Properties

Label 483.2.r.a.34.20
Level 483483
Weight 22
Character 483.34
Analytic conductor 3.8573.857
Analytic rank 00
Dimension 320320
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(34,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 483=3723 483 = 3 \cdot 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 483.r (of order 2222, degree 1010, 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: 3.856774417633.85677441763
Analytic rank: 00
Dimension: 320320
Relative dimension: 3232 over Q(ζ22)\Q(\zeta_{22})
Twist minimal: yes
Sato-Tate group: SU(2)[C22]\mathrm{SU}(2)[C_{22}]

Embedding invariants

Embedding label 34.20
Character χ\chi == 483.34
Dual form 483.2.r.a.412.20

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.2272140.146021i)q2+(0.989821+0.142315i)q3+(0.800526+1.75291i)q4+(1.039960.305361i)q5+(0.2456820.112199i)q6+(1.80110+1.93805i)q7+(0.150947+1.04986i)q8+(0.959493+0.281733i)q9+(0.1917050.221239i)q10+(2.429393.78020i)q11+(1.04184+1.62114i)q12+(2.38102+2.06316i)q13+(0.126238+0.703351i)q14+(1.072840.154251i)q15+(2.336302.69624i)q16+(2.18750+4.78996i)q17+(0.2591490.0760930i)q18+(2.28938+5.01305i)q19+(0.297249+2.06741i)q20+(2.05858+1.66200i)q211.21366iq22+(0.277290+4.78781i)q23+1.06065iq24+(3.21799+2.06807i)q25+(0.842265+0.121099i)q26+(0.909632+0.415415i)q27+(1.955404.70862i)q28+(0.7780251.70364i)q29+(0.2212390.191705i)q30+(6.661650.957801i)q31+(2.959930.869114i)q32+(2.942643.39599i)q33+(1.19647+0.768923i)q34+(1.28128+2.56549i)q35+(1.26195+1.45637i)q36+(2.085777.10348i)q37+(0.211833+1.47333i)q38+(2.06316+2.38102i)q39+(0.477566+1.04572i)q40+(3.1160210.6122i)q41+(0.225050+0.678226i)q42+(1.394000.200427i)q43+(4.68155+7.28464i)q44+1.08387q45+(0.636118+1.12835i)q46+1.11953iq47+(1.928813.00128i)q48+(0.5120796.98124i)q49+(0.429187+0.939789i)q50+(1.48355+5.05252i)q51+(5.52260+2.52209i)q52+(1.39483+1.20863i)q53+(0.2673400.0384377i)q54+(1.372154.67312i)q55+(2.306551.59836i)q56+(2.97951+4.63621i)q57+(0.4255460.273482i)q58+(9.62852+8.34316i)q59+(0.588447+2.00407i)q60+(1.6612011.5539i)q61+(1.373761.19037i)q62+(2.27415+1.35212i)q63+(6.046791.77550i)q64+(3.10618+1.41855i)q65+(0.1727211.20130i)q66+(5.581298.68465i)q6710.1475q68+(0.955844+4.69961i)q69+(0.0834932+0.770008i)q70+(8.577285.51229i)q71+(0.150947+1.04986i)q72+(12.5808+5.74545i)q73+(0.5633451.91858i)q74+(3.47955+1.58906i)q75+(6.954708.02616i)q76+(2.95065+11.5168i)q77+(0.816458+0.239734i)q78+(6.670145.77971i)q79+(3.253002.09058i)q80+(0.841254+0.540641i)q81+(2.257611.95623i)q82+(0.695752+0.204291i)q83+(1.265394.93898i)q84+(3.73760+4.31342i)q85+(0.346003+0.158014i)q86+(0.5276531.79702i)q87+(4.33539+1.97990i)q88+(1.6637511.5717i)q89+(0.2462700.158268i)q90+(8.28696+0.898568i)q91+(8.170614.31883i)q92+6.73016q93+(0.163475+0.254371i)q94+(0.850087+5.91249i)q95+(2.806111.28151i)q96+(7.694642.25935i)q97+(1.135761.51146i)q98+(3.395992.94264i)q99+O(q100)q+(0.227214 - 0.146021i) q^{2} +(0.989821 + 0.142315i) q^{3} +(-0.800526 + 1.75291i) q^{4} +(1.03996 - 0.305361i) q^{5} +(0.245682 - 0.112199i) q^{6} +(-1.80110 + 1.93805i) q^{7} +(0.150947 + 1.04986i) q^{8} +(0.959493 + 0.281733i) q^{9} +(0.191705 - 0.221239i) q^{10} +(2.42939 - 3.78020i) q^{11} +(-1.04184 + 1.62114i) q^{12} +(2.38102 + 2.06316i) q^{13} +(-0.126238 + 0.703351i) q^{14} +(1.07284 - 0.154251i) q^{15} +(-2.33630 - 2.69624i) q^{16} +(2.18750 + 4.78996i) q^{17} +(0.259149 - 0.0760930i) q^{18} +(-2.28938 + 5.01305i) q^{19} +(-0.297249 + 2.06741i) q^{20} +(-2.05858 + 1.66200i) q^{21} -1.21366i q^{22} +(-0.277290 + 4.78781i) q^{23} +1.06065i q^{24} +(-3.21799 + 2.06807i) q^{25} +(0.842265 + 0.121099i) q^{26} +(0.909632 + 0.415415i) q^{27} +(-1.95540 - 4.70862i) q^{28} +(-0.778025 - 1.70364i) q^{29} +(0.221239 - 0.191705i) q^{30} +(6.66165 - 0.957801i) q^{31} +(-2.95993 - 0.869114i) q^{32} +(2.94264 - 3.39599i) q^{33} +(1.19647 + 0.768923i) q^{34} +(-1.28128 + 2.56549i) q^{35} +(-1.26195 + 1.45637i) q^{36} +(2.08577 - 7.10348i) q^{37} +(0.211833 + 1.47333i) q^{38} +(2.06316 + 2.38102i) q^{39} +(0.477566 + 1.04572i) q^{40} +(-3.11602 - 10.6122i) q^{41} +(-0.225050 + 0.678226i) q^{42} +(-1.39400 - 0.200427i) q^{43} +(4.68155 + 7.28464i) q^{44} +1.08387 q^{45} +(0.636118 + 1.12835i) q^{46} +1.11953i q^{47} +(-1.92881 - 3.00128i) q^{48} +(-0.512079 - 6.98124i) q^{49} +(-0.429187 + 0.939789i) q^{50} +(1.48355 + 5.05252i) q^{51} +(-5.52260 + 2.52209i) q^{52} +(-1.39483 + 1.20863i) q^{53} +(0.267340 - 0.0384377i) q^{54} +(1.37215 - 4.67312i) q^{55} +(-2.30655 - 1.59836i) q^{56} +(-2.97951 + 4.63621i) q^{57} +(-0.425546 - 0.273482i) q^{58} +(9.62852 + 8.34316i) q^{59} +(-0.588447 + 2.00407i) q^{60} +(-1.66120 - 11.5539i) q^{61} +(1.37376 - 1.19037i) q^{62} +(-2.27415 + 1.35212i) q^{63} +(6.04679 - 1.77550i) q^{64} +(3.10618 + 1.41855i) q^{65} +(0.172721 - 1.20130i) q^{66} +(-5.58129 - 8.68465i) q^{67} -10.1475 q^{68} +(-0.955844 + 4.69961i) q^{69} +(0.0834932 + 0.770008i) q^{70} +(8.57728 - 5.51229i) q^{71} +(-0.150947 + 1.04986i) q^{72} +(12.5808 + 5.74545i) q^{73} +(-0.563345 - 1.91858i) q^{74} +(-3.47955 + 1.58906i) q^{75} +(-6.95470 - 8.02616i) q^{76} +(2.95065 + 11.5168i) q^{77} +(0.816458 + 0.239734i) q^{78} +(-6.67014 - 5.77971i) q^{79} +(-3.25300 - 2.09058i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-2.25761 - 1.95623i) q^{82} +(0.695752 + 0.204291i) q^{83} +(-1.26539 - 4.93898i) q^{84} +(3.73760 + 4.31342i) q^{85} +(-0.346003 + 0.158014i) q^{86} +(-0.527653 - 1.79702i) q^{87} +(4.33539 + 1.97990i) q^{88} +(1.66375 - 11.5717i) q^{89} +(0.246270 - 0.158268i) q^{90} +(-8.28696 + 0.898568i) q^{91} +(-8.17061 - 4.31883i) q^{92} +6.73016 q^{93} +(0.163475 + 0.254371i) q^{94} +(-0.850087 + 5.91249i) q^{95} +(-2.80611 - 1.28151i) q^{96} +(7.69464 - 2.25935i) q^{97} +(-1.13576 - 1.51146i) q^{98} +(3.39599 - 2.94264i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 320q+4q236q4+12q8+32q94q18+52q2368q2588q28+24q32+28q35+14q3644q37+110q4244q43154q44+40q4616q49++44q99+O(q100) 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49}+ \cdots + 44 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/483Z)×\left(\mathbb{Z}/483\mathbb{Z}\right)^\times.

