Properties

Label 169.4.c.h.22.2
Level 169169
Weight 44
Character 169.22
Analytic conductor 9.9719.971
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,4,Mod(22,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 169=132 169 = 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 169.c (of order 33, degree 22, not 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: 9.971322790979.97132279097
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 22.2
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 169.22
Dual form 169.4.c.h.146.2

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+(0.8660251.50000i)q2+(1.00000+1.73205i)q3+(2.50000+4.33013i)q41.73205q5+(1.73205+3.00000i)q6+(6.9282012.0000i)q7+22.5167q8+(11.5000+19.9186i)q9+(1.50000+2.59808i)q10+(6.92820+12.0000i)q1110.0000q1224.0000q14+(1.732053.00000i)q15+(0.500000+0.866025i)q16+(58.5000+101.325i)q17+39.8372q18+(57.1577+99.0000i)q19+(4.330137.50000i)q20+27.7128q21+(12.0000+20.7846i)q22+(39.0000+67.5500i)q23+(22.5167+39.0000i)q24122.000q25100.000q27+(34.641060.0000i)q28+(70.5000122.110i)q29+(3.000005.19615i)q30+155.885q31+(90.9327+157.500i)q32+(13.856424.0000i)q33+202.650q34+(12.0000+20.7846i)q35+(57.5000+99.5929i)q36+(71.8801124.500i)q37+198.000q3839.0000q40+(135.966235.500i)q41+(24.000041.5692i)q42+(52.0000+90.0666i)q4369.2820q44+(19.918634.5000i)q45+(67.5500+117.000i)q46301.377q47+(1.000001.73205i)q48+(75.5000130.770i)q49+(105.655+183.000i)q50234.000q51+93.0000q53+(86.6025+150.000i)q54+(12.000020.7846i)q55+(156.000270.200i)q56228.631q57+(122.110211.500i)q58+(142.028246.000i)q59+17.3205q60+(72.5000125.574i)q61+(135.000233.827i)q62+(159.349276.000i)q63+307.000q6448.0000q66+(393.176+681.000i)q67+(292.500+506.625i)q68+(78.0000135.100i)q69+41.5692q70+(528.275915.000i)q71+(258.942+448.500i)q72458.993q73+(124.500215.640i)q74+(122.000211.310i)q75+(285.788+495.000i)q76+192.000q77+1276.00q79+(0.8660251.50000i)q80+(210.500+364.597i)q81+(235.500407.898i)q82789.815q83+(69.2820+120.000i)q84+(101.325175.500i)q85+180.133q86+(141.000+244.219i)q87+(156.000+270.200i)q88+(488.438846.000i)q8969.0000q90390.000q92+(155.885+270.000i)q93+(261.000+452.065i)q94+(99.0000171.473i)q95363.731q96+(100.459174.000i)q97+(130.770226.500i)q98318.697q99+O(q100)q+(0.866025 - 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(2.50000 + 4.33013i) q^{4} -1.73205 q^{5} +(1.73205 + 3.00000i) q^{6} +(-6.92820 - 12.0000i) q^{7} +22.5167 q^{8} +(11.5000 + 19.9186i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-6.92820 + 12.0000i) q^{11} -10.0000 q^{12} -24.0000 q^{14} +(1.73205 - 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(58.5000 + 101.325i) q^{17} +39.8372 q^{18} +(57.1577 + 99.0000i) q^{19} +(-4.33013 - 7.50000i) q^{20} +27.7128 q^{21} +(12.0000 + 20.7846i) q^{22} +(-39.0000 + 67.5500i) q^{23} +(-22.5167 + 39.0000i) q^{24} -122.000 q^{25} -100.000 q^{27} +(34.6410 - 60.0000i) q^{28} +(70.5000 - 122.110i) q^{29} +(-3.00000 - 5.19615i) q^{30} +155.885 q^{31} +(90.9327 + 157.500i) q^{32} +(-13.8564 - 24.0000i) q^{33} +202.650 q^{34} +(12.0000 + 20.7846i) q^{35} +(-57.5000 + 99.5929i) q^{36} +(71.8801 - 124.500i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(135.966 - 235.500i) q^{41} +(24.0000 - 41.5692i) q^{42} +(52.0000 + 90.0666i) q^{43} -69.2820 q^{44} +(-19.9186 - 34.5000i) q^{45} +(67.5500 + 117.000i) q^{46} -301.377 q^{47} +(-1.00000 - 1.73205i) q^{48} +(75.5000 - 130.770i) q^{49} +(-105.655 + 183.000i) q^{50} -234.000 q^{51} +93.0000 q^{53} +(-86.6025 + 150.000i) q^{54} +(12.0000 - 20.7846i) q^{55} +(-156.000 - 270.200i) q^{56} -228.631 q^{57} +(-122.110 - 211.500i) q^{58} +(-142.028 - 246.000i) q^{59} +17.3205 q^{60} +(-72.5000 - 125.574i) q^{61} +(135.000 - 233.827i) q^{62} +(159.349 - 276.000i) q^{63} +307.000 q^{64} -48.0000 q^{66} +(-393.176 + 681.000i) q^{67} +(-292.500 + 506.625i) q^{68} +(-78.0000 - 135.100i) q^{69} +41.5692 q^{70} +(-528.275 - 915.000i) q^{71} +(258.942 + 448.500i) q^{72} -458.993 q^{73} +(-124.500 - 215.640i) q^{74} +(122.000 - 211.310i) q^{75} +(-285.788 + 495.000i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(0.866025 - 1.50000i) q^{80} +(-210.500 + 364.597i) q^{81} +(-235.500 - 407.898i) q^{82} -789.815 q^{83} +(69.2820 + 120.000i) q^{84} +(-101.325 - 175.500i) q^{85} +180.133 q^{86} +(141.000 + 244.219i) q^{87} +(-156.000 + 270.200i) q^{88} +(488.438 - 846.000i) q^{89} -69.0000 q^{90} -390.000 q^{92} +(-155.885 + 270.000i) q^{93} +(-261.000 + 452.065i) q^{94} +(-99.0000 - 171.473i) q^{95} -363.731 q^{96} +(-100.459 - 174.000i) q^{97} +(-130.770 - 226.500i) q^{98} -318.697 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q3+10q4+46q96q1040q1296q142q16+234q17+48q22156q23488q25400q27+282q2912q30+48q35230q36+792q38+396q95+O(q100) 4 q - 4 q^{3} + 10 q^{4} + 46 q^{9} - 6 q^{10} - 40 q^{12} - 96 q^{14} - 2 q^{16} + 234 q^{17} + 48 q^{22} - 156 q^{23} - 488 q^{25} - 400 q^{27} + 282 q^{29} - 12 q^{30} + 48 q^{35} - 230 q^{36} + 792 q^{38}+ \cdots - 396 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/169Z)×\left(\mathbb{Z}/169\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.866025 1.50000i 0.306186 0.530330i −0.671339 0.741151i 0.734280π-0.734280\pi
0.977525 + 0.210821i 0.0676136π0.0676136\pi
33 −1.00000 + 1.73205i −0.192450 + 0.333333i −0.946062 0.323987i 0.894977π-0.894977\pi
0.753612 + 0.657320i 0.228310π0.228310\pi
44 2.50000 + 4.33013i 0.312500 + 0.541266i
55 −1.73205 −0.154919 −0.0774597 0.996995i 0.524681π-0.524681\pi
−0.0774597 + 0.996995i 0.524681π0.524681\pi
66 1.73205 + 3.00000i 0.117851 + 0.204124i
77 −6.92820 12.0000i −0.374088 0.647939i 0.616102 0.787666i 0.288711π-0.288711\pi
−0.990190 + 0.139727i 0.955377π0.955377\pi
88 22.5167 0.995105
99 11.5000 + 19.9186i 0.425926 + 0.737725i
1010 −1.50000 + 2.59808i −0.0474342 + 0.0821584i
1111 −6.92820 + 12.0000i −0.189903 + 0.328921i −0.945218 0.326441i 0.894151π-0.894151\pi
0.755315 + 0.655362i 0.227484π0.227484\pi
1212 −10.0000 −0.240563
1313 0 0
1414 −24.0000 −0.458162
1515 1.73205 3.00000i 0.0298142 0.0516398i
1616 −0.500000 + 0.866025i −0.00781250 + 0.0135316i
1717 58.5000 + 101.325i 0.834608 + 1.44558i 0.894349 + 0.447369i 0.147639π0.147639\pi
−0.0597414 + 0.998214i 0.519028π0.519028\pi
1818 39.8372 0.521651
1919 57.1577 + 99.0000i 0.690151 + 1.19538i 0.971788 + 0.235856i 0.0757893π0.0757893\pi
−0.281637 + 0.959521i 0.590877π0.590877\pi
2020 −4.33013 7.50000i −0.0484123 0.0838525i
2121 27.7128 0.287973
2222 12.0000 + 20.7846i 0.116291 + 0.201422i
2323 −39.0000 + 67.5500i −0.353568 + 0.612398i −0.986872 0.161506i 0.948365π-0.948365\pi
0.633304 + 0.773903i 0.281698π0.281698\pi
2424 −22.5167 + 39.0000i −0.191508 + 0.331702i
2525 −122.000 −0.976000
2626 0 0
2727 −100.000 −0.712778
2828 34.6410 60.0000i 0.233805 0.404962i
2929 70.5000 122.110i 0.451432 0.781903i −0.547043 0.837104i 0.684247π-0.684247\pi
0.998475 + 0.0552014i 0.0175801π0.0175801\pi
3030 −3.00000 5.19615i −0.0182574 0.0316228i
3131 155.885 0.903151 0.451576 0.892233i 0.350862π-0.350862\pi
0.451576 + 0.892233i 0.350862π0.350862\pi
3232 90.9327 + 157.500i 0.502337 + 0.870073i
3333 −13.8564 24.0000i −0.0730937 0.126602i
3434 202.650 1.02218
3535 12.0000 + 20.7846i 0.0579534 + 0.100378i
3636 −57.5000 + 99.5929i −0.266204 + 0.461078i
