Properties

Label 725.2.y.a.18.2
Level 725725
Weight 22
Character 725.18
Analytic conductor 5.7895.789
Analytic rank 00
Dimension 120120
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [725,2,Mod(18,725)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(725, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([21, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("725.18");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 725=5229 725 = 5^{2} \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 725.y (of order 2828, degree 1212, 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: 5.789154146545.78915414654
Analytic rank: 00
Dimension: 120120
Relative dimension: 1010 over Q(ζ28)\Q(\zeta_{28})
Twist minimal: yes
Sato-Tate group: SU(2)[C28]\mathrm{SU}(2)[C_{28}]

Embedding invariants

Embedding label 18.2
Character χ\chi == 725.18
Dual form 725.2.y.a.282.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.616210.778326i)q2+(0.677001+0.539890i)q3+(0.759368+0.952217i)q4+(0.6739651.39950i)q6+(0.005599110.0496935i)q7+(0.312179+1.36775i)q8+(0.5007142.19377i)q9+(1.354290.850959i)q11+1.05463iq12+(2.02300+3.21958i)q13+(0.0296284+0.0846731i)q14+(1.102044.82834i)q163.45060q17+(0.898211+3.93532i)q18+(2.86087+0.322342i)q19+(0.02303840.0366654i)q21+(2.85115+0.321247i)q22+(0.506191+0.177124i)q23+(0.527087+1.09451i)q24+(0.7637066.77808i)q26+(1.972534.09601i)q27+(0.04306720.0430672i)q28+(5.374910.332224i)q29+(0.5728691.63716i)q31+(3.78973+4.75217i)q32+(1.37628+0.155070i)q33+(5.57689+2.68569i)q34+(1.708722.14267i)q36+(5.956031.35942i)q37+(4.372882.74766i)q38+(0.368650+3.27185i)q39+(1.91127+1.91127i)q41+(0.0657726+0.0413277i)q42+(1.10572+2.29605i)q43+(1.83870+0.643391i)q44+(0.6802510.680251i)q46+(3.59355+0.820205i)q47+(3.352852.67381i)q48+(6.822061.55709i)q49+(2.336051.86294i)q51+(1.52954+4.37118i)q52+(1.117213.19279i)q53+(6.37606+5.08474i)q54+(0.06622020.0231715i)q56+(1.76278+1.76278i)q57+(8.945563.64649i)q584.31330iq59+(7.719550.869785i)q61+(0.348372+3.09188i)q62+(0.106213+0.0371654i)q63+(0.8996370.433242i)q64+(2.103671.32182i)q66+(4.544057.23181i)q67+(2.620273.28571i)q68+(0.247064+0.393200i)q69+(8.28838+1.89177i)q71+(2.844211.36970i)q72+(1.984540.955706i)q73+(10.68432.43862i)q74+(1.86551+2.96894i)q76+(0.04987000.0625350i)q77+(3.142395.00108i)q78+(1.97211+1.23916i)q79+(2.53525+1.22091i)q81+(4.576611.60143i)q82+(1.2779911.3425i)q83+(0.05240800.00590497i)q844.57151iq86+(3.81818+2.67694i)q87+(1.58668+1.58668i)q88+(2.11636+0.740547i)q89+(0.1486650.118557i)q91+(0.215725+0.616506i)q92+(0.4960561.41765i)q93+(5.169554.12258i)q94+(5.13130+1.17119i)q96+(8.135996.48824i)q97+(12.23782.79320i)q98+(2.544932.54493i)q99+O(q100)q+(-1.61621 - 0.778326i) q^{2} +(0.677001 + 0.539890i) q^{3} +(0.759368 + 0.952217i) q^{4} +(-0.673965 - 1.39950i) q^{6} +(-0.00559911 - 0.0496935i) q^{7} +(0.312179 + 1.36775i) q^{8} +(-0.500714 - 2.19377i) q^{9} +(1.35429 - 0.850959i) q^{11} +1.05463i q^{12} +(2.02300 + 3.21958i) q^{13} +(-0.0296284 + 0.0846731i) q^{14} +(1.10204 - 4.82834i) q^{16} -3.45060 q^{17} +(-0.898211 + 3.93532i) q^{18} +(2.86087 + 0.322342i) q^{19} +(0.0230384 - 0.0366654i) q^{21} +(-2.85115 + 0.321247i) q^{22} +(0.506191 + 0.177124i) q^{23} +(-0.527087 + 1.09451i) q^{24} +(-0.763706 - 6.77808i) q^{26} +(1.97253 - 4.09601i) q^{27} +(0.0430672 - 0.0430672i) q^{28} +(5.37491 - 0.332224i) q^{29} +(-0.572869 - 1.63716i) q^{31} +(-3.78973 + 4.75217i) q^{32} +(1.37628 + 0.155070i) q^{33} +(5.57689 + 2.68569i) q^{34} +(1.70872 - 2.14267i) q^{36} +(5.95603 - 1.35942i) q^{37} +(-4.37288 - 2.74766i) q^{38} +(-0.368650 + 3.27185i) q^{39} +(-1.91127 + 1.91127i) q^{41} +(-0.0657726 + 0.0413277i) q^{42} +(1.10572 + 2.29605i) q^{43} +(1.83870 + 0.643391i) q^{44} +(-0.680251 - 0.680251i) q^{46} +(3.59355 + 0.820205i) q^{47} +(3.35285 - 2.67381i) q^{48} +(6.82206 - 1.55709i) q^{49} +(-2.33605 - 1.86294i) q^{51} +(-1.52954 + 4.37118i) q^{52} +(-1.11721 - 3.19279i) q^{53} +(-6.37606 + 5.08474i) q^{54} +(0.0662202 - 0.0231715i) q^{56} +(1.76278 + 1.76278i) q^{57} +(-8.94556 - 3.64649i) q^{58} -4.31330i q^{59} +(7.71955 - 0.869785i) q^{61} +(-0.348372 + 3.09188i) q^{62} +(-0.106213 + 0.0371654i) q^{63} +(0.899637 - 0.433242i) q^{64} +(-2.10367 - 1.32182i) q^{66} +(4.54405 - 7.23181i) q^{67} +(-2.62027 - 3.28571i) q^{68} +(0.247064 + 0.393200i) q^{69} +(8.28838 + 1.89177i) q^{71} +(2.84421 - 1.36970i) q^{72} +(1.98454 - 0.955706i) q^{73} +(-10.6843 - 2.43862i) q^{74} +(1.86551 + 2.96894i) q^{76} +(-0.0498700 - 0.0625350i) q^{77} +(3.14239 - 5.00108i) q^{78} +(1.97211 + 1.23916i) q^{79} +(-2.53525 + 1.22091i) q^{81} +(4.57661 - 1.60143i) q^{82} +(1.27799 - 11.3425i) q^{83} +(0.0524080 - 0.00590497i) q^{84} -4.57151i q^{86} +(3.81818 + 2.67694i) q^{87} +(1.58668 + 1.58668i) q^{88} +(-2.11636 + 0.740547i) q^{89} +(0.148665 - 0.118557i) q^{91} +(0.215725 + 0.616506i) q^{92} +(0.496056 - 1.41765i) q^{93} +(-5.16955 - 4.12258i) q^{94} +(-5.13130 + 1.17119i) q^{96} +(8.13599 - 6.48824i) q^{97} +(-12.2378 - 2.79320i) q^{98} +(-2.54493 - 2.54493i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 120q20q4+28q912q11+20q16+4q19+4q21+12q2932q3140q3416q36184q394q41+36q44+76q4684q49+112q51+168q54+208q99+O(q100) 120 q - 20 q^{4} + 28 q^{9} - 12 q^{11} + 20 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{29} - 32 q^{31} - 40 q^{34} - 16 q^{36} - 184 q^{39} - 4 q^{41} + 36 q^{44} + 76 q^{46} - 84 q^{49} + 112 q^{51} + 168 q^{54}+ \cdots - 208 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/725Z)×\left(\mathbb{Z}/725\mathbb{Z}\right)^\times.

