Properties

Label 357.2.bl.a.10.15
Level 357357
Weight 22
Character 357.10
Analytic conductor 2.8512.851
Analytic rank 00
Dimension 384384
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [357,2,Mod(10,357)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(357, base_ring=CyclotomicField(48))
 
chi = DirichletCharacter(H, H._module([0, 8, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("357.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 357=3717 357 = 3 \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 357.bl (of order 4848, degree 1616, 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: 2.850659352162.85065935216
Analytic rank: 00
Dimension: 384384
Relative dimension: 2424 over Q(ζ48)\Q(\zeta_{48})
Twist minimal: yes
Sato-Tate group: SU(2)[C48]\mathrm{SU}(2)[C_{48}]

Embedding invariants

Embedding label 10.15
Character χ\chi == 357.10
Dual form 357.2.bl.a.250.15

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5592460.0736262i)q2+(0.4422890.896873i)q3+(1.62452+0.435288i)q4+(1.946511.70704i)q5+(0.3133820.469009i)q6+(2.538140.746878i)q7+(1.91873+0.794762i)q8+(0.608761+0.793353i)q9+(0.9628951.09797i)q10+(0.9580760.0627956i)q11+(1.10890+1.26446i)q12+(3.776083.77608i)q13+(1.364460.604562i)q14+(2.391920.990765i)q15+(1.898481.09609i)q16+(3.073122.74881i)q17+(0.282036+0.488501i)q18+(0.4170083.16749i)q19+(2.41908+3.62041i)q20+(1.792451.94606i)q21+(0.5311770.105658i)q22+(3.586881.76885i)q23+(1.56143+1.36934i)q24+(0.2222721.68832i)q25+(2.389781.83374i)q26+(0.980785+0.195090i)q27+(3.79815+2.31814i)q28+(0.353142+1.77536i)q29+(1.410620.377974i)q30+(9.230674.55206i)q31+(4.276313.28133i)q32+(0.4800660.831499i)q33+(1.516251.76352i)q34+(3.665575.78652i)q35+(0.6436061.55380i)q36+(0.606978+9.26070i)q37+(0.4664201.74070i)q38+(1.71655+5.05678i)q39+(2.37812+4.82236i)q40+(1.08348+5.44704i)q41+(1.145700.956354i)q42+(0.3684990.889635i)q43+(1.52908+0.519051i)q44+(0.169328+2.58345i)q45+(2.136180.725136i)q46+(3.22686+12.0428i)q47+(1.822731.21791i)q48+(5.884353.79137i)q490.960552iq50+(3.824541.54043i)q51+(7.77799+4.49062i)q52+(0.111916+0.145852i)q53+(0.562864+0.0368921i)q54+(1.757711.75771i)q55+(4.27641+3.45027i)q56+(2.65640+1.77495i)q57+(0.328206+0.966865i)q58+(11.58041.52459i)q59+(4.31698+0.568341i)q60+(3.35591+9.88621i)q61+(4.827073.22534i)q62+(0.952586+2.46832i)q63+(0.950284+0.950284i)q64+(13.79610.904245i)q65+(0.3296950.429667i)q66+(5.04673+2.91373i)q67+(3.79581+5.80317i)q68+3.99932iq69+(1.623923.50597i)q70+(3.654862.44210i)q71+(0.5375192.00605i)q72+(9.25085+3.14024i)q73+(0.342380+5.22370i)q74+(1.61252+0.547376i)q75+(2.05621+4.96412i)q76+(2.384830.874950i)q77+(0.587661+2.95437i)q78+(6.4313113.0414i)q79+(1.824345.37432i)q80+(0.2588190.965926i)q81+(0.204890+3.12601i)q82+(6.07736+14.6721i)q83+(3.75895+2.38117i)q84+(1.2895210.5965i)q85+(0.2715820.470394i)q86+(1.436081.10195i)q87+(1.78838+0.881930i)q88+(9.93227+2.66134i)q89+(0.284906+1.43232i)q90+(12.40456.76397i)q91+(6.59690+1.31220i)q92+(8.165246.26541i)q93+(0.917943+6.97247i)q94+(6.218755.45370i)q95+(4.834302.38401i)q96+(5.250251.04434i)q97+(3.011662.55355i)q98+(0.533421+0.798320i)q99+O(q100)q+(0.559246 - 0.0736262i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(-1.62452 + 0.435288i) q^{4} +(1.94651 - 1.70704i) q^{5} +(-0.313382 - 0.469009i) q^{6} +(2.53814 - 0.746878i) q^{7} +(-1.91873 + 0.794762i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.962895 - 1.09797i) q^{10} +(0.958076 - 0.0627956i) q^{11} +(1.10890 + 1.26446i) q^{12} +(-3.77608 - 3.77608i) q^{13} +(1.36446 - 0.604562i) q^{14} +(-2.39192 - 0.990765i) q^{15} +(1.89848 - 1.09609i) q^{16} +(3.07312 - 2.74881i) q^{17} +(-0.282036 + 0.488501i) q^{18} +(-0.417008 - 3.16749i) q^{19} +(-2.41908 + 3.62041i) q^{20} +(-1.79245 - 1.94606i) q^{21} +(0.531177 - 0.105658i) q^{22} +(-3.58688 - 1.76885i) q^{23} +(1.56143 + 1.36934i) q^{24} +(0.222272 - 1.68832i) q^{25} +(-2.38978 - 1.83374i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-3.79815 + 2.31814i) q^{28} +(0.353142 + 1.77536i) q^{29} +(-1.41062 - 0.377974i) q^{30} +(9.23067 - 4.55206i) q^{31} +(4.27631 - 3.28133i) q^{32} +(-0.480066 - 0.831499i) q^{33} +(1.51625 - 1.76352i) q^{34} +(3.66557 - 5.78652i) q^{35} +(0.643606 - 1.55380i) q^{36} +(-0.606978 + 9.26070i) q^{37} +(-0.466420 - 1.74070i) q^{38} +(-1.71655 + 5.05678i) q^{39} +(-2.37812 + 4.82236i) q^{40} +(-1.08348 + 5.44704i) q^{41} +(-1.14570 - 0.956354i) q^{42} +(-0.368499 - 0.889635i) q^{43} +(-1.52908 + 0.519051i) q^{44} +(0.169328 + 2.58345i) q^{45} +(-2.13618 - 0.725136i) q^{46} +(-3.22686 + 12.0428i) q^{47} +(-1.82273 - 1.21791i) q^{48} +(5.88435 - 3.79137i) q^{49} -0.960552i q^{50} +(-3.82454 - 1.54043i) q^{51} +(7.77799 + 4.49062i) q^{52} +(0.111916 + 0.145852i) q^{53} +(0.562864 + 0.0368921i) q^{54} +(1.75771 - 1.75771i) q^{55} +(-4.27641 + 3.45027i) q^{56} +(-2.65640 + 1.77495i) q^{57} +(0.328206 + 0.966865i) q^{58} +(-11.5804 - 1.52459i) q^{59} +(4.31698 + 0.568341i) q^{60} +(3.35591 + 9.88621i) q^{61} +(4.82707 - 3.22534i) q^{62} +(-0.952586 + 2.46832i) q^{63} +(-0.950284 + 0.950284i) q^{64} +(-13.7961 - 0.904245i) q^{65} +(-0.329695 - 0.429667i) q^{66} +(5.04673 + 2.91373i) q^{67} +(-3.79581 + 5.80317i) q^{68} +3.99932i q^{69} +(1.62392 - 3.50597i) q^{70} +(-3.65486 - 2.44210i) q^{71} +(0.537519 - 2.00605i) q^{72} +(9.25085 + 3.14024i) q^{73} +(0.342380 + 5.22370i) q^{74} +(-1.61252 + 0.547376i) q^{75} +(2.05621 + 4.96412i) q^{76} +(2.38483 - 0.874950i) q^{77} +(-0.587661 + 2.95437i) q^{78} +(6.43131 - 13.0414i) q^{79} +(1.82434 - 5.37432i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.204890 + 3.12601i) q^{82} +(-6.07736 + 14.6721i) q^{83} +(3.75895 + 2.38117i) q^{84} +(1.28952 - 10.5965i) q^{85} +(-0.271582 - 0.470394i) q^{86} +(1.43608 - 1.10195i) q^{87} +(-1.78838 + 0.881930i) q^{88} +(9.93227 + 2.66134i) q^{89} +(0.284906 + 1.43232i) q^{90} +(-12.4045 - 6.76397i) q^{91} +(6.59690 + 1.31220i) q^{92} +(-8.16524 - 6.26541i) q^{93} +(-0.917943 + 6.97247i) q^{94} +(-6.21875 - 5.45370i) q^{95} +(-4.83430 - 2.38401i) q^{96} +(5.25025 - 1.04434i) q^{97} +(3.01166 - 2.55355i) q^{98} +(-0.533421 + 0.798320i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 384q16q11+32q1464q2216q2548q2864q3064q3532q3748q4264q44+32q4664q49+80q5632q58288q61528q68+176q70++32q99+O(q100) 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/357Z)×\left(\mathbb{Z}/357\mathbb{Z}\right)^\times.

