Properties

Label 538.3.c.b.187.3
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 187.3
Character χ\chi == 538.187
Dual form 538.3.c.b.351.3

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+(3.243213.24321i)q3+2.00000iq4+4.65083q5+6.48641iq6+(4.880174.88017i)q7+(2.000002.00000i)q8+12.0368iq9+(4.650834.65083i)q10+17.7265iq11+(6.486416.48641i)q12+4.34344iq139.76035q14+(15.083615.0836i)q154.00000q16+(11.343611.3436i)q17+(12.036812.0368i)q18+(7.80386+7.80386i)q19+9.30167iq2031.6548q21+(17.726517.7265i)q2240.0305q2312.9728q243.36973q25+(4.343444.34344i)q26+(9.848849.84884i)q27+(9.76035+9.76035i)q28+(3.41094+3.41094i)q29+30.1672iq30+(41.6217+41.6217i)q31+(4.00000+4.00000i)q32+(57.490657.4906i)q33+22.6871iq34+(22.696922.6969i)q3524.0735q363.25116q37+15.6077q38+(14.086714.0867i)q39+(9.301679.30167i)q40+11.4842q41+(31.6548+31.6548i)q428.80977iq4335.4530q44+55.9810iq45+(40.0305+40.0305i)q4641.4763q47+(12.9728+12.9728i)q48+1.36783iq49+(3.36973+3.36973i)q50+73.5790iq518.68688q5217.5716q5319.6977q54+82.4429iq5519.5207iq56+50.6191q57+6.82188q58+(5.47396+5.47396i)q59+(30.167230.1672i)q60+27.1650q61+83.2434q62+(58.7415+58.7415i)q638.00000iq64+20.2006iq65114.981q66+2.74007q67+(22.687122.6871i)q68+(129.827+129.827i)q6945.3938q70+(61.4762+61.4762i)q71+(24.0735+24.0735i)q7279.1820iq73+(3.25116+3.25116i)q74+(10.9287+10.9287i)q75+(15.607715.6077i)q76+(86.5083+86.5083i)q7728.1734q78+6.12702iq7918.6033q80+44.4472q81+(11.484211.4842i)q82+(58.781558.7815i)q8363.3096iq84+(52.757052.7570i)q85+(8.80977+8.80977i)q86+22.1247q87+(35.4530+35.4530i)q88+113.961iq89+(55.981055.9810i)q90+(21.1967+21.1967i)q9180.0610iq92+269.975q93+(41.4763+41.4763i)q94+(36.2945+36.2945i)q9525.9456iq969.11196iq97+(1.367831.36783i)q98213.369q99+O(q100)q+(-1.00000 - 1.00000i) q^{2} +(-3.24321 - 3.24321i) q^{3} +2.00000i q^{4} +4.65083 q^{5} +6.48641i q^{6} +(4.88017 - 4.88017i) q^{7} +(2.00000 - 2.00000i) q^{8} +12.0368i q^{9} +(-4.65083 - 4.65083i) q^{10} +17.7265i q^{11} +(6.48641 - 6.48641i) q^{12} +4.34344i q^{13} -9.76035 q^{14} +(-15.0836 - 15.0836i) q^{15} -4.00000 q^{16} +(-11.3436 - 11.3436i) q^{17} +(12.0368 - 12.0368i) q^{18} +(-7.80386 + 7.80386i) q^{19} +9.30167i q^{20} -31.6548 q^{21} +(17.7265 - 17.7265i) q^{22} -40.0305 q^{23} -12.9728 q^{24} -3.36973 q^{25} +(4.34344 - 4.34344i) q^{26} +(9.84884 - 9.84884i) q^{27} +(9.76035 + 9.76035i) q^{28} +(-3.41094 + 3.41094i) q^{29} +30.1672i q^{30} +(-41.6217 + 41.6217i) q^{31} +(4.00000 + 4.00000i) q^{32} +(57.4906 - 57.4906i) q^{33} +22.6871i q^{34} +(22.6969 - 22.6969i) q^{35} -24.0735 q^{36} -3.25116 q^{37} +15.6077 q^{38} +(14.0867 - 14.0867i) q^{39} +(9.30167 - 9.30167i) q^{40} +11.4842 q^{41} +(31.6548 + 31.6548i) q^{42} -8.80977i q^{43} -35.4530 q^{44} +55.9810i q^{45} +(40.0305 + 40.0305i) q^{46} -41.4763 q^{47} +(12.9728 + 12.9728i) q^{48} +1.36783i q^{49} +(3.36973 + 3.36973i) q^{50} +73.5790i q^{51} -8.68688 q^{52} -17.5716 q^{53} -19.6977 q^{54} +82.4429i q^{55} -19.5207i q^{56} +50.6191 q^{57} +6.82188 q^{58} +(-5.47396 + 5.47396i) q^{59} +(30.1672 - 30.1672i) q^{60} +27.1650 q^{61} +83.2434 q^{62} +(58.7415 + 58.7415i) q^{63} -8.00000i q^{64} +20.2006i q^{65} -114.981 q^{66} +2.74007 q^{67} +(22.6871 - 22.6871i) q^{68} +(129.827 + 129.827i) q^{69} -45.3938 q^{70} +(-61.4762 + 61.4762i) q^{71} +(24.0735 + 24.0735i) q^{72} -79.1820i q^{73} +(3.25116 + 3.25116i) q^{74} +(10.9287 + 10.9287i) q^{75} +(-15.6077 - 15.6077i) q^{76} +(86.5083 + 86.5083i) q^{77} -28.1734 q^{78} +6.12702i q^{79} -18.6033 q^{80} +44.4472 q^{81} +(-11.4842 - 11.4842i) q^{82} +(58.7815 - 58.7815i) q^{83} -63.3096i q^{84} +(-52.7570 - 52.7570i) q^{85} +(-8.80977 + 8.80977i) q^{86} +22.1247 q^{87} +(35.4530 + 35.4530i) q^{88} +113.961i q^{89} +(55.9810 - 55.9810i) q^{90} +(21.1967 + 21.1967i) q^{91} -80.0610i q^{92} +269.975 q^{93} +(41.4763 + 41.4763i) q^{94} +(-36.2945 + 36.2945i) q^{95} -25.9456i q^{96} -9.11196i q^{97} +(1.36783 - 1.36783i) q^{98} -213.369 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 −3.24321 3.24321i −1.08107 1.08107i −0.996410 0.0846584i 0.973020π-0.973020\pi
−0.0846584 0.996410i 0.526980π-0.526980\pi
44 2.00000i 0.500000i
55 4.65083 0.930167 0.465083 0.885267i 0.346024π-0.346024\pi
0.465083 + 0.885267i 0.346024π0.346024\pi
66 6.48641i 1.08107i
77 4.88017 4.88017i 0.697168 0.697168i −0.266631 0.963799i 0.585911π-0.585911\pi
0.963799 + 0.266631i 0.0859105π0.0859105\pi
88 2.00000 2.00000i 0.250000 0.250000i
99 12.0368i 1.33742i
1010 −4.65083 4.65083i −0.465083 0.465083i
1111 17.7265i 1.61150i 0.592257 + 0.805749i 0.298237π0.298237\pi
−0.592257 + 0.805749i 0.701763π0.701763\pi
1212 6.48641 6.48641i 0.540534 0.540534i
1313 4.34344i 0.334111i 0.985947 + 0.167055i 0.0534259π0.0534259\pi
−0.985947 + 0.167055i 0.946574π0.946574\pi
1414 −9.76035 −0.697168
1515 −15.0836 15.0836i −1.00557 1.00557i
1616 −4.00000 −0.250000
1717 −11.3436 11.3436i −0.667268 0.667268i 0.289815 0.957083i 0.406406π-0.406406\pi
−0.957083 + 0.289815i 0.906406π0.906406\pi
1818 12.0368 12.0368i 0.668709 0.668709i
1919 −7.80386 + 7.80386i −0.410730 + 0.410730i −0.881993 0.471263i 0.843798π-0.843798\pi
0.471263 + 0.881993i 0.343798π0.343798\pi
2020 9.30167i 0.465083i
2121 −31.6548 −1.50737
2222 17.7265 17.7265i 0.805749 0.805749i
2323 −40.0305 −1.74046 −0.870229 0.492648i 0.836029π-0.836029\pi
−0.870229 + 0.492648i 0.836029π0.836029\pi
2424 −12.9728 −0.540534
2525 −3.36973 −0.134789
2626 4.34344 4.34344i 0.167055 0.167055i
2727 9.84884 9.84884i 0.364772 0.364772i
2828 9.76035 + 9.76035i 0.348584 + 0.348584i
2929 −3.41094 + 3.41094i −0.117619 + 0.117619i −0.763466 0.645848i 0.776504π-0.776504\pi
0.645848 + 0.763466i 0.276504π0.276504\pi
3030 30.1672i 1.00557i
3131 −41.6217 + 41.6217i −1.34263 + 1.34263i −0.449208 + 0.893427i 0.648294π0.648294\pi
−0.893427 + 0.449208i 0.851706π0.851706\pi
3232 4.00000 + 4.00000i 0.125000 + 0.125000i
3333 57.4906 57.4906i 1.74214 1.74214i
3434 22.6871i 0.667268i
3535 22.6969 22.6969i 0.648482 0.648482i
3636 −24.0735 −0.668709
3737 −3.25116 −0.0878691 −0.0439346 0.999034i 0.513989π-0.513989\pi
−0.0439346 + 0.999034i 0.513989π0.513989\pi
3838 15.6077 0.410730
3939 14.0867 14.0867i 0.361197 0.361197i
4040 9.30167 9.30167i 0.232542 0.232542i
4141 11.4842 0.280103 0.140052 0.990144i 0.455273π-0.455273\pi
0.140052 + 0.990144i 0.455273π0.455273\pi
4242 31.6548 + 31.6548i 0.753686 + 0.753686i
4343 8.80977i 0.204878i −0.994739 0.102439i 0.967335π-0.967335\pi
0.994739 0.102439i 0.0326647π-0.0326647\pi
4444 −35.4530 −0.805749
4545 55.9810i 1.24402i
4646 40.0305 + 40.0305i 0.870229 + 0.870229i
4747 −41.4763 −0.882475 −0.441237 0.897390i 0.645460π-0.645460\pi
−0.441237 + 0.897390i 0.645460π0.645460\pi
4848 12.9728 + 12.9728i 0.270267 + 0.270267i
4949 1.36783i 0.0279148i
5050 3.36973 + 3.36973i 0.0673947 + 0.0673947i
