Properties

Label 312.2.bt.c.115.7
Level 312312
Weight 22
Character 312.115
Analytic conductor 2.4912.491
Analytic rank 00
Dimension 4848
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 312=23313 312 = 2^{3} \cdot 3 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 312.bt (of order 1212, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.491332543062.49133254306
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 115.7
Character χ\chi == 312.115
Dual form 312.2.bt.c.19.7

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.157821+1.40538i)q2+(0.5000000.866025i)q3+(1.95019+0.443596i)q4+(2.14006+2.14006i)q5+(1.138180.839367i)q6+(1.949330.522322i)q7+(0.9312012.67074i)q8+(0.500000+0.866025i)q9+(3.345352.66986i)q10+(5.459971.46299i)q11+(1.35926+1.46711i)q12+(2.42353+2.66955i)q13+(1.04171+2.65712i)q14+(2.92338+0.783318i)q15+(3.606441.73019i)q16+(5.676183.27715i)q17+(1.296010.566013i)q18+(1.560340.418091i)q19+(3.224205.12285i)q20+(1.427011.42701i)q21+(1.194377.90422i)q22+(0.192056+0.332651i)q23+(1.84733+2.14182i)q244.15975iq25+(4.134212.98468i)q26+1.00000q27+(3.56986+1.88334i)q28+(0.554113+0.319917i)q29+(0.639489+4.23209i)q30+(4.55111+4.55111i)q31+(3.00075+4.79536i)q32+(1.46299+5.45997i)q33+(3.709828.49440i)q34+(3.05389+5.28950i)q35+(0.5909271.91071i)q36+(0.777993+2.90351i)q37+(0.833830+2.12688i)q38+(3.52366+0.764069i)q39+(7.70839+3.72273i)q40+(0.4517621.68600i)q41+(1.780282.23070i)q42+(5.38062+3.10650i)q43+(11.2969+0.431087i)q44+(0.7833182.92338i)q45+(0.437191+0.322411i)q46+(4.53305+4.53305i)q47+(3.301612.25818i)q48+(2.53510+1.46364i)q49+(5.846030.656495i)q50+6.55429iq51+(3.542146.28118i)q52+3.23972iq53+(0.157821+1.40538i)q54+(14.81568.55378i)q55+(3.210214.71978i)q56+(1.142251.14225i)q57+(0.5370560.728250i)q58+(1.99499+7.44540i)q59+(6.048610.230813i)q60+(6.352023.66734i)q61+(7.114295.67777i)q62+(0.522322+1.94933i)q63+(6.26573+4.97400i)q64+(0.52648310.8995i)q65+(7.44244+2.91776i)q66+(2.233998.33737i)q67+(12.5233+3.87311i)q68+(0.1920560.332651i)q69+(7.915723.45709i)q70+(3.68585+13.7558i)q71+(2.77853+0.528927i)q72+(3.28631+3.28631i)q73+(4.203320.635142i)q74+(3.60245+2.07987i)q75+(2.85748+1.50751i)q7611.4074q77+(0.517700+5.07267i)q7815.2352iq79+(4.01530+11.4207i)q80+(0.5000000.866025i)q81+(2.44077+0.368812i)q82+(2.70458+2.70458i)q83+(3.41595+2.14992i)q84+(19.16075.13409i)q85+(3.51664+8.05209i)q86+(0.554113+0.319917i)q87+(1.17705+15.9445i)q88+(16.3179+4.37236i)q89+(3.984841.56223i)q90+(3.32991+6.46970i)q91+(0.5221080.563536i)q92+(6.21693+1.66582i)q93+(5.65524+7.08606i)q94+(2.44448+4.23396i)q95+(2.652534.99640i)q96+(5.55609+1.48875i)q97+(2.457073.33179i)q98+(3.996973.99697i)q99+O(q100)q+(0.157821 + 1.40538i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.95019 + 0.443596i) q^{4} +(-2.14006 + 2.14006i) q^{5} +(1.13818 - 0.839367i) q^{6} +(1.94933 - 0.522322i) q^{7} +(-0.931201 - 2.67074i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.34535 - 2.66986i) q^{10} +(-5.45997 - 1.46299i) q^{11} +(1.35926 + 1.46711i) q^{12} +(-2.42353 + 2.66955i) q^{13} +(1.04171 + 2.65712i) q^{14} +(2.92338 + 0.783318i) q^{15} +(3.60644 - 1.73019i) q^{16} +(-5.67618 - 3.27715i) q^{17} +(-1.29601 - 0.566013i) q^{18} +(1.56034 - 0.418091i) q^{19} +(3.22420 - 5.12285i) q^{20} +(-1.42701 - 1.42701i) q^{21} +(1.19437 - 7.90422i) q^{22} +(0.192056 + 0.332651i) q^{23} +(-1.84733 + 2.14182i) q^{24} -4.15975i q^{25} +(-4.13421 - 2.98468i) q^{26} +1.00000 q^{27} +(-3.56986 + 1.88334i) q^{28} +(-0.554113 + 0.319917i) q^{29} +(-0.639489 + 4.23209i) q^{30} +(-4.55111 + 4.55111i) q^{31} +(3.00075 + 4.79536i) q^{32} +(1.46299 + 5.45997i) q^{33} +(3.70982 - 8.49440i) q^{34} +(-3.05389 + 5.28950i) q^{35} +(0.590927 - 1.91071i) q^{36} +(-0.777993 + 2.90351i) q^{37} +(0.833830 + 2.12688i) q^{38} +(3.52366 + 0.764069i) q^{39} +(7.70839 + 3.72273i) q^{40} +(0.451762 - 1.68600i) q^{41} +(1.78028 - 2.23070i) q^{42} +(5.38062 + 3.10650i) q^{43} +(11.2969 + 0.431087i) q^{44} +(-0.783318 - 2.92338i) q^{45} +(-0.437191 + 0.322411i) q^{46} +(4.53305 + 4.53305i) q^{47} +(-3.30161 - 2.25818i) q^{48} +(-2.53510 + 1.46364i) q^{49} +(5.84603 - 0.656495i) q^{50} +6.55429i q^{51} +(3.54214 - 6.28118i) q^{52} +3.23972i q^{53} +(0.157821 + 1.40538i) q^{54} +(14.8156 - 8.55378i) q^{55} +(-3.21021 - 4.71978i) q^{56} +(-1.14225 - 1.14225i) q^{57} +(-0.537056 - 0.728250i) q^{58} +(1.99499 + 7.44540i) q^{59} +(-6.04861 - 0.230813i) q^{60} +(-6.35202 - 3.66734i) q^{61} +(-7.11429 - 5.67777i) q^{62} +(-0.522322 + 1.94933i) q^{63} +(-6.26573 + 4.97400i) q^{64} +(-0.526483 - 10.8995i) q^{65} +(-7.44244 + 2.91776i) q^{66} +(2.23399 - 8.33737i) q^{67} +(12.5233 + 3.87311i) q^{68} +(0.192056 - 0.332651i) q^{69} +(-7.91572 - 3.45709i) q^{70} +(3.68585 + 13.7558i) q^{71} +(2.77853 + 0.528927i) q^{72} +(-3.28631 + 3.28631i) q^{73} +(-4.20332 - 0.635142i) q^{74} +(-3.60245 + 2.07987i) q^{75} +(-2.85748 + 1.50751i) q^{76} -11.4074 q^{77} +(-0.517700 + 5.07267i) q^{78} -15.2352i q^{79} +(-4.01530 + 11.4207i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.44077 + 0.368812i) q^{82} +(2.70458 + 2.70458i) q^{83} +(3.41595 + 2.14992i) q^{84} +(19.1607 - 5.13409i) q^{85} +(-3.51664 + 8.05209i) q^{86} +(0.554113 + 0.319917i) q^{87} +(1.17705 + 15.9445i) q^{88} +(16.3179 + 4.37236i) q^{89} +(3.98484 - 1.56223i) q^{90} +(-3.32991 + 6.46970i) q^{91} +(-0.522108 - 0.563536i) q^{92} +(6.21693 + 1.66582i) q^{93} +(-5.65524 + 7.08606i) q^{94} +(-2.44448 + 4.23396i) q^{95} +(2.65253 - 4.99640i) q^{96} +(-5.55609 + 1.48875i) q^{97} +(-2.45707 - 3.33179i) q^{98} +(3.99697 - 3.99697i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+2q224q3+2q64q824q96q10+20q1128q14+4q16+12q174q18+20q19+4q20+14q22+2q2412q26+48q272q28++8q99+O(q100) 48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/312Z)×\left(\mathbb{Z}/312\mathbb{Z}\right)^\times.