3737 71.8801 124.500i 0.319379 0.553180i −0.660980 0.750404i 0.729859π-0.729859\pi
0.980359 + 0.197223i 0.0631924π0.0631924\pi
3838 198.000 0.845259
3939 0 0
4040 −39.0000 −0.154161
4141 135.966 235.500i 0.517910 0.897047i −0.481873 0.876241i 0.660043π-0.660043\pi
0.999784 0.0208059i 0.00662322π-0.00662322\pi
4242 24.0000 41.5692i 0.0881733 0.152721i
4343 52.0000 + 90.0666i 0.184417 + 0.319419i 0.943380 0.331714i 0.107627π-0.107627\pi
−0.758963 + 0.651134i 0.774294π0.774294\pi
4444 −69.2820 −0.237379
4545 −19.9186 34.5000i −0.0659842 0.114288i
4646 67.5500 + 117.000i 0.216515 + 0.375015i
4747 −301.377 −0.935326 −0.467663 0.883907i 0.654904π-0.654904\pi
−0.467663 + 0.883907i 0.654904π0.654904\pi
4848 −1.00000 1.73205i −0.00300703 0.00520833i
4949 75.5000 130.770i 0.220117 0.381253i
5050 −105.655 + 183.000i −0.298838 + 0.517602i
5151 −234.000 −0.642481
5252 0 0
5353 93.0000 0.241029 0.120514 0.992712i 0.461546π-0.461546\pi
0.120514 + 0.992712i 0.461546π0.461546\pi
5454 −86.6025 + 150.000i −0.218243 + 0.378008i
5555 12.0000 20.7846i 0.0294196 0.0509563i
5656 −156.000 270.200i −0.372257 0.644768i
5757 −228.631 −0.531279
5858 −122.110 211.500i −0.276444 0.478816i
5959 −142.028 246.000i −0.313398 0.542822i 0.665698 0.746222i 0.268134π-0.268134\pi
−0.979096 + 0.203400i 0.934801π0.934801\pi
6060 17.3205 0.0372678
6161 −72.5000 125.574i −0.152175 0.263575i 0.779852 0.625964i 0.215294π-0.215294\pi
−0.932027 + 0.362389i 0.881961π0.881961\pi
6262 135.000 233.827i 0.276533 0.478968i
6363 159.349 276.000i 0.318667 0.551948i
6464 307.000 0.599609
6565 0 0
6666 −48.0000 −0.0895211
6767 −393.176 + 681.000i −0.716926 + 1.24175i 0.245286 + 0.969451i 0.421118π0.421118\pi
−0.962212 + 0.272301i 0.912215π0.912215\pi
6868 −292.500 + 506.625i −0.521630 + 0.903490i
6969 −78.0000 135.100i −0.136088 0.235712i
7070 41.5692 0.0709782
7171 −528.275 915.000i −0.883025 1.52944i −0.847961 0.530059i 0.822170π-0.822170\pi
−0.0350641 0.999385i 0.511164π-0.511164\pi
7272 258.942 + 448.500i 0.423841 + 0.734114i
7373 −458.993 −0.735906 −0.367953 0.929844i 0.619941π-0.619941\pi
−0.367953 + 0.929844i 0.619941π0.619941\pi
7474 −124.500 215.640i −0.195579 0.338752i
7575 122.000 211.310i 0.187831 0.325333i
7676 −285.788 + 495.000i −0.431344 + 0.747110i
7777 192.000 0.284161
7878 0 0
7979 1276.00 1.81723 0.908615 0.417634i 0.137141π-0.137141\pi
0.908615 + 0.417634i 0.137141π0.137141\pi
8080 0.866025 1.50000i 0.00121031 0.00209631i
8181 −210.500 + 364.597i −0.288752 + 0.500133i
8282 −235.500 407.898i −0.317154 0.549327i
8383 −789.815 −1.04450 −0.522250 0.852793i 0.674907π-0.674907\pi
−0.522250 + 0.852793i 0.674907π0.674907\pi
8484 69.2820 + 120.000i 0.0899915 + 0.155870i
8585 −101.325 175.500i −0.129297 0.223949i
8686 180.133 0.225864
8787 141.000 + 244.219i 0.173756 + 0.300955i
8888 −156.000 + 270.200i −0.188973 + 0.327311i
8989 488.438 846.000i 0.581734 1.00759i −0.413540 0.910486i 0.635708π-0.635708\pi
0.995274 0.0971073i 0.0309590π-0.0309590\pi
9090 −69.0000 −0.0808138
9191 0 0
9292 −390.000 −0.441960
9393 −155.885 + 270.000i −0.173812 + 0.301050i
9494 −261.000 + 452.065i −0.286384 + 0.496032i
9595 −99.0000 171.473i −0.106918 0.185187i
9696 −363.731 −0.386699
9797 −100.459 174.000i −0.105155 0.182134i 0.808646 0.588295i 0.200201π-0.200201\pi
−0.913802 + 0.406161i 0.866867π0.866867\pi
9898 −130.770 226.500i −0.134793 0.233469i
9999 −318.697 −0.323538
100100 −305.000 528.275i −0.305000 0.528275i
101101 214.500 371.525i 0.211322 0.366021i −0.740806 0.671719i 0.765556π-0.765556\pi
0.952129 + 0.305698i 0.0988897π0.0988897\pi
102102 −202.650 + 351.000i −0.196719 + 0.340727i
103103 −182.000 −0.174107 −0.0870534 0.996204i 0.527745π-0.527745\pi
−0.0870534 + 0.996204i 0.527745π0.527745\pi
104104 0 0
105105 −48.0000 −0.0446126
106106 80.5404 139.500i 0.0737997 0.127825i
107107 753.000 1304.23i 0.680330 1.17837i −0.294551 0.955636i 0.595170π-0.595170\pi
0.974880 0.222729i 0.0714967π-0.0714967\pi
108108 −250.000 433.013i −0.222743 0.385802i
109109 1551.92 1.36373 0.681866 0.731477i 0.261169π-0.261169\pi
0.681866 + 0.731477i 0.261169π0.261169\pi
110110 −20.7846 36.0000i −0.0180158 0.0312042i
111111 143.760 + 249.000i 0.122929 + 0.212919i
112112 13.8564 0.0116902
113113 343.500 + 594.959i 0.285962 + 0.495302i 0.972842 0.231470i 0.0743534π-0.0743534\pi
−0.686880 + 0.726771i 0.741020π0.741020\pi
114114 −198.000 + 342.946i −0.162670 + 0.281753i
115115 67.5500 117.000i 0.0547745 0.0948722i
116116 705.000 0.564290
117117 0 0
118118 −492.000 −0.383833
119119 810.600 1404.00i 0.624433 1.08155i
120120 39.0000 67.5500i 0.0296683 0.0513870i
121121 569.500 + 986.403i 0.427874 + 0.741099i
122122 −251.147 −0.186376
123123 271.932 + 471.000i 0.199344 + 0.345273i
124124 389.711 + 675.000i 0.282235 + 0.488845i
125125 427.817 0.306121
126126 −276.000 478.046i −0.195143 0.337998i
127127 143.000 247.683i 0.0999149 0.173058i −0.811734 0.584027i 0.801476π-0.801476\pi
0.911649 + 0.410969i 0.134810π0.134810\pi
128128 −461.592 + 799.500i −0.318745 + 0.552082i
129129 −208.000 −0.141964
130130 0 0
131131 −1974.00 −1.31656 −0.658279 0.752774i 0.728715π-0.728715\pi
−0.658279 + 0.752774i 0.728715π0.728715\pi
132132 69.2820 120.000i 0.0456835 0.0791262i
133133 792.000 1371.78i 0.516354 0.894352i
134134 681.000 + 1179.53i 0.439026 + 0.760415i
135135 173.205 0.110423
136136 1317.22 + 2281.50i 0.830523 + 1.43851i
137137 −423.486 733.500i −0.264094 0.457424i 0.703232 0.710961i 0.251740π-0.251740\pi
−0.967326 + 0.253536i 0.918406π0.918406\pi
138138 −270.200 −0.166674
139139 −118.000 204.382i −0.0720045 0.124716i 0.827775 0.561060i 0.189606π-0.189606\pi
−0.899780 + 0.436344i 0.856273π0.856273\pi
140140 −60.0000 + 103.923i −0.0362209 + 0.0627364i
141141 301.377 522.000i 0.180004 0.311775i
142142 −1830.00 −1.08148
143143 0 0
144144 −23.0000 −0.0133102
145145 −122.110 + 211.500i −0.0699355 + 0.121132i
146146 −397.500 + 688.490i −0.225324 + 0.390273i
147147 151.000 + 261.540i 0.0847229 + 0.146744i
148148 718.801 0.399224
149149 23.3827 + 40.5000i 0.0128563 + 0.0222677i 0.872382 0.488825i 0.162574π-0.162574\pi
−0.859526 + 0.511093i 0.829241π0.829241\pi
150150 −211.310 366.000i −0.115023 0.199225i
151151 1770.16 0.953995 0.476998 0.878905i 0.341725π-0.341725\pi
0.476998 + 0.878905i 0.341725π0.341725\pi
152152 1287.00 + 2229.15i 0.686773 + 1.18953i
153153 −1345.50 + 2330.47i −0.710962 + 1.23142i
154154 166.277 288.000i 0.0870063 0.150699i
155155 −270.000 −0.139916
156156 0 0
157157 1211.00 0.615594 0.307797 0.951452i 0.400408π-0.400408\pi
0.307797 + 0.951452i 0.400408π0.400408\pi
158158 1105.05 1914.00i 0.556411 0.963732i
159159 −93.0000 + 161.081i −0.0463860 + 0.0803430i
160160 −157.500 272.798i −0.0778217 0.134791i
161161 1080.80 0.529062
162162 364.597 + 631.500i 0.176824 + 0.306267i
163163 −502.295 870.000i −0.241367 0.418059i 0.719737 0.694247i 0.244262π-0.244262\pi
−0.961104 + 0.276187i 0.910929π0.910929\pi
164164 1359.66 0.647388
165165 24.0000 + 41.5692i 0.0113236 + 0.0196131i
166166 −684.000 + 1184.72i −0.319811 + 0.553930i
167167 −457.261 + 792.000i −0.211880 + 0.366987i −0.952303 0.305154i 0.901292π-0.901292\pi
0.740423 + 0.672141i 0.234625π0.234625\pi
168168 624.000 0.286563
169169 0 0
170170 −351.000 −0.158356