5151 73.5790i 1.44272i
5252 −8.68688 −0.167055
5353 −17.5716 −0.331540 −0.165770 0.986164i 0.553011π-0.553011\pi
−0.165770 + 0.986164i 0.553011π0.553011\pi
5454 −19.6977 −0.364772
5555 82.4429i 1.49896i
5656 19.5207i 0.348584i
5757 50.6191 0.888054
5858 6.82188 0.117619
5959 −5.47396 + 5.47396i −0.0927790 + 0.0927790i −0.751973 0.659194i 0.770898π-0.770898\pi
0.659194 + 0.751973i 0.270898π0.270898\pi
6060 30.1672 30.1672i 0.502787 0.502787i
6161 27.1650 0.445329 0.222664 0.974895i 0.428525π-0.428525\pi
0.222664 + 0.974895i 0.428525π0.428525\pi
6262 83.2434 1.34263
6363 58.7415 + 58.7415i 0.932404 + 0.932404i
6464 8.00000i 0.125000i
6565 20.2006i 0.310779i
6666 −114.981 −1.74214
6767 2.74007 0.0408965 0.0204483 0.999791i 0.493491π-0.493491\pi
0.0204483 + 0.999791i 0.493491π0.493491\pi
6868 22.6871 22.6871i 0.333634 0.333634i
6969 129.827 + 129.827i 1.88155 + 1.88155i
7070 −45.3938 −0.648482
7171 −61.4762 + 61.4762i −0.865863 + 0.865863i −0.992011 0.126149i 0.959738π-0.959738\pi
0.126149 + 0.992011i 0.459738π0.459738\pi
7272 24.0735 + 24.0735i 0.334355 + 0.334355i
7373 79.1820i 1.08468i −0.840158 0.542342i 0.817538π-0.817538\pi
0.840158 0.542342i 0.182462π-0.182462\pi
7474 3.25116 + 3.25116i 0.0439346 + 0.0439346i
7575 10.9287 + 10.9287i 0.145717 + 0.145717i
7676 −15.6077 15.6077i −0.205365 0.205365i
7777 86.5083 + 86.5083i 1.12348 + 1.12348i
7878 −28.1734 −0.361197
7979 6.12702i 0.0775572i 0.999248 + 0.0387786i 0.0123467π0.0123467\pi
−0.999248 + 0.0387786i 0.987653π0.987653\pi
8080 −18.6033 −0.232542
8181 44.4472 0.548731
8282 −11.4842 11.4842i −0.140052 0.140052i
8383 58.7815 58.7815i 0.708210 0.708210i −0.257948 0.966159i 0.583046π-0.583046\pi
0.966159 + 0.257948i 0.0830464π0.0830464\pi
8484 63.3096i 0.753686i
8585 −52.7570 52.7570i −0.620671 0.620671i
8686 −8.80977 + 8.80977i −0.102439 + 0.102439i
8787 22.1247 0.254307
8888 35.4530 + 35.4530i 0.402875 + 0.402875i
8989 113.961i 1.28046i 0.768181 + 0.640232i 0.221162π0.221162\pi
−0.768181 + 0.640232i 0.778838π0.778838\pi
9090 55.9810 55.9810i 0.622011 0.622011i
9191 21.1967 + 21.1967i 0.232931 + 0.232931i
9292 80.0610i 0.870229i
9393 269.975 2.90296
9494 41.4763 + 41.4763i 0.441237 + 0.441237i
9595 −36.2945 + 36.2945i −0.382047 + 0.382047i
9696 25.9456i 0.270267i
9797 9.11196i 0.0939378i −0.998896 0.0469689i 0.985044π-0.985044\pi
0.998896 0.0469689i 0.0149562π-0.0149562\pi
9898 1.36783 1.36783i 0.0139574 0.0139574i
9999 −213.369 −2.15525
100100 6.73947i 0.0673947i
101101 2.08356 + 2.08356i 0.0206293 + 0.0206293i 0.717346 0.696717i 0.245357π-0.245357\pi
−0.696717 + 0.717346i 0.745357π0.745357\pi
102102 73.5790 73.5790i 0.721362 0.721362i
103103 45.5958i 0.442677i −0.975197 0.221339i 0.928957π-0.928957\pi
0.975197 0.221339i 0.0710426π-0.0710426\pi
104104 8.68688 + 8.68688i 0.0835277 + 0.0835277i
105105 −147.221 −1.40211
106106 17.5716 + 17.5716i 0.165770 + 0.165770i
107107 −83.6935 + 83.6935i −0.782182 + 0.782182i −0.980199 0.198016i 0.936550π-0.936550\pi
0.198016 + 0.980199i 0.436550π0.436550\pi
108108 19.6977 + 19.6977i 0.182386 + 0.182386i
109109 17.4640 17.4640i 0.160220 0.160220i −0.622444 0.782664i 0.713860π-0.713860\pi
0.782664 + 0.622444i 0.213860π0.213860\pi
110110 82.4429 82.4429i 0.749481 0.749481i
111111 10.5442 + 10.5442i 0.0949925 + 0.0949925i
112112 −19.5207 + 19.5207i −0.174292 + 0.174292i
113113 90.7656 90.7656i 0.803236 0.803236i −0.180364 0.983600i 0.557728π-0.557728\pi
0.983600 + 0.180364i 0.0577276π0.0577276\pi
114114 −50.6191 50.6191i −0.444027 0.444027i
115115 −186.175 −1.61892
116116 −6.82188 6.82188i −0.0588093 0.0588093i
117117 −52.2810 −0.446846
118118 10.9479 0.0927790
119119 −110.717 −0.930395
120120 −60.3345 −0.502787
121121 −193.228 −1.59693
122122 −27.1650 27.1650i −0.222664 0.222664i
123123 −37.2457 37.2457i −0.302811 0.302811i
124124 −83.2434 83.2434i −0.671317 0.671317i
125125 −131.943 −1.05554
126126 117.483i 0.932404i
127127 195.393i 1.53853i −0.638930 0.769265i 0.720623π-0.720623\pi
0.638930 0.769265i 0.279377π-0.279377\pi
128128 −8.00000 + 8.00000i −0.0625000 + 0.0625000i
129129 −28.5719 + 28.5719i −0.221488 + 0.221488i
130130 20.2006 20.2006i 0.155389 0.155389i
131131 −51.8047 −0.395455 −0.197728 0.980257i 0.563356π-0.563356\pi
−0.197728 + 0.980257i 0.563356π0.563356\pi
132132 114.981 + 114.981i 0.871070 + 0.871070i
133133 76.1684i 0.572695i
134134 −2.74007 2.74007i −0.0204483 0.0204483i
135135 45.8053 45.8053i 0.339299 0.339299i
136136 −45.3742 −0.333634
137137 −110.932 + 110.932i −0.809726 + 0.809726i −0.984592 0.174866i 0.944051π-0.944051\pi
0.174866 + 0.984592i 0.444051π0.444051\pi
138138 259.654i 1.88155i
139139 −64.5863 64.5863i −0.464650 0.464650i 0.435526 0.900176i 0.356562π-0.356562\pi
−0.900176 + 0.435526i 0.856562π0.856562\pi
140140 45.3938 + 45.3938i 0.324241 + 0.324241i
141141 134.516 + 134.516i 0.954015 + 0.954015i
142142 122.952 0.865863
143143 −76.9939 −0.538419
144144 48.1470i 0.334355i
145145 −15.8637 + 15.8637i −0.109405 + 0.109405i
146146 −79.1820 + 79.1820i −0.542342 + 0.542342i
147147 4.43614 4.43614i 0.0301778 0.0301778i
148148 6.50231i 0.0439346i
149149 230.957i 1.55005i −0.631932 0.775024i 0.717738π-0.717738\pi
0.631932 0.775024i 0.282262π-0.282262\pi
150150 21.8575i 0.145717i
151151 251.195i 1.66354i −0.555120 0.831770i 0.687328π-0.687328\pi
0.555120 0.831770i 0.312672π-0.312672\pi
152152 31.2155i 0.205365i
153153 136.540 136.540i 0.892416 0.892416i
154154 173.017i 1.12348i
155155 −193.576 + 193.576i −1.24887 + 1.24887i
156156 28.1734 + 28.1734i 0.180598 + 0.180598i
157157 192.662 + 192.662i 1.22714 + 1.22714i 0.965040 + 0.262104i 0.0844165π0.0844165\pi
0.262104 + 0.965040i 0.415583π0.415583\pi
158158 6.12702 6.12702i 0.0387786 0.0387786i
159159 56.9884 + 56.9884i 0.358417 + 0.358417i
160160 18.6033 + 18.6033i 0.116271 + 0.116271i
161161 −195.356 + 195.356i −1.21339 + 1.21339i
162162 −44.4472 44.4472i −0.274366 0.274366i
163163 −128.235 + 128.235i −0.786715 + 0.786715i −0.980954 0.194239i 0.937776π-0.937776\pi
0.194239 + 0.980954i 0.437776π0.437776\pi
164164 22.9685i 0.140052i
165165 267.379 267.379i 1.62048 1.62048i
166166 −117.563 −0.708210
167167 203.727 + 203.727i 1.21992 + 1.21992i 0.967659 + 0.252262i 0.0811745π0.0811745\pi
0.252262 + 0.967659i 0.418826π0.418826\pi
168168 −63.3096 + 63.3096i −0.376843 + 0.376843i
169169 150.135 0.888370
170170 105.514i 0.620671i
171171 −93.9332 93.9332i −0.549317 0.549317i
172172 17.6195 0.102439
173173 −300.872 −1.73914 −0.869571 0.493808i 0.835605π-0.835605\pi
−0.869571 + 0.493808i 0.835605π0.835605\pi
174174 −22.1247 22.1247i −0.127154 0.127154i
175175 −16.4449 + 16.4449i −0.0939708 + 0.0939708i
176176 70.9059i 0.402875i
177177 35.5064 0.200601
178178 113.961 113.961i 0.640232 0.640232i
179179 7.39567 + 7.39567i 0.0413166 + 0.0413166i 0.727463 0.686147i 0.240699π-0.240699\pi
