Properties

Label 30.3.d.a.11.4
Level 3030
Weight 33
Character 30.11
Analytic conductor 0.8170.817
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [30,3,Mod(11,30)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("30.11"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 30=235 30 = 2 \cdot 3 \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 30.d (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: 0.8174407930810.817440793081
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,5)\Q(\sqrt{-2}, \sqrt{-5})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x44x2+9 x^{4} - 4x^{2} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 11.4
Root 1.581140.707107i1.58114 - 0.707107i of defining polynomial
Character χ\chi == 30.11
Dual form 30.3.d.a.11.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.41421iq2+(2.581141.52896i)q32.00000q4+2.23607iq5+(2.16228+3.65028i)q67.48683q72.82843iq8+(4.324567.89292i)q93.16228q108.48528iq11+(5.16228+3.05792i)q1210.0000q1310.5880iq14+(3.41886+5.77160i)q15+4.00000q16+30.3870iq17+(11.1623+6.11584i)q18+26.9737q194.47214iq20+(19.3246+11.4471i)q21+12.0000q229.17377iq23+(4.324567.30056i)q245.00000q2514.1421iq26+(0.90569426.9848i)q27+14.9737q28+26.8328iq29+(8.16228+4.83500i)q30+8.00000q31+5.65685iq32+(12.973721.9017i)q3342.9737q3416.7411iq35+(8.64911+15.7858i)q36+15.9473q37+38.1465iq38+(25.8114+15.2896i)q39+6.32456q4047.3575iq41+(16.188627.3290i)q4214.4605q43+16.9706iq44+(17.6491+9.67000i)q45+12.9737q4645.8688iq47+(10.32466.11584i)q48+7.05267q497.07107iq50+(46.4605+78.4330i)q51+20.0000q52+30.3870iq53+(38.16231.28084i)q54+18.9737q55+21.1760iq56+(69.622841.2417i)q5737.9473q58+24.0789iq59+(6.8377211.5432i)q6053.9473q61+11.3137iq62+(32.3772+59.0930i)q638.00000q6422.3607iq65+(30.973718.3475i)q66110.460q6760.7739iq68+(14.026323.6788i)q69+23.6754q7015.5936iq71+(22.324612.2317i)q72+87.9473q73+22.5529iq74+(12.9057+7.64481i)q7553.9473q76+63.5279iq77+(21.622836.5028i)q7846.9737q79+8.94427iq80+(43.596468.2668i)q81+66.9737q8226.1443iq83+(38.649122.8942i)q8467.9473q8520.4502iq86+(41.0263+69.2592i)q8724.0000q8860.7739iq89+(13.6754+24.9596i)q90+74.8683q91+18.3475iq92+(20.649112.2317i)q93+64.8683q94+60.3150iq95+(8.64911+14.6011i)q96+36.0527q97+9.97398iq98+(66.973736.6951i)q99+O(q100)q+1.41421i q^{2} +(2.58114 - 1.52896i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(2.16228 + 3.65028i) q^{6} -7.48683 q^{7} -2.82843i q^{8} +(4.32456 - 7.89292i) q^{9} -3.16228 q^{10} -8.48528i q^{11} +(-5.16228 + 3.05792i) q^{12} -10.0000 q^{13} -10.5880i q^{14} +(3.41886 + 5.77160i) q^{15} +4.00000 q^{16} +30.3870i q^{17} +(11.1623 + 6.11584i) q^{18} +26.9737 q^{19} -4.47214i q^{20} +(-19.3246 + 11.4471i) q^{21} +12.0000 q^{22} -9.17377i q^{23} +(-4.32456 - 7.30056i) q^{24} -5.00000 q^{25} -14.1421i q^{26} +(-0.905694 - 26.9848i) q^{27} +14.9737 q^{28} +26.8328i q^{29} +(-8.16228 + 4.83500i) q^{30} +8.00000 q^{31} +5.65685i q^{32} +(-12.9737 - 21.9017i) q^{33} -42.9737 q^{34} -16.7411i q^{35} +(-8.64911 + 15.7858i) q^{36} +15.9473 q^{37} +38.1465i q^{38} +(-25.8114 + 15.2896i) q^{39} +6.32456 q^{40} -47.3575i q^{41} +(-16.1886 - 27.3290i) q^{42} -14.4605 q^{43} +16.9706i q^{44} +(17.6491 + 9.67000i) q^{45} +12.9737 q^{46} -45.8688i q^{47} +(10.3246 - 6.11584i) q^{48} +7.05267 q^{49} -7.07107i q^{50} +(46.4605 + 78.4330i) q^{51} +20.0000 q^{52} +30.3870i q^{53} +(38.1623 - 1.28084i) q^{54} +18.9737 q^{55} +21.1760i q^{56} +(69.6228 - 41.2417i) q^{57} -37.9473 q^{58} +24.0789i q^{59} +(-6.83772 - 11.5432i) q^{60} -53.9473 q^{61} +11.3137i q^{62} +(-32.3772 + 59.0930i) q^{63} -8.00000 q^{64} -22.3607i q^{65} +(30.9737 - 18.3475i) q^{66} -110.460 q^{67} -60.7739i q^{68} +(-14.0263 - 23.6788i) q^{69} +23.6754 q^{70} -15.5936i q^{71} +(-22.3246 - 12.2317i) q^{72} +87.9473 q^{73} +22.5529i q^{74} +(-12.9057 + 7.64481i) q^{75} -53.9473 q^{76} +63.5279i q^{77} +(-21.6228 - 36.5028i) q^{78} -46.9737 q^{79} +8.94427i q^{80} +(-43.5964 - 68.2668i) q^{81} +66.9737 q^{82} -26.1443i q^{83} +(38.6491 - 22.8942i) q^{84} -67.9473 q^{85} -20.4502i q^{86} +(41.0263 + 69.2592i) q^{87} -24.0000 q^{88} -60.7739i q^{89} +(-13.6754 + 24.9596i) q^{90} +74.8683 q^{91} +18.3475i q^{92} +(20.6491 - 12.2317i) q^{93} +64.8683 q^{94} +60.3150i q^{95} +(8.64911 + 14.6011i) q^{96} +36.0527 q^{97} +9.97398i q^{98} +(-66.9737 - 36.6951i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q38q44q6+8q78q98q1240q13+20q15+16q16+32q18+32q1952q21+48q22+8q2420q25+28q2716q2820q30+192q99+O(q100) 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 8 q^{12} - 40 q^{13} + 20 q^{15} + 16 q^{16} + 32 q^{18} + 32 q^{19} - 52 q^{21} + 48 q^{22} + 8 q^{24} - 20 q^{25} + 28 q^{27} - 16 q^{28} - 20 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/30Z)×\left(\mathbb{Z}/30\mathbb{Z}\right)^\times.