171171 −1314.63 + 2277.00i −0.587906 + 1.01828i
172172 −260.000 + 450.333i −0.115261 + 0.199637i
173173 1287.00 + 2229.15i 0.565600 + 0.979648i 0.996994 + 0.0774841i 0.0246887π0.0246887\pi
−0.431394 + 0.902164i 0.641978π0.641978\pi
174174 488.438 0.212807
175175 845.241 + 1464.00i 0.365110 + 0.632389i
176176 −6.92820 12.0000i −0.00296723 0.00513940i
177177 568.113 0.241254
178178 −846.000 1465.31i −0.356238 0.617022i
179179 1872.00 3242.40i 0.781675 1.35390i −0.149290 0.988793i 0.547699π-0.547699\pi
0.930965 0.365108i 0.118968π-0.118968\pi
180180 99.5929 172.500i 0.0412401 0.0714299i
181181 637.000 0.261590 0.130795 0.991409i 0.458247π-0.458247\pi
0.130795 + 0.991409i 0.458247π0.458247\pi
182182 0 0
183183 290.000 0.117144
184184 −878.150 + 1521.00i −0.351837 + 0.609400i
185185 −124.500 + 215.640i −0.0494780 + 0.0856983i
186186 270.000 + 467.654i 0.106437 + 0.184355i
187187 −1621.20 −0.633978
188188 −753.442 1305.00i −0.292289 0.506260i
189189 692.820 + 1200.00i 0.266642 + 0.461837i
190190 −342.946 −0.130947
191191 1299.00 + 2249.93i 0.492106 + 0.852353i 0.999959 0.00909077i 0.00289372π-0.00289372\pi
−0.507852 + 0.861444i 0.669560π0.669560\pi
192192 −307.000 + 531.740i −0.115395 + 0.199870i
193193 −558.586 + 967.500i −0.208331 + 0.360840i −0.951189 0.308609i 0.900137π-0.900137\pi
0.742858 + 0.669449i 0.233470π0.233470\pi
194194 −348.000 −0.128788
195195 0 0
196196 755.000 0.275146
197197 1025.37 1776.00i 0.370837 0.642308i −0.618858 0.785503i 0.712404π-0.712404\pi
0.989695 + 0.143195i 0.0457375π0.0457375\pi
198198 −276.000 + 478.046i −0.0990630 + 0.171582i
199199 −1261.00 2184.12i −0.449196 0.778030i 0.549138 0.835732i 0.314956π-0.314956\pi
−0.998334 + 0.0577019i 0.981623π0.981623\pi
200200 −2747.03 −0.971223
201201 −786.351 1362.00i −0.275945 0.477951i
202202 −371.525 643.500i −0.129408 0.224141i
203203 −1953.75 −0.675500
204204 −585.000 1013.25i −0.200775 0.347753i
205205 −235.500 + 407.898i −0.0802343 + 0.138970i
206206 −157.617 + 273.000i −0.0533091 + 0.0923340i
207207 −1794.00 −0.602375
208208 0 0
209209 −1584.00 −0.524247
210210 −41.5692 + 72.0000i −0.0136598 + 0.0236594i
211211 −521.000 + 902.398i −0.169986 + 0.294425i −0.938415 0.345511i 0.887706π-0.887706\pi
0.768428 + 0.639936i 0.221039π0.221039\pi
212212 232.500 + 402.702i 0.0753215 + 0.130461i
213213 2113.10 0.679753
214214 −1304.23 2259.00i −0.416615 0.721598i
215215 −90.0666 156.000i −0.0285697 0.0494842i
216216 −2251.67 −0.709289
217217 −1080.00 1870.61i −0.337858 0.585187i
218218 1344.00 2327.88i 0.417556 0.723228i
219219 458.993 795.000i 0.141625 0.245302i
220220 120.000 0.0367745
221221 0 0
222222 498.000 0.150557
223223 −1203.78 + 2085.00i −0.361483 + 0.626107i −0.988205 0.153136i 0.951063π-0.951063\pi
0.626722 + 0.779243i 0.284396π0.284396\pi
224224 1260.00 2182.38i 0.375836 0.650967i
225225 −1403.00 2430.07i −0.415704 0.720020i
226226 1189.92 0.350231
227227 −1203.78 2085.00i −0.351971 0.609631i 0.634624 0.772821i 0.281155π-0.281155\pi
−0.986595 + 0.163190i 0.947822π0.947822\pi
228228 −571.577 990.000i −0.166025 0.287563i
229229 −2508.01 −0.723729 −0.361864 0.932231i 0.617860π-0.617860\pi
−0.361864 + 0.932231i 0.617860π0.617860\pi
230230 −117.000 202.650i −0.0335424 0.0580971i
231231 −192.000 + 332.554i −0.0546869 + 0.0947205i
232232 1587.42 2749.50i 0.449222 0.778076i
233233 5850.00 1.64483 0.822417 0.568885i 0.192625π-0.192625\pi
0.822417 + 0.568885i 0.192625π0.192625\pi
234234 0 0
235235 522.000 0.144900
236236 710.141 1230.00i 0.195874 0.339263i
237237 −1276.00 + 2210.10i −0.349726 + 0.605744i
238238 −1404.00 2431.80i −0.382386 0.662312i
239239 −5383.21 −1.45695 −0.728475 0.685072i 0.759771π-0.759771\pi
−0.728475 + 0.685072i 0.759771π0.759771\pi
240240 1.73205 + 3.00000i 0.000465847 + 0.000806872i
241241 2458.65 + 4258.50i 0.657159 + 1.13823i 0.981348 + 0.192240i 0.0615753π0.0615753\pi
−0.324189 + 0.945992i 0.605091π0.605091\pi
242242 1972.81 0.524036
243243 −1771.00 3067.46i −0.467530 0.809785i
244244 362.500 627.868i 0.0951094 0.164734i
245245 −130.770 + 226.500i −0.0341003 + 0.0590635i
246246 942.000 0.244145
247247 0 0
248248 3510.00 0.898731
249249 789.815 1368.00i 0.201014 0.348167i
250250 370.500 641.725i 0.0937299 0.162345i
251251 −1989.00 3445.05i −0.500178 0.866333i −1.00000 0.000205037i 0.999935π-0.999935\pi
0.499822 0.866128i 0.333399π-0.333399\pi
252252 1593.49 0.398334
253253 −540.400 936.000i −0.134287 0.232592i
254254 −247.683 429.000i −0.0611852 0.105976i
255255 405.300 0.0995328
256256 2027.50 + 3511.73i 0.494995 + 0.857357i
257257 1033.50 1790.07i 0.250848 0.434482i −0.712911 0.701254i 0.752624π-0.752624\pi
0.963760 + 0.266772i 0.0859572π0.0859572\pi
258258 −180.133 + 312.000i −0.0434675 + 0.0752879i
259259 −1992.00 −0.477903
260260 0 0
261261 3243.00 0.769106
262262 −1709.53 + 2961.00i −0.403112 + 0.698211i
263263 1026.00 1777.08i 0.240555 0.416653i −0.720318 0.693644i 0.756004π-0.756004\pi
0.960872 + 0.276991i 0.0893373π0.0893373\pi
264264 −312.000 540.400i −0.0727359 0.125982i
265265 −161.081 −0.0373400
266266 −1371.78 2376.00i −0.316201 0.547676i
267267 976.877 + 1692.00i 0.223910 + 0.387823i
268268 −3931.76 −0.896157
269269 −1665.00 2883.86i −0.377386 0.653652i 0.613295 0.789854i 0.289844π-0.289844\pi
−0.990681 + 0.136202i 0.956510π0.956510\pi
270270 150.000 259.808i 0.0338100 0.0585607i
271271 −1402.96 + 2430.00i −0.314479 + 0.544694i −0.979327 0.202285i 0.935163π-0.935163\pi
0.664848 + 0.746979i 0.268496π0.268496\pi
272272 −117.000 −0.0260815
273273 0 0
274274 −1467.00 −0.323448
275275 845.241 1464.00i 0.185345 0.321027i
276276 390.000 675.500i 0.0850552 0.147320i
277277 188.500 + 326.492i 0.0408876 + 0.0708194i 0.885745 0.464172i 0.153648π-0.153648\pi
−0.844857 + 0.534992i 0.820315π0.820315\pi
278278 −408.764 −0.0881872
279279 1792.67 + 3105.00i 0.384676 + 0.666278i
280280 270.200 + 468.000i 0.0576698 + 0.0998870i
281281 36.3731 0.00772183 0.00386092 0.999993i 0.498771π-0.498771\pi
0.00386092 + 0.999993i 0.498771π0.498771\pi
282282 −522.000 904.131i −0.110229 0.190923i
283283 −3562.00 + 6169.56i −0.748194 + 1.29591i 0.200493 + 0.979695i 0.435745π0.435745\pi
−0.948688 + 0.316215i 0.897588π0.897588\pi
284284 2641.38 4575.00i 0.551891 0.955902i
285285 396.000 0.0823053
286286 0 0
287287 −3768.00 −0.774976
288288 −2091.45 + 3622.50i −0.427917 + 0.741173i
289289 −4388.00 + 7600.24i −0.893141 + 1.54696i
290290 211.500 + 366.329i 0.0428266 + 0.0741778i
291291 401.836 0.0809486
292292 −1147.48 1987.50i −0.229971 0.398321i
293293 −4161.25 7207.50i −0.829703 1.43709i −0.898271 0.439441i 0.855177π-0.855177\pi
0.0685685 0.997646i 0.478157π-0.478157\pi
294294 523.079 0.103764
295295 246.000 + 426.084i 0.0485514 + 0.0840936i
296296 1618.50 2803.32i 0.317816 0.550473i
297297 692.820 1200.00i 0.135359 0.234448i
298298 81.0000 0.0157457
299299 0 0
300300 1220.00 0.234789
301301 720.533 1248.00i 0.137976 0.238982i
302302 1533.00 2655.23i 0.292100 0.505932i
303303 429.000 + 743.050i 0.0813380 + 0.140882i
304304 −114.315 −0.0215672
305305 125.574 + 217.500i 0.0235748 + 0.0408328i
306306 2330.47 + 4036.50i 0.435374 + 0.754089i
307307 2220.49 0.412801 0.206401 0.978468i 0.433825π-0.433825\pi
0.206401 + 0.978468i 0.433825π0.433825\pi
308308 480.000 + 831.384i 0.0888004 + 0.153807i
