Properties

Label 40.5.g.a.11.15
Level 4040
Weight 55
Character 40.11
Analytic conductor 4.1354.135
Analytic rank 00
Dimension 1616
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,5,Mod(11,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.11");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 40=235 40 = 2^{3} \cdot 5
Weight: k k == 5 5
Character orbit: [χ][\chi] == 40.g (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.134798523354.13479852335
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x166x15+14x1484x13+628x121392x11+2016x1018048x9++4294967296 x^{16} - 6 x^{15} + 14 x^{14} - 84 x^{13} + 628 x^{12} - 1392 x^{11} + 2016 x^{10} - 18048 x^{9} + \cdots + 4294967296 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 22555 2^{25}\cdot 5^{5}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 11.15
Root 3.73120+1.44159i-3.73120 + 1.44159i of defining polynomial
Character χ\chi == 40.11
Dual form 40.5.g.a.11.16

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+(3.731201.44159i)q2+7.09911q3+(11.843710.7577i)q4+11.1803iq5+(26.488210.2340i)q6+2.59084iq7+(28.682857.2127i)q830.6027q9+(16.1174+41.7160i)q107.95663q11+(84.079376.3700i)q12+54.6467iq13+(3.73492+9.66694i)q14+79.3704iq15+(24.5442254.821i)q1628.7782q17+(114.185+44.1165i)q18316.702q19+(120.275+132.416i)q20+18.3927iq21+(29.6878+11.4702i)q22+846.949iq23+(203.623406.159i)q24125.000q25+(78.7780+203.898i)q26792.279q27+(27.8715+30.6850i)q28766.738iq29+(114.419+296.147i)q30+1194.00iq31+(275.767986.169i)q3256.4850q33+(107.377+41.4862i)q3428.9665q35+(362.448+329.214i)q362436.16iq37+(1181.68+456.554i)q38+387.943iq39+(639.658+320.684i)q40+2433.43q41+(26.5146+68.6266i)q42+2338.16q43+(94.2356+85.5950i)q44342.149iq45+(1220.95+3160.13i)q462192.51iq47+(174.2421809.00i)q48+2394.29q49+(466.400+180.198i)q50204.299q51+(587.872+647.216i)q523041.70iq53+(2956.15+1142.14i)q5488.9578iq55+(148.229+74.3127i)q562248.30q57+(1105.322860.85i)q58+455.150q59+(853.842+940.036i)q60+3920.95iq61+(1721.25+4455.04i)q6279.2868iq63+(2450.593282.05i)q64610.969q65+(210.756+81.4280i)q664822.82q67+(340.839+309.587i)q68+6012.58iq69+(108.080+41.7577i)q70+874.716iq71+(877.773+1750.86i)q727682.80q73+(3511.939089.78i)q74887.388q75+(3750.91+3406.98i)q7620.6144iq77+(559.253+1447.49i)q78+1475.37iq79+(2848.98+274.413i)q803145.66q81+(9079.623508.01i)q82+6849.50q83+(197.863+217.836i)q84321.750iq85+(8724.143370.66i)q865443.16iq87+(228.219+455.220i)q88+13113.1q89+(493.2371276.62i)q90141.581q91+(9111.21+10031.0i)q92+8476.32iq93+(3160.708180.70i)q943540.84iq95+(1957.707000.92i)q968603.40q97+(8933.563451.57i)q98+243.494q99+O(q100)q+(3.73120 - 1.44159i) q^{2} +7.09911 q^{3} +(11.8437 - 10.7577i) q^{4} +11.1803i q^{5} +(26.4882 - 10.2340i) q^{6} +2.59084i q^{7} +(28.6828 - 57.2127i) q^{8} -30.6027 q^{9} +(16.1174 + 41.7160i) q^{10} -7.95663 q^{11} +(84.0793 - 76.3700i) q^{12} +54.6467i q^{13} +(3.73492 + 9.66694i) q^{14} +79.3704i q^{15} +(24.5442 - 254.821i) q^{16} -28.7782 q^{17} +(-114.185 + 44.1165i) q^{18} -316.702 q^{19} +(120.275 + 132.416i) q^{20} +18.3927i q^{21} +(-29.6878 + 11.4702i) q^{22} +846.949i q^{23} +(203.623 - 406.159i) q^{24} -125.000 q^{25} +(78.7780 + 203.898i) q^{26} -792.279 q^{27} +(27.8715 + 30.6850i) q^{28} -766.738i q^{29} +(114.419 + 296.147i) q^{30} +1194.00i q^{31} +(-275.767 - 986.169i) q^{32} -56.4850 q^{33} +(-107.377 + 41.4862i) q^{34} -28.9665 q^{35} +(-362.448 + 329.214i) q^{36} -2436.16i q^{37} +(-1181.68 + 456.554i) q^{38} +387.943i q^{39} +(639.658 + 320.684i) q^{40} +2433.43 q^{41} +(26.5146 + 68.6266i) q^{42} +2338.16 q^{43} +(-94.2356 + 85.5950i) q^{44} -342.149i q^{45} +(1220.95 + 3160.13i) q^{46} -2192.51i q^{47} +(174.242 - 1809.00i) q^{48} +2394.29 q^{49} +(-466.400 + 180.198i) q^{50} -204.299 q^{51} +(587.872 + 647.216i) q^{52} -3041.70i q^{53} +(-2956.15 + 1142.14i) q^{54} -88.9578i q^{55} +(148.229 + 74.3127i) q^{56} -2248.30 q^{57} +(-1105.32 - 2860.85i) q^{58} +455.150 q^{59} +(853.842 + 940.036i) q^{60} +3920.95i q^{61} +(1721.25 + 4455.04i) q^{62} -79.2868i q^{63} +(-2450.59 - 3282.05i) q^{64} -610.969 q^{65} +(-210.756 + 81.4280i) q^{66} -4822.82 q^{67} +(-340.839 + 309.587i) q^{68} +6012.58i q^{69} +(-108.080 + 41.7577i) q^{70} +874.716i q^{71} +(-877.773 + 1750.86i) q^{72} -7682.80 q^{73} +(-3511.93 - 9089.78i) q^{74} -887.388 q^{75} +(-3750.91 + 3406.98i) q^{76} -20.6144i q^{77} +(559.253 + 1447.49i) q^{78} +1475.37i q^{79} +(2848.98 + 274.413i) q^{80} -3145.66 q^{81} +(9079.62 - 3508.01i) q^{82} +6849.50 q^{83} +(197.863 + 217.836i) q^{84} -321.750i q^{85} +(8724.14 - 3370.66i) q^{86} -5443.16i q^{87} +(-228.219 + 455.220i) q^{88} +13113.1 q^{89} +(-493.237 - 1276.62i) q^{90} -141.581 q^{91} +(9111.21 + 10031.0i) q^{92} +8476.32i q^{93} +(-3160.70 - 8180.70i) q^{94} -3540.84i q^{95} +(-1957.70 - 7000.92i) q^{96} -8603.40 q^{97} +(8933.56 - 3451.57i) q^{98} +243.494 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q6q2+8q4+84q6216q8+432q950q10+192q11+260q12+972q14824q16806q18704q19300q201100q221256q242000q25++2624q99+O(q100) 16 q - 6 q^{2} + 8 q^{4} + 84 q^{6} - 216 q^{8} + 432 q^{9} - 50 q^{10} + 192 q^{11} + 260 q^{12} + 972 q^{14} - 824 q^{16} - 806 q^{18} - 704 q^{19} - 300 q^{20} - 1100 q^{22} - 1256 q^{24} - 2000 q^{25}+ \cdots + 2624 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 3.73120 1.44159i 0.932799 0.360397i
33 7.09911 0.788789 0.394395 0.918941i 0.370954π-0.370954\pi
0.394395 + 0.918941i 0.370954π0.370954\pi
44 11.8437 10.7577i 0.740228 0.672356i
55 11.1803i 0.447214i
66 26.4882 10.2340i 0.735782 0.284277i
77 2.59084i 0.0528743i 0.999650 + 0.0264372i 0.00841619π0.00841619\pi
−0.999650 + 0.0264372i 0.991584π0.991584\pi
88 28.6828 57.2127i 0.448169 0.893949i
99 −30.6027 −0.377811
1010 16.1174 + 41.7160i 0.161174 + 0.417160i
1111 −7.95663 −0.0657573 −0.0328786 0.999459i 0.510467π-0.510467\pi
−0.0328786 + 0.999459i 0.510467π0.510467\pi
1212 84.0793 76.3700i 0.583884 0.530347i
1313 54.6467i 0.323353i 0.986844 + 0.161677i 0.0516901π0.0516901\pi
−0.986844 + 0.161677i 0.948310π0.948310\pi
1414 3.73492 + 9.66694i 0.0190557 + 0.0493211i
1515 79.3704i 0.352757i
1616 24.5442 254.821i 0.0958759 0.995393i
1717 −28.7782 −0.0995785 −0.0497892 0.998760i 0.515855π-0.515855\pi
−0.0497892 + 0.998760i 0.515855π0.515855\pi
1818 −114.185 + 44.1165i −0.352422 + 0.136162i
1919 −316.702 −0.877291 −0.438646 0.898660i 0.644542π-0.644542\pi
−0.438646 + 0.898660i 0.644542π0.644542\pi
2020 120.275 + 132.416i 0.300687 + 0.331040i
2121 18.3927i 0.0417067i
2222 −29.6878 + 11.4702i −0.0613383 + 0.0236987i
2323 846.949i 1.60104i 0.599308 + 0.800519i 0.295443π0.295443\pi
−0.599308 + 0.800519i 0.704557π0.704557\pi
2424 203.623 406.159i 0.353511 0.705137i
2525 −125.000 −0.200000
2626 78.7780 + 203.898i 0.116535 + 0.301624i
2727 −792.279 −1.08680
2828 27.8715 + 30.6850i 0.0355503 + 0.0391391i
2929 766.738i 0.911698i −0.890057 0.455849i 0.849336π-0.849336\pi
0.890057 0.455849i 0.150664π-0.150664\pi
3030 114.419 + 296.147i 0.127133 + 0.329052i
3131 1194.00i 1.24245i 0.783631 + 0.621227i 0.213366π0.213366\pi
−0.783631 + 0.621227i 0.786634π0.786634\pi
3232 −275.767 986.169i −0.269304 0.963055i
