Properties

Label 84.6.e.a.71.49
Level 8484
Weight 66
Character 84.71
Analytic conductor 13.47213.472
Analytic rank 00
Dimension 6060
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,6,Mod(71,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.71");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 84=2237 84 = 2^{2} \cdot 3 \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 84.e (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 13.472240864313.4722408643
Analytic rank: 00
Dimension: 6060
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 71.49
Character χ\chi == 84.71
Dual form 84.6.e.a.71.50

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(4.400933.55413i)q2+(2.02884+15.4559i)q3+(6.7363731.2829i)q444.2997iq5+(46.0033+75.2309i)q649.0000iq7+(81.5372161.616i)q8+(234.76862.7150i)q9+(157.447194.960i)q10+344.560q11+(469.838+167.584i)q12378.416q13+(174.152215.646i)q14+(684.690+89.8770i)q15+(933.243421.466i)q161696.09iq17+(1256.09+558.389i)q182579.78iq19+(1385.82298.419i)q20+(757.337+99.4133i)q21+(1516.381224.61i)q22+526.327q23+(2663.34932.335i)q24+1162.54q25+(1665.38+1344.94i)q26+(1445.623501.30i)q27+(1532.86330.082i)q28+6045.46iq29+(3332.702037.93i)q302887.35iq31+(5605.08+1462.02i)q32+(699.058+5325.47i)q33+(6028.117464.37i)q342170.68q35+(3543.39+6921.75i)q363591.74q37+(9168.8511353.4i)q38+(767.7475848.75i)q39+(7159.53+3612.07i)q40+12630.3iq41+(3686.322254.16i)q42+21579.3iq43+(2321.0810778.8i)q44+(2778.25+10400.1i)q45+(2316.331870.63i)q46+16221.6q47+(8407.5313569.0i)q482401.00q49+(5116.264131.82i)q50+(26214.5+3441.10i)q51+(2549.15+11838.0i)q5221958.7iq53+(6081.9820546.9i)q5415263.9iq55+(7919.18+3995.32i)q56+(39872.7+5233.96i)q57+(21486.3+26605.6i)q587005.98q59+(7423.9320813.6i)q60+7136.98q61+(10262.012707.0i)q62+(3073.04+11503.6i)q63+(19471.4+26355.4i)q64+16763.7iq65+(15850.9+25921.6i)q66+18300.1iq67+(53058.611425.5i)q68+(1067.83+8134.83i)q69+(9553.02+7714.88i)q70+77638.4q71+(9006.55+43055.8i)q7253127.5q73+(15807.0+12765.5i)q74+(2358.61+17968.1i)q75+(80702.917378.3i)q7616883.4iq77+(17408.428468.6i)q788353.39iq79+(18670.8+41342.3i)q80+(51182.7+29446.9i)q81+(44889.7+55585.1i)q82+76137.1q83+(8211.6423022.0i)q8475136.1q85+(76695.5+94968.9i)q86+(93437.812265.3i)q87+(28094.455686.3i)q88+9040.37iq89+(24736.5+55644.5i)q90+18542.4iq91+(3545.5316465.0i)q92+(44626.5+5857.98i)q93+(71390.357653.7i)q94114283.q95+(11224.989597.6i)q9652693.1q97+(10566.6+8533.46i)q98+(80891.521609.1i)q99+O(q100)q+(4.40093 - 3.55413i) q^{2} +(-2.02884 + 15.4559i) q^{3} +(6.73637 - 31.2829i) q^{4} -44.2997i q^{5} +(46.0033 + 75.2309i) q^{6} -49.0000i q^{7} +(-81.5372 - 161.616i) q^{8} +(-234.768 - 62.7150i) q^{9} +(-157.447 - 194.960i) q^{10} +344.560 q^{11} +(469.838 + 167.584i) q^{12} -378.416 q^{13} +(-174.152 - 215.646i) q^{14} +(684.690 + 89.8770i) q^{15} +(-933.243 - 421.466i) q^{16} -1696.09i q^{17} +(-1256.09 + 558.389i) q^{18} -2579.78i q^{19} +(-1385.82 - 298.419i) q^{20} +(757.337 + 99.4133i) q^{21} +(1516.38 - 1224.61i) q^{22} +526.327 q^{23} +(2663.34 - 932.335i) q^{24} +1162.54 q^{25} +(-1665.38 + 1344.94i) q^{26} +(1445.62 - 3501.30i) q^{27} +(-1532.86 - 330.082i) q^{28} +6045.46i q^{29} +(3332.70 - 2037.93i) q^{30} -2887.35i q^{31} +(-5605.08 + 1462.02i) q^{32} +(-699.058 + 5325.47i) q^{33} +(-6028.11 - 7464.37i) q^{34} -2170.68 q^{35} +(-3543.39 + 6921.75i) q^{36} -3591.74 q^{37} +(-9168.85 - 11353.4i) q^{38} +(767.747 - 5848.75i) q^{39} +(-7159.53 + 3612.07i) q^{40} +12630.3i q^{41} +(3686.32 - 2254.16i) q^{42} +21579.3i q^{43} +(2321.08 - 10778.8i) q^{44} +(-2778.25 + 10400.1i) q^{45} +(2316.33 - 1870.63i) q^{46} +16221.6 q^{47} +(8407.53 - 13569.0i) q^{48} -2401.00 q^{49} +(5116.26 - 4131.82i) q^{50} +(26214.5 + 3441.10i) q^{51} +(-2549.15 + 11838.0i) q^{52} -21958.7i q^{53} +(-6081.98 - 20546.9i) q^{54} -15263.9i q^{55} +(-7919.18 + 3995.32i) q^{56} +(39872.7 + 5233.96i) q^{57} +(21486.3 + 26605.6i) q^{58} -7005.98 q^{59} +(7423.93 - 20813.6i) q^{60} +7136.98 q^{61} +(-10262.0 - 12707.0i) q^{62} +(-3073.04 + 11503.6i) q^{63} +(-19471.4 + 26355.4i) q^{64} +16763.7i q^{65} +(15850.9 + 25921.6i) q^{66} +18300.1i q^{67} +(-53058.6 - 11425.5i) q^{68} +(-1067.83 + 8134.83i) q^{69} +(-9553.02 + 7714.88i) q^{70} +77638.4 q^{71} +(9006.55 + 43055.8i) q^{72} -53127.5 q^{73} +(-15807.0 + 12765.5i) q^{74} +(-2358.61 + 17968.1i) q^{75} +(-80702.9 - 17378.3i) q^{76} -16883.4i q^{77} +(-17408.4 - 28468.6i) q^{78} -8353.39i q^{79} +(-18670.8 + 41342.3i) q^{80} +(51182.7 + 29446.9i) q^{81} +(44889.7 + 55585.1i) q^{82} +76137.1 q^{83} +(8211.64 - 23022.0i) q^{84} -75136.1 q^{85} +(76695.5 + 94968.9i) q^{86} +(-93437.8 - 12265.3i) q^{87} +(-28094.4 - 55686.3i) q^{88} +9040.37i q^{89} +(24736.5 + 55644.5i) q^{90} +18542.4i q^{91} +(3545.53 - 16465.0i) q^{92} +(44626.5 + 5857.98i) q^{93} +(71390.3 - 57653.7i) q^{94} -114283. q^{95} +(-11224.9 - 89597.6i) q^{96} -52693.1 q^{97} +(-10566.6 + 8533.46i) q^{98} +(-80891.5 - 21609.1i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 60q20q4114q6+44q9+668q10+786q123004q163320q18+7120q22+16466q2437500q257448q2835236q309424q33+43360q34+50524q36++232584q97+O(q100) 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/84Z)×\left(\mathbb{Z}/84\mathbb{Z}\right)^\times.

nn 2929 4343 7373
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 4.40093 3.55413i 0.777982 0.628287i
33 −2.02884 + 15.4559i −0.130150 + 0.991494i
44 6.73637 31.2829i 0.210511 0.977591i
55 44.2997i 0.792456i −0.918152 0.396228i 0.870319π-0.870319\pi
0.918152 0.396228i 0.129681π-0.129681\pi
66 46.0033 + 75.2309i 0.521688 + 0.853136i
77 49.0000i 0.377964i
88 −81.5372 161.616i −0.450434 0.892810i
99 −234.768 62.7150i −0.966122 0.258087i
1010 −157.447 194.960i −0.497890 0.616517i
1111 344.560 0.858584 0.429292 0.903166i 0.358763π-0.358763\pi
0.429292 + 0.903166i 0.358763π0.358763\pi
1212 469.838 + 167.584i 0.941878 + 0.335955i
1313 −378.416 −0.621029 −0.310514 0.950569i 0.600501π-0.600501\pi
−0.310514 + 0.950569i 0.600501π0.600501\pi
1414 −174.152 215.646i −0.237470 0.294049i
1515 684.690 + 89.8770i 0.785716 + 0.103138i
1616 −933.243 421.466i −0.911370 0.411588i
1717 1696.09i 1.42340i −0.702485 0.711699i 0.747926π-0.747926\pi
0.702485 0.711699i 0.252074π-0.252074\pi
1818 −1256.09 + 558.389i −0.913778 + 0.406215i
1919 2579.78i 1.63945i −0.572758 0.819724i 0.694127π-0.694127\pi
0.572758 0.819724i 0.305873π-0.305873\pi
2020 −1385.82 298.419i −0.774698 0.166821i
2121 757.337 + 99.4133i 0.374750 + 0.0491922i
2222 1516.38 1224.61i 0.667963 0.539437i
2323 526.327 0.207461 0.103730 0.994605i 0.466922π-0.466922\pi
0.103730 + 0.994605i 0.466922π0.466922\pi
2424 2663.34 932.335i 0.943840 0.330403i
2525 1162.54 0.372013
2626 −1665.38 + 1344.94i −0.483149 + 0.390184i
2727 1445.62 3501.30i 0.381632 0.924314i
2828 −1532.86 330.082i −0.369495 0.0795658i
2929 6045.46i 1.33486i 0.744675 + 0.667428i 0.232605π0.232605\pi
−0.744675 + 0.667428i 0.767395π0.767395\pi
3030 3332.70 2037.93i 0.676073 0.413415i
3131 2887.35i 0.539629i −0.962912 0.269815i 0.913038π-0.913038\pi
0.962912 0.269815i 0.0869625π-0.0869625\pi
3232 −5605.08 + 1462.02i −0.967625 + 0.252393i
3333 −699.058 + 5325.47i −0.111745 + 0.851281i
3434 −6028.11 7464.37i −0.894302 1.10738i
3535 −2170.68 −0.299520
3636 −3543.39 + 6921.75i −0.455683 + 0.890142i
3737 −3591.74 −0.431321 −0.215660 0.976468i 0.569190π-0.569190\pi
−0.215660 + 0.976468i 0.569190π0.569190\pi
3838 −9168.85 11353.4i −1.03004 1.27546i
3939 767.747 5848.75i 0.0808271 0.615746i
4040 −7159.53 + 3612.07i −0.707513 + 0.356949i
4141 12630.3i 1.17342i 0.809796 + 0.586711i 0.199578π0.199578\pi
