Properties

Label 684.2.bs.a.23.4
Level 684684
Weight 22
Character 684.23
Analytic conductor 5.4625.462
Analytic rank 00
Dimension 696696
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(23,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 15, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 684=223219 684 = 2^{2} \cdot 3^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 684.bs (of order 1818, degree 66, 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: 5.461767498265.46176749826
Analytic rank: 00
Dimension: 696696
Relative dimension: 116116 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 23.4
Character χ\chi == 684.23
Dual form 684.2.bs.a.119.4

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+(1.40831+0.129087i)q2+(0.3562161.69503i)q3+(1.966670.363589i)q4+(1.53473+0.270614i)q5+(0.720469+2.34114i)q60.923751iq7+(2.72275+0.765918i)q8+(2.74622+1.20759i)q9+(2.126440.579223i)q10+(1.38916+2.40610i)q11+(1.316853.20404i)q12+(5.07753+4.26056i)q13+(0.119244+1.30093i)q14+(1.00539+2.50501i)q15+(3.735611.43012i)q16+(0.788778+2.16715i)q17+(3.711642.05516i)q18+(3.664242.36079i)q19+(2.91992+1.09022i)q20+(1.56578+0.329055i)q21+(1.645783.56786i)q22+(8.659253.15171i)q23+(2.26814+4.34230i)q24+(2.41630+0.879461i)q25+(7.700725.34474i)q26+(3.02515+4.22475i)q27+(0.3358661.81672i)q28+(3.100173.69463i)q29+(1.739273.39804i)q30+(3.56920+2.06068i)q31+(5.07628+2.49627i)q32+(4.57324+1.49757i)q33+(0.8310933.15384i)q34+(0.249980+1.41771i)q35+(4.96185+3.37343i)q365.89377q37+(4.85564+3.79773i)q38+(5.4130510.1242i)q39+(3.971421.91229i)q40+(0.1799220.494332i)q41+(2.162630.665534i)q42+(2.048485.62815i)q43+(1.85720+5.23710i)q44+(3.887912.59649i)q45+(11.7881+5.55638i)q46+(2.45486+2.05987i)q47+(3.754785.82251i)q48+6.14668q49+(3.289371.55047i)q50+(3.95435+0.565024i)q51+(11.5349+6.53298i)q52+(3.83515+4.57056i)q53+(4.805705.55925i)q54+(1.480864.06864i)q55+(0.707518+2.51514i)q56+(5.306865.37004i)q57+(3.88907+5.60338i)q58+(2.016391.69196i)q59+(2.88808+4.56098i)q60+(2.4170613.7078i)q61+(4.760543.36282i)q62+(1.11551+2.53682i)q63+(6.826744.17081i)q64+(8.945615.16475i)q65+(6.633861.51870i)q66+(14.1422+2.49365i)q67+(0.763316+4.54887i)q68+(8.4267913.5550i)q69+(0.5350571.96430i)q70+(7.018285.88904i)q71+(6.552355.39135i)q72+(1.56692+8.88643i)q73+(8.300260.760810i)q74+(2.35143+3.78241i)q75+(6.348015.97518i)q76+(2.22264+1.28324i)q77+(6.31634+14.9568i)q78+(6.78987+8.09186i)q79+(5.34613+3.20576i)q80+(6.083456.63262i)q81+(0.189574+0.719399i)q824.95989q83+(2.95974+1.21645i)q84+(0.6240993.53944i)q85+(2.15837+8.19062i)q86+(7.366833.93877i)q87+(1.939477.61520i)q88+(4.70122+0.828952i)q89+(5.14021+4.15855i)q90+(3.935694.69038i)q91+(15.88409.34679i)q92+(4.76432+5.31584i)q93+(3.723102.58404i)q94+(4.98476+4.61477i)q95+(6.03950+7.71521i)q96+(0.862927+4.89390i)q97+(8.65644+0.793458i)q98+(0.9093618.28522i)q99+O(q100)q+(-1.40831 + 0.129087i) q^{2} +(-0.356216 - 1.69503i) q^{3} +(1.96667 - 0.363589i) q^{4} +(-1.53473 + 0.270614i) q^{5} +(0.720469 + 2.34114i) q^{6} -0.923751i q^{7} +(-2.72275 + 0.765918i) q^{8} +(-2.74622 + 1.20759i) q^{9} +(2.12644 - 0.579223i) q^{10} +(-1.38916 + 2.40610i) q^{11} +(-1.31685 - 3.20404i) q^{12} +(5.07753 + 4.26056i) q^{13} +(0.119244 + 1.30093i) q^{14} +(1.00539 + 2.50501i) q^{15} +(3.73561 - 1.43012i) q^{16} +(-0.788778 + 2.16715i) q^{17} +(3.71164 - 2.05516i) q^{18} +(3.66424 - 2.36079i) q^{19} +(-2.91992 + 1.09022i) q^{20} +(-1.56578 + 0.329055i) q^{21} +(1.64578 - 3.56786i) q^{22} +(8.65925 - 3.15171i) q^{23} +(2.26814 + 4.34230i) q^{24} +(-2.41630 + 0.879461i) q^{25} +(-7.70072 - 5.34474i) q^{26} +(3.02515 + 4.22475i) q^{27} +(-0.335866 - 1.81672i) q^{28} +(3.10017 - 3.69463i) q^{29} +(-1.73927 - 3.39804i) q^{30} +(-3.56920 + 2.06068i) q^{31} +(-5.07628 + 2.49627i) q^{32} +(4.57324 + 1.49757i) q^{33} +(0.831093 - 3.15384i) q^{34} +(0.249980 + 1.41771i) q^{35} +(-4.96185 + 3.37343i) q^{36} -5.89377 q^{37} +(-4.85564 + 3.79773i) q^{38} +(5.41305 - 10.1242i) q^{39} +(3.97142 - 1.91229i) q^{40} +(0.179922 - 0.494332i) q^{41} +(2.16263 - 0.665534i) q^{42} +(2.04848 - 5.62815i) q^{43} +(-1.85720 + 5.23710i) q^{44} +(3.88791 - 2.59649i) q^{45} +(-11.7881 + 5.55638i) q^{46} +(2.45486 + 2.05987i) q^{47} +(-3.75478 - 5.82251i) q^{48} +6.14668 q^{49} +(3.28937 - 1.55047i) q^{50} +(3.95435 + 0.565024i) q^{51} +(11.5349 + 6.53298i) q^{52} +(-3.83515 + 4.57056i) q^{53} +(-4.80570 - 5.55925i) q^{54} +(1.48086 - 4.06864i) q^{55} +(0.707518 + 2.51514i) q^{56} +(-5.30686 - 5.37004i) q^{57} +(-3.88907 + 5.60338i) q^{58} +(2.01639 - 1.69196i) q^{59} +(2.88808 + 4.56098i) q^{60} +(2.41706 - 13.7078i) q^{61} +(4.76054 - 3.36282i) q^{62} +(1.11551 + 2.53682i) q^{63} +(6.82674 - 4.17081i) q^{64} +(-8.94561 - 5.16475i) q^{65} +(-6.63386 - 1.51870i) q^{66} +(14.1422 + 2.49365i) q^{67} +(-0.763316 + 4.54887i) q^{68} +(-8.42679 - 13.5550i) q^{69} +(-0.535057 - 1.96430i) q^{70} +(7.01828 - 5.88904i) q^{71} +(6.55235 - 5.39135i) q^{72} +(1.56692 + 8.88643i) q^{73} +(8.30026 - 0.760810i) q^{74} +(2.35143 + 3.78241i) q^{75} +(6.34801 - 5.97518i) q^{76} +(2.22264 + 1.28324i) q^{77} +(-6.31634 + 14.9568i) q^{78} +(6.78987 + 8.09186i) q^{79} +(-5.34613 + 3.20576i) q^{80} +(6.08345 - 6.63262i) q^{81} +(-0.189574 + 0.719399i) q^{82} -4.95989 q^{83} +(-2.95974 + 1.21645i) q^{84} +(0.624099 - 3.53944i) q^{85} +(-2.15837 + 8.19062i) q^{86} +(-7.36683 - 3.93877i) q^{87} +(1.93947 - 7.61520i) q^{88} +(4.70122 + 0.828952i) q^{89} +(-5.14021 + 4.15855i) q^{90} +(3.93569 - 4.69038i) q^{91} +(15.8840 - 9.34679i) q^{92} +(4.76432 + 5.31584i) q^{93} +(-3.72310 - 2.58404i) q^{94} +(-4.98476 + 4.61477i) q^{95} +(6.03950 + 7.71521i) q^{96} +(0.862927 + 4.89390i) q^{97} +(-8.65644 + 0.793458i) q^{98} +(0.909361 - 8.28522i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 696q9q23q418q56q618q912q103q126q139q143q1612q1818q20+24q21+9q22+45q246q25+72q2618q29++45q98+O(q100) 696 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 18 q^{9} - 12 q^{10} - 3 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 12 q^{18} - 18 q^{20} + 24 q^{21} + 9 q^{22} + 45 q^{24} - 6 q^{25} + 72 q^{26} - 18 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/684Z)×\left(\mathbb{Z}/684\mathbb{Z}\right)^\times.

