Properties

Label 1183.2.e.g.508.1
Level 11831183
Weight 22
Character 1183.508
Analytic conductor 9.4469.446
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1183,2,Mod(170,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.170");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1183=7132 1183 = 7 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1183.e (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 9.446302559129.44630255912
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12x11+7x102x9+33x811x7+55x6+17x5+47x4+x3+8x2+x+1 x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 508.1
Root 0.181721+0.314749i-0.181721 + 0.314749i of defining polynomial
Character χ\chi == 1183.508
Dual form 1183.2.e.g.170.1

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+(1.194022.06810i)q2+(1.375742.38285i)q3+(1.85136+3.20665i)q4+(0.491140+0.850679i)q56.57063q6+(1.69505+2.03145i)q7+4.06616q8+(2.285323.95828i)q9+(1.172862.03145i)q10+(0.293901+0.509052i)q11+(5.09398+8.82303i)q12+(2.177335.93113i)q14+2.70272q15+(1.152351.99593i)q16+(3.227105.58950i)q17+(5.45742+9.45253i)q18+(1.913453.31419i)q193.63711q20+(7.172601.24430i)q21+1.40369q22+(4.130017.15338i)q23+(5.593989.68906i)q24+(2.017563.49452i)q254.32156q27+(9.65231+1.67448i)q283.96018q29+(3.227105.58950i)q30+(1.49436+2.58831i)q31+(1.314302.27644i)q32+(0.808663+1.40065i)q3315.4129q34+(0.895609+2.43967i)q35+16.9238q36+(0.877941+1.52064i)q37+(4.56938+7.91440i)q38+(1.99705+3.45900i)q403.67169q41+(11.137613.3479i)q42+6.38085q43+(1.088231.88488i)q44+(2.244823.88814i)q45+(9.86261+17.0825i)q46+(2.170303.75906i)q476.34134q48+(1.25361+6.88683i)q499.63603q50+(8.8793015.3794i)q51+(0.212770+0.368529i)q53+(5.16002+8.93742i)q540.577387q55+(6.89235+8.26022i)q5610.5296q57+(4.72853+8.19006i)q58+(3.004315.20362i)q59+(5.00371+8.66669i)q60+(1.103371.91109i)q61+7.13717q62+(4.1673511.3520i)q6310.8866q64+(1.931123.34479i)q66+(3.506516.07346i)q67+(11.9491+20.6964i)q6822.7272q69+(6.114861.06080i)q703.60253q71+(9.2924716.0950i)q72+(2.467144.27321i)q73+(2.096563.63134i)q74+(5.551289.61510i)q75+14.1699q76+(1.53229+0.265822i)q77+(1.392702.41223i)q79+(1.131931.96056i)q80+(0.9106091.57722i)q81+(4.38406+7.59342i)q82+2.86819q83+(9.28903+25.3037i)q84+6.33983q85+(7.6188513.1962i)q86+(5.44818+9.43652i)q87+(1.19505+2.06989i)q88+(1.046561.81269i)q8910.7214q90+30.5845q92+(4.11170+7.12167i)q93+(5.18275+8.97679i)q94+(1.879543.25546i)q95+(3.616286.26357i)q967.69704q97+(15.73955.63041i)q98+2.68663q99+O(q100)q+(-1.19402 - 2.06810i) q^{2} +(1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} -6.57063 q^{6} +(1.69505 + 2.03145i) q^{7} +4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(1.17286 - 2.03145i) q^{10} +(-0.293901 + 0.509052i) q^{11} +(5.09398 + 8.82303i) q^{12} +(2.17733 - 5.93113i) q^{14} +2.70272 q^{15} +(-1.15235 - 1.99593i) q^{16} +(3.22710 - 5.58950i) q^{17} +(-5.45742 + 9.45253i) q^{18} +(-1.91345 - 3.31419i) q^{19} -3.63711 q^{20} +(7.17260 - 1.24430i) q^{21} +1.40369 q^{22} +(-4.13001 - 7.15338i) q^{23} +(5.59398 - 9.68906i) q^{24} +(2.01756 - 3.49452i) q^{25} -4.32156 q^{27} +(-9.65231 + 1.67448i) q^{28} -3.96018 q^{29} +(-3.22710 - 5.58950i) q^{30} +(-1.49436 + 2.58831i) q^{31} +(1.31430 - 2.27644i) q^{32} +(0.808663 + 1.40065i) q^{33} -15.4129 q^{34} +(-0.895609 + 2.43967i) q^{35} +16.9238 q^{36} +(0.877941 + 1.52064i) q^{37} +(-4.56938 + 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} -3.67169 q^{41} +(-11.1376 - 13.3479i) q^{42} +6.38085 q^{43} +(-1.08823 - 1.88488i) q^{44} +(2.24482 - 3.88814i) q^{45} +(-9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} -6.34134 q^{48} +(-1.25361 + 6.88683i) q^{49} -9.63603 q^{50} +(-8.87930 - 15.3794i) q^{51} +(-0.212770 + 0.368529i) q^{53} +(5.16002 + 8.93742i) q^{54} -0.577387 q^{55} +(6.89235 + 8.26022i) q^{56} -10.5296 q^{57} +(4.72853 + 8.19006i) q^{58} +(3.00431 - 5.20362i) q^{59} +(-5.00371 + 8.66669i) q^{60} +(-1.10337 - 1.91109i) q^{61} +7.13717 q^{62} +(4.16735 - 11.3520i) q^{63} -10.8866 q^{64} +(1.93112 - 3.34479i) q^{66} +(3.50651 - 6.07346i) q^{67} +(11.9491 + 20.6964i) q^{68} -22.7272 q^{69} +(6.11486 - 1.06080i) q^{70} -3.60253 q^{71} +(-9.29247 - 16.0950i) q^{72} +(2.46714 - 4.27321i) q^{73} +(2.09656 - 3.63134i) q^{74} +(-5.55128 - 9.61510i) q^{75} +14.1699 q^{76} +(-1.53229 + 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} +(1.13193 - 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(-9.28903 + 25.3037i) q^{84} +6.33983 q^{85} +(-7.61885 - 13.1962i) q^{86} +(-5.44818 + 9.43652i) q^{87} +(-1.19505 + 2.06989i) q^{88} +(-1.04656 - 1.81269i) q^{89} -10.7214 q^{90} +30.5845 q^{92} +(4.11170 + 7.12167i) q^{93} +(-5.18275 + 8.97679i) q^{94} +(1.87954 - 3.25546i) q^{95} +(-3.61628 - 6.26357i) q^{96} -7.69704 q^{97} +(15.7395 - 5.63041i) q^{98} +2.68663 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q2q2+q34q4q518q6+6q7+6q8+3q9+4q104q11+5q122q144q15+8q16+5q173q18+q192q20+9q21++20q99+O(q100) 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21}+ \cdots + 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1183Z)×\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times.

nn 339339 10161016
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.19402 2.06810i −0.844299 1.46237i −0.886229 0.463248i 0.846684π-0.846684\pi
0.0419302 0.999121i 0.486649π-0.486649\pi
33 1.37574 2.38285i 0.794283 1.37574i −0.129010 0.991643i 0.541180π-0.541180\pi
0.923293 0.384096i 0.125487π-0.125487\pi
44 −1.85136 + 3.20665i −0.925680 + 1.60333i
55 0.491140 + 0.850679i 0.219644 + 0.380435i 0.954699 0.297572i 0.0961769π-0.0961769\pi
−0.735055 + 0.678008i 0.762844π0.762844\pi
66 −6.57063 −2.68245
77 1.69505 + 2.03145i 0.640669 + 0.767817i
88 4.06616 1.43761
99 −2.28532 3.95828i −0.761772 1.31943i
1010 1.17286 2.03145i 0.370891 0.642402i
1111 −0.293901 + 0.509052i −0.0886146 + 0.153485i −0.906926 0.421291i 0.861577π-0.861577\pi
0.818311 + 0.574775i 0.194911π0.194911\pi
1212 5.09398 + 8.82303i 1.47051 + 2.54699i
1313 0 0
1414 2.17733 5.93113i 0.581916 1.58516i
1515 2.70272 0.697840
1616 −1.15235 1.99593i −0.288088 0.498983i
1717 3.22710 5.58950i 0.782687 1.35565i −0.147685 0.989035i 0.547182π-0.547182\pi
0.930371 0.366619i 0.119485π-0.119485\pi
1818 −5.45742 + 9.45253i −1.28633 + 2.22798i
1919 −1.91345 3.31419i −0.438975 0.760327i 0.558636 0.829413i 0.311325π-0.311325\pi
−0.997611 + 0.0690863i 0.977992π0.977992\pi
2020 −3.63711 −0.813282
2121 7.17260 1.24430i 1.56519 0.271528i
2222 1.40369 0.299269
2323 −4.13001 7.15338i −0.861166 1.49158i −0.870805 0.491629i 0.836402π-0.836402\pi
0.00963902 0.999954i 0.496932π-0.496932\pi
2424 5.59398 9.68906i 1.14187 1.97777i
2525 2.01756 3.49452i 0.403513 0.698904i
2626 0 0
2727 −4.32156 −0.831685
2828 −9.65231 + 1.67448i −1.82412 + 0.316447i
2929 −3.96018 −0.735387 −0.367694 0.929947i 0.619853π-0.619853\pi
−0.367694 + 0.929947i 0.619853π0.619853\pi
3030 −3.22710 5.58950i −0.589185 1.02050i
3131 −1.49436 + 2.58831i −0.268395 + 0.464874i −0.968448 0.249218i 0.919827π-0.919827\pi
0.700053 + 0.714091i 0.253160π0.253160\pi
3232 1.31430 2.27644i 0.232338 0.402421i
3333 0.808663 + 1.40065i 0.140770 + 0.243821i
3434 −15.4129 −2.64329
3535 −0.895609 + 2.43967i −0.151386 + 0.412380i
3636 16.9238 2.82063
3737 0.877941 + 1.52064i 0.144333 + 0.249991i 0.929124 0.369769i 0.120563π-0.120563\pi