nn 176176 552552
χ(n)\chi(n) e(1128)e\left(\frac{11}{28}\right) e(34)e\left(\frac{3}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.61621 0.778326i −1.14283 0.550360i −0.235960 0.971763i 0.575824π-0.575824\pi
−0.906874 + 0.421403i 0.861538π0.861538\pi
33 0.677001 + 0.539890i 0.390866 + 0.311706i 0.799130 0.601159i 0.205294π-0.205294\pi
−0.408263 + 0.912864i 0.633865π0.633865\pi
44 0.759368 + 0.952217i 0.379684 + 0.476108i
55 0 0
66 −0.673965 1.39950i −0.275145 0.571345i
77 −0.00559911 0.0496935i −0.00211626 0.0187824i 0.992610 0.121351i 0.0387226π-0.0387226\pi
−0.994726 + 0.102568i 0.967294π0.967294\pi
88 0.312179 + 1.36775i 0.110372 + 0.483572i
99 −0.500714 2.19377i −0.166905 0.731257i
1010 0 0
1111 1.35429 0.850959i 0.408335 0.256574i −0.312166 0.950027i 0.601055π-0.601055\pi
0.720501 + 0.693454i 0.243912π0.243912\pi
1212 1.05463i 0.304444i
1313 2.02300 + 3.21958i 0.561079 + 0.892951i 0.999984 0.00558163i 0.00177670π-0.00177670\pi
−0.438906 + 0.898533i 0.644634π0.644634\pi
1414 −0.0296284 + 0.0846731i −0.00791852 + 0.0226298i
1515 0 0
1616 1.10204 4.82834i 0.275509 1.20708i
1717 −3.45060 −0.836892 −0.418446 0.908242i 0.637425π-0.637425\pi
−0.418446 + 0.908242i 0.637425π0.637425\pi
1818 −0.898211 + 3.93532i −0.211710 + 0.927563i
1919 2.86087 + 0.322342i 0.656328 + 0.0739504i 0.433847 0.900987i 0.357156π-0.357156\pi
0.222481 + 0.974937i 0.428584π0.428584\pi
2020 0 0
2121 0.0230384 0.0366654i 0.00502739 0.00800105i
2222 −2.85115 + 0.321247i −0.607867 + 0.0684902i
2323 0.506191 + 0.177124i 0.105548 + 0.0369329i 0.382536 0.923940i 0.375051π-0.375051\pi
−0.276988 + 0.960873i 0.589336π0.589336\pi
2424 −0.527087 + 1.09451i −0.107591 + 0.223416i
2525 0 0
2626 −0.763706 6.77808i −0.149775 1.32929i
2727 1.97253 4.09601i 0.379614 0.788277i
2828 0.0430672 0.0430672i 0.00813893 0.00813893i
2929 5.37491 0.332224i 0.998095 0.0616925i
3030 0 0
3131 −0.572869 1.63716i −0.102890 0.294043i 0.880918 0.473270i 0.156926π-0.156926\pi
−0.983808 + 0.179226i 0.942641π0.942641\pi
3232 −3.78973 + 4.75217i −0.669936 + 0.840073i
3333 1.37628 + 0.155070i 0.239580 + 0.0269942i
3434 5.57689 + 2.68569i 0.956429 + 0.460592i
3535 0 0
3636 1.70872 2.14267i 0.284787 0.357111i
3737 5.95603 1.35942i 0.979165 0.223488i 0.297154 0.954830i 0.403963π-0.403963\pi
0.682011 + 0.731342i 0.261106π0.261106\pi
3838 −4.37288 2.74766i −0.709374 0.445729i
3939 −0.368650 + 3.27185i −0.0590312 + 0.523916i
4040 0 0
4141 −1.91127 + 1.91127i −0.298490 + 0.298490i −0.840422 0.541932i 0.817693π-0.817693\pi
0.541932 + 0.840422i 0.317693π0.317693\pi
4242 −0.0657726 + 0.0413277i −0.0101489 + 0.00637700i
4343 1.10572 + 2.29605i 0.168621 + 0.350144i 0.968106 0.250541i 0.0806086π-0.0806086\pi
−0.799485 + 0.600686i 0.794894π0.794894\pi
4444 1.83870 + 0.643391i 0.277195 + 0.0969948i
4545 0 0
4646 −0.680251 0.680251i −0.100298 0.100298i
4747 3.59355 + 0.820205i 0.524173 + 0.119639i 0.476416 0.879220i 0.341936π-0.341936\pi
0.0477571 + 0.998859i 0.484793π0.484793\pi
4848 3.35285 2.67381i 0.483942 0.385931i
4949 6.82206 1.55709i 0.974580 0.222441i
5050 0 0
5151 −2.33605 1.86294i −0.327113 0.260864i
5252 −1.52954 + 4.37118i −0.212109 + 0.606173i
5353 −1.11721 3.19279i −0.153460 0.438563i 0.841328 0.540524i 0.181774π-0.181774\pi
−0.994788 + 0.101961i 0.967488π0.967488\pi
5454 −6.37606 + 5.08474i −0.867672 + 0.691945i
5555 0 0
5656 0.0662202 0.0231715i 0.00884905 0.00309642i
5757 1.76278 + 1.76278i 0.233486 + 0.233486i
5858 −8.94556 3.64649i −1.17461 0.478807i
5959 4.31330i 0.561544i −0.959774 0.280772i 0.909410π-0.909410\pi
0.959774 0.280772i 0.0905905π-0.0905905\pi
6060 0 0
6161 7.71955 0.869785i 0.988387 0.111365i 0.397057 0.917794i 0.370031π-0.370031\pi
0.591330 + 0.806429i 0.298603π0.298603\pi
6262 −0.348372 + 3.09188i −0.0442432 + 0.392670i
6363 −0.106213 + 0.0371654i −0.0133815 + 0.00468240i
6464 0.899637 0.433242i 0.112455 0.0541553i
6565 0 0
6666 −2.10367 1.32182i −0.258944 0.162705i
6767 4.54405 7.23181i 0.555144 0.883506i −0.444783 0.895639i 0.646719π-0.646719\pi
0.999926 + 0.0121324i 0.00386195π0.00386195\pi
6868 −2.62027 3.28571i −0.317754 0.398451i
6969 0.247064 + 0.393200i 0.0297430 + 0.0473358i
7070 0 0
7171 8.28838 + 1.89177i 0.983650 + 0.224512i 0.683956 0.729524i 0.260258π-0.260258\pi
0.299694 + 0.954035i 0.403115π0.403115\pi
7272 2.84421 1.36970i 0.335194 0.161421i
7373 1.98454 0.955706i 0.232273 0.111857i −0.314127 0.949381i 0.601712π-0.601712\pi
0.546401 + 0.837524i 0.315998π0.315998\pi
7474 −10.6843 2.43862i −1.24202 0.283483i
7575 0 0
7676 1.86551 + 2.96894i 0.213989 + 0.340561i
7777 −0.0498700 0.0625350i −0.00568321 0.00712652i
7878 3.14239 5.00108i 0.355805 0.566261i
7979 1.97211 + 1.23916i 0.221880 + 0.139416i 0.638386 0.769717i 0.279603π-0.279603\pi
−0.416506 + 0.909133i 0.636745π0.636745\pi
8080 0 0
8181 −2.53525 + 1.22091i −0.281695 + 0.135657i
8282 4.57661 1.60143i 0.505402 0.176848i
8383 1.27799 11.3425i 0.140278 1.24500i −0.704432 0.709772i 0.748798π-0.748798\pi
0.844709 0.535226i 0.179773π-0.179773\pi
8484 0.0524080 0.00590497i 0.00571819 0.000644285i
8585 0 0
8686 4.57151i 0.492959i
8787 3.81818 + 2.67694i 0.409352 + 0.286998i
8888 1.58668 + 1.58668i 0.169141 + 0.169141i
8989 −2.11636 + 0.740547i −0.224334 + 0.0784978i −0.440106 0.897946i 0.645059π-0.645059\pi
0.215772 + 0.976444i 0.430773π0.430773\pi
9090 0 0
9191 0.148665 0.118557i 0.0155844 0.0124281i
9292 0.215725 + 0.616506i 0.0224909 + 0.0642752i
9393 0.496056 1.41765i 0.0514386 0.147003i
9494 −5.16955 4.12258i −0.533199 0.425212i
9595 0 0
9696 −5.13130 + 1.17119i −0.523711 + 0.119534i
9797 8.13599 6.48824i 0.826085 0.658781i −0.116336 0.993210i 0.537115π-0.537115\pi
0.942421 + 0.334429i 0.108544π0.108544\pi
9898 −12.2378 2.79320i −1.23621 0.282156i
9999 −2.54493 2.54493i −0.255775 0.255775i
100100 0 0
101101 −10.7478 3.76081i −1.06944 0.374215i −0.262555 0.964917i 0.584565π-0.584565\pi
−0.806890 + 0.590702i 0.798851π0.798851\pi
102102 2.32558 + 4.82912i 0.230267 + 0.478154i
103103 0.578374 0.363416i 0.0569889 0.0358085i −0.503236 0.864149i 0.667857π-0.667857\pi
0.560225 + 0.828340i 0.310715π0.310715\pi
104104 −3.77204 + 3.77204i −0.369879 + 0.369879i
105105 0 0
106106 −0.679392 + 6.02977i −0.0659884 + 0.585663i
107107 −11.2056 7.04093i −1.08328 0.680673i −0.132706 0.991156i 0.542366π-0.542366\pi
−0.950579 + 0.310483i 0.899509π0.899509\pi
108108 5.39816 1.23210i 0.519438 0.118558i
109109 10.9158 13.6879i 1.04554 1.31107i 0.0966979 0.995314i 0.469172π-0.469172\pi
0.948842 0.315752i 0.102257π-0.102257\pi
110110 0 0
111111 4.76617 + 2.29527i 0.452385 + 0.217857i
112112 −0.246107 0.0277296i −0.0232549 0.00262020i
113113 1.65404 2.07410i 0.155599 0.195114i −0.697922 0.716174i 0.745892π-0.745892\pi
0.853520 + 0.521060i 0.174463π0.174463\pi
114114 −1.47701 4.22104i −0.138334 0.395337i
115115 0 0
116116 4.39788 + 4.86580i 0.408333 + 0.451778i
117117 6.05009 6.05009i 0.559331 0.559331i
118118 −3.35716 + 6.97121i −0.309051 + 0.641752i
119119 0.0193203 + 0.171472i 0.00177109 + 0.0157188i
120120 0 0
121121 −3.66274 + 7.60576i −0.332976 + 0.691433i
122122 −13.1534 4.60258i −1.19085 0.416698i
123123 −2.32581 + 0.262056i −0.209711 + 0.0236288i
124124 1.12392 1.78870i 0.100931 0.160630i
125125 0 0
126126 0.200589 + 0.0226009i 0.0178699 + 0.00201345i
127127 −2.65798 + 11.6454i −0.235857 + 1.03336i 0.708828 + 0.705381i 0.249224π0.249224\pi
−0.944686 + 0.327977i 0.893633π0.893633\pi
128128 10.3653 0.916172
129129 −0.491041 + 2.15139i −0.0432338 + 0.189420i
130130 0 0
131131 −5.93311 + 16.9558i −0.518378 + 1.48144i 0.325833 + 0.945427i 0.394355π0.394355\pi
−0.844211 + 0.536011i 0.819930π0.819930\pi
132132 0.897444 + 1.42827i 0.0781125 + 0.124315i
133133 0.143971i 0.0124839i
