Properties

Label 72.5.p.b.67.40
Level 7272
Weight 55
Character 72.67
Analytic conductor 7.4437.443
Analytic rank 00
Dimension 8888
Inner twists 44

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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] = [72,5,Mod(43,72)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(72, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 5, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("72.43"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Level: N N == 72=2332 72 = 2^{3} \cdot 3^{2}
Weight: k k == 5 5
Character orbit: [χ][\chi] == 72.p (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [88] 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: 7.442637342047.44263734204
Analytic rank: 00
Dimension: 8888
Relative dimension: 4444 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 67.40
Character χ\chi == 72.67
Dual form 72.5.p.b.43.40

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+(3.83772+1.12779i)q2+(8.904831.30534i)q3+(13.4562+8.65626i)q4+(23.238113.4165i)q5+(35.6464+5.03320i)q6+(52.216530.1472i)q7+(41.8787+48.3960i)q8+(77.592223.2478i)q9+(74.050377.6964i)q10+(92.8475+160.817i)q11+(131.125+59.5176i)q12+(166.02695.8552i)q13+(234.39256.8075i)q14+(224.44489.1381i)q15+(106.138+232.961i)q16425.178q17+(323.9951.71102i)q18114.203q19+(196.559381.690i)q20+(425.627336.616i)q21+(174.956+721.881i)q22+(239.080+138.033i)q23+(436.096+376.292i)q24+(47.5051+82.2813i)q25+(529.057555.107i)q26+(660.599308.302i)q27+(963.597+46.3326i)q28+(757.999+437.631i)q29+(760.826595.212i)q30+(910.769525.833i)q31+(144.600+1013.74i)q32+(1036.71+1310.85i)q33+(1631.71479.510i)q341617.88q35+(1245.33+358.831i)q36+194.549iq37+(438.278128.796i)q38+(1603.56636.853i)q39+(323.8751686.50i)q40+(1420.332460.08i)q41+(2013.07811.824i)q42+(449.077777.825i)q43+(142.695+2967.69i)q44+(2115.00500.783i)q45+(761.849+799.362i)q46+(348.382+201.138i)q47+(1249.24+1935.93i)q48+(617.2081069.03i)q49+(89.5157+369.348i)q50+(3786.14+555.004i)q51+(1404.332727.01i)q52+4662.79iq53+(2882.89438.162i)q544982.75iq55+(3645.76+1264.54i)q56+(1016.96+149.074i)q57+(3402.54+824.644i)q58+(1769.31+3064.53i)q59+(2248.563142.31i)q60+(1797.64+1037.87i)q61+(2902.253045.15i)q62+(3350.733553.10i)q63+(588.347+4053.52i)q64+(2572.08+4454.98i)q65+(2500.26+6199.85i)q66+(1465.532538.37i)q67+(5721.283680.45i)q68+(2309.14+917.077i)q69+(6208.971824.62i)q70+3035.73iq71+(4374.56+2781.56i)q72+5570.78q73+(219.410+746.624i)q74+(530.431+670.691i)q75+(1536.73988.567i)q76+(9696.34+5598.18i)q77+(5435.774252.54i)q78+(9323.765383.08i)q79+(659.0656837.56i)q80+(5480.083607.69i)q81+(8225.267839.27i)q82+(1407.362437.61i)q83+(8641.15845.242i)q84+(9880.31+5704.40i)q85+(846.2133491.54i)q86+(6178.59+4886.48i)q87+(3894.55+11228.2i)q881868.54q89+(7551.984307.13i)q9011559.1q91+(2022.26+3926.93i)q92+(8796.643493.58i)q93+(1563.83+379.012i)q94+(2653.85+1532.20i)q95+(2610.92+8838.43i)q96+(1255.93+2175.33i)q97+(3574.313406.58i)q98+(10942.9+10319.6i)q99+O(q100)q+(3.83772 + 1.12779i) q^{2} +(8.90483 - 1.30534i) q^{3} +(13.4562 + 8.65626i) q^{4} +(-23.2381 - 13.4165i) q^{5} +(35.6464 + 5.03320i) q^{6} +(52.2165 - 30.1472i) q^{7} +(41.8787 + 48.3960i) q^{8} +(77.5922 - 23.2478i) q^{9} +(-74.0503 - 77.6964i) q^{10} +(92.8475 + 160.817i) q^{11} +(131.125 + 59.5176i) q^{12} +(-166.026 - 95.8552i) q^{13} +(234.392 - 56.8075i) q^{14} +(-224.444 - 89.1381i) q^{15} +(106.138 + 232.961i) q^{16} -425.178 q^{17} +(323.995 - 1.71102i) q^{18} -114.203 q^{19} +(-196.559 - 381.690i) q^{20} +(425.627 - 336.616i) q^{21} +(174.956 + 721.881i) q^{22} +(239.080 + 138.033i) q^{23} +(436.096 + 376.292i) q^{24} +(47.5051 + 82.2813i) q^{25} +(-529.057 - 555.107i) q^{26} +(660.599 - 308.302i) q^{27} +(963.597 + 46.3326i) q^{28} +(-757.999 + 437.631i) q^{29} +(-760.826 - 595.212i) q^{30} +(-910.769 - 525.833i) q^{31} +(144.600 + 1013.74i) q^{32} +(1036.71 + 1310.85i) q^{33} +(-1631.71 - 479.510i) q^{34} -1617.88 q^{35} +(1245.33 + 358.831i) q^{36} +194.549i q^{37} +(-438.278 - 128.796i) q^{38} +(-1603.56 - 636.853i) q^{39} +(-323.875 - 1686.50i) q^{40} +(1420.33 - 2460.08i) q^{41} +(2013.07 - 811.824i) q^{42} +(-449.077 - 777.825i) q^{43} +(-142.695 + 2967.69i) q^{44} +(-2115.00 - 500.783i) q^{45} +(761.849 + 799.362i) q^{46} +(-348.382 + 201.138i) q^{47} +(1249.24 + 1935.93i) q^{48} +(617.208 - 1069.03i) q^{49} +(89.5157 + 369.348i) q^{50} +(-3786.14 + 555.004i) q^{51} +(-1404.33 - 2727.01i) q^{52} +4662.79i q^{53} +(2882.89 - 438.162i) q^{54} -4982.75i q^{55} +(3645.76 + 1264.54i) q^{56} +(-1016.96 + 149.074i) q^{57} +(-3402.54 + 824.644i) q^{58} +(-1769.31 + 3064.53i) q^{59} +(-2248.56 - 3142.31i) q^{60} +(-1797.64 + 1037.87i) q^{61} +(-2902.25 - 3045.15i) q^{62} +(3350.73 - 3553.10i) q^{63} +(-588.347 + 4053.52i) q^{64} +(2572.08 + 4454.98i) q^{65} +(2500.26 + 6199.85i) q^{66} +(1465.53 - 2538.37i) q^{67} +(-5721.28 - 3680.45i) q^{68} +(2309.14 + 917.077i) q^{69} +(-6208.97 - 1824.62i) q^{70} +3035.73i q^{71} +(4374.56 + 2781.56i) q^{72} +5570.78 q^{73} +(-219.410 + 746.624i) q^{74} +(530.431 + 670.691i) q^{75} +(-1536.73 - 988.567i) q^{76} +(9696.34 + 5598.18i) q^{77} +(-5435.77 - 4252.54i) q^{78} +(9323.76 - 5383.08i) q^{79} +(659.065 - 6837.56i) q^{80} +(5480.08 - 3607.69i) q^{81} +(8225.26 - 7839.27i) q^{82} +(-1407.36 - 2437.61i) q^{83} +(8641.15 - 845.242i) q^{84} +(9880.31 + 5704.40i) q^{85} +(-846.213 - 3491.54i) q^{86} +(-6178.59 + 4886.48i) q^{87} +(-3894.55 + 11228.2i) q^{88} -1868.54 q^{89} +(-7551.98 - 4307.13i) q^{90} -11559.1 q^{91} +(2022.26 + 3926.93i) q^{92} +(-8796.64 - 3493.58i) q^{93} +(-1563.83 + 379.012i) q^{94} +(2653.85 + 1532.20i) q^{95} +(2610.92 + 8838.43i) q^{96} +(1255.93 + 2175.33i) q^{97} +(3574.31 - 3406.58i) q^{98} +(10942.9 + 10319.6i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 88q+7q218q3+31q49q6386q8+30q936q10+44q11+612q12318q14+511q161156q17+234q18+860q191164q20+215q22561q24+11742q99+O(q100) 88 q + 7 q^{2} - 18 q^{3} + 31 q^{4} - 9 q^{6} - 386 q^{8} + 30 q^{9} - 36 q^{10} + 44 q^{11} + 612 q^{12} - 318 q^{14} + 511 q^{16} - 1156 q^{17} + 234 q^{18} + 860 q^{19} - 1164 q^{20} + 215 q^{22} - 561 q^{24}+ \cdots - 11742 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/72Z)×\left(\mathbb{Z}/72\mathbb{Z}\right)^\times.