−0.784791 + 0.619760i 0.787230π0.787230\pi
3838 −4.56938 + 7.91440i −0.741252 + 1.28389i
3939 0 0
4040 1.99705 + 3.45900i 0.315762 + 0.546916i
4141 −3.67169 −0.573421 −0.286710 0.958017i 0.592562π-0.592562\pi
−0.286710 + 0.958017i 0.592562π0.592562\pi
4242 −11.1376 13.3479i −1.71856 2.05963i
4343 6.38085 0.973070 0.486535 0.873661i 0.338261π-0.338261\pi
0.486535 + 0.873661i 0.338261π0.338261\pi
4444 −1.08823 1.88488i −0.164058 0.284156i
4545 2.24482 3.88814i 0.334638 0.579610i
4646 −9.86261 + 17.0825i −1.45416 + 2.51868i
4747 −2.17030 3.75906i −0.316570 0.548316i 0.663200 0.748442i 0.269198π-0.269198\pi
−0.979770 + 0.200127i 0.935865π0.935865\pi
4848 −6.34134 −0.915294
4949 −1.25361 + 6.88683i −0.179087 + 0.983833i
5050 −9.63603 −1.36274
5151 −8.87930 15.3794i −1.24335 2.15355i
5252 0 0
5353 −0.212770 + 0.368529i −0.0292263 + 0.0506214i −0.880269 0.474476i 0.842638π-0.842638\pi
0.851042 + 0.525097i 0.175971π0.175971\pi
5454 5.16002 + 8.93742i 0.702190 + 1.21623i
5555 −0.577387 −0.0778548
5656 6.89235 + 8.26022i 0.921029 + 1.10382i
5757 −10.5296 −1.39468
5858 4.72853 + 8.19006i 0.620887 + 1.07541i
5959 3.00431 5.20362i 0.391128 0.677454i −0.601470 0.798895i 0.705418π-0.705418\pi
0.992599 + 0.121441i 0.0387516π0.0387516\pi
6060 −5.00371 + 8.66669i −0.645977 + 1.11886i
6161 −1.10337 1.91109i −0.141272 0.244691i 0.786704 0.617331i 0.211786π-0.211786\pi
−0.927976 + 0.372640i 0.878453π0.878453\pi
6262 7.13717 0.906422
6363 4.16735 11.3520i 0.525036 1.43022i
6464 −10.8866 −1.36083
6565 0 0
6666 1.93112 3.34479i 0.237704 0.411716i
6767 3.50651 6.07346i 0.428389 0.741991i −0.568341 0.822793i 0.692415π-0.692415\pi
0.996730 + 0.0808015i 0.0257480π0.0257480\pi
6868 11.9491 + 20.6964i 1.44904 + 2.50980i
6969 −22.7272 −2.73604
7070 6.11486 1.06080i 0.730866 0.126790i
7171 −3.60253 −0.427542 −0.213771 0.976884i 0.568575π-0.568575\pi
−0.213771 + 0.976884i 0.568575π0.568575\pi
7272 −9.29247 16.0950i −1.09513 1.89682i
7373 2.46714 4.27321i 0.288756 0.500141i −0.684757 0.728772i 0.740092π-0.740092\pi
0.973513 + 0.228631i 0.0734249π0.0734249\pi
7474 2.09656 3.63134i 0.243720 0.422135i
7575 −5.55128 9.61510i −0.641007 1.11026i
7676 14.1699 1.62540
7777 −1.53229 + 0.265822i −0.174621 + 0.0302932i
7878 0 0
7979 −1.39270 2.41223i −0.156691 0.271397i 0.776982 0.629522i 0.216749π-0.216749\pi
−0.933674 + 0.358125i 0.883416π0.883416\pi
8080 1.13193 1.96056i 0.126554 0.219198i
8181 0.910609 1.57722i 0.101179 0.175247i
8282 4.38406 + 7.59342i 0.484138 + 0.838552i
8383 2.86819 0.314825 0.157412 0.987533i 0.449685π-0.449685\pi
0.157412 + 0.987533i 0.449685π0.449685\pi
8484 −9.28903 + 25.3037i −1.01352 + 2.76086i
8585 6.33983 0.687651
8686 −7.61885 13.1962i −0.821562 1.42299i
8787 −5.44818 + 9.43652i −0.584106 + 1.01170i
8888 −1.19505 + 2.06989i −0.127393 + 0.220651i
8989 −1.04656 1.81269i −0.110935 0.192145i 0.805213 0.592986i 0.202051π-0.202051\pi
−0.916147 + 0.400842i 0.868718π0.868718\pi
9090 −10.7214 −1.13014
9191 0 0
9292 30.5845 3.18866
9393 4.11170 + 7.12167i 0.426363 + 0.738483i
9494 −5.18275 + 8.97679i −0.534560 + 0.925885i
9595 1.87954 3.25546i 0.192837 0.334003i
9696 −3.61628 6.26357i −0.369085 0.639273i
9797 −7.69704 −0.781516 −0.390758 0.920493i 0.627787π-0.627787\pi
−0.390758 + 0.920493i 0.627787π0.627787\pi
9898 15.7395 5.63041i 1.58993 0.568758i
9999 2.68663 0.270016
100100 7.47047 + 12.9392i 0.747047 + 1.29392i
101101 1.31866 2.28399i 0.131212 0.227265i −0.792932 0.609310i 0.791447π-0.791447\pi
0.924144 + 0.382045i 0.124780π0.124780\pi
102102 −21.2041 + 36.7266i −2.09952 + 3.63647i
103103 5.43095 + 9.40669i 0.535128 + 0.926868i 0.999157 + 0.0410486i 0.0130699π0.0130699\pi
−0.464029 + 0.885820i 0.653597π0.653597\pi
104104 0 0
105105 4.58125 + 5.49045i 0.447084 + 0.535813i
106106 1.01621 0.0987027
107107 7.99024 + 13.8395i 0.772446 + 1.33792i 0.936219 + 0.351418i 0.114300π0.114300\pi
−0.163773 + 0.986498i 0.552366π0.552366\pi
108108 8.00077 13.8577i 0.769874 1.33346i
109109 4.61738 7.99754i 0.442265 0.766026i −0.555592 0.831455i 0.687508π-0.687508\pi
0.997857 + 0.0654294i 0.0208417π0.0208417\pi
110110 0.689410 + 1.19409i 0.0657327 + 0.113852i
111111 4.83127 0.458564
112112 2.10135 5.72416i 0.198559 0.540882i
113113 10.1802 0.957677 0.478838 0.877903i 0.341058π-0.341058\pi
0.478838 + 0.877903i 0.341058π0.341058\pi
114114 12.5726 + 21.7763i 1.17753 + 2.03954i
115115 4.05682 7.02662i 0.378301 0.655236i
116116 7.33173 12.6989i 0.680734 1.17907i
117117 0 0
118118 −14.3488 −1.32092
119119 16.8249 2.91878i 1.54234 0.267564i
120120 10.9897 1.00322
121121 5.32724 + 9.22706i 0.484295 + 0.838823i
122122 −2.63489 + 4.56376i −0.238552 + 0.413184i
123123 −5.05128 + 8.74908i −0.455459 + 0.788878i
124124 −5.53320 9.58378i −0.496896 0.860649i
125125 8.87502 0.793806
126126 −28.4530 + 4.93601i −2.53479 + 0.439735i
127127 4.25026 0.377149 0.188575 0.982059i 0.439613π-0.439613\pi
0.188575 + 0.982059i 0.439613π0.439613\pi
128128 10.3702 + 17.9617i 0.916606 + 1.58761i
129129 8.77838 15.2046i 0.772893 1.33869i
130130 0 0
131131 1.08478 + 1.87890i 0.0947779 + 0.164160i 0.909516 0.415669i 0.136453π-0.136453\pi
−0.814738 + 0.579829i 0.803119π0.803119\pi
132132 −5.98851 −0.521233
133133 3.48923 9.50479i 0.302555 0.824170i
134134 −16.7474 −1.44675
135135 −2.12249 3.67626i −0.182675 0.316402i
136136 13.1219 22.7278i 1.12519 1.94889i
137137 4.18158 7.24271i 0.357257 0.618787i −0.630245 0.776396i 0.717045π-0.717045\pi
0.987501 + 0.157610i 0.0503788π0.0503788\pi
138138 27.1367 + 47.0022i 2.31003 + 4.00110i
139139 −0.576914 −0.0489332 −0.0244666 0.999701i 0.507789π-0.507789\pi
−0.0244666 + 0.999701i 0.507789π0.507789\pi
140140 −6.16508 7.38862i −0.521045 0.624452i
141141 −11.9430 −1.00579
142142 4.30149 + 7.45040i 0.360973 + 0.625224i
143143 0 0
144144 −5.26698 + 9.12267i −0.438915 + 0.760223i
145145 −1.94500 3.36885i −0.161524 0.279767i
146146 −11.7832 −0.975187
147147 14.6856 + 12.4616i 1.21125 + 1.02782i
148148 −6.50154 −0.534423
149149 1.40331 + 2.43061i 0.114964 + 0.199123i 0.917765 0.397123i 0.129991π-0.129991\pi
−0.802801 + 0.596246i 0.796658π0.796658\pi
150150 −13.2567 + 22.9612i −1.08240 + 1.87478i
151151 −11.5054 + 19.9280i −0.936300 + 1.62172i −0.164000 + 0.986460i 0.552440π0.552440\pi
−0.772300 + 0.635258i 0.780894π0.780894\pi
152152 −7.78039 13.4760i −0.631073 1.09305i
153153 −29.4998 −2.38492
154154 2.37933 + 2.85154i 0.191732 + 0.229784i
155155 −2.93576 −0.235806
156156 0 0
157157 −11.2880 + 19.5513i −0.900879 + 1.56037i −0.0745227 + 0.997219i 0.523743π0.523743\pi
−0.826356 + 0.563148i 0.809590π0.809590\pi
158158 −3.32583 + 5.76050i −0.264588 + 0.458281i
159159 0.585433 + 1.01400i 0.0464278 + 0.0804154i
160160 2.58203 0.204127
161161 7.53119 20.5153i 0.593541 1.61683i
162162 −4.34913 −0.341700
163163 4.08857 + 7.08161i 0.320242 + 0.554675i 0.980538 0.196331i 0.0629026π-0.0629026\pi
−0.660296 + 0.751005i 0.729569π0.729569\pi
164164 6.79761 11.7738i 0.530804 0.919380i
165165 −0.794333 + 1.37583i −0.0618388 + 0.107108i
166166 −3.42467 5.93170i −0.265806 0.460389i
167167 2.32771 0.180124 0.0900619 0.995936i 0.471293π-0.471293\pi
0.0900619 + 0.995936i 0.471293π0.471293\pi
168168 29.1649 5.05953i 2.25012 0.390351i
169169 0 0
170170 −7.56988 13.1114i −0.580583 1.00560i
171171 −8.74566 + 15.1479i −0.668798 + 1.15839i
172172 −11.8133 + 20.4611i −0.900752 + 1.56015i