nn 325325 343343 533533
χ(n)\chi(n) e(19)e\left(\frac{1}{9}\right) 1-1 e(56)e\left(\frac{5}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.40831 + 0.129087i −0.995825 + 0.0912784i
33 −0.356216 1.69503i −0.205662 0.978623i
44 1.96667 0.363589i 0.983337 0.181795i
55 −1.53473 + 0.270614i −0.686352 + 0.121022i −0.505940 0.862569i 0.668854π-0.668854\pi
−0.180412 + 0.983591i 0.557743π0.557743\pi
66 0.720469 + 2.34114i 0.294130 + 0.955765i
77 0.923751i 0.349145i −0.984644 0.174573i 0.944146π-0.944146\pi
0.984644 0.174573i 0.0558544π-0.0558544\pi
88 −2.72275 + 0.765918i −0.962638 + 0.270793i
99 −2.74622 + 1.20759i −0.915407 + 0.402530i
1010 2.12644 0.579223i 0.672440 0.183166i
1111 −1.38916 + 2.40610i −0.418848 + 0.725467i −0.995824 0.0912948i 0.970899π-0.970899\pi
0.576976 + 0.816761i 0.304233π0.304233\pi
1212 −1.31685 3.20404i −0.380143 0.924928i
1313 5.07753 + 4.26056i 1.40825 + 1.18167i 0.957292 + 0.289122i 0.0933634π0.0933634\pi
0.450962 + 0.892543i 0.351081π0.351081\pi
1414 0.119244 + 1.30093i 0.0318694 + 0.347688i
1515 1.00539 + 2.50501i 0.259592 + 0.646790i
1616 3.73561 1.43012i 0.933901 0.357531i
1717 −0.788778 + 2.16715i −0.191307 + 0.525611i −0.997848 0.0655666i 0.979115π-0.979115\pi
0.806541 + 0.591178i 0.201337π0.201337\pi
1818 3.71164 2.05516i 0.874843 0.484407i
1919 3.66424 2.36079i 0.840635 0.541602i
2020 −2.91992 + 1.09022i −0.652914 + 0.243781i
2121 −1.56578 + 0.329055i −0.341681 + 0.0718057i
2222 1.64578 3.56786i 0.350880 0.760670i
2323 8.65925 3.15171i 1.80558 0.657177i 0.807881 0.589346i 0.200614π-0.200614\pi
0.997697 0.0678308i 0.0216078π-0.0216078\pi
2424 2.26814 + 4.34230i 0.462982 + 0.886368i
2525 −2.41630 + 0.879461i −0.483260 + 0.175892i
2626 −7.70072 5.34474i −1.51024 1.04819i
2727 3.02515 + 4.22475i 0.582190 + 0.813053i
2828 −0.335866 1.81672i −0.0634727 0.343327i
2929 3.10017 3.69463i 0.575686 0.686076i −0.397101 0.917775i 0.629984π-0.629984\pi
0.972788 + 0.231698i 0.0744283π0.0744283\pi
3030 −1.73927 3.39804i −0.317546 0.620395i
3131 −3.56920 + 2.06068i −0.641048 + 0.370109i −0.785018 0.619473i 0.787346π-0.787346\pi
0.143970 + 0.989582i 0.454013π0.454013\pi
3232 −5.07628 + 2.49627i −0.897368 + 0.441283i
3333 4.57324 + 1.49757i 0.796099 + 0.260694i
3434 0.831093 3.15384i 0.142531 0.540879i
3535 0.249980 + 1.41771i 0.0422544 + 0.239636i
3636 −4.96185 + 3.37343i −0.826975 + 0.562239i
3737 −5.89377 −0.968930 −0.484465 0.874811i 0.660986π-0.660986\pi
−0.484465 + 0.874811i 0.660986π0.660986\pi
3838 −4.85564 + 3.79773i −0.787690 + 0.616072i
3939 5.41305 10.1242i 0.866781 1.62117i
4040 3.97142 1.91229i 0.627936 0.302360i
4141 0.179922 0.494332i 0.0280991 0.0772018i −0.924850 0.380332i 0.875810π-0.875810\pi
0.952949 + 0.303131i 0.0980318π0.0980318\pi
4242 2.16263 0.665534i 0.333701 0.102694i
4343 2.04848 5.62815i 0.312390 0.858285i −0.679783 0.733414i 0.737926π-0.737926\pi
0.992173 0.124872i 0.0398519π-0.0398519\pi
4444 −1.85720 + 5.23710i −0.279983 + 0.789522i
4545 3.88791 2.59649i 0.579576 0.387062i
4646 −11.7881 + 5.55638i −1.73805 + 0.819243i
4747 2.45486 + 2.05987i 0.358078 + 0.300463i 0.804024 0.594597i 0.202688π-0.202688\pi
−0.445946 + 0.895060i 0.647133π0.647133\pi
4848 −3.75478 5.82251i −0.541955 0.840407i
4949 6.14668 0.878098
5050 3.28937 1.55047i 0.465187 0.219269i
5151 3.95435 + 0.565024i 0.553719 + 0.0791192i
5252 11.5349 + 6.53298i 1.59961 + 0.905962i
5353 −3.83515 + 4.57056i −0.526799 + 0.627814i −0.962174 0.272435i 0.912171π-0.912171\pi
0.435375 + 0.900249i 0.356616π0.356616\pi
5454 −4.80570 5.55925i −0.653973 0.756518i
5555 1.48086 4.06864i 0.199680 0.548616i
5656 0.707518 + 2.51514i 0.0945461 + 0.336100i
5757 −5.30686 5.37004i −0.702910 0.711279i
5858 −3.88907 + 5.60338i −0.510659 + 0.735760i
5959 2.01639 1.69196i 0.262512 0.220274i −0.502026 0.864853i 0.667412π-0.667412\pi
0.764538 + 0.644579i 0.222967π0.222967\pi
6060 2.88808 + 4.56098i 0.372849 + 0.588820i
6161 2.41706 13.7078i 0.309473 1.75511i −0.292190 0.956360i 0.594384π-0.594384\pi
0.601663 0.798750i 0.294505π-0.294505\pi
6262 4.76054 3.36282i 0.604589 0.427078i
6363 1.11551 + 2.53682i 0.140542 + 0.319610i
6464 6.82674 4.17081i 0.853342 0.521351i
6565 −8.94561 5.16475i −1.10957 0.640608i
6666 −6.63386 1.51870i −0.816572 0.186939i
6767 14.1422 + 2.49365i 1.72774 + 0.304647i 0.947244 0.320512i 0.103855π-0.103855\pi
0.780497 + 0.625160i 0.214966π0.214966\pi
6868 −0.763316 + 4.54887i −0.0925657 + 0.551631i
6969 −8.42679 13.5550i −1.01447 1.63182i
7070 −0.535057 1.96430i −0.0639516 0.234779i
7171 7.01828 5.88904i 0.832917 0.698900i −0.123042 0.992401i 0.539265π-0.539265\pi
0.955959 + 0.293502i 0.0948206π0.0948206\pi
7272 6.55235 5.39135i 0.772202 0.635377i
7373 1.56692 + 8.88643i 0.183394 + 1.04008i 0.928002 + 0.372576i 0.121525π0.121525\pi
−0.744608 + 0.667502i 0.767364π0.767364\pi
7474 8.30026 0.760810i 0.964885 0.0884423i
7575 2.35143 + 3.78241i 0.271520 + 0.436755i
7676 6.34801 5.97518i 0.728167 0.685400i
7777 2.22264 + 1.28324i 0.253293 + 0.146239i
7878 −6.31634 + 14.9568i −0.715185 + 1.69352i
7979 6.78987 + 8.09186i 0.763921 + 0.910405i 0.998089 0.0617909i 0.0196812π-0.0196812\pi
−0.234169 + 0.972196i 0.575237π0.575237\pi
8080 −5.34613 + 3.20576i −0.597716 + 0.358415i
8181 6.08345 6.63262i 0.675939 0.736958i
8282 −0.189574 + 0.719399i −0.0209350 + 0.0794443i
8383 −4.95989 −0.544419 −0.272209 0.962238i 0.587754π-0.587754\pi
−0.272209 + 0.962238i 0.587754π0.587754\pi
8484 −2.95974 + 1.21645i −0.322934 + 0.132725i
8585 0.624099 3.53944i 0.0676931 0.383907i
8686 −2.15837 + 8.19062i −0.232743 + 0.883217i
8787 −7.36683 3.93877i −0.789807 0.422281i
8888 1.93947 7.61520i 0.206748 0.811783i
8989 4.70122 + 0.828952i 0.498328 + 0.0878687i 0.417162 0.908832i 0.363025π-0.363025\pi
0.0811656 + 0.996701i 0.474136π0.474136\pi
9090 −5.14021 + 4.15855i −0.541826 + 0.438349i
9191 3.93569 4.69038i 0.412573 0.491685i
9292 15.8840 9.34679i 1.65602 0.974470i
9393 4.76432 + 5.31584i 0.494037 + 0.551227i
9494 −3.72310 2.58404i −0.384009 0.266524i
9595 −4.98476 + 4.61477i −0.511426 + 0.473465i
9696 6.03950 + 7.71521i 0.616404 + 0.787430i
9797 0.862927 + 4.89390i 0.0876170 + 0.496900i 0.996761 + 0.0804190i 0.0256258π0.0256258\pi
−0.909144 + 0.416481i 0.863263π0.863263\pi
9898 −8.65644 + 0.793458i −0.874432 + 0.0801513i
9999 0.909361 8.28522i 0.0913942 0.832696i
100100 −4.43231 + 2.60815i −0.443231 + 0.260815i
101101 6.30923 + 17.3345i 0.627792 + 1.72484i 0.687060 + 0.726601i 0.258901π0.258901\pi
−0.0592682 + 0.998242i 0.518877π0.518877\pi
102102 −5.64188 0.285274i −0.558630 0.0282463i
103103 5.98769i 0.589985i 0.955500 + 0.294992i 0.0953171π0.0953171\pi
−0.955500 + 0.294992i 0.904683π0.904683\pi
104104 −17.0881 7.71145i −1.67563 0.756170i
105105 2.31400 0.928734i 0.225824 0.0906351i
106106 4.81108 6.93183i 0.467294 0.673279i
107107 −1.86630 + 3.23252i −0.180422 + 0.312499i −0.942024 0.335545i 0.891080π-0.891080\pi
0.761603 + 0.648044i 0.224413π0.224413\pi
108108 7.48555 + 7.20879i 0.720297 + 0.693666i
109109 −7.04749 + 5.91355i −0.675028 + 0.566415i −0.914549 0.404476i 0.867454π-0.867454\pi
0.239521 + 0.970891i 0.423010π0.423010\pi
110110 −1.56031 + 5.92107i −0.148769 + 0.564552i
111111 2.09946 + 9.99009i 0.199272 + 0.948217i
112112 −1.32108 3.45077i −0.124830 0.326067i
113113 3.09693 + 1.78802i 0.291335 + 0.168202i 0.638544 0.769586i 0.279537π-0.279537\pi
−0.347209 + 0.937788i 0.612870π0.612870\pi
114114 8.16690 + 6.87763i 0.764900 + 0.644149i
115115 −12.4367 + 7.18034i −1.15973 + 0.669570i
116116 4.75368 8.39333i 0.441369 0.779301i
117117 −19.0890 5.56884i −1.76478 0.514839i
118118 −2.62130 + 2.64309i −0.241310 + 0.243316i
119119 2.00191 + 0.728634i 0.183514 + 0.0667938i
120120 −4.65607 6.05046i −0.425039 0.552329i
121121 1.64045 + 2.84135i 0.149132 + 0.258304i
122122 −1.63447 + 19.6169i −0.147978 + 1.77603i
123123 −0.901997 0.128884i −0.0813303 0.0116210i
124124 −6.27022 + 5.35041i −0.563082 + 0.480481i
125125 10.2185 5.89963i 0.913967 0.527679i
126126 −1.89846 3.42863i −0.169128 0.305447i
127127 −16.6675 2.93892i −1.47900 0.260787i −0.624821 0.780768i 0.714828π-0.714828\pi
−0.854178 + 0.519981i 0.825939π0.825939\pi
128128 −9.07576 + 6.75503i −0.802192 + 0.597066i
129129 −10.2696 1.46739i −0.904185 0.129196i
130130 13.2649 + 6.11881i 1.16341 + 0.536655i
131131 12.9688 10.8821i 1.13309 0.950777i 0.133901 0.990995i 0.457250π-0.457250\pi
0.999191 + 0.0402176i 0.0128051π0.0128051\pi
132132 9.53858 + 1.28246i 0.830226 + 0.111623i
133133 −2.18078 3.38485i −0.189098 0.293504i
134134 −20.2385 1.68626i −1.74834 0.145670i
135135 −5.78606 5.66520i −0.497985 0.487583i
136136 0.487786 6.50475i 0.0418273 0.557777i
137137 7.30728 + 1.28847i 0.624303 + 0.110081i 0.476846 0.878987i 0.341780π-0.341780\pi