nn 3737 5555 6565
χ(n)\chi(n) 1-1 1-1 e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 3.83772 + 1.12779i 0.959430 + 0.281947i
33 8.90483 1.30534i 0.989426 0.145038i
44 13.4562 + 8.65626i 0.841012 + 0.541016i
55 −23.2381 13.4165i −0.929523 0.536660i −0.0428621 0.999081i 0.513648π-0.513648\pi
−0.886661 + 0.462421i 0.846981π0.846981\pi
66 35.6464 + 5.03320i 0.990178 + 0.139811i
77 52.2165 30.1472i 1.06564 0.615249i 0.138655 0.990341i 0.455722π-0.455722\pi
0.926988 + 0.375092i 0.122389π0.122389\pi
88 41.8787 + 48.3960i 0.654355 + 0.756188i
99 77.5922 23.2478i 0.957928 0.287009i
1010 −74.0503 77.6964i −0.740503 0.776964i
1111 92.8475 + 160.817i 0.767335 + 1.32906i 0.939003 + 0.343908i 0.111751π0.111751\pi
−0.171669 + 0.985155i 0.554916π0.554916\pi
1212 131.125 + 59.5176i 0.910587 + 0.413316i
1313 −166.026 95.8552i −0.982402 0.567190i −0.0794078 0.996842i 0.525303π-0.525303\pi
−0.902995 + 0.429652i 0.858636π0.858636\pi
1414 234.392 56.8075i 1.19588 0.289834i
1515 −224.444 89.1381i −0.997530 0.396169i
1616 106.138 + 232.961i 0.414603 + 0.910002i
1717 −425.178 −1.47120 −0.735602 0.677414i 0.763101π-0.763101\pi
−0.735602 + 0.677414i 0.763101π0.763101\pi
1818 323.995 1.71102i 0.999986 0.00528092i
1919 −114.203 −0.316351 −0.158175 0.987411i 0.550561π-0.550561\pi
−0.158175 + 0.987411i 0.550561π0.550561\pi
2020 −196.559 381.690i −0.491398 0.954224i
2121 425.627 336.616i 0.965140 0.763302i
2222 174.956 + 721.881i 0.361479 + 1.49149i
2323 239.080 + 138.033i 0.451946 + 0.260931i 0.708652 0.705558i 0.249304π-0.249304\pi
−0.256705 + 0.966490i 0.582637π0.582637\pi
2424 436.096 + 376.292i 0.757112 + 0.653285i
2525 47.5051 + 82.2813i 0.0760082 + 0.131650i
2626 −529.057 555.107i −0.782629 0.821164i
2727 660.599 308.302i 0.906171 0.422911i
2828 963.597 + 46.3326i 1.22908 + 0.0590978i
2929 −757.999 + 437.631i −0.901306 + 0.520369i −0.877624 0.479350i 0.840872π-0.840872\pi
−0.0236825 + 0.999720i 0.507539π0.507539\pi
3030 −760.826 595.212i −0.845362 0.661347i
3131 −910.769 525.833i −0.947730 0.547172i −0.0553551 0.998467i 0.517629π-0.517629\pi
−0.892375 + 0.451294i 0.850962π0.850962\pi
3232 144.600 + 1013.74i 0.141211 + 0.989980i
3333 1036.71 + 1310.85i 0.951986 + 1.20372i
3434 −1631.71 479.510i −1.41152 0.414801i
3535 −1617.88 −1.32072
3636 1245.33 + 358.831i 0.960906 + 0.276876i
3737 194.549i 0.142110i 0.997472 + 0.0710551i 0.0226366π0.0226366\pi
−0.997472 + 0.0710551i 0.977363π0.977363\pi
3838 −438.278 128.796i −0.303517 0.0891940i
3939 −1603.56 636.853i −1.05428 0.418707i
4040 −323.875 1686.50i −0.202422 1.05406i
4141 1420.33 2460.08i 0.844930 1.46346i −0.0407524 0.999169i 0.512975π-0.512975\pi
0.885682 0.464292i 0.153691π-0.153691\pi
4242 2013.07 811.824i 1.14119 0.460217i
4343 −449.077 777.825i −0.242876 0.420673i 0.718656 0.695365i 0.244757π-0.244757\pi
−0.961532 + 0.274692i 0.911424π0.911424\pi
4444 −142.695 + 2967.69i −0.0737063 + 1.53290i
4545 −2115.00 500.783i −1.04444 0.247300i
4646 761.849 + 799.362i 0.360042 + 0.377770i
4747 −348.382 + 201.138i −0.157710 + 0.0910540i −0.576778 0.816901i 0.695690π-0.695690\pi
0.419068 + 0.907955i 0.362357π0.362357\pi
4848 1249.24 + 1935.93i 0.542204 + 0.840247i
4949 617.208 1069.03i 0.257063 0.445246i
5050 89.5157 + 369.348i 0.0358063 + 0.147739i
5151 −3786.14 + 555.004i −1.45565 + 0.213381i
5252 −1404.33 2727.01i −0.519353 1.00851i
5353 4662.79i 1.65995i 0.557802 + 0.829974i 0.311645π0.311645\pi
−0.557802 + 0.829974i 0.688355π0.688355\pi
5454 2882.89 438.162i 0.988646 0.150261i
5555 4982.75i 1.64719i
5656 3645.76 + 1264.54i 1.16255 + 0.403235i
5757 −1016.96 + 149.074i −0.313006 + 0.0458830i
5858 −3402.54 + 824.644i −1.01146 + 0.245138i
5959 −1769.31 + 3064.53i −0.508276 + 0.880359i 0.491678 + 0.870777i 0.336384π0.336384\pi
−0.999954 + 0.00958239i 0.996950π0.996950\pi
6060 −2248.56 3142.31i −0.624601 0.872863i
6161 −1797.64 + 1037.87i −0.483107 + 0.278922i −0.721710 0.692195i 0.756644π-0.756644\pi
0.238604 + 0.971117i 0.423310π0.423310\pi
6262 −2902.25 3045.15i −0.755007 0.792183i
6363 3350.73 3553.10i 0.844226 0.895213i
6464 −588.347 + 4053.52i −0.143639 + 0.989630i
6565 2572.08 + 4454.98i 0.608777 + 1.05443i
6666 2500.26 + 6199.85i 0.573980 + 1.42329i
6767 1465.53 2538.37i 0.326471 0.565465i −0.655338 0.755336i 0.727474π-0.727474\pi
0.981809 + 0.189871i 0.0608070π0.0608070\pi
6868 −5721.28 3680.45i −1.23730 0.795945i
6969 2309.14 + 917.077i 0.485013 + 0.192623i
7070 −6208.97 1824.62i −1.26714 0.372372i
7171 3035.73i 0.602208i 0.953591 + 0.301104i 0.0973551π0.0973551\pi
−0.953591 + 0.301104i 0.902645π0.902645\pi
7272 4374.56 + 2781.56i 0.843858 + 0.536567i
7373 5570.78 1.04537 0.522685 0.852526i 0.324930π-0.324930\pi
0.522685 + 0.852526i 0.324930π0.324930\pi
7474 −219.410 + 746.624i −0.0400675 + 0.136345i
7575 530.431 + 670.691i 0.0942988 + 0.119234i
7676 −1536.73 988.567i −0.266055 0.171151i
7777 9696.34 + 5598.18i 1.63541 + 0.944204i
7878 −5435.77 4252.54i −0.893454 0.698970i
7979 9323.76 5383.08i 1.49395 0.862535i 0.493978 0.869475i 0.335542π-0.335542\pi
0.999976 + 0.00694001i 0.00220909π0.00220909\pi
8080 659.065 6837.56i 0.102979 1.06837i
8181 5480.08 3607.69i 0.835251 0.549868i
8282 8225.26 7839.27i 1.22327 1.16586i
8383 −1407.36 2437.61i −0.204291 0.353842i 0.745616 0.666376i 0.232155π-0.232155\pi
−0.949906 + 0.312534i 0.898822π0.898822\pi
8484 8641.15 845.242i 1.22465 0.119791i
8585 9880.31 + 5704.40i 1.36752 + 0.789537i
8686 −846.213 3491.54i −0.114415 0.472085i
8787 −6178.59 + 4886.48i −0.816302 + 0.645591i
8888 −3894.55 + 11228.2i −0.502911 + 1.44993i
8989 −1868.54 −0.235897 −0.117949 0.993020i 0.537632π-0.537632\pi
−0.117949 + 0.993020i 0.537632π0.537632\pi
9090 −7551.98 4307.13i −0.932344 0.531744i
9191 −11559.1 −1.39585
9292 2022.26 + 3926.93i 0.238924 + 0.463957i
9393 −8796.64 3493.58i −1.01707 0.403929i
9494 −1563.83 + 379.012i −0.176984 + 0.0428941i
9595 2653.85 + 1532.20i 0.294055 + 0.169773i
9696 2610.92 + 8838.43i 0.283303 + 0.959031i
9797 1255.93 + 2175.33i 0.133481 + 0.231197i 0.925016 0.379927i 0.124051π-0.124051\pi
−0.791535 + 0.611124i 0.790718π0.790718\pi
9898 3574.31 3406.58i 0.372169 0.354704i
9999 10942.9 + 10319.6i 1.11650 + 1.05291i
100100 −73.0097 + 1518.41i −0.00730097 + 0.151841i
101101 4729.31 2730.47i 0.463612 0.267667i −0.249950 0.968259i 0.580414π-0.580414\pi
0.713562 + 0.700592i 0.247081π0.247081\pi
102102 −15156.1 2140.01i −1.45675 0.205691i
103103 9762.25 + 5636.24i 0.920186 + 0.531270i 0.883694 0.468064i 0.155048π-0.155048\pi
0.0364916 + 0.999334i 0.488382π0.488382\pi
104104 −2313.95 12049.3i −0.213938 1.11402i
105105 −14407.0 + 2111.89i −1.30675 + 0.191555i
106106 −5258.63 + 17894.5i −0.468017 + 1.59260i
107107 4850.33 0.423647 0.211823 0.977308i 0.432060π-0.432060\pi
0.211823 + 0.977308i 0.432060π0.432060\pi
108108 11557.9 + 1569.74i 0.990903 + 0.134580i
109109 17364.2i 1.46151i −0.682639 0.730756i 0.739168π-0.739168\pi
0.682639 0.730756i 0.260832π-0.260832\pi
110110 5619.48 19122.4i 0.464420 1.58037i
111111 253.953 + 1732.43i 0.0206114 + 0.140608i
112112 12565.3 + 8964.61i 1.00170 + 0.714653i
113113 6670.25 11553.2i 0.522378 0.904786i −0.477283 0.878750i 0.658378π-0.658378\pi
0.999661 0.0260362i 0.00828850π-0.00828850\pi
114114 −4070.91 574.805i −0.313244 0.0442294i
115115 −3703.83 6415.23i −0.280063 0.485083i
116116 −13988.0 672.586i −1.03954 0.0499841i
117117 −15110.7 3577.88i −1.10386 0.261369i
118118 −10246.2 + 9765.41i −0.735869 + 0.701337i
119119 −22201.3 + 12817.9i −1.56778 + 0.905157i
120120 −5085.51 14595.2i −0.353161 1.01356i
121121 −9920.81 + 17183.3i −0.677605 + 1.17365i
122122 −8069.33 + 1955.69i −0.542148 + 0.131396i
123123 9436.53 23760.6i 0.623738 1.57053i
124124 −7703.74 14959.6i −0.501024 0.972916i
125125 14221.2i 0.910158i
126126 16866.3 9856.90i 1.06238 0.620868i
127127 1492.37i 0.0925269i −0.998929 0.0462634i 0.985269π-0.985269\pi
0.998929 0.0462634i 0.0147314π-0.0147314\pi
128128 −6829.42 + 14892.8i −0.416835 + 0.908982i
129129 −5014.29 6340.20i −0.301321 0.380999i
130130 4846.67 + 19997.7i 0.286785 + 1.18330i
131131 −3213.86 + 5566.56i −0.187277 + 0.324373i −0.944341 0.328967i 0.893299π-0.893299\pi
0.757065 + 0.653340i 0.226633π0.226633\pi
132132 2603.18 + 26613.1i 0.149402 + 1.52738i
133133 −5963.26 + 3442.89i −0.337117 + 0.194635i
134134 8487.04 8088.76i 0.472657 0.450477i
135135 −19487.4 1698.59i −1.06927 0.0932010i
136136 −17805.9 20576.9i −0.962690 1.11251i
137137 −10678.8 18496.2i −0.568959 0.985466i −0.996669 0.0815500i 0.974013π-0.974013\pi
