Properties

Label 338.4.e.i.23.9
Level 338338
Weight 44
Character 338.23
Analytic conductor 19.94319.943
Analytic rank 00
Dimension 2424
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,4,Mod(23,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 338=2132 338 = 2 \cdot 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 338.e (of order 66, 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: 19.942645581919.9426455819
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 23.9
Character χ\chi == 338.23
Dual form 338.4.e.i.147.9

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+(1.732051.00000i)q2+(1.679082.90825i)q3+(2.000003.46410i)q4+6.80407iq5+(5.816493.35815i)q6+(13.4563+7.76902i)q78.00000iq8+(7.8614013.6163i)q9+(6.80407+11.7850i)q10+(16.9750+9.80052i)q1113.4326q12+31.0761q14+(19.787911.4246i)q15+(8.0000013.8564i)q16+(62.9859109.095i)q1731.4456iq18+(84.1839+48.6036i)q19+(23.5700+13.6081i)q2052.1791iq21+(19.6010+33.9500i)q22+(64.9251+112.454i)q23+(23.2660+13.4326i)q24+78.7047q25143.470q27+(53.825331.0761i)q28+(73.9704128.121i)q29+(22.849139.5758i)q30172.602iq31+(27.712816.0000i)q32+(57.0047+32.9117i)q33251.944iq34+(52.8609+91.5578i)q35+(31.445654.4654i)q36+(191.625110.635i)q37+194.414q38+54.4325q40+(24.3297+14.0468i)q41+(52.179190.3769i)q42+(180.884313.301i)q43+78.4042iq44+(92.6465+53.4895i)q45+(224.907+129.850i)q46456.486iq47+(26.8652+46.5319i)q48+(50.784887.9618i)q49+(136.32178.7047i)q50423.033q51643.067q53+(248.497+143.470i)q54+(66.6834115.499i)q55+(62.1521107.651i)q56326.437iq57+(256.241147.941i)q58+(269.267+155.461i)q5991.3964iq60+(405.728+702.742i)q61+(172.602298.956i)q62+(211.571122.151i)q6364.0000q64+131.647q66+(6.066113.50227i)q67+(251.944436.379i)q68+(218.028377.636i)q69+211.444iq70+(736.799+425.391i)q71+(108.93162.8912i)q72+1127.56iq73+(221.269383.249i)q74+(132.151228.893i)q75+(336.735194.414i)q76304.562q77+278.080q79+(94.279954.4325i)q80+(28.6389+49.6041i)q81+(28.0935+48.6594i)q82417.276iq83+(180.754104.358i)q84+(742.288+428.560i)q85723.537iq86+(248.404+430.249i)q87+(78.4042+135.800i)q88+(280.827162.136i)q89+213.958q90+519.401q92+(501.970+289.812i)q93+(456.486790.657i)q94+(330.702+572.793i)q95+107.461iq96+(71.0986+41.0488i)q97+(175.924101.570i)q98+308.183iq99+O(q100)q+(1.73205 - 1.00000i) q^{2} +(-1.67908 - 2.90825i) q^{3} +(2.00000 - 3.46410i) q^{4} +6.80407i q^{5} +(-5.81649 - 3.35815i) q^{6} +(13.4563 + 7.76902i) q^{7} -8.00000i q^{8} +(7.86140 - 13.6163i) q^{9} +(6.80407 + 11.7850i) q^{10} +(-16.9750 + 9.80052i) q^{11} -13.4326 q^{12} +31.0761 q^{14} +(19.7879 - 11.4246i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(62.9859 - 109.095i) q^{17} -31.4456i q^{18} +(84.1839 + 48.6036i) q^{19} +(23.5700 + 13.6081i) q^{20} -52.1791i q^{21} +(-19.6010 + 33.9500i) q^{22} +(64.9251 + 112.454i) q^{23} +(-23.2660 + 13.4326i) q^{24} +78.7047 q^{25} -143.470 q^{27} +(53.8253 - 31.0761i) q^{28} +(-73.9704 - 128.121i) q^{29} +(22.8491 - 39.5758i) q^{30} -172.602i q^{31} +(-27.7128 - 16.0000i) q^{32} +(57.0047 + 32.9117i) q^{33} -251.944i q^{34} +(-52.8609 + 91.5578i) q^{35} +(-31.4456 - 54.4654i) q^{36} +(191.625 - 110.635i) q^{37} +194.414 q^{38} +54.4325 q^{40} +(-24.3297 + 14.0468i) q^{41} +(-52.1791 - 90.3769i) q^{42} +(180.884 - 313.301i) q^{43} +78.4042i q^{44} +(92.6465 + 53.4895i) q^{45} +(224.907 + 129.850i) q^{46} -456.486i q^{47} +(-26.8652 + 46.5319i) q^{48} +(-50.7848 - 87.9618i) q^{49} +(136.321 - 78.7047i) q^{50} -423.033 q^{51} -643.067 q^{53} +(-248.497 + 143.470i) q^{54} +(-66.6834 - 115.499i) q^{55} +(62.1521 - 107.651i) q^{56} -326.437i q^{57} +(-256.241 - 147.941i) q^{58} +(269.267 + 155.461i) q^{59} -91.3964i q^{60} +(-405.728 + 702.742i) q^{61} +(-172.602 - 298.956i) q^{62} +(211.571 - 122.151i) q^{63} -64.0000 q^{64} +131.647 q^{66} +(6.06611 - 3.50227i) q^{67} +(-251.944 - 436.379i) q^{68} +(218.028 - 377.636i) q^{69} +211.444i q^{70} +(736.799 + 425.391i) q^{71} +(-108.931 - 62.8912i) q^{72} +1127.56i q^{73} +(221.269 - 383.249i) q^{74} +(-132.151 - 228.893i) q^{75} +(336.735 - 194.414i) q^{76} -304.562 q^{77} +278.080 q^{79} +(94.2799 - 54.4325i) q^{80} +(28.6389 + 49.6041i) q^{81} +(-28.0935 + 48.6594i) q^{82} -417.276i q^{83} +(-180.754 - 104.358i) q^{84} +(742.288 + 428.560i) q^{85} -723.537i q^{86} +(-248.404 + 430.249i) q^{87} +(78.4042 + 135.800i) q^{88} +(280.827 - 162.136i) q^{89} +213.958 q^{90} +519.401 q^{92} +(-501.970 + 289.812i) q^{93} +(-456.486 - 790.657i) q^{94} +(-330.702 + 572.793i) q^{95} +107.461i q^{96} +(71.0986 + 41.0488i) q^{97} +(-175.924 - 101.570i) q^{98} +308.183i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q18q3+48q4226q9+72q10144q12+200q14192q16+198q17148q22+534q231472q25+2676q27+238q29+472q301228q35+904q36+8186q95+O(q100) 24 q - 18 q^{3} + 48 q^{4} - 226 q^{9} + 72 q^{10} - 144 q^{12} + 200 q^{14} - 192 q^{16} + 198 q^{17} - 148 q^{22} + 534 q^{23} - 1472 q^{25} + 2676 q^{27} + 238 q^{29} + 472 q^{30} - 1228 q^{35} + 904 q^{36}+ \cdots - 8186 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/338Z)×\left(\mathbb{Z}/338\mathbb{Z}\right)^\times.

nn 171171
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\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 1.73205 1.00000i 0.612372 0.353553i
33 −1.67908 2.90825i −0.323139 0.559692i 0.657995 0.753022i 0.271405π-0.271405\pi
−0.981134 + 0.193330i 0.938071π0.938071\pi
44 2.00000 3.46410i 0.250000 0.433013i
55 6.80407i 0.608574i 0.952580 + 0.304287i 0.0984182π0.0984182\pi
−0.952580 + 0.304287i 0.901582π0.901582\pi
66 −5.81649 3.35815i −0.395762 0.228493i
77 13.4563 + 7.76902i 0.726574 + 0.419487i 0.817167 0.576400i 0.195543π-0.195543\pi
−0.0905938 + 0.995888i 0.528876π0.528876\pi
88 8.00000i 0.353553i
99 7.86140 13.6163i 0.291163 0.504309i
1010 6.80407 + 11.7850i 0.215163 + 0.372674i
1111 −16.9750 + 9.80052i −0.465287 + 0.268633i −0.714265 0.699876i 0.753239π-0.753239\pi
0.248978 + 0.968509i 0.419905π0.419905\pi
1212 −13.4326 −0.323139
1313 0 0
1414 31.0761 0.593245
1515 19.7879 11.4246i 0.340614 0.196654i
1616 −8.00000 13.8564i −0.125000 0.216506i
1717 62.9859 109.095i 0.898607 1.55643i 0.0693317 0.997594i 0.477913π-0.477913\pi
0.829276 0.558840i 0.188753π-0.188753\pi
1818 31.4456i 0.411767i
1919 84.1839 + 48.6036i 1.01648 + 0.586865i 0.913082 0.407776i 0.133695π-0.133695\pi
0.103397 + 0.994640i 0.467029π0.467029\pi
2020 23.5700 + 13.6081i 0.263520 + 0.152144i
2121 52.1791i 0.542210i
2222 −19.6010 + 33.9500i −0.189953 + 0.329007i
2323 64.9251 + 112.454i 0.588600 + 1.01949i 0.994416 + 0.105531i 0.0336542π0.0336542\pi
−0.405816 + 0.913955i 0.633012π0.633012\pi
2424 −23.2660 + 13.4326i −0.197881 + 0.114247i
2525 78.7047 0.629637
2626 0 0
2727 −143.470 −1.02262
2828 53.8253 31.0761i 0.363287 0.209744i
2929 −73.9704 128.121i −0.473654 0.820393i 0.525891 0.850552i 0.323732π-0.323732\pi
−0.999545 + 0.0301591i 0.990399π0.990399\pi
3030 22.8491 39.5758i 0.139055 0.240851i
3131 172.602i 1.00001i −0.866023 0.500004i 0.833332π-0.833332\pi
0.866023 0.500004i 0.166668π-0.166668\pi
3232 −27.7128 16.0000i −0.153093 0.0883883i
3333 57.0047 + 32.9117i 0.300704 + 0.173612i
3434 251.944i 1.27082i
3535 −52.8609 + 91.5578i −0.255289 + 0.442174i
3636 −31.4456 54.4654i −0.145581 0.252155i
