Properties

Label 684.2.o.a.11.59
Level 684684
Weight 22
Character 684.11
Analytic conductor 5.4625.462
Analytic rank 00
Dimension 232232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(11,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 684=223219 684 = 2^{2} \cdot 3^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 684.o (of order 66, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.461767498265.46176749826
Analytic rank: 00
Dimension: 232232
Relative dimension: 116116 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 11.59
Character χ\chi == 684.11
Dual form 684.2.o.a.311.59

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+(0.0259174+1.41398i)q2+(0.706340+1.58148i)q3+(1.998660.0732931i)q43.02562iq5+(2.25448+0.957760i)q6+(3.37115+1.94633i)q7+(0.1554352.82415i)q8+(2.00217+2.23413i)q9+(4.27815+0.0784162i)q10+(1.505662.60787i)q11+(1.295823.21261i)q12+(2.00787+3.47774i)q13+(2.83944+4.71628i)q14+(4.784962.13712i)q15+(3.98926+0.292976i)q16+(4.32629+2.49779i)q17+(3.107112.88892i)q18+(2.72273+3.40393i)q19+(0.221757+6.04718i)q20+(0.696914+6.70618i)q21+(3.64845+2.19655i)q22+(2.39004+4.13967i)q23+(4.576141.74899i)q244.15438q25+(4.865402.92922i)q26+(4.947441.58834i)q27+(6.595114.13713i)q28+0.434362iq29+(2.89782+6.82121i)q30+(2.216901.27993i)q31+(0.517652+5.63312i)q32+(5.18781+0.539123i)q33+(3.64394+6.05254i)q34+(5.8888610.1998i)q35+(4.165394.31851i)q363.09614q37+(4.88364+3.76166i)q38+(6.918220.718950i)q39+(8.544810.470286i)q400.413929iq41+(9.464311.15923i)q42+(1.63331+0.942994i)q43+(3.20043+5.10189i)q44+(6.75962+6.05780i)q45+(5.791463.48675i)q46+12.3628q47+(2.35443+6.51588i)q48+(4.07641+7.06056i)q49+(0.1076715.87419i)q50+(0.894370+8.60624i)q51+(4.267946.80364i)q52+(9.321445.38174i)q53+(2.374106.95440i)q54+(7.890434.55554i)q55+(6.020739.21810i)q56+(3.46008+6.71028i)q57+(0.6141770.0112575i)q5810.5919q59+(9.72013+3.92066i)q606.42411q61+(1.75233+3.16782i)q62+(11.0980+3.63468i)q63+(7.951680.877943i)q64+(10.5223+6.07506i)q65+(0.896762+7.32146i)q66+(11.16986.44889i)q67+(8.463705.30930i)q68+(8.235000.855791i)q69+(14.2697+8.59106i)q70+(4.869188.43367i)q71+(5.99831+6.00169i)q72+(0.2980780.516286i)q73+(0.08024384.37786i)q74+(2.934406.57007i)q75+(5.192327.00284i)q76+(10.15165.86101i)q77+(1.195889.76356i)q78+(11.66796.73648i)q79+(0.88643312.0700i)q80+(0.9826448.94620i)q81+(0.585286+0.0107280i)q82+(1.873993.24584i)q83+(1.8844113.3523i)q84+(7.5573513.0897i)q85+(1.291042.33391i)q86+(0.686935+0.306807i)q87+(7.131004.65756i)q88+(12.3615+7.13690i)q89+(8.74078+9.40094i)q90+(13.5377+7.81597i)q91+(5.080288.09861i)q92+(3.59007+2.60193i)q93+(0.320410+17.4806i)q94+(10.29908.23795i)q95+(9.27431+3.16024i)q96+(1.434962.48542i)q97+(10.0891+5.58096i)q98+(2.81174+8.58523i)q99+O(q100)q+(-0.0259174 + 1.41398i) q^{2} +(0.706340 + 1.58148i) q^{3} +(-1.99866 - 0.0732931i) q^{4} -3.02562i q^{5} +(-2.25448 + 0.957760i) q^{6} +(3.37115 + 1.94633i) q^{7} +(0.155435 - 2.82415i) q^{8} +(-2.00217 + 2.23413i) q^{9} +(4.27815 + 0.0784162i) q^{10} +(1.50566 - 2.60787i) q^{11} +(-1.29582 - 3.21261i) q^{12} +(-2.00787 + 3.47774i) q^{13} +(-2.83944 + 4.71628i) q^{14} +(4.78496 - 2.13712i) q^{15} +(3.98926 + 0.292976i) q^{16} +(4.32629 + 2.49779i) q^{17} +(-3.10711 - 