173173 4.06686 + 7.04401i 0.309198 + 0.535546i 0.978187 0.207726i 0.0666061π-0.0666061\pi
−0.668989 + 0.743272i 0.733273π0.733273\pi
174174 26.0209 1.97264
175175 10.5188 1.82480i 0.795149 0.137942i
176176 1.35471 0.102115
177177 −8.26630 14.3177i −0.621333 1.07618i
178178 −2.49922 + 4.32877i −0.187324 + 0.324455i
179179 10.4963 18.1801i 0.784528 1.35884i −0.144752 0.989468i 0.546239π-0.546239\pi
0.929281 0.369375i 0.120428π-0.120428\pi
180180 8.31194 + 14.3967i 0.619536 + 1.07307i
181181 −1.60807 −0.119527 −0.0597635 0.998213i 0.519035π-0.519035\pi
−0.0597635 + 0.998213i 0.519035π0.519035\pi
182182 0 0
183183 −6.07180 −0.448841
184184 −16.7933 29.0868i −1.23802 2.14431i
185185 −0.862384 + 1.49369i −0.0634037 + 0.109818i
186186 9.81889 17.0068i 0.719956 1.24700i
187187 1.89690 + 3.28552i 0.138715 + 0.240261i
188188 16.0720 1.17217
189189 −7.32526 8.77905i −0.532834 0.638582i
190190 −8.97683 −0.651247
191191 5.78111 + 10.0132i 0.418307 + 0.724529i 0.995769 0.0918886i 0.0292904π-0.0292904\pi
−0.577463 + 0.816417i 0.695957π0.695957\pi
192192 −14.9771 + 25.9412i −1.08088 + 1.87214i
193193 11.7894 20.4199i 0.848621 1.46985i −0.0338178 0.999428i 0.510767π-0.510767\pi
0.882439 0.470427i 0.155900π-0.155900\pi
194194 9.19041 + 15.9183i 0.659833 + 1.14286i
195195 0 0
196196 −19.7628 16.7699i −1.41163 1.19785i
197197 1.47094 0.104800 0.0524002 0.998626i 0.483313π-0.483313\pi
0.0524002 + 0.998626i 0.483313π0.483313\pi
198198 −3.20788 5.55622i −0.227974 0.394863i
199199 −4.69700 + 8.13543i −0.332961 + 0.576706i −0.983091 0.183117i 0.941381π-0.941381\pi
0.650130 + 0.759823i 0.274714π0.274714\pi
200200 8.20374 14.2093i 0.580092 1.00475i
201201 −9.64810 16.7110i −0.680524 1.17870i
202202 −6.29802 −0.443127
203203 −6.71271 8.04493i −0.471140 0.564643i
204204 65.7551 4.60378
205205 −1.80331 3.12343i −0.125949 0.218150i
206206 12.9693 22.4635i 0.903615 1.56511i
207207 −18.8767 + 32.6955i −1.31202 + 2.27249i
208208 0 0
209209 2.24946 0.155598
210210 5.88472 16.0302i 0.406084 1.10619i
211211 −8.94219 −0.615605 −0.307803 0.951450i 0.599594π-0.599594\pi
−0.307803 + 0.951450i 0.599594π0.599594\pi
212212 −0.787829 1.36456i −0.0541083 0.0937184i
213213 −4.95615 + 8.58430i −0.339589 + 0.588186i
214214 19.0810 33.0493i 1.30435 2.25920i
215215 3.13389 + 5.42805i 0.213729 + 0.370190i
216216 −17.5722 −1.19563
217217 −7.79104 + 1.35159i −0.528890 + 0.0917518i
218218 −22.0530 −1.49362
219219 −6.78827 11.7576i −0.458709 0.794507i
220220 1.06895 1.85148i 0.0720686 0.124827i
221221 0 0
222222 −5.76863 9.99156i −0.387165 0.670589i
223223 −21.8196 −1.46115 −0.730574 0.682833i 0.760748π-0.760748\pi
−0.730574 + 0.682833i 0.760748π0.760748\pi
224224 6.85229 1.18873i 0.457838 0.0794256i
225225 −18.4431 −1.22954
226226 −12.1554 21.0538i −0.808565 1.40048i
227227 −9.27627 + 16.0670i −0.615687 + 1.06640i 0.374576 + 0.927196i 0.377788π0.377788\pi
−0.990263 + 0.139206i 0.955545π0.955545\pi
228228 19.4941 33.7648i 1.29103 2.23613i
229229 9.67525 + 16.7580i 0.639359 + 1.10740i 0.985574 + 0.169247i 0.0541334π0.0541334\pi
−0.346215 + 0.938155i 0.612533π0.612533\pi
230230 −19.3757 −1.27759
231231 −1.47462 + 4.01692i −0.0970230 + 0.264294i
232232 −16.1027 −1.05720
233233 −8.08170 13.9979i −0.529450 0.917034i −0.999410 0.0343462i 0.989065π-0.989065\pi
0.469960 0.882688i 0.344268π-0.344268\pi
234234 0 0
235235 2.13184 3.69245i 0.139066 0.240869i
236236 11.1241 + 19.2676i 0.724119 + 1.25421i
237237 −7.66398 −0.497829
238238 −26.1256 31.3105i −1.69347 2.02956i
239239 −16.1037 −1.04166 −0.520831 0.853660i 0.674378π-0.674378\pi
−0.520831 + 0.853660i 0.674378π0.674378\pi
240240 −3.11449 5.39445i −0.201039 0.348210i
241241 −2.00300 + 3.46930i −0.129025 + 0.223477i −0.923299 0.384082i 0.874518π-0.874518\pi
0.794274 + 0.607559i 0.207851π0.207851\pi
242242 12.7217 22.0346i 0.817779 1.41643i
243243 −8.98786 15.5674i −0.576572 0.998651i
244244 8.17095 0.523092
245245 −6.47418 + 2.31598i −0.413620 + 0.147962i
246246 24.1253 1.53817
247247 0 0
248248 −6.07631 + 10.5245i −0.385846 + 0.668305i
249249 3.94588 6.83446i 0.250060 0.433116i
250250 −10.5969 18.3544i −0.670209 1.16084i
251251 3.24688 0.204941 0.102471 0.994736i 0.467325π-0.467325\pi
0.102471 + 0.994736i 0.467325π0.467325\pi
252252 28.6867 + 34.3799i 1.80709 + 2.16573i
253253 4.85525 0.305247
254254 −5.07489 8.78996i −0.318427 0.551531i
255255 8.72195 15.1069i 0.546190 0.946029i
256256 13.8778 24.0371i 0.867365 1.50232i
257257 13.4462 + 23.2895i 0.838751 + 1.45276i 0.890940 + 0.454122i 0.150047π0.150047\pi
−0.0521891 + 0.998637i 0.516620π0.516620\pi
258258 −41.9262 −2.61021
259259 −1.60095 + 4.36106i −0.0994784 + 0.270983i
260260 0 0
261261 9.05027 + 15.6755i 0.560198 + 0.970291i
262262 2.59050 4.48688i 0.160042 0.277200i
263263 1.90353 3.29701i 0.117377 0.203302i −0.801351 0.598195i 0.795885π-0.795885\pi
0.918727 + 0.394893i 0.129218π0.129218\pi
264264 3.28815 + 5.69525i 0.202372 + 0.350518i
265265 −0.418000 −0.0256775
266266 −23.8231 + 4.13282i −1.46069 + 0.253399i
267267 −5.75915 −0.352455
268268 12.9836 + 22.4883i 0.793102 + 1.37369i
269269 11.9190 20.6444i 0.726716 1.25871i −0.231548 0.972824i 0.574379π-0.574379\pi
0.958264 0.285886i 0.0922878π-0.0922878\pi
270270 −5.06859 + 8.77905i −0.308464 + 0.534276i
271271 4.95068 + 8.57482i 0.300732 + 0.520883i 0.976302 0.216413i 0.0694357π-0.0694357\pi
−0.675570 + 0.737296i 0.736102π0.736102\pi
272272 −14.8750 −0.901931
273273 0 0
274274 −19.9715 −1.20653
275275 1.18593 + 2.05409i 0.0715142 + 0.123866i
276276 42.0763 72.8783i 2.53270 4.38676i
277277 −5.89289 + 10.2068i −0.354069 + 0.613266i −0.986958 0.160977i 0.948536π-0.948536\pi
0.632889 + 0.774243i 0.281869π0.281869\pi
278278 0.688846 + 1.19312i 0.0413142 + 0.0715584i
279279 13.6603 0.817823
280280 −3.64169 + 9.92010i −0.217633 + 0.592840i
281281 −12.9976 −0.775372 −0.387686 0.921791i 0.626726π-0.626726\pi
−0.387686 + 0.921791i 0.626726π0.626726\pi
282282 14.2602 + 24.6994i 0.849184 + 1.47083i
283283 8.40249 14.5535i 0.499476 0.865118i −0.500524 0.865723i 0.666859π-0.666859\pi
1.00000 0.000604910i 0.000192549π0.000192549\pi
284284 6.66959 11.5521i 0.395767 0.685489i
285285 −5.17151 8.95733i −0.306334 0.530586i
286286 0 0
287287 −6.22369 7.45886i −0.367373 0.440283i
288288 −12.0144 −0.707955
289289 −12.3283 21.3533i −0.725197 1.25608i
290290 −4.64474 + 8.04493i −0.272749 + 0.472414i
291291 −10.5891 + 18.3409i −0.620746 + 1.07516i
292292 9.13512 + 15.8225i 0.534592 + 0.925941i
293293 14.0956 0.823476 0.411738 0.911302i 0.364922π-0.364922\pi
0.411738 + 0.911302i 0.364922π0.364922\pi
294294 8.23701 45.2508i 0.480392 2.63908i
295295 5.90215 0.343637
296296 3.56985 + 6.18316i 0.207493 + 0.359389i
297297 1.27011 2.19990i 0.0736994 0.127651i
298298 3.35116 5.80438i 0.194128 0.336239i
299299 0 0
300300 41.1097 2.37347
301301 10.8159 + 12.9624i 0.623416 + 0.747140i
302302 54.9508 3.16207
303303 −3.62827 6.28434i −0.208439 0.361026i
304304 −4.40993 + 7.63822i −0.252927 + 0.438082i
305305 1.08382 1.87723i 0.0620593 0.107490i
306306 35.2233 + 61.0085i 2.01358 + 3.48762i
307307 −15.8786 −0.906240 −0.453120 0.891450i 0.649689π-0.649689\pi
−0.453120 + 0.891450i 0.649689π0.649689\pi
308308 1.98443 5.40566i 0.113073 0.308016i
309309 29.8863 1.70017
310310 3.50535 + 6.07145i 0.199091 + 0.344835i
311311 14.3017 24.7713i 0.810975 1.40465i −0.101208 0.994865i 0.532271π-0.532271\pi