3737 191.625 110.635i 0.851430 0.491573i −0.00970317 0.999953i 0.503089π-0.503089\pi
0.861133 + 0.508380i 0.169755π0.169755\pi
3838 194.414 0.829952
3939 0 0
4040 54.4325 0.215163
4141 −24.3297 + 14.0468i −0.0926746 + 0.0535057i −0.545621 0.838032i 0.683706π-0.683706\pi
0.452946 + 0.891538i 0.350373π0.350373\pi
4242 −52.1791 90.3769i −0.191700 0.332035i
4343 180.884 313.301i 0.641502 1.11111i −0.343596 0.939118i 0.611645π-0.611645\pi
0.985098 0.171996i 0.0550217π-0.0550217\pi
4444 78.4042i 0.268633i
4545 92.6465 + 53.4895i 0.306910 + 0.177194i
4646 224.907 + 129.850i 0.720885 + 0.416203i
4747 456.486i 1.41671i −0.705857 0.708354i 0.749438π-0.749438\pi
0.705857 0.708354i 0.250562π-0.250562\pi
4848 −26.8652 + 46.5319i −0.0807846 + 0.139923i
4949 −50.7848 87.9618i −0.148061 0.256448i
5050 136.321 78.7047i 0.385573 0.222610i
5151 −423.033 −1.16150
5252 0 0
5353 −643.067 −1.66664 −0.833321 0.552789i 0.813563π-0.813563\pi
−0.833321 + 0.552789i 0.813563π0.813563\pi
5454 −248.497 + 143.470i −0.626225 + 0.361551i
5555 −66.6834 115.499i −0.163483 0.283162i
5656 62.1521 107.651i 0.148311 0.256883i
5757 326.437i 0.758554i
5858 −256.241 147.941i −0.580105 0.334924i
5959 269.267 + 155.461i 0.594163 + 0.343040i 0.766742 0.641956i 0.221877π-0.221877\pi
−0.172579 + 0.984996i 0.555210π0.555210\pi
6060 91.3964i 0.196654i
6161 −405.728 + 702.742i −0.851610 + 1.47503i 0.0281456 + 0.999604i 0.491040π0.491040\pi
−0.879755 + 0.475427i 0.842294π0.842294\pi
6262 −172.602 298.956i −0.353556 0.612378i
6363 211.571 122.151i 0.423103 0.244278i
6464 −64.0000 −0.125000
6565 0 0
6666 131.647 0.245524
6767 6.06611 3.50227i 0.0110611 0.00638612i −0.494459 0.869201i 0.664634π-0.664634\pi
0.505520 + 0.862815i 0.331301π0.331301\pi
6868 −251.944 436.379i −0.449304 0.778217i
6969 218.028 377.636i 0.380399 0.658870i
7070 211.444i 0.361034i
7171 736.799 + 425.391i 1.23158 + 0.711051i 0.967358 0.253412i 0.0815528π-0.0815528\pi
0.264218 + 0.964463i 0.414886π0.414886\pi
7272 −108.931 62.8912i −0.178300 0.102942i
7373 1127.56i 1.80782i 0.427728 + 0.903908i 0.359314π0.359314\pi
−0.427728 + 0.903908i 0.640686π0.640686\pi
7474 221.269 383.249i 0.347595 0.602052i
7575 −132.151 228.893i −0.203460 0.352403i
7676 336.735 194.414i 0.508240 0.293432i
7777 −304.562 −0.450754
7878 0 0
7979 278.080 0.396031 0.198015 0.980199i 0.436550π-0.436550\pi
0.198015 + 0.980199i 0.436550π0.436550\pi
8080 94.2799 54.4325i 0.131760 0.0760718i
8181 28.6389 + 49.6041i 0.0392852 + 0.0680440i
8282 −28.0935 + 48.6594i −0.0378343 + 0.0655309i
8383 417.276i 0.551832i −0.961182 0.275916i 0.911019π-0.911019\pi
0.961182 0.275916i 0.0889811π-0.0889811\pi
8484 −180.754 104.358i −0.234784 0.135553i
8585 742.288 + 428.560i 0.947205 + 0.546869i
8686 723.537i 0.907221i
8787 −248.404 + 430.249i −0.306112 + 0.530201i
8888 78.4042 + 135.800i 0.0949763 + 0.164504i
8989 280.827 162.136i 0.334467 0.193105i −0.323355 0.946278i 0.604811π-0.604811\pi
0.657823 + 0.753173i 0.271478π0.271478\pi
9090 213.958 0.250591
9191 0 0
9292 519.401 0.588600
9393 −501.970 + 289.812i −0.559697 + 0.323141i
9494 −456.486 790.657i −0.500882 0.867553i
9595 −330.702 + 572.793i −0.357151 + 0.618603i
9696 107.461i 0.114247i
9797 71.0986 + 41.0488i 0.0744224 + 0.0429678i 0.536749 0.843742i 0.319652π-0.319652\pi
−0.462327 + 0.886709i 0.652985π0.652985\pi
9898 −175.924 101.570i −0.181336 0.104695i
9999 308.183i 0.312865i
100100 157.409 272.641i 0.157409 0.272641i
101101 358.261 + 620.526i 0.352953 + 0.611333i 0.986765 0.162154i 0.0518442π-0.0518442\pi
−0.633812 + 0.773487i 0.718511π0.718511\pi
102102 −732.714 + 423.033i −0.711270 + 0.410652i
103103 935.493 0.894921 0.447460 0.894304i 0.352329π-0.352329\pi
0.447460 + 0.894304i 0.352329π0.352329\pi
104104 0 0
105105 355.030 0.329975
106106 −1113.82 + 643.067i −1.02061 + 0.589247i
107107 599.382 + 1038.16i 0.541536 + 0.937969i 0.998816 + 0.0486457i 0.0154905π0.0154905\pi
−0.457280 + 0.889323i 0.651176π0.651176\pi
108108 −286.939 + 496.994i −0.255655 + 0.442808i
109109 119.517i 0.105024i 0.998620 + 0.0525120i 0.0167228π0.0167228\pi
−0.998620 + 0.0525120i 0.983277π0.983277\pi
110110 −230.998 133.367i −0.200225 0.115600i
111111 −643.505 371.528i −0.550260 0.317693i
112112 248.609i 0.209744i
113113 303.346 525.410i 0.252534 0.437402i −0.711689 0.702495i 0.752069π-0.752069\pi
0.964223 + 0.265093i 0.0854026π0.0854026\pi
114114 −326.437 565.405i −0.268189 0.464518i
115115 −765.141 + 441.754i −0.620433 + 0.358207i
116116 −591.764 −0.473654
117117 0 0
118118 621.846 0.485132
119119 1695.12 978.677i 1.30581 0.753909i
120120 −91.3964 158.303i −0.0695276 0.120425i
121121 −473.400 + 819.952i −0.355672 + 0.616042i
122122 1622.91i 1.20436i
123123 81.7029 + 47.1712i 0.0598935 + 0.0345795i
124124 −597.911 345.204i −0.433016 0.250002i
125125 1386.02i 0.991755i
126126 244.301 423.142i 0.172731 0.299179i
127127 928.966 + 1609.02i 0.649074 + 1.12423i 0.983344 + 0.181752i 0.0581769π0.0581769\pi
−0.334270 + 0.942477i 0.608490π0.608490\pi
128128 −110.851 + 64.0000i −0.0765466 + 0.0441942i
129129 −1214.87 −0.829176
130130 0 0
131131 −1867.72 −1.24568 −0.622838 0.782351i 0.714020π-0.714020\pi
−0.622838 + 0.782351i 0.714020π0.714020\pi
132132 228.019 131.647i 0.150352 0.0868058i
133133 755.204 + 1308.05i 0.492365 + 0.852801i
134134 7.00454 12.1322i 0.00451567 0.00782137i
135135 976.178i 0.622341i
136136 −872.758 503.887i −0.550282 0.317706i
137137 −456.522 263.573i −0.284695 0.164369i 0.350852 0.936431i 0.385892π-0.385892\pi
−0.635547 + 0.772062i 0.719225π0.719225\pi
138138 872.113i 0.537965i
139139 747.477 1294.67i 0.456116 0.790017i −0.542635 0.839969i 0.682573π-0.682573\pi
0.998752 + 0.0499516i 0.0159067π0.0159067\pi
140140 211.444 + 366.231i 0.127645 + 0.221087i
141141 −1327.57 + 766.475i −0.792921 + 0.457793i
142142 1701.56 1.00558
143143 0 0
144144 −251.565 −0.145581
145145 871.741 503.300i 0.499270 0.288254i
146146 1127.56 + 1952.99i 0.639159 + 1.10706i
147147 −170.543 + 295.389i −0.0956881 + 0.165737i
148148 885.077i 0.491573i
149149 −1505.71 869.319i −0.827867 0.477969i 0.0252549 0.999681i 0.491960π-0.491960\pi
−0.853122 + 0.521712i 0.825294π0.825294\pi
150150 −457.785 264.302i −0.249187 0.143868i
151151 1923.77i 1.03678i 0.855144 + 0.518391i 0.173469π0.173469\pi
−0.855144 + 0.518391i 0.826531π0.826531\pi
152152 388.829 673.471i 0.207488 0.359380i
153153 −990.315 1715.28i −0.523282 0.906352i
154154 −527.516 + 304.562i −0.276029 + 0.159365i
155155 1174.40 0.608579
156156 0 0
157157 275.052 0.139819 0.0699093 0.997553i 0.477729π-0.477729\pi
0.0699093 + 0.997553i 0.477729π0.477729\pi
158158 481.649 278.080i 0.242518 0.140018i
159159 1079.76 + 1870.20i 0.538556 + 0.932807i
160160 108.865 188.560i 0.0537909 0.0931685i
161161 2017.62i 0.987642i
162162 99.2082 + 57.2779i 0.0481144 + 0.0277788i
163163 −3353.63 1936.22i −1.61151 0.930407i −0.989020 0.147780i 0.952787π-0.952787\pi
−0.622491 0.782627i 0.713879π-0.713879\pi
164164 112.374i 0.0535057i
165165 −223.933 + 387.864i −0.105656 + 0.183001i
166166 −417.276 722.744i −0.195102 0.337926i
167167 616.965 356.205i 0.285881 0.165054i −0.350202 0.936674i 0.613887π-0.613887\pi
0.636083 + 0.771621i 0.280554π0.280554\pi