−0.686147 + 0.727463i 0.740699π0.740699\pi
180180 −111.962 −0.622011
181181 200.292 200.292i 1.10659 1.10659i 0.112991 0.993596i 0.463957π-0.463957\pi
0.993596 0.112991i 0.0360432π-0.0360432\pi
182182 42.3935i 0.232931i
183183 −88.1018 88.1018i −0.481431 0.481431i
184184 −80.0610 + 80.0610i −0.435114 + 0.435114i
185185 −15.1206 −0.0817329
186186 −269.975 269.975i −1.45148 1.45148i
187187 201.081 201.081i 1.07530 1.07530i
188188 82.9526i 0.441237i
189189 96.1281i 0.508614i
190190 72.5890 0.382047
191191 89.3960i 0.468042i 0.972232 + 0.234021i 0.0751884π0.0751884\pi
−0.972232 + 0.234021i 0.924812π0.924812\pi
192192 −25.9456 + 25.9456i −0.135134 + 0.135134i
193193 151.033 151.033i 0.782554 0.782554i −0.197707 0.980261i 0.563350π-0.563350\pi
0.980261 + 0.197707i 0.0633496π0.0633496\pi
194194 −9.11196 + 9.11196i −0.0469689 + 0.0469689i
195195 65.5148 65.5148i 0.335973 0.335973i
196196 −2.73565 −0.0139574
197197 −53.3615 + 53.3615i −0.270871 + 0.270871i −0.829451 0.558580i 0.811346π-0.811346\pi
0.558580 + 0.829451i 0.311346π0.311346\pi
198198 213.369 + 213.369i 1.07762 + 1.07762i
199199 97.4643i 0.489770i 0.969552 + 0.244885i 0.0787503π0.0787503\pi
−0.969552 + 0.244885i 0.921250π0.921250\pi
200200 −6.73947 + 6.73947i −0.0336973 + 0.0336973i
201201 −8.88660 8.88660i −0.0442120 0.0442120i
202202 4.16713i 0.0206293i
203203 33.2919i 0.164000i
204204 −147.158 −0.721362
205205 53.4113 0.260543
206206 −45.5958 + 45.5958i −0.221339 + 0.221339i
207207 481.838i 2.32772i
208208 17.3738i 0.0835277i
209209 −138.335 138.335i −0.661890 0.661890i
210210 147.221 + 147.221i 0.701054 + 0.701054i
211211 186.048i 0.881745i −0.897570 0.440872i 0.854669π-0.854669\pi
0.897570 0.440872i 0.145331π-0.145331\pi
212212 35.1432i 0.165770i
213213 398.760 1.87211
214214 167.387 0.782182
215215 40.9728i 0.190571i
216216 39.3954i 0.182386i
217217 406.242i 1.87208i
218218 −34.9279 −0.160220
219219 −256.803 + 256.803i −1.17262 + 1.17262i
220220 −164.886 −0.749481
221221 49.2701 49.2701i 0.222942 0.222942i
222222 21.0883i 0.0949925i
223223 −164.625 + 164.625i −0.738230 + 0.738230i −0.972235 0.234005i 0.924817π-0.924817\pi
0.234005 + 0.972235i 0.424817π0.424817\pi
224224 39.0414 0.174292
225225 40.5607i 0.180270i
226226 −181.531 −0.803236
227227 49.7130 49.7130i 0.219000 0.219000i −0.589077 0.808077i 0.700509π-0.700509\pi
0.808077 + 0.589077i 0.200509π0.200509\pi
228228 101.238i 0.444027i
229229 255.416 + 255.416i 1.11535 + 1.11535i 0.992414 + 0.122938i 0.0392318π0.0392318\pi
0.122938 + 0.992414i 0.460768π0.460768\pi
230230 186.175 + 186.175i 0.809458 + 0.809458i
231231 561.128i 2.42913i
232232 13.6438i 0.0588093i
233233 417.135i 1.79028i 0.445786 + 0.895140i 0.352924π0.352924\pi
−0.445786 + 0.895140i 0.647076π0.647076\pi
234234 52.2810 + 52.2810i 0.223423 + 0.223423i
235235 −192.899 −0.820849
236236 −10.9479 10.9479i −0.0463895 0.0463895i
237237 19.8712 19.8712i 0.0838447 0.0838447i
238238 110.717 + 110.717i 0.465198 + 0.465198i
239239 361.322 1.51181 0.755904 0.654683i 0.227198π-0.227198\pi
0.755904 + 0.654683i 0.227198π0.227198\pi
240240 60.3345 + 60.3345i 0.251394 + 0.251394i
241241 −146.401 + 146.401i −0.607472 + 0.607472i −0.942285 0.334813i 0.891327π-0.891327\pi
0.334813 + 0.942285i 0.391327π0.391327\pi
242242 193.228 + 193.228i 0.798463 + 0.798463i
243243 −232.791 232.791i −0.957988 0.957988i
244244 54.3301i 0.222664i
245245 6.36153i 0.0259654i
246246 74.4915i 0.302811i
247247 −33.8956 33.8956i −0.137229 0.137229i
248248 166.487i 0.671317i
249249 −381.281 −1.53125
250250 131.943 + 131.943i 0.527772 + 0.527772i
251251 −156.154 156.154i −0.622127 0.622127i 0.323948 0.946075i 0.394990π-0.394990\pi
−0.946075 + 0.323948i 0.894990π0.894990\pi
252252 −117.483 + 117.483i −0.466202 + 0.466202i
253253 709.600i 2.80474i
254254 −195.393 + 195.393i −0.769265 + 0.769265i
255255 342.204i 1.34198i
256256 16.0000 0.0625000
257257 128.944 + 128.944i 0.501726 + 0.501726i 0.911974 0.410248i 0.134558π-0.134558\pi
−0.410248 + 0.911974i 0.634558π0.634558\pi
258258 57.1438 0.221488
259259 −15.8662 + 15.8662i −0.0612595 + 0.0612595i
260260 −40.4013 −0.155389
261261 −41.0566 41.0566i −0.157305 0.157305i
262262 51.8047 + 51.8047i 0.197728 + 0.197728i
263263 9.95329 0.0378452 0.0189226 0.999821i 0.493976π-0.493976\pi
0.0189226 + 0.999821i 0.493976π0.493976\pi
264264 229.962i 0.871070i
265265 −81.7227 −0.308388
266266 76.1684 76.1684i 0.286347 0.286347i
267267 369.600 369.600i 1.38427 1.38427i
268268 5.48014i 0.0204483i
269269 −263.956 + 51.8506i −0.981247 + 0.192753i
270270 −91.6107 −0.339299
271271 190.256 + 190.256i 0.702051 + 0.702051i 0.964851 0.262799i 0.0846457π-0.0846457\pi
−0.262799 + 0.964851i 0.584646π0.584646\pi
272272 45.3742 + 45.3742i 0.166817 + 0.166817i
273273 137.491i 0.503629i
274274 221.865 0.809726
275275 59.7335i 0.217213i
276276 −259.654 + 259.654i −0.940777 + 0.940777i
277277 172.223 172.223i 0.621745 0.621745i −0.324232 0.945977i 0.605106π-0.605106\pi
0.945977 + 0.324232i 0.105106π0.105106\pi
278278 129.173i 0.464650i
279279 −500.990 500.990i −1.79566 1.79566i
280280 90.7875i 0.324241i
281281 69.4108 69.4108i 0.247014 0.247014i −0.572730 0.819744i 0.694116π-0.694116\pi
0.819744 + 0.572730i 0.194116π0.194116\pi
282282 269.032i 0.954015i
283283 75.3669 0.266314 0.133157 0.991095i 0.457489π-0.457489\pi
0.133157 + 0.991095i 0.457489π0.457489\pi
284284 −122.952 122.952i −0.432931 0.432931i
285285 235.421 0.826038
286286 76.9939 + 76.9939i 0.269210 + 0.269210i
287287 56.0450 56.0450i 0.195279 0.195279i
288288 −48.1470 + 48.1470i −0.167177 + 0.167177i
289289 31.6474i 0.109507i
290290 31.7274 0.109405
291291 −29.5520 + 29.5520i −0.101553 + 0.101553i
292292 158.364 0.542342
293293 −52.8258 −0.180293 −0.0901463 0.995929i 0.528733π-0.528733\pi
−0.0901463 + 0.995929i 0.528733π0.528733\pi
294294 −8.87228 −0.0301778
295295 −25.4585 + 25.4585i −0.0862999 + 0.0862999i
296296 −6.50231 + 6.50231i −0.0219673 + 0.0219673i
297297 174.585 + 174.585i 0.587829 + 0.587829i
298298 −230.957 + 230.957i −0.775024 + 0.775024i
299299 173.870i 0.581506i
300300 −21.8575 + 21.8575i −0.0728583 + 0.0728583i
301301 −42.9932 42.9932i −0.142835 0.142835i
302302 −251.195 + 251.195i −0.831770 + 0.831770i
303303 13.5149i 0.0446035i
304304 31.2155 31.2155i 0.102682 0.102682i
305305 126.340 0.414230
306306 −273.079 −0.892416
307307 −71.2554 −0.232102 −0.116051 0.993243i 0.537024π-0.537024\pi
−0.116051 + 0.993243i 0.537024π0.537024\pi
308308 −173.017 + 173.017i −0.561742 + 0.561742i
309309 −147.876 + 147.876i −0.478564 + 0.478564i
310310 387.151 1.24887
311311 357.948 + 357.948i 1.15096 + 1.15096i 0.986361 + 0.164595i 0.0526319π0.0526319\pi
0.164595 + 0.986361i 0.447368π0.447368\pi
312312 56.3467i 0.180598i
313313 −325.811 −1.04093 −0.520465 0.853883i 0.674241π-0.674241\pi