nn 7979 145145 157157 209209
χ(n)\chi(n) 1-1 e(712)e\left(\frac{7}{12}\right) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.157821 + 1.40538i 0.111596 + 0.993754i
33 −0.500000 0.866025i −0.288675 0.500000i
44 −1.95019 + 0.443596i −0.975093 + 0.221798i
55 −2.14006 + 2.14006i −0.957066 + 0.957066i −0.999116 0.0420497i 0.986611π-0.986611\pi
0.0420497 + 0.999116i 0.486611π0.486611\pi
66 1.13818 0.839367i 0.464662 0.342670i
77 1.94933 0.522322i 0.736778 0.197419i 0.129133 0.991627i 0.458781π-0.458781\pi
0.607646 + 0.794208i 0.292114π0.292114\pi
88 −0.931201 2.67074i −0.329229 0.944250i
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 −3.34535 2.66986i −1.05789 0.844283i
1111 −5.45997 1.46299i −1.64624 0.441109i −0.687685 0.726010i 0.741373π-0.741373\pi
−0.958557 + 0.284900i 0.908039π0.908039\pi
1212 1.35926 + 1.46711i 0.392384 + 0.423519i
1313 −2.42353 + 2.66955i −0.672168 + 0.740399i
1414 1.04171 + 2.65712i 0.278408 + 0.710145i
1515 2.92338 + 0.783318i 0.754814 + 0.202252i
1616 3.60644 1.73019i 0.901611 0.432548i
1717 −5.67618 3.27715i −1.37668 0.794825i −0.384919 0.922950i 0.625771π-0.625771\pi
−0.991758 + 0.128126i 0.959104π0.959104\pi
1818 −1.29601 0.566013i −0.305471 0.133411i
1919 1.56034 0.418091i 0.357966 0.0959166i −0.0753542 0.997157i 0.524009π-0.524009\pi
0.433320 + 0.901240i 0.357342π0.357342\pi
2020 3.22420 5.12285i 0.720952 1.14550i
2121 −1.42701 1.42701i −0.311399 0.311399i
2222 1.19437 7.90422i 0.254640 1.68518i
2323 0.192056 + 0.332651i 0.0400465 + 0.0693626i 0.885354 0.464918i 0.153916π-0.153916\pi
−0.845307 + 0.534280i 0.820583π0.820583\pi
2424 −1.84733 + 2.14182i −0.377085 + 0.437196i
2525 4.15975i 0.831950i
2626 −4.13421 2.98468i −0.810786 0.585343i
2727 1.00000 0.192450
2828 −3.56986 + 1.88334i −0.674640 + 0.355918i
2929 −0.554113 + 0.319917i −0.102896 + 0.0594072i −0.550565 0.834792i 0.685588π-0.685588\pi
0.447669 + 0.894199i 0.352254π0.352254\pi
3030 −0.639489 + 4.23209i −0.116754 + 0.772670i
3131 −4.55111 + 4.55111i −0.817403 + 0.817403i −0.985731 0.168328i 0.946163π-0.946163\pi
0.168328 + 0.985731i 0.446163π0.446163\pi
3232 3.00075 + 4.79536i 0.530462 + 0.847709i
3333 1.46299 + 5.45997i 0.254674 + 0.950458i
3434 3.70982 8.49440i 0.636228 1.45678i
3535 −3.05389 + 5.28950i −0.516202 + 0.894088i
3636 0.590927 1.91071i 0.0984878 0.318451i
3737 −0.777993 + 2.90351i −0.127901 + 0.477334i −0.999926 0.0121269i 0.996140π-0.996140\pi
0.872025 + 0.489461i 0.162806π0.162806\pi
3838 0.833830 + 2.12688i 0.135265 + 0.345026i
3939 3.52366 + 0.764069i 0.564238 + 0.122349i
4040 7.70839 + 3.72273i 1.21880 + 0.588615i
4141 0.451762 1.68600i 0.0705534 0.263309i −0.921635 0.388058i 0.873146π-0.873146\pi
0.992188 + 0.124749i 0.0398126π0.0398126\pi
4242 1.78028 2.23070i 0.274703 0.344205i
4343 5.38062 + 3.10650i 0.820537 + 0.473737i 0.850602 0.525811i 0.176238π-0.176238\pi
−0.0300644 + 0.999548i 0.509571π0.509571\pi
4444 11.2969 + 0.431087i 1.70308 + 0.0649888i
4545 −0.783318 2.92338i −0.116770 0.435792i
4646 −0.437191 + 0.322411i −0.0644603 + 0.0475370i
4747 4.53305 + 4.53305i 0.661213 + 0.661213i 0.955666 0.294453i 0.0951375π-0.0951375\pi
−0.294453 + 0.955666i 0.595138π0.595138\pi
4848 −3.30161 2.25818i −0.476546 0.325940i
4949 −2.53510 + 1.46364i −0.362158 + 0.209092i
5050 5.84603 0.656495i 0.826753 0.0928424i
5151 6.55429i 0.917785i
5252 3.54214 6.28118i 0.491206 0.871043i
5353 3.23972i 0.445009i 0.974932 + 0.222505i 0.0714233π0.0714233\pi
−0.974932 + 0.222505i 0.928577π0.928577\pi
5454 0.157821 + 1.40538i 0.0214767 + 0.191248i
5555 14.8156 8.55378i 1.99773 1.15339i
5656 −3.21021 4.71978i −0.428982 0.630707i
5757 −1.14225 1.14225i −0.151294 0.151294i
5858 −0.537056 0.728250i −0.0705189 0.0956239i
5959 1.99499 + 7.44540i 0.259726 + 0.969309i 0.965400 + 0.260773i 0.0839774π0.0839774\pi
−0.705675 + 0.708536i 0.749356π0.749356\pi
6060 −6.04861 0.230813i −0.780873 0.0297979i
6161 −6.35202 3.66734i −0.813292 0.469555i 0.0348055 0.999394i 0.488919π-0.488919\pi
−0.848098 + 0.529840i 0.822252π0.822252\pi
6262 −7.11429 5.67777i −0.903516 0.721078i
6363 −0.522322 + 1.94933i −0.0658064 + 0.245593i
6464 −6.26573 + 4.97400i −0.783216 + 0.621750i
6565 −0.526483 10.8995i −0.0653021 1.35192i
6666 −7.44244 + 2.91776i −0.916100 + 0.359151i
6767 2.23399 8.33737i 0.272925 1.01857i −0.684293 0.729207i 0.739889π-0.739889\pi
0.957219 0.289365i 0.0934441π-0.0934441\pi
6868 12.5233 + 3.87311i 1.51868 + 0.469683i
6969 0.192056 0.332651i 0.0231209 0.0400465i
7070 −7.91572 3.45709i −0.946110 0.413201i
7171 3.68585 + 13.7558i 0.437431 + 1.63251i 0.735182 + 0.677870i 0.237097π0.237097\pi
−0.297752 + 0.954643i 0.596237π0.596237\pi
7272 2.77853 + 0.528927i 0.327453 + 0.0623347i
7373 −3.28631 + 3.28631i −0.384633 + 0.384633i −0.872768 0.488135i 0.837677π-0.837677\pi
0.488135 + 0.872768i 0.337677π0.337677\pi
7474 −4.20332 0.635142i −0.488626 0.0738337i
7575 −3.60245 + 2.07987i −0.415975 + 0.240163i
7676 −2.85748 + 1.50751i −0.327776 + 0.172924i
7777 −11.4074 −1.30000
7878 −0.517700 + 5.07267i −0.0586180 + 0.574367i
7979 15.2352i 1.71409i −0.515243 0.857044i 0.672298π-0.672298\pi
0.515243 0.857044i 0.327702π-0.327702\pi
8080 −4.01530 + 11.4207i −0.448925 + 1.27688i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 2.44077 + 0.368812i 0.269538 + 0.0407285i
8383 2.70458 + 2.70458i 0.296866 + 0.296866i 0.839785 0.542919i 0.182681π-0.182681\pi
−0.542919 + 0.839785i 0.682681π0.682681\pi
8484 3.41595 + 2.14992i 0.372711 + 0.234575i
8585 19.1607 5.13409i 2.07827 0.556871i
8686 −3.51664 + 8.05209i −0.379209 + 0.868279i
8787 0.554113 + 0.319917i 0.0594072 + 0.0342987i
8888 1.17705 + 15.9445i 0.125474 + 1.69969i
8989 16.3179 + 4.37236i 1.72969 + 0.463469i 0.980112 0.198445i 0.0635892π-0.0635892\pi
0.749579 + 0.661915i 0.230256π0.230256\pi
9090 3.98484 1.56223i 0.420039 0.164673i
9191 −3.32991 + 6.46970i −0.349069 + 0.678209i
9292 −0.522108 0.563536i −0.0544336 0.0587527i
9393 6.21693 + 1.66582i 0.644665 + 0.172738i
9494 −5.65524 + 7.08606i −0.583294 + 0.730871i
9595 −2.44448 + 4.23396i −0.250798 + 0.434395i
9696 2.65253 4.99640i 0.270723 0.509943i
9797 −5.55609 + 1.48875i −0.564135 + 0.151160i −0.529606 0.848244i 0.677660π-0.677660\pi
−0.0345298 + 0.999404i 0.510993π0.510993\pi
9898 −2.45707 3.33179i −0.248201 0.336562i
9999 3.99697 3.99697i 0.401711 0.401711i
100100 1.84525 + 8.11228i 0.184525 + 0.811228i
101101 −8.39225 14.5358i −0.835060 1.44637i −0.893981 0.448104i 0.852099π-0.852099\pi
0.0589207 0.998263i 0.481234π-0.481234\pi
102102 −9.21127 + 1.03440i −0.912052 + 0.102421i
103103 −12.5606 −1.23764 −0.618818 0.785534i 0.712388π-0.712388\pi
−0.618818 + 0.785534i 0.712388π0.712388\pi
104104 9.38647 + 3.98675i 0.920419 + 0.390933i
105105 6.10779 0.596059
106106 −4.55303 + 0.511295i −0.442230 + 0.0496613i
107107 −7.99878 13.8543i −0.773271 1.33934i −0.935761 0.352634i 0.885286π-0.885286\pi
0.162490 0.986710i 0.448047π-0.448047\pi
108108 −1.95019 + 0.443596i −0.187657 + 0.0426851i
109109 −10.1481 + 10.1481i −0.972008 + 0.972008i −0.999619 0.0276109i 0.991210π-0.991210\pi
0.0276109 + 0.999619i 0.491210π0.491210\pi
110110 14.3595 + 19.4716i 1.36913 + 1.85654i
111111 2.90351 0.777993i 0.275589 0.0738438i
112112 6.12644 5.25644i 0.578894 0.496687i
113113 −5.09342 + 8.82207i −0.479149 + 0.829910i −0.999714 0.0239117i 0.992388π-0.992388\pi
0.520565 + 0.853822i 0.325721π0.325721\pi
114114 1.42502 1.78556i 0.133465 0.167233i
115115 −1.12291 0.300882i −0.104712 0.0280574i
116116 0.938709 0.869701i 0.0871569 0.0807497i
117117 −1.10013 3.43362i −0.101707 0.317438i
118118 −10.1488 + 3.97876i −0.934270 + 0.366274i
119119 −12.7765 3.42345i −1.17122 0.313827i
120120 −0.630217 8.53703i −0.0575307 0.779320i
121121 18.1446 + 10.4758i 1.64951 + 0.952344i
122122 4.15152 9.50578i 0.375861 0.860613i
123123 −1.68600 + 0.451762i −0.152022 + 0.0407340i
124124 6.85665 10.8944i 0.615745 0.978342i
125125 −1.79819 1.79819i −0.160835 0.160835i
126126 −2.82199 0.426416i −0.251402 0.0379881i
127127 −4.84623 8.39392i −0.430034 0.744840i 0.566842 0.823826i 0.308165π-0.308165\pi
−0.996876 + 0.0789864i 0.974832π0.974832\pi
128128 −7.97922 8.02073i −0.705270 0.708939i
129129 6.21301i 0.547025i
130130 15.2349 2.46008i 1.33619 0.215763i
131131 4.01978 0.351210 0.175605 0.984461i 0.443812π-0.443812\pi
0.175605 + 0.984461i 0.443812π0.443812\pi
132132 −5.27513 9.99897i −0.459141 0.870298i
133133 2.82324 1.63000i 0.244806 0.141339i
134134 12.0697 + 1.82380i 1.04267 + 0.157552i
135135 −2.14006 + 2.14006i −0.184187 + 0.184187i
136136 −3.46674 + 18.2113i −0.297271 + 1.56161i