nn 77 1111
χ(n)\chi(n) 11 1-1

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 1.41421i 0.707107i
33 2.58114 1.52896i 0.860380 0.509654i
44 −2.00000 −0.500000
55 2.23607i 0.447214i
66 2.16228 + 3.65028i 0.360380 + 0.608380i
77 −7.48683 −1.06955 −0.534774 0.844995i 0.679603π-0.679603\pi
−0.534774 + 0.844995i 0.679603π0.679603\pi
88 2.82843i 0.353553i
99 4.32456 7.89292i 0.480506 0.876991i
1010 −3.16228 −0.316228
1111 8.48528i 0.771389i −0.922627 0.385695i 0.873962π-0.873962\pi
0.922627 0.385695i 0.126038π-0.126038\pi
1212 −5.16228 + 3.05792i −0.430190 + 0.254827i
1313 −10.0000 −0.769231 −0.384615 0.923077i 0.625666π-0.625666\pi
−0.384615 + 0.923077i 0.625666π0.625666\pi
1414 10.5880i 0.756284i
1515 3.41886 + 5.77160i 0.227924 + 0.384773i
1616 4.00000 0.250000
1717 30.3870i 1.78747i 0.448596 + 0.893734i 0.351924π0.351924\pi
−0.448596 + 0.893734i 0.648076π0.648076\pi
1818 11.1623 + 6.11584i 0.620127 + 0.339769i
1919 26.9737 1.41967 0.709833 0.704370i 0.248770π-0.248770\pi
0.709833 + 0.704370i 0.248770π0.248770\pi
2020 4.47214i 0.223607i
2121 −19.3246 + 11.4471i −0.920217 + 0.545099i
2222 12.0000 0.545455
2323 9.17377i 0.398859i −0.979912 0.199430i 0.936091π-0.936091\pi
0.979912 0.199430i 0.0639090π-0.0639090\pi
2424 −4.32456 7.30056i −0.180190 0.304190i
2525 −5.00000 −0.200000
2626 14.1421i 0.543928i
2727 −0.905694 26.9848i −0.0335442 0.999437i
2828 14.9737 0.534774
2929 26.8328i 0.925270i 0.886549 + 0.462635i 0.153096π0.153096\pi
−0.886549 + 0.462635i 0.846904π0.846904\pi
3030 −8.16228 + 4.83500i −0.272076 + 0.161167i
3131 8.00000 0.258065 0.129032 0.991640i 0.458813π-0.458813\pi
0.129032 + 0.991640i 0.458813π0.458813\pi
3232 5.65685i 0.176777i
3333 −12.9737 21.9017i −0.393141 0.663688i
3434 −42.9737 −1.26393
3535 16.7411i 0.478316i
3636 −8.64911 + 15.7858i −0.240253 + 0.438496i
3737 15.9473 0.431009 0.215504 0.976503i 0.430860π-0.430860\pi
0.215504 + 0.976503i 0.430860π0.430860\pi
3838 38.1465i 1.00386i
3939 −25.8114 + 15.2896i −0.661830 + 0.392041i
4040 6.32456 0.158114
4141 47.3575i 1.15506i −0.816369 0.577531i 0.804016π-0.804016\pi
0.816369 0.577531i 0.195984π-0.195984\pi
4242 −16.1886 27.3290i −0.385443 0.650692i
4343 −14.4605 −0.336291 −0.168145 0.985762i 0.553778π-0.553778\pi
−0.168145 + 0.985762i 0.553778π0.553778\pi
4444 16.9706i 0.385695i
4545 17.6491 + 9.67000i 0.392202 + 0.214889i
4646 12.9737 0.282036
4747 45.8688i 0.975933i −0.872862 0.487966i 0.837739π-0.837739\pi
0.872862 0.487966i 0.162261π-0.162261\pi
4848 10.3246 6.11584i 0.215095 0.127413i
4949 7.05267 0.143932
5050 7.07107i 0.141421i
5151 46.4605 + 78.4330i 0.910990 + 1.53790i
5252 20.0000 0.384615
5353 30.3870i 0.573339i 0.958030 + 0.286670i 0.0925482π0.0925482\pi
−0.958030 + 0.286670i 0.907452π0.907452\pi
5454 38.1623 1.28084i 0.706709 0.0237194i
5555 18.9737 0.344976
5656 21.1760i 0.378142i
5757 69.6228 41.2417i 1.22145 0.723538i
5858 −37.9473 −0.654264
5959 24.0789i 0.408116i 0.978959 + 0.204058i 0.0654132π0.0654132\pi
−0.978959 + 0.204058i 0.934587π0.934587\pi
6060 −6.83772 11.5432i −0.113962 0.192387i
6161 −53.9473 −0.884382 −0.442191 0.896921i 0.645799π-0.645799\pi
−0.442191 + 0.896921i 0.645799π0.645799\pi
6262 11.3137i 0.182479i
6363 −32.3772 + 59.0930i −0.513924 + 0.937984i
6464 −8.00000 −0.125000
6565 22.3607i 0.344010i
6666 30.9737 18.3475i 0.469298 0.277993i
6767 −110.460 −1.64866 −0.824332 0.566107i 0.808449π-0.808449\pi
−0.824332 + 0.566107i 0.808449π0.808449\pi
6868 60.7739i 0.893734i
6969 −14.0263 23.6788i −0.203280 0.343171i
7070 23.6754 0.338221
7171 15.5936i 0.219628i −0.993952 0.109814i 0.964974π-0.964974\pi
0.993952 0.109814i 0.0350255π-0.0350255\pi
7272 −22.3246 12.2317i −0.310063 0.169885i
7373 87.9473 1.20476 0.602379 0.798210i 0.294220π-0.294220\pi
0.602379 + 0.798210i 0.294220π0.294220\pi
7474 22.5529i 0.304769i
7575 −12.9057 + 7.64481i −0.172076 + 0.101931i
7676 −53.9473 −0.709833
7777 63.5279i 0.825037i
7878 −21.6228 36.5028i −0.277215 0.467985i
7979 −46.9737 −0.594603 −0.297302 0.954784i 0.596087π-0.596087\pi
−0.297302 + 0.954784i 0.596087π0.596087\pi
8080 8.94427i 0.111803i
8181 −43.5964 68.2668i −0.538228 0.842799i
8282 66.9737 0.816752
8383 26.1443i 0.314992i −0.987520 0.157496i 0.949658π-0.949658\pi
0.987520 0.157496i 0.0503421π-0.0503421\pi
8484 38.6491 22.8942i 0.460108 0.272549i
8585 −67.9473 −0.799380
8686 20.4502i 0.237793i
8787 41.0263 + 69.2592i 0.471567 + 0.796083i
8888 −24.0000 −0.272727
8989 60.7739i 0.682853i −0.939908 0.341427i 0.889090π-0.889090\pi
0.939908 0.341427i 0.110910π-0.110910\pi
9090 −13.6754 + 24.9596i −0.151949 + 0.277329i
9191 74.8683 0.822729
9292 18.3475i 0.199430i
9393 20.6491 12.2317i 0.222033 0.131524i
9494 64.8683 0.690089
9595 60.3150i 0.634894i
9696 8.64911 + 14.6011i 0.0900949 + 0.152095i
9797 36.0527 0.371677 0.185838 0.982580i 0.440500π-0.440500\pi
0.185838 + 0.982580i 0.440500π0.440500\pi
9898 9.97398i 0.101775i
9999 −66.9737 36.6951i −0.676502 0.370657i
100100 10.0000 0.100000
101101 48.1577i 0.476809i 0.971166 + 0.238405i 0.0766245π0.0766245\pi
−0.971166 + 0.238405i 0.923376π0.923376\pi
102102 −110.921 + 65.7051i −1.08746 + 0.644167i
103103 140.408 1.36318 0.681591 0.731733i 0.261288π-0.261288\pi
0.681591 + 0.731733i 0.261288π0.261288\pi
104104 28.2843i 0.271964i
105105 −25.5964 43.2110i −0.243776 0.411534i
106106 −42.9737 −0.405412
107107 43.1149i 0.402943i 0.979494 + 0.201471i 0.0645723π0.0645723\pi
−0.979494 + 0.201471i 0.935428π0.935428\pi
108108 1.81139 + 53.9696i 0.0167721 + 0.499719i
109109 133.842 1.22791 0.613954 0.789342i 0.289578π-0.289578\pi
0.613954 + 0.789342i 0.289578π0.289578\pi
110110 26.8328i 0.243935i
111111 41.1623 24.3829i 0.370831 0.219665i
112112 −29.9473 −0.267387
113113 7.90852i 0.0699869i −0.999388 0.0349935i 0.988859π-0.988859\pi
0.999388 0.0349935i 0.0111410π-0.0111410\pi
114114 58.3246 + 98.4615i 0.511619 + 0.863697i
115115 20.5132 0.178375
116116 53.6656i 0.462635i
117117 −43.2456 + 78.9292i −0.369620 + 0.674609i
118118 −34.0527 −0.288582
119119 227.502i 1.91178i
120120 16.3246 9.67000i 0.136038 0.0805833i
121121 49.0000 0.404959
122122 76.2930i 0.625353i
123123 −72.4078 122.236i −0.588682 0.993792i
124124 −16.0000 −0.129032
125125 11.1803i 0.0894427i
126126 −83.5701 45.7883i −0.663255 0.363399i
127127 −134.460 −1.05874 −0.529372 0.848390i 0.677572π-0.677572\pi
−0.529372 + 0.848390i 0.677572π0.677572\pi
128128 11.3137i 0.0883883i
129129 −37.3246 + 22.1095i −0.289338 + 0.171392i
130130 31.6228 0.243252
131131 220.394i 1.68240i 0.540727 + 0.841198i 0.318149π0.318149\pi
−0.540727 + 0.841198i 0.681851π0.681851\pi
132132 25.9473 + 43.8034i 0.196571 + 0.331844i
133133 −201.947 −1.51840
134134 156.215i 1.16578i
135135 60.3399 2.02519i 0.446962 0.0150014i
136136 85.9473 0.631966
137137 95.5153i 0.697192i −0.937273 0.348596i 0.886659π-0.886659\pi
0.937273 0.348596i 0.113341π-0.113341\pi
138138 33.4868 19.8362i 0.242658 0.143741i