3333 −56.4850 −0.0518686
3434 −107.377 + 41.4862i −0.0928867 + 0.0358878i
3535 −28.9665 −0.0236461
3636 −362.448 + 329.214i −0.279666 + 0.254023i
3737 2436.16i 1.77952i −0.456432 0.889758i 0.650873π-0.650873\pi
0.456432 0.889758i 0.349127π-0.349127\pi
3838 −1181.68 + 456.554i −0.818336 + 0.316173i
3939 387.943i 0.255058i
4040 639.658 + 320.684i 0.399786 + 0.200427i
4141 2433.43 1.44761 0.723806 0.690004i 0.242391π-0.242391\pi
0.723806 + 0.690004i 0.242391π0.242391\pi
4242 26.5146 + 68.6266i 0.0150310 + 0.0389040i
4343 2338.16 1.26455 0.632277 0.774742i 0.282120π-0.282120\pi
0.632277 + 0.774742i 0.282120π0.282120\pi
4444 −94.2356 + 85.5950i −0.0486754 + 0.0442123i
4545 342.149i 0.168962i
4646 1220.95 + 3160.13i 0.577009 + 1.49345i
4747 2192.51i 0.992537i −0.868169 0.496269i 0.834703π-0.834703\pi
0.868169 0.496269i 0.165297π-0.165297\pi
4848 174.242 1809.00i 0.0756259 0.785156i
4949 2394.29 0.997204
5050 −466.400 + 180.198i −0.186560 + 0.0720794i
5151 −204.299 −0.0785464
5252 587.872 + 647.216i 0.217408 + 0.239355i
5353 3041.70i 1.08284i −0.840752 0.541420i 0.817887π-0.817887\pi
0.840752 0.541420i 0.182113π-0.182113\pi
5454 −2956.15 + 1142.14i −1.01377 + 0.391680i
5555 88.9578i 0.0294075i
5656 148.229 + 74.3127i 0.0472669 + 0.0236967i
5757 −2248.30 −0.691998
5858 −1105.32 2860.85i −0.328573 0.850431i
5959 455.150 0.130753 0.0653764 0.997861i 0.479175π-0.479175\pi
0.0653764 + 0.997861i 0.479175π0.479175\pi
6060 853.842 + 940.036i 0.237178 + 0.261121i
6161 3920.95i 1.05374i 0.849947 + 0.526868i 0.176634π0.176634\pi
−0.849947 + 0.526868i 0.823366π0.823366\pi
6262 1721.25 + 4455.04i 0.447776 + 1.15896i
6363 79.2868i 0.0199765i
6464 −2450.59 3282.05i −0.598288 0.801281i
6565 −610.969 −0.144608
6666 −210.756 + 81.4280i −0.0483830 + 0.0186933i
6767 −4822.82 −1.07436 −0.537182 0.843466i 0.680511π-0.680511\pi
−0.537182 + 0.843466i 0.680511π0.680511\pi
6868 −340.839 + 309.587i −0.0737108 + 0.0669521i
6969 6012.58i 1.26288i
7070 −108.080 + 41.7577i −0.0220571 + 0.00852198i
7171 874.716i 0.173520i 0.996229 + 0.0867602i 0.0276514π0.0276514\pi
−0.996229 + 0.0867602i 0.972349π0.972349\pi
7272 −877.773 + 1750.86i −0.169323 + 0.337744i
7373 −7682.80 −1.44170 −0.720848 0.693093i 0.756248π-0.756248\pi
−0.720848 + 0.693093i 0.756248π0.756248\pi
7474 −3511.93 9089.78i −0.641332 1.65993i
7575 −887.388 −0.157758
7676 −3750.91 + 3406.98i −0.649396 + 0.589852i
7777 20.6144i 0.00347687i
7878 559.253 + 1447.49i 0.0919220 + 0.237918i
7979 1475.37i 0.236400i 0.992990 + 0.118200i 0.0377123π0.0377123\pi
−0.992990 + 0.118200i 0.962288π0.962288\pi
8080 2848.98 + 274.413i 0.445153 + 0.0428770i
8181 −3145.66 −0.479448
8282 9079.62 3508.01i 1.35033 0.521714i
8383 6849.50 0.994266 0.497133 0.867674i 0.334386π-0.334386\pi
0.497133 + 0.867674i 0.334386π0.334386\pi
8484 197.863 + 217.836i 0.0280417 + 0.0308725i
8585 321.750i 0.0445328i
8686 8724.14 3370.66i 1.17957 0.455741i
8787 5443.16i 0.719138i
8888 −228.219 + 455.220i −0.0294704 + 0.0587836i
8989 13113.1 1.65548 0.827740 0.561111i 0.189626π-0.189626\pi
0.827740 + 0.561111i 0.189626π0.189626\pi
9090 −493.237 1276.62i −0.0608935 0.157608i
9191 −141.581 −0.0170971
9292 9111.21 + 10031.0i 1.07647 + 1.18513i
9393 8476.32i 0.980035i
9494 −3160.70 8180.70i −0.357707 0.925838i
9595 3540.84i 0.392337i
9696 −1957.70 7000.92i −0.212424 0.759648i
9797 −8603.40 −0.914380 −0.457190 0.889369i 0.651144π-0.651144\pi
−0.457190 + 0.889369i 0.651144π0.651144\pi
9898 8933.56 3451.57i 0.930191 0.359389i
9999 243.494 0.0248438
100100 −1480.46 + 1344.71i −0.148046 + 0.134471i
101101 7164.77i 0.702360i −0.936308 0.351180i 0.885781π-0.885781\pi
0.936308 0.351180i 0.114219π-0.114219\pi
102102 −762.281 + 294.515i −0.0732680 + 0.0283079i
103103 8010.36i 0.755053i 0.925999 + 0.377527i 0.123225π0.123225\pi
−0.925999 + 0.377527i 0.876775π0.876775\pi
104104 3126.49 + 1567.42i 0.289061 + 0.144917i
105105 −205.636 −0.0186518
106106 −4384.88 11349.2i −0.390252 1.01007i
107107 −2003.50 −0.174994 −0.0874969 0.996165i 0.527887π-0.527887\pi
−0.0874969 + 0.996165i 0.527887π0.527887\pi
108108 −9383.48 + 8523.10i −0.804482 + 0.730718i
109109 20282.4i 1.70713i 0.520985 + 0.853566i 0.325565π0.325565\pi
−0.520985 + 0.853566i 0.674435π0.674435\pi
110110 −128.240 331.919i −0.0105984 0.0274313i
111111 17294.5i 1.40366i
112112 660.200 + 63.5902i 0.0526307 + 0.00506937i
113113 −570.501 −0.0446786 −0.0223393 0.999750i 0.507111π-0.507111\pi
−0.0223393 + 0.999750i 0.507111π0.507111\pi
114114 −8388.85 + 3241.12i −0.645495 + 0.249394i
115115 −9469.18 −0.716006
116116 −8248.33 9080.98i −0.612985 0.674865i
117117 1672.34i 0.122166i
118118 1698.25 656.139i 0.121966 0.0471229i
119119 74.5597i 0.00526514i
120120 4541.00 + 2276.57i 0.315347 + 0.158095i
121121 −14577.7 −0.995676
122122 5652.39 + 14629.8i 0.379763 + 0.982923i
123123 17275.2 1.14186
124124 12844.7 + 14141.3i 0.835371 + 0.919700i
125125 1397.54i 0.0894427i
126126 −114.299 295.834i −0.00719947 0.0186341i
127127 6367.53i 0.394788i −0.980324 0.197394i 0.936752π-0.936752\pi
0.980324 0.197394i 0.0632478π-0.0632478\pi
128128 −13875.0 8713.22i −0.846862 0.531813i
129129 16598.8 0.997467
130130 −2279.64 + 880.765i −0.134890 + 0.0521162i
131131 17348.8 1.01094 0.505472 0.862843i 0.331319π-0.331319\pi
0.505472 + 0.862843i 0.331319π0.331319\pi
132132 −668.988 + 607.648i −0.0383946 + 0.0348742i
133133 820.525i 0.0463862i
134134 −17994.9 + 6952.52i −1.00217 + 0.387198i
135135 8857.95i 0.486033i
136136 −825.440 + 1646.48i −0.0446280 + 0.0890180i
137137 −425.657 −0.0226787 −0.0113394 0.999936i 0.503610π-0.503610\pi
−0.0113394 + 0.999936i 0.503610π0.503610\pi
138138 8667.66 + 22434.1i 0.455138 + 1.17801i
139139 −21843.4 −1.13055 −0.565276 0.824902i 0.691230π-0.691230\pi
−0.565276 + 0.824902i 0.691230π0.691230\pi
140140 −343.069 + 311.613i −0.0175035 + 0.0158986i
141141 15564.9i 0.782903i
142142 1260.98 + 3263.74i 0.0625362 + 0.161860i
143143 434.804i 0.0212628i
144144 −751.119 + 7798.20i −0.0362230 + 0.376071i
145145 8572.39 0.407724
146146 −28666.0 + 11075.4i −1.34481 + 0.519583i
147147 16997.3 0.786584
148148 −26207.4 28853.0i −1.19647 1.31725i
149149 19745.1i 0.889381i −0.895684 0.444690i 0.853314π-0.853314\pi
0.895684 0.444690i 0.146686π-0.146686\pi
150150 −3311.02 + 1279.25i −0.147156 + 0.0568554i
151151 28379.1i 1.24464i 0.782761 + 0.622322i 0.213811π0.213811\pi
−0.782761 + 0.622322i 0.786189π0.786189\pi
152152 −9083.92 + 18119.4i −0.393175 + 0.784253i
153153 880.690 0.0376218
154154 −29.7174 76.9163i −0.00125305 0.00324322i
155155 −13349.3 −0.555642
156156 4173.37 + 4594.66i 0.171489 + 0.188801i
157157 4457.00i 0.180819i −0.995905 0.0904094i 0.971182π-0.971182\pi
0.995905 0.0904094i 0.0288176π-0.0288176\pi
158158 2126.87 + 5504.90i 0.0851977 + 0.220513i
159159 21593.3i 0.854133i
160160 11025.7 3083.17i 0.430691 0.120436i
161161 −2194.31 −0.0846538
162162 −11737.1 + 4534.74i −0.447228 + 0.172791i
163163 −1910.59 −0.0719107 −0.0359553 0.999353i 0.511447π-0.511447\pi
−0.0359553 + 0.999353i 0.511447π0.511447\pi
164164 28820.8 26178.1i 1.07156 0.973310i
165165 631.521i 0.0231964i
166166 25556.8 9874.15i 0.927451 0.358330i