nn 5252 190190 239239
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(316)e\left(\frac{3}{16}\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 0.559246 0.0736262i 0.395447 0.0520616i 0.0698192 0.997560i 0.477758π-0.477758\pi
0.325628 + 0.945498i 0.394424π0.394424\pi
33 −0.442289 0.896873i −0.255355 0.517810i
44 −1.62452 + 0.435288i −0.812258 + 0.217644i
55 1.94651 1.70704i 0.870505 0.763413i −0.102369 0.994746i 0.532642π-0.532642\pi
0.972874 + 0.231334i 0.0743090π0.0743090\pi
66 −0.313382 0.469009i −0.127937 0.191472i
77 2.53814 0.746878i 0.959328 0.282293i
88 −1.91873 + 0.794762i −0.678372 + 0.280991i
99 −0.608761 + 0.793353i −0.202920 + 0.264451i
1010 0.962895 1.09797i 0.304494 0.347209i
1111 0.958076 0.0627956i 0.288871 0.0189336i 0.0797210 0.996817i 0.474597π-0.474597\pi
0.209150 + 0.977884i 0.432930π0.432930\pi
1212 1.10890 + 1.26446i 0.320113 + 0.365019i
1313 −3.77608 3.77608i −1.04730 1.04730i −0.998825 0.0484722i 0.984565π-0.984565\pi
−0.0484722 0.998825i 0.515435π-0.515435\pi
1414 1.36446 0.604562i 0.364667 0.161576i
1515 −2.39192 0.990765i −0.617591 0.255814i
1616 1.89848 1.09609i 0.474620 0.274022i
1717 3.07312 2.74881i 0.745341 0.666684i
1818 −0.282036 + 0.488501i −0.0664765 + 0.115141i
1919 −0.417008 3.16749i −0.0956682 0.726672i −0.970304 0.241891i 0.922233π-0.922233\pi
0.874635 0.484781i 0.161101π-0.161101\pi
2020 −2.41908 + 3.62041i −0.540923 + 0.809548i
2121 −1.79245 1.94606i −0.391144 0.424664i
2222 0.531177 0.105658i 0.113247 0.0225263i
2323 −3.58688 1.76885i −0.747916 0.368831i 0.0280499 0.999607i 0.491070π-0.491070\pi
−0.775966 + 0.630775i 0.782737π0.782737\pi
2424 1.56143 + 1.36934i 0.318726 + 0.279515i
2525 0.222272 1.68832i 0.0444543 0.337664i
2626 −2.38978 1.83374i −0.468674 0.359626i
2727 0.980785 + 0.195090i 0.188752 + 0.0375451i
2828 −3.79815 + 2.31814i −0.717783 + 0.438087i
2929 0.353142 + 1.77536i 0.0655768 + 0.329677i 0.999622 0.0274769i 0.00874727π-0.00874727\pi
−0.934046 + 0.357154i 0.883747π0.883747\pi
3030 −1.41062 0.377974i −0.257542 0.0690083i
3131 9.23067 4.55206i 1.65788 0.817574i 0.660083 0.751193i 0.270521π-0.270521\pi
0.997794 0.0663814i 0.0211454π-0.0211454\pi
3232 4.27631 3.28133i 0.755952 0.580062i
3333 −0.480066 0.831499i −0.0835688 0.144745i
3434 1.51625 1.76352i 0.260034 0.302442i
3535 3.66557 5.78652i 0.619594 0.978101i
3636 0.643606 1.55380i 0.107268 0.258967i
3737 −0.606978 + 9.26070i −0.0997866 + 1.52245i 0.595288 + 0.803512i 0.297038π0.297038\pi
−0.695075 + 0.718938i 0.744629π0.744629\pi
3838 −0.466420 1.74070i −0.0756633 0.282379i
3939 −1.71655 + 5.05678i −0.274867 + 0.809733i
4040 −2.37812 + 4.82236i −0.376014 + 0.762481i
4141 −1.08348 + 5.44704i −0.169212 + 0.850685i 0.799149 + 0.601133i 0.205284π0.205284\pi
−0.968361 + 0.249553i 0.919716π0.919716\pi
4242 −1.14570 0.956354i −0.176785 0.147569i
4343 −0.368499 0.889635i −0.0561955 0.135668i 0.893288 0.449485i 0.148392π-0.148392\pi
−0.949484 + 0.313817i 0.898392π0.898392\pi
4444 −1.52908 + 0.519051i −0.230517 + 0.0782499i
4545 0.169328 + 2.58345i 0.0252420 + 0.385118i
4646 −2.13618 0.725136i −0.314963 0.106915i
4747 −3.22686 + 12.0428i −0.470685 + 1.75662i 0.166631 + 0.986019i 0.446711π0.446711\pi
−0.637316 + 0.770602i 0.719956π0.719956\pi
4848 −1.82273 1.21791i −0.263088 0.175790i
4949 5.88435 3.79137i 0.840621 0.541624i
5050 0.960552i 0.135843i
5151 −3.82454 1.54043i −0.535542 0.215703i
5252 7.77799 + 4.49062i 1.07861 + 0.622737i
5353 0.111916 + 0.145852i 0.0153729 + 0.0200343i 0.800977 0.598696i 0.204314π-0.204314\pi
−0.785604 + 0.618730i 0.787647π0.787647\pi
5454 0.562864 + 0.0368921i 0.0765961 + 0.00502037i
5555 1.75771 1.75771i 0.237009 0.237009i
5656 −4.27641 + 3.45027i −0.571459 + 0.461062i
5757 −2.65640 + 1.77495i −0.351848 + 0.235098i
5858 0.328206 + 0.966865i 0.0430956 + 0.126956i
5959 −11.5804 1.52459i −1.50764 0.198485i −0.669038 0.743228i 0.733294π-0.733294\pi
−0.838603 + 0.544743i 0.816627π0.816627\pi
6060 4.31698 + 0.568341i 0.557319 + 0.0733725i
6161 3.35591 + 9.88621i 0.429681 + 1.26580i 0.919195 + 0.393803i 0.128841π0.128841\pi
−0.489514 + 0.871996i 0.662826π0.662826\pi
6262 4.82707 3.22534i 0.613038 0.409619i
6363 −0.952586 + 2.46832i −0.120015 + 0.310978i
6464 −0.950284 + 0.950284i −0.118785 + 0.118785i
6565 −13.7961 0.904245i −1.71120 0.112158i
6666 −0.329695 0.429667i −0.0405827 0.0528884i
6767 5.04673 + 2.91373i 0.616556 + 0.355969i 0.775527 0.631314i 0.217484π-0.217484\pi
−0.158971 + 0.987283i 0.550818π0.550818\pi
6868 −3.79581 + 5.80317i −0.460309 + 0.703738i
6969 3.99932i 0.481461i
7070 1.62392 3.50597i 0.194095 0.419044i
7171 −3.65486 2.44210i −0.433752 0.289824i 0.319462 0.947599i 0.396498π-0.396498\pi
−0.753214 + 0.657775i 0.771498π0.771498\pi
7272 0.537519 2.00605i 0.0633472 0.236415i
7373 9.25085 + 3.14024i 1.08273 + 0.367537i 0.805093 0.593149i 0.202115π-0.202115\pi
0.277637 + 0.960686i 0.410449π0.410449\pi
7474 0.342380 + 5.22370i 0.0398008 + 0.607243i
7575 −1.61252 + 0.547376i −0.186197 + 0.0632055i
7676 2.05621 + 4.96412i 0.235863 + 0.569424i
7777 2.38483 0.874950i 0.271777 0.0997098i
7878 −0.587661 + 2.95437i −0.0665395 + 0.334517i
7979 6.43131 13.0414i 0.723579 1.46727i −0.154115 0.988053i 0.549253π-0.549253\pi
0.877695 0.479221i 0.159081π-0.159081\pi
8080 1.82434 5.37432i 0.203967 0.600868i
8181 −0.258819 0.965926i −0.0287577 0.107325i
8282 −0.204890 + 3.12601i −0.0226263 + 0.345210i
8383 −6.07736 + 14.6721i −0.667077 + 1.61047i 0.119399 + 0.992846i 0.461903π0.461903\pi
−0.786476 + 0.617620i 0.788097π0.788097\pi
8484 3.75895 + 2.38117i 0.410135 + 0.259807i
8585 1.28952 10.5965i 0.139868 1.14935i
8686 −0.271582 0.470394i −0.0292854 0.0507238i
8787 1.43608 1.10195i 0.153964 0.118141i
8888 −1.78838 + 0.881930i −0.190642 + 0.0940141i
8989 9.93227 + 2.66134i 1.05282 + 0.282102i 0.743416 0.668829i 0.233204π-0.233204\pi
0.309402 + 0.950931i 0.399871π0.399871\pi
9090 0.284906 + 1.43232i 0.0300317 + 0.150980i
9191 −12.4045 6.76397i −1.30035 0.709056i
9292 6.59690 + 1.31220i 0.687774 + 0.136807i
9393 −8.16524 6.26541i −0.846696 0.649693i
9494 −0.917943 + 6.97247i −0.0946786 + 0.719155i
9595 −6.21875 5.45370i −0.638030 0.559537i
9696 −4.83430 2.38401i −0.493398 0.243317i
9797 5.25025 1.04434i 0.533082 0.106037i 0.0787930 0.996891i 0.474893π-0.474893\pi
0.454289 + 0.890854i 0.349893π0.349893\pi
9898 3.01166 2.55355i 0.304223 0.257947i
9999 −0.533421 + 0.798320i −0.0536108 + 0.0802342i
100100 0.373822 + 2.83946i 0.0373822 + 0.283946i
101101 3.62332 6.27577i 0.360533 0.624462i −0.627515 0.778604i 0.715928π-0.715928\pi
0.988049 + 0.154142i 0.0492613π0.0492613\pi
102102 −2.25227 0.579893i −0.223008 0.0574180i
103103 9.46233 5.46308i 0.932351 0.538293i 0.0447966 0.998996i 0.485736π-0.485736\pi
0.887554 + 0.460703i 0.152403π0.152403\pi
104104 10.2463 + 4.24418i 1.00474 + 0.416176i
105105 −6.81101 0.728234i −0.664687 0.0710683i
106106 0.0733273 + 0.0733273i 0.00712218 + 0.00712218i
107107 −6.98828 7.96861i −0.675583 0.770355i 0.307888 0.951423i 0.400378π-0.400378\pi
−0.983471 + 0.181068i 0.942045π0.942045\pi
108108 −1.67822 + 0.109996i −0.161487 + 0.0105844i
109109 −1.92030 + 2.18968i −0.183931 + 0.209733i −0.836456 0.548034i 0.815376π-0.815376\pi
0.652525 + 0.757767i 0.273710π0.273710\pi
110110 0.853579 1.11241i 0.0813855 0.106064i
111111 8.57413 3.55152i 0.813820 0.337095i
112112 3.99997 4.19996i 0.377961 0.396859i
113113 7.27876 + 10.8934i 0.684728 + 1.02477i 0.997196 + 0.0748391i 0.0238443π0.0238443\pi
−0.312468 + 0.949928i 0.601156π0.601156\pi
114114 −1.35490 + 1.18821i −0.126898 + 0.111286i
115115 −10.0014 + 2.67987i −0.932635 + 0.249899i
116116 −1.34648 2.73039i −0.125017 0.253510i
117117 5.29450 0.697034i 0.489477 0.0644408i
118118 −6.58855 −0.606525
119119 5.74699 9.27211i 0.526826 0.849973i
120120 5.37686 0.490838
121121 −9.99193 + 1.31546i −0.908357 + 0.119587i
122122 2.60467 + 5.28174i 0.235815 + 0.478186i
123123 5.36452 1.43742i 0.483702 0.129608i
124124 −13.0139 + 11.4129i −1.16868 + 1.02491i
125125 4.74246 + 7.09759i 0.424178 + 0.634828i
126126 −0.350998 + 1.45053i −0.0312694 + 0.129224i
127127 −10.9584 + 4.53911i −0.972398 + 0.402781i −0.811604 0.584207i 0.801405π-0.801405\pi
−0.160794 + 0.986988i 0.551405π0.551405\pi
128128 −7.02413 + 9.15403i −0.620851 + 0.809109i
129129 −0.634906 + 0.723972i −0.0559004 + 0.0637422i
130130 −7.78200 + 0.510059i −0.682526 + 0.0447351i
131131 −6.63518 7.56597i −0.579718 0.661042i 0.385433 0.922736i 0.374052π-0.374052\pi
−0.965151 + 0.261694i 0.915719π0.915719\pi
132132 1.14182 + 1.14182i 0.0993823 + 0.0993823i
133133 −3.42415 7.72809i −0.296912 0.670110i
134134 3.03689 + 1.25792i 0.262347 + 0.108668i
135135 2.24213 1.29450i 0.192972 0.111413i
136136 −3.71182 + 7.71660i −0.318286 + 0.661693i
