Properties

Label 40.6.f.a.29.18
Level 4040
Weight 66
Character 40.29
Analytic conductor 6.4156.415
Analytic rank 00
Dimension 2828
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] = [40,6,Mod(29,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.29"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 40=235 40 = 2^{3} \cdot 5
Weight: k k == 6 6
Character orbit: [χ][\chi] == 40.f (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.415352792526.41535279252
Analytic rank: 00
Dimension: 2828
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 29.18
Character χ\chi == 40.29
Dual form 40.6.f.a.29.17

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+(1.42014+5.47569i)q27.17847q3+(27.9664+15.5525i)q4+(1.28331+55.8870i)q5+(10.194439.3071i)q6146.905iq7+(124.877131.049i)q8191.470q9+(307.842+72.3401i)q10+42.4351iq11+(200.756111.643i)q12605.383q13+(804.405208.625i)q14+(9.21223401.183i)q15+(540.241869.894i)q16409.138iq17+(271.9131048.43i)q18+2096.86iq19+(833.2911582.92i)q20+1054.55iq21+(232.362+60.2637i)q22+3048.59iq23+(896.424+940.730i)q24+(3121.71143.441i)q25+(859.7283314.89i)q26+3118.83q27+(2284.73+4108.40i)q28+4594.96iq29+(2209.84519.291i)q305118.83q31+(5530.49+1722.83i)q32304.619iq33+(2240.32581.033i)q34+(8210.06+188.525i)q35+(5354.722977.82i)q3611248.5q37+(11481.8+2977.83i)q38+4345.73q39+(7484.186810.80i)q40+11002.0q41+(5774.40+1497.61i)q42+8413.16q43+(659.9711186.76i)q44+(245.71510700.7i)q45+(16693.2+4329.42i)q463975.72iq47+(3878.11+6244.51i)q484774.02q49+(3647.8117297.2i)q50+2936.99iq51+(16930.49415.21i)q5238273.5q53+(4429.16+17077.7i)q54+(2371.5754.4575i)q55+(19251.7+18345.0i)q5615052.2iq57+(25160.6+6525.47i)q5836611.0iq59+(5981.75+11362.9i)q603181.32iq61+(7269.4428029.1i)q62+28127.8iq63+(1579.62+32729.9i)q64+(776.89733833.0i)q65+(1668.00432.601i)q66+41894.6q67+(6363.11+11442.1i)q6821884.2iq69+(10627.1+45223.5i)q70+72161.6q71+(23910.1+25091.9i)q72+48275.5iq73+(15974.461593.2i)q74+(22409.1+1029.69i)q75+(32611.358641.7i)q76+6233.92q77+(6171.53+23795.9i)q7839428.9q79+(47922.4+31308.8i)q80+24138.7q81+(15624.4+60243.7i)q8246504.5q83+(16400.929492.0i)q84+(22865.5+525.053i)q85+(11947.8+46067.9i)q8632984.8iq87+(5561.075299.16i)q8838217.3q89+(58942.413850.9i)q90+88933.7iq91+(47413.285258.2i)q92+36745.3q93+(21769.85646.07i)q94+(117187.2690.93i)q95+(39700.412367.3i)q96+95979.0iq97+(6779.7626141.1i)q988125.03iq99+O(q100)q+(1.42014 + 5.47569i) q^{2} -7.17847 q^{3} +(-27.9664 + 15.5525i) q^{4} +(-1.28331 + 55.8870i) q^{5} +(-10.1944 - 39.3071i) q^{6} -146.905i q^{7} +(-124.877 - 131.049i) q^{8} -191.470 q^{9} +(-307.842 + 72.3401i) q^{10} +42.4351i q^{11} +(200.756 - 111.643i) q^{12} -605.383 q^{13} +(804.405 - 208.625i) q^{14} +(9.21223 - 401.183i) q^{15} +(540.241 - 869.894i) q^{16} -409.138i q^{17} +(-271.913 - 1048.43i) q^{18} +2096.86i q^{19} +(-833.291 - 1582.92i) q^{20} +1054.55i q^{21} +(-232.362 + 60.2637i) q^{22} +3048.59i q^{23} +(896.424 + 940.730i) q^{24} +(-3121.71 - 143.441i) q^{25} +(-859.728 - 3314.89i) q^{26} +3118.83 q^{27} +(2284.73 + 4108.40i) q^{28} +4594.96i q^{29} +(2209.84 - 519.291i) q^{30} -5118.83 q^{31} +(5530.49 + 1722.83i) q^{32} -304.619i q^{33} +(2240.32 - 581.033i) q^{34} +(8210.06 + 188.525i) q^{35} +(5354.72 - 2977.82i) q^{36} -11248.5 q^{37} +(-11481.8 + 2977.83i) q^{38} +4345.73 q^{39} +(7484.18 - 6810.80i) q^{40} +11002.0 q^{41} +(-5774.40 + 1497.61i) q^{42} +8413.16 q^{43} +(-659.971 - 1186.76i) q^{44} +(245.715 - 10700.7i) q^{45} +(-16693.2 + 4329.42i) q^{46} -3975.72i q^{47} +(-3878.11 + 6244.51i) q^{48} -4774.02 q^{49} +(-3647.81 - 17297.2i) q^{50} +2936.99i q^{51} +(16930.4 - 9415.21i) q^{52} -38273.5 q^{53} +(4429.16 + 17077.7i) q^{54} +(-2371.57 - 54.4575i) q^{55} +(-19251.7 + 18345.0i) q^{56} -15052.2i q^{57} +(-25160.6 + 6525.47i) q^{58} -36611.0i q^{59} +(5981.75 + 11362.9i) q^{60} -3181.32i q^{61} +(-7269.44 - 28029.1i) q^{62} +28127.8i q^{63} +(-1579.62 + 32729.9i) q^{64} +(776.897 - 33833.0i) q^{65} +(1668.00 - 432.601i) q^{66} +41894.6 q^{67} +(6363.11 + 11442.1i) q^{68} -21884.2i q^{69} +(10627.1 + 45223.5i) q^{70} +72161.6 q^{71} +(23910.1 + 25091.9i) q^{72} +48275.5i q^{73} +(-15974.4 - 61593.2i) q^{74} +(22409.1 + 1029.69i) q^{75} +(-32611.3 - 58641.7i) q^{76} +6233.92 q^{77} +(6171.53 + 23795.9i) q^{78} -39428.9 q^{79} +(47922.4 + 31308.8i) q^{80} +24138.7 q^{81} +(15624.4 + 60243.7i) q^{82} -46504.5 q^{83} +(-16400.9 - 29492.0i) q^{84} +(22865.5 + 525.053i) q^{85} +(11947.8 + 46067.9i) q^{86} -32984.8i q^{87} +(5561.07 - 5299.16i) q^{88} -38217.3 q^{89} +(58942.4 - 13850.9i) q^{90} +88933.7i q^{91} +(-47413.2 - 85258.2i) q^{92} +36745.3 q^{93} +(21769.8 - 5646.07i) q^{94} +(-117187. - 2690.93i) q^{95} +(-39700.4 - 12367.3i) q^{96} +95979.0i q^{97} +(-6779.76 - 26141.1i) q^{98} -8125.03i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q12q4156q6+1940q916q10692q14488q15+1560q16+2732q202224q24+1556q259976q2615012q30+4368q31+13016q3434116q36+236176q96+O(q100) 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36}+ \cdots - 236176 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/40Z)×\left(\mathbb{Z}/40\mathbb{Z}\right)^\times.

nn 1717 2121 3131
χ(n)\chi(n) 1-1 1-1 11

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 1.42014 + 5.47569i 0.251047 + 0.967975i
33 −7.17847 −0.460499 −0.230250 0.973132i 0.573954π-0.573954\pi
−0.230250 + 0.973132i 0.573954π0.573954\pi
44 −27.9664 + 15.5525i −0.873951 + 0.486015i
55 −1.28331 + 55.8870i −0.0229566 + 0.999736i
66 −10.1944 39.3071i −0.115607 0.445751i
77 146.905i 1.13316i −0.824007 0.566580i 0.808266π-0.808266\pi
0.824007 0.566580i 0.191734π-0.191734\pi
88 −124.877 131.049i −0.689853 0.723950i
99 −191.470 −0.787941
1010 −307.842 + 72.3401i −0.973483 + 0.228760i
1111 42.4351i 0.105741i 0.998601 + 0.0528705i 0.0168371π0.0168371\pi
−0.998601 + 0.0528705i 0.983163π0.983163\pi
1212 200.756 111.643i 0.402453 0.223809i
1313 −605.383 −0.993510 −0.496755 0.867891i 0.665475π-0.665475\pi
−0.496755 + 0.867891i 0.665475π0.665475\pi
1414 804.405 208.625i 1.09687 0.284476i
1515 9.21223 401.183i 0.0105715 0.460378i
1616 540.241 869.894i 0.527579 0.849506i
1717 409.138i 0.343359i −0.985153 0.171679i 0.945081π-0.945081\pi
0.985153 0.171679i 0.0549193π-0.0549193\pi
1818 −271.913 1048.43i −0.197810 0.762707i
1919 2096.86i 1.33256i 0.745704 + 0.666278i 0.232114π0.232114\pi
−0.745704 + 0.666278i 0.767886π0.767886\pi
2020 −833.291 1582.92i −0.465824 0.884878i
2121 1054.55i 0.521819i
2222 −232.362 + 60.2637i −0.102355 + 0.0265460i
2323 3048.59i 1.20166i 0.799379 + 0.600828i 0.205162π0.205162\pi
−0.799379 + 0.600828i 0.794838π0.794838\pi
2424 896.424 + 940.730i 0.317677 + 0.333378i
2525 −3121.71 143.441i −0.998946 0.0459011i
2626 −859.728 3314.89i −0.249418 0.961693i
2727 3118.83 0.823345
2828 2284.73 + 4108.40i 0.550732 + 0.990325i
2929 4594.96i 1.01458i 0.861775 + 0.507290i 0.169353π0.169353\pi
−0.861775 + 0.507290i 0.830647π0.830647\pi
3030 2209.84 519.291i 0.448288 0.105344i
3131 −5118.83 −0.956679 −0.478339 0.878175i 0.658761π-0.658761\pi
−0.478339 + 0.878175i 0.658761π0.658761\pi
3232 5530.49 + 1722.83i 0.954747 + 0.297418i
3333 304.619i 0.0486937i
3434 2240.32 581.033i 0.332363 0.0861992i
3535 8210.06 + 188.525i 1.13286 + 0.0260135i
3636 5354.72 2977.82i 0.688621 0.382951i
3737 −11248.5 −1.35080 −0.675398 0.737454i 0.736028π-0.736028\pi
−0.675398 + 0.737454i 0.736028π0.736028\pi
3838 −11481.8 + 2977.83i −1.28988 + 0.334534i
3939 4345.73 0.457510
4040 7484.18 6810.80i 0.739596 0.673052i
4141 11002.0 1.02215 0.511073 0.859537i 0.329248π-0.329248\pi