167167 50764.6i 1.82024i 0.414347 + 0.910119i 0.364010π0.364010\pi
−0.414347 + 0.910119i 0.635990π0.635990\pi
168168 1052.29 + 527.554i 0.0372837 + 0.0186917i
169169 25574.7 0.895443
170170 −463.830 1200.51i −0.0160495 0.0415402i
171171 9691.94 0.331450
172172 27692.4 25153.2i 0.936059 0.850230i
173173 42367.9i 1.41561i −0.706407 0.707806i 0.749685π-0.749685\pi
0.706407 0.707806i 0.250315π-0.250315\pi
174174 −7846.78 20309.5i −0.259175 0.670811i
175175 323.855i 0.0105749i
176176 −195.289 + 2027.51i −0.00630454 + 0.0654544i
177177 3231.16 0.103136
178178 48927.4 18903.6i 1.54423 0.596630i
179179 −51902.2 −1.61987 −0.809934 0.586521i 0.800497π-0.800497\pi
−0.809934 + 0.586521i 0.800497π0.800497\pi
180180 −3680.73 4052.29i −0.113603 0.125071i
181181 8176.63i 0.249584i 0.992183 + 0.124792i 0.0398264π0.0398264\pi
−0.992183 + 0.124792i 0.960174π0.960174\pi
182182 −528.266 + 204.101i −0.0159481 + 0.00616173i
183183 27835.2i 0.831175i
184184 48456.2 + 24292.9i 1.43125 + 0.717536i
185185 27237.1 0.795824
186186 12219.4 + 31626.8i 0.353201 + 0.914175i
187187 228.977 0.00654801
188188 −23586.4 25967.4i −0.667338 0.734704i
189189 2052.67i 0.0574640i
190190 −5104.43 13211.6i −0.141397 0.365971i
191191 38144.4i 1.04560i 0.852456 + 0.522799i 0.175112π0.175112\pi
−0.852456 + 0.522799i 0.824888π0.824888\pi
192192 −17397.0 23299.6i −0.471923 0.632042i
193193 −35295.2 −0.947547 −0.473774 0.880647i 0.657109π-0.657109\pi
−0.473774 + 0.880647i 0.657109π0.657109\pi
194194 −32101.0 + 12402.5i −0.852932 + 0.329539i
195195 −4337.33 −0.114065
196196 28357.1 25757.0i 0.738159 0.670476i
197197 6283.20i 0.161901i −0.996718 0.0809503i 0.974204π-0.974204\pi
0.996718 0.0809503i 0.0257955π-0.0257955\pi
198198 908.525 351.018i 0.0231743 0.00895364i
199199 20814.6i 0.525609i 0.964849 + 0.262805i 0.0846474π0.0846474\pi
−0.964849 + 0.262805i 0.915353π0.915353\pi
200200 −3585.36 + 7151.59i −0.0896339 + 0.178790i
201201 −34237.7 −0.847448
202202 −10328.6 26733.2i −0.253128 0.655161i
203203 1986.50 0.0482054
204204 −2419.65 + 2197.79i −0.0581423 + 0.0528111i
205205 27206.6i 0.647391i
206206 11547.6 + 29888.2i 0.272119 + 0.704313i
207207 25918.9i 0.604890i
208208 13925.1 + 1341.26i 0.321864 + 0.0310018i
209209 2519.88 0.0576883
210210 −767.269 + 296.442i −0.0173984 + 0.00672205i
211211 21192.8 0.476017 0.238009 0.971263i 0.423505π-0.423505\pi
0.238009 + 0.971263i 0.423505π0.423505\pi
212212 −32721.7 36024.8i −0.728054 0.801549i
213213 6209.70i 0.136871i
214214 −7475.47 + 2888.23i −0.163234 + 0.0630672i
215215 26141.4i 0.565526i
216216 −22724.8 + 45328.4i −0.487072 + 0.971546i
217217 −3093.46 −0.0656939
218218 29238.9 + 75677.7i 0.615245 + 1.59241i
219219 −54541.0 −1.13720
220220 −956.981 1053.59i −0.0197723 0.0217683i
221221 1572.63i 0.0321990i
222222 −24931.6 64529.3i −0.505876 1.30934i
223223 46813.2i 0.941365i −0.882303 0.470683i 0.844008π-0.844008\pi
0.882303 0.470683i 0.155992π-0.155992\pi
224224 2555.01 714.468i 0.0509209 0.0142392i
225225 3825.34 0.0755622
226226 −2128.65 + 822.427i −0.0416762 + 0.0161020i
227227 1993.76 0.0386920 0.0193460 0.999813i 0.493842π-0.493842\pi
0.0193460 + 0.999813i 0.493842π0.493842\pi
228228 −26628.1 + 24186.5i −0.512237 + 0.465269i
229229 45591.9i 0.869394i 0.900577 + 0.434697i 0.143144π0.143144\pi
−0.900577 + 0.434697i 0.856856π0.856856\pi
230230 −35331.4 + 13650.6i −0.667890 + 0.258046i
231231 146.344i 0.00274252i
232232 −43867.2 21992.2i −0.815011 0.408595i
233233 −82293.2 −1.51584 −0.757918 0.652350i 0.773783π-0.773783\pi
−0.757918 + 0.652350i 0.773783π0.773783\pi
234234 −2410.82 6239.82i −0.0440284 0.113957i
235235 24513.1 0.443876
236236 5390.64 4896.36i 0.0967869 0.0879123i
237237 10473.8i 0.186470i
238238 −107.484 278.197i −0.00189754 0.00491132i
239239 104832.i 1.83527i −0.397426 0.917634i 0.630097π-0.630097\pi
0.397426 0.917634i 0.369903π-0.369903\pi
240240 20225.2 + 1948.08i 0.351132 + 0.0338209i
241241 10146.4 0.174693 0.0873467 0.996178i 0.472161π-0.472161\pi
0.0873467 + 0.996178i 0.472161π0.472161\pi
242242 −54392.2 + 21015.0i −0.928766 + 0.358838i
243243 41843.3 0.708620
244244 42180.3 + 46438.4i 0.708485 + 0.780005i
245245 26768.9i 0.445963i
246246 64457.2 24903.7i 1.06513 0.411523i
247247 17306.7i 0.283675i
248248 68311.9 + 34247.3i 1.11069 + 0.556830i
249249 48625.3 0.784267
250250 −2014.68 5214.51i −0.0322349 0.0834321i
251251 14884.6 0.236260 0.118130 0.992998i 0.462310π-0.462310\pi
0.118130 + 0.992998i 0.462310π0.462310\pi
252252 −852.942 939.045i −0.0134313 0.0147872i
253253 6738.86i 0.105280i
254254 −9179.35 23758.5i −0.142280 0.368257i
255255 2284.14i 0.0351270i
256256 −64331.2 12508.8i −0.981616 0.190868i
257257 63894.6 0.967382 0.483691 0.875239i 0.339296π-0.339296\pi
0.483691 + 0.875239i 0.339296π0.339296\pi
258258 61933.6 23928.7i 0.930436 0.359484i
259259 6311.70 0.0940907
260260 −7236.10 + 6572.61i −0.107043 + 0.0972280i
261261 23464.3i 0.344450i
262262 64731.8 25009.8i 0.943007 0.364341i
263263 46265.3i 0.668874i 0.942418 + 0.334437i 0.108546π0.108546\pi
−0.942418 + 0.334437i 0.891454π0.891454\pi
264264 −1620.15 + 3231.66i −0.0232459 + 0.0463679i
265265 34007.2 0.484261
266266 −1182.86 3061.54i −0.0167174 0.0432690i
267267 93091.0 1.30583
268268 −57119.9 + 51882.4i −0.795275 + 0.722355i
269269 87276.9i 1.20613i −0.797691 0.603066i 0.793946π-0.793946\pi
0.797691 0.603066i 0.206054π-0.206054\pi
270270 −12769.5 33050.8i −0.175165 0.453371i
271271 142380.i 1.93869i −0.245696 0.969347i 0.579016π-0.579016\pi
0.245696 0.969347i 0.420984π-0.420984\pi
272272 −706.338 + 7333.27i −0.00954717 + 0.0991197i
273273 −1005.10 −0.0134860
274274 −1588.21 + 613.622i −0.0211547 + 0.00817334i
275275 994.579 0.0131515
276276 64681.5 + 71210.9i 0.849106 + 0.934821i
277277 75663.5i 0.986114i 0.869997 + 0.493057i 0.164121π0.164121\pi
−0.869997 + 0.493057i 0.835879π0.835879\pi
278278 −81501.9 + 31489.1i −1.05458 + 0.407447i
279279 36539.6i 0.469413i
280280 −830.841 + 1657.25i −0.0105975 + 0.0211384i
281281 43571.0 0.551804 0.275902 0.961186i 0.411023π-0.411023\pi
0.275902 + 0.961186i 0.411023π0.411023\pi
282282 −22438.2 58075.7i −0.282156 0.730291i
283283 67132.6 0.838225 0.419112 0.907934i 0.362341π-0.362341\pi
0.419112 + 0.907934i 0.362341π0.362341\pi
284284 9409.93 + 10359.8i 0.116667 + 0.128445i
285285 25136.8i 0.309471i
286286 −626.807 1622.34i −0.00766305 0.0198339i
287287 6304.64i 0.0765415i
288288 8439.21 + 30179.4i 0.101746 + 0.363853i
289289 −82692.8 −0.990084
290290 31985.3 12357.9i 0.380324 0.146942i
291291 −61076.4 −0.721253
292292 −90992.4 + 82649.2i −1.06718 + 0.969333i
293293 42456.8i 0.494552i −0.968945 0.247276i 0.920465π-0.920465\pi
0.968945 0.247276i 0.0795355π-0.0795355\pi
294294 63420.3 24503.1i 0.733725 0.283482i
295295 5088.73i 0.0584744i
296296 −139379. 69876.0i −1.59080 0.797525i
297297 6303.87 0.0714652
298298 −28464.3 73673.0i −0.320530 0.829614i
299299 −46283.0 −0.517701
300300 −10509.9 + 9546.25i −0.116777 + 0.106069i
301301 6057.80i 0.0668624i
302302 40911.0 + 105888.i 0.448566 + 1.16100i
303303 50863.5i 0.554014i
304304 −7773.21 + 80702.2i −0.0841110 + 0.873250i
305305 −43837.5 −0.471245
306306 3286.03 1269.59i 0.0350936 0.0135588i