0.427710 0.903916i 0.359320π-0.359320\pi
138138 7827.58 + 6123.71i 0.411026 + 0.321556i
139139 −10328.6 + 17889.6i −0.534578 + 0.925916i 0.464606 + 0.885518i 0.346196π0.346196\pi
−0.999184 + 0.0403986i 0.987137π0.987137\pi
140140 −21770.5 14004.8i −1.11074 0.714530i
141141 −2839.73 + 2245.86i −0.142836 + 0.112965i
142142 −3423.65 + 11650.3i −0.169790 + 0.577776i
143143 35599.6i 1.74090i
144144 13651.3 + 15608.4i 0.658339 + 0.752721i
145145 23485.9 1.11705
146146 21379.1 + 6282.65i 1.00296 + 0.294739i
147147 4100.67 10325.2i 0.189767 0.477822i
148148 −1684.07 + 2617.89i −0.0768839 + 0.119516i
149149 −4499.97 2598.06i −0.202692 0.117025i 0.395218 0.918587i 0.370669π-0.370669\pi
−0.597911 + 0.801563i 0.704002π0.704002\pi
150150 1279.25 + 3172.14i 0.0568555 + 0.140984i
151151 17647.9 10189.0i 0.773998 0.446868i −0.0603013 0.998180i 0.519206π-0.519206\pi
0.834299 + 0.551313i 0.185873π0.185873\pi
152152 −4782.66 5526.95i −0.207006 0.239221i
153153 −32990.5 + 9884.43i −1.40931 + 0.422249i
154154 30898.3 + 32419.7i 1.30285 + 1.36700i
155155 14109.7 + 24438.7i 0.587291 + 1.01722i
156156 −16065.0 22450.4i −0.660134 0.922519i
157157 −7737.56 4467.28i −0.313910 0.181236i 0.334765 0.942302i 0.391343π-0.391343\pi
−0.648675 + 0.761066i 0.724676π0.724676\pi
158158 41853.0 10143.5i 1.67653 0.406327i
159159 6086.55 + 41521.4i 0.240756 + 1.64240i
160160 10240.6 25497.4i 0.400024 0.995991i
161161 16645.2 0.642151
162162 25099.7 7664.93i 0.956399 0.292064i
163163 38000.8 1.43027 0.715134 0.698987i 0.246366π-0.246366\pi
0.715134 + 0.698987i 0.246366π0.246366\pi
164164 40407.3 20808.6i 1.50235 0.773668i
165165 −6504.21 44370.6i −0.238906 1.62977i
166166 −2651.94 10942.1i −0.0962381 0.397085i
167167 11942.4 + 6894.97i 0.428213 + 0.247229i 0.698585 0.715527i 0.253813π-0.253813\pi
−0.270372 + 0.962756i 0.587147π0.587147\pi
168168 34115.6 + 6501.57i 1.20874 + 0.230356i
169169 4095.92 + 7094.35i 0.143410 + 0.248393i
170170 31484.5 + 33034.8i 1.08943 + 1.14307i
171171 −8861.23 + 2654.96i −0.303041 + 0.0907956i
172172 690.178 14353.9i 0.0233294 0.485191i
173173 9687.10 5592.85i 0.323669 0.186871i −0.329358 0.944205i 0.606832π-0.606832\pi
0.653027 + 0.757335i 0.273499π0.273499\pi
174174 −29222.6 + 11784.8i −0.965207 + 0.389246i
175175 4961.10 + 2864.29i 0.161995 + 0.0935279i
176176 −27609.2 + 38698.6i −0.891310 + 1.24931i
177177 −11755.1 + 29598.7i −0.375215 + 0.944770i
178178 −7170.94 2107.31i −0.226327 0.0665104i
179179 7133.34 0.222632 0.111316 0.993785i 0.464493π-0.464493\pi
0.111316 + 0.993785i 0.464493π0.464493\pi
180180 −24124.9 25046.6i −0.744595 0.773042i
181181 26104.7i 0.796822i 0.917207 + 0.398411i 0.130438π0.130438\pi
−0.917207 + 0.398411i 0.869562π0.869562\pi
182182 −44360.4 13036.1i −1.33922 0.393556i
183183 −14652.9 + 11588.6i −0.437544 + 0.346041i
184184 3332.12 + 17351.1i 0.0984202 + 0.512498i
185185 2610.17 4520.94i 0.0762649 0.132095i
186186 −29819.0 23328.1i −0.861921 0.674301i
187187 −39476.7 68375.7i −1.12891 1.95532i
188188 −6429.00 309.125i −0.181898 0.00874619i
189189 25199.7 36013.7i 0.705459 1.00819i
190190 8456.73 + 8873.13i 0.234259 + 0.245793i
191191 −39532.9 + 22824.3i −1.08366 + 0.625649i −0.931880 0.362766i 0.881832π-0.881832\pi
−0.151776 + 0.988415i 0.548499π0.548499\pi
192192 52.1133 + 36864.0i 0.00141366 + 0.999999i
193193 −6039.50 + 10460.7i −0.162139 + 0.280832i −0.935635 0.352968i 0.885173π-0.885173\pi
0.773497 + 0.633800i 0.218506π0.218506\pi
194194 2366.59 + 9764.72i 0.0628810 + 0.259452i
195195 28719.2 + 36313.4i 0.755273 + 0.954987i
196196 17559.1 9042.44i 0.457078 0.235382i
197197 70123.2i 1.80688i −0.428714 0.903440i 0.641033π-0.641033\pi
0.428714 0.903440i 0.358967π-0.358967\pi
198198 30357.3 + 51945.0i 0.774342 + 1.32499i
199199 53477.1i 1.35040i −0.737636 0.675198i 0.764058π-0.764058\pi
0.737636 0.675198i 0.235942π-0.235942\pi
200200 −1992.63 + 5744.89i −0.0498158 + 0.143622i
201201 9736.85 24516.8i 0.241005 0.606837i
202202 21229.2 5145.12i 0.520271 0.126094i
203203 −26386.7 + 45703.1i −0.640314 + 1.10906i
204204 −55751.3 25305.6i −1.33966 0.608073i
205205 −66011.3 + 38111.6i −1.57076 + 0.906880i
206206 31108.3 + 32640.0i 0.733065 + 0.769159i
207207 21759.7 + 5152.19i 0.507822 + 0.120241i
208208 4708.73 48851.4i 0.108837 1.12915i
209209 −10603.4 18365.7i −0.242747 0.420450i
210210 −57671.6 8143.12i −1.30775 0.184651i
211211 16582.5 28721.8i 0.372465 0.645128i −0.617479 0.786587i 0.711846π-0.711846\pi
0.989944 + 0.141459i 0.0451793π0.0451793\pi
212212 −40362.3 + 62743.5i −0.898058 + 1.39604i
213213 3962.67 + 27032.7i 0.0873431 + 0.595840i
214214 18614.2 + 5470.14i 0.406460 + 0.119446i
215215 24100.2i 0.521367i
216216 42585.6 + 19059.1i 0.912757 + 0.408502i
217217 −63409.5 −1.34659
218218 19583.1 66639.0i 0.412068 1.40222i
219219 49606.9 7271.79i 1.03432 0.151619i
220220 43132.0 67048.9i 0.891157 1.38531i
221221 70590.6 + 40755.5i 1.44531 + 0.834453i
222222 −979.204 + 6934.97i −0.0198686 + 0.140714i
223223 −53609.6 + 30951.5i −1.07804 + 0.622404i −0.930366 0.366633i 0.880510π-0.880510\pi
−0.147669 + 0.989037i 0.547177π0.547177\pi
224224 38111.9 + 48574.6i 0.759564 + 0.968085i
225225 5598.88 + 5280.00i 0.110595 + 0.104296i
226226 38628.1 36815.4i 0.756287 0.720796i
227227 −121.231 209.978i −0.00235268 0.00407496i 0.864847 0.502036i 0.167416π-0.167416\pi
−0.867199 + 0.497961i 0.834082π0.834082\pi
228228 −14974.8 6797.06i −0.288065 0.130753i
229229 −10175.3 5874.70i −0.194033 0.112025i 0.399836 0.916587i 0.369067π-0.369067\pi
−0.593869 + 0.804562i 0.702400π0.702400\pi
230230 −6979.27 28797.0i −0.131933 0.544366i
231231 93651.8 + 37193.8i 1.75506 + 0.697023i
232232 −52923.6 18356.7i −0.983271 0.341050i
233233 −34752.2 −0.640134 −0.320067 0.947395i 0.603705π-0.603705\pi
−0.320067 + 0.947395i 0.603705π0.603705\pi
234234 −53955.7 30772.6i −0.985384 0.561994i
235235 10794.3 0.195460
236236 −50335.5 + 25921.3i −0.903755 + 0.465408i
237237 75999.8 60106.1i 1.35306 1.07009i
238238 −99658.3 + 24153.3i −1.75938 + 0.426405i
239239 −41098.0 23728.0i −0.719491 0.415398i 0.0950746 0.995470i 0.469691π-0.469691\pi
−0.814565 + 0.580072i 0.803024π0.803024\pi
240240 −3056.51 61747.6i −0.0530644 1.07201i
241241 34530.8 + 59809.0i 0.594527 + 1.02975i 0.993613 + 0.112838i 0.0359942π0.0359942\pi
−0.399086 + 0.916914i 0.630672π0.630672\pi
242242 −57452.4 + 54756.3i −0.981020 + 0.934983i
243243 44090.0 39279.2i 0.746667 0.665198i
244244 −33173.5 1595.08i −0.557200 0.0267918i
245245 −28685.4 + 16561.5i −0.477891 + 0.275911i
246246 63011.6 80544.2i 1.04124 1.33096i
247247 18960.6 + 10946.9i 0.310784 + 0.179431i
248248 −12693.6 66098.8i −0.206387 1.07471i
249249 −15714.2 19869.5i −0.253451 0.320470i
250250 −16038.5 + 54577.1i −0.256616 + 0.873233i
251251 −59187.9 −0.939475 −0.469738 0.882806i 0.655652π-0.655652\pi
−0.469738 + 0.882806i 0.655652π0.655652\pi
252252 75844.7 18806.4i 1.19433 0.296145i
253253 51263.9i 0.800887i
254254 1683.07 5727.28i 0.0260876 0.0887731i
255255 95428.8 + 37899.5i 1.46757 + 0.582846i
256256 −43005.3 + 49452.1i −0.656208 + 0.754580i
257257 26280.3 45518.9i 0.397891 0.689168i −0.595574 0.803300i 0.703075π-0.703075\pi
0.993466 + 0.114132i 0.0364087π0.0364087\pi
258258 −12093.0 29987.0i −0.181676 0.450498i
259259 5865.11 + 10158.7i 0.0874332 + 0.151439i
260260 −3952.98 + 82211.6i −0.0584761 + 1.21615i
261261 −48640.8 + 51578.5i −0.714035 + 0.757160i
262262 −18611.8 + 17738.4i −0.271135 + 0.258411i
263263 37110.2 21425.6i 0.536515 0.309757i −0.207150 0.978309i 0.566419π-0.566419\pi
0.743665 + 0.668552i 0.233086π0.233086\pi
264264 −20023.6 + 105069.i −0.287299 + 1.50754i
265265 62558.4 108354.i 0.890828 1.54296i
266266 −26768.2 + 6487.57i −0.378317 + 0.0916893i
267267 −16639.0 + 2439.09i −0.233403 + 0.0342141i
268268 41693.3 21470.8i 0.580492 0.298937i
269269 10584.0i 0.146267i −0.997322 0.0731333i 0.976700π-0.976700\pi
0.997322 0.0731333i 0.0232998π-0.0232998\pi
270270 −72871.5 28496.3i −0.999608 0.390896i
271271 93339.2i 1.27094i 0.772125 + 0.635471i 0.219194π0.219194\pi
−0.772125 + 0.635471i 0.780806π0.780806\pi
272272 −45127.7 99049.7i −0.609966 1.33880i
273273 −102932. + 15088.6i −1.38109 + 0.202452i
274274 −20122.4 83026.7i −0.268028 1.10590i
275275 −8821.46 + 15279.2i −0.116647 + 0.202039i
276276 23133.9 + 32328.9i 0.303689 + 0.424398i
277277 −20273.5 + 11704.9i −0.264222 + 0.152549i −0.626259 0.779615i 0.715415π-0.715415\pi
0.362037 + 0.932164i 0.382081π0.382081\pi