2.88892i) q^{18} +(2.72273 + 3.40393i) q^{19} +(-0.221757 + 6.04718i) q^{20} +(-0.696914 + 6.70618i) q^{21} +(3.64845 + 2.19655i) q^{22} +(-2.39004 + 4.13967i) q^{23} +(4.57614 - 1.74899i) q^{24} -4.15438 q^{25} +(-4.86540 - 2.92922i) q^{26} +(-4.94744 - 1.58834i) q^{27} +(-6.59511 - 4.13713i) q^{28} +0.434362i q^{29} +(2.89782 + 6.82121i) q^{30} +(2.21690 - 1.27993i) q^{31} +(-0.517652 + 5.63312i) q^{32} +(5.18781 + 0.539123i) q^{33} +(-3.64394 + 6.05254i) q^{34} +(5.88886 - 10.1998i) q^{35} +(4.16539 - 4.31851i) q^{36} -3.09614 q^{37} +(-4.88364 + 3.76166i) q^{38} +(-6.91822 - 0.718950i) q^{39} +(-8.54481 - 0.470286i) q^{40} -0.413929i q^{41} +(-9.46431 - 1.15923i) q^{42} +(-1.63331 + 0.942994i) q^{43} +(-3.20043 + 5.10189i) q^{44} +(6.75962 + 6.05780i) q^{45} +(-5.79146 - 3.48675i) q^{46} +12.3628 q^{47} +(2.35443 + 6.51588i) q^{48} +(4.07641 + 7.06056i) q^{49} +(0.107671 - 5.87419i) q^{50} +(-0.894370 + 8.60624i) q^{51} +(4.26794 - 6.80364i) q^{52} +(9.32144 - 5.38174i) q^{53} +(2.37410 - 6.95440i) q^{54} +(-7.89043 - 4.55554i) q^{55} +(6.02073 - 9.21810i) q^{56} +(-3.46008 + 6.71028i) q^{57} +(-0.614177 - 0.0112575i) q^{58} -10.5919 q^{59} +(-9.72013 + 3.92066i) q^{60} -6.42411 q^{61} +(1.75233 + 3.16782i) q^{62} +(-11.0980 + 3.63468i) q^{63} +(-7.95168 - 0.877943i) q^{64} +(10.5223 + 6.07506i) q^{65} +(-0.896762 + 7.32146i) q^{66} +(-11.1698 - 6.44889i) q^{67} +(-8.46370 - 5.30930i) q^{68} +(-8.23500 - 0.855791i) q^{69} +(14.2697 + 8.59106i) q^{70} +(4.86918 - 8.43367i) q^{71} +(5.99831 + 6.00169i) q^{72} +(0.298078 - 0.516286i) q^{73} +(0.0802438 - 4.37786i) q^{74} +(-2.93440 - 6.57007i) q^{75} +(-5.19232 - 7.00284i) q^{76} +(10.1516 - 5.86101i) q^{77} +(1.19588 - 9.76356i) q^{78} +(11.6679 - 6.73648i) q^{79} +(0.886433 - 12.0700i) q^{80} +(-0.982644 - 8.94620i) q^{81} +(0.585286 + 0.0107280i) q^{82} +(1.87399 - 3.24584i) q^{83} +(1.88441 - 13.3523i) q^{84} +(7.55735 - 13.0897i) q^{85} +(-1.29104 - 2.33391i) q^{86} +(-0.686935 + 0.306807i) q^{87} +(-7.13100 - 4.65756i) q^{88} +(-12.3615 + 7.13690i) q^{89} +(-8.74078 + 9.40094i) q^{90} +(-13.5377 + 7.81597i) q^{91} +(5.08028 - 8.09861i) q^{92} +(3.59007 + 2.60193i) q^{93} +(-0.320410 + 17.4806i) q^{94} +(10.2990 - 8.23795i) q^{95} +(-9.27431 + 3.16024i) q^{96} +(-1.43496 - 2.48542i) q^{97} +(-10.0891 + 5.58096i) q^{98} +(2.81174 + 8.58523i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 232q3q2+q4+3q6+2q10q12+2q13+q1612q1716q1827q2014q21+6q2210q24204q256q289q303q3212q33+162q98+O(q100) 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 325325 343343 533533
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 1-1 e(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.0259174 + 1.41398i −0.0183264 + 0.999832i
33 0.706340 + 1.58148i 0.407805 + 0.913069i
44 −1.99866 0.0732931i −0.999328 0.0366466i
55 3.02562i 1.35310i −0.736397 0.676549i 0.763475π-0.763475\pi
0.736397 0.676549i 0.236525π-0.236525\pi
66 −2.25448 + 0.957760i −0.920389 + 0.391004i
77 3.37115 + 1.94633i 1.27417 + 0.735644i 0.975771 0.218796i 0.0702129π-0.0702129\pi
0.298403 + 0.954440i 0.403546π0.403546\pi
88 0.155435 2.82415i 0.0549545 0.998489i
99 −2.00217 + 2.23413i −0.667389 + 0.744709i
1010 4.27815 + 0.0784162i 1.35287 + 0.0247974i