307307 −22580.4 −0.239582 −0.119791 0.992799i 0.538223π-0.538223\pi
−0.119791 + 0.992799i 0.538223π0.538223\pi
308308 −221.763 244.149i −0.00233769 0.00257368i
309309 56866.4i 0.595578i
310310 −49808.9 + 19244.2i −0.518303 + 0.200252i
311311 104096.i 1.07625i 0.842865 + 0.538125i 0.180867π0.180867\pi
−0.842865 + 0.538125i 0.819133π0.819133\pi
312312 22195.3 + 11127.3i 0.228008 + 0.114309i
313313 −84004.7 −0.857462 −0.428731 0.903432i 0.641039π-0.641039\pi
−0.428731 + 0.903432i 0.641039π0.641039\pi
314314 −6425.16 16629.9i −0.0651665 0.168668i
315315 886.453 0.00893377
316316 15871.6 + 17473.8i 0.158945 + 0.174990i
317317 52955.1i 0.526974i 0.964663 + 0.263487i 0.0848726π0.0848726\pi
−0.964663 + 0.263487i 0.915127π0.915127\pi
318318 −31128.7 80569.0i −0.307827 0.796735i
319319 6100.65i 0.0599508i
320320 36694.4 27398.4i 0.358344 0.267563i
321321 −14223.1 −0.138033
322322 −8187.40 + 3163.29i −0.0789650 + 0.0305089i
323323 9114.11 0.0873593
324324 −37256.1 + 33840.0i −0.354901 + 0.322359i
325325 6830.84i 0.0646706i
326326 −7128.80 + 2754.29i −0.0670782 + 0.0259164i
327327 143987.i 1.34657i
328328 69797.8 139223.i 0.648775 1.29409i
329329 5680.46 0.0524797
330330 −910.393 2356.33i −0.00835990 0.0216375i
331331 −61731.5 −0.563444 −0.281722 0.959496i 0.590906π-0.590906\pi
−0.281722 + 0.959496i 0.590906π0.590906\pi
332332 81123.1 73684.8i 0.735984 0.668501i
333333 74553.0i 0.672321i
334334 73181.6 + 189413.i 0.656008 + 1.69792i
335335 53920.8i 0.480471i
336336 4686.83 + 451.433i 0.0415146 + 0.00399867i
337337 −15465.0 −0.136173 −0.0680865 0.997679i 0.521689π-0.521689\pi
−0.0680865 + 0.997679i 0.521689π0.521689\pi
338338 95424.4 36868.2i 0.835268 0.322715i
339339 −4050.05 −0.0352420
340340 −3461.28 3810.69i −0.0299419 0.0329645i
341341 9500.20i 0.0817004i
342342 36162.5 13971.8i 0.309177 0.119454i
343343 12423.8i 0.105601i
344344 67065.1 133773.i 0.566735 1.13045i
345345 −67222.7 −0.564778
346346 −61077.0 158083.i −0.510182 1.32048i
347347 −74344.2 −0.617431 −0.308715 0.951154i 0.599899π-0.599899\pi
−0.308715 + 0.951154i 0.599899π0.599899\pi
348348 −58555.8 64466.8i −0.483516 0.532326i
349349 82400.1i 0.676514i 0.941054 + 0.338257i 0.109837π0.109837\pi
−0.941054 + 0.338257i 0.890163π0.890163\pi
350350 −466.866 1208.37i −0.00381115 0.00986422i
351351 43295.4i 0.351421i
352352 2194.18 + 7846.58i 0.0177087 + 0.0633279i
353353 153677. 1.23327 0.616635 0.787249i 0.288495π-0.288495\pi
0.616635 + 0.787249i 0.288495π0.288495\pi
354354 12056.1 4658.00i 0.0962055 0.0371700i
355355 −9779.62 −0.0776007
356356 155307. 141066.i 1.22543 1.11307i
357357 529.307i 0.00415309i
358358 −193657. + 74821.5i −1.51101 + 0.583795i
359359 235554.i 1.82768i 0.406072 + 0.913841i 0.366898π0.366898\pi
−0.406072 + 0.913841i 0.633102π0.633102\pi
360360 −19575.2 9813.80i −0.151044 0.0757237i
361361 −30020.8 −0.230360
362362 11787.3 + 30508.6i 0.0899493 + 0.232812i
363363 −103489. −0.785379
364364 −1676.84 + 1523.08i −0.0126557 + 0.0114953i
365365 85896.3i 0.644746i
366366 40126.9 + 103859.i 0.299553 + 0.775319i
367367 112718.i 0.836878i −0.908245 0.418439i 0.862577π-0.862577\pi
0.908245 0.418439i 0.137423π-0.137423\pi
368368 215820. + 20787.7i 1.59366 + 0.153501i
369369 −74469.7 −0.546924
370370 101627. 39264.6i 0.742344 0.286812i
371371 7880.56 0.0572545
372372 91185.6 + 100391.i 0.658932 + 0.725449i
373373 16080.3i 0.115578i −0.998329 0.0577892i 0.981595π-0.981595\pi
0.998329 0.0577892i 0.0184051π-0.0184051\pi
374374 854.359 330.091i 0.00610798 0.00235988i
375375 9921.30i 0.0705515i
376376 −125440. 62887.6i −0.887277 0.444825i
377377 41899.7 0.294801
378378 −2959.10 7658.92i −0.0207098 0.0536023i
379379 208815. 1.45373 0.726864 0.686781i 0.240977π-0.240977\pi
0.726864 + 0.686781i 0.240977π0.240977\pi
380380 −38091.2 41936.4i −0.263790 0.290419i
381381 45203.8i 0.311404i
382382 54988.5 + 142324.i 0.376830 + 0.975332i
383383 96057.8i 0.654840i 0.944879 + 0.327420i 0.106179π0.106179\pi
−0.944879 + 0.327420i 0.893821π0.893821\pi
384384 −98500.0 61856.1i −0.667996 0.419488i
385385 230.476 0.00155490
386386 −131693. + 50881.1i −0.883871 + 0.341493i
387387 −71554.0 −0.477763
388388 −101896. + 92552.7i −0.676850 + 0.614788i
389389 168851.i 1.11584i −0.829893 0.557922i 0.811599π-0.811599\pi
0.829893 0.557922i 0.188401π-0.188401\pi
390390 −16183.4 + 6252.64i −0.106400 + 0.0411087i
391391 24373.6i 0.159429i
392392 68675.0 136984.i 0.446917 0.891449i
393393 123161. 0.797422
394394 −9057.78 23443.9i −0.0583485 0.151021i
395395 −16495.1 −0.105721
396396 2883.86 2619.44i 0.0183901 0.0167039i
397397 189472.i 1.20216i −0.799188 0.601081i 0.794737π-0.794737\pi
0.799188 0.601081i 0.205263π-0.205263\pi
398398 30006.1 + 77663.5i 0.189428 + 0.490288i
399399 5824.99i 0.0365889i
400400 −3068.03 + 31852.6i −0.0191752 + 0.199079i
401401 120359. 0.748494 0.374247 0.927329i 0.377901π-0.377901\pi
0.374247 + 0.927329i 0.377901π0.377901\pi
402402 −127748. + 49356.7i −0.790499 + 0.305417i
403403 −65248.1 −0.401751
404404 −77076.4 84857.1i −0.472236 0.519907i
405405 35169.5i 0.214415i
406406 7412.01 2863.71i 0.0449660 0.0173731i
407407 19383.6i 0.117016i
408408 −5859.88 + 11688.5i −0.0352021 + 0.0702165i
409409 150488. 0.899615 0.449807 0.893126i 0.351493π-0.351493\pi
0.449807 + 0.893126i 0.351493π0.351493\pi
410410 39220.7 + 101513.i 0.233318 + 0.603886i
411411 −3021.79 −0.0178887
412412 86173.0 + 94871.9i 0.507664 + 0.558912i
413413 1179.22i 0.00691346i
414414 −37364.4 96708.6i −0.218000 0.564241i
415415 76579.7i 0.444649i
416416 53890.9 15069.8i 0.311407 0.0870802i
417417 −155068. −0.891767
418418 9402.17 3632.63i 0.0538116 0.0207907i
419419 288889. 1.64552 0.822761 0.568388i 0.192433π-0.192433\pi
0.822761 + 0.568388i 0.192433π0.192433\pi
420420 −2435.48 + 2212.17i −0.0138066 + 0.0125406i
421421 182304.i 1.02857i −0.857620 0.514284i 0.828058π-0.828058\pi
0.857620 0.514284i 0.171942π-0.171942\pi
422422 79074.4 30551.2i 0.444029 0.171555i
423423 67096.9i 0.374992i
424424 −174024. 87244.6i −0.968004 0.485296i
425425 3597.27 0.0199157
426426 8951.83 + 23169.6i 0.0493279 + 0.127673i
427427 −10158.6 −0.0557155
428428 −23728.8 + 21553.1i −0.129535 + 0.117658i
429429 3086.72i 0.0167719i
430430 37685.2 + 97538.8i 0.203814 + 0.527522i
431431 100495.i 0.540992i 0.962721 + 0.270496i 0.0871877π0.0871877\pi
−0.962721 + 0.270496i 0.912812π0.912812\pi
432432 −19445.9 + 201889.i −0.104198 + 1.08180i
433433 328152. 1.75025 0.875124 0.483898i 0.160779π-0.160779\pi
0.875124 + 0.483898i 0.160779π0.160779\pi
434434 −11542.3 + 4459.49i −0.0612792 + 0.0236759i
435435 60856.3 0.321608
436436 218192. + 240218.i 1.14780 + 1.26367i
437437 268230.i 1.40458i
438438 −203503. + 78625.6i −1.06077 + 0.409842i
439439 155253.i 0.805582i 0.915292 + 0.402791i 0.131960π0.131960\pi
−0.915292 + 0.402791i 0.868040π0.868040\pi
440440 −5089.52 2551.56i −0.0262888 0.0131796i
441441 −73271.7 −0.376755
442442 −2267.09 5867.80i −0.0116044 0.0300352i
443443 −337851. −1.72154 −0.860772 0.508991i 0.830019π-0.830019\pi
−0.860772 + 0.508991i 0.830019π0.830019\pi
444444 −186049. 204831.i −0.943761 1.03903i
445445 146608.i 0.740353i
446446 −67485.2 174669.i −0.339265 0.878105i