137137 −1.31484 4.90704i −0.112334 0.419237i 0.886739 0.462270i 0.152965π-0.152965\pi
−0.999074 + 0.0430325i 0.986298π0.986298\pi
138138 0.497812 + 0.217413i 0.0423766 + 0.0185074i
139139 0.331332 0.573884i 0.0281032 0.0486762i −0.851632 0.524141i 0.824387π-0.824387\pi
0.879735 + 0.475464i 0.157720π0.157720\pi
140140 3.60925 11.6702i 0.305038 0.986312i
141141 1.65921 6.19226i 0.139731 0.521482i
142142 −18.7504 + 7.35098i −1.57350 + 0.616880i
143143 17.1379 11.0300i 1.43315 0.922377i
144144 −0.304834 + 3.98837i −0.0254028 + 0.332364i
145145 0.501194 1.87048i 0.0416219 0.155335i
146146 −5.13716 4.09986i −0.425154 0.339307i
147147 2.53510 + 1.46364i 0.209092 + 0.120719i
148148 0.229244 6.00750i 0.0188438 0.493813i
149149 −3.58167 13.3670i −0.293421 1.09506i −0.942463 0.334311i 0.891496π-0.891496\pi
0.649041 0.760753i 0.275170π-0.275170\pi
150150 −3.49156 4.73456i −0.285084 0.386575i
151151 4.87170 + 4.87170i 0.396453 + 0.396453i 0.876980 0.480527i 0.159555π-0.159555\pi
−0.480527 + 0.876980i 0.659555π0.659555\pi
152152 −2.56960 3.77793i −0.208422 0.306431i
153153 5.67618 3.27715i 0.458892 0.264942i
154154 −1.80033 16.0318i −0.145075 1.29188i
155155 19.4793i 1.56462i
156156 −7.21073 + 0.0730082i −0.577321 + 0.00584534i
157157 14.3369i 1.14421i 0.820182 + 0.572103i 0.193872π0.193872\pi
−0.820182 + 0.572103i 0.806128π0.806128\pi
158158 21.4112 2.40442i 1.70338 0.191286i
159159 2.80568 1.61986i 0.222505 0.128463i
160160 −16.6842 3.84060i −1.31900 0.303626i
161161 0.548133 + 0.548133i 0.0431989 + 0.0431989i
162162 1.13818 0.839367i 0.0894242 0.0659469i
163163 −4.18581 15.6217i −0.327858 1.22358i −0.911408 0.411505i 0.865003π-0.865003\pi
0.583550 0.812077i 0.301663π-0.301663\pi
164164 −0.133117 + 3.48841i −0.0103947 + 0.272399i
165165 −14.8156 8.55378i −1.15339 0.665911i
166166 −3.37412 + 4.22780i −0.261883 + 0.328141i
167167 0.0673496 0.251352i 0.00521167 0.0194502i −0.963271 0.268531i 0.913462π-0.913462\pi
0.968483 + 0.249081i 0.0801285π0.0801285\pi
168168 −2.48234 + 5.14001i −0.191517 + 0.396560i
169169 −1.25296 12.9395i −0.0963817 0.995344i
170170 10.2393 + 26.1178i 0.785319 + 2.00314i
171171 −0.418091 + 1.56034i −0.0319722 + 0.119322i
172172 −11.8712 3.67143i −0.905174 0.279944i
173173 −10.4951 + 18.1780i −0.797927 + 1.38205i 0.123038 + 0.992402i 0.460736π0.460736\pi
−0.920964 + 0.389647i 0.872597π0.872597\pi
174174 −0.362155 + 0.829229i −0.0274549 + 0.0628637i
175175 −2.17273 8.10873i −0.164243 0.612963i
176176 −22.2223 + 4.17057i −1.67507 + 0.314369i
177177 5.45041 5.45041i 0.409678 0.409678i
178178 −3.56953 + 23.6229i −0.267547 + 1.77061i
179179 17.9236 10.3482i 1.33967 0.773459i 0.352912 0.935656i 0.385191π-0.385191\pi
0.986758 + 0.162197i 0.0518580π0.0518580\pi
180180 2.82442 + 5.35366i 0.210520 + 0.399038i
181181 9.07419 0.674479 0.337240 0.941419i 0.390507π-0.390507\pi
0.337240 + 0.941419i 0.390507π0.390507\pi
182182 −9.61791 3.65874i −0.712927 0.271204i
183183 7.33468i 0.542195i
184184 0.709583 0.822698i 0.0523112 0.0606501i
185185 −4.54874 7.87865i −0.334430 0.579250i
186186 −1.35995 + 9.00005i −0.0997164 + 0.659915i
187187 26.1973 + 26.1973i 1.91574 + 1.91574i
188188 −10.8511 6.82944i −0.791399 0.498088i
189189 1.94933 0.522322i 0.141793 0.0379933i
190190 −6.33611 2.76721i −0.459670 0.200755i
191191 −5.46209 3.15354i −0.395223 0.228182i 0.289198 0.957269i 0.406611π-0.406611\pi
−0.684421 + 0.729087i 0.739945π0.739945\pi
192192 7.44047 + 2.93928i 0.536970 + 0.212124i
193193 −13.7202 3.67630i −0.987598 0.264626i −0.271357 0.962479i 0.587472π-0.587472\pi
−0.716241 + 0.697853i 0.754139π0.754139\pi
194194 −2.96913 7.57346i −0.213171 0.543743i
195195 −9.17602 + 5.90571i −0.657109 + 0.422917i
196196 4.29465 3.97894i 0.306761 0.284210i
197197 24.3259 + 6.51810i 1.73315 + 0.464395i 0.980904 0.194491i 0.0623056π-0.0623056\pi
0.752242 + 0.658887i 0.228972π0.228972\pi
198198 6.24807 + 4.98646i 0.444031 + 0.354372i
199199 −0.773978 + 1.34057i −0.0548659 + 0.0950305i −0.892154 0.451732i 0.850806π-0.850806\pi
0.837288 + 0.546762i 0.184140π0.184140\pi
200200 −11.1096 + 3.87356i −0.785569 + 0.273902i
201201 −8.33737 + 2.23399i −0.588073 + 0.157574i
202202 19.1039 14.0884i 1.34414 0.991253i
203203 −0.913051 + 0.913051i −0.0640836 + 0.0640836i
204204 −2.90746 12.7821i −0.203563 0.894925i
205205 2.64135 + 4.57495i 0.184480 + 0.319528i
206206 −1.98233 17.6525i −0.138116 1.22991i
207207 −0.384113 −0.0266977
208208 −4.12152 + 13.8207i −0.285776 + 0.958296i
209209 −9.13105 −0.631608
210210 0.963936 + 8.58376i 0.0665179 + 0.592336i
211211 0.803291 + 1.39134i 0.0553009 + 0.0957839i 0.892351 0.451343i 0.149055π-0.149055\pi
−0.837050 + 0.547127i 0.815722π0.815722\pi
212212 −1.43713 6.31805i −0.0987023 0.433925i
213213 10.0699 10.0699i 0.689981 0.689981i
214214 18.2082 13.4278i 1.24468 0.917906i
215215 −18.1630 + 4.86676i −1.23871 + 0.331910i
216216 −0.931201 2.67074i −0.0633602 0.181721i
217217 −6.49447 + 11.2488i −0.440874 + 0.763616i
218218 −15.8635 12.6603i −1.07441 0.857464i
219219 4.48918 + 1.20287i 0.303351 + 0.0812825i
220220 −25.0987 + 23.2536i −1.69215 + 1.56776i
221221 22.5049 7.21056i 1.51384 0.485035i
222222 1.55161 + 3.95775i 0.104137 + 0.265627i
223223 −10.5079 2.81559i −0.703663 0.188546i −0.110792 0.993844i 0.535339π-0.535339\pi
−0.592871 + 0.805298i 0.702006π0.702006\pi
224224 8.35418 + 7.78040i 0.558187 + 0.519850i
225225 3.60245 + 2.07987i 0.240163 + 0.138658i
226226 −13.2022 5.76589i −0.878198 0.383541i
227227 −15.9677 + 4.27853i −1.05981 + 0.283976i −0.746301 0.665609i 0.768172π-0.768172\pi
−0.313511 + 0.949585i 0.601505π0.601505\pi
228228 2.73429 + 1.72089i 0.181082 + 0.113969i
229229 19.9869 + 19.9869i 1.32077 + 1.32077i 0.913150 + 0.407624i 0.133643π0.133643\pi
0.407624 + 0.913150i 0.366357π0.366357\pi
230230 0.245636 1.62560i 0.0161967 0.107189i
231231 5.70372 + 9.87913i 0.375277 + 0.649999i
232232 1.37041 + 1.18199i 0.0899717 + 0.0776012i
233233 20.8253i 1.36431i 0.731209 + 0.682154i 0.238957π0.238957\pi
−0.731209 + 0.682154i 0.761043π0.761043\pi
234234 4.65191 2.08799i 0.304105 0.136496i
235235 −19.4020 −1.26565
236236 −7.19335 13.6349i −0.468248 0.887559i
237237 −13.1940 + 7.61758i −0.857044 + 0.494815i
238238 2.79485 18.4961i 0.181163 1.19893i
239239 −3.93608 + 3.93608i −0.254604 + 0.254604i −0.822855 0.568251i 0.807620π-0.807620\pi
0.568251 + 0.822855i 0.307620π0.307620\pi
240240 11.8983 2.23301i 0.768032 0.144140i
241241 2.05467 + 7.66812i 0.132353 + 0.493947i 0.999995 0.00324247i 0.00103211π-0.00103211\pi
−0.867642 + 0.497189i 0.834365π0.834365\pi
242242 −11.8589 + 27.1534i −0.762317 + 1.74548i
243243 −0.500000 + 0.866025i −0.0320750 + 0.0555556i
244244 14.0144 + 4.33426i 0.897182 + 0.277472i
245245 2.29299 8.55757i 0.146494 0.546723i
246246 −0.900984 2.29817i −0.0574446 0.146526i
247247 −2.66542 + 5.17865i −0.169596 + 0.329509i
248248 16.3928 + 7.91684i 1.04095 + 0.502720i
249249 0.989944 3.69452i 0.0627352 0.234131i
250250 2.24335 2.81093i 0.141882 0.177779i
251251 1.68623 + 0.973546i 0.106434 + 0.0614497i 0.552272 0.833664i 0.313761π-0.313761\pi
−0.445838 + 0.895114i 0.647094π0.647094\pi
252252 0.153908 4.03326i 0.00969528 0.254071i
253253 −0.561954 2.09724i −0.0353298 0.131853i
254254 11.0318 8.13553i 0.692197 0.510469i
255255 −14.0266 14.0266i −0.878380 0.878380i
256256 10.0129 12.4797i 0.625805 0.779979i
257257 −12.0543 + 6.95958i −0.751930 + 0.434127i −0.826391 0.563097i 0.809610π-0.809610\pi
0.0744612 + 0.997224i 0.476276π0.476276\pi
258258 8.73164 0.980542i 0.543608 0.0610459i
259259 6.06627i 0.376939i
260260 5.86173 + 21.0225i 0.363529 + 1.30376i
261261 0.639835i 0.0396048i
262262 0.634405 + 5.64932i 0.0391937 + 0.349016i
263263 −4.34520 + 2.50870i −0.267936 + 0.154693i −0.627949 0.778254i 0.716106π-0.716106\pi
0.360013 + 0.932947i 0.382772π0.382772\pi
264264 13.2198 8.99161i 0.813624 0.553395i
265265 −6.93320 6.93320i −0.425903 0.425903i
266266 2.73633 + 3.71047i 0.167775 + 0.227504i
267267 −4.37236 16.3179i −0.267584 0.998638i
268268 −0.658270 + 17.2504i −0.0402102 + 1.05374i
269269 −4.67208 2.69743i −0.284862 0.164465i 0.350760 0.936465i 0.385923π-0.385923\pi
−0.635622 + 0.772000i 0.719256π0.719256\pi
270270 −3.34535 2.66986i −0.203592 0.162482i
271271 1.53068 5.71257i 0.0929822 0.347014i −0.903724 0.428116i 0.859177π-0.859177\pi
0.996706 + 0.0811022i 0.0258440π0.0258440\pi
272272 −26.1409 1.99797i −1.58503 0.121145i
273273 7.26788 0.351062i 0.439872 0.0212473i
274274 6.68875 2.62228i 0.404082 0.158418i
275275 −6.08569 + 22.7121i −0.366981 + 1.36959i
276276 −0.226983 + 0.733927i −0.0136627 + 0.0441772i