0.511073 + 0.859537i 0.329248π0.329248\pi
4242 −5774.40 + 1497.61i −0.505107 + 0.131001i
4343 8413.16 0.693886 0.346943 0.937886i 0.387220π-0.387220\pi
0.346943 + 0.937886i 0.387220π0.387220\pi
4444 −659.971 1186.76i −0.0513917 0.0924125i
4545 245.715 10700.7i 0.0180884 0.787733i
4646 −16693.2 + 4329.42i −1.16317 + 0.301672i
4747 3975.72i 0.262525i −0.991348 0.131263i 0.958097π-0.958097\pi
0.991348 0.131263i 0.0419031π-0.0419031\pi
4848 −3878.11 + 6244.51i −0.242950 + 0.391197i
4949 −4774.02 −0.284049
5050 −3647.81 17297.2i −0.206351 0.978478i
5151 2936.99i 0.158116i
5252 16930.4 9415.21i 0.868279 0.482860i
5353 −38273.5 −1.87158 −0.935790 0.352558i 0.885312π-0.885312\pi
−0.935790 + 0.352558i 0.885312π0.885312\pi
5454 4429.16 + 17077.7i 0.206698 + 0.796977i
5555 −2371.57 54.4575i −0.105713 0.00242746i
5656 −19251.7 + 18345.0i −0.820350 + 0.781713i
5757 15052.2i 0.613641i
5858 −25160.6 + 6525.47i −0.982088 + 0.254707i
5959 36611.0i 1.36924i −0.728898 0.684622i 0.759967π-0.759967\pi
0.728898 0.684622i 0.240033π-0.240033\pi
6060 5981.75 + 11362.9i 0.214511 + 0.407485i
6161 3181.32i 0.109467i −0.998501 0.0547335i 0.982569π-0.982569\pi
0.998501 0.0547335i 0.0174309π-0.0174309\pi
6262 −7269.44 28029.1i −0.240172 0.926041i
6363 28127.8i 0.892862i
6464 −1579.62 + 32729.9i −0.0482062 + 0.998837i
6565 776.897 33833.0i 0.0228076 0.993248i
6666 1668.00 432.601i 0.0471342 0.0122244i
6767 41894.6 1.14017 0.570087 0.821584i 0.306909π-0.306909\pi
0.570087 + 0.821584i 0.306909π0.306909\pi
6868 6363.11 + 11442.1i 0.166877 + 0.300079i
6969 21884.2i 0.553361i
7070 10627.1 + 45223.5i 0.259221 + 1.10311i
7171 72161.6 1.69887 0.849435 0.527693i 0.176943π-0.176943\pi
0.849435 + 0.527693i 0.176943π0.176943\pi
7272 23910.1 + 25091.9i 0.543563 + 0.570429i
7373 48275.5i 1.06028i 0.847911 + 0.530138i 0.177860π0.177860\pi
−0.847911 + 0.530138i 0.822140π0.822140\pi
7474 −15974.4 61593.2i −0.339113 1.30754i
7575 22409.1 + 1029.69i 0.460014 + 0.0211374i
7676 −32611.3 58641.7i −0.647642 1.16459i
7777 6233.92 0.119821
7878 6171.53 + 23795.9i 0.114857 + 0.442859i
7979 −39428.9 −0.710798 −0.355399 0.934715i 0.615655π-0.615655\pi
−0.355399 + 0.934715i 0.615655π0.615655\pi
8080 47922.4 + 31308.8i 0.837170 + 0.546942i
8181 24138.7 0.408791
8282 15624.4 + 60243.7i 0.256607 + 0.989412i
8383 −46504.5 −0.740968 −0.370484 0.928839i 0.620808π-0.620808\pi
−0.370484 + 0.928839i 0.620808π0.620808\pi
8484 −16400.9 29492.0i −0.253612 0.456044i
8585 22865.5 + 525.053i 0.343268 + 0.00788235i
8686 11947.8 + 46067.9i 0.174198 + 0.671664i
8787 32984.8i 0.467213i
8888 5561.07 5299.16i 0.0765512 0.0729458i
8989 −38217.3 −0.511428 −0.255714 0.966752i 0.582311π-0.582311\pi
−0.255714 + 0.966752i 0.582311π0.582311\pi
9090 58942.4 13850.9i 0.767047 0.180249i
9191 88933.7i 1.12580i
9292 −47413.2 85258.2i −0.584022 1.05019i
9393 36745.3 0.440550
9494 21769.8 5646.07i 0.254118 0.0659062i
9595 −117187. 2690.93i −1.33220 0.0305910i
9696 −39700.4 12367.3i −0.439660 0.136961i
9797 95979.0i 1.03573i 0.855462 + 0.517865i 0.173273π0.173273\pi
−0.855462 + 0.517865i 0.826727π0.826727\pi
9898 −6779.76 26141.1i −0.0713098 0.274953i
9999 8125.03i 0.0833177i
100100 89533.8 44538.7i 0.895338 0.445387i
101101 83900.0i 0.818386i 0.912448 + 0.409193i 0.134190π0.134190\pi
−0.912448 + 0.409193i 0.865810π0.865810\pi
102102 −16082.0 + 4170.93i −0.153053 + 0.0396947i
103103 10693.4i 0.0993165i −0.998766 0.0496583i 0.984187π-0.984187\pi
0.998766 0.0496583i 0.0158132π-0.0158132\pi
104104 75598.3 + 79334.8i 0.685376 + 0.719251i
105105 −58935.7 1353.32i −0.521681 0.0119792i
106106 −54353.6 209574.i −0.469855 1.81164i
107107 −109794. −0.927081 −0.463540 0.886076i 0.653421π-0.653421\pi
−0.463540 + 0.886076i 0.653421π0.653421\pi
108108 −87222.4 + 48505.5i −0.719563 + 0.400158i
109109 135615.i 1.09330i 0.837361 + 0.546651i 0.184097π0.184097\pi
−0.837361 + 0.546651i 0.815903π0.815903\pi
110110 −3069.76 13063.3i −0.0241893 0.102937i
111111 80746.9 0.622040
112112 −127792. 79364.0i −0.962625 0.597831i
113113 195440.i 1.43985i −0.694050 0.719927i 0.744175π-0.744175\pi
0.694050 0.719927i 0.255825π-0.255825\pi
114114 82421.5 21376.3i 0.593989 0.154053i
115115 −170377. 3912.30i −1.20134 0.0275859i
116116 −71462.9 128504.i −0.493101 0.886693i
117117 115913. 0.782827
118118 200470. 51992.6i 1.32539 0.343745i
119119 −60104.4 −0.389080
120120 −53725.0 + 48891.1i −0.340583 + 0.309940i
121121 159250. 0.988819
122122 17420.0 4517.92i 0.105961 0.0274814i
123123 −78977.7 −0.470697
124124 143155. 79610.4i 0.836090 0.464960i
125125 12022.6 174279.i 0.0688214 0.997629i
126126 −154019. + 39945.3i −0.864268 + 0.224150i
127127 171245.i 0.942126i −0.882100 0.471063i 0.843870π-0.843870\pi
0.882100 0.471063i 0.156130π-0.156130\pi
128128 −181462. + 37831.4i −0.978952 + 0.204093i
129129 −60393.6 −0.319534
130130 186363. 43793.5i 0.967165 0.227275i
131131 111420.i 0.567265i 0.958933 + 0.283632i 0.0915395π0.0915395\pi
−0.958933 + 0.283632i 0.908460π0.908460\pi
132132 4737.58 + 8519.11i 0.0236658 + 0.0425559i
133133 308039. 1.51000
134134 59496.1 + 229402.i 0.286238 + 1.10366i
135135 −4002.43 + 174302.i −0.0189012 + 0.823128i
136136 −53617.1 + 51091.9i −0.248574 + 0.236867i
137137 282243.i 1.28476i 0.766387 + 0.642379i 0.222052π0.222052\pi
−0.766387 + 0.642379i 0.777948π0.777948\pi
138138 119831. 31078.6i 0.535640 0.138920i
139139 44060.1i 0.193423i −0.995312 0.0967117i 0.969168π-0.969168\pi
0.995312 0.0967117i 0.0308325π-0.0308325\pi
140140 −232538. + 122414.i −1.00271 + 0.527852i
141141 28539.6i 0.120893i
142142 102479. + 395135.i 0.426496 + 1.64446i
143143 25689.5i 0.105055i
144144 −103440. + 166558.i −0.415701 + 0.669360i
145145 −256798. 5896.77i −1.01431 0.0232913i
146146 −264342. + 68557.8i −1.02632 + 0.266180i
147147 34270.1 0.130804
148148 314580. 174942.i 1.18053 0.656506i
149149 251552.i 0.928244i −0.885771 0.464122i 0.846370π-0.846370\pi
0.885771 0.464122i 0.153630π-0.153630\pi
150150 26185.7 + 124167.i 0.0950246 + 0.450588i
151151 95790.0 0.341883 0.170942 0.985281i 0.445319π-0.445319\pi
0.170942 + 0.985281i 0.445319π0.445319\pi
152152 274791. 261849.i 0.964703 0.919267i
153153 78337.6i 0.270546i
154154 8853.02 + 34135.0i 0.0300808 + 0.115984i
155155 6569.06 286076.i 0.0219621 0.956427i
156156 −121534. + 67586.8i −0.399841 + 0.222357i
157157 −178462. −0.577824 −0.288912 0.957356i 0.593294π-0.593294\pi
−0.288912 + 0.957356i 0.593294π0.593294\pi
158158 −55994.4 215900.i −0.178444 0.688035i
159159 274745. 0.861861
160160 −103381. + 306871.i −0.319257 + 0.947668i
161161 447853. 1.36167
162162 34280.3 + 132176.i 0.102626 + 0.395699i
163163 147330. 0.434332 0.217166 0.976135i 0.430319π-0.430319\pi
0.217166 + 0.976135i 0.430319π0.430319\pi
164164 −307687. + 171109.i −0.893305 + 0.496778i
165165 17024.2 + 390.922i 0.0486808 + 0.00111784i
166166 −66042.7 254644.i −0.186018 0.717239i
167167 310989.i 0.862888i −0.902140 0.431444i 0.858004π-0.858004\pi
0.902140 0.431444i 0.141996π-0.141996\pi
168168 138198. 131689.i 0.377770 0.359978i
169169 −4803.84 −0.0129381
170170 29597.1 + 125950.i 0.0785466 + 0.334254i
171171 401485.i 1.04997i
172172 −235286. + 130845.i −0.606422 + 0.337239i
173173 −120278. −0.305542 −0.152771 0.988262i 0.548820π-0.548820\pi
−0.152771 + 0.988262i 0.548820π0.548820\pi
174174 180614. 46842.9i 0.452251 0.117293i
175175 −21072.2 + 458594.i −0.0520133 + 1.13196i
176176 36914.0 + 22925.2i 0.0898276 + 0.0557868i
177177 262811.i 0.630536i
178178 −54273.8 209266.i −0.128393 0.495050i
179179 180544.i 0.421162i 0.977576 + 0.210581i 0.0675356π0.0675356\pi