447447 140173.i 0.701534i
448448 8503.26 6349.09i 0.0423672 0.0316341i
449449 −245472. −1.21761 −0.608806 0.793319i 0.708351π-0.708351\pi
−0.608806 + 0.793319i 0.708351π0.708351\pi
450450 14273.1 5514.56i 0.0704844 0.0272324i
451451 −19361.9 −0.0951910
452452 −6756.82 + 6137.28i −0.0330724 + 0.0300399i
453453 201466.i 0.981762i
454454 7439.12 2874.18i 0.0360919 0.0139445i
455455 1582.92i 0.00764605i
456456 −64487.7 + 128631.i −0.310132 + 0.618611i
457457 −115007. −0.550671 −0.275336 0.961348i 0.588789π-0.588789\pi
−0.275336 + 0.961348i 0.588789π0.588789\pi
458458 65724.7 + 170112.i 0.313327 + 0.810970i
459459 22800.4 0.108222
460460 −112150. + 101866.i −0.530008 + 0.481410i
461461 115456.i 0.543270i 0.962400 + 0.271635i 0.0875644π0.0875644\pi
−0.962400 + 0.271635i 0.912436π0.912436\pi
462462 −210.967 546.037i −0.000988395 0.00255822i
463463 308334.i 1.43833i −0.694837 0.719167i 0.744524π-0.744524\pi
0.694837 0.719167i 0.255476π-0.255476\pi
464464 −195381. 18819.0i −0.907498 0.0874099i
465465 −94768.1 −0.438285
466466 −307052. + 118633.i −1.41397 + 0.546302i
467467 −234153. −1.07366 −0.536829 0.843691i 0.680378π-0.680378\pi
−0.536829 + 0.843691i 0.680378π0.680378\pi
468468 −17990.5 19806.6i −0.0821393 0.0904311i
469469 12495.2i 0.0568063i
470470 91463.0 35337.7i 0.414047 0.159972i
471471 31640.7i 0.142628i
472472 13055.0 26040.4i 0.0585994 0.116886i
473473 −18603.9 −0.0831536
474474 15098.9 + 39079.8i 0.0672030 + 0.173939i
475475 39587.8 0.175458
476476 −802.090 883.059i −0.00354005 0.00389741i
477477 93084.2i 0.409109i
478478 −151125. 391150.i −0.661425 1.71194i
479479 175880.i 0.766558i 0.923633 + 0.383279i 0.125205π0.125205\pi
−0.923633 + 0.383279i 0.874795π0.874795\pi
480480 78272.6 21887.7i 0.339725 0.0949988i
481481 133128. 0.575412
482482 37858.1 14626.9i 0.162954 0.0629589i
483483 −15577.6 −0.0667740
484484 −172653. + 156822.i −0.737028 + 0.669448i
485485 96188.9i 0.408923i
486486 156126. 60320.7i 0.661000 0.255384i
487487 289085.i 1.21890i −0.792826 0.609449i 0.791391π-0.791391\pi
0.792826 0.609449i 0.208609π-0.208609\pi
488488 224328. + 112464.i 0.941985 + 0.472252i
489489 −13563.5 −0.0567224
490490 38589.8 + 99880.2i 0.160724 + 0.415994i
491491 182813. 0.758304 0.379152 0.925334i 0.376216π-0.376216\pi
0.379152 + 0.925334i 0.376216π0.376216\pi
492492 204602. 185841.i 0.845237 0.767736i
493493 22065.3i 0.0907855i
494494 −24949.2 64574.8i −0.102236 0.264612i
495495 2722.35i 0.0111105i
496496 304255. + 29305.8i 1.23673 + 0.119121i
497497 −2266.25 −0.00917477
498498 181431. 70097.7i 0.731563 0.282647i
499499 463712. 1.86229 0.931145 0.364650i 0.118811π-0.118811\pi
0.931145 + 0.364650i 0.118811π0.118811\pi
500500 −15034.3 16552.0i −0.0601373 0.0662080i
501501 360383.i 1.43578i
502502 55537.3 21457.4i 0.220383 0.0851472i
503503 173588.i 0.686094i −0.939318 0.343047i 0.888541π-0.888541\pi
0.939318 0.343047i 0.111459π-0.111459\pi
504504 −4536.21 2274.17i −0.0178580 0.00895286i
505505 80104.6 0.314105
506506 −9714.65 25144.0i −0.0379425 0.0982050i
507507 181558. 0.706316
508508 −68499.9 75414.8i −0.265438 0.292233i
509509 231066.i 0.891867i 0.895066 + 0.445934i 0.147128π0.147128\pi
−0.895066 + 0.445934i 0.852872π0.852872\pi
510510 −3292.78 8522.56i −0.0126597 0.0327665i
511511 19904.9i 0.0762287i
512512 −258065. + 46066.4i −0.984439 + 0.175729i
513513 250917. 0.953443
514514 238403. 92109.7i 0.902373 0.348641i
515515 −89558.5 −0.337670
516516 196591. 178565.i 0.738353 0.670653i
517517 17445.0i 0.0652665i
518518 23550.2 9098.87i 0.0877678 0.0339100i
519519 300774.i 1.11662i
520520 −17524.3 + 34955.2i −0.0648089 + 0.129272i
521521 39770.4 0.146516 0.0732578 0.997313i 0.476660π-0.476660\pi
0.0732578 + 0.997313i 0.476660π0.476660\pi
522522 33825.8 + 87549.8i 0.124139 + 0.321302i
523523 −71651.8 −0.261953 −0.130977 0.991385i 0.541811π-0.541811\pi
−0.130977 + 0.991385i 0.541811π0.541811\pi
524524 205473. 186633.i 0.748329 0.679713i
525525 2299.08i 0.00834134i
526526 66695.5 + 172625.i 0.241060 + 0.623925i
527527 34361.1i 0.123722i
528528 −1386.38 + 14393.5i −0.00497295 + 0.0516297i
529529 −437481. −1.56332
530530 126888. 49024.4i 0.451718 0.174526i
531531 −13928.8 −0.0493998
532532 −8826.95 9718.01i −0.0311880 0.0343364i
533533 132979.i 0.468090i
534534 347341. 134199.i 1.21807 0.470615i
535535 22399.9i 0.0782596i
536536 −138332. + 275927.i −0.481498 + 0.960427i
537537 −368459. −1.27774
538538 −125817. 325647.i −0.434686 1.12508i
539539 −19050.5 −0.0655734
540540 −95291.1 104911.i −0.326787 0.359775i
541541 335147.i 1.14509i 0.819873 + 0.572546i 0.194044π0.194044\pi
−0.819873 + 0.572546i 0.805956π0.805956\pi
542542 −205253. 531246.i −0.698699 1.80841i
543543 58046.7i 0.196869i
544544 7936.07 + 28380.1i 0.0268168 + 0.0958996i
545545 −226764. −0.763452
546546 −3750.22 + 1448.94i −0.0125797 + 0.00486031i
547547 −174207. −0.582225 −0.291112 0.956689i 0.594025π-0.594025\pi
−0.291112 + 0.956689i 0.594025π0.594025\pi
548548 −5041.34 + 4579.09i −0.0167874 + 0.0152482i
549549 119992.i 0.398113i
550550 3710.97 1433.77i 0.0122677 0.00473974i
551551 242828.i 0.799825i
552552 343996. + 172458.i 1.12895 + 0.565985i
553553 −3822.45 −0.0124995
554554 109076. + 282315.i 0.355392 + 0.919846i
555555 193359. 0.627738
556556 −258705. + 234984.i −0.836866 + 0.760132i
557557 179035.i 0.577069i 0.957470 + 0.288534i 0.0931680π0.0931680\pi
−0.957470 + 0.288534i 0.906832π0.906832\pi
558558 −52675.0 136336.i −0.169175 0.437868i
559559 127773.i 0.408898i
560560 −710.960 + 7381.26i −0.00226709 + 0.0235372i
561561 1625.53 0.00516500
562562 162572. 62811.4i 0.514722 0.198868i
563563 −126413. −0.398819 −0.199410 0.979916i 0.563902π-0.563902\pi
−0.199410 + 0.979916i 0.563902π0.563902\pi
564564 −167442. 184345.i −0.526389 0.579527i
565565 6378.40i 0.0199809i
566566 250485. 96777.5i 0.781895 0.302094i
567567 8149.90i 0.0253505i
568568 50044.9 + 25089.4i 0.155118 + 0.0777665i
569569 −160597. −0.496035 −0.248017 0.968756i 0.579779π-0.579779\pi
−0.248017 + 0.968756i 0.579779π0.579779\pi
570570 −36236.9 93790.3i −0.111532 0.288674i
571571 −372210. −1.14160 −0.570802 0.821088i 0.693367π-0.693367\pi
−0.570802 + 0.821088i 0.693367π0.693367\pi
572572 −4677.48 5149.66i −0.0142962 0.0157393i
573573 270791.i 0.824756i
574574 9088.69 + 23523.9i 0.0275853 + 0.0713978i
575575 105869.i 0.320208i
576576 74994.6 + 100440.i 0.226040 + 0.302733i
577577 328066. 0.985393 0.492696 0.870201i 0.336011π-0.336011\pi
0.492696 + 0.870201i 0.336011π0.336011\pi
578578 −308543. + 119209.i −0.923550 + 0.356823i
579579 −250564. −0.747415
580580 101528. 92219.2i 0.301809 0.274135i
581581 17746.0i 0.0525712i
582582 −227888. + 88047.0i −0.672784 + 0.259937i
583583 24201.7i 0.0712047i
584584 −220365. + 439554.i −0.646125 + 1.28880i
585585 18697.3 0.0546345
586586 −61205.2 158415.i −0.178235 0.461318i
587587 128807. 0.373822 0.186911 0.982377i 0.440152π-0.440152\pi
0.186911 + 0.982377i 0.440152π0.440152\pi
588588 201310. 182852.i 0.582252 0.528864i
589589 378142.i 1.08999i
590590 7335.85 + 18987.1i 0.0210740 + 0.0545449i
591591 44605.1i 0.127706i
592592 −620784. 59793.6i −1.77132 0.170613i