nn 323323 346346 442442
χ(n)\chi(n) 11 1-1 e(922)e\left(\frac{9}{22}\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 0.227214 0.146021i 0.160664 0.103253i −0.457838 0.889036i 0.651376π-0.651376\pi
0.618502 + 0.785783i 0.287740π0.287740\pi
33 0.989821 + 0.142315i 0.571474 + 0.0821655i
44 −0.800526 + 1.75291i −0.400263 + 0.876454i
55 1.03996 0.305361i 0.465086 0.136562i −0.0407898 0.999168i 0.512987π-0.512987\pi
0.505876 + 0.862606i 0.331169π0.331169\pi
66 0.245682 0.112199i 0.100299 0.0458051i
77 −1.80110 + 1.93805i −0.680752 + 0.732514i
88 0.150947 + 1.04986i 0.0533678 + 0.371181i
99 0.959493 + 0.281733i 0.319831 + 0.0939109i
1010 0.191705 0.221239i 0.0606224 0.0699620i
1111 2.42939 3.78020i 0.732488 1.13977i −0.252575 0.967577i 0.581277π-0.581277\pi
0.985063 0.172196i 0.0550862π-0.0550862\pi
1212 −1.04184 + 1.62114i −0.300754 + 0.467983i
1313 2.38102 + 2.06316i 0.660375 + 0.572218i 0.919241 0.393695i 0.128803π-0.128803\pi
−0.258866 + 0.965913i 0.583349π0.583349\pi
1414 −0.126238 + 0.703351i −0.0337385 + 0.187978i
1515 1.07284 0.154251i 0.277005 0.0398274i
1616 −2.33630 2.69624i −0.584075 0.674059i
1717 2.18750 + 4.78996i 0.530547 + 1.16174i 0.965290 + 0.261182i 0.0841122π0.0841122\pi
−0.434742 + 0.900555i 0.643161π0.643161\pi
1818 0.259149 0.0760930i 0.0610820 0.0179353i
1919 −2.28938 + 5.01305i −0.525221 + 1.15007i 0.442204 + 0.896914i 0.354197π0.354197\pi
−0.967425 + 0.253158i 0.918531π0.918531\pi
2020 −0.297249 + 2.06741i −0.0664669 + 0.462287i
2121 −2.05858 + 1.66200i −0.449219 + 0.362678i
2222 1.21366i 0.258752i
2323 −0.277290 + 4.78781i −0.0578190 + 0.998327i
2424 1.06065i 0.216505i
2525 −3.21799 + 2.06807i −0.643597 + 0.413615i
2626 0.842265 + 0.121099i 0.165182 + 0.0237495i
2727 0.909632 + 0.415415i 0.175059 + 0.0799467i
2828 −1.95540 4.70862i −0.369535 0.889846i
2929 −0.778025 1.70364i −0.144476 0.316358i 0.823535 0.567265i 0.191998π-0.191998\pi
−0.968011 + 0.250907i 0.919271π0.919271\pi
3030 0.221239 0.191705i 0.0403926 0.0350004i
3131 6.66165 0.957801i 1.19647 0.172026i 0.484853 0.874596i 0.338873π-0.338873\pi
0.711615 + 0.702569i 0.247964π0.247964\pi
3232 −2.95993 0.869114i −0.523247 0.153639i
3333 2.94264 3.39599i 0.512248 0.591165i
3434 1.19647 + 0.768923i 0.205192 + 0.131869i
3535 −1.28128 + 2.56549i −0.216575 + 0.433647i
3636 −1.26195 + 1.45637i −0.210325 + 0.242728i
3737 2.08577 7.10348i 0.342899 1.16781i −0.589921 0.807461i 0.700841π-0.700841\pi
0.932819 0.360344i 0.117341π-0.117341\pi
3838 0.211833 + 1.47333i 0.0343639 + 0.239006i
3939 2.06316 + 2.38102i 0.330370 + 0.381268i
4040 0.477566 + 1.04572i 0.0755098 + 0.165343i
4141 −3.11602 10.6122i −0.486640 1.65734i −0.726983 0.686655i 0.759078π-0.759078\pi
0.240343 0.970688i 0.422740π-0.422740\pi
4242 −0.225050 + 0.678226i −0.0347260 + 0.104653i
4343 −1.39400 0.200427i −0.212583 0.0305649i 0.0352003 0.999380i 0.488793π-0.488793\pi
−0.247784 + 0.968815i 0.579702π0.579702\pi
4444 4.68155 + 7.28464i 0.705771 + 1.09820i
4545 1.08387 0.161574
4646 0.636118 + 1.12835i 0.0937905 + 0.166365i
4747 1.11953i 0.163300i 0.996661 + 0.0816498i 0.0260189π0.0260189\pi
−0.996661 + 0.0816498i 0.973981π0.973981\pi
4848 −1.92881 3.00128i −0.278399 0.433198i
4949 −0.512079 6.98124i −0.0731541 0.997321i
5050 −0.429187 + 0.939789i −0.0606963 + 0.132906i
5151 1.48355 + 5.05252i 0.207739 + 0.707495i
5252 −5.52260 + 2.52209i −0.765847 + 0.349750i
5353 −1.39483 + 1.20863i −0.191595 + 0.166018i −0.745376 0.666645i 0.767730π-0.767730\pi
0.553781 + 0.832662i 0.313184π0.313184\pi
5454 0.267340 0.0384377i 0.0363804 0.00523071i
5555 1.37215 4.67312i 0.185021 0.630123i
5656 −2.30655 1.59836i −0.308226 0.213590i
5757 −2.97951 + 4.63621i −0.394646 + 0.614081i
5858 −0.425546 0.273482i −0.0558769 0.0359099i
5959 9.62852 + 8.34316i 1.25353 + 1.08619i 0.992676 + 0.120808i 0.0385486π0.0385486\pi
0.260851 + 0.965379i 0.415997π0.415997\pi
6060 −0.588447 + 2.00407i −0.0759682 + 0.258724i
6161 −1.66120 11.5539i −0.212695 1.47932i −0.764106 0.645090i 0.776820π-0.776820\pi
0.551412 0.834233i 0.314089π-0.314089\pi
6262 1.37376 1.19037i 0.174468 0.151177i
6363 −2.27415 + 1.35212i −0.286517 + 0.170351i
6464 6.04679 1.77550i 0.755849 0.221937i
6565 3.10618 + 1.41855i 0.385275 + 0.175949i
6666 0.172721 1.20130i 0.0212605 0.147870i
6767 −5.58129 8.68465i −0.681863 1.06100i −0.993831 0.110907i 0.964625π-0.964625\pi
0.311968 0.950093i 0.399012π-0.399012\pi
6868 −10.1475 −1.23057
6969 −0.955844 + 4.69961i −0.115070 + 0.565767i
7070 0.0834932 + 0.770008i 0.00997934 + 0.0920336i
7171 8.57728 5.51229i 1.01794 0.654188i 0.0785010 0.996914i 0.474987π-0.474987\pi
0.939435 + 0.342726i 0.111350π0.111350\pi
7272 −0.150947 + 1.04986i −0.0177893 + 0.123727i
7373 12.5808 + 5.74545i 1.47247 + 0.672454i 0.980204 0.197992i 0.0634420π-0.0634420\pi
0.492265 + 0.870446i 0.336169π0.336169\pi
7474 −0.563345 1.91858i −0.0654875 0.223030i
7575 −3.47955 + 1.58906i −0.401784 + 0.183488i
7676 −6.95470 8.02616i −0.797759 0.920663i
7777 2.95065 + 11.5168i 0.336258 + 1.31246i
7878 0.816458 + 0.239734i 0.0924456 + 0.0271445i
7979 −6.67014 5.77971i −0.750450 0.650268i 0.193221 0.981155i 0.438107π-0.438107\pi
−0.943670 + 0.330887i 0.892652π0.892652\pi
8080 −3.25300 2.09058i −0.363696 0.233733i
8181 0.841254 + 0.540641i 0.0934726 + 0.0600712i
8282 −2.25761 1.95623i −0.249311 0.216029i
8383 0.695752 + 0.204291i 0.0763688 + 0.0224239i 0.319694 0.947521i 0.396420π-0.396420\pi
−0.243325 + 0.969945i 0.578238π0.578238\pi
8484 −1.26539 4.93898i −0.138065 0.538887i
8585 3.73760 + 4.31342i 0.405399 + 0.467856i
8686 −0.346003 + 0.158014i −0.0373104 + 0.0170391i
8787 −0.527653 1.79702i −0.0565704 0.192661i
8888 4.33539 + 1.97990i 0.462154 + 0.211059i
8989 1.66375 11.5717i 0.176358 1.22659i −0.688747 0.725002i 0.741839π-0.741839\pi
0.865104 0.501592i 0.167252π-0.167252\pi
9090 0.246270 0.158268i 0.0259591 0.0166829i
9191 −8.28696 + 0.898568i −0.868709 + 0.0941955i
9292 −8.17061 4.31883i −0.851845 0.450269i
9393 6.73016 0.697885
9494 0.163475 + 0.254371i 0.0168611 + 0.0262364i
9595 −0.850087 + 5.91249i −0.0872171 + 0.606608i
9696 −2.80611 1.28151i −0.286398 0.130794i
9797 7.69464 2.25935i 0.781272 0.229402i 0.133310 0.991074i 0.457439π-0.457439\pi
0.647963 + 0.761672i 0.275621π0.275621\pi
9898 −1.13576 1.51146i −0.114729 0.152680i
9999 3.39599 2.94264i 0.341309 0.295746i
100100 −1.04906 7.29638i −0.104906 0.729638i
101101 2.70718 9.21979i 0.269374 0.917404i −0.708058 0.706154i 0.750429π-0.750429\pi
0.977432 0.211250i 0.0677533π-0.0677533\pi
102102 1.07486 + 0.931371i 0.106427 + 0.0922195i
103103 −8.38523 5.38886i −0.826221 0.530980i 0.0578537 0.998325i 0.481574π-0.481574\pi
−0.884075 + 0.467345i 0.845211π0.845211\pi
104104 −1.80662 + 2.81116i −0.177154 + 0.275657i
105105 −1.63334 + 2.35703i −0.159398 + 0.230023i
106106 −0.140439 + 0.478292i −0.0136407 + 0.0464558i
107107 −5.56322 + 0.799870i −0.537816 + 0.0773263i −0.405870 0.913931i 0.633032π-0.633032\pi
−0.131946 + 0.991257i 0.542123π0.542123\pi
108108 −1.45637 + 1.26195i −0.140139 + 0.121431i
109109 −2.82030 + 1.28799i −0.270135 + 0.123367i −0.545878 0.837865i 0.683804π-0.683804\pi
0.275742 + 0.961232i 0.411076π0.411076\pi
110110 −0.370603 1.26216i −0.0353356 0.120342i
111111 3.07547 6.73434i 0.291911 0.639196i
112112 9.43335 + 0.328320i 0.891368 + 0.0310233i
113113 4.77648 + 7.43234i 0.449333 + 0.699176i 0.989843 0.142161i 0.0454052π-0.0454052\pi
−0.540510 + 0.841337i 0.681769π0.681769\pi
114114 1.48848i 0.139409i
115115 1.17364 + 5.06383i 0.109442 + 0.472204i
116116 3.60915 0.335101
117117 1.70331 + 2.65040i 0.157471 + 0.245029i
118118 3.40601 + 0.489711i 0.313549 + 0.0450815i
119119 −13.2231 4.38771i −1.21216 0.402221i
120120 0.323883 + 1.10304i 0.0295663 + 0.100694i
121121 −3.81843 8.36119i −0.347130 0.760108i
122122 −2.06456 2.38263i −0.186917 0.215713i
123123 −1.57403 10.9476i −0.141925 0.987113i
124124 −3.65389 + 12.4440i −0.328129 + 1.11751i
125125 −6.26400 + 7.22904i −0.560269 + 0.646585i
126126 −0.319281 + 0.639295i −0.0284438 + 0.0569529i
127127 −7.42569 4.77220i −0.658924 0.423465i 0.167994 0.985788i 0.446271π-0.446271\pi
−0.826917 + 0.562323i 0.809908π0.809908\pi
128128 5.15500 5.94919i 0.455642 0.525839i
129129 −1.35129 0.396774i −0.118974 0.0349340i
130130 0.912905 0.131256i 0.0800671 0.0115119i
131131 −14.9580 + 12.9612i −1.30689 + 1.13243i −0.324439 + 0.945907i 0.605175π0.605175\pi
−0.982451 + 0.186520i 0.940279π0.940279\pi
132132 3.59719 + 7.87675i 0.313095 + 0.685583i
133133 −5.59214 13.4659i −0.484900 1.16765i
134134 −2.53629 1.15828i −0.219102 0.100061i
135135 1.07284 + 0.154251i 0.0923351 + 0.0132758i