168168 −417.433 −0.191700
169169 0 0
170170 1714.24 0.773390
171171 1323.61 764.184i 0.591922 0.341746i
172172 −723.537 1253.20i −0.320751 0.555557i
173173 −405.847 + 702.947i −0.178358 + 0.308925i −0.941318 0.337520i 0.890412π-0.890412\pi
0.762960 + 0.646446i 0.223745π0.223745\pi
174174 993.617i 0.432907i
175175 1059.08 + 611.458i 0.457478 + 0.264125i
176176 271.600 + 156.808i 0.116322 + 0.0671584i
177177 1044.13i 0.443398i
178178 324.271 561.654i 0.136546 0.236504i
179179 431.918 + 748.105i 0.180353 + 0.312380i 0.942001 0.335611i 0.108943π-0.108943\pi
−0.761648 + 0.647991i 0.775609π0.775609\pi
180180 370.586 213.958i 0.153455 0.0885971i
181181 −1426.89 −0.585965 −0.292982 0.956118i 0.594648π-0.594648\pi
−0.292982 + 0.956118i 0.594648π0.594648\pi
182182 0 0
183183 2725.00 1.10075
184184 899.628 519.401i 0.360443 0.208102i
185185 752.765 + 1303.83i 0.299159 + 0.518158i
186186 −579.625 + 1003.94i −0.228495 + 0.395766i
187187 2469.18i 0.965584i
188188 −1581.31 912.972i −0.613453 0.354177i
189189 −1930.58 1114.62i −0.743009 0.428977i
190190 1322.81i 0.505087i
191191 392.215 679.337i 0.148585 0.257357i −0.782120 0.623128i 0.785862π-0.785862\pi
0.930705 + 0.365772i 0.119195π0.119195\pi
192192 107.461 + 186.128i 0.0403923 + 0.0699615i
193193 −2609.25 + 1506.45i −0.973149 + 0.561848i −0.900195 0.435487i 0.856576π-0.856576\pi
−0.0729543 + 0.997335i 0.523243π0.523243\pi
194194 164.195 0.0607656
195195 0 0
196196 −406.278 −0.148061
197197 −2363.64 + 1364.65i −0.854836 + 0.493540i −0.862280 0.506433i 0.830964π-0.830964\pi
0.00744371 + 0.999972i 0.497631π0.497631\pi
198198 308.183 + 533.789i 0.110614 + 0.191590i
199199 −480.802 + 832.774i −0.171272 + 0.296652i −0.938865 0.344286i 0.888121π-0.888121\pi
0.767593 + 0.640938i 0.221454π0.221454\pi
200200 629.637i 0.222610i
201201 −20.3709 11.7612i −0.00714853 0.00412720i
202202 1241.05 + 716.521i 0.432277 + 0.249576i
203203 2298.71i 0.794768i
204204 −846.065 + 1465.43i −0.290375 + 0.502944i
205205 −95.5751 165.541i −0.0325622 0.0563994i
206206 1620.32 935.493i 0.548025 0.316402i
207207 2041.61 0.685515
208208 0 0
209209 −1905.36 −0.630606
210210 614.930 355.030i 0.202068 0.116664i
211211 −1888.57 3271.10i −0.616183 1.06726i −0.990176 0.139829i 0.955345π-0.955345\pi
0.373992 0.927432i 0.377989π-0.377989\pi
212212 −1286.13 + 2227.65i −0.416661 + 0.721677i
213213 2857.06i 0.919072i
214214 2076.32 + 1198.76i 0.663244 + 0.382924i
215215 2131.72 + 1230.75i 0.676195 + 0.390401i
216216 1147.76i 0.361551i
217217 1340.95 2322.59i 0.419491 0.726580i
218218 119.517 + 207.009i 0.0371316 + 0.0643139i
219219 3279.21 1893.25i 1.01182 0.584175i
220220 −533.467 −0.163483
221221 0 0
222222 −1486.11 −0.449285
223223 −3781.34 + 2183.15i −1.13550 + 0.655582i −0.945313 0.326165i 0.894243π-0.894243\pi
−0.190189 + 0.981747i 0.560910π0.560910\pi
224224 −248.609 430.603i −0.0741556 0.128441i
225225 618.729 1071.67i 0.183327 0.317532i
226226 1213.38i 0.357137i
227227 1582.22 + 913.495i 0.462624 + 0.267096i 0.713147 0.701015i 0.247269π-0.247269\pi
−0.250523 + 0.968111i 0.580603π0.580603\pi
228228 −1130.81 652.873i −0.328464 0.189639i
229229 4376.52i 1.26292i 0.775409 + 0.631459i 0.217544π0.217544\pi
−0.775409 + 0.631459i 0.782456π0.782456\pi
230230 −883.509 + 1530.28i −0.253291 + 0.438712i
231231 511.382 + 885.740i 0.145656 + 0.252283i
232232 −1024.96 + 591.764i −0.290053 + 0.167462i
233233 −4723.89 −1.32821 −0.664104 0.747641i 0.731187π-0.731187\pi
−0.664104 + 0.747641i 0.731187π0.731187\pi
234234 0 0
235235 3105.96 0.862172
236236 1077.07 621.846i 0.297081 0.171520i
237237 −466.918 808.725i −0.127973 0.221655i
238238 1957.35 3390.24i 0.533094 0.923346i
239239 2312.19i 0.625788i 0.949788 + 0.312894i 0.101298π0.101298\pi
−0.949788 + 0.312894i 0.898702π0.898702\pi
240240 −316.606 182.793i −0.0851536 0.0491634i
241241 6190.00 + 3573.80i 1.65449 + 0.955223i 0.975191 + 0.221364i 0.0710510π0.0710510\pi
0.679303 + 0.733858i 0.262282π0.262282\pi
242242 1893.60i 0.502996i
243243 −1840.67 + 3188.13i −0.485921 + 0.841640i
244244 1622.91 + 2810.97i 0.425805 + 0.737515i
245245 598.498 345.543i 0.156068 0.0901058i
246246 188.685 0.0489028
247247 0 0
248248 −1380.82 −0.353556
249249 −1213.54 + 700.639i −0.308856 + 0.178318i
250250 1386.02 + 2400.66i 0.350638 + 0.607324i
251251 −1369.27 + 2371.64i −0.344332 + 0.596401i −0.985232 0.171224i 0.945228π-0.945228\pi
0.640900 + 0.767624i 0.278561π0.278561\pi
252252 977.206i 0.244278i
253253 −2204.21 1272.60i −0.547736 0.316236i
254254 3218.03 + 1857.93i 0.794950 + 0.458965i
255255 2878.34i 0.706858i
256256 −128.000 + 221.703i −0.0312500 + 0.0541266i
257257 −3028.18 5244.96i −0.734991 1.27304i −0.954727 0.297483i 0.903853π-0.903853\pi
0.219736 0.975559i 0.429481π-0.429481\pi
258258 −2104.22 + 1214.87i −0.507764 + 0.293158i
259259 3438.09 0.824835
260260 0 0
261261 −2326.05 −0.551642
262262 −3234.99 + 1867.72i −0.762817 + 0.440413i
263263 −2667.09 4619.54i −0.625323 1.08309i −0.988478 0.151362i 0.951634π-0.951634\pi
0.363156 0.931728i 0.381699π-0.381699\pi
264264 263.293 456.037i 0.0613810 0.106315i
265265 4375.47i 1.01428i
266266 2616.10 + 1510.41i 0.603021 + 0.348154i
267267 −943.060 544.476i −0.216159 0.124799i
268268 28.0181i 0.00638612i
269269 −309.630 + 536.295i −0.0701803 + 0.121556i −0.898980 0.437989i 0.855691π-0.855691\pi
0.828800 + 0.559545i 0.189024π0.189024\pi
270270 −976.178 1690.79i −0.220031 0.381104i
271271 −1134.37 + 654.928i −0.254273 + 0.146805i −0.621719 0.783240i 0.713566π-0.713566\pi
0.367446 + 0.930045i 0.380232π0.380232\pi
272272 −2015.55 −0.449304
273273 0 0
274274 −1054.29 −0.232453
275275 −1336.01 + 771.347i −0.292962 + 0.169142i
276276 −872.113 1510.54i −0.190199 0.329435i
277277 3291.31 5700.72i 0.713920 1.23655i −0.249454 0.968387i 0.580251π-0.580251\pi
0.963375 0.268159i 0.0864154π-0.0864154\pi
278278 2989.91i 0.645046i
279279 −2350.21 1356.89i −0.504313 0.291165i
280280 732.462 + 422.887i 0.156332 + 0.0902584i
281281 7406.25i 1.57231i −0.618028 0.786156i 0.712068π-0.712068\pi
0.618028 0.786156i 0.287932π-0.287932\pi
282282 −1532.95 + 2655.15i −0.323709 + 0.560680i
283283 1109.97 + 1922.53i 0.233149 + 0.403825i 0.958733 0.284308i 0.0917638π-0.0917638\pi
−0.725584 + 0.688133i 0.758430π0.758430\pi
284284 2947.20 1701.56i 0.615788 0.355526i
285285 2221.10 0.461637
286286 0 0
287287 −436.518 −0.0897799
288288 −435.723 + 251.565i −0.0891501 + 0.0514708i
289289 −5477.95 9488.08i −1.11499 1.93122i
290290 1006.60 1743.48i 0.203826 0.353037i
291291 275.696i 0.0555382i
292292 3905.97 + 2255.11i 0.782807 + 0.451954i
293293 1951.28 + 1126.57i 0.389062 + 0.224625i 0.681754 0.731582i 0.261218π-0.261218\pi
−0.292691 + 0.956207i 0.594551π0.594551\pi
294294 682.172i 0.135323i
295295 −1057.77 + 1832.11i −0.208765 + 0.361592i
296296 −885.077 1533.00i −0.173797 0.301026i
297297 2435.40 1406.08i 0.475812 0.274710i
298298 −3477.28 −0.675950
299299 0 0
300300 −1057.21 −0.203460
301301 4868.07 2810.58i 0.932197 0.538204i
302302 1923.77 + 3332.06i 0.366558 + 0.634897i
303303 1203.09 2083.82i 0.228105 0.395090i
304304 1555.31i 0.293432i
305305 −4781.50 2760.60i −0.897666 0.518268i
306306 −3430.55 1980.63i −0.640887 0.370017i