−0.977576 + 0.210581i 0.932464π0.932464\pi
180180 159550. + 303080.i 0.367041 + 0.697231i
181181 149699.i 0.339643i 0.985475 + 0.169821i 0.0543191π0.0543191\pi
−0.985475 + 0.169821i 0.945681π0.945681\pi
182182 −486974. + 126298.i −1.08975 + 0.282630i
183183 22837.0i 0.0504095i
184184 399515. 380698.i 0.869938 0.828965i
185185 14435.3 628643.i 0.0310097 1.35044i
186186 52183.4 + 201206.i 0.110599 + 0.426441i
187187 17361.8 0.0363071
188188 61832.2 + 111187.i 0.127591 + 0.229434i
189189 458171.i 0.932981i
190190 −151687. 645502.i −0.304835 1.29722i
191191 213909. 0.424273 0.212136 0.977240i 0.431958π-0.431958\pi
0.212136 + 0.977240i 0.431958π0.431958\pi
192192 11339.3 234951.i 0.0221989 0.459964i
193193 729587.i 1.40988i −0.709265 0.704942i 0.750973π-0.750973\pi
0.709265 0.704942i 0.249027π-0.249027\pi
194194 −525551. + 136303.i −1.00256 + 0.260017i
195195 −5576.93 + 242869.i −0.0105029 + 0.457390i
196196 133512. 74247.8i 0.248245 0.138052i
197197 −922110. −1.69285 −0.846423 0.532512i 0.821248π-0.821248\pi
−0.846423 + 0.532512i 0.821248π0.821248\pi
198198 44490.2 11538.7i 0.0806494 0.0209167i
199199 −985328. −1.76379 −0.881897 0.471442i 0.843734π-0.843734\pi
−0.881897 + 0.471442i 0.843734π0.843734\pi
200200 371031. + 427009.i 0.655896 + 0.754852i
201201 −300739. −0.525049
202202 −459410. + 119149.i −0.792177 + 0.205454i
203203 675021. 1.14968
204204 −45677.4 82137.0i −0.0768469 0.138186i
205205 −14119.0 + 614870.i −0.0234650 + 1.02188i
206206 58553.6 15186.0i 0.0961359 0.0249331i
207207 583713.i 0.946833i
208208 −327053. + 526619.i −0.524155 + 0.843992i
209209 −88980.5 −0.140906
210210 −76286.4 324636.i −0.119371 0.507982i
211211 932526.i 1.44197i 0.692953 + 0.720983i 0.256309π0.256309\pi
−0.692953 + 0.720983i 0.743691π0.743691\pi
212212 1.07037e6 595247.i 1.63567 0.909615i
213213 −518010. −0.782328
214214 −155922. 601196.i −0.232741 0.897391i
215215 −10796.7 + 470186.i −0.0159293 + 0.693703i
216216 −389469. 408719.i −0.567987 0.596060i
217217 751980.i 1.08407i
218218 −742584. + 192591.i −1.05829 + 0.274470i
219219 346544.i 0.488257i
220220 67171.3 35360.8i 0.0935679 0.0492567i
221221 247686.i 0.341130i
222222 114672. + 442145.i 0.156161 + 0.602119i
223223 748564.i 1.00801i 0.863699 + 0.504007i 0.168142π0.168142\pi
−0.863699 + 0.504007i 0.831858π0.831858\pi
224224 253092. 812455.i 0.337022 1.08188i
225225 597712. + 27464.6i 0.787110 + 0.0361674i
226226 1.07017e6 277552.i 1.39374 0.361471i
227227 1.47117e6 1.89495 0.947475 0.319829i 0.103626π-0.103626\pi
0.947475 + 0.319829i 0.103626π0.103626\pi
228228 234100. + 420957.i 0.298238 + 0.536292i
229229 835029.i 1.05223i 0.850412 + 0.526117i 0.176353π0.176353\pi
−0.850412 + 0.526117i 0.823647π0.823647\pi
230230 −220536. 938486.i −0.274890 1.16979i
231231 −44750.0 −0.0551777
232232 602164. 573803.i 0.734505 0.699911i
233233 284718.i 0.343577i 0.985134 + 0.171789i 0.0549546π0.0549546\pi
−0.985134 + 0.171789i 0.945045π0.945045\pi
234234 164612. + 634701.i 0.196526 + 0.757757i
235235 222191. + 5102.09i 0.262456 + 0.00602669i
236236 569391. + 1.02388e6i 0.665473 + 1.19665i
237237 283039. 0.327322
238238 −85356.5 329113.i −0.0976774 0.376620i
239239 800635. 0.906650 0.453325 0.891345i 0.350238π-0.350238\pi
0.453325 + 0.891345i 0.350238π0.350238\pi
240240 −344010. 224749.i −0.385516 0.251866i
241241 −1.50596e6 −1.67021 −0.835107 0.550088i 0.814594π-0.814594\pi
−0.835107 + 0.550088i 0.814594π0.814594\pi
242242 226157. + 872005.i 0.248240 + 0.957152i
243243 −931154. −1.01159
244244 49477.4 + 88970.2i 0.0532026 + 0.0956688i
245245 6126.56 266805.i 0.00652081 0.283975i
246246 −112159. 432458.i −0.118167 0.455623i
247247 1.26940e6i 1.32391i
248248 639222. + 670817.i 0.659968 + 0.692587i
249249 333831. 0.341215
250250 971370. 181667.i 0.982957 0.183835i
251251 1.10255e6i 1.10463i −0.833637 0.552313i 0.813745π-0.813745\pi
0.833637 0.552313i 0.186255π-0.186255\pi
252252 −437457. 786634.i −0.433944 0.780317i
253253 −129367. −0.127064
254254 937686. 243192.i 0.911955 0.236518i
255255 −164139. 3769.08i −0.158075 0.00362981i
256256 −464854. 939905.i −0.443320 0.896364i
257257 1.41038e6i 1.33200i 0.745953 + 0.665999i 0.231994π0.231994\pi
−0.745953 + 0.665999i 0.768006π0.768006\pi
258258 −85767.2 330697.i −0.0802181 0.309301i
259259 1.65246e6i 1.53067i
260260 504460. + 958272.i 0.462800 + 0.879135i
261261 879794.i 0.799429i
262262 −610103. + 158232.i −0.549098 + 0.142410i
263263 1.68879e6i 1.50552i 0.658298 + 0.752758i 0.271277π0.271277\pi
−0.658298 + 0.752758i 0.728723π0.728723\pi
264264 −39920.0 + 38039.8i −0.0352518 + 0.0335915i
265265 49116.9 2.13899e6i 0.0429651 1.87109i
266266 437457. + 1.68673e6i 0.379081 + 1.46164i
267267 274342. 0.235512
268268 −1.17164e6 + 651565.i −0.996456 + 0.554141i
269269 305848.i 0.257706i −0.991664 0.128853i 0.958870π-0.958870\pi
0.991664 0.128853i 0.0411295π-0.0411295\pi
270270 −960107. + 225616.i −0.801512 + 0.188348i
271271 −1.25325e6 −1.03661 −0.518306 0.855195i 0.673437π-0.673437\pi
−0.518306 + 0.855195i 0.673437π0.673437\pi
272272 −355907. 221034.i −0.291685 0.181149i
273273 638408.i 0.518432i
274274 −1.54547e6 + 400823.i −1.24361 + 0.322535i
275275 6086.93 132470.i 0.00485363 0.105630i
276276 340354. + 612024.i 0.268942 + 0.483610i
277277 483396. 0.378533 0.189267 0.981926i 0.439389π-0.439389\pi
0.189267 + 0.981926i 0.439389π0.439389\pi
278278 241260. 62571.4i 0.187229 0.0485584i
279279 980100. 0.753806
280280 −1.00054e6 1.09946e6i −0.762674 0.838079i
281281 88721.8 0.0670293 0.0335147 0.999438i 0.489330π-0.489330\pi
0.0335147 + 0.999438i 0.489330π0.489330\pi
282282 −156274. + 40530.1i −0.117021 + 0.0303497i
283283 −1.76445e6 −1.30961 −0.654807 0.755796i 0.727250π-0.727250\pi
−0.654807 + 0.755796i 0.727250π0.727250\pi
284284 −2.01810e6 + 1.12229e6i −1.48473 + 0.825676i
285285 841224. + 19316.7i 0.613479 + 0.0140871i
286286 140668. 36482.6i 0.101690 0.0263737i
287287 1.61625e6i 1.15825i
288288 −1.05892e6 329869.i −0.752284 0.234347i
289289 1.25246e6 0.882105
290290 −332400. 1.41452e6i −0.232095 0.987677i
291291 688982.i 0.476953i
292292 −750803. 1.35009e6i −0.515310 0.926630i
293293 −9124.96 −0.00620957 −0.00310479 0.999995i 0.500988π-0.500988\pi
−0.00310479 + 0.999995i 0.500988π0.500988\pi
294294 48668.3 + 187653.i 0.0328381 + 0.126615i
295295 2.04608e6 + 46983.3i 1.36888 + 0.0314332i
296296 1.40467e6 + 1.47410e6i 0.931850 + 0.977908i
297297 132348.i 0.0870614i
298298 1.37742e6 357238.i 0.898517 0.233033i
299299 1.84557e6i 1.19386i
300300 −642716. + 319720.i −0.412302 + 0.205100i
301301 1.23593e6i 0.786283i
302302 136035. + 524516.i 0.0858288 + 0.330934i
303303 602273.i 0.376866i
304304 1.82405e6 + 1.13281e6i 1.13201 + 0.703029i
305305 177795. + 4082.64i 0.109438 + 0.00251299i
306306 −428952. + 111250.i −0.261882 + 0.0679199i
307307 −2.64214e6 −1.59996 −0.799980 0.600026i 0.795157π-0.795157\pi
−0.799980 + 0.600026i 0.795157π0.795157\pi
308308 −174340. + 96952.9i −0.104718 + 0.0582350i
309309 76762.0i 0.0457352i
310310 1.57579e6 370297.i 0.931311 0.218849i
311311 −1.40253e6 −0.822262 −0.411131 0.911576i 0.634866π-0.634866\pi
−0.411131 + 0.911576i 0.634866π0.634866\pi
312312 −542680. 569503.i −0.315615 0.331214i
313313 1.35907e6i 0.784115i 0.919941 + 0.392058i 0.128237π0.128237\pi
−0.919941 + 0.392058i 0.871763π0.871763\pi
314314 −253440. 977201.i −0.145061 0.559319i
315315 −1.57198e6 36096.8i −0.892627 0.0204971i
316316 1.10268e6 613216.i 0.621203 0.345458i
317317 300344. 0.167869 0.0839344 0.996471i 0.473251π-0.473251\pi
0.0839344 + 0.996471i 0.473251π0.473251\pi