1111 1.50566 2.60787i 0.453972 0.786303i −0.544656 0.838660i 0.683340π-0.683340\pi
0.998628 + 0.0523562i 0.0166731π0.0166731\pi
1212 −1.29582 3.21261i −0.374071 0.927400i
1313 −2.00787 + 3.47774i −0.556884 + 0.964551i 0.440870 + 0.897571i 0.354670π0.354670\pi
−0.997754 + 0.0669803i 0.978664π0.978664\pi
1414 −2.83944 + 4.71628i −0.758872 + 1.26048i
1515 4.78496 2.13712i 1.23547 0.551801i
1616 3.98926 + 0.292976i 0.997314 + 0.0732439i
1717 4.32629 + 2.49779i 1.04928 + 0.605802i 0.922448 0.386122i 0.126186π-0.126186\pi
0.126832 + 0.991924i 0.459519π0.459519\pi
1818 −3.10711 2.88892i −0.732353 0.680925i
1919 2.72273 + 3.40393i 0.624637 + 0.780915i
2020 −0.221757 + 6.04718i −0.0495864 + 1.35219i
2121 −0.696914 + 6.70618i −0.152079 + 1.46341i
2222 3.64845 + 2.19655i 0.777852 + 0.468306i
2323 −2.39004 + 4.13967i −0.498358 + 0.863182i −0.999998 0.00189485i 0.999397π-0.999397\pi
0.501640 + 0.865076i 0.332730π0.332730\pi
2424 4.57614 1.74899i 0.934100 0.357012i
2525 −4.15438 −0.830875
2626 −4.86540 2.92922i −0.954183 0.574467i
2727 −4.94744 1.58834i −0.952136 0.305676i
2828 −6.59511 4.13713i −1.24636 0.781844i
2929 0.434362i 0.0806590i 0.999186 + 0.0403295i 0.0128408π0.0128408\pi
−0.999186 + 0.0403295i 0.987159π0.987159\pi
3030 2.89782 + 6.82121i 0.529067 + 1.24538i
3131 2.21690 1.27993i 0.398167 0.229882i −0.287525 0.957773i 0.592833π-0.592833\pi
0.685693 + 0.727891i 0.259499π0.259499\pi
3232 −0.517652 + 5.63312i −0.0915087 + 0.995804i
3333 5.18781 + 0.539123i 0.903081 + 0.0938493i
3434 −3.64394 + 6.05254i −0.624930 + 1.03800i
3535 5.88886 10.1998i 0.995399 1.72408i
3636 4.16539 4.31851i 0.694232 0.719751i
3737 −3.09614 −0.509002 −0.254501 0.967073i 0.581911π-0.581911\pi
−0.254501 + 0.967073i 0.581911π0.581911\pi
3838 −4.88364 + 3.76166i −0.792231 + 0.610221i
3939 −6.91822 0.718950i −1.10780 0.115124i
4040 −8.54481 0.470286i −1.35105 0.0743588i
4141 0.413929i 0.0646449i −0.999477 0.0323224i 0.989710π-0.989710\pi
0.999477 0.0323224i 0.0102903π-0.0102903\pi
4242 −9.46431 1.15923i −1.46037 0.178872i
4343 −1.63331 + 0.942994i −0.249078 + 0.143805i −0.619342 0.785121i 0.712601π-0.712601\pi
0.370264 + 0.928927i 0.379267π0.379267\pi
4444 −3.20043 + 5.10189i −0.482483 + 0.769139i
4545 6.75962 + 6.05780i 1.00766 + 0.903044i
4646 −5.79146 3.48675i −0.853904 0.514093i
4747 12.3628 1.80329 0.901647 0.432474i 0.142359π-0.142359\pi
0.901647 + 0.432474i 0.142359π0.142359\pi
4848 2.35443 + 6.51588i 0.339833 + 0.940486i
4949 4.07641 + 7.06056i 0.582345 + 1.00865i
5050 0.107671 5.87419i 0.0152269 0.830736i
5151 −0.894370 + 8.60624i −0.125237 + 1.20511i
5252 4.26794 6.80364i 0.591857 0.943495i
5353 9.32144 5.38174i 1.28040 0.739238i 0.303477 0.952839i 0.401852π-0.401852\pi
0.976921 + 0.213600i 0.0685190π0.0685190\pi
5454 2.37410 6.95440i 0.323074 0.946374i
5555 −7.89043 4.55554i −1.06395 0.614269i
5656 6.02073 9.21810i 0.804554 1.23182i
5757 −3.46008 + 6.71028i −0.458299 + 0.888798i
5858 −0.614177 0.0112575i −0.0806454 0.00147819i
5959 −10.5919 −1.37895 −0.689477 0.724308i 0.742160π-0.742160\pi
−0.689477 + 0.724308i 0.742160π0.742160\pi
6060 −9.72013 + 3.92066i −1.25486 + 0.506154i
6161 −6.42411 −0.822524 −0.411262 0.911517i 0.634912π-0.634912\pi
−0.411262 + 0.911517i 0.634912π0.634912\pi