139139 −76.8157 −0.552631 −0.276315 0.961067i 0.589113π-0.589113\pi
−0.276315 + 0.961067i 0.589113π0.589113\pi
140140 33.4821i 0.239158i
141141 −70.1317 118.394i −0.497388 0.839673i
142142 22.0527 0.155300
143143 84.8528i 0.593376i
144144 17.2982 31.5717i 0.120127 0.219248i
145145 −60.0000 −0.413793
146146 124.376i 0.851893i
147147 18.2039 10.7833i 0.123836 0.0733555i
148148 −31.8947 −0.215504
149149 276.237i 1.85394i 0.375139 + 0.926969i 0.377595π0.377595\pi
−0.375139 + 0.926969i 0.622405π0.622405\pi
150150 −10.8114 18.2514i −0.0720759 0.121676i
151151 18.0527 0.119554 0.0597770 0.998212i 0.480961π-0.480961\pi
0.0597770 + 0.998212i 0.480961π0.480961\pi
152152 76.2930i 0.501928i
153153 239.842 + 131.410i 1.56759 + 0.858890i
154154 −89.8420 −0.583390
155155 17.8885i 0.115410i
156156 51.6228 30.5792i 0.330915 0.196021i
157157 103.842 0.661414 0.330707 0.943733i 0.392713π-0.392713\pi
0.330707 + 0.943733i 0.392713π0.392713\pi
158158 66.4308i 0.420448i
159159 46.4605 + 78.4330i 0.292204 + 0.493289i
160160 −12.6491 −0.0790569
161161 68.6825i 0.426599i
162162 96.5438 61.6547i 0.595949 0.380584i
163163 −11.3815 −0.0698251 −0.0349126 0.999390i 0.511115π-0.511115\pi
−0.0349126 + 0.999390i 0.511115π0.511115\pi
164164 94.7151i 0.577531i
165165 48.9737 29.0100i 0.296810 0.175818i
166166 36.9737 0.222733
167167 252.270i 1.51060i −0.655382 0.755298i 0.727492π-0.727492\pi
0.655382 0.755298i 0.272508π-0.272508\pi
168168 32.3772 + 54.6581i 0.192722 + 0.325346i
169169 −69.0000 −0.408284
170170 96.0920i 0.565247i
171171 116.649 212.901i 0.682159 1.24504i
172172 28.9210 0.168145
173173 11.8160i 0.0683005i −0.999417 0.0341502i 0.989128π-0.989128\pi
0.999417 0.0341502i 0.0108725π-0.0108725\pi
174174 −97.9473 + 58.0200i −0.562916 + 0.333448i
175175 37.4342 0.213910
176176 33.9411i 0.192847i
177177 36.8157 + 62.1509i 0.207998 + 0.351135i
178178 85.9473 0.482850
179179 69.0358i 0.385675i 0.981231 + 0.192837i 0.0617690π0.0617690\pi
−0.981231 + 0.192837i 0.938231π0.938231\pi
180180 −35.2982 19.3400i −0.196101 0.107444i
181181 −189.684 −1.04798 −0.523989 0.851725i 0.675557π-0.675557\pi
−0.523989 + 0.851725i 0.675557π0.675557\pi
182182 105.880i 0.581757i
183183 −139.246 + 82.4834i −0.760905 + 0.450729i
184184 −25.9473 −0.141018
185185 35.6593i 0.192753i
186186 17.2982 + 29.2023i 0.0930012 + 0.157001i
187187 257.842 1.37883
188188 91.7377i 0.487966i
189189 6.78078 + 202.031i 0.0358771 + 1.06895i
190190 −85.2982 −0.448938
191191 108.708i 0.569153i −0.958653 0.284577i 0.908147π-0.908147\pi
0.958653 0.284577i 0.0918530π-0.0918530\pi
192192 −20.6491 + 12.2317i −0.107547 + 0.0637067i
193193 −167.947 −0.870193 −0.435097 0.900384i 0.643286π-0.643286\pi
−0.435097 + 0.900384i 0.643286π0.643286\pi
194194 50.9862i 0.262815i
195195 −34.1886 57.7160i −0.175326 0.295980i
196196 −14.1053 −0.0719660
197197 171.659i 0.871367i −0.900100 0.435684i 0.856507π-0.856507\pi
0.900100 0.435684i 0.143493π-0.143493\pi
198198 51.8947 94.7151i 0.262094 0.478359i
199199 35.0790 0.176276 0.0881382 0.996108i 0.471908π-0.471908\pi
0.0881382 + 0.996108i 0.471908π0.471908\pi
200200 14.1421i 0.0707107i
201201 −285.114 + 168.890i −1.41848 + 0.840248i
202202 −68.1053 −0.337155
203203 200.893i 0.989620i
204204 −92.9210 156.866i −0.455495 0.768951i
205205 105.895 0.516559
206206 198.567i 0.963916i
207207 −72.4078 39.6725i −0.349796 0.191654i
208208 −40.0000 −0.192308
209209 228.879i 1.09512i
210210 61.1096 36.1988i 0.290998 0.172375i
211211 −58.1580 −0.275630 −0.137815 0.990458i 0.544008π-0.544008\pi
−0.137815 + 0.990458i 0.544008π0.544008\pi
212212 60.7739i 0.286670i
213213 −23.8420 40.2492i −0.111934 0.188963i
214214 −60.9737 −0.284924
215215 32.3347i 0.150394i
216216 −76.3246 + 2.56169i −0.353354 + 0.0118597i
217217 −59.8947 −0.276012
218218 189.281i 0.868262i
219219 227.004 134.468i 1.03655 0.614009i
220220 −37.9473 −0.172488
221221 303.870i 1.37498i
222222 34.4826 + 58.2123i 0.155327 + 0.262217i
223223 99.3815 0.445657 0.222828 0.974858i 0.428471π-0.428471\pi
0.222828 + 0.974858i 0.428471π0.428471\pi
224224 42.3519i 0.189071i
225225 −21.6228 + 39.4646i −0.0961012 + 0.175398i
226226 11.1843 0.0494882
227227 216.951i 0.955733i 0.878432 + 0.477867i 0.158590π0.158590\pi
−0.878432 + 0.477867i 0.841410π0.841410\pi
228228 −139.246 + 82.4834i −0.610726 + 0.361769i
229229 325.684 1.42220 0.711100 0.703090i 0.248197π-0.248197\pi
0.711100 + 0.703090i 0.248197π0.248197\pi
230230 29.0100i 0.126130i
231231 97.1317 + 163.974i 0.420483 + 0.709845i
232232 75.8947 0.327132
233233 51.7119i 0.221939i 0.993824 + 0.110970i 0.0353957π0.0353957\pi
−0.993824 + 0.110970i 0.964604π0.964604\pi
234234 −111.623 61.1584i −0.477020 0.261361i
235235 102.566 0.436450
236236 48.1577i 0.204058i
237237 −121.246 + 71.8209i −0.511585 + 0.303042i
238238 321.737 1.35183
239239 410.047i 1.71568i 0.513917 + 0.857840i 0.328194π0.328194\pi
−0.513917 + 0.857840i 0.671806π0.671806\pi
240240 13.6754 + 23.0864i 0.0569810 + 0.0961934i
241241 445.526 1.84866 0.924328 0.381599i 0.124627π-0.124627\pi
0.924328 + 0.381599i 0.124627π0.124627\pi
242242 69.2965i 0.286349i
243243 −216.906 109.549i −0.892616 0.450818i
244244 107.895 0.442191
245245 15.7702i 0.0643683i
246246 172.868 102.400i 0.702717 0.416261i
247247 −269.737 −1.09205
248248 22.6274i 0.0912396i
249249 −39.9737 67.4821i −0.160537 0.271013i
250250 15.8114 0.0632456
251251 237.364i 0.945675i 0.881150 + 0.472838i 0.156770π0.156770\pi
−0.881150 + 0.472838i 0.843230π0.843230\pi
252252 64.7544 118.186i 0.256962 0.468992i
253253 −77.8420 −0.307676
254254 190.156i 0.748645i
255255 −175.381 + 103.889i −0.687771 + 0.407407i
256256 16.0000 0.0625000
257257 318.887i 1.24080i 0.784284 + 0.620402i 0.213030π0.213030\pi
−0.784284 + 0.620402i 0.786970π0.786970\pi
258258 −31.2676 52.7849i −0.121192 0.204593i
259259 −119.395 −0.460985
260260 44.7214i 0.172005i
261261 211.789 + 116.040i 0.811453 + 0.444598i
262262 −311.684 −1.18963
263263 36.2300i 0.137757i 0.997625 + 0.0688784i 0.0219420π0.0219420\pi
−0.997625 + 0.0688784i 0.978058π0.978058\pi
264264 −61.9473 + 36.6951i −0.234649 + 0.138996i
265265 −67.9473 −0.256405
266266 285.597i 1.07367i
267267 −92.9210 156.866i −0.348019 0.587513i
268268 220.921 0.824332
269269 528.041i 1.96298i −0.191518 0.981489i 0.561341π-0.561341\pi
0.191518 0.981489i 0.438659π-0.438659\pi
270270 2.86406 + 85.3334i 0.0106076 + 0.316050i
271271 −475.895 −1.75607 −0.878034 0.478597i 0.841145π-0.841145\pi
−0.878034 + 0.478597i 0.841145π0.841145\pi
272272 121.548i 0.446867i
273273 193.246 114.471i 0.707859 0.419307i
274274 135.079 0.492989
275275 42.4264i 0.154278i
276276 28.0527 + 47.3575i 0.101640 + 0.171585i
277277 188.158 0.679271 0.339635 0.940557i 0.389696π-0.389696\pi
0.339635 + 0.940557i 0.389696π0.389696\pi
278278 108.634i 0.390769i
279279 34.5964 63.1434i 0.124002 0.226320i
280280 −47.3509 −0.169110