134134 −12.9728 + 8.15138i −1.12068 + 0.704172i
135135 0 0
136136 −1.07721 4.71954i −0.0923696 0.404698i
137137 2.03582 + 8.91949i 0.173932 + 0.762044i 0.984355 + 0.176199i 0.0563801π0.0563801\pi
−0.810423 + 0.585845i 0.800763π0.800763\pi
138138 −0.0932697 0.827791i −0.00793964 0.0704663i
139139 8.09430 + 16.8080i 0.686550 + 1.42564i 0.894306 + 0.447455i 0.147670π0.147670\pi
−0.207756 + 0.978181i 0.566616π0.566616\pi
140140 0 0
141141 1.99002 + 2.49540i 0.167590 + 0.210151i
142142 −11.9234 9.50856i −1.00059 0.797941i
143143 5.47947 + 2.63877i 0.458216 + 0.220665i
144144 −11.1441 −0.928673
145145 0 0
146146 −3.95129 −0.327011
147147 5.45919 + 2.62901i 0.450267 + 0.216837i
148148 5.81728 + 4.63913i 0.478177 + 0.381334i
149149 −7.09534 8.89728i −0.581273 0.728893i 0.401056 0.916053i 0.368643π-0.368643\pi
−0.982329 + 0.187160i 0.940072π0.940072\pi
150150 0 0
151151 7.35606 + 15.2750i 0.598627 + 1.24306i 0.951574 + 0.307419i 0.0994654π0.0994654\pi
−0.352947 + 0.935643i 0.614820π0.614820\pi
152152 0.452221 + 4.01357i 0.0366800 + 0.325544i
153153 1.72776 + 7.56982i 0.139681 + 0.611984i
154154 0.0319278 + 0.139885i 0.00257282 + 0.0112722i
155155 0 0
156156 −3.39546 + 2.13351i −0.271854 + 0.170817i
157157 21.8717i 1.74555i −0.488120 0.872776i 0.662317π-0.662317\pi
0.488120 0.872776i 0.337683π-0.337683\pi
158158 −2.22288 3.53769i −0.176843 0.281444i
159159 0.967406 2.76469i 0.0767203 0.219254i
160160 0 0
161161 0.00596768 0.0261461i 0.000470319 0.00206060i
162162 5.04777 0.396591
163163 −2.63820 + 11.5587i −0.206640 + 0.905347i 0.760145 + 0.649754i 0.225128π0.225128\pi
−0.966784 + 0.255593i 0.917729π0.917729\pi
164164 −3.27130 0.368587i −0.255446 0.0287818i
165165 0 0
166166 −10.8936 + 17.3371i −0.845510 + 1.34562i
167167 −24.4686 + 2.75695i −1.89344 + 0.213339i −0.980743 0.195302i 0.937431π-0.937431\pi
−0.912695 + 0.408641i 0.866003π0.866003\pi
168168 0.0573412 + 0.0200645i 0.00442397 + 0.00154801i
169169 −0.632702 + 1.31382i −0.0486694 + 0.101063i
170170 0 0
171171 −0.725331 6.43749i −0.0554674 0.492287i
172172 −1.34669 + 2.79643i −0.102684 + 0.213226i
173173 −8.89672 + 8.89672i −0.676405 + 0.676405i −0.959185 0.282780i 0.908744π-0.908744\pi
0.282780 + 0.959185i 0.408744π0.408744\pi
174174 −4.08745 7.29829i −0.309869 0.553282i
175175 0 0
176176 −2.61624 7.47678i −0.197206 0.563583i
177177 2.32871 2.92011i 0.175036 0.219489i
178178 3.99687 + 0.450339i 0.299578 + 0.0337544i
179179 1.78074 + 0.857561i 0.133099 + 0.0640971i 0.499248 0.866459i 0.333610π-0.333610\pi
−0.366149 + 0.930556i 0.619324π0.619324\pi
180180 0 0
181181 −8.08934 + 10.1437i −0.601276 + 0.753976i −0.985576 0.169232i 0.945871π-0.945871\pi
0.384300 + 0.923208i 0.374443π0.374443\pi
182182 −0.332550 + 0.0759024i −0.0246503 + 0.00562626i
183183 5.69573 + 3.57886i 0.421040 + 0.264557i
184184 −0.0842383 + 0.747636i −0.00621013 + 0.0551165i
185185 0 0
186186 −1.90512 + 1.90512i −0.139690 + 0.139690i
187187 −4.67312 + 2.93632i −0.341732 + 0.214725i
188188 1.94781 + 4.04468i 0.142059 + 0.294988i
189189 −0.214589 0.0750880i −0.0156091 0.00546185i
190190 0 0
191191 9.41763 + 9.41763i 0.681436 + 0.681436i 0.960324 0.278888i 0.0899658π-0.0899658\pi
−0.278888 + 0.960324i 0.589966π0.589966\pi
192192 0.842958 + 0.192400i 0.0608353 + 0.0138853i
193193 −8.89678 + 7.09495i −0.640404 + 0.510705i −0.889003 0.457901i 0.848601π-0.848601\pi
0.248599 + 0.968607i 0.420030π0.420030\pi
194194 −18.1994 + 4.15391i −1.30664 + 0.298233i
195195 0 0
196196 6.66314 + 5.31367i 0.475938 + 0.379548i
197197 −7.58813 + 21.6856i −0.540632 + 1.54504i 0.272022 + 0.962291i 0.412308π0.412308\pi
−0.812654 + 0.582746i 0.801978π0.801978\pi
198198 2.13235 + 6.09392i 0.151540 + 0.433076i
199199 1.71680 1.36910i 0.121701 0.0970531i −0.560748 0.827986i 0.689486π-0.689486\pi
0.682449 + 0.730933i 0.260915π0.260915\pi
200200 0 0
201201 6.98070 2.44265i 0.492381 0.172292i
202202 14.4435 + 14.4435i 1.01624 + 1.01624i
203203 −0.0466041 0.265238i −0.00327097 0.0186160i
204204 3.63909i 0.254787i
205205 0 0
206206 −1.21763 + 0.137194i −0.0848363 + 0.00955876i
207207 0.135112 1.19916i 0.00939096 0.0833471i
208208 17.7746 6.21962i 1.23245 0.431253i
209209 4.14875 1.99793i 0.286975 0.138200i
210210 0 0
211211 8.46368 + 5.31808i 0.582664 + 0.366112i 0.790880 0.611971i 0.209623π-0.209623\pi
−0.208216 + 0.978083i 0.566766π0.566766\pi
212212 2.19186 3.48832i 0.150537 0.239579i
213213 4.58989 + 5.75554i 0.314494 + 0.394363i
214214 12.6304 + 20.1012i 0.863399 + 1.37409i
215215 0 0
216216 6.21809 + 1.41924i 0.423087 + 0.0965669i
217217 −0.0781489 + 0.0376345i −0.00530509 + 0.00255480i
218218 −28.2958 + 13.6266i −1.91644 + 0.922907i
219219 1.85951 + 0.424422i 0.125654 + 0.0286798i
220220 0 0
221221 −6.98055 11.1095i −0.469562 0.747304i
222222 −5.91667 7.41927i −0.397101 0.497949i
223223 −3.30385 + 5.25804i −0.221242 + 0.352105i −0.938840 0.344352i 0.888098π-0.888098\pi
0.717598 + 0.696457i 0.245241π0.245241\pi
224224 0.257371 + 0.161717i 0.0171963 + 0.0108052i
225225 0 0
226226 −4.28759 + 2.06480i −0.285207 + 0.137348i
227227 −9.71679 + 3.40005i −0.644926 + 0.225669i −0.632870 0.774258i 0.718123π-0.718123\pi
−0.0120560 + 0.999927i 0.503838π0.503838\pi
228228 −0.339950 + 3.01714i −0.0225138 + 0.199815i
229229 2.88517 0.325080i 0.190657 0.0214819i −0.0161195 0.999870i 0.505131π-0.505131\pi
0.206777 + 0.978388i 0.433703π0.433703\pi
230230 0 0
231231 0.0692605i 0.00455701i
232232 2.13233 + 7.24780i 0.139995 + 0.475842i
233233 9.72899 + 9.72899i 0.637367 + 0.637367i 0.949905 0.312538i 0.101179π-0.101179\pi
−0.312538 + 0.949905i 0.601179π0.601179\pi
234234 −14.4872 + 5.06928i −0.947055 + 0.331389i
235235 0 0
236236 4.10720 3.27538i 0.267356 0.213209i
237237 0.666111 + 1.90364i 0.0432686 + 0.123654i
238238 0.102236 0.292173i 0.00662695 0.0189387i
239239 −13.8791 11.0682i −0.897762 0.715941i 0.0616058 0.998101i 0.480378π-0.480378\pi
−0.959368 + 0.282160i 0.908949π0.908949\pi
240240 0 0
241241 −18.2239 + 4.15948i −1.17390 + 0.267935i −0.764625 0.644475i 0.777076π-0.777076\pi
−0.409276 + 0.912411i 0.634219π0.634219\pi
242242 11.8395 9.44171i 0.761074 0.606936i
243243 −15.6722 3.57709i −1.00538 0.229470i
244244 6.69020 + 6.69020i 0.428296 + 0.428296i
245245 0 0
246246 3.96296 + 1.38670i 0.252669 + 0.0884128i
247247 4.74972 + 9.86289i 0.302217 + 0.627561i
248248 2.06039 1.29463i 0.130835 0.0822090i
249249 6.98888 6.98888i 0.442902 0.442902i
250250 0 0
251251 −0.444851 + 3.94816i −0.0280788 + 0.249206i 0.971830 + 0.235684i 0.0757329π0.0757329\pi
−0.999909 + 0.0135222i 0.995696π0.995696\pi
252252 −0.116044 0.0729152i −0.00731008 0.00459323i
253253 0.836257 0.190870i 0.0525750 0.0119999i
254254 13.3597 16.7526i 0.838265 1.05115i
255255 0 0
256256 −18.5518 8.93407i −1.15949 0.558380i
257257 −24.4713 2.75726i −1.52648 0.171993i −0.691542 0.722336i 0.743068π-0.743068\pi
−0.834939 + 0.550343i 0.814497π0.814497\pi
258258 2.46811 3.09491i 0.153658 0.192681i
259259 −0.100903 0.288364i −0.00626980 0.0179181i
260260 0 0
261261 −3.42012 11.6250i −0.211700 0.719568i
262262 22.7863 22.7863i 1.40774 1.40774i
263263 3.52401 7.31769i 0.217300 0.451228i −0.763613 0.645674i 0.776577π-0.776577\pi
0.980913 + 0.194446i 0.0622908π0.0622908\pi
264264 0.217551 + 1.93082i 0.0133893 + 0.118834i
265265 0 0
266266 −0.112057 + 0.232688i −0.00687063 + 0.0142670i
267267 −1.83259 0.641251i −0.112153 0.0392439i
268268 10.3369 1.16468i 0.631424 0.0711444i
269269 4.23287 6.73657i 0.258083 0.410736i −0.692400 0.721514i 0.743447π-0.743447\pi
0.950483 + 0.310778i 0.100589π0.100589\pi
270270 0 0
271271 25.3607 + 2.85746i 1.54055 + 0.173579i 0.841013 0.541015i 0.181960π-0.181960\pi
0.699539 + 0.714594i 0.253389π0.253389\pi
272272 −3.80268 + 16.6606i −0.230571 + 1.01020i
273273 0.164654 0.00996531