0.147457 + 0.989068i 0.452891π0.452891\pi
138138 13.6173 + 18.0018i 1.15918 + 1.53241i
139139 9.16881 10.9270i 0.777688 0.926812i −0.221139 0.975242i 0.570977π-0.570977\pi
0.998827 + 0.0484299i 0.0154218π0.0154218\pi
140140 1.00709 + 2.69728i 0.0851149 + 0.227962i
141141 2.61707 4.89480i 0.220397 0.412217i
142142 −9.12371 + 9.19956i −0.765645 + 0.772010i
143143 −17.3048 + 6.29845i −1.44710 + 0.526703i
144144 −8.53179 + 8.43851i −0.710983 + 0.703210i
145145 −3.75810 + 6.50922i −0.312093 + 0.540561i
146146 −3.35383 12.3126i −0.277565 1.01900i
147147 −2.18955 10.4188i −0.180591 0.859327i
148148 −11.5911 + 2.14291i −0.952784 + 0.176146i
149149 2.42366 6.65894i 0.198554 0.545522i −0.799958 0.600056i 0.795145π-0.795145\pi
0.998512 + 0.0545339i 0.0173673π0.0173673\pi
150150 −3.79981 5.02326i −0.310253 0.410148i
151151 −12.5306 + 7.23454i −1.01973 + 0.588739i −0.914024 0.405659i 0.867042π-0.867042\pi
−0.105701 + 0.994398i 0.533709π0.533709\pi
152152 −8.16865 + 9.23434i −0.662565 + 0.749004i
153153 −0.450873 6.90399i −0.0364509 0.558154i
154154 −3.29581 1.52029i −0.265584 0.122508i
155155 4.92012 4.12847i 0.395193 0.331606i
156156 6.96464 21.8792i 0.557617 1.75174i
157157 1.64561 + 9.33269i 0.131334 + 0.744830i 0.977343 + 0.211662i 0.0678875π0.0678875\pi
−0.846009 + 0.533168i 0.821001π0.821001\pi
158158 −10.6068 10.5194i −0.843832 0.836875i
159159 9.11335 + 4.87257i 0.722736 + 0.386420i
160160 7.11519 5.20482i 0.562505 0.411477i
161161 −2.91139 7.99899i −0.229450 0.630409i
162162 −7.71119 + 10.1261i −0.605848 + 0.795580i
163163 3.45838 1.99670i 0.270881 0.156393i −0.358407 0.933565i 0.616680π-0.616680\pi
0.629288 + 0.777172i 0.283347π0.283347\pi
164164 0.174114 1.03761i 0.0135960 0.0810236i
165165 −7.42396 1.06079i −0.577954 0.0825821i
166166 6.98506 0.640258i 0.542146 0.0496936i
167167 −11.0372 + 4.01722i −0.854086 + 0.310862i −0.731705 0.681621i 0.761275π-0.761275\pi
−0.122381 + 0.992483i 0.539053π0.539053\pi
168168 4.01120 2.09520i 0.309471 0.161648i
169169 5.37158 + 30.4637i 0.413198 + 2.34336i
170170 −0.422029 + 5.06520i −0.0323681 + 0.388483i
171171 −7.21196 + 10.9081i −0.551512 + 0.834167i
172172 1.98235 11.8135i 0.151153 0.900774i
173173 −1.66408 + 0.293422i −0.126517 + 0.0223084i −0.236548 0.971620i 0.576016π-0.576016\pi
0.110031 + 0.993928i 0.464905π0.464905\pi
174174 10.8832 + 4.59605i 0.825055 + 0.348425i
175175 0.812403 + 2.23206i 0.0614119 + 0.168728i
176176 −1.74835 + 10.9749i −0.131787 + 0.827265i
177177 −3.58618 2.81514i −0.269554 0.211599i
178178 −6.72778 0.560554i −0.504268 0.0420153i
179179 −9.24340 16.0100i −0.690884 1.19665i −0.971549 0.236840i 0.923888π-0.923888\pi
0.280665 0.959806i 0.409445π-0.409445\pi
180180 6.70220 6.52006i 0.499553 0.485976i
181181 2.09610 0.762920i 0.155802 0.0567074i −0.262942 0.964812i 0.584693π-0.584693\pi
0.418744 + 0.908104i 0.362470π0.362470\pi
182182 −4.93721 + 7.11355i −0.365970 + 0.527291i
183183 −24.0961 + 0.785976i −1.78124 + 0.0581010i
184184 −21.1630 + 15.2136i −1.56016 + 1.12156i
185185 9.04535 1.59494i 0.665027 0.117262i
186186 −7.39584 6.87134i −0.542289 0.503831i
187187 −4.11864 4.90840i −0.301185 0.358938i
188188 5.57685 + 3.15853i 0.406733 + 0.230360i
189189 3.90261 2.79448i 0.283873 0.203269i
190190 6.42438 7.14249i 0.466074 0.518171i
191191 1.83482 + 3.17800i 0.132763 + 0.229952i 0.924741 0.380598i 0.124282π-0.124282\pi
−0.791978 + 0.610550i 0.790948π0.790948\pi
192192 −9.50142 10.0858i −0.685706 0.727879i
193193 −7.02060 2.55529i −0.505354 0.183934i 0.0767467 0.997051i 0.475547π-0.475547\pi
−0.582100 + 0.813117i 0.697769π0.697769\pi
194194 −1.84701 6.78074i −0.132607 0.486829i
195195 −5.56781 + 17.0028i −0.398719 + 1.21760i
196196 12.0885 2.23487i 0.863466 0.159633i
197197 8.74347 + 5.04805i 0.622947 + 0.359658i 0.778015 0.628245i 0.216227π-0.216227\pi
−0.155069 + 0.987904i 0.549560π0.549560\pi
198198 −0.211146 + 11.7855i −0.0150055 + 0.837562i
199199 −2.36247 6.49084i −0.167471 0.460124i 0.827359 0.561673i 0.189842π-0.189842\pi
−0.994830 + 0.101550i 0.967620π0.967620\pi
200200 5.90538 4.24524i 0.417574 0.300184i
201201 −0.810879 24.8596i −0.0571950 1.75346i
202202 −11.1230 23.5978i −0.782612 1.66034i
203203 −3.41292 2.86378i −0.239540 0.200998i
204204 7.98235 0.326540i 0.558876 0.0228624i
205205 −0.142359 + 0.807356i −0.00994276 + 0.0563882i
206206 −0.772934 8.43253i −0.0538529 0.587522i
207207 −19.9742 + 19.1121i −1.38830 + 1.32838i
208208 25.0608 + 8.65426i 1.73765 + 0.600065i
209209 0.590058 + 12.0961i 0.0408152 + 0.836702i
210210 −3.13895 + 1.60665i −0.216608 + 0.110870i
211211 −13.0273 15.5253i −0.896833 1.06880i −0.997269 0.0738607i 0.976468π-0.976468\pi
0.100435 0.994944i 0.467976π-0.467976\pi
212212 −5.88069 + 10.3832i −0.403887 + 0.713122i
213213 −12.4821 9.79839i −0.855259 0.671375i
214214 2.21105 4.79330i 0.151144 0.327663i
215215 −1.62081 + 9.19204i −0.110538 + 0.626892i
216216 −11.4725 9.18592i −0.780607 0.625023i
217217 1.90356 + 3.29706i 0.129222 + 0.223819i
218218 9.16169 9.23785i 0.620508 0.625666i
219219 14.5046 5.82145i 0.980127 0.393377i
220220 1.43306 8.54012i 0.0966170 0.575774i
221221 −13.2383 + 7.64314i −0.890505 + 0.514133i
222222 −4.24628 13.7981i −0.284992 0.926070i
223223 −7.95864 + 21.8662i −0.532950 + 1.46427i 0.322594 + 0.946537i 0.395445π0.395445\pi
−0.855544 + 0.517730i 0.826777π0.826777\pi
224224 2.30594 + 4.68922i 0.154072 + 0.313312i
225225 5.57366 5.33309i 0.371577 0.355540i
226226 −4.59225 2.11831i −0.305472 0.140908i
227227 3.46465 + 6.00095i 0.229957 + 0.398297i 0.957795 0.287452i 0.0928081π-0.0928081\pi
−0.727838 + 0.685749i 0.759475π0.759475\pi
228228 −12.3893 8.63159i −0.820504 0.571641i
229229 1.22633 2.12406i 0.0810380 0.140362i −0.822658 0.568537i 0.807510π-0.807510\pi
0.903696 + 0.428175i 0.140843π0.140843\pi
230230 16.5879 11.7176i 1.09377 0.772633i
231231 1.38339 4.22454i 0.0910201 0.277954i
232232 −5.61119 + 12.4340i −0.368393 + 0.816335i
233233 16.9594 + 20.2114i 1.11105 + 1.32409i 0.940903 + 0.338676i 0.109979π0.109979\pi
0.170144 + 0.985419i 0.445577π0.445577\pi
234234 27.6021 + 5.37850i 1.80441 + 0.351604i
235235 −4.32497 2.49702i −0.282130 0.162888i
236236 3.35041 4.06066i 0.218093 0.264327i
237237 11.2972 14.3915i 0.733834 0.934826i
238238 −2.91336 0.767723i −0.188845 0.0497641i
239239 12.3262 0.797318 0.398659 0.917099i 0.369476π-0.369476\pi
0.398659 + 0.917099i 0.369476π0.369476\pi
240240 7.33822 + 7.91989i 0.473680 + 0.511227i
241241 −14.2999 + 5.20472i −0.921134 + 0.335266i −0.758690 0.651452i 0.774160π-0.774160\pi
−0.162445 + 0.986718i 0.551938π0.551938\pi
242242 −2.67705 3.78974i −0.172087 0.243614i
243243 −13.4095 7.94895i −0.860219 0.509925i
244244 −0.230452 27.8377i −0.0147532 1.78212i
245245 −9.43350 + 1.66338i −0.602684 + 0.106269i
246246 1.28693 + 0.0650717i 0.0820516 + 0.00414882i
247247 28.6636 + 3.62475i 1.82382 + 0.230637i
248248 8.13974 8.34444i 0.516874 0.529872i
249249 1.76679 + 8.40714i 0.111966 + 0.532781i
250250 −13.6292 + 9.62759i −0.861986 + 0.608902i
251251 −12.4729 10.4660i −0.787281 0.660607i 0.157790 0.987473i 0.449563π-0.449563\pi
−0.945071 + 0.326865i 0.894008π0.894008\pi
252252 3.11621 + 4.58351i 0.196303 + 0.288734i
253253 −4.44578 + 25.2133i −0.279504 + 1.58514i
254254 23.8523 + 1.98736i 1.49663 + 0.124698i
255255 −6.22176 + 0.202944i −0.389622 + 0.0127088i
256256 11.9095 10.6847i 0.744344 0.667797i
257257 8.50189 + 1.49911i 0.530334 + 0.0935121i 0.432402 0.901681i 0.357666π-0.357666\pi
0.0979317 + 0.995193i 0.468777π0.468777\pi
258258 14.6521 + 0.740865i 0.912203 + 0.0461242i
259259 5.44438i 0.338297i
260260 −19.4709 6.90485i −1.20754 0.428220i
261261 −4.05213 + 13.8900i −0.250821 + 0.859770i
262262 −16.8594 + 16.9995i −1.04158 + 1.05023i
263263 −17.5461 + 14.7229i −1.08194 + 0.907856i −0.996080 0.0884517i 0.971808π-0.971808\pi
−0.0858597 + 0.996307i 0.527364π0.527364\pi
264264 −13.5988 0.574788i −0.836949 0.0353757i
265265 4.64907 8.05242i 0.285590 0.494656i
266266 3.50815 + 4.48541i 0.215099 + 0.275018i
267267 −0.269557 8.26397i −0.0164966 0.505747i
268268 28.7197 0.237754i 1.75433 0.0145231i
269269 −0.983121 + 0.173351i −0.0599420 + 0.0105694i −0.203539 0.979067i 0.565244π-0.565244\pi
0.143597 + 0.989636i 0.454133π0.454133\pi
270270 8.87987 + 7.23145i 0.540412 + 0.440092i
271271 −8.24020 9.82029i −0.500557 0.596540i 0.455313 0.890331i 0.349527π-0.349527\pi
−0.955870 + 0.293791i 0.905083π0.905083\pi
272272 0.152725 + 9.22366i 0.00926034 + 0.559267i
273273 −9.35226 5.00031i −0.566025 0.302632i
274274 −10.4572 0.871290i −0.631745 0.0526365i
275275 1.24056 7.03557i 0.0748087 0.424261i
276276 −21.5012 23.5943i −1.29422 1.42021i