0.912183 0.409784i 0.134396π-0.134396\pi
312312 0 0
313313 9.28962 + 16.0901i 0.525080 + 0.909465i 0.999573 + 0.0292063i 0.00929798π0.00929798\pi
−0.474493 + 0.880259i 0.657369π0.657369\pi
314314 53.9122 3.04244
315315 11.7037 2.03035i 0.659427 0.114397i
316316 10.3136 0.580184
317317 15.3223 + 26.5389i 0.860584 + 1.49057i 0.871366 + 0.490633i 0.163234π0.163234\pi
−0.0107826 + 0.999942i 0.503432π0.503432\pi
318318 1.39804 2.42147i 0.0783979 0.135789i
319319 1.16390 2.01594i 0.0651660 0.112871i
320320 −5.34685 9.26102i −0.298898 0.517707i
321321 43.9700 2.45416
322322 −51.4200 + 8.92033i −2.86552 + 0.497110i
323323 −24.6995 −1.37432
324324 3.37173 + 5.84001i 0.187318 + 0.324445i
325325 0 0
326326 9.76366 16.9112i 0.540759 0.936622i
327327 −12.7046 22.0051i −0.702568 1.21688i
328328 −14.9297 −0.824353
329329 3.95760 10.7807i 0.218190 0.594357i
330330 3.79379 0.208842
331331 13.6138 + 23.5799i 0.748284 + 1.29607i 0.948644 + 0.316344i 0.102455π0.102455\pi
−0.200360 + 0.979722i 0.564211π0.564211\pi
332332 −5.31005 + 9.19728i −0.291427 + 0.504766i
333333 4.01275 6.95028i 0.219897 0.380873i
334334 −2.77933 4.81395i −0.152078 0.263407i
335335 6.88876 0.376373
336336 −10.7489 12.8821i −0.586400 0.702779i
337337 −12.3160 −0.670898 −0.335449 0.942058i 0.608888π-0.608888\pi
−0.335449 + 0.942058i 0.608888π0.608888\pi
338338 0 0
339339 14.0054 24.2580i 0.760666 1.31751i
340340 −11.7373 + 20.3296i −0.636545 + 1.10253i
341341 −0.878389 1.52141i −0.0475674 0.0823892i
342342 41.7699 2.25866
343343 −16.1152 + 9.12688i −0.870140 + 0.492805i
344344 25.9456 1.39889
345345 −11.1623 19.3336i −0.600956 1.04089i
346346 9.71182 16.8214i 0.522111 0.904322i
347347 −3.07253 + 5.32177i −0.164942 + 0.285688i −0.936635 0.350308i 0.886077π-0.886077\pi
0.771693 + 0.635996i 0.219410π0.219410\pi
348348 −20.1731 34.9408i −1.08139 1.87302i
349349 −13.0313 −0.697547 −0.348774 0.937207i 0.613402π-0.613402\pi
−0.348774 + 0.937207i 0.613402π0.613402\pi
350350 −16.3336 19.5752i −0.873065 1.04634i
351351 0 0
352352 0.772550 + 1.33810i 0.0411771 + 0.0713208i
353353 15.8332 27.4240i 0.842718 1.45963i −0.0448710 0.998993i 0.514288π-0.514288\pi
0.887589 0.460637i 0.152379π-0.152379\pi
354354 −19.7402 + 34.1911i −1.04918 + 1.81724i
355355 −1.76935 3.06460i −0.0939072 0.162652i
356356 7.75021 0.410761
357357 16.1917 44.1067i 0.856954 2.33438i
358358 −50.1310 −2.64950
359359 9.96610 + 17.2618i 0.525991 + 0.911043i 0.999542 + 0.0302764i 0.00963874π0.00963874\pi
−0.473551 + 0.880767i 0.657028π0.657028\pi
360360 9.12780 15.8098i 0.481077 0.833251i
361361 2.17744 3.77144i 0.114602 0.198497i
362362 1.92007 + 3.32566i 0.100917 + 0.174793i
363363 29.3156 1.53867
364364 0 0
365365 4.84684 0.253695
366366 7.24984 + 12.5571i 0.378955 + 0.656370i
367367 −9.85950 + 17.0772i −0.514662 + 0.891420i 0.485194 + 0.874407i 0.338749π0.338749\pi
−0.999855 + 0.0170133i 0.994584π0.994584\pi
368368 −9.51844 + 16.4864i −0.496183 + 0.859414i
369369 8.39096 + 14.5336i 0.436816 + 0.756588i
370370 4.11881 0.214127
371371 −1.10931 + 0.192442i −0.0575923 + 0.00999109i
372372 −30.4490 −1.57870
373373 −8.77345 15.1961i −0.454272 0.786823i 0.544374 0.838843i 0.316767π-0.316767\pi
−0.998646 + 0.0520202i 0.983434π0.983434\pi
374374 4.52986 7.84595i 0.234234 0.405704i
375375 12.2097 21.1478i 0.630507 1.09207i
376376 −8.82478 15.2850i −0.455103 0.788262i
377377 0 0
378378 −9.40946 + 25.6317i −0.483971 + 1.31835i
379379 11.7014 0.601058 0.300529 0.953773i 0.402837π-0.402837\pi
0.300529 + 0.953773i 0.402837π0.402837\pi
380380 6.95942 + 12.0541i 0.357010 + 0.618360i
381381 5.84725 10.1277i 0.299563 0.518859i
382382 13.8055 23.9119i 0.706352 1.22344i
383383 −10.7644 18.6445i −0.550036 0.952690i −0.998271 0.0587748i 0.981281π-0.981281\pi
0.448235 0.893916i 0.352053π-0.352053\pi
384384 57.0669 2.91218
385385 −0.978699 1.17293i −0.0498791 0.0597783i
386386 −56.3072 −2.86596
387387 −14.5823 25.2572i −0.741258 1.28390i
388388 14.2500 24.6817i 0.723435 1.25303i
389389 −13.2455 + 22.9419i −0.671574 + 1.16320i 0.305884 + 0.952069i 0.401048π0.401048\pi
−0.977458 + 0.211131i 0.932285π0.932285\pi
390390 0 0
391391 −53.3118 −2.69609
392392 −5.09738 + 28.0030i −0.257457 + 1.41436i
393393 5.96951 0.301122
394394 −1.75633 3.04206i −0.0884828 0.153257i
395395 1.36802 2.36949i 0.0688327 0.119222i
396396 −4.97392 + 8.61508i −0.249949 + 0.432924i
397397 −16.8995 29.2707i −0.848160 1.46906i −0.882849 0.469658i 0.844377π-0.844377\pi
0.0346887 0.999398i 0.488956π-0.488956\pi
398398 22.4332 1.12447
399399 −17.8482 21.3904i −0.893529 1.07086i
400400 −9.29977 −0.464989
401401 10.8059 + 18.7164i 0.539623 + 0.934655i 0.998924 + 0.0463741i 0.0147666π0.0147666\pi
−0.459301 + 0.888281i 0.651900π0.651900\pi
402402 −23.0400 + 39.9065i −1.14913 + 1.99035i
403403 0 0
404404 4.88264 + 8.45697i 0.242920 + 0.420750i
405405 1.78895 0.0888934
406406 −8.62262 + 23.4884i −0.427934 + 1.16571i
407407 −1.03211 −0.0511599
408408 −36.1047 62.5351i −1.78745 3.09595i
409409 3.87109 6.70492i 0.191413 0.331537i −0.754306 0.656523i 0.772026π-0.772026\pi
0.945719 + 0.324986i 0.105360π0.105360\pi
410410 −4.30637 + 7.45886i −0.212677 + 0.368367i
411411 −11.5055 19.9282i −0.567526 0.982984i
412412 −40.2186 −1.98143
413413 15.6634 2.71728i 0.770744 0.133709i
414414 90.1567 4.43096
415415 1.40868 + 2.43991i 0.0691495 + 0.119770i
416416 0 0
417417 −0.793683 + 1.37470i −0.0388668 + 0.0673193i
418418 −2.68589 4.65211i −0.131371 0.227542i
419419 −8.10194 −0.395806 −0.197903 0.980222i 0.563413π-0.563413\pi
−0.197903 + 0.980222i 0.563413π0.563413\pi
420420 −26.0875 + 4.52565i −1.27294 + 0.220829i
421421 32.1124 1.56506 0.782530 0.622612i 0.213929π-0.213929\pi
0.782530 + 0.622612i 0.213929π0.213929\pi
422422 10.6771 + 18.4933i 0.519755 + 0.900242i
423423 −9.91963 + 17.1813i −0.482309 + 0.835384i
424424 −0.865159 + 1.49850i −0.0420158 + 0.0727735i
425425 −13.0218 22.5543i −0.631648 1.09405i
426426 23.6709 1.14686
427427 2.01203 5.48085i 0.0973690 0.265237i
428428 −59.1713 −2.86015
429429 0 0
430430 7.48384 12.9624i 0.360903 0.625102i
431431 −14.7640 + 25.5721i −0.711159 + 1.23176i 0.253263 + 0.967397i 0.418496π0.418496\pi
−0.964422 + 0.264366i 0.914837π0.914837\pi
432432 4.97996 + 8.62554i 0.239598 + 0.414997i
433433 22.0910 1.06163 0.530813 0.847489i 0.321887π-0.321887\pi
0.530813 + 0.847489i 0.321887π0.321887\pi
434434 12.0979 + 14.4988i 0.580716 + 0.695967i
435435 −10.7033 −0.513183
436436 17.0969 + 29.6127i 0.818792 + 1.41819i
437437 −15.8051 + 27.3752i −0.756060 + 1.30953i
438438 −16.2106 + 28.0777i −0.774575 + 1.34160i
439439 3.17790 + 5.50428i 0.151673 + 0.262705i 0.931843 0.362863i 0.118201π-0.118201\pi
−0.780170 + 0.625568i 0.784867π0.784867\pi
440440 −2.34775 −0.111924
441441 30.1249 10.7764i 1.43452 0.513164i
442442 0 0
443443 6.78135 + 11.7456i 0.322192 + 0.558052i 0.980940 0.194311i 0.0622472π-0.0622472\pi
−0.658748 + 0.752363i 0.728914π0.728914\pi
444444 −8.94443 + 15.4922i −0.424484 + 0.735227i
445445 1.02801 1.78057i 0.0487324 0.0844070i
446446 26.0530 + 45.1251i 1.23365 + 2.13674i
447447 7.72237 0.365255
448448 −18.4534 22.1157i −0.871839 1.04487i
449449 −21.9118 −1.03408 −0.517041 0.855961i 0.672966π-0.672966\pi
−0.517041 + 0.855961i 0.672966π0.672966\pi
450450 22.0214 + 38.1421i 1.03810 + 1.79804i
451451 1.07911 1.86908i 0.0508134 0.0880115i