−0.809796 + 0.586711i 0.800422π0.800422\pi
4242 3686.32 2254.16i 0.322455 0.197180i
4343 21579.3i 1.77978i 0.456176 + 0.889889i 0.349219π0.349219\pi
−0.456176 + 0.889889i 0.650781π0.650781\pi
4444 2321.08 10778.8i 0.180742 0.839345i
4545 −2778.25 + 10400.1i −0.204522 + 0.765609i
4646 2316.33 1870.63i 0.161401 0.130345i
4747 16221.6 1.07115 0.535575 0.844488i 0.320095π-0.320095\pi
0.535575 + 0.844488i 0.320095π0.320095\pi
4848 8407.53 13569.0i 0.526702 0.850050i
4949 −2401.00 −0.142857
5050 5116.26 4131.82i 0.289419 0.233731i
5151 26214.5 + 3441.10i 1.41129 + 0.185256i
5252 −2549.15 + 11838.0i −0.130734 + 0.607112i
5353 21958.7i 1.07379i −0.843650 0.536893i 0.819598π-0.819598\pi
0.843650 0.536893i 0.180402π-0.180402\pi
5454 −6081.98 20546.9i −0.283831 0.958874i
5555 15263.9i 0.680391i
5656 −7919.18 + 3995.32i −0.337450 + 0.170248i
5757 39872.7 + 5233.96i 1.62550 + 0.213375i
5858 21486.3 + 26605.6i 0.838672 + 1.03849i
5959 −7005.98 −0.262023 −0.131011 0.991381i 0.541822π-0.541822\pi
−0.131011 + 0.991381i 0.541822π0.541822\pi
6060 7423.93 20813.6i 0.266229 0.746397i
6161 7136.98 0.245578 0.122789 0.992433i 0.460816π-0.460816\pi
0.122789 + 0.992433i 0.460816π0.460816\pi
6262 −10262.0 12707.0i −0.339042 0.419822i
6363 −3073.04 + 11503.6i −0.0975475 + 0.365160i
6464 −19471.4 + 26355.4i −0.594219 + 0.804303i
6565 16763.7i 0.492138i
6666 15850.9 + 25921.6i 0.447913 + 0.732489i
6767 18300.1i 0.498042i 0.968498 + 0.249021i 0.0801088π0.0801088\pi
−0.968498 + 0.249021i 0.919891π0.919891\pi
6868 −53058.6 11425.5i −1.39150 0.299641i
6969 −1067.83 + 8134.83i −0.0270011 + 0.205696i
7070 −9553.02 + 7714.88i −0.233021 + 0.188185i
7171 77638.4 1.82781 0.913904 0.405931i 0.133053π-0.133053\pi
0.913904 + 0.405931i 0.133053π0.133053\pi
7272 9006.55 + 43055.8i 0.204752 + 0.978814i
7373 −53127.5 −1.16684 −0.583422 0.812169i 0.698287π-0.698287\pi
−0.583422 + 0.812169i 0.698287π0.698287\pi
7474 −15807.0 + 12765.5i −0.335560 + 0.270993i
7575 −2358.61 + 17968.1i −0.0484176 + 0.368849i
7676 −80702.9 17378.3i −1.60271 0.345123i
7777 16883.4i 0.324514i
7878 −17408.4 28468.6i −0.323983 0.529822i
7979 8353.39i 0.150590i −0.997161 0.0752948i 0.976010π-0.976010\pi
0.997161 0.0752948i 0.0239898π-0.0239898\pi
8080 −18670.8 + 41342.3i −0.326166 + 0.722221i
8181 51182.7 + 29446.9i 0.866783 + 0.498686i
8282 44889.7 + 55585.1i 0.737246 + 0.912901i
8383 76137.1 1.21311 0.606556 0.795041i 0.292551π-0.292551\pi
0.606556 + 0.795041i 0.292551π0.292551\pi
8484 8211.64 23022.0i 0.126979 0.355996i
8585 −75136.1 −1.12798
8686 76695.5 + 94968.9i 1.11821 + 1.38464i
8787 −93437.8 12265.3i −1.32350 0.173732i
8888 −28094.4 55686.3i −0.386735 0.766553i
8989 9040.37i 0.120979i 0.998169 + 0.0604897i 0.0192662π0.0192662\pi
−0.998169 + 0.0604897i 0.980734π0.980734\pi
9090 24736.5 + 55644.5i 0.321908 + 0.724129i
9191 18542.4i 0.234727i
9292 3545.53 16465.0i 0.0436728 0.202812i
9393 44626.5 + 5857.98i 0.535039 + 0.0702329i
9494 71390.3 57653.7i 0.833335 0.672989i
9595 −114283. −1.29919
9696 −11224.9 89597.6i −0.124310 0.992243i
9797 −52693.1 −0.568623 −0.284311 0.958732i 0.591765π-0.591765\pi
−0.284311 + 0.958732i 0.591765π0.591765\pi
9898 −10566.6 + 8533.46i −0.111140 + 0.0897553i
9999 −80891.5 21609.1i −0.829497 0.221589i
100100 7831.30 36367.7i 0.0783130 0.363677i
101101 82630.2i 0.806000i −0.915200 0.403000i 0.867967π-0.867967\pi
0.915200 0.403000i 0.132033π-0.132033\pi
102102 127598. 78025.7i 1.21435 0.742570i
103103 69948.5i 0.649659i −0.945773 0.324829i 0.894693π-0.894693\pi
0.945773 0.324829i 0.105307π-0.105307\pi
104104 30855.0 + 61158.1i 0.279732 + 0.554461i
105105 4403.97 33549.8i 0.0389827 0.296973i
106106 −78044.2 96638.9i −0.674646 0.835386i
107107 46494.7 0.392594 0.196297 0.980544i 0.437108π-0.437108\pi
0.196297 + 0.980544i 0.437108π0.437108\pi
108108 −99792.6 68809.3i −0.823264 0.567659i
109109 122497. 0.987552 0.493776 0.869589i 0.335616π-0.335616\pi
0.493776 + 0.869589i 0.335616π0.335616\pi
110110 −54249.8 67175.3i −0.427480 0.529331i
111111 7287.07 55513.4i 0.0561365 0.427652i
112112 −20651.9 + 45728.9i −0.155566 + 0.344465i
113113 58741.6i 0.432762i 0.976309 + 0.216381i 0.0694254π0.0694254\pi
−0.976309 + 0.216381i 0.930575π0.930575\pi
114114 194079. 118678.i 1.39867 0.855281i
115115 23316.1i 0.164404i
116116 189120. + 40724.4i 1.30494 + 0.281002i
117117 88839.9 + 23732.4i 0.599989 + 0.160279i
118118 −30832.8 + 24900.1i −0.203849 + 0.164625i
119119 −83108.3 −0.537994
120120 −41302.1 117985.i −0.261830 0.747952i
121121 −42329.5 −0.262833
122122 31409.3 25365.7i 0.191055 0.154294i
123123 −195212. 25624.9i −1.16344 0.152721i
124124 −90324.8 19450.3i −0.527537 0.113598i
125125 189937.i 1.08726i
126126 27361.1 + 61548.6i 0.153535 + 0.345375i
127127 125876.i 0.692520i −0.938139 0.346260i 0.887451π-0.887451\pi
0.938139 0.346260i 0.112549π-0.112549\pi
128128 7978.36 + 185192.i 0.0430416 + 0.999073i
129129 −333527. 43781.0i −1.76464 0.231639i
130130 59580.4 + 73775.9i 0.309204 + 0.382874i
131131 74756.6 0.380602 0.190301 0.981726i 0.439054π-0.439054\pi
0.190301 + 0.981726i 0.439054π0.439054\pi
132132 161887. + 57742.9i 0.808682 + 0.288445i
133133 −126409. −0.619653
134134 65040.8 + 80537.4i 0.312913 + 0.387468i
135135 −155106. 64040.5i −0.732479 0.302427i
136136 −274115. + 138294.i −1.27082 + 0.641146i
137137 368808.i 1.67880i −0.543513 0.839401i 0.682906π-0.682906\pi
0.543513 0.839401i 0.317094π-0.317094\pi
138138 24212.8 + 39596.1i 0.108230 + 0.176992i
139139 409405.i 1.79728i 0.438687 + 0.898640i 0.355444π0.355444\pi
−0.438687 + 0.898640i 0.644556π0.644556\pi
140140 −14622.5 + 67905.3i −0.0630524 + 0.292808i
141141 −32911.1 + 250719.i −0.139410 + 1.06204i
142142 341681. 275937.i 1.42200 1.14839i
143143 −130387. −0.533205
144144 192663. + 157475.i 0.774269 + 0.632857i
145145 267812. 1.05781
146146 −233811. + 188822.i −0.907783 + 0.733112i
147147 4871.25 37109.5i 0.0185929 0.141642i
148148 −24195.3 + 112360.i −0.0907979 + 0.421655i
149149 394571.i 1.45599i −0.685580 0.727997i 0.740452π-0.740452\pi
0.685580 0.727997i 0.259548π-0.259548\pi
150150 53480.7 + 87459.0i 0.194075 + 0.317378i
151151 8762.51i 0.0312742i −0.999878 0.0156371i 0.995022π-0.995022\pi
0.999878 0.0156371i 0.00497765π-0.00497765\pi
152152 −416933. + 210348.i −1.46372 + 0.738463i
153153 −106370. + 398187.i −0.367360 + 1.37518i
154154 −60005.9 74302.8i −0.203888 0.252466i
155155 −127909. −0.427633
156156 −177794. 63416.7i −0.584933 0.208637i
157157 413913. 1.34017 0.670085 0.742284i 0.266258π-0.266258\pi
0.670085 + 0.742284i 0.266258π0.266258\pi
158158 −29689.0 36762.7i −0.0946135 0.117156i
159159 339391. + 44550.8i 1.06465 + 0.139754i
160160 64766.9 + 248303.i 0.200011 + 0.766800i
161161 25790.0i 0.0784128i
162162 329909. 52315.8i 0.987659 0.156619i
163163 156479.i 0.461304i 0.973036 + 0.230652i 0.0740859π0.0740859\pi
−0.973036 + 0.230652i 0.925914π0.925914\pi
164164 395113. + 85082.4i 1.14713 + 0.247019i
165165 235917. + 30968.0i 0.674603 + 0.0885530i
166166 335074. 270601.i 0.943779 0.762182i
167167 256467. 0.711607 0.355804 0.934561i 0.384207π-0.384207\pi
0.355804 + 0.934561i 0.384207π0.384207\pi
168168 −45684.4 130504.i −0.124881 0.356738i
169169 −228094. −0.614323
170170 −330669. + 267043.i −0.877548 + 0.708695i
171171 −161791. + 605648.i −0.423120 + 1.58391i
172172 675063. + 145366.i 1.73990 + 0.374664i
173173 40911.6i 0.103928i −0.998649 0.0519638i 0.983452π-0.983452\pi
0.998649 0.0519638i 0.0165480π-0.0165480\pi
174174 −454805. + 278111.i −1.13881 + 0.696378i
175175 56964.5i 0.140608i
176176 −321558. 145220.i −0.782488 0.353383i
177177 14214.0 108283.i 0.0341023 0.259794i
178178 32130.6 + 39786.0i 0.0760097 + 0.0941198i