277277 2.57456 4.45926i 0.154690 0.267931i −0.778256 0.627947i 0.783895π-0.783895\pi
0.932946 + 0.360016i 0.117229π0.117229\pi
278278 0.858816 + 0.375076i 0.0515083 + 0.0224956i
279279 −1.66582 6.21693i −0.0997301 0.372198i
280280 16.9707 + 3.23057i 1.01419 + 0.193064i
281281 5.33135 5.33135i 0.318042 0.318042i −0.529973 0.848015i 0.677798π-0.677798\pi
0.848015 + 0.529973i 0.177798π0.177798\pi
282282 8.96433 + 1.35455i 0.533818 + 0.0806625i
283283 9.16044 5.28878i 0.544532 0.314385i −0.202382 0.979307i 0.564868π-0.564868\pi
0.746913 + 0.664921i 0.231535π0.231535\pi
284284 −13.2901 25.1913i −0.788624 1.49483i
285285 4.88896 0.289597
286286 18.2061 + 22.3446i 1.07655 + 1.32126i
287287 3.52254i 0.207929i
288288 −5.65328 + 0.201040i −0.333123 + 0.0118464i
289289 12.9794 + 22.4809i 0.763493 + 1.32241i
290290 2.70784 + 0.409167i 0.159010 + 0.0240271i
291291 4.06734 + 4.06734i 0.238432 + 0.238432i
292292 4.95111 7.86670i 0.289742 0.460364i
293293 −25.2375 + 6.76237i −1.47439 + 0.395062i −0.904434 0.426613i 0.859707π-0.859707\pi
−0.569957 + 0.821675i 0.693040π0.693040\pi
294294 −1.65688 + 3.79378i −0.0966313 + 0.221258i
295295 −20.2031 11.6642i −1.17627 0.679118i
296296 8.47899 0.625933i 0.492832 0.0363816i
297297 −5.45997 1.46299i −0.316819 0.0848915i
298298 18.2204 7.14318i 1.05548 0.413794i
299299 −1.35348 0.293489i −0.0782740 0.0169729i
300300 6.10282 5.65417i 0.352346 0.326444i
301301 12.1112 + 3.24519i 0.698079 + 0.187050i
302302 −6.07773 + 7.61544i −0.349734 + 0.438219i
303303 −8.39225 + 14.5358i −0.482122 + 0.835060i
304304 4.90389 4.20750i 0.281257 0.241317i
305305 21.4421 5.74538i 1.22777 0.328980i
306306 5.50146 + 7.45999i 0.314497 + 0.426459i
307307 −0.147072 + 0.147072i −0.00839384 + 0.00839384i −0.711291 0.702897i 0.751889π-0.751889\pi
0.702897 + 0.711291i 0.251889π0.251889\pi
308308 22.2466 5.06030i 1.26762 0.288337i
309309 6.28032 + 10.8778i 0.357275 + 0.618818i
310310 27.3758 3.07424i 1.55484 0.174605i
311311 22.9534 1.30157 0.650785 0.759262i 0.274440π-0.274440\pi
0.650785 + 0.759262i 0.274440π0.274440\pi
312312 −1.24061 10.1223i −0.0702356 0.573062i
313313 −24.8668 −1.40556 −0.702778 0.711410i 0.748057π-0.748057\pi
−0.702778 + 0.711410i 0.748057π0.748057\pi
314314 −20.1487 + 2.26265i −1.13706 + 0.127689i
315315 −3.05389 5.28950i −0.172067 0.298029i
316316 6.75826 + 29.7114i 0.380182 + 1.67139i
317317 −6.82966 + 6.82966i −0.383592 + 0.383592i −0.872395 0.488802i 0.837434π-0.837434\pi
0.488802 + 0.872395i 0.337434π0.337434\pi
318318 2.71931 + 3.68740i 0.152491 + 0.206779i
319319 3.49348 0.936074i 0.195597 0.0524101i
320320 2.76439 24.0537i 0.154534 1.34464i
321321 −7.99878 + 13.8543i −0.446448 + 0.773271i
322322 −0.683828 + 0.856841i −0.0381082 + 0.0477499i
323323 −10.2269 2.74029i −0.569040 0.152474i
324324 1.35926 + 1.46711i 0.0755144 + 0.0815062i
325325 11.1046 + 10.0813i 0.615975 + 0.559210i
326326 21.2937 8.34807i 1.17935 0.462357i
327327 13.8625 + 3.71445i 0.766598 + 0.205409i
328328 −4.92355 + 0.363465i −0.271858 + 0.0200690i
329329 11.2041 + 6.46870i 0.617703 + 0.356631i
330330 9.68310 22.1715i 0.533037 1.22050i
331331 15.6172 4.18461i 0.858398 0.230007i 0.197334 0.980336i 0.436772π-0.436772\pi
0.661064 + 0.750329i 0.270105π0.270105\pi
332332 −6.47417 4.07469i −0.355316 0.223628i
333333 −2.12552 2.12552i −0.116478 0.116478i
334334 0.363874 + 0.0549831i 0.0199103 + 0.00300854i
335335 13.0616 + 22.6234i 0.713632 + 1.23605i
336336 −7.61543 2.67743i −0.415456 0.146066i
337337 3.86354i 0.210460i 0.994448 + 0.105230i 0.0335579π0.0335579\pi
−0.994448 + 0.105230i 0.966442π0.966442\pi
338338 17.9871 3.80301i 0.978371 0.206856i
339339 10.1868 0.553274
340340 −35.0895 + 18.5121i −1.90299 + 1.00396i
341341 31.5071 18.1906i 1.70621 0.985079i
342342 −2.25885 0.341323i −0.122145 0.0184566i
343343 −14.1663 + 14.1663i −0.764910 + 0.764910i
344344 3.28623 17.2630i 0.177182 0.930761i
345345 0.300882 + 1.12291i 0.0161990 + 0.0604554i
346346 −27.2034 11.8807i −1.46246 0.638711i
347347 2.98579 5.17154i 0.160286 0.277623i −0.774685 0.632347i 0.782092π-0.782092\pi
0.934971 + 0.354724i 0.115425π0.115425\pi
348348 −1.22254 0.378095i −0.0655349 0.0202680i
349349 −2.28028 + 8.51010i −0.122060 + 0.455535i −0.999718 0.0237529i 0.992439π-0.992439\pi
0.877658 + 0.479288i 0.159105π0.159105\pi
350350 11.0529 4.33324i 0.590805 0.231621i
351351 −2.42353 + 2.66955i −0.129359 + 0.142490i
352352 −9.36839 30.5726i −0.499337 1.62952i
353353 5.18074 19.3348i 0.275743 1.02909i −0.679599 0.733584i 0.737846π-0.737846\pi
0.955342 0.295503i 0.0954873π-0.0954873\pi
354354 8.52009 + 6.79971i 0.452838 + 0.361401i
355355 −37.3263 21.5503i −1.98107 1.14377i
356356 −33.7624 1.28836i −1.78941 0.0682832i
357357 3.42345 + 12.7765i 0.181188 + 0.676204i
358358 17.3718 + 23.5563i 0.918130 + 1.24499i
359359 −4.68016 4.68016i −0.247009 0.247009i 0.572733 0.819742i 0.305883π-0.305883\pi
−0.819742 + 0.572733i 0.805883π0.805883\pi
360360 −7.07817 + 4.81430i −0.373053 + 0.253736i
361361 −14.1946 + 8.19528i −0.747086 + 0.431330i
362362 1.43210 + 12.7527i 0.0752693 + 0.670266i
363363 20.9516i 1.09967i
364364 3.62401 14.0942i 0.189950 0.738739i
365365 14.0658i 0.736238i
366366 −10.3080 + 1.15756i −0.538808 + 0.0605069i
367367 −2.27876 + 1.31564i −0.118950 + 0.0686760i −0.558295 0.829643i 0.688544π-0.688544\pi
0.439344 + 0.898319i 0.355211π0.355211\pi
368368 1.26819 + 0.867395i 0.0661090 + 0.0452161i
369369 1.23424 + 1.23424i 0.0642519 + 0.0642519i
370370 10.3546 7.63613i 0.538311 0.396983i
371371 1.69218 + 6.31528i 0.0878534 + 0.327873i
372372 −12.8631 0.490852i −0.666921 0.0254495i
373373 −19.0380 10.9916i −0.985750 0.569123i −0.0817490 0.996653i 0.526051π-0.526051\pi
−0.904001 + 0.427530i 0.859384π0.859384\pi
374374 −32.6827 + 40.9517i −1.68998 + 2.11756i
375375 −0.658183 + 2.45637i −0.0339884 + 0.126847i
376376 7.88542 16.3278i 0.406659 0.842041i
377377 0.488878 2.25456i 0.0251785 0.116116i
378378 1.04171 + 2.65712i 0.0535796 + 0.136667i
379379 2.00036 7.46544i 0.102752 0.383474i −0.895329 0.445406i 0.853059π-0.853059\pi
0.998080 + 0.0619317i 0.0197261π0.0197261\pi
380380 2.88902 9.34137i 0.148203 0.479202i
381381 −4.84623 + 8.39392i −0.248280 + 0.430034i
382382 3.56989 8.17400i 0.182651 0.418218i
383383 4.12761 + 15.4044i 0.210911 + 0.787130i 0.987566 + 0.157204i 0.0502481π0.0502481\pi
−0.776655 + 0.629926i 0.783085π0.783085\pi
384384 −2.95655 + 10.9206i −0.150876 + 0.557288i
385385 24.4127 24.4127i 1.24418 1.24418i
386386 3.00128 19.8622i 0.152761 1.01096i
387387 −5.38062 + 3.10650i −0.273512 + 0.157912i
388388 10.1750 5.36800i 0.516557 0.272519i
389389 31.6884 1.60667 0.803333 0.595531i 0.203058π-0.203058\pi
0.803333 + 0.595531i 0.203058π0.203058\pi
390390 −9.74793 11.9638i −0.493606 0.605808i
391391 2.51759i 0.127320i
392392 6.26970 + 5.40766i 0.316668 + 0.273128i
393393 −2.00989 3.48123i −0.101386 0.175605i
394394 −5.32127 + 35.2158i −0.268082 + 1.77415i
395395 32.6042 + 32.6042i 1.64050 + 1.64050i
396396 −6.02179 + 9.56788i −0.302607 + 0.480804i
397397 2.55011 0.683299i 0.127986 0.0342938i −0.194257 0.980951i 0.562230π-0.562230\pi
0.322244 + 0.946657i 0.395563π0.395563\pi
398398 −2.00616 0.876164i −0.100560 0.0439181i
399399 −2.82324 1.63000i −0.141339 0.0816018i
400400 −7.19716 15.0019i −0.359858 0.750095i
401401 20.1455 + 5.39796i 1.00602 + 0.269561i 0.723964 0.689838i 0.242318π-0.242318\pi
0.282052 + 0.959399i 0.408985π0.408985\pi
402402 −4.45542 11.3646i −0.222216 0.566815i
403403 −1.11963 23.1792i −0.0557727 1.15464i
404404 22.8145 + 24.6247i 1.13506 + 1.22513i
405405 2.92338 + 0.783318i 0.145264 + 0.0389234i
406406 −1.42728 1.13908i −0.0708348 0.0565318i
407407 8.49563 14.7149i 0.421113 0.729389i
408408 17.5048 6.10337i 0.866618 0.302162i
409409 −30.9777 + 8.30045i −1.53175 + 0.410431i −0.923589 0.383384i 0.874759π-0.874759\pi
−0.608160 + 0.793815i 0.708092π0.708092\pi
410410 −6.01268 + 4.43412i −0.296945 + 0.218986i
411411 −3.59221 + 3.59221i −0.177190 + 0.177190i
412412 24.4956 5.57185i 1.20681 0.274506i
413413 7.77780 + 13.4715i 0.382720 + 0.662891i
414414 −0.0606210 0.539824i −0.00297936 0.0265309i
415415 −11.5759 −0.568241
416416 −20.0739 3.61110i −0.984202 0.177049i
417417 −0.662664 −0.0324508
418418 −1.44107 12.8326i −0.0704850 0.627662i
419419 −4.29484 7.43889i −0.209817 0.363413i 0.741840 0.670577i 0.233953π-0.233953\pi
−0.951657 + 0.307164i 0.900620π0.900620\pi
420420 −11.9113 + 2.70939i −0.581213 + 0.132205i
421421 9.64411 9.64411i 0.470025 0.470025i −0.431898 0.901923i 0.642156π-0.642156\pi
0.901923 + 0.431898i 0.142156π0.142156\pi