318318 390176. + 1.50442e6i 0.216368 + 0.834259i
319319 −194987. −0.107283
320320 −1.82715e6 130283.i −0.997468 0.0711234i
321321 788150. 0.426920
322322 636013. + 2.45231e6i 0.341842 + 1.31806i
323323 857906. 0.457545
324324 −675073. + 375416.i −0.357263 + 0.198678i
325325 1.88983e6 + 86836.8i 0.992463 + 0.0456032i
326326 209228. + 806732.i 0.109038 + 0.420422i
327327 973505.i 0.503464i
328328 −1.37390e6 1.44180e6i −0.705130 0.739982i
329329 −584052. −0.297483
330330 22036.2 + 93774.7i 0.0111391 + 0.0474024i
331331 2.37543e6i 1.19172i −0.803090 0.595858i 0.796812π-0.796812\pi
0.803090 0.595858i 0.203188π-0.203188\pi
332332 1.30056e6 723259.i 0.647570 0.360121i
333333 2.15374e6 1.06435
334334 1.70288e6 441647.i 0.835253 0.216625i
335335 −53763.9 + 2.34136e6i −0.0261745 + 1.13987i
336336 917348. + 569712.i 0.443288 + 0.275301i
337337 3.69929e6i 1.77437i 0.461416 + 0.887184i 0.347341π0.347341\pi
−0.461416 + 0.887184i 0.652659π0.652659\pi
338338 −6822.11 26304.4i −0.00324808 0.0125238i
339339 1.40296e6i 0.663051i
340340 −647632. + 340931.i −0.303830 + 0.159945i
341341 217218.i 0.101160i
342342 2.19841e6 570164.i 1.01635 0.263593i
343343 1.76770e6i 0.811286i
344344 −1.05061e6 1.10254e6i −0.478679 0.502339i
345345 1.22304e6 + 28084.3i 0.553215 + 0.0127033i
346346 −170811. 658605.i −0.0767054 0.295757i
347347 1.98355e6 0.884339 0.442170 0.896931i 0.354209π-0.354209\pi
0.442170 + 0.896931i 0.354209π0.354209\pi
348348 512994. + 922466.i 0.227072 + 0.408321i
349349 1.51829e6i 0.667256i 0.942705 + 0.333628i 0.108273π0.108273\pi
−0.942705 + 0.333628i 0.891727π0.891727\pi
350350 −2.54104e6 + 535881.i −1.10877 + 0.233829i
351351 −1.88809e6 −0.818001
352352 −73108.4 + 234687.i −0.0314493 + 0.100956i
353353 2.06194e6i 0.880724i −0.897820 0.440362i 0.854850π-0.854850\pi
0.897820 0.440362i 0.145150π-0.145150\pi
354354 −1.43907e6 + 373227.i −0.610343 + 0.158294i
355355 −92605.9 + 4.03289e6i −0.0390003 + 1.69842i
356356 1.06880e6 594373.i 0.446963 0.248562i
357357 431458. 0.179171
358358 −988602. + 256397.i −0.407675 + 0.105732i
359359 1.33255e6 0.545691 0.272846 0.962058i 0.412035π-0.412035\pi
0.272846 + 0.962058i 0.412035π0.412035\pi
360360 −1.43299e6 + 1.30406e6i −0.582757 + 0.530325i
361361 −1.92072e6 −0.775705
362362 −819705. + 212593.i −0.328766 + 0.0852663i
363363 −1.14317e6 −0.455350
364364 −1.38314e6 2.48716e6i −0.547158 0.983898i
365365 −2.69797e6 61952.6i −1.06000 0.0243404i
366366 −125049. + 32431.7i −0.0487951 + 0.0126552i
367367 313330.i 0.121433i 0.998155 + 0.0607166i 0.0193386π0.0193386\pi
−0.998155 + 0.0607166i 0.980661π0.980661\pi
368368 2.65195e6 + 1.64698e6i 1.02081 + 0.633969i
369369 −2.10655e6 −0.805390
370370 3.46276e6 813716.i 1.31498 0.309007i
371371 5.62256e6i 2.12080i
372372 −1.02764e6 + 571481.i −0.385019 + 0.214114i
373373 2.93069e6 1.09068 0.545341 0.838215i 0.316400π-0.316400\pi
0.545341 + 0.838215i 0.316400π0.316400\pi
374374 24656.2 + 95068.1i 0.00911480 + 0.0351444i
375375 −86303.9 + 1.25105e6i −0.0316922 + 0.459407i
376376 −521014. + 496475.i −0.190055 + 0.181104i
377377 2.78171e6i 1.00800i
378378 2.50880e6 650665.i 0.903102 0.234222i
379379 4.10811e6i 1.46907i −0.678569 0.734537i 0.737399π-0.737399\pi
0.678569 0.734537i 0.262601π-0.262601\pi
380380 3.31916e6 1.74729e6i 1.17915 0.620736i
381381 1.22928e6i 0.433848i
382382 303780. + 1.17130e6i 0.106512 + 0.410685i
383383 958991.i 0.334055i 0.985952 + 0.167027i 0.0534168π0.0534168\pi
−0.985952 + 0.167027i 0.946583π0.946583\pi
384384 1.30262e6 271572.i 0.450806 0.0939846i
385385 −8000.07 + 348395.i −0.00275069 + 0.119790i
386386 3.99499e6 1.03611e6i 1.36473 0.353948i
387387 −1.61086e6 −0.546741
388388 −1.49271e6 2.68419e6i −0.503380 0.905178i
389389 647634.i 0.216998i 0.994097 + 0.108499i 0.0346044π0.0346044\pi
−0.994097 + 0.108499i 0.965396π0.965396\pi
390390 −1.33780e6 + 314370.i −0.445379 + 0.104660i
391391 1.24730e6 0.412599
392392 596164. + 625630.i 0.195952 + 0.205637i
393393 799827.i 0.261225i
394394 −1.30952e6 5.04919e6i −0.424984 1.63863i
395395 50599.6 2.20356e6i 0.0163175 0.710611i
396396 126364. + 227228.i 0.0404936 + 0.0728155i
397397 −2.06284e6 −0.656885 −0.328443 0.944524i 0.606524π-0.606524\pi
−0.328443 + 0.944524i 0.606524π0.606524\pi
398398 −1.39930e6 5.39535e6i −0.442796 1.70731i
399399 −2.21125e6 −0.695352
400400 −1.81125e6 + 2.63806e6i −0.566017 + 0.824394i
401401 −1.92225e6 −0.596964 −0.298482 0.954415i 0.596480π-0.596480\pi
−0.298482 + 0.954415i 0.596480π0.596480\pi
402402 −427091. 1.64676e6i −0.131812 0.508234i
403403 3.09885e6 0.950470
404404 −1.30485e6 2.34638e6i −0.397748 0.715229i
405405 −30977.5 + 1.34904e6i −0.00938446 + 0.408683i
406406 958623. + 3.69621e6i 0.288624 + 1.11286i
407407 477330.i 0.142834i
408408 384889. 366761.i 0.114468 0.109077i
409409 1.40471e6 0.415221 0.207610 0.978212i 0.433431π-0.433431\pi
0.207610 + 0.978212i 0.433431π0.433431\pi
410410 −3.38689e6 + 795888.i −0.995042 + 0.233826i
411411 2.02607e6i 0.591630i
412412 166308. + 299055.i 0.0482693 + 0.0867977i
413413 −5.37833e6 −1.55157
414414 3.19623e6 828952.i 0.916511 0.237700i
415415 59679.8 2.59899e6i 0.0170101 0.740773i
416416 −3.34807e6 1.04297e6i −0.948551 0.295487i
417417 316284.i 0.0890712i
418418 −126364. 487230.i −0.0353740 0.136393i
419419 4.03594e6i 1.12308i 0.827451 + 0.561538i 0.189790π0.189790\pi
−0.827451 + 0.561538i 0.810210π0.810210\pi
420420 1.66927e6 878748.i 0.461746 0.243075i
421421 594910.i 0.163586i 0.996649 + 0.0817929i 0.0260646π0.0260646\pi
−0.996649 + 0.0817929i 0.973935π0.973935\pi
422422 −5.10623e6 + 1.32432e6i −1.39579 + 0.362001i
423423 761229.i 0.206854i
424424 4.77947e6 + 5.01570e6i 1.29111 + 1.35493i
425425 −58687.2 + 1.27721e6i −0.0157605 + 0.342997i
426426 −735645. 2.83646e6i −0.196401 0.757274i
427427 −467352. −0.124044
428428 3.07053e6 1.70756e6i 0.810223 0.450575i
429429 184411.i 0.0483776i
430430 −2.58993e6 + 608609.i −0.675486 + 0.158733i
431431 4.15801e6 1.07818 0.539091 0.842247i 0.318768π-0.318768\pi
0.539091 + 0.842247i 0.318768π0.318768\pi
432432 1.68492e6 2.71305e6i 0.434380 0.699436i
433433 2.27636e6i 0.583474i −0.956499 0.291737i 0.905767π-0.905767\pi
0.956499 0.291737i 0.0942333π-0.0942333\pi
434434 −4.11761e6 + 1.06792e6i −1.04935 + 0.272153i
435435 1.84342e6 + 42329.8i 0.467090 + 0.0107256i
436436 −2.10914e6 3.79265e6i −0.531361 0.955492i
437437 −6.39247e6 −1.60127
438438 1.89757e6 492140.i 0.472620 0.122575i
439439 −1.28126e6 −0.317305 −0.158653 0.987334i 0.550715π-0.550715\pi
−0.158653 + 0.987334i 0.550715π0.550715\pi
440440 289017. + 317592.i 0.0711692 + 0.0782056i
441441 914079. 0.223814
442442 −1.35625e6 + 351748.i −0.330205 + 0.0856398i
443443 6.01266e6 1.45565 0.727825 0.685763i 0.240531π-0.240531\pi
0.727825 + 0.685763i 0.240531π0.240531\pi
444444 −2.25820e6 + 1.25581e6i −0.543632 + 0.302320i
445445 49044.7 2.13585e6i 0.0117407 0.511294i
446446 −4.09891e6 + 1.06306e6i −0.975733 + 0.253059i
447447 1.80576e6i 0.427455i
448448 4.80818e6 + 232054.i 1.13184 + 0.0546253i
449449 2.11543e6 0.495202 0.247601 0.968862i 0.420358π-0.420358\pi
0.247601 + 0.968862i 0.420358π0.420358\pi
450450 698445. + 3.31189e6i 0.162593 + 0.770983i
451451 466872.i 0.108083i
452452 3.03958e6 + 5.46577e6i 0.699790 + 1.25836i
453453 −687625. −0.157437
454454 2.08926e6 + 8.05567e6i 0.475722 + 1.83426i
455455 −4.97024e6 114130.i −1.12551 0.0258447i
456456 −1.97258e6 + 1.87967e6i −0.444245 + 0.423322i
457457 1.35964e6i 0.304533i 0.988339 + 0.152267i 0.0486573π0.0486573\pi
−0.988339 + 0.152267i 0.951343π0.951343\pi