278278 −59813.9 + 57007.0i −0.773949 + 0.737630i
279279 −82892.9 19627.2i −1.06490 0.252144i
280280 −67754.7 78298.9i −0.864219 0.998711i
281281 −3736.40 6471.63i −0.0473195 0.0819598i 0.841396 0.540420i 0.181735π-0.181735\pi
−0.888715 + 0.458460i 0.848401π0.848401\pi
282282 −13430.9 + 5416.38i −0.168891 + 0.0681100i
283283 −45059.8 + 78045.9i −0.562622 + 0.974490i 0.434645 + 0.900602i 0.356874π0.356874\pi
−0.997267 + 0.0738877i 0.976459π0.976459\pi
284284 −26278.0 + 40849.4i −0.325804 + 0.506464i
285285 25632.1 + 10179.8i 0.315569 + 0.125328i
286286 40148.8 136621.i 0.490840 1.67027i
287287 171276.i 2.07937i
288288 34787.0 + 75296.6i 0.419403 + 0.907800i
289289 97255.3 1.16444
290290 90132.3 + 26487.1i 1.07173 + 0.314947i
291291 14023.4 + 17731.5i 0.165602 + 0.209392i
292292 74961.5 + 48222.1i 0.879170 + 0.565562i
293293 118256. + 68274.9i 1.37748 + 0.795290i 0.991856 0.127365i 0.0406518π-0.0406518\pi
0.385627 + 0.922655i 0.373985π0.373985\pi
294294 27381.9 35000.7i 0.316788 0.404932i
295295 82230.6 47475.8i 0.944907 0.545543i
296296 −9415.39 + 8147.46i −0.107462 + 0.0929905i
297297 110915. + 77610.2i 1.25741 + 0.879844i
298298 −14339.6 15045.6i −0.161475 0.169425i
299299 −26462.3 45834.0i −0.295995 0.512679i
300300 1331.91 + 13616.5i 0.0147990 + 0.151294i
301301 −46898.5 27076.9i −0.517638 0.298858i
302302 79218.8 19199.6i 0.868589 0.210512i
303303 38549.5 30487.7i 0.419888 0.332078i
304304 −12121.3 26604.7i −0.131160 0.287880i
305305 55698.2 0.598745
306306 −137756. + 727.487i −1.47118 + 0.00776931i
307307 −168794. −1.79094 −0.895468 0.445126i 0.853159π-0.853159\pi
−0.895468 + 0.445126i 0.853159π0.853159\pi
308308 82016.5 + 159264.i 0.864569 + 1.67887i
309309 94288.5 + 37446.7i 0.987510 + 0.392190i
310310 26587.4 + 109701.i 0.276664 + 1.14153i
311311 −68907.1 39783.5i −0.712431 0.411323i 0.0995292 0.995035i 0.468266π-0.468266\pi
−0.811961 + 0.583712i 0.801600π0.801600\pi
312312 −36333.8 104276.i −0.373252 1.07122i
313313 93373.0 + 161727.i 0.953087 + 1.65080i 0.738686 + 0.674049i 0.235446π0.235446\pi
0.214401 + 0.976746i 0.431220π0.431220\pi
314314 −24656.4 25870.5i −0.250075 0.262389i
315315 −125535. + 37612.1i −1.26515 + 0.379059i
316316 172060. + 8273.15i 1.72308 + 0.0828508i
317317 −95810.6 + 55316.3i −0.953443 + 0.550471i −0.894149 0.447770i 0.852218π-0.852218\pi
−0.0592945 + 0.998241i 0.518885π0.518885\pi
318318 −23468.8 + 166212.i −0.232079 + 1.64364i
319319 −140757. 81265.8i −1.38321 0.798595i
320320 68056.2 86302.5i 0.664611 0.842798i
321321 43191.4 6331.36i 0.419167 0.0614450i
322322 63879.6 + 18772.2i 0.616099 + 0.181052i
323323 48556.4 0.465417
324324 104970. 1108.72i 0.999944 0.0105617i
325325 18214.4i 0.172444i
326326 145836. + 42856.8i 1.37224 + 0.403259i
327327 −22666.3 154626.i −0.211975 1.44606i
328328 178539. 34286.8i 1.65954 0.318698i
329329 −12127.5 + 21005.5i −0.112042 + 0.194062i
330330 25079.2 177617.i 0.230296 1.63101i
331331 −35525.1 61531.2i −0.324249 0.561616i 0.657111 0.753794i 0.271778π-0.271778\pi
−0.981360 + 0.192178i 0.938445π0.938445\pi
332332 2162.94 44983.5i 0.0196231 0.408110i
333333 4522.83 + 15095.5i 0.0407870 + 0.136131i
334334 38055.7 + 39929.5i 0.341135 + 0.357932i
335335 −68112.2 + 39324.6i −0.606925 + 0.350408i
336336 123594. + 63426.3i 1.09476 + 0.561812i
337337 −3370.32 + 5837.57i −0.0296764 + 0.0514011i −0.880482 0.474079i 0.842781π-0.842781\pi
0.850806 + 0.525480i 0.176114π0.176114\pi
338338 7718.10 + 31845.5i 0.0675581 + 0.278749i
339339 44316.6 111586.i 0.385626 0.970984i
340340 83572.7 + 162286.i 0.722947 + 1.40386i
341341 195289.i 1.67946i
342342 −37001.1 + 195.403i −0.316346 + 0.00167062i
343343 70338.5i 0.597868i
344344 18836.8 54307.9i 0.159181 0.458929i
345345 −41356.1 52291.7i −0.347457 0.439334i
346346 43483.9 10538.8i 0.363225 0.0880318i
347347 43353.9 75091.2i 0.360055 0.623634i −0.627914 0.778283i 0.716091π-0.716091\pi
0.987970 + 0.154648i 0.0494245π0.0494245\pi
348348 −125439. + 12269.9i −1.03580 + 0.101317i
349349 −108745. + 62783.7i −0.892805 + 0.515461i −0.874859 0.484378i 0.839046π-0.839046\pi
−0.0179461 + 0.999839i 0.505713π0.505713\pi
350350 15809.0 + 16587.4i 0.129053 + 0.135408i
351351 −139229. 12135.7i −1.13010 0.0985031i
352352 −149600. + 117377.i −1.20739 + 0.947323i
353353 24176.0 + 41874.1i 0.194015 + 0.336044i 0.946577 0.322477i 0.104516π-0.104516\pi
−0.752562 + 0.658521i 0.771182π0.771182\pi
354354 −78493.9 + 100334.i −0.626368 + 0.800650i
355355 40728.9 70544.5i 0.323181 0.559766i
356356 −25143.5 16174.6i −0.198392 0.127624i
357357 −180967. + 143122.i −1.41992 + 1.12297i
358358 27375.8 + 8044.89i 0.213600 + 0.0627702i
359359 59745.2i 0.463568i −0.972767 0.231784i 0.925544π-0.925544\pi
0.972767 0.231784i 0.0744563π-0.0744563\pi
360360 −64337.4 123329.i −0.496431 0.951616i
361361 −117279. −0.899922
362362 −29440.5 + 100183.i −0.224661 + 0.764495i
363363 −65913.0 + 165965.i −0.500216 + 1.25951i
364364 −155541. 100058.i −1.17393 0.755179i
365365 −129454. 74740.4i −0.971696 0.561009i
366366 −69303.2 + 27948.4i −0.517358 + 0.208639i
367367 145654. 84093.5i 1.08141 0.624353i 0.150135 0.988666i 0.452029π-0.452029\pi
0.931277 + 0.364312i 0.118696π0.118696\pi
368368 −6780.64 + 70346.7i −0.0500697 + 0.519455i
369369 53014.9 223902.i 0.389355 1.64439i
370370 15115.7 14406.4i 0.110415 0.105233i
371371 140570. + 243475.i 1.02128 + 1.76891i
372372 −88127.9 123156.i −0.636836 0.889961i
373373 233844. + 135010.i 1.68077 + 0.970393i 0.961150 + 0.276026i 0.0890175π0.0890175\pi
0.719620 + 0.694368i 0.244316π0.244316\pi
374374 −74387.4 306928.i −0.531810 2.19429i
375375 18563.6 + 126638.i 0.132008 + 0.900534i
376376 −24324.1 8436.87i −0.172052 0.0596768i
377377 167797. 1.18059
378378 137325. 109790.i 0.961095 0.768389i
379379 110475. 0.769102 0.384551 0.923104i 0.374356π-0.374356\pi
0.384551 + 0.923104i 0.374356π0.374356\pi
380380 22447.6 + 43590.0i 0.155454 + 0.301870i
381381 −1948.05 13289.3i −0.0134199 0.0915485i
382382 −177457. + 43008.7i −1.21609 + 0.294733i
383383 174715. + 100872.i 1.19106 + 0.687659i 0.958547 0.284934i 0.0919718π-0.0919718\pi
0.232513 + 0.972593i 0.425305π0.425305\pi
384384 −41374.7 + 141532.i −0.280590 + 0.959828i
385385 −150216. 260182.i −1.01343 1.75532i
386386 −34975.4 + 33334.1i −0.234740 + 0.223725i
387387 −52927.6 49913.1i −0.353395 0.333267i
388388 −1930.21 + 40143.3i −0.0128216 + 0.266655i
389389 −28286.6 + 16331.2i −0.186931 + 0.107925i −0.590545 0.807005i 0.701087π-0.701087\pi
0.403614 + 0.914929i 0.367754π0.367754\pi
390390 69262.7 + 171750.i 0.455376 + 1.12919i
391391 −101651. 58688.5i −0.664905 0.383883i
392392 77584.9 14899.4i 0.504900 0.0969610i
393393 −21352.6 + 53764.5i −0.138250 + 0.348105i
394394 79084.0 269113.i 0.509444 1.73358i
395395 −288888. −1.85155
396396 57920.1 + 233587.i 0.369351 + 1.48956i
397397 157999.i 1.00247i −0.865310 0.501237i 0.832878π-0.832878\pi
0.865310 0.501237i 0.167122π-0.167122\pi
398398 60310.7 205230.i 0.380740 1.29561i
399399 −48607.7 + 38442.5i −0.305323 + 0.241471i
400400 −14126.2 + 19800.0i −0.0882886 + 0.123750i
401401 −71882.8 + 124505.i −0.447029 + 0.774277i −0.998191 0.0601210i 0.980851π-0.980851\pi
0.551162 + 0.834398i 0.314185π0.314185\pi
402402 65017.0 83107.6i 0.402323 0.514267i
403403 100808. + 174604.i 0.620702 + 1.07509i
404404 87274.2 + 4196.40i 0.534716 + 0.0257107i
405405 −175749. + 10312.1i −1.07148 + 0.0628690i
406406 −152808. + 145637.i −0.927031 + 0.883527i
407407 −31286.7 + 18063.4i −0.188873 + 0.109046i
408408 −185419. 159991.i −1.11387 0.961116i
409409 −6867.24 + 11894.4i −0.0410521 + 0.0711044i −0.885821 0.464026i 0.846404π-0.846404\pi
0.844769 + 0.535131i 0.179738π0.179738\pi
410410 −296315. + 71815.2i −1.76273 + 0.427217i
411411 −119237. 150766.i −0.705873 0.892525i
412412 82574.1 + 160347.i 0.486462 + 0.944640i
413413 213359.i 1.25086i
414414 77696.9 + 44312.9i 0.453318 + 0.258541i
415415 75527.3i 0.438538i
416416 73164.8 182168.i 0.422781 1.05265i
417417 −68622.2 + 172787.i −0.394632 + 0.993660i
418418 −19980.4 82440.7i −0.114354 0.471834i
419419 135489. 234673.i 0.771748 1.33671i −0.164857 0.986318i 0.552716π-0.552716\pi
0.936604 0.350389i 0.113951π-0.113951\pi
420420 −212144. 96292.3i −1.20263 0.545875i
421421 206716. 119347.i 1.16630 0.673362i 0.213493 0.976945i 0.431516π-0.431516\pi
0.952805 + 0.303582i 0.0981828π0.0981828\pi
422422 96031.0 91524.5i 0.539246 0.513940i
423423 −22355.7 + 23705.8i −0.124942 + 0.132487i
424424 −225661. + 195272.i −1.25523 + 1.08619i