309309 182.000 315.233i 0.0335069 0.0580356i
310310 −233.827 + 405.000i −0.0428402 + 0.0742015i
311311 −4914.00 −0.895972 −0.447986 0.894041i 0.647859π-0.647859\pi
−0.447986 + 0.894041i 0.647859π0.647859\pi
312312 0 0
313313 −518.000 −0.0935434 −0.0467717 0.998906i 0.514893π-0.514893\pi
−0.0467717 + 0.998906i 0.514893π0.514893\pi
314314 1048.76 1816.50i 0.188487 0.326468i
315315 −276.000 + 478.046i −0.0493677 + 0.0855074i
316316 3190.00 + 5525.24i 0.567885 + 0.983605i
317317 3916.17 0.693861 0.346930 0.937891i 0.387224π-0.387224\pi
0.346930 + 0.937891i 0.387224π0.387224\pi
318318 161.081 + 279.000i 0.0284055 + 0.0491998i
319319 976.877 + 1692.00i 0.171456 + 0.296971i
320320 −531.740 −0.0928911
321321 1506.00 + 2608.47i 0.261859 + 0.453553i
322322 936.000 1621.20i 0.161991 0.280577i
323323 −6687.45 + 11583.0i −1.15201 + 1.99534i
324324 −2105.00 −0.360940
325325 0 0
326326 −1740.00 −0.295613
327327 −1551.92 + 2688.00i −0.262450 + 0.454577i
328328 3061.50 5302.67i 0.515375 0.892656i
329329 2088.00 + 3616.52i 0.349894 + 0.606034i
330330 83.1384 0.0138685
331331 3727.37 + 6456.00i 0.618958 + 1.07207i 0.989676 + 0.143321i 0.0457781π0.0457781\pi
−0.370719 + 0.928745i 0.620889π0.620889\pi
332332 −1974.54 3420.00i −0.326406 0.565352i
333333 3306.48 0.544127
334334 792.000 + 1371.78i 0.129749 + 0.224733i
335335 681.000 1179.53i 0.111066 0.192371i
336336 −13.8564 + 24.0000i −0.00224979 + 0.00389675i
337337 3575.00 0.577871 0.288936 0.957349i 0.406699π-0.406699\pi
0.288936 + 0.957349i 0.406699π0.406699\pi
338338 0 0
339339 −1374.00 −0.220134
340340 506.625 877.500i 0.0808106 0.139968i
341341 −1080.00 + 1870.61i −0.171511 + 0.297066i
342342 2277.00 + 3943.88i 0.360018 + 0.623569i
343343 −6845.06 −1.07755
344344 1170.87 + 2028.00i 0.183514 + 0.317856i
345345 135.100 + 234.000i 0.0210827 + 0.0365163i
346346 4458.30 0.692716
347347 3483.00 + 6032.73i 0.538839 + 0.933297i 0.998967 + 0.0454442i 0.0144703π0.0144703\pi
−0.460128 + 0.887853i 0.652196π0.652196\pi
348348 −705.000 + 1221.10i −0.108598 + 0.188097i
349349 3325.54 5760.00i 0.510063 0.883455i −0.489869 0.871796i 0.662955π-0.662955\pi
0.999932 0.0116588i 0.00371121π-0.00371121\pi
350350 2928.00 0.447166
351351 0 0
352352 −2520.00 −0.381581
353353 2815.45 4876.50i 0.424508 0.735269i −0.571867 0.820347i 0.693781π-0.693781\pi
0.996374 + 0.0850777i 0.0271139π0.0271139\pi
354354 492.000 852.169i 0.0738687 0.127944i
355355 915.000 + 1584.83i 0.136798 + 0.236940i
356356 4884.38 0.727168
357357 1621.20 + 2808.00i 0.240344 + 0.416289i
358358 −3242.40 5616.00i −0.478676 0.829092i
359359 7129.12 1.04808 0.524040 0.851694i 0.324424π-0.324424\pi
0.524040 + 0.851694i 0.324424π0.324424\pi
360360 −448.500 776.825i −0.0656612 0.113729i
361361 −3104.50 + 5377.15i −0.452617 + 0.783956i
362362 551.658 955.500i 0.0800953 0.138729i
363363 −2278.00 −0.329377
364364 0 0
365365 795.000 0.114006
366366 251.147 435.000i 0.0358680 0.0621252i
367367 −1.00000 + 1.73205i −0.000142233 + 0.000246355i −0.866097 0.499877i 0.833379π-0.833379\pi
0.865954 + 0.500123i 0.166712π0.166712\pi
368368 −39.0000 67.5500i −0.00552450 0.00956871i
369369 6254.44 0.882366
370370 215.640 + 373.500i 0.0302989 + 0.0524793i
371371 −644.323 1116.00i −0.0901660 0.156172i
372372 −1558.85 −0.217264
373373 −1749.50 3030.22i −0.242857 0.420641i 0.718670 0.695351i 0.244751π-0.244751\pi
−0.961527 + 0.274711i 0.911418π0.911418\pi
374374 −1404.00 + 2431.80i −0.194115 + 0.336218i
375375 −427.817 + 741.000i −0.0589129 + 0.102040i
376376 −6786.00 −0.930748
377377 0 0
378378 2400.00 0.326568
379379 2759.16 4779.00i 0.373953 0.647706i −0.616216 0.787577i 0.711335π-0.711335\pi
0.990170 + 0.139871i 0.0446686π0.0446686\pi
380380 495.000 857.365i 0.0668236 0.115742i
381381 286.000 + 495.367i 0.0384573 + 0.0666100i
382382 4499.87 0.602705
383383 3682.34 + 6378.00i 0.491276 + 0.850915i 0.999950 0.0100443i 0.00319724π-0.00319724\pi
−0.508673 + 0.860960i 0.669864π0.669864\pi
384384 −923.183 1599.00i −0.122685 0.212496i
385385 −332.554 −0.0440221
386386 967.500 + 1675.76i 0.127576 + 0.220969i
387387 −1196.00 + 2071.53i −0.157096 + 0.272098i
388388 502.295 870.000i 0.0657220 0.113834i
389389 1209.00 0.157580 0.0787901 0.996891i 0.474894π-0.474894\pi
0.0787901 + 0.996891i 0.474894π0.474894\pi
390390 0 0
391391 −9126.00 −1.18036
392392 1700.01 2944.50i 0.219039 0.379387i
393393 1974.00 3419.07i 0.253372 0.438853i
394394 −1776.00 3076.12i −0.227090 0.393332i
395395 −2210.10 −0.281524
396396 −796.743 1380.00i −0.101106 0.175120i
397397 5847.40 + 10128.0i 0.739226 + 1.28038i 0.952844 + 0.303460i 0.0981419π0.0981419\pi
−0.213618 + 0.976917i 0.568525π0.568525\pi
398398 −4368.23 −0.550150
399399 1584.00 + 2743.57i 0.198745 + 0.344236i
400400 61.0000 105.655i 0.00762500 0.0132069i
401401 1490.43 2581.50i 0.185607 0.321481i −0.758174 0.652053i 0.773908π-0.773908\pi
0.943781 + 0.330571i 0.107241π0.107241\pi
402402 −2724.00 −0.337962
403403 0 0
404404 2145.00 0.264153
405405 364.597 631.500i 0.0447332 0.0774802i
406406 −1692.00 + 2930.63i −0.206829 + 0.358238i
407407 996.000 + 1725.12i 0.121302 + 0.210101i
408408 −5268.90 −0.639337
409409 −21.6506 37.5000i −0.00261749 0.00453363i 0.864714 0.502265i 0.167500π-0.167500\pi
−0.867331 + 0.497731i 0.834167π0.834167\pi
410410 407.898 + 706.500i 0.0491333 + 0.0851013i
411411 1693.95 0.203300
412412 −455.000 788.083i −0.0544084 0.0942380i
413413 −1968.00 + 3408.68i −0.234477 + 0.406126i
414414 −1553.65 + 2691.00i −0.184439 + 0.319458i
415415 1368.00 0.161813
416416 0 0
417417 472.000 0.0554291
418418 −1371.78 + 2376.00i −0.160517 + 0.278024i
419419 4731.00 8194.33i 0.551610 0.955416i −0.446549 0.894759i 0.647347π-0.647347\pi
0.998159 0.0606569i 0.0193195π-0.0193195\pi
420420 −120.000 207.846i −0.0139414 0.0241473i
421421 7068.50 0.818284 0.409142 0.912471i 0.365828π-0.365828\pi
0.409142 + 0.912471i 0.365828π0.365828\pi
422422 902.398 + 1563.00i 0.104095 + 0.180298i
423423 −3465.83 6003.00i −0.398380 0.690014i
424424 2094.05 0.239849
425425 −7137.00 12361.6i −0.814577 1.41089i
426426 1830.00 3169.65i 0.208131 0.360493i
427427 −1004.59 + 1740.00i −0.113854 + 0.197200i
428428 7530.00 0.850412
429429 0 0
430430 −312.000 −0.0349906
431431 −4964.06 + 8598.00i −0.554780 + 0.960907i 0.443140 + 0.896452i 0.353864π0.353864\pi
−0.997921 + 0.0644552i 0.979469π0.979469\pi
432432 50.0000 86.6025i 0.00556858 0.00964506i
433433 −3308.50 5730.49i −0.367197 0.636004i 0.621929 0.783074i 0.286349π-0.286349\pi
−0.989126 + 0.147070i 0.953016π0.953016\pi
434434 −3741.23 −0.413790
435435 −244.219 423.000i −0.0269182 0.0466237i
436436 3879.79 + 6720.00i 0.426166 + 0.738141i
437437 −8916.60 −0.976061
438438 −795.000 1376.98i −0.0867273 0.150216i
439439 6994.00 12114.0i 0.760377 1.31701i −0.182280 0.983247i 0.558348π-0.558348\pi
0.942656 0.333765i 0.108319π-0.108319\pi
440440 270.200 468.000i 0.0292756 0.0507069i
441441 3473.00 0.375013
442442 0 0
443443 2004.00 0.214928 0.107464 0.994209i 0.465727π-0.465727\pi
0.107464 + 0.994209i 0.465727π0.465727\pi
444444 −718.801 + 1245.00i −0.0768306 + 0.133075i
445445 −846.000 + 1465.31i −0.0901219 + 0.156096i
446446 2085.00 + 3611.33i 0.221362 + 0.383411i
447447 −93.5307 −0.00989676
448448 −2126.96 3684.00i −0.224307 0.388510i