179179 380158. 0.886811 0.443406 0.896321i 0.353770π-0.353770\pi
0.443406 + 0.896321i 0.353770π0.353770\pi
180180 306631. + 156971.i 0.705399 + 0.361109i
181181 −658395. −1.49379 −0.746896 0.664941i 0.768457π-0.768457\pi
−0.746896 + 0.664941i 0.768457π0.768457\pi
182182 65902.1 + 81603.8i 0.147476 + 0.182613i
183183 −14479.8 + 110308.i −0.0319621 + 0.243489i
184184 −42915.2 85062.7i −0.0934473 0.185223i
185185 159113.i 0.341803i
186186 217218. 132828.i 0.460377 0.281518i
187187 584404.i 1.22211i
188188 109275. 507460.i 0.225489 1.04715i
189189 −171564. 70835.4i −0.349358 0.144243i
190190 −502952. + 406177.i −1.01075 + 0.816265i
191191 −165125. −0.327514 −0.163757 0.986501i 0.552361π-0.552361\pi
−0.163757 + 0.986501i 0.552361π0.552361\pi
192192 −367841. 354418.i −0.720124 0.693845i
193193 769958. 1.48790 0.743950 0.668235i 0.232950π-0.232950\pi
0.743950 + 0.668235i 0.232950π0.232950\pi
194194 −231899. + 187278.i −0.442378 + 0.357258i
195195 −259098. 34010.9i −0.487952 0.0640519i
196196 −16174.0 + 75110.3i −0.0300731 + 0.139656i
197197 647382.i 1.18849i 0.804285 + 0.594244i 0.202549π0.202549\pi
−0.804285 + 0.594244i 0.797451π0.797451\pi
198198 −432799. + 192399.i −0.784555 + 0.348770i
199199 129883.i 0.232499i 0.993220 + 0.116249i 0.0370872π0.0370872\pi
−0.993220 + 0.116249i 0.962913π0.962913\pi
200200 −94790.3 187885.i −0.167567 0.332137i
201201 −282844. 37128.0i −0.493806 0.0648203i
202202 −293678. 363650.i −0.506399 0.627054i
203203 296227. 0.504528
204204 284238. 796886.i 0.478197 1.34067i
205205 559518. 0.929886
206206 −248606. 307838.i −0.408172 0.505423i
207207 −123564. 33008.6i −0.200432 0.0535428i
208208 353154. + 159490.i 0.565987 + 0.255608i
209209 888887.i 1.40761i
210210 −99858.6 163303.i −0.156256 0.255532i
211211 448543.i 0.693581i 0.937943 + 0.346791i 0.112729π0.112729\pi
−0.937943 + 0.346791i 0.887271π0.887271\pi
212212 −686934. 147922.i −1.04972 0.226044i
213213 −157516. + 1.19997e6i −0.237890 + 1.81226i
214214 204620. 165248.i 0.305431 0.246662i
215215 955955. 1.41040
216216 −683737. + 51850.7i −0.997137 + 0.0756172i
217217 −141480. −0.203961
218218 539101. 435370.i 0.768297 0.620466i
219219 107787. 821132.i 0.151865 1.15692i
220220 −477499. 102823.i −0.665144 0.143230i
221221 641828.i 0.883971i
222222 −165232. 270210.i −0.225015 0.367975i
223223 1.18883e6i 1.60087i −0.599420 0.800435i 0.704602π-0.704602\pi
0.599420 0.800435i 0.295398π-0.295398\pi
224224 71638.9 + 274649.i 0.0953958 + 0.365728i
225225 −272927. 72908.8i −0.359410 0.0960115i
226226 208775. + 258518.i 0.271899 + 0.336681i
227227 1.08067e6 1.39197 0.695983 0.718058i 0.254969π-0.254969\pi
0.695983 + 0.718058i 0.254969π0.254969\pi
228228 432330. 1.21208e6i 0.550780 1.54416i
229229 773995. 0.975325 0.487663 0.873032i 0.337850π-0.337850\pi
0.487663 + 0.873032i 0.337850π0.337850\pi
230230 −82868.3 102612.i −0.103293 0.127903i
231231 260948. + 34253.8i 0.321754 + 0.0422356i
232232 977042. 492930.i 1.19177 0.601264i
233233 713125.i 0.860550i 0.902698 + 0.430275i 0.141583π0.141583\pi
−0.902698 + 0.430275i 0.858417π0.858417\pi
234234 475326. 211304.i 0.567482 0.252271i
235235 718613.i 0.848839i
236236 −47194.8 + 219168.i −0.0551588 + 0.256151i
237237 129109. + 16947.7i 0.149309 + 0.0195993i
238238 −365754. + 295378.i −0.418549 + 0.338014i
239239 −1.44920e6 −1.64110 −0.820549 0.571577i 0.806332π-0.806332\pi
−0.820549 + 0.571577i 0.806332π0.806332\pi
240240 −601101. 372451.i −0.673627 0.417389i
241241 −1.01525e6 −1.12598 −0.562988 0.826465i 0.690348π-0.690348\pi
−0.562988 + 0.826465i 0.690348π0.690348\pi
242242 −186289. + 150444.i −0.204479 + 0.165135i
243243 −558969. + 731329.i −0.607256 + 0.794506i
244244 48077.3 223266.i 0.0516970 0.240075i
245245 106363.i 0.113208i
246246 −950190. + 581036.i −1.00109 + 0.612161i
247247 976229.i 1.01814i
248248 −466642. + 235427.i −0.481786 + 0.243067i
249249 −154470. + 1.17676e6i −0.157887 + 1.20279i
250250 −675059. 835897.i −0.683111 0.845869i
251251 708118. 0.709449 0.354724 0.934971i 0.384575π-0.384575\pi
0.354724 + 0.934971i 0.384575π0.384575\pi
252252 339166. + 173626.i 0.336442 + 0.172232i
253253 181351. 0.178122
254254 −447378. 553970.i −0.435101 0.538768i
255255 152439. 1.16129e6i 0.146807 1.11839i
256256 693308. + 786661.i 0.661190 + 0.750218i
257257 1.30567e6i 1.23310i −0.787314 0.616552i 0.788529π-0.788529\pi
0.787314 0.616552i 0.211471π-0.211471\pi
258258 −1.62343e6 + 992719.i −1.51839 + 0.928490i
259259 175995.i 0.163024i
260260 524418. + 112927.i 0.481110 + 0.103601i
261261 379141. 1.41928e6i 0.344508 1.28963i
262262 328999. 265695.i 0.296102 0.239127i
263263 358891. 0.319943 0.159972 0.987122i 0.448860π-0.448860\pi
0.159972 + 0.987122i 0.448860π0.448860\pi
264264 917680. 321245.i 0.810366 0.283679i
265265 −972765. −0.850929
266266 −556317. + 449274.i −0.482079 + 0.389320i
267267 −139727. 18341.5i −0.119950 0.0157455i
268268 572480. + 123276.i 0.486882 + 0.104844i
269269 680424.i 0.573322i 0.958032 + 0.286661i 0.0925454π0.0925454\pi
−0.958032 + 0.286661i 0.907455π0.907455\pi
270270 −910220. + 269430.i −0.759866 + 0.224924i
271271 122132.i 0.101020i 0.998724 + 0.0505098i 0.0160846π0.0160846\pi
−0.998724 + 0.0505098i 0.983915π0.983915\pi
272272 −714844. + 1.58286e6i −0.585854 + 1.29724i
273273 −286589. 37619.6i −0.232730 0.0305498i
274274 −1.31079e6 1.62310e6i −1.05477 1.30608i
275275 400565. 0.319405
276276 247288. + 88204.2i 0.195403 + 0.0696974i
277277 1.45307e6 1.13786 0.568928 0.822387i 0.307358π-0.307358\pi
0.568928 + 0.822387i 0.307358π0.307358\pi
278278 1.45508e6 + 1.80176e6i 1.12921 + 1.39825i
279279 −181080. + 677857.i −0.139271 + 0.521348i
280280 176991. + 350817.i 0.134914 + 0.267415i
281281 2.25718e6i 1.70530i 0.522484 + 0.852649i 0.325005π0.325005\pi
−0.522484 + 0.852649i 0.674995π0.674995\pi
282282 746249. + 1.22037e6i 0.558806 + 0.913836i
283283 568122.i 0.421672i −0.977521 0.210836i 0.932381π-0.932381\pi
0.977521 0.210836i 0.0676187π-0.0676187\pi
284284 523000. 2.42876e6i 0.384774 1.78685i
285285 231862. 1.76635e6i 0.169090 1.28814i
286286 −573825. + 463412.i −0.414824 + 0.335006i
287287 618885. 0.443512
288288 1.40758e6 + 8288.07i 0.999983 + 0.00588806i
289289 −1.45686e6 −1.02606
290290 1.17862e6 951837.i 0.822960 0.664611i
291291 106906. 814417.i 0.0740064 0.563786i
292292 −357887. + 1.66199e6i −0.245634 + 1.14070i
293293 2.31878e6i 1.57794i −0.614430 0.788972i 0.710614π-0.710614\pi
0.614430 0.788972i 0.289386π-0.289386\pi
294294 −110454. 180629.i −0.0745269 0.121877i
295295 310362.i 0.207641i
296296 292860. + 580482.i 0.194281 + 0.385087i
297297 498103. 1.20641e6i 0.327664 0.793602i
298298 −1.40236e6 1.73648e6i −0.914782 1.13274i
299299 −199171. −0.128839
300300 546205. + 194824.i 0.350391 + 0.124980i
301301 1.05739e6 0.672693
302302 −31143.1 38563.2i −0.0196492 0.0243308i
303303 1.27712e6 + 167644.i 0.799145 + 0.104901i
304304 −1.08729e6 + 2.40756e6i −0.674778 + 1.49414i
305305 316166.i 0.194610i
306306 947078. + 2.13044e6i 0.578205 + 1.30067i
307307 1.29505e6i 0.784224i 0.919917 + 0.392112i 0.128256π0.128256\pi
−0.919917 + 0.392112i 0.871744π0.871744\pi
308308 −528163. 113733.i −0.317242 0.0683140i
309309 1.08111e6 + 141914.i 0.644133 + 0.0845532i
310310 −562917. + 454604.i −0.332690 + 0.268676i
311311 −2.90926e6 −1.70562 −0.852810 0.522221i 0.825103π-0.825103\pi
−0.852810 + 0.522221i 0.825103π0.825103\pi
312312 −1.00785e6 + 352811.i −0.586152 + 0.205190i
313313 −1.86057e6 −1.07346 −0.536728 0.843755i 0.680340π-0.680340\pi
−0.536728 + 0.843755i 0.680340π0.680340\pi
314314 1.82160e6 1.47110e6i 1.04263 0.842011i
315315 509606. + 136134.i 0.289373 + 0.0773022i