458458 −4.57236e6 + 1.18586e6i −1.01854 + 0.264161i
459459 1.27603e6i 0.282703i
460460 4.82567e6 2.54036e6i 1.06332 0.559759i
461461 2.06438e6i 0.452415i −0.974079 0.226208i 0.927367π-0.927367\pi
0.974079 0.226208i 0.0726328π-0.0726328\pi
462462 −63551.2 245037.i −0.0138522 0.0534106i
463463 1.48917e6i 0.322843i −0.986886 0.161421i 0.948392π-0.948392\pi
0.986886 0.161421i 0.0516078π-0.0516078\pi
464464 3.99712e6 + 2.48239e6i 0.861892 + 0.535272i
465465 −47155.8 + 2.05359e6i −0.0101135 + 0.440434i
466466 −1.55903e6 + 404338.i −0.332574 + 0.0862541i
467467 7.05856e6 1.49770 0.748849 0.662741i 0.230607π-0.230607\pi
0.748849 + 0.662741i 0.230607π0.230607\pi
468468 −3.24166e6 + 1.80273e6i −0.684152 + 0.380465i
469469 6.15452e6i 1.29200i
470470 287604. + 1.22389e6i 0.0600552 + 0.255564i
471471 1.28108e6 0.266087
472472 −4.79783e6 + 4.57186e6i −0.991264 + 0.944577i
473473 357014.i 0.0733722i
474474 401954. + 1.54983e6i 0.0821732 + 0.316839i
475475 300776. 6.54578e6i 0.0611658 1.33115i
476476 1.68090e6 934772.i 0.340037 0.189099i
477477 7.32821e6 1.47469
478478 1.13701e6 + 4.38403e6i 0.227612 + 0.877614i
479479 1.47482e6 0.293697 0.146849 0.989159i 0.453087π-0.453087\pi
0.146849 + 0.989159i 0.453087π0.453087\pi
480480 742117. 2.20287e6i 0.147018 0.436400i
481481 6.80964e6 1.34203
482482 −2.13867e6 8.24619e6i −0.419302 1.61672i
483483 −3.21490e6 −0.627046
484484 −4.45366e6 + 2.47673e6i −0.864179 + 0.480580i
485485 −5.36397e6 123171.i −1.03546 0.0237769i
486486 −1.32237e6 5.09871e6i −0.253958 0.979196i
487487 9.13416e6i 1.74520i 0.488433 + 0.872602i 0.337569π0.337569\pi
−0.488433 + 0.872602i 0.662431π0.662431\pi
488488 −416909. + 397273.i −0.0792486 + 0.0755161i
489489 −1.05760e6 −0.200009
490490 1.46964e6 345353.i 0.276517 0.0649790i
491491 4.74188e6i 0.887660i −0.896111 0.443830i 0.853619π-0.853619\pi
0.896111 0.443830i 0.146381π-0.146381\pi
492492 2.20872e6 1.22830e6i 0.411366 0.228766i
493493 1.87997e6 0.348365
494494 6.95087e6 1.80273e6i 1.28151 0.332363i
495495 454083. + 10427.0i 0.0832957 + 0.00191269i
496496 −2.76540e6 + 4.45284e6i −0.504724 + 0.812704i
497497 1.06009e7i 1.92509i
498498 474086. + 1.82796e6i 0.0856611 + 0.330288i
499499 539009.i 0.0969046i 0.998825 + 0.0484523i 0.0154289π0.0154289\pi
−0.998825 + 0.0484523i 0.984571π0.984571\pi
500500 2.37423e6 + 5.06093e6i 0.424716 + 0.905327i
501501 2.23243e6i 0.397359i
502502 6.03724e6 1.56578e6i 1.06925 0.277313i
503503 2.21657e6i 0.390627i −0.980741 0.195313i 0.937428π-0.937428\pi
0.980741 0.195313i 0.0625724π-0.0625724\pi
504504 3.68612e6 3.51251e6i 0.646387 0.615943i
505505 −4.68891e6 107670.i −0.818171 0.0187874i
506506 −183719. 708376.i −0.0318991 0.122995i
507507 34484.2 0.00595800
508508 2.66329e6 + 4.78912e6i 0.457887 + 0.823372i
509509 3.35132e6i 0.573352i 0.958028 + 0.286676i 0.0925503π0.0925503\pi
−0.958028 + 0.286676i 0.907450π0.907450\pi
510510 −212462. 904129.i −0.0361706 0.153924i
511511 7.09190e6 1.20146
512512 4.48648e6 3.88019e6i 0.756363 0.654152i
513513 6.53974e6i 1.09715i
514514 −7.72281e6 + 2.00293e6i −1.28934 + 0.334394i
515515 597620. + 13722.9i 0.0992903 + 0.00227997i
516516 1.68899e6 939270.i 0.279257 0.155298i
517517 168710. 0.0277597
518518 −9.04834e6 + 2.34671e6i −1.48165 + 0.384269i
519519 863411. 0.140702
520520 −4.53080e6 + 4.12315e6i −0.734795 + 0.668683i
521521 5.01924e6 0.810109 0.405054 0.914293i 0.367253π-0.367253\pi
0.405054 + 0.914293i 0.367253π0.367253\pi
522522 4.81748e6 1.24943e6i 0.773827 0.200694i
523523 −3.44581e6 −0.550855 −0.275428 0.961322i 0.588819π-0.588819\pi
−0.275428 + 0.961322i 0.588819π0.588819\pi
524524 −1.73286e6 3.11602e6i −0.275699 0.495761i
525525 151266. 3.29200e6i 0.0239521 0.521269i
526526 −9.24727e6 + 2.39831e6i −1.45730 + 0.377955i
527527 2.09431e6i 0.328484i
528528 −264986. 164568.i −0.0413655 0.0256898i
529529 −2.85758e6 −0.443975
530530 1.17822e7 2.76871e6i 1.82195 0.428142i
531531 7.00988e6i 1.07888i
532532 −8.61474e6 + 4.79076e6i −1.31966 + 0.733881i
533533 −6.66044e6 −1.01551
534534 389603. + 1.50221e6i 0.0591247 + 0.227970i
535535 140900. 6.13603e6i 0.0212826 0.926836i
536536 −5.23166e6 5.49024e6i −0.786552 0.825429i
537537 1.29603e6i 0.193945i
538538 1.67473e6 434346.i 0.249453 0.0646963i
539539 202586.i 0.0300357i
540540 −2.59889e6 4.93684e6i −0.383534 0.728559i
541541 3.97667e6i 0.584153i 0.956395 + 0.292076i 0.0943461π0.0943461\pi
−0.956395 + 0.292076i 0.905654π0.905654\pi
542542 −1.77979e6 6.86244e6i −0.260238 1.00341i
543543 1.07461e6i 0.156405i
544544 704875. 2.26274e6i 0.102121 0.327821i
545545 −7.57908e6 174036.i −1.09301 0.0250985i
546546 3.49573e6 906627.i 0.501829 0.130151i
547547 −9.20664e6 −1.31563 −0.657814 0.753181i 0.728519π-0.728519\pi
−0.657814 + 0.753181i 0.728519π0.728519\pi
548548 −4.38957e6 7.89332e6i −0.624411 1.12281i
549549 609127.i 0.0862535i
550550 734009. 154795.i 0.103465 0.0218198i
551551 −9.63498e6 −1.35198
552552 −2.86790e6 + 2.73283e6i −0.400606 + 0.381738i
553553 5.79229e6i 0.805448i
554554 686489. + 2.64693e6i 0.0950296 + 0.366410i
555555 −103624. + 4.51270e6i −0.0142799 + 0.621876i
556556 685244. + 1.23220e6i 0.0940066 + 0.169042i
557557 6.00805e6 0.820531 0.410266 0.911966i 0.365436π-0.365436\pi
0.410266 + 0.911966i 0.365436π0.365436\pi
558558 1.39188e6 + 5.36672e6i 0.189241 + 0.729665i
559559 −5.09319e6 −0.689383
560560 4.59941e6 7.04003e6i 0.619773 0.948647i
561561 −124631. −0.0167194
562562 125997. + 485814.i 0.0168275 + 0.0648827i
563563 −3.22469e6 −0.428763 −0.214381 0.976750i 0.568774π-0.568774\pi
−0.214381 + 0.976750i 0.568774π0.568774\pi
564564 −443861. 798150.i −0.0587556 0.105654i
565565 1.09226e7 + 250811.i 1.43947 + 0.0330542i
566566 −2.50576e6 9.66158e6i −0.328775 1.26767i
567567 3.54609e6i 0.463225i
568568 −9.01130e6 9.45669e6i −1.17197 1.22990i
569569 −3.74802e6 −0.485312 −0.242656 0.970112i 0.578019π-0.578019\pi
−0.242656 + 0.970112i 0.578019π0.578019\pi
570570 1.08888e6 + 4.63372e6i 0.140376 + 0.597369i
571571 4.37966e6i 0.562148i 0.959686 + 0.281074i 0.0906906π0.0906906\pi
−0.959686 + 0.281074i 0.909309π0.909309\pi
572572 399535. + 718444.i 0.0510582 + 0.0918127i
573573 −1.53554e6 −0.195377
574574 8.85009e6 2.29530e6i 1.12116 0.290776i
575575 437293. 9.51681e6i 0.0551573 1.20039i
576576 302449. 6.26678e6i 0.0379836 0.787025i
577577 1.03145e7i 1.28976i −0.764284 0.644880i 0.776907π-0.776907\pi
0.764284 0.644880i 0.223093π-0.223093\pi
578578 1.77867e6 + 6.85810e6i 0.221450 + 0.853855i
579579 5.23732e6i 0.649251i
580580 7.27344e6 3.82893e6i 0.897779 0.472615i
581581 6.83173e6i 0.839635i
582582 3.77266e6 978449.i 0.461679 0.119738i
583583 1.62414e6i 0.197903i
584584 6.32645e6 6.02848e6i 0.767587 0.731435i
585585 −148752. + 6.47800e6i −0.0179710 + 0.782620i
586586 −12958.7 49965.5i −0.00155890 0.00601071i
587587 −5.88489e6 −0.704925 −0.352463 0.935826i 0.614656π-0.614656\pi
−0.352463 + 0.935826i 0.614656π0.614656\pi
588588 −958413. + 532985.i −0.114317 + 0.0635729i
589589 1.07335e7i 1.27483i
590590 2.64844e6 + 1.12704e7i 0.313228 + 1.33294i
591591 6.61934e6 0.779554
592592 −6.07689e6 + 9.78498e6i −0.712652 + 1.14751i
593593 1.07458e7i 1.25488i 0.778664 + 0.627442i 0.215898π0.215898\pi
−0.778664 + 0.627442i 0.784102π0.784102\pi
594594 −724696. + 187952.i −0.0842732 + 0.0218565i
595595 77132.8 3.35905e6i 0.00893196 0.388977i
596596 3.91226e6 + 7.03501e6i 0.451140 + 0.811239i
597597 7.07314e6 0.812226
598598 1.01058e7 2.62096e6i 1.15562 0.299714i
599599 1.01249e6 0.115299 0.0576493 0.998337i 0.481639π-0.481639\pi
0.0576493 + 0.998337i 0.481639π0.481639\pi
600600 −2.66343e6 3.06527e6i −0.302039 0.347608i