136136 −4.69859 + 3.01960i −0.402901 + 0.258929i
137137 2.80847i 0.239944i 0.992777 + 0.119972i 0.0382805π0.0382805\pi
−0.992777 + 0.119972i 0.961719π0.961719\pi
138138 0.469063 + 1.20739i 0.0399293 + 0.102780i
139139 11.5201i 0.977123i 0.872529 + 0.488562i 0.162478π0.162478\pi
−0.872529 + 0.488562i 0.837522π0.837522\pi
140140 −3.47137 4.29970i −0.293385 0.363391i
141141 −0.159325 + 1.10813i −0.0134176 + 0.0933214i
142142 1.14396 2.50493i 0.0959994 0.210209i
143143 13.5836 3.98850i 1.13592 0.333535i
144144 −1.48205 3.24523i −0.123504 0.270436i
145145 −1.32934 1.53415i −0.110396 0.127404i
146146 3.69748 0.531618i 0.306006 0.0439970i
147147 0.486668 6.98306i 0.0401397 0.575953i
148148 10.7820 + 9.34269i 0.886278 + 0.767964i
149149 −6.27446 + 9.76325i −0.514024 + 0.799836i −0.997129 0.0757260i 0.975873π-0.975873\pi
0.483105 + 0.875562i 0.339509π0.339509\pi
150150 −0.558565 + 0.869144i −0.0456066 + 0.0709653i
151151 −5.69807 + 6.57593i −0.463703 + 0.535141i −0.938649 0.344873i 0.887922π-0.887922\pi
0.474947 + 0.880015i 0.342467π0.342467\pi
152152 −5.60857 1.64683i −0.454915 0.133575i
153153 0.749405 + 5.21223i 0.0605858 + 0.421384i
154154 2.35213 + 2.18591i 0.189540 + 0.176146i
155155 6.63541 3.03029i 0.532969 0.243399i
156156 −5.82532 + 1.71047i −0.466399 + 0.136947i
157157 7.41817 16.2435i 0.592034 1.29637i −0.342171 0.939638i 0.611162π-0.611162\pi
0.934205 0.356736i 0.116111π-0.116111\pi
158158 −2.35951 0.339246i −0.187712 0.0269890i
159159 −1.55264 + 0.997820i −0.123132 + 0.0791323i
160160 −3.34362 −0.264336
161161 −8.77959 9.16072i −0.691928 0.721966i
162162 0.270089 0.0212202
163163 −19.1315 + 12.2951i −1.49849 + 0.963024i −0.503404 + 0.864051i 0.667919π0.667919\pi
−0.995090 + 0.0989727i 0.968444π0.968444\pi
164164 21.0966 + 3.03324i 1.64737 + 0.236856i
165165 2.02324 4.43027i 0.157509 0.344896i
166166 0.187915 0.0551769i 0.0145851 0.00428256i
167167 7.73632 3.53306i 0.598654 0.273396i −0.0929524 0.995671i 0.529630π-0.529630\pi
0.691607 + 0.722274i 0.256903π0.256903\pi
168168 −2.05560 1.91035i −0.158593 0.147386i
169169 −0.437494 3.04284i −0.0336534 0.234064i
170170 1.47908 + 0.434298i 0.113441 + 0.0333091i
171171 −3.60899 + 4.16499i −0.275986 + 0.318505i
172172 1.46727 2.28311i 0.111878 0.174085i
173173 5.25864 8.18260i 0.399807 0.622112i −0.581731 0.813382i 0.697624π-0.697624\pi
0.981538 + 0.191270i 0.0612605π0.0612605\pi
174174 −0.382294 0.331259i −0.0289816 0.0251127i
175175 1.78788 9.96143i 0.135151 0.753013i
176176 −15.8681 + 2.28149i −1.19610 + 0.171974i
177177 8.34316 + 9.62852i 0.627110 + 0.723724i
178178 −1.31168 2.87218i −0.0983148 0.215279i
179179 21.6927 6.36954i 1.62139 0.476082i 0.659996 0.751269i 0.270558π-0.270558\pi
0.961391 + 0.275187i 0.0887399π0.0887399\pi
180180 −0.867666 + 1.89992i −0.0646720 + 0.141612i
181181 −1.43926 + 10.0103i −0.106979 + 0.744058i 0.863757 + 0.503909i 0.168105π0.168105\pi
−0.970736 + 0.240149i 0.922804π0.922804\pi
182182 −1.75170 + 1.41424i −0.129845 + 0.104830i
183183 11.6727i 0.862871i
184184 −5.06838 + 0.431590i −0.373646 + 0.0318172i
185185 8.02429i 0.589957i
186186 1.52918 0.982747i 0.112125 0.0720585i
187187 23.4213 + 3.36748i 1.71274 + 0.246254i
188188 −1.96242 0.896209i −0.143124 0.0653628i
189189 −2.44343 + 1.01471i −0.177734 + 0.0738092i
190190 0.670198 + 1.46753i 0.0486212 + 0.106466i
191191 14.4740 12.5418i 1.04730 0.907495i 0.0514701 0.998675i 0.483609π-0.483609\pi
0.995834 + 0.0911800i 0.0290639π0.0290639\pi
192192 6.23792 0.896878i 0.450183 0.0647266i
193193 4.26226 + 1.25151i 0.306804 + 0.0900857i 0.431510 0.902108i 0.357981π-0.357981\pi
−0.124707 + 0.992194i 0.539799π0.539799\pi
194194 1.41841 1.63694i 0.101836 0.117525i
195195 2.87269 + 1.84616i 0.205717 + 0.132206i
196196 12.6474 + 4.69104i 0.903387 + 0.335074i
197197 −1.25209 + 1.44499i −0.0892079 + 0.102951i −0.798598 0.601864i 0.794425π-0.794425\pi
0.709391 + 0.704816i 0.248970π0.248970\pi
198198 0.341926 1.16449i 0.0242996 0.0827570i
199199 −1.29091 8.97847i −0.0915102 0.636467i −0.983024 0.183475i 0.941265π-0.941265\pi
0.891514 0.452993i 0.149644π-0.149644\pi
200200 −2.65693 3.06626i −0.187873 0.216817i
201201 −4.28852 9.39055i −0.302489 0.662359i
202202 −0.731179 2.49017i −0.0514456 0.175208i
203203 4.70304 + 1.56057i 0.330089 + 0.109531i
204204 −10.0442 1.44414i −0.703237 0.101110i
205205 −6.48109 10.0848i −0.452659 0.704351i
206206 −2.69213 −0.187569
207207 −1.61494 + 4.51575i −0.112246 + 0.313866i
208208 11.2399i 0.779350i
209209 13.3885 + 20.8330i 0.926104 + 1.44105i
210210 −0.0269402 + 0.774053i −0.00185905 + 0.0534147i
211211 −7.86869 + 17.2300i −0.541703 + 1.18616i 0.418847 + 0.908057i 0.362434π0.362434\pi
−0.960550 + 0.278108i 0.910293π0.910293\pi
212212 −1.00201 3.41255i −0.0688186 0.234375i
213213 9.27446 4.23550i 0.635476 0.290212i
214214 −1.14724 + 0.994089i −0.0784237 + 0.0679546i
215215 −1.51092 + 0.217237i −0.103044 + 0.0148154i
216216 −0.298821 + 1.01769i −0.0203322 + 0.0692451i
217217 −10.1420 + 14.6357i −0.688486 + 0.993537i
218218 −0.452736 + 0.704471i −0.0306632 + 0.0477128i
219219 11.6351 + 7.47740i 0.786224 + 0.505276i
220220 7.09310 + 6.14621i 0.478217 + 0.414377i
221221 −4.67399 + 15.9182i −0.314407 + 1.07077i
222222 −0.284569 1.97922i −0.0190990 0.132836i
223223 −16.9528 + 14.6897i −1.13524 + 0.983695i −0.999975 0.00711417i 0.997735π-0.997735\pi
−0.135269 + 0.990809i 0.543190π0.543190\pi
224224 7.01552 4.17113i 0.468744 0.278695i
225225 −3.67028 + 1.07769i −0.244685 + 0.0718461i
226226 2.17056 + 0.991262i 0.144384 + 0.0659378i
227227 −1.51829 + 10.5599i −0.100772 + 0.700888i 0.875322 + 0.483541i 0.160649π0.160649\pi
−0.976094 + 0.217347i 0.930260π0.930260\pi
228228 −5.74167 8.93422i −0.380252 0.591683i
229229 −3.49933 −0.231242 −0.115621 0.993293i 0.536886π-0.536886\pi
−0.115621 + 0.993293i 0.536886π0.536886\pi
230230 1.00609 + 0.979194i 0.0663399 + 0.0645661i
231231 1.28161 + 11.8195i 0.0843235 + 0.777665i
232232 1.67114 1.07398i 0.109716 0.0705100i
233233 1.77046 12.3138i 0.115986 0.806704i −0.845917 0.533315i 0.820946π-0.820946\pi
0.961904 0.273389i 0.0881447π-0.0881447\pi
234234 0.774030 + 0.353487i 0.0505999 + 0.0231082i
235235 0.341860 + 1.16427i 0.0223005 + 0.0759484i
236236 −22.3327 + 10.1990i −1.45373 + 0.663898i
237237 −5.77971 6.67014i −0.375433 0.433272i
238238 −3.64517 + 0.933907i −0.236281 + 0.0605362i
239239 −10.9628 3.21897i −0.709124 0.208218i −0.0927711 0.995687i 0.529572π-0.529572\pi
−0.616353 + 0.787470i 0.711391π0.711391\pi
240240 −2.92237 2.53225i −0.188638 0.163456i
241241 15.9870 + 10.2742i 1.02981 + 0.661821i 0.942447 0.334355i 0.108518π-0.108518\pi
0.0873668 + 0.996176i 0.472155π0.472155\pi
242242 −2.08851 1.34220i −0.134255 0.0862801i
243243 0.755750 + 0.654861i 0.0484814 + 0.0420093i
244244 21.5827 + 6.33726i 1.38169 + 0.405702i
245245 −2.66435 7.10388i −0.170219 0.453850i
246246 −1.95623 2.25761i −0.124724 0.143940i
247247 −15.7938 + 7.21278i −1.00493 + 0.458938i
248248 2.01111 + 6.84922i 0.127706 + 0.434926i
249249 0.659597 + 0.301228i 0.0418003 + 0.0190895i
250250 −0.367672 + 2.55721i −0.0232536 + 0.161732i
251251 −8.72513 + 5.60730i −0.550725 + 0.353930i −0.786221 0.617946i 0.787965π-0.787965\pi
0.235495 + 0.971875i 0.424329π0.424329\pi
252252 −0.549617 5.06879i −0.0346226 0.319304i
253253 17.4252 + 12.6797i 1.09551 + 0.797163i
254254 −2.38406 −0.149589
255255 3.08569 + 4.80143i 0.193233 + 0.300677i
256256 −1.49118 + 10.3714i −0.0931986 + 0.648210i
257257 24.9774 + 11.4068i 1.55805 + 0.711538i 0.993497 0.113859i 0.0363213π-0.0363213\pi
0.564553 + 0.825397i 0.309049π0.309049\pi
258258 −0.364969 + 0.107165i −0.0227220 + 0.00667177i
259259 10.0102 + 16.8364i 0.622005 + 1.04616i
260260 −4.97316 + 4.30927i −0.308422 + 0.267249i
261261 −0.266540 1.85382i −0.0164984 0.114749i
262262 −1.50606 + 5.12916i −0.0930445 + 0.316880i
263263 −4.71585 4.08631i −0.290792 0.251972i 0.497232 0.867618i 0.334350π-0.334350\pi
−0.788023 + 0.615645i 0.788895π0.788895\pi
264264 4.00949 + 2.57674i 0.246767 + 0.158587i
265265 −1.08151 + 1.68286i −0.0664364 + 0.103377i
266266 −3.23692 2.24307i −0.198469 0.137532i
267267 3.29364 11.2171i 0.201567 0.686476i
268268 19.6914 2.83119i 1.20284 0.172942i
269269 −9.73091 + 8.43188i −0.593304 + 0.514101i −0.898954 0.438043i 0.855672π-0.855672\pi
0.305650 + 0.952144i 0.401126π0.401126\pi
270270 0.266287 0.121609i 0.0162057 0.00740090i
271271 0.363936 + 1.23945i 0.0221076 + 0.0752915i 0.969808 0.243870i 0.0784170π-0.0784170\pi
−0.947700 + 0.319161i 0.896599π0.896599\pi
272272 7.80421 17.0888i 0.473199 1.03616i
273273 −8.33049 0.289935i −0.504184 0.0175477i