452452 −18.8473 + 32.6445i −0.886502 + 1.53547i
453453 31.6570 + 54.8315i 1.48737 + 2.57621i
454454 44.3041 2.07930
455455 0 0
456456 −42.8151 −2.00500
457457 7.60732 + 13.1763i 0.355855 + 0.616359i 0.987264 0.159091i 0.0508563π-0.0508563\pi
−0.631409 + 0.775450i 0.717523π0.717523\pi
458458 23.1049 40.0188i 1.07962 1.86996i
459459 −13.9461 + 24.1554i −0.650949 + 1.12748i
460460 15.0213 + 26.0176i 0.700371 + 1.21308i
461461 16.2163 0.755267 0.377633 0.925955i 0.376738π-0.376738\pi
0.377633 + 0.925955i 0.376738π0.376738\pi
462462 10.0681 1.74662i 0.468412 0.0812600i
463463 1.44769 0.0672799 0.0336400 0.999434i 0.489290π-0.489290\pi
0.0336400 + 0.999434i 0.489290π0.489290\pi
464464 4.56353 + 7.90426i 0.211856 + 0.366946i
465465 −4.03884 + 6.99547i −0.187297 + 0.324407i
466466 −19.2994 + 33.4275i −0.894027 + 1.54850i
467467 −7.00337 12.1302i −0.324078 0.561319i 0.657248 0.753675i 0.271721π-0.271721\pi
−0.981325 + 0.192356i 0.938387π0.938387\pi
468468 0 0
469469 18.2817 3.17150i 0.844169 0.146446i
470470 −10.1818 −0.469652
471471 31.0586 + 53.7951i 1.43111 + 2.47875i
472472 12.2160 21.1588i 0.562288 0.973912i
473473 −1.87534 + 3.24818i −0.0862282 + 0.149352i
474474 9.15094 + 15.8499i 0.420316 + 0.728009i
475475 −15.4420 −0.708528
476476 −21.7895 + 59.3553i −0.998719 + 2.72055i
477477 1.94499 0.0890550
478478 19.2281 + 33.3041i 0.879474 + 1.52329i
479479 −15.0122 + 26.0018i −0.685923 + 1.18805i 0.287223 + 0.957864i 0.407268π0.407268\pi
−0.973146 + 0.230189i 0.926065π0.926065\pi
480480 3.55219 6.15258i 0.162135 0.280826i
481481 0 0
482482 9.56649 0.435742
483483 −38.5238 46.1693i −1.75289 2.10078i
484484 −39.4506 −1.79321
485485 −3.78033 6.54772i −0.171656 0.297317i
486486 −21.4633 + 37.1756i −0.973597 + 1.68632i
487487 −14.2452 + 24.6733i −0.645510 + 1.11806i 0.338674 + 0.940904i 0.390022π0.390022\pi
−0.984184 + 0.177152i 0.943312π0.943312\pi
488488 −4.48649 7.77082i −0.203094 0.351769i
489489 22.4992 1.01745
490490 12.5200 + 10.6239i 0.565595 + 0.479941i
491491 −28.4677 −1.28473 −0.642365 0.766399i 0.722047π-0.722047\pi
−0.642365 + 0.766399i 0.722047π0.722047\pi
492492 −18.7035 32.3954i −0.843218 1.46050i
493493 −12.7799 + 22.1354i −0.575578 + 0.996930i
494494 0 0
495495 1.31951 + 2.28546i 0.0593076 + 0.102724i
496496 6.88812 0.309286
497497 −6.10647 7.31838i −0.273913 0.328274i
498498 −18.8458 −0.844501
499499 −13.1164 22.7183i −0.587172 1.01701i −0.994601 0.103775i 0.966908π-0.966908\pi
0.407429 0.913237i 0.366425π-0.366425\pi
500500 −16.4309 + 28.4591i −0.734811 + 1.27273i
501501 3.20233 5.54659i 0.143069 0.247803i
502502 −3.87684 6.71488i −0.173032 0.299700i
503503 8.53175 0.380412 0.190206 0.981744i 0.439084π-0.439084\pi
0.190206 + 0.981744i 0.439084π0.439084\pi
504504 16.9451 46.1591i 0.754795 2.05609i
505505 2.59059 0.115280
506506 −5.79726 10.0412i −0.257720 0.446384i
507507 0 0
508508 −7.86876 + 13.6291i −0.349120 + 0.604693i
509509 −6.51298 11.2808i −0.288683 0.500014i 0.684813 0.728719i 0.259884π-0.259884\pi
−0.973496 + 0.228706i 0.926551π0.926551\pi
510510 −41.6567 −1.84459
511511 12.8627 2.23142i 0.569014 0.0987124i
512512 −24.8008 −1.09605
513513 8.26908 + 14.3225i 0.365089 + 0.632352i
514514 32.1100 55.6162i 1.41631 2.45312i
515515 −5.33472 + 9.24000i −0.235076 + 0.407163i
516516 32.5039 + 56.2984i 1.43090 + 2.47840i
517517 2.55141 0.112211
518518 10.9307 1.89625i 0.480266 0.0833164i
519519 22.3798 0.982363
520520 0 0
521521 −2.23285 + 3.86741i −0.0978230 + 0.169434i −0.910783 0.412885i 0.864521π-0.864521\pi
0.812960 + 0.582319i 0.197855π0.197855\pi
522522 21.6124 37.4337i 0.945948 1.63843i
523523 1.45406 + 2.51850i 0.0635815 + 0.110126i 0.896064 0.443925i 0.146414π-0.146414\pi
−0.832482 + 0.554051i 0.813081π0.813081\pi
524524 −8.03330 −0.350936
525525 10.1229 27.5752i 0.441801 1.20348i
526526 −9.09140 −0.396404
527527 9.64490 + 16.7055i 0.420138 + 0.727701i
528528 1.86373 3.22807i 0.0811084 0.140484i
529529 −22.6139 + 39.1684i −0.983213 + 1.70297i
530530 0.499100 + 0.864466i 0.0216795 + 0.0375500i
531531 −27.4632 −1.19180
532532 24.0187 + 28.7855i 1.04134 + 1.24801i
533533 0 0
534534 6.87654 + 11.9105i 0.297577 + 0.515418i
535535 −7.84866 + 13.5943i −0.339327 + 0.587732i
536536 14.2581 24.6957i 0.615854 1.06669i
537537 −28.8803 50.0221i −1.24628 2.15861i
538538 −56.9262 −2.45426
539539 −3.13732 2.66220i −0.135134 0.114669i
540540 15.7180 0.676394
541541 −9.23193 15.9902i −0.396912 0.687471i 0.596431 0.802664i 0.296585π-0.296585\pi
−0.993343 + 0.115193i 0.963251π0.963251\pi
542542 11.8224 20.4770i 0.507815 0.879562i
543543 −2.21229 + 3.83180i −0.0949384 + 0.164438i
544544 −8.48277 14.6926i −0.363696 0.629940i
545545 9.07112 0.388564
546546 0 0
547547 34.9817 1.49571 0.747856 0.663861i 0.231083π-0.231083\pi
0.747856 + 0.663861i 0.231083π0.231083\pi
548548 15.4832 + 26.8177i 0.661411 + 1.14560i
549549 −5.04310 + 8.73491i −0.215234 + 0.372797i
550550 2.83204 4.90524i 0.120759 0.209160i
551551 7.57760 + 13.1248i 0.322817 + 0.559135i
552552 −92.4127 −3.93334
553553 2.53964 6.91806i 0.107996 0.294186i
554554 28.1449 1.19576
555555 2.37283 + 4.10986i 0.100721 + 0.174454i
556556 1.06808 1.84996i 0.0452965 0.0784559i
557557 0.0265706 0.0460217i 0.00112583 0.00195000i −0.865462 0.500975i 0.832975π-0.832975\pi
0.866588 + 0.499025i 0.166308π0.166308\pi
558558 −16.3107 28.2510i −0.690487 1.19596i
559559 0 0
560560 5.90148 1.02379i 0.249383 0.0432629i
561561 10.4385 0.440716
562562 15.5194 + 26.8804i 0.654646 + 1.13388i
563563 −3.99253 + 6.91527i −0.168265 + 0.291444i −0.937810 0.347149i 0.887150π-0.887150\pi
0.769545 + 0.638593i 0.220483π0.220483\pi
564564 22.1109 38.2972i 0.931037 1.61260i
565565 4.99992 + 8.66012i 0.210348 + 0.364334i
566566 −40.1309 −1.68683
567567 4.74758 0.823608i 0.199380 0.0345883i
568568 −14.6485 −0.614637
569569 13.3621 + 23.1438i 0.560167 + 0.970237i 0.997481 + 0.0709285i 0.0225962π0.0225962\pi
−0.437315 + 0.899308i 0.644070π0.644070\pi
570570 −12.3498 + 21.3904i −0.517275 + 0.895946i
571571 −6.74647 + 11.6852i −0.282331 + 0.489012i −0.971958 0.235153i 0.924441π-0.924441\pi
0.689627 + 0.724164i 0.257774π0.257774\pi
572572 0 0
573573 31.8132 1.32902
574574 −7.99447 + 21.7772i −0.333683 + 0.908964i
575575 −33.3302 −1.38996
576576 24.8794 + 43.0923i 1.03664 + 1.79551i
577577 6.00662 10.4038i 0.250059 0.433115i −0.713483 0.700673i 0.752883π-0.752883\pi
0.963542 + 0.267558i 0.0862167π0.0862167\pi
578578 −29.4406 + 50.9925i −1.22457 + 2.12101i
579579 −32.4383 56.1848i −1.34809 2.33496i
580580 14.4036 0.598078
581581 4.86172 + 5.82659i 0.201698 + 0.241728i
582582 50.5745 2.09638
583583 −0.125067 0.216622i −0.00517974 0.00897158i
584584 10.0318 17.3756i 0.415118 0.719005i
585585 0 0
586586 −16.8305 29.1512i −0.695260 1.20422i
587587 −10.4235 −0.430225 −0.215113 0.976589i 0.569012π-0.569012\pi
−0.215113 + 0.976589i 0.569012π0.569012\pi
588588 −67.1486 + 24.0207i −2.76916 + 0.990599i
589589 11.4375 0.471275
590590 −7.04728 12.2062i −0.290132 0.502523i
591591 2.02364 3.50504i 0.0832412 0.144178i
592592 2.02339 3.50462i 0.0831610 0.144039i
593593 −11.1751 19.3558i −0.458905 0.794847i 0.539998 0.841666i 0.318425π-0.318425\pi
−0.998903 + 0.0468194i 0.985091π0.985091\pi
594594 −6.06615 −0.248897
595595 10.7463 + 12.8791i 0.440557 + 0.527991i
596596 −10.3921 −0.425679
597597 12.9237 + 22.3845i 0.528931 + 0.916135i
598598 0 0