422422 −1.82859 + 1.34851i −0.0890142 + 0.0656445i
423423 −6.19226 + 1.65921i −0.301078 + 0.0806735i
424424 8.65245 3.01683i 0.420200 0.146510i
425425 −13.6321 + 23.6115i −0.661254 + 1.14533i
426426 15.7413 + 12.5628i 0.762671 + 0.608672i
427427 −14.2977 3.83106i −0.691915 0.185398i
428428 21.7448 + 23.4702i 1.05107 + 1.13447i
429429 −18.1213 9.32689i −0.874902 0.450306i
430430 −9.70615 24.7578i −0.468072 1.19393i
431431 −21.6924 5.81246i −1.04489 0.279976i −0.304749 0.952433i 0.598573π-0.598573\pi
−0.740137 + 0.672456i 0.765239π0.765239\pi
432432 3.60644 1.73019i 0.173515 0.0832438i
433433 −0.162501 0.0938199i −0.00780929 0.00450870i 0.496090 0.868271i 0.334769π-0.334769\pi
−0.503900 + 0.863762i 0.668102π0.668102\pi
434434 −16.8337 7.35192i −0.808046 0.352903i
435435 −1.87048 + 0.501194i −0.0896827 + 0.0240304i
436436 15.2890 24.2922i 0.732208 1.16339i
437437 0.438751 + 0.438751i 0.0209883 + 0.0209883i
438438 −0.982006 + 6.49884i −0.0469221 + 0.310527i
439439 8.34993 + 14.4625i 0.398520 + 0.690257i 0.993544 0.113451i 0.0361905π-0.0361905\pi
−0.595023 + 0.803708i 0.702857π0.702857\pi
440440 −36.6412 31.6033i −1.74680 1.50663i
441441 2.92728i 0.139395i
442442 13.6853 + 30.4900i 0.650945 + 1.45026i
443443 −30.9433 −1.47016 −0.735081 0.677979i 0.762856π-0.762856\pi
−0.735081 + 0.677979i 0.762856π0.762856\pi
444444 −5.31727 + 2.80522i −0.252346 + 0.133130i
445445 −44.2784 + 25.5642i −2.09900 + 1.21186i
446446 2.29861 15.2120i 0.108842 0.720309i
447447 −9.78529 + 9.78529i −0.462828 + 0.462828i
448448 −9.61596 + 12.9687i −0.454311 + 0.612713i
449449 6.57967 + 24.5557i 0.310514 + 1.15885i 0.928094 + 0.372346i 0.121446π0.121446\pi
−0.617580 + 0.786508i 0.711887π0.711887\pi
450450 −2.35447 + 5.39106i −0.110991 + 0.254137i
451451 −4.93321 + 8.54458i −0.232296 + 0.402349i
452452 6.01968 19.4641i 0.283142 0.915514i
453453 1.78316 6.65486i 0.0837804 0.312673i
454454 −8.53299 21.7654i −0.400473 1.02150i
455455 −6.71935 20.9718i −0.315008 0.983173i
456456 −1.98698 + 4.11430i −0.0930490 + 0.192670i
457457 7.33011 27.3564i 0.342888 1.27968i −0.552172 0.833730i 0.686201π-0.686201\pi
0.895060 0.445946i 0.147133π-0.147133\pi
458458 −24.9349 + 31.2436i −1.16513 + 1.45992i
459459 −5.67618 3.27715i −0.264942 0.152964i
460460 2.32335 + 0.0886583i 0.108327 + 0.00413371i
461461 5.14616 + 19.2057i 0.239681 + 0.894500i 0.975983 + 0.217847i 0.0699035π0.0699035\pi
−0.736302 + 0.676653i 0.763430π0.763430\pi
462462 −12.9838 + 9.57503i −0.604060 + 0.445471i
463463 17.2055 + 17.2055i 0.799606 + 0.799606i 0.983033 0.183427i 0.0587191π-0.0587191\pi
−0.183427 + 0.983033i 0.558719π0.558719\pi
464464 −1.44486 + 2.11249i −0.0670760 + 0.0980697i
465465 −16.8696 + 9.73966i −0.782308 + 0.451666i
466466 −29.2674 + 3.28666i −1.35579 + 0.152252i
467467 27.3110i 1.26380i 0.775049 + 0.631901i 0.217725π0.217725\pi
−0.775049 + 0.631901i 0.782275π0.782275\pi
468468 3.66859 + 6.20817i 0.169581 + 0.286973i
469469 17.4192i 0.804342i
470470 −3.06204 27.2672i −0.141241 1.25774i
471471 12.4161 7.16843i 0.572103 0.330304i
472472 18.0270 12.2613i 0.829761 0.564371i
473473 −24.8332 24.8332i −1.14183 1.14183i
474474 −12.7879 17.3404i −0.587367 0.796471i
475475 −1.73915 6.49061i −0.0797978 0.297810i
476476 26.4352 + 1.00876i 1.21165 + 0.0462363i
477477 −2.80568 1.61986i −0.128463 0.0741682i
478478 −6.15288 4.91049i −0.281426 0.224600i
479479 0.729765 2.72352i 0.0333438 0.124441i −0.947248 0.320502i 0.896148π-0.896148\pi
0.980592 + 0.196061i 0.0628151π0.0628151\pi
480480 5.01603 + 16.3692i 0.228950 + 0.747149i
481481 −5.86556 9.11364i −0.267447 0.415546i
482482 −10.4523 + 4.09777i −0.476091 + 0.186649i
483483 0.200631 0.748763i 0.00912900 0.0340699i
484484 −40.0323 12.3808i −1.81965 0.562766i
485485 8.70437 15.0764i 0.395245 0.684584i
486486 −1.29601 0.566013i −0.0587880 0.0256749i
487487 −4.75278 17.7376i −0.215369 0.803767i −0.986036 0.166530i 0.946744π-0.946744\pi
0.770668 0.637237i 0.219923π-0.219923\pi
488488 −3.87951 + 20.3796i −0.175617 + 0.922543i
489489 −11.4358 + 11.4358i −0.517147 + 0.517147i
490490 12.3885 + 1.87197i 0.559656 + 0.0845668i
491491 −2.95448 + 1.70577i −0.133334 + 0.0769803i −0.565183 0.824965i 0.691195π-0.691195\pi
0.431849 + 0.901946i 0.357861π0.357861\pi
492492 3.08761 1.62892i 0.139200 0.0734376i
493493 4.19366 0.188873
494494 −7.69863 2.92862i −0.346378 0.131765i
495495 17.1076i 0.768927i
496496 −8.53903 + 24.2876i −0.383414 + 1.09055i
497497 14.3699 + 24.8894i 0.644579 + 1.11644i
498498 5.34844 + 0.808175i 0.239669 + 0.0362152i
499499 15.4529 + 15.4529i 0.691767 + 0.691767i 0.962621 0.270853i 0.0873059π-0.0873059\pi
−0.270853 + 0.962621i 0.587306π0.587306\pi
500500 4.30447 + 2.70913i 0.192502 + 0.121156i
501501 −0.251352 + 0.0673496i −0.0112296 + 0.00300896i
502502 −1.10208 + 2.52344i −0.0491882 + 0.112627i
503503 −32.5066 18.7677i −1.44940 0.836809i −0.450950 0.892549i 0.648915π-0.648915\pi
−0.998445 + 0.0557399i 0.982248π0.982248\pi
504504 5.69255 0.420233i 0.253566 0.0187187i
505505 49.0675 + 13.1476i 2.18348 + 0.585061i
506506 2.85873 1.12075i 0.127086 0.0498233i
507507 −10.5794 + 7.55484i −0.469849 + 0.335522i
508508 13.1746 + 14.2199i 0.584527 + 0.630907i
509509 −20.9745 5.62011i −0.929680 0.249107i −0.237962 0.971275i 0.576479π-0.576479\pi
−0.691718 + 0.722168i 0.743146π0.743146\pi
510510 17.4990 21.9264i 0.774870 0.970917i
511511 −4.68959 + 8.12261i −0.207455 + 0.359323i
512512 19.1189 + 12.1024i 0.844945 + 0.534854i
513513 1.56034 0.418091i 0.0688905 0.0184592i
514514 −11.6833 15.8426i −0.515327 0.698786i
515515 26.8806 26.8806i 1.18450 1.18450i
516516 2.75607 + 12.1165i 0.121329 + 0.533400i
517517 −18.1185 31.3821i −0.796849 1.38018i
518518 −8.52541 + 0.957383i −0.374585 + 0.0420650i
519519 20.9902 0.921366
520520 −28.6196 + 11.5557i −1.25505 + 0.506753i
521521 −25.5951 −1.12134 −0.560671 0.828039i 0.689457π-0.689457\pi
−0.560671 + 0.828039i 0.689457π0.689457\pi
522522 0.899211 0.100979i 0.0393574 0.00441974i
523523 −4.87205 8.43864i −0.213040 0.368996i 0.739624 0.673020i 0.235003π-0.235003\pi
−0.952664 + 0.304024i 0.901670π0.901670\pi
524524 −7.83932 + 1.78316i −0.342462 + 0.0778977i
525525 −5.93600 + 5.93600i −0.259068 + 0.259068i
526526 −4.21144 5.71073i −0.183628 0.249000i
527527 40.7476 10.9183i 1.77499 0.475608i
528528 14.7230 + 17.1598i 0.640736 + 0.746785i
529529 11.4262 19.7908i 0.496793 0.860470i
530530 8.64958 10.8380i 0.375714 0.470772i
531531 −7.44540 1.99499i −0.323103 0.0865752i
532532 −4.78277 + 4.43117i −0.207359 + 0.192116i
533533 3.40600 + 5.29208i 0.147530 + 0.229225i
534534 22.2428 8.72013i 0.962539 0.377357i
535535 46.7670 + 12.5312i 2.02191 + 0.541770i
536536 −24.3473 + 1.79735i −1.05164 + 0.0776338i
537537 −17.9236 10.3482i −0.773459 0.446557i
538538 3.05356 6.99176i 0.131648 0.301436i
539539 15.9829 4.28260i 0.688431 0.184465i
540540 3.22420 5.12285i 0.138747 0.220452i
541541 −6.38555 6.38555i −0.274536 0.274536i 0.556387 0.830923i 0.312187π-0.312187\pi
−0.830923 + 0.556387i 0.812187π0.812187\pi
542542 8.26991 + 1.24962i 0.355223 + 0.0536759i
543543 −4.53710 7.85848i −0.194705 0.337240i
544544 −1.31768 37.0533i −0.0564950 1.58865i
545545 43.4350i 1.86055i
546546 1.64040 + 10.1587i 0.0702026 + 0.434753i
547547 27.2746 1.16618 0.583090 0.812408i 0.301844π-0.301844\pi
0.583090 + 0.812408i 0.301844π0.301844\pi
548548 4.74093 + 8.98639i 0.202522 + 0.383879i
549549 6.35202 3.66734i 0.271097 0.156518i
550550 −32.8796 4.96826i −1.40199 0.211847i
551551 −0.730848 + 0.730848i −0.0311352 + 0.0311352i
552552 −1.06727 0.203168i −0.0454260 0.00864739i
553553 −7.95765 29.6984i −0.338394 1.26290i
554554 6.67327 + 2.91446i 0.283520 + 0.123824i
555555 −4.54874 + 7.87865i −0.193083 + 0.334430i
556556 −0.391586 + 1.26616i −0.0166069 + 0.0536970i
557557 −0.477883 + 1.78348i −0.0202486 + 0.0755686i −0.975311 0.220837i 0.929121π-0.929121\pi
0.955062 + 0.296405i 0.0957879π0.0957879\pi
558558 8.47424 3.32227i 0.358743 0.140643i
559559 −21.3331 + 6.83511i −0.902293 + 0.289094i
560560 −1.86186 + 24.3601i −0.0786779 + 1.02940i
561561 9.58889 35.7862i 0.404843 1.51090i
562562 8.33397 + 6.65117i 0.351547 + 0.280563i
563563 25.0364 + 14.4548i 1.05516 + 0.609196i 0.924089 0.382177i 0.124826π-0.124826\pi
0.131069 + 0.991373i 0.458159π0.458159\pi
564564 −0.488904 + 12.8121i −0.0205866 + 0.539485i
565565 −7.97954 29.7800i −0.335702 1.25286i
566566 8.87845 + 12.0392i 0.373189 + 0.506046i
567567 −1.42701 1.42701i −0.0599288 0.0599288i
568568 33.3059 22.6534i 1.39749 0.950515i
569569 16.6849 9.63300i 0.699465 0.403837i −0.107683 0.994185i 0.534343π-0.534343\pi