−0.520465 + 0.853883i 0.674241π0.674241\pi
314314 385.323i 1.22714i
315315 273.197 + 273.197i 0.867292 + 0.867292i
316316 −12.2540 −0.0387786
317317 −65.7703 65.7703i −0.207477 0.207477i 0.595717 0.803194i 0.296868π-0.296868\pi
−0.803194 + 0.595717i 0.796868π0.796868\pi
318318 113.977i 0.358417i
319319 −60.4639 60.4639i −0.189542 0.189542i
320320 37.2067i 0.116271i
321321 542.870 1.69119
322322 390.712 1.21339
323323 177.047 0.548134
324324 88.8944i 0.274366i
325325 14.6362i 0.0450346i
326326 256.469 0.786715
327327 −113.278 −0.346417
328328 22.9685 22.9685i 0.0700258 0.0700258i
329329 −202.412 + 202.412i −0.615233 + 0.615233i
330330 −534.759 −1.62048
331331 226.887 0.685459 0.342729 0.939434i 0.388649π-0.388649\pi
0.342729 + 0.939434i 0.388649π0.388649\pi
332332 117.563 + 117.563i 0.354105 + 0.354105i
333333 39.1334i 0.117518i
334334 407.454i 1.21992i
335335 12.7436 0.0380406
336336 126.619 0.376843
337337 195.474 195.474i 0.580042 0.580042i −0.354873 0.934915i 0.615476π-0.615476\pi
0.934915 + 0.354873i 0.115476π0.115476\pi
338338 −150.135 150.135i −0.444185 0.444185i
339339 −588.743 −1.73671
340340 105.514 105.514i 0.310335 0.310335i
341341 −737.806 737.806i −2.16365 2.16365i
342342 187.866i 0.549317i
343343 245.804 + 245.804i 0.716629 + 0.716629i
344344 −17.6195 17.6195i −0.0512196 0.0512196i
345345 603.805 + 603.805i 1.75016 + 1.75016i
346346 300.872 + 300.872i 0.869571 + 0.869571i
347347 −366.063 −1.05494 −0.527468 0.849575i 0.676859π-0.676859\pi
−0.527468 + 0.849575i 0.676859π0.676859\pi
348348 44.2495i 0.127154i
349349 404.957 1.16034 0.580168 0.814497i 0.302987π-0.302987\pi
0.580168 + 0.814497i 0.302987π0.302987\pi
350350 32.8898 0.0939708
351351 42.7779 + 42.7779i 0.121874 + 0.121874i
352352 −70.9059 + 70.9059i −0.201437 + 0.201437i
353353 186.759i 0.529062i −0.964377 0.264531i 0.914783π-0.914783\pi
0.964377 0.264531i 0.0852171π-0.0852171\pi
354354 −35.5064 35.5064i −0.100300 0.100300i
355355 −285.916 + 285.916i −0.805397 + 0.805397i
356356 −227.923 −0.640232
357357 359.078 + 359.078i 1.00582 + 1.00582i
358358 14.7913i 0.0413166i
359359 −137.869 + 137.869i −0.384037 + 0.384037i −0.872554 0.488518i 0.837538π-0.837538\pi
0.488518 + 0.872554i 0.337538π0.337538\pi
360360 111.962 + 111.962i 0.311006 + 0.311006i
361361 239.199i 0.662602i
362362 −400.585 −1.10659
363363 626.678 + 626.678i 1.72639 + 1.72639i
364364 −42.3935 + 42.3935i −0.116466 + 0.116466i
365365 368.262i 1.00894i
366366 176.204i 0.481431i
367367 −405.724 + 405.724i −1.10552 + 1.10552i −0.111783 + 0.993733i 0.535656π0.535656\pi
−0.993733 + 0.111783i 0.964344π0.964344\pi
368368 160.122 0.435114
369369 138.233i 0.374615i
370370 15.1206 + 15.1206i 0.0408665 + 0.0408665i
371371 −85.7525 + 85.7525i −0.231139 + 0.231139i
372372 539.951i 1.45148i
373373 −460.015 460.015i −1.23328 1.23328i −0.962695 0.270588i 0.912782π-0.912782\pi
−0.270588 0.962695i 0.587218π-0.587218\pi
374374 −402.163 −1.07530
375375 427.918 + 427.918i 1.14111 + 1.14111i
376376 −82.9526 + 82.9526i −0.220619 + 0.220619i
377377 −14.8152 14.8152i −0.0392976 0.0392976i
378378 −96.1281 + 96.1281i −0.254307 + 0.254307i
379379 241.236 241.236i 0.636508 0.636508i −0.313184 0.949692i 0.601396π-0.601396\pi
0.949692 + 0.313184i 0.101396π0.101396\pi
380380 −72.5890 72.5890i −0.191024 0.191024i
381381 −633.701 + 633.701i −1.66326 + 1.66326i
382382 89.3960 89.3960i 0.234021 0.234021i
383383 −197.526 197.526i −0.515733 0.515733i 0.400544 0.916277i 0.368821π-0.368821\pi
−0.916277 + 0.400544i 0.868821π0.868821\pi
384384 51.8913 0.135134
385385 402.336 + 402.336i 1.04503 + 1.04503i
386386 −302.066 −0.782554
387387 106.041 0.274008
388388 18.2239 0.0469689
389389 −585.938 −1.50627 −0.753134 0.657867i 0.771459π-0.771459\pi
−0.753134 + 0.657867i 0.771459π0.771459\pi
390390 −131.030 −0.335973
391391 454.088 + 454.088i 1.16135 + 1.16135i
392392 2.73565 + 2.73565i 0.00697870 + 0.00697870i
393393 168.013 + 168.013i 0.427514 + 0.427514i
394394 106.723 0.270871
395395 28.4958i 0.0721412i
396396 426.739i 1.07762i
397397 34.3580 34.3580i 0.0865440 0.0865440i −0.662509 0.749054i 0.730509π-0.730509\pi
0.749054 + 0.662509i 0.230509π0.230509\pi
398398 97.4643 97.4643i 0.244885 0.244885i
399399 247.030 247.030i 0.619122 0.619122i
400400 13.4789 0.0336973
401401 −117.728 117.728i −0.293587 0.293587i 0.544909 0.838495i 0.316564π-0.316564\pi
−0.838495 + 0.544909i 0.816564π0.816564\pi
402402 17.7732i 0.0442120i
403403 −180.781 180.781i −0.448589 0.448589i
404404 −4.16713 + 4.16713i −0.0103147 + 0.0103147i
405405 206.717 0.510411
406406 33.2919 33.2919i 0.0819998 0.0819998i
407407 57.6316i 0.141601i
408408 147.158 + 147.158i 0.360681 + 0.360681i
409409 108.614 + 108.614i 0.265560 + 0.265560i 0.827308 0.561748i 0.189871π-0.189871\pi
−0.561748 + 0.827308i 0.689871π0.689871\pi
410410 −53.4113 53.4113i −0.130271 0.130271i
411411 719.553 1.75074
412412 91.1915 0.221339
413413 53.4277i 0.129365i
414414 −481.838 + 481.838i −1.16386 + 1.16386i
415415 273.383 273.383i 0.658754 0.658754i
416416 −17.3738 + 17.3738i −0.0417639 + 0.0417639i
417417 418.933i 1.00464i
418418 276.670i 0.661890i
419419 201.551i 0.481030i 0.970645 + 0.240515i 0.0773162π0.0773162\pi
−0.970645 + 0.240515i 0.922684π0.922684\pi
420420 294.443i 0.701054i
421421 689.634i 1.63809i −0.573733 0.819043i 0.694505π-0.694505\pi
0.573733 0.819043i 0.305495π-0.305495\pi
422422 −186.048 + 186.048i −0.440872 + 0.440872i
423423 499.240i 1.18024i
424424 −35.1432 + 35.1432i −0.0828850 + 0.0828850i
425425 38.2248 + 38.2248i 0.0899406 + 0.0899406i
426426 −398.760 398.760i −0.936057 0.936057i
427427 132.570 132.570i 0.310469 0.310469i
428428 −167.387 167.387i −0.391091 0.391091i
429429 249.707 + 249.707i 0.582068 + 0.582068i
430430 −40.9728 + 40.9728i −0.0952856 + 0.0952856i
431431 −124.538 124.538i −0.288951 0.288951i 0.547714 0.836665i 0.315498π-0.315498\pi
−0.836665 + 0.547714i 0.815498π0.815498\pi
432432 −39.3954 + 39.3954i −0.0911930 + 0.0911930i
433433 10.7776i 0.0248905i 0.999923 + 0.0124452i 0.00396155π0.00396155\pi
−0.999923 + 0.0124452i 0.996038π0.996038\pi
434434 406.242 406.242i 0.936042 0.936042i
435435 102.899 0.236548
436436 34.9279 + 34.9279i 0.0801099 + 0.0801099i
437437 312.393 312.393i 0.714857 0.714857i
438438 513.607 1.17262
439439 659.978i 1.50337i −0.659524 0.751684i 0.729242π-0.729242\pi
0.659524 0.751684i 0.270758π-0.270758\pi
440440 164.886 + 164.886i 0.374741 + 0.374741i
441441 −16.4642 −0.0373338
442442 −98.5402 −0.222942
443443 69.5007 + 69.5007i 0.156886 + 0.156886i 0.781185 0.624299i 0.214615π-0.214615\pi
−0.624299 + 0.781185i 0.714615π0.714615\pi
444444 −21.0883 + 21.0883i −0.0474963 + 0.0474963i
445445 530.016i 1.19105i
446446 329.251 0.738230
447447 −749.042 + 749.042i −1.67571 + 1.67571i
448448 −39.0414 39.0414i −0.0871459 0.0871459i