6262 1.75233 + 3.16782i 0.222547 + 0.402314i
6363 −11.0980 + 3.63468i −1.39821 + 0.457927i
6464 −7.95168 0.877943i −0.993960 0.109743i
6565 10.5223 + 6.07506i 1.30513 + 0.753519i
6666 −0.896762 + 7.32146i −0.110384 + 0.901210i
6767 −11.1698 6.44889i −1.36461 0.787858i −0.374376 0.927277i 0.622143π-0.622143\pi
−0.990233 + 0.139420i 0.955476π0.955476\pi
6868 −8.46370 5.30930i −1.02637 0.643848i
6969 −8.23500 0.855791i −0.991377 0.103025i
7070 14.2697 + 8.59106i 1.70555 + 1.02683i
7171 4.86918 8.43367i 0.577866 1.00089i −0.417858 0.908512i 0.637219π-0.637219\pi
0.995724 0.0923804i 0.0294476π-0.0294476\pi
7272 5.99831 + 6.00169i 0.706908 + 0.707306i
7373 0.298078 0.516286i 0.0348874 0.0604267i −0.848055 0.529909i 0.822226π-0.822226\pi
0.882942 + 0.469482i 0.155559π0.155559\pi
7474 0.0802438 4.37786i 0.00932815 0.508916i
7575 −2.93440 6.57007i −0.338835 0.758646i
7676 −5.19232 7.00284i −0.595600 0.803281i
7777 10.1516 5.86101i 1.15688 0.667924i
7878 1.19588 9.76356i 0.135407 1.10551i
7979 11.6679 6.73648i 1.31274 0.757913i 0.330195 0.943913i 0.392886π-0.392886\pi
0.982550 + 0.185999i 0.0595522π0.0595522\pi
8080 0.886433 12.0700i 0.0991062 1.34946i
8181 −0.982644 8.94620i −0.109183 0.994022i
8282 0.585286 + 0.0107280i 0.0646340 + 0.00118471i
8383 1.87399 3.24584i 0.205697 0.356277i −0.744658 0.667446i 0.767387π-0.767387\pi
0.950354 + 0.311169i 0.100721π0.100721\pi
8484 1.88441 13.3523i 0.205606 1.45685i
8585 7.55735 13.0897i 0.819710 1.41978i
8686 −1.29104 2.33391i −0.139216 0.251672i
8787 −0.686935 + 0.306807i −0.0736472 + 0.0328932i
8888 −7.13100 4.65756i −0.760167 0.496497i
8989 −12.3615 + 7.13690i −1.31031 + 0.756510i −0.982148 0.188111i 0.939764π-0.939764\pi
−0.328165 + 0.944620i 0.606430π0.606430\pi
9090 −8.74078 + 9.40094i −0.921359 + 0.990946i
9191 −13.5377 + 7.81597i −1.41913 + 0.819337i
9292 5.08028 8.09861i 0.529656 0.844339i
9393 3.59007 + 2.60193i 0.372273 + 0.269807i
9494 −0.320410 + 17.4806i −0.0330478 + 1.80299i
9595 10.2990 8.23795i 1.05665 0.845196i
9696 −9.27431 + 3.16024i −0.946556 + 0.322541i
9797 −1.43496 2.48542i −0.145698 0.252357i 0.783935 0.620843i 0.213210π-0.213210\pi
−0.929633 + 0.368486i 0.879876π0.879876\pi
9898 −10.0891 + 5.58096i −1.01915 + 0.563762i
9999 2.81174 + 8.58523i 0.282591 + 0.862848i
100100 8.30317 + 0.304487i 0.830317 + 0.0304487i
101101 5.37149i 0.534483i 0.963630 + 0.267241i 0.0861121π0.0861121\pi
−0.963630 + 0.267241i 0.913888π0.913888\pi
102102 −12.1458 1.48767i −1.20262 0.147301i
103103 7.02928 4.05836i 0.692615 0.399882i −0.111976 0.993711i 0.535718π-0.535718\pi
0.804591 + 0.593829i 0.202385π0.202385\pi
104104 9.50957 + 6.21110i 0.932490 + 0.609049i
105105 20.2903 + 2.10860i 1.98013 + 0.205778i
106106 7.36806 + 13.3198i 0.715649 + 1.29373i
107107 −6.23445 −0.602707 −0.301354 0.953512i 0.597438π-0.597438\pi
−0.301354 + 0.953512i 0.597438π0.597438\pi
108108 9.77182 + 3.53716i 0.940294 + 0.340363i
109109 −8.83890 + 15.3094i −0.846613 + 1.46638i 0.0376005 + 0.999293i 0.488029π0.488029\pi
−0.884213 + 0.467083i 0.845305π0.845305\pi
110110 6.64593 11.0388i 0.633664 1.05251i
111111 −2.18692 4.89648i −0.207574 0.464754i
112112 12.8781 + 8.75208i 1.21687 + 0.826994i
