.579773π0.579773\pi
884884 250.929 + 250.929i 0.283856 + 0.283856i
885885 −1227.55 −1.38706
886886 615.226i 0.694386i
887887 −961.847 −1.08438 −0.542191 0.840255i 0.682405π-0.682405\pi
−0.542191 + 0.840255i 0.682405π0.682405\pi
888888 −142.205 −0.160140
889889 65.7804 + 65.7804i 0.0739938 + 0.0739938i
890890 −490.232 + 490.232i −0.550822 + 0.550822i
891891 275.168i 0.308830i
892892 −473.723 473.723i −0.531080 0.531080i
893893 −1606.19 + 1606.19i −1.79865 + 1.79865i
894894 1016.00 1.13646
895895 41.5784 + 41.5784i 0.0464564 + 0.0464564i
896896 14.2621i 0.0159175i
897897 −531.173 + 531.173i −0.592167 + 0.592167i
898898 41.1705 + 41.1705i 0.0458468 + 0.0458468i
899899 2065.54i 2.29760i
900900 465.164 0.516849
901901 136.921 + 136.921i 0.151965 + 0.151965i
902902 123.126 123.126i 0.136503 0.136503i
903903 183.906i 0.203662i
904904 610.348i 0.675164i
905905 −686.087 + 686.087i −0.758107 + 0.758107i
906906 1861.52 2.05466
907907 74.5646i 0.0822102i −0.999155 0.0411051i 0.986912π-0.986912\pi
0.999155 0.0411051i 0.0130878π-0.0130878\pi
908908 475.772 + 475.772i 0.523978 + 0.523978i
909909 575.944 575.944i 0.633602 0.633602i
910910 43.6396i 0.0479556i
911911 −968.971 968.971i −1.06363 1.06363i −0.997833 0.0658019i 0.979039π-0.979039\pi
−0.0658019 0.997833i 0.520961π-0.520961\pi
912912 574.881 0.630352
913913 −75.5020 75.5020i −0.0826966 0.0826966i
914914 339.800 339.800i 0.371772 0.371772i
915915 1093.76 + 1093.76i 1.19536 + 1.19536i
916916 −213.611 + 213.611i −0.233200 + 0.233200i
917917 38.2592 38.2592i 0.0417222 0.0417222i
918918 −1358.09 1358.09i −1.47940 1.47940i
919919 529.117 529.117i 0.575753 0.575753i −0.357977 0.933730i 0.616533π-0.616533\pi
0.933730 + 0.357977i 0.116533π0.116533\pi
920920 147.691 147.691i 0.160534 0.160534i
921921 −2137.97 2137.97i −2.32136 2.32136i
922922 428.287 0.464520
923923 75.3820 + 75.3820i 0.0816707 + 0.0816707i
924924 −34.1960 −0.0370087
925925 −116.811 −0.126282
926926 −549.830 −0.593769
927927 1012.83 1.09259
928928 265.287 0.285870
929929 690.119 + 690.119i 0.742862 + 0.742862i 0.973128 0.230265i 0.0739595π-0.0739595\pi
−0.230265 + 0.973128i 0.573959π0.573959\pi
930930 830.294 + 830.294i 0.892790 + 0.892790i
931931 911.540 + 911.540i 0.979097 + 0.979097i
932932 −55.7632 −0.0598317
933933 2726.31i 2.92209i
934934 149.334i 0.159887i
935935 167.287 167.287i 0.178916 0.178916i
936936 259.980 259.980i 0.277757 0.277757i
937937 313.024 313.024i 0.334071 0.334071i −0.520060 0.854130i 0.674090π-0.674090\pi
0.854130 + 0.520060i 0.174090π0.174090\pi
938938 −38.7414 −0.0413022
939939 −1325.19 1325.19i −1.41127 1.41127i
940940 595.886i 0.633922i
941941 −235.189 235.189i −0.249935 0.249935i 0.571009 0.820944i 0.306552π-0.306552\pi
−0.820944 + 0.571009i 0.806552π0.806552\pi
942942 348.121 348.121i 0.369555 0.369555i
943943 −993.528 −1.05358
944944 −184.181 + 184.181i −0.195107 + 0.195107i
945945 236.189i 0.249935i