449449 −476.210 −1.06060 −0.530301 0.847810i 0.677921π-0.677921\pi
−0.530301 + 0.847810i 0.677921π0.677921\pi
450450 −40.5607 + 40.5607i −0.0901349 + 0.0901349i
451451 203.575i 0.451386i
452452 181.531 + 181.531i 0.401618 + 0.401618i
453453 −814.675 + 814.675i −1.79840 + 1.79840i
454454 −99.4260 −0.219000
455455 98.5826 + 98.5826i 0.216665 + 0.216665i
456456 101.238 101.238i 0.222013 0.222013i
457457 411.084i 0.899527i 0.893148 + 0.449763i 0.148492π0.148492\pi
−0.893148 + 0.449763i 0.851508π0.851508\pi
458458 510.832i 1.11535i
459459 −223.442 −0.486801
460460 372.351i 0.809458i
461461 −496.304 + 496.304i −1.07658 + 1.07658i −0.0797675 + 0.996813i 0.525418π0.525418\pi
−0.996813 + 0.0797675i 0.974582π0.974582\pi
462462 −561.128 + 561.128i −1.21456 + 1.21456i
463463 −527.308 + 527.308i −1.13889 + 1.13889i −0.150245 + 0.988649i 0.548006π0.548006\pi
−0.988649 + 0.150245i 0.951994π0.951994\pi
464464 13.6438 13.6438i 0.0294046 0.0294046i
465465 1255.61 2.70024
466466 417.135 417.135i 0.895140 0.895140i
467467 410.785 + 410.785i 0.879625 + 0.879625i 0.993496 0.113871i 0.0363250π-0.0363250\pi
−0.113871 + 0.993496i 0.536325π0.536325\pi
468468 104.562i 0.223423i
469469 13.3720 13.3720i 0.0285117 0.0285117i
470470 192.899 + 192.899i 0.410424 + 0.410424i
471471 1249.68i 2.65325i
472472 21.8958i 0.0463895i
473473 156.166 0.330161
474474 −39.7424 −0.0838447
475475 26.2969 26.2969i 0.0553620 0.0553620i
476476 221.434i 0.465198i
477477 211.505i 0.443408i
478478 −361.322 361.322i −0.755904 0.755904i
479479 476.992 + 476.992i 0.995808 + 0.995808i 0.999991 0.00418306i 0.00133151π-0.00133151\pi
−0.00418306 + 0.999991i 0.501332π0.501332\pi
480480 120.669i 0.251394i
481481 14.1212i 0.0293580i
482482 292.801 0.607472
483483 1267.16 2.62352
484484 386.456i 0.798463i
485485 42.3782i 0.0873778i
486486 465.582i 0.957988i
487487 −29.8493 −0.0612923 −0.0306461 0.999530i 0.509756π-0.509756\pi
−0.0306461 + 0.999530i 0.509756π0.509756\pi
488488 54.3301 54.3301i 0.111332 0.111332i
489489 831.782 1.70098
490490 6.36153 6.36153i 0.0129827 0.0129827i
491491 648.671i 1.32112i −0.750772 0.660561i 0.770318π-0.770318\pi
0.750772 0.660561i 0.229682π-0.229682\pi
492492 74.4915 74.4915i 0.151405 0.151405i
493493 77.3843 0.156966
494494 67.7913i 0.137229i
495495 −992.346 −2.00474
496496 166.487 166.487i 0.335659 0.335659i
497497 600.029i 1.20730i
498498 381.281 + 381.281i 0.765624 + 0.765624i
499499 −589.524 589.524i −1.18141 1.18141i −0.979379 0.202031i 0.935246π-0.935246\pi
−0.202031 0.979379i 0.564754π-0.564754\pi
500500 263.886i 0.527772i
501501 1321.46i 2.63764i
502502 312.308i 0.622127i
503503 −388.751 388.751i −0.772865 0.772865i 0.205742 0.978606i 0.434039π-0.434039\pi
−0.978606 + 0.205742i 0.934039π0.934039\pi
504504 234.966 0.466202
505505 9.69031 + 9.69031i 0.0191887 + 0.0191887i
506506 −709.600 + 709.600i −1.40237 + 1.40237i
507507 −486.917 486.917i −0.960389 0.960389i
508508 390.787 0.769265
509509 11.4967 + 11.4967i 0.0225869 + 0.0225869i 0.718310 0.695723i 0.244916π-0.244916\pi
−0.695723 + 0.718310i 0.744916π0.744916\pi
510510 342.204 342.204i 0.670988 0.670988i
511511 −386.422 386.422i −0.756207 0.756207i
512512 −16.0000 16.0000i −0.0312500 0.0312500i
513513 153.718i 0.299645i
514514 257.887i 0.501726i
515515 212.058i 0.411764i
516516 −57.1438 57.1438i −0.110744 0.110744i
517517 735.229i 1.42211i
518518 31.7324 0.0612595
519519 975.788 + 975.788i 1.88013 + 1.88013i
520520 40.4013 + 40.4013i 0.0776947 + 0.0776947i
521521 513.038 513.038i 0.984717 0.984717i −0.0151678 0.999885i 0.504828π-0.504828\pi
0.999885 + 0.0151678i 0.00482826π0.00482826\pi
522522 82.1133i 0.157305i
523523 152.358 152.358i 0.291316 0.291316i −0.546284 0.837600i 0.683958π-0.683958\pi
0.837600 + 0.546284i 0.183958π0.183958\pi
524524 103.609i 0.197728i
525525 106.668 0.203178
526526 −9.95329 9.95329i −0.0189226 0.0189226i
527527 944.276 1.79179
528528 −229.962 + 229.962i −0.435535 + 0.435535i
529529 1073.44 2.02919
530530 81.7227 + 81.7227i 0.154194 + 0.154194i
531531 −65.8888 65.8888i −0.124084 0.124084i
532532 −152.337 −0.286347
533533 49.8811i 0.0935856i
534534 −739.200 −1.38427
535535 −389.245 + 389.245i −0.727560 + 0.727560i
536536 5.48014 5.48014i 0.0102241 0.0102241i
537537 47.9713i 0.0893321i
538538 315.806 + 212.105i 0.587000 + 0.394247i
539539 −24.2467 −0.0449847
540540 91.6107 + 91.6107i 0.169649 + 0.169649i
541541 −591.764 591.764i −1.09383 1.09383i −0.995115 0.0987185i 0.968526π-0.968526\pi
−0.0987185 0.995115i 0.531474π-0.531474\pi
542542 380.512i 0.702051i
543543 −1299.18 −2.39259
544544 90.7485i 0.166817i
545545 81.2220 81.2220i 0.149031 0.149031i
546546 −137.491 + 137.491i −0.251815 + 0.251815i
547547 131.614i 0.240611i −0.992737 0.120305i 0.961613π-0.961613\pi
0.992737 0.120305i 0.0383873π-0.0383873\pi
548548 −221.865 221.865i −0.404863 0.404863i
549549 326.979i 0.595590i
550550 −59.7335 + 59.7335i −0.108606 + 0.108606i
551551 53.2370i 0.0966188i
552552 519.309 0.940777
553553 29.9009 + 29.9009i 0.0540704 + 0.0540704i
554554 −344.447 −0.621745
555555 49.0392 + 49.0392i 0.0883589 + 0.0883589i
556556 129.173 129.173i 0.232325 0.232325i
557557 −319.474 + 319.474i −0.573563 + 0.573563i −0.933122 0.359559i 0.882927π-0.882927\pi
0.359559 + 0.933122i 0.382927π0.382927\pi
558558 1001.98i 1.79566i
559559 38.2647 0.0684521
560560 −90.7875 + 90.7875i −0.162121 + 0.162121i
561561 −1304.30 −2.32495
562562 −138.822 −0.247014
563563 −1020.14 −1.81198 −0.905989 0.423300i 0.860872π-0.860872\pi
−0.905989 + 0.423300i 0.860872π0.860872\pi
564564 −269.032 + 269.032i −0.477008 + 0.477008i
565565 422.136 422.136i 0.747143 0.747143i
566566 −75.3669 75.3669i −0.133157 0.133157i
567567 216.910 216.910i 0.382557 0.382557i
568568 245.905i 0.432931i
569569 −748.079 + 748.079i −1.31473 + 1.31473i −0.396836 + 0.917889i 0.629892π0.629892\pi
−0.917889 + 0.396836i 0.870108π0.870108\pi
570570 −235.421 235.421i −0.413019 0.413019i
571571 366.353 366.353i 0.641599 0.641599i −0.309350 0.950948i 0.600111π-0.600111\pi
0.950948 + 0.309350i 0.100111π0.100111\pi
572572 153.988i 0.269210i
573573 289.930 289.930i 0.505985 0.505985i
574574 −112.090 −0.195279
575575 134.892 0.234595
576576 96.2941 0.167177
577577 −783.122 + 783.122i −1.35723 + 1.35723i −0.479917 + 0.877314i 0.659333π0.659333\pi
−0.877314 + 0.479917i 0.840667π0.840667\pi
578578 −31.6474 + 31.6474i −0.0547534 + 0.0547534i
579579 −979.661 −1.69199
580580 −31.7274 31.7274i −0.0547024 0.0547024i
581581 573.727i 0.987483i
582582 59.1039 0.101553
583583 311.483i 0.534276i
584584 −158.364 158.364i −0.271171 0.271171i
585585 −243.150 −0.415641
586586 52.8258 + 52.8258i 0.0901463 + 0.0901463i
587587 312.119i 0.531718i 0.964012 + 0.265859i 0.0856556π0.0856556\pi
−0.964012 + 0.265859i 0.914344π0.914344\pi
588588 8.87228 + 8.87228i 0.0150889 + 0.0150889i