316316 −261319. 56271.5i −0.147215 0.0317008i
317317 229634.i 0.128348i −0.997939 0.0641738i 0.979559π-0.979559\pi
0.997939 0.0641738i 0.0204412π-0.0204412\pi
318318 1.65198e6 1.01018e6i 0.916086 0.560182i
319319 2.08302e6i 1.14609i
320320 1.16754e6 + 862575.i 0.637375 + 0.470893i
321321 −94330.4 + 718616.i −0.0510963 + 0.389255i
322322 −91661.0 113500.i −0.0492657 0.0610037i
323323 −4.37553e6 −2.33359
324324 1.26597e6 1.40278e6i 0.669979 0.742380i
325325 −439925. −0.231031
326326 556146. + 688653.i 0.289831 + 0.358886i
327327 −248527. + 1.89330e6i −0.128530 + 0.979152i
328328 2.04126e6 1.02984e6i 1.04764 0.528549i
329329 794860.i 0.404856i
330330 1.14832e6 702189.i 0.580466 0.354952i
331331 768951.i 0.385770i 0.981221 + 0.192885i 0.0617845π0.0617845\pi
−0.981221 + 0.192885i 0.938216π0.938216\pi
332332 512887. 2.38179e6i 0.255374 1.18593i
333333 843224. + 225256.i 0.416708 + 0.111318i
334334 1.12869e6 911516.i 0.553617 0.447093i
335335 810687. 0.394677
336336 −664880. 411969.i −0.321289 0.199075i
337337 −342359. −0.164213 −0.0821064 0.996624i 0.526165π-0.526165\pi
−0.0821064 + 0.996624i 0.526165π0.526165\pi
338338 −1.00383e6 + 810675.i −0.477932 + 0.385971i
339339 −907902. 119177.i −0.429081 0.0563241i
340340 −506144. + 2.35048e6i −0.237453 + 1.10270i
341341 994866.i 0.463317i
342342 1.44052e6 + 3.24044e6i 0.665969 + 1.49809i
343343 117649.i 0.0539949i
344344 3.48756e6 1.75952e6i 1.58900 0.801672i
345345 360370. + 47304.7i 0.163005 + 0.0213972i
346346 −145405. 180049.i −0.0652964 0.0808538i
347347 −3.46788e6 −1.54611 −0.773055 0.634339i 0.781272π-0.781272\pi
−0.773055 + 0.634339i 0.781272π0.781272\pi
348348 −1.01312e6 + 2.84038e6i −0.448451 + 1.25727i
349349 2.86639e6 1.25971 0.629856 0.776712i 0.283114π-0.283114\pi
0.629856 + 0.776712i 0.283114π0.283114\pi
350350 −202459. 250697.i −0.0883420 0.109390i
351351 −547047. + 1.32495e6i −0.237005 + 0.574026i
352352 −1.93129e6 + 503753.i −0.830787 + 0.216701i
353353 3.99256e6i 1.70535i 0.522438 + 0.852677i 0.325022π0.325022\pi
−0.522438 + 0.852677i 0.674978π0.674978\pi
354354 −322298. 527066.i −0.136694 0.223541i
355355 3.43935e6i 1.44846i
356356 282809. + 60899.3i 0.118268 + 0.0254675i
357357 168614. 1.28451e6i 0.0700200 0.533418i
358358 1.67305e6 1.35113e6i 0.689923 0.557172i
359359 2.03633e6 0.833896 0.416948 0.908930i 0.363100π-0.363100\pi
0.416948 + 0.908930i 0.363100π0.363100\pi
360360 1.90736e6 398987.i 0.775667 0.162257i
361361 −4.17914e6 −1.68779
362362 −2.89755e6 + 2.34002e6i −1.16214 + 0.938529i
363363 85879.9 654239.i 0.0342078 0.260597i
364364 580061. + 124908.i 0.229467 + 0.0494127i
365365 2.35353e6i 0.924673i
366366 328325. + 536922.i 0.128115 + 0.209512i
367367 2.00386e6i 0.776610i 0.921531 + 0.388305i 0.126939π0.126939\pi
−0.921531 + 0.388305i 0.873061π0.873061\pi
368368 −491191. 221829.i −0.189073 0.0853884i
369369 792110. 2.96519e6i 0.302845 1.13367i
370370 565507. + 700244.i 0.214750 + 0.265916i
371371 −1.07598e6 −0.405853
372372 483876. 1.35659e6i 0.181291 0.508265i
373373 −642838. −0.239237 −0.119619 0.992820i 0.538167π-0.538167\pi
−0.119619 + 0.992820i 0.538167π0.538167\pi
374374 −2.07705e6 2.57192e6i −0.767833 0.950777i
375375 2.93563e6 + 385351.i 1.07801 + 0.141507i
376376 −1.32267e6 2.62167e6i −0.482482 0.956332i
377377 2.28770e6i 0.828983i
378378 −1.00680e6 + 298017.i −0.362420 + 0.107278i
379379 1.88523e6i 0.674167i −0.941475 0.337083i 0.890560π-0.890560\pi
0.941475 0.337083i 0.109440π-0.109440\pi
380380 −769853. + 3.57511e6i −0.273495 + 1.27008i
381381 1.94552e6 + 255382.i 0.686630 + 0.0901317i
382382 −726705. + 586876.i −0.254800 + 0.205773i
383383 −3.44186e6 −1.19894 −0.599469 0.800398i 0.704622π-0.704622\pi
−0.599469 + 0.800398i 0.704622π0.704622\pi
384384 −2.87849e6 252413.i −0.996177 0.0873541i
385385 −747930. −0.257163
386386 3.38853e6 2.73653e6i 1.15756 0.934829i
387387 1.35335e6 5.06612e6i 0.459337 1.71948i
388388 −354960. + 1.64839e6i −0.119702 + 0.555881i
389389 125849.i 0.0421672i −0.999778 0.0210836i 0.993288π-0.993288\pi
0.999778 0.0210836i 0.00671162π-0.00671162\pi
390390 −1.26115e6 + 771187.i −0.419861 + 0.256743i
391391 892696.i 0.295299i
392392 195771. + 388040.i 0.0643477 + 0.127544i
393393 −151669. + 1.15543e6i −0.0495355 + 0.377365i
394394 2.30088e6 + 2.84908e6i 0.746711 + 0.924622i
395395 −370052. −0.119336
396396 −1.22091e6 + 2.38496e6i −0.391242 + 0.764262i
397397 −4.93089e6 −1.57018 −0.785090 0.619382i 0.787383π-0.787383\pi
−0.785090 + 0.619382i 0.787383π0.787383\pi
398398 461622. + 571607.i 0.146076 + 0.180880i
399399 256464. 1.95376e6i 0.0806481 0.614383i
400400 −1.08493e6 489972.i −0.339041 0.153116i
401401 862477.i 0.267847i 0.990992 + 0.133923i 0.0427576π0.0427576\pi
−0.990992 + 0.133923i 0.957242π0.957242\pi
402402 −1.37673e6 + 841864.i −0.424898 + 0.259823i
403403 1.09262e6i 0.335125i
404404 −2.58491e6 556627.i −0.787939 0.169672i
405405 1.30449e6 2.26737e6i 0.395187 0.686887i
406406 1.30368e6 1.05283e6i 0.392513 0.316988i
407407 −1.23757e6 −0.370325
408408 −1.58132e6 4.51726e6i −0.470295 1.34346i
409409 2.19083e6 0.647592 0.323796 0.946127i 0.395041π-0.395041\pi
0.323796 + 0.946127i 0.395041π0.395041\pi
410410 2.46240e6 1.98860e6i 0.723435 0.584235i
411411 5.70025e6 + 748254.i 1.66452 + 0.218497i
412412 −2.18819e6 471198.i −0.635101 0.136761i
413413 343293.i 0.0990352i
414414 −661115. + 293895.i −0.189573 + 0.0842736i
415415 3.37285e6i 0.961339i
416416 2.12105e6 553252.i 0.600923 0.156744i
417417 −6.32770e6 830617.i −1.78199 0.233916i
418418 −3.15922e6 3.91193e6i −0.884380 1.09509i
419419 3.66270e6 1.01921 0.509607 0.860407i 0.329791π-0.329791\pi
0.509607 + 0.860407i 0.329791π0.329791\pi
420420 −1.01987e6 363773.i −0.282112 0.100625i
421421 6.00951e6 1.65247 0.826236 0.563325i 0.190478π-0.190478\pi
0.826236 + 0.563325i 0.190478π0.190478\pi
422422 1.59418e6 + 1.97400e6i 0.435768 + 0.539594i
423423 −3.80831e6 1.01734e6i −1.03486 0.276449i
424424 −3.54888e6 + 1.79045e6i −0.958687 + 0.483670i
425425 1.97177e6i 0.529522i
426426 3.57162e6 + 5.84081e6i 0.953546 + 1.55937i
427427 349712.i 0.0928198i
428428 313205. 1.45449e6i 0.0826456 0.383797i
429429 264535. 2.01525e6i 0.0693968 0.528670i
430430 4.20709e6 3.39759e6i 1.09726 0.886134i
431431 1.12043e6 0.290529 0.145265 0.989393i 0.453597π-0.453597\pi
0.145265 + 0.989393i 0.453597π0.453597\pi
432432 −2.82480e6 + 2.65828e6i −0.728245 + 0.685317i
433433 543582. 0.139330 0.0696651 0.997570i 0.477807π-0.477807\pi
0.0696651 + 0.997570i 0.477807π0.477807\pi
434434 −622645. + 502839.i −0.158678 + 0.128146i
435435 −543348. + 4.13926e6i −0.137675 + 1.04882i
436436 825186. 3.83207e6i 0.207891 0.965422i
437437 1.35780e6i 0.340121i
438438 −2.44404e6 3.99684e6i −0.608729 0.995476i
439439 1.09494e6i 0.271163i −0.990766 0.135582i 0.956710π-0.956710\pi
0.990766 0.135582i 0.0432903π-0.0432903\pi
440440 −2.46689e6 + 1.24457e6i −0.607459 + 0.306471i
441441 563677. + 150579.i 0.138017 + 0.0368695i
442442 2.28114e6 + 2.82464e6i 0.555387 + 0.687713i
443443 3.16516e6 0.766278 0.383139 0.923691i 0.374843π-0.374843\pi
0.383139 + 0.923691i 0.374843π0.374843\pi
444444 −1.68753e6 601919.i −0.406252 0.144904i
445445 400485. 0.0958709
446446 −4.22524e6 5.23194e6i −1.00581 1.24545i
447447 6.09844e6 + 800522.i 1.44361 + 0.189498i
448448 1.29142e6 + 954097.i 0.303998 + 0.224594i
449449 7.74623e6i 1.81332i 0.421862 + 0.906660i 0.361377π0.361377\pi
−0.421862 + 0.906660i 0.638623π0.638623\pi
450450 −1.46026e6 + 649150.i −0.339937 + 0.151117i
451451 4.35190e6i 1.00748i
452452 1.83761e6 + 395705.i 0.423065 + 0.0911014i
453453 135432. + 17777.8i 0.0310082 + 0.00407035i
454454 4.75595e6 3.84084e6i 1.08292 0.874554i