449449 4541.44 + 7866.00i 0.477336 + 0.826769i 0.999663 0.0259758i 0.00826929π-0.00826929\pi
−0.522327 + 0.852745i 0.674936π0.674936\pi
450450 −4860.13 −0.509131
451451 1884.00 + 3263.18i 0.196705 + 0.340704i
452452 −1717.50 + 2974.80i −0.178727 + 0.309563i
453453 −1770.16 + 3066.00i −0.183596 + 0.317998i
454454 −4170.00 −0.431074
455455 0 0
456456 −5148.00 −0.528678
457457 1261.80 2185.50i 0.129156 0.223705i −0.794194 0.607665i 0.792106π-0.792106\pi
0.923350 + 0.383959i 0.125440π0.125440\pi
458458 −2172.00 + 3762.01i −0.221596 + 0.383815i
459459 −5850.00 10132.5i −0.594890 1.03038i
460460 675.500 0.0684681
461461 −9793.88 16963.5i −0.989472 1.71382i −0.620072 0.784545i 0.712897π-0.712897\pi
−0.369400 0.929270i 0.620437π-0.620437\pi
462462 332.554 + 576.000i 0.0334887 + 0.0580042i
463463 −8632.54 −0.866497 −0.433249 0.901274i 0.642633π-0.642633\pi
−0.433249 + 0.901274i 0.642633π0.642633\pi
464464 70.5000 + 122.110i 0.00705362 + 0.0122172i
465465 270.000 467.654i 0.0269268 0.0466385i
466466 5066.25 8775.00i 0.503625 0.872305i
467467 −5460.00 −0.541025 −0.270512 0.962716i 0.587193π-0.587193\pi
−0.270512 + 0.962716i 0.587193π0.587193\pi
468468 0 0
469469 10896.0 1.07277
470470 452.065 783.000i 0.0443664 0.0768449i
471471 −1211.00 + 2097.51i −0.118471 + 0.205198i
472472 −3198.00 5539.10i −0.311864 0.540165i
473473 −1441.07 −0.140085
474474 2210.10 + 3828.00i 0.214163 + 0.370941i
475475 −6973.24 12078.0i −0.673587 1.16669i
476476 8106.00 0.780542
477477 1069.50 + 1852.43i 0.102660 + 0.177813i
478478 −4662.00 + 8074.82i −0.446098 + 0.772665i
479479 1276.52 2211.00i 0.121766 0.210904i −0.798698 0.601732i 0.794478π-0.794478\pi
0.920464 + 0.390827i 0.127811π0.127811\pi
480480 630.000 0.0599072
481481 0 0
482482 8517.00 0.804852
483483 −1080.80 + 1872.00i −0.101818 + 0.176354i
484484 −2847.50 + 4932.01i −0.267421 + 0.463187i
485485 174.000 + 301.377i 0.0162906 + 0.0282161i
486486 −6134.92 −0.572605
487487 −5414.39 9378.00i −0.503798 0.872603i −0.999990 0.00439074i 0.998602π-0.998602\pi
0.496193 0.868212i 0.334731π-0.334731\pi
488488 −1632.46 2827.50i −0.151430 0.262285i
489489 2009.18 0.185804
490490 226.500 + 392.310i 0.0208821 + 0.0361689i
491491 5694.00 9862.30i 0.523354 0.906475i −0.476277 0.879295i 0.658014π-0.658014\pi
0.999631 0.0271797i 0.00865264π-0.00865264\pi
492492 −1359.66 + 2355.00i −0.124590 + 0.215796i
493493 16497.0 1.50707
494494 0 0
495495 552.000 0.0501223
496496 −77.9423 + 135.000i −0.00705587 + 0.0122211i
497497 −7320.00 + 12678.6i −0.660658 + 1.14429i
498498 −1368.00 2369.45i −0.123095 0.213208i
499499 −17677.3 −1.58586 −0.792931 0.609311i 0.791446π-0.791446\pi
−0.792931 + 0.609311i 0.791446π0.791446\pi
500500 1069.54 + 1852.50i 0.0956627 + 0.165693i
501501 −914.523 1584.00i −0.0815526 0.141253i
502502 −6890.10 −0.612590
503503 −1938.00 3356.71i −0.171792 0.297552i 0.767255 0.641343i 0.221622π-0.221622\pi
−0.939046 + 0.343791i 0.888289π0.888289\pi
504504 3588.00 6214.60i 0.317108 0.549246i
505505 −371.525 + 643.500i −0.0327379 + 0.0567037i
506506 −1872.00 −0.164467
507507 0 0
508508 1430.00 0.124894
509509 −8532.95 + 14779.5i −0.743058 + 1.28701i 0.208039 + 0.978120i 0.433292π0.433292\pi
−0.951097 + 0.308893i 0.900042π0.900042\pi
510510 351.000 607.950i 0.0304756 0.0527852i
511511 3180.00 + 5507.92i 0.275293 + 0.476822i
512512 −361.999 −0.0312465
513513 −5715.77 9900.00i −0.491925 0.852038i
514514 −1790.07 3100.50i −0.153612 0.266065i
515515 315.233 0.0269725
516516 −520.000 900.666i −0.0443638 0.0768404i
517517 2088.00 3616.52i 0.177621 0.307649i
518518 −1725.12 + 2988.00i −0.146327 + 0.253446i
519519 −5148.00 −0.435399
520520 0 0
521521 2121.00 0.178355 0.0891773 0.996016i 0.471576π-0.471576\pi
0.0891773 + 0.996016i 0.471576π0.471576\pi
522522 2808.52 4864.50i 0.235490 0.407880i
523523 5732.00 9928.12i 0.479241 0.830069i −0.520476 0.853876i 0.674245π-0.674245\pi
0.999717 + 0.0238072i 0.00757878π0.00757878\pi
524524 −4935.00 8547.67i −0.411425 0.712608i
525525 −3380.96 −0.281062
526526 −1777.08 3078.00i −0.147309 0.255147i
527527 9119.25 + 15795.0i 0.753777 + 1.30558i
528528 27.7128 0.00228418
529529 3041.50 + 5268.03i 0.249979 + 0.432977i
530530 −139.500 + 241.621i −0.0114330 + 0.0198025i
531531 3266.65 5658.00i 0.266969 0.462404i
532532 7920.00 0.645443
533533 0 0
534534 3384.00 0.274232
535535 −1304.23 + 2259.00i −0.105396 + 0.182552i
536536 −8853.00 + 15333.8i −0.713417 + 1.23567i
537537 3744.00 + 6484.80i 0.300867 + 0.521117i
538538 −5767.73 −0.462202
539539 1046.16 + 1812.00i 0.0836016 + 0.144802i
540540 433.013 + 750.000i 0.0345072 + 0.0597683i
541541 4764.87 0.378665 0.189333 0.981913i 0.439368π-0.439368\pi
0.189333 + 0.981913i 0.439368π0.439368\pi
542542 2430.00 + 4208.88i 0.192578 + 0.333555i
543543 −637.000 + 1103.32i −0.0503431 + 0.0871968i
544544 −10639.1 + 18427.5i −0.838508 + 1.45234i
545545 −2688.00 −0.211268
546546 0 0
547547 6554.00 0.512301 0.256151 0.966637i 0.417546π-0.417546\pi
0.256151 + 0.966637i 0.417546π0.417546\pi
548548 2117.43 3667.50i 0.165059 0.285890i
549549 1667.50 2888.19i 0.129631 0.224527i
550550 −1464.00 2535.72i −0.113500 0.196588i
551551 16118.5 1.24622
552552 −1756.30 3042.00i −0.135422 0.234558i
553553 −8840.39 15312.0i −0.679804 1.17745i
554554 652.983 0.0500769
555555 −249.000 431.281i −0.0190441 0.0329853i
556556 590.000 1021.91i 0.0450028 0.0779472i
557557 9056.03 15685.5i 0.688898 1.19321i −0.283297 0.959032i 0.591428π-0.591428\pi
0.972195 0.234174i 0.0752386π-0.0752386\pi
558558 6210.00 0.471130
559559 0 0
560560 −24.0000 −0.00181104
561561 1621.20 2808.00i 0.122009 0.211326i
562562 31.5000 54.5596i 0.00236432 0.00409512i
563563 −6084.00 10537.8i −0.455435 0.788837i 0.543278 0.839553i 0.317183π-0.317183\pi
−0.998713 + 0.0507160i 0.983850π0.983850\pi
564564 3013.77 0.225005
565565 −594.959 1030.50i −0.0443011 0.0767318i
566566 6169.56 + 10686.0i 0.458173 + 0.793580i
567567 5833.55 0.432074
568568 −11895.0 20602.7i −0.878703 1.52196i
569569 −3861.00 + 6687.45i −0.284467 + 0.492711i −0.972480 0.232988i 0.925150π-0.925150\pi
0.688013 + 0.725698i 0.258483π0.258483\pi
570570 342.946 594.000i 0.0252008 0.0436490i
571571 −11440.0 −0.838440 −0.419220 0.907885i 0.637696π-0.637696\pi
−0.419220 + 0.907885i 0.637696π0.637696\pi
572572 0 0
573573 −5196.00 −0.378824
574574 −3263.18 + 5652.00i −0.237287 + 0.410993i
575575 4758.00 8241.10i 0.345082 0.597700i
576576 3530.50 + 6115.01i 0.255389 + 0.442347i
577577 15444.7 1.11433 0.557167 0.830400i 0.311888π-0.311888\pi
0.557167 + 0.830400i 0.311888π0.311888\pi
578578 7600.24 + 13164.0i 0.546935 + 0.947319i
579579 −1117.17 1935.00i −0.0801867 0.138887i
580580 −1221.10 −0.0874194
581581 5472.00 + 9477.78i 0.390735 + 0.676772i
582582 348.000 602.754i 0.0247853 0.0429295i
583583 −644.323 + 1116.00i −0.0457721 + 0.0792796i
584584 −10335.0 −0.732304
585585 0 0
586586 −14415.0 −1.01617
587587 −7035.59 + 12186.0i −0.494702 + 0.856848i −0.999981 0.00610719i 0.998056π-0.998056\pi
0.505280 + 0.862956i 0.331389π0.331389\pi
588588 −755.000 + 1307.70i −0.0529518 + 0.0917153i
589589 8910.00 + 15432.6i 0.623311 + 1.07961i
590590 852.169 0.0594631
591591 2050.75 + 3552.00i 0.142735 + 0.247225i
592592 71.8801 + 124.500i 0.00499029 + 0.00864344i