274274 0.410097 + 0.638124i 0.0247749 + 0.0385505i
275275 17.1888i 1.03652i
276276 −7.47281 5.43767i −0.449810 0.327309i
277277 12.3157 0.739977 0.369988 0.929036i 0.379362π-0.379362\pi
0.369988 + 0.929036i 0.379362π0.379362\pi
278278 1.68218 + 2.61753i 0.100891 + 0.156989i
279279 6.66165 + 0.957801i 0.398823 + 0.0573421i
280280 −2.88681 0.957905i −0.172520 0.0572458i
281281 −6.69105 22.7876i −0.399155 1.35940i −0.876805 0.480846i 0.840329π-0.840329\pi
0.477650 0.878550i 0.341489π-0.341489\pi
282282 0.125610 + 0.275047i 0.00747995 + 0.0163788i
283283 6.30384 + 7.27502i 0.374724 + 0.432455i 0.911519 0.411258i 0.134911π-0.134911\pi
−0.536795 + 0.843713i 0.680365π0.680365\pi
284284 2.79619 + 19.4479i 0.165923 + 1.15402i
285285 −1.68287 + 5.73132i −0.0996845 + 0.339494i
286286 2.50397 2.88973i 0.148063 0.170873i
287287 26.1792 + 13.0746i 1.54531 + 0.771769i
288288 −2.59517 1.66782i −0.152922 0.0982771i
289289 −7.02595 + 8.10838i −0.413291 + 0.476963i
290290 −0.526063 0.154466i −0.0308915 0.00907056i
291291 7.93786 1.14129i 0.465326 0.0669037i
292292 −20.1425 + 17.4536i −1.17875 + 1.02139i
293293 −0.898909 1.96834i −0.0525148 0.114991i 0.881556 0.472080i 0.156497π-0.156497\pi
−0.934071 + 0.357089i 0.883769π0.883769\pi
294294 −0.909098 1.65771i −0.0530197 0.0966797i
295295 12.5610 + 5.73642i 0.731330 + 0.333987i
296296 7.77250 + 1.11752i 0.451767 + 0.0649543i
297297 3.78020 2.42939i 0.219349 0.140967i
298298 3.13455i 0.181579i
299299 −10.5383 + 10.8278i −0.609443 + 0.626185i
300300 7.37141i 0.425589i
301301 2.89917 2.34066i 0.167106 0.134913i
302302 −0.334454 + 2.32618i −0.0192457 + 0.133857i
303303 3.99173 8.74068i 0.229319 0.502139i
304304 18.8651 5.53928i 1.08199 0.317700i
305305 −5.25570 11.5084i −0.300940 0.658968i
306306 0.931371 + 1.07486i 0.0532430 + 0.0614457i
307307 16.5084 2.37356i 0.942187 0.135466i 0.345931 0.938260i 0.387563π-0.387563\pi
0.596256 + 0.802794i 0.296654π0.296654\pi
308308 −22.5499 4.04728i −1.28490 0.230615i
309309 −7.53297 6.52735i −0.428536 0.371328i
310310 1.06517 1.65744i 0.0604975 0.0941360i
311311 −8.90159 + 13.8511i −0.504763 + 0.785426i −0.996346 0.0854041i 0.972782π-0.972782\pi
0.491584 + 0.870830i 0.336418π0.336418\pi
312312 −2.18830 + 2.52544i −0.123888 + 0.142975i
313313 −32.5568 9.55955i −1.84022 0.540338i −0.840224 0.542240i 0.817576π-0.817576\pi
−0.999998 + 0.00190234i 0.999394π0.999394\pi
314314 −0.686392 4.77396i −0.0387353 0.269410i
315315 −1.95216 + 2.10059i −0.109992 + 0.118355i
316316 15.4709 7.06533i 0.870307 0.397456i
317317 3.56166 1.04580i 0.200043 0.0587378i −0.180176 0.983634i 0.557667π-0.557667\pi
0.380219 + 0.924897i 0.375849π0.375849\pi
318318 −0.207078 + 0.453437i −0.0116123 + 0.0254275i
319319 −8.33022 1.19770i −0.466403 0.0670586i
320320 5.74628 3.69291i 0.321227 0.206440i
321321 −5.62042 −0.313701
322322 −3.33250 0.799434i −0.185713 0.0445507i
323323 −29.0204 −1.61474
324324 −1.62114 + 1.04184i −0.0900633 + 0.0578802i
325325 −11.9288 1.71511i −0.661693 0.0951371i
326326 −2.55159 + 5.58721i −0.141320 + 0.309447i
327327 −2.97489 + 0.873506i −0.164512 + 0.0483050i
328328 10.6709 4.87325i 0.589204 0.269080i
329329 −2.16970 2.01638i −0.119619 0.111166i
330330 −0.187207 1.30205i −0.0103054 0.0716757i
331331 −4.66719 1.37041i −0.256532 0.0753246i 0.150938 0.988543i 0.451771π-0.451771\pi
−0.407470 + 0.913219i 0.633589π0.633589\pi
332332 −0.915072 + 1.05605i −0.0502211 + 0.0579582i
333333 4.00256 6.22811i 0.219339 0.341298i
334334 1.24190 1.93243i 0.0679535 0.105738i
335335 −8.45630 7.32742i −0.462017 0.400340i
336336 9.29061 + 1.66748i 0.506844 + 0.0909687i
337337 −1.60868 + 0.231293i −0.0876302 + 0.0125993i −0.185990 0.982552i 0.559549π-0.559549\pi
0.0983602 + 0.995151i 0.468640π0.468640\pi
338338 −0.543724 0.627491i −0.0295747 0.0341310i
339339 3.67013 + 8.03645i 0.199334 + 0.436480i
340340 −10.5531 + 3.09866i −0.572320 + 0.168048i
341341 12.5631 27.5093i 0.680328 1.48971i
342342 −0.211833 + 1.47333i −0.0114546 + 0.0796687i
343343 14.4523 + 11.5815i 0.780351 + 0.625341i
344344 1.49376i 0.0805381i
345345 0.441036 + 5.17931i 0.0237446 + 0.278845i
346346 2.62707i 0.141232i
347347 18.0057 11.5716i 0.966598 0.621195i 0.0407812 0.999168i 0.487015π-0.487015\pi
0.925816 + 0.377974i 0.123379π0.123379\pi
348348 3.57241 + 0.513636i 0.191502 + 0.0275338i
349349 −23.7180 10.8316i −1.26959 0.579804i −0.337262 0.941411i 0.609501π-0.609501\pi
−0.932331 + 0.361607i 0.882228π0.882228\pi
350350 −1.04835 2.52444i −0.0560366 0.134937i
351351 1.30878 + 2.86583i 0.0698575 + 0.152967i
352352 −10.4762 + 9.07771i −0.558385 + 0.483844i
353353 13.1611 1.89228i 0.700495 0.100716i 0.217140 0.976140i 0.430327π-0.430327\pi
0.483355 + 0.875424i 0.339418π0.339418\pi
354354 3.30165 + 0.969452i 0.175481 + 0.0515258i
355355 7.23684 8.35175i 0.384091 0.443265i
356356 18.9522 + 12.1798i 1.00446 + 0.645530i
357357 −12.4641 6.22489i −0.659669 0.329456i
358358 3.99878 4.61484i 0.211342 0.243902i
359359 4.06200 13.8339i 0.214384 0.730125i −0.780139 0.625606i 0.784852π-0.784852\pi
0.994523 0.104518i 0.0333301π-0.0333301\pi
360360 0.163607 + 1.13791i 0.00862283 + 0.0599731i
361361 −7.44704 8.59434i −0.391950 0.452334i
362362 1.13469 + 2.48463i 0.0596382 + 0.130589i
363363 −2.58964 8.81950i −0.135921 0.462904i
364364 5.05882 15.2456i 0.265154 0.799087i
365365 14.8380 + 2.13338i 0.776657 + 0.111666i
366366 −1.70446 2.65220i −0.0890937 0.138633i
367367 −5.90645 −0.308314 −0.154157 0.988046i 0.549266π-0.549266\pi
−0.154157 + 0.988046i 0.549266π0.549266\pi
368368 13.5569 10.4381i 0.706702 0.544125i
369369 11.0602i 0.575770i
370370 −1.17172 1.82323i −0.0609147 0.0947851i
371371 0.169848 4.88011i 0.00881807 0.253363i
372372 −5.38767 + 11.7973i −0.279338 + 0.611664i
373373 1.94395 + 6.62049i 0.100654 + 0.342796i 0.994387 0.105803i 0.0337413π-0.0337413\pi
−0.893733 + 0.448599i 0.851923π0.851923\pi
374374 5.81336 2.65487i 0.300602 0.137280i
375375 −7.22904 + 6.26400i −0.373306 + 0.323472i
376376 −1.17534 + 0.168989i −0.0606137 + 0.00871494i
377377 1.66239 5.66158i 0.0856175 0.291586i
378378 −0.407012 + 0.587349i −0.0209345 + 0.0302100i
379379 2.26030 3.51710i 0.116104 0.180661i −0.778338 0.627846i 0.783937π-0.783937\pi
0.894442 + 0.447185i 0.147573π0.147573\pi
380380 −9.68353 6.22322i −0.496754 0.319245i
381381 −6.67096 5.78042i −0.341763 0.296140i
382382 1.45732 4.96319i 0.0745632 0.253939i
383383 −5.18273 36.0467i −0.264825 1.84190i −0.495178 0.868792i 0.664897π-0.664897\pi
0.230353 0.973107i 0.426012π-0.426012\pi
384384 5.94919 5.15500i 0.303593 0.263065i
385385 6.58535 + 11.0760i 0.335621 + 0.564488i
386386 1.15119 0.338020i 0.0585940 0.0172048i
387387 −1.28107 0.585044i −0.0651203 0.0297395i
388388 −2.19933 + 15.2967i −0.111654 + 0.776571i
389389 −0.566956 0.882200i −0.0287458 0.0447293i 0.826583 0.562814i 0.190281π-0.190281\pi
−0.855329 + 0.518085i 0.826645π0.826645\pi
390390 0.922293 0.0467021
391391 −23.5400 + 9.14514i −1.19047 + 0.462489i
392392 7.25203 1.59141i 0.366283 0.0803782i
393393 −16.6504 + 10.7005i −0.839900 + 0.539771i
394394 −0.0734928 + 0.511154i −0.00370252 + 0.0257516i
395395 −8.70161 3.97389i −0.437826 0.199948i
396396 2.43960 + 8.30851i 0.122594 + 0.417518i
397397 2.14138 0.977934i 0.107473 0.0490811i −0.360953 0.932584i 0.617549π-0.617549\pi
0.468426 + 0.883503i 0.344821π0.344821\pi
398398 −1.60436 1.85153i −0.0804194 0.0928089i
399399 −3.61881 14.1247i −0.181167 0.707121i
400400 13.0942 + 3.84481i 0.654710 + 0.192240i
401401 16.9334 + 14.6729i 0.845614 + 0.732728i 0.965596 0.260048i 0.0837383π-0.0837383\pi
−0.119982 + 0.992776i 0.538284π0.538284\pi
402402 −2.34563 1.50745i −0.116990 0.0751846i
403403 17.8376 + 11.4635i 0.888554 + 0.571039i
404404 13.9943 + 12.1261i 0.696242 + 0.603297i
405405 1.03996 + 0.305361i 0.0516763 + 0.0151735i
406406 1.29647 0.332161i 0.0643428 0.0164849i
407407 −21.7854 25.1417i −1.07986 1.24623i
408408 −5.08050 + 2.32019i −0.251522 + 0.114866i
409409 −1.29893 4.42376i −0.0642281 0.218741i 0.921125 0.389267i 0.127272π-0.127272\pi
−0.985353 + 0.170526i 0.945453π0.945453\pi
410410 −2.94519 1.34502i −0.145452 0.0664259i
411411 −0.399688 + 2.77989i −0.0197151 + 0.137122i
412412 16.1588 10.3846i 0.796086 0.511613i
413413 −33.5114 + 3.63369i −1.64899 + 0.178802i
414414 0.292459 + 1.26185i 0.0143736 + 0.0620168i
415415 0.785941 0.0385803
416416 −5.25452 8.17619i −0.257624 0.400871i
417417 −1.63948 + 11.4029i −0.0802858 + 0.558400i
418418 6.08412 + 2.77852i 0.297584 + 0.135902i
419419 −22.6903 + 6.66248i −1.10849 + 0.325483i −0.784222 0.620480i 0.786938π-0.786938\pi
−0.324273 + 0.945964i 0.605120π0.605120\pi