425425 −20198.1 34984.2i −0.111824 0.193684i
426426 −15279.4 + 108213.i −0.0841953 + 0.596293i
427427 −62577.6 + 108388.i −0.343213 + 0.594462i
428428 65267.1 + 41985.7i 0.356292 + 0.229200i
429429 −46469.8 317009.i −0.252497 1.72249i
430430 −27179.9 + 92489.8i −0.146998 + 0.500215i
431431 208255.i 1.12109i 0.828124 + 0.560545i 0.189408π0.189408\pi
−0.828124 + 0.560545i 0.810592π0.810592\pi
432432 141937. + 121171.i 0.760551 + 0.649278i
433433 −275527. −1.46957 −0.734783 0.678303i 0.762716π-0.762716\pi
−0.734783 + 0.678303i 0.762716π0.762716\pi
434434 −243348. 71512.4i −1.29196 0.379666i
435435 209138. 30657.2i 1.10523 0.162014i
436436 150309. 233656.i 0.790701 1.22915i
437437 −27303.5 15763.7i −0.142974 0.0825458i
438438 198578. + 28038.9i 1.03510 + 0.146155i
439439 5755.89 3323.16i 0.0298664 0.0172434i −0.484992 0.874518i 0.661178π-0.661178\pi
0.514859 + 0.857275i 0.327844π0.327844\pi
440440 241145. 208671.i 1.24559 1.07785i
441441 23037.8 97297.4i 0.118458 0.500293i
442442 224943. + 236019.i 1.15141 + 1.20810i
443443 −122953. 212960.i −0.626514 1.08515i −0.988246 0.152872i 0.951148π-0.951148\pi
0.361732 0.932282i 0.382186π-0.382186\pi
444444 −11579.1 + 25510.2i −0.0587365 + 0.129404i
445445 43421.3 + 25069.3i 0.219272 + 0.126597i
446446 −240645. + 58323.1i −1.20978 + 0.293205i
447447 −43462.9 17261.3i −0.217522 0.0863890i
448448 91481.0 + 229398.i 0.455801 + 1.14297i
449449 −282931. −1.40342 −0.701711 0.712462i 0.747580π-0.747580\pi
−0.701711 + 0.712462i 0.747580π0.747580\pi
450450 15532.2 + 26577.5i 0.0767024 + 0.131247i
451451 527495. 2.59338
452452 189764. 97722.9i 0.928830 0.478321i
453453 143852. 113768.i 0.701000 0.554402i
454454 −228.440 942.561i −0.00110831 0.00457296i
455455 268610. + 155082.i 1.29748 + 0.749099i
456456 −49803.4 42973.6i −0.239513 0.206667i
457457 108539. + 187995.i 0.519702 + 0.900150i 0.999738 + 0.0229008i 0.00729020π0.00729020\pi
−0.480036 + 0.877249i 0.659376π0.659376\pi
458458 −32424.5 34021.0i −0.154576 0.162187i
459459 −280872. + 131083.i −1.33316 + 0.622188i
460460 5692.35 118386.i 0.0269015 0.559479i
461461 86601.0 49999.1i 0.407494 0.235267i −0.282219 0.959350i 0.591070π-0.591070\pi
0.689712 + 0.724084i 0.257737π0.257737\pi
462462 317463. + 248359.i 1.48734 + 1.16358i
463463 6135.09 + 3542.10i 0.0286193 + 0.0165234i 0.514241 0.857645i 0.328074π-0.328074\pi
−0.485622 + 0.874169i 0.661407π0.661407\pi
464464 −182403. 130134.i −0.847222 0.604444i
465465 157545. + 199204.i 0.728617 + 0.921282i
466466 −133369. 39193.1i −0.614164 0.180484i
467467 429771. 1.97062 0.985312 0.170765i 0.0546240π-0.0546240\pi
0.985312 + 0.170765i 0.0546240π0.0546240\pi
468468 −172362. 178947.i −0.786955 0.817020i
469469 176727.i 0.803445i
470470 41425.5 + 12173.7i 0.187530 + 0.0551093i
471471 −74733.0 29680.2i −0.336876 0.133790i
472472 −222407. + 42711.2i −0.998309 + 0.191716i
473473 83391.4 144438.i 0.372734 0.645594i
474474 359453. 144959.i 1.59987 0.645191i
475475 −5425.21 9396.74i −0.0240453 0.0416476i
476476 −409700. 19699.6i −1.80822 0.0869449i
477477 108399. + 361796.i 0.476420 + 1.59011i
478478 −130963. 137411.i −0.573181 0.601403i
479479 49730.6 28712.0i 0.216747 0.125139i −0.387696 0.921787i 0.626729π-0.626729\pi
0.604443 + 0.796648i 0.293396π0.293396\pi
480480 57908.1 240417.i 0.251337 1.04348i
481481 18648.5 32300.2i 0.0806036 0.139609i
482482 65067.6 + 268474.i 0.280073 + 1.15560i
483483 148223. 21727.7i 0.635361 0.0931365i
484484 −282240. + 145345.i −1.20483 + 0.620455i
485485 67400.6i 0.286537i
486486 213504. 101019.i 0.903925 0.427690i
487487 265572.i 1.11976i 0.828574 + 0.559879i 0.189152π0.189152\pi
−0.828574 + 0.559879i 0.810848π0.810848\pi
488488 −125512. 43534.0i −0.527040 0.182805i
489489 338391. 49604.1i 1.41514 0.207444i
490490 −128765. + 31207.5i −0.536295 + 0.129977i
491491 −77229.5 + 133765.i −0.320347 + 0.554857i −0.980560 0.196222i 0.937133π-0.937133\pi
0.660213 + 0.751079i 0.270466π0.270466\pi
492492 332658. 238042.i 1.37426 0.983386i
493493 322284. 186071.i 1.32601 0.765570i
494494 60419.7 + 63394.7i 0.247585 + 0.259776i
495495 −115838. 386623.i −0.472759 1.57789i
496496 25830.7 267984.i 0.104996 1.08930i
497497 91518.7 + 158515.i 0.370508 + 0.641738i
498498 −37898.2 93975.7i −0.152813 0.378928i
499499 −98724.4 + 170996.i −0.396482 + 0.686727i −0.993289 0.115658i 0.963102π-0.963102\pi
0.596807 + 0.802385i 0.296436π0.296436\pi
500500 −123103. + 191364.i −0.492410 + 0.765454i
501501 115346. + 45809.6i 0.459543 + 0.182507i
502502 −227147. 66751.3i −0.901361 0.264882i
503503 343592.i 1.35802i 0.734127 + 0.679012i 0.237592π0.237592\pi
−0.734127 + 0.679012i 0.762408π0.762408\pi
504504 312280. + 13362.8i 1.22937 + 0.0526063i
505505 −146533. −0.574584
506506 −57814.8 + 196737.i −0.225807 + 0.768395i
507507 45734.1 + 57827.4i 0.177920 + 0.224966i
508508 12918.3 20081.6i 0.0500585 0.0778162i
509509 73009.5 + 42152.1i 0.281802 + 0.162698i 0.634239 0.773137i 0.281314π-0.281314\pi
−0.352437 + 0.935836i 0.614647π0.614647\pi
510510 323486. + 253071.i 1.24370 + 0.972976i
511511 290887. 167943.i 1.11399 0.643163i
512512 −220814. + 141283.i −0.842337 + 0.538951i
513513 −75442.1 + 35208.9i −0.286668 + 0.133788i
514514 152192. 145050.i 0.576058 0.549025i
515515 −151237. 261951.i −0.570222 0.987654i
516516 −12590.9 128720.i −0.0472885 0.483444i
517517 −64692.7 37350.4i −0.242033 0.139738i
518518 11051.8 + 45600.7i 0.0411884 + 0.169946i
519519 78961.4 62448.4i 0.293143 0.231839i
520520 −107888. + 311047.i −0.398993 + 1.15032i
521521 −397536. −1.46454 −0.732270 0.681015i 0.761539π-0.761539\pi
−0.732270 + 0.681015i 0.761539π0.761539\pi
522522 −244839. + 143087.i −0.898546 + 0.525122i
523523 −286663. −1.04802 −0.524008 0.851714i 0.675564π-0.675564\pi
−0.524008 + 0.851714i 0.675564π0.675564\pi
524524 −91431.9 + 47084.8i −0.332993 + 0.171482i
525525 47916.7 + 19030.1i 0.173847 + 0.0690435i
526526 166582. 40373.0i 0.602084 0.145922i
527527 387239. + 223572.i 1.39430 + 0.805002i
528528 −195341. + 380644.i −0.700688 + 1.36537i
529529 −101814. 176348.i −0.363830 0.630171i
530530 362282. 345281.i 1.28972 1.22920i
531531 −66040.9 + 278916.i −0.234220 + 0.989200i
532532 −110045. 5291.31i −0.388820 0.0186956i
533533 −471622. + 272291.i −1.66012 + 0.958472i
534534 −66606.8 9404.74i −0.233580 0.0329810i
535535 −112712. 65074.5i −0.393789 0.227354i
536536 184222. 35378.0i 0.641226 0.123141i
537537 63521.2 9311.47i 0.220278 0.0322901i
538538 11936.5 40618.4i 0.0412394 0.140333i
539539 229225. 0.789012
540540 −247523. 191544.i −0.848843 0.656873i
541541 412153.i 1.40820i −0.710101 0.704100i 0.751351π-0.751351\pi
0.710101 0.704100i 0.248649π-0.248649\pi
542542 −105267. + 358210.i −0.358338 + 1.21938i
543543 34075.6 + 232458.i 0.115570 + 0.788397i
544544 −61480.7 431020.i −0.207750 1.45646i
545545 −232967. + 403511.i −0.784335 + 1.35851i
546546 −412039. 58179.1i −1.38214 0.195156i
547547 −168911. 292563.i −0.564527 0.977789i −0.997094 0.0761869i 0.975725π-0.975725\pi
0.432567 0.901602i 0.357608π-0.357608\pi
548548 16412.0 341327.i 0.0546514 1.13660i
549549 −115355. + 122322.i −0.382728 + 0.405843i
550550 −51086.0 + 48688.7i −0.168879 + 0.160954i
551551 86565.4 49978.6i 0.285129 0.164619i
552552 52321.1 + 150159.i 0.171711 + 0.492804i
553553 324569. 562171.i 1.06135 1.83831i
554554 −91004.7 + 22056.0i −0.296513 + 0.0718633i
555555 17341.7 43665.4i 0.0562997 0.141759i
556556 −293841. + 151320.i −0.950522 + 0.489492i
557557 251395.i 0.810302i 0.914250 + 0.405151i 0.132781π0.132781\pi
−0.914250 + 0.405151i 0.867219π0.867219\pi
558558 −295985. 168809.i −0.950606 0.542160i
559559 172186.i 0.551027i
560560 −171719. 376902.i −0.547574 1.20186i
561561 −440787. 557343.i −1.40057 1.77091i
562562 −7040.63 29050.2i −0.0222915 0.0919763i
563563 −32923.4 + 57025.0i −0.103870 + 0.179907i −0.913276 0.407342i 0.866456π-0.866456\pi
0.809406 + 0.587249i 0.199789π0.199789\pi
564564 −57652.7 + 5639.34i −0.181243 + 0.0177284i
565565 −310007. + 178983.i −0.971125 + 0.560679i
566566 −260946. + 248701.i −0.814550 + 0.776326i
567567 177389. 353590.i 0.551773 1.09985i
568568 −146917. + 127132.i −0.455382 + 0.394057i
569569 59792.5 + 103564.i 0.184681 + 0.319877i 0.943469 0.331461i 0.107541π-0.107541\pi
−0.758788 + 0.651338i 0.774208π0.774208\pi
570570 86888.3 + 67974.8i 0.267431 + 0.209218i
571571 14325.3 24812.2i 0.0439372 0.0761014i −0.843220 0.537568i 0.819343π-0.819343\pi
0.887158 + 0.461466i 0.152677π0.152677\pi
572572 308160. 479036.i 0.941854 1.46412i