593593 −210780. −0.599405 −0.299703 0.954033i 0.596887π-0.596887\pi
−0.299703 + 0.954033i 0.596887π0.596887\pi
594594 23521.0 9087.58i 0.0666627 0.0257558i
595595 833.603 0.00235464
596596 −212412. 233855.i −0.597980 0.658345i
597597 147765.i 0.414595i
598598 −172691. + 66720.9i −0.482911 + 0.186578i
599599 187457.i 0.522453i −0.965278 0.261226i 0.915873π-0.915873\pi
0.965278 0.261226i 0.0841269π-0.0841269\pi
600600 −25452.8 + 50769.9i −0.0707023 + 0.141027i
601601 14463.8 0.0400436 0.0200218 0.999800i 0.493626π-0.493626\pi
0.0200218 + 0.999800i 0.493626π0.493626\pi
602602 8732.85 + 22602.9i 0.0240970 + 0.0623692i
603603 147591. 0.405907
604604 305294. + 336113.i 0.836843 + 0.921321i
605605 162984.i 0.445280i
606606 −73324.1 189782.i −0.199665 0.516784i
607607 579553.i 1.57295i 0.617620 + 0.786477i 0.288097π0.288097\pi
−0.617620 + 0.786477i 0.711903π0.711903\pi
608608 87336.0 + 312322.i 0.236258 + 0.844880i
609609 14102.4 0.0380239
610610 −163566. + 63195.6i −0.439577 + 0.169835i
611611 119814. 0.320940
612612 10430.6 9474.19i 0.0278488 0.0252953i
613613 377775.i 1.00534i −0.864479 0.502669i 0.832352π-0.832352\pi
0.864479 0.502669i 0.167648π-0.167648\pi
614614 −84251.9 + 32551.6i −0.223482 + 0.0863448i
615615 193143.i 0.510656i
616616 −1179.40 591.279i −0.00310814 0.00155823i
617617 699981. 1.83872 0.919361 0.393414i 0.128706π-0.128706\pi
0.919361 + 0.393414i 0.128706π0.128706\pi
618618 81977.9 + 212180.i 0.214644 + 0.555555i
619619 −117981. −0.307915 −0.153957 0.988077i 0.549202π-0.549202\pi
−0.153957 + 0.988077i 0.549202π0.549202\pi
620620 −158105. + 143608.i −0.411302 + 0.373589i
621621 671020.i 1.74001i
622622 150064. + 388403.i 0.387877 + 1.00393i
623623 33973.9i 0.0875324i
624624 98855.8 + 9521.75i 0.253883 + 0.0244539i
625625 15625.0 0.0400000
626626 −313438. + 121100.i −0.799840 + 0.309027i
627627 17888.9 0.0455039
628628 −47947.0 52787.2i −0.121575 0.133847i
629629 70108.2i 0.177202i
630630 3307.53 1277.90i 0.00833341 0.00321970i
631631 749113.i 1.88143i −0.339193 0.940717i 0.610154π-0.610154\pi
0.339193 0.940717i 0.389846π-0.389846\pi
632632 84409.9 + 42317.8i 0.211329 + 0.105947i
633633 150450. 0.375478
634634 76339.3 + 197586.i 0.189920 + 0.491561i
635635 71191.1 0.176554
636636 −232295. 255744.i −0.574281 0.632254i
637637 130840.i 0.322449i
638638 8794.62 + 22762.7i 0.0216061 + 0.0559220i
639639 26768.7i 0.0655579i
640640 97416.8 155127.i 0.237834 0.378728i
641641 190520. 0.463686 0.231843 0.972753i 0.425525π-0.425525\pi
0.231843 + 0.972753i 0.425525π0.425525\pi
642642 −53069.1 + 20503.8i −0.128757 + 0.0497467i
643643 272152. 0.658248 0.329124 0.944287i 0.393247π-0.393247\pi
0.329124 + 0.944287i 0.393247π0.393247\pi
644644 −25988.7 + 23605.7i −0.0626631 + 0.0569174i
645645 185581.i 0.446081i
646646 34006.5 13138.8i 0.0814887 0.0314840i
647647 26959.8i 0.0644034i −0.999481 0.0322017i 0.989748π-0.989748\pi
0.999481 0.0322017i 0.0102519π-0.0102519\pi
648648 −90226.4 + 179971.i −0.214874 + 0.428602i
649649 −3621.46 −0.00859794
650650 −9847.25 25487.2i −0.0233071 0.0603247i
651651 −21960.8 −0.0518187
652652 −22628.4 + 20553.6i −0.0532303 + 0.0483495i
653653 497282.i 1.16621i −0.812397 0.583104i 0.801838π-0.801838\pi
0.812397 0.583104i 0.198162π-0.198162\pi
654654 207570. + 537244.i 0.485299 + 1.25608i
655655 193965.i 0.452108i
656656 59726.8 620089.i 0.138791 1.44094i
657657 235115. 0.544689
658658 21194.9 8188.88i 0.0489530 0.0189135i
659659 150938. 0.347558 0.173779 0.984785i 0.444402π-0.444402\pi
0.173779 + 0.984785i 0.444402π0.444402\pi
660660 −6793.71 7479.52i −0.0155962 0.0171706i
661661 535544.i 1.22572i −0.790191 0.612861i 0.790018π-0.790018\pi
0.790191 0.612861i 0.209982π-0.209982\pi
662662 −230332. + 88991.3i −0.525580 + 0.203063i
663663 11164.3i 0.0253982i
664664 196463. 391879.i 0.445600 0.888823i
665665 9173.75 0.0207445
666666 107475. + 278172.i 0.242302 + 0.627141i
667667 649388. 1.45966
668668 546110. + 601239.i 1.22385 + 1.34739i
669669 332332.i 0.742539i
670670 −77731.6 201189.i −0.173160 0.448183i
671671 31197.5i 0.0692908i
672672 18138.3 5072.09i 0.0401659 0.0112318i
673673 −189265. −0.417868 −0.208934 0.977930i 0.566999π-0.566999\pi
−0.208934 + 0.977930i 0.566999π0.566999\pi
674674 −57703.1 + 22294.2i −0.127022 + 0.0490763i
675675 99034.9 0.217361
676676 302898. 275125.i 0.662832 0.602056i
677677 464037.i 1.01245i 0.862400 + 0.506227i 0.168960π0.168960\pi
−0.862400 + 0.506227i 0.831040π0.831040\pi
678678 −15111.5 + 5838.50i −0.0328737 + 0.0127011i
679679 22290.0i 0.0483472i
680680 −18408.2 9228.70i −0.0398101 0.0199583i
681681 14153.9 0.0305199
682682 −13695.4 35447.1i −0.0294446 0.0762100i
683683 −42942.9 −0.0920556 −0.0460278 0.998940i 0.514656π-0.514656\pi
−0.0460278 + 0.998940i 0.514656π0.514656\pi
684684 114788. 104263.i 0.245349 0.222853i
685685 4758.99i 0.0101422i
686686 17910.0 + 46355.8i 0.0380582 + 0.0985044i
687687 323661.i 0.685769i
688688 57388.3 595812.i 0.121240 1.25873i
689689 166219. 0.350140
690690 −250821. + 96907.4i −0.526824 + 0.203544i
691691 −695800. −1.45723 −0.728615 0.684924i 0.759836π-0.759836\pi
−0.728615 + 0.684924i 0.759836π0.759836\pi
692692 −455780. 501790.i −0.951795 1.04788i
693693 630.855i 0.00131360i
694694 −277393. + 107174.i −0.575939 + 0.222520i
695695 244216.i 0.505598i
696696 −311418. 156125.i −0.642872 0.322296i
697697 −70029.8 −0.144151
698698 118787. + 307451.i 0.243814 + 0.631052i
699699 −584208. −1.19568
700700 −3483.93 3835.63i −0.00711007 0.00782781i
701701 243528.i 0.495580i 0.968814 + 0.247790i 0.0797043π0.0797043\pi
−0.968814 + 0.247790i 0.920296π0.920296\pi
702702 −62414.2 161544.i −0.126651 0.327805i
703703 771536.i 1.56115i
704704 19498.4 + 26114.0i 0.0393418 + 0.0526901i
705705 174021. 0.350125
706706 573397. 221538.i 1.15039 0.444467i
707707 18562.8 0.0371368
708708 38268.7 34759.8i 0.0763445 0.0693443i
709709 210565.i 0.418883i 0.977821 + 0.209442i 0.0671646π0.0671646\pi
−0.977821 + 0.209442i 0.932835π0.932835\pi
710710 −36489.7 + 14098.2i −0.0723858 + 0.0279670i
711711 45150.3i 0.0893144i
712712 376120. 750234.i 0.741936 1.47991i
713713 −1.01126e6 −1.98922
714714 −763.042 1974.95i −0.00149676 0.00387400i
715715 4861.25 0.00950903
716716 −614712. + 558348.i −1.19907 + 1.08913i
717717 744216.i 1.44764i
718718 339571. + 878897.i 0.658691 + 1.70486i
719719 174495.i 0.337539i 0.985656 + 0.168770i 0.0539794π0.0539794\pi
−0.985656 + 0.168770i 0.946021π0.946021\pi
720720 −87186.5 8397.77i −0.168184 0.0161994i
721721 −20753.6 −0.0399229
722722 −112013. + 43277.6i −0.214880 + 0.0830211i
723723 72030.1 0.137796
724724 87961.6 + 96841.1i 0.167809 + 0.184749i
725725 95842.3i 0.182340i
726726 −386136. + 149188.i −0.732601 + 0.283048i
727727 511384.i 0.967561i 0.875189 + 0.483781i 0.160737π0.160737\pi
−0.875189 + 0.483781i 0.839263π0.839263\pi
728728 −4060.94 + 8100.23i −0.00766239 + 0.0152839i
729729 551848. 1.03840
730730 −123827. 320496.i −0.232365 0.601419i
731731 −67288.0 −0.125922
732732 299443. + 329671.i 0.558845 + 0.615259i
733733 384728.i 0.716055i 0.933711 + 0.358027i 0.116551π0.116551\pi
−0.933711 + 0.358027i 0.883449π0.883449\pi
734734 −162493. 420574.i −0.301608 0.780639i