946946 −70.8232 70.8232i −0.0748660 0.0748660i
947947 268.643 + 268.643i 0.283678 + 0.283678i 0.834574 0.550896i 0.185714π-0.185714\pi
−0.550896 + 0.834574i 0.685714π0.685714\pi
948948 −461.852 461.852i −0.487185 0.487185i
949949 285.330 0.300664
950950 472.223 0.497077
951951 1790.50i 1.88275i
952952 65.1763 65.1763i 0.0684625 0.0684625i
953953 956.368 956.368i 1.00353 1.00353i 0.00354000 0.999994i 0.498873π-0.498873\pi
0.999994 0.00354000i 0.00112682π-0.00112682\pi
954954 141.860 141.860i 0.148700 0.148700i
955955 152.719i 0.159915i
956956 732.475i 0.766187i
957957 636.076i 0.664656i
958958 480.043i 0.501089i
959959 140.632i 0.146645i
960960 −106.638 + 106.638i −0.111082 + 0.111082i
961961 978.934i 1.01866i
962962 −65.2856 + 65.2856i −0.0678644 + 0.0678644i
963963 −1150.15 1150.15i −1.19434 1.19434i
964964 −41.6485 41.6485i −0.0432038 0.0432038i
965965 −801.411 + 801.411i −0.830478 + 0.830478i
966966 137.967 + 137.967i 0.142823 + 0.142823i
967967 −545.790 545.790i −0.564415 0.564415i 0.366143 0.930559i 0.380678π-0.380678\pi
−0.930559 + 0.366143i 0.880678π0.880678\pi
968968 228.831 228.831i 0.236396 0.236396i
969969 −2627.15 2627.15i −2.71119 2.71119i
970970 349.497 349.497i 0.360306 0.360306i
971971 14.0166i 0.0144352i −0.999974 0.00721760i 0.997703π-0.997703\pi
0.999974 0.00721760i 0.00229745π-0.00229745\pi
972972 −132.936 + 132.936i −0.136765 + 0.136765i
973973 −146.005 −0.150057
974974 421.501 + 421.501i 0.432753 + 0.432753i
975975 315.039 315.039i 0.323117 0.323117i
976976 328.214 0.336285
977977 1638.23i 1.67680i −0.545057 0.838399i 0.683492π-0.683492\pi
0.545057 0.838399i 0.316508π-0.316508\pi
978978 1169.26 + 1169.26i 1.19556 + 1.19556i
979979 −352.720 −0.360286
980980 −338.175 −0.345076
981981 799.902 + 799.902i 0.815394 + 0.815394i
982982 960.328 960.328i 0.977930 0.977930i
983983 385.358i 0.392022i −0.980602 0.196011i 0.937201π-0.937201\pi
0.980602 0.196011i 0.0627989π-0.0627989\pi
984984 717.362 0.729026
985985 144.756 144.756i 0.146961 0.146961i
986986 −1212.33 1212.33i −1.22955 1.22955i
987987 556.652 0.563984
988988 263.925 263.925i 0.267131 0.267131i
989989 571.486i 0.577842i
990990 −173.322 173.322i −0.175072 0.175072i
991991 359.520 359.520i 0.362785 0.362785i −0.502052 0.864837i 0.667422π-0.667422\pi
0.864837 + 0.502052i 0.167422π0.167422\pi
992992 249.154 0.251164
993993 1949.85 + 1949.85i 1.96359 + 1.96359i
994994 19.5798 19.5798i 0.0196979 0.0196979i
995995 289.459i 0.290913i
996996 439.892i 0.441659i
997997 592.073 0.593854 0.296927 0.954900i 0.404038π-0.404038\pi
0.296927 + 0.954900i 0.404038π0.404038\pi
998998 288.711i 0.289289i
999999 353.343 353.343i 0.353697 0.353697i
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 538.3.c.b.187.2 46
269.82 odd 4 inner 538.3.c.b.351.2 yes 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
538.3.c.b.187.2 46 1.1 even 1 trivial
538.3.c.b.351.2 yes 46 269.82 odd 4 inner