113113 −10.0674 + 5.81240i −0.947058 + 0.546784i −0.892166 0.451708i 0.850815π-0.850815\pi
−0.0548923 + 0.998492i 0.517482π0.517482\pi
114114 −9.39850 5.06638i −0.880250 0.474510i
115115 12.5251 + 7.23136i 1.16797 + 0.674328i
116116 0.0318357 0.868140i 0.00295587 0.0806048i
117117 −3.74961 11.4489i −0.346651 1.05845i
118118 0.274516 14.9768i 0.0252712 1.37872i
119119 9.72304 + 16.8408i 0.891310 + 1.54379i
120120 −5.29179 13.8456i −0.483072 1.26393i
121121 0.965999 + 1.67316i 0.0878181 + 0.152105i
122122 0.166496 9.08354i 0.0150739 0.822385i
123123 0.654621 0.292375i 0.0590252 0.0263625i
124124 −4.52464 + 2.39566i −0.406324 + 0.215136i
125125 2.55854i 0.228843i
126126 −4.85172 15.7864i −0.432226 1.40637i
127127 5.52271 3.18854i 0.490062 0.282937i −0.234538 0.972107i 0.575358π-0.575358\pi
0.724600 + 0.689170i 0.242025π0.242025\pi
128128 1.44748 11.2207i 0.127940 0.991782i
129129 −2.64500 1.91698i −0.232880 0.168781i
130130 −8.86270 + 14.7209i −0.777310 + 1.29110i
131131 9.96122 0.870316 0.435158 0.900354i 0.356693π-0.356693\pi
0.435158 + 0.900354i 0.356693π0.356693\pi
132132 −10.3291 1.45775i −0.899036 0.126881i
133133 2.55355 + 16.7745i 0.221421 + 1.45453i
134134 9.40807 15.6267i 0.812734 1.34994i
135135 −4.80571 + 14.9691i −0.413610 + 1.28833i
136136 7.72659 11.8299i 0.662549 1.01440i
137137 17.9170i 1.53075i −0.643585 0.765375i 0.722554π-0.722554\pi
0.643585 0.765375i 0.277446π-0.277446\pi
138138 1.42350 11.6219i 0.121176 0.989323i
139139 12.9933 + 7.50170i 1.10208 + 0.636286i 0.936766 0.349955i 0.113803π-0.113803\pi
0.165313 + 0.986241i 0.447137π0.447137\pi
140140 −12.5174 + 19.9543i −1.05791 + 1.68645i
141141 8.73231 + 19.5515i 0.735393 + 1.64653i
142142 11.7988 + 7.10349i 0.990134 + 0.596111i
143143 6.04633 + 10.4726i 0.505620 + 0.875759i
144144 −8.64171 + 8.32592i −0.720142 + 0.693826i
145145 1.31421 0.109140
146146 0.722290 + 0.434856i 0.0597772 + 0.0359889i
147147 −8.28681 + 11.4339i −0.683484 + 0.943054i
148148 6.18811 + 0.226926i 0.508660 + 0.0186532i
149149 17.7470i 1.45389i −0.686695 0.726946i 0.740939π-0.740939\pi
0.686695 0.726946i 0.259061π-0.259061\pi
150150 9.36597 3.97889i 0.764728 0.324875i
151151 2.78743 + 1.60932i 0.226838 + 0.130965i 0.609112 0.793084i 0.291526π-0.291526\pi
−0.382275 + 0.924049i 0.624859π0.624859\pi
152152 10.0364 7.16032i 0.814061 0.580779i
153153 −14.2423 + 4.66450i −1.15142 + 0.377102i
154154 8.02423 + 14.5060i 0.646611 + 1.16893i
155155 −3.87258 6.70751i −0.311053 0.538760i
156156 13.7745 + 1.94399i 1.10284 + 0.155644i
157157 −2.50724 −0.200100 −0.100050 0.994982i 0.531900π-0.531900\pi
−0.100050 + 0.994982i 0.531900π0.531900\pi
158158 9.22282 + 16.6728i 0.733728 + 1.32641i
159159 15.0952 + 10.9404i 1.19713 + 0.867626i
160160 17.0437 + 1.56622i 1.34742 + 0.123820i
161161 −16.1144 + 9.30363i −1.26999 + 0.733229i
162162 12.6752 1.15757i 0.995856 0.0909476i
163163 18.7315i 1.46717i −0.679600 0.733583i 0.737847π-0.737847\pi
0.679600 0.733583i 0.262153π-0.262153\pi
164164 −0.0303382 + 0.827302i −0.00236901 + 0.0646014i
165165 1.63118 15.6963i 0.126987 1.22196i
166166 4.54097 + 2.73389i 0.352448 + 0.212191i
167167 8.16353 14.1397i 0.631713 1.09416i −0.355488 0.934681i 0.615685π-0.615685\pi
0.987201 0.159479i 0.0509813π-0.0509813\pi