277277 4.50871 7.80931i 0.270902 0.469216i −0.698191 0.715911i 0.746011π-0.746011\pi
0.969093 + 0.246695i 0.0793447π0.0793447\pi
278278 −11.5020 + 16.5721i −0.689844 + 0.993929i
279279 7.31336 9.96922i 0.437839 0.596842i
280280 −1.76648 3.66860i −0.105568 0.219241i
281281 17.3218 + 3.05430i 1.03333 + 0.182204i 0.664497 0.747291i 0.268646π-0.268646\pi
0.368834 + 0.929495i 0.379757π0.379757\pi
282282 −3.05379 + 7.23123i −0.181851 + 0.430613i
283283 13.7683 + 16.4084i 0.818441 + 0.975380i 0.999968 0.00800637i 0.00254853π-0.00254853\pi
−0.181527 + 0.983386i 0.558104π0.558104\pi
284284 11.6615 14.1336i 0.691981 0.838674i
285285 9.59780 + 6.80544i 0.568525 + 0.403120i
286286 23.5575 11.1040i 1.39299 0.656593i
287287 −0.456640 0.166203i −0.0269546 0.00981068i
288288 10.9261 12.9854i 0.643827 0.765171i
289289 8.94839 + 7.50859i 0.526376 + 0.441682i
290290 4.45231 9.65211i 0.261449 0.566792i
291291 7.98790 3.20597i 0.468259 0.187937i
292292 6.31262 + 16.9070i 0.369418 + 0.989406i
293293 17.6678i 1.03216i −0.856540 0.516081i 0.827390π-0.827390\pi
0.856540 0.516081i 0.172610π-0.172610\pi
294294 4.42849 + 14.3902i 0.258275 + 0.839255i
295295 −2.63675 + 3.14236i −0.153518 + 0.182955i
296296 16.0473 4.51415i 0.932729 0.262380i
297297 −14.3676 + 1.40994i −0.833692 + 0.0818132i
298298 −2.55368 + 9.69072i −0.147930 + 0.561368i
299299 57.3956 + 20.8903i 3.31928 + 1.20812i
300300 5.99974 + 6.58381i 0.346395 + 0.380116i
301301 −5.19901 1.89229i −0.299666 0.109070i
302302 16.7131 11.8060i 0.961729 0.679360i
303303 27.1349 16.8691i 1.55886 0.969105i
304304 10.3120 14.0593i 0.591431 0.806355i
305305 21.6919i 1.24208i
306306 1.52618 + 9.66475i 0.0872462 + 0.552497i
307307 19.3822 3.41760i 1.10620 0.195053i 0.409426 0.912344i 0.365729π-0.365729\pi
0.696774 + 0.717291i 0.254618π0.254618\pi
308308 4.83777 + 1.71559i 0.275658 + 0.0977547i
309309 10.1493 2.13291i 0.577373 0.121337i
310310 −6.39612 + 6.44928i −0.363275 + 0.366295i
311311 −4.90302 8.49229i −0.278025 0.481553i 0.692869 0.721064i 0.256346π-0.256346\pi
−0.970894 + 0.239510i 0.923013π0.923013\pi
312312 −6.98405 + 31.7117i −0.395394 + 1.79532i
313313 −17.2879 14.5062i −0.977168 0.819942i 0.00649137 0.999979i 0.497934π-0.497934\pi
−0.983660 + 0.180037i 0.942378π0.942378\pi
314314 −3.52225 12.9309i −0.198772 0.729733i
315315 −2.39851 3.59147i −0.135141 0.202356i
316316 16.2956 + 13.4453i 0.916698 + 0.756358i
317317 −4.66484 12.8166i −0.262004 0.719849i −0.999032 0.0439874i 0.985994π-0.985994\pi
0.737028 0.675862i 0.236228π-0.236228\pi
318318 −13.4634 5.68568i −0.754991 0.318837i
319319 4.58303 + 12.5918i 0.256600 + 0.705003i
320320 −9.34852 + 8.24848i −0.522598 + 0.461104i
321321 6.14400 + 2.01194i 0.342925 + 0.112296i
322322 5.13271 + 10.8892i 0.286035 + 0.606833i
323323 2.22590 + 9.80310i 0.123853 + 0.545459i
324324 9.55260 15.2561i 0.530700 0.847560i
325325 −16.0158 5.82928i −0.888398 0.323351i
326326 −4.61272 + 3.25840i −0.255475 + 0.180466i
327327 12.5340 + 9.83918i 0.693134 + 0.544108i
328328 −0.111265 + 1.48375i −0.00614359 + 0.0819264i
329329 1.90281 2.26768i 0.104905 0.125021i
330330 10.5922 + 0.535578i 0.583080 + 0.0294826i
331331 −4.35892 2.51662i −0.239588 0.138326i 0.375399 0.926863i 0.377506π-0.377506\pi
−0.614987 + 0.788537i 0.710839π0.710839\pi
332332 −9.75448 + 1.80336i −0.535347 + 0.0989724i
333333 16.1856 7.11727i 0.886965 0.390024i
334334 15.0253 7.08226i 0.822146 0.387524i
335335 −22.3792 −1.22271
336336 −5.37855 + 3.46848i −0.293424 + 0.189221i
337337 4.24028 + 24.0478i 0.230983 + 1.30997i 0.850911 + 0.525310i 0.176050π0.176050\pi
−0.619928 + 0.784658i 0.712838π0.712838\pi
338338 −11.4973 42.2089i −0.625371 2.29586i
339339 1.92755 5.88630i 0.104690 0.319700i
340340 −0.0595041 7.18784i −0.00322706 0.389816i
341341 11.4505i 0.620079i
342342 8.74857 16.2930i 0.473068 0.881026i
343343 12.1443i 0.655729i
344344 −1.26679 + 16.8930i −0.0683010 + 0.910811i
345345 16.6010 + 18.5228i 0.893768 + 0.997233i
346346 2.30566 0.628039i 0.123953 0.0337636i
347347 −1.13690 6.44768i −0.0610320 0.346130i −0.999998 0.00211914i 0.999325π-0.999325\pi
0.938966 0.344011i 0.111786π-0.111786\pi
348348 −15.9202 5.06777i −0.853414 0.271661i
349349 −29.3532 −1.57124 −0.785620 0.618709i 0.787656π-0.787656\pi
−0.785620 + 0.618709i 0.787656π0.787656\pi
350350 −1.43224 3.03856i −0.0765567 0.162418i
351351 −2.63950 + 34.3401i −0.140886 + 1.83294i
352352 1.04549 15.6818i 0.0557250 0.835841i
353353 −6.38333 3.68542i −0.339750 0.196155i 0.320411 0.947279i 0.396179π-0.396179\pi
−0.660162 + 0.751124i 0.729512π0.729512\pi
354354 5.41385 + 3.50166i 0.287743 + 0.186111i
355355 −9.17751 + 10.9373i −0.487091 + 0.580493i
356356 9.54716 0.0790355i 0.505998 0.00418887i
357357 0.521942 3.65283i 0.0276241 0.193328i
358358 15.0843 + 21.3539i 0.797228 + 1.12859i
359359 −0.0856158 0.0311616i −0.00451863 0.00164465i 0.339760 0.940512i 0.389654π-0.389654\pi
−0.344278 + 0.938868i 0.611876π0.611876\pi
360360 −8.59712 + 10.0474i −0.453108 + 0.529546i
361361 7.85337 17.3010i 0.413335 0.910579i
362362 −2.85348 + 1.34501i −0.149976 + 0.0706920i
363363 4.23180 3.79274i 0.222112 0.199067i
364364 6.03485 10.6554i 0.316312 0.558495i
365365 −4.80959 13.2142i −0.251745 0.691665i
366366 33.8334 4.21740i 1.76850 0.220447i
367367 −10.7034 29.4074i −0.558713 1.53505i −0.821506 0.570200i 0.806866π-0.806866\pi
0.262793 0.964852i 0.415356π-0.415356\pi
368368 27.8402 24.1573i 1.45127 1.25929i
369369 0.102845 + 1.57482i 0.00535391 + 0.0819818i
370370 −12.5328 + 3.41381i −0.651548 + 0.177475i
371371 4.22206 + 3.54273i 0.219198 + 0.183929i
372372 11.3026 + 8.72227i 0.586014 + 0.452229i
373373 −5.94496 10.2970i −0.307819 0.533157i 0.670066 0.742301i 0.266266π-0.266266\pi
−0.977885 + 0.209144i 0.932932π0.932932\pi
374374 6.43393 + 6.38089i 0.332691 + 0.329948i
375375 −13.6400 15.2190i −0.704367 0.785906i
376376 −8.26165 3.72829i −0.426062 0.192272i
377377 31.4824 5.55119i 1.62143 0.285901i
378378 −5.13536 + 4.43927i −0.264134 + 0.228332i
379379 9.53183i 0.489617i 0.969571 + 0.244809i 0.0787251π0.0787251\pi
−0.969571 + 0.244809i 0.921275π0.921275\pi
380380 −8.12552 + 10.8881i −0.416830 + 0.558550i
381381 0.955674 + 29.2987i 0.0489607 + 1.50102i
382382 −2.99424 4.23876i −0.153198 0.216874i
383383 −27.5194 10.0162i −1.40618 0.511806i −0.476171 0.879353i 0.657976π-0.657976\pi
−0.930005 + 0.367547i 0.880198π0.880198\pi
384384 14.6829 + 12.9774i 0.749283 + 0.662250i
385385 −3.75841 1.36795i −0.191546 0.0697172i
386386 10.2170 + 2.69237i 0.520033 + 0.137038i
387387 1.17093 + 17.9299i 0.0595218 + 0.911427i
388388 3.47647 + 9.31095i 0.176491 + 0.472692i
389389 5.81882 6.93460i 0.295026 0.351598i −0.598087 0.801432i 0.704072π-0.704072\pi
0.893113 + 0.449833i 0.148517π0.148517\pi
390390 5.64636 24.6639i 0.285914 1.24891i
391391 21.2519i 1.07475i
392392 −16.7359 + 4.70786i −0.845290 + 0.237783i
393393 −23.0652 18.1061i −1.16349 0.913332i
394394 −12.9652 5.98055i −0.653175 0.301296i
395395 −12.6104 10.5814i −0.634498 0.532407i
396396 −1.22400 16.6250i −0.0615084 0.835436i
397397 −8.11706 2.95437i −0.407384 0.148276i 0.130196 0.991488i 0.458439π-0.458439\pi
−0.537580 + 0.843213i 0.680661π0.680661\pi
398398 4.16498 + 8.83615i 0.208771 + 0.442916i
399399 −4.96058 + 4.90221i −0.248339 + 0.245418i
400400 −7.76860 + 6.74092i −0.388430 + 0.337046i
401401 2.44680 + 2.91598i 0.122187 + 0.145617i 0.823670 0.567069i 0.191923π-0.191923\pi
−0.701483 + 0.712686i 0.747478π0.747478\pi
402402 4.35102 + 34.9054i 0.217009 + 1.74092i
403403 −26.9024 4.74362i −1.34010 0.236296i
404404 18.7108 + 31.7972i 0.930897 + 1.58197i
405405 −7.54157 + 11.8256i −0.374743 + 0.587616i
406406 5.17613 + 3.59253i 0.256887 + 0.178294i
407407 8.18741 14.1810i 0.405835 0.702926i
408408 −11.1995 + 1.49029i −0.554456 + 0.0737802i
409409 1.92495 10.9169i 0.0951825 0.539807i −0.899509 0.436903i 0.856075π-0.856075\pi
0.994691 0.102904i 0.0328135π-0.0328135\pi
410410 0.0962659 1.15538i 0.00475423 0.0570604i
411411 −0.418982 12.8450i −0.0206669 0.633597i
412412 2.17706 + 11.7758i 0.107256 + 0.580154i
413413 −1.56295 1.86265i −0.0769076 0.0916549i
414414 25.6628 29.4942i 1.26126 1.44956i
415415 7.61209 1.34222i 0.373663 0.0658869i
416416 −36.4105 8.95286i −1.78517 0.438950i
417417 −21.7875 11.6490i −1.06694 0.570454i
418418 −2.39243 16.9588i −0.117018 0.829483i
419419 4.74761 8.22311i 0.231936 0.401725i −0.726442 0.687228i 0.758827π-0.758827\pi
0.958378 + 0.285503i 0.0921607π0.0921607\pi
420420 4.21321 2.66786i 0.205584 0.130178i
421421 −10.0496 + 8.43265i −0.489790 + 0.410982i −0.853951 0.520354i 0.825800π-0.825800\pi
0.364161 + 0.931336i 0.381356π0.381356\pi
422422 20.3505 + 20.1828i 0.990648 + 0.982481i