274274 3.65197 16.0003i 0.220623 0.966614i
275275 0 0
276276 −0.186799 + 0.533842i −0.0112440 + 0.0321335i
277277 9.73540 + 15.4938i 0.584943 + 0.930932i 0.999779 + 0.0210355i 0.00669631π0.00669631\pi
−0.414835 + 0.909896i 0.636161π0.636161\pi
278278 33.4653i 2.00711i
279279 −3.30472 + 2.07650i −0.197849 + 0.124317i
280280 0 0
281281 −5.32480 23.3295i −0.317651 1.39172i −0.841660 0.540007i 0.818422π-0.818422\pi
0.524009 0.851712i 0.324436π-0.324436\pi
282282 −1.27405 5.58198i −0.0758686 0.332402i
283283 −3.51609 31.2062i −0.209010 1.85501i −0.461148 0.887323i 0.652562π-0.652562\pi
0.252138 0.967691i 0.418866π-0.418866\pi
284284 4.49255 + 9.32888i 0.266584 + 0.553567i
285285 0 0
286286 −6.80215 8.52963i −0.402220 0.504367i
287287 0.105679 + 0.0842763i 0.00623804 + 0.00497467i
288288 12.3228 + 5.93433i 0.726125 + 0.349683i
289289 −5.09339 −0.299611
290290 0 0
291291 9.01101 0.528234
292292 2.41704 + 1.16398i 0.141446 + 0.0681170i
293293 −4.76687 3.80145i −0.278483 0.222083i 0.474280 0.880374i 0.342708π-0.342708\pi
−0.752764 + 0.658291i 0.771280π0.771280\pi
294294 −6.77698 8.49807i −0.395242 0.495617i
295295 0 0
296296 3.71870 + 7.72196i 0.216145 + 0.448830i
297297 −0.814146 7.22574i −0.0472415 0.419280i
298298 4.54259 + 19.9024i 0.263145 + 1.15291i
299299 0.453758 + 1.98804i 0.0262415 + 0.114972i
300300 0 0
301301 0.107908 0.0678028i 0.00621969 0.00390809i
302302 30.4131i 1.75007i
303303 −5.24583 8.34869i −0.301365 0.479620i
304304 4.70915 13.4580i 0.270089 0.771869i
305305 0 0
306306 3.09936 13.5792i 0.177179 0.776271i
307307 −16.3838 −0.935075 −0.467538 0.883973i 0.654859π-0.654859\pi
−0.467538 + 0.883973i 0.654859π0.654859\pi
308308 0.0216772 0.0949741i 0.00123517 0.00541165i
309309 0.587764 + 0.0662251i 0.0334367 + 0.00376741i
310310 0 0
311311 10.3934 16.5410i 0.589354 0.937951i −0.410308 0.911947i 0.634579π-0.634579\pi
0.999662 0.0260043i 0.00827836π-0.00827836\pi
312312 −4.59016 + 0.517186i −0.259866 + 0.0292799i
313313 −17.7270 6.20293i −1.00199 0.350610i −0.221079 0.975256i 0.570958π-0.570958\pi
−0.780908 + 0.624646i 0.785243π0.785243\pi
314314 −17.0233 + 35.3493i −0.960682 + 1.99488i
315315 0 0
316316 0.317609 + 2.81886i 0.0178669 + 0.158573i
317317 1.86736 3.87760i 0.104881 0.217788i −0.841923 0.539597i 0.818577π-0.818577\pi
0.946805 + 0.321809i 0.104291π0.104291\pi
318318 −3.71536 + 3.71536i −0.208347 + 0.208347i
319319 6.99650 5.02376i 0.391729 0.281276i
320320 0 0
321321 −3.78486 10.8165i −0.211250 0.603718i
322322 −0.0299953 + 0.0376129i −0.00167157 + 0.00209608i
323323 −9.87169 1.11227i −0.549276 0.0618885i
324324 −3.08776 1.48699i −0.171542 0.0826105i
325325 0 0
326326 13.2603 16.6279i 0.734421 0.920935i
327327 14.7799 3.37343i 0.817333 0.186551i
328328 −3.21080 2.01748i −0.177287 0.111397i
329329 0.0206381 0.183168i 0.00113782 0.0100984i
330330 0 0
331331 −7.44773 + 7.44773i −0.409364 + 0.409364i −0.881517 0.472153i 0.843477π-0.843477\pi
0.472153 + 0.881517i 0.343477π0.343477\pi
332332 11.7709 7.39618i 0.646015 0.405918i
333333 −5.96453 12.3855i −0.326854 0.678720i
334334 41.6923 + 14.5888i 2.28130 + 0.798261i
335335 0 0
336336 −0.151644 0.151644i −0.00827285 0.00827285i
337337 23.2516 + 5.30703i 1.26660 + 0.289092i 0.802479 0.596681i 0.203514π-0.203514\pi
0.464118 + 0.885773i 0.346371π0.346371\pi
338338 2.04516 1.63096i 0.111242 0.0887125i
339339 2.23957 0.511166i 0.121637 0.0277627i
340340 0 0
341341 −2.16899 1.72971i −0.117458 0.0936693i
342342 −3.83818 + 10.9689i −0.207545 + 0.593130i
343343 −0.231191 0.660705i −0.0124831 0.0356747i
344344 −2.79523 + 2.22912i −0.150709 + 0.120186i
345345 0 0
346346 21.3035 7.45443i 1.14529 0.400753i
347347 22.4557 + 22.4557i 1.20549 + 1.20549i 0.972474 + 0.233012i 0.0748581π0.0748581\pi
0.233012 + 0.972474i 0.425142π0.425142\pi
348348 0.350372 + 5.66852i 0.0187819 + 0.303864i
349349 9.37948i 0.502072i −0.967978 0.251036i 0.919229π-0.919229\pi
0.967978 0.251036i 0.0807713π-0.0807713\pi
350350 0 0
351351 17.1779 1.93548i 0.916886 0.103308i
352352 −1.08850 + 9.66074i −0.0580175 + 0.514919i
353353 29.8092 10.4307i 1.58658 0.555169i 0.614319 0.789058i 0.289431π-0.289431\pi
0.972263 + 0.233889i 0.0751452π0.0751452\pi
354354 −6.03648 + 2.90702i −0.320835 + 0.154506i
355355 0 0
356356 −2.31226 1.45289i −0.122549 0.0770029i
357357 −0.0794962 + 0.126518i −0.00420739 + 0.00669602i
358358 −2.21060 2.77200i −0.116834 0.146505i
359359 10.9969 + 17.5015i 0.580397 + 0.923696i 0.999873 + 0.0159298i 0.00507083π0.00507083\pi
−0.419476 + 0.907766i 0.637786π0.637786\pi
360360 0 0
361361 −10.4430 2.38354i −0.549631 0.125450i
362362 20.9692 10.0982i 1.10212 0.530752i
363363 −6.58595 + 3.17163i −0.345673 + 0.166467i
364364 0.225783 + 0.0515335i 0.0118343 + 0.00270109i
365365 0 0
366366 −6.41998 10.2173i −0.335578 0.534069i
367367 −18.7845 23.5550i −0.980542 1.22956i −0.973288 0.229588i 0.926262π-0.926262\pi
−0.00725434 0.999974i 0.502309π-0.502309\pi
368368 1.41305 2.24886i 0.0736606 0.117230i
369369 5.14989 + 3.23589i 0.268093 + 0.168454i
370370 0 0
371371 −0.152405 + 0.0733946i −0.00791250 + 0.00381046i
372372 1.72660 0.604162i 0.0895199 0.0313244i
373373 4.14321 36.7720i 0.214527 1.90398i −0.177652 0.984093i 0.556850π-0.556850\pi
0.392179 0.919889i 0.371721π-0.371721\pi
374374 9.83816 1.10849i 0.508719 0.0573189i
375375 0 0
376376 5.17112i 0.266680i
377377 11.9430 + 16.6329i 0.615098 + 0.856636i
378378 0.288379 + 0.288379i 0.0148326 + 0.0148326i
379379 −22.8719 + 8.00324i −1.17485 + 0.411099i −0.845949 0.533264i 0.820965π-0.820965\pi
−0.328904 + 0.944363i 0.606679π0.606679\pi
380380 0 0
381381 −8.08666 + 6.44890i −0.414292 + 0.330387i
382382 −7.89089 22.5509i −0.403733 1.15380i
383383 1.63819 4.68168i 0.0837077 0.239223i −0.894420 0.447228i 0.852411π-0.852411\pi
0.978128 + 0.208005i 0.0666970π0.0666970\pi
384384 7.01732 + 5.59612i 0.358101 + 0.285576i
385385 0 0
386386 19.9013 4.54233i 1.01295 0.231199i
387387 4.48336 3.57536i 0.227902 0.181746i
388388 12.3564 + 2.82027i 0.627302 + 0.143178i
389389 23.2351 + 23.2351i 1.17807 + 1.17807i 0.980236 + 0.197832i 0.0633900π0.0633900\pi
0.197832 + 0.980236i 0.436610π0.436610\pi
390390 0 0
391391 −1.74666 0.611183i −0.0883324 0.0309088i
392392 4.25941 + 8.84476i 0.215133 + 0.446728i
393393 −13.1710 + 8.27589i −0.664389 + 0.417463i
394394 29.1425 29.1425i 1.46818 1.46818i
395395 0 0
396396 0.490787 4.35585i 0.0246630 0.218890i
397397 −17.7209 11.1348i −0.889386 0.558838i 0.00805748 0.999968i 0.497435π-0.497435\pi
−0.897444 + 0.441129i 0.854578π0.854578\pi
398398 −3.84032 + 0.876528i −0.192498 + 0.0439364i
399399 0.0777286 0.0974686i 0.00389130 0.00487953i
400400 0 0
401401 −11.6907 5.62994i −0.583806 0.281146i 0.118578 0.992945i 0.462166π-0.462166\pi
−0.702383 + 0.711799i 0.747881π0.747881\pi
402402 −13.1835 1.48542i −0.657532 0.0740861i
403403 4.11207 5.15638i 0.204837 0.256857i
404404 −4.58041 13.0901i −0.227884 0.651255i
405405 0 0
406406 −0.131119 + 0.464953i −0.00650735 + 0.0230752i
407407 6.90940 6.90940i 0.342486 0.342486i
408408 1.81877 3.77671i 0.0900423 0.186975i
409409 −0.292252 2.59381i −0.0144509 0.128256i 0.984415 0.175859i 0.0562702π-0.0562702\pi
−0.998866 + 0.0476033i 0.984842π0.984842\pi
410410 0 0
411411 −3.43730 + 7.13762i −0.169549 + 0.352073i
412412 0.785249 + 0.274771i 0.0386865 + 0.0135370i
413413 −0.214343 + 0.0241507i −0.0105471 + 0.00118838i
414414 −1.15171 + 1.83293i −0.0566032 + 0.0900835i
415415 0 0
416416 −22.9666 2.58772i −1.12603 0.126873i
417417 −3.59462 + 15.7491i −0.176029 + 0.771235i
418418 −8.26031 −0.404025
419419 −3.84687 + 16.8542i −0.187932 + 0.823384i 0.789773 + 0.613399i 0.210198π0.210198\pi
−0.977705 + 0.209984i 0.932659π0.932659\pi
420420 0 0