281281 24.4322i 0.0869473i 0.999055 + 0.0434736i 0.0138424π0.0138424\pi
−0.999055 + 0.0434736i 0.986158π0.986158\pi
282282 167.434 99.1812i 0.593738 0.351706i
283283 198.460 0.701274 0.350637 0.936511i 0.385965π-0.385965\pi
0.350637 + 0.936511i 0.385965π0.385965\pi
284284 31.1872i 0.109814i
285285 92.2192 + 155.681i 0.323576 + 0.546250i
286286 −120.000 −0.419580
287287 354.558i 1.23539i
288288 44.6491 + 24.4634i 0.155032 + 0.0849423i
289289 −634.368 −2.19504
290290 84.8528i 0.292596i
291291 93.0569 55.1231i 0.319783 0.189427i
292292 −175.895 −0.602379
293293 513.825i 1.75367i −0.480794 0.876834i 0.659651π-0.659651\pi
0.480794 0.876834i 0.340349π-0.340349\pi
294294 15.2498 + 25.7442i 0.0518702 + 0.0875654i
295295 −53.8420 −0.182515
296296 45.1059i 0.152385i
297297 −228.974 + 7.68507i −0.770955 + 0.0258757i
298298 −390.658 −1.31093
299299 91.7377i 0.306815i
300300 25.8114 15.2896i 0.0860380 0.0509654i
301301 108.263 0.359679
302302 25.5303i 0.0845375i
303303 73.6313 + 124.302i 0.243008 + 0.410237i
304304 107.895 0.354917
305305 120.630i 0.395508i
306306 −185.842 + 339.188i −0.607327 + 1.10846i
307307 −11.3815 −0.0370733 −0.0185366 0.999828i 0.505901π-0.505901\pi
−0.0185366 + 0.999828i 0.505901π0.505901\pi
308308 127.056i 0.412519i
309309 362.412 214.678i 1.17285 0.694751i
310310 −25.2982 −0.0816072
311311 518.756i 1.66802i −0.551746 0.834012i 0.686038π-0.686038\pi
0.551746 0.834012i 0.313962π-0.313962\pi
312312 43.2456 + 73.0056i 0.138608 + 0.233992i
313313 −46.3160 −0.147974 −0.0739872 0.997259i 0.523572π-0.523572\pi
−0.0739872 + 0.997259i 0.523572π0.523572\pi
314314 146.855i 0.467690i
315315 −132.136 72.3977i −0.419479 0.229834i
316316 93.9473 0.297302
317317 39.0957i 0.123330i 0.998097 + 0.0616651i 0.0196411π0.0196411\pi
−0.998097 + 0.0616651i 0.980359π0.980359\pi
318318 −110.921 + 65.7051i −0.348808 + 0.206620i
319319 227.684 0.713743
320320 17.8885i 0.0559017i
321321 65.9210 + 111.286i 0.205361 + 0.346684i
322322 −97.1317 −0.301651
323323 819.648i 2.53761i
324324 87.1929 + 136.534i 0.269114 + 0.421400i
325325 50.0000 0.153846
326326 16.0959i 0.0493738i
327327 345.465 204.639i 1.05647 0.625808i
328328 −133.947 −0.408376
329329 343.412i 1.04381i
330330 41.0263 + 69.2592i 0.124322 + 0.209876i
331331 −445.421 −1.34568 −0.672841 0.739787i 0.734926π-0.734926\pi
−0.672841 + 0.739787i 0.734926π0.734926\pi
332332 52.2887i 0.157496i
333333 68.9651 125.871i 0.207102 0.377991i
334334 356.763 1.06815
335335 246.997i 0.737305i
336336 −77.2982 + 45.7883i −0.230054 + 0.136275i
337337 325.684 0.966421 0.483211 0.875504i 0.339471π-0.339471\pi
0.483211 + 0.875504i 0.339471π0.339471\pi
338338 97.5807i 0.288700i
339339 −12.0918 20.4130i −0.0356691 0.0602153i
340340 135.895 0.399690
341341 67.8823i 0.199068i
342342 301.088 + 164.967i 0.880373 + 0.482359i
343343 314.053 0.915605
344344 40.9005i 0.118897i
345345 52.9473 31.3638i 0.153471 0.0909097i
346346 16.7103 0.0482957
347347 51.8236i 0.149348i −0.997208 0.0746738i 0.976208π-0.976208\pi
0.997208 0.0746738i 0.0237916π-0.0237916\pi
348348 −82.0527 138.518i −0.235784 0.398042i
349349 −97.5787 −0.279595 −0.139798 0.990180i 0.544645π-0.544645\pi
−0.139798 + 0.990180i 0.544645π0.544645\pi
350350 52.9399i 0.151257i
351351 9.05694 + 269.848i 0.0258033 + 0.768798i
352352 48.0000 0.136364
353353 569.797i 1.61416i 0.590445 + 0.807078i 0.298952π0.298952\pi
−0.590445 + 0.807078i 0.701048π0.701048\pi
354354 −87.8947 + 52.0652i −0.248290 + 0.147077i
355355 34.8683 0.0982206
356356 121.548i 0.341427i
357357 −347.842 587.215i −0.974347 1.64486i
358358 −97.6313 −0.272713
359359 274.283i 0.764019i −0.924158 0.382010i 0.875232π-0.875232\pi
0.924158 0.382010i 0.124768π-0.124768\pi
360360 27.3509 49.9192i 0.0759747 0.138665i
361361 366.579 1.01545
362362 268.254i 0.741032i
363363 126.476 74.9191i 0.348418 0.206389i
364364 −149.737 −0.411364
365365 196.656i 0.538784i
366366 −116.649 196.923i −0.318713 0.538041i
367367 461.828 1.25839 0.629194 0.777248i 0.283385π-0.283385\pi
0.629194 + 0.777248i 0.283385π0.283385\pi
368368 36.6951i 0.0997149i
369369 −373.789 204.800i −1.01298 0.555014i
370370 −50.4299 −0.136297
371371 227.502i 0.613213i
372372 −41.2982 + 24.4634i −0.111017 + 0.0657618i
373373 −491.947 −1.31889 −0.659447 0.751751i 0.729209π-0.729209\pi
−0.659447 + 0.751751i 0.729209π0.729209\pi
374374 364.644i 0.974983i
375375 −17.0943 28.8580i −0.0455848 0.0769547i
376376 −129.737 −0.345044
377377 268.328i 0.711746i
378378 −285.715 + 9.58947i −0.755859 + 0.0253690i
379379 −258.763 −0.682752 −0.341376 0.939927i 0.610893π-0.610893\pi
−0.341376 + 0.939927i 0.610893π0.610893\pi
380380 120.630i 0.317447i
381381 −347.061 + 205.585i −0.910922 + 0.539593i
382382 153.737 0.402452
383383 522.422i 1.36402i −0.731341 0.682012i 0.761105π-0.761105\pi
0.731341 0.682012i 0.238895π-0.238895\pi
384384 −17.2982 29.2023i −0.0450475 0.0760475i
385385 −142.053 −0.368968
386386 237.513i 0.615320i
387387 −62.5352 + 114.136i −0.161590 + 0.294924i
388388 −72.1053 −0.185838
389389 610.847i 1.57030i 0.619306 + 0.785150i 0.287414π0.287414\pi
−0.619306 + 0.785150i 0.712586π0.712586\pi
390390 81.6228 48.3500i 0.209289 0.123974i
391391 278.763 0.712949
392392 19.9480i 0.0508876i
393393 336.974 + 568.867i 0.857439 + 1.44750i
394394 242.763 0.616150
395395 105.036i 0.265915i
396396 133.947 + 73.3901i 0.338251 + 0.185329i
397397 −214.000 −0.539043 −0.269521 0.962994i 0.586865π-0.586865\pi
−0.269521 + 0.962994i 0.586865π0.586865\pi
398398 49.6092i 0.124646i
399399 −521.254 + 308.770i −1.30640 + 0.773859i
400400 −20.0000 −0.0500000
401401 454.557i 1.13356i 0.823869 + 0.566780i 0.191811π0.191811\pi
−0.823869 + 0.566780i 0.808189π0.808189\pi
402402 −238.846 403.212i −0.594145 1.00301i
403403 −80.0000 −0.198511
404404 96.3155i 0.238405i
405405 152.649 97.4846i 0.376911 0.240703i
406406 284.105 0.699767
407407 135.318i 0.332476i
408408 221.842 131.410i 0.543730 0.322084i
409409 −573.842 −1.40304 −0.701518 0.712651i 0.747494π-0.747494\pi
−0.701518 + 0.712651i 0.747494π0.747494\pi
410410 149.758i 0.365263i
411411 −146.039 246.538i −0.355326 0.599850i
412412 −280.816 −0.681591
413413 180.274i 0.436500i
414414 56.1053 102.400i 0.135520 0.247343i
415415 58.4605 0.140869
416416 56.5685i 0.135982i
417417 −198.272 + 117.448i −0.475472 + 0.281650i
418418 323.684 0.774364
419419 97.9159i 0.233690i 0.993150 + 0.116845i 0.0372780π0.0372780\pi
−0.993150 + 0.116845i 0.962722π0.962722\pi
420420 51.1929 + 86.4220i 0.121888 + 0.205767i
421421 717.315 1.70384 0.851918 0.523675i 0.175439π-0.175439\pi
0.851918 + 0.523675i 0.175439π0.175439\pi
422422 82.2478i 0.194900i
423423 −362.039 198.362i −0.855885 0.468942i
424424 85.9473 0.202706
425425 151.935i 0.357494i
426426 56.9210 33.7177i 0.133617 0.0791495i
427427 403.895 0.945889
428428 86.2298i 0.201471i
429429 129.737 + 219.017i 0.302416 + 0.510529i
430430 45.7281 0.106344
431431 293.077i 0.679994i 0.940427 + 0.339997i 0.110426π0.110426\pi