455455 821422. 0.186011
456456 −2.40522e6 6.87082e6i −0.541679 1.54738i
457457 −1.10785e6 −0.248135 −0.124068 0.992274i 0.539594π-0.539594\pi
−0.124068 + 0.992274i 0.539594π0.539594\pi
458458 3.40630e6 2.75088e6i 0.758785 0.612784i
459459 −5.93851e6 2.45190e6i −1.31567 0.543214i
460460 −729395. 157066.i −0.160719 0.0346088i
461461 2.76440e6i 0.605826i 0.953018 + 0.302913i 0.0979592π0.0979592\pi
−0.953018 + 0.302913i 0.902041π0.902041\pi
462462 1.27016e6 776694.i 0.276855 0.169295i
463463 7.08557e6i 1.53611i −0.640384 0.768055i 0.721225π-0.721225\pi
0.640384 0.768055i 0.278775π-0.278775\pi
464464 2.54796e6 5.64188e6i 0.549411 1.21655i
465465 259507. 1.97694e6i 0.0556565 0.423995i
466466 2.53454e6 + 3.13841e6i 0.540672 + 0.669492i
467467 7.00008e6 1.48529 0.742644 0.669686i 0.233571π-0.233571\pi
0.742644 + 0.669686i 0.233571π0.233571\pi
468468 1.34088e6 2.61930e6i 0.282992 0.552804i
469469 896704. 0.188242
470470 −2.55404e6 3.16256e6i −0.533314 0.660381i
471471 −839764. + 6.39739e6i −0.174424 + 1.32877i
472472 571248. + 1.13228e6i 0.118024 + 0.233936i
473473 7.43536e6i 1.52809i
474474 628434. 384284.i 0.128473 0.0785608i
475475 2.99909e6i 0.609896i
476476 −559848. + 2.59987e6i −0.113254 + 0.525938i
477477 −1.37714e6 + 5.15520e6i −0.277130 + 1.03741i
478478 −6.37784e6 + 5.15065e6i −1.27674 + 1.03108i
479479 2.35991e6 0.469956 0.234978 0.972001i 0.424498π-0.424498\pi
0.234978 + 0.972001i 0.424498π0.424498\pi
480480 −3.96914e6 + 497261.i −0.786310 + 0.0985103i
481481 1.35917e6 0.267863
482482 −4.46803e6 + 3.60831e6i −0.875988 + 0.707435i
483483 398607. + 52323.8i 0.0777458 + 0.0102054i
484484 −285147. + 1.32419e6i −0.0553294 + 0.256943i
485485 2.33428e6i 0.450609i
486486 139253. + 5.20517e6i 0.0267432 + 0.999642i
487487 7.32192e6i 1.39895i 0.714656 + 0.699476i 0.246583π0.246583\pi
−0.714656 + 0.699476i 0.753417π0.753417\pi
488488 −581929. 1.15345e6i −0.110617 0.219255i
489489 −2.41852e6 317471.i −0.457380 0.0600389i
490490 378029. + 468098.i 0.0711271 + 0.0880738i
491491 −714702. −0.133789 −0.0668947 0.997760i 0.521309π-0.521309\pi
−0.0668947 + 0.997760i 0.521309π0.521309\pi
492492 −2.11664e6 + 5.93420e6i −0.394217 + 1.10522i
493493 1.02536e7 1.90003
494494 3.46964e6 + 4.29632e6i 0.639687 + 0.792098i
495495 −957275. + 3.58346e6i −0.175600 + 0.657340i
496496 −1.21692e6 + 2.69460e6i −0.222105 + 0.491802i
497497 3.80428e6i 0.690846i
498498 3.50256e6 + 5.72786e6i 0.632866 + 1.03495i
499499 1.06401e7i 1.91291i 0.291881 + 0.956455i 0.405719π0.405719\pi
−0.291881 + 0.956455i 0.594281π0.594281\pi
500500 −5.94177e6 1.27948e6i −1.06290 0.228881i
501501 −520331. + 3.96392e6i −0.0926159 + 0.705554i
502502 3.11638e6 2.51674e6i 0.551938 0.445737i
503503 −3.63711e6 −0.640968 −0.320484 0.947254i 0.603845π-0.603845\pi
−0.320484 + 0.947254i 0.603845π0.603845\pi
504504 2.10973e6 441321.i 0.369957 0.0773888i
505505 −3.66049e6 −0.638720
506506 798113. 644545.i 0.138576 0.111912i
507507 462767. 3.52539e6i 0.0799544 0.609098i
508508 −3.93776e6 847944.i −0.677002 0.145783i
509509 6.58725e6i 1.12696i 0.826129 + 0.563481i 0.190538π0.190538\pi
−0.826129 + 0.563481i 0.809462π0.809462\pi
510510 −3.45651e6 5.65256e6i −0.588454 0.962321i
511511 2.60325e6i 0.441025i
512512 5.84709e6 + 997935.i 0.985746 + 0.168239i
513513 −9.03256e6 3.72938e6i −1.51537 0.625667i
514514 −4.64051e6 5.74615e6i −0.774743 0.959333i
515515 −3.09869e6 −0.514826
516516 −3.61635e6 + 1.01388e7i −0.597925 + 1.67633i
517517 5.58932e6 0.919672
518518 625509. + 774542.i 0.102426 + 0.126830i
519519 632324. + 83003.1i 0.103044 + 0.0135262i
520520 2.70928e6 1.36687e6i 0.439386 0.221676i
521521 4.47912e6i 0.722934i 0.932385 + 0.361467i 0.117724π0.117724\pi
−0.932385 + 0.361467i 0.882276π0.882276\pi
522522 −3.37572e6 7.59365e6i −0.542238 1.21976i
523523 3.99101e6i 0.638012i −0.947753 0.319006i 0.896651π-0.896651\pi
0.947753 0.319006i 0.103349π-0.103349\pi
524524 503588. 2.33861e6i 0.0801211 0.372074i
525525 880436. + 115572.i 0.139412 + 0.0183001i
526526 1.57945e6 1.27554e6i 0.248910 0.201016i
527527 −4.89721e6 −0.768107
528528 2.89690e6 4.67533e6i 0.452218 0.729839i
529529 −6.15932e6 −0.956960
530530 −4.28107e6 + 3.45733e6i −0.662007 + 0.534627i
531531 1.64478e6 + 439380.i 0.253146 + 0.0676245i
532532 −851537. + 3.95444e6i −0.130444 + 0.605768i
533533 4.77952e6i 0.728729i
534534 −680116. + 415887.i −0.103212 + 0.0631135i
535535 2.05970e6i 0.311114i
536536 2.95758e6 1.49214e6i 0.444657 0.224335i
537537 −771280. + 5.87567e6i −0.115419 + 0.879268i
538538 2.41831e6 + 2.99450e6i 0.360211 + 0.446034i
539539 −827288. −0.122655
540540 −3.04823e6 + 4.42078e6i −0.449845 + 0.652400i
541541 1.18244e7 1.73694 0.868470 0.495742i 0.165104π-0.165104\pi
0.868470 + 0.495742i 0.165104π0.165104\pi
542542 434072. + 537493.i 0.0634692 + 0.0785914i
543543 1.33578e6 1.01761e7i 0.194417 1.48109i
544544 2.47971e6 + 9.50671e6i 0.359256 + 1.37731i
545545 5.42658e6i 0.782592i
546546 −1.39496e6 + 853012.i −0.200254 + 0.122454i
547547 5.03397e6i 0.719353i 0.933077 + 0.359677i 0.117113π0.117113\pi
−0.933077 + 0.359677i 0.882887π0.882887\pi
548548 −1.15374e7 2.48443e6i −1.64118 0.353407i
549549 −1.67553e6 447596.i −0.237258 0.0633804i
550550 1.76286e6 1.42366e6i 0.248491 0.200678i
551551 1.55959e7 2.18843
552552 1.40179e6 490713.i 0.195810 0.0685456i
553553 −409316. −0.0569175
554554 6.39486e6 5.16440e6i 0.885231 0.714900i
555555 −2.45923e6 322815.i −0.338896 0.0444857i
556556 1.28074e7 + 2.75790e6i 1.75701 + 0.378348i
557557 1.14297e7i 1.56098i −0.625167 0.780491i 0.714969π-0.714969\pi
0.625167 0.780491i 0.285031π-0.285031\pi
558558 1.61227e6 + 3.62678e6i 0.219206 + 0.493101i
559559 8.16596e6i 1.10529i
560560 2.02577e6 + 914870.i 0.272974 + 0.123279i
561561 9.03247e6 + 1.18566e6i 1.21171 + 0.159058i
562562 8.02230e6 + 9.93369e6i 1.07142 + 1.32669i
563563 5.20508e6 0.692080 0.346040 0.938220i 0.387526π-0.387526\pi
0.346040 + 0.938220i 0.387526π0.387526\pi
564564 7.62153e6 + 2.71849e6i 1.00889 + 0.359858i
565565 2.60223e6 0.342945
566566 −2.01918e6 2.50026e6i −0.264931 0.328053i
567567 1.44290e6 2.50795e6i 0.188486 0.327613i
568568 −6.33042e6 1.25476e7i −0.823306 1.63188i
569569 1.36150e7i 1.76294i −0.472243 0.881468i 0.656556π-0.656556\pi
0.472243 0.881468i 0.343444π-0.343444\pi
570570 −5.25740e6 8.59763e6i −0.677773 1.10839i
571571 2.37109e6i 0.304340i 0.988354 + 0.152170i 0.0486260π0.0486260\pi
−0.988354 + 0.152170i 0.951374π0.951374\pi
572572 −878335. + 4.07889e6i −0.112246 + 0.521257i
573573 335013. 2.55215e6i 0.0426261 0.324728i
574574 2.72367e6 2.19960e6i 0.345044 0.278653i
575575 611876. 0.0771781
576576 6.22413e6 4.96625e6i 0.781668 0.623695i
577577 −9.60114e6 −1.20056 −0.600279 0.799791i 0.704944π-0.704944\pi
−0.600279 + 0.799791i 0.704944π0.704944\pi
578578 −6.41153e6 + 5.17786e6i −0.798256 + 0.644660i
579579 −1.56212e6 + 1.19004e7i −0.193651 + 1.47525i
580580 1.80408e6 8.37793e6i 0.222682 1.03411i
581581 3.73072e6i 0.458513i
582582 −2.42406e6 3.96415e6i −0.296644 0.485113i
583583 7.56610e6i 0.921936i
584584 4.33187e6 + 8.58625e6i 0.525586 + 1.04177i
585585 1.05134e6 3.93558e6i 0.127014 0.475465i
586586 −8.24125e6 1.02048e7i −0.991401 1.22761i
587587 −9.44610e6 −1.13151 −0.565753 0.824575i 0.691415π-0.691415\pi
−0.565753 + 0.824575i 0.691415π0.691415\pi
588588 −1.12808e6 402370.i −0.134554 0.0479935i
589589 −7.44872e6 −0.884695
590590 1.10307e6 + 1.36588e6i 0.130458 + 0.161541i
591591 −1.00058e7 1.31344e6i −1.17838 0.154682i
592592 3.35196e6 + 1.51380e6i 0.393093 + 0.177527i
593593 2.55949e6i 0.298894i −0.988770 0.149447i 0.952251π-0.952251\pi
0.988770 0.149447i 0.0477493π-0.0477493\pi