735735 190036.i 0.351771i
736736 835234. 233560.i 1.54189 0.431165i
737737 38373.4 0.0706473
738738 −277861. + 107355.i −0.510170 + 0.197110i
739739 −66307.5 −0.121415 −0.0607077 0.998156i 0.519336π-0.519336\pi
−0.0607077 + 0.998156i 0.519336π0.519336\pi
740740 322586. 293008.i 0.589091 0.535077i
741741 122862.i 0.223760i
742742 29403.9 11360.5i 0.0534069 0.0206343i
743743 786533.i 1.42475i −0.701798 0.712376i 0.747619π-0.747619\pi
0.701798 0.712376i 0.252381π-0.252381\pi
744744 484953. + 243125.i 0.876101 + 0.439222i
745745 220757. 0.397743
746746 −23181.2 59998.8i −0.0416541 0.107811i
747747 −209613. −0.375645
748748 2711.93 2463.27i 0.00484702 0.00440259i
749749 5190.76i 0.00925268i
750750 −14302.4 37018.3i −0.0254265 0.0658104i
751751 743780.i 1.31876i 0.751811 + 0.659379i 0.229181π0.229181\pi
−0.751811 + 0.659379i 0.770819π0.770819\pi
752752 −558698. 53813.6i −0.987965 0.0951604i
753753 105667. 0.186359
754754 156336. 60402.1i 0.274990 0.106245i
755755 −317288. −0.556622
756756 −22082.0 24311.1i −0.0386362 0.0425365i
757757 378393.i 0.660315i 0.943926 + 0.330158i 0.107102π0.107102\pi
−0.943926 + 0.330158i 0.892898π0.892898\pi
758758 779130. 301025.i 1.35604 0.523919i
759759 47839.9i 0.0830437i
760760 −202581. 101561.i −0.350729 0.175833i
761761 −487660. −0.842070 −0.421035 0.907044i 0.638333π-0.638333\pi
−0.421035 + 0.907044i 0.638333π0.638333\pi
762762 −65165.2 168664.i −0.112229 0.290478i
763763 −52548.6 −0.0902634
764764 410346. + 451770.i 0.703013 + 0.773981i
765765 9846.41i 0.0168250i
766766 138476. + 358410.i 0.236002 + 0.610834i
767767 24872.5i 0.0422793i
768768 −456694. 88800.9i −0.774288 0.150555i
769769 −264950. −0.448034 −0.224017 0.974585i 0.571917π-0.571917\pi
−0.224017 + 0.974585i 0.571917π0.571917\pi
770770 859.950 332.251i 0.00145041 0.000560382i
771771 453595. 0.763061
772772 −418024. + 379695.i −0.701401 + 0.637089i
773773 515794.i 0.863212i −0.902062 0.431606i 0.857947π-0.857947\pi
0.902062 0.431606i 0.142053π-0.142053\pi
774774 −266982. + 103151.i −0.445657 + 0.172184i
775775 149250.i 0.248491i
776776 −246770. + 492224.i −0.409797 + 0.817408i
777777 44807.4 0.0742178
778778 −243413. 630015.i −0.402147 1.04086i
779779 −770674. −1.26998
780780 −51369.8 + 46659.7i −0.0844343 + 0.0766924i
781781 6959.79i 0.0114102i
782782 −35136.7 90942.8i −0.0574576 0.148715i
783783 607471.i 0.990836i
784784 58765.9 610114.i 0.0956078 0.992610i
785785 49830.8 0.0808646
786786 459538. 177547.i 0.743834 0.287388i
787787 −537891. −0.868449 −0.434225 0.900805i 0.642978π-0.642978\pi
−0.434225 + 0.900805i 0.642978π0.642978\pi
788788 −67592.7 74416.1i −0.108855 0.119843i
789789 328443.i 0.527601i
790790 −61546.6 + 23779.2i −0.0986166 + 0.0381016i
791791 1478.08i 0.00236235i
792792 6984.11 13931.0i 0.0111342 0.0222091i
793793 −214267. −0.340729
794794 −273140. 706955.i −0.433255 1.12138i
795795 241421. 0.381980
796796 223917. + 246521.i 0.353396 + 0.389071i
797797 839237.i 1.32120i 0.750739 + 0.660599i 0.229698π0.229698\pi
−0.750739 + 0.660599i 0.770302π0.770302\pi
798798 −8397.24 21734.2i −0.0131865 0.0341301i
799799 63096.6i 0.0988353i
800800 34470.9 + 123271.i 0.0538607 + 0.192611i
801801 −401295. −0.625459
802802 449081. 173507.i 0.698194 0.269755i
803803 61129.2 0.0948021
804804 −405500. + 368319.i −0.627305 + 0.569786i
805805 24533.1i 0.0378583i
806806 −243453. + 94060.8i −0.374753 + 0.144790i
807807 619588.i 0.951384i
808808 −409916. 205506.i −0.627874 0.314776i
809809 514568. 0.786223 0.393111 0.919491i 0.371399π-0.371399\pi
0.393111 + 0.919491i 0.371399π0.371399\pi
810810 −50699.9 131224.i −0.0772747 0.200007i
811811 174798. 0.265763 0.132881 0.991132i 0.457577π-0.457577\pi
0.132881 + 0.991132i 0.457577π0.457577\pi
812812 23527.4 21370.1i 0.0356830 0.0324112i
813813 1.01077e6i 1.52922i
814814 27943.2 + 72324.1i 0.0421723 + 0.109153i
815815 21361.1i 0.0321594i
816816 −5014.37 + 52059.7i −0.00753071 + 0.0781846i
817817 −740500. −1.10938
818818 561502. 216942.i 0.839160 0.324218i
819819 4332.76 0.00645947
820820 292680. + 322226.i 0.435277 + 0.479217i
821821 1.02886e6i 1.52641i 0.646159 + 0.763203i 0.276374π0.276374\pi
−0.646159 + 0.763203i 0.723626π0.723626\pi
822822 −11274.9 + 4356.17i −0.0166866 + 0.00644705i
823823 54452.4i 0.0803928i −0.999192 0.0401964i 0.987202π-0.987202\pi
0.999192 0.0401964i 0.0127984π-0.0127984\pi
824824 458294. + 229760.i 0.674979 + 0.338392i
825825 7060.62 0.0103737
826826 1699.95 + 4399.91i 0.00249159 + 0.00644887i
827827 1.20898e6 1.76770 0.883848 0.467773i 0.154944π-0.154944\pi
0.883848 + 0.467773i 0.154944π0.154944\pi
828828 −278828. 306975.i −0.406701 0.447757i
829829 366682.i 0.533556i 0.963758 + 0.266778i 0.0859591π0.0859591\pi
−0.963758 + 0.266778i 0.914041π0.914041\pi
830830 110396. + 285734.i 0.160250 + 0.414769i
831831 537143.i 0.777836i
832832 179353. 133917.i 0.259097 0.193458i
833833 −68903.2 −0.0993001
834834 −578591. + 223545.i −0.831839 + 0.321390i
835835 −567566. −0.814035
836836 29844.6 27108.1i 0.0427025 0.0387870i
837837 945980.i 1.35030i
838838 1.07790e6 416459.i 1.53494 0.593041i
839839 1.27074e6i 1.80523i −0.430444 0.902617i 0.641643π-0.641643\pi
0.430444 0.902617i 0.358357π-0.358357\pi
840840 −5898.23 + 11765.0i −0.00835917 + 0.0166738i
841841 119393. 0.168806
842842 −262808. 680214.i −0.370693 0.959448i
843843 309315. 0.435257
844844 251000. 227985.i 0.352362 0.320053i
845845 285934.i 0.400454i
846846 96726.0 + 250352.i 0.135146 + 0.349792i
847847 37768.5i 0.0526457i
848848 −775088. 74656.2i −1.07785 0.103818i
849849 476581. 0.661183
850850 13422.1 5185.78i 0.0185773 0.00717755i
851851 2.06330e6 2.84907
852852 66802.1 + 73545.6i 0.0920260 + 0.101316i
853853 927864.i 1.27522i 0.770358 + 0.637612i 0.220077π0.220077\pi
−0.770358 + 0.637612i 0.779923π0.779923\pi
854854 −37903.6 + 14644.4i −0.0519714 + 0.0200797i
855855 108359.i 0.148229i
856856 −57466.2 + 114626.i −0.0784269 + 0.156435i
857857 155651. 0.211928 0.105964 0.994370i 0.466207π-0.466207\pi
0.105964 + 0.994370i 0.466207π0.466207\pi
858858 −4449.77 11517.1i −0.00604454 0.0156448i
859859 −1.04127e6 −1.41116 −0.705578 0.708632i 0.749313π-0.749313\pi
−0.705578 + 0.708632i 0.749313π0.749313\pi
860860 281221. + 309610.i 0.380234 + 0.418618i
861861 44757.3i 0.0603751i
862862 144873. + 374967.i 0.194972 + 0.504637i
863863 1.42220e6i 1.90959i −0.297264 0.954795i 0.596074π-0.596074\pi
0.297264 0.954795i 0.403926π-0.403926\pi
864864 218484. + 781321.i 0.292680 + 1.04665i
865865 473687. 0.633081
866866 1.22440e6 473060.i 1.63263 0.630784i
867867 −587045. −0.780968
868868 −36637.9 + 33278.5i −0.0486285 + 0.0441697i
869869 11739.0i 0.0155450i
870870 227067. 87729.7i 0.299996 0.115907i
871871 263551.i 0.347399i
872872 1.16041e6 + 581758.i 1.52609 + 0.765084i
873873 263287. 0.345463
874874 −386678. 1.00082e6i −0.506205 1.31019i
875875 3620.81 0.00472922
876876 −645965. + 586735.i −0.841784 + 0.764600i
877877 577824.i 0.751271i −0.926768 0.375635i 0.877424π-0.877424\pi
0.926768 0.375635i 0.122576π-0.122576\pi
878878 223810. + 579278.i 0.290329 + 0.751446i
879879 301405.i 0.390098i
880880 −22668.3 2183.40i −0.0292721 0.00281947i