421421 −3.22153 + 9.20660i −0.157008 + 0.448702i −0.995337 0.0964625i 0.969247π-0.969247\pi
0.838329 + 0.545165i 0.183533π0.183533\pi
422422 −9.53990 15.1827i −0.464395 0.739080i
423423 8.29412i 0.403274i
424424 4.01816 2.52478i 0.195139 0.122614i
425425 0 0
426426 −2.93854 12.8746i −0.142373 0.623777i
427427 −0.0864453 0.378741i −0.00418338 0.0183286i
428428 −1.80466 16.0168i −0.0872315 0.774201i
429429 2.28496 + 4.74476i 0.110319 + 0.229079i
430430 0 0
431431 −10.7212 13.4440i −0.516424 0.647575i 0.453422 0.891296i 0.350203π-0.350203\pi
−0.969845 + 0.243721i 0.921632π0.921632\pi
432432 −17.6031 14.0380i −0.846929 0.675404i
433433 4.96082 + 2.38901i 0.238402 + 0.114808i 0.549271 0.835645i 0.314906π-0.314906\pi
−0.310869 + 0.950453i 0.600620π0.600620\pi
434434 0.155597 0.00746889
435435 0 0
436436 21.3229 1.02118
437437 1.39105 + 0.669894i 0.0665430 + 0.0320454i
438438 −2.67503 2.13326i −0.127818 0.101931i
439439 2.44429 + 3.06504i 0.116659 + 0.146286i 0.836732 0.547612i 0.184463π-0.184463\pi
−0.720073 + 0.693898i 0.755892π0.755892\pi
440440 0 0
441441 −6.83180 14.1864i −0.325324 0.675542i
442442 2.63524 + 23.3884i 0.125346 + 1.11247i
443443 7.11646 + 31.1792i 0.338113 + 1.48137i 0.802988 + 0.595995i 0.203242π0.203242\pi
−0.464875 + 0.885376i 0.653901π0.653901\pi
444444 1.43368 + 6.28138i 0.0680396 + 0.298101i
445445 0 0
446446 9.43219 5.92664i 0.446627 0.280634i
447447 9.85416i 0.466086i
448448 −0.0265665 0.0422803i −0.00125515 0.00199756i
449449 2.93533 8.38870i 0.138527 0.395887i −0.853631 0.520878i 0.825605π-0.825605\pi
0.992158 + 0.124991i 0.0398902π0.0398902\pi
450450 0 0
451451 −0.962009 + 4.21484i −0.0452992 + 0.198469i
452452 3.23101 0.151974
453453 −3.26677 + 14.3127i −0.153486 + 0.672467i
454454 18.3507 + 2.06763i 0.861243 + 0.0970388i
455455 0 0
456456 −1.86073 + 2.96134i −0.0871368 + 0.138677i
457457 −30.5147 + 3.43818i −1.42742 + 0.160831i −0.791614 0.611021i 0.790759π-0.790759\pi
−0.635802 + 0.771852i 0.719331π0.719331\pi
458458 −4.91606 1.72020i −0.229712 0.0803798i
459459 −6.80641 + 14.1337i −0.317696 + 0.659703i
460460 0 0
461461 −0.686954 6.09689i −0.0319946 0.283960i −0.999514 0.0311644i 0.990078π-0.990078\pi
0.967520 0.252796i 0.0813501π-0.0813501\pi
462462 −0.0539073 + 0.111940i −0.00250799 + 0.00520790i
463463 −8.48374 + 8.48374i −0.394273 + 0.394273i −0.876207 0.481935i 0.839934π-0.839934\pi
0.481935 + 0.876207i 0.339934π0.339934\pi
464464 4.31925 26.3180i 0.200516 1.22178i
465465 0 0
466466 −8.15177 23.2964i −0.377624 1.07919i
467467 3.56319 4.46810i 0.164885 0.206759i −0.692524 0.721395i 0.743501π-0.743501\pi
0.857409 + 0.514636i 0.172073π0.172073\pi
468468 10.3552 + 1.16675i 0.478671 + 0.0539332i
469469 −0.384816 0.185318i −0.0177692 0.00855718i
470470 0 0
471471 11.8083 14.8072i 0.544099 0.682278i
472472 5.89951 1.34652i 0.271547 0.0619788i
473473 3.45131 + 2.16860i 0.158692 + 0.0997125i
474474 0.405074 3.59513i 0.0186057 0.165130i
475475 0 0
476476 −0.148607 + 0.148607i −0.00681141 + 0.00681141i
477477 −6.44485 + 4.04957i −0.295090 + 0.185417i
478478 13.8168 + 28.6910i 0.631967 + 1.31229i
479479 −0.512120 0.179198i −0.0233993 0.00818778i 0.318554 0.947905i 0.396803π-0.396803\pi
−0.341953 + 0.939717i 0.611088π0.611088\pi
480480 0 0
481481 16.4258 + 16.4258i 0.748952 + 0.748952i
482482 32.6910 + 7.46151i 1.48904 + 0.339863i
483483 0.0181562 0.0144791i 0.000826134 0.000658820i
484484 −10.0237 + 2.28784i −0.455623 + 0.103993i
485485 0 0
486486 22.5455 + 17.9795i 1.02269 + 0.815565i
487487 −12.2890 + 35.1198i −0.556866 + 1.59143i 0.229261 + 0.973365i 0.426369π0.426369\pi
−0.786127 + 0.618065i 0.787917π0.787917\pi
488488 3.59953 + 10.2869i 0.162943 + 0.465665i
489489 −8.02648 + 6.40091i −0.362970 + 0.289459i
490490 0 0
491491 17.2250 6.02730i 0.777355 0.272008i 0.0877005 0.996147i 0.472048π-0.472048\pi
0.689654 + 0.724139i 0.257762π0.257762\pi
492492 −2.01568 2.01568i −0.0908737 0.0908737i
493493 −18.5466 + 1.14637i −0.835298 + 0.0516300i
494494 19.6373i 0.883526i
495495 0 0
496496 −8.53610 + 0.961788i −0.383282 + 0.0431856i
497497 0.0476010 0.422471i 0.00213520 0.0189504i
498498 −16.7351 + 5.85588i −0.749920 + 0.262408i
499499 −8.25425 + 3.97504i −0.369511 + 0.177947i −0.609419 0.792849i 0.708597π-0.708597\pi
0.239908 + 0.970796i 0.422883π0.422883\pi
500500 0 0
501501 −18.0537 11.3439i −0.806581 0.506808i
502502 3.79193 6.03483i 0.169242 0.269348i
503503 11.8551 + 14.8659i 0.528594 + 0.662836i 0.972409 0.233282i 0.0749466π-0.0749466\pi
−0.443815 + 0.896119i 0.646375π0.646375\pi
504504 −0.0839903 0.133670i −0.00374122 0.00595413i
505505 0 0
506506 −1.50013 0.342394i −0.0666888 0.0152213i
507507 −1.13766 + 0.547867i −0.0505251 + 0.0243316i
508508 −13.1073 + 6.31214i −0.581542 + 0.280056i
509509 −36.0022 8.21727i −1.59577 0.364224i −0.670014 0.742348i 0.733712π-0.733712\pi
−0.925755 + 0.378124i 0.876569π0.876569\pi
510510 0 0
511511 −0.0586040 0.0932678i −0.00259249 0.00412592i
512512 10.1047 + 12.6709i 0.446568 + 0.559978i
513513 6.96347 11.0823i 0.307445 0.489295i
514514 37.4048 + 23.5030i 1.64986 + 1.03667i
515515 0 0
516516 −2.42147 + 1.16612i −0.106599 + 0.0513356i
517517 5.56469 1.94717i 0.244735 0.0856363i
518518 −0.0613609 + 0.544593i −0.00269604 + 0.0239280i
519519 −10.8263 + 1.21984i −0.475224 + 0.0535448i
520520 0 0
521521 12.6825i 0.555630i −0.960635 0.277815i 0.910390π-0.910390\pi
0.960635 0.277815i 0.0896102π-0.0896102\pi
522522 −3.52039 + 21.4504i −0.154083 + 0.938858i
523523 24.6658 + 24.6658i 1.07856 + 1.07856i 0.996639 + 0.0819190i 0.0261049π0.0261049\pi
0.0819190 + 0.996639i 0.473895π0.473895\pi
524524 −20.6510 + 7.22611i −0.902145 + 0.315674i
525525 0 0
526526 −11.3911 + 9.08410i −0.496676 + 0.396086i
527527 1.97674 + 5.64919i 0.0861081 + 0.246083i
528528 2.26544 6.47426i 0.0985907 0.281756i
529529 −17.7573 14.1609i −0.772055 0.615693i
530530 0 0
531531 −9.46240 + 2.15973i −0.410633 + 0.0937244i
532532 0.137092 0.109327i 0.00594368 0.00473993i
533533 −10.0200 2.28700i −0.434014 0.0990609i
534534 2.46275 + 2.46275i 0.106574 + 0.106574i
535535 0 0
536536 11.3098 + 3.95749i 0.488511 + 0.170937i
537537 0.742576 + 1.54197i 0.0320445 + 0.0665411i
538538 −12.0845 + 7.59317i −0.520998 + 0.327365i
539539 7.91405 7.91405i 0.340882 0.340882i
540540 0 0
541541 1.45294 12.8952i 0.0624669 0.554409i −0.923032 0.384724i 0.874297π-0.874297\pi
0.985498 0.169685i 0.0542749π-0.0542749\pi
542542 −38.7642 24.3572i −1.66506 1.04623i
543543 −10.9530 + 2.49995i −0.470037 + 0.107283i
544544 13.0768 16.3978i 0.560664 0.703051i
545545 0 0
546546 −0.266116 0.128155i −0.0113887 0.00548451i
547547 12.2767 + 1.38325i 0.524913 + 0.0591435i 0.370445 0.928854i 0.379205π-0.379205\pi
0.154468 + 0.987998i 0.450634π0.450634\pi
548548 −6.94736 + 8.71171i −0.296776 + 0.372146i
549549 −5.77340 16.4994i −0.246403 0.704178i
550550 0 0
551551 15.4840 + 0.782110i 0.659640 + 0.0333190i
552552 −0.460671 + 0.460671i −0.0196074 + 0.0196074i
553553 0.0505361 0.104939i 0.00214901 0.00446247i
554554 −3.67523 32.6186i −0.156146 1.38583i
555555 0 0
556556 −9.85830 + 20.4710i −0.418085 + 0.868163i
557557 −17.3588 6.07412i −0.735518 0.257369i −0.0635804 0.997977i 0.520252π-0.520252\pi
−0.671937 + 0.740608i 0.734538π0.734538\pi
558558 6.95732 0.783902i 0.294527 0.0331852i
559559 −5.15545 + 8.20485i −0.218052 + 0.347028i
560560 0 0
561561 −4.74899 0.535083i −0.200503 0.0225912i
562562 −9.55194 + 41.8498i −0.402924 + 1.76533i
563563 33.1694 1.39792 0.698962 0.715159i 0.253646π-0.253646\pi
0.698962 + 0.715159i 0.253646π0.253646\pi
564564 −0.865009 + 3.78985i −0.0364235 + 0.159582i
565565 0 0
566566 −18.6058 + 53.1724i −0.782062 + 2.23500i
567567 0.0748666 + 0.119150i 0.00314410 + 0.00500381i
568568 11.9270i 0.500445i