589589 649.620i 1.10292i
590590 50.9170 0.0862999
591591 346.125 0.585659
592592 13.0046 0.0219673
593593 698.996i 1.17875i −0.807861 0.589373i 0.799375π-0.799375\pi
0.807861 0.589373i 0.200625π-0.200625\pi
594594 349.171i 0.587829i
595595 −514.927 −0.865423
596596 461.914 0.775024
597597 316.097 316.097i 0.529475 0.529475i
598598 −173.870 + 173.870i −0.290753 + 0.290753i
599599 −527.549 −0.880716 −0.440358 0.897822i 0.645148π-0.645148\pi
−0.440358 + 0.897822i 0.645148π0.645148\pi
600600 43.7150 0.0728583
601601 −291.321 291.321i −0.484728 0.484728i 0.421910 0.906638i 0.361360π-0.361360\pi
−0.906638 + 0.421910i 0.861360π0.861360\pi
602602 85.9864i 0.142835i
603603 32.9815i 0.0546958i
604604 502.389 0.831770
605605 −898.672 −1.48541
606606 −13.5149 + 13.5149i −0.0223017 + 0.0223017i
607607 −218.193 218.193i −0.359461 0.359461i 0.504153 0.863614i 0.331805π-0.331805\pi
−0.863614 + 0.504153i 0.831805π0.831805\pi
608608 −62.4309 −0.102682
609609 107.973 107.973i 0.177295 0.177295i
610610 −126.340 126.340i −0.207115 0.207115i
611611 180.150i 0.294844i
612612 273.079 + 273.079i 0.446208 + 0.446208i
613613 452.233 + 452.233i 0.737738 + 0.737738i 0.972140 0.234402i 0.0753132π-0.0753132\pi
−0.234402 + 0.972140i 0.575313π0.575313\pi
614614 71.2554 + 71.2554i 0.116051 + 0.116051i
615615 −173.224 173.224i −0.281665 0.281665i
616616 346.033 0.561742
617617 267.924i 0.434236i 0.976145 + 0.217118i 0.0696656π0.0696656\pi
−0.976145 + 0.217118i 0.930334π0.930334\pi
618618 295.753 0.478564
619619 −296.911 −0.479663 −0.239831 0.970815i 0.577092π-0.577092\pi
−0.239831 + 0.970815i 0.577092π0.577092\pi
620620 −387.151 387.151i −0.624437 0.624437i
621621 −394.254 + 394.254i −0.634870 + 0.634870i
622622 715.895i 1.15096i
623623 556.151 + 556.151i 0.892699 + 0.892699i
624624 −56.3467 + 56.3467i −0.0902992 + 0.0902992i
625625 −529.402 −0.847042
626626 325.811 + 325.811i 0.520465 + 0.520465i
627627 897.298i 1.43110i
628628 −385.323 + 385.323i −0.613572 + 0.613572i
629629 36.8797 + 36.8797i 0.0586322 + 0.0586322i
630630 546.394i 0.867292i
631631 284.390 0.450698 0.225349 0.974278i 0.427648π-0.427648\pi
0.225349 + 0.974278i 0.427648π0.427648\pi
632632 12.2540 + 12.2540i 0.0193893 + 0.0193893i
633633 −603.392 + 603.392i −0.953227 + 0.953227i
634634 131.541i 0.207477i
635635 908.742i 1.43109i
636636 −113.977 + 113.977i −0.179209 + 0.179209i
637637 −5.94107 −0.00932665
638638 120.928i 0.189542i
639639 −739.975 739.975i −1.15802 1.15802i
640640 −37.2067 + 37.2067i −0.0581354 + 0.0581354i
641641 124.117i 0.193630i 0.995302 + 0.0968152i 0.0308656π0.0308656\pi
−0.995302 + 0.0968152i 0.969134π0.969134\pi
642642 −542.870 542.870i −0.845593 0.845593i
643643 −418.214 −0.650410 −0.325205 0.945644i 0.605433π-0.605433\pi
−0.325205 + 0.945644i 0.605433π0.605433\pi
644644 −390.712 390.712i −0.606695 0.606695i
645645 −132.883 + 132.883i −0.206020 + 0.206020i
646646 −177.047 177.047i −0.274067 0.274067i
647647 277.424 277.424i 0.428786 0.428786i −0.459429 0.888215i 0.651946π-0.651946\pi
0.888215 + 0.459429i 0.151946π0.151946\pi
648648 88.8944 88.8944i 0.137183 0.137183i
649649 −97.0340 97.0340i −0.149513 0.149513i
650650 −14.6362 + 14.6362i −0.0225173 + 0.0225173i
651651 1317.53 1317.53i 2.02385 2.02385i
652652 −256.469 256.469i −0.393357 0.393357i
653653 −157.807 −0.241665 −0.120832 0.992673i 0.538556π-0.538556\pi
−0.120832 + 0.992673i 0.538556π0.538556\pi
654654 113.278 + 113.278i 0.173209 + 0.173209i
655655 −240.935 −0.367840
656656 −45.9369 −0.0700258
657657 953.094 1.45068
658658 404.823 0.615233
659659 −300.321 −0.455723 −0.227861 0.973694i 0.573173π-0.573173\pi
−0.227861 + 0.973694i 0.573173π0.573173\pi
660660 534.759 + 534.759i 0.810241 + 0.810241i
661661 644.216 + 644.216i 0.974608 + 0.974608i 0.999686 0.0250771i 0.00798313π-0.00798313\pi
−0.0250771 + 0.999686i 0.507983π0.507983\pi
662662 −226.887 226.887i −0.342729 0.342729i
663663 −319.586 −0.482030
664664 235.126i 0.354105i
665665 354.247i 0.532702i
666666 −39.1334 + 39.1334i −0.0587589 + 0.0587589i
667667 136.542 136.542i 0.204710 0.204710i
668668 −407.454 + 407.454i −0.609960 + 0.609960i
669669 1067.83 1.59616
670670 −12.7436 12.7436i −0.0190203 0.0190203i
671671 481.541i 0.717646i
672672 −126.619 126.619i −0.188421 0.188421i
673673 435.829 435.829i 0.647591 0.647591i −0.304819 0.952410i 0.598596π-0.598596\pi
0.952410 + 0.304819i 0.0985961π0.0985961\pi
674674 −390.948 −0.580042
675675 −33.1880 + 33.1880i −0.0491674 + 0.0491674i
676676 300.269i 0.444185i
677677 878.629 + 878.629i 1.29783 + 1.29783i 0.929825 + 0.368002i 0.119958π0.119958\pi
0.368002 + 0.929825i 0.380042π0.380042\pi
678678 588.743 + 588.743i 0.868353 + 0.868353i
679679 −44.4680 44.4680i −0.0654904 0.0654904i
680680 −211.028 −0.310335
681681 −322.459 −0.473508
682682 1475.61i 2.16365i
683683 41.5498 41.5498i 0.0608343 0.0608343i −0.676035 0.736869i 0.736303π-0.736303\pi
0.736869 + 0.676035i 0.236303π0.236303\pi
684684 187.866 187.866i 0.274659 0.274659i
685685 −515.928 + 515.928i −0.753180 + 0.753180i
686686 491.607i 0.716629i
687687 1656.73i 2.41155i
688688 35.2391i 0.0512196i
689689 76.3213i 0.110771i
690690 1207.61i 1.75016i
691691 −47.9903 + 47.9903i −0.0694505 + 0.0694505i −0.740979 0.671528i 0.765638π-0.765638\pi
0.671528 + 0.740979i 0.265638π0.265638\pi
692692 601.743i 0.869571i
693693 −1041.28 + 1041.28i −1.50257 + 1.50257i
694694 366.063 + 366.063i 0.527468 + 0.527468i
695695 −300.380 300.380i −0.432202 0.432202i
696696 44.2495 44.2495i 0.0635768 0.0635768i
697697 −130.272 130.272i −0.186904 0.186904i
698698 −404.957 404.957i −0.580168 0.580168i
699699 1352.85 1352.85i 1.93541 1.93541i
700700 −32.8898 32.8898i −0.0469854 0.0469854i
701701 165.521 165.521i 0.236121 0.236121i −0.579121 0.815242i 0.696604π-0.696604\pi
0.815242 + 0.579121i 0.196604π0.196604\pi
702702 85.5558i 0.121874i
703703 25.3716 25.3716i 0.0360904 0.0360904i
704704 141.812 0.201437
705705 625.613 + 625.613i 0.887394 + 0.887394i
706706 −186.759 + 186.759i −0.264531 + 0.264531i
707707 20.3363 0.0287642
708708 71.0127i 0.100300i
709709 705.800 + 705.800i 0.995486 + 0.995486i 0.999990 0.00450375i 0.00143359π-0.00143359\pi
−0.00450375 + 0.999990i 0.501434π0.501434\pi
710710 571.832 0.805397
711711 −73.7495 −0.103726
712712 227.923 + 227.923i 0.320116 + 0.320116i
713713 1666.14 1666.14i 2.33680 2.33680i
714714 718.156i 1.00582i
715715 −358.086 −0.500820
716716 −14.7913 + 14.7913i −0.0206583 + 0.0206583i
717717 −1171.84 1171.84i −1.63437 1.63437i
718718 275.738 0.384037
719719 −482.421 + 482.421i −0.670962 + 0.670962i −0.957938 0.286976i 0.907350π-0.907350\pi
0.286976 + 0.957938i 0.407350π0.407350\pi
720720 223.924i 0.311006i
721721 −222.515 222.515i −0.308620 0.308620i
722722 239.199 239.199i 0.331301 0.331301i
723723 949.615 1.31344
724724 400.585 + 400.585i 0.553294 + 0.553294i