881881 −95874.2 −0.123524 −0.0617618 0.998091i 0.519672π-0.519672\pi
−0.0617618 + 0.998091i 0.519672π0.519672\pi
882882 −273391. + 105627.i −0.351437 + 0.135781i
883883 1.28768e6 1.65153 0.825765 0.564014i 0.190744π-0.190744\pi
0.825765 + 0.564014i 0.190744π0.190744\pi
884884 −16917.9 18625.7i −0.0216492 0.0238346i
885885 36125.5i 0.0461240i
886886 −1.26059e6 + 487042.i −1.60585 + 0.620439i
887887 1.17289e6i 1.49077i −0.666633 0.745386i 0.732265π-0.732265\pi
0.666633 0.745386i 0.267735π-0.267735\pi
888888 −989468. 496057.i −1.25480 0.629079i
889889 16497.3 0.0208741
890890 211349. + 547025.i 0.266821 + 0.690601i
891891 25028.8 0.0315272
892892 −503601. 554439.i −0.632932 0.696825i
893893 694374.i 0.870744i
894894 −202071. 523012.i −0.252831 0.654390i
895895 580284.i 0.724427i
896896 22574.6 35947.9i 0.0281193 0.0447772i
897897 −328568. −0.408357
898898 −915903. + 353869.i −1.13579 + 0.438823i
899899 915484. 1.13274
900900 45306.0 41151.8i 0.0559333 0.0508047i
901901 87534.6i 0.107828i
902902 −72243.2 + 27911.9i −0.0887940 + 0.0343065i
903903 43005.0i 0.0527404i
904904 −16363.6 + 32639.9i −0.0200236 + 0.0399404i
905905 −91417.5 −0.111617
906906 290431. + 751711.i 0.353824 + 0.915787i
907907 410980. 0.499581 0.249791 0.968300i 0.419638π-0.419638\pi
0.249791 + 0.968300i 0.419638π0.419638\pi
908908 23613.4 21448.3i 0.0286409 0.0260148i
909909 219261.i 0.265359i
910910 −2281.92 5906.20i −0.00275561 0.00713223i
911911 67611.8i 0.0814678i −0.999170 0.0407339i 0.987030π-0.987030\pi
0.999170 0.0407339i 0.0129696π-0.0129696\pi
912912 −55182.8 + 572914.i −0.0663459 + 0.688810i
913913 −54498.9 −0.0653802
914914 −429114. + 165793.i −0.513666 + 0.198460i
915915 −311207. −0.371713
916916 490463. + 539974.i 0.584542 + 0.643550i
917917 44948.0i 0.0534529i
918918 85072.6 32868.7i 0.100950 0.0390029i
919919 423513.i 0.501459i −0.968057 0.250729i 0.919330π-0.919330\pi
0.968057 0.250729i 0.0806705π-0.0806705\pi
920920 −271603. + 541757.i −0.320892 + 0.640072i
921921 −160301. −0.188980
922922 166440. + 430790.i 0.195793 + 0.506762i
923923 −47800.4 −0.0561084
924924 −1574.32 1733.24i −0.00184395 0.00203009i
925925 304520.i 0.355903i
926926 −444491. 1.15046e6i −0.518371 1.34168i
927927 245139.i 0.285268i
928928 −756133. + 211441.i −0.878016 + 0.245524i
929929 963117. 1.11596 0.557979 0.829855i 0.311577π-0.311577\pi
0.557979 + 0.829855i 0.311577π0.311577\pi
930930 −353599. + 136617.i −0.408832 + 0.157956i
931931 −758276. −0.874839
932932 −974652. + 885285.i −1.12206 + 1.01918i
933933 738989.i 0.848935i
934934 −873671. + 337552.i −1.00151 + 0.386943i
935935 2560.04i 0.00292836i
936936 −95678.9 47967.4i −0.109211 0.0547513i
937937 −1.35035e6 −1.53804 −0.769019 0.639226i 0.779255π-0.779255\pi
−0.769019 + 0.639226i 0.779255π0.779255\pi
938938 −18012.9 46621.9i −0.0204728 0.0529889i
939939 −596358. −0.676357
940940 290324. 263704.i 0.328570 0.298443i
941941 651491.i 0.735748i −0.929876 0.367874i 0.880086π-0.880086\pi
0.929876 0.367874i 0.119914π-0.119914\pi
942942 −45612.9 118058.i −0.0514027 0.133043i
943943 2.06099e6i 2.31768i
944944 11171.3 115982.i 0.0125360 0.130150i
945945 22949.6 0.0256987
946946 −69414.7 + 26819.1i −0.0775656 + 0.0299683i
947947 −1.31859e6 −1.47032 −0.735158 0.677896i 0.762892π-0.762892\pi
−0.735158 + 0.677896i 0.762892π0.762892\pi
948948 112674. + 124048.i 0.125374 + 0.138030i
949949 419840.i 0.466177i
950950 147710. 57069.2i 0.163667 0.0632346i
951951 375934.i 0.415671i
952952 −4265.76 2138.58i −0.00470677 0.00235968i
953953 −76396.5 −0.0841178 −0.0420589 0.999115i 0.513392π-0.513392\pi
−0.0420589 + 0.999115i 0.513392π0.513392\pi
954954 134189. + 347316.i 0.147442 + 0.381617i
955955 −426468. −0.467605
956956 −1.12775e6 1.24160e6i −1.23395 1.35852i
957957 43309.2i 0.0472886i
958958 253546. + 656242.i 0.276265 + 0.715044i
959959 1102.81i 0.00119912i
960960 260497. 194504.i 0.282658 0.211051i
961961 −502111. −0.543692
962962 496727. 191916.i 0.536744 0.207377i
963963 61312.6 0.0661146
964964 120170. 109151.i 0.129313 0.117456i
965965 394612.i 0.423756i
966966 −58123.2 + 22456.5i −0.0622867 + 0.0240651i
967967 462106.i 0.494184i −0.968992 0.247092i 0.920525π-0.920525\pi
0.968992 0.247092i 0.0794749π-0.0794749\pi
968968 −418130. + 834029.i −0.446232 + 0.890083i
969969 64702.0 0.0689081
970970 −138665. 358900.i −0.147375 0.381443i
971971 901828. 0.956501 0.478250 0.878223i 0.341271π-0.341271\pi
0.478250 + 0.878223i 0.341271π0.341271\pi
972972 495577. 450137.i 0.524540 0.476444i
973973 56592.7i 0.0597771i
974974 −416741. 1.07863e6i −0.439287 1.13699i
975975 48492.8i 0.0510115i
976976 999139. + 96236.6i 1.04888 + 0.101028i
977977 46500.7 0.0487159 0.0243580 0.999703i 0.492246π-0.492246\pi
0.0243580 + 0.999703i 0.492246π0.492246\pi
978978 −50608.1 + 19553.0i −0.0529106 + 0.0204426i
979979 −104336. −0.108860
980980 287972. + 317042.i 0.299846 + 0.330115i
981981 620697.i 0.644973i
982982 682110. 263540.i 0.707345 0.273290i
983983 649309.i 0.671961i 0.941869 + 0.335981i 0.109068π0.109068\pi
−0.941869 + 0.335981i 0.890932π0.890932\pi
984984 495502. 988361.i 0.511747 1.02076i
985985 70248.3 0.0724042
986986 31809.1 + 82330.1i 0.0327188 + 0.0846846i
987987 40326.2 0.0413955
988988 −186180. 204975.i −0.190730 0.209984i
989989 1.98030e6i 2.02460i
990990 3924.50 + 10157.6i 0.00400419 + 0.0103639i
991991 194704.i 0.198257i −0.995075 0.0991285i 0.968395π-0.968395\pi
0.995075 0.0991285i 0.0316055π-0.0316055\pi
992992 1.17748e6 329265.i 1.19655 0.334597i
993993 −438238. −0.444439
994994 −8455.83 + 3267.00i −0.00855822 + 0.00330656i
995995 −232715. −0.235060
996996 575902. 523096.i 0.580537 0.527306i
997997 1.72172e6i 1.73210i −0.499959 0.866049i 0.666652π-0.666652\pi
0.499959 0.866049i 0.333348π-0.333348\pi
998998 1.73020e6 668481.i 1.73714 0.671163i
999999 1.93012e6i 1.93398i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 40.5.g.a.11.15 16
3.2 odd 2 360.5.g.a.91.2 16
4.3 odd 2 160.5.g.a.111.6 16
5.2 odd 4 200.5.e.e.99.20 32
5.3 odd 4 200.5.e.e.99.13 32
5.4 even 2 200.5.g.h.51.2 16
8.3 odd 2 inner 40.5.g.a.11.16 yes 16
8.5 even 2 160.5.g.a.111.5 16
12.11 even 2 1440.5.g.a.271.5 16
20.3 even 4 800.5.e.e.399.17 32
20.7 even 4 800.5.e.e.399.16 32
20.19 odd 2 800.5.g.h.751.12 16
24.5 odd 2 1440.5.g.a.271.12 16
24.11 even 2 360.5.g.a.91.1 16
40.3 even 4 200.5.e.e.99.19 32
40.13 odd 4 800.5.e.e.399.15 32
40.19 odd 2 200.5.g.h.51.1 16
40.27 even 4 200.5.e.e.99.14 32
40.29 even 2 800.5.g.h.751.11 16
40.37 odd 4 800.5.e.e.399.18 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.5.g.a.11.15 16 1.1 even 1 trivial
40.5.g.a.11.16 yes 16 8.3 odd 2 inner
160.5.g.a.111.5 16 8.5 even 2
160.5.g.a.111.6 16 4.3 odd 2
200.5.e.e.99.13 32 5.3 odd 4
200.5.e.e.99.14 32 40.27 even 4
200.5.e.e.99.19 32 40.3 even 4
200.5.e.e.99.20 32 5.2 odd 4
200.5.g.h.51.1 16 40.19 odd 2
200.5.g.h.51.2 16 5.4 even 2
360.5.g.a.91.1 16 24.11 even 2
360.5.g.a.91.2 16 3.2 odd 2
800.5.e.e.399.15 32 40.13 odd 4
800.5.e.e.399.16 32 20.7 even 4
800.5.e.e.399.17 32 20.3 even 4
800.5.e.e.399.18 32 40.37 odd 4
800.5.g.h.751.11 16 40.29 even 2
800.5.g.h.751.12 16 20.19 odd 2
1440.5.g.a.271.5 16 12.11 even 2
1440.5.g.a.271.12 16 24.5 odd 2