593593 −26938.6 −1.86549 −0.932745 0.360538i 0.882593π-0.882593\pi
−0.932745 + 0.360538i 0.882593π0.882593\pi
594594 −1200.00 2078.46i −0.0828899 0.143570i
595595 −1404.00 + 2431.80i −0.0967368 + 0.167553i
596596 −116.913 + 202.500i −0.00803517 + 0.0139173i
597597 5044.00 0.345791
598598 0 0
599599 −10554.0 −0.719908 −0.359954 0.932970i 0.617208π-0.617208\pi
−0.359954 + 0.932970i 0.617208π0.617208\pi
600600 2747.03 4758.00i 0.186912 0.323741i
601601 7415.50 12844.0i 0.503302 0.871745i −0.496691 0.867928i 0.665452π-0.665452\pi
0.999993 0.00381713i 0.00121503π-0.00121503\pi
602602 −1248.00 2161.60i −0.0844928 0.146346i
603603 −18086.1 −1.22143
604604 4425.39 + 7665.00i 0.298123 + 0.516365i
605605 −986.403 1708.50i −0.0662859 0.114811i
606606 1486.10 0.0996183
607607 3977.00 + 6888.37i 0.265933 + 0.460610i 0.967808 0.251691i 0.0809866π-0.0809866\pi
−0.701874 + 0.712301i 0.747653π0.747653\pi
608608 −10395.0 + 18004.7i −0.693377 + 1.20096i
609609 1953.75 3384.00i 0.130000 0.225167i
610610 435.000 0.0288732
611611 0 0
612612 −13455.0 −0.888703
613613 12610.2 21841.5i 0.830866 1.43910i −0.0664859 0.997787i 0.521179π-0.521179\pi
0.897352 0.441315i 0.145488π-0.145488\pi
614614 1923.00 3330.73i 0.126394 0.218921i
615615 −471.000 815.796i −0.0308822 0.0534895i
616616 4323.20 0.282771
617617 8692.30 + 15055.5i 0.567162 + 0.982353i 0.996845 + 0.0793731i 0.0252918π0.0252918\pi
−0.429683 + 0.902980i 0.641375π0.641375\pi
618618 −315.233 546.000i −0.0205187 0.0355394i
619619 8209.92 0.533093 0.266547 0.963822i 0.414117π-0.414117\pi
0.266547 + 0.963822i 0.414117π0.414117\pi
620620 −675.000 1169.13i −0.0437236 0.0757316i
621621 3900.00 6755.00i 0.252015 0.436504i
622622 −4255.65 + 7371.00i −0.274334 + 0.475161i
623623 −13536.0 −0.870479
624624 0 0
625625 14509.0 0.928576
626626 −448.601 + 777.000i −0.0286417 + 0.0496089i
627627 1584.00 2743.57i 0.100891 0.174749i
628628 3027.50 + 5243.78i 0.192373 + 0.333200i
629629 16819.9 1.06622
630630 478.046 + 828.000i 0.0302314 + 0.0523624i
631631 6432.84 + 11142.0i 0.405843 + 0.702941i 0.994419 0.105501i 0.0336445π-0.0336445\pi
−0.588576 + 0.808442i 0.700311π0.700311\pi
632632 28731.3 1.80834
633633 −1042.00 1804.80i −0.0654278 0.113324i
634634 3391.50 5874.25i 0.212451 0.367975i
635635 −247.683 + 429.000i −0.0154788 + 0.0268100i
636636 −930.000 −0.0579825
637637 0 0
638638 3384.00 0.209990
639639 12150.3 21045.0i 0.752206 1.30286i
640640 799.500 1384.77i 0.0493797 0.0855282i
641641 3100.50 + 5370.22i 0.191049 + 0.330907i 0.945598 0.325337i 0.105478π-0.105478\pi
−0.754549 + 0.656244i 0.772144π0.772144\pi
642642 5216.94 0.320710
643643 8410.84 + 14568.0i 0.515849 + 0.893477i 0.999831 + 0.0183989i 0.00585689π0.00585689\pi
−0.483981 + 0.875078i 0.660810π0.660810\pi
644644 2702.00 + 4680.00i 0.165332 + 0.286363i
645645 360.267 0.0219930
646646 11583.0 + 20062.3i 0.705460 + 1.22189i
647647 −6747.00 + 11686.1i −0.409972 + 0.710092i −0.994886 0.101003i 0.967795π-0.967795\pi
0.584914 + 0.811095i 0.301128π0.301128\pi
648648 −4739.76 + 8209.50i −0.287338 + 0.497685i
649649 3936.00 0.238061
650650 0 0
651651 4320.00 0.260083
652652 2511.47 4350.00i 0.150854 0.261287i
653653 5667.00 9815.53i 0.339612 0.588226i −0.644747 0.764396i 0.723037π-0.723037\pi
0.984360 + 0.176170i 0.0563708π0.0563708\pi
654654 2688.00 + 4655.75i 0.160717 + 0.278371i
655655 3419.07 0.203960
656656 135.966 + 235.500i 0.00809235 + 0.0140164i
657657 −5278.42 9142.50i −0.313441 0.542896i
658658 7233.04 0.428531
659659 −6618.00 11462.7i −0.391200 0.677578i 0.601408 0.798942i 0.294607π-0.294607\pi
−0.992608 + 0.121364i 0.961273π0.961273\pi
660660 −120.000 + 207.846i −0.00707726 + 0.0122582i
661661 5926.21 10264.5i 0.348718 0.603998i −0.637304 0.770613i 0.719950π-0.719950\pi
0.986022 + 0.166615i 0.0532836π0.0532836\pi
662662 12912.0 0.758065
663663 0 0
664664 −17784.0 −1.03939
665665 −1371.78 + 2376.00i −0.0799932 + 0.138552i
666666 2863.50 4959.73i 0.166604 0.288567i
667667 5499.00 + 9524.55i 0.319224 + 0.552911i
668668 −4572.61 −0.264850
669669 −2407.55 4170.00i −0.139135 0.240989i
670670 −1179.53 2043.00i −0.0680136 0.117803i
671671 2009.18 0.115594
672672 2520.00 + 4364.77i 0.144659 + 0.250557i
673673 4010.50 6946.39i 0.229708 0.397866i −0.728014 0.685563i 0.759556π-0.759556\pi
0.957722 + 0.287697i 0.0928896π0.0928896\pi
674674 3096.04 5362.50i 0.176936 0.306463i
675675 12200.0 0.695671
676676 0 0
677677 −21630.0 −1.22793 −0.613965 0.789333i 0.710426π-0.710426\pi
−0.613965 + 0.789333i 0.710426π0.710426\pi
678678 −1189.92 + 2061.00i −0.0674020 + 0.116744i
679679 −1392.00 + 2411.01i −0.0786746 + 0.136268i
680680 −2281.50 3951.67i −0.128664 0.222853i
681681 4815.10 0.270947
682682 1870.61 + 3240.00i 0.105029 + 0.181915i
683683 −13269.2 22983.0i −0.743387 1.28758i −0.950945 0.309361i 0.899885π-0.899885\pi
0.207557 0.978223i 0.433449π-0.433449\pi
684684 −13146.3 −0.734883
685685 733.500 + 1270.46i 0.0409133 + 0.0708639i
686686 −5928.00 + 10267.6i −0.329930 + 0.571456i
687687 2508.01 4344.00i 0.139282 0.241243i
688688 −104.000 −0.00576303
689689 0 0
690690 468.000 0.0258210
691691 −415.692 + 720.000i −0.0228852 + 0.0396383i −0.877241 0.480050i 0.840619π-0.840619\pi
0.854356 + 0.519688i 0.173952π0.173952\pi
692692 −6435.00 + 11145.7i −0.353500 + 0.612280i
693693 2208.00 + 3824.37i 0.121032 + 0.209633i
694694 12065.5 0.659941
695695 204.382 + 354.000i 0.0111549 + 0.0193208i
696696 3174.85 + 5499.00i 0.172906 + 0.299481i
697697 31816.0 1.72901
698698 −5760.00 9976.61i −0.312348 0.541003i
699699 −5850.00 + 10132.5i −0.316548 + 0.548278i
700700 −4226.20 + 7320.00i −0.228194 + 0.395243i
701701 −30186.0 −1.62640 −0.813202 0.581981i 0.802278π-0.802278\pi
−0.813202 + 0.581981i 0.802278π0.802278\pi
702702 0 0
703703 16434.0 0.881679
704704 −2126.96 + 3684.00i −0.113868 + 0.197224i
705705 −522.000 + 904.131i −0.0278860 + 0.0483000i
706706 −4876.50 8446.35i −0.259957 0.450258i
707707 −5944.40 −0.316212
708708 1420.28 + 2460.00i 0.0753919 + 0.130583i
709709 −5940.07 10288.5i −0.314646 0.544983i 0.664716 0.747096i 0.268552π-0.268552\pi
−0.979362 + 0.202113i 0.935219π0.935219\pi
710710 3169.65 0.167542
711711 14674.0 + 25416.1i 0.774006 + 1.34062i
712712 10998.0 19049.1i 0.578887 1.00266i
713713 −6079.50 + 10530.0i −0.319325 + 0.553088i
714714 5616.00 0.294361
715715 0 0
716716 18720.0 0.977094
717717 5383.21 9324.00i 0.280390 0.485650i
718718 6174.00 10693.7i 0.320908 0.555828i
719719 9204.00 + 15941.8i 0.477401 + 0.826883i 0.999665 0.0259014i 0.00824561π-0.00824561\pi
−0.522264 + 0.852784i 0.674912π0.674912\pi
720720 39.8372 0.00206201
721721 1260.93 + 2184.00i 0.0651312 + 0.112811i
722722 5377.15 + 9313.50i 0.277170 + 0.480073i
723723 −9834.58 −0.505881
724724 1592.50 + 2758.29i 0.0817470 + 0.141590i
725725 −8601.00 + 14897.4i −0.440597 + 0.763137i
726726 −1972.81 + 3417.00i −0.100851 + 0.174679i
727727 −21112.0 −1.07703 −0.538515 0.842616i 0.681014π-0.681014\pi
−0.538515 + 0.842616i 0.681014π0.681014\pi
728728 0 0
729729 −4283.00 −0.217599
730730 688.490 1192.50i 0.0349071 0.0604608i
731731 −6084.00 + 10537.8i −0.307832 + 0.533180i
732732 725.000 + 1255.74i 0.0366076 + 0.0634062i
733733 −23959.5 −1.20732 −0.603658 0.797243i 0.706291π-0.706291\pi
−0.603658 + 0.797243i 0.706291π0.706291\pi