168168 18.8309 + 3.01056i 1.45284 + 0.232270i
169169 −1.56311 2.70738i −0.120239 0.208260i
170170 18.3127 + 11.0252i 1.40452 + 0.845592i
171171 −13.0562 0.732312i −0.998431 0.0560013i
172172 3.33355 1.76501i 0.254181 0.134581i
173173 −4.54638 + 2.62485i −0.345655 + 0.199564i −0.662770 0.748823i 0.730619π-0.730619\pi
0.317115 + 0.948387i 0.397286π0.397286\pi
174174 −0.416014 0.979262i −0.0315380 0.0742376i
175175 −14.0050 8.08579i −1.05868 0.611229i
176176 6.77049 9.96235i 0.510345 0.750941i
177177 −7.48151 16.7510i −0.562345 1.25908i
178178 −9.77103 17.6638i −0.732369 1.32396i
179179 −9.00022 −0.672708 −0.336354 0.941736i 0.609194π-0.609194\pi
−0.336354 + 0.941736i 0.609194π0.609194\pi
180180 −13.0662 12.6029i −0.973894 0.939364i
181181 6.89054 + 11.9348i 0.512170 + 0.887104i 0.999900 + 0.0141097i 0.00449141π0.00449141\pi
−0.487731 + 0.872994i 0.662175π0.662175\pi
182182 −10.7007 19.3445i −0.793192 1.43391i
183183 −4.53761 10.1596i −0.335430 0.751021i
184184 11.3196 + 7.39329i 0.834490 + 0.545041i
185185 9.36773i 0.688729i
186186 −3.77211 + 5.00884i −0.276584 + 0.367266i
187187 13.0278 7.52161i 0.952688 0.550035i
188188 −24.7089 0.906105i −1.80208 0.0660845i
189189 −13.5871 14.9839i −0.988317 1.08992i
190190 11.3813 + 14.7760i 0.825689 + 1.07197i
191191 −7.15070 + 12.3854i −0.517406 + 0.896174i 0.482389 + 0.875957i 0.339769π0.339769\pi
−0.999796 + 0.0202169i 0.993564π0.993564\pi
192192 −4.22814 13.1956i −0.305140 0.952308i
193193 −4.54467 −0.327132 −0.163566 0.986532i 0.552300π-0.552300\pi
−0.163566 + 0.986532i 0.552300π0.552300\pi
194194 3.55152 1.96458i 0.254984 0.141049i
195195 −2.17527 + 20.9319i −0.155774 + 1.49896i
196196 −7.62986 14.4104i −0.544990 1.02931i
197197 19.3601i 1.37935i −0.724121 0.689673i 0.757754π-0.757754\pi
0.724121 0.689673i 0.242246π-0.242246\pi
198198 −12.2122 + 3.75323i −0.867882 + 0.266730i
199199 −5.50195 + 3.17655i −0.390023 + 0.225180i −0.682170 0.731194i 0.738964π-0.738964\pi
0.292147 + 0.956373i 0.405630π0.405630\pi
200200 −0.645734 + 11.7326i −0.0456603 + 0.829620i
201201 2.30912 22.2200i 0.162873 1.56727i
202202 −7.59515 0.139215i −0.534393 0.00979512i
203203 −0.845412 + 1.46430i −0.0593363 + 0.102774i
204204 2.41832 17.1354i 0.169316 1.19972i
205205 −1.25239 −0.0874709
206206 5.55624 + 10.0444i 0.387121 + 0.699827i
207207 −4.46329 13.6280i −0.310220 0.947210i
208208 −9.02881 + 13.2853i −0.626036 + 0.921172i
209209 12.9765 1.97539i 0.897604 0.136641i
210210 −3.50738 + 28.6354i −0.242032 + 1.97603i
211211 3.70510i 0.255070i −0.991834 0.127535i 0.959294π-0.959294\pi
0.991834 0.127535i 0.0407065π-0.0407065\pi
212212 −19.0248 + 10.0730i −1.30663 + 0.691820i
213213 16.7770 + 1.74349i 1.14954 + 0.119462i
214214 0.161581 8.81537i 0.0110454 0.602606i
215215 2.85314 + 4.94179i 0.194583 + 0.337027i
216216 −5.25472 + 13.7254i −0.357538 + 0.933898i
217217 9.96467 0.676446
218218 −21.4181 12.8948i −1.45061 0.873344i
219219 1.02704 + 0.106731i 0.0694010 + 0.00721223i
220220 15.4364 + 9.68328i 1.04072 + 0.652847i
221221 −17.3733 + 10.0305i −1.16865 + 0.674723i
222222 6.98019 2.96535i 0.468480 0.199022i
223223 −10.0726 + 5.81541i −0.674511 + 0.389429i −0.797784 0.602944i 0.793994π-0.793994\pi
0.123273 + 0.992373i 0.460661π0.460661\pi