137137 −2.26000 + 3.91443i −0.193084 + 0.334432i −0.946271 0.323375i 0.895182π-0.895182\pi
0.753186 + 0.657807i 0.228516π0.228516\pi
138138 0.294454 + 2.23660i 0.0250656 + 0.190392i
139139 −1.19426 + 1.78734i −0.101296 + 0.151600i −0.878655 0.477457i 0.841559π-0.841559\pi
0.777359 + 0.629057i 0.216559π0.216559\pi
140140 −3.43597 + 10.9959i −0.290392 + 0.929321i
141141 12.2281 2.43231i 1.02979 0.204838i
142142 −2.22377 1.09664i −0.186615 0.0920282i
143143 −3.85490 3.38065i −0.322363 0.282704i
144144 −0.286136 + 2.17342i −0.0238447 + 0.181118i
145145 3.71801 + 2.85293i 0.308764 + 0.236923i
146146 5.40471 + 1.07506i 0.447297 + 0.0889729i
147147 −6.00295 3.60063i −0.495115 0.296975i
148148 −3.04502 15.3084i −0.250299 1.25834i
149149 9.97363 + 2.67243i 0.817072 + 0.218934i 0.643066 0.765811i 0.277662π-0.277662\pi
0.174006 + 0.984745i 0.444329π0.444329\pi
150150 −0.861493 + 0.424841i −0.0703406 + 0.0346881i
151151 6.40253 4.91283i 0.521030 0.399801i −0.314489 0.949261i 0.601833π-0.601833\pi
0.835520 + 0.549460i 0.185167π0.185167\pi
152152 3.31752 + 5.74612i 0.269087 + 0.466072i
153153 0.309980 + 4.11144i 0.0250604 + 0.332390i
154154 1.26929 0.664899i 0.102282 0.0535791i
155155 10.1970 24.6178i 0.819044 1.97735i
156156 0.587402 8.96202i 0.0470298 0.717536i
157157 0.473522 + 1.76721i 0.0377912 + 0.141039i 0.982244 0.187609i 0.0600738π-0.0600738\pi
−0.944453 + 0.328648i 0.893407π0.893407\pi
158158 2.63650 7.76687i 0.209749 0.617899i
159159 0.0813115 0.164883i 0.00644842 0.0130761i
160160 2.72251 13.6870i 0.215233 1.08205i
161161 −10.4251 1.81064i −0.821615 0.142699i
162162 −0.215861 0.521135i −0.0169596 0.0409442i
163163 −4.57124 + 1.55173i −0.358047 + 0.121541i −0.494666 0.869083i 0.664710π-0.664710\pi
0.136619 + 0.990624i 0.456376π0.456376\pi
164164 −0.610894 9.32044i −0.0477028 0.727804i
165165 −2.35386 0.799026i −0.183247 0.0622041i
166166 −2.31850 + 8.65274i −0.179950 + 0.671583i
167167 −2.02483 1.35295i −0.156686 0.104694i 0.474756 0.880118i 0.342536π-0.342536\pi
−0.631442 + 0.775423i 0.717536π0.717536\pi
168168 4.98586 + 2.30938i 0.384668 + 0.178172i
169169 15.5176i 1.19366i
170170 −0.0590221 6.02101i −0.00452679 0.461790i
171171 2.76680 + 1.59741i 0.211582 + 0.122157i
172172 0.985879 + 1.28482i 0.0751726 + 0.0979668i
173173 −15.5591 1.01980i −1.18294 0.0775338i −0.538793 0.842438i 0.681120π-0.681120\pi
−0.644144 + 0.764904i 0.722786π0.722786\pi
174174 0.721993 0.721993i 0.0547341 0.0547341i
175175 −0.696812 4.45121i −0.0526740 0.336480i
176176 1.75006 1.16935i 0.131916 0.0881431i
177177 3.75452 + 11.0605i 0.282207 + 0.831355i
178178 5.75053 + 0.757071i 0.431020 + 0.0567449i
179179 4.93527 + 0.649740i 0.368879 + 0.0485639i 0.312687 0.949856i 0.398771π-0.398771\pi
0.0561919 + 0.998420i 0.482104π0.482104\pi
180180 −1.39962 4.12315i −0.104322 0.307322i
181181 1.69387 1.13181i 0.125905 0.0841268i −0.491023 0.871146i 0.663377π-0.663377\pi
0.616928 + 0.787020i 0.288377π0.288377\pi
182182 −7.43518 2.86943i −0.551132 0.212696i
183183 7.38239 7.38239i 0.545722 0.545722i
184184 8.28805 + 0.543227i 0.611003 + 0.0400473i
185185 14.6269 + 19.0622i 1.07539 + 1.40148i
186186 −5.02768 2.90273i −0.368647 0.212839i
187187 2.77167 2.82655i 0.202684 0.206697i
188188 20.9683i 1.52927i
189189 2.63508 0.237359i 0.191674 0.0172654i
190190 −3.87935 2.59210i −0.281437 0.188050i
191191 0.174072 0.649645i 0.0125954 0.0470066i −0.959342 0.282246i 0.908921π-0.908921\pi
0.971938 + 0.235239i 0.0755873π0.0755873\pi
192192 1.27258 + 0.431984i 0.0918408 + 0.0311757i
193193 −0.118027 1.80075i −0.00849578 0.129621i 0.991504 0.130075i 0.0415219π-0.0415219\pi
−1.00000 0.000454761i 0.999855π0.999855\pi
194194 2.85929 0.970598i 0.205285 0.0696849i
195195 5.29087 + 12.7733i 0.378887 + 0.914714i
196196 −7.90888 + 8.72052i −0.564920 + 0.622894i
197197 −1.20363 + 6.05108i −0.0857554 + 0.431122i 0.913926 + 0.405881i 0.133035π0.133035\pi
−0.999681 + 0.0252407i 0.991965π0.991965\pi
198198 −0.239536 + 0.485731i −0.0170231 + 0.0345194i
199199 8.04185 23.6905i 0.570072 1.67938i −0.152685 0.988275i 0.548792π-0.548792\pi
0.722757 0.691103i 0.242875π-0.242875\pi
200200 0.915335 + 3.41608i 0.0647240 + 0.241553i
201201 0.381134 5.81498i 0.0268831 0.410157i
202202 1.56427 3.77647i 0.110061 0.265712i
203203 2.22230 + 4.24237i 0.155975 + 0.297756i
204204 6.88355 + 0.837678i 0.481945 + 0.0586492i
205205 7.18932 + 12.4523i 0.502124 + 0.869705i
206206 4.88955 3.75188i 0.340671 0.261406i
207207 3.58688 1.76885i 0.249305 0.122944i
208208 −11.3077 3.02990i −0.784050 0.210085i
209209 −0.598430 3.00851i −0.0413943 0.208103i
210210 −3.86265 + 0.0942069i −0.266548 + 0.00650089i
211211 −14.0629 2.79728i −0.968130 0.192573i −0.314391 0.949294i 0.601800π-0.601800\pi
−0.653738 + 0.756721i 0.726800π0.726800\pi
212212 −0.245298 0.188223i −0.0168471 0.0129272i
213213 −0.573749 + 4.35806i −0.0393127 + 0.298609i
214214 −4.49487 3.94189i −0.307263 0.269462i
215215 −2.23593 1.10264i −0.152489 0.0751993i
216216 −2.03691 + 0.405166i −0.138594 + 0.0275681i
217217 20.0289 18.4480i 1.35965 1.25233i
218218 −0.912702 + 1.36595i −0.0618160 + 0.0925141i
219219 −1.27515 9.68573i −0.0861667 0.654501i
220220 −2.09032 + 3.62054i −0.140929 + 0.244096i
221221 −21.9841 1.22462i −1.47881 0.0823770i
222222 4.53357 2.61746i 0.304273 0.175672i
223223 −1.19419 0.494648i −0.0799686 0.0331241i 0.342341 0.939576i 0.388780π-0.388780\pi
−0.422309 + 0.906452i 0.638780π0.638780\pi
224224 8.40314 11.5224i 0.561458 0.769870i
225225 1.20412 + 1.20412i 0.0802750 + 0.0802750i
226226 4.87266 + 5.55620i 0.324124 + 0.369593i
227227 0.0159556 0.00104578i 0.00105901 6.94111e-5i −0.0648736 0.997893i 0.520664π-0.520664\pi
0.0659326 + 0.997824i 0.478998π0.478998\pi
228228 3.54275 4.03973i 0.234624 0.267538i
229229 −2.99180 + 3.89899i −0.197704 + 0.257653i −0.881676 0.471855i 0.843584π-0.843584\pi
0.683972 + 0.729508i 0.260251π0.260251\pi
230230 −5.39593 + 2.23507i −0.355797 + 0.147376i
231231 −1.83950 1.75191i −0.121030 0.115267i
232232 −2.08857 3.12577i −0.137122 0.205217i
233233 11.6916 10.2533i 0.765943 0.671714i −0.184423 0.982847i 0.559042π-0.559042\pi
0.950366 + 0.311133i 0.100708π0.100708\pi
234234 2.90961 0.779628i 0.190207 0.0509658i
235235 14.2764 + 28.9498i 0.931293 + 1.88848i
236236 19.4762 2.56409i 1.26779 0.166908i
237237 −14.5410 −0.944538
238238 2.53131 5.60852i 0.164081 0.363547i
239239 −17.9141 −1.15877 −0.579384 0.815055i 0.696707π-0.696707\pi
−0.579384 + 0.815055i 0.696707π0.696707\pi
240240 −5.62697 + 0.740805i −0.363219 + 0.0478187i
241241 −8.25636 16.7423i −0.531839 1.07846i −0.982585 0.185811i 0.940509π-0.940509\pi
0.450746 0.892652i 0.351158π-0.351158\pi
242242 −5.49110 + 1.47133i −0.352981 + 0.0945810i
243243 −0.751840 + 0.659346i −0.0482305 + 0.0422971i
244244 −9.75508 14.5995i −0.624505 0.934638i
245245 4.98191 17.4248i 0.318283 1.11323i
246246 2.89426 1.19884i 0.184531 0.0764352i
247247 −10.3860 + 13.5354i −0.660848 + 0.861234i
248248 −14.0933 + 16.0703i −0.894926 + 1.02047i
249249 15.8469 1.03866i 1.00426 0.0658225i
250250 3.17477 + 3.62013i 0.200790 + 0.228957i
251251 2.44973 + 2.44973i 0.154625 + 0.154625i 0.780180 0.625555i 0.215127π-0.215127\pi
−0.625555 + 0.780180i 0.715127π0.715127\pi
252252 0.473064 4.42447i 0.0298002 0.278715i
253253 −3.54758 1.46945i −0.223034 0.0923838i
254254 −5.79423 + 3.34530i −0.363562 + 0.209903i
255255 −10.0741 + 3.53019i −0.630863 + 0.221069i
256256 −1.91034 + 3.30880i −0.119396 + 0.206800i
257257 −2.91195 22.1184i −0.181642 1.37971i −0.802905 0.596107i 0.796713π-0.796713\pi
0.621263 0.783602i 0.286620π-0.286620\pi
258258 −0.301766 + 0.451624i −0.0187871 + 0.0281169i
259259 5.37601 + 23.9583i 0.334049 + 1.48870i
260260 22.8056 4.53632i 1.41434 0.281330i
261261 −1.62347 0.800607i −0.100490 0.0495563i
262262 −4.26775 3.74272i −0.263663 0.231226i
263263 −0.344039 + 2.61323i −0.0212143 + 0.161139i −0.998773 0.0495250i 0.984229π-0.984229\pi
0.977559 + 0.210664i 0.0675626π0.0675626\pi
264264 1.58196 + 1.21388i 0.0973628 + 0.0747091i
265265 0.466822 + 0.0928567i 0.0286766 + 0.00570414i
266266 −2.48393 4.06980i −0.152300 0.249535i
267267 −2.00604 10.0851i −0.122768 0.617196i
268268 −9.46680 2.53662i −0.578277 0.154949i
269269 5.22766 2.57800i 0.318736 0.157183i −0.275882 0.961191i 0.588970π-0.588970\pi
0.594618 + 0.804008i 0.297303π0.297303\pi
270270 1.15860 0.889022i 0.0705099 0.0541042i
271271 −0.375161 0.649798i −0.0227894 0.0394724i 0.854406 0.519606i 0.173921π-0.173921\pi
−0.877195 + 0.480134i 0.840588π0.840588\pi
272272 2.82132 8.58696i 0.171067 0.520661i
273273 −0.580043 + 14.1169i −0.0351058 + 0.854393i
274274 −0.975690 + 2.35552i −0.0589436 + 0.142302i
275275 0.106934 1.63150i 0.00644836 0.0983830i