0.807148 + 0.590349i 0.201010π0.201010\pi
570570 0.771579 + 6.87084i 0.0323179 + 0.287788i
571571 12.8987i 0.539793i 0.962889 + 0.269897i 0.0869895π0.0869895\pi
−0.962889 + 0.269897i 0.913011π0.913011\pi
572572 −28.5293 + 29.1129i −1.19287 + 1.21727i
573573 6.30707i 0.263482i
574574 4.95051 0.555930i 0.206630 0.0232041i
575575 1.38375 0.798906i 0.0577062 0.0333167i
576576 −1.17474 7.91328i −0.0489476 0.329720i
577577 6.51540 + 6.51540i 0.271240 + 0.271240i 0.829599 0.558360i 0.188569π-0.188569\pi
−0.558360 + 0.829599i 0.688569π0.688569\pi
578578 −29.5458 + 21.7889i −1.22895 + 0.906299i
579579 3.67630 + 13.7202i 0.152782 + 0.570190i
580580 −0.147682 + 3.87011i −0.00613217 + 0.160698i
581581 6.68478 + 3.85946i 0.277331 + 0.160117i
582582 −5.07425 + 6.35807i −0.210334 + 0.263550i
583583 4.73969 17.6887i 0.196298 0.732593i
584584 11.8371 + 5.71667i 0.489822 + 0.236557i
585585 9.70250 + 4.99381i 0.401149 + 0.206469i
586586 −13.4867 34.4010i −0.557131 1.42109i
587587 −8.38093 + 31.2780i −0.345918 + 1.29098i 0.545618 + 0.838034i 0.316295π0.316295\pi
−0.891536 + 0.452949i 0.850372π0.850372\pi
588588 −5.59319 1.72981i −0.230659 0.0713362i
589589 −5.19848 + 9.00403i −0.214200 + 0.371005i
590590 13.2042 30.2338i 0.543609 1.24471i
591591 −6.51810 24.3259i −0.268119 1.00063i
592592 2.21784 + 11.8174i 0.0911525 + 0.485693i
593593 −5.55065 + 5.55065i −0.227938 + 0.227938i −0.811831 0.583893i 0.801529π-0.801529\pi
0.583893 + 0.811831i 0.301529π0.301529\pi
594594 1.19437 7.90422i 0.0490054 0.324314i
595595 34.6689 20.0161i 1.42129 0.820580i
596596 12.9144 + 24.4792i 0.528996 + 1.00271i
597597 1.54796 0.0633537
598598 0.198855 1.94848i 0.00813179 0.0796792i
599599 26.2642i 1.07313i −0.843860 0.536564i 0.819722π-0.819722\pi
0.843860 0.536564i 0.180278π-0.180278\pi
600600 8.90941 + 7.68443i 0.363725 + 0.313716i
601601 13.1909 + 22.8473i 0.538067 + 0.931959i 0.999008 + 0.0445287i 0.0141786π0.0141786\pi
−0.460941 + 0.887431i 0.652488π0.652488\pi
602602 −2.64932 + 17.5330i −0.107978 + 0.714592i
603603 6.10338 + 6.10338i 0.248549 + 0.248549i
604604 −11.6618 7.33964i −0.474511 0.298646i
605605 −61.2495 + 16.4117i −2.49014 + 0.667232i
606606 −21.7528 9.50025i −0.883647 0.385921i
607607 25.3345 + 14.6269i 1.02830 + 0.593688i 0.916496 0.400043i 0.131005π-0.131005\pi
0.111801 + 0.993731i 0.464338π0.464338\pi
608608 6.68707 + 6.22780i 0.271197 + 0.252570i
609609 1.24725 + 0.334200i 0.0505411 + 0.0135425i
610610 11.4585 + 29.2275i 0.463939 + 1.18339i
611611 −23.0872 + 1.11519i −0.934007 + 0.0451156i
612612 −9.61588 + 8.90898i −0.388699 + 0.360124i
613613 −42.9715 11.5142i −1.73560 0.465053i −0.754140 0.656714i 0.771946π-0.771946\pi
−0.981461 + 0.191661i 0.938613π0.938613\pi
614614 −0.229903 0.183481i −0.00927813 0.00740469i
615615 2.64135 4.57495i 0.106509 0.184480i
616616 10.6226 + 30.4663i 0.427998 + 1.22752i
617617 12.9985 3.48295i 0.523301 0.140218i 0.0125082 0.999922i 0.496018π-0.496018\pi
0.510793 + 0.859704i 0.329352π0.329352\pi
618618 −14.2963 + 10.5430i −0.575082 + 0.424101i
619619 14.3690 14.3690i 0.577539 0.577539i −0.356686 0.934224i 0.616093π-0.616093\pi
0.934224 + 0.356686i 0.116093π0.116093\pi
620620 8.64096 + 37.9883i 0.347029 + 1.52565i
621621 0.192056 + 0.332651i 0.00770696 + 0.0133488i
622622 3.62253 + 32.2583i 0.145250 + 1.29344i
623623 34.0927 1.36590
624624 14.0299 3.34103i 0.561645 0.133748i
625625 28.4952 1.13981
626626 −3.92450 34.9473i −0.156855 1.39678i
627627 4.56552 + 7.90772i 0.182329 + 0.315804i
628628 −6.35978 27.9595i −0.253783 1.11571i
629629 13.9313 13.9313i 0.555476 0.555476i
630630 6.95179 5.12667i 0.276966 0.204252i
631631 18.6313 4.99223i 0.741699 0.198738i 0.131866 0.991268i 0.457903π-0.457903\pi
0.609833 + 0.792530i 0.291237π0.291237\pi
632632 −40.6892 + 14.1870i −1.61853 + 0.564328i
633633 0.803291 1.39134i 0.0319280 0.0553009i
634634 −10.6761 8.52041i −0.424004 0.338389i
635635 28.3348 + 7.59228i 1.12443 + 0.301290i
636636 −4.75303 + 4.40361i −0.188470 + 0.174615i
637637 2.23665 10.3148i 0.0886192 0.408686i
638638 1.86688 + 4.76193i 0.0739106 + 0.188527i
639639 −13.7558 3.68585i −0.544171 0.145810i
640640 34.2409 + 0.0888356i 1.35349 + 0.00351154i
641641 9.68124 + 5.58947i 0.382386 + 0.220771i 0.678856 0.734271i 0.262476π-0.262476\pi
−0.296470 + 0.955042i 0.595809π0.595809\pi
642642 −20.7329 9.05482i −0.818263 0.357365i
643643 −29.4413 + 7.88878i −1.16105 + 0.311103i −0.787386 0.616460i 0.788566π-0.788566\pi
−0.373666 + 0.927563i 0.621899π0.621899\pi
644644 −1.31211 0.825811i −0.0517044 0.0325415i
645645 13.2962 + 13.2962i 0.523539 + 0.523539i
646646 2.23713 14.8052i 0.0880187 0.582501i
647647 4.73251 + 8.19695i 0.186054 + 0.322255i 0.943931 0.330142i 0.107097π-0.107097\pi
−0.757877 + 0.652397i 0.773763π0.773763\pi
648648 −1.84733 + 2.14182i −0.0725700 + 0.0841384i
649649 43.5703i 1.71028i
650650 −12.4155 + 17.1973i −0.486976 + 0.674533i
651651 12.9889 0.509077
652652 15.0928 + 28.6083i 0.591080 + 1.12039i
653653 −2.68322 + 1.54916i −0.105003 + 0.0606233i −0.551582 0.834121i 0.685976π-0.685976\pi
0.446579 + 0.894744i 0.352642π0.352642\pi
654654 −3.03242 + 20.0683i −0.118577 + 0.784733i
655655 −8.60259 + 8.60259i −0.336131 + 0.336131i
656656 −1.28785 6.86210i −0.0502819 0.267920i
657657 −1.20287 4.48918i −0.0469285 0.175140i
658658 −7.32274 + 16.7669i −0.285470 + 0.653643i
659659 16.9703 29.3934i 0.661068 1.14500i −0.319267 0.947665i 0.603437π-0.603437\pi
0.980335 0.197339i 0.0632299π-0.0632299\pi
660660 32.6875 + 10.1093i 1.27236 + 0.393505i
661661 −7.79236 + 29.0815i −0.303088 + 1.13114i 0.631491 + 0.775383i 0.282443π0.282443\pi
−0.934579 + 0.355756i 0.884223π0.884223\pi
662662 8.34569 + 21.2877i 0.324364 + 0.827368i
663663 −17.4970 15.8846i −0.679527 0.616905i
664664 4.70472 9.74174i 0.182579 0.378053i
665665 −2.55361 + 9.53020i −0.0990247 + 0.369565i
666666 2.65171 3.32261i 0.102752 0.128748i
667667 −0.212842 0.122884i −0.00824127 0.00475810i
668668 −0.0198453 + 0.520059i −0.000767837 + 0.0201217i
669669 2.81559 + 10.5079i 0.108857 + 0.406260i
670670 −29.7331 + 21.9270i −1.14869 + 0.847113i
671671 29.3165 + 29.3165i 1.13175 + 1.13175i
672672 2.56094 11.1251i 0.0987903 0.429161i
673673 −26.6178 + 15.3678i −1.02604 + 0.592386i −0.915848 0.401524i 0.868481π-0.868481\pi
−0.110194 + 0.993910i 0.535147π0.535147\pi
674674 −5.42974 + 0.609747i −0.209146 + 0.0234866i
675675 4.15975i 0.160109i
676676 8.18341 + 24.6786i 0.314747 + 0.949176i
677677 21.4417i 0.824072i −0.911168 0.412036i 0.864818π-0.864818\pi
0.911168 0.412036i 0.135182π-0.135182\pi
678678 1.60770 + 14.3164i 0.0617432 + 0.549818i
679679 −10.0531 + 5.80413i −0.385801 + 0.222742i
680680 −31.5543 46.3924i −1.21005 1.77907i
681681 11.6892 + 11.6892i 0.447929 + 0.447929i
682682 30.5372 + 41.4086i 1.16933 + 1.58562i
683683 −1.79418 6.69597i −0.0686524 0.256214i 0.923067 0.384640i 0.125674π-0.125674\pi
−0.991719 + 0.128426i 0.959008π0.959008\pi
684684 0.123195 3.22841i 0.00471048 0.123441i
685685 13.3152 + 7.68755i 0.508749 + 0.293726i
686686 −22.1448 17.6733i −0.845493 0.674771i
687687 7.31573 27.3027i 0.279112 1.04166i
688688 24.7798 + 1.89393i 0.944720 + 0.0722055i
689689 −8.64858 7.85157i −0.329485 0.299121i
690690 −1.53063 + 0.600072i −0.0582700 + 0.0228444i
691691 −6.26415 + 23.3781i −0.238300 + 0.889346i 0.738334 + 0.674435i 0.235613π0.235613\pi
−0.976634 + 0.214911i 0.931054π0.931054\pi
692692 12.4037 40.1061i 0.471516 1.52460i
693693 5.70372 9.87913i 0.216666 0.375277i
694694 7.73920 + 3.38000i 0.293776 + 0.128303i
695695 0.519076 + 1.93722i 0.0196897 + 0.0734829i
696696 0.338426 1.77780i 0.0128280 0.0673874i
697697 −8.08956 + 8.08956i −0.306414 + 0.306414i
698698 −12.3198 1.86158i −0.466311 0.0704619i
699699 18.0352 10.4126i 0.682154 0.393842i
700700 7.83423 + 14.8497i 0.296106 + 0.561267i
701701 −19.1039 −0.721544 −0.360772 0.932654i 0.617487π-0.617487\pi
−0.360772 + 0.932654i 0.617487π0.617487\pi
702702 −4.13421 2.98468i −0.156036 0.112649i
703703 4.85572i 0.183137i
704704 41.4876 17.9911i 1.56362 0.678066i
705705 9.70101 + 16.8026i 0.365361 + 0.632824i
706706 27.9904 + 4.22948i 1.05343 + 0.159179i
707707 −23.9517 23.9517i −0.900795 0.900795i
708708 −8.21153 + 13.0471i −0.308608 + 0.490340i
709709 14.7947 3.96424i 0.555628 0.148880i 0.0299311 0.999552i 0.490471π-0.490471\pi
0.525697 + 0.850672i 0.323805π0.323805\pi
710710 24.3955 55.8587i 0.915548 2.09634i
711711 13.1940 + 7.61758i 0.494815 + 0.285681i
712712 −3.51778 47.6524i −0.131834 1.78585i
713713 −2.38800 0.639863i −0.0894313 0.0239631i