423423 −9.22906 2.69239i −0.448732 0.130909i
424424 6.94149 15.3819i 0.337109 0.747011i
425425 5.93018i 0.287656i
426426 18.8435 + 12.1879i 0.912970 + 0.590505i
427427 −12.6626 2.23276i −0.612788 0.108051i
428428 −2.49508 + 7.03587i −0.120604 + 0.340092i
429429 16.8403 + 27.0885i 0.813057 + 1.30785i
430430 1.09602 13.1545i 0.0528549 0.634365i
431431 −6.17077 + 34.9962i −0.297236 + 1.68571i 0.360739 + 0.932667i 0.382524π0.382524\pi
−0.657975 + 0.753040i 0.728587π0.728587\pi
432432 17.3427 + 11.4557i 0.834399 + 0.551161i
433433 13.6868 + 11.4846i 0.657744 + 0.551913i 0.909410 0.415901i 0.136534π-0.136534\pi
−0.251666 + 0.967814i 0.580978π0.580978\pi
434434 −3.10640 4.39755i −0.149112 0.211089i
435435 12.3720 + 4.05138i 0.593191 + 0.194249i
436436 −11.7100 + 14.1924i −0.560808 + 0.679693i
437437 24.2891 31.9913i 1.16190 1.53035i
438438 −19.6754 + 10.0708i −0.940128 + 0.481200i
439439 −2.19392 + 0.386847i −0.104710 + 0.0184632i −0.225758 0.974184i 0.572486π-0.572486\pi
0.121048 + 0.992647i 0.461375π0.461375\pi
440440 −0.915777 + 12.2121i −0.0436580 + 0.582190i
441441 −16.8801 + 7.42268i −0.803816 + 0.353461i
442442 17.6570 12.4728i 0.839858 0.593271i
443443 −1.78605 + 0.650069i −0.0848578 + 0.0308857i −0.384100 0.923291i 0.625488π-0.625488\pi
0.299242 + 0.954177i 0.403266π0.403266\pi
444444 7.76124 + 18.8839i 0.368332 + 0.896190i
445445 −7.43943 −0.352663
446446 8.38559 31.8217i 0.397069 1.50680i
447447 −12.1504 1.73613i −0.574695 0.0821164i
448448 −3.85279 6.30621i −0.182027 0.297940i
449449 −15.2853 8.82496i −0.721357 0.416476i 0.0938950 0.995582i 0.470068π-0.470068\pi
−0.815252 + 0.579107i 0.803402π0.803402\pi
450450 −7.16100 + 8.23014i −0.337573 + 0.387972i
451451 0.939472 + 1.11962i 0.0442380 + 0.0527208i
452452 6.74076 + 2.39043i 0.317059 + 0.112436i
453453 16.7263 + 18.6626i 0.785871 + 0.876846i
454454 −5.65395 8.00396i −0.265353 0.375644i
455455 −4.77094 + 8.26352i −0.223665 + 0.387400i
456456 18.5623 + 10.5566i 0.869257 + 0.494360i
457457 8.30445 + 14.3837i 0.388466 + 0.672842i 0.992243 0.124311i 0.0396719π-0.0396719\pi
−0.603778 + 0.797153i 0.706339π0.706339\pi
458458 −1.45286 + 3.14964i −0.0678877 + 0.147173i
459459 −11.5418 + 3.22355i −0.538726 + 0.150463i
460460 −21.8482 + 18.6432i −1.01868 + 0.869245i
461461 9.66396 26.5515i 0.450095 1.23663i −0.482562 0.875862i 0.660294π-0.660294\pi
0.932657 0.360765i 0.117484π-0.117484\pi
462462 −1.40290 + 6.12804i −0.0652689 + 0.285102i
463463 −10.6965 + 6.17564i −0.497109 + 0.287006i −0.727519 0.686088i 0.759327π-0.759327\pi
0.230410 + 0.973094i 0.425993π0.425993\pi
464464 6.29722 18.2353i 0.292341 0.846553i
465465 −8.75048 6.86909i −0.405794 0.318547i
466466 −26.4931 26.2747i −1.22727 1.21715i
467467 −5.58533 9.67408i −0.258458 0.447663i 0.707371 0.706843i 0.249881π-0.249881\pi
−0.965829 + 0.259180i 0.916548π0.916548\pi
468468 −39.5666 4.01152i −1.82897 0.185433i
469469 2.30351 13.0638i 0.106366 0.603232i
470470 6.41324 + 2.95829i 0.295821 + 0.136456i
471471 15.2330 6.11380i 0.701897 0.281709i
472472 −4.19424 + 6.15117i −0.193056 + 0.283130i
473473 10.6962 + 12.7473i 0.491813 + 0.586120i
474474 −14.0523 + 21.7260i −0.645442 + 0.997906i
475475 −6.77769 + 8.92693i −0.310982 + 0.409595i
476476 4.20202 + 0.705114i 0.192599 + 0.0323188i
477477 5.01281 17.1831i 0.229521 0.786758i
478478 −17.3592 + 1.59116i −0.793989 + 0.0727779i
479479 0.0619290 0.351217i 0.00282961 0.0160475i −0.983360 0.181666i 0.941851π-0.941851\pi
0.986190 + 0.165619i 0.0529621π0.0529621\pi
480480 −11.3568 10.2064i −0.518367 0.465856i
481481 −29.9258 25.1107i −1.36450 1.14495i
482482 19.4668 9.17578i 0.886687 0.417946i
483483 −12.5214 + 7.78425i −0.569743 + 0.354196i
484484 4.25932 + 4.99155i 0.193605 + 0.226889i
485485 −2.64872 7.27730i −0.120272 0.330445i
486486 19.9108 + 9.46359i 0.903173 + 0.429277i
487487 6.34428 + 3.66287i 0.287487 + 0.165981i 0.636808 0.771022i 0.280254π-0.280254\pi
−0.349321 + 0.937003i 0.613588π0.613588\pi
488488 3.91803 + 39.1743i 0.177361 + 1.77334i
489489 −4.61638 5.15078i −0.208760 0.232926i
490490 13.0706 3.56030i 0.590468 0.160838i
491491 −19.9588 7.26441i −0.900728 0.327838i −0.150183 0.988658i 0.547986π-0.547986\pi
−0.750544 + 0.660820i 0.770209π0.770209\pi
492492 −1.82079 + 0.0744847i −0.0820877 + 0.00335803i
493493 5.56148 + 9.63277i 0.250477 + 0.433838i
494494 −40.8351 1.40467i −1.83726 0.0631990i
495495 0.846477 + 12.9617i 0.0380463 + 0.582584i
496496 −10.3861 + 12.8023i −0.466350 + 0.574840i
497497 −5.44000 6.48314i −0.244017 0.290809i
498498 −3.57345 11.6118i −0.160130 0.520337i
499499 14.3357 2.52778i 0.641756 0.113159i 0.156706 0.987645i 0.449913π-0.449913\pi
0.485050 + 0.874487i 0.338801π0.338801\pi
500500 17.9513 15.3180i 0.802808 0.685041i
501501 10.7409 + 17.2774i 0.479869 + 0.771896i
502502 18.9167 + 13.1293i 0.844294 + 0.585988i
503503 35.1333 12.7875i 1.56652 0.570166i 0.594300 0.804243i 0.297429π-0.297429\pi
0.972218 + 0.234078i 0.0752070π0.0752070\pi
504504 −4.98026 6.05274i −0.221839 0.269611i
505505 −14.3739 24.8963i −0.639631 1.10787i
506506 3.00633 36.0820i 0.133647 1.60404i
507507 49.7233 19.9566i 2.20829 0.886305i
508508 −33.8480 + 0.280208i −1.50176 + 0.0124322i
509509 3.96195 + 10.8854i 0.175610 + 0.482485i 0.996003 0.0893145i 0.0284676π-0.0284676\pi
−0.820393 + 0.571800i 0.806245π0.806245\pi
510510 8.73597 1.08896i 0.386835 0.0482198i
511511 8.20885 1.44744i 0.363138 0.0640310i
512512 −15.3930 + 16.5848i −0.680281 + 0.732951i
513513 21.0586 + 8.33878i 0.929760 + 0.368166i
514514 −12.1668 1.01373i −0.536655 0.0447138i
515515 −1.62036 9.18949i −0.0714014 0.404937i
516516 −20.7304 + 0.848035i −0.912605 + 0.0373327i
517517 −8.36645 + 3.04514i −0.367956 + 0.133925i
518518 −0.702799 7.66737i −0.0308792 0.336885i
519519 1.09013 + 2.71613i 0.0478513 + 0.119225i
520520 28.3124 + 7.21072i 1.24158 + 0.316211i
521521 10.4089 6.00955i 0.456020 0.263283i −0.254349 0.967112i 0.581861π-0.581861\pi
0.710369 + 0.703829i 0.248528π0.248528\pi
522522 3.91363 20.0845i 0.171295 0.879075i
523523 0.612547 + 1.68296i 0.0267848 + 0.0735906i 0.952364 0.304963i 0.0986439π-0.0986439\pi
−0.925580 + 0.378553i 0.876422π0.876422\pi
524524 21.5488 26.1169i 0.941365 1.14092i
525525 3.49400 2.17214i 0.152491 0.0947999i
526526 22.8098 22.9994i 0.994556 1.00282i
527527 −1.65049 9.36042i −0.0718967 0.407746i
528528 19.2255 0.945953i 0.836685 0.0411673i
529529 47.4303 39.7987i 2.06219 1.73038i
530530 −5.50786 + 11.9404i −0.239246 + 0.518659i
531531 −3.49427 + 7.08146i −0.151638 + 0.307309i
532532 −5.51957 5.86398i −0.239304 0.254236i
533533 3.01969 1.74342i 0.130797 0.0755159i
534534 1.44639 + 11.6034i 0.0625915 + 0.502130i
535535 1.98949 5.46609i 0.0860133 0.236320i
536536 −40.4155 + 4.04217i −1.74569 + 0.174595i
537537 −23.8448 + 21.3708i −1.02898 + 0.922219i
538538 1.36216 0.371040i 0.0587270 0.0159967i
539539 −8.53875 + 14.7895i −0.367790 + 0.637031i
540540 −13.4391 9.03785i −0.578326 0.388927i
541541 −0.349822 + 0.127325i −0.0150400 + 0.00547412i −0.349529 0.936925i 0.613658π-0.613658\pi
0.334489 + 0.942400i 0.391436π0.391436\pi
542542 12.8724 + 12.7663i 0.552918 + 0.548360i
543543 −2.03983 3.28119i −0.0875377 0.140809i
544544 −1.40574 12.9701i −0.0602706 0.556087i
545545 9.21571 10.9829i 0.394758 0.470454i
546546 13.8164 + 5.83473i 0.591286 + 0.249703i
547547 36.8553 + 6.49858i 1.57582 + 0.277859i 0.892083 0.451871i 0.149243π-0.149243\pi
0.683735 + 0.729730i 0.260354π0.260354\pi
548548 14.8395 0.122848i 0.633912 0.00524779i
549549 9.91569 + 40.5636i 0.423191 + 1.73121i
550550 −0.838893 + 10.0684i −0.0357705 + 0.429318i
551551 2.63752 20.8569i 0.112362 0.888533i
552552 33.3260 + 30.4525i 1.41845 + 1.29614i
553553 7.47486 6.27215i 0.317863 0.266719i
554554 −5.34158 + 11.5799i −0.226942 + 0.491985i
555555 −5.92556 14.7639i −0.251526 0.626695i
556556 14.0591 24.8234i 0.596240 1.05275i
557557 −36.9065 6.50761i −1.56378 0.275736i −0.676315 0.736613i 0.736424π-0.736424\pi
−0.887464 + 0.460876i 0.847535π0.847535\pi
558558 −9.01258 + 14.9838i −0.381533 + 0.634316i
559559 34.3803 19.8495i 1.45413 0.839543i
560560 2.96132 + 4.93850i 0.125139 + 0.208690i
561561 −6.85274 + 8.72965i −0.289323 + 0.368566i
562562 −24.7887 2.06538i −1.04565 0.0871227i
563563 11.9058 + 20.6214i 0.501769 + 0.869089i 0.999998 + 0.00204371i 0.000650534π0.000650534\pi
−0.498229 + 0.867045i 0.666016π0.666016\pi
564564 3.36722 10.5780i 0.141786 0.445415i
565565 −5.23682 1.90605i −0.220315 0.0801880i
566566 −21.5082 21.3308i −0.904055 0.896602i
567567 −6.12689 5.61959i −0.257305 0.236001i
568568 −14.5985 + 21.4098i −0.612540 + 0.898335i
569569 −22.6542 + 13.0794i −0.949715 + 0.548318i −0.892992 0.450072i 0.851398π-0.851398\pi