224224 −12.7090 + 17.9825i −0.849156 + 1.20151i
225225 8.31776 9.28140i 0.554517 0.618760i
226226 −7.95767 14.3857i −0.529336 0.956920i
227227 −1.26292 + 2.18744i −0.0838227 + 0.145185i −0.904889 0.425648i 0.860046π-0.860046\pi
0.821066 + 0.570833i 0.193380π0.193380\pi
228228 7.40732 13.1579i 0.490562 0.871406i
229229 −13.4497 23.2956i −0.888782 1.53942i −0.841316 0.540544i 0.818219π-0.818219\pi
−0.0474665 0.998873i 0.515115π-0.515115\pi
230230 −10.5496 + 17.5227i −0.695619 + 1.15542i
231231 16.4395 + 11.9147i 1.08164 + 0.783927i
232232 1.22670 + 0.0675149i 0.0805371 + 0.00443257i
233233 4.82101 + 2.78341i 0.315835 + 0.182347i 0.649534 0.760332i 0.274964π-0.274964\pi
−0.333700 + 0.942679i 0.608297π0.608297\pi
234234 16.2856 5.00513i 1.06462 0.327196i
235235 37.4050i 2.44003i
236236 21.1697 + 0.776317i 1.37803 + 0.0505339i
237237 18.8951 + 13.6944i 1.22737 + 0.889545i
238238 −24.0645 + 13.3117i −1.55987 + 0.862868i
239239 0.139802 + 0.242144i 0.00904302 + 0.0156630i 0.870512 0.492148i 0.163788π-0.163788\pi
−0.861468 + 0.507811i 0.830455π0.830455\pi
240240 19.7146 7.12362i 1.27257 0.459828i
241241 −14.7801 −0.952069 −0.476034 0.879427i 0.657926π-0.657926\pi
−0.476034 + 0.879427i 0.657926π0.657926\pi
242242 −2.39084 + 1.32254i −0.153689 + 0.0850158i
243243 13.4542 7.87309i 0.863085 0.505059i
244244 12.8396 + 0.470843i 0.821971 + 0.0301427i
245245 21.3626 12.3337i 1.36480 0.787970i
246246 0.396445 + 0.933196i 0.0252764 + 0.0594984i
247247 −17.3049 + 2.63429i −1.10108 + 0.167616i
248248 −3.27013 6.45982i −0.207654 0.410199i
249249 6.45690 + 0.671009i 0.409190 + 0.0425235i
250250 3.61771 + 0.0663106i 0.228804 + 0.00419385i
251251 −3.57806 6.19739i −0.225845 0.391176i 0.730727 0.682669i 0.239181π-0.239181\pi
−0.956573 + 0.291494i 0.905848π0.905848\pi
252252 22.4474 6.45108i 1.41405 0.406380i
253253 7.19716 + 12.4658i 0.452482 + 0.783721i
254254 4.36539 + 7.89163i 0.273909 + 0.495165i
255255 26.0392 + 2.70602i 1.63064 + 0.169458i
256256 15.8283 + 2.33751i 0.989271 + 0.146094i
257257 −18.0122 10.3993i −1.12357 0.648693i −0.181260 0.983435i 0.558018π-0.558018\pi
−0.942310 + 0.334742i 0.891351π0.891351\pi
258258 2.77912 3.69029i 0.173020 0.229747i
259259 −10.4375 6.02611i −0.648556 0.374444i
260260 −20.5852 12.9132i −1.27664 0.800841i
261261 −0.970419 0.869666i −0.0600675 0.0538309i
262262 −0.258169 + 14.0849i −0.0159497 + 0.870169i
263263 4.49769 + 7.79022i 0.277339 + 0.480366i 0.970723 0.240203i 0.0772141π-0.0772141\pi
−0.693383 + 0.720569i 0.743881π0.743881\pi
264264 2.32893 14.5674i 0.143336 0.896559i
265265 −16.2831 28.2031i −1.00026 1.73251i
266266 −23.7849 + 3.17591i −1.45835 + 0.194727i
267267 −20.0183 14.5084i −1.22510 0.887897i
268268 21.8520 + 13.7078i 1.33482 + 0.837337i
269269 −9.99790 5.77229i −0.609583 0.351943i 0.163219 0.986590i 0.447812π-0.447812\pi
−0.772802 + 0.634647i 0.781146π0.781146\pi
270270 −21.0414 7.18312i −1.28054 0.437151i
271271 0.0117891 + 0.00680646i 0.000716139 + 0.000413463i 0.500358 0.865819i 0.333202π-0.333202\pi
−0.499642 + 0.866232i 0.666535π0.666535\pi
272272 16.5269 + 11.2318i 1.00209 + 0.681028i
273273 −21.9230 15.8888i −1.32684 0.961636i
274274 25.3342 + 0.464361i 1.53049 + 0.0280531i
275275 −6.25506 + 10.8341i −0.377194 + 0.653320i