276276 −1.74085 6.49695i −0.104787 0.391071i
277277 −2.80472 + 8.26244i −0.168519 + 0.496442i −0.998077 0.0619785i 0.980259π-0.980259\pi
0.829558 + 0.558420i 0.188592π0.188592\pi
278278 −0.536292 + 1.08749i −0.0321647 + 0.0652235i
279279 −2.00788 + 10.0943i −0.120209 + 0.604330i
280280 −2.43431 + 14.0160i −0.145478 + 0.837616i
281281 9.95495 + 24.0334i 0.593863 + 1.43371i 0.879745 + 0.475447i 0.157714π0.157714\pi
−0.285882 + 0.958265i 0.592286π0.592286\pi
282282 6.65941 2.26057i 0.396562 0.134615i
283283 0.827228 + 12.6211i 0.0491736 + 0.750244i 0.949252 + 0.314516i 0.101842π0.101842\pi
−0.900079 + 0.435728i 0.856491π0.856491\pi
284284 7.00040 + 2.37632i 0.415397 + 0.141008i
285285 −2.14079 + 7.98953i −0.126809 + 0.473259i
286286 −2.40474 1.60680i −0.142195 0.0950118i
287287 1.31824 + 14.6346i 0.0778131 + 0.863854i
288288 5.39017i 0.317619i
289289 1.88811 16.8948i 0.111065 0.993813i
290290 2.28934 + 1.32175i 0.134434 + 0.0776157i
291291 −3.25876 4.24690i −0.191032 0.248958i
292292 −16.3951 1.07459i −0.959449 0.0628856i
293293 −15.4640 + 15.4640i −0.903417 + 0.903417i −0.995730 0.0923128i 0.970574π-0.970574\pi
0.0923128 + 0.995730i 0.470574π0.470574\pi
294294 −3.62223 1.57167i −0.211253 0.0916614i
295295 −25.1439 + 16.8006i −1.46394 + 0.978170i
296296 −6.19543 18.2511i −0.360102 1.06083i
297297 0.951918 + 0.125322i 0.0552359 + 0.00727194i
298298 5.77448 + 0.760224i 0.334506 + 0.0440386i
299299 6.86501 + 20.2237i 0.397014 + 1.16957i
300300 2.38129 1.59113i 0.137484 0.0918639i
301301 −1.59975 1.98280i −0.0922081 0.114287i
302302 3.21888 3.21888i 0.185226 0.185226i
303303 −7.23112 0.473952i −0.415417 0.0272279i
304304 −4.26352 5.55633i −0.244530 0.318678i
305305 23.4085 + 13.5149i 1.34037 + 0.773861i
306306 0.476065 + 2.27648i 0.0272148 + 0.130138i
307307 23.4740i 1.33973i −0.742483 0.669865i 0.766352π-0.766352\pi
0.742483 0.669865i 0.233648π-0.233648\pi
308308 −3.49335 + 2.45946i −0.199052 + 0.140141i
309309 −9.08477 6.07025i −0.516814 0.345324i
310310 3.89013 14.5182i 0.220945 0.824576i
311311 32.5369 + 11.0448i 1.84500 + 0.626293i 0.995044 + 0.0994387i 0.0317047π0.0317047\pi
0.849956 + 0.526854i 0.176629π0.176629\pi
312312 −0.725358 11.0668i −0.0410653 0.626535i
313313 −11.6407 + 3.95148i −0.657970 + 0.223351i −0.630402 0.776269i 0.717110π-0.717110\pi
−0.0275685 + 0.999620i 0.508776π0.508776\pi
314314 0.394929 + 0.953442i 0.0222871 + 0.0538058i
315315 2.35930 + 6.43070i 0.132932 + 0.362329i
316316 −4.77100 + 23.9855i −0.268390 + 1.34929i
317317 −5.70016 + 11.5588i −0.320153 + 0.649205i −0.996147 0.0877016i 0.972048π-0.972048\pi
0.675994 + 0.736907i 0.263714π0.263714\pi
318318 0.0333334 0.0981971i 0.00186925 0.00550662i
319319 0.449822 + 1.67876i 0.0251852 + 0.0939924i
320320 −0.227561 + 3.47191i −0.0127210 + 0.194086i
321321 −4.05599 + 9.79203i −0.226383 + 0.546538i
322322 −5.96352 0.245033i −0.332334 0.0136551i
323323 −9.98833 8.58779i −0.555766 0.477838i
324324 0.840911 + 1.45650i 0.0467173 + 0.0809167i
325325 −7.21455 + 5.53592i −0.400191 + 0.307078i
326326 −2.44220 + 1.20436i −0.135261 + 0.0667033i
327327 2.81319 + 0.753792i 0.155570 + 0.0416848i
328328 −2.25019 11.3125i −0.124246 0.624628i
329329 0.804267 + 32.9764i 0.0443407 + 1.81805i
330330 −1.37521 0.273547i −0.0757030 0.0150583i
331331 11.5706 + 8.87842i 0.635976 + 0.488002i 0.875710 0.482837i 0.160394π-0.160394\pi
−0.239734 + 0.970839i 0.577060π0.577060\pi
332332 3.48621 26.4804i 0.191331 1.45330i
333333 −6.97750 6.11911i −0.382365 0.335325i
334334 −1.23199 0.607551i −0.0674116 0.0332437i
335335 14.7974 2.94338i 0.808466 0.160814i
336336 −5.53597 1.72987i −0.302012 0.0943721i
337337 −7.62186 + 11.4069i −0.415189 + 0.621374i −0.978837 0.204641i 0.934397π-0.934397\pi
0.563648 + 0.826015i 0.309397π0.309397\pi
338338 1.14250 + 8.67816i 0.0621439 + 0.472029i
339339 6.55071 11.3462i 0.355786 0.616239i
340340 2.51769 + 17.7755i 0.136541 + 0.964014i
341341 8.55783 4.94087i 0.463433 0.267563i
342342 1.66493 + 0.689637i 0.0900292 + 0.0372913i
343343 12.1036 14.0179i 0.653535 0.756897i
344344 1.41410 + 1.41410i 0.0762429 + 0.0762429i
345345 6.82700 + 7.78470i 0.367553 + 0.419114i
346346 −8.77646 + 0.575239i −0.471825 + 0.0309251i
347347 −6.94736 + 7.92194i −0.372954 + 0.425272i −0.907621 0.419790i 0.862104π-0.862104\pi
0.534667 + 0.845063i 0.320437π0.320437\pi
348348 −1.85328 + 2.41524i −0.0993462 + 0.129470i
349349 17.9575 7.43826i 0.961245 0.398161i 0.153799 0.988102i 0.450849π-0.450849\pi
0.807446 + 0.589941i 0.200849π0.200849\pi
350350 −0.717415 2.43802i −0.0383474 0.130318i
351351 −2.96685 4.44020i −0.158359 0.237000i
352352 3.89098 3.41229i 0.207390 0.181876i
353353 −10.8165 + 2.89827i −0.575704 + 0.154259i −0.534911 0.844908i 0.679655π-0.679655\pi
−0.0407925 + 0.999168i 0.512988π0.512988\pi
354354 2.91404 + 5.90909i 0.154880 + 0.314065i
355355 −11.2830 + 1.48543i −0.598839 + 0.0788386i
356356 −17.2936 −0.916558
357357 −10.8577 1.05337i −0.574652 0.0557502i
358358 2.80787 0.148400
359359 12.4910 1.64447i 0.659249 0.0867918i 0.206524 0.978442i 0.433785π-0.433785\pi
0.452726 + 0.891650i 0.350452π0.350452\pi
360360 −2.37812 4.82236i −0.125338 0.254160i
361361 8.49350 2.27583i 0.447026 0.119780i
362362 0.863962 0.757674i 0.0454088 0.0398225i
363363 5.59912 + 8.37967i 0.293878 + 0.439819i
364364 23.0956 + 5.58864i 1.21054 + 0.292924i
365365 23.3674 9.67909i 1.22310 0.506627i
366366 3.58503 4.67211i 0.187393 0.244215i
367367 −5.60280 + 6.38877i −0.292464 + 0.333491i −0.879348 0.476180i 0.842021π-0.842021\pi
0.586884 + 0.809671i 0.300354π0.300354\pi
368368 −8.74842 + 0.573402i −0.456043 + 0.0298906i
369369 −3.66185 4.17554i −0.190628 0.217370i
370370 9.58352 + 9.58352i 0.498224 + 0.498224i
371371 0.392994 + 0.286606i 0.0204032 + 0.0148798i
372372 15.9918 + 6.62403i 0.829137 + 0.343440i
373373 1.25769 0.726125i 0.0651205 0.0375973i −0.467086 0.884212i 0.654696π-0.654696\pi
0.532207 + 0.846614i 0.321363π0.321363\pi
374374 1.34194 1.78480i 0.0693899 0.0922899i
375375 4.26810 7.39257i 0.220404 0.381750i
376376 −3.37970 25.6714i −0.174295 1.32390i
377377 5.37043 8.03741i 0.276591 0.413948i
378378 1.45618 0.326753i 0.0748980 0.0168064i
379379 14.6723 2.91851i 0.753668 0.149914i 0.196718 0.980460i 0.436972π-0.436972\pi
0.556950 + 0.830546i 0.311972π0.311972\pi
380380 12.4764 + 6.15267i 0.640025 + 0.315625i
381381 8.91777 + 7.82067i 0.456871 + 0.400665i
382382 0.0495181 0.376127i 0.00253357 0.0192444i
383383 11.0945 + 8.51313i 0.566904 + 0.435000i 0.852033 0.523489i 0.175370π-0.175370\pi
−0.285129 + 0.958489i 0.592036π0.592036\pi
384384 11.3167 + 2.25103i 0.577502 + 0.114872i
385385 3.14852 5.77411i 0.160464 0.294276i
386386 −0.198588 0.998371i −0.0101079 0.0508157i
387387 0.930122 + 0.249226i 0.0472808 + 0.0126688i
388388 −8.07452 + 3.98191i −0.409922 + 0.202151i
389389 4.74045 3.63747i 0.240350 0.184427i −0.481562 0.876412i 0.659930π-0.659930\pi
0.721912 + 0.691985i 0.243264π0.243264\pi
390390 3.89935 + 6.75387i 0.197451 + 0.341995i
391391 −15.8851 + 4.42375i −0.803346 + 0.223718i
392392 −8.27721 + 11.9512i −0.418062 + 0.603629i
393393 −3.85105 + 9.29726i −0.194260 + 0.468985i
394394 −0.227610 + 3.47266i −0.0114668 + 0.174950i
395395 −9.74364 36.3637i −0.490256 1.82966i
396396 0.519051 1.52908i 0.0260833 0.0768390i
397397 −3.81627 + 7.73863i −0.191533 + 0.388391i −0.971363 0.237601i 0.923639π-0.923639\pi
0.779830 + 0.625992i 0.215306π0.215306\pi
398398 2.75313 13.8409i 0.138002 0.693783i
399399 −5.41665 + 6.48908i −0.271172 + 0.324860i
400400 −1.42857 3.44887i −0.0714284 0.172443i
401401 −21.1509 + 7.17975i −1.05622 + 0.358540i −0.794918 0.606716i 0.792486π-0.792486\pi
−0.261306 + 0.965256i 0.584153π0.584153\pi
402402 −0.214987 3.28007i −0.0107226 0.163595i
403403 −52.0447 17.6668i −2.59253 0.880046i
404404 −3.15437 + 11.7723i −0.156936 + 0.585692i
405405 −2.15267 1.43837i −0.106967 0.0714731i
406406 1.55516 + 2.20891i 0.0771815 + 0.109626i
407407 8.91057i 0.441681i
408408 8.56251 0.0839357i 0.423907 0.00415544i
409409 21.2862 + 12.2896i 1.05253 + 0.607681i 0.923358 0.383941i 0.125433π-0.125433\pi
0.129177 + 0.991622i 0.458767π0.458767\pi
410410 4.93742 + 6.43457i 0.243842 + 0.317781i
411411 4.51031 + 0.295622i 0.222477 + 0.0145819i
412412 −12.9937 + 12.9937i −0.640153 + 0.640153i
413413 −30.5314 + 4.77952i −1.50235 + 0.235185i
414414 1.87571 1.25331i 0.0921863 0.0615969i
415415 13.2162 + 38.9336i 0.648756 + 1.91117i
416416 −28.5383 3.75713i −1.39920 0.184209i
417417 2.13123 + 0.280581i 0.104367 + 0.0137401i
418418 −0.556175 1.63844i −0.0272034 0.0801386i
419419 −17.0551 + 11.3958i −0.833196 + 0.556724i −0.897402 0.441213i 0.854548π-0.854548\pi
0.0642067 + 0.997937i 0.479548π0.479548\pi
420420 11.3816 1.78172i 0.555365 0.0869392i