−0.0567226 + 0.998390i 0.518065π0.518065\pi
570570 −14.3952 8.34522i −0.602947 0.349543i
571571 −7.20784 4.16145i −0.301639 0.174151i 0.341540 0.939867i 0.389051π-0.389051\pi
−0.643179 + 0.765716i 0.722385π0.722385\pi
572572 −31.7429 + 18.6788i −1.32724 + 0.781002i
573573 4.73320 4.24213i 0.197732 0.177217i
574574 0.664545 + 0.175120i 0.0277376 + 0.00730935i
575575 −18.1515 + 15.2309i −0.756971 + 0.635174i
576576 −13.7111 + 19.6979i −0.571295 + 0.820744i
577577 6.57688 11.3915i 0.273799 0.474234i −0.696032 0.718010i 0.745053π-0.745053\pi
0.969831 + 0.243777i 0.0783864π0.0783864\pi
578578 −13.5714 9.41930i −0.564494 0.391791i
579579 −1.83043 + 12.8103i −0.0760699 + 0.532379i
580580 −5.02427 + 14.1679i −0.208621 + 0.588290i
581581 4.58170i 0.190081i
582582 −10.8356 + 5.54613i −0.449149 + 0.229895i
583583 −5.66957 15.5770i −0.234810 0.645134i
584584 −11.0726 22.9954i −0.458187 0.951556i
585585 30.8035 + 3.38090i 1.27357 + 0.139783i
586586 2.28068 + 24.8817i 0.0942140 + 1.02785i
587587 −3.14631 17.8436i −0.129862 0.736484i −0.978301 0.207191i 0.933568π-0.933568\pi
0.848439 0.529294i 0.177543π-0.177543\pi
588588 −8.09428 19.6942i −0.333803 0.812177i
589589 −8.21361 + 15.9770i −0.338436 + 0.658320i
590590 3.30773 4.76579i 0.136177 0.196204i
591591 5.44200 16.6186i 0.223854 0.683598i
592592 −22.0168 + 8.42881i −0.904885 + 0.346422i
593593 −2.40098 + 2.86137i −0.0985963 + 0.117503i −0.813086 0.582143i 0.802214π-0.802214\pi
0.714490 + 0.699646i 0.246659π0.246659\pi
594594 20.0520 3.84031i 0.822744 0.157570i
595595 −3.26956 0.576512i −0.134039 0.0236347i
596596 2.34542 13.9772i 0.0960722 0.572527i
597597 −10.1606 + 6.31659i −0.415845 + 0.258521i
598598 −83.5275 22.0110i −3.41569 0.900096i
599599 1.71314 9.71569i 0.0699969 0.396972i −0.929600 0.368571i 0.879847π-0.879847\pi
0.999597 0.0284014i 0.00904166π-0.00904166\pi
600600 −9.29938 8.49755i −0.379646 0.346911i
601601 −22.8190 −0.930808 −0.465404 0.885098i 0.654091π-0.654091\pi
−0.465404 + 0.885098i 0.654091π0.654091\pi
602602 7.56609 + 1.99380i 0.308371 + 0.0812612i
603603 −41.8488 + 10.2299i −1.70422 + 0.416592i
604604 −22.0132 + 18.7840i −0.895703 + 0.764309i
605605 −3.28656 3.91677i −0.133618 0.159239i
606606 −36.0367 + 27.2597i −1.46389 + 1.10735i
607607 −11.2946 6.52094i −0.458434 0.264677i 0.252952 0.967479i 0.418599π-0.418599\pi
−0.711385 + 0.702802i 0.751932π0.751932\pi
608608 −12.7076 + 21.1310i −0.515360 + 0.856974i
609609 −3.63844 + 6.80511i −0.147437 + 0.275757i
610610 −2.80015 30.5490i −0.113375 1.23689i
611611 3.68843 + 20.9181i 0.149218 + 0.846256i
612612 −3.39694 13.4140i −0.137313 0.542227i
613613 −7.69123 + 6.45371i −0.310646 + 0.260663i −0.784759 0.619801i 0.787213π-0.787213\pi
0.474113 + 0.880464i 0.342769π0.342769\pi
614614 −26.8550 + 7.31503i −1.08378 + 0.295211i
615615 1.41920 0.0462919i 0.0572277 0.00186667i
616616 −7.03455 1.79158i −0.283430 0.0721850i
617617 −28.2352 4.97862i −1.13671 0.200432i −0.426541 0.904468i 0.640268π-0.640268\pi
−0.710164 + 0.704036i 0.751379π0.751379\pi
618618 −14.0180 + 4.31395i −0.563887 + 0.173532i
619619 −18.6165 10.7482i −0.748259 0.432007i 0.0768057 0.997046i 0.475528π-0.475528\pi
−0.825064 + 0.565039i 0.808861π0.808861\pi
620620 8.17519 9.90825i 0.328324 0.397925i
621621 39.5107 + 27.0488i 1.58551 + 1.08543i
622622 8.00122 + 11.3269i 0.320820 + 0.454165i
623623 0.765745 4.34275i 0.0306789 0.173989i
624624 5.74214 45.5614i 0.229869 1.82392i
625625 −4.23714 + 3.55538i −0.169486 + 0.142215i
626626 26.2193 + 18.1977i 1.04793 + 0.727324i
627627 20.2929 5.30898i 0.810422 0.212020i
628628 6.62963 + 17.7560i 0.264551 + 0.708543i
629629 4.64888 12.7727i 0.185363 0.509280i
630630 3.84146 + 4.74828i 0.153047 + 0.189176i
631631 −22.3141 + 26.5929i −0.888309 + 1.05865i 0.109597 + 0.993976i 0.465044π0.465044\pi
−0.997907 + 0.0646699i 0.979401π0.979401\pi
632632 −24.6848 16.8316i −0.981910 0.669526i
633633 −21.6752 + 27.6119i −0.861513 + 1.09747i
634634 8.22400 + 17.4475i 0.326617 + 0.692929i
635635 26.3754 1.04668
636636 19.6946 + 6.26924i 0.780942 + 0.248592i
637637 31.2100 + 26.1883i 1.23658 + 1.03762i
638638 −8.07975 17.1415i −0.319881 0.678638i
639639 −12.1622 + 24.6478i −0.481129 + 0.975052i
640640 12.1008 12.8232i 0.478328 0.506881i
641641 1.14366 3.14218i 0.0451718 0.124109i −0.915056 0.403328i 0.867853π-0.867853\pi
0.960227 + 0.279219i 0.0900756π0.0900756\pi
642642 −8.91238 2.04033i −0.351744 0.0805252i
643643 −10.8591 + 29.8351i −0.428241 + 1.17658i 0.518639 + 0.854993i 0.326439π0.326439\pi
−0.946880 + 0.321588i 0.895783π0.895783\pi
644644 −8.63410 14.6728i −0.340231 0.578191i
645645 16.1581 0.527051i 0.636225 0.0207526i
646646 −4.40021 13.5185i −0.173124 0.531877i
647647 43.8882 1.72542 0.862711 0.505697i 0.168765π-0.168765\pi
0.862711 + 0.505697i 0.168765π0.168765\pi
648648 −11.4837 + 22.7184i −0.451121 + 0.892463i
649649 1.26992 + 7.20205i 0.0498486 + 0.282705i
650650 23.3077 + 6.14200i 0.914204 + 0.240909i
651651 4.91052 4.40104i 0.192458 0.172490i
652652 6.07552 5.18428i 0.237936 0.203032i
653653 −28.2822 + 16.3287i −1.10677 + 0.638992i −0.937990 0.346662i 0.887315π-0.887315\pi
−0.168777 + 0.985654i 0.553982π0.553982\pi
654654 −18.9219 12.2386i −0.739906 0.478568i
655655 −16.9588 + 20.2107i −0.662635 + 0.789697i
656656 −0.0348371 2.10394i −0.00136016 0.0821451i
657657 −15.0343 22.5119i −0.586543 0.878272i
658658 −2.38701 + 3.43922i −0.0930555 + 0.134075i
659659 −21.7954 + 7.93288i −0.849029 + 0.309021i −0.729644 0.683827i 0.760314π-0.760314\pi
−0.119384 + 0.992848i 0.538092π0.538092\pi
660660 −14.9862 + 0.613052i −0.583337 + 0.0238630i
661661 20.2091 7.35550i 0.786042 0.286096i 0.0823521 0.996603i 0.473757π-0.473757\pi
0.703690 + 0.710508i 0.251535π0.251535\pi
662662 6.46357 + 2.98150i 0.251214 + 0.115879i
663663 17.6710 + 19.7166i 0.686285 + 0.765731i
664664 13.5045 3.79887i 0.524078 0.147425i
665665 4.26290 + 4.60468i 0.165308 + 0.178562i
666666 −21.8756 + 12.1127i −0.847662 + 0.469356i
667667 15.2007 41.7636i 0.588573 1.61709i
668668 −20.2460 + 11.9136i −0.783341 + 0.460950i
669669 39.8987 + 5.70100i 1.54257 + 0.220413i
670670 31.5169 2.88887i 1.21760 0.111607i
671671 29.6248 + 24.8581i 1.14365 + 0.959637i
672672 7.12693 5.57899i 0.274927 0.215214i
673673 19.1121 33.1031i 0.736717 1.27603i −0.217248 0.976116i 0.569708π-0.569708\pi
0.953966 0.299915i 0.0969585π-0.0969585\pi
674674 −9.07589 33.3194i −0.349590 1.28342i
675675 −11.0252 7.54776i −0.424358 0.290513i
676676 21.6404 + 57.9591i 0.832323 + 2.22920i
677677 1.79454i 0.0689698i 0.999405 + 0.0344849i 0.0109791π0.0109791\pi
−0.999405 + 0.0344849i 0.989021π0.989021\pi
678678 −1.95475 + 8.53856i −0.0750716 + 0.327921i
679679 4.52075 0.797130i 0.173490 0.0305910i
680680 1.01166 + 10.1150i 0.0387953 + 0.387894i
681681 8.93760 8.01031i 0.342490 0.306956i
682682 1.47811 + 16.1258i 0.0565998 + 0.617490i
683683 −18.3934 −0.703803 −0.351901 0.936037i 0.614465π-0.614465\pi
−0.351901 + 0.936037i 0.614465π0.614465\pi
684684 −10.2175 + 24.0750i −0.390675 + 0.920529i
685685 −11.5634 −0.441814
686686 1.56767 + 17.1029i 0.0598538 + 0.652991i
687687 −4.03718 1.32203i −0.154028 0.0504386i
688688 −0.396632 23.9541i −0.0151215 0.913243i
689689 −38.9462 + 6.86727i −1.48373 + 0.261622i
690690 −25.7704 23.9428i −0.981063 0.911488i
691691 20.9229i 0.795945i −0.917397 0.397973i 0.869714π-0.869714\pi
0.917397 0.397973i 0.130286π-0.130286\pi
692692 −3.16601 + 1.18210i −0.120354 + 0.0449369i
693693 −7.65348 0.840023i −0.290732 0.0319098i
694694 2.43342 + 8.93358i 0.0923714 + 0.339114i
695695 −11.1147 + 19.2511i −0.421603 + 0.730237i
696696 23.0748 + 5.08190i 0.874648 + 0.192629i
697697 0.929373 + 0.779837i 0.0352025 + 0.0295384i
698698 41.3384 3.78912i 1.56468 0.143420i
699699 28.2177 35.9463i 1.06729 1.35961i
700700 2.40928 + 4.09435i 0.0910623 + 0.154752i
701701 −13.9837 + 38.4199i −0.528157 + 1.45110i 0.333081 + 0.942898i 0.391912π0.391912\pi
−0.861238 + 0.508201i 0.830311π0.830311\pi
702702 −0.715634 48.7022i −0.0270098 1.83815i
703703 −21.5962 + 13.9139i −0.814517 + 0.524774i
704704 0.551935 + 22.2198i 0.0208018 + 0.837438i
705705 −2.69189 + 8.22042i −0.101383 + 0.309599i
706706 9.46545 + 4.36621i 0.356237 + 0.164324i
707707 16.0127 5.82815i 0.602220 0.219190i
708708 −8.07640 4.23256i −0.303530 0.159069i
709709 4.58118 1.66741i 0.172050 0.0626210i −0.254559 0.967057i 0.581930π-0.581930\pi
0.426609 + 0.904436i 0.359708π0.359708\pi
710710 11.5129 16.5878i 0.432072 0.622531i
711711 −28.4181 14.0226i −1.06576 0.525890i
712712 −13.4352 + 1.34372i −0.503504 + 0.0503581i
713713 −24.4120 + 29.0930i −0.914235 + 1.08954i
714714 −0.263522 + 5.21170i −0.00986206 + 0.195043i
715715 24.8538 14.3494i 0.929480 0.536636i