734734 1.73205 + 3.00000i 8.70997e−5 + 0.000150861i
735735 −261.540 453.000i −0.0131252 0.0227335i
736736 −14185.5 −0.710441
737737 −5448.00 9436.21i −0.272293 0.471625i
738738 5416.50 9381.65i 0.270168 0.467945i
739739 −1583.09 + 2742.00i −0.0788025 + 0.136490i −0.902734 0.430200i 0.858443π-0.858443\pi
0.823931 + 0.566690i 0.191776π0.191776\pi
740740 −1245.00 −0.0618474
741741 0 0
742742 −2232.00 −0.110430
743743 −15051.5 + 26070.0i −0.743185 + 1.28723i 0.207852 + 0.978160i 0.433353π0.433353\pi
−0.951038 + 0.309075i 0.899981π0.899981\pi
744744 −3510.00 + 6079.50i −0.172961 + 0.299577i
745745 −40.5000 70.1481i −0.00199168 0.00344970i
746746 −6060.45 −0.297438
747747 −9082.87 15732.0i −0.444880 0.770554i
748748 −4053.00 7020.00i −0.198118 0.343151i
749749 −20867.7 −1.01801
750750 741.000 + 1283.45i 0.0360767 + 0.0624866i
751751 14248.0 24678.3i 0.692299 1.19910i −0.278783 0.960354i 0.589931π-0.589931\pi
0.971083 0.238744i 0.0767356π-0.0767356\pi
752752 150.688 261.000i 0.00730724 0.0126565i
753753 7956.00 0.385037
754754 0 0
755755 −3066.00 −0.147792
756756 −3464.10 + 6000.00i −0.166651 + 0.288648i
757757 −8711.00 + 15087.9i −0.418239 + 0.724411i −0.995762 0.0919633i 0.970686π-0.970686\pi
0.577524 + 0.816374i 0.304019π0.304019\pi
758758 −4779.00 8277.47i −0.228999 0.396638i
759759 2161.60 0.103374
760760 −2229.15 3861.00i −0.106394 0.184281i
761761 20663.4 + 35790.0i 0.984292 + 1.70484i 0.645040 + 0.764149i 0.276841π0.276841\pi
0.339252 + 0.940695i 0.389826π0.389826\pi
762762 990.733 0.0471004
763763 −10752.0 18623.0i −0.510155 0.883615i
764764 −6495.00 + 11249.7i −0.307567 + 0.532721i
765765 2330.47 4036.50i 0.110142 0.190771i
766766 12756.0 0.601688
767767 0 0
768768 −8110.00 −0.381047
769769 −7035.59 + 12186.0i −0.329922 + 0.571441i −0.982496 0.186283i 0.940356π-0.940356\pi
0.652574 + 0.757725i 0.273689π0.273689\pi
770770 −288.000 + 498.831i −0.0134790 + 0.0233462i
771771 2067.00 + 3580.15i 0.0965515 + 0.167232i
772772 −5585.86 −0.260414
773773 −100.459 174.000i −0.00467433 0.00809618i 0.863679 0.504043i 0.168155π-0.168155\pi
−0.868353 + 0.495946i 0.834821π0.834821\pi
774774 2071.53 + 3588.00i 0.0962012 + 0.166625i
775775 −19017.9 −0.881476
776776 −2262.00 3917.90i −0.104641 0.181243i
777777 1992.00 3450.25i 0.0919725 0.159301i
778778 1047.02 1813.50i 0.0482489 0.0835696i
779779 31086.0 1.42975
780780 0 0
781781 14640.0 0.670756
782782 −7903.35 + 13689.0i −0.361411 + 0.625982i
783783 −7050.00 + 12211.0i −0.321771 + 0.557323i
784784 75.5000 + 130.770i 0.00343932 + 0.00595708i
785785 −2097.51 −0.0953675
786786 −3419.07 5922.00i −0.155158 0.268741i
787787 −3451.98 5979.00i −0.156353 0.270811i 0.777198 0.629256i 0.216640π-0.216640\pi
−0.933551 + 0.358445i 0.883307π0.883307\pi
788788 10253.7 0.463546
789789 2052.00 + 3554.17i 0.0925895 + 0.160370i
790790 −1914.00 + 3315.15i −0.0861988 + 0.149301i
791791 4759.68 8244.00i 0.213950 0.370573i
792792 −7176.00 −0.321955
793793 0 0
794794 20256.0 0.905363
795795 161.081 279.000i 0.00718609 0.0124467i
796796 6305.00 10920.6i 0.280747 0.486268i
797797 −15639.0 27087.5i −0.695059 1.20388i −0.970161 0.242462i 0.922045π-0.922045\pi
0.275102 0.961415i 0.411288π-0.411288\pi
798798 5487.14 0.243412
799799 −17630.5 30537.0i −0.780631 1.35209i
800800 −11093.8 19215.0i −0.490281 0.849191i
801801 22468.2 0.991103
802802 −2581.50 4471.29i −0.113661 0.196866i
803803 3180.00 5507.92i 0.139751 0.242055i
804804 3931.76 6810.00i 0.172466 0.298719i
805805 −1872.00 −0.0819619
806806 0 0
807807 6660.00 0.290512
808808 4829.82 8365.50i 0.210288 0.364229i
809809 −4024.50 + 6970.64i −0.174900 + 0.302935i −0.940127 0.340826i 0.889293π-0.889293\pi
0.765227 + 0.643761i 0.222627π0.222627\pi
810810 −631.500 1093.79i −0.0273934 0.0474467i
811811 14026.1 0.607305 0.303653 0.952783i 0.401794π-0.401794\pi
0.303653 + 0.952783i 0.401794π0.401794\pi
812812 −4884.38 8460.00i −0.211094 0.365625i
813813 −2805.92 4860.00i −0.121043 0.209653i
814814 3450.25 0.148564
815815 870.000 + 1506.88i 0.0373924 + 0.0647655i
816816 117.000 202.650i 0.00501939 0.00869383i
817817 −5944.40 + 10296.0i −0.254551 + 0.440895i
818818 −75.0000 −0.00320576
819819 0 0
820820 −2355.00 −0.100293
821821 −4018.36 + 6960.00i −0.170818 + 0.295866i −0.938706 0.344718i 0.887974π-0.887974\pi
0.767888 + 0.640584i 0.221308π0.221308\pi
822822 1467.00 2540.92i 0.0622476 0.107816i
823823 −20150.0 34900.8i −0.853445 1.47821i −0.878081 0.478513i 0.841176π-0.841176\pi
0.0246361 0.999696i 0.492157π-0.492157\pi
824824 −4098.03 −0.173255
825825 1690.48 + 2928.00i 0.0713394 + 0.123563i
826826 3408.68 + 5904.00i 0.143587 + 0.248700i
827827 −39525.4 −1.66195 −0.830975 0.556310i 0.812217π-0.812217\pi
−0.830975 + 0.556310i 0.812217π0.812217\pi
828828 −4485.00 7768.25i −0.188242 0.326045i
829829 −6155.50 + 10661.6i −0.257888 + 0.446676i −0.965676 0.259750i 0.916360π-0.916360\pi
0.707788 + 0.706425i 0.249693π0.249693\pi
830830 1184.72 2052.00i 0.0495450 0.0858144i
831831 −754.000 −0.0314753
832832 0 0
833833 17667.0 0.734844
834834 408.764 708.000i 0.0169716 0.0293957i
835835 792.000 1371.78i 0.0328243 0.0568534i
836836 −3960.00 6858.92i −0.163827 0.283757i
837837 −15588.5 −0.643747
838838 −8194.33 14193.0i −0.337791 0.585070i
839839 10733.5 + 18591.0i 0.441671 + 0.764997i 0.997814 0.0660899i 0.0210524π-0.0210524\pi
−0.556142 + 0.831087i 0.687719π0.687719\pi
840840 −1080.80 −0.0443942
841841 2254.00 + 3904.04i 0.0924187 + 0.160074i
842842 6121.50 10602.7i 0.250547 0.433961i
843843 −36.3731 + 63.0000i −0.00148607 + 0.00257394i
844844 −5210.00 −0.212483
845845 0 0
846846 −12006.0 −0.487913
847847 7891.22 13668.0i 0.320125 0.554472i
848848 −46.5000 + 80.5404i −0.00188304 + 0.00326152i
849849 −7124.00 12339.1i −0.287980 0.498796i
850850 −24723.3 −0.997649
851851 5606.65 + 9711.00i 0.225844 + 0.391174i
852852 5282.75 + 9150.00i 0.212423 + 0.367927i
853853 −774.227 −0.0310774 −0.0155387 0.999879i 0.504946π-0.504946\pi
−0.0155387 + 0.999879i 0.504946π0.504946\pi
854854 1740.00 + 3013.77i 0.0697208 + 0.120760i
855855 2277.00 3943.88i 0.0910781 0.157752i
856856 16955.0 29367.0i 0.676999 1.17260i
857857 −13923.0 −0.554960 −0.277480 0.960731i 0.589499π-0.589499\pi
−0.277480 + 0.960731i 0.589499π0.589499\pi
858858 0 0
859859 −22358.0 −0.888062 −0.444031 0.896011i 0.646452π-0.646452\pi
−0.444031 + 0.896011i 0.646452π0.646452\pi
860860 450.333 780.000i 0.0178561 0.0309277i
861861 3768.00 6526.37i 0.149144 0.258325i
862862 8598.00 + 14892.2i 0.339732 + 0.588433i
863863 −2230.88 −0.0879955 −0.0439977 0.999032i 0.514009π-0.514009\pi
−0.0439977 + 0.999032i 0.514009π0.514009\pi
864864 −9093.27 15750.0i −0.358055 0.620169i
865865 −2229.15 3861.00i −0.0876224 0.151766i
866866 −11461.0 −0.449723
867867 −8776.00 15200.5i −0.343770 0.595427i
868868 5400.00 9353.07i 0.211161 0.365742i
869869 −8840.39 + 15312.0i −0.345097 + 0.597726i
870870 −846.000 −0.0329679
871871 0 0
872872 34944.0 1.35706
873873 2310.56 4002.00i 0.0895767 0.155151i
874874 −7722.00 + 13374.9i −0.298856 + 0.517635i
875875 −2964.00 5133.80i −0.114516 0.198348i
876876 4589.93 0.177031
877877 8377.06 + 14509.5i 0.322547 + 0.558667i 0.981013 0.193943i 0.0621278π-0.0621278\pi
−0.658466 + 0.752610i 0.728794π0.728794\pi
878878 −12114.0 20982.0i −0.465634 0.806501i