421421 −10.3441 + 10.3441i −0.504141 + 0.504141i −0.912722 0.408581i 0.866024π-0.866024\pi
0.408581 + 0.912722i 0.366024π0.366024\pi
422422 −8.07057 0.528973i −0.392869 0.0257500i
423423 −7.58980 9.89122i −0.369029 0.480928i
424424 −0.330654 0.190903i −0.0160580 0.00927109i
425425 −3.95780 5.79939i −0.191982 0.281312i
426426 2.47947i 0.120131i
427427 15.9016 + 22.5862i 0.769531 + 1.09302i
428428 14.8212 + 9.90322i 0.716411 + 0.478690i
429429 −1.32704 + 4.95258i −0.0640700 + 0.239113i
430430 −1.33162 0.452024i −0.0642163 0.0217985i
431431 −1.01662 15.5107i −0.0489690 0.747123i −0.949781 0.312914i 0.898695π-0.898695\pi
0.900812 0.434208i 0.142972π-0.142972\pi
432432 2.07584 0.704651i 0.0998737 0.0339025i
433433 −6.10014 14.7270i −0.293154 0.707736i −1.00000 0.000368770i 0.999883π-0.999883\pi
0.706846 0.707367i 0.250117π-0.250117\pi
434434 9.84285 11.7916i 0.472472 0.566015i
435435 0.914282 4.59640i 0.0438365 0.220381i
436436 2.16641 4.39305i 0.103752 0.210389i
437437 −4.10706 + 12.0990i −0.196468 + 0.578775i
438438 −1.42625 5.32282i −0.0681487 0.254334i
439439 0.883317 13.4768i 0.0421584 0.643213i −0.923533 0.383520i 0.874712π-0.874712\pi
0.965691 0.259693i 0.0836215π-0.0836215\pi
440440 −1.97560 + 4.76952i −0.0941830 + 0.227378i
441441 −0.574271 + 6.97640i −0.0273462 + 0.332210i
442442 −12.3847 + 0.933738i −0.589079 + 0.0444134i
443443 3.22627 + 5.58807i 0.153285 + 0.265497i 0.932433 0.361342i 0.117681π-0.117681\pi
−0.779148 + 0.626840i 0.784348π0.784348\pi
444444 −12.3829 + 9.50172i −0.587665 + 0.450932i
445445 23.8763 11.7745i 1.13184 0.558164i
446446 −0.704263 0.188707i −0.0333478 0.00893552i
447447 −2.01440 10.1271i −0.0952778 0.478994i
448448 −1.70221 + 3.12170i −0.0804219 + 0.147487i
449449 −25.2874 5.02997i −1.19339 0.237379i −0.441860 0.897084i 0.645681π-0.645681\pi
−0.751525 + 0.659705i 0.770681π0.770681\pi
450450 0.762057 + 0.584747i 0.0359237 + 0.0275652i
451451 −0.696010 + 5.28672i −0.0327738 + 0.248942i
452452 −16.5662 14.5282i −0.779210 0.683349i
453453 −7.23795 3.56936i −0.340069 0.167703i
454454 0.00884610 0.00175960i 0.000415168 8.25821e-5i
455455 −35.6919 + 8.00890i −1.67326 + 0.375463i
456456 3.68623 5.51684i 0.172624 0.258350i
457457 2.28445 + 17.3521i 0.106862 + 0.811696i 0.958003 + 0.286759i 0.0925779π0.0925779\pi
−0.851141 + 0.524937i 0.824089π0.824089\pi
458458 −1.38609 + 2.40077i −0.0647676 + 0.112181i
459459 3.55033 2.09645i 0.165715 0.0978541i
460460 15.0809 8.70697i 0.703151 0.405965i
461461 29.5926 + 12.2577i 1.37827 + 0.570896i 0.944017 0.329897i 0.107014π-0.107014\pi
0.434248 + 0.900793i 0.357014π0.357014\pi
462462 −1.15772 0.844315i −0.0538621 0.0392811i
463463 −10.4152 10.4152i −0.484035 0.484035i 0.422383 0.906418i 0.361194π-0.361194\pi
−0.906418 + 0.422383i 0.861194π0.861194\pi
464464 2.61638 + 2.98341i 0.121463 + 0.138502i
465465 −26.5890 + 1.74274i −1.23304 + 0.0808175i
466466 5.78358 6.59491i 0.267919 0.305503i
467467 11.2185 14.6202i 0.519128 0.676541i −0.458059 0.888922i 0.651455π-0.651455\pi
0.977187 + 0.212381i 0.0681218π0.0681218\pi
468468 −8.29759 + 3.43697i −0.383556 + 0.158874i
469469 14.9855 + 3.62618i 0.691967 + 0.167441i
470470 10.1155 + 15.1389i 0.466594 + 0.698307i
471471 1.37553 1.20631i 0.0633810 0.0555837i
472472 23.4313 6.27840i 1.07851 0.288987i
473473 −0.408915 0.829198i −0.0188019 0.0381265i
474474 −8.13199 + 1.07060i −0.373515 + 0.0491741i
475475 −5.44043 −0.249624
476476 −5.30004 + 17.5643i −0.242927 + 0.805058i
477477 −0.183843 −0.00841758
478478 −10.0184 + 1.31895i −0.458231 + 0.0603272i
479479 5.35277 + 10.8543i 0.244574 + 0.495947i 0.984198 0.177074i 0.0566630π-0.0566630\pi
−0.739623 + 0.673021i 0.764996π0.764996\pi
480480 −13.4796 + 3.61185i −0.615257 + 0.164858i
481481 37.2612 32.6772i 1.69896 1.48995i
482482 −5.85001 8.75516i −0.266461 0.398786i
483483 2.98700 + 10.1508i 0.135913 + 0.461879i
484484 15.6594 6.48635i 0.711793 0.294834i
485485 8.43692 10.9952i 0.383101 0.499267i
486486 −0.371918 + 0.424092i −0.0168706 + 0.0192372i
487487 −2.55068 + 0.167180i −0.115582 + 0.00757567i −0.123085 0.992396i 0.539279π-0.539279\pi
0.00750215 + 0.999972i 0.497612π0.497612\pi
488488 −14.2963 16.3018i −0.647161 0.737946i
489489 3.41351 + 3.41351i 0.154364 + 0.154364i
490490 1.50320 10.1115i 0.0679075 0.456792i
491491 −13.3348 5.52347i −0.601793 0.249271i 0.0609223 0.998143i 0.480596π-0.480596\pi
−0.662715 + 0.748872i 0.730596π0.730596\pi
492492 −8.08906 + 4.67022i −0.364683 + 0.210550i
493493 5.96538 + 4.48518i 0.268667 + 0.202002i
494494 −4.81180 + 8.33428i −0.216493 + 0.374977i
495495 0.324459 + 2.46451i 0.0145833 + 0.110771i
496496 12.5348 18.7596i 0.562828 0.842331i
497497 −11.1005 3.46867i −0.497926 0.155591i
498498 8.78585 1.74761i 0.393703 0.0783125i
499499 9.38784 + 4.62957i 0.420257 + 0.207248i 0.640107 0.768286i 0.278890π-0.278890\pi
−0.219850 + 0.975534i 0.570557π0.570557\pi
500500 −10.7937 9.46582i −0.482709 0.423324i
501501 −0.317863 + 2.41441i −0.0142011 + 0.107868i
502502 1.55036 + 1.18964i 0.0691961 + 0.0530961i
503503 −17.5791 3.49670i −0.783813 0.155910i −0.213068 0.977037i 0.568346π-0.568346\pi
−0.570745 + 0.821127i 0.693346π0.693346\pi
504504 −0.133972 5.49310i −0.00596759 0.244682i
505505 −3.66018 18.4010i −0.162876 0.818833i
506506 −2.09216 0.560593i −0.0930079 0.0249214i
507507 13.9173 6.86326i 0.618089 0.304808i
508508 15.8262 12.1439i 0.702176 0.538798i
509509 −17.2110 29.8103i −0.762864 1.32132i −0.941368 0.337381i 0.890459π-0.890459\pi
0.178504 0.983939i 0.442874π-0.442874\pi
510510 −5.37397 + 2.71596i −0.237963 + 0.120265i
511511 25.8254 + 1.06113i 1.14245 + 0.0469415i
512512 8.00637 19.3291i 0.353835 0.854233i
513513 0.208951 3.18798i 0.00922543 0.140753i
514514 −3.25699 12.1553i −0.143660 0.536145i
515515 9.09280 26.7865i 0.400677 1.18036i
516516 0.716279 1.45247i 0.0315324 0.0639415i
517517 −2.33534 + 11.7405i −0.102708 + 0.516348i
518518 4.77048 + 13.0028i 0.209603 + 0.571310i
519519 5.96699 + 14.4056i 0.261922 + 0.632335i
520520 27.1896 9.22962i 1.19234 0.404746i
521521 2.62269 + 40.0145i 0.114902 + 1.75307i 0.534329 + 0.845277i 0.320564π0.320564\pi
−0.419427 + 0.907789i 0.637769π0.637769\pi
522522 −0.966865 0.328206i −0.0423185 0.0143652i
523523 11.5346 43.0478i 0.504374 1.88235i 0.0349270 0.999390i 0.488880π-0.488880\pi
0.469447 0.882960i 0.344453π-0.344453\pi
524524 14.0723 + 9.40283i 0.614753 + 0.410765i
525525 −3.68398 + 2.59367i −0.160782 + 0.113197i
526526 1.48677i 0.0648263i
527527 15.8542 39.3624i 0.690619 1.71465i
528528 −1.82279 1.05239i −0.0793267 0.0457993i
529529 −4.26466 5.55781i −0.185420 0.241644i
530530 0.267905 + 0.0175594i 0.0116371 + 0.000762733i
531531 8.25925 8.25925i 0.358421 0.358421i
532532 8.92654 + 11.0639i 0.387014 + 0.479682i
533533 24.6598 16.4772i 1.06814 0.713705i
534534 −1.86440 5.49234i −0.0806803 0.237677i
535535 −27.2055 3.58167i −1.17620 0.154849i
536536 −11.9990 1.57970i −0.518278 0.0682326i
537537 −1.60008 4.71368i −0.0690485 0.203410i
538538 2.73374 1.82663i 0.117860 0.0787515i
539539 5.39957 4.00193i 0.232576 0.172375i
540540 −3.07890 + 3.07890i −0.132495 + 0.132495i
541541 −1.19994 0.0786481i −0.0515894 0.00338135i 0.0395866 0.999216i 0.487396π-0.487396\pi
−0.0911760 + 0.995835i 0.529063π0.529063\pi
542542 −0.257649 0.335775i −0.0110670 0.0144228i
543543 −1.76427 1.01860i −0.0757121 0.0437124i
544544 4.12186 21.8387i 0.176723 0.936325i
545545 7.54026i 0.322989i
546546 0.714986 + 7.93753i 0.0305986 + 0.339695i
547547 −7.65371 5.11404i −0.327249 0.218661i 0.381082 0.924541i 0.375552π-0.375552\pi
−0.708331 + 0.705880i 0.750552π0.750552\pi
548548 1.96750 7.34280i 0.0840473 0.313669i
549549 −9.88621 3.35591i −0.421933 0.143227i
550550 −0.0603185 0.920282i −0.00257199 0.0392410i
551551 5.47618 1.85891i 0.233293 0.0791924i
552552 −3.17850 7.67359i −0.135286 0.326610i
553553 6.58326 37.9044i 0.279949 1.61186i
554554 −0.960197 + 4.82724i −0.0407949 + 0.205090i
555555 10.6270 21.5495i 0.451092 0.914724i
556556 1.16209 3.42341i 0.0492837 0.145185i
557557 −10.9699 40.9403i −0.464811 1.73470i −0.657516 0.753441i 0.728393π-0.728393\pi
0.192705 0.981257i 0.438274π-0.438274\pi
558558 −0.379695 + 5.79303i −0.0160738 + 0.245239i
559559 −1.96785 + 4.75081i −0.0832313 + 0.200938i
560560 0.616467 15.0034i 0.0260505 0.634008i
561561 −3.76093 1.23568i −0.158787 0.0521706i
562562 7.33676 + 12.7076i 0.309482 + 0.536039i
563563 11.3329 8.69605i 0.477625 0.366495i −0.341714 0.939804i 0.611007π-0.611007\pi
0.819339 + 0.573309i 0.194341π0.194341\pi
564564 −18.8059 + 9.27405i −0.791872 + 0.390508i
565565 32.7637 + 8.77901i 1.37838 + 0.369336i
566566 1.39186 + 6.99737i 0.0585044 + 0.294121i
567567 −1.37835 2.25835i −0.0578852 0.0948419i
568568 8.95356 + 1.78097i 0.375683 + 0.0747280i