−0.940427 + 0.339997i 0.889574π0.889574\pi
432432 −3.62278 107.939i −0.00838606 0.249859i
433433 487.526 1.12593 0.562963 0.826482i 0.309661π-0.309661\pi
0.562963 + 0.826482i 0.309661π0.309661\pi
434434 84.7038i 0.195170i
435435 −154.868 + 91.7377i −0.356019 + 0.210891i
436436 −267.684 −0.613954
437437 247.450i 0.566247i
438438 190.167 + 321.033i 0.434170 + 0.732951i
439439 257.237 0.585961 0.292981 0.956118i 0.405353π-0.405353\pi
0.292981 + 0.956118i 0.405353π0.405353\pi
440440 53.6656i 0.121967i
441441 30.4997 55.6662i 0.0691602 0.126227i
442442 429.737 0.972255
443443 293.096i 0.661615i −0.943698 0.330808i 0.892679π-0.892679\pi
0.943698 0.330808i 0.107321π-0.107321\pi
444444 −82.3246 + 48.7657i −0.185416 + 0.109833i
445445 135.895 0.305381
446446 140.547i 0.315127i
447447 422.355 + 713.005i 0.944866 + 1.59509i
448448 59.8947 0.133693
449449 585.614i 1.30426i −0.758106 0.652132i 0.773875π-0.773875\pi
0.758106 0.652132i 0.226125π-0.226125\pi
450450 −55.8114 30.5792i −0.124025 0.0679538i
451451 −401.842 −0.891002
452452 15.8170i 0.0349935i
453453 46.5964 27.6018i 0.102862 0.0609312i
454454 −306.816 −0.675805
455455 167.411i 0.367936i
456456 −116.649 196.923i −0.255809 0.431849i
457457 −813.052 −1.77911 −0.889554 0.456831i 0.848984π-0.848984\pi
−0.889554 + 0.456831i 0.848984π0.848984\pi
458458 460.587i 1.00565i
459459 819.986 27.5213i 1.78646 0.0599593i
460460 −41.0263 −0.0891877
461461 554.074i 1.20190i 0.799288 + 0.600948i 0.205210π0.205210\pi
−0.799288 + 0.600948i 0.794790π0.794790\pi
462462 −231.895 + 137.365i −0.501937 + 0.297327i
463463 −449.723 −0.971324 −0.485662 0.874147i 0.661421π-0.661421\pi
−0.485662 + 0.874147i 0.661421π0.661421\pi
464464 107.331i 0.231317i
465465 27.3509 + 46.1728i 0.0588191 + 0.0992964i
466466 −73.1317 −0.156935
467467 30.7221i 0.0657862i −0.999459 0.0328931i 0.989528π-0.989528\pi
0.999459 0.0328931i 0.0104721π-0.0104721\pi
468468 86.4911 157.858i 0.184810 0.337304i
469469 826.999 1.76332
470470 145.050i 0.308617i
471471 268.031 158.770i 0.569067 0.337092i
472472 68.1053 0.144291
473473 122.701i 0.259411i
474474 −101.570 171.467i −0.214283 0.361745i
475475 −134.868 −0.283933
476476 455.004i 0.955891i
477477 239.842 + 131.410i 0.502813 + 0.275493i
478478 −579.895 −1.21317
479479 735.242i 1.53495i −0.641078 0.767476i 0.721512π-0.721512\pi
0.641078 0.767476i 0.278488π-0.278488\pi
480480 −32.6491 + 19.3400i −0.0680190 + 0.0402917i
481481 −159.473 −0.331545
482482 630.069i 1.30720i
483483 105.013 + 177.279i 0.217418 + 0.367037i
484484 −98.0000 −0.202479
485485 80.6162i 0.166219i
486486 154.925 306.751i 0.318776 0.631175i
487487 −92.6185 −0.190182 −0.0950909 0.995469i 0.530314π-0.530314\pi
−0.0950909 + 0.995469i 0.530314π0.530314\pi
488488 152.586i 0.312676i
489489 −29.3772 + 17.4019i −0.0600761 + 0.0355866i
490490 −22.3025 −0.0455153
491491 898.323i 1.82958i −0.403933 0.914789i 0.632357π-0.632357\pi
0.403933 0.914789i 0.367643π-0.367643\pi
492492 144.816 + 244.473i 0.294341 + 0.496896i
493493 −815.368 −1.65389
494494 381.465i 0.772197i
495495 82.0527 149.758i 0.165763 0.302541i
496496 32.0000 0.0645161
497497 116.747i 0.234903i
498498 95.4342 56.5313i 0.191635 0.113517i
499499 136.921 0.274391 0.137195 0.990544i 0.456191π-0.456191\pi
0.137195 + 0.990544i 0.456191π0.456191\pi
500500 22.3607i 0.0447214i
501501 −385.710 651.143i −0.769881 1.29969i
502502 −335.684 −0.668693
503503 443.077i 0.880868i −0.897785 0.440434i 0.854825π-0.854825\pi
0.897785 0.440434i 0.145175π-0.145175\pi
504504 167.140 + 91.5766i 0.331627 + 0.181700i
505505 −107.684 −0.213236
506506 110.085i 0.217560i
507507 −178.099 + 105.498i −0.351279 + 0.208083i
508508 268.921 0.529372
509509 213.062i 0.418590i 0.977853 + 0.209295i 0.0671168π0.0671168\pi
−0.977853 + 0.209295i 0.932883π0.932883\pi
510510 −146.921 248.027i −0.288080 0.486327i
511511 −658.447 −1.28855
512512 22.6274i 0.0441942i
513513 −24.4299 727.879i −0.0476216 1.41887i
514514 −450.974 −0.877381
515515 313.961i 0.609634i
516516 74.6491 44.2191i 0.144669 0.0856959i
517517 −389.210 −0.752824
518518 168.850i 0.325965i
519519 −18.0662 30.4987i −0.0348096 0.0587643i
520520 −63.2456 −0.121626
521521 3.20085i 0.00614366i 0.999995 + 0.00307183i 0.000977795π0.000977795\pi
−0.999995 + 0.00307183i 0.999022π0.999022\pi
522522 −164.105 + 299.515i −0.314378 + 0.573784i
523523 966.644 1.84827 0.924134 0.382069i 0.124788π-0.124788\pi
0.924134 + 0.382069i 0.124788π0.124788\pi
524524 440.788i 0.841198i
525525 96.6228 57.2354i 0.184043 0.109020i
526526 −51.2370 −0.0974088
527527 243.096i 0.461282i
528528 −51.8947 87.6068i −0.0982853 0.165922i
529529 444.842 0.840911
530530 96.0920i 0.181306i
531531 190.053 + 104.130i 0.357915 + 0.196102i
532532 403.895 0.759200
533533 473.575i 0.888509i
534534 221.842 131.410i 0.415434 0.246086i
535535 −96.4078 −0.180202
536536 312.429i 0.582891i
537537 105.553 + 178.191i 0.196561 + 0.331827i
538538 746.763 1.38804
539539 59.8439i 0.111028i
540540 −120.680 + 4.05039i −0.223481 + 0.00750072i
541541 −186.105 −0.344002 −0.172001 0.985097i 0.555023π-0.555023\pi
−0.172001 + 0.985097i 0.555023π0.555023\pi
542542 673.017i 1.24173i
543543 −489.601 + 290.019i −0.901659 + 0.534106i
544544 −171.895 −0.315983
545545 299.280i 0.549137i
546546 161.886 + 273.290i 0.296495 + 0.500532i
547547 −309.434 −0.565693 −0.282847 0.959165i 0.591279π-0.591279\pi
−0.282847 + 0.959165i 0.591279π0.591279\pi
548548 191.031i 0.348596i
549549 −233.298 + 425.802i −0.424951 + 0.775596i
550550 −60.0000 −0.109091
551551 723.779i 1.31357i
552552 −66.9737 + 39.6725i −0.121329 + 0.0718704i
553553 351.684 0.635957
554554 266.096i 0.480317i
555555 54.5217 + 92.0417i 0.0982373 + 0.165841i
556556 153.631 0.276315
557557 4.00106i 0.00718323i 0.999994 + 0.00359161i 0.00114325π0.00114325\pi
−0.999994 + 0.00359161i 0.998857π0.998857\pi
558558 89.2982 + 48.9268i 0.160033 + 0.0876824i
559559 144.605 0.258685
560560 66.9643i 0.119579i
561561 665.526 394.230i 1.18632 0.702728i
562562 −34.5523 −0.0614810
563563 166.970i 0.296572i −0.988945 0.148286i 0.952624π-0.952624\pi
0.988945 0.148286i 0.0473756π-0.0473756\pi
564564 140.263 + 236.788i 0.248694 + 0.419836i
565565 17.6840 0.0312991
566566 280.666i 0.495875i
567567 326.399 + 511.102i 0.575660 + 0.901414i
568568 −44.1053 −0.0776502
569569 156.289i 0.274673i −0.990524 0.137337i 0.956146π-0.956146\pi
0.990524 0.137337i 0.0438542π-0.0438542\pi
570570 −220.167 + 130.418i −0.386257 + 0.228803i
571571 −144.105 −0.252374 −0.126187 0.992006i 0.540274π-0.540274\pi
−0.126187 + 0.992006i 0.540274π0.540274\pi
572572 169.706i 0.296688i
573573 −166.211 280.591i −0.290071 0.489688i
574574 −501.421 −0.873555
575575 45.8688i 0.0797719i
576576 −34.5964 + 63.1434i −0.0600633 + 0.109624i
577577 532.947 0.923651 0.461826 0.886971i 0.347195π-0.347195\pi
0.461826 + 0.886971i 0.347195π0.347195\pi
578578 897.132i 1.55213i