420420 −2.82413 4.74996i −0.137803 0.231774i
421421 0.466757 0.404448i 0.0227484 0.0197116i −0.643412 0.765520i 0.722482π-0.722482\pi
0.666161 + 0.745808i 0.267936π0.267936\pi
422422 0.728078 + 5.06390i 0.0354423 + 0.246507i
423423 −0.315407 + 1.07418i −0.0153356 + 0.0522282i
424424 −1.47943 1.28194i −0.0718477 0.0622564i
425425 −16.9454 10.8901i −0.821970 0.528248i
426426 1.48881 2.31663i 0.0721331 0.112241i
427427 25.3840 + 17.5902i 1.22842 + 0.851250i
428428 3.05140 10.3921i 0.147495 0.502322i
429429 14.0129 2.01476i 0.676551 0.0972733i
430430 −0.311579 + 0.269985i −0.0150257 + 0.0130198i
431431 9.67073 4.41648i 0.465823 0.212734i −0.168655 0.985675i 0.553942π-0.553942\pi
0.634478 + 0.772941i 0.281215π0.281215\pi
432432 −1.00512 3.42312i −0.0483588 0.164695i
433433 7.20625 15.7795i 0.346310 0.758314i −0.653689 0.756764i 0.726779π-0.726779\pi
0.999999 0.00154997i 0.000493372π-0.000493372\pi
434434 −0.167282 + 4.80639i −0.00802980 + 0.230714i
435435 −1.09748 1.70772i −0.0526202 0.0818787i
436436 5.97479i 0.286140i
437437 −23.3667 12.3512i −1.11778 0.590838i
438438 3.73550 0.178489
439439 7.28174 + 11.3306i 0.347538 + 0.540780i 0.970385 0.241564i 0.0776603π-0.0776603\pi
−0.622847 + 0.782344i 0.714024π0.714024\pi
440440 5.11324 + 0.735172i 0.243764 + 0.0350480i
441441 1.47551 6.84272i 0.0702623 0.325844i
442442 1.26240 + 4.29932i 0.0600460 + 0.204498i
443443 −2.45335 5.37209i −0.116562 0.255236i 0.842354 0.538924i 0.181169π-0.181169\pi
−0.958916 + 0.283689i 0.908442π0.908442\pi
444444 9.34269 + 10.7820i 0.443384 + 0.511693i
445445 −1.80329 12.5422i −0.0854843 0.594556i
446446 −1.70690 + 5.81317i −0.0808241 + 0.275262i
447447 −7.60005 + 8.77092i −0.359470 + 0.414850i
448448 −7.44987 + 14.9168i −0.351973 + 0.704754i
449449 8.93655 + 5.74317i 0.421742 + 0.271037i 0.734252 0.678877i 0.237533π-0.237533\pi
−0.312510 + 0.949915i 0.601170π0.601170\pi
450450 −0.676572 + 0.780805i −0.0318939 + 0.0368075i
451451 −47.6861 14.0019i −2.24545 0.659324i
452452 −16.8519 + 2.42294i −0.792647 + 0.113965i
453453 −6.57593 + 5.69807i −0.308964 + 0.267719i
454454 1.19700 + 2.62106i 0.0561780 + 0.123013i
455455 −8.34376 + 3.46500i −0.391161 + 0.162441i
456456 −5.31712 2.42825i −0.248997 0.113713i
457457 −32.2218 4.63280i −1.50727 0.216713i −0.661374 0.750057i 0.730026π-0.730026\pi
−0.845899 + 0.533344i 0.820935π0.820935\pi
458458 −0.795095 + 0.510976i −0.0371523 + 0.0238764i
459459 5.26583i 0.245788i
460460 −9.81595 1.99644i −0.457671 0.0930847i
461461 4.03455i 0.187908i 0.995577 + 0.0939540i 0.0299507π0.0299507\pi
−0.995577 + 0.0939540i 0.970049π0.970049\pi
462462 2.01710 + 2.49841i 0.0938438 + 0.116236i
463463 −4.02965 + 28.0268i −0.187274 + 1.30252i 0.651755 + 0.758430i 0.274033π0.274033\pi
−0.839028 + 0.544088i 0.816876π0.816876\pi
464464 −2.77571 + 6.07795i −0.128859 + 0.282162i
465465 6.99913 2.05513i 0.324577 0.0953043i
466466 −1.39581 3.05639i −0.0646594 0.141584i
467467 2.48941 + 2.87293i 0.115196 + 0.132943i 0.810419 0.585851i 0.199240π-0.199240\pi
−0.695223 + 0.718795i 0.744694π0.744694\pi
468468 −6.00945 + 0.864028i −0.277787 + 0.0399397i
469469 26.8837 + 4.82511i 1.24138 + 0.222803i
470470 0.247683 + 0.214619i 0.0114248 + 0.00989961i
471471 9.65436 15.0225i 0.444849 0.692199i
472472 −7.30575 + 11.3680i −0.336274 + 0.523253i
473473 −4.14422 + 4.78269i −0.190552 + 0.219908i
474474 −2.28721 0.671586i −0.105055 0.0308470i
475475 −3.00016 20.8665i −0.137657 0.957422i
476476 18.2767 19.6664i 0.837711 0.901408i
477477 −1.67884 + 0.766701i −0.0768688 + 0.0351048i
478478 −2.96093 + 0.869409i −0.135430 + 0.0397658i
479479 −4.15124 + 9.08995i −0.189675 + 0.415330i −0.980448 0.196780i 0.936952π-0.936952\pi
0.790773 + 0.612110i 0.209679π0.209679\pi
480480 −3.30958 0.475846i −0.151061 0.0217193i
481481 19.6219 12.6102i 0.894681 0.574977i
482482 5.13272 0.233789
483483 −7.38652 10.3169i −0.336098 0.469437i
484484 17.7131 0.805143
485485 7.31224 4.69929i 0.332032 0.213384i
486486 0.267340 + 0.0384377i 0.0121268 + 0.00174357i
487487 8.16380 17.8762i 0.369937 0.810049i −0.629516 0.776987i 0.716747π-0.716747\pi
0.999453 0.0330617i 0.0105258π-0.0105258\pi
488488 11.8792 3.48805i 0.537746 0.157897i
489489 −20.6865 + 9.44722i −0.935477 + 0.427218i
490490 −1.64269 1.22505i −0.0742093 0.0553420i
491491 4.89665 + 34.0570i 0.220983 + 1.53697i 0.734333 + 0.678790i 0.237495π0.237495\pi
−0.513350 + 0.858180i 0.671596π0.671596\pi
492492 20.4502 + 6.00472i 0.921967 + 0.270714i
493493 6.45843 7.45343i 0.290873 0.335685i
494494 −2.53534 + 3.94507i −0.114071 + 0.177497i
495495 2.63314 4.09724i 0.118351 0.184157i
496496 −18.1461 15.7237i −0.814784 0.706014i
497497 −4.76546 + 26.5514i −0.213760 + 1.19099i
498498 0.193855 0.0278722i 0.00868686 0.00124898i
499499 8.97398 + 10.3565i 0.401731 + 0.463622i 0.920185 0.391483i 0.128038π-0.128038\pi
−0.518455 + 0.855105i 0.673492π0.673492\pi
500500 −7.65735 16.7673i −0.342447 0.749854i
501501 8.16038 2.39610i 0.364579 0.107050i
502502 −1.16368 + 2.54811i −0.0519377 + 0.113728i
503503 −3.88849 + 27.0450i −0.173379 + 1.20588i 0.698302 + 0.715804i 0.253939π0.253939\pi
−0.871681 + 0.490074i 0.836970π0.836970\pi
504504 −1.76281 2.18344i −0.0785218 0.0972583i
505505 10.4149i 0.463458i
506506 5.81075 + 0.336534i 0.258319 + 0.0149608i
507507 3.07413i 0.136527i
508508 14.3097 9.19628i 0.634890 0.408019i
509509 2.11143 + 0.303578i 0.0935875 + 0.0134558i 0.188949 0.981987i 0.439492π-0.439492\pi
−0.0953620 + 0.995443i 0.530401π0.530401\pi
510510 1.40222 + 0.640373i 0.0620914 + 0.0283562i
511511 −33.7942 + 14.0341i −1.49497 + 0.620830i
512512 7.71584 + 16.8953i 0.340995 + 0.746675i
513513 −4.16499 + 3.60899i −0.183889 + 0.159341i
514514 7.34085 1.05546i 0.323791 0.0465541i
515515 −10.3659 3.04370i −0.456776 0.134122i
516516 1.77725 2.05106i 0.0782391 0.0902928i
517517 4.23203 + 2.71976i 0.186124 + 0.119615i
518518 4.73294 + 2.36376i 0.207953 + 0.103857i
519519 6.36962 7.35093i 0.279595 0.322670i
520520 −1.02040 + 3.47518i −0.0447477 + 0.152397i
521521 −5.45094 37.9121i −0.238810 1.66096i −0.657968 0.753046i 0.728584π-0.728584\pi
0.419158 0.907913i 0.362325π-0.362325\pi
522522 −0.331259 0.382294i −0.0144988 0.0167325i
523523 −6.97867 15.2812i −0.305156 0.668199i 0.693476 0.720479i 0.256078π-0.256078\pi
−0.998632 + 0.0522808i 0.983351π0.983351\pi
524524 −10.7455 36.5959i −0.469420 1.59870i
525525 3.18734 9.60559i 0.139107 0.419222i
526526 −1.66819 0.239850i −0.0727367 0.0104580i
527527 19.1602 + 29.8139i 0.834632 + 1.29871i
528528 −16.0313 −0.697671
529529 −22.8462 2.65522i −0.993314 0.115444i
530530 0.540291i 0.0234688i
531531 6.88796 + 10.7179i 0.298912 + 0.465116i
532532 28.0812 + 0.977342i 1.21747 + 0.0423731i
533533 14.4754 31.6966i 0.626997 1.37293i
534534 −0.889577 3.02962i −0.0384958 0.131105i
535535 −5.54130 + 2.53063i −0.239571 + 0.109409i
536536 8.27518 7.17049i 0.357433 0.309718i
537537 22.3783 3.21752i 0.965697 0.138846i
538538 −0.979761 + 3.33676i −0.0422405 + 0.143858i
539539 −27.6345 15.0244i −1.19030 0.647146i
540540 −1.12922 + 1.75710i −0.0485940 + 0.0756137i
541541 −38.3527 24.6478i −1.64891 1.05969i −0.931955 0.362574i 0.881898π-0.881898\pi
−0.716957 0.697117i 0.754466π-0.754466\pi
542542 0.263678 + 0.228478i 0.0113259 + 0.00981398i
543543 −2.84922 + 9.70355i −0.122272 + 0.416419i
544544 −2.31183 16.0791i −0.0991190 0.689388i
545545 −2.53971 + 2.20067i −0.108789 + 0.0942663i
546546 −1.93514 + 1.15055i −0.0828162 + 0.0492391i
547547 11.3960 3.34618i 0.487260 0.143072i −0.0288693 0.999583i 0.509191π-0.509191\pi
0.516129 + 0.856511i 0.327372π0.327372\pi
548548 −4.92300 2.24826i −0.210300 0.0960408i
549549 1.66120 11.5539i 0.0708982 0.493108i
550550 2.50993 + 3.90553i 0.107024 + 0.166532i
551551 10.3216 0.439716
552552 −5.07821 0.294109i −0.216143 0.0125181i
553553 23.2150 2.51723i 0.987201 0.107044i
554554 2.79829 1.79835i 0.118888 0.0764046i
555555 1.14198 7.94261i 0.0484741 0.337145i
556556 −20.1937 9.22215i −0.856403 0.391106i
557557 1.50719 + 5.13302i 0.0638617 + 0.217493i 0.985241 0.171171i 0.0547550π-0.0547550\pi
−0.921380 + 0.388664i 0.872937π0.872937\pi
558558 1.65348 0.755118i 0.0699973 0.0319667i
559559 −2.90563 3.35327i −0.122895 0.141828i
560560 9.91061 2.53914i 0.418800 0.107298i
561561 22.7037 + 6.66640i 0.958550 + 0.281456i
562562 −4.84778 4.20063i −0.204491 0.177193i
563563 11.6071 + 7.45945i 0.489182 + 0.314378i 0.761876 0.647722i 0.224278π-0.224278\pi
−0.272694 + 0.962101i 0.587915π0.587915\pi
564564 −1.81491 1.16637i −0.0764213 0.0491130i
565565 7.23692 + 6.27082i 0.304459 + 0.263816i
566566 2.49463 + 0.732488i 0.104857 + 0.0307888i