307307 6633.50i 1.23321i −0.787274 0.616603i 0.788509π-0.788509\pi
0.787274 0.616603i 0.211491π-0.211491\pi
308308 −609.123 + 1055.03i −0.112688 + 0.195182i
309309 −1570.76 2720.64i −0.289183 0.500880i
310310 2034.11 1174.40i 0.372677 0.215165i
311311 −815.823 −0.148749 −0.0743747 0.997230i 0.523696π-0.523696\pi
−0.0743747 + 0.997230i 0.523696π0.523696\pi
312312 0 0
313313 6169.43 1.11411 0.557055 0.830475i 0.311931π-0.311931\pi
0.557055 + 0.830475i 0.311931π0.311931\pi
314314 476.403 275.052i 0.0856210 0.0494333i
315315 831.122 + 1439.54i 0.148662 + 0.257489i
316316 556.160 963.297i 0.0990077 0.171486i
317317 8846.56i 1.56742i 0.621126 + 0.783711i 0.286676π0.286676\pi
−0.621126 + 0.783711i 0.713324π0.713324\pi
318318 3740.39 + 2159.52i 0.659594 + 0.380817i
319319 2511.30 + 1449.90i 0.440770 + 0.254479i
320320 435.460i 0.0760718i
321321 2012.82 3486.30i 0.349983 0.606188i
322322 2017.62 + 3494.61i 0.349184 + 0.604805i
323323 10604.8 6122.68i 1.82683 1.05472i
324324 229.111 0.0392852
325325 0 0
326326 −7744.87 −1.31579
327327 347.584 200.678i 0.0587812 0.0339373i
328328 112.374 + 194.638i 0.0189171 + 0.0327654i
329329 3546.45 6142.63i 0.594292 1.02934i
330330 895.732i 0.149420i
331331 8236.93 + 4755.60i 1.36780 + 0.789701i 0.990647 0.136449i 0.0435688π-0.0435688\pi
0.377156 + 0.926150i 0.376902π0.376902\pi
332332 −1445.49 834.553i −0.238950 0.137958i
333333 3478.97i 0.572512i
334334 712.409 1233.93i 0.116710 0.202148i
335335 23.8297 + 41.2742i 0.00388643 + 0.00673149i
336336 −723.015 + 417.433i −0.117392 + 0.0677763i
337337 4745.81 0.767124 0.383562 0.923515i 0.374697π-0.374697\pi
0.383562 + 0.923515i 0.374697π0.374697\pi
338338 0 0
339339 −2037.36 −0.326414
340340 2969.15 1714.24i 0.473603 0.273435i
341341 1691.59 + 2929.92i 0.268636 + 0.465291i
342342 1528.37 2647.21i 0.241651 0.418552i
343343 6907.74i 1.08741i
344344 −2506.40 1447.07i −0.392838 0.226805i
345345 2569.46 + 1483.48i 0.400972 + 0.231501i
346346 1623.39i 0.252237i
347347 −4692.18 + 8127.10i −0.725906 + 1.25731i 0.232693 + 0.972550i 0.425246π0.425246\pi
−0.958600 + 0.284757i 0.908087π0.908087\pi
348348 993.617 + 1720.99i 0.153056 + 0.265101i
349349 −8063.42 + 4655.42i −1.23675 + 0.714036i −0.968428 0.249294i 0.919802π-0.919802\pi
−0.268319 + 0.963330i 0.586468π0.586468\pi
350350 2445.83 0.373529
351351 0 0
352352 627.233 0.0949763
353353 1066.95 616.005i 0.160873 0.0928800i −0.417402 0.908722i 0.637059π-0.637059\pi
0.578275 + 0.815842i 0.303726π0.303726\pi
354354 −1044.13 1808.48i −0.156765 0.271525i
355355 −2894.39 + 5013.23i −0.432727 + 0.749506i
356356 1297.08i 0.193105i
357357 −5692.47 3286.55i −0.843914 0.487234i
358358 1496.21 + 863.837i 0.220886 + 0.127528i
359359 6179.13i 0.908417i −0.890895 0.454209i 0.849922π-0.849922\pi
0.890895 0.454209i 0.150078π-0.150078\pi
360360 427.916 741.172i 0.0626476 0.108509i
361361 1295.12 + 2243.21i 0.188820 + 0.327046i
362362 −2471.44 + 1426.89i −0.358829 + 0.207170i
363363 3179.50 0.459725
364364 0 0
365365 −7671.97 −1.10019
366366 4719.83 2725.00i 0.674070 0.389174i
367367 235.037 + 407.095i 0.0334300 + 0.0579025i 0.882256 0.470769i 0.156024π-0.156024\pi
−0.848826 + 0.528672i 0.822690π0.822690\pi
368368 1038.80 1799.26i 0.147150 0.254871i
369369 441.709i 0.0623156i
370370 2607.65 + 1505.53i 0.366393 + 0.211537i
371371 −8653.32 4996.00i −1.21094 0.699135i
372372 2318.50i 0.323141i
373373 2559.15 4432.59i 0.355249 0.615310i −0.631911 0.775041i 0.717729π-0.717729\pi
0.987161 + 0.159731i 0.0510626π0.0510626\pi
374374 2469.18 + 4276.74i 0.341386 + 0.591297i
375375 4030.89 2327.23i 0.555078 0.320474i
376376 −3651.89 −0.500882
377377 0 0
378378 −4458.48 −0.606665
379379 −428.638 + 247.474i −0.0580940 + 0.0335406i −0.528766 0.848768i 0.677345π-0.677345\pi
0.470672 + 0.882308i 0.344012π0.344012\pi
380380 1322.81 + 2291.17i 0.178575 + 0.309302i
381381 3119.61 5403.33i 0.419482 0.726564i
382382 1568.86i 0.210131i
383383 3727.82 + 2152.26i 0.497343 + 0.287141i 0.727616 0.685985i 0.240628π-0.240628\pi
−0.230272 + 0.973126i 0.573962π0.573962\pi
384384 372.256 + 214.922i 0.0494703 + 0.0285617i
385385 2072.26i 0.274317i
386386 −3012.90 + 5218.50i −0.397286 + 0.688120i
387387 −2844.01 4925.96i −0.373563 0.647030i
388388 284.394 164.195i 0.0372112 0.0214839i
389389 −5599.48 −0.729832 −0.364916 0.931040i 0.618902π-0.618902\pi
−0.364916 + 0.931040i 0.618902π0.618902\pi
390390 0 0
391391 16357.5 2.11568
392392 −703.694 + 406.278i −0.0906682 + 0.0523473i
393393 3136.05 + 5431.79i 0.402526 + 0.697195i
394394 −2729.30 + 4727.29i −0.348985 + 0.604460i
395395 1892.07i 0.241014i
396396 1067.58 + 616.367i 0.135474 + 0.0782161i
397397 8493.19 + 4903.55i 1.07371 + 0.619904i 0.929192 0.369598i 0.120505π-0.120505\pi
0.144514 + 0.989503i 0.453838π0.453838\pi
398398 1923.21i 0.242215i
399399 2536.09 4392.64i 0.318204 0.551145i
400400 −629.637 1090.56i −0.0787047 0.136321i
401401 −12694.6 + 7329.22i −1.58089 + 0.912728i −0.586161 + 0.810194i 0.699362π0.699362\pi
−0.994730 + 0.102534i 0.967305π0.967305\pi
402402 −47.0446 −0.00583675
403403 0 0
404404 2866.08 0.352953
405405 −337.509 + 194.861i −0.0414098 + 0.0239080i
406406 −2298.71 3981.48i −0.280993 0.486694i
407407 −2168.55 + 3756.04i −0.264106 + 0.457445i
408408 3384.26i 0.410652i
409409 −9253.81 5342.69i −1.11876 0.645914i −0.177673 0.984090i 0.556857π-0.556857\pi
−0.941083 + 0.338175i 0.890190π0.890190\pi
410410 −331.082 191.150i −0.0398804 0.0230250i
411411 1770.24i 0.212456i
412412 1870.99 3240.64i 0.223730 0.387512i
413413 2415.57 + 4183.88i 0.287802 + 0.498488i
414414 3536.17 2041.61i 0.419790 0.242366i
415415 2839.18 0.335830
416416 0 0
417417 −5020.29 −0.589555
418418 −3300.18 + 1905.36i −0.386166 + 0.222953i
419419 −3205.07 5551.34i −0.373694 0.647257i 0.616437 0.787405i 0.288576π-0.288576\pi
−0.990131 + 0.140147i 0.955242π0.955242\pi
420420 710.060 1229.86i 0.0824938 0.142883i
421421 2672.97i 0.309436i −0.987959 0.154718i 0.950553π-0.950553\pi
0.987959 0.154718i 0.0494469π-0.0494469\pi
422422 −6542.21 3777.14i −0.754667 0.435707i
423423 −6215.67 3588.62i −0.714459 0.412493i
424424 5144.53i 0.589247i
425425 4957.28 8586.27i 0.565797 0.979989i
426426 −2857.06 4948.57i −0.324941 0.562814i
427427 −10919.2 + 6304.22i −1.23751 + 0.714479i
428428 4795.05 0.541536
429429 0 0
430430 4922.99 0.552111
431431 −4482.32 + 2587.87i −0.500941 + 0.289218i −0.729102 0.684405i 0.760062π-0.760062\pi
0.228161 + 0.973623i 0.426729π0.426729\pi
432432 1147.76 + 1987.98i 0.127828 + 0.221404i
433433 −2085.98 + 3613.02i −0.231515 + 0.400995i −0.958254 0.285918i 0.907701π-0.907701\pi
0.726739 + 0.686913i 0.241035π0.241035\pi
434434 5363.80i 0.593250i
435435 −2927.44 1690.16i −0.322667 0.186292i
436436 414.018 + 239.033i 0.0454768 + 0.0262560i
437437 12622.4i 1.38172i
438438 3786.51 6558.43i 0.413074 0.715465i
439439 5332.27 + 9235.77i 0.579717 + 1.00410i 0.995512 + 0.0946401i 0.0301700π0.0301700\pi
−0.415795 + 0.909458i 0.636497π0.636497\pi
440440 −923.992 + 533.467i −0.100113 + 0.0578001i
441441 −1596.96 −0.172439
442442 0 0
443443 2122.16 0.227600 0.113800 0.993504i 0.463698π-0.463698\pi
0.113800 + 0.993504i 0.463698π0.463698\pi
444444 −2574.02 + 1486.11i −0.275130 + 0.158846i
445445 1103.18 + 1910.77i 0.117519 + 0.203548i