569569 −8.14411 6.24920i −0.341419 0.261980i 0.423792 0.905759i 0.360699π-0.360699\pi
−0.765211 + 0.643780i 0.777365π0.777365\pi
570570 −0.608990 + 4.62573i −0.0255078 + 0.193751i
571571 −0.951907 0.834800i −0.0398361 0.0349353i 0.639196 0.769044i 0.279267π-0.279267\pi
−0.679032 + 0.734108i 0.737600π0.737600\pi
572572 7.73390 + 3.81394i 0.323370 + 0.159469i
573573 −0.659638 + 0.131210i −0.0275568 + 0.00548139i
574574 1.81471 + 8.08730i 0.0757445 + 0.337557i
575575 −3.78365 + 5.66263i −0.157789 + 0.236148i
576576 −0.175415 1.33241i −0.00730894 0.0555169i
577577 −1.52690 + 2.64466i −0.0635655 + 0.110099i −0.896057 0.443939i 0.853581π-0.853581\pi
0.832491 + 0.554038i 0.186914π0.186914\pi
578578 −0.187983 9.58738i −0.00781904 0.398782i
579579 −1.56284 + 0.902305i −0.0649493 + 0.0374985i
580580 −7.28182 3.01623i −0.302361 0.125242i
581581 −4.46699 + 41.7788i −0.185322 + 1.73328i
582582 −2.13513 2.13513i −0.0885042 0.0885042i
583583 0.116383 + 0.132710i 0.00482010 + 0.00549627i
584584 −20.2456 + 1.32697i −0.837768 + 0.0549102i
585585 9.11592 10.3947i 0.376897 0.429769i
586586 −7.50964 + 9.78675i −0.310220 + 0.404287i
587587 −16.2163 + 6.71703i −0.669320 + 0.277242i −0.691355 0.722516i 0.742986π-0.742986\pi
0.0220343 + 0.999757i 0.492986π0.492986\pi
588588 11.3192 + 3.23627i 0.466796 + 0.133462i
589589 −18.2679 27.3398i −0.752714 1.12652i
590590 −12.8247 + 11.2469i −0.527983 + 0.463029i
591591 5.95940 1.59682i 0.245137 0.0656843i
592592 8.99820 + 18.2465i 0.369824 + 0.749928i
593593 16.3231 2.14898i 0.670311 0.0882481i 0.212314 0.977202i 0.431900π-0.431900\pi
0.457998 + 0.888953i 0.348567π0.348567\pi
594594 0.541583 0.0222214
595595 −4.64132 27.8586i −0.190276 1.14209i
596596 −17.3656 −0.711323
597597 −24.8042 + 3.26554i −1.01517 + 0.133650i
598598 5.32822 + 10.8046i 0.217887 + 0.441832i
599599 42.9228 11.5011i 1.75378 0.469923i 0.768351 0.640029i 0.221077π-0.221077\pi
0.985426 + 0.170105i 0.0544108π0.0544108\pi
600600 2.65894 2.33183i 0.108551 0.0951966i
601601 3.24051 + 4.84976i 0.132183 + 0.197826i 0.891657 0.452712i 0.149543π-0.149543\pi
−0.759474 + 0.650538i 0.774543π0.774543\pi
602602 −1.04064 0.991088i −0.0424133 0.0403937i
603603 −5.38387 + 2.23007i −0.219248 + 0.0908156i
604604 −8.26252 + 10.7679i −0.336197 + 0.438140i
605605 −17.2038 + 19.6172i −0.699435 + 0.797553i
606606 −4.07887 + 0.267343i −0.165693 + 0.0108601i
607607 29.4639 + 33.5971i 1.19590 + 1.36366i 0.914759 + 0.403999i 0.132380π0.132380\pi
0.281143 + 0.959666i 0.409287π0.409287\pi
608608 −12.1768 12.1768i −0.493835 0.493835i
609609 2.82197 3.86948i 0.114352 0.156799i
610610 14.0862 + 5.83468i 0.570332 + 0.236239i
611611 57.6594 33.2897i 2.33265 1.34676i
612612 −2.29323 6.54416i −0.0926982 0.264532i
613613 −15.8887 + 27.5200i −0.641738 + 1.11152i 0.343306 + 0.939224i 0.388453π0.388453\pi
−0.985045 + 0.172300i 0.944880π0.944880\pi
614614 −1.72830 13.1277i −0.0697485 0.529792i
615615 7.98835 11.9554i 0.322121 0.482089i
616616 −3.88046 + 3.57416i −0.156348 + 0.144007i
617617 −28.4985 + 5.66871i −1.14731 + 0.228214i −0.731894 0.681419i 0.761363π-0.761363\pi
−0.415414 + 0.909632i 0.636363π0.636363\pi
618618 −5.52755 2.72589i −0.222351 0.109651i
619619 12.6375 + 11.0828i 0.507944 + 0.445455i 0.874560 0.484918i 0.161150π-0.161150\pi
−0.366616 + 0.930372i 0.619484π0.619484\pi
620620 −5.84940 + 44.4306i −0.234918 + 1.78438i
621621 −3.17287 2.43463i −0.127323 0.0976983i
622622 19.0093 + 3.78119i 0.762205 + 0.151612i
623623 27.1972 0.663318i 1.08963 0.0265753i
624624 2.28385 + 11.4817i 0.0914271 + 0.459635i
625625 29.5714 + 7.92365i 1.18286 + 0.316946i
626626 −6.21907 + 3.06691i −0.248564 + 0.122578i
627627 −2.43357 + 1.86735i −0.0971875 + 0.0745746i
628628 −1.53849 2.66474i −0.0613924 0.106335i
629629 23.5906 + 30.1277i 0.940618 + 1.20127i
630630 1.79290 + 3.42264i 0.0714308 + 0.136361i
631631 −10.8204 + 26.1228i −0.430755 + 1.03993i 0.548290 + 0.836288i 0.315279π0.315279\pi
−0.979045 + 0.203646i 0.934721π0.934721\pi
632632 −1.97510 + 30.1342i −0.0785654 + 1.19868i
633633 3.71105 + 13.8498i 0.147501 + 0.550482i
634634 −2.33676 + 6.88388i −0.0928047 + 0.273394i
635635 −13.5821 + 27.5418i −0.538990 + 1.09296i
636636 −0.0603201 + 0.303250i −0.00239185 + 0.0120246i
637637 −36.5363 7.90327i −1.44762 0.313139i
638638 0.375162 + 0.905720i 0.0148528 + 0.0358578i
639639 4.16239 1.41294i 0.164662 0.0558951i
640640 1.95378 + 29.8089i 0.0772298 + 1.17830i
641641 −31.5986 10.7263i −1.24807 0.423662i −0.382268 0.924052i 0.624857π-0.624857\pi
−0.865800 + 0.500390i 0.833190π0.833190\pi
642642 −1.54735 + 5.77478i −0.0610690 + 0.227912i
643643 −39.8908 26.6542i −1.57314 1.05114i −0.966668 0.256032i 0.917585π-0.917585\pi
−0.606470 0.795106i 0.707415π-0.707415\pi
644644 17.7239 1.59651i 0.698421 0.0629114i
645645 2.49303i 0.0981629i
646646 −6.21823 4.06729i −0.244653 0.160025i
647647 −22.2303 12.8347i −0.873963 0.504583i −0.00529975 0.999986i 0.501687π-0.501687\pi
−0.868663 + 0.495403i 0.835020π0.835020\pi
648648 1.26428 + 1.64765i 0.0496658 + 0.0647257i
649649 −11.1907 0.733474i −0.439272 0.0287914i
650650 −3.62712 + 3.62712i −0.142267 + 0.142267i
651651 −25.4040 9.80407i −0.995663 0.384252i
652652 6.75060 4.51061i 0.264374 0.176649i
653653 5.79848 + 17.0818i 0.226912 + 0.668462i 0.999439 + 0.0334801i 0.0106590π0.0106590\pi
−0.772527 + 0.634982i 0.781008π0.781008\pi
654654 1.62877 + 0.214431i 0.0636898 + 0.00838492i
655655 −25.8309 3.40070i −1.00930 0.132876i
656656 3.91346 + 11.5287i 0.152795 + 0.450120i
657657 −8.12288 + 5.42754i −0.316904 + 0.211748i
658658 2.87771 + 18.3827i 0.112185 + 0.716633i
659659 −12.5511 + 12.5511i −0.488923 + 0.488923i −0.907966 0.419043i 0.862366π-0.862366\pi
0.419043 + 0.907966i 0.362366π0.362366\pi
660660 4.17168 + 0.273427i 0.162383 + 0.0106431i
661661 −11.7357 15.2943i −0.456467 0.594879i 0.507252 0.861798i 0.330661π-0.330661\pi
−0.963719 + 0.266918i 0.913995π0.913995\pi
662662 7.12449 + 4.11332i 0.276901 + 0.159869i
663663 8.62498 + 20.2586i 0.334966 + 0.786777i
664664 32.9817i 1.27994i
665665 −19.8573 9.19762i −0.770034 0.356668i
666666 −4.35267 2.90836i −0.168662 0.112697i
667667 1.87368 6.99267i 0.0725491 0.270757i
668668 3.87829 + 1.31650i 0.150056 + 0.0509370i
669669 0.0845386 + 1.28981i 0.00326845 + 0.0498669i
670670 8.05866 2.73555i 0.311333 0.105683i
671671 3.83603 + 9.26100i 0.148088 + 0.357517i
672672 −14.0507 2.44033i −0.542018 0.0941380i
673673 3.82921 19.2507i 0.147605 0.742061i −0.834094 0.551622i 0.814009π-0.814009\pi
0.981699 0.190439i 0.0609911π-0.0609911\pi
674674 −3.42265 + 6.94044i −0.131835 + 0.267336i
675675 0.547376 1.61252i 0.0210685 0.0620658i
676676 −6.75462 25.2086i −0.259793 0.969561i
677677 0.793971 12.1137i 0.0305148 0.465566i −0.955070 0.296381i 0.904220π-0.904220\pi
0.985584 0.169184i 0.0541133π-0.0541133\pi
678678 2.82808 6.82760i 0.108612 0.262212i
679679 12.5459 6.57198i 0.481467 0.252209i
680680 5.94748 + 21.3567i 0.228075 + 0.818991i
681681 −0.00799491 0.0138476i −0.000306366 0.000530641i
682682 4.42216 3.39324i 0.169333 0.129934i
683683 5.41443 2.67010i 0.207178 0.102169i −0.335740 0.941955i 0.608986π-0.608986\pi
0.542917 + 0.839786i 0.317320π0.317320\pi
684684 −5.19004 1.39067i −0.198446 0.0531735i
685685 2.28299 + 11.4774i 0.0872286 + 0.438528i
686686 5.73683 8.73061i 0.219033 0.333336i
687687 4.82014 + 0.958786i 0.183900 + 0.0365800i
688688 −1.67470 1.28505i −0.0638475 0.0489919i
689689 0.128145 0.973355i 0.00488192 0.0370819i
690690 4.39113 + 3.85092i 0.167168 + 0.146602i
691691 −24.9597 12.3088i −0.949511 0.468247i −0.0995149 0.995036i 0.531729π-0.531729\pi
−0.849996 + 0.526789i 0.823396π0.823396\pi
692692 25.7199 5.11601i 0.977725 0.194482i
693693 −0.757651 + 2.42465i −0.0287808 + 0.0921049i
694694 −3.30202 + 4.94182i −0.125343 + 0.187589i
695695 0.726424 + 5.51773i 0.0275548 + 0.209300i
696696 −1.87967 + 3.25568i −0.0712486 + 0.123406i
697697 11.6432 + 19.7177i 0.441018 + 0.746861i
698698 9.49504 5.48196i 0.359392 0.207495i
699699 −14.3669 5.95098i −0.543408 0.225087i
700700 3.06954 + 6.92775i 0.116018 + 0.261844i
701701 1.41724 + 1.41724i 0.0535283 + 0.0535283i 0.733364 0.679836i 0.237949π-0.237949\pi
−0.679836 + 0.733364i 0.737949π0.737949\pi
702702 −1.98611 2.26473i −0.0749610 0.0854767i
703703 29.5863 1.93919i 1.11587 0.0731379i
704704 −0.850770 + 0.970118i −0.0320646 + 0.0365627i
705705 19.6500 25.6083i 0.740060 0.964465i
706706 −5.83569 + 2.41722i −0.219629 + 0.0909734i
707707 4.50927 18.6350i 0.169588 0.700840i
708708 −10.9138 16.3336i −0.410164 0.613855i
709709 −7.69108 + 6.74490i −0.288845 + 0.253310i −0.791489 0.611183i 0.790694π-0.790694\pi
0.502644 + 0.864493i 0.332360π0.332360\pi
710710 −6.20060 + 1.66145i −0.232704 + 0.0623530i