567567 −2.56297 + 0.656644i −0.107635 + 0.0275764i
568568 7.08184 + 8.17288i 0.297147 + 0.342926i
569569 21.2851 9.72056i 0.892316 0.407507i 0.0841443 0.996454i 0.473184π-0.473184\pi
0.808172 + 0.588946i 0.200457π0.200457\pi
570570 0.454525 + 1.54797i 0.0190380 + 0.0648373i
571571 −43.2169 19.7365i −1.80857 0.825946i −0.949261 0.314489i 0.898167π-0.898167\pi
−0.859309 0.511457i 0.829106π-0.829106\pi
572572 −3.88254 + 27.0036i −0.162337 + 1.12908i
573573 16.1116 10.3543i 0.673072 0.432557i
574574 7.85744 0.851994i 0.327963 0.0355616i
575575 −9.00923 15.9806i −0.375711 0.666435i
576576 6.30207 0.262586
577577 7.29062 + 11.3444i 0.303513 + 0.472275i 0.959188 0.282768i 0.0912525π-0.0912525\pi
−0.655676 + 0.755043i 0.727616π0.727616\pi
578578 −0.412395 + 2.86827i −0.0171534 + 0.119304i
579579 4.04076 + 1.84535i 0.167928 + 0.0766903i
580580 3.75339 1.10209i 0.155851 0.0457620i
581581 −1.64905 + 0.980454i −0.0684140 + 0.0406761i
582582 1.63694 1.41841i 0.0678532 0.0587952i
583583 1.18027 + 8.20896i 0.0488818 + 0.339981i
584584 −4.13288 + 14.0753i −0.171020 + 0.582440i
585585 2.58071 + 2.23620i 0.106699 + 0.0924554i
586586 −0.491664 0.315973i −0.0203104 0.0130527i
587587 0.327769 0.510018i 0.0135285 0.0210507i −0.834423 0.551124i 0.814199π-0.814199\pi
0.847952 + 0.530073i 0.177836π0.177836\pi
588588 11.8511 + 6.44321i 0.488730 + 0.265713i
589589 −10.4496 + 35.5880i −0.430567 + 1.46638i
590590 3.69167 0.530782i 0.151984 0.0218520i
591591 −1.44499 + 1.25209i −0.0594390 + 0.0515042i
592592 −24.0257 + 10.9722i −0.987448 + 0.450953i
593593 5.35710 + 18.2446i 0.219990 + 0.749217i 0.993338 + 0.115235i 0.0367622π0.0367622\pi
−0.773348 + 0.633981i 0.781420π0.781420\pi
594594 0.504171 1.10398i 0.0206864 0.0452968i
595595 −15.0914 0.525243i −0.618687 0.0215329i
596596 −12.0912 18.8143i −0.495275 0.770663i
597597 9.07080i 0.371243i
598598 −0.813352 + 3.99902i −0.0332605 + 0.163532i
599599 −45.3081 −1.85124 −0.925620 0.378453i 0.876456π-0.876456\pi
−0.925620 + 0.378453i 0.876456π0.876456\pi
600600 −2.19351 3.41317i −0.0895498 0.139342i
601601 −5.12812 0.737313i −0.209181 0.0300756i 0.0369278 0.999318i 0.488243π-0.488243\pi
−0.246108 + 0.969242i 0.579152π0.579152\pi
602602 0.316946 0.955170i 0.0129178 0.0389298i
603603 −2.90846 9.90529i −0.118441 0.403375i
604604 −6.96554 15.2524i −0.283424 0.620611i
605605 −6.52421 7.52934i −0.265247 0.306111i
606606 −0.369349 2.56888i −0.0150038 0.104354i
607607 −3.79079 + 12.9103i −0.153864 + 0.524011i −0.999959 0.00901974i 0.997129π-0.997129\pi
0.846096 + 0.533031i 0.178947π0.178947\pi
608608 11.1333 12.8485i 0.451516 0.521077i
609609 4.43308 + 2.21400i 0.179637 + 0.0897157i
610610 −2.87463 1.84742i −0.116391 0.0747997i
611611 −2.30976 + 2.66561i −0.0934429 + 0.107839i
612612 −9.73647 2.85889i −0.393574 0.115564i
613613 7.30054 1.04966i 0.294866 0.0423953i 0.00670569 0.999978i 0.497865π-0.497865\pi
0.288160 + 0.957582i 0.406956π0.406956\pi
614614 3.40435 2.94989i 0.137389 0.119048i
615615 −4.97991 10.9045i −0.200809 0.439711i
616616 −11.6456 + 4.83619i −0.469215 + 0.194856i
617617 33.3461 + 15.2286i 1.34246 + 0.613082i 0.951592 0.307363i 0.0994467π-0.0994467\pi
0.390871 + 0.920446i 0.372174π0.372174\pi
618618 −2.66473 0.383130i −0.107191 0.0154117i
619619 −11.1866 + 7.18916i −0.449626 + 0.288957i −0.745791 0.666180i 0.767928π-0.767928\pi
0.296166 + 0.955137i 0.404292π0.404292\pi
620620 14.0571i 0.564546i
621621 −2.24116 + 4.23995i −0.0899346 + 0.170143i
622622 4.44699i 0.178308i
623623 19.4299 + 24.0662i 0.778442 + 0.964191i
624624 1.59961 11.1255i 0.0640357 0.445378i
625625 3.63841 7.96701i 0.145537 0.318681i
626626 −8.79326 + 2.58193i −0.351449 + 0.103195i
627627 10.2874 + 22.5263i 0.410840 + 0.899614i
628628 22.5350 + 26.0067i 0.899243 + 1.03778i
629629 38.5881 5.54812i 1.53861 0.221218i
630630 −0.136825 + 0.762340i −0.00545125 + 0.0303724i
631631 5.37572 + 4.65809i 0.214004 + 0.185435i 0.755266 0.655419i 0.227508π-0.227508\pi
−0.541262 + 0.840854i 0.682053π0.682053\pi
632632 5.06104 7.87514i 0.201318 0.313256i
633633 −10.2407 + 15.9348i −0.407031 + 0.633353i
634634 0.656549 0.757698i 0.0260749 0.0300920i
635635 −9.17971 2.69541i −0.364286 0.106964i
636636 −0.506159 3.52041i −0.0200705 0.139594i
637637 13.1842 17.6790i 0.522376 0.700466i
638638 −2.06763 + 0.944255i −0.0818582 + 0.0373834i
639639 9.78283 2.87250i 0.387003 0.113634i
640640 3.54437 7.76108i 0.140103 0.306784i
641641 25.9394 + 3.72952i 1.02454 + 0.147307i 0.634045 0.773296i 0.281393π-0.281393\pi
0.390499 + 0.920603i 0.372302π0.372302\pi
642642 −1.27704 + 0.820702i −0.0504006 + 0.0323905i
643643 −18.8578 −0.743678 −0.371839 0.928297i 0.621273π-0.621273\pi
−0.371839 + 0.928297i 0.621273π0.621273\pi
644644 23.0862 8.05641i 0.909723 0.317467i
645645 −1.52645 −0.0601040
646646 −6.59382 + 4.23759i −0.259430 + 0.166726i
647647 13.4429 + 1.93280i 0.528496 + 0.0759863i 0.401398 0.915904i 0.368525π-0.368525\pi
0.127098 + 0.991890i 0.459434π0.459434\pi
648648 −0.440612 + 0.964806i −0.0173089 + 0.0379011i
649649 54.9302 16.1290i 2.15620 0.633117i
650650 −2.96084 + 1.35217i −0.116134 + 0.0530365i
651651 −12.1217 + 13.0434i −0.475086 + 0.511211i
652652 −6.23685 43.3783i −0.244254 1.69882i
653653 −17.4593 5.12651i −0.683235 0.200616i −0.0783464 0.996926i 0.524964π-0.524964\pi
−0.604888 + 0.796310i 0.706782π0.706782\pi
654654 −0.548385 + 0.632870i −0.0214435 + 0.0247472i
655655 −11.5980 + 18.0468i −0.453171 + 0.705147i
656656 −21.3330 + 33.1948i −0.832913 + 1.29604i
657657 10.4525 + 9.05713i 0.407790 + 0.353352i
658658 −0.787418 0.141326i −0.0306968 0.00550947i
659659 7.42513 1.06757i 0.289242 0.0415867i 0.00383348 0.999993i 0.498780π-0.498780\pi
0.285409 + 0.958406i 0.407871π0.407871\pi
660660 6.14621 + 7.09310i 0.239241 + 0.276099i
661661 −7.89523 17.2882i −0.307089 0.672431i 0.691671 0.722213i 0.256875π-0.256875\pi
−0.998760 + 0.0497815i 0.984148π0.984148\pi
662662 −1.26056 + 0.370133i −0.0489930 + 0.0143856i
663663 −6.89181 + 15.0909i −0.267656 + 0.586084i
664664 −0.109455 + 0.761279i −0.00424769 + 0.0295434i
665665 −9.92760 12.2965i −0.384976 0.476837i
666666 1.99957i 0.0774818i
667667 8.37243 3.25264i 0.324182 0.125943i
668668 16.3894i 0.634123i
669669 −18.8708 + 12.1275i −0.729588 + 0.468878i
670670 −2.99135 0.430091i −0.115566 0.0166159i
671671 −47.7117 21.7892i −1.84189 0.841163i
672672 7.53772 3.13026i 0.290774 0.120753i
673673 −3.26764 7.15514i −0.125958 0.275810i 0.836138 0.548518i 0.184808π-0.184808\pi
−0.962097 + 0.272708i 0.912081π0.912081\pi
674674 −0.331740 + 0.287454i −0.0127781 + 0.0110723i
675675 −3.78629 + 0.544387i −0.145734 + 0.0209535i
676676 5.68404 + 1.66898i 0.218617 + 0.0641917i
677677 1.86548 2.15288i 0.0716963 0.0827420i −0.718768 0.695250i 0.755294π-0.755294\pi
0.790465 + 0.612508i 0.209839π0.209839\pi
678678 2.00740 + 1.29008i 0.0770936 + 0.0495450i
679679 −9.48008 + 18.9819i −0.363812 + 0.728459i
680680 −3.96430 + 4.57505i −0.152024 + 0.175445i
681681 −3.00567 + 10.2364i −0.115178 + 0.392259i
682682 −1.16244 8.08495i −0.0445122 0.309589i
683683 4.52163 + 5.21824i 0.173015 + 0.199670i 0.835634 0.549287i 0.185100π-0.185100\pi
−0.662619 + 0.748957i 0.730555π0.730555\pi
684684 −4.41176 9.66041i −0.168688 0.369375i
685685 0.857599 + 2.92072i 0.0327672 + 0.111595i
686686 4.97491 + 0.521126i 0.189943 + 0.0198967i
687687 −3.46371 0.498006i −0.132149 0.0190001i
688688 2.71641 + 4.22682i 0.103562 + 0.161146i
689689 −5.81471 −0.221523
690690 0.856499 + 1.11241i 0.0326064 + 0.0423487i
691691 1.87878i 0.0714722i 0.999361 + 0.0357361i 0.0113776π0.0113776\pi
−0.999361 + 0.0357361i 0.988622π0.988622\pi
692692 10.1337 + 15.7683i 0.385224 + 0.599421i
693693 −0.413528 + 11.8816i −0.0157086 + 0.451344i
694694 2.40145 5.25844i 0.0911577 0.199608i
695695 3.51780 + 11.9805i 0.133438 + 0.454447i
696696 1.80697 0.825217i 0.0684931 0.0312798i
697697 44.0156 38.1398i 1.66721 1.44465i
698698 −6.97069 + 1.00223i −0.263845 + 0.0379351i
699699 3.50487 11.9365i 0.132566 0.451480i
700700 16.0302 + 11.1084i 0.605885 + 0.419857i
701701 −20.2576 + 31.5215i −0.765120 + 1.19055i 0.211877 + 0.977296i 0.432042π0.432042\pi
−0.976997 + 0.213253i 0.931594π0.931594\pi
702702 0.715845 + 0.460045i 0.0270178 + 0.0173633i
703703 30.8350 + 26.7187i 1.16296 + 1.00771i
704704 7.97826 27.1714i 0.300692 1.02406i
705705 0.172687 + 1.20107i 0.00650379 + 0.0452348i
706706 2.71407 2.35175i 0.102145 0.0885094i
707707 12.9925 + 21.8524i 0.488634 + 0.821844i
708708 −23.5568 + 6.91691i −0.885320 + 0.259953i
709709 −36.7527 16.7844i −1.38027 0.630350i −0.419519 0.907746i 0.637801π-0.637801\pi