599599 −0.579463 + 1.00366i −0.0236762 + 0.0410084i −0.877621 0.479356i 0.840870π-0.840870\pi
0.853945 + 0.520364i 0.174204π0.174204\pi
600600 −22.5724 39.0966i −0.921515 1.59611i
601601 42.1813 1.72061 0.860306 0.509778i 0.170272π-0.170272\pi
0.860306 + 0.509778i 0.170272π0.170272\pi
602602 13.8932 37.8456i 0.566245 1.54247i
603603 −32.0540 −1.30534
604604 −42.6014 73.7879i −1.73343 3.00239i
605605 −5.23284 + 9.06355i −0.212745 + 0.368486i
606606 −8.66444 + 15.0072i −0.351969 + 0.609628i
607607 9.07844 + 15.7243i 0.368482 + 0.638230i 0.989328 0.145702i 0.0465441π-0.0465441\pi
−0.620846 + 0.783932i 0.713211π0.713211\pi
608608 −10.0594 −0.407962
609609 −28.4048 + 4.92765i −1.15102 + 0.199679i
610610 −5.17640 −0.209586
611611 0 0
612612 54.6147 94.5955i 2.20767 3.82380i
613613 −0.451323 + 0.781714i −0.0182288 + 0.0315731i −0.874996 0.484130i 0.839136π-0.839136\pi
0.856767 + 0.515703i 0.172469π0.172469\pi
614614 18.9594 + 32.8386i 0.765137 + 1.32526i
615615 −9.92354 −0.400156
616616 −6.23055 + 1.08087i −0.251036 + 0.0435497i
617617 26.0436 1.04848 0.524238 0.851572i 0.324350π-0.324350\pi
0.524238 + 0.851572i 0.324350π0.324350\pi
618618 −35.6848 61.8079i −1.43545 2.48628i
619619 13.4171 23.2390i 0.539277 0.934056i −0.459666 0.888092i 0.652031π-0.652031\pi
0.998943 0.0459638i 0.0146359π-0.0146359\pi
620620 5.43515 9.41396i 0.218281 0.378074i
621621 17.8481 + 30.9138i 0.716218 + 1.24053i
622622 −68.3060 −2.73882
623623 1.90843 5.19863i 0.0764596 0.208279i
624624 0 0
625625 −5.72894 9.92281i −0.229158 0.396912i
626626 22.1839 38.4237i 0.886649 1.53572i
627627 3.09467 5.36012i 0.123589 0.214063i
628628 −41.7962 72.3932i −1.66785 2.88880i
629629 11.3328 0.451869
630630 −18.1734 21.7801i −0.724044 0.867739i
631631 33.6121 1.33808 0.669039 0.743228i 0.266706π-0.266706\pi
0.669039 + 0.743228i 0.266706π0.266706\pi
632632 −5.66296 9.80853i −0.225260 0.390162i
633633 −12.3021 + 21.3079i −0.488965 + 0.846913i
634634 36.5901 63.3760i 1.45318 2.51698i
635635 2.08747 + 3.61561i 0.0828388 + 0.143481i
636636 −4.33539 −0.171909
637637 0 0
638638 −5.55889 −0.220078
639639 8.23293 + 14.2598i 0.325690 + 0.564111i
640640 −10.1865 + 17.6435i −0.402655 + 0.697419i
641641 −10.5921 + 18.3460i −0.418361 + 0.724622i −0.995775 0.0918294i 0.970729π-0.970729\pi
0.577414 + 0.816452i 0.304062π0.304062\pi
642642 −52.5010 90.9343i −2.07205 3.58889i
643643 −0.661539 −0.0260886 −0.0130443 0.999915i 0.504152π-0.504152\pi
−0.0130443 + 0.999915i 0.504152π0.504152\pi
644644 51.8423 + 62.1310i 2.04287 + 2.44831i
645645 17.2457 0.679047
646646 29.4917 + 51.0811i 1.16034 + 2.00976i
647647 20.0162 34.6690i 0.786916 1.36298i −0.140931 0.990019i 0.545010π-0.545010\pi
0.927848 0.372960i 0.121657π-0.121657\pi
648648 3.70268 6.41323i 0.145455 0.251936i
649649 1.76594 + 3.05870i 0.0693193 + 0.120065i
650650 0 0
651651 −7.49781 + 20.4243i −0.293862 + 0.800492i
652652 −30.2777 −1.18577
653653 −6.35602 11.0089i −0.248730 0.430813i 0.714444 0.699693i 0.246680π-0.246680\pi
−0.963174 + 0.268880i 0.913347π0.913347\pi
654654 −30.3391 + 52.5489i −1.18635 + 2.05482i
655655 −1.06556 + 1.84560i −0.0416349 + 0.0721138i
656656 4.23107 + 7.32844i 0.165196 + 0.286127i
657657 −22.5527 −0.879867
658658 −27.0209 + 4.68759i −1.05339 + 0.182741i
659659 −14.1904 −0.552781 −0.276391 0.961045i 0.589138π-0.589138\pi
−0.276391 + 0.961045i 0.589138π0.589138\pi
660660 −2.94119 5.09430i −0.114486 0.198295i
661661 25.0890 43.4554i 0.975848 1.69022i 0.298742 0.954334i 0.403433π-0.403433\pi
0.677106 0.735885i 0.263234π-0.263234\pi
662662 32.5104 56.3096i 1.26355 2.18853i
663663 0 0
664664 11.6625 0.452594
665665 9.79923 1.69997i 0.379998 0.0659219i
666666 −19.1652 −0.742635
667667 16.3556 + 28.3287i 0.633290 + 1.09689i
668668 −4.30944 + 7.46417i −0.166737 + 0.288797i
669669 −30.0181 + 51.9928i −1.16057 + 2.01016i
670670 −8.22530 14.2466i −0.317771 0.550396i
671671 1.29713 0.0500751
672672 6.59439 17.9634i 0.254384 0.692952i
673673 −1.87427 −0.0722479 −0.0361240 0.999347i 0.511501π-0.511501\pi
−0.0361240 + 0.999347i 0.511501π0.511501\pi
674674 14.7056 + 25.4708i 0.566438 + 0.981100i
675675 −8.71902 + 15.1018i −0.335595 + 0.581268i
676676 0 0
677677 1.00439 + 1.73966i 0.0386020 + 0.0668607i 0.884681 0.466197i 0.154376π-0.154376\pi
−0.846079 + 0.533058i 0.821043π0.821043\pi
678678 −66.8906 −2.56892
679679 −13.0469 15.6362i −0.500693 0.600062i
680680 25.7788 0.988571
681681 25.5234 + 44.2079i 0.978061 + 1.69405i
682682 −2.09762 + 3.63319i −0.0803222 + 0.139122i
683683 −7.05061 + 12.2120i −0.269784 + 0.467280i −0.968806 0.247820i 0.920286π-0.920286\pi
0.699022 + 0.715100i 0.253619π0.253619\pi
684684 −32.3828 56.0886i −1.23819 2.14460i
685685 8.21497 0.313878
686686 38.1172 + 22.4302i 1.45532 + 0.856390i
687687 53.2425 2.03133
688688 −7.35298 12.7357i −0.280330 0.485546i
689689 0 0
690690 −26.6559 + 46.1693i −1.01477 + 1.75764i
691691 −17.8460 30.9102i −0.678895 1.17588i −0.975314 0.220822i 0.929126π-0.929126\pi
0.296419 0.955058i 0.404207π-0.404207\pi
692692 −30.1169 −1.14487
693693 4.55397 + 5.45776i 0.172991 + 0.207323i
694694 14.6746 0.557041
695695 −0.283346 0.490769i −0.0107479 0.0186159i
696696 −22.1532 + 38.3704i −0.839714 + 1.45443i
697697 −11.8489 + 20.5229i −0.448809 + 0.777360i
698698 15.5596 + 26.9500i 0.588938 + 1.02007i
699699 −44.4732 −1.68213
700700 −13.6226 + 37.1086i −0.514888 + 1.40257i
701701 −6.15865 −0.232609 −0.116305 0.993214i 0.537105π-0.537105\pi
−0.116305 + 0.993214i 0.537105π0.537105\pi
702702 0 0
703703 3.35979 5.81932i 0.126717 0.219480i
704704 3.19959 5.54185i 0.120589 0.208866i
705705 −5.86571 10.1597i −0.220915 0.382637i
706706 −75.6207 −2.84602
707707 6.87501 1.19268i 0.258561 0.0448552i
708708 61.2156 2.30062
709709 17.0185 + 29.4770i 0.639144 + 1.10703i 0.985621 + 0.168972i 0.0540447π0.0540447\pi
−0.346477 + 0.938059i 0.612622π0.612622\pi
710710 −4.22527 + 7.31838i −0.158571 + 0.274654i
711711 −6.36553 + 11.0254i −0.238726 + 0.413486i
712712 −4.25547 7.37069i −0.159480 0.276228i
713713 24.6869 0.924530
714714 −110.550 + 19.1782i −4.13724 + 0.717727i
715715 0 0
716716 38.8648 + 67.3158i 1.45244 + 2.51571i
717717 −22.1545 + 38.3727i −0.827375 + 1.43306i
718718 23.7994 41.2218i 0.888187 1.53838i
719719 11.4824 + 19.8881i 0.428222 + 0.741702i 0.996715 0.0809859i 0.0258069π-0.0258069\pi
−0.568493 + 0.822688i 0.692474π0.692474\pi
720720 −10.3473 −0.385621
721721 −9.90351 + 26.9775i −0.368826 + 1.00470i
722722 −10.3996 −0.387034
723723 5.51122 + 9.54571i 0.204964 + 0.355009i
724724 2.97712 5.15653i 0.110644 0.191641i
725725 −7.98992 + 13.8389i −0.296738 + 0.513966i
726726 −35.0034 60.6276i −1.29910 2.25010i
727727 1.06558 0.0395203 0.0197601 0.999805i 0.493710π-0.493710\pi
0.0197601 + 0.999805i 0.493710π0.493710\pi
728728 0 0
729729 −43.9962 −1.62949
730730 −5.78721 10.0237i −0.214194 0.370996i
731731 20.5916 35.6658i 0.761609 1.31915i
732732 11.2411 19.4702i 0.415483 0.719637i
733733 −13.1689 22.8092i −0.486404 0.842476i 0.513474 0.858105i 0.328358π-0.328358\pi
−0.999878 + 0.0156289i 0.995025π0.995025\pi
734734 47.0897 1.73811
735735 −3.38816 + 18.6132i −0.124974 + 0.686558i
736736 −21.7123 −0.800326
737737 2.06114 + 3.57000i 0.0759230 + 0.131502i
738738 20.0379 34.7067i 0.737606 1.27757i
739739 17.1075 29.6310i 0.629308 1.08999i −0.358383 0.933575i 0.616672π-0.616672\pi
0.987691 0.156419i 0.0499950π-0.0499950\pi