579579 −433.495 + 256.785i −0.748697 + 0.443497i
580580 120.000 0.206897
581581 195.738i 0.336899i
582582 77.9559 + 131.602i 0.133945 + 0.226121i
583583 257.842 0.442268
584584 248.753i 0.425946i
585585 −176.491 96.7000i −0.301694 0.165299i
586586 726.658 1.24003
587587 190.342i 0.324262i −0.986769 0.162131i 0.948163π-0.948163\pi
0.986769 0.162131i 0.0518368π-0.0518368\pi
588588 −36.4078 + 21.5665i −0.0619181 + 0.0366777i
589589 215.789 0.366366
590590 76.1441i 0.129058i
591591 −262.460 443.077i −0.444096 0.749707i
592592 63.7893 0.107752
593593 345.719i 0.583001i −0.956571 0.291500i 0.905846π-0.905846\pi
0.956571 0.291500i 0.0941544π-0.0941544\pi
594594 −10.8683 323.818i −0.0182969 0.545148i
595595 508.710 0.854975
596596 552.473i 0.926969i
597597 90.5438 53.6344i 0.151665 0.0898399i
598598 −129.737 −0.216951
599599 704.055i 1.17538i 0.809085 + 0.587692i 0.199963π0.199963\pi
−0.809085 + 0.587692i 0.800037π0.800037\pi
600600 21.6228 + 36.5028i 0.0360380 + 0.0608380i
601601 338.474 0.563185 0.281592 0.959534i 0.409137π-0.409137\pi
0.281592 + 0.959534i 0.409137π0.409137\pi
602602 153.107i 0.254331i
603603 −477.693 + 871.856i −0.792193 + 1.44586i
604604 −36.1053 −0.0597770
605605 109.567i 0.181103i
606606 −175.789 + 104.130i −0.290081 + 0.171832i
607607 −816.513 −1.34516 −0.672581 0.740024i 0.734814π-0.734814\pi
−0.672581 + 0.740024i 0.734814π0.734814\pi
608608 152.586i 0.250964i
609609 −307.157 518.532i −0.504363 0.851449i
610610 170.596 0.279666
611611 458.688i 0.750717i
612612 −479.684 262.820i −0.783797 0.429445i
613613 −229.263 −0.374001 −0.187001 0.982360i 0.559877π-0.559877\pi
−0.187001 + 0.982360i 0.559877π0.559877\pi
614614 16.0959i 0.0262148i
615615 273.329 161.909i 0.444437 0.263266i
616616 179.684 0.291695
617617 1072.25i 1.73785i −0.494945 0.868924i 0.664812π-0.664812\pi
0.494945 0.868924i 0.335188π-0.335188\pi
618618 303.601 + 512.528i 0.491263 + 0.829334i
619619 −80.7103 −0.130388 −0.0651941 0.997873i 0.520767π-0.520767\pi
−0.0651941 + 0.997873i 0.520767π0.520767\pi
620620 35.7771i 0.0577050i
621621 −247.552 + 8.30863i −0.398635 + 0.0133794i
622622 733.631 1.17947
623623 455.004i 0.730344i
624624 −103.246 + 61.1584i −0.165458 + 0.0980103i
625625 25.0000 0.0400000
626626 65.5007i 0.104634i
627627 −349.947 590.769i −0.558130 0.942215i
628628 −207.684 −0.330707
629629 484.591i 0.770415i
630630 102.386 186.868i 0.162517 0.296617i
631631 492.894 0.781131 0.390566 0.920575i 0.372279π-0.372279\pi
0.390566 + 0.920575i 0.372279π0.372279\pi
632632 132.862i 0.210224i
633633 −150.114 + 88.9213i −0.237147 + 0.140476i
634634 −55.2897 −0.0872077
635635 300.663i 0.473485i
636636 −92.9210 156.866i −0.146102 0.246645i
637637 −70.5267 −0.110717
638638 321.994i 0.504692i
639639 −123.079 67.4353i −0.192612 0.105533i
640640 25.2982 0.0395285
641641 65.4816i 0.102155i 0.998695 + 0.0510777i 0.0162656π0.0162656\pi
−0.998695 + 0.0510777i 0.983734π0.983734\pi
642642 −157.381 + 93.2264i −0.245143 + 0.145212i
643643 −428.619 −0.666592 −0.333296 0.942822i 0.608161π-0.608161\pi
−0.333296 + 0.942822i 0.608161π0.608161\pi
644644 137.365i 0.213300i
645645 −49.4384 83.4602i −0.0766487 0.129396i
646646 −1159.16 −1.79436
647647 462.801i 0.715303i −0.933855 0.357652i 0.883578π-0.883578\pi
0.933855 0.357652i 0.116422π-0.116422\pi
648648 −193.088 + 123.309i −0.297975 + 0.190292i
649649 204.316 0.314817
650650 70.7107i 0.108786i
651651 −154.596 + 91.5766i −0.237475 + 0.140671i
652652 22.7630 0.0349126
653653 425.064i 0.650941i −0.945552 0.325470i 0.894477π-0.894477\pi
0.945552 0.325470i 0.105523π-0.105523\pi
654654 289.404 + 488.561i 0.442513 + 0.747035i
655655 −492.816 −0.752390
656656 189.430i 0.288765i
657657 380.333 694.161i 0.578894 1.05656i
658658 −485.658 −0.738083
659659 182.769i 0.277343i 0.990338 + 0.138671i 0.0442831π0.0442831\pi
−0.990338 + 0.138671i 0.955717π0.955717\pi
660660 −97.9473 + 58.0200i −0.148405 + 0.0879091i
661661 −482.053 −0.729278 −0.364639 0.931149i 0.618808π-0.618808\pi
−0.364639 + 0.931149i 0.618808π0.618808\pi
662662 629.920i 0.951541i
663663 −464.605 784.330i −0.700762 1.18300i
664664 −73.9473 −0.111366
665665 451.568i 0.679050i
666666 178.009 + 97.5314i 0.267280 + 0.146444i
667667 246.158 0.369052
668668 504.539i 0.755298i
669669 256.517 151.950i 0.383434 0.227131i
670670 349.307 0.521353
671671 457.758i 0.682203i
672672 −64.7544 109.316i −0.0963608 0.162673i
673673 184.579 0.274264 0.137132 0.990553i 0.456212π-0.456212\pi
0.137132 + 0.990553i 0.456212π0.456212\pi
674674 460.587i 0.683363i
675675 4.52847 + 134.924i 0.00670885 + 0.199887i
676676 138.000 0.204142
677677 1065.85i 1.57437i 0.616715 + 0.787187i 0.288463π0.288463\pi
−0.616715 + 0.787187i 0.711537π0.711537\pi
678678 28.8683 17.1004i 0.0425787 0.0252219i
679679 −269.920 −0.397526
680680 192.184i 0.282624i
681681 331.710 + 559.982i 0.487093 + 0.822293i
682682 96.0000 0.140762
683683 788.926i 1.15509i 0.816359 + 0.577545i 0.195989π0.195989\pi
−0.816359 + 0.577545i 0.804011π0.804011\pi
684684 −233.298 + 425.802i −0.341079 + 0.622518i
685685 213.579 0.311794
686686 444.138i 0.647431i
687687 840.636 497.958i 1.22363 0.724830i
688688 −57.8420 −0.0840727
689689 303.870i 0.441030i
690690 44.3552 + 74.8788i 0.0642828 + 0.108520i
691691 932.000 1.34877 0.674385 0.738380i 0.264409π-0.264409\pi
0.674385 + 0.738380i 0.264409π0.264409\pi
692692 23.6320i 0.0341502i
693693 501.421 + 274.730i 0.723551 + 0.396436i
694694 73.2897 0.105605
695695 171.765i 0.247144i
696696 195.895 116.040i 0.281458 0.166724i
697697 1439.05 2.06464
698698 137.997i 0.197704i
699699 79.0655 + 133.476i 0.113112 + 0.190952i
700700 −74.8683 −0.106955
701701 1352.75i 1.92974i −0.262721 0.964872i 0.584620π-0.584620\pi
0.262721 0.964872i 0.415380π-0.415380\pi
702702 −381.623 + 12.8084i −0.543622 + 0.0182457i
703703 430.158 0.611889
704704 67.8823i 0.0964237i
705705 264.737 156.819i 0.375513 0.222439i
706706 −805.815 −1.14138
707707 360.549i 0.509970i
708708 −73.6313 124.302i −0.103999 0.175568i
709709 −269.473 −0.380075 −0.190038 0.981777i 0.560861π-0.560861\pi
−0.190038 + 0.981777i 0.560861π0.560861\pi
710710 49.3113i 0.0694525i
711711 −203.140 + 370.759i −0.285711 + 0.521462i
712712 −171.895 −0.241425
713713 73.3901i 0.102931i
714714 830.447 491.923i 1.16309 0.688968i
715715 −189.737 −0.265366
716716 138.072i 0.192837i
717717 626.947 + 1058.39i 0.874403 + 1.47614i
718718 387.895 0.540243
719719 537.103i 0.747014i 0.927627 + 0.373507i 0.121845π0.121845\pi
−0.927627 + 0.373507i 0.878155π0.878155\pi
720720 70.5964 + 38.6800i 0.0980506 + 0.0537222i
721721 −1051.21 −1.45799
722722 518.421i 0.718034i
723723 1149.96 681.192i 1.59055 0.942174i
724724 379.368 0.523989
725725 134.164i 0.185054i
726726 105.952 + 178.864i 0.145939 + 0.246369i
727727 −1117.83 −1.53759 −0.768795 0.639495i 0.779144π-0.779144\pi
−0.768795 + 0.639495i 0.779144π0.779144\pi
728728 211.760i 0.290879i