573573 −322240. + 254851.i −0.981454 + 0.776205i
574574 193162. 657308.i 0.586271 1.99501i
575575 26229.0i 0.0793317i
576576 48584.2 + 328199.i 0.146437 + 0.989220i
577577 −101252. −0.304126 −0.152063 0.988371i 0.548592π-0.548592\pi
−0.152063 + 0.988371i 0.548592π0.548592\pi
578578 373239. + 109683.i 1.11720 + 0.328310i
579579 −40125.9 + 101035.i −0.119693 + 0.301379i
580580 316031. + 203300.i 0.939450 + 0.604340i
581581 −146975. 84855.8i −0.435401 0.251379i
582582 33820.4 + 83864.0i 0.0998465 + 0.247588i
583583 −749854. + 432929.i −2.20617 + 1.27374i
584584 233297. + 269604.i 0.684043 + 0.790496i
585585 303142. + 285876.i 0.885796 + 0.835346i
586586 376832. + 395387.i 1.09737 + 1.15140i
587587 −36792.0 63725.7i −0.106777 0.184943i 0.807686 0.589613i 0.200720π-0.200720\pi
−0.914463 + 0.404670i 0.867386π0.867386\pi
588588 144557. 103442.i 0.418105 0.299187i
589589 104012. + 60051.5i 0.299815 + 0.173098i
590590 369121. 89460.5i 1.06039 0.256997i
591591 −91535.0 624436.i −0.262067 1.78778i
592592 −45322.2 + 20649.1i −0.129321 + 0.0589194i
593593 295880. 0.841407 0.420704 0.907198i 0.361783π-0.361783\pi
0.420704 + 0.907198i 0.361783π0.361783\pi
594594 338133. + 422935.i 0.958329 + 1.19867i
595595 687887. 1.94305
596596 −38063.1 73913.0i −0.107155 0.208079i
597597 −69806.0 476204.i −0.195859 1.33612i
598598 −49863.9 205742.i −0.139439 0.575335i
599599 −528443. 305097.i −1.47280 0.850323i −0.473271 0.880917i 0.656927π-0.656927\pi
−0.999532 + 0.0305942i 0.990260π0.990260\pi
600600 −10245.0 + 53758.4i −0.0284583 + 0.149329i
601601 56375.3 + 97644.9i 0.156077 + 0.270334i 0.933451 0.358705i 0.116782π-0.116782\pi
−0.777373 + 0.629039i 0.783448π0.783448\pi
602602 −149446. 156805.i −0.412375 0.432680i
603603 54702.2 231028.i 0.150442 0.635375i
604604 325673. + 15659.3i 0.892704 + 0.0429239i
605605 461081. 266205.i 1.25970 0.727287i
606606 182326. 73527.8i 0.496482 0.200220i
607607 −121995. 70434.1i −0.331105 0.191164i 0.325226 0.945636i 0.394560π-0.394560\pi
−0.656332 + 0.754472i 0.727893π0.727893\pi
608608 −16513.7 115772.i −0.0446722 0.313181i
609609 −175311. + 441422.i −0.472687 + 1.19020i
610610 213754. + 62815.7i 0.574454 + 0.168814i
611611 77120.6 0.206580
612612 −529488. 152567.i −1.41369 0.407341i
613613 471219.i 1.25401i −0.779014 0.627006i 0.784280π-0.784280\pi
0.779014 0.627006i 0.215720π-0.215720\pi
614614 −647784. 190363.i −1.71828 0.504948i
615615 −538071. + 425545.i −1.42262 + 1.12511i
616616 135140. + 703709.i 0.356143 + 1.85452i
617617 −189422. + 328089.i −0.497577 + 0.861828i −0.999996 0.00279589i 0.999110π-0.999110\pi
0.502419 + 0.864624i 0.332443π0.332443\pi
618618 319621. + 250047.i 0.836871 + 0.654704i
619619 90319.8 + 156439.i 0.235723 + 0.408284i 0.959483 0.281768i 0.0909209π-0.0909209\pi
−0.723760 + 0.690052i 0.757588π0.757588\pi
620620 −21684.9 + 450988.i −0.0564123 + 1.17323i
621621 200491. + 17475.5i 0.519892 + 0.0453156i
622622 −219579. 230391.i −0.567557 0.595503i
623623 −97568.6 + 56331.3i −0.251382 + 0.145135i
624624 −21837.5 441160.i −0.0560832 1.13299i
625625 220490. 381899.i 0.564454 0.977663i
626626 175946. + 725967.i 0.448984 + 1.85254i
627627 −118395. 149702.i −0.301161 0.380797i
628628 −65448.1 127091.i −0.165950 0.322252i
629629 82717.9i 0.209073i
630630 −524186. + 2768.22i −1.32070 + 0.00697461i
631631 115341.i 0.289685i −0.989455 0.144842i 0.953733π-0.953733\pi
0.989455 0.144842i 0.0462675π-0.0462675\pi
632632 650987. + 225797.i 1.62981 + 0.565306i
633633 110173. 277408.i 0.274958 0.692328i
634634 −430079. + 104234.i −1.06997 + 0.259318i
635635 −20022.3 + 34679.7i −0.0496555 + 0.0860058i
636636 −277518. + 611407.i −0.686084 + 1.51153i
637637 −204945. + 118325.i −0.505078 + 0.291607i
638638 −448534. 470619.i −1.10193 1.15619i
639639 70573.9 + 235549.i 0.172839 + 0.576871i
640640 358511. 254452.i 0.875272 0.621221i
641641 71144.9 + 123227.i 0.173152 + 0.299908i 0.939520 0.342493i 0.111271π-0.111271\pi
−0.766368 + 0.642402i 0.777938π0.777938\pi
642642 172897. + 24412.7i 0.419486 + 0.0592306i
643643 −150535. + 260734.i −0.364095 + 0.630631i −0.988630 0.150365i 0.951955π-0.951955\pi
0.624535 + 0.780996i 0.285288π0.285288\pi
644644 223981. + 144085.i 0.540057 + 0.347414i
645645 31459.1 + 214608.i 0.0756182 + 0.515854i
646646 186346. + 54761.3i 0.446535 + 0.131223i
647647 562947.i 1.34480i −0.740186 0.672402i 0.765263π-0.765263\pi
0.740186 0.672402i 0.234737π-0.234737\pi
648648 404096. + 114129.i 0.962354 + 0.271798i
649649 −657103. −1.56007
650650 20542.0 69902.0i 0.0486201 0.165448i
651651 −564651. + 82771.3i −1.33235 + 0.195307i
652652 511346. + 328945.i 1.20287 + 0.773798i
653653 −658714. 380308.i −1.54479 0.891887i −0.998526 0.0542753i 0.982715π-0.982715\pi
−0.546267 0.837611i 0.683952π-0.683952\pi
654654 87397.6 618972.i 0.204336 1.44716i
655655 149368. 86237.4i 0.348156 0.201008i
656656 723853. + 69771.3i 1.68206 + 0.162132i
657657 432249. 129508.i 1.00139 0.300031i
658658 −70231.7 + 66935.9i −0.162211 + 0.154599i
659659 −207982. 360235.i −0.478911 0.829497i 0.520797 0.853681i 0.325635π-0.325635\pi
−0.999708 + 0.0241831i 0.992302π0.992302\pi
660660 296561. 653362.i 0.680811 1.49991i
661661 317798. + 183481.i 0.727358 + 0.419940i 0.817455 0.575993i 0.195384π-0.195384\pi
−0.0900969 + 0.995933i 0.528718π0.528718\pi
662662 −66941.2 276204.i −0.152749 0.630253i
663663 681798. + 270776.i 1.55106 + 0.616003i
664664 59032.5 170195.i 0.133892 0.386020i
665665 184766. 0.417810
666666 332.877 + 63033.0i 0.000750473 + 0.142108i
667667 −241629. −0.543123
668668 101015. + 196157.i 0.226378 + 0.439593i
669669 −436982. + 345597.i −0.976364 + 0.772179i
670670 −305745. + 74100.8i −0.681099 + 0.165072i
671671 −333813. 192727.i −0.741409 0.428053i
672672 402787. + 382800.i 0.891942 + 0.847682i
673673 208572. + 361257.i 0.460496 + 0.797602i 0.998986 0.0450300i 0.0143383π-0.0143383\pi
−0.538490 + 0.842632i 0.681005π0.681005\pi
674674 −19517.9 + 18602.0i −0.0429648 + 0.0409486i
675675 56749.3 + 39709.0i 0.124553 + 0.0871528i
676676 −6294.95 + 130918.i −0.0137752 + 0.286488i
677677 270633. 156250.i 0.590477 0.340912i −0.174809 0.984602i 0.555931π-0.555931\pi
0.765286 + 0.643690i 0.222597π0.222597\pi
678678 295920. 378258.i 0.643747 0.822865i
679679 131160. + 75725.3i 0.284487 + 0.164249i
680680 137705. + 717061.i 0.297804 + 1.55074i
681681 −1353.64 1711.57i −0.00291882 0.00369064i
682682 220244. 749464.i 0.473517 1.61132i
683683 −140348. −0.300860 −0.150430 0.988621i 0.548066π-0.548066\pi
−0.150430 + 0.988621i 0.548066π0.548066\pi
684684 −142220. 40979.5i −0.303983 0.0875899i
685685 573088.i 1.22135i
686686 −79326.8 + 269940.i −0.168567 + 0.573612i
687687 −98277.7 39031.0i −0.208229 0.0826982i
688688 133538. 187174.i 0.282117 0.395430i
689689 446953. 774145.i 0.941506 1.63074i
690690 −99739.2 247322.i −0.209492 0.519475i
691691 6583.82 + 11403.5i 0.0137887 + 0.0238827i 0.872837 0.488011i 0.162277π-0.162277\pi
−0.859049 + 0.511894i 0.828944π0.828944\pi
692692 178765. + 8595.54i 0.373310 + 0.0179499i
693693 882505. + 208957.i 1.83760 + 0.435101i
694694 251067. 239285.i 0.521279 0.496817i
695695 480033. 277147.i 0.993805 0.573773i
696696 −495238. 94379.8i −1.02234 0.194832i
697697 −603892. + 1.04597e6i −1.24306 + 2.15305i
698698 −488138. + 118306.i −1.00192 + 0.242826i
699699 −309463. + 45363.6i −0.633365 + 0.0928439i
700700 41963.5 + 81487.1i 0.0856398 + 0.166300i
701701 143500.i 0.292022i −0.989283 0.146011i 0.953357π-0.953357\pi
0.989283 0.146011i 0.0466434π-0.0466434\pi
702702 −520635. 203594.i −1.05648 0.413134i
703703 22218.0i 0.0449567i
704704 −706500. + 281744.i −1.42550 + 0.568472i
705705 96121.3 14090.3i 0.193393 0.0283492i
706706 45555.8 + 187967.i 0.0913976 + 0.377113i
707707 164632. 285151.i 0.329363 0.570474i
708708 −414393. + 296530.i −0.826696 + 0.591565i
709709 −386361. + 223066.i −0.768602 + 0.443752i −0.832376 0.554212i 0.813020π-0.813020\pi
0.0637739 + 0.997964i 0.479686π0.479686\pi
710710 235865. 224796.i 0.467893 0.445936i
711711 598306. 634441.i 1.18354 1.25502i
712712 −78252.1 90429.9i −0.154360 0.178382i
713713 −145164. 251432.i −0.285549 0.494585i
714714 −855912. + 345169.i −1.67893 + 0.677074i
715715 −477623. + 827267.i −0.934271 + 1.61820i
716716 95987.6 + 61748.0i 0.187236 + 0.120447i
717717 −396944. 157646.i −0.772131 0.306652i
718718 67379.8 229285.i 0.130702 0.444761i
719719 316954.i 0.613110i 0.951853 + 0.306555i 0.0991763π0.0991763\pi
−0.951853 + 0.306555i 0.900824π0.900824\pi
720720 −107820. 545863.i −0.207985 1.05298i