714714 −17.4155 + 6.82765i −0.651760 + 0.255518i
715715 −13.0714 + 60.2813i −0.488841 + 2.25439i
716716 −30.3639 + 28.1317i −1.13475 + 1.05133i
717717 5.37678 + 1.44070i 0.200800 + 0.0538041i
718718 5.83878 7.31603i 0.217901 0.273032i
719719 13.6019 23.5592i 0.507266 0.878610i −0.492699 0.870200i 0.663990π-0.663990\pi
0.999965 0.00840997i 0.00267701π-0.00267701\pi
720720 −7.88300 9.18773i −0.293782 0.342406i
721721 −24.4849 + 6.56070i −0.911864 + 0.244333i
722722 −13.7577 18.6555i −0.512008 0.694285i
723723 5.61345 5.61345i 0.208766 0.208766i
724724 −17.6964 + 4.02528i −0.657680 + 0.149598i
725725 1.33078 + 2.30497i 0.0494238 + 0.0856045i
726726 29.4449 3.30659i 1.09280 0.122719i
727727 13.8943 0.515313 0.257656 0.966237i 0.417050π-0.417050\pi
0.257656 + 0.966237i 0.417050π0.417050\pi
728728 20.3797 + 2.86874i 0.755322 + 0.106323i
729729 1.00000 0.0370370
730730 19.7678 2.21988i 0.731640 0.0821614i
731731 −20.3609 35.2662i −0.753076 1.30437i
732732 −3.25364 14.3040i −0.120258 0.528690i
733733 −4.98282 + 4.98282i −0.184045 + 0.184045i −0.793116 0.609071i 0.791542π-0.791542\pi
0.609071 + 0.793116i 0.291542π0.291542\pi
734734 −2.20862 2.99489i −0.0815215 0.110543i
735735 −8.55757 + 2.29299i −0.315651 + 0.0845784i
736736 −1.01887 + 1.91918i −0.0375561 + 0.0707420i
737737 −24.3950 + 42.2534i −0.898602 + 1.55643i
738738 −1.53978 + 1.92936i −0.0566803 + 0.0710208i
739739 −10.6069 2.84210i −0.390180 0.104548i 0.0583951 0.998294i 0.481402π-0.481402\pi
−0.448575 + 0.893745i 0.648068π0.648068\pi
740740 12.3658 + 13.3470i 0.454577 + 0.490646i
741741 5.81755 0.281007i 0.213713 0.0103230i
742742 −8.60831 + 3.37483i −0.316021 + 0.123894i
743743 −6.08271 1.62986i −0.223153 0.0597937i 0.145510 0.989357i 0.453518π-0.453518\pi
−0.368663 + 0.929563i 0.620184π0.620184\pi
744744 −1.34023 18.1550i −0.0491353 0.665595i
745745 36.2711 + 20.9412i 1.32887 + 0.767224i
746746 12.4428 28.4903i 0.455562 1.04310i
747747 −3.69452 + 0.989944i −0.135176 + 0.0362202i
748748 −62.7107 39.4686i −2.29293 1.44311i
749749 −22.8287 22.8287i −0.834141 0.834141i
750750 −3.55601 0.537330i −0.129847 0.0196205i
751751 −1.52313 2.63814i −0.0555798 0.0962670i 0.836897 0.547361i 0.184367π-0.184367\pi
−0.892477 + 0.451094i 0.851034π0.851034\pi
752752 24.1912 + 8.50515i 0.882163 + 0.310151i
753753 1.94709i 0.0709560i
754754 3.24567 + 0.331242i 0.118200 + 0.0120631i
755755 −20.8515 −0.758863
756756 −3.56986 + 1.88334i −0.129834 + 0.0684965i
757757 0.430375 0.248477i 0.0156422 0.00903105i −0.492158 0.870506i 0.663792π-0.663792\pi
0.507801 + 0.861475i 0.330459π0.330459\pi
758758 10.8075 + 1.63306i 0.392545 + 0.0593155i
759759 −1.53529 + 1.53529i −0.0557274 + 0.0557274i
760760 13.5841 + 2.58590i 0.492748 + 0.0938005i
761761 10.3019 + 38.4472i 0.373444 + 1.39371i 0.855605 + 0.517629i 0.173185π0.173185\pi
−0.482161 + 0.876082i 0.660148π0.660148\pi
762762 −12.5615 5.48606i −0.455055 0.198739i
763763 −14.4814 + 25.0825i −0.524261 + 0.908047i
764764 12.0510 + 3.72702i 0.435989 + 0.134839i
765765 −5.13409 + 19.1607i −0.185624 + 0.692757i
766766 −20.9977 + 8.23200i −0.758676 + 0.297434i
767767 −24.7108 12.7185i −0.892255 0.459237i
768768 −15.8142 2.43158i −0.570644 0.0877420i
769769 −4.72877 + 17.6480i −0.170524 + 0.636404i 0.826747 + 0.562574i 0.190189π0.190189\pi
−0.997271 + 0.0738298i 0.976478π0.976478\pi
770770 38.1619 + 30.4562i 1.37526 + 1.09757i
771771 12.0543 + 6.95958i 0.434127 + 0.250643i
772772 28.3876 + 1.08326i 1.02169 + 0.0389875i
773773 2.76848 + 10.3321i 0.0995752 + 0.371620i 0.997673 0.0681754i 0.0217178π-0.0217178\pi
−0.898098 + 0.439795i 0.855051π0.855051\pi
774774 −5.21499 7.07155i −0.187449 0.254182i
775775 18.9315 + 18.9315i 0.680038 + 0.680038i
776776 9.14990 + 13.4526i 0.328462 + 0.482919i
777777 5.25354 3.03313i 0.188470 0.108813i
778778 5.00109 + 44.5342i 0.179298 + 1.59663i
779779 2.81960i 0.101023i
780780 15.2752 15.5877i 0.546940 0.558128i
781781 80.4986i 2.88047i
782782 3.53817 0.397328i 0.126525 0.0142084i
783783 −0.554113 + 0.319917i −0.0198024 + 0.0114329i
784784 −6.61033 + 9.66476i −0.236083 + 0.345170i
785785 −30.6818 30.6818i −1.09508 1.09508i
786786 4.57525 3.37407i 0.163194 0.120349i
787787 8.91143 + 33.2579i 0.317658 + 1.18552i 0.921489 + 0.388404i 0.126974π0.126974\pi
−0.603831 + 0.797113i 0.706360π0.706360\pi
788788 −50.3314 1.92063i −1.79298 0.0684196i
789789 4.34520 + 2.50870i 0.154693 + 0.0893121i
790790 −40.6757 + 50.9669i −1.44718 + 1.81332i
791791 −5.32081 + 19.8575i −0.189186 + 0.706053i
792792 −14.3969 6.95290i −0.511570 0.247060i
793793 25.1845 8.06909i 0.894327 0.286542i
794794 1.36275 + 3.47603i 0.0483624 + 0.123360i
795795 −2.53773 + 9.47093i −0.0900040 + 0.335899i
796796 0.914729 2.95769i 0.0324217 0.104833i
797797 −11.1615 + 19.3323i −0.395362 + 0.684786i −0.993147 0.116870i 0.962714π-0.962714\pi
0.597786 + 0.801656i 0.296047π0.296047\pi
798798 1.84520 4.22496i 0.0653193 0.149562i
799799 −10.8749 40.5859i −0.384728 1.43582i
800800 19.9475 12.4824i 0.705251 0.441318i
801801 −11.9455 + 11.9455i −0.422074 + 0.422074i
802802 −4.40681 + 29.1639i −0.155610 + 1.02981i
803803 22.7510 13.1353i 0.802864 0.463534i
804804 15.2684 8.05512i 0.538476 0.284082i
805805 −2.34608 −0.0826884
806806 32.3988 5.23166i 1.14120 0.184277i
807807 5.39486i 0.189908i
808808 −31.0065 + 35.9493i −1.09081 + 1.26469i
809809 −7.83338 13.5678i −0.275407 0.477019i 0.694831 0.719173i 0.255479π-0.255479\pi
−0.970238 + 0.242154i 0.922146π0.922146\pi
810810 −0.639489 + 4.23209i −0.0224693 + 0.148700i
811811 −18.7650 18.7650i −0.658930 0.658930i 0.296197 0.955127i 0.404281π-0.404281\pi
−0.955127 + 0.296197i 0.904281π0.904281\pi
812812 1.37559 2.18564i 0.0482738 0.0767011i
813813 −5.71257 + 1.53068i −0.200349 + 0.0536833i
814814 22.0208 + 9.61728i 0.771827 + 0.337085i
815815 42.3892 + 24.4734i 1.48483 + 0.857267i
816816 11.3402 + 23.6377i 0.396985 + 0.827485i
817817 9.69438 + 2.59760i 0.339163 + 0.0908786i
818818 −16.5542 42.2255i −0.578804 1.47638i
819819 −3.93797 6.11864i −0.137604 0.213802i
820820 −7.18055 7.75031i −0.250756 0.270652i
821821 −27.3688 7.33344i −0.955177 0.255939i −0.252619 0.967566i 0.581292π-0.581292\pi
−0.702558 + 0.711627i 0.747959π0.747959\pi
822822 −5.61534 4.48149i −0.195857 0.156310i
823823 4.58266 7.93739i 0.159741 0.276680i −0.775034 0.631920i 0.782267π-0.782267\pi
0.934775 + 0.355239i 0.115601π0.115601\pi
824824 11.6965 + 33.5462i 0.407466 + 1.16864i
825825 22.7121 6.08569i 0.790734 0.211876i
826826 −17.7051 + 13.0568i −0.616040 + 0.454306i
827827 −10.5467 + 10.5467i −0.366745 + 0.366745i −0.866289 0.499543i 0.833501π-0.833501\pi
0.499543 + 0.866289i 0.333501π0.333501\pi
828828 0.749091 0.170391i 0.0260327 0.00592150i
829829 −5.56947 9.64660i −0.193436 0.335040i 0.752951 0.658077i 0.228630π-0.228630\pi
−0.946387 + 0.323036i 0.895296π0.895296\pi
830830 −1.82692 16.2686i −0.0634135 0.564691i
831831 −5.14911 −0.178621
832832 1.90689 28.7813i 0.0661095 0.997812i
833833 19.1863 0.664765
834834 −0.104582 0.931295i −0.00362138 0.0322481i
835835 0.393777 + 0.682042i 0.0136272 + 0.0236030i
836836 17.8072 4.05050i 0.615876 0.140089i
837837 −4.55111 + 4.55111i −0.157309 + 0.157309i
838838 9.77665 7.20990i 0.337729 0.249062i
839839 −22.8055 + 6.11071i −0.787332 + 0.210965i −0.630015 0.776583i 0.716951π-0.716951\pi
−0.157317 + 0.987548i 0.550285π0.550285\pi
840840 −5.68758 16.3123i −0.196240 0.562829i
841841 −14.2953 + 24.7602i −0.492942 + 0.853800i
842842 15.0757 + 12.0316i 0.519542 + 0.414636i
843843 −7.28276 1.95141i −0.250832 0.0672101i
844844 −2.18376 2.35704i −0.0751682 0.0811325i
845845 30.3727 + 25.0099i 1.04485 + 0.860367i
846846 −3.30909 8.44061i −0.113769 0.290194i
847847 40.8416 + 10.9435i 1.40333 + 0.376022i
848848 5.60533 + 11.6839i 0.192488 + 0.401225i
849849 −9.16044 5.28878i −0.314385 0.181511i
850850 −35.3346 15.4319i −1.21197 0.529310i
851851 −1.11528 + 0.298837i −0.0382311 + 0.0102440i
852852 −15.1713 + 24.1052i −0.519759 + 0.825832i
853853 9.07626 + 9.07626i 0.310765 + 0.310765i 0.845206 0.534441i 0.179478π-0.179478\pi
−0.534441 + 0.845206i 0.679478π0.679478\pi
854854 3.12762 20.6984i 0.107025 0.708283i
855855 −2.44448 4.23396i −0.0835994 0.144798i
856856 −29.5528 + 34.2638i −1.01009 + 1.17111i
857857 35.2366i 1.20366i −0.798625 0.601829i 0.794439π-0.794439\pi
0.798625 0.601829i 0.205561π-0.205561\pi
858858 10.2479 26.9392i 0.349858 0.919690i
859859 −51.5506 −1.75888 −0.879441 0.476008i 0.842083π-0.842083\pi
−0.879441 + 0.476008i 0.842083π0.842083\pi
860860 33.2623 17.5481i 1.13424 0.598386i
861861 −3.05061 + 1.76127i −0.103964 + 0.0600239i