569569 12.1703 7.64712i 0.510207 0.320584i −0.252208 0.967673i 0.581157π-0.581157\pi
0.762414 + 0.647089i 0.224014π0.224014\pi
570570 0 0
571571 2.48794 + 10.9004i 0.104117 + 0.456166i 0.999931 + 0.0117373i 0.00373617π0.00373617\pi
−0.895814 + 0.444429i 0.853407π0.853407\pi
572572 1.64825 + 7.22144i 0.0689166 + 0.301944i
573573 1.29126 + 11.4602i 0.0539430 + 0.478758i
574574 −0.105205 0.218461i −0.00439119 0.00911839i
575575 0 0
576576 −1.40090 1.75667i −0.0583707 0.0731945i
577577 −20.7764 16.5686i −0.864933 0.689761i 0.0869530 0.996212i 0.472287π-0.472287\pi
−0.951886 + 0.306451i 0.900858π0.900858\pi
578578 8.23200 + 3.96432i 0.342406 + 0.164894i
579579 −9.85362 −0.409502
580580 0 0
581581 −0.570802 −0.0236809
582582 −14.5637 7.01350i −0.603684 0.290719i
583583 −4.22996 3.37328i −0.175187 0.139707i
584584 1.92670 + 2.41600i 0.0797273 + 0.0999749i
585585 0 0
586586 4.74549 + 9.85412i 0.196035 + 0.407070i
587587 0.901390 + 8.00006i 0.0372044 + 0.330198i 0.998503 + 0.0546906i 0.0174172π0.0174172\pi
−0.961299 + 0.275507i 0.911154π0.911154\pi
588588 1.64215 + 7.19472i 0.0677210 + 0.296705i
589589 −1.11117 4.86837i −0.0457851 0.200598i
590590 0 0
591591 −16.8450 + 10.5844i −0.692912 + 0.435385i
592592 30.2558i 1.24351i
593593 20.3482 + 32.3840i 0.835600 + 1.32985i 0.942030 + 0.335529i 0.108915π0.108915\pi
−0.106430 + 0.994320i 0.533942π0.533942\pi
594594 −4.30815 + 12.3120i −0.176766 + 0.505167i
595595 0 0
596596 3.08416 13.5126i 0.126332 0.553498i
597597 1.90144 0.0778207
598598 0.813978 3.56627i 0.0332861 0.145836i
599599 −46.8364 5.27719i −1.91368 0.215620i −0.926625 0.375986i 0.877304π-0.877304\pi
−0.987058 + 0.160366i 0.948733π0.948733\pi
600600 0 0
601601 1.29346 2.05853i 0.0527614 0.0839693i −0.819302 0.573362i 0.805639π-0.805639\pi
0.872063 + 0.489393i 0.162782π0.162782\pi
602602 −0.227174 + 0.0255964i −0.00925893 + 0.00104323i
603603 −18.1402 6.34753i −0.738727 0.258492i
604604 −8.95917 + 18.6039i −0.364543 + 0.756982i
605605 0 0
606606 1.98036 + 17.5762i 0.0804468 + 0.713985i
607607 12.2672 25.4732i 0.497912 1.03392i −0.488943 0.872316i 0.662617π-0.662617\pi
0.986855 0.161609i 0.0516683π-0.0516683\pi
608608 −12.3737 + 12.3737i −0.501821 + 0.501821i
609609 0.111648 0.204727i 0.00452421 0.00829596i
610610 0 0
611611 4.62903 + 13.2290i 0.187270 + 0.535188i
612612 −5.89610 + 7.39348i −0.238336 + 0.298864i
613613 −23.5041 2.64828i −0.949323 0.106963i −0.376296 0.926499i 0.622802π-0.622802\pi
−0.573027 + 0.819536i 0.694231π0.694231\pi
614614 26.4797 + 12.7520i 1.06864 + 0.514628i
615615 0 0
616616 0.0699637 0.0877317i 0.00281892 0.00353481i
617617 17.3434 3.95851i 0.698218 0.159364i 0.141344 0.989961i 0.454858π-0.454858\pi
0.556874 + 0.830597i 0.312001π0.312001\pi
618618 −0.898406 0.564506i −0.0361392 0.0227078i
619619 −5.39810 + 47.9094i −0.216968 + 1.92564i 0.137360 + 0.990521i 0.456138π0.456138\pi
−0.354328 + 0.935121i 0.615290π0.615290\pi
620620 0 0
621621 1.72398 1.72398i 0.0691809 0.0691809i
622622 −29.6721 + 18.6442i −1.18974 + 0.747566i
623623 0.0486501 + 0.101023i 0.00194912 + 0.00404740i
624624 15.3914 + 5.38567i 0.616147 + 0.215599i
625625 0 0
626626 23.8226 + 23.8226i 0.952143 + 0.952143i
627627 3.88737 + 0.887268i 0.155247 + 0.0354341i
628628 20.8266 16.6087i 0.831072 0.662758i
629629 −20.5518 + 4.69082i −0.819455 + 0.187035i
630630 0 0
631631 24.3390 + 19.4097i 0.968921 + 0.772688i 0.973825 0.227300i 0.0729896π-0.0729896\pi
−0.00490424 + 0.999988i 0.501561π0.501561\pi
632632 −1.07921 + 3.08419i −0.0429285 + 0.122683i
633633 2.85874 + 8.16980i 0.113625 + 0.324721i
634634 −6.03608 + 4.81361i −0.239723 + 0.191173i
635635 0 0
636636 3.36720 1.17823i 0.133518 0.0467200i
637637 18.8142 + 18.8142i 0.745445 + 0.745445i
638638 −15.2179 + 2.67390i −0.602484 + 0.105861i
639639 19.1301i 0.756773i
640640 0 0
641641 −47.2768 + 5.32682i −1.86732 + 0.210397i −0.971993 0.235010i 0.924488π-0.924488\pi
−0.895328 + 0.445406i 0.853059π0.853059\pi
642642 −2.30164 + 20.4276i −0.0908384 + 0.806213i
643643 0.213571 0.0747317i 0.00842241 0.00294713i −0.326065 0.945348i 0.605723π-0.605723\pi
0.334487 + 0.942400i 0.391437π0.391437\pi
644644 0.0294284 0.0141720i 0.00115964 0.000558455i
645645 0 0
646646 15.0890 + 9.48106i 0.593670 + 0.373028i
647647 22.1007 35.1731i 0.868868 1.38280i −0.0543507 0.998522i 0.517309π-0.517309\pi
0.923219 0.384274i 0.125548π-0.125548\pi
648648 −2.46136 3.08644i −0.0966912 0.121247i
649649 −3.67044 5.84148i −0.144078 0.229298i
650650 0 0
651651 −0.0732253 0.0167132i −0.00286993 0.000655042i
652652 −13.0097 + 6.26516i −0.509501 + 0.245363i
653653 15.6929 7.55731i 0.614111 0.295740i −0.100853 0.994901i 0.532157π-0.532157\pi
0.714964 + 0.699161i 0.246443π0.246443\pi
654654 −26.5131 6.05145i −1.03675 0.236630i
655655 0 0
656656 7.12197 + 11.3346i 0.278066 + 0.442540i
657657 −3.09029 3.87510i −0.120564 0.151182i
658658 −0.175920 + 0.279976i −0.00685809 + 0.0109146i
659659 36.8444 + 23.1509i 1.43526 + 0.901831i 0.999999 + 0.00152434i 0.000485211π0.000485211\pi
0.435257 + 0.900306i 0.356658π0.356658\pi
660660 0 0
661661 −10.9914 + 5.29320i −0.427518 + 0.205882i −0.635254 0.772303i 0.719105π-0.719105\pi
0.207736 + 0.978185i 0.433390π0.433390\pi
662662 17.8339 6.24034i 0.693133 0.242538i
663663 1.27206 11.2898i 0.0494027 0.438461i
664664 15.9126 1.79292i 0.617528 0.0695787i
665665 0 0
666666 24.6599i 0.955552i
667667 2.77957 + 0.783855i 0.107626 + 0.0303510i
668668 −21.2059 21.2059i −0.820480 0.820480i
669669 −5.07547 + 1.77598i −0.196229 + 0.0686635i
670670 0 0
671671 9.71439 7.74697i 0.375020 0.299068i
672672 0.0869310 + 0.248434i 0.00335344 + 0.00958357i
673673 10.4404 29.8369i 0.402447 1.15013i −0.547253 0.836967i 0.684326π-0.684326\pi
0.949700 0.313161i 0.101388π-0.101388\pi
674674 −33.4489 26.6746i −1.28841 1.02747i
675675 0 0
676676 −1.73149 + 0.395202i −0.0665959 + 0.0152001i
677677 21.1289 16.8498i 0.812051 0.647589i −0.126794 0.991929i 0.540469π-0.540469\pi
0.938845 + 0.344340i 0.111897π0.111897\pi
678678 −4.01747 0.916961i −0.154290 0.0352157i
679679 −0.367977 0.367977i −0.0141217 0.0141217i
680680 0 0
681681 −8.41393 2.94416i −0.322422 0.112821i
682682 2.15927 + 4.48377i 0.0826827 + 0.171692i
683683 11.2393 7.06210i 0.430058 0.270224i −0.299561 0.954077i 0.596840π-0.596840\pi
0.729619 + 0.683854i 0.239697π0.239697\pi
684684 5.57909 5.57909i 0.213322 0.213322i
685685 0 0
686686 −0.140591 + 1.24778i −0.00536779 + 0.0476405i
687687 2.12877 + 1.33759i 0.0812175 + 0.0510323i
688688 12.3046 2.80845i 0.469110 0.107071i
689689 8.01935 10.0559i 0.305513 0.383101i
690690 0 0
691691 −17.7230 8.53497i −0.674216 0.324685i 0.0652598 0.997868i 0.479212π-0.479212\pi
−0.739476 + 0.673183i 0.764927π0.764927\pi
692692 −15.2275 1.71573i −0.578862 0.0652221i
693693 −0.112217 + 0.140716i −0.00426277 + 0.00534534i
694694 −18.8153 53.7711i −0.714219 2.04112i
695695 0 0
696696 −2.46942 + 6.05799i −0.0936033 + 0.229628i
697697 6.59502 6.59502i 0.249804 0.249804i
698698 −7.30030 + 15.1592i −0.276320 + 0.573785i
699699 1.33395 + 11.8391i 0.0504545 + 0.447796i
700700 0 0
701701 1.46305 3.03806i 0.0552588 0.114746i −0.871511 0.490376i 0.836859π-0.836859\pi
0.926770 + 0.375630i 0.122574π0.122574\pi
702702 −29.2695 10.2418i −1.10471 0.386553i
703703 17.4776 1.96925i 0.659180 0.0742717i
704704 0.849702 1.35229i 0.0320243 0.0509664i
705705 0 0
706706 −56.2964 6.34308i −2.11874 0.238725i
707707 −0.126710 + 0.555152i −0.00476541 + 0.0208786i
708708 4.54892 0.170959
709709 −0.0430267 + 0.188512i −0.00161590 + 0.00707973i −0.975729 0.218980i 0.929727π-0.929727\pi
0.974114 + 0.226059i 0.0725843π0.0725843\pi
710710 0 0
711711 1.73097 4.94683i 0.0649165 0.185521i
712712 −1.67357 2.66346i −0.0627195 0.0998175i
713713 0.930187i 0.0348358i