601601 7.16049e6 0.808643 0.404321 0.914617i 0.367508π-0.367508\pi
0.404321 + 0.914617i 0.367508π0.367508\pi
602602 6.76759e6 1.75520e6i 0.761102 0.197394i
603603 −8.02154e6 −0.898390
604604 −2.67890e6 + 1.48977e6i −0.298789 + 0.166160i
605605 −204368. + 8.90001e6i −0.0226999 + 0.988558i
606606 3.29786e6 855311.i 0.364797 0.0946112i
607607 1.22036e7i 1.34437i 0.740385 + 0.672183i 0.234643π0.234643\pi
−0.740385 + 0.672183i 0.765357π0.765357\pi
608608 −3.61253e6 + 1.15967e7i −0.396326 + 1.27225i
609609 −4.84562e6 −0.529427
610610 230137. + 979346.i 0.0250416 + 0.106564i
611611 2.40683e6i 0.260821i
612612 −1.21834e6 2.19082e6i −0.131489 0.236444i
613613 1.15888e7 1.24563 0.622815 0.782369i 0.285989π-0.285989\pi
0.622815 + 0.782369i 0.285989π0.285989\pi
614614 −3.75220e6 1.44675e7i −0.401666 1.54872i
615615 101353. 4.41382e6i 0.0108056 0.470573i
616616 −778471. 816948.i −0.0826591 0.0867447i
617617 1.47499e6i 0.155983i −0.996954 0.0779915i 0.975149π-0.975149\pi
0.996954 0.0779915i 0.0248507π-0.0248507\pi
618618 −420325. + 109013.i −0.0442705 + 0.0114817i
619619 6.94510e6i 0.728537i −0.931294 0.364269i 0.881319π-0.881319\pi
0.931294 0.364269i 0.118681π-0.118681\pi
620620 4.26547e6 + 8.10268e6i 0.445644 + 0.846544i
621621 9.50803e6i 0.989377i
622622 −1.99178e6 7.67981e6i −0.206427 0.795929i
623623 5.61430e6i 0.579530i
624624 2.34774e6 3.78032e6i 0.241373 0.388658i
625625 9.72447e6 + 895561.i 0.995786 + 0.0917055i
626626 −7.44183e6 + 1.93006e6i −0.759004 + 0.196850i
627627 638744. 0.0648870
628628 4.99093e6 2.77552e6i 0.504990 0.280831i
629629 4.60218e6i 0.463807i
630630 −2.03477e6 8.65893e6i −0.204251 0.869186i
631631 3.38551e6 0.338494 0.169247 0.985574i 0.445867π-0.445867\pi
0.169247 + 0.985574i 0.445867π0.445867\pi
632632 4.92374e6 + 5.16711e6i 0.490346 + 0.514582i
633633 6.69411e6i 0.664024i
634634 426529. + 1.64459e6i 0.0421430 + 0.162493i
635635 9.57037e6 + 219761.i 0.941878 + 0.0216280i
636636 −7.68364e6 + 4.27296e6i −0.753224 + 0.418877i
637637 2.89011e6 0.282206
638638 −276909. 1.06769e6i −0.0269330 0.103847i
639639 −1.38167e7 −1.33861
640640 −1.88141e6 1.01899e7i −0.181566 0.983379i
641641 −6.43478e6 −0.618570 −0.309285 0.950969i 0.600090π-0.600090\pi
−0.309285 + 0.950969i 0.600090π0.600090\pi
642642 1.11928e6 + 4.31567e6i 0.107177 + 0.413248i
643643 819506. 0.0781672 0.0390836 0.999236i 0.487556π-0.487556\pi
0.0390836 + 0.999236i 0.487556π0.487556\pi
644644 −1.25248e7 + 6.96522e6i −1.19003 + 0.661790i
645645 77504.0 3.37522e6i 0.00733541 0.319450i
646646 1.21834e6 + 4.69763e6i 0.114865 + 0.442892i
647647 1.00673e7i 0.945482i 0.881201 + 0.472741i 0.156735π0.156735\pi
−0.881201 + 0.472741i 0.843265π0.843265\pi
648648 −3.01436e6 3.16335e6i −0.282006 0.295944i
649649 1.55359e6 0.144785
650650 2.20833e6 + 1.04714e7i 0.205012 + 0.972127i
651651 5.39807e6i 0.499213i
652652 −4.12029e6 + 2.29134e6i −0.379584 + 0.211092i
653653 3.73524e6 0.342796 0.171398 0.985202i 0.445172π-0.445172\pi
0.171398 + 0.985202i 0.445172π0.445172\pi
654654 5.33061e6 1.38251e6i 0.487341 0.126393i
655655 −6.22694e6 142987.i −0.567115 0.0130225i
656656 5.94375e6 9.57059e6i 0.539263 0.868319i
657657 9.24328e6i 0.835435i
658658 −829434. 3.19809e6i −0.0746822 0.287956i
659659 2.11585e6i 0.189789i 0.995487 + 0.0948947i 0.0302514π0.0302514\pi
−0.995487 + 0.0948947i 0.969749π0.969749\pi
660660 −482187. + 253836.i −0.0430879 + 0.0226827i
661661 1.89096e7i 1.68337i −0.539970 0.841684i 0.681565π-0.681565\pi
0.539970 0.841684i 0.318435π-0.318435\pi
662662 1.30071e7 3.37344e6i 1.15355 0.299177i
663663 1.77800e6i 0.157090i
664664 5.80733e6 + 6.09436e6i 0.511159 + 0.536424i
665665 −395310. + 1.72154e7i −0.0346644 + 1.50960i
666666 3.05861e6 + 1.17932e7i 0.267201 + 1.03026i
667667 −1.40082e7 −1.21918
668668 4.83665e6 + 8.69726e6i 0.419376 + 0.754121i
669669 5.37355e6i 0.464190i
670670 −1.28969e7 + 3.03066e6i −1.10994 + 0.260826i
671671 135000. 0.0115752
672672 −1.81681e6 + 5.83218e6i −0.155198 + 0.498205i
673673 2.10683e6i 0.179304i 0.995973 + 0.0896522i 0.0285755π0.0285755\pi
−0.995973 + 0.0896522i 0.971424π0.971424\pi
674674 −2.02562e7 + 5.25350e6i −1.71754 + 0.445450i
675675 −9.73606e6 447368.i −0.822477 0.0377925i
676676 134346. 74711.6i 0.0113073 0.00628813i
677677 −5.17934e6 −0.434313 −0.217156 0.976137i 0.569678π-0.569678\pi
−0.217156 + 0.976137i 0.569678π0.569678\pi
678678 −7.68220e6 + 1.99240e6i −0.641817 + 0.166457i
679679 1.40998e7 1.17365
680680 −2.78656e6 3.06207e6i −0.231098 0.253947i
681681 −1.05607e7 −0.872623
682682 1.18942e6 308479.i 0.0979206 0.0253960i
683683 8.80956e6 0.722608 0.361304 0.932448i 0.382332π-0.382332\pi
0.361304 + 0.932448i 0.382332π0.382332\pi
684684 6.24408e6 + 1.12281e7i 0.510303 + 0.917626i
685685 −1.57737e7 362206.i −1.28442 0.0294937i
686686 9.67940e6 2.51038e6i 0.785304 0.203671i
687687 5.99423e6i 0.484553i
688688 4.54514e6 7.31856e6i 0.366080 0.589460i
689689 2.31701e7 1.85943
690690 1.58311e6 + 6.73689e6i 0.126587 + 0.538688i
691691 5.78539e6i 0.460933i −0.973080 0.230466i 0.925975π-0.925975\pi
0.973080 0.230466i 0.0740252π-0.0740252\pi
692692 3.36374e6 1.87062e6i 0.267028 0.148498i
693693 −1.19361e6 −0.0944122
694694 2.81691e6 + 1.08613e7i 0.222011 + 0.856018i
695695 2.46239e6 + 56543.0i 0.193372 + 0.00444034i
696696 −4.32262e6 + 4.11903e6i −0.338239 + 0.322308i
697697 4.50135e6i 0.350963i
698698 −8.31371e6 + 2.15619e6i −0.645887 + 0.167513i
699699 2.04384e6i 0.158217i
700700 −6.54295e6 1.31529e7i −0.504694 1.01456i
701701 2.01716e7i 1.55041i −0.631711 0.775204i 0.717647π-0.717647\pi
0.631711 0.775204i 0.282353π-0.282353\pi
702702 −2.68134e6 1.03386e7i −0.205357 0.791805i
703703 2.35865e7i 1.80001i
704704 −1.38890e6 67031.4i −0.105618 0.00509738i
705705 −1.59499e6 36625.2i −0.120861 0.00277528i
706706 1.12906e7 2.92824e6i 0.852519 0.221103i
707707 1.23253e7 0.927362
708708 −4.08735e6 7.34987e6i −0.306450 0.551057i
709709 1.71661e7i 1.28250i 0.767334 + 0.641248i 0.221583π0.221583\pi
−0.767334 + 0.641248i 0.778417π0.778417\pi
710710 −2.22144e7 + 5.22018e6i −1.65382 + 0.388633i
711711 7.54943e6 0.560067
712712 4.77245e6 + 5.00833e6i 0.352810 + 0.370248i
713713 1.56052e7i 1.14960i
714714 612729. + 2.36253e6i 0.0449804 + 0.173433i
715715 1.43571e6 + 32967.7i 0.105027 + 0.00241170i
716716 −2.80790e6 5.04916e6i −0.204691 0.368075i
717717 −5.74733e6 −0.417511
718718 1.89240e6 + 7.29663e6i 0.136994 + 0.528215i
719719 1.37927e7 0.995009 0.497505 0.867461i 0.334250π-0.334250\pi
0.497505 + 0.867461i 0.334250π0.334250\pi
720720 −9.17569e6 5.99468e6i −0.659641 0.430958i
721721 −1.57091e6 −0.112541
722722 −2.72769e6 1.05173e7i −0.194739 0.750863i
723723 1.08105e7 0.769132
724724 −2.32819e6 4.18654e6i −0.165071 0.296831i
725725 659105. 1.43441e7i 0.0465704 1.01351i
726726 −1.62346e6 6.25966e6i −0.114314 0.440767i
727727 9.10175e6i 0.638688i 0.947639 + 0.319344i 0.103463π0.103463\pi
−0.947639 + 0.319344i 0.896537π0.896537\pi
728728 1.16547e7 1.11058e7i 0.815026 0.776640i
729729 818554. 0.0570465
730730 −3.49225e6 1.48612e7i −0.242549 1.03216i
731731 3.44215e6i 0.238252i
732732 −355172. 638670.i −0.0244997 0.0440554i
733733 −1.79637e7 −1.23491 −0.617456 0.786605i 0.711837π-0.711837\pi
−0.617456 + 0.786605i 0.711837π0.711837\pi
734734 −1.71570e6 + 444972.i −0.117544 + 0.0304855i
735735 −43979.3 + 1.91525e6i −0.00300283 + 0.130770i
736736 −5.25220e6 + 1.68602e7i −0.357394 + 1.14728i
737737 1.77780e6i 0.120563i
738738 −2.99159e6 1.15348e7i −0.202191 0.779598i
739739 1.38839e7i 0.935192i −0.883942 0.467596i 0.845120π-0.845120\pi