729729 −727.359 + 48.8800i −0.997750 + 0.0670507i
730730 −278.114 −0.380978
731731 439.411i 0.601109i
732732 278.491 164.967i 0.380452 0.225364i
733733 7.52599 0.0102674 0.00513369 0.999987i 0.498366π-0.498366\pi
0.00513369 + 0.999987i 0.498366π0.498366\pi
734734 653.124i 0.889815i
735735 24.1121 + 40.7052i 0.0328056 + 0.0553812i
736736 51.8947 0.0705091
737737 937.288i 1.27176i
738738 289.631 528.618i 0.392454 0.716284i
739739 −823.079 −1.11377 −0.556887 0.830588i 0.688004π-0.688004\pi
−0.556887 + 0.830588i 0.688004π0.688004\pi
740740 71.3186i 0.0963765i
741741 −696.228 + 412.417i −0.939579 + 0.556568i
742742 321.737 0.433607
743743 3.21898i 0.00433241i 0.999998 + 0.00216620i 0.000689524π0.000689524\pi
−0.999998 + 0.00216620i 0.999310π0.999310\pi
744744 −34.5964 58.4045i −0.0465006 0.0785007i
745745 −617.684 −0.829106
746746 695.719i 0.932599i
747747 −206.355 113.063i −0.276245 0.151356i
748748 −515.684 −0.689417
749749 322.794i 0.430967i
750750 40.8114 24.1750i 0.0544152 0.0322333i
751751 1185.63 1.57874 0.789368 0.613920i 0.210408π-0.210408\pi
0.789368 + 0.613920i 0.210408π0.210408\pi
752752 183.475i 0.243983i
753753 362.921 + 612.671i 0.481967 + 0.813639i
754754 379.473 0.503280
755755 40.3670i 0.0534662i
756756 −13.5616 404.061i −0.0179386 0.534473i
757757 −863.315 −1.14044 −0.570221 0.821491i 0.693143π-0.693143\pi
−0.570221 + 0.821491i 0.693143π0.693143\pi
758758 365.946i 0.482779i
759759 −200.921 + 119.017i −0.264718 + 0.156808i
760760 170.596 0.224469
761761 570.597i 0.749800i −0.927065 0.374900i 0.877677π-0.877677\pi
0.927065 0.374900i 0.122323π-0.122323\pi
762762 −290.741 490.819i −0.381550 0.644119i
763763 −1002.05 −1.31331
764764 217.416i 0.284577i
765765 −293.842 + 536.303i −0.384107 + 0.701050i
766766 738.816 0.964511
767767 240.789i 0.313936i
768768 41.2982 24.4634i 0.0537737 0.0318534i
769769 −741.684 −0.964479 −0.482239 0.876040i 0.660176π-0.660176\pi
−0.482239 + 0.876040i 0.660176π0.660176\pi
770770 200.893i 0.260900i
771771 487.565 + 823.090i 0.632380 + 1.06756i
772772 335.895 0.435097
773773 623.203i 0.806214i 0.915153 + 0.403107i 0.132070π0.132070\pi
−0.915153 + 0.403107i 0.867930π0.867930\pi
774774 −161.412 88.4382i −0.208543 0.114261i
775775 −40.0000 −0.0516129
776776 101.972i 0.131408i
777777 −308.175 + 182.550i −0.396622 + 0.234943i
778778 −863.868 −1.11037
779779 1277.41i 1.63980i
780780 68.3772 + 115.432i 0.0876631 + 0.147990i
781781 −132.316 −0.169419
782782 394.230i 0.504131i
783783 724.078 24.3023i 0.924749 0.0310375i
784784 28.2107 0.0359830
785785 232.198i 0.295793i
786786 −804.500 + 476.553i −1.02354 + 0.606301i
787787 335.303 0.426052 0.213026 0.977046i 0.431668π-0.431668\pi
0.213026 + 0.977046i 0.431668π0.431668\pi
788788 343.319i 0.435684i
789789 55.3943 + 93.5147i 0.0702083 + 0.118523i
790790 148.544 0.188030
791791 59.2098i 0.0748543i
792792 −103.789 + 189.430i −0.131047 + 0.239179i
793793 539.473 0.680294
794794 302.642i 0.381161i
795795 −175.381 + 103.889i −0.220606 + 0.130678i
796796 −70.1580 −0.0881382
797797 550.520i 0.690740i 0.938467 + 0.345370i 0.112247π0.112247\pi
−0.938467 + 0.345370i 0.887753π0.887753\pi
798798 −436.666 737.165i −0.547201 0.923765i
799799 1393.81 1.74445
800800 28.2843i 0.0353553i
801801 −479.684 262.820i −0.598856 0.328115i
802802 −642.841 −0.801548
803803 746.258i 0.929337i
804804 570.228 337.780i 0.709239 0.420124i
805805 −153.579 −0.190781
806806 113.137i 0.140369i
807807 −807.354 1362.95i −1.00044 1.68891i
808808 136.211 0.168578
809809 560.288i 0.692569i −0.938130 0.346284i 0.887443π-0.887443\pi
0.938130 0.346284i 0.112557π-0.112557\pi
810810 137.864 + 215.878i 0.170203 + 0.266517i
811811 −237.842 −0.293270 −0.146635 0.989191i 0.546844π-0.546844\pi
−0.146635 + 0.989191i 0.546844π0.546844\pi
812812 401.786i 0.494810i
813813 −1228.35 + 727.624i −1.51089 + 0.894987i
814814 191.368 0.235096
815815 25.4498i 0.0312267i
816816 185.842 + 313.732i 0.227748 + 0.384475i
817817 −390.053 −0.477421
818818 811.535i 0.992097i
819819 323.772 590.930i 0.395326 0.721526i
820820 −211.789 −0.258280
821821 65.4816i 0.0797584i 0.999205 + 0.0398792i 0.0126973π0.0126973\pi
−0.999205 + 0.0398792i 0.987303π0.987303\pi
822822 348.658 206.531i 0.424158 0.251254i
823823 521.512 0.633673 0.316836 0.948480i 0.397379π-0.397379\pi
0.316836 + 0.948480i 0.397379π0.397379\pi
824824 397.133i 0.481958i
825825 64.8683 + 109.508i 0.0786283 + 0.132738i
826826 254.947 0.308652
827827 987.512i 1.19409i 0.802208 + 0.597045i 0.203658π0.203658\pi
−0.802208 + 0.597045i 0.796342π0.796342\pi
828828 144.816 + 79.3449i 0.174898 + 0.0958272i
829829 333.631 0.402450 0.201225 0.979545i 0.435508π-0.435508\pi
0.201225 + 0.979545i 0.435508π0.435508\pi
830830 82.6756i 0.0996092i
831831 485.662 287.686i 0.584431 0.346193i
832832 80.0000 0.0961538
833833 214.309i 0.257274i
834834 −166.097 280.399i −0.199157 0.336210i
835835 564.092 0.675559
836836 457.758i 0.547558i
837837 −7.24555 215.878i −0.00865657 0.257919i
838838 −138.474 −0.165243
839839 129.363i 0.154187i −0.997024 0.0770934i 0.975436π-0.975436\pi
0.997024 0.0770934i 0.0245640π-0.0245640\pi
840840 −122.219 + 72.3977i −0.145499 + 0.0861877i
841841 121.000 0.143876
842842 1014.44i 1.20479i
843843 37.3559 + 63.0629i 0.0443130 + 0.0748077i
844844 116.316 0.137815
845845 154.289i 0.182590i
846846 280.527 512.001i 0.331592 0.605202i
847847 −366.855 −0.433123
848848 121.548i 0.143335i
849849 512.254 303.438i 0.603362 0.357407i
850850 214.868 0.252786
851851 146.297i 0.171912i
852852 47.6840 + 80.4984i 0.0559671 + 0.0944817i
853853 1080.42 1.26661 0.633306 0.773902i 0.281697π-0.281697\pi
0.633306 + 0.773902i 0.281697π0.281697\pi
854854 571.193i 0.668845i
855855 476.061 + 260.835i 0.556797 + 0.305071i
856856 121.947 0.142462
857857 702.548i 0.819776i 0.912136 + 0.409888i 0.134432π0.134432\pi
−0.912136 + 0.409888i 0.865568π0.865568\pi
858858 −309.737 + 183.475i −0.360998 + 0.213841i
859859 −281.132 −0.327278 −0.163639 0.986520i 0.552323π-0.552323\pi
−0.163639 + 0.986520i 0.552323π0.552323\pi
860860 64.6693i 0.0751969i
861861 542.105 + 915.163i 0.629623 + 1.06291i
862862 −414.474 −0.480828
863863 419.221i 0.485772i 0.970055 + 0.242886i 0.0780941π0.0780941\pi
−0.970055 + 0.242886i 0.921906π0.921906\pi
864864 152.649 5.12338i 0.176677 0.00592984i
865865 26.4213 0.0305449
866866 689.466i 0.796150i
867867 −1637.39 + 969.924i −1.88857 + 1.11871i
868868 119.789 0.138006
869869 398.585i 0.458671i
870870 −129.737 219.017i −0.149123 0.251744i
871871 1104.60 1.26820
872872 378.562i 0.434131i
873873 155.912 284.561i 0.178593 0.325958i
874874 349.947 0.400397
875875 83.7053i 0.0956632i
876876 −454.009 + 268.936i −0.518275 + 0.307005i
877877 1079.42 1.23081 0.615405 0.788211i 0.288992π-0.288992\pi
0.615405 + 0.788211i 0.288992π0.288992\pi
878878 363.788i 0.414337i
879879 −785.618 1326.25i −0.893763 1.50882i
880880 75.8947 0.0862439