446446 −4366.31 + 7562.67i −0.463567 + 0.802921i
447447 5838.62i 0.617801i
448448 −861.205 497.217i −0.0908217 0.0524359i
449449 −13237.6 7642.71i −1.39136 0.803300i −0.397891 0.917433i 0.630258π-0.630258\pi
−0.993466 + 0.114132i 0.963591π0.963591\pi
450450 2474.92i 0.259264i
451451 275.331 476.887i 0.0287469 0.0497910i
452452 −1213.38 2101.64i −0.126267 0.218701i
453453 5594.79 3230.16i 0.580279 0.335024i
454454 3653.98 0.377731
455455 0 0
456456 −2611.49 −0.268189
457457 −7390.60 + 4266.96i −0.756494 + 0.436762i −0.828035 0.560676i 0.810541π-0.810541\pi
0.0715418 + 0.997438i 0.477208π0.477208\pi
458458 4376.52 + 7580.35i 0.446509 + 0.773376i
459459 −9036.57 + 15651.8i −0.918935 + 1.59164i
460460 3534.04i 0.358207i
461461 5375.22 + 3103.39i 0.543057 + 0.313534i 0.746317 0.665591i 0.231820π-0.231820\pi
−0.203260 + 0.979125i 0.565154π0.565154\pi
462462 1771.48 + 1022.76i 0.178391 + 0.102994i
463463 14278.3i 1.43319i 0.697487 + 0.716597i 0.254302π0.254302\pi
−0.697487 + 0.716597i 0.745698π0.745698\pi
464464 −1183.53 + 2049.93i −0.118414 + 0.205098i
465465 −1971.90 3415.43i −0.196655 0.340617i
466466 −8182.02 + 4723.89i −0.813357 + 0.469592i
467467 1787.57 0.177129 0.0885643 0.996070i 0.471772π-0.471772\pi
0.0885643 + 0.996070i 0.471772π0.471772\pi
468468 0 0
469469 108.837 0.0107156
470470 5379.68 3105.96i 0.527971 0.304824i
471471 −461.833 799.918i −0.0451807 0.0782553i
472472 1243.69 2154.14i 0.121283 0.210068i
473473 7091.04i 0.689315i
474474 −1617.45 933.835i −0.156734 0.0904905i
475475 6625.66 + 3825.33i 0.640013 + 0.369512i
476476 7829.42i 0.753909i
477477 −5055.41 + 8756.22i −0.485264 + 0.840503i
478478 2312.19 + 4004.83i 0.221249 + 0.383215i
479479 11895.4 6867.79i 1.13468 0.655109i 0.189574 0.981866i 0.439289π-0.439289\pi
0.945108 + 0.326757i 0.105956π0.105956\pi
480480 −731.171 −0.0695276
481481 0 0
482482 14295.2 1.35089
483483 5867.72 3387.73i 0.552776 0.319145i
484484 1893.60 + 3279.81i 0.177836 + 0.308021i
485485 −279.299 + 483.760i −0.0261491 + 0.0452915i
486486 7362.67i 0.687197i
487487 14738.9 + 8509.51i 1.37142 + 0.791792i 0.991107 0.133064i 0.0424816π-0.0424816\pi
0.380317 + 0.924856i 0.375815π0.375815\pi
488488 5621.94 + 3245.83i 0.521502 + 0.301089i
489489 13004.2i 1.20260i
490490 691.086 1197.00i 0.0637144 0.110357i
491491 −6821.33 11814.9i −0.626970 1.08594i −0.988156 0.153451i 0.950961π-0.950961\pi
0.361186 0.932494i 0.382372π-0.382372\pi
492492 326.811 188.685i 0.0299467 0.0172898i
493493 −18636.4 −1.70252
494494 0 0
495495 −2096.90 −0.190401
496496 −2391.65 + 1380.82i −0.216508 + 0.125001i
497497 6609.74 + 11448.4i 0.596554 + 1.03326i
498498 −1401.28 + 2427.08i −0.126090 + 0.218394i
499499 4507.63i 0.404387i 0.979346 + 0.202194i 0.0648070π0.0648070\pi
−0.979346 + 0.202194i 0.935193π0.935193\pi
500500 4801.31 + 2772.04i 0.429443 + 0.247939i
501501 −2071.86 1196.19i −0.184758 0.106670i
502502 5477.07i 0.486959i
503503 4794.70 8304.67i 0.425020 0.736157i −0.571402 0.820670i 0.693600π-0.693600\pi
0.996422 + 0.0845135i 0.0269336π0.0269336\pi
504504 −977.206 1692.57i −0.0863655 0.149589i
505505 −4222.10 + 2437.63i −0.372041 + 0.214798i
506506 −5090.40 −0.447225
507507 0 0
508508 7431.73 0.649074
509509 8997.81 5194.89i 0.783539 0.452376i −0.0541444 0.998533i 0.517243π-0.517243\pi
0.837683 + 0.546157i 0.183910π0.183910\pi
510510 −2878.34 4985.44i −0.249912 0.432860i
511511 −8760.01 + 15172.8i −0.758356 + 1.31351i
512512 512.000i 0.0441942i
513513 −12077.8 6973.14i −1.03947 0.600140i
514514 −10489.9 6056.36i −0.900177 0.519717i
515515 6365.15i 0.544626i
516516 −2429.75 + 4208.45i −0.207294 + 0.359044i
517517 4473.80 + 7748.85i 0.380575 + 0.659176i
518518 5954.94 3438.09i 0.505106 0.291623i
519519 2725.79 0.230538
520520 0 0
521521 −3202.79 −0.269322 −0.134661 0.990892i 0.542995π-0.542995\pi
−0.134661 + 0.990892i 0.542995π0.542995\pi
522522 −4028.83 + 2326.05i −0.337810 + 0.195035i
523523 3828.77 + 6631.62i 0.320115 + 0.554456i 0.980512 0.196461i 0.0629450π-0.0629450\pi
−0.660396 + 0.750917i 0.729612π0.729612\pi
524524 −3735.44 + 6469.97i −0.311419 + 0.539393i
525525 4106.74i 0.341396i
526526 −9239.07 5334.18i −0.765861 0.442170i
527527 −18830.0 10871.5i −1.55645 0.898615i
528528 1053.17i 0.0868058i
529529 −2347.03 + 4065.17i −0.192901 + 0.334114i
530530 −4375.47 7578.54i −0.358600 0.621114i
531531 4233.63 2444.29i 0.345996 0.199761i
532532 6041.63 0.492365
533533 0 0
534534 −2177.90 −0.176493
535535 −7063.70 + 4078.23i −0.570823 + 0.329565i
536536 −28.0181 48.5288i −0.00225783 0.00391068i
537537 1450.45 2512.25i 0.116558 0.201884i
538538 1238.52i 0.0992499i
539539 1724.14 + 995.434i 0.137781 + 0.0795480i
540540 −3381.58 1952.36i −0.269481 0.155585i
541541 6536.41i 0.519450i 0.965683 + 0.259725i 0.0836319π0.0836319\pi
−0.965683 + 0.259725i 0.916368π0.916368\pi
542542 −1309.86 + 2268.74i −0.103807 + 0.179798i
543543 2395.85 + 4149.74i 0.189348 + 0.327960i
544544 −3491.03 + 2015.55i −0.275141 + 0.158853i
545545 −813.200 −0.0639149
546546 0 0
547547 −2020.69 −0.157950 −0.0789748 0.996877i 0.525165π-0.525165\pi
−0.0789748 + 0.996877i 0.525165π0.525165\pi
548548 −1826.09 + 1054.29i −0.142348 + 0.0821845i
549549 6379.19 + 11049.1i 0.495914 + 0.858949i
550550 −1542.69 + 2672.02i −0.119601 + 0.207155i
551551 14380.9i 1.11188i
552552 −3021.09 1744.23i −0.232946 0.134491i
553553 3741.94 + 2160.41i 0.287746 + 0.166130i
554554 13165.3i 1.00964i
555555 2527.90 4378.45i 0.193339 0.334874i
556556 −2989.91 5178.67i −0.228058 0.395008i
557557 −8698.31 + 5021.97i −0.661686 + 0.382025i −0.792919 0.609327i 0.791440π-0.791440\pi
0.131233 + 0.991352i 0.458106π0.458106\pi
558558 −5427.58 −0.411770
559559 0 0
560560 1691.55 0.127645
561561 7180.98 4145.94i 0.540430 0.312017i
562562 −7406.25 12828.0i −0.555896 0.962841i
563563 4184.05 7246.99i 0.313209 0.542494i −0.665846 0.746089i 0.731929π-0.731929\pi
0.979055 + 0.203595i 0.0652626π0.0652626\pi
564564 6131.80i 0.457793i
565565 3574.93 + 2063.98i 0.266192 + 0.153686i
566566 3845.06 + 2219.95i 0.285548 + 0.164861i
567567 889.985i 0.0659186i
568568 3403.13 5894.39i 0.251395 0.435428i
569569 −7049.80 12210.6i −0.519408 0.899640i −0.999746 0.0225569i 0.992819π-0.992819\pi
0.480338 0.877084i 0.340514π-0.340514\pi
570570 3847.05 2221.10i 0.282693 0.163213i
571571 7703.05 0.564558 0.282279 0.959332i 0.408910π-0.408910\pi
0.282279 + 0.959332i 0.408910π0.408910\pi
572572 0 0
573573 −2634.24 −0.192054
574574 −756.071 + 436.518i −0.0549788 + 0.0317420i
575575 5109.91 + 8850.62i 0.370605 + 0.641907i
576576 −503.130 + 871.446i −0.0363954 + 0.0630386i
577577 14074.3i 1.01546i 0.861517 + 0.507729i 0.169515π0.169515\pi
−0.861517 + 0.507729i 0.830485π0.830485\pi
578578 −18976.2 10955.9i −1.36558 0.788417i
579579 8762.26 + 5058.89i 0.628924 + 0.363109i
580580 4026.40i 0.288254i
581581 3241.83 5615.01i 0.231486 0.400946i
582582 −275.696 477.520i −0.0196357 0.0340100i
583583 10916.1 6302.39i 0.775467 0.447716i
584584 9020.45 0.639159
585585 0 0
586586 4506.30 0.317668
587587 3806.69 2197.79i 0.267664 0.154536i −0.360162 0.932890i 0.617278π-0.617278\pi
0.627826 + 0.778354i 0.283945π0.283945\pi
588588 682.172 + 1181.56i 0.0478441 + 0.0828684i