721721 679667. 1.30745
722722 −450083. 132265.i −0.863412 0.253730i
723723 385562. + 487515.i 0.737594 + 0.932634i
724724 −225969. + 351270.i −0.431094 + 0.670137i
725725 −72017.6 41579.4i −0.137013 0.0791047i
726726 −440128. + 562591.i −0.835038 + 1.06738i
727727 429578. 248017.i 0.812779 0.469258i −0.0351407 0.999382i 0.511188π-0.511188\pi
0.847920 + 0.530124i 0.177855π0.177855\pi
728728 −484079. 559412.i −0.913383 1.05553i
729729 341341. 407328.i 0.642293 0.766459i
730730 −412518. 432829.i −0.774100 0.812215i
731731 190938. + 330714.i 0.357320 + 0.618896i
732732 −297486. + 29098.9i −0.555194 + 0.0543068i
733733 607822. + 350926.i 1.13128 + 0.653143i 0.944256 0.329213i 0.106783π-0.106783\pi
0.187021 + 0.982356i 0.440117π0.440117\pi
734734 653820. 158461.i 1.21357 0.294123i
735735 −233820. + 184922.i −0.432820 + 0.342306i
736736 −105358. + 262324.i −0.194497 + 0.484264i
737737 544283. 1.00205
738738 455970. 799485.i 0.837190 1.46790i
739739 591401. 1.08291 0.541456 0.840729i 0.317873π-0.317873\pi
0.541456 + 0.840729i 0.317873π0.317873\pi
740740 74257.3 38240.4i 0.135605 0.0698327i
741741 183131. + 72730.3i 0.333522 + 0.132458i
742742 264882. + 1.09292e6i 0.481110 + 1.98509i
743743 76816.9 + 44350.2i 0.139149 + 0.0803375i 0.567958 0.823057i 0.307734π-0.307734\pi
−0.428810 + 0.903395i 0.641067π0.641067\pi
744744 −199316. 572029.i −0.360078 1.03341i
745745 69713.8 + 120748.i 0.125605 + 0.217554i
746746 745165. + 781856.i 1.33898 + 1.40491i
747747 −165869. 156422.i −0.297251 0.280321i
748748 60671.0 1.26180e6i 0.108437 2.25521i
749749 253267. 146224.i 0.451456 0.260648i
750750 −71578.3 + 506935.i −0.127250 + 0.901219i
751751 −692048. 399554.i −1.22703 0.708428i −0.260626 0.965440i 0.583929π-0.583929\pi
−0.966408 + 0.257011i 0.917262π0.917262\pi
752752 −83834.0 59810.7i −0.148246 0.105765i
753753 −527058. + 77260.6i −0.929541 + 0.136260i
754754 643957. + 189239.i 1.13270 + 0.332864i
755755 −546805. −0.959264
756756 650836. 266472.i 1.13875 0.466238i
757757 1.07119e6i 1.86927i 0.355603 + 0.934637i 0.384275π0.384275\pi
−0.355603 + 0.934637i 0.615725π0.615725\pi
758758 423971. + 124592.i 0.737900 + 0.216846i
759759 66917.1 + 456497.i 0.116159 + 0.792418i
760760 36987.4 + 192602.i 0.0640363 + 0.333453i
761761 173781. 300998.i 0.300078 0.519750i −0.676075 0.736832i 0.736321π-0.736321\pi
0.976153 + 0.217082i 0.0696540π0.0696540\pi
762762 7511.38 53197.5i 0.0129363 0.0916181i
763763 −523483. 906699.i −0.899194 1.55745i
764764 −729535. 35078.2i −1.24985 0.0600967i
765765 899249. + 212922.i 1.53659 + 0.363829i
766766 556747. + 584160.i 0.948856 + 0.995576i
767767 587502. 339195.i 0.998662 0.576578i
768768 −318403. + 496500.i −0.539827 + 0.841776i
769769 307338. 532324.i 0.519712 0.900168i −0.480025 0.877255i 0.659372π-0.659372\pi
0.999737 0.0229135i 0.00729422π-0.00729422\pi
770770 −283058. 1.16792e6i −0.477412 1.96984i
771771 174604. 439643.i 0.293728 0.739590i
772772 −171819. + 88482.1i −0.288295 + 0.148464i
773773 558543.i 0.934755i 0.884058 + 0.467378i 0.154801π0.154801\pi
−0.884058 + 0.467378i 0.845199π0.845199\pi
774774 −146830. 251243.i −0.245094 0.419385i
775775 99919.0i 0.166358i
776776 −52680.6 + 151882.i −0.0874838 + 0.252222i
777777 65488.4 + 82805.2i 0.108473 + 0.137156i
778778 −126974. + 30773.6i −0.209776 + 0.0508416i
779779 −162205. + 280947.i −0.267294 + 0.462967i
780780 72113.9 + 737241.i 0.118530 + 1.21177i
781781 −488195. + 281860.i −0.800371 + 0.462095i
782782 −323922. 339871.i −0.529696 0.555777i
783783 −365811. + 522791.i −0.596668 + 0.852716i
784784 314552. + 30319.4i 0.511754 + 0.0493274i
785785 119871. + 207622.i 0.194524 + 0.336925i
786786 −142580. + 182252.i −0.230788 + 0.295004i
787787 171055. 296276.i 0.276176 0.478351i −0.694255 0.719729i 0.744266π-0.744266\pi
0.970431 + 0.241378i 0.0775994π0.0775994\pi
788788 607005. 943592.i 0.977552 1.51961i
789789 302492. 239233.i 0.485915 0.384297i
790790 −1.10867e6 325804.i −1.77643 0.522039i
791791 804358.i 1.28557i
792792 −41154.9 + 961763.i −0.0656102 + 1.53327i
793793 397940. 0.632807
794794 178189. 606356.i 0.282644 0.961805i
795795 415632. 1.04654e6i 0.657620 1.65585i
796796 462911. 719598.i 0.730586 1.13570i
797797 −639205. 369045.i −1.00629 0.580982i −0.0961872 0.995363i 0.530665π-0.530665\pi
−0.910103 + 0.414381i 0.863998π0.863998\pi
798798 −229898. + 92712.4i −0.361018 + 0.145590i
799799 148124. 85519.6i 0.232024 0.133959i
800800 −76542.5 + 60055.7i −0.119598 + 0.0938370i
801801 −144984. + 43439.4i −0.225972 + 0.0677047i
802802 −416280. + 396745.i −0.647198 + 0.616827i
803803 517233. + 895874.i 0.802149 + 1.38936i
804804 343245. 245618.i 0.530997 0.379969i
805805 −386802. 223320.i −0.596894 0.344617i
806806 189955. + 783770.i 0.292403 + 1.20648i
807807 −13815.8 94248.7i −0.0212142 0.144720i
808808 330201. + 114531.i 0.505773 + 0.175429i
809809 −869283. −1.32820 −0.664101 0.747643i 0.731185π-0.731185\pi
−0.664101 + 0.747643i 0.731185π0.731185\pi
810810 −686106. 158632.i −1.04573 0.241781i
811811 −524099. −0.796841 −0.398420 0.917203i 0.630441π-0.630441\pi
−0.398420 + 0.917203i 0.630441π0.630441\pi
812812 −750682. + 386580.i −1.13853 + 0.586309i
813813 121840. + 831170.i 0.184335 + 1.25750i
814814 −140441. + 34037.5i −0.211956 + 0.0513699i
815815 −883065. 509838.i −1.32947 0.767568i
816816 −531149. 823114.i −0.797693 1.23617i
817817 51285.8 + 88829.7i 0.0768340 + 0.133080i
818818 −39768.9 + 37902.6i −0.0594343 + 0.0566452i
819819 −896892. + 268722.i −1.33713 + 0.400623i
820820 −1.21817e6 58573.0i −1.81167 0.0871104i
821821 176424. 101858.i 0.261741 0.151116i −0.363388 0.931638i 0.618380π-0.618380\pi
0.625128 + 0.780522i 0.285047π0.285047\pi
822822 −287565. 713072.i −0.425592 1.05533i
823823 840341. + 485171.i 1.24067 + 0.716300i 0.969230 0.246156i 0.0791675π-0.0791675\pi
0.271438 + 0.962456i 0.412501π0.412501\pi
824824 136059. + 708493.i 0.200389 + 1.04347i
825825 −58609.0 + 147574.i −0.0861106 + 0.216821i
826826 −240623. + 818811.i −0.352677 + 1.20012i
827827 −876265. −1.28122 −0.640611 0.767865i 0.721319π-0.721319\pi
−0.640611 + 0.767865i 0.721319π0.721319\pi
828828 248203. + 257686.i 0.362032 + 0.375864i
829829 728747.i 1.06040i −0.847874 0.530198i 0.822118π-0.822118\pi
0.847874 0.530198i 0.177882π-0.177882\pi
830830 −85178.6 + 289853.i −0.123644 + 0.420747i
831831 −165253. + 130694.i −0.239303 + 0.189258i
832832 486232. 616594.i 0.702420 0.890744i
833833 −262423. + 454530.i −0.378192 + 0.655047i
834834 −458219. + 585715.i −0.658781 + 0.842082i
835835 −185013. 320451.i −0.265356 0.459610i
836836 16296.2 338918.i 0.0233171 0.484934i
837837 −763768. 66572.7i −1.09021 0.0950266i
838838 784630. 747809.i 1.11732 1.06488i
839839 −261880. + 151197.i −0.372031 + 0.214792i −0.674345 0.738416i 0.735574π-0.735574\pi
0.302314 + 0.953208i 0.402241π0.402241\pi
840840 −705552. 608796.i −0.999932 0.862806i
841841 29400.8 50923.6i 0.0415687 0.0719991i
842842 927916. 224891.i 1.30883 0.317210i
843843 −41719.7 52751.5i −0.0587065 0.0742300i
844844 471760. 242943.i 0.662272 0.341051i
845845 219812.i 0.307849i
846846 −112530. + 65764.0i −0.157227 + 0.0918856i
847847 1.19634e6i 1.66758i
848848 −1.08625e6 + 494902.i −1.51056 + 0.688220i
849849 −299374. + 753805.i −0.415334 + 1.04579i
850850 −38060.1 157039.i −0.0526783 0.217355i
851851 −26854.1 + 46512.7i −0.0370810 + 0.0642262i
852852 −180679. + 398059.i −0.248902 + 0.548363i
853853 −613667. + 354301.i −0.843402 + 0.486938i −0.858419 0.512949i 0.828553π-0.828553\pi
0.0150171 + 0.999887i 0.495220π0.495220\pi
854854 −362394. + 345387.i −0.496895 + 0.473577i
855855 241538. + 57190.7i 0.330410 + 0.0782336i
856856 203126. + 234737.i 0.277215 + 0.320357i
857857 −506749. 877715.i −0.689972 1.19507i −0.971847 0.235615i 0.924290π-0.924290\pi
0.281875 0.959451i 0.409044π-0.409044\pi
858858 179180. 1.26900e6i 0.243397 1.72380i
859859 187918. 325483.i 0.254672 0.441105i −0.710134 0.704066i 0.751366π-0.751366\pi
0.964806 + 0.262961i 0.0846991π0.0846991\pi
860860 −208617. + 324297.i −0.282068 + 0.438476i
861861 −223574. 1.52518e6i −0.301588 2.05738i
862862 −234867. + 799224.i −0.316087 + 1.07561i
863863 771077.i 1.03532i 0.855585 + 0.517662i 0.173198π0.173198\pi
−0.855585 + 0.517662i 0.826802π0.826802\pi
864864 408060. + 625095.i 0.546634 + 0.837372i
865865 −300146. −0.401144
866866 −1.05740e6 310736.i −1.40995 0.414339i
867867 866042. 126952.i 1.15213 0.168889i
868868 −853251. 548889.i −1.13250 0.728526i