881881 748.212i 0.849275i −0.905363 0.424638i 0.860401π-0.860401\pi
0.905363 0.424638i 0.139599π-0.139599\pi
882882 78.7238 + 43.1330i 0.0892561 + 0.0489037i
883883 −875.749 −0.991788 −0.495894 0.868383i 0.665160π-0.665160\pi
−0.495894 + 0.868383i 0.665160π0.665160\pi
884884 607.739i 0.687488i
885885 −138.974 + 82.3223i −0.157032 + 0.0930196i
886886 414.500 0.467833
887887 1015.05i 1.14436i 0.820127 + 0.572182i 0.193903π0.193903\pi
−0.820127 + 0.572182i 0.806097π0.806097\pi
888888 −68.9651 116.425i −0.0776634 0.131109i
889889 1006.68 1.13238
890890 192.184i 0.215937i
891891 −579.263 + 369.928i −0.650126 + 0.415183i
892892 −198.763 −0.222828
893893 1237.25i 1.38550i
894894 −1008.34 + 597.300i −1.12790 + 0.668121i
895895 −154.369 −0.172479
896896 84.7038i 0.0945355i
897897 140.263 + 236.788i 0.156369 + 0.263977i
898898 828.184 0.922254
899899 214.663i 0.238779i
900900 43.2456 78.9292i 0.0480506 0.0876991i
901901 −923.368 −1.02483
902902 568.290i 0.630034i
903903 279.443 165.530i 0.309460 0.183312i
904904 −22.3687 −0.0247441
905905 424.146i 0.468670i
906906 39.0349 + 65.8973i 0.0430849 + 0.0727343i
907907 1504.70 1.65898 0.829491 0.558520i 0.188631π-0.188631\pi
0.829491 + 0.558520i 0.188631π0.188631\pi
908908 433.903i 0.477867i
909909 380.105 + 208.261i 0.418158 + 0.229110i
910910 −236.754 −0.260170
911911 1002.19i 1.10010i −0.835131 0.550051i 0.814608π-0.814608\pi
0.835131 0.550051i 0.185392π-0.185392\pi
912912 278.491 164.967i 0.305363 0.180885i
913913 −221.842 −0.242981
914914 1149.83i 1.25802i
915915 −184.438 311.363i −0.201572 0.340287i
916916 −651.368 −0.711100
917917 1650.05i 1.79940i
918918 38.9210 + 1159.64i 0.0423976 + 1.26322i
919919 −780.289 −0.849063 −0.424532 0.905413i 0.639561π-0.639561\pi
−0.424532 + 0.905413i 0.639561π0.639561\pi
920920 58.0200i 0.0630652i
921921 −29.3772 + 17.4019i −0.0318971 + 0.0188945i
922922 −783.579 −0.849868
923923 155.936i 0.168945i
924924 −194.263 327.949i −0.210242 0.354923i
925925 −79.7367 −0.0862018
926926 636.005i 0.686830i
927927 607.201 1108.23i 0.655018 1.19550i
928928 −151.789 −0.163566
929929 1093.84i 1.17744i 0.808339 + 0.588718i 0.200367π0.200367\pi
−0.808339 + 0.588718i 0.799633π0.799633\pi
930930 −65.2982 + 38.6800i −0.0702131 + 0.0415914i
931931 190.236 0.204335
932932 103.424i 0.110970i
933933 −793.157 1338.98i −0.850115 1.43513i
934934 43.4477 0.0465179
935935 576.552i 0.616633i
936936 223.246 + 122.317i 0.238510 + 0.130680i
937937 −407.947 −0.435376 −0.217688 0.976018i 0.569852π-0.569852\pi
−0.217688 + 0.976018i 0.569852π0.569852\pi
938938 1169.55i 1.24686i
939939 −119.548 + 70.8154i −0.127314 + 0.0754157i
940940 −205.132 −0.218225
941941 671.008i 0.713079i 0.934280 + 0.356540i 0.116044π0.116044\pi
−0.934280 + 0.356540i 0.883956π0.883956\pi
942942 224.535 + 379.053i 0.238360 + 0.402391i
943943 −434.447 −0.460707
944944 96.3155i 0.102029i
945945 −451.754 + 15.1623i −0.478047 + 0.0160447i
946946 −173.526 −0.183431
947947 1608.13i 1.69813i −0.528290 0.849064i 0.677167π-0.677167\pi
0.528290 0.849064i 0.322833π-0.322833\pi
948948 242.491 143.642i 0.255792 0.151521i
949949 −879.473 −0.926737
950950 190.733i 0.200771i
951951 59.7758 + 100.911i 0.0628557 + 0.106111i
952952 −643.473 −0.675917
953953 695.440i 0.729737i −0.931059 0.364869i 0.881114π-0.881114\pi
0.931059 0.364869i 0.118886π-0.118886\pi
954954 −185.842 + 339.188i −0.194803 + 0.355543i
955955 243.079 0.254533
956956 820.095i 0.857840i
957957 587.684 348.120i 0.614090 0.363762i
958958 1039.79 1.08538
959959 715.107i 0.745680i
960960 −27.3509 46.1728i −0.0284905 0.0480967i
961961 −897.000 −0.933403
962962 225.529i 0.234438i
963963 340.302 + 186.453i 0.353377 + 0.193617i
964964 −891.052 −0.924328
965965 375.542i 0.389162i
966966 −250.710 + 148.511i −0.259534 + 0.153738i
967967 −1030.07 −1.06522 −0.532609 0.846361i 0.678788π-0.678788\pi
−0.532609 + 0.846361i 0.678788π0.678788\pi
968968 138.593i 0.143175i
969969 1253.21 + 2115.63i 1.29330 + 2.18331i
970970 −114.009 −0.117535
971971 1165.24i 1.20004i 0.799986 + 0.600019i 0.204840π0.204840\pi
−0.799986 + 0.600019i 0.795160π0.795160\pi
972972 433.811 + 219.097i 0.446308 + 0.225409i
973973 575.106 0.591065
974974 130.982i 0.134479i
975975 129.057 76.4481i 0.132366 0.0784083i
976976 −215.789 −0.221096
977977 726.440i 0.743541i 0.928325 + 0.371771i 0.121249π0.121249\pi
−0.928325 + 0.371771i 0.878751π0.878751\pi
978978 −24.6100 41.5457i −0.0251636 0.0424802i
979979 −515.684 −0.526746
980980 31.5405i 0.0321842i
981981 578.807 1056.40i 0.590017 1.07686i
982982 1270.42 1.29371
983983 1024.21i 1.04192i 0.853581 + 0.520960i 0.174426π0.174426\pi
−0.853581 + 0.520960i 0.825574π0.825574\pi
984984 −345.737 + 204.800i −0.351358 + 0.208130i
985985 383.842 0.389687
986986 1153.10i 1.16948i
987987 525.064 + 886.395i 0.531980 + 0.898070i
988988 539.473 0.546026
989989 132.657i 0.134133i
990990 211.789 + 116.040i 0.213929 + 0.117212i
991991 −1797.89 −1.81422 −0.907111 0.420892i 0.861717π-0.861717\pi
−0.907111 + 0.420892i 0.861717π0.861717\pi
992992 45.2548i 0.0456198i
993993 −1149.69 + 681.031i −1.15780 + 0.685832i
994994 −165.105 −0.166101
995995 78.4390i 0.0788332i
996996 79.9473 + 134.964i 0.0802684 + 0.135506i
997997 901.368 0.904080 0.452040 0.891998i 0.350696π-0.350696\pi
0.452040 + 0.891998i 0.350696π0.350696\pi
998998 193.636i 0.194024i
999999 −14.4434 430.336i −0.0144579 0.430766i
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 30.3.d.a.11.4 yes 4
3.2 odd 2 inner 30.3.d.a.11.2 4
4.3 odd 2 240.3.l.c.161.2 4
5.2 odd 4 150.3.b.b.149.1 8
5.3 odd 4 150.3.b.b.149.8 8
5.4 even 2 150.3.d.c.101.1 4
8.3 odd 2 960.3.l.f.641.3 4
8.5 even 2 960.3.l.e.641.2 4
9.2 odd 6 810.3.h.a.701.2 8
9.4 even 3 810.3.h.a.431.2 8
9.5 odd 6 810.3.h.a.431.3 8
9.7 even 3 810.3.h.a.701.3 8
12.11 even 2 240.3.l.c.161.1 4
15.2 even 4 150.3.b.b.149.7 8
15.8 even 4 150.3.b.b.149.2 8
15.14 odd 2 150.3.d.c.101.3 4
20.3 even 4 1200.3.c.k.449.3 8
20.7 even 4 1200.3.c.k.449.6 8
20.19 odd 2 1200.3.l.u.401.3 4
24.5 odd 2 960.3.l.e.641.1 4
24.11 even 2 960.3.l.f.641.4 4
60.23 odd 4 1200.3.c.k.449.5 8
60.47 odd 4 1200.3.c.k.449.4 8
60.59 even 2 1200.3.l.u.401.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.3.d.a.11.2 4 3.2 odd 2 inner
30.3.d.a.11.4 yes 4 1.1 even 1 trivial
150.3.b.b.149.1 8 5.2 odd 4
150.3.b.b.149.2 8 15.8 even 4
150.3.b.b.149.7 8 15.2 even 4
150.3.b.b.149.8 8 5.3 odd 4
150.3.d.c.101.1 4 5.4 even 2
150.3.d.c.101.3 4 15.14 odd 2
240.3.l.c.161.1 4 12.11 even 2
240.3.l.c.161.2 4 4.3 odd 2
810.3.h.a.431.2 8 9.4 even 3
810.3.h.a.431.3 8 9.5 odd 6
810.3.h.a.701.2 8 9.2 odd 6
810.3.h.a.701.3 8 9.7 even 3
960.3.l.e.641.1 4 24.5 odd 2
960.3.l.e.641.2 4 8.5 even 2
960.3.l.f.641.3 4 8.3 odd 2
960.3.l.f.641.4 4 24.11 even 2
1200.3.c.k.449.3 8 20.3 even 4
1200.3.c.k.449.4 8 60.47 odd 4
1200.3.c.k.449.5 8 60.23 odd 4
1200.3.c.k.449.6 8 20.7 even 4
1200.3.l.u.401.3 4 20.19 odd 2
1200.3.l.u.401.4 4 60.59 even 2