862862 4.74520 31.4034i 0.161622 1.06960i
863863 1.05809 1.05809i 0.0360179 0.0360179i −0.688868 0.724886i 0.741892π-0.741892\pi
0.724886 + 0.688868i 0.241892π0.241892\pi
864864 3.00075 + 4.79536i 0.102087 + 0.163142i
865865 −16.4420 61.3623i −0.559044 2.08638i
866866 0.106207 0.243182i 0.00360905 0.00826367i
867867 12.9794 22.4809i 0.440803 0.763493i
868868 7.67552 24.8181i 0.260524 0.842381i
869869 −22.2889 + 83.1834i −0.756100 + 2.82180i
870870 −0.999569 2.54964i −0.0338886 0.0864408i
871871 16.8428 + 26.1696i 0.570698 + 0.886725i
872872 36.5527 + 17.6530i 1.23783 + 0.597805i
873873 1.48875 5.55609i 0.0503865 0.188045i
874874 −0.547368 + 0.685856i −0.0185150 + 0.0231994i
875875 −4.44450 2.56603i −0.150252 0.0867478i
876876 −9.28832 0.354439i −0.313823 0.0119754i
877877 5.39910 + 20.1497i 0.182315 + 0.680407i 0.995189 + 0.0979688i 0.0312346π0.0312346\pi
−0.812875 + 0.582438i 0.802099π0.802099\pi
878878 −19.0075 + 14.0173i −0.641472 + 0.473061i
879879 18.4751 + 18.4751i 0.623151 + 0.623151i
880880 38.6319 56.4825i 1.30228 1.90402i
881881 −8.27395 + 4.77697i −0.278756 + 0.160940i −0.632860 0.774266i 0.718119π-0.718119\pi
0.354104 + 0.935206i 0.384786π0.384786\pi
882882 4.11395 0.461986i 0.138524 0.0155559i
883883 35.6265i 1.19893i 0.800403 + 0.599463i 0.204619π0.204619\pi
−0.800403 + 0.599463i 0.795381π0.795381\pi
884884 −40.6902 + 24.0450i −1.36856 + 0.808722i
885885 23.3285i 0.784178i
886886 −4.88350 43.4872i −0.164065 1.46098i
887887 −14.9150 + 8.61120i −0.500798 + 0.289136i −0.729043 0.684468i 0.760035π-0.760035\pi
0.228245 + 0.973604i 0.426701π0.426701\pi
888888 −4.78157 7.03006i −0.160459 0.235913i
889889 −13.8312 13.8312i −0.463885 0.463885i
890890 −42.9154 58.1935i −1.43853 1.95065i
891891 1.46299 + 5.45997i 0.0490121 + 0.182916i
892892 21.7414 + 0.829645i 0.727956 + 0.0277786i
893893 8.96830 + 5.17785i 0.300113 + 0.173270i
894894 −15.2964 12.2077i −0.511587 0.408288i
895895 −16.2118 + 60.5034i −0.541902 + 2.02240i
896896 −19.7435 11.4673i −0.659586 0.383097i
897897 0.422573 + 1.31890i 0.0141093 + 0.0440366i
898898 −33.4716 + 13.1223i −1.11696 + 0.437898i
899899 1.06585 3.97781i 0.0355481 0.132667i
900900 −7.94807 2.45811i −0.264936 0.0819369i
901901 10.6170 18.3892i 0.353705 0.612634i
902902 −12.7869 5.58453i −0.425759 0.185944i
903903 −3.24519 12.1112i −0.107993 0.403036i
904904 28.3045 + 5.38810i 0.941393 + 0.179206i
905905 −19.4194 + 19.4194i −0.645521 + 0.645521i
906906 9.63403 + 1.45575i 0.320069 + 0.0483640i
907907 19.3561 11.1752i 0.642708 0.371068i −0.142949 0.989730i 0.545658π-0.545658\pi
0.785657 + 0.618662i 0.212325π0.212325\pi
908908 29.2420 15.4271i 0.970430 0.511967i
909909 16.7845 0.556707
910910 28.4129 12.7530i 0.941878 0.422759i
911911 18.2434i 0.604431i 0.953240 + 0.302215i 0.0977262π0.0977262\pi
−0.953240 + 0.302215i 0.902274π0.902274\pi
912912 −6.09575 2.14314i −0.201850 0.0709665i
913913 −10.8101 18.7237i −0.357763 0.619664i
914914 39.6029 + 5.98419i 1.30995 + 0.197939i
915915 −15.6967 15.6967i −0.518916 0.518916i
916916 −47.8444 30.1121i −1.58082 0.994932i
917917 7.83589 2.09962i 0.258764 0.0693356i
918918 3.70982 8.49440i 0.122442 0.280357i
919919 35.3967 + 20.4363i 1.16763 + 0.674131i 0.953121 0.302591i 0.0978516π-0.0978516\pi
0.214509 + 0.976722i 0.431185π0.431185\pi
920920 0.242074 + 3.27918i 0.00798095 + 0.108111i
921921 0.200904 + 0.0538321i 0.00662001 + 0.00177383i
922922 −26.1792 + 10.2634i −0.862165 + 0.338006i
923923 −45.6545 23.4981i −1.50274 0.773449i
924924 −15.5057 16.7360i −0.510099 0.550574i
925925 12.0779 + 3.23626i 0.397118 + 0.106407i
926926 −21.4649 + 26.8956i −0.705379 + 0.883845i
927927 6.28032 10.8778i 0.206273 0.357275i
928928 −3.19687 1.69718i −0.104943 0.0557128i
929929 −7.06937 + 1.89423i −0.231939 + 0.0621477i −0.372916 0.927865i 0.621642π-0.621642\pi
0.140978 + 0.990013i 0.454975π0.454975\pi
930930 −16.3503 22.1711i −0.536147 0.727018i
931931 −3.34368 + 3.34368i −0.109585 + 0.109585i
932932 −9.23801 40.6131i −0.302601 1.33033i
933933 −11.4767 19.8783i −0.375731 0.650785i
934934 −38.3823 + 4.31024i −1.25591 + 0.141035i
935935 −112.128 −3.66698
936936 −8.14586 + 6.13555i −0.266256 + 0.200547i
937937 36.3958 1.18900 0.594499 0.804096i 0.297350π-0.297350\pi
0.594499 + 0.804096i 0.297350π0.297350\pi
938938 24.4805 2.74911i 0.799318 0.0897615i
939939 12.4334 + 21.5353i 0.405749 + 0.702778i
940940 37.8375 8.60666i 1.23412 0.280718i
941941 2.60051 2.60051i 0.0847743 0.0847743i −0.663448 0.748222i 0.730908π-0.730908\pi
0.748222 + 0.663448i 0.230908π0.230908\pi
942942 12.0339 + 16.3180i 0.392085 + 0.531669i
943943 0.647614 0.173528i 0.0210892 0.00565084i
944944 20.0768 + 23.3997i 0.653444 + 0.761596i
945945 −3.05389 + 5.28950i −0.0993432 + 0.172067i
946946 30.9809 38.8193i 1.00728 1.26212i
947947 29.5599 + 7.92054i 0.960567 + 0.257383i 0.704840 0.709366i 0.251019π-0.251019\pi
0.255726 + 0.966749i 0.417685π0.417685\pi
948948 22.3517 20.7085i 0.725948 0.672581i
949949 −0.808473 16.7374i −0.0262441 0.543320i
950950 8.84730 3.46852i 0.287044 0.112534i
951951 9.32950 + 2.49983i 0.302530 + 0.0810626i
952952 2.75433 + 37.3106i 0.0892684 + 1.20924i
953953 −17.9259 10.3495i −0.580677 0.335254i 0.180725 0.983534i 0.442156π-0.442156\pi
−0.761402 + 0.648279i 0.775489π0.775489\pi
954954 1.83372 4.19869i 0.0593690 0.135938i
955955 18.4380 4.94044i 0.596639 0.159869i
956956 5.93005 9.42211i 0.191791 0.304733i
957957 −2.55740 2.55740i −0.0826691 0.0826691i
958958 3.94275 + 0.595769i 0.127385 + 0.0192484i
959959 −5.12611 8.87869i −0.165531 0.286708i
960960 −22.2133 + 9.63284i −0.716932 + 0.310898i
961961 10.4251i 0.336295i
962962 11.8824 9.68167i 0.383105 0.312149i
963963 15.9976 0.515514
964964 −7.40853 14.0428i −0.238613 0.452288i
965965 37.2295 21.4945i 1.19846 0.691932i
966966 1.08396 + 0.163792i 0.0348759 + 0.00526991i
967967 −11.7809 + 11.7809i −0.378848 + 0.378848i −0.870687 0.491838i 0.836325π-0.836325\pi
0.491838 + 0.870687i 0.336325π0.336325\pi
968968 11.0819 58.2146i 0.356184 1.87109i
969969 2.74029 + 10.2269i 0.0880308 + 0.328535i
970970 22.5618 + 9.85357i 0.724416 + 0.316379i
971971 16.7807 29.0650i 0.538517 0.932739i −0.460467 0.887677i 0.652318π-0.652318\pi
0.998984 0.0450621i 0.0143486π-0.0143486\pi
972972 0.590927 1.91071i 0.0189540 0.0612860i
973973 0.346124 1.29175i 0.0110962 0.0414117i
974974 24.1780 9.47882i 0.774712 0.303721i
975975 3.17834 14.6576i 0.101788 0.469417i
976976 −29.2534 2.23586i −0.936378 0.0715680i
977977 1.82586 6.81419i 0.0584143 0.218005i −0.930549 0.366168i 0.880669π-0.880669\pi
0.988963 + 0.148163i 0.0473361π0.0473361\pi
978978 −17.8765 14.2669i −0.571628 0.456205i
979979 −82.6983 47.7459i −2.64305 1.52597i
980980 −0.675656 + 17.7060i −0.0215830 + 0.565598i
981981 −3.71445 13.8625i −0.118593 0.442596i
982982 −2.86353 3.88296i −0.0913790 0.123910i
983983 −34.9395 34.9395i −1.11440 1.11440i −0.992549 0.121848i 0.961118π-0.961118\pi
−0.121848 0.992549i 0.538882π-0.538882\pi
984984 2.77655 + 4.08219i 0.0885131 + 0.130135i
985985 −66.0081 + 38.1098i −2.10319 + 1.21428i
986986 0.661847 + 5.89369i 0.0210775 + 0.187693i
987987 12.9374i 0.411802i
988988 2.90082 11.2817i 0.0922875 0.358918i
989989 2.38650i 0.0758861i
990990 −24.0426 + 2.69993i −0.764124 + 0.0858094i
991991 −50.5421 + 29.1805i −1.60552 + 0.926950i −0.615169 + 0.788395i 0.710912π0.710912\pi
−0.990355 + 0.138554i 0.955755π0.955755\pi
992992 −35.4809 8.16750i −1.12652 0.259318i
993993 −11.4326 11.4326i −0.362802 0.362802i
994994 −32.7112 + 24.1232i −1.03754 + 0.765143i
995995 −1.21254 4.52527i −0.0384402 0.143461i
996996 −0.291698 + 7.64414i −0.00924280 + 0.242214i
997997 3.45063 + 1.99222i 0.109283 + 0.0630943i 0.553645 0.832753i 0.313236π-0.313236\pi
−0.444363 + 0.895847i 0.646570π0.646570\pi
998998 −19.2784 + 24.1560i −0.610248 + 0.764645i
999999 −0.777993 + 2.90351i −0.0246146 + 0.0918630i
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 312.2.bt.c.115.7 yes 48
3.2 odd 2 936.2.ed.c.739.6 48
8.3 odd 2 inner 312.2.bt.c.115.3 yes 48
13.6 odd 12 inner 312.2.bt.c.19.3 48
24.11 even 2 936.2.ed.c.739.10 48
39.32 even 12 936.2.ed.c.19.10 48
104.19 even 12 inner 312.2.bt.c.19.7 yes 48
312.227 odd 12 936.2.ed.c.19.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
312.2.bt.c.19.3 48 13.6 odd 12 inner
312.2.bt.c.19.7 yes 48 104.19 even 12 inner
312.2.bt.c.115.3 yes 48 8.3 odd 2 inner
312.2.bt.c.115.7 yes 48 1.1 even 1 trivial
936.2.ed.c.19.6 48 312.227 odd 12
936.2.ed.c.19.10 48 39.32 even 12
936.2.ed.c.739.6 48 3.2 odd 2
936.2.ed.c.739.10 48 24.11 even 2