711711 6.43131 + 13.0414i 0.241193 + 0.489091i
712712 −21.1724 + 2.78740i −0.793470 + 0.104462i
713713 −41.1612 −1.54150
714714 −6.14970 + 0.210320i −0.230147 + 0.00787104i
715715 −13.2745 −0.496438
716716 −8.30024 + 1.09275i −0.310195 + 0.0408379i
717717 7.92321 + 16.0667i 0.295898 + 0.600021i
718718 6.86446 1.83933i 0.256179 0.0686431i
719719 −1.41456 + 1.24054i −0.0527542 + 0.0462642i −0.685317 0.728245i 0.740336π-0.740336\pi
0.632563 + 0.774509i 0.282003π0.282003\pi
720720 3.15315 + 4.71903i 0.117511 + 0.175868i
721721 19.9365 20.9333i 0.742474 0.779596i
722722 4.58240 1.89809i 0.170539 0.0706396i
723723 −11.3640 + 14.8098i −0.422631 + 0.550783i
724724 −2.25906 + 2.57597i −0.0839574 + 0.0957350i
725725 3.07588 0.201604i 0.114235 0.00748737i
726726 3.74825 + 4.27406i 0.139111 + 0.158625i
727727 27.5414 + 27.5414i 1.02145 + 1.02145i 0.999765 + 0.0216897i 0.00690460π0.00690460\pi
0.0216897 + 0.999765i 0.493095π0.493095\pi
728728 29.1766 + 3.11956i 1.08136 + 0.115619i
729729 0.923880 + 0.382683i 0.0342178 + 0.0141735i
730730 12.3555 7.13344i 0.457297 0.264021i
731731 −3.57787 1.72102i −0.132332 0.0636542i
732732 −8.77934 + 15.2063i −0.324494 + 0.562040i
733733 3.14145 + 23.8617i 0.116032 + 0.881351i 0.946142 + 0.323751i 0.104944π0.104944\pi
−0.830110 + 0.557599i 0.811723π0.811723\pi
734734 −2.66297 + 3.98541i −0.0982919 + 0.147104i
735735 −17.8312 + 3.23863i −0.657715 + 0.119459i
736736 −21.1428 + 4.20556i −0.779333 + 0.155019i
737737 5.01812 + 2.47466i 0.184845 + 0.0911554i
738738 −2.35530 2.06555i −0.0866999 0.0760338i
739739 4.74342 36.0299i 0.174490 1.32538i −0.650186 0.759775i 0.725309π-0.725309\pi
0.824676 0.565605i 0.191357π-0.191357\pi
740740 −32.0592 24.5999i −1.17852 0.904310i
741741 16.7331 + 3.32842i 0.614707 + 0.122273i
742742 0.240882 + 0.131349i 0.00884305 + 0.00482196i
743743 −5.31459 26.7183i −0.194973 0.980198i −0.947041 0.321112i 0.895943π-0.895943\pi
0.752068 0.659086i 0.229057π-0.229057\pi
744744 20.6464 + 5.53218i 0.756932 + 0.202819i
745745 23.9757 11.8235i 0.878402 0.433180i
746746 0.649894 0.498681i 0.0237943 0.0182580i
747747 −7.94046 13.7533i −0.290526 0.503206i
748748 −3.27226 + 5.79824i −0.119646 + 0.212005i
749749 −23.6888 15.0061i −0.865572 0.548310i
750750 1.84263 4.44851i 0.0672834 0.162437i
751751 −2.90976 + 44.3944i −0.106179 + 1.61997i 0.529701 + 0.848185i 0.322304π0.322304\pi
−0.635879 + 0.771788i 0.719362π0.719362\pi
752752 7.07383 + 26.3999i 0.257956 + 0.962705i
753753 1.11361 3.28058i 0.0405821 0.119551i
754754 2.41163 4.89030i 0.0878263 0.178094i
755755 4.07616 20.4923i 0.148347 0.745790i
756756 −4.17741 + 1.53261i −0.151931 + 0.0557406i
757757 13.7761 + 33.2584i 0.500700 + 1.20880i 0.949103 + 0.314965i 0.101993π0.101993\pi
−0.448403 + 0.893831i 0.648007π0.648007\pi
758758 7.99058 2.71243i 0.290231 0.0985201i
759759 0.251140 + 3.83165i 0.00911579 + 0.139080i
760760 16.2665 + 5.52172i 0.590046 + 0.200294i
761761 −3.56257 + 13.2957i −0.129143 + 0.481968i −0.999953 0.00965066i 0.996928π-0.996928\pi
0.870810 + 0.491619i 0.163595π0.163595\pi
762762 5.56303 + 3.71710i 0.201527 + 0.134656i
763763 −3.23857 + 6.99195i −0.117244 + 0.253126i
764764 1.13113i 0.0409228i
765765 7.62178 + 7.47380i 0.275566 + 0.270216i
766766 6.83136 + 3.94409i 0.246827 + 0.142506i
767767 37.9716 + 49.4856i 1.37108 + 1.78682i
768768 3.81250 + 0.249884i 0.137572 + 0.00901692i
769769 −10.9451 + 10.9451i −0.394691 + 0.394691i −0.876356 0.481665i 0.840032π-0.840032\pi
0.481665 + 0.876356i 0.340032π0.340032\pi
770770 1.33567 3.46096i 0.0481344 0.124724i
771771 −18.5495 + 12.3944i −0.668044 + 0.446372i
772772 0.975580 + 2.87397i 0.0351119 + 0.103436i
773773 −31.2636 4.11593i −1.12447 0.148040i −0.454727 0.890631i 0.650263π-0.650263\pi
−0.669745 + 0.742591i 0.733597π0.733597\pi
774774 0.538517 + 0.0708971i 0.0193566 + 0.00254834i
775775 −5.63362 16.5961i −0.202366 0.596150i
776776 −9.24378 + 6.17650i −0.331832 + 0.221723i
777777 19.1098 15.4181i 0.685561 0.553121i
778778 2.38327 2.38327i 0.0854442 0.0854442i
779779 17.7053 + 1.16047i 0.634357 + 0.0415780i
780780 −14.1552 18.4474i −0.506836 0.660522i
781781 −3.65499 2.11021i −0.130786 0.0755092i
782782 −8.55800 + 3.64352i −0.306033 + 0.130292i
783783 1.81014i 0.0646893i
784784 7.01564 13.6476i 0.250559 0.487414i
785785 3.93842 + 2.63157i 0.140568 + 0.0939246i
786786 −1.46916 + 5.48299i −0.0524033 + 0.195572i
787787 −41.8475 14.2053i −1.49170 0.506365i −0.547806 0.836606i 0.684537π-0.684537\pi
−0.943897 + 0.330241i 0.892870π0.892870\pi
788788 −0.678637 10.3540i −0.0241755 0.368846i
789789 2.49590 0.847245i 0.0888565 0.0301627i
790790 −8.12641 19.6189i −0.289125 0.698009i
791791 26.6106 + 22.2127i 0.946164 + 0.789794i
792792 0.389013 1.95570i 0.0138230 0.0694928i
793793 24.6589 50.0033i 0.875664 1.77567i
794794 −1.56447 + 4.60878i −0.0555209 + 0.163559i
795795 −0.123189 0.459749i −0.00436908 0.0163056i
796796 −2.75192 + 41.9862i −0.0975392 + 1.48816i
797797 15.5493 37.5393i 0.550784 1.32971i −0.366107 0.930573i 0.619310π-0.619310\pi
0.916891 0.399138i 0.130690π-0.130690\pi
798798 −2.55147 + 4.02780i −0.0903212 + 0.142583i
799799 23.1868 + 45.8789i 0.820290 + 1.62308i
800800 −4.58943 7.94913i −0.162261 0.281044i
801801 −8.15777 + 6.25968i −0.288241 + 0.221175i
802802 −11.2999 + 5.57251i −0.399014 + 0.196772i
803803 9.06021 + 2.42768i 0.319728 + 0.0856708i
804804 1.91203 + 9.61244i 0.0674322 + 0.339005i
805805 −23.3834 + 14.2717i −0.824158 + 0.503011i
806806 −30.4066 6.04824i −1.07103 0.213040i
807807 −4.62427 3.54832i −0.162782 0.124907i
808808 −1.96441 + 14.9211i −0.0691076 + 0.524924i
809809 12.8591 + 11.2771i 0.452102 + 0.396483i 0.854889 0.518811i 0.173625π-0.173625\pi
−0.402787 + 0.915294i 0.631958π0.631958\pi
810810 −1.30977 0.645909i −0.0460208 0.0226949i
811811 −33.4977 + 6.66311i −1.17626 + 0.233973i −0.744255 0.667896i 0.767195π-0.767195\pi
−0.432009 + 0.901869i 0.642195π0.642195\pi
812812 −5.45682 5.92446i −0.191497 0.207908i
813813 −0.416856 + 0.623870i −0.0146198 + 0.0218801i
814814 0.656051 + 4.98320i 0.0229946 + 0.174661i
815815 −6.24909 + 10.8237i −0.218896 + 0.379139i
816816 −8.94924 + 1.26755i −0.313286 + 0.0443732i
817817 −2.66424 + 1.53820i −0.0932100 + 0.0538148i
818818 12.8091 + 5.30568i 0.447858 + 0.185509i
819819 12.9176 5.72352i 0.451378 0.199996i
820820 −17.0995 17.0995i −0.597140 0.597140i
821821 16.8874 + 19.2564i 0.589373 + 0.672052i 0.967256 0.253802i 0.0816811π-0.0816811\pi
−0.377883 + 0.925853i 0.623348π0.623348\pi
822822 2.54414 0.166752i 0.0887371 0.00581614i
823823 −24.5693 + 28.0159i −0.856432 + 0.976573i −0.999914 0.0130795i 0.995837π-0.995837\pi
0.143483 + 0.989653i 0.454170π0.454170\pi
824824 −13.8138 + 18.0024i −0.481225 + 0.627145i
825825 −1.51054 + 0.625687i −0.0525903 + 0.0217836i
826826 −16.7227 + 4.92084i −0.581857 + 0.171218i
827827 −11.0441 16.5287i −0.384042 0.574760i 0.588206 0.808711i 0.299834π-0.299834\pi
−0.972248 + 0.233951i 0.924834π0.924834\pi
828828 −5.05698 + 4.43485i −0.175742 + 0.154122i
829829 −28.0681 + 7.52082i −0.974845 + 0.261209i −0.710872 0.703321i 0.751700π-0.751700\pi
−0.263973 + 0.964530i 0.585033π0.585033\pi
830830 10.2576 + 20.8004i 0.356047 + 0.721993i
831831 8.65085 1.13891i 0.300095 0.0395082i
832832 7.17670 0.248807
833833 7.66156 27.8263i 0.265457 0.964123i
834834 1.21254 0.0419868
835835 −6.25089 + 0.822945i −0.216321 + 0.0284792i
836836 2.28173 + 4.62688i 0.0789152 + 0.160024i
837837 9.94137 2.66378i 0.343624 0.0920737i
838838 −8.69896 + 7.62879i −0.300501 + 0.263532i
839839 −1.71714 2.56988i −0.0592822 0.0887220i 0.800644 0.599140i 0.204491π-0.204491\pi
−0.859926 + 0.510418i 0.829491π0.829491\pi
840840 13.6472 4.01585i 0.470874 0.138560i
841841 23.7653 9.84391i 0.819493 0.339445i
842842 −5.02330 + 6.54650i −0.173114 + 0.225607i
843843 17.1519 19.5580i 0.590744 0.673614i
844844 24.0630 1.57717i 0.828283 0.0542886i
845845 26.4892 + 30.2051i 0.911256 + 1.03909i
846846 −4.97282 4.97282i −0.170969 0.170969i
847847 −24.3785 + 10.8016i −0.837654 + 0.371147i
848848 0.372337 + 0.154227i 0.0127861 + 0.00529618i
849849 10.9536 6.32407i 0.375927 0.217041i
850850 −2.64037 2.95189i −0.0905641 0.101249i
851851 18.5580 32.1433i 0.636159 1.10186i
852852 −0.964945 7.32948i −0.0330585 0.251104i
853853 32.0534 47.9713i 1.09749 1.64250i 0.418796 0.908080i 0.362452π-0.362452\pi
0.678690 0.734424i 0.262548π-0.262548\pi
854854 10.5558 + 11.4604i 0.361213 + 0.392168i
855855 8.11244 1.61366i 0.277440 0.0551862i
856856 19.7417 + 9.73555i 0.674759 + 0.332754i
857857 −23.1965 20.3428i −0.792376 0.694895i 0.164184 0.986430i 0.447501π-0.447501\pi
−0.956560 + 0.291534i 0.905834π0.905834\pi
858858 −0.377502 + 2.86741i −0.0128877 + 0.0978919i