589589 8389.08 14530.3i 0.586869 1.01649i
590590 4231.08i 0.295239i
591591 7937.48 + 4582.71i 0.552461 + 0.318963i
592592 −3066.00 1770.15i −0.212857 0.122893i
593593 9239.06i 0.639802i −0.947451 0.319901i 0.896350π-0.896350\pi
0.947451 0.319901i 0.103650π-0.103650\pi
594594 2812.16 4870.80i 0.194249 0.336450i
595595 6658.98 + 11533.7i 0.458810 + 0.794681i
596596 −6022.82 + 3477.28i −0.413933 + 0.238985i
597597 3229.21 0.221378
598598 0 0
599599 −15261.0 −1.04098 −0.520492 0.853867i 0.674251π-0.674251\pi
−0.520492 + 0.853867i 0.674251π0.674251\pi
600600 −1831.14 + 1057.21i −0.124593 + 0.0719340i
601601 −8195.48 14195.0i −0.556241 0.963437i −0.997806 0.0662077i 0.978910π-0.978910\pi
0.441565 0.897229i 0.354423π-0.354423\pi
602602 5621.17 9736.15i 0.380568 0.659162i
603603 110.131i 0.00743761i
604604 6664.13 + 3847.54i 0.448940 + 0.259195i
605605 −5579.01 3221.04i −0.374907 0.216453i
606606 4812.38i 0.322590i
607607 −7031.79 + 12179.4i −0.470200 + 0.814411i −0.999419 0.0340744i 0.989152π-0.989152\pi
0.529219 + 0.848485i 0.322485π0.322485\pi
608608 −1555.31 2693.88i −0.103744 0.179690i
609609 −6685.22 + 3859.71i −0.444825 + 0.256820i
610610 −11042.4 −0.732941
611611 0 0
612612 −7922.52 −0.523282
613613 −6391.17 + 3689.94i −0.421104 + 0.243125i −0.695550 0.718478i 0.744839π-0.744839\pi
0.274445 + 0.961603i 0.411506π0.411506\pi
614614 −6633.50 11489.6i −0.436004 0.755181i
615615 −320.956 + 555.912i −0.0210442 + 0.0364496i
616616 2436.49i 0.159365i
617617 −9868.51 5697.59i −0.643908 0.371761i 0.142210 0.989836i 0.454579π-0.454579\pi
−0.786118 + 0.618076i 0.787912π0.787912\pi
618618 −5441.29 3141.53i −0.354176 0.204483i
619619 5223.75i 0.339192i 0.985514 + 0.169596i 0.0542464π0.0542464\pi
−0.985514 + 0.169596i 0.945754π0.945754\pi
620620 2348.79 4068.23i 0.152145 0.263523i
621621 −9314.78 16133.7i −0.601915 1.04255i
622622 −1413.05 + 815.823i −0.0910901 + 0.0525909i
623623 5038.53 0.324020
624624 0 0
625625 407.511 0.0260807
626626 10685.8 6169.43i 0.682251 0.393898i
627627 3199.25 + 5541.26i 0.203773 + 0.352945i
628628 550.103 952.807i 0.0349546 0.0605432i
629629 27873.7i 1.76693i
630630 2879.09 + 1662.24i 0.182072 + 0.105120i
631631 16565.8 + 9564.25i 1.04512 + 0.603402i 0.921280 0.388900i 0.127145π-0.127145\pi
0.123843 + 0.992302i 0.460478π0.460478\pi
632632 2224.64i 0.140018i
633633 −6342.12 + 10984.9i −0.398225 + 0.689746i
634634 8846.56 + 15322.7i 0.554167 + 0.959846i
635635 −10947.9 + 6320.75i −0.684177 + 0.395010i
636636 8638.07 0.538556
637637 0 0
638638 5799.59 0.359887
639639 11584.5 6688.34i 0.717179 0.414064i
640640 −435.460 754.239i −0.0268954 0.0465843i
641641 930.204 1611.16i 0.0573180 0.0992777i −0.835943 0.548817i 0.815078π-0.815078\pi
0.893261 + 0.449539i 0.148412π0.148412\pi
642642 8051.26i 0.494950i
643643 8284.94 + 4783.31i 0.508128 + 0.293368i 0.732064 0.681236i 0.238557π-0.238557\pi
−0.223936 + 0.974604i 0.571891π0.571891\pi
644644 6989.23 + 4035.23i 0.427662 + 0.246911i
645645 8266.08i 0.504615i
646646 12245.4 21209.6i 0.745801 1.29176i
647647 11478.5 + 19881.3i 0.697473 + 1.20806i 0.969340 + 0.245724i 0.0790256π0.0790256\pi
−0.271867 + 0.962335i 0.587641π0.587641\pi
648648 396.833 229.111i 0.0240572 0.0138894i
649649 −6094.41 −0.368608
650650 0 0
651651 −9006.22 −0.542215
652652 −13414.5 + 7744.87i −0.805756 + 0.465203i
653653 2049.77 + 3550.30i 0.122838 + 0.212763i 0.920886 0.389832i 0.127467π-0.127467\pi
−0.798047 + 0.602595i 0.794134π0.794134\pi
654654 401.356 695.168i 0.0239973 0.0415646i
655655 12708.1i 0.758086i
656656 389.275 + 224.748i 0.0231687 + 0.0133764i
657657 15353.2 + 8864.17i 0.911698 + 0.526369i
658658 14185.8i 0.840455i
659659 −14231.6 + 24649.9i −0.841252 + 1.45709i 0.0475845 + 0.998867i 0.484848π0.484848\pi
−0.888837 + 0.458224i 0.848486π0.848486\pi
660660 895.732 + 1551.45i 0.0528278 + 0.0915004i
661661 −7094.82 + 4096.20i −0.417483 + 0.241034i −0.694000 0.719975i 0.744153π-0.744153\pi
0.276517 + 0.961009i 0.410820π0.410820\pi
662662 19022.4 1.11681
663663 0 0
664664 −3338.21 −0.195102
665665 −8900.07 + 5138.46i −0.518992 + 0.299640i
666666 −3478.97 6025.75i −0.202413 0.350590i
667667 9605.07 16636.5i 0.557586 0.965767i
668668 2849.64i 0.165054i
669669 12698.3 + 7331.37i 0.733849 + 0.423688i
670670 82.5484 + 47.6593i 0.00475988 + 0.00274812i
671671 15905.4i 0.915083i
672672 −834.866 + 1446.03i −0.0479251 + 0.0830086i
673673 17137.1 + 29682.2i 0.981553 + 1.70010i 0.656354 + 0.754453i 0.272098π0.272098\pi
0.325199 + 0.945646i 0.394569π0.394569\pi
674674 8219.99 4745.81i 0.469766 0.271219i
675675 −11291.7 −0.643880
676676 0 0
677677 −11531.2 −0.654623 −0.327311 0.944917i 0.606143π-0.606143\pi
−0.327311 + 0.944917i 0.606143π0.606143\pi
678678 −3528.82 + 2037.36i −0.199887 + 0.115405i
679679 637.817 + 1104.73i 0.0360489 + 0.0624385i
680680 3428.48 5938.30i 0.193347 0.334888i
681681 6135.32i 0.345236i
682682 5859.84 + 3383.18i 0.329010 + 0.189954i
683683 −6534.72 3772.82i −0.366097 0.211366i 0.305655 0.952142i 0.401125π-0.401125\pi
−0.671752 + 0.740776i 0.734458π0.734458\pi
684684 6113.48i 0.341746i
685685 1793.37 3106.20i 0.100031 0.173258i
686686 −6907.74 11964.5i −0.384459 0.665902i
687687 12728.0 7348.51i 0.706846 0.408098i
688688 −5788.29 −0.320751
689689 0 0
690690 5933.92 0.327392
691691 29859.0 17239.1i 1.64384 0.949069i 0.664383 0.747392i 0.268694π-0.268694\pi
0.979452 0.201677i 0.0646391π-0.0646391\pi
692692 1623.39 + 2811.79i 0.0891791 + 0.154463i
693693 −2394.28 + 4147.02i −0.131243 + 0.227319i
694694 18768.7i 1.02659i
695695 8809.01 + 5085.88i 0.480784 + 0.277581i
696696 3441.99 + 1987.23i 0.187454 + 0.108227i
697697 3538.99i 0.192323i
698698 −9310.83 + 16126.8i −0.504900 + 0.874512i
699699 7931.77 + 13738.2i 0.429195 + 0.743387i
700700 4236.30 2445.83i 0.228739 0.132063i
701701 −1042.89 −0.0561905 −0.0280952 0.999605i 0.508944π-0.508944\pi
−0.0280952 + 0.999605i 0.508944π0.508944\pi
702702 0 0
703703 21508.9 1.15395
704704 1086.40 627.233i 0.0581609 0.0335792i
705705 −5215.15 9032.90i −0.278601 0.482551i
706706 1232.01 2133.91i 0.0656761 0.113754i
707707 11133.3i 0.592238i
708708 −3616.96 2088.25i −0.191997 0.110849i
709709 16263.8 + 9389.88i 0.861492 + 0.497383i 0.864512 0.502613i 0.167628π-0.167628\pi
−0.00301951 + 0.999995i 0.500961π0.500961\pi
710710 11577.6i 0.611969i
711711 2186.10 3786.43i 0.115310 0.199722i
712712 −1297.08 2246.62i −0.0682729 0.118252i
713713 19409.7 11206.2i 1.01949 0.588605i
714714 −13146.2 −0.689053
715715 0 0
716716 3455.35 0.180353
717717 6724.42 3882.35i 0.350249 0.202216i
718718 −6179.13 10702.6i −0.321174 0.556290i
719719 17256.2 29888.6i 0.895059 1.55029i 0.0613275 0.998118i 0.480467π-0.480467\pi
0.833732 0.552170i 0.186200π-0.186200\pi
720720 1711.66i 0.0885971i
721721 12588.3 + 7267.86i 0.650226 + 0.375408i
722722 4486.41 + 2590.23i 0.231256 + 0.133516i
723723 24002.7i 1.23468i
724724 −2853.77 + 4942.88i −0.146491 + 0.253730i
725725 −5821.82 10083.7i −0.298230 0.516550i
726726 5507.05 3179.50i 0.281523 0.162537i
727727 6114.86 0.311950 0.155975 0.987761i 0.450148π-0.450148\pi
0.155975 + 0.987761i 0.450148π0.450148\pi
728728 0 0
729729 13909.0 0.706650
730730 −13288.2 + 7671.97i −0.673726 + 0.388976i