740740 −3.19317 5.53073i −0.117383 0.203314i
741741 0 0
742742 1.72252 + 2.06438i 0.0632358 + 0.0757857i
743743 −22.4782 −0.824644 −0.412322 0.911038i 0.635282π-0.635282\pi
−0.412322 + 0.911038i 0.635282π0.635282\pi
744744 16.7188 + 28.9579i 0.612942 + 1.06165i
745745 −1.37845 + 2.38754i −0.0505023 + 0.0874726i
746746 −20.9513 + 36.2888i −0.767083 + 1.32863i
747747 −6.55472 11.3531i −0.239825 0.415388i
748748 −14.0474 −0.513623
749749 −14.5705 + 39.6905i −0.532393 + 1.45026i
750750 −58.3145 −2.12934
751751 21.2712 + 36.8428i 0.776197 + 1.34441i 0.934119 + 0.356961i 0.116187π0.116187\pi
−0.157923 + 0.987451i 0.550480π0.550480\pi
752752 −5.00189 + 8.66353i −0.182400 + 0.315927i
753753 4.46686 7.73683i 0.162781 0.281946i
754754 0 0
755755 −22.6031 −0.822612
756756 41.7131 7.23637i 1.51709 0.263184i
757757 −11.2380 −0.408454 −0.204227 0.978924i 0.565468π-0.565468\pi
−0.204227 + 0.978924i 0.565468π0.565468\pi
758758 −13.9716 24.1996i −0.507473 0.878969i
759759 6.67956 11.5693i 0.242453 0.419941i
760760 7.64252 13.2372i 0.277223 0.480165i
761761 6.40422 + 11.0924i 0.232153 + 0.402101i 0.958441 0.285289i 0.0920897π-0.0920897\pi
−0.726289 + 0.687390i 0.758756π0.758756\pi
762762 −27.9269 −1.01168
763763 24.0733 4.17623i 0.871513 0.151190i
764764 −42.8117 −1.54887
765765 −14.4885 25.0948i −0.523833 0.907306i
766766 −25.7058 + 44.5238i −0.928789 + 1.60871i
767767 0 0
768768 −38.1846 66.1377i −1.37787 2.38654i
769769 51.3517 1.85179 0.925895 0.377781i 0.123313π-0.123313\pi
0.925895 + 0.377781i 0.123313π0.123313\pi
770770 −1.25716 + 3.42455i −0.0453049 + 0.123412i
771771 73.9938 2.66482
772772 43.6529 + 75.6091i 1.57110 + 2.72123i
773773 10.0023 17.3245i 0.359759 0.623120i −0.628162 0.778083i 0.716192π-0.716192\pi
0.987920 + 0.154963i 0.0495257π0.0495257\pi
774774 −34.8230 + 60.3151i −1.25169 + 2.16798i
775775 6.02993 + 10.4441i 0.216602 + 0.375165i
776776 −31.2974 −1.12351
777777 8.18925 + 9.81450i 0.293788 + 0.352093i
778778 63.2615 2.26804
779779 7.02558 + 12.1687i 0.251717 + 0.435987i
780780 0 0
781781 1.05879 1.83388i 0.0378864 0.0656212i
782782 63.6552 + 110.254i 2.27631 + 3.94268i
783783 17.1142 0.611611
784784 15.1903 5.43394i 0.542509 0.194069i
785785 −22.1759 −0.791492
786786 −7.12771 12.3456i −0.254237 0.440351i
787787 14.6596 25.3911i 0.522558 0.905096i −0.477098 0.878850i 0.658311π-0.658311\pi
0.999656 0.0262462i 0.00835537π-0.00835537\pi
788788 −2.72325 + 4.71680i −0.0970117 + 0.168029i
789789 −5.23752 9.07166i −0.186461 0.322959i
790790 −6.53378 −0.232462
791791 17.2560 + 20.6807i 0.613553 + 0.735321i
792792 10.9243 0.388177
793793 0 0
794794 −40.3566 + 69.8996i −1.43220 + 2.48064i
795795 −0.575059 + 0.996031i −0.0203952 + 0.0353256i
796796 −17.3917 30.1232i −0.616431 1.06769i
797797 3.10100 0.109843 0.0549215 0.998491i 0.482509π-0.482509\pi
0.0549215 + 0.998491i 0.482509π0.482509\pi
798798 −22.9264 + 62.4525i −0.811588 + 2.21079i
799799 −28.0151 −0.991102
800800 −5.30338 9.18572i −0.187503 0.324764i
801801 −4.78343 + 8.28514i −0.169014 + 0.292741i
802802 25.8050 44.6956i 0.911206 1.57826i
803803 1.45019 + 2.51180i 0.0511761 + 0.0886395i
804804 71.4484 2.51979
805805 21.1508 3.66923i 0.745467 0.129323i
806806 0 0
807807 −32.7950 56.8025i −1.15444 1.99954i
808808 5.36189 9.28707i 0.188631 0.326718i
809809 −3.99501 + 6.91957i −0.140457 + 0.243279i −0.927669 0.373404i 0.878191π-0.878191\pi
0.787212 + 0.616683i 0.211524π0.211524\pi
810810 −2.13603 3.69972i −0.0750526 0.129995i
811811 48.2554 1.69448 0.847239 0.531213i 0.178263π-0.178263\pi
0.847239 + 0.531213i 0.178263π0.178263\pi
812812 38.2249 6.63125i 1.34143 0.232711i
813813 27.2434 0.955466
814814 1.23236 + 2.13451i 0.0431942 + 0.0748146i
815815 −4.01612 + 6.95612i −0.140679 + 0.243662i
816816 −20.4642 + 35.4449i −0.716389 + 1.24082i
817817 −12.2094 21.1473i −0.427153 0.739851i
818818 −18.4886 −0.646439
819819 0 0
820820 13.3543 0.466353
821821 −13.7760 23.8607i −0.480785 0.832743i 0.518972 0.854791i 0.326315π-0.326315\pi
−0.999757 + 0.0220477i 0.992981π0.992981\pi
822822 −27.4756 + 47.5892i −0.958323 + 1.65986i
823823 −10.2137 + 17.6907i −0.356028 + 0.616659i −0.987293 0.158908i 0.949203π-0.949203\pi
0.631265 + 0.775567i 0.282536π0.282536\pi
824824 22.0831 + 38.2491i 0.769303 + 1.33247i
825825 6.52611 0.227210
826826 −24.3220 29.1490i −0.846270 1.01422i
827827 27.7142 0.963719 0.481859 0.876249i 0.339962π-0.339962\pi
0.481859 + 0.876249i 0.339962π0.339962\pi
828828 −69.8953 121.062i −2.42903 4.20720i
829829 −4.62832 + 8.01648i −0.160748 + 0.278424i −0.935137 0.354286i 0.884724π-0.884724\pi
0.774389 + 0.632710i 0.218057π0.218057\pi
830830 3.36398 5.82659i 0.116766 0.202244i
831831 16.2142 + 28.0837i 0.562463 + 0.974214i
832832 0 0
833833 34.4484 + 29.2315i 1.19357 + 1.01281i
834834 3.79069 0.131261
835835 1.14323 + 1.98014i 0.0395632 + 0.0685255i
836836 −4.16456 + 7.21323i −0.144034 + 0.249475i
837837 6.45797 11.1855i 0.223220 0.386628i
838838 9.67387 + 16.7556i 0.334178 + 0.578814i
839839 30.3739 1.04862 0.524312 0.851526i 0.324323π-0.324323\pi
0.524312 + 0.851526i 0.324323π0.324323\pi
840840 18.6281 + 22.3251i 0.642731 + 0.770288i
841841 −13.3170 −0.459205
842842 −38.3428 66.4116i −1.32138 2.28869i
843843 −17.8813 + 30.9713i −0.615865 + 1.06671i
844844 16.5552 28.6745i 0.569854 0.987016i
845845 0 0
846846 47.3769 1.62885
847847 −9.71440 + 26.4624i −0.333791 + 0.909258i
848848 0.980745 0.0336789
849849 −23.1193 40.0437i −0.793451 1.37430i
850850 −31.0964 + 53.8606i −1.06660 + 1.84740i
851851 7.25180 12.5605i 0.248589 0.430568i
852852 −18.3512 31.7853i −0.628703 1.08894i
853853 5.30773 0.181733 0.0908666 0.995863i 0.471036π-0.471036\pi
0.0908666 + 0.995863i 0.471036π0.471036\pi
854854 −13.7374 + 2.38315i −0.470082 + 0.0815498i
855855 −17.1814 −0.587591
856856 32.4896 + 56.2737i 1.11047 + 1.92340i
857857 8.31857 14.4082i 0.284157 0.492175i −0.688247 0.725476i 0.741620π-0.741620\pi
0.972404 + 0.233302i 0.0749529π0.0749529\pi
858858 0 0
859859 5.29426 + 9.16993i 0.180638 + 0.312874i 0.942098 0.335338i 0.108850π-0.108850\pi
−0.761460 + 0.648212i 0.775517π0.775517\pi
860860 −23.2078 −0.791381
861861 −26.3355 + 4.56868i −0.897512 + 0.155700i
862862 70.5142 2.40172
863863 −28.0316 48.5522i −0.954207 1.65273i −0.736173 0.676793i 0.763369π-0.763369\pi
−0.218033 0.975941i 0.569964π-0.569964\pi
864864 −5.67984 + 9.83777i −0.193232 + 0.334688i
865865 −3.99480 + 6.91919i −0.135827 + 0.235260i
866866 −26.3771 45.6864i −0.896329 1.55249i
867867 −67.8424 −2.30405
868868 10.0900 27.4854i 0.342476 0.932916i
869869 1.63727 0.0555405
870870 12.7799 + 22.1354i 0.433279 + 0.750462i
871871 0 0
872872 18.7750 32.5193i 0.635803 1.10124i
873873 17.5902 + 30.4671i 0.595337 + 1.03115i
874874 75.4863 2.55336
875875 15.0436 + 18.0292i 0.508567 + 0.609498i
876876 50.2702 1.69847
877877 −1.83026 3.17010i −0.0618033 0.107047i 0.833468 0.552567i 0.186352π-0.186352\pi
−0.895272 + 0.445521i 0.853018π0.853018\pi
878878 7.58894 13.1444i 0.256114 0.443603i
879879 19.3919 33.5878i 0.654073 1.13289i
880880 0.665353 + 1.15242i 0.0224290 + 0.0388482i
881881 10.2299 0.344653 0.172326 0.985040i 0.444872π-0.444872\pi
0.172326 + 0.985040i 0.444872π0.444872\pi
882882 −58.2565 49.4341i −1.96160 1.66453i
883883 −3.98979 −0.134267 −0.0671335 0.997744i 0.521385π-0.521385\pi
−0.0671335 + 0.997744i 0.521385π0.521385\pi