859859 −11.4383 8.77692i −0.390270 0.299465i 0.394925 0.918713i 0.370771π-0.370771\pi
−0.785195 + 0.619249i 0.787437π0.787437\pi
860860 4.11227 + 0.817981i 0.140227 + 0.0278929i
861861 12.5423 7.65501i 0.427442 0.260882i
862862 −1.71053 8.59943i −0.0582610 0.292898i
863863 −35.6889 9.56282i −1.21486 0.325522i −0.406196 0.913786i 0.633145π-0.633145\pi
−0.808669 + 0.588264i 0.799812π0.799812\pi
864864 4.83430 2.38401i 0.164466 0.0811057i
865865 −32.0268 + 24.5750i −1.08894 + 0.835576i
866866 −4.49577 7.78691i −0.152773 0.264610i
867867 −15.9876 + 5.77899i −0.542967 + 0.196265i
868868 −24.5071 + 38.6874i −0.831827 + 1.31313i
869869 5.34274 12.8985i 0.181240 0.437552i
870870 0.172893 2.63784i 0.00586162 0.0894311i
871871 −8.05438 30.0593i −0.272912 1.01852i
872872 1.94425 5.72757i 0.0658406 0.193960i
873873 −2.36762 + 4.80105i −0.0801317 + 0.162491i
874874 −1.40606 + 7.06872i −0.0475605 + 0.239103i
875875 17.3381 + 14.4727i 0.586134 + 0.489265i
876876 6.28758 + 15.1796i 0.212438 + 0.512870i
877877 −25.2384 + 8.56730i −0.852242 + 0.289297i −0.713175 0.700986i 0.752744π-0.752744\pi
−0.139067 + 0.990283i 0.544410π0.544410\pi
878878 −0.498254 7.60189i −0.0168153 0.256551i
879879 20.7088 + 7.02969i 0.698491 + 0.237106i
880880 1.41037 5.26357i 0.0475436 0.177435i
881881 −28.5048 19.0463i −0.960350 0.641685i −0.0266129 0.999646i 0.508472π-0.508472\pi
−0.933737 + 0.357961i 0.883472π0.883472\pi
882882 0.192487 + 3.94381i 0.00648138 + 0.132795i
883883 30.3589i 1.02166i 0.859682 + 0.510829i 0.170662π0.170662\pi
−0.859682 + 0.510829i 0.829338π0.829338\pi
884884 36.2465 7.57998i 1.21910 0.254942i
885885 26.1889 + 15.1202i 0.880330 + 0.508259i
886886 2.21571 + 2.88757i 0.0744382 + 0.0970097i
887887 29.5141 + 1.93445i 0.990985 + 0.0649526i 0.552263 0.833670i 0.313764π-0.313764\pi
0.438722 + 0.898623i 0.355431π0.355431\pi
888888 −13.6288 + 13.6288i −0.457352 + 0.457352i
889889 −24.4238 + 19.7055i −0.819147 + 0.660900i
890890 12.4858 8.34275i 0.418525 0.279650i
891891 −0.308624 0.909178i −0.0103393 0.0304586i
892892 2.15529 + 0.283749i 0.0721644 + 0.00950062i
893893 39.4910 + 5.19909i 1.32152 + 0.173981i
894894 −1.87216 5.51521i −0.0626144 0.184456i
895895 10.7157 7.15998i 0.358185 0.239332i
896896 −10.9913 + 28.4804i −0.367194 + 0.951463i
897897 15.1017 15.1017i 0.504233 0.504233i
898898 −14.5122 0.951180i −0.484279 0.0317413i
899899 11.3413 + 14.7803i 0.378253 + 0.492949i
900900 −2.48026 1.43198i −0.0826753 0.0477326i
901901 0.744852 + 0.140585i 0.0248146 + 0.00468355i
902902 3.00782i 0.100150i
903903 −1.07076 + 2.31174i −0.0356328 + 0.0769299i
904904 −22.6236 15.1166i −0.752450 0.502771i
905905 1.36509 5.09459i 0.0453772 0.169350i
906906 −4.31060 1.46325i −0.143210 0.0486132i
907907 0.581382 + 8.87017i 0.0193045 + 0.294529i 0.996585 + 0.0825776i 0.0263152π0.0263152\pi
−0.977280 + 0.211952i 0.932018π0.932018\pi
908908 −0.0254649 + 0.00864416i −0.000845082 + 0.000286867i
909909 2.77317 + 6.69502i 0.0919801 + 0.222060i
910910 −19.3709 + 7.10680i −0.642138 + 0.235588i
911911 −2.15595 + 10.8387i −0.0714297 + 0.359101i −0.999925 0.0122427i 0.996103π-0.996103\pi
0.928495 + 0.371344i 0.121103π0.121103\pi
912912 −3.09761 + 6.28134i −0.102572 + 0.207996i
913913 −4.90124 + 14.4386i −0.162207 + 0.477847i
914914 2.55514 + 9.53589i 0.0845164 + 0.315419i
915915 1.76783 26.9719i 0.0584428 0.891664i
916916 3.16305 7.63628i 0.104510 0.252310i
917917 −22.4919 14.2479i −0.742748 0.470506i
918918 1.83116 1.43383i 0.0604372 0.0473235i
919919 5.39679 + 9.34751i 0.178024 + 0.308346i 0.941203 0.337840i 0.109696π-0.109696\pi
−0.763180 + 0.646186i 0.776363π0.776363\pi
920920 17.0601 13.0907i 0.562454 0.431586i
921921 −21.0532 + 10.3823i −0.693725 + 0.342108i
922922 17.4520 + 4.67626i 0.574752 + 0.154004i
923923 4.57949 + 23.0226i 0.150736 + 0.757799i
924924 3.75089 + 2.04530i 0.123395 + 0.0672853i
925925 15.5001 + 3.08317i 0.509641 + 0.101374i
926926 −6.59149 5.05783i −0.216610 0.166210i
927927 −1.42615 + 10.8327i −0.0468409 + 0.355792i
928928 7.33569 + 6.43323i 0.240806 + 0.211181i
929929 −30.5653 15.0731i −1.00282 0.494534i −0.134695 0.990887i 0.543005π-0.543005\pi
−0.868120 + 0.496354i 0.834672π0.834672\pi
930930 −14.7415 + 2.93227i −0.483393 + 0.0961528i
931931 −14.4629 17.0576i −0.474003 0.559040i
932932 −14.5301 + 21.7458i −0.475949 + 0.712308i
933933 −4.48494 34.0665i −0.146830 1.11529i
934934 5.19745 9.00225i 0.170066 0.294563i
935935 0.570043 10.2332i 0.0186424 0.334663i
936936 −9.60471 + 5.54528i −0.313940 + 0.181253i
937937 18.5699 + 7.69191i 0.606652 + 0.251284i 0.664796 0.747025i 0.268518π-0.268518\pi
−0.0581441 + 0.998308i 0.518518π0.518518\pi
938938 8.64758 + 0.924599i 0.282353 + 0.0301892i
939939 8.69251 + 8.69251i 0.283669 + 0.283669i
940940 −35.7938 40.8150i −1.16747 1.33124i
941941 60.6618 3.97599i 1.97752 0.129613i 0.979947 0.199259i 0.0638534π-0.0638534\pi
0.997572 + 0.0696453i 0.0221867π0.0221867\pi
942942 0.680444 0.775897i 0.0221700 0.0252801i
943943 13.5213 17.6214i 0.440316 0.573830i
944944 −23.6562 + 9.79874i −0.769945 + 0.318922i
945945 4.72403 4.96022i 0.153673 0.161356i
946946 −0.289735 0.433619i −0.00942009 0.0140982i
947947 −45.7130 + 40.0892i −1.48547 + 1.30273i −0.640445 + 0.768004i 0.721250π0.721250\pi
−0.845029 + 0.534721i 0.820417π0.820417\pi
948948 23.6221 6.32951i 0.767209 0.205573i
949949 −23.0742 46.7898i −0.749019 1.51886i
950950 −3.04254 + 0.400558i −0.0987130 + 0.0129958i
951951 12.8879 0.417918
952952 −3.65778 + 22.3581i −0.118549 + 0.724631i
953953 −47.5702 −1.54095 −0.770476 0.637470i 0.779981π-0.779981\pi
−0.770476 + 0.637470i 0.779981π0.779981\pi
954954 −0.102813 + 0.0135356i −0.00332870 + 0.000438232i
955955 −0.770139 1.56169i −0.0249211 0.0505350i
956956 29.1018 7.79779i 0.941218 0.252199i
957957 1.30668 1.14593i 0.0422390 0.0370426i
958958 3.79268 + 5.67614i 0.122536 + 0.183388i
959959 −2.81259 + 11.6233i −0.0908234 + 0.375336i
960960 3.21451 1.33149i 0.103748 0.0429738i
961961 45.6124 59.4432i 1.47137 1.91752i
962962 18.4323 21.0180i 0.594280 0.677647i
963963 10.5761 0.693196i 0.340811 0.0223379i
964964 20.7003 + 23.6042i 0.666712 + 0.760239i
965965 −3.30369 3.30369i −0.106350 0.106350i
966966 2.41784 + 5.45690i 0.0777926 + 0.175573i
967967 7.30054 + 3.02398i 0.234769 + 0.0972447i 0.496967 0.867770i 0.334447π-0.334447\pi
−0.262197 + 0.965014i 0.584447π0.584447\pi
968968 18.1263 10.4652i 0.582601 0.336365i
969969 −3.28443 + 12.7565i −0.105511 + 0.409799i
970970 3.90878 6.77021i 0.125503 0.217378i
971971 −5.68905 43.2127i −0.182570 1.38676i −0.799937 0.600084i 0.795134π-0.795134\pi
0.617366 0.786676i 0.288200π-0.288200\pi
972972 0.934371 1.39838i 0.0299700 0.0448532i
973973 −1.69629 + 5.42850i −0.0543805 + 0.174030i
974974 −1.41415 + 0.281292i −0.0453123 + 0.00901317i
975975 8.15593 + 4.02206i 0.261199 + 0.128809i
976976 17.2073 + 15.0904i 0.550791 + 0.483031i
977977 7.75319 58.8913i 0.248047 1.88410i −0.185013 0.982736i 0.559233π-0.559233\pi
0.433060 0.901365i 0.357434π-0.357434\pi
978978 2.16032 + 1.65767i 0.0690793 + 0.0530064i
979979 9.68299 + 1.92607i 0.309470 + 0.0615573i
980980 −0.508411 + 30.4754i −0.0162406 + 0.973500i
981981 −0.568187 2.85647i −0.0181408 0.0912000i
982982 −7.86413 2.10719i −0.250954 0.0672430i
983983 −8.22481 + 4.05603i −0.262331 + 0.129367i −0.568699 0.822546i 0.692553π-0.692553\pi
0.306368 + 0.951913i 0.400886π0.400886\pi
984984 −9.15063 + 7.02153i −0.291711 + 0.223838i
985985 7.98656 + 13.8331i 0.254473 + 0.440760i
986986 3.66634 + 2.06911i 0.116760 + 0.0658940i
987987 29.2199 15.3064i 0.930080 0.487209i
988988 10.9805 26.5093i 0.349337 0.843374i
989989 −0.251872 + 3.84283i −0.00800908 + 0.122195i
990990 0.362905 + 1.35438i 0.0115339 + 0.0430450i
991991 1.53268 4.51513i 0.0486872 0.143428i −0.919867 0.392230i 0.871704π-0.871704\pi
0.968554 + 0.248802i 0.0800370π0.0800370\pi
992992 24.5364 49.7549i 0.779031 1.57972i
993993 2.84527 14.3042i 0.0902920 0.453929i
994994 −6.46331 1.12255i −0.205004 0.0356052i
995995 −24.7872 59.8416i −0.785807 1.89711i
996996 −25.2914 + 8.58529i −0.801390 + 0.272035i
997997 −1.85524 28.3054i −0.0587559 0.896442i −0.920905 0.389787i 0.872549π-0.872549\pi
0.862149 0.506655i 0.169118π-0.169118\pi
998998 5.59097 + 1.89788i 0.176979 + 0.0600763i
999999 −2.40199 + 8.96434i −0.0759956 + 0.283619i
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 357.2.bl.a.10.15 384
7.5 odd 6 inner 357.2.bl.a.61.10 yes 384
17.12 odd 16 inner 357.2.bl.a.199.10 yes 384
119.12 even 48 inner 357.2.bl.a.250.15 yes 384
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
357.2.bl.a.10.15 384 1.1 even 1 trivial
357.2.bl.a.61.10 yes 384 7.5 odd 6 inner
357.2.bl.a.199.10 yes 384 17.12 odd 16 inner
357.2.bl.a.250.15 yes 384 119.12 even 48 inner