0.883942 0.467596i 0.154880π-0.154880\pi
740740 9.37325e6 + 1.78054e7i 0.629232 + 1.19529i
741741 9.11238e6i 0.609658i
742742 −3.07874e7 + 7.98480e6i −2.05288 + 0.532420i
743743 2.37521e6i 0.157845i −0.996881 0.0789225i 0.974852π-0.974852\pi
0.996881 0.0789225i 0.0251480π-0.0251480\pi
744744 −4.58864e6 4.81544e6i −0.303914 0.318936i
745745 1.40585e7 + 322820.i 0.927999 + 0.0213093i
746746 4.16198e6 + 1.60476e7i 0.273812 + 1.05575i
747747 8.90419e6 0.583839
748748 −485548. + 270019.i −0.0317306 + 0.0176458i
749749 1.61292e7i 1.05053i
750750 −6.97295e6 + 1.30409e6i −0.452651 + 0.0846556i
751751 −1.99260e7 −1.28920 −0.644600 0.764520i 0.722976π-0.722976\pi
−0.644600 + 0.764520i 0.722976π0.722976\pi
752752 −3.45845e6 2.14785e6i −0.223017 0.138503i
753753 7.91465e6i 0.508679i
754754 1.52318e7 3.95041e6i 0.975714 0.253054i
755755 −122929. + 5.35341e6i −0.00784848 + 0.341793i
756756 7.12568e6 + 1.28134e7i 0.453442 + 0.815379i
757757 −1.30771e7 −0.829413 −0.414707 0.909955i 0.636116π-0.636116\pi
−0.414707 + 0.909955i 0.636116π0.636116\pi
758758 2.24947e7 5.83407e6i 1.42203 0.368807i
759759 928660. 0.0585130
760760 1.42813e7 + 1.56933e7i 0.896879 + 0.985552i
761761 −1.75251e7 −1.09698 −0.548492 0.836156i 0.684798π-0.684798\pi
−0.548492 + 0.836156i 0.684798π0.684798\pi
762762 −6.73115e6 + 1.74574e6i −0.419954 + 0.108916i
763763 1.99224e7 1.23888
764764 −5.98226e6 + 3.32681e6i −0.370794 + 0.206203i
765765 −4.37805e6 100532.i −0.270475 0.00621082i
766766 −5.25114e6 + 1.36190e6i −0.323356 + 0.0838634i
767767 2.21637e7i 1.36036i
768768 3.33694e6 + 6.74708e6i 0.204148 + 0.412775i
769769 −3.13820e7 −1.91366 −0.956830 0.290647i 0.906129π-0.906129\pi
−0.956830 + 0.290647i 0.906129π0.906129\pi
770770 −1.91906e6 + 450963.i −0.116644 + 0.0274103i
771771 1.01244e7i 0.613384i
772772 1.13469e7 + 2.04039e7i 0.685225 + 1.23217i
773773 103265. 0.00621590 0.00310795 0.999995i 0.499011π-0.499011\pi
0.00310795 + 0.999995i 0.499011π0.499011\pi
774774 −2.28765e6 8.82060e6i −0.137258 0.529232i
775775 1.59795e7 + 734250.i 0.955671 + 0.0439126i
776776 1.25779e7 1.19855e7i 0.749817 0.714502i
777777 1.18621e7i 0.704870i
778778 −3.54625e6 + 919729.i −0.210049 + 0.0544767i
779779 2.30697e7i 1.36207i
780780 −3.62125e6 6.87893e6i −0.213119 0.404841i
781781 3.06218e6i 0.179640i
782782 1.77133e6 + 6.82981e6i 0.103582 + 0.399385i
783783 1.43309e7i 0.835350i
784784 −2.57912e6 + 4.15289e6i −0.149859 + 0.241302i
785785 229022. 9.97368e6i 0.0132649 0.577672i
786786 4.37960e6 1.13586e6i 0.252859 0.0655798i
787787 5.01823e6 0.288811 0.144405 0.989519i 0.453873π-0.453873\pi
0.144405 + 0.989519i 0.453873π0.453873\pi
788788 2.57881e7 1.43411e7i 1.47946 0.822748i
789789 1.21229e7i 0.693288i
790790 1.21379e7 2.85229e6i 0.691950 0.162602i
791791 −2.87111e7 −1.63158
792792 −1.06478e6 + 1.01463e6i −0.0603178 + 0.0574769i
793793 1.92592e6i 0.108757i
794794 −2.92952e6 1.12955e7i −0.164909 0.635849i
795795 −352584. + 1.53547e7i −0.0197854 + 0.861634i
796796 2.75561e7 1.53243e7i 1.54147 0.857230i
797797 9.61578e6 0.536215 0.268107 0.963389i 0.413602π-0.413602\pi
0.268107 + 0.963389i 0.413602π0.413602\pi
798798 −3.14027e6 1.21081e7i −0.174566 0.673084i
799799 −1.62662e6 −0.0901403
800800 −1.70174e7 6.17146e6i −0.940089 0.340928i
801801 7.31745e6 0.402975
802802 −2.72985e6 1.05256e7i −0.149866 0.577846i
803803 −2.04857e6 −0.112115
804804 8.41060e6 4.67724e6i 0.458867 0.255182i
805805 −574736. + 2.50291e7i −0.0312592 + 1.36131i
806806 4.40080e6 + 1.69684e7i 0.238613 + 0.920031i
807807 2.19552e6i 0.118673i
808808 1.09950e7 1.04771e7i 0.592470 0.564566i
809809 2.06325e7 1.10836 0.554181 0.832396i 0.313032π-0.313032\pi
0.554181 + 0.832396i 0.313032π0.313032\pi
810810 −7.43092e6 + 1.74620e6i −0.397951 + 0.0935149i
811811 3.18795e7i 1.70200i 0.525164 + 0.851001i 0.324004π0.324004\pi
−0.525164 + 0.851001i 0.675996π0.675996\pi
812812 −1.88779e7 + 1.04982e7i −1.00476 + 0.558762i
813813 8.99645e6 0.477359
814814 2.61371e6 677875.i 0.138260 0.0358582i
815815 −189070. + 8.23381e6i −0.00997078 + 0.434217i
816816 2.55487e6 + 1.58668e6i 0.134321 + 0.0834189i
817817 1.76412e7i 0.924642i
818818 1.99488e6 + 7.69177e6i 0.104240 + 0.401923i
819819 1.70281e7i 0.887067i
820820 −9.16788e6 1.74153e7i −0.476140 0.904474i
821821 7.88522e6i 0.408278i −0.978942 0.204139i 0.934561π-0.934561\pi
0.978942 0.204139i 0.0654394π-0.0654394\pi
822822 1.10941e7 2.87730e6i 0.572683 0.148527i
823823 51764.9i 0.00266401i −0.999999 0.00133200i 0.999576π-0.999576\pi
0.999999 0.00133200i 0.000423990π-0.000423990\pi
824824 −1.40135e6 + 1.33535e6i −0.0719002 + 0.0685138i
825825 −43694.9 + 950932.i −0.00223509 + 0.0486423i
826826 −7.63796e6 2.94501e7i −0.389518 1.50188i
827827 5.24793e6 0.266824 0.133412 0.991061i 0.457407π-0.457407\pi
0.133412 + 0.991061i 0.457407π0.457407\pi
828828 9.07818e6 + 1.63244e7i 0.460175 + 0.827485i
829829 6.76109e6i 0.341689i 0.985298 + 0.170844i 0.0546495π0.0546495\pi
−0.985298 + 0.170844i 0.945350π0.945350\pi
830830 1.43160e7 3.36414e6i 0.721320 0.169504i
831831 −3.47004e6 −0.174314
832832 956277. 1.98141e7i 0.0478934 0.992355i
833833 1.95323e6i 0.0975308i
834834 −1.73188e6 + 449167.i −0.0862187 + 0.0223611i
835835 1.73802e7 + 399097.i 0.862660 + 0.0198090i
836836 2.48847e6 1.38387e6i 0.123145 0.0684823i
837837 −1.59647e7 −0.787677
838838 −2.20995e7 + 5.73158e6i −1.08711 + 0.281945i
839839 −5.32681e6 −0.261254 −0.130627 0.991432i 0.541699π-0.541699\pi
−0.130627 + 0.991432i 0.541699π0.541699\pi
840840 7.18234e6 + 7.89245e6i 0.351211 + 0.385935i
841841 −602476. −0.0293731
842842 −3.25754e6 + 844853.i −0.158347 + 0.0410678i
843843 −636887. −0.0308669
844844 −1.45031e7 2.60794e7i −0.700816 1.26021i
845845 6164.83 268472.i 0.000297016 0.0129347i
846846 −4.16826e6 + 1.08105e6i −0.200230 + 0.0519302i
847847 2.33946e7i 1.12049i
848848 −2.06769e7 + 3.32939e7i −0.987407 + 1.58992i
849849 1.26660e7 0.603076
850850 −7.07695e6 + 1.49246e6i −0.335969 + 0.0708525i
851851 3.42920e7i 1.62319i
852852 1.44869e7 8.05633e6i 0.683716 0.380223i
853853 −8.20548e6 −0.386128 −0.193064 0.981186i 0.561843π-0.561843\pi
−0.193064 + 0.981186i 0.561843π0.561843\pi
854854 −663704. 2.55907e6i −0.0311408 0.120071i
855855 2.24378e7 + 515231.i 1.04970 + 0.0241039i
856856 1.37107e7 + 1.43883e7i 0.639549 + 0.671160i
857857 5.45868e6i 0.253884i 0.991910 + 0.126942i 0.0405162π0.0405162\pi
−0.991910 + 0.126942i 0.959484π0.959484\pi
858858 −1.00978e6 + 261889.i −0.0468283 + 0.0121451i
859859 3.18230e7i 1.47149i 0.677257 + 0.735747i 0.263169π0.263169\pi
−0.677257 + 0.735747i 0.736831π0.736831\pi
860860 −7.01061e6 1.33173e7i −0.323229 0.614004i
861861 1.16022e7i 0.533375i
862862 5.90494e6 + 2.27680e7i 0.270675 + 1.04365i
863863 9.28914e6i 0.424569i −0.977208 0.212285i 0.931910π-0.931910\pi
0.977208 0.212285i 0.0680904π-0.0680904\pi
864864 1.72486e7 + 5.37320e6i 0.786086 + 0.244877i
865865 154354. 6.72196e6i 0.00701420 0.305461i
866866 1.24647e7 3.23275e6i 0.564789 0.146480i
867867 −8.99077e6 −0.406208
868868 −1.16951e7 2.10302e7i −0.526874 0.947423i
869869 1.67317e6i 0.0751606i
870870 2.38612e6 + 1.01541e7i 0.106880 + 0.454824i
871871 −2.53623e7 −1.13277
872872 1.77721e7 1.69351e7i 0.791495 0.754217i
873873 1.83771e7i 0.816094i
874874 −9.07819e6 3.50032e7i −0.401995 1.54999i
875875 −2.56024e7 1.76618e6i −1.13047 0.0779856i
876876 5.38961e6 + 9.69159e6i 0.237300 + 0.426712i
877877 1.60806e7 0.705997 0.352999 0.935624i 0.385162π-0.385162\pi
0.352999 + 0.935624i 0.385162π0.385162\pi
878878 −1.81957e6 7.01580e6i −0.0796585 0.307143i
879879 65503.2 0.00285950