884884 0 0
885885 8.11982 14.0639i 0.272945 0.472754i
886886 16.1941 28.0490i 0.544052 0.942325i
887887 7.11039 + 12.3155i 0.238743 + 0.413516i 0.960354 0.278784i 0.0899312π-0.0899312\pi
−0.721611 + 0.692299i 0.756598π0.756598\pi
888888 19.6447 0.659234
889889 7.20440 + 8.63420i 0.241628 + 0.289582i
890890 −4.90986 −0.164579
891891 0.535258 + 0.927094i 0.0179318 + 0.0310588i
892892 40.3960 69.9678i 1.35256 2.34270i
893893 −8.30550 + 14.3855i −0.277933 + 0.481394i
894894 −9.22065 15.9706i −0.308385 0.534138i
895895 20.6206 0.689269
896896 −18.9104 + 51.5127i −0.631753 + 1.72092i
897897 0 0
898898 26.1631 + 45.3158i 0.873074 + 1.51221i
899899 5.91794 10.2502i 0.197374 0.341862i
900900 34.1448 59.1405i 1.13816 1.97135i
901901 1.37326 + 2.37856i 0.0457500 + 0.0792413i
902902 −5.15392 −0.171607
903903 45.7672 7.93969i 1.52304 0.264216i
904904 41.3945 1.37676
905905 −0.789789 1.36795i −0.0262535 0.0454723i
906906 75.5980 130.940i 2.51158 4.35018i
907907 −21.7126 + 37.6074i −0.720956 + 1.24873i 0.239661 + 0.970857i 0.422964π0.422964\pi
−0.960617 + 0.277876i 0.910370π0.910370\pi
908908 −34.3474 59.4915i −1.13986 1.97429i
909909 −12.0542 −0.399814
910910 0 0
911911 24.8617 0.823706 0.411853 0.911250i 0.364882π-0.364882\pi
0.411853 + 0.911250i 0.364882π0.364882\pi
912912 12.1338 + 21.0164i 0.401791 + 0.695923i
913913 −0.842964 + 1.46006i −0.0278980 + 0.0483208i
914914 18.1666 31.4654i 0.600896 1.04078i
915915 −2.98210 5.16516i −0.0985853 0.170755i
916916 −71.6495 −2.36737
917917 −1.97814 + 5.38852i −0.0653238 + 0.177944i
918918 66.6076 2.19838
919919 0.831637 + 1.44044i 0.0274332 + 0.0475157i 0.879416 0.476054i 0.157933π-0.157933\pi
−0.851983 + 0.523570i 0.824600π0.824600\pi
920920 16.4957 28.5714i 0.543847 0.941971i
921921 −21.8448 + 37.8363i −0.719811 + 1.24675i
922922 −19.3625 33.5369i −0.637671 1.10448i
923923 0 0
924924 −10.1508 12.1654i −0.333937 0.400211i
925925 7.08521 0.232960
926926 −1.72857 2.99397i −0.0568044 0.0983880i
927927 24.8229 42.9945i 0.815291 1.41212i
928928 −5.20488 + 9.01512i −0.170859 + 0.295936i
929929 4.74761 + 8.22310i 0.155764 + 0.269791i 0.933337 0.359002i 0.116883π-0.116883\pi
−0.777573 + 0.628793i 0.783549π0.783549\pi
930930 19.2898 0.632537
931931 25.2230 9.02289i 0.826649 0.295713i
932932 59.8486 1.96040
933933 −39.3508 68.1576i −1.28829 2.23138i
934934 −16.7243 + 28.9674i −0.547236 + 0.947841i
935935 −1.86328 + 3.22730i −0.0609359 + 0.105544i
936936 0 0
937937 −6.41678 −0.209627 −0.104813 0.994492i 0.533425π-0.533425\pi
−0.104813 + 0.994492i 0.533425π0.533425\pi
938938 −28.3876 34.0215i −0.926889 1.11084i
939939 51.1203 1.66825
940940 7.89361 + 13.6721i 0.257461 + 0.445936i
941941 −25.7593 + 44.6164i −0.839730 + 1.45445i 0.0503911 + 0.998730i 0.483953π0.483953\pi
−0.890121 + 0.455725i 0.849380π0.849380\pi
942942 74.1691 128.465i 2.41656 4.18561i
943943 15.1641 + 26.2650i 0.493810 + 0.855305i
944944 −13.8481 −0.450717
945945 3.87043 10.5432i 0.125905 0.342970i
946946 8.95676 0.291209
947947 −4.20109 7.27651i −0.136517 0.236455i 0.789659 0.613546i 0.210258π-0.210258\pi
−0.926176 + 0.377091i 0.876924π0.876924\pi
948948 14.1888 24.5757i 0.460831 0.798182i
949949 0 0
950950 18.4380 + 31.9356i 0.598209 + 1.03613i
951951 84.3177 2.73419
952952 68.4128 11.8682i 2.21727 0.384652i
953953 −36.0911 −1.16910 −0.584552 0.811356i 0.698730π-0.698730\pi
−0.584552 + 0.811356i 0.698730π0.698730\pi
954954 −2.32235 4.02244i −0.0751890 0.130231i
955955 −5.67867 + 9.83575i −0.183758 + 0.318277i
956956 29.8138 51.6390i 0.964246 1.67012i
957957 −3.20245 5.54681i −0.103521 0.179303i
958958 71.6991 2.31649
959959 21.8012 3.78207i 0.703998 0.122129i
960960 −29.4235 −0.949639
961961 11.0338 + 19.1111i 0.355928 + 0.616486i
962962 0 0
963963 36.5205 63.2553i 1.17686 2.03837i
964964 −7.41656 12.8459i −0.238871 0.413737i
965965 23.1610 0.745580
966966 −49.4847 + 134.798i −1.59214 + 4.33706i
967967 −3.18338 −0.102371 −0.0511853 0.998689i 0.516300π-0.516300\pi
−0.0511853 + 0.998689i 0.516300π0.516300\pi
968968 21.6614 + 37.5187i 0.696225 + 1.20590i
969969 −33.9801 + 58.8553i −1.09160 + 1.89070i
970970 −9.02756 + 15.6362i −0.289857 + 0.502048i
971971 −18.8738 32.6904i −0.605690 1.04909i −0.991942 0.126692i 0.959564π-0.959564\pi
0.386253 0.922393i 0.373769π-0.373769\pi
972972 66.5591 2.13488
973973 −0.977898 1.17197i −0.0313500 0.0375718i
974974 68.0359 2.18001
975975 0 0
976976 −2.54294 + 4.40451i −0.0813977 + 0.140985i
977977 −10.6538 + 18.4530i −0.340846 + 0.590363i −0.984590 0.174878i 0.944047π-0.944047\pi
0.643744 + 0.765241i 0.277380π0.277380\pi
978978 −26.8645 46.5307i −0.859032 1.48789i
979979 1.23034 0.0393217
980980 4.55951 25.0482i 0.145648 0.800134i
981981 −42.2087 −1.34762
982982 33.9910 + 58.8741i 1.08470 + 1.87875i
983983 −11.0158 + 19.0799i −0.351350 + 0.608556i −0.986486 0.163844i 0.947611π-0.947611\pi
0.635136 + 0.772400i 0.280944π0.280944\pi
984984 −20.5393 + 35.5752i −0.654770 + 1.13409i
985985 0.722439 + 1.25130i 0.0230188 + 0.0398698i
986986 61.0378 1.94384
987987 −20.2441 24.2618i −0.644376 0.772260i
988988 0 0
989989 −26.3529 45.6446i −0.837975 1.45141i
990990 3.15104 5.45776i 0.100147 0.173459i
991991 11.0129 19.0750i 0.349838 0.605937i −0.636383 0.771374i 0.719570π-0.719570\pi
0.986220 + 0.165437i 0.0529033π0.0529033\pi
992992 3.92808 + 6.80364i 0.124717 + 0.216016i
993993 74.9164 2.37740
994994 −7.84390 + 21.3671i −0.248793 + 0.677723i
995995 −9.22753 −0.292532
996996 14.6105 + 25.3061i 0.462951 + 0.801855i
997997 −5.04102 + 8.73130i −0.159651 + 0.276523i −0.934743 0.355325i 0.884370π-0.884370\pi
0.775092 + 0.631848i 0.217703π0.217703\pi
998998 −31.3225 + 54.2522i −0.991497 + 1.71732i
999999 −3.79408 6.57153i −0.120039 0.207914i
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 1183.2.e.g.508.1 12
7.2 even 3 inner 1183.2.e.g.170.1 12
7.3 odd 6 8281.2.a.cf.1.6 6
7.4 even 3 8281.2.a.ce.1.6 6
13.4 even 6 91.2.g.b.81.6 yes 12
13.10 even 6 91.2.h.b.74.1 yes 12
13.12 even 2 1183.2.e.h.508.6 12
39.17 odd 6 819.2.n.d.172.1 12
39.23 odd 6 819.2.s.d.802.6 12
91.4 even 6 637.2.f.k.393.6 12
91.10 odd 6 637.2.f.j.295.6 12
91.17 odd 6 637.2.f.j.393.6 12
91.23 even 6 91.2.g.b.9.6 12
91.25 even 6 8281.2.a.bz.1.1 6
91.30 even 6 91.2.h.b.16.1 yes 12
91.38 odd 6 8281.2.a.ca.1.1 6
91.51 even 6 1183.2.e.h.170.6 12
91.62 odd 6 637.2.h.l.165.1 12
91.69 odd 6 637.2.g.l.263.6 12
91.75 odd 6 637.2.g.l.373.6 12
91.82 odd 6 637.2.h.l.471.1 12
91.88 even 6 637.2.f.k.295.6 12
273.23 odd 6 819.2.n.d.100.1 12
273.212 odd 6 819.2.s.d.289.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.6 12 91.23 even 6
91.2.g.b.81.6 yes 12 13.4 even 6
91.2.h.b.16.1 yes 12 91.30 even 6
91.2.h.b.74.1 yes 12 13.10 even 6
637.2.f.j.295.6 12 91.10 odd 6
637.2.f.j.393.6 12 91.17 odd 6
637.2.f.k.295.6 12 91.88 even 6
637.2.f.k.393.6 12 91.4 even 6
637.2.g.l.263.6 12 91.69 odd 6
637.2.g.l.373.6 12 91.75 odd 6
637.2.h.l.165.1 12 91.62 odd 6
637.2.h.l.471.1 12 91.82 odd 6
819.2.n.d.100.1 12 273.23 odd 6
819.2.n.d.172.1 12 39.17 odd 6
819.2.s.d.289.6 12 273.212 odd 6
819.2.s.d.802.6 12 39.23 odd 6
1183.2.e.g.170.1 12 7.2 even 3 inner
1183.2.e.g.508.1 12 1.1 even 1 trivial
1183.2.e.h.170.6 12 91.51 even 6
1183.2.e.h.508.6 12 13.12 even 2
8281.2.a.bz.1.1 6 91.25 even 6
8281.2.a.ca.1.1 6 91.38 odd 6
8281.2.a.ce.1.6 6 7.4 even 3
8281.2.a.cf.1.6 6 7.3 odd 6