731731 −22786.3 39467.0i −1.15292 1.99691i
732732 5449.99 9439.66i 0.275188 0.476639i
733733 20350.9i 1.02548i −0.858543 0.512742i 0.828630π-0.828630\pi
0.858543 0.512742i 0.171370π-0.171370\pi
734734 814.191 + 470.073i 0.0409432 + 0.0236386i
735735 −2009.85 1160.39i −0.100863 0.0582333i
736736 4155.20i 0.208102i
737737 −68.6481 + 118.902i −0.00343105 + 0.00594276i
738738 441.709 + 765.062i 0.0220319 + 0.0381603i
739739 −9284.97 + 5360.68i −0.462183 + 0.266841i −0.712962 0.701203i 0.752647π-0.752647\pi
0.250779 + 0.968044i 0.419313π0.419313\pi
740740 6022.12 0.299159
741741 0 0
742742 −19984.0 −0.988727
743743 −24012.1 + 13863.4i −1.18562 + 0.684519i −0.957308 0.289069i 0.906654π-0.906654\pi
−0.228313 + 0.973588i 0.573321π0.573321\pi
744744 2318.50 + 4015.76i 0.114248 + 0.197883i
745745 5914.91 10244.9i 0.290880 0.503818i
746746 10236.6i 0.502398i
747747 −5681.78 3280.38i −0.278294 0.160673i
748748 8553.49 + 4938.36i 0.418110 + 0.241396i
749749 18626.4i 0.908671i
750750 4654.47 8061.78i 0.226610 0.392499i
751751 −15684.0 27165.5i −0.762075 1.31995i −0.941779 0.336232i 0.890847π-0.890847\pi
0.179704 0.983721i 0.442486π-0.442486\pi
752752 −6325.25 + 3651.89i −0.306726 + 0.177089i
753753 9196.41 0.445068
754754 0 0
755755 −13089.4 −0.630959
756756 −7722.31 + 4458.48i −0.371505 + 0.214488i
757757 −4458.12 7721.68i −0.214046 0.370739i 0.738931 0.673781i 0.235331π-0.235331\pi
−0.952977 + 0.303042i 0.901998π0.901998\pi
758758 −494.948 + 857.275i −0.0237168 + 0.0410787i
759759 8547.17i 0.408752i
760760 4582.34 + 2645.62i 0.218709 + 0.126272i
761761 9762.51 + 5636.39i 0.465034 + 0.268487i 0.714158 0.699984i 0.246810π-0.246810\pi
−0.249125 + 0.968471i 0.580143π0.580143\pi
762762 12478.4i 0.593237i
763763 −928.527 + 1608.26i −0.0440563 + 0.0763077i
764764 −1568.86 2717.35i −0.0742924 0.128678i
765765 11670.8 6738.17i 0.551582 0.318456i
766766 8609.02 0.406079
767767 0 0
768768 859.687 0.0403923
769769 −8009.36 + 4624.21i −0.375585 + 0.216844i −0.675896 0.736997i 0.736243π-0.736243\pi
0.300311 + 0.953841i 0.402910π0.402910\pi
770770 −2072.26 3589.26i −0.0969857 0.167984i
771771 −10169.1 + 17613.4i −0.475008 + 0.822738i
772772 12051.6i 0.561848i
773773 11568.3 + 6678.95i 0.538269 + 0.310770i 0.744377 0.667759i 0.232746π-0.232746\pi
−0.206108 + 0.978529i 0.566080π0.566080\pi
774774 −9851.93 5688.01i −0.457520 0.264149i
775775 13584.6i 0.629643i
776776 328.390 568.789i 0.0151914 0.0263123i
777777 −5772.81 9998.81i −0.266536 0.461654i
778778 −9698.58 + 5599.48i −0.446929 + 0.258035i
779779 −2730.89 −0.125602
780780 0 0
781781 −16676.2 −0.764049
782782 28331.9 16357.5i 1.29559 0.748007i
783783 10612.5 + 18381.4i 0.484369 + 0.838951i
784784 −812.556 + 1407.39i −0.0370151 + 0.0641121i
785785 1871.47i 0.0850899i
786786 10863.6 + 6272.09i 0.492991 + 0.284629i
787787 43.1767 + 24.9281i 0.00195563 + 0.00112909i 0.500977 0.865460i 0.332974π-0.332974\pi
−0.499022 + 0.866589i 0.666307π0.666307\pi
788788 10917.2i 0.493540i
789789 −8956.50 + 15513.1i −0.404132 + 0.699977i
790790 1892.07 + 3277.17i 0.0852114 + 0.147590i
791791 8163.84 4713.40i 0.366969 0.211870i
792792 2465.47 0.110614
793793 0 0
794794 19614.2 0.876677
795795 −12724.9 + 7346.75i −0.567682 + 0.327751i
796796 1923.21 + 3331.09i 0.0856361 + 0.148326i
797797 −5756.94 + 9971.31i −0.255861 + 0.443164i −0.965129 0.261775i 0.915692π-0.915692\pi
0.709268 + 0.704939i 0.249026π0.249026\pi
798798 10144.4i 0.450008i
799799 −49800.2 28752.2i −2.20501 1.27306i
800800 −2181.13 1259.27i −0.0963932 0.0556526i
801801 5098.45i 0.224900i
802802 −14658.4 + 25389.2i −0.645396 + 1.11786i
803803 −11050.6 19140.3i −0.485640 0.841153i
804804 −81.4837 + 47.0446i −0.00357426 + 0.00206360i
805805 −13728.0 −0.601054
806806 0 0
807807 2079.57 0.0907118
808808 4964.20 2866.08i 0.216139 0.124788i
809809 −6503.80 11264.9i −0.282647 0.489559i 0.689389 0.724391i 0.257879π-0.257879\pi
−0.972036 + 0.234833i 0.924546π0.924546\pi
810810 −389.722 + 675.019i −0.0169055 + 0.0292812i
811811 1032.74i 0.0447156i 0.999750 + 0.0223578i 0.00711731π0.00711731\pi
−0.999750 + 0.0223578i 0.992883π0.992883\pi
812812 −7962.97 4597.42i −0.344145 0.198692i
813813 3809.39 + 2199.35i 0.164331 + 0.0948765i
814814 8674.21i 0.373502i
815815 13174.2 22818.3i 0.566222 0.980724i
816816 3384.26 + 5861.71i 0.145187 + 0.251472i
817817 30455.1 17583.2i 1.30415 0.752949i
818818 −21370.8 −0.913461
819819 0 0
820820 −764.601 −0.0325622
821821 −4408.83 + 2545.44i −0.187417 + 0.108205i −0.590773 0.806838i 0.701177π-0.701177\pi
0.403356 + 0.915043i 0.367844π0.367844\pi
822822 1770.24 + 3066.14i 0.0751145 + 0.130102i
823823 10894.9 18870.5i 0.461447 0.799250i −0.537586 0.843209i 0.680664π-0.680664\pi
0.999033 + 0.0439588i 0.0139970π0.0139970\pi
824824 7483.94i 0.316402i
825825 4486.53 + 2590.30i 0.189335 + 0.109312i
826826 8367.77 + 4831.13i 0.352484 + 0.203507i
827827 22544.8i 0.947955i 0.880537 + 0.473977i 0.157182π0.157182\pi
−0.880537 + 0.473977i 0.842818π0.842818\pi
828828 4083.22 7072.34i 0.171379 0.296837i
829829 −5248.91 9091.38i −0.219906 0.380888i 0.734873 0.678205i 0.237242π-0.237242\pi
−0.954779 + 0.297316i 0.903908π0.903908\pi
830830 4917.60 2839.18i 0.205653 0.118734i
831831 −22105.5 −0.922780
832832 0 0
833833 −12794.9 −0.532193
834834 −8695.39 + 5020.29i −0.361027 + 0.208439i
835835 2423.64 + 4197.87i 0.100447 + 0.173980i
836836 −3810.72 + 6600.37i −0.157651 + 0.273060i
837837 24763.2i 1.02263i
838838 −11102.7 6410.14i −0.457680 0.264242i
839839 −12499.5 7216.59i −0.514340 0.296954i 0.220276 0.975438i 0.429304π-0.429304\pi
−0.734616 + 0.678483i 0.762637π0.762637\pi
840840 2840.24i 0.116664i
841841 1251.25 2167.22i 0.0513037 0.0888607i
842842 −2672.97 4629.72i −0.109402 0.189490i
843843 −21539.2 + 12435.7i −0.880011 + 0.508075i
844844 −15108.6 −0.616183
845845 0 0
846846 −14354.5 −0.583353
847847 −12740.4 + 7355.70i −0.516844 + 0.298400i
848848 5144.53 + 8910.60i 0.208330 + 0.360839i
849849 3727.46 6456.15i 0.150679 0.260983i
850850 19829.1i 0.800158i
851851 24882.5 + 14365.9i 1.00230 + 0.578681i
852852 −9897.14 5714.11i −0.397970 0.229768i
853853 4097.21i 0.164462i 0.996613 + 0.0822309i 0.0262045π0.0262045\pi
−0.996613 + 0.0822309i 0.973796π0.973796\pi
854854 −12608.4 + 21838.5i −0.505213 + 0.875055i
855855 5199.56 + 9005.91i 0.207978 + 0.360229i
856856 8305.27 4795.05i 0.331622 0.191462i
857857 5188.52 0.206810 0.103405 0.994639i 0.467026π-0.467026\pi
0.103405 + 0.994639i 0.467026π0.467026\pi
858858 0 0
859859 6351.40 0.252278 0.126139 0.992013i 0.459741π-0.459741\pi
0.126139 + 0.992013i 0.459741π0.459741\pi
860860 8526.87 4922.99i 0.338098 0.195201i
861861 732.947 + 1269.50i 0.0290114 + 0.0502491i
862862 −5175.73 + 8964.63i −0.204508 + 0.354219i
863863 19337.4i 0.762751i −0.924420 0.381376i 0.875450π-0.875450\pi
0.924420 0.381376i 0.124550π-0.124550\pi
864864 3975.95 + 2295.52i 0.156556 + 0.0903878i
865865 −4782.90 2761.41i −0.188004 0.108544i
866866 8343.92i 0.327411i
867867 −18395.8 + 31862.4i −0.720593 + 1.24810i
868868 −5363.80 9290.37i −0.209745 0.363290i
869869 −4720.41 + 2725.33i −0.184268 + 0.106387i
870870 −6760.63 −0.263456
871871 0 0
872872 956.134 0.0371316
873873 1117.87 645.402i 0.0433381 0.0250212i