880880 −1.32859e6 + 2.03359e6i −0.0578342 + 0.0885233i
881881 −1.74471e7 −0.757327 −0.378663 0.925535i 0.623616π-0.623616\pi
−0.378663 + 0.925535i 0.623616π0.623616\pi
882882 1.29812e6 + 5.00522e6i 0.0561879 + 0.216646i
883883 −2.18862e7 −0.944645 −0.472323 0.881426i 0.656584π-0.656584\pi
−0.472323 + 0.881426i 0.656584π0.656584\pi
884884 −3.85212e6 6.92688e6i −0.165794 0.298131i
885885 −1.46877e7 337268.i −0.630370 0.0144750i
886886 8.53880e6 + 3.29235e7i 0.365437 + 1.40903i
887887 4.00556e7i 1.70944i −0.519088 0.854721i 0.673728π-0.673728\pi
0.519088 0.854721i 0.326272π-0.326272\pi
888888 −1.00834e7 1.05818e7i −0.429116 0.450326i
889889 −2.51567e7 −1.06758
890890 1.17649e7 2.76464e6i 0.497867 0.116994i
891891 1.02433e6i 0.0432260i
892892 −1.16420e7 2.09347e7i −0.489910 0.880955i
893893 8.33653e6 0.349830
894894 −9.88778e6 + 2.56442e6i −0.413766 + 0.107311i
895895 −1.00900e7 231694.i −0.421051 0.00966846i
896896 5.55762e6 + 2.66577e7i 0.231270 + 1.10931i
897897 1.32484e7i 0.549770i
898898 3.00420e6 + 1.15834e7i 0.124319 + 0.479343i
899899 2.35208e7i 0.970628i
900900 −1.71430e7 + 8.52781e6i −0.705473 + 0.350939i
901901 1.56592e7i 0.642623i
902902 −2.55645e6 + 663022.i −0.104621 + 0.0271339i
903903 8.87211e6i 0.362083i
904904 −2.56123e7 + 2.44060e7i −1.04238 + 0.993287i
905905 −8.36622e6 192111.i −0.339553 0.00779704i
906906 −976522. 3.76523e6i −0.0395241 0.152395i
907907 1.61797e7 0.653060 0.326530 0.945187i 0.394121π-0.394121\pi
0.326530 + 0.945187i 0.394121π0.394121\pi
908908 −4.11433e7 + 2.28803e7i −1.65609 + 0.920974i
909909 1.60643e7i 0.644840i
910910 −6.43348e6 2.73776e7i −0.257539 1.09595i
911911 3.81429e7 1.52271 0.761356 0.648334i 0.224534π-0.224534\pi
0.761356 + 0.648334i 0.224534π0.224534\pi
912912 −1.30939e7 8.13185e6i −0.521291 0.323744i
913913 1.97342e6i 0.0783508i
914914 −7.44500e6 + 1.93088e6i −0.294781 + 0.0764523i
915915 −1.27629e6 29307.1i −0.0503962 0.00115723i
916916 −1.29868e7 2.33528e7i −0.511402 0.919601i
917917 1.63682e7 0.642801
918918 6.98716e6 1.81214e6i 0.273649 0.0709717i
919919 −5.75041e6 −0.224600 −0.112300 0.993674i 0.535822π-0.535822\pi
−0.112300 + 0.993674i 0.535822π0.535822\pi
920920 2.07634e7 + 2.28162e7i 0.808776 + 0.888739i
921921 1.89665e7 0.736780
922922 1.13039e7 2.93170e6i 0.437927 0.113578i
923923 −4.36854e7 −1.68784
924924 1.25150e6 695973.i 0.0482225 0.0268171i
925925 3.51144e7 + 1.61349e6i 1.34937 + 0.0620030i
926926 8.15422e6 2.11482e6i 0.312504 0.0810487i
927927 2.04745e6i 0.0782555i
928928 −7.91632e6 + 2.54124e7i −0.301754 + 0.968668i
929929 1.58033e7 0.600771 0.300386 0.953818i 0.402885π-0.402885\pi
0.300386 + 0.953818i 0.402885π0.402885\pi
930930 −1.13118e7 + 2.65816e6i −0.428868 + 0.100780i
931931 1.00104e7i 0.378512i
932932 −4.42806e6 7.96254e6i −0.166984 0.300270i
933933 1.00680e7 0.378651
934934 1.00241e7 + 3.86505e7i 0.375993 + 1.44973i
935935 −22280.7 + 970300.i −0.000833488 + 0.0362975i
936936 −1.44748e7 1.51902e7i −0.540035 0.566727i
937937 1.61564e7i 0.601167i 0.953756 + 0.300583i 0.0971814π0.0971814\pi
−0.953756 + 0.300583i 0.902819π0.902819\pi
938938 3.37003e7 8.74026e6i 1.25062 0.324353i
939939 9.75602e6i 0.361084i
940940 −6.29323e6 + 3.31293e6i −0.232303 + 0.122290i
941941 4.39614e7i 1.61844i −0.587504 0.809221i 0.699889π-0.699889\pi
0.587504 0.809221i 0.300111π-0.300111\pi
942942 1.81931e6 + 7.01481e6i 0.0668005 + 0.257566i
943943 3.35407e7i 1.22827i
944944 −3.18476e7 1.97788e7i −1.16318 0.722385i
945945 2.56058e7 + 587976.i 0.932735 + 0.0214181i
946946 −1.95490e6 + 507008.i −0.0710225 + 0.0184199i
947947 −4.52665e7 −1.64022 −0.820111 0.572205i 0.806088π-0.806088\pi
−0.820111 + 0.572205i 0.806088π0.806088\pi
948948 −7.91558e6 + 4.40195e6i −0.286063 + 0.159083i
949949 2.92252e7i 1.05340i
950950 3.62698e7 7.64895e6i 1.30388 0.274975i
951951 −2.15601e6 −0.0773035
952952 7.50564e6 + 7.87661e6i 0.268408 + 0.281674i
953953 3.21216e6i 0.114569i 0.998358 + 0.0572843i 0.0182441π0.0182441\pi
−0.998358 + 0.0572843i 0.981756π0.981756\pi
954954 1.04071e7 + 4.01270e7i 0.370218 + 1.42747i
955955 −274512. + 1.19547e7i −0.00973986 + 0.424161i
956956 −2.23909e7 + 1.24518e7i −0.792367 + 0.440645i
957957 1.39971e6 0.0494036
958958 2.09444e6 + 8.07565e6i 0.0737318 + 0.284292i
959959 4.14628e7 1.45583
960960 1.31161e7 + 935232.i 0.459333 + 0.0327523i
961961 −2.42676e6 −0.0847654
962962 9.67063e6 + 3.72875e7i 0.336912 + 1.29905i
963963 2.10221e7 0.730485
964964 4.21164e7 2.34215e7i 1.45968 0.811748i
965965 4.07744e7 + 936288.i 1.40951 + 0.0323662i
966966 −4.56560e6 1.76038e7i −0.157418 0.606965i
967967 4.06241e6i 0.139707i −0.997557 0.0698533i 0.977747π-0.977747\pi
0.997557 0.0698533i 0.0222531π-0.0222531\pi
968968 −1.98866e7 2.08696e7i −0.682139 0.715855i
969969 −6.15845e6 −0.210699
970970 −6.94313e6 2.95464e7i −0.236933 1.00827i
971971 2.41409e7i 0.821685i 0.911706 + 0.410842i 0.134765π0.134765\pi
−0.911706 + 0.410842i 0.865235π0.865235\pi
972972 2.60410e7 1.44817e7i 0.884082 0.491649i
973973 −6.47264e6 −0.219179
974974 −5.00158e7 + 1.29718e7i −1.68931 + 0.438128i
975975 −1.35661e7 623355.i −0.457028 0.0210002i
976976 −2.76741e6 1.71868e6i −0.0929928 0.0577526i
977977 1.48416e7i 0.497443i 0.968575 + 0.248722i 0.0800104π0.0800104\pi
−0.968575 + 0.248722i 0.919990π0.919990\pi
978978 −1.50194e6 5.79110e6i −0.0502118 0.193604i
979979 1.62175e6i 0.0540790i
980980 3.97814e6 + 7.55687e6i 0.132317 + 0.251349i
981981 2.59661e7i 0.861457i
982982 2.59651e7 6.73412e6i 0.859233 0.222845i
983983 3.34107e7i 1.10281i 0.834237 + 0.551406i 0.185908π0.185908\pi
−0.834237 + 0.551406i 0.814092π0.814092\pi
984984 9.86247e6 + 1.03499e7i 0.324712 + 0.340761i
985985 1.18336e6 5.15339e7i 0.0388620 1.69240i
986986 2.66982e6 + 1.02942e7i 0.0874560 + 0.337208i
987987 4.19260e6 0.136991
988988 1.97424e7 + 3.55007e7i 0.643438 + 1.15703i
989989 2.56483e7i 0.833812i
990990 587766. + 2.50123e6i 0.0190597 + 0.0811083i
991991 5.15057e7 1.66599 0.832993 0.553284i 0.186626π-0.186626\pi
0.832993 + 0.553284i 0.186626π0.186626\pi
992992 −2.83096e7 8.81886e6i −0.913387 0.284533i
993993 1.70520e7i 0.548784i
994994 5.80472e7 1.50547e7i 1.86344 0.483288i
995995 1.26448e6 5.50670e7i 0.0404907 1.76333i
996996 −9.33606e6 + 5.19190e6i −0.298205 + 0.165836i
997997 −1.18985e7 −0.379102 −0.189551 0.981871i 0.560703π-0.560703\pi
−0.189551 + 0.981871i 0.560703π0.560703\pi
998998 −2.95144e6 + 765466.i −0.0938012 + 0.0243276i
999999 −3.50821e7 −1.11217
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 40.6.f.a.29.18 yes 28
4.3 odd 2 160.6.f.a.49.18 28
5.2 odd 4 200.6.d.e.101.4 28
5.3 odd 4 200.6.d.e.101.25 28
5.4 even 2 inner 40.6.f.a.29.11 28
8.3 odd 2 160.6.f.a.49.12 28
8.5 even 2 inner 40.6.f.a.29.12 yes 28
20.3 even 4 800.6.d.e.401.22 28
20.7 even 4 800.6.d.e.401.7 28
20.19 odd 2 160.6.f.a.49.11 28
40.3 even 4 800.6.d.e.401.21 28
40.13 odd 4 200.6.d.e.101.26 28
40.19 odd 2 160.6.f.a.49.17 28
40.27 even 4 800.6.d.e.401.8 28
40.29 even 2 inner 40.6.f.a.29.17 yes 28
40.37 odd 4 200.6.d.e.101.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.f.a.29.11 28 5.4 even 2 inner
40.6.f.a.29.12 yes 28 8.5 even 2 inner
40.6.f.a.29.17 yes 28 40.29 even 2 inner
40.6.f.a.29.18 yes 28 1.1 even 1 trivial
160.6.f.a.49.11 28 20.19 odd 2
160.6.f.a.49.12 28 8.3 odd 2
160.6.f.a.49.17 28 40.19 odd 2
160.6.f.a.49.18 28 4.3 odd 2
200.6.d.e.101.3 28 40.37 odd 4
200.6.d.e.101.4 28 5.2 odd 4
200.6.d.e.101.25 28 5.3 odd 4
200.6.d.e.101.26 28 40.13 odd 4
800.6.d.e.401.7 28 20.7 even 4
800.6.d.e.401.8 28 40.27 even 4
800.6.d.e.401.21 28 40.3 even 4
800.6.d.e.401.22 28 20.3 even 4