594594 −2.09561e6 7.07963e6i −0.243693 0.823274i
595595 3.68167e6i 0.426336i
596596 −1.23433e7 2.65797e6i −1.42337 0.306503i
597597 −2.00746e6 263513.i −0.230521 0.0302598i
598598 −876536. + 707878.i −0.100234 + 0.0809479i
599599 −6.35830e6 −0.724059 −0.362030 0.932167i 0.617916π-0.617916\pi
−0.362030 + 0.932167i 0.617916π0.617916\pi
600600 3.09624e6 1.08388e6i 0.351121 0.122914i
601601 −4.70528e6 −0.531373 −0.265687 0.964059i 0.585599π-0.585599\pi
−0.265687 + 0.964059i 0.585599π0.585599\pi
602602 4.65348e6 3.75808e6i 0.523343 0.422644i
603603 1.14769e6 4.29627e6i 0.128538 0.481169i
604604 −274117. 59027.5i −0.0305734 0.00658358i
605605 1.87518e6i 0.208284i
606606 6.21635e6 3.80126e6i 0.687628 0.420481i
607607 1.14458e7i 1.26089i −0.776236 0.630443i 0.782873π-0.782873\pi
0.776236 0.630443i 0.217127π-0.217127\pi
608608 3.77168e6 + 1.44598e7i 0.413786 + 1.58637i
609609 −600999. + 4.57845e6i −0.0656644 + 0.500236i
610610 −1.12369e6 1.39142e6i −0.122271 0.151403i
611611 −6.13853e6 −0.665214
612612 1.17399e7 + 6.00990e6i 1.26703 + 0.648618i
613613 −5.56627e6 −0.598292 −0.299146 0.954207i 0.596702π-0.596702\pi
−0.299146 + 0.954207i 0.596702π0.596702\pi
614614 4.60277e6 + 5.69942e6i 0.492718 + 0.610112i
615615 −1.13517e6 + 8.64784e6i −0.121025 + 0.921977i
616616 −2.72863e6 + 1.37663e6i −0.289730 + 0.146172i
617617 9.77784e6i 1.03402i −0.855979 0.517011i 0.827045π-0.827045\pi
0.855979 0.517011i 0.172955π-0.172955\pi
618618 5.26229e6 3.21786e6i 0.554247 0.338919i
619619 401672.i 0.0421352i −0.999778 0.0210676i 0.993293π-0.993293\pi
0.999778 0.0210676i 0.00670652π-0.00670652\pi
620620 −861640. + 4.00136e6i −0.0900216 + 0.418050i
621621 760869. 1.84283e6i 0.0791737 0.191759i
622622 −1.28035e7 + 1.03399e7i −1.32694 + 1.07162i
623623 442978. 0.0457259
624624 −3.18155e6 + 5.13473e6i −0.327097 + 0.527905i
625625 −4.78118e6 −0.489593
626626 −8.18822e6 + 6.61269e6i −0.835130 + 0.674439i
627627 1.37385e7 + 1.80341e6i 1.39563 + 0.183200i
628628 2.78827e6 1.29484e7i 0.282121 1.31014i
629629 6.09190e6i 0.613941i
630630 2.72658e6 1.21209e6i 0.273695 0.121670i
631631 1.37179e6i 0.137155i −0.997646 0.0685777i 0.978154π-0.978154\pi
0.997646 0.0685777i 0.0218461π-0.0218461\pi
632632 −1.35004e6 + 681112.i −0.134448 + 0.0678307i
633633 −6.93261e6 910022.i −0.687682 0.0902698i
634634 −816148. 1.01060e6i −0.0806391 0.0998521i
635635 −5.57625e6 −0.548792
636636 3.67994e6 1.03170e7i 0.360744 1.01138i
637637 908578. 0.0887184
638638 7.40332e6 + 9.16723e6i 0.720070 + 0.891634i
639639 −1.82270e7 4.86909e6i −1.76588 0.471733i
640640 8.20394e6 353439.i 0.791722 0.0341086i
641641 5.19717e6i 0.499599i −0.968298 0.249800i 0.919635π-0.919635\pi
0.968298 0.249800i 0.0803647π-0.0803647\pi
642642 2.13891e6 + 3.49784e6i 0.204812 + 0.334937i
643643 406989.i 0.0388200i −0.999812 0.0194100i 0.993821π-0.993821\pi
0.999812 0.0194100i 0.00617878π-0.00617878\pi
644644 −806787. 173731.i −0.0766556 0.0165068i
645645 −1.93948e6 + 1.47751e7i −0.183564 + 1.39840i
646646 −1.92564e7 + 1.55512e7i −1.81549 + 1.46616i
647647 −4.46242e6 −0.419092 −0.209546 0.977799i 0.567199π-0.567199\pi
−0.209546 + 0.977799i 0.567199π0.567199\pi
648648 585797. 1.06729e7i 0.0548037 0.998497i
649649 −2.41398e6 −0.224969
650650 −1.93608e6 + 1.56355e6i −0.179738 + 0.145154i
651651 287041. 2.18670e6i 0.0265455 0.202226i
652652 4.89512e6 + 1.05410e6i 0.450967 + 0.0971098i
653653 1.37929e6i 0.126582i −0.997995 0.0632909i 0.979840π-0.979840\pi
0.997995 0.0632909i 0.0201596π-0.0201596\pi
654654 5.63528e6 + 9.21558e6i 0.515194 + 0.842516i
655655 3.31169e6i 0.301611i
656656 5.32325e6 1.17871e7i 0.482967 1.06942i
657657 1.24726e7 + 3.33190e6i 1.12731 + 0.301147i
658658 −2.82503e6 3.49812e6i −0.254366 0.314971i
659659 −1.17955e7 −1.05804 −0.529022 0.848608i 0.677441π-0.677441\pi
−0.529022 + 0.848608i 0.677441π0.677441\pi
660660 2.55799e6 7.17155e6i 0.228580 0.640845i
661661 1.10195e6 0.0980980 0.0490490 0.998796i 0.484381π-0.484381\pi
0.0490490 + 0.998796i 0.484381π0.484381\pi
662662 2.73295e6 + 3.38410e6i 0.242374 + 0.300122i
663663 −9.92000e6 1.30217e6i −0.876452 0.115049i
664664 −6.20801e6 1.23050e7i −0.546427 1.08308i
665665 5.59987e6i 0.491048i
666666 4.51156e6 2.00559e6i 0.394131 0.175209i
667667 3.18188e6i 0.276930i
668668 1.72766e6 8.02304e6i 0.149801 0.695661i
669669 1.83743e7 + 2.41194e6i 1.58725 + 0.208354i
670670 3.56778e6 2.88129e6i 0.307051 0.247970i
671671 2.45912e6 0.210850
672672 −4.39028e6 + 550022.i −0.375033 + 0.0469848i
673673 1.37263e7 1.16820 0.584098 0.811683i 0.301448π-0.301448\pi
0.584098 + 0.811683i 0.301448π0.301448\pi
674674 −1.50670e6 + 1.21679e6i −0.127755 + 0.103173i
675675 1.68059e6 4.07040e6i 0.141972 0.343857i
676676 −1.53652e6 + 7.13545e6i −0.129322 + 0.600557i
677677 8.78449e6i 0.736622i −0.929703 0.368311i 0.879936π-0.879936\pi
0.929703 0.368311i 0.120064π-0.120064\pi
678678 −4.41918e6 + 2.70231e6i −0.369205 + 0.225767i
679679 2.58196e6i 0.214919i
680680 6.12639e6 + 1.21432e7i 0.508080 + 1.00707i
681681 −2.19251e6 + 1.67027e7i −0.181165 + 1.38013i
682682 −3.53588e6 4.37833e6i −0.291096 0.360452i
683683 2.47234e6 0.202795 0.101398 0.994846i 0.467669π-0.467669\pi
0.101398 + 0.994846i 0.467669π0.467669\pi
684684 1.78565e7 + 9.14115e6i 1.45934 + 0.747069i
685685 −1.63381e7 −1.33038
686686 418139. + 517765.i 0.0339243 + 0.0420071i
687687 −1.57031e6 + 1.19628e7i −0.126939 + 0.967029i
688688 9.09495e6 2.01387e7i 0.732536 1.62204i
689689 8.30955e6i 0.666852i
690690 1.75409e6 1.07262e6i 0.140259 0.0857674i
691691 1.79021e6i 0.142629i −0.997454 0.0713146i 0.977281π-0.977281\pi
0.997454 0.0713146i 0.0227194π-0.0227194\pi
692692 −1.27983e6 275595.i −0.101599 0.0218780i
693693 −1.05884e6 + 3.96368e6i −0.0837528 + 0.313520i
694694 −1.52619e7 + 1.23253e7i −1.20285 + 0.971400i
695695 1.81365e7 1.42427
696696 5.63639e6 + 1.61011e7i 0.441040 + 1.25989i
697697 2.14221e7 1.67025
698698 1.26148e7 1.01875e7i 0.980033 0.791460i
699699 −1.10220e7 1.44682e6i −0.853230 0.112001i
700700 −1.78202e6 383734.i −0.137457 0.0295995i
701701 2.41968e7i 1.85979i −0.367829 0.929894i 0.619899π-0.619899\pi
0.367829 0.929894i 0.380101π-0.380101\pi
702702 2.30152e6 + 7.77528e6i 0.176267 + 0.595488i
703703 9.26588e6i 0.707128i
704704 −6.70905e6 + 9.08102e6i −0.510187 + 0.690562i
705705 1.11068e7 + 1.45795e6i 0.841619 + 0.110477i
706706 1.41901e7 + 1.75710e7i 1.07145 + 1.32673i
707707 −4.04888e6 −0.304639
708708 −3.29167e6 1.17409e6i −0.246793 0.0880277i
709709 2.75535e6 0.205855 0.102928 0.994689i 0.467179π-0.467179\pi
0.102928 + 0.994689i 0.467179π0.467179\pi
710710 −1.22239e7 1.51364e7i −0.910047 1.12687i
711711 −523883. + 1.96111e6i −0.0388652 + 0.145488i
712712 1.46107e6 737127.i 0.108012 0.0544932i
713713 1.51969e6i 0.111952i
714714 −3.82326e6 6.25232e6i −0.280665 0.458982i
715715 5.77610e6i 0.422542i
716716 2.56088e6 1.18924e7i 0.186684 0.866939i
717717 2.94020e6 2.23987e7i 0.213589 1.62714i
718718 8.96174e6 7.23737e6i 0.648756 0.523926i
719719 −7.78137e6 −0.561350 −0.280675 0.959803i 0.590558π-0.590558\pi
−0.280675 + 0.959803i 0.590558π0.590558\pi
720720 6.97609e6 8.53490e6i 0.501511 0.613574i
721721 −3.42748e6 −0.245548
722722 −1.83921e7 + 1.48532e7i −1.31307 + 1.06042i
723723 2.05977e6 1.56915e7i 0.146546 1.11640i
724724 −4.43519e6 + 2.05965e7i −0.314460 + 1.46032i
725725 7.02809e6i 0.496583i
726726 −1.94730e6 3.18449e6i −0.137117 0.224232i
727727 1.69934e7i 1.19246i 0.802812 + 0.596232i 0.203336π0.203336\pi
−0.802812 + 0.596232i 0.796664π0.796664\pi
728728 2.99675e6 1.51190e6i 0.209566 0.105729i
729729 −1.01693e7 1.01231e7i −0.708714 0.705496i
730730 8.36475e6 + 1.03577e7i 0.580960 + 0.719378i