716716 −23.9998 28.1257i −0.896915 1.05111i
717717 −4.39081 20.8933i −0.163978 0.780274i
718718 0.124596 + 0.0328333i 0.00464989 + 0.00122533i
719719 −8.79161 49.8597i −0.327872 1.85945i −0.488675 0.872466i 0.662520π-0.662520\pi
0.160804 0.986986i 0.448591π-0.448591\pi
720720 10.8104 15.2597i 0.402880 0.568694i
721721 5.53114 0.205990
722722 −8.82665 + 25.3789i −0.328494 + 0.944506i
723723 13.9160 + 22.3846i 0.517541 + 0.832492i
724724 3.84496 2.26253i 0.142897 0.0840864i
725725 −4.24164 + 11.6538i −0.157531 + 0.432812i
726726 −5.47009 + 5.88763i −0.203014 + 0.218510i
727727 2.44059 6.70547i 0.0905165 0.248692i −0.886171 0.463358i 0.846644π-0.846644\pi
0.976687 + 0.214666i 0.0688665π0.0688665\pi
728728 −7.12346 + 15.7851i −0.264013 + 0.585036i
729729 −8.69699 + 25.5610i −0.322111 + 0.946702i
730730 8.47918 + 17.9889i 0.313828 + 0.665798i
731731 10.5813 + 8.87872i 0.391362 + 0.328391i
732732 −47.1035 + 10.3069i −1.74099 + 0.380952i
733733 34.6414 1.27951 0.639754 0.768580i 0.279036π-0.279036\pi
0.639754 + 0.768580i 0.279036π0.279036\pi
734734 18.8698 + 40.0330i 0.696498 + 1.47765i
735735 6.17984 + 15.3975i 0.227947 + 0.567945i
736736 −36.0892 + 37.6148i −1.33027 + 1.38650i
737737 −25.6457 + 30.5634i −0.944673 + 1.12582i
738738 −0.348127 2.20456i −0.0128147 0.0811508i
739739 2.61591 7.18715i 0.0962278 0.264384i −0.882234 0.470811i 0.843961π-0.843961\pi
0.978462 + 0.206427i 0.0661836π0.0661836\pi
740740 17.2093 6.42552i 0.632628 0.236207i
741741 −4.06640 49.8767i −0.149383 1.83227i
742742 −6.40329 4.44424i −0.235072 0.163153i
743743 −19.6371 + 16.4775i −0.720416 + 0.604501i −0.927500 0.373822i 0.878047π-0.878047\pi
0.207084 + 0.978323i 0.433603π0.433603\pi
744744 −17.0435 10.8246i −0.624847 0.396850i
745745 −1.91765 + 10.8756i −0.0702574 + 0.398449i
746746 9.70156 + 13.7339i 0.355199 + 0.502835i
747747 13.6209 5.98952i 0.498364 0.219145i
748748 −9.88466 8.15573i −0.361419 0.298203i
749749 2.98604 + 1.72399i 0.109108 + 0.0629933i
750750 21.1739 + 19.6723i 0.773163 + 0.718332i
751751 3.09433 + 0.545614i 0.112914 + 0.0199097i 0.229819 0.973233i 0.426186π-0.426186\pi
−0.116906 + 0.993143i 0.537298π0.537298\pi
752752 12.1162 + 4.18412i 0.441834 + 0.152579i
753753 −13.2971 + 24.8700i −0.484572 + 0.906313i
754754 −43.6204 + 11.8818i −1.58856 + 0.432709i
755755 17.2733 14.4940i 0.628640 0.527492i
756756 6.65912 6.91478i 0.242190 0.251488i
757757 −0.841987 4.77515i −0.0306025 0.173556i 0.965676 0.259751i 0.0836403π-0.0836403\pi
−0.996278 + 0.0861949i 0.972529π0.972529\pi
758758 −1.23044 13.4238i −0.0446914 0.487573i
759759 44.3208 1.44567i 1.60874 0.0524745i
760760 10.0377 16.3828i 0.364107 0.594266i
761761 0.433654 + 0.250370i 0.0157199 + 0.00907591i 0.507839 0.861452i 0.330444π-0.330444\pi
−0.492119 + 0.870528i 0.663778π0.663778\pi
762762 −5.12796 41.1382i −0.185767 1.49028i
763763 5.46265 + 6.51013i 0.197761 + 0.235683i
764764 4.76398 + 5.58297i 0.172355 + 0.201985i
765765 2.56029 + 10.4737i 0.0925674 + 0.378679i
766766 40.0488 + 10.5536i 1.44702 + 0.381316i
767767 17.4470 0.629974
768768 −22.3533 16.3808i −0.806604 0.591092i
769769 3.35061 19.0022i 0.120826 0.685239i −0.862874 0.505420i 0.831338π-0.831338\pi
0.983700 0.179819i 0.0575512π-0.0575512\pi
770770 5.46959 + 1.44134i 0.197110 + 0.0519421i
771771 −0.487479 14.9449i −0.0175561 0.538229i
772772 −14.7363 2.47280i −0.530371 0.0889982i
773773 11.9875 + 2.11372i 0.431160 + 0.0760252i 0.385017 0.922910i 0.374196π-0.374196\pi
0.0461436 + 0.998935i 0.485307π0.485307\pi
774774 −3.96355 25.0997i −0.142467 0.902189i
775775 6.81198 8.11820i 0.244693 0.291614i
776776 −6.09786 12.6639i −0.218901 0.454609i
777777 9.22836 1.93938i 0.331065 0.0695747i
778778 −7.29954 + 10.5172i −0.261701 + 0.377060i
779779 −0.507734 2.23611i −0.0181915 0.0801171i
780780 −4.76802 + 35.4633i −0.170723 + 1.26979i
781781 4.42008 + 25.0675i 0.158163 + 0.896986i
782782 −2.74334 29.9292i −0.0981017 1.07027i
783783 24.9874 + 1.92061i 0.892975 + 0.0686371i
784784 22.9616 8.79051i 0.820057 0.313947i
785785 −5.05112 13.8778i −0.180282 0.495321i
786786 34.8202 + 22.5216i 1.24200 + 0.803318i
787787 3.58252i 0.127703i −0.997959 0.0638514i 0.979662π-0.979662\pi
0.997959 0.0638514i 0.0203384π-0.0203384\pi
788788 19.0310 + 6.74883i 0.677950 + 0.240417i
789789 31.2060 + 24.4966i 1.11096 + 0.872101i
790790 19.1253 + 13.2740i 0.680446 + 0.472269i
791791 1.65168 2.86080i 0.0587270 0.101718i
792792 3.86984 + 23.2551i 0.137509 + 0.826334i
793793 70.6758 59.3040i 2.50977 2.10595i
794794 11.8127 + 3.11286i 0.419217 + 0.110471i
795795 −15.3051 5.01188i −0.542817 0.177753i
796796 −7.00621 11.9064i −0.248329 0.422011i
797797 15.1583 + 8.75164i 0.536934 + 0.309999i 0.743835 0.668363i 0.233005π-0.233005\pi
−0.206902 + 0.978362i 0.566338π0.566338\pi
798798 6.35321 7.54418i 0.224901 0.267061i
799799 −6.40038 + 3.69526i −0.226429 + 0.130729i
800800 10.0704 10.4961i 0.356044 0.371094i
801801 −13.9116 + 3.40067i −0.491543 + 0.120157i
802802 −3.82226 3.79075i −0.134969 0.133856i
803803 −23.5583 8.57453i −0.831356 0.302589i
804804 −10.6334 48.5959i −0.375012 1.71385i
805805 6.63284 + 11.4884i 0.233777 + 0.404914i
806806 38.4993 + 3.20773i 1.35608 + 0.112988i
807807 0.644038 + 1.60466i 0.0226712 + 0.0564869i
808808 −30.4552 42.3650i −1.07141 1.49040i
809809 8.50204 4.90866i 0.298916 0.172579i −0.343040 0.939321i 0.611457π-0.611457\pi
0.641956 + 0.766742i 0.278123π0.278123\pi
810810 9.09434 17.6276i 0.319542 0.619369i
811811 16.9636 + 2.99113i 0.595671 + 0.105033i 0.463352 0.886174i 0.346647π-0.346647\pi
0.132319 + 0.991207i 0.457758π0.457758\pi
812812 −7.75334 4.39122i −0.272089 0.154102i
813813 −13.7103 + 17.4655i −0.480843 + 0.612542i
814814 −9.69982 + 21.0281i −0.339979 + 0.737036i
815815 −4.76734 + 4.00028i −0.166993 + 0.140124i
816816 15.5799 3.54449i 0.545407 0.124082i
817817 −5.78074 25.4590i −0.202242 0.890696i
818818 −1.30169 + 15.6229i −0.0455125 + 0.546241i
819819 −5.14422 + 17.6335i −0.179754 + 0.616165i
820820 0.0135730 + 1.63957i 0.000473991 + 0.0572561i
821821 −20.3189 3.58278i −0.709136 0.125040i −0.192565 0.981284i 0.561681π-0.561681\pi
−0.516571 + 0.856244i 0.672792π0.672792\pi
822822 2.24818 + 18.0356i 0.0784142 + 0.629065i
823823 −0.217887 + 0.259668i −0.00759507 + 0.00905145i −0.769829 0.638251i 0.779658π-0.779658\pi
0.762234 + 0.647302i 0.224103π0.224103\pi
824824 −4.58608 16.3030i −0.159764 0.567942i
825825 −12.3674 + 0.403403i −0.430577 + 0.0140447i
826826 2.44156 + 2.42143i 0.0849526 + 0.0842522i
827827 35.6500 12.9755i 1.23967 0.451204i 0.362773 0.931878i 0.381830π-0.381830\pi
0.876900 + 0.480674i 0.159608π0.159608\pi
828828 −32.3338 + 44.8497i −1.12368 + 1.55863i
829829 8.75620 15.1662i 0.304115 0.526743i −0.672949 0.739689i 0.734973π-0.734973\pi
0.977064 + 0.212946i 0.0683059π0.0683059\pi
830830 −10.5469 + 2.87288i −0.366089 + 0.0997191i
831831 −14.8431 4.86057i −0.514900 0.168611i
832832 52.4329 + 7.90828i 1.81779 + 0.274170i
833833 −4.84837 + 13.3208i −0.167986 + 0.461538i
834834 32.1873 + 13.5929i 1.11456 + 0.470684i
835835 15.8520 9.15218i 0.548583 0.316724i
836836 5.55845 + 23.5745i 0.192243 + 0.815339i
837837 −19.5032 8.84513i −0.674130 0.305732i
838838 −5.62461 + 12.1935i −0.194299 + 0.421219i
839839 −23.0465 + 19.3383i −0.795654 + 0.667633i −0.947138 0.320827i 0.896039π-0.896039\pi
0.151484 + 0.988460i 0.451595π0.451595\pi
840840 −5.58912 + 4.30105i −0.192843 + 0.148400i
841841 0.996505 + 5.65146i 0.0343622 + 0.194878i
842842 13.0645 13.1731i 0.450231 0.453974i
843843 −0.993191 30.4488i −0.0342073 1.04871i
844844 −31.2652 25.7966i −1.07619 0.887955i
845845 −16.4878 45.3000i −0.567199 1.55837i
846846 13.3449 + 2.60037i 0.458808 + 0.0894025i
847847 2.62470 1.51537i 0.0901857 0.0520687i
848848 −7.79016 + 22.5585i −0.267515 + 0.774663i
849849 22.9082 29.1826i 0.786207 1.00154i
850850 0.765510 + 8.35153i 0.0262568 + 0.286455i
851851 −51.0356 + 18.5754i −1.74948 + 0.636758i
852852 −28.1108 14.7319i −0.963059 0.504706i
853853 0.363805 + 2.06324i 0.0124564 + 0.0706440i 0.990402 0.138214i 0.0441363π-0.0441363\pi
−0.977946 + 0.208858i 0.933025π0.933025\pi
854854 18.1211 + 1.50984i 0.620093 + 0.0516657i
855855 8.11650 18.6927i 0.277579 0.639278i
856856 2.60561 10.2308i 0.0890580 0.349681i
857857 12.1488 2.14217i 0.414996 0.0731750i 0.0377482 0.999287i 0.487982π-0.487982\pi
0.377248 + 0.926112i 0.376870π0.376870\pi
858858 −27.2131 35.9752i −0.929041 1.22817i
859859 0.957068 + 2.62952i 0.0326548 + 0.0897182i 0.954949 0.296771i 0.0959098π-0.0959098\pi
−0.922294 + 0.386489i 0.873688π0.873688\pi
860860 0.154534 + 18.6671i 0.00526956 + 0.636541i
861861 −0.119056 + 0.833221i −0.00405743 + 0.0283961i