714714 0.226955 0.142605i 0.00849356 0.00533686i
715715 0 0
716716 0.535655 + 2.34686i 0.0200184 + 0.0877062i
717717 −3.42053 14.9863i −0.127742 0.559675i
718718 −4.15148 36.8454i −0.154932 1.37506i
719719 −10.8827 22.5981i −0.405856 0.842768i −0.999282 0.0378799i 0.987940π-0.987940\pi
0.593427 0.804888i 0.297775π-0.297775\pi
720720 0 0
721721 −0.0212978 0.0267066i −0.000793171 0.000994605i
722722 15.0229 + 11.9804i 0.559094 + 0.445863i
723723 −14.5832 7.02291i −0.542356 0.261185i
724724 −15.8018 −0.587269
725725 0 0
726726 13.1128 0.486663
727727 13.0524 + 6.28573i 0.484088 + 0.233125i 0.659978 0.751285i 0.270566π-0.270566\pi
−0.175889 + 0.984410i 0.556280π0.556280\pi
728728 0.208566 + 0.166326i 0.00772996 + 0.00616444i
729729 −3.41554 4.28295i −0.126501 0.158628i
730730 0 0
731731 −3.81539 7.92274i −0.141117 0.293033i
732732 0.917298 + 8.14124i 0.0339043 + 0.300909i
733733 −4.89262 21.4360i −0.180713 0.791755i −0.981292 0.192528i 0.938332π-0.938332\pi
0.800579 0.599228i 0.204526π-0.204526\pi
734734 12.0262 + 52.6903i 0.443896 + 1.94484i
735735 0 0
736736 −2.76005 + 1.73425i −0.101737 + 0.0639255i
737737 13.6608i 0.503202i
738738 −5.80474 9.23819i −0.213675 0.340062i
739739 −12.6498 + 36.1512i −0.465332 + 1.32984i 0.437257 + 0.899337i 0.355950π0.355950\pi
−0.902588 + 0.430505i 0.858336π0.858336\pi
740740 0 0
741741 −2.10931 + 9.24151i −0.0774876 + 0.339495i
742742 0.303444 0.0111398
743743 −5.87833 + 25.7547i −0.215655 + 0.944847i 0.744992 + 0.667074i 0.232453π0.232453\pi
−0.960647 + 0.277773i 0.910404π0.910404\pi
744744 2.09384 + 0.235919i 0.0767640 + 0.00864922i
745745 0 0
746746 −35.3169 + 56.2066i −1.29304 + 2.05787i
747747 −25.5227 + 2.87572i −0.933827 + 0.105217i
748748 −6.34463 2.22008i −0.231982 0.0811742i
749749 −0.287147 + 0.596267i −0.0104921 + 0.0217871i
750750 0 0
751751 2.42708 + 21.5409i 0.0885654 + 0.786039i 0.956971 + 0.290184i 0.0937167π0.0937167\pi
−0.868405 + 0.495855i 0.834855π0.834855\pi
752752 7.92045 16.4470i 0.288829 0.599760i
753753 −2.43274 + 2.43274i −0.0886539 + 0.0886539i
754754 −6.35669 36.1778i −0.231497 1.31752i
755755 0 0
756756 −0.0914520 0.261355i −0.00332608 0.00950538i
757757 −12.2870 + 15.4075i −0.446580 + 0.559993i −0.953264 0.302138i 0.902300π-0.902300\pi
0.506684 + 0.862132i 0.330871π0.330871\pi
758758 43.1950 + 4.86691i 1.56891 + 0.176774i
759759 0.669195 + 0.322267i 0.0242902 + 0.0116976i
760760 0 0
761761 11.8638 14.8768i 0.430063 0.539282i −0.518831 0.854877i 0.673633π-0.673633\pi
0.948894 + 0.315595i 0.102204π0.102204\pi
762762 18.0891 4.12872i 0.655299 0.149568i
763763 −0.741319 0.465802i −0.0268376 0.0168632i
764764 −1.81618 + 16.1191i −0.0657072 + 0.583167i
765765 0 0
766766 −6.29154 + 6.29154i −0.227323 + 0.227323i
767767 13.8870 8.72580i 0.501432 0.315070i
768768 −7.73616 16.0643i −0.279155 0.579670i
769769 24.2753 + 8.49430i 0.875390 + 0.306312i 0.730317 0.683109i 0.239372π-0.239372\pi
0.145073 + 0.989421i 0.453658π0.453658\pi
770770 0 0
771771 −15.0785 15.0785i −0.543039 0.543039i
772772 −13.5119 3.08399i −0.486302 0.110995i
773773 5.38261 4.29249i 0.193599 0.154390i −0.521893 0.853011i 0.674774π-0.674774\pi
0.715492 + 0.698621i 0.246203π0.246203\pi
774774 −10.0289 + 2.28902i −0.360480 + 0.0822771i
775775 0 0
776776 11.4142 + 9.10249i 0.409745 + 0.326760i
777777 0.0873735 0.249699i 0.00313451 0.00895791i
778778 −19.4684 55.6374i −0.697975 1.99470i
779779 −6.08397 + 4.85181i −0.217981 + 0.173834i
780780 0 0
781781 12.8347 4.49106i 0.459263 0.160703i
782782 2.34727 + 2.34727i 0.0839383 + 0.0839383i
783783 9.24139 22.6710i 0.330260 0.810195i
784784 34.6552i 1.23768i
785785 0 0
786786 27.7285 3.12425i 0.989042 0.111438i
787787 4.01476 35.6320i 0.143111 1.27014i −0.692740 0.721187i 0.743597π-0.743597\pi
0.835851 0.548957i 0.184975π-0.184975\pi
788788 −26.4116 + 9.24182i −0.940874 + 0.329226i
789789 6.33651 3.05150i 0.225586 0.108636i
790790 0 0
791791 −0.112330 0.0705817i −0.00399400 0.00250960i
792792 2.68634 4.27529i 0.0954550 0.151916i
793793 18.4170 + 23.0942i 0.654006 + 0.820098i
794794 19.9742 + 31.7888i 0.708859 + 1.12814i
795795 0 0
796796 2.60736 + 0.595114i 0.0924156 + 0.0210933i
797797 39.7334 19.1346i 1.40743 0.677782i 0.432775 0.901502i 0.357534π-0.357534\pi
0.974654 + 0.223720i 0.0718200π0.0718200\pi
798798 −0.201488 + 0.0970316i −0.00713261 + 0.00343488i
799799 −12.3999 2.83019i −0.438677 0.100125i
800800 0 0
801801 2.68428 + 4.27201i 0.0948445 + 0.150944i
802802 14.5127 + 18.1984i 0.512461 + 0.642606i
803803 1.87439 2.98307i 0.0661457 0.105270i
804804 7.62686 + 4.79227i 0.268978 + 0.169010i
805805 0 0
806806 −10.6593 + 5.13326i −0.375459 + 0.180811i
807807 6.50266 2.27538i 0.228905 0.0800972i
808808 1.78860 15.8743i 0.0629229 0.558456i
809809 −27.0462 + 3.04738i −0.950895 + 0.107140i −0.573765 0.819020i 0.694518π-0.694518\pi
−0.377130 + 0.926160i 0.623089π0.623089\pi
810810 0 0
811811 15.8296i 0.555851i −0.960603 0.277926i 0.910353π-0.910353\pi
0.960603 0.277926i 0.0896469π-0.0896469\pi
812812 0.217174 0.245790i 0.00762132 0.00862554i
813813 15.6265 + 15.6265i 0.548045 + 0.548045i
814814 −16.5448 + 5.78928i −0.579895 + 0.202914i
815815 0 0
816816 −11.5693 + 9.22623i −0.405007 + 0.322983i
817817 2.42320 + 6.92511i 0.0847770 + 0.242279i
818818 −1.54649 + 4.41961i −0.0540717 + 0.154528i
819819 −0.334525 0.266775i −0.0116892 0.00932186i
820820 0 0
821821 −9.19783 + 2.09935i −0.321007 + 0.0732677i −0.379988 0.924991i 0.624072π-0.624072\pi
0.0589814 + 0.998259i 0.481215π0.481215\pi
822822 11.1108 8.86056i 0.387533 0.309048i
823823 −38.7440 8.84307i −1.35053 0.308250i −0.514763 0.857332i 0.672120π-0.672120\pi
−0.835768 + 0.549083i 0.814977π0.814977\pi
824824 0.677618 + 0.677618i 0.0236059 + 0.0236059i
825825 0 0
826826 0.365221 + 0.127796i 0.0127077 + 0.00444660i
827827 19.2297 + 39.9309i 0.668683 + 1.38853i 0.908570 + 0.417734i 0.137175π0.137175\pi
−0.239887 + 0.970801i 0.577110π0.577110\pi
828828 1.24446 0.781944i 0.0432479 0.0271744i
829829 17.1511 17.1511i 0.595681 0.595681i −0.343479 0.939160i 0.611606π-0.611606\pi
0.939160 + 0.343479i 0.111606π0.111606\pi
830830 0 0
831831 −1.77408 + 15.7454i −0.0615420 + 0.546200i
832832 3.21482 + 2.02001i 0.111454 + 0.0700312i
833833 −23.5402 + 5.37289i −0.815618 + 0.186160i
834834 18.0676 22.6560i 0.625629 0.784514i
835835 0 0
836836 5.05290 + 2.43335i 0.174758 + 0.0841591i
837837 −7.83584 0.882887i −0.270846 0.0305170i
838838 19.3355 24.2459i 0.667932 0.837561i
839839 −11.9236 34.0758i −0.411650 1.17643i −0.944012 0.329911i 0.892981π-0.892981\pi
0.532362 0.846517i 0.321305π-0.321305\pi
840840 0 0
841841 28.7793 3.57135i 0.992388 0.123150i
842842 12.3724 12.3724i 0.426381 0.426381i
843843 8.99045 18.6689i 0.309648 0.642990i
844844 1.36308 + 12.0976i 0.0469190 + 0.416418i
845845 0 0
846846 −6.45553 + 13.4051i −0.221946 + 0.460875i
847847 0.398465 + 0.139429i 0.0136914 + 0.00479083i
848848 −16.6471 + 1.87567i −0.571663 + 0.0644109i
849849 14.4675 23.0249i 0.496524 0.790213i
850850 0 0
851851 3.25567 + 0.366826i 0.111603 + 0.0125746i
852852 −1.99511 + 8.74114i −0.0683513 + 0.299467i
853853 −6.64060 −0.227370 −0.113685 0.993517i 0.536265π-0.536265\pi
−0.113685 + 0.993517i 0.536265π0.536265\pi
854854 −0.155071 + 0.679409i −0.00530641 + 0.0232489i
855855 0 0
856856 6.13207 17.5244i 0.209590 0.598973i
857857 4.11164 + 6.54364i 0.140451 + 0.223527i 0.909541 0.415614i 0.136433π-0.136433\pi
−0.769090 + 0.639140i 0.779290π0.779290\pi
858858 9.44698i 0.322514i
859859 −24.3070 + 15.2731i −0.829346 + 0.521113i −0.878536 0.477677i 0.841479π-0.841479\pi
0.0491898 + 0.998789i 0.484336π0.484336\pi
860860 0 0
861861 0.0260449 + 0.114110i 0.000887608 + 0.00388887i
862862 6.86396 + 30.0730i 0.233787 + 1.02429i