725725 11.4940 11.4940i 0.0158537 0.0158537i
726726 1253.36i 1.72639i
727727 903.795i 1.24318i −0.783341 0.621592i 0.786486π-0.786486\pi
0.783341 0.621592i 0.213514π-0.213514\pi
728728 84.7870 0.116466
729729 1109.95i 1.52257i
730730 −368.262 + 368.262i −0.504469 + 0.504469i
731731 −99.9341 + 99.9341i −0.136709 + 0.136709i
732732 176.204 176.204i 0.240715 0.240715i
733733 52.7615 52.7615i 0.0719802 0.0719802i −0.670200 0.742180i 0.733792π-0.733792\pi
0.742180 + 0.670200i 0.233792π0.233792\pi
734734 811.449 1.10552
735735 20.6318 20.6318i 0.0280704 0.0280704i
736736 −160.122 160.122i −0.217557 0.217557i
737737 48.5718i 0.0659047i
738738 138.233 138.233i 0.187308 0.187308i
739739 963.523 + 963.523i 1.30382 + 1.30382i 0.925795 + 0.378025i 0.123397π0.123397\pi
0.378025 + 0.925795i 0.376603π0.376603\pi
740740 30.2412i 0.0408665i
741741 219.861i 0.296708i
742742 171.505 0.231139
743743 440.376 0.592700 0.296350 0.955079i 0.404230π-0.404230\pi
0.296350 + 0.955079i 0.404230π0.404230\pi
744744 539.951 539.951i 0.725740 0.725740i
745745 1074.14i 1.44180i
746746 920.030i 1.23328i
747747 707.538 + 707.538i 0.947173 + 0.947173i
748748 402.163 + 402.163i 0.537651 + 0.537651i
749749 816.878i 1.09062i
750750 855.836i 1.14111i
751751 1037.35 1.38129 0.690643 0.723196i 0.257328π-0.257328\pi
0.690643 + 0.723196i 0.257328π0.257328\pi
752752 165.905 0.220619
753753 1012.88i 1.34512i
754754 29.6304i 0.0392976i
755755 1168.26i 1.54737i
756756 192.256 0.254307
757757 −66.0668 + 66.0668i −0.0872745 + 0.0872745i −0.749396 0.662122i 0.769656π-0.769656\pi
0.662122 + 0.749396i 0.269656π0.269656\pi
758758 −482.473 −0.636508
759759 −2301.38 + 2301.38i −3.03212 + 3.03212i
760760 145.178i 0.191024i
761761 −613.704 + 613.704i −0.806444 + 0.806444i −0.984094 0.177649i 0.943151π-0.943151\pi
0.177649 + 0.984094i 0.443151π0.443151\pi
762762 1267.40 1.66326
763763 170.454i 0.223400i
764764 −178.792 −0.234021
765765 635.024 635.024i 0.830096 0.830096i
766766 395.051i 0.515733i
767767 −23.7758 23.7758i −0.0309985 0.0309985i
768768 −51.8913 51.8913i −0.0675668 0.0675668i
769769 657.413i 0.854894i −0.904040 0.427447i 0.859413π-0.859413\pi
0.904040 0.427447i 0.140587π-0.140587\pi
770770 804.672i 1.04503i
771771 836.381i 1.08480i
772772 302.066 + 302.066i 0.391277 + 0.391277i
773773 −239.707 −0.310099 −0.155050 0.987907i 0.549554π-0.549554\pi
−0.155050 + 0.987907i 0.549554π0.549554\pi
774774 −106.041 106.041i −0.137004 0.137004i
775775 140.254 140.254i 0.180973 0.180973i
776776 −18.2239 18.2239i −0.0234844 0.0234844i
777777 102.915 0.132451
778778 585.938 + 585.938i 0.753134 + 0.753134i
779779 −89.6214 + 89.6214i −0.115047 + 0.115047i
780780 131.030 + 131.030i 0.167987 + 0.167987i
781781 −1089.76 1089.76i −1.39534 1.39534i
782782 908.177i 1.16135i
783783 67.1876i 0.0858079i
784784 5.47130i 0.00697870i
785785 896.037 + 896.037i 1.14145 + 1.14145i
786786 336.026i 0.427514i
787787 −1402.92 −1.78262 −0.891308 0.453398i 0.850211π-0.850211\pi
−0.891308 + 0.453398i 0.850211π0.850211\pi
788788 −106.723 106.723i −0.135435 0.135435i
789789 −32.2806 32.2806i −0.0409133 0.0409133i
790790 28.4958 28.4958i 0.0360706 0.0360706i
791791 885.904i 1.11998i
792792 −426.739 + 426.739i −0.538812 + 0.538812i
793793 117.990i 0.148789i
794794 −68.7160 −0.0865440
795795 265.043 + 265.043i 0.333388 + 0.333388i
796796 −194.929 −0.244885
797797 −18.3790 + 18.3790i −0.0230603 + 0.0230603i −0.718543 0.695483i 0.755191π-0.755191\pi
0.695483 + 0.718543i 0.255191π0.255191\pi
798798 −494.060 −0.619122
799799 470.489 + 470.489i 0.588847 + 0.588847i
800800 −13.4789 13.4789i −0.0168487 0.0168487i
801801 −1371.73 −1.71252
802802 235.456i 0.293587i
803803 1403.62 1.74797
804804 17.7732 17.7732i 0.0221060 0.0221060i
805805 −908.568 + 908.568i −1.12866 + 1.12866i
806806 361.563i 0.448589i
807807 1024.22 + 687.900i 1.26917 + 0.852416i
808808 8.33426 0.0103147
809809 910.227 + 910.227i 1.12513 + 1.12513i 0.990959 + 0.134167i 0.0428359π0.0428359\pi
0.134167 + 0.990959i 0.457164π0.457164\pi
810810 −206.717 206.717i −0.255206 0.255206i
811811 196.995i 0.242904i 0.992597 + 0.121452i 0.0387551π0.0387551\pi
−0.992597 + 0.121452i 0.961245π0.961245\pi
812812 −66.5839 −0.0819998
813813 1234.08i 1.51793i
814814 −57.6316 + 57.6316i −0.0708005 + 0.0708005i
815815 −596.397 + 596.397i −0.731776 + 0.731776i
816816 294.316i 0.360681i
817817 68.7503 + 68.7503i 0.0841496 + 0.0841496i
818818 217.228i 0.265560i
819819 −255.140 + 255.140i −0.311527 + 0.311527i
820820 106.823i 0.130271i
821821 1604.12 1.95386 0.976929 0.213563i 0.0685068π-0.0685068\pi
0.976929 + 0.213563i 0.0685068π0.0685068\pi
822822 −719.553 719.553i −0.875369 0.875369i
823823 −1149.18 −1.39632 −0.698162 0.715939i 0.745999π-0.745999\pi
−0.698162 + 0.715939i 0.745999π0.745999\pi
824824 −91.1915 91.1915i −0.110669 0.110669i
825825 −193.728 + 193.728i −0.234822 + 0.234822i
826826 53.4277 53.4277i 0.0646825 0.0646825i
827827 1447.99i 1.75089i 0.483316 + 0.875446i 0.339432π0.339432\pi
−0.483316 + 0.875446i 0.660568π0.660568\pi
828828 963.676 1.16386
829829 −202.788 + 202.788i −0.244617 + 0.244617i −0.818757 0.574140i 0.805337π-0.805337\pi
0.574140 + 0.818757i 0.305337π0.305337\pi
830830 −546.766 −0.658754
831831 −1117.11 −1.34430
832832 34.7475 0.0417639
833833 15.5160 15.5160i 0.0186267 0.0186267i
834834 418.933 418.933i 0.502318 0.502318i
835835 947.500 + 947.500i 1.13473 + 1.13473i
836836 276.670 276.670i 0.330945 0.330945i
837837 819.851i 0.979511i
838838 201.551 201.551i 0.240515 0.240515i
839839 −173.794 173.794i −0.207144 0.207144i 0.595908 0.803052i 0.296792π-0.296792\pi
−0.803052 + 0.595908i 0.796792π0.796792\pi
840840 −294.443 + 294.443i −0.350527 + 0.350527i
841841 817.731i 0.972332i
842842 −689.634 + 689.634i −0.819043 + 0.819043i
843843 −450.227 −0.534077
844844 372.096 0.440872
845845 698.251 0.826332
846846 −499.240 + 499.240i −0.590119 + 0.590119i
847847 −942.987 + 942.987i −1.11333 + 1.11333i
848848 70.2865 0.0828850
849849 −244.430 244.430i −0.287904 0.287904i
850850 76.4495i 0.0899406i
851851 130.145 0.152932
852852 797.520i 0.936057i
853853 385.375 + 385.375i 0.451788 + 0.451788i 0.895948 0.444160i 0.146498π-0.146498\pi
−0.444160 + 0.895948i 0.646498π0.646498\pi
854854 −265.140 −0.310469
855855 −436.868 436.868i −0.510957 0.510957i
856856 334.774i 0.391091i
857857 749.750 + 749.750i 0.874854 + 0.874854i 0.992997 0.118143i 0.0376941π-0.0376941\pi
−0.118143 + 0.992997i 0.537694π0.537694\pi
858858 499.414i 0.582068i
859859 −89.1312 −0.103762 −0.0518808 0.998653i 0.516522π-0.516522\pi
−0.0518808 + 0.998653i 0.516522π0.516522\pi
860860 81.9456 0.0952856
861861 −363.531 −0.422220
862862 249.076i 0.288951i
863863 1389.87i 1.61051i 0.592928 + 0.805256i 0.297972π0.297972\pi
−0.592928 + 0.805256i 0.702028π0.702028\pi
864864 78.7908 0.0911930