731731 3.66004e7 2.53333
732732 3.35322e6 + 1.19605e6i 0.231305 + 0.0825031i
733733 −1.94968e7 −1.34031 −0.670153 0.742223i 0.733772π-0.733772\pi
−0.670153 + 0.742223i 0.733772π0.733772\pi
734734 7.12198e6 + 8.81886e6i 0.487934 + 0.604188i
735735 −1.64394e6 215795.i −0.112245 0.0147341i
736736 −2.95010e6 + 769500.i −0.200744 + 0.0523617i
737737 6.30547e6i 0.427611i
738738 −7.05263e6 1.58648e7i −0.476662 1.07225i
739739 2.33899e7i 1.57549i 0.616000 + 0.787747i 0.288752π0.288752\pi
−0.616000 + 0.787747i 0.711248π0.711248\pi
740740 4.97751e6 + 1.07184e6i 0.334143 + 0.0719534i
741741 −1.50885e7 1.98062e6i −1.00948 0.132512i
742742 −4.73531e6 + 3.82416e6i −0.315746 + 0.254992i
743743 2.36878e7 1.57417 0.787085 0.616844i 0.211589π-0.211589\pi
0.787085 + 0.616844i 0.211589π0.211589\pi
744744 −2.69198e6 7.69000e6i −0.178295 0.509324i
745745 −1.74794e7 −1.15381
746746 −2.82908e6 + 2.28473e6i −0.186122 + 0.150310i
747747 −1.78745e7 4.77494e6i −1.17201 0.313088i
748748 −1.82819e7 3.93676e6i −1.19472 0.257267i
749749 2.27824e6i 0.148387i
750750 1.42891e7 8.73771e6i 0.927581 0.567211i
751751 9.85141e6i 0.637380i 0.947859 + 0.318690i 0.103243π0.103243\pi
−0.947859 + 0.318690i 0.896757π0.896757\pi
752752 −1.51387e7 6.83687e6i −0.976213 0.440872i
753753 −1.43666e6 + 1.09446e7i −0.0923350 + 0.703415i
754754 −8.13078e6 1.00680e7i −0.520839 0.644934i
755755 −388176. −0.0247834
756756 −3.37166e6 + 4.88984e6i −0.214555 + 0.311164i
757757 −1.86760e7 −1.18452 −0.592262 0.805745i 0.701765π-0.701765\pi
−0.592262 + 0.805745i 0.701765π0.701765\pi
758758 −6.70036e6 8.29678e6i −0.423570 0.524489i
759759 −367933. + 2.80294e6i −0.0231827 + 0.176607i
760760 9.31833e6 + 1.84700e7i 0.585200 + 1.15993i
761761 3.39083e6i 0.212248i 0.994353 + 0.106124i 0.0338441π0.0338441\pi
−0.994353 + 0.106124i 0.966156π0.966156\pi
762762 9.46974e6 5.79070e6i 0.590814 0.361280i
763763 6.00236e6i 0.373259i
764764 −1.11234e6 + 5.16560e6i −0.0689455 + 0.320175i
765765 1.76395e7 + 4.71216e6i 1.08977 + 0.291116i
766766 −1.51474e7 + 1.22328e7i −0.932752 + 0.753277i
767767 2.65118e6 0.162724
768768 −1.35651e7 + 9.11967e6i −0.829891 + 0.557925i
769769 3.88330e6 0.236802 0.118401 0.992966i 0.462223π-0.462223\pi
0.118401 + 0.992966i 0.462223π0.462223\pi
770770 −3.29159e6 + 2.65824e6i −0.200068 + 0.161572i
771771 2.01802e7 + 2.64899e6i 1.22262 + 0.160489i
772772 5.18672e6 2.40866e7i 0.313220 1.45456i
773773 4.33830e6i 0.261139i 0.991439 + 0.130569i 0.0416805π0.0416805\pi
−0.991439 + 0.130569i 0.958320π0.958320\pi
774774 −1.20496e7 2.71056e7i −0.722973 1.62632i
775775 3.35667e6i 0.200749i
776776 4.29645e6 + 8.51604e6i 0.256127 + 0.507672i
777777 −2.72016e6 357066.i −0.161637 0.0212176i
778778 −447282. 553851.i −0.0264931 0.0328053i
779779 3.25834e7 1.92377
780780 −2.80934e6 + 7.87623e6i −0.165336 + 0.463534i
781781 2.67511e7 1.56933
782782 −3.17276e6 3.92869e6i −0.185532 0.229737i
783783 2.11669e7 + 8.73944e6i 1.23383 + 0.509424i
784784 2.24072e6 + 1.01194e6i 0.130196 + 0.0587983i
785785 1.83362e7i 1.06203i
786786 3.43905e6 + 5.62401e6i 0.198556 + 0.324706i
787787 127599.i 0.00734365i −0.999993 0.00367182i 0.998831π-0.998831\pi
0.999993 0.00367182i 0.00116878π-0.00116878\pi
788788 2.02520e7 + 4.36100e6i 1.16186 + 0.250190i
789789 −728133. + 5.54697e6i −0.0416407 + 0.317222i
790790 −1.62857e6 + 1.31521e6i −0.0928410 + 0.0749771i
791791 2.87834e6 0.163569
792792 3.10330e6 + 1.48353e7i 0.175797 + 0.840394i
793793 −2.70075e6 −0.152511
794794 −2.17005e7 + 1.75250e7i −1.22157 + 0.986523i
795795 1.97359e6 1.50349e7i 0.110749 0.843691i
796796 4.06313e6 + 874941.i 0.227289 + 0.0489436i
797797 2.09099e7i 1.16602i 0.812464 + 0.583011i 0.198126π0.198126\pi
−0.812464 + 0.583011i 0.801874π0.801874\pi
798798 −5.81523e6 9.50987e6i −0.323266 0.528649i
799799 2.75133e7i 1.52467i
800800 −6.51613e6 + 1.69966e6i −0.359969 + 0.0938937i
801801 566967. 2.12239e6i 0.0312231 0.116881i
802802 3.06535e6 + 3.79570e6i 0.168285 + 0.208380i
803803 −1.83056e7 −1.00183
804804 −3.06681e6 + 8.59807e6i −0.167320 + 0.469095i
805805 −1.14249e6 −0.0621387
806806 3.88332e6 + 4.80855e6i 0.210555 + 0.260721i
807807 −1.05165e7 1.38047e6i −0.568446 0.0746180i
808808 −1.33543e7 + 6.73743e6i −0.719605 + 0.363050i
809809 2.83460e6i 0.152272i 0.997097 + 0.0761361i 0.0242584π0.0242584\pi
−0.997097 + 0.0761361i 0.975742π0.975742\pi
810810 −2.31757e6 1.46149e7i −0.124114 0.782677i
811811 4.12579e6i 0.220270i 0.993917 + 0.110135i 0.0351283π0.0351283\pi
−0.993917 + 0.110135i 0.964872π0.964872\pi
812812 1.99550e6 9.26686e6i 0.106209 0.493222i
813813 −1.88765e6 247786.i −0.100160 0.0131477i
814814 −5.44645e6 + 4.39848e6i −0.288106 + 0.232670i
815815 6.93197e6 0.365563
816816 −2.30142e7 1.42599e7i −1.20996 0.749707i
817817 5.56697e7 2.91786
818818 9.64171e6 7.78650e6i 0.503815 0.406873i
819819 1.16289e6 4.35316e6i 0.0605798 0.226775i
820820 3.76912e6 1.75034e7i 0.195752 0.909049i
821821 3.09426e7i 1.60214i 0.598573 + 0.801068i 0.295735π0.295735\pi
−0.598573 + 0.801068i 0.704265π0.704265\pi
822822 2.77458e7 1.69664e7i 1.43225 0.875811i
823823 3.78985e7i 1.95039i −0.221343 0.975196i 0.571044π-0.571044\pi
0.221343 0.975196i 0.428956π-0.428956\pi
824824 −1.13048e7 + 5.70340e6i −0.580022 + 0.292628i
825825 −812683. + 6.19108e6i −0.0415706 + 0.316688i
826826 1.22011e6 + 1.51081e6i 0.0622225 + 0.0770476i
827827 −8.10586e6 −0.412131 −0.206066 0.978538i 0.566066π-0.566066\pi
−0.206066 + 0.978538i 0.566066π0.566066\pi
828828 −1.86498e6 + 3.64310e6i −0.0945363 + 0.184669i
829829 −5.94605e6 −0.300498 −0.150249 0.988648i 0.548008π-0.548008\pi
−0.150249 + 0.988648i 0.548008π0.548008\pi
830830 −1.19875e7 1.48437e7i −0.603996 0.747904i
831831 −2.94805e6 + 2.24585e7i −0.148092 + 1.12818i
832832 7.36829e6 9.97332e6i 0.369027 0.499495i
833833 4.07231e6i 0.203342i
834834 −3.07999e7 + 1.88340e7i −1.53332 + 0.937620i
835835 1.13614e7i 0.563918i
836836 −2.78070e7 5.98787e6i −1.37606 0.296317i
837837 −1.01095e7 4.17402e6i −0.498787 0.205940i
838838 1.61193e7 1.30177e7i 0.792931 0.640359i
839839 −1.52217e7 −0.746548 −0.373274 0.927721i 0.621765π-0.621765\pi
−0.373274 + 0.927721i 0.621765π0.621765\pi
840840 −5.78126e6 + 2.02380e6i −0.282699 + 0.0989624i
841841 −1.60364e7 −0.781838
842842 2.64474e7 2.13586e7i 1.28559 1.03823i
843843 −3.48867e7 4.57946e6i −1.69079 0.221945i
844844 1.40317e7 + 3.02155e6i 0.678039 + 0.146007i
845845 1.01045e7i 0.486824i
846846 −2.03759e7 + 9.05799e6i −0.978792 + 0.435117i
847847 2.07415e6i 0.0993415i
848848 −9.25487e6 + 2.04928e7i −0.441958 + 0.978617i
849849 8.78081e6 + 1.15263e6i 0.418086 + 0.0548808i
850850 −7.00793e6 8.67763e6i −0.332692 0.411959i
851851 −1.89043e6 −0.0894821
852852 3.64774e7 + 1.30110e7i 1.72157 + 0.614061i
853853 −1.14805e7 −0.540240 −0.270120 0.962827i 0.587063π-0.587063\pi
−0.270120 + 0.962827i 0.587063π0.587063\pi
854854 −1.24292e6 1.53906e6i −0.0583175 0.0722121i
855855 2.68300e7 + 7.16727e6i 1.25518 + 0.335304i
856856 −3.79105e6 7.51428e6i −0.176838 0.350512i
857857 7.23435e6i 0.336471i −0.985747 0.168236i 0.946193π-0.946193\pi
0.985747 0.168236i 0.0538069π-0.0538069\pi
858858 −5.99824e6 9.80915e6i −0.278167 0.454897i
859859 3.67531e6i 0.169946i 0.996383 + 0.0849729i 0.0270804π0.0270804\pi
−0.996383 + 0.0849729i 0.972920π0.972920\pi
860860 6.43966e6 2.99051e7i 0.296905 1.37879i
861861 −1.25562e6 + 9.56541e6i −0.0577232 + 0.439740i
862862 4.93092e6 3.98214e6i 0.226027 0.182536i
863863 −3.05585e6 −0.139670 −0.0698352 0.997559i 0.522247π-0.522247\pi
−0.0698352 + 0.997559i 0.522247π0.522247\pi
864864 −2.98386e6 + 2.17386e7i −0.135986 + 0.990711i
865865 −1.81237e6 −0.0823581