−0.960756 + 0.277396i 0.910529π0.910529\pi
710710 0.424774 2.95437i 0.0159415 0.110875i
711711 −4.77162 7.42479i −0.178950 0.278451i
712712 12.3998 0.464701
713713 2.73856 + 32.1603i 0.102560 + 1.20441i
714714 −3.74097 + 0.405640i −0.140002 + 0.0151807i
715715 12.9085 8.29579i 0.482751 0.310245i
716716 −6.20033 + 43.1242i −0.231717 + 1.61163i
717717 −10.3931 4.74637i −0.388138 0.177256i
718718 −1.09710 3.73639i −0.0409435 0.139441i
719719 28.7094 13.1112i 1.07068 0.488964i 0.199486 0.979901i 0.436073π-0.436073\pi
0.871195 + 0.490937i 0.163345π0.163345\pi
720720 −2.53225 2.92237i −0.0943712 0.108910i
721721 25.5465 6.54512i 0.951402 0.243753i
722722 −2.94703 0.865325i −0.109677 0.0322041i
723723 14.3621 + 12.4448i 0.534133 + 0.462829i
724724 −16.3949 10.5364i −0.609312 0.391581i
725725 6.02693 + 3.87327i 0.223834 + 0.143850i
726726 −1.87624 1.62577i −0.0696337 0.0603379i
727727 33.7177 + 9.90040i 1.25052 + 0.367186i 0.838958 0.544196i 0.183165π-0.183165\pi
0.411562 + 0.911382i 0.364984π0.364984\pi
728728 −2.19426 8.56450i −0.0813247 0.317422i
729729 0.654861 + 0.755750i 0.0242541 + 0.0279907i
730730 3.68292 1.68193i 0.136311 0.0622511i
731731 −2.08934 7.11565i −0.0772772 0.263182i
732732 20.4612 + 9.34430i 0.756267 + 0.345375i
733733 −4.24969 + 29.5572i −0.156966 + 1.09172i 0.747218 + 0.664579i 0.231389π0.231389\pi
−0.904184 + 0.427143i 0.859520π0.859520\pi
734734 −1.34202 + 0.862467i −0.0495350 + 0.0318342i
735735 −1.62624 7.41075i −0.0599847 0.273350i
736736 4.98191 13.9306i 0.183636 0.513488i
737737 −46.3888 −1.70875
738738 −1.61502 2.51303i −0.0594498 0.0925058i
739739 3.72120 25.8815i 0.136887 0.952067i −0.799392 0.600809i 0.794845π-0.794845\pi
0.936279 0.351257i 0.114246π-0.114246\pi
740740 14.0658 + 6.42365i 0.517070 + 0.236138i
741741 −16.6595 + 4.89168i −0.612003 + 0.179700i
742742 −0.674009 1.13363i −0.0247436 0.0416168i
743743 −7.25393 + 6.28557i −0.266121 + 0.230595i −0.777691 0.628646i 0.783609π-0.783609\pi
0.511570 + 0.859241i 0.329064π0.329064\pi
744744 1.01590 + 7.06572i 0.0372446 + 0.259042i
745745 −3.54390 + 12.0694i −0.129838 + 0.442189i
746746 1.40843 + 1.22041i 0.0515661 + 0.0446823i
747747 0.610014 + 0.392032i 0.0223192 + 0.0143437i
748748 −24.6522 + 38.3596i −0.901376 + 1.40257i
749749 8.46972 12.2224i 0.309477 0.446598i
750750 −0.727859 + 2.47886i −0.0265777 + 0.0905152i
751751 −23.5208 + 3.38177i −0.858284 + 0.123403i −0.557386 0.830254i 0.688196π-0.688196\pi
−0.300898 + 0.953656i 0.597287π0.597287\pi
752752 3.01850 2.61555i 0.110074 0.0953792i
753753 −9.43432 + 4.30851i −0.343806 + 0.157011i
754754 −0.448994 1.52913i −0.0163514 0.0556877i
755755 −3.91776 + 8.57870i −0.142582 + 0.312211i
756756 0.177341 5.09541i 0.00644984 0.185318i
757757 −5.87141 9.13609i −0.213400 0.332057i 0.718007 0.696036i 0.245054π-0.245054\pi
−0.931407 + 0.363979i 0.881418π0.881418\pi
758758 1.12918i 0.0410138i
759759 15.4434 + 15.0305i 0.560559 + 0.545571i
760760 −6.33559 −0.229816
761761 15.0257 + 23.3805i 0.544682 + 0.847541i 0.999064 0.0432657i 0.0137762π-0.0137762\pi
−0.454382 + 0.890807i 0.650140π0.650140\pi
762762 −2.35980 0.339287i −0.0854864 0.0122911i
763763 2.58345 7.78567i 0.0935273 0.281860i
764764 10.3978 + 35.4117i 0.376180 + 1.28115i
765765 2.37097 + 5.19169i 0.0857225 + 0.187706i
766766 −6.44117 7.43351i −0.232729 0.268584i
767767 5.71237 + 39.7304i 0.206262 + 1.43458i
768768 −2.95200 + 10.0536i −0.106521 + 0.362778i
769769 −12.0360 + 13.8903i −0.434030 + 0.500897i −0.930060 0.367408i 0.880245π-0.880245\pi
0.496030 + 0.868305i 0.334791π0.334791\pi
770770 3.11362 + 1.55503i 0.112207 + 0.0560393i
771771 23.0998 + 14.8454i 0.831921 + 0.534643i
772772 −5.60583 + 6.46947i −0.201758 + 0.232841i
773773 −35.6254 10.4606i −1.28136 0.376241i −0.430955 0.902373i 0.641823π-0.641823\pi
−0.850402 + 0.526133i 0.823641π0.823641\pi
774774 −0.376505 + 0.0541333i −0.0135332 + 0.00194578i
775775 −19.4563 + 16.8590i −0.698891 + 0.605593i
776776 3.53348 + 7.73725i 0.126845 + 0.277751i
777777 7.51227 + 18.0896i 0.269501 + 0.648962i
778778 −0.257640 0.117660i −0.00923685 0.00421833i
779779 60.3331 + 8.67459i 2.16166 + 0.310800i
780780 −5.53581 + 3.55765i −0.198214 + 0.127384i
781781 45.8153i 1.63940i
782782 −4.01322 + 5.51524i −0.143513 + 0.197225i
783783 1.87289i 0.0669315i
784784 −17.6267 + 17.6910i −0.629525 + 0.631821i
785785 2.75449 19.1579i 0.0983120 0.683775i
786786 −2.22068 + 4.86262i −0.0792091 + 0.173444i
787787 −17.9026 + 5.25668i −0.638159 + 0.187380i −0.584777 0.811194i 0.698818π-0.698818\pi
−0.0533816 + 0.998574i 0.517000π0.517000\pi
788788 −1.53060 3.35156i −0.0545255 0.119394i
789789 −4.08631 4.71585i −0.145476 0.167889i
790790 −2.55740 + 0.367698i −0.0909882 + 0.0130821i
791791 −23.0072 4.12934i −0.818041 0.146822i
792792 3.60197 + 3.12112i 0.127990 + 0.110904i
793793 19.8822 30.9373i 0.706038 1.09862i
794794 0.343751 0.534887i 0.0121993 0.0189824i
795795 −1.30999 + 1.51181i −0.0464607 + 0.0536185i
796796 16.7718 + 4.92466i 0.594462 + 0.174550i
797797 4.31039 + 29.9794i 0.152682 + 1.06193i 0.911700 + 0.410856i 0.134770π0.134770\pi
−0.759018 + 0.651069i 0.774321π0.774321\pi
798798 −2.88475 2.68091i −0.102119 0.0949030i
799799 −5.36248 + 2.44896i −0.189711 + 0.0866381i
800800 11.3224 3.32456i 0.400307 0.117541i
801801 4.85648 10.6342i 0.171595 0.375741i
802802 5.99005 + 0.861239i 0.211516 + 0.0304114i
803803 52.2825 33.5999i 1.84501 1.18572i
804804 19.8939 0.701602
805805 −11.9278 6.84589i −0.420399 0.241286i
806806 5.72687 0.201720
807807 −10.8318 + 6.96120i −0.381299 + 0.245046i
808808 10.0881 + 1.45045i 0.354899 + 0.0510268i
809809 −22.6825 + 49.6678i −0.797475 + 1.74623i −0.143582 + 0.989638i 0.545862π0.545862\pi
−0.653892 + 0.756588i 0.726865π0.726865\pi
810810 0.280883 0.0824748i 0.00986924 0.00289787i
811811 −17.4723 + 7.97932i −0.613534 + 0.280192i −0.697846 0.716248i 0.745858π-0.745858\pi
0.0843118 + 0.996439i 0.473131π0.473131\pi
812812 −6.50044 + 6.99472i −0.228121 + 0.245466i
813813 0.183839 + 1.27863i 0.00644753 + 0.0448436i
814814 −8.62118 2.53141i −0.302172 0.0887258i
815815 −16.1416 + 18.6285i −0.565417 + 0.652526i
816816 10.1568 15.8042i 0.355558 0.553259i
817817 4.19616 6.52935i 0.146805 0.228433i
818818 −0.941098 0.815466i −0.0329047 0.0285121i
819819 −8.20443 1.47254i −0.286686 0.0514546i
820820 22.8660 3.28763i 0.798514 0.114809i
821821 1.30591 + 1.50710i 0.0455766 + 0.0525981i 0.778080 0.628165i 0.216194π-0.216194\pi
−0.732504 + 0.680763i 0.761648π0.761648\pi
822822 0.315109 + 0.689992i 0.0109907 + 0.0240662i
823823 −7.99543 + 2.34767i −0.278703 + 0.0818347i −0.418097 0.908402i 0.637303π-0.637303\pi
0.139394 + 0.990237i 0.455485π0.455485\pi
824824 4.39182 9.61674i 0.152996 0.335015i
825825 −2.44622 + 17.0138i −0.0851664 + 0.592345i
826826 −7.08365 + 5.71900i −0.246472 + 0.198990i
827827 47.9455i 1.66723i 0.552347 + 0.833614i 0.313732π0.313732\pi
−0.552347 + 0.833614i 0.686268π0.686268\pi
828828 −6.62289 6.44581i −0.230161 0.224008i
829829 32.2563i 1.12031i −0.828389 0.560153i 0.810742π-0.810742\pi
0.828389 0.560153i 0.189258π-0.189258\pi
830830 0.178576 0.114764i 0.00619848 0.00398352i
831831 12.1903 + 1.75270i 0.422877 + 0.0608006i
832832 18.0606 + 8.24802i 0.626140 + 0.285949i
833833 32.3197 17.7243i 1.11981 0.614112i
834834 1.29255 + 2.83028i 0.0447572 + 0.0980047i
835835 6.96664 6.03663i 0.241091 0.208906i
836836 −47.2361 + 6.79153i −1.63370 + 0.234890i
837837 6.45754 + 1.89610i 0.223205 + 0.0655390i
838838 −4.18269 + 4.82708i −0.144489 + 0.166749i
839839 −16.0212 10.2962i −0.553115 0.355465i 0.234034 0.972228i 0.424807π-0.424807\pi
−0.787149 + 0.616763i 0.788444π0.788444\pi
840840 −2.72110 1.35899i −0.0938869 0.0468896i
841841 16.6939 19.2658i 0.575652 0.664338i
842842 0.0469957 0.160053i 0.00161958 0.00551577i
843843 −3.37993 23.5079i −0.116411 0.809656i
844844 −23.9036 27.5862i −0.822795 0.949556i
845845 −1.38414 3.03085i −0.0476160 0.104264i
846846 0.0851880 + 0.290124i 0.00292882 + 0.00997466i
847847 23.0818 + 7.65903i 0.793099 + 0.263167i
848848 6.51749 + 0.937074i 0.223812 + 0.0321792i
849849 5.20433 + 8.09810i 0.178612 + 0.277926i
850850 −5.44041 −0.186604
851851 33.4318 + 11.9560i 1.14603 + 0.409846i
852852 19.6479i 0.673126i
853853 24.3308 + 37.8595i 0.833071 + 1.29628i 0.952837 + 0.303481i 0.0981489π0.0981489\pi
−0.119767 + 0.992802i 0.538215π0.538215\pi
854854 8.33614 + 0.290132i 0.285257 + 0.00992811i
855855 −2.48139 + 5.43349i −0.0848618 + 0.185821i
856856 −1.67950 5.71985i −0.0574042 0.195501i
857857 0.391463 0.178775i 0.0133721 0.00610685i −0.408718 0.912661i 0.634024π-0.634024\pi
0.422090 + 0.906554i 0.361297π0.361297\pi