863863 −0.144916 1.28617i −0.00493300 0.0437816i 0.991005 0.133828i 0.0427270π-0.0427270\pi
−0.995938 + 0.0900465i 0.971298π0.971298\pi
864864 11.9896 + 24.8966i 0.407893 + 0.846999i
865865 0 0
866866 −6.15831 7.72228i −0.209268 0.262414i
867867 −3.44823 2.74987i −0.117108 0.0933905i
868868 −0.0951799 0.0458362i −0.00323062 0.00155578i
869869 3.72530 0.126372
870870 0 0
871871 32.4760 1.10041
872872 22.1293 + 10.6569i 0.749393 + 0.360888i
873873 −18.3075 14.5998i −0.619616 0.494127i
874874 −1.72683 2.16538i −0.0584110 0.0732451i
875875 0 0
876876 1.00791 + 2.09295i 0.0340542 + 0.0707143i
877877 −5.07240 45.0188i −0.171283 1.52018i −0.725743 0.687966i 0.758504π-0.758504\pi
0.554460 0.832210i 0.312925π-0.312925\pi
878878 −1.56488 6.85620i −0.0528122 0.231385i
879879 −1.17481 5.14717i −0.0396253 0.173610i
880880 0 0
881881 −29.8952 + 18.7844i −1.00720 + 0.632863i −0.931300 0.364252i 0.881325π-0.881325\pi
−0.0758960 + 0.997116i 0.524182π0.524182\pi
882882 28.2456i 0.951078i
883883 15.5925 + 24.8153i 0.524729 + 0.835101i 0.998974 0.0452919i 0.0144218π-0.0144218\pi
−0.474245 + 0.880393i 0.657279π0.657279\pi
884884 5.27783 15.0832i 0.177513 0.507302i
885885 0 0
886886 12.7659 55.9312i 0.428880 1.87904i
887887 −31.6025 −1.06111 −0.530555 0.847651i 0.678016π-0.678016\pi
−0.530555 + 0.847651i 0.678016π0.678016\pi
888888 −1.65145 + 7.23546i −0.0554189 + 0.242806i
889889 0.593581 + 0.0668805i 0.0199081 + 0.00224310i
890890 0 0
891891 −2.39453 + 3.81087i −0.0802198 + 0.127669i
892892 −7.51563 + 0.846808i −0.251642 + 0.0283532i
893893 10.0163 + 3.50485i 0.335182 + 0.117285i
894894 −7.66976 + 15.9264i −0.256515 + 0.532659i
895895 0 0
896896 −0.0580365 0.515088i −0.00193886 0.0172079i
897897 −0.766131 + 1.59089i −0.0255804 + 0.0531182i
898898 −11.2733 + 11.2733i −0.376194 + 0.376194i
899899 −3.62302 8.60929i −0.120835 0.287136i
900900 0 0
901901 3.85502 + 11.0170i 0.128429 + 0.367030i
902902 4.83533 6.06331i 0.160999 0.201886i
903903 0.109660 + 0.0123557i 0.00364924 + 0.000411171i
904904 3.35319 + 1.61481i 0.111526 + 0.0537079i
905905 0 0
906906 16.4197 20.5897i 0.545508 0.684046i
907907 5.78318 1.31997i 0.192027 0.0438290i −0.125426 0.992103i 0.540030π-0.540030\pi
0.317453 + 0.948274i 0.397172π0.397172\pi
908908 −10.6162 6.67060i −0.352311 0.221372i
909909 −2.86880 + 25.4613i −0.0951520 + 0.844497i
910910 0 0
911911 −3.72458 + 3.72458i −0.123401 + 0.123401i −0.766110 0.642709i 0.777810π-0.777810\pi
0.642709 + 0.766110i 0.277810π0.277810\pi
912912 10.4539 6.56864i 0.346164 0.217509i
913913 −7.92120 16.4486i −0.262154 0.544368i
914914 51.9942 + 18.1936i 1.71982 + 0.601789i
915915 0 0
916916 2.50045 + 2.50045i 0.0826171 + 0.0826171i
917917 0.875815 + 0.199899i 0.0289220 + 0.00660125i
918918 22.0012 17.5454i 0.726148 0.579084i
919919 −33.9679 + 7.75296i −1.12050 + 0.255747i −0.742359 0.670002i 0.766293π-0.766293\pi
−0.378140 + 0.925749i 0.623436π0.623436\pi
920920 0 0
921921 −11.0919 8.84547i −0.365489 0.291468i
922922 −3.63510 + 10.3885i −0.119716 + 0.342128i
923923 10.6767 + 30.5122i 0.351427 + 1.00432i
924924 0.0659510 0.0525942i 0.00216963 0.00173022i
925925 0 0
926926 20.3146 7.10840i 0.667580 0.233596i
927927 −1.08685 1.08685i −0.0356969 0.0356969i
928928 −18.7907 + 26.8015i −0.616834 + 0.879803i
929929 2.84350i 0.0932921i 0.998911 + 0.0466460i 0.0148533π0.0148533\pi
−0.998911 + 0.0466460i 0.985147π0.985147\pi
930930 0 0
931931 20.0189 2.25559i 0.656093 0.0739240i
932932 −1.87623 + 16.6520i −0.0614579 + 0.545454i
933933 15.9666 5.58696i 0.522723 0.182909i
934934 −9.23651 + 4.44807i −0.302228 + 0.145545i
935935 0 0
936936 10.1637 + 6.38628i 0.332211 + 0.208742i
937937 −17.6180 + 28.0389i −0.575555 + 0.915990i 0.424390 + 0.905480i 0.360489π0.360489\pi
−0.999945 + 0.0105107i 0.996654π0.996654\pi
938938 0.477707 + 0.599025i 0.0155977 + 0.0195589i
939939 −8.65226 13.7700i −0.282356 0.449367i
940940 0 0
941941 −36.8079 8.40116i −1.19990 0.273870i −0.424554 0.905403i 0.639569π-0.639569\pi
−0.775349 + 0.631533i 0.782426π0.782426\pi
942942 −30.6095 + 14.7408i −0.997313 + 0.480281i
943943 −1.30600 + 0.628936i −0.0425292 + 0.0204810i
944944 −20.8261 4.75341i −0.677831 0.154710i
945945 0 0
946946 −3.89017 6.19117i −0.126480 0.201292i
947947 −5.12052 6.42093i −0.166394 0.208652i 0.691642 0.722240i 0.256887π-0.256887\pi
−0.858037 + 0.513588i 0.828316π0.828316\pi
948948 −1.30685 + 2.07984i −0.0424446 + 0.0675501i
949949 7.09170 + 4.45601i 0.230206 + 0.144648i
950950 0 0
951951 3.35768 1.61697i 0.108880 0.0524339i
952952 −0.228499 + 0.0799553i −0.00740570 + 0.00259137i
953953 −2.26419 + 20.0953i −0.0733444 + 0.650950i 0.902226 + 0.431263i 0.141932π0.141932\pi
−0.975571 + 0.219687i 0.929497π0.929497\pi
954954 13.5681 1.52876i 0.439285 0.0494955i
955955 0 0
956956 21.6207i 0.699263i
957957 7.44891 + 0.376251i 0.240789 + 0.0121625i
958958 0.688219 + 0.688219i 0.0222353 + 0.0222353i
959959 0.431842 0.151108i 0.0139449 0.00487953i
960960 0 0
961961 21.8846 17.4524i 0.705956 0.562981i
962962 −13.7629 39.3322i −0.443735 1.26812i
963963 −9.83541 + 28.1080i −0.316942 + 0.905767i
964964 −17.7993 14.1945i −0.573278 0.457174i
965965 0 0
966966 −0.0406136 + 0.00926979i −0.00130672 + 0.000298251i
967967 −9.18359 + 7.32367i −0.295324 + 0.235513i −0.759931 0.650004i 0.774767π-0.774767\pi
0.464606 + 0.885517i 0.346196π0.346196\pi
968968 −11.5462 2.63534i −0.371109 0.0847031i
969969 −6.08264 6.08264i −0.195402 0.195402i
970970 0 0
971971 25.2257 + 8.82685i 0.809531 + 0.283267i 0.703135 0.711057i 0.251783π-0.251783\pi
0.106396 + 0.994324i 0.466069π0.466069\pi
972972 −8.49483 17.6397i −0.272472 0.565794i
973973 0.789927 0.496344i 0.0253239 0.0159121i
974974 47.1962 47.1962i 1.51226 1.51226i
975975 0 0
976976 4.30761 38.2311i 0.137883 1.22375i
977977 12.8225 + 8.05689i 0.410227 + 0.257763i 0.721299 0.692624i 0.243545π-0.243545\pi
−0.311072 + 0.950386i 0.600688π0.600688\pi
978978 17.9545 4.09799i 0.574121 0.131039i
979979 −2.23600 + 2.80385i −0.0714629 + 0.0896116i
980980 0 0
981981 −35.4939 17.0929i −1.13323 0.545736i
982982 −32.5305 3.66531i −1.03809 0.116965i
983983 −5.50262 + 6.90007i −0.175506 + 0.220078i −0.861802 0.507244i 0.830664π-0.830664\pi
0.686296 + 0.727323i 0.259236π0.259236\pi
984984 −1.08450 3.09931i −0.0345724 0.0988024i
985985 0 0
986986 30.8675 + 12.5826i 0.983022 + 0.400710i
987987 0.112863 0.112863i 0.00359246 0.00359246i
988988 −5.78483 + 12.0123i −0.184040 + 0.382163i
989989 0.153020 + 1.35809i 0.00486575 + 0.0431847i
990990 0 0
991991 11.0604 22.9671i 0.351345 0.729575i −0.648145 0.761517i 0.724455π-0.724455\pi
0.999490 + 0.0319421i 0.0101692π0.0101692\pi
992992 9.95110 + 3.48204i 0.315948 + 0.110555i
993993 −9.06307 + 1.02116i −0.287608 + 0.0324056i
994994 −0.405753 + 0.645753i −0.0128697 + 0.0204820i
995995 0 0
996996 11.9621 + 1.34780i 0.379032 + 0.0427067i
997997 3.55020 15.5544i 0.112436 0.492614i −0.887083 0.461609i 0.847272π-0.847272\pi
0.999519 0.0310044i 0.00987059π-0.00987059\pi
998998 16.4345 0.520225
999999 6.18025 27.0774i 0.195534 0.856692i
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 725.2.y.a.18.2 120
5.2 odd 4 725.2.bd.a.482.9 yes 120
5.3 odd 4 725.2.bd.a.482.2 yes 120
5.4 even 2 inner 725.2.y.a.18.9 yes 120
29.21 odd 28 725.2.bd.a.543.9 yes 120
145.79 odd 28 725.2.bd.a.543.2 yes 120
145.108 even 28 inner 725.2.y.a.282.9 yes 120
145.137 even 28 inner 725.2.y.a.282.2 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
725.2.y.a.18.2 120 1.1 even 1 trivial
725.2.y.a.18.9 yes 120 5.4 even 2 inner
725.2.y.a.282.2 yes 120 145.137 even 28 inner
725.2.y.a.282.9 yes 120 145.108 even 28 inner
725.2.bd.a.482.2 yes 120 5.3 odd 4
725.2.bd.a.482.9 yes 120 5.2 odd 4
725.2.bd.a.543.2 yes 120 145.79 odd 28
725.2.bd.a.543.9 yes 120 29.21 odd 28