869869 1.73138e6 + 999610.i 2.29272 + 1.32371i
870870 837188. + 118209.i 1.10607 + 0.156176i
871871 −486632. + 280957.i −0.641453 + 0.370343i
872872 840359. 727191.i 1.10518 0.956347i
873873 148022. + 139591.i 0.194221 + 0.183159i
874874 −87005.2 91289.2i −0.113900 0.119508i
875875 428730. + 742582.i 0.559974 + 0.969903i
876876 730466. + 331559.i 0.951901 + 0.432069i
877877 121036. + 69880.4i 0.157368 + 0.0908566i 0.576616 0.817015i 0.304373π-0.304373\pi
−0.419248 + 0.907872i 0.637706π0.637706\pi
878878 25837.3 6261.96i 0.0335165 0.00812309i
879879 1.14217e6 + 453612.i 1.47827 + 0.587093i
880880 1.16079e6 528862.i 1.49895 0.682931i
881881 764399. 0.984846 0.492423 0.870356i 0.336111π-0.336111\pi
0.492423 + 0.870356i 0.336111π0.336111\pi
882882 198143. 347419.i 0.254708 0.446597i
883883 −276974. −0.355237 −0.177618 0.984099i 0.556839π-0.556839\pi
−0.177618 + 0.984099i 0.556839π0.556839\pi
884884 597091. + 1.15946e6i 0.764075 + 1.48372i
885885 670277. 530104.i 0.855791 0.676822i
886886 −231685. 955947.i −0.295141 1.21777i
887887 −284311. 164147.i −0.361365 0.208634i 0.308314 0.951285i 0.400235π-0.400235\pi
−0.669679 + 0.742650i 0.733568π0.733568\pi
888888 −73207.3 + 84842.1i −0.0928385 + 0.107593i
889889 −44990.7 77926.1i −0.0569271 0.0986006i
890890 138366. + 145179.i 0.174682 + 0.183283i
891891 1.08899e6 + 546324.i 1.37173 + 0.688168i
892892 −989306. 47568.8i −1.24337 0.0597850i
893893 39786.1 22970.5i 0.0498917 0.0288050i
894894 −147331. 115261.i −0.184340 0.144214i
895895 −165765. 95704.5i −0.206941 0.119478i
896896 92366.8 + 983536.i 0.115054 + 1.22511i
897897 −295472. 373602.i −0.367224 0.464327i
898898 −1.08581e6 319086.i −1.34649 0.395690i
899899 920482. 1.13893
900900 29634.6 + 119514.i 0.0365860 + 0.147548i
901901 1.98252e6i 2.44212i
902902 2.02438e6 + 594902.i 2.48816 + 0.731193i
903903 −452968. 179896.i −0.555510 0.220621i
904904 838471. 161020.i 1.02601 0.197035i
905905 350234. 606623.i 0.427623 0.740664i
906906 680368. 274377.i 0.828873 0.334265i
907907 2523.63 + 4371.06i 0.00306769 + 0.00531339i 0.867555 0.497341i 0.165690π-0.165690\pi
−0.864487 + 0.502654i 0.832357π0.832357\pi
908908 186.318 3874.92i 0.000225986 0.00469992i
909909 303480. 321809.i 0.367284 0.389466i
910910 855951. + 898097.i 1.03363 + 1.08453i
911911 124609. 71943.0i 0.150145 0.0866865i −0.423045 0.906109i 0.639039π-0.639039\pi
0.573191 + 0.819422i 0.305705π0.305705\pi
912912 −142666. 221088.i −0.171527 0.265813i
913913 261339. 452653.i 0.313518 0.543030i
914914 204524. + 843882.i 0.244823 + 1.01016i
915915 495984. 72705.4i 0.592414 0.0868409i
916916 −86067.6 167131.i −0.102577 0.199189i
917917 387555.i 0.460887i
918918 −1.22574e6 + 186297.i −1.45450 + 0.221065i
919919 1.50889e6i 1.78660i −0.449466 0.893298i 0.648386π-0.648386\pi
0.449466 0.893298i 0.351614π-0.351614\pi
920920 155360. 447912.i 0.183553 0.529197i
921921 −1.50308e6 + 220334.i −1.77200 + 0.259754i
922922 388739. 94215.2i 0.457294 0.110830i
923923 290990. 504010.i 0.341566 0.591610i
924924 938238. + 1.31116e6i 1.09893 + 1.53572i
925925 −16007.7 + 9242.07i −0.0187088 + 0.0108015i
926926 19550.0 + 20512.7i 0.0227995 + 0.0239221i
927927 888504. + 210377.i 1.03395 + 0.244816i
928928 −553250. 705131.i −0.642429 0.818793i
929929 489589. + 847994.i 0.567284 + 0.982565i 0.996833 + 0.0795211i 0.0253391π0.0253391\pi
−0.429549 + 0.903043i 0.641328π0.641328\pi
930930 379954. + 942167.i 0.439304 + 1.08934i
931931 −70486.7 + 122087.i −0.0813220 + 0.140854i
932932 −467633. 300824.i −0.538361 0.346323i
933933 −665537. 264318.i −0.764556 0.303643i
934934 1.64934e6 + 484690.i 1.89068 + 0.555611i
935935 2.11856e6i 2.42335i
936936 −459663. 881136.i −0.524672 1.00575i
937937 75553.9 0.0860553 0.0430276 0.999074i 0.486300π-0.486300\pi
0.0430276 + 0.999074i 0.486300π0.486300\pi
938938 199310. 678227.i 0.226529 0.770849i
939939 1.04258e6 + 1.31827e6i 1.18244 + 1.49511i
940940 145250. + 93438.1i 0.164384 + 0.105747i
941941 −33992.9 19625.8i −0.0383892 0.0221640i 0.480683 0.876895i 0.340389π-0.340389\pi
−0.519072 + 0.854731i 0.673722π0.673722\pi
942942 −253331. 198187.i −0.285488 0.223344i
943943 679142. 392103.i 0.763726 0.440937i
944944 −901706. 86914.4i −1.01186 0.0975322i
945945 −1.06877e6 + 498796.i −1.19680 + 0.558546i
946946 482928. 460266.i 0.539635 0.514311i
947947 −313680. 543310.i −0.349773 0.605825i 0.636436 0.771330i 0.280408π-0.280408\pi
−0.986209 + 0.165504i 0.947075π0.947075\pi
948948 1.54296e6 150926.i 1.71688 0.167938i
949949 −924894. 533988.i −1.02697 0.592924i
950950 −10222.9 42180.5i −0.0113273 0.0467374i
951951 −780971. + 617648.i −0.863522 + 0.682936i
952952 −1.55010e6 537656.i −1.71035 0.593240i
953953 −884152. −0.973512 −0.486756 0.873538i 0.661820π-0.661820\pi
−0.486756 + 0.873538i 0.661820π0.661820\pi
954954 7978.12 + 1.51072e6i 0.00876605 + 1.65992i
955955 1.22489e6 1.34304
956956 −347628. 675043.i −0.380363 0.738611i
957957 −1.35949e6 539923.i −1.48441 0.589533i
958958 223233. 54103.1i 0.243236 0.0589509i
959959 −1.11522e6 643871.i −1.21261 0.700103i
960960 493374. 857346.i 0.535346 0.930280i
961961 91239.2 + 158031.i 0.0987949 + 0.171118i
962962 107996. 102928.i 0.116696 0.111220i
963963 376348. 112759.i 0.405823 0.121591i
964964 −53069.6 + 1.10371e6i −0.0571074 + 1.18768i
965965 280693. 162058.i 0.301423 0.174027i
966966 593342. + 83778.7i 0.635844 + 0.0897799i
967967 −415020. 239612.i −0.443829 0.256245i 0.261391 0.965233i 0.415819π-0.415819\pi
−0.705220 + 0.708988i 0.749152π0.749152\pi
968968 −1.24708e6 + 239489.i −1.33089 + 0.255584i
969969 432387. 63382.9i 0.460495 0.0675032i
970970 76013.4 258664.i 0.0807880 0.274912i
971971 37374.6 0.0396404 0.0198202 0.999804i 0.493691π-0.493691\pi
0.0198202 + 0.999804i 0.493691π0.493691\pi
972972 933294. 146895.i 0.987839 0.155480i
973973 1.24551e6i 1.31559i
974974 −299508. + 1.01919e6i −0.315712 + 1.07433i
975975 −23776.1 162197.i −0.0250110 0.170621i
976976 −432581. 308622.i −0.454117 0.323986i
977977 −380919. + 659770.i −0.399064 + 0.691200i −0.993611 0.112861i 0.963998π-0.963998\pi
0.594546 + 0.804061i 0.297332π0.297332\pi
978978 1.35459e6 + 191266.i 1.41622 + 0.199968i
979979 −173489. 300492.i −0.181012 0.313522i
980980 −529358. 25453.1i −0.551184 0.0265026i
981981 −403679. 1.34733e6i −0.419467 1.40002i
982982 −447244. + 426256.i −0.463790 + 0.442026i
983983 −958351. + 553304.i −0.991785 + 0.572607i −0.905807 0.423690i 0.860735π-0.860735\pi
−0.0859774 + 0.996297i 0.527401π0.527401\pi
984984 1.54511e6 538373.i 1.59576 0.556024i
985985 −940809. + 1.62953e6i −0.969681 + 1.67954i
986986 1.44669e6 350620.i 1.48806 0.360648i
987987 −80574.1 + 202881.i −0.0827106 + 0.208260i
988988 160378. + 311432.i 0.164298 + 0.319043i
989989 247949.i 0.253496i
990990 −8525.58 1.61439e6i −0.00869868 1.64717i
991991 306890.i 0.312489i 0.987718 + 0.156245i 0.0499388π0.0499388\pi
−0.987718 + 0.156245i 0.950061π0.950061\pi
992992 401360. 999317.i 0.407860 1.01550i
993993 −396664. 501553.i −0.402277 0.508649i
994994 172452. + 711550.i 0.174540 + 0.720166i
995995 −717475. + 1.24270e6i −0.724704 + 1.25522i
996996 −39458.3 403394.i −0.0397759 0.406640i
997997 13764.4 7946.86i 0.0138473 0.00799476i −0.493060 0.869995i 0.664122π-0.664122\pi
0.506908 + 0.862000i 0.330788π0.330788\pi
998998 −571723. + 544894.i −0.574017 + 0.547080i
999999 59979.8 + 128519.i 0.0601000 + 0.128776i
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 72.5.p.b.67.40 yes 88
3.2 odd 2 216.5.p.b.91.5 88
4.3 odd 2 288.5.t.b.175.3 88
8.3 odd 2 inner 72.5.p.b.67.18 yes 88
8.5 even 2 288.5.t.b.175.4 88
9.2 odd 6 216.5.p.b.19.27 88
9.7 even 3 inner 72.5.p.b.43.18 88
12.11 even 2 864.5.t.b.847.36 88
24.5 odd 2 864.5.t.b.847.9 88
24.11 even 2 216.5.p.b.91.27 88
36.7 odd 6 288.5.t.b.79.4 88
36.11 even 6 864.5.t.b.559.9 88
72.11 even 6 216.5.p.b.19.5 88
72.29 odd 6 864.5.t.b.559.36 88
72.43 odd 6 inner 72.5.p.b.43.40 yes 88
72.61 even 6 288.5.t.b.79.3 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.5.p.b.43.18 88 9.7 even 3 inner
72.5.p.b.43.40 yes 88 72.43 odd 6 inner
72.5.p.b.67.18 yes 88 8.3 odd 2 inner
72.5.p.b.67.40 yes 88 1.1 even 1 trivial
216.5.p.b.19.5 88 72.11 even 6
216.5.p.b.19.27 88 9.2 odd 6
216.5.p.b.91.5 88 3.2 odd 2
216.5.p.b.91.27 88 24.11 even 2
288.5.t.b.79.3 88 72.61 even 6
288.5.t.b.79.4 88 36.7 odd 6
288.5.t.b.175.3 88 4.3 odd 2
288.5.t.b.175.4 88 8.5 even 2
864.5.t.b.559.9 88 36.11 even 6
864.5.t.b.559.36 88 72.29 odd 6
864.5.t.b.847.9 88 24.5 odd 2
864.5.t.b.847.36 88 12.11 even 2