862862 4.17280 50.0820i 0.142126 1.70580i
863863 9.44017 + 16.3509i 0.321347 + 0.556589i 0.980766 0.195186i 0.0625311π-0.0625311\pi
−0.659419 + 0.751775i 0.729198π0.729198\pi
864864 −25.9026 13.8944i −0.881225 0.472697i
865865 2.47450 0.900646i 0.0841356 0.0306229i
866866 −20.7577 14.4070i −0.705376 0.489571i
867867 9.53969 17.8424i 0.323985 0.605961i
868868 4.94245 + 5.79212i 0.167758 + 0.196597i
869869 −28.9021 + 5.09621i −0.980435 + 0.172877i
870870 −17.9466 4.10854i −0.608445 0.139292i
871871 61.1830 + 72.9151i 2.07311 + 2.47063i
872872 14.6593 21.4989i 0.496426 0.728046i
873873 −8.27962 12.3977i −0.280223 0.419597i
874874 −30.0769 + 48.1890i −1.01737 + 1.63002i
875875 −5.44979 9.43932i −0.184237 0.319107i
876876 26.4091 16.7226i 0.892281 0.565004i
877877 −18.7708 6.83202i −0.633845 0.230701i 0.00505884 0.999987i 0.498390π-0.498390\pi
−0.638904 + 0.769286i 0.720612π0.720612\pi
878878 3.03978 0.828007i 0.102588 0.0279439i
879879 −29.9473 + 6.29355i −1.01010 + 0.212276i
880880 −0.286729 17.3167i −0.00966564 0.583745i
881881 −19.9891 11.5407i −0.673451 0.388817i 0.123932 0.992291i 0.460450π-0.460450\pi
−0.797383 + 0.603473i 0.793783π0.793783\pi
882882 22.8143 12.6324i 0.768198 0.425357i
883883 −13.3436 36.6612i −0.449047 1.23375i −0.933388 0.358868i 0.883163π-0.883163\pi
0.484341 0.874879i 0.339059π-0.339059\pi
884884 −23.2565 + 19.8449i −0.782199 + 0.667455i
885885 6.26564 + 3.35000i 0.210617 + 0.112609i
886886 2.43140 1.14605i 0.0816843 0.0385024i
887887 −1.56981 1.31723i −0.0527091 0.0442282i 0.616053 0.787705i 0.288731π-0.288731\pi
−0.668762 + 0.743477i 0.733175π0.733175\pi
888888 −13.3679 25.5925i −0.448597 0.858828i
889889 −2.71483 + 15.3966i −0.0910526 + 0.516385i
890890 10.4770 0.960334i 0.351190 0.0321905i
891891 7.50786 + 23.8512i 0.251523 + 0.799045i
892892 −7.70173 + 45.8973i −0.257873 + 1.53676i
893893 13.8581 + 1.75247i 0.463744 + 0.0586442i
894894 17.3357 + 0.876553i 0.579791 + 0.0293163i
895895 18.5187 + 22.0697i 0.619011 + 0.737708i
896896 6.23997 + 8.38375i 0.208463 + 0.280081i
897897 14.9643 104.729i 0.499644 3.49678i
898898 22.6656 + 10.4551i 0.756361 + 0.348893i
899899 −3.45166 + 19.5754i −0.115119 + 0.652875i
900900 9.02251 12.5150i 0.300750 0.417166i
901901 −6.88000 11.9165i −0.229206 0.396996i
902902 −1.46760 1.45550i −0.0488656 0.0484628i
903903 −1.35550 + 9.48652i −0.0451082 + 0.315692i
904904 −9.80165 2.49632i −0.325998 0.0830264i
905905 −3.01050 + 1.73811i −0.100072 + 0.0577768i
906906 −25.9650 24.1236i −0.862628 0.801452i
907907 1.25354 3.44407i 0.0416231 0.114359i −0.917140 0.398566i 0.869508π-0.869508\pi
0.958763 + 0.284207i 0.0917303π0.0917303\pi
908908 8.99572 + 10.5422i 0.298533 + 0.349855i
909909 −38.2595 39.9853i −1.26899 1.32623i
910910 5.65225 12.2535i 0.187370 0.406198i
911911 −10.1210 17.5300i −0.335322 0.580795i 0.648225 0.761449i 0.275512π-0.275512\pi
−0.983547 + 0.180654i 0.942178π0.942178\pi
912912 −27.5041 12.4709i −0.910753 0.412952i
913913 6.89010 11.9340i 0.228029 0.394958i
914914 −13.5520 19.1847i −0.448260 0.634575i
915915 36.7684 7.72702i 1.21553 0.255447i
916916 1.63950 4.62322i 0.0541706 0.152755i
917917 −10.0524 11.9800i −0.331959 0.395614i
918918 15.8383 6.02966i 0.522743 0.199009i
919919 −25.3019 14.6081i −0.834633 0.481876i 0.0208033 0.999784i 0.493378π-0.493378\pi
−0.855436 + 0.517908i 0.826711π0.826711\pi
920920 28.3625 29.0758i 0.935084 0.958600i
921921 −12.6972 31.6359i −0.418386 1.04244i
922922 −10.1824 + 38.6402i −0.335339 + 1.27255i
923923 60.7261 1.99882
924924 1.18467 8.81127i 0.0389728 0.289869i
925925 14.2411 5.18334i 0.468245 0.170427i
926926 14.2668 10.0780i 0.468837 0.331183i
927927 −7.23069 16.4435i −0.237487 0.540076i
928928 −6.51449 + 26.4939i −0.213849 + 0.869704i
929929 46.5540 8.20873i 1.52739 0.269320i 0.654056 0.756446i 0.273066π-0.273066\pi
0.873331 + 0.487126i 0.161955π0.161955\pi
930930 13.2101 + 8.54424i 0.433176 + 0.280177i
931931 22.5230 14.5110i 0.738160 0.475579i
932932 40.7023 + 33.5830i 1.33325 + 1.10005i
933933 −12.6481 + 11.3358i −0.414080 + 0.371119i
934934 9.11467 + 12.9031i 0.298241 + 0.422202i
935935 7.64928 + 6.41851i 0.250158 + 0.209908i
936936 56.2399 + 0.541919i 1.83826 + 0.0177132i
937937 −7.21371 + 40.9110i −0.235662 + 1.33650i 0.605554 + 0.795804i 0.292952π0.292952\pi
−0.841216 + 0.540700i 0.818160π0.818160\pi
938938 −1.55768 + 18.6953i −0.0508601 + 0.610423i
939939 −18.4302 + 34.4707i −0.601448 + 1.12491i
940940 −9.41370 3.33832i −0.307041 0.108884i
941941 28.3624 + 5.00106i 0.924588 + 0.163030i 0.615620 0.788043i 0.288906π-0.288906\pi
0.308967 + 0.951073i 0.400017π0.400017\pi
942942 −20.6635 + 10.5765i −0.673253 + 0.344601i
943943 4.84761i 0.157860i
944944 5.11275 9.20417i 0.166406 0.299570i
945945 −5.23323 + 5.34488i −0.170237 + 0.173869i
946946 −16.7091 16.5714i −0.543260 0.538781i
947947 30.7056 25.7651i 0.997798 0.837252i 0.0111204 0.999938i 0.496460π-0.496460\pi
0.986678 + 0.162686i 0.0520158π0.0520158\pi
948948 16.9854 32.4109i 0.551660 1.05266i
949949 −29.9050 + 51.7971i −0.970759 + 1.68140i
950950 8.39274 13.4468i 0.272296 0.436271i
951951 −20.0627 + 12.4725i −0.650577 + 0.404448i
952952 −6.00877 0.450592i −0.194745 0.0146038i
953953 −25.0363 + 4.41458i −0.811006 + 0.143002i −0.563747 0.825947i 0.690641π-0.690641\pi
−0.247258 + 0.968950i 0.579530π0.579530\pi
954954 −4.84148 + 24.8462i −0.156749 + 0.804424i
955955 −3.67597 4.38085i −0.118952 0.141761i
956956 24.2417 4.48169i 0.784032 0.144948i
957957 19.7108 12.2537i 0.637160 0.396107i
958958 −0.0418777 + 0.502616i −0.00135301 + 0.0162388i
959959 1.19023 6.75010i 0.0384344 0.217972i
960960 17.3115 + 12.9077i 0.558725 + 0.416595i
961961 −7.00718 + 12.1368i −0.226038 + 0.391510i
962962 45.3863 + 31.5007i 1.46331 + 1.01562i
963963 1.22170 11.1309i 0.0393686 0.358689i
964964 −26.2308 + 15.4353i −0.844836 + 0.497136i
965965 11.4662 + 2.02180i 0.369111 + 0.0650842i
966966 16.6292 12.5790i 0.535035 0.404722i
967967 −11.9214 14.2074i −0.383368 0.456880i 0.539506 0.841982i 0.318611π-0.318611\pi
−0.922874 + 0.385102i 0.874166π0.874166\pi
968968 −6.64279 6.47983i −0.213507 0.208270i
969969 15.8236 7.26498i 0.508327 0.233385i
970970 4.66962 + 9.90677i 0.149933 + 0.318087i
971971 −5.21874 1.89947i −0.167477 0.0609567i 0.256921 0.966432i 0.417292π-0.417292\pi
−0.424398 + 0.905476i 0.639514π0.639514\pi
972972 −29.2622 10.7574i −0.938586 0.345045i
973973 −10.0938 8.46969i −0.323592 0.271526i
974974 −9.40755 4.33950i −0.301437 0.139046i
975975 −4.17568 + 29.2237i −0.133729 + 0.935908i
976976 −10.5747 54.6638i −0.338488 1.74975i
977977 28.0711i 0.898073i 0.893514 + 0.449036i 0.148233π0.148233\pi
−0.893514 + 0.449036i 0.851767π0.851767\pi
978978 7.16619 + 6.65798i 0.229150 + 0.212899i
979979 −8.52530 + 10.1601i −0.272470 + 0.324717i
980980 −17.9478 + 6.70125i −0.573322 + 0.214063i
981981 12.2128 24.7504i 0.389925 0.790220i
982982 29.0459 + 7.65411i 0.926892 + 0.244253i
983983 −25.4508 9.26332i −0.811753 0.295454i −0.0974052 0.995245i 0.531054π-0.531054\pi
−0.714348 + 0.699791i 0.753276π0.753276\pi
984984 2.55463 0.339939i 0.0814385 0.0108368i
985985 −14.7849 5.38128i −0.471088 0.171462i
986986 −9.07576 12.8480i −0.289031 0.409164i
987987 −4.52158 2.41752i −0.143923 0.0769506i
988988 57.6898 3.29308i 1.83536 0.104767i
989989 55.1918i 1.75500i
990990 −2.86529 18.1448i −0.0910647 0.576679i
991991 −11.0066 + 1.94076i −0.349635 + 0.0616501i −0.345708 0.938342i 0.612361π-0.612361\pi
−0.00392729 + 0.999992i 0.501250π0.501250\pi
992992 12.9743 19.3703i 0.411933 0.615008i
993993 −2.71302 + 8.28494i −0.0860951 + 0.262915i
994994 8.49810 + 8.42804i 0.269543 + 0.267321i
995995 5.38227 + 9.32237i 0.170630 + 0.295539i
996996 6.53145 + 15.8917i 0.206957 + 0.503548i
997997 19.0387 + 15.9753i 0.602961 + 0.505944i 0.892396 0.451253i 0.149023π-0.149023\pi
−0.289435 + 0.957198i 0.593467π0.593467\pi
998998 −19.8629 + 5.41045i −0.628748 + 0.171265i
999999 −17.8295 24.8997i −0.564101 0.787792i
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 684.2.bs.a.23.4 696
4.3 odd 2 inner 684.2.bs.a.23.11 yes 696
9.2 odd 6 684.2.ch.a.479.37 yes 696
19.5 even 9 684.2.ch.a.347.30 yes 696
36.11 even 6 684.2.ch.a.479.30 yes 696
76.43 odd 18 684.2.ch.a.347.37 yes 696
171.119 odd 18 inner 684.2.bs.a.119.11 yes 696
684.119 even 18 inner 684.2.bs.a.119.4 yes 696
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.2.bs.a.23.4 696 1.1 even 1 trivial
684.2.bs.a.23.11 yes 696 4.3 odd 2 inner
684.2.bs.a.119.4 yes 696 684.119 even 18 inner
684.2.bs.a.119.11 yes 696 171.119 odd 18 inner
684.2.ch.a.347.30 yes 696 19.5 even 9
684.2.ch.a.347.37 yes 696 76.43 odd 18
684.2.ch.a.479.30 yes 696 36.11 even 6
684.2.ch.a.479.37 yes 696 9.2 odd 6