879879 16645.0 0.638706
880880 12.0000 + 20.7846i 0.000459682 + 0.000796192i
881881 8677.50 15029.9i 0.331842 0.574766i −0.651031 0.759051i 0.725663π-0.725663\pi
0.982873 + 0.184284i 0.0589967π0.0589967\pi
882882 3007.71 5209.50i 0.114824 0.198881i
883883 46982.0 1.79057 0.895283 0.445497i 0.146973π-0.146973\pi
0.895283 + 0.445497i 0.146973π0.146973\pi
884884 0 0
885885 −984.000 −0.0373749
886886 1735.51 3006.00i 0.0658079 0.113983i
887887 4458.00 7721.48i 0.168754 0.292291i −0.769228 0.638975i 0.779359π-0.779359\pi
0.937982 + 0.346684i 0.112692π0.112692\pi
888888 3237.00 + 5606.65i 0.122327 + 0.211877i
889889 −3962.93 −0.149508
890890 1465.31 + 2538.00i 0.0551882 + 0.0955887i
891891 −2916.77 5052.00i −0.109670 0.189953i
892892 −12037.8 −0.451854
893893 −17226.0 29836.3i −0.645516 1.11807i
894894 −81.0000 + 140.296i −0.00303025 + 0.00524855i
895895 −3242.40 + 5616.00i −0.121097 + 0.209745i
896896 12792.0 0.476954
897897 0 0
898898 15732.0 0.584614
899899 10989.9 19035.0i 0.407711 0.706177i
900900 7015.00 12150.3i 0.259815 0.450012i
901901 5440.50 + 9423.22i 0.201165 + 0.348427i
902902 6526.37 0.240914
903903 1441.07 + 2496.00i 0.0531071 + 0.0919841i
904904 7734.47 + 13396.5i 0.284563 + 0.492877i
905905 −1103.32 −0.0405254
906906 3066.00 + 5310.47i 0.112429 + 0.194733i
907907 −15418.0 + 26704.8i −0.564439 + 0.977637i 0.432662 + 0.901556i 0.357574π0.357574\pi
−0.997102 + 0.0760813i 0.975759π0.975759\pi
908908 6018.88 10425.0i 0.219982 0.381020i
909909 9867.00 0.360031
910910 0 0
911911 −27480.0 −0.999400 −0.499700 0.866199i 0.666556π-0.666556\pi
−0.499700 + 0.866199i 0.666556π0.666556\pi
912912 114.315 198.000i 0.00415061 0.00718907i
913913 5472.00 9477.78i 0.198354 0.343558i
914914 −2185.50 3785.40i −0.0790918 0.136991i
915915 −502.295 −0.0181479
916916 −6270.02 10860.0i −0.226165 0.391730i
917917 13676.3 + 23688.0i 0.492509 + 0.853050i
918918 −20265.0 −0.728589
919919 14221.0 + 24631.5i 0.510454 + 0.884133i 0.999927 + 0.0121140i 0.00385609π0.00385609\pi
−0.489472 + 0.872019i 0.662811π0.662811\pi
920920 1521.00 2634.45i 0.0545064 0.0944078i
921921 −2220.49 + 3846.00i −0.0794437 + 0.137600i
922922 −33927.0 −1.21185
923923 0 0
924924 −1920.00 −0.0683586
925925 −8769.37 + 15189.0i −0.311714 + 0.539904i
926926 −7476.00 + 12948.8i −0.265310 + 0.459530i
927927 −2093.00 3625.18i −0.0741566 0.128443i
928928 25643.0 0.907083
929929 −3489.22 6043.50i −0.123227 0.213435i 0.797812 0.602907i 0.205991π-0.205991\pi
−0.921038 + 0.389472i 0.872658π0.872658\pi
930930 −467.654 810.000i −0.0164892 0.0285602i
931931 17261.6 0.607655
932932 14625.0 + 25331.2i 0.514011 + 0.890292i
933933 4914.00 8511.30i 0.172430 0.298657i
934934 −4728.50 + 8190.00i −0.165654 + 0.286922i
935935 2808.00 0.0982154
936936 0 0
937937 −38465.0 −1.34109 −0.670543 0.741871i 0.733939π-0.733939\pi
−0.670543 + 0.741871i 0.733939π0.733939\pi
938938 9436.21 16344.0i 0.328468 0.568924i
939939 518.000 897.202i 0.0180024 0.0311811i
940940 1305.00 + 2260.33i 0.0452813 + 0.0784295i
941941 4884.38 0.169210 0.0846049 0.996415i 0.473037π-0.473037\pi
0.0846049 + 0.996415i 0.473037π0.473037\pi
942942 2097.51 + 3633.00i 0.0725485 + 0.125658i
943943 10605.3 + 18369.0i 0.366233 + 0.634334i
944944 284.056 0.00979369
945945 −1200.00 2078.46i −0.0413079 0.0715475i
946946 −1248.00 + 2161.60i −0.0428922 + 0.0742914i
947947 −10882.5 + 18849.0i −0.373424 + 0.646790i −0.990090 0.140435i 0.955150π-0.955150\pi
0.616665 + 0.787225i 0.288483π0.288483\pi
948948 −12760.0 −0.437158
949949 0 0
950950 −24156.0 −0.824973
951951 −3916.17 + 6783.00i −0.133534 + 0.231287i
952952 18252.0 31613.4i 0.621377 1.07626i
953953 3237.00 + 5606.65i 0.110028 + 0.190574i 0.915781 0.401677i 0.131573π-0.131573\pi
−0.805753 + 0.592251i 0.798239π0.798239\pi
954954 3704.86 0.125733
955955 −2249.93 3897.00i −0.0762368 0.132046i
956956 −13458.0 23310.0i −0.455297 0.788598i
957957 −3907.51 −0.131987
958958 −2211.00 3829.56i −0.0745659 0.129152i
959959 −5868.00 + 10163.7i −0.197589 + 0.342234i
960960 531.740 921.000i 0.0178769 0.0309637i
961961 −5491.00 −0.184317
962962 0 0
963963 34638.0 1.15908
964964 −12293.2 + 21292.5i −0.410724 + 0.711395i
965965 967.500 1675.76i 0.0322745 0.0559011i
966966 1872.00 + 3242.40i 0.0623505 + 0.107994i
967967 7541.35 0.250789 0.125395 0.992107i 0.459980π-0.459980\pi
0.125395 + 0.992107i 0.459980π0.459980\pi
968968 12823.2 + 22210.5i 0.425779 + 0.737472i
969969 −13374.9 23166.0i −0.443409 0.768007i
970970 602.754 0.0199518
971971 −17499.0 30309.2i −0.578342 1.00172i −0.995670 0.0929611i 0.970367π-0.970367\pi
0.417328 0.908756i 0.362967π-0.362967\pi
972972 8855.00 15337.3i 0.292206 0.506116i
973973 −1635.06 + 2832.00i −0.0538720 + 0.0933091i
974974 −18756.0 −0.617024
975975 0 0
976976 145.000 0.00475547
977977 −12608.5 + 21838.5i −0.412877 + 0.715123i −0.995203 0.0978318i 0.968809π-0.968809\pi
0.582326 + 0.812955i 0.302143π0.302143\pi
978978 1740.00 3013.77i 0.0568907 0.0985375i
979979 6768.00 + 11722.5i 0.220946 + 0.382690i
980980 −1307.70 −0.0426254
981981 17847.1 + 30912.0i 0.580849 + 1.00606i
982982 −9862.30 17082.0i −0.320487 0.555100i
983983 56440.6 1.83131 0.915654 0.401967i 0.131673π-0.131673\pi
0.915654 + 0.401967i 0.131673π0.131673\pi
984984 6123.00 + 10605.3i 0.198368 + 0.343583i
985985 −1776.00 + 3076.12i −0.0574498 + 0.0995060i
986986 14286.8 24745.5i 0.461445 0.799247i
987987 −8352.00 −0.269349
988988 0 0
989989 −8112.00 −0.260816
990990 478.046 828.000i 0.0153468 0.0265814i
991991 −29641.0 + 51339.7i −0.950129 + 1.64567i −0.204987 + 0.978765i 0.565715π0.565715\pi
−0.745142 + 0.666906i 0.767618π0.767618\pi
992992 14175.0 + 24551.8i 0.453686 + 0.785808i
993993 −14909.5 −0.476474
994994 12678.6 + 21960.0i 0.404569 + 0.700733i
995995 2184.12 + 3783.00i 0.0695891 + 0.120532i
996996 7898.15 0.251268
997997 18855.5 + 32658.7i 0.598957 + 1.03742i 0.992975 + 0.118321i 0.0377511π0.0377511\pi
−0.394019 + 0.919102i 0.628916π0.628916\pi
998998 −15309.0 + 26516.0i −0.485569 + 0.841030i
999999 −7188.01 + 12450.0i −0.227646 + 0.394295i
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 169.4.c.h.22.2 4
13.2 odd 12 13.4.e.b.10.1 yes 2
13.3 even 3 inner 169.4.c.h.146.2 4
13.4 even 6 169.4.a.i.1.2 2
13.5 odd 4 169.4.e.a.147.1 2
13.6 odd 12 169.4.b.d.168.2 2
13.7 odd 12 169.4.b.d.168.1 2
13.8 odd 4 13.4.e.b.4.1 2
13.9 even 3 169.4.a.i.1.1 2
13.10 even 6 inner 169.4.c.h.146.1 4
13.11 odd 12 169.4.e.a.23.1 2
13.12 even 2 inner 169.4.c.h.22.1 4
39.2 even 12 117.4.q.a.10.1 2
39.8 even 4 117.4.q.a.82.1 2
39.17 odd 6 1521.4.a.o.1.1 2
39.35 odd 6 1521.4.a.o.1.2 2
52.15 even 12 208.4.w.b.49.1 2
52.47 even 4 208.4.w.b.17.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.e.b.4.1 2 13.8 odd 4
13.4.e.b.10.1 yes 2 13.2 odd 12
117.4.q.a.10.1 2 39.2 even 12
117.4.q.a.82.1 2 39.8 even 4
169.4.a.i.1.1 2 13.9 even 3
169.4.a.i.1.2 2 13.4 even 6
169.4.b.d.168.1 2 13.7 odd 12
169.4.b.d.168.2 2 13.6 odd 12
169.4.c.h.22.1 4 13.12 even 2 inner
169.4.c.h.22.2 4 1.1 even 1 trivial
169.4.c.h.146.1 4 13.10 even 6 inner
169.4.c.h.146.2 4 13.3 even 3 inner
169.4.e.a.23.1 2 13.11 odd 12
169.4.e.a.147.1 2 13.5 odd 4
208.4.w.b.17.1 2 52.47 even 4
208.4.w.b.49.1 2 52.15 even 12
1521.4.a.o.1.1 2 39.17 odd 6
1521.4.a.o.1.2 2 39.35 odd 6