858858 2.88973 2.50397i 0.0986538 0.0854840i
859859 44.1198 6.34347i 1.50535 0.216436i 0.660249 0.751046i 0.270451π-0.270451\pi
0.845099 + 0.534610i 0.179542π0.179542\pi
860860 0.828731 2.82240i 0.0282595 0.0962430i
861861 24.0520 + 16.6672i 0.819690 + 0.568016i
862862 1.55242 2.41562i 0.0528757 0.0822762i
863863 −34.6908 22.2944i −1.18089 0.758912i −0.205340 0.978691i 0.565830π-0.565830\pi
−0.975550 + 0.219779i 0.929466π0.929466\pi
864864 −2.33140 2.02017i −0.0793160 0.0687277i
865865 2.97015 10.1154i 0.100988 0.343934i
866866 −0.666783 4.63758i −0.0226582 0.157591i
867867 −8.10838 + 7.02595i −0.275375 + 0.238614i
868868 −17.5361 29.4943i −0.595214 1.00110i
869869 −38.0528 + 11.1733i −1.29085 + 0.379029i
870870 −0.498726 0.227760i −0.0169084 0.00772180i
871871 4.62871 32.1934i 0.156838 1.09083i
872872 −1.77792 2.76650i −0.0602079 0.0936854i
873873 8.01949 0.271418
874874 −7.11277 + 0.605676i −0.240593 + 0.0204873i
875875 −2.72816 25.1602i −0.0922286 0.850569i
876876 −22.4214 + 14.4093i −0.757548 + 0.486846i
877877 5.48040 38.1171i 0.185060 1.28712i −0.659518 0.751689i 0.729240π-0.729240\pi
0.844578 0.535433i 0.179851π-0.179851\pi
878878 3.30902 + 1.51118i 0.111674 + 0.0509998i
879879 −0.609636 2.07623i −0.0205625 0.0700295i
880880 −15.8056 + 7.21817i −0.532806 + 0.243324i
881881 −23.7570 27.4171i −0.800395 0.923705i 0.198008 0.980200i 0.436553π-0.436553\pi
−0.998403 + 0.0564951i 0.982007π0.982007\pi
882882 −0.663928 1.77022i −0.0223556 0.0596063i
883883 −27.5009 8.07500i −0.925480 0.271745i −0.215937 0.976407i 0.569280π-0.569280\pi
−0.709543 + 0.704662i 0.751099π0.751099\pi
884884 −24.1614 20.9360i −0.812636 0.704153i
885885 11.6168 + 7.46565i 0.390494 + 0.250955i
886886 −1.34187 0.862371i −0.0450812 0.0289719i
887887 7.78761 + 6.74800i 0.261482 + 0.226576i 0.775728 0.631067i 0.217383π-0.217383\pi
−0.514246 + 0.857643i 0.671928π0.671928\pi
888888 7.53434 + 2.21228i 0.252836 + 0.0742394i
889889 22.6232 5.79615i 0.758757 0.194397i
890890 −2.24116 2.58643i −0.0751238 0.0866975i
891891 4.08746 1.86668i 0.136935 0.0625362i
892892 −12.1785 41.4762i −0.407767 1.38873i
893893 −5.61223 2.56302i −0.187806 0.0857683i
894894 −0.446093 + 3.10264i −0.0149196 + 0.103768i
895895 20.6146 13.2482i 0.689070 0.442839i
896896 2.24515 + 20.7057i 0.0750053 + 0.691730i
897897 −11.9719 + 9.21779i −0.399731 + 0.307773i
898898 2.86913 0.0957442
899899 −6.81468 10.6039i −0.227282 0.353658i
900900 1.04906 7.29638i 0.0349687 0.243213i
901901 −8.84048 4.03731i −0.294519 0.134502i
902902 −12.8795 + 3.78177i −0.428841 + 0.125919i
903903 3.20277 1.90424i 0.106582 0.0633690i
904904 −7.08192 + 6.13652i −0.235541 + 0.204097i
905905 1.55997 + 10.8498i 0.0518551 + 0.360660i
906906 −0.662100 + 2.25491i −0.0219968 + 0.0749142i
907907 −2.07024 1.79388i −0.0687413 0.0595647i 0.619812 0.784750i 0.287209π-0.287209\pi
−0.688554 + 0.725185i 0.741754π0.741754\pi
908908 −17.2952 11.1149i −0.573960 0.368862i
909909 5.19503 8.08363i 0.172308 0.268117i
910910 −1.38985 + 2.00566i −0.0460732 + 0.0664870i
911911 14.4023 49.0498i 0.477170 1.62509i −0.271704 0.962381i 0.587587π-0.587587\pi
0.748874 0.662712i 0.230595π-0.230595\pi
912912 19.4614 2.79812i 0.644430 0.0926551i
913913 2.46251 2.13378i 0.0814973 0.0706178i
914914 −7.99772 + 3.65244i −0.264541 + 0.120812i
915915 −3.56439 12.1392i −0.117835 0.401310i
916916 2.80130 6.13400i 0.0925576 0.202673i
917917 1.82143 52.3339i 0.0601491 1.72822i
918918 0.768923 + 1.19647i 0.0253782 + 0.0394893i
919919 15.7075i 0.518142i 0.965858 + 0.259071i 0.0834163π0.0834163\pi
−0.965858 + 0.259071i 0.916584π0.916584\pi
920920 −5.13915 + 1.99653i −0.169433 + 0.0658235i
921921 16.6782 0.549566
922922 0.589131 + 0.916706i 0.0194020 + 0.0301901i
923923 31.7954 + 4.57149i 1.04656 + 0.150472i
924924 −21.7444 7.21527i −0.715339 0.237365i
925925 7.97855 + 27.1724i 0.262333 + 0.893424i
926926 3.17692 + 6.95649i 0.104400 + 0.228605i
927927 −6.52735 7.53297i −0.214386 0.247415i
928928 0.822245 + 5.71884i 0.0269915 + 0.187730i
929929 −11.2088 + 38.1736i −0.367748 + 1.25244i 0.543091 + 0.839674i 0.317254π0.317254\pi
−0.910839 + 0.412762i 0.864564π0.864564\pi
930930 1.29020 1.48898i 0.0423075 0.0488254i
931931 36.1697 + 13.4157i 1.18541 + 0.439681i
932932 20.1677 + 12.9610i 0.660613 + 0.424551i
933933 −10.7822 + 12.4433i −0.352994 + 0.407376i
934934 0.985137 + 0.289262i 0.0322347 + 0.00946496i
935935 25.3856 3.64990i 0.830199 0.119365i
936936 −2.52544 + 2.18830i −0.0825465 + 0.0715269i
937937 6.51140 + 14.2580i 0.212718 + 0.465788i 0.985672 0.168675i 0.0539487π-0.0539487\pi
−0.772954 + 0.634463i 0.781221π0.781221\pi
938938 6.81292 2.82927i 0.222450 0.0923789i
939939 −30.8650 14.0956i −1.00724 0.459992i
940940 −2.31452 0.332778i −0.0754913 0.0108540i
941941 −5.11296 + 3.28590i −0.166678 + 0.107117i −0.621320 0.783557i 0.713403π-0.713403\pi
0.454643 + 0.890674i 0.349767π0.349767\pi
942942 4.82305i 0.157144i
943943 51.6731 11.9762i 1.68271 0.390000i
944944 45.4529i 1.47937i
945945 −2.23123 + 1.80139i −0.0725820 + 0.0585993i
946946 −0.243250 + 1.69184i −0.00790872 + 0.0550064i
947947 20.4952 44.8782i 0.666004 1.45835i −0.210815 0.977526i 0.567612π-0.567612\pi
0.876819 0.480820i 0.159661π-0.159661\pi
948948 16.3190 4.79168i 0.530015 0.155626i
949949 18.1012 + 39.6362i 0.587591 + 1.28664i
950950 −3.72864 4.30308i −0.120973 0.139610i
951951 3.67424 0.528276i 0.119145 0.0171305i
952952 2.61049 14.5447i 0.0846065 0.471397i
953953 −22.2093 19.2445i −0.719431 0.623391i 0.216208 0.976347i 0.430631π-0.430631\pi
−0.935640 + 0.352956i 0.885176π0.885176\pi
954954 −0.269501 + 0.419351i −0.00872541 + 0.0135770i
955955 11.2227 17.4629i 0.363158 0.565085i
956956 14.4186 16.6399i 0.466330 0.538173i
957957 −8.07498 2.37103i −0.261027 0.0766444i
958958 0.384108 + 2.67153i 0.0124100 + 0.0863132i
959959 −5.44297 5.05834i −0.175763 0.163342i
960960 6.21335 2.83754i 0.200535 0.0915812i
961961 13.7160 4.02737i 0.442451 0.129915i
962962 2.61700 5.73043i 0.0843754 0.184756i
963963 −5.56322 0.799870i −0.179272 0.0257754i
964964 −30.8078 + 19.7990i −0.992252 + 0.637682i
965965 4.81476 0.154993
966966 −3.18481 1.26556i −0.102470 0.0407188i
967967 4.46220 0.143495 0.0717473 0.997423i 0.477142π-0.477142\pi
0.0717473 + 0.997423i 0.477142π0.477142\pi
968968 8.20169 5.27090i 0.263612 0.169413i
969969 −28.7250 4.13003i −0.922779 0.132676i
970970 0.975244 2.13549i 0.0313132 0.0685663i
971971 10.0015 2.93670i 0.320963 0.0942431i −0.117283 0.993099i 0.537418π-0.537418\pi
0.438245 + 0.898855i 0.355600π0.355600\pi
972972 −1.75291 + 0.800526i −0.0562245 + 0.0256769i
973973 −22.3266 20.7489i −0.715757 0.665178i
974974 −0.755384 5.25381i −0.0242041 0.168343i
975975 −11.5633 3.39530i −0.370323 0.108737i
976976 −27.2710 + 31.4724i −0.872922 + 1.00741i
977977 −5.06030 + 7.87398i −0.161893 + 0.251911i −0.912718 0.408591i 0.866020π-0.866020\pi
0.750824 + 0.660502i 0.229657π0.229657\pi
978978 −3.32077 + 5.16721i −0.106186 + 0.165229i
979979 −39.7013 34.4014i −1.26886 1.09947i
980980 14.5853 + 1.01649i 0.465911 + 0.0324706i
981981 −3.06892 + 0.441244i −0.0979831 + 0.0140878i
982982 6.08563 + 7.02319i 0.194200 + 0.224119i
983983 −8.62034 18.8759i −0.274946 0.602048i 0.720906 0.693033i 0.243726π-0.243726\pi
−0.995852 + 0.0909847i 0.970999π0.970999\pi
984984 11.2559 3.30502i 0.358824 0.105360i
985985 −0.860887 + 1.88508i −0.0274302 + 0.0600637i
986986 0.379084 2.63659i 0.0120725 0.0839661i
987987 −1.86065 2.30463i −0.0592252 0.0733573i
988988 33.4591i 1.06448i
989989 1.34615 6.61864i 0.0428051 0.210460i
990990 1.31544i 0.0418075i
991991 −35.0553 + 22.5286i −1.11357 + 0.715646i −0.962068 0.272811i 0.912046π-0.912046\pi
−0.151499 + 0.988457i 0.548410π0.548410\pi
992992 −20.5505 2.95471i −0.652478 0.0938122i
993993 −4.42465 2.02067i −0.140412 0.0641241i
994994 2.79429 + 6.72870i 0.0886296 + 0.213421i
995995 −4.08418 8.94310i −0.129477 0.283515i
996996 −1.05605 + 0.915072i −0.0334622 + 0.0289952i
997997 −59.5532 + 8.56246i −1.88607 + 0.271176i −0.986272 0.165131i 0.947195π-0.947195\pi
−0.899798 + 0.436307i 0.856286π0.856286\pi
998998 3.55129 + 1.04275i 0.112414 + 0.0330077i
999999 4.84818 5.59509i 0.153390 0.177021i
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 483.2.r.a.34.20 yes 320
7.6 odd 2 inner 483.2.r.a.34.19 320
23.21 odd 22 inner 483.2.r.a.412.19 yes 320
161.90 even 22 inner 483.2.r.a.412.20 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.r.a.34.19 320 7.6 odd 2 inner
483.2.r.a.34.20 yes 320 1.1 even 1 trivial
483.2.r.a.412.19 yes 320 23.21 odd 22 inner
483.2.r.a.412.20 yes 320 161.90 even 22 inner