866866 2.39227e6 1.93196e6i 0.108396 0.0875394i
867867 2.95574e6 2.25170e7i 0.133542 1.01733i
868868 −953063. + 4.42592e6i −0.0429361 + 0.199390i
869869 2.87824e6i 0.129294i
870870 1.23202e7 + 2.01477e7i 0.551849 + 0.902460i
871871 6.92505e6i 0.309298i
872872 −9.98808e6 1.97975e7i −0.444827 0.881696i
873873 1.23706e7 + 3.30465e6i 0.549359 + 0.146754i
874874 −4.82581e6 5.97560e6i −0.213694 0.264608i
875875 −9.30689e6 −0.410946
876876 −2.49613e7 8.90335e6i −1.09902 0.392007i
877877 −2.33195e6 −0.102381 −0.0511906 0.998689i 0.516302π-0.516302\pi
−0.0511906 + 0.998689i 0.516302π0.516302\pi
878878 −3.89157e6 4.81877e6i −0.170368 0.210960i
879879 3.58388e7 + 4.70445e6i 1.56452 + 0.205370i
880880 −6.43321e6 + 1.42449e7i −0.280041 + 0.620087i
881881 2.44678e7i 1.06207i 0.847348 + 0.531037i 0.178198π0.178198\pi
−0.847348 + 0.531037i 0.821802π0.821802\pi
882882 3.01588e6 1.34069e6i 0.130540 0.0580307i
883883 1.21881e7i 0.526060i −0.964788 0.263030i 0.915278π-0.915278\pi
0.964788 0.263030i 0.0847218π-0.0847218\pi
884884 2.00782e7 + 4.32359e6i 0.864162 + 0.186086i
885885 −4.79692e6 629676.i −0.205875 0.0270246i
886886 1.39296e7 1.12494e7i 0.596150 0.481442i
887887 −2.95279e7 −1.26015 −0.630077 0.776533i 0.716977π-0.716977\pi
−0.630077 + 0.776533i 0.716977π0.716977\pi
888888 −9.56602e6 + 3.34870e6i −0.407098 + 0.142510i
889889 −6.16791e6 −0.261748
890890 1.76251e6 1.42338e6i 0.0745858 0.0602344i
891891 1.76355e7 + 1.01462e7i 0.744206 + 0.428164i
892892 −3.71899e7 8.00836e6i −1.56500 0.337001i
893893 4.18482e7i 1.75609i
894894 2.96839e7 1.81516e7i 1.24216 0.759575i
895895 1.68409e7i 0.702759i
896896 9.07441e6 390940.i 0.377614 0.0162682i
897897 404086. 3.07836e6i 0.0167684 0.127743i
898898 2.75311e7 + 3.40906e7i 1.13929 + 1.41073i
899899 1.74554e7 0.720327
900900 −4.11933e6 + 8.04681e6i −0.169520 + 0.331144i
901901 −3.72440e7 −1.52842
902902 1.54672e7 + 1.91524e7i 0.632988 + 0.783803i
903903 −2.14527e6 + 1.63428e7i −0.0875512 + 0.666971i
904904 9.49357e6 4.78962e6i 0.386374 0.194931i
905905 2.91667e7i 1.18376i
906906 659212. 403105.i 0.0266812 0.0163154i
907907 185741.i 0.00749703i 0.999993 + 0.00374852i 0.00119319π0.00119319\pi
−0.999993 + 0.00374852i 0.998807π0.998807\pi
908908 7.27979e6 3.38065e7i 0.293025 1.36077i
909909 −5.18215e6 + 1.93989e7i −0.208018 + 0.778694i
910910 3.61502e6 2.91944e6i 0.144713 0.116868i
911911 6.75595e6 0.269706 0.134853 0.990866i 0.456944π-0.456944\pi
0.134853 + 0.990866i 0.456944π0.456944\pi
912912 −3.50049e7 2.16895e7i −1.39361 0.863502i
913913 2.62338e7 1.04156
914914 −4.87555e6 + 3.93742e6i −0.193045 + 0.155900i
915915 4.88661e6 + 641450.i 0.192955 + 0.0253285i
916916 5.21391e6 2.42128e7i 0.205317 0.953469i
917917 3.66308e6i 0.143854i
918918 −3.48493e7 + 1.03156e7i −1.36486 + 0.404005i
919919 2.92608e7i 1.14287i 0.820647 + 0.571436i 0.193613π0.193613\pi
−0.820647 + 0.571436i 0.806387π0.806387\pi
920920 −3.76825e6 + 1.90113e6i −0.146781 + 0.0740529i
921921 −2.00161e7 2.62745e6i −0.777554 0.102067i
922922 9.82502e6 + 1.21659e7i 0.380633 + 0.471322i
923923 −2.93796e7 −1.13512
924924 2.82940e6 7.93247e6i 0.109022 0.305653i
925925 −4.17554e6 −0.160457
926926 −2.51830e7 3.11831e7i −0.965117 1.19507i
927927 −4.38682e6 + 1.64216e7i −0.167668 + 0.627649i
928928 −8.83857e6 3.38853e7i −0.336909 1.29164i
929929 1.00655e7i 0.382644i 0.981527 + 0.191322i 0.0612774π0.0612774\pi
−0.981527 + 0.191322i 0.938723π0.938723\pi
930930 −5.88423e6 9.62269e6i −0.223091 0.364829i
931931 6.19404e6i 0.234207i
932932 2.23086e7 + 4.80387e6i 0.841266 + 0.181156i
933933 5.90244e6 4.49652e7i 0.221987 1.69111i
934934 3.08069e7 2.48792e7i 1.15553 0.933187i
935935 −2.58889e7 −0.968466
936936 −3.40823e6 1.62930e7i −0.127157 0.607872i
937937 4.80624e6 0.178837 0.0894183 0.995994i 0.471499π-0.471499\pi
0.0894183 + 0.995994i 0.471499π0.471499\pi
938938 3.94633e6 3.18700e6i 0.146449 0.118270i
939939 3.77480e6 2.87567e7i 0.139711 1.06433i
940940 −2.24803e7 4.84084e6i −0.829818 0.178690i
941941 1.75486e7i 0.646055i 0.946390 + 0.323028i 0.104701π0.104701\pi
−0.946390 + 0.323028i 0.895299π0.895299\pi
942942 1.90414e7 + 3.11391e7i 0.699151 + 1.14335i
943943 6.64767e6i 0.243439i
944944 6.53828e6 + 2.95278e6i 0.238800 + 0.107845i
945945 −3.13799e6 + 7.60021e6i −0.114307 + 0.276851i
946946 2.64262e7 + 3.27225e7i 0.960079 + 1.18883i
947947 −3.50620e7 −1.27046 −0.635231 0.772322i 0.719095π-0.719095\pi
−0.635231 + 0.772322i 0.719095π0.719095\pi
948948 1.39990e6 3.92474e6i 0.0505913 0.141837i
949949 2.01043e7 0.724643
950950 −1.06592e7 1.31988e7i −0.383190 0.474488i
951951 3.54919e6 + 465891.i 0.127256 + 0.0167045i
952952 6.77642e6 + 1.34316e7i 0.242330 + 0.480326i
953953 5.57491e7i 1.98841i −0.107500 0.994205i 0.534284π-0.534284\pi
0.107500 0.994205i 0.465716π-0.465716\pi
954954 1.22615e7 + 2.75822e7i 0.436188 + 0.981202i
955955 7.31499e6i 0.259541i
956956 −9.76236e6 + 4.53353e7i −0.345470 + 1.60432i
957957 −3.21949e7 4.22612e6i −1.13634 0.149163i
958958 1.03858e7 8.38742e6i 0.365617 0.295267i
959959 −1.80716e7 −0.634527
960960 −1.57006e7 + 1.62952e7i −0.549842 + 0.570667i
961961 2.02923e7 0.708800
962962 5.98162e6 4.83067e6i 0.208392 0.168294i
963963 −1.09155e7 2.91592e6i −0.379294 0.101323i
964964 −6.83907e6 + 3.17599e7i −0.237031 + 1.10074i
965965 3.41089e7i 1.17910i
966966 1.94021e6 1.18643e6i 0.0668968 0.0409070i
967967 2.91267e7i 1.00167i 0.865542 + 0.500836i 0.166974π0.166974\pi
−0.865542 + 0.500836i 0.833026π0.833026\pi
968968 3.45143e6 + 6.84112e6i 0.118389 + 0.234660i
969969 8.87725e6 6.76276e7i 0.303717 2.31374i
970970 8.29634e6 + 1.02730e7i 0.283111 + 0.350565i
971971 1.85833e7 0.632522 0.316261 0.948672i 0.397572π-0.397572\pi
0.316261 + 0.948672i 0.397572π0.397572\pi
972972 1.91127e7 + 2.24127e7i 0.648868 + 0.760901i
973973 2.00608e7 0.679308
974974 2.60230e7 + 3.22233e7i 0.878943 + 1.08836i
975975 892537. 6.79941e6i 0.0300687 0.229066i
976976 −6.66053e6 3.00800e6i −0.223813 0.101077i
977977 2.11129e7i 0.707639i −0.935314 0.353820i 0.884883π-0.884883\pi
0.935314 0.353820i 0.115117π-0.115117\pi
978978 −1.17721e7 + 7.19856e6i −0.393555 + 0.240657i
979979 3.11495e6i 0.103871i
980980 3.32736e6 + 716503.i 0.110671 + 0.0238316i
981981 −2.87584e7 7.68241e6i −0.954095 0.254874i
982982 −3.14535e6 + 2.54014e6i −0.104086 + 0.0840581i
983983 3.96350e7 1.30826 0.654132 0.756380i 0.273034π-0.273034\pi
0.654132 + 0.756380i 0.273034π0.273034\pi
984984 1.17757e7 + 3.36388e7i 0.387702 + 1.10752i
985985 2.86788e7 0.941825
986986 4.51255e7 3.64427e7i 1.47819 1.19376i
987987 1.22853e7 + 1.61265e6i 0.401413 + 0.0526922i
988988 3.05393e7 + 6.57624e6i 0.995330 + 0.214331i
989989 1.13578e7i 0.369234i
990990 8.52319e6 + 1.91729e7i 0.276385 + 0.621726i
991991 9.73754e6i 0.314967i −0.987522 0.157484i 0.949662π-0.949662\pi
0.987522 0.157484i 0.0503381π-0.0503381\pi
992992 4.22137e6 + 1.61838e7i 0.136199 + 0.522159i
993993 −1.18848e7 1.56008e6i −0.382489 0.0502081i
994994 −1.35209e7 1.67424e7i −0.434050 0.537466i
995995 5.75379e6 0.184245
996996 3.57721e7 + 1.27594e7i 1.14260 + 0.407551i
997997 −2.00990e7 −0.640377 −0.320188 0.947354i 0.603746π-0.603746\pi
−0.320188 + 0.947354i 0.603746π0.603746\pi
998998 3.78163e7 + 4.68263e7i 1.20186 + 1.48821i
999999 −5.19229e6 + 1.25757e7i −0.164606 + 0.398676i
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 84.6.e.a.71.49 yes 60
3.2 odd 2 inner 84.6.e.a.71.12 yes 60
4.3 odd 2 inner 84.6.e.a.71.11 60
12.11 even 2 inner 84.6.e.a.71.50 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.e.a.71.11 60 4.3 odd 2 inner
84.6.e.a.71.12 yes 60 3.2 odd 2 inner
84.6.e.a.71.49 yes 60 1.1 even 1 trivial
84.6.e.a.71.50 yes 60 12.11 even 2 inner