874874 12622.4 + 21862.6i 0.488510 + 0.846124i
875875 −10768.0 + 18650.7i −0.416029 + 0.720583i
876876 15146.0i 0.584175i
877877 −14740.2 8510.28i −0.567552 0.327676i 0.188619 0.982050i 0.439599π-0.439599\pi
−0.756171 + 0.654374i 0.772932π0.772932\pi
878878 18471.5 + 10664.5i 0.710005 + 0.409921i
879879 7566.42i 0.290340i
880880 −1066.93 + 1847.98i −0.0408709 + 0.0707904i
881881 −7506.10 13000.9i −0.287045 0.497177i 0.686058 0.727547i 0.259340π-0.259340\pi
−0.973103 + 0.230370i 0.926006π0.926006\pi
882882 −2766.01 + 1596.96i −0.105597 + 0.0609664i
883883 46753.9 1.78187 0.890936 0.454129i 0.150049π-0.150049\pi
0.890936 + 0.454129i 0.150049π0.150049\pi
884884 0 0
885885 7104.31 0.269840
886886 3675.69 2122.16i 0.139376 0.0804688i
887887 5953.40 + 10311.6i 0.225361 + 0.390337i 0.956428 0.291969i 0.0943104π-0.0943104\pi
−0.731066 + 0.682306i 0.760977π0.760977\pi
888888 −2972.22 + 5148.04i −0.112321 + 0.194546i
889889 28868.6i 1.08911i
890890 3821.53 + 2206.36i 0.143930 + 0.0830982i
891891 −972.292 561.353i −0.0365578 0.0211067i
892892 17465.2i 0.655582i
893893 22186.8 38428.8i 0.831416 1.44006i
894894 5838.62 + 10112.8i 0.218426 + 0.378324i
895895 −5090.15 + 2938.80i −0.190106 + 0.109758i
896896 −1988.87 −0.0741556
897897 0 0
898898 −30570.8 −1.13604
899899 −22113.9 + 12767.5i −0.820400 + 0.473658i
900900 −2474.92 4286.68i −0.0916636 0.158766i
901901 −40504.1 + 70155.2i −1.49766 + 2.59402i
902902 1101.32i 0.0406542i
903903 −16347.7 9438.37i −0.602457 0.347829i
904904 −4203.28 2426.77i −0.154645 0.0892843i
905905 9708.63i 0.356603i
906906 6460.31 11189.6i 0.236898 0.410319i
907907 14577.2 + 25248.5i 0.533660 + 0.924326i 0.999227 + 0.0393134i 0.0125171π0.0125171\pi
−0.465567 + 0.885013i 0.654150π0.654150\pi
908908 6328.88 3653.98i 0.231312 0.133548i
909909 11265.7 0.411068
910910 0 0
911911 −6426.94 −0.233737 −0.116868 0.993147i 0.537286π-0.537286\pi
−0.116868 + 0.993147i 0.537286π0.537286\pi
912912 −4523.24 + 2611.49i −0.164232 + 0.0948193i
913913 4089.52 + 7083.26i 0.148240 + 0.256760i
914914 −8533.93 + 14781.2i −0.308837 + 0.534922i
915915 18541.1i 0.669889i
916916 15160.7 + 8753.03i 0.546860 + 0.315730i
917917 −25132.7 14510.4i −0.905075 0.522545i
918918 36146.3i 1.29957i
919919 13666.7 23671.5i 0.490560 0.849674i −0.509381 0.860541i 0.670126π-0.670126\pi
0.999941 + 0.0108669i 0.00345909π0.00345909\pi
920920 3534.04 + 6121.13i 0.126645 + 0.219356i
921921 −19291.9 + 11138.2i −0.690216 + 0.398496i
922922 12413.5 0.443404
923923 0 0
924924 4091.06 0.145656
925925 15081.8 8707.46i 0.536092 0.309513i
926926 14278.3 + 24730.8i 0.506711 + 0.877649i
927927 7354.28 12738.0i 0.260568 0.451317i
928928 4734.11i 0.167462i
929929 −7564.48 4367.36i −0.267150 0.154239i 0.360442 0.932782i 0.382626π-0.382626\pi
−0.627592 + 0.778542i 0.715959π0.715959\pi
930930 −6830.87 3943.80i −0.240853 0.139056i
931931 9873.29i 0.347566i
932932 −9447.78 + 16364.0i −0.332052 + 0.575131i
933933 1369.83 + 2372.61i 0.0480667 + 0.0832539i
934934 3096.17 1787.57i 0.108469 0.0626244i
935935 −16800.5 −0.587630
936936 0 0
937937 38518.8 1.34296 0.671480 0.741023i 0.265659π-0.265659\pi
0.671480 + 0.741023i 0.265659π0.265659\pi
938938 188.511 108.837i 0.00656193 0.00378853i
939939 −10358.9 17942.2i −0.360012 0.623559i
940940 6211.92 10759.4i 0.215543 0.373332i
941941 33183.6i 1.14958i 0.818301 + 0.574790i 0.194916π0.194916\pi
−0.818301 + 0.574790i 0.805084π0.805084\pi
942942 −1599.84 923.666i −0.0553349 0.0319476i
943943 −3159.21 1823.97i −0.109097 0.0629870i
944944 4974.77i 0.171520i
945945 7583.94 13135.8i 0.261064 0.452176i
946946 7091.04 + 12282.0i 0.243710 + 0.422118i
947947 −24763.2 + 14297.1i −0.849733 + 0.490594i −0.860561 0.509348i 0.829887π-0.829887\pi
0.0108276 + 0.999941i 0.496553π0.496553\pi
948948 −3735.34 −0.127973
949949 0 0
950950 15301.3 0.522569
951951 25728.0 14854.1i 0.877274 0.506494i
952952 −7829.42 13560.9i −0.266547 0.461673i
953953 −4792.89 + 8301.53i −0.162914 + 0.282175i −0.935913 0.352232i 0.885423π-0.885423\pi
0.772999 + 0.634408i 0.218756π0.218756\pi
954954 20221.6i 0.686268i
955955 4622.25 + 2668.66i 0.156621 + 0.0904249i
956956 8009.67 + 4624.38i 0.270974 + 0.156447i
957957 9737.96i 0.328927i
958958 13735.6 23790.7i 0.463232 0.802342i
959959 −4095.40 7093.45i −0.137901 0.238852i
960960 −1266.43 + 731.171i −0.0425768 + 0.0245817i
961961 −0.495919 −1.66466e−5
962962 0 0
963963 18847.9 0.630701
964964 24760.0 14295.2i 0.827247 0.477611i
965965 −10250.0 17753.5i −0.341926 0.592233i
966966 6775.46 11735.4i 0.225670 0.390871i
967967 5738.23i 0.190826i 0.995438 + 0.0954132i 0.0304172π0.0304172\pi
−0.995438 + 0.0954132i 0.969583π0.969583\pi
968968 6559.62 + 3787.20i 0.217804 + 0.125749i
969969 −35612.5 20560.9i −1.18064 0.681642i
970970 1117.19i 0.0369804i
971971 23508.0 40717.0i 0.776938 1.34570i −0.156760 0.987637i 0.550105π-0.550105\pi
0.933699 0.358060i 0.116562π-0.116562\pi
972972 7362.67 + 12752.5i 0.242961 + 0.420820i
973973 20116.6 11614.3i 0.662804 0.382670i
974974 34038.1 1.11976
975975 0 0
976976 12983.3 0.425805
977977 −31456.5 + 18161.4i −1.03007 + 0.594713i −0.917006 0.398874i 0.869401π-0.869401\pi
−0.113068 + 0.993587i 0.536068π0.536068\pi
978978 13004.2 + 22524.0i 0.425184 + 0.736440i
979979 −3178.03 + 5504.50i −0.103749 + 0.179698i
980980 2764.34i 0.0901058i
981981 1627.38 + 939.569i 0.0529646 + 0.0305791i
982982 −23629.8 13642.7i −0.767879 0.443335i
983983 33276.4i 1.07971i 0.841759 + 0.539854i 0.181520π0.181520\pi
−0.841759 + 0.539854i 0.818480π0.818480\pi
984984 377.369 653.623i 0.0122257 0.0211755i
985985 −9285.17 16082.4i −0.300356 0.520231i
986986 −32279.2 + 18636.4i −1.04257 + 0.601930i
987987 −23819.0 −0.768154
988988 0 0
989989 46975.7 1.51035
990990 −3631.94 + 2096.90i −0.116596 + 0.0673170i
991991 23175.4 + 40141.0i 0.742877 + 1.28670i 0.951180 + 0.308636i 0.0998725π0.0998725\pi
−0.208303 + 0.978064i 0.566794π0.566794\pi
992992 −2761.63 + 4783.29i −0.0883891 + 0.153094i
993993 31940.0i 1.02073i
994994 22896.8 + 13219.5i 0.730627 + 0.421827i
995995 −5666.25 3271.41i −0.180535 0.104232i
996996 5605.11i 0.178318i
997997 −9198.72 + 15932.6i −0.292203 + 0.506110i −0.974330 0.225123i 0.927722π-0.927722\pi
0.682127 + 0.731233i 0.261055π0.261055\pi
998998 4507.63 + 7807.44i 0.142972 + 0.247636i
999999 −27492.3 + 15872.7i −0.870690 + 0.502693i
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 338.4.e.i.23.9 24
13.2 odd 12 338.4.a.o.1.4 yes 6
13.3 even 3 338.4.b.h.337.10 12
13.4 even 6 inner 338.4.e.i.147.9 24
13.5 odd 4 338.4.c.o.315.3 12
13.6 odd 12 338.4.c.o.191.3 12
13.7 odd 12 338.4.c.p.191.3 12
13.8 odd 4 338.4.c.p.315.3 12
13.9 even 3 inner 338.4.e.i.147.6 24
13.10 even 6 338.4.b.h.337.4 12
13.11 odd 12 338.4.a.n.1.4 6
13.12 even 2 inner 338.4.e.i.23.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
338.4.a.n.1.4 6 13.11 odd 12
338.4.a.o.1.4 yes 6 13.2 odd 12
338.4.b.h.337.4 12 13.10 even 6
338.4.b.h.337.10 12 13.3 even 3
338.4.c.o.191.3 12 13.6 odd 12
338.4.c.o.315.3 12 13.5 odd 4
338.4.c.p.191.3 12 13.7 odd 12
338.4.c.p.315.3 12 13.8 odd 4
338.4.e.i.23.6 24 13.12 even 2 inner
338.4.e.i.23.9 24 1.1 even 1 trivial
338.4.e.i.147.6 24 13.9 even 3 inner
338.4.e.i.147.9 24 13.4 even 6 inner