865865 −1399.30 −1.61769
866866 10.7776 10.7776i 0.0124452 0.0124452i
867867 −102.639 + 102.639i −0.118384 + 0.118384i
868868 −812.484 −0.936042
869869 −108.611 −0.124983
870870 −102.899 102.899i −0.118274 0.118274i
871871 11.9013i 0.0136640i
872872 69.8558i 0.0801099i
873873 109.679 0.125634
874874 −624.785 −0.714857
875875 −643.904 + 643.904i −0.735891 + 0.735891i
876876 −513.607 513.607i −0.586309 0.586309i
877877 95.5592 0.108961 0.0544807 0.998515i 0.482650π-0.482650\pi
0.0544807 + 0.998515i 0.482650π0.482650\pi
878878 −659.978 + 659.978i −0.751684 + 0.751684i
879879 171.325 + 171.325i 0.194909 + 0.194909i
880880 329.772i 0.374741i
881881 −1045.37 1045.37i −1.18657 1.18657i −0.978010 0.208556i 0.933124π-0.933124\pi
−0.208556 0.978010i 0.566876π-0.566876\pi
882882 16.4642 + 16.4642i 0.0186669 + 0.0186669i
883883 574.613 + 574.613i 0.650751 + 0.650751i 0.953174 0.302423i 0.0977954π-0.0977954\pi
−0.302423 + 0.953174i 0.597795π0.597795\pi
884884 98.5402 + 98.5402i 0.111471 + 0.111471i
885885 165.134 0.186592
886886 139.001i 0.156886i
887887 −548.626 −0.618519 −0.309259 0.950978i 0.600081π-0.600081\pi
−0.309259 + 0.950978i 0.600081π0.600081\pi
888888 42.1767 0.0474963
889889 −953.553 953.553i −1.07261 1.07261i
890890 530.016 530.016i 0.595523 0.595523i
891891 787.893i 0.884279i
892892 −329.251 329.251i −0.369115 0.369115i
893893 323.675 323.675i 0.362458 0.362458i
894894 1498.08 1.67571
895895 34.3960 + 34.3960i 0.0384313 + 0.0384313i
896896 78.0828i 0.0871459i
897897 −563.897 + 563.897i −0.628648 + 0.628648i
898898 476.210 + 476.210i 0.530301 + 0.530301i
899899 283.938i 0.315838i
900900 81.1214 0.0901349
901901 199.325 + 199.325i 0.221226 + 0.221226i
902902 203.575 203.575i 0.225693 0.225693i
903903 278.872i 0.308828i
904904 363.063i 0.401618i
905905 931.526 931.526i 1.02931 1.02931i
906906 1629.35 1.79840
907907 76.3254i 0.0841515i −0.999114 0.0420758i 0.986603π-0.986603\pi
0.999114 0.0420758i 0.0133971π-0.0133971\pi
908908 99.4260 + 99.4260i 0.109500 + 0.109500i
909909 −25.0794 + 25.0794i −0.0275901 + 0.0275901i
910910 197.165i 0.216665i
911911 −836.780 836.780i −0.918529 0.918529i 0.0783937 0.996922i 0.475021π-0.475021\pi
−0.996922 + 0.0783937i 0.975021π0.975021\pi
912912 −202.476 −0.222013
913913 1041.99 + 1041.99i 1.14128 + 1.14128i
914914 411.084 411.084i 0.449763 0.449763i
915915 −409.747 409.747i −0.447811 0.447811i
916916 −510.832 + 510.832i −0.557676 + 0.557676i
917917 −252.816 + 252.816i −0.275699 + 0.275699i
918918 223.442 + 223.442i 0.243401 + 0.243401i
919919 −560.470 + 560.470i −0.609869 + 0.609869i −0.942912 0.333042i 0.891925π-0.891925\pi
0.333042 + 0.942912i 0.391925π0.391925\pi
920920 −372.351 + 372.351i −0.404729 + 0.404729i
921921 231.096 + 231.096i 0.250918 + 0.250918i
922922 992.608 1.07658
923923 −267.019 267.019i −0.289294 0.289294i
924924 1122.26 1.21456
925925 10.9555 0.0118438
926926 1054.62 1.13889
927927 548.825 0.592045
928928 −27.2875 −0.0294046
929929 1227.95 + 1227.95i 1.32180 + 1.32180i 0.912319 + 0.409481i 0.134290π0.134290\pi
0.409481 + 0.912319i 0.365710π0.365710\pi
930930 −1255.61 1255.61i −1.35012 1.35012i
931931 −10.6743 10.6743i −0.0114654 0.0114654i
932932 −834.270 −0.895140
933933 2321.79i 2.48853i
934934 821.570i 0.879625i
935935 935.196 935.196i 1.00021 1.00021i
936936 −104.562 + 104.562i −0.111712 + 0.111712i
937937 105.483 105.483i 0.112575 0.112575i −0.648576 0.761150i 0.724635π-0.724635\pi
0.761150 + 0.648576i 0.224635π0.224635\pi
938938 −26.7440 −0.0285117
939939 1056.67 + 1056.67i 1.12532 + 1.12532i
940940 385.799i 0.410424i
941941 −826.783 826.783i −0.878621 0.878621i 0.114771 0.993392i 0.463387π-0.463387\pi
−0.993392 + 0.114771i 0.963387π0.963387\pi
942942 −1249.68 + 1249.68i −1.32663 + 1.32663i
943943 −459.720 −0.487508
944944 21.8958 21.8958i 0.0231947 0.0231947i
945945 447.076i 0.473096i
946946 −156.166 156.166i −0.165081 0.165081i
947947 1189.52 + 1189.52i 1.25609 + 1.25609i 0.952945 + 0.303145i 0.0980365π0.0980365\pi
0.303145 + 0.952945i 0.401964π0.401964\pi
948948 39.7424 + 39.7424i 0.0419223 + 0.0419223i
949949 343.922 0.362405
950950 −52.5939 −0.0553620
951951 426.613i 0.448594i
952952 −221.434 + 221.434i −0.232599 + 0.232599i
953953 482.280 482.280i 0.506065 0.506065i −0.407251 0.913316i 0.633513π-0.633513\pi
0.913316 + 0.407251i 0.133513π0.133513\pi
954954 −211.505 + 211.505i −0.221704 + 0.221704i
955955 415.766i 0.435357i
956956 722.644i 0.755904i
957957 392.194i 0.409816i
958958 953.984i 0.995808i
959959 1082.74i 1.12903i
960960 −120.669 + 120.669i −0.125697 + 0.125697i
961961 2503.73i 2.60534i
962962 −14.1212 + 14.1212i −0.0146790 + 0.0146790i
963963 −1007.40 1007.40i −1.04610 1.04610i
964964 −292.801 292.801i −0.303736 0.303736i
965965 702.429 702.429i 0.727906 0.727906i
966966 −1267.16 1267.16i −1.31176 1.31176i
967967 1278.70 + 1278.70i 1.32233 + 1.32233i 0.911884 + 0.410448i 0.134628π0.134628\pi
0.410448 + 0.911884i 0.365372π0.365372\pi
968968 −386.456 + 386.456i −0.399232 + 0.399232i
969969 −574.200 574.200i −0.592570 0.592570i
970970 −42.3782 + 42.3782i −0.0436889 + 0.0436889i
971971 103.072i 0.106151i −0.998591 0.0530754i 0.983098π-0.983098\pi
0.998591 0.0530754i 0.0169024π-0.0169024\pi
972972 465.582 465.582i 0.478994 0.478994i
973973 −630.385 −0.647878
974974 29.8493 + 29.8493i 0.0306461 + 0.0306461i
975975 −47.4684 + 47.4684i −0.0486855 + 0.0486855i
976976 −108.660 −0.111332
977977 1372.54i 1.40485i −0.711759 0.702424i 0.752101π-0.752101\pi
0.711759 0.702424i 0.247899π-0.247899\pi
978978 −831.782 831.782i −0.850492 0.850492i
979979 −2020.13 −2.06347
980980 −12.7231 −0.0129827
981981 210.210 + 210.210i 0.214281 + 0.214281i
982982 −648.671 + 648.671i −0.660561 + 0.660561i
983983 1395.65i 1.41979i 0.704309 + 0.709894i 0.251257π0.251257\pi
−0.704309 + 0.709894i 0.748743π0.748743\pi
984984 −148.983 −0.151405
985985 −248.176 + 248.176i −0.251955 + 0.251955i
986986 −77.3843 77.3843i −0.0784831 0.0784831i
987987 1312.92 1.33022
988988 67.7913 67.7913i 0.0686146 0.0686146i
989989 352.660i 0.356582i
990990 992.346 + 992.346i 1.00237 + 1.00237i
991991 −842.735 + 842.735i −0.850388 + 0.850388i −0.990181 0.139793i 0.955356π-0.955356\pi
0.139793 + 0.990181i 0.455356π0.455356\pi
992992 −332.973 −0.335659
993993 −735.840 735.840i −0.741028 0.741028i
994994 600.029 600.029i 0.603651 0.603651i
995995 453.290i 0.455568i
996996 762.561i 0.765624i
997997 724.949 0.727131 0.363565 0.931569i 0.381559π-0.381559\pi
0.363565 + 0.931569i 0.381559π0.381559\pi
998998 1179.05i 1.18141i
999999 −32.0201 + 32.0201i −0.0320522 + 0.0320522i
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.187.3 46
269.82 odd 4 inner 538.3.c.b.351.3 yes 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
538.3.c.b.187.3 46 1.1 even 1 trivial
538.3.c.b.351.3 yes 46 269.82 odd 4 inner