276276 16.3962 + 2.31400i 0.986936 + 0.139286i
277277 4.86773 8.43115i 0.292473 0.506579i −0.681921 0.731426i 0.738855π-0.738855\pi
0.974394 + 0.224847i 0.0721883π0.0721883\pi
278278 −10.9440 + 18.1778i −0.656376 + 1.09023i
279279 −1.57909 + 7.51548i −0.0945375 + 0.449940i
280280 −27.8905 18.2164i −1.66677 1.08864i
281281 11.5527i 0.689174i 0.938754 + 0.344587i 0.111981π0.111981\pi
−0.938754 + 0.344587i 0.888019π0.888019\pi
282282 −27.8716 + 11.8405i −1.65973 + 0.705094i
283283 22.5259i 1.33902i −0.742802 0.669511i 0.766504π-0.766504\pi
0.742802 0.669511i 0.233496π-0.233496\pi
284284 −10.3500 + 16.4991i −0.614157 + 0.979044i
285285 20.3028 + 10.4689i 1.20263 + 0.620123i
286286 −14.9646 + 8.27795i −0.884878 + 0.489485i
287287 0.805643 1.39542i 0.0475556 0.0823688i
288288 −11.5487 12.4350i −0.680512 0.732737i
289289 3.97787 + 6.88987i 0.233992 + 0.405287i
290290 −0.0340610 + 1.85827i −0.00200013 + 0.109121i
291291 2.91708 4.02492i 0.171002 0.235945i
292292 −0.633595 + 1.01003i −0.0370784 + 0.0591076i
293293 16.3725 9.45267i 0.956492 0.552231i 0.0614006 0.998113i 0.480443π-0.480443\pi
0.895092 + 0.445882i 0.147110π0.147110\pi
294294 −15.9525 12.0137i −0.930370 0.700652i
295295 32.0472i 1.86586i
296296 −0.481247 + 8.74396i −0.0279719 + 0.508232i
297297 −11.5913 + 10.5108i −0.672597 + 0.609899i
298298 25.0938 + 0.459956i 1.45365 + 0.0266445i
299299 −9.59780 16.6239i −0.555055 0.961384i
300300 5.38332 + 13.3464i 0.310806 + 0.770554i
301301 −7.34152 −0.423158
302302 −2.34778 + 3.89964i −0.135100 + 0.224399i
303303 −8.49491 + 3.79409i −0.488020 + 0.217965i
304304 9.86441 + 14.3768i 0.565762 + 0.824568i
305305 19.4369i 1.11296i
306306 −6.22636 20.2592i −0.355937 1.15814i
307307 24.8145 + 14.3266i 1.41624 + 0.817664i 0.995966 0.0897351i 0.0286020π-0.0286020\pi
0.420270 + 0.907399i 0.361935π0.361935\pi
308308 −20.7191 + 10.9701i −1.18058 + 0.625080i
309309 11.3833 + 8.25010i 0.647572 + 0.469332i
310310 9.58462 5.30189i 0.544370 0.301127i
311311 0.926512 + 1.60477i 0.0525377 + 0.0909979i 0.891098 0.453811i 0.149936π-0.149936\pi
−0.838561 + 0.544808i 0.816602π0.816602\pi
312312 −3.10576 + 19.4264i −0.175829 + 1.09980i
313313 −4.47592 −0.252994 −0.126497 0.991967i 0.540373π-0.540373\pi
−0.126497 + 0.991967i 0.540373π0.540373\pi
314314 0.0649811 3.54518i 0.00366710 0.200066i
315315 10.9972 + 33.5782i 0.619620 + 1.89192i
316316 −23.8139 + 12.6087i −1.33964 + 0.709297i
317317 26.9184i 1.51189i −0.654638 0.755943i 0.727179π-0.727179\pi
0.654638 0.755943i 0.272821π-0.272821\pi
318318 −15.8606 + 21.0607i −0.889420 + 1.18103i
319319 1.13276 + 0.654000i 0.0634224 + 0.0366169i
320320 −2.65632 + 24.0588i −0.148493 + 1.34493i
321321 −4.40364 9.85967i −0.245787 0.550313i
322322 −12.7375 23.0264i −0.709831 1.28321i
323323 3.27705 + 21.5272i 0.182340 + 1.19781i
324324 1.30827 + 17.9524i 0.0726819 + 0.997355i
325325 8.34146 14.4478i 0.462701 0.801421i
326326 26.4859 + 0.485472i 1.46692 + 0.0268878i
327327 −30.4548 3.16490i −1.68416 0.175019i
328328 −1.16900 0.0643389i −0.0645472 0.00355252i
329329 41.6766 + 24.0620i 2.29771 + 1.32658i
330330 22.1520 + 2.71326i 1.21943 + 0.149360i
331331 −24.8192 14.3294i −1.36419 0.787613i −0.374007 0.927426i 0.622017π-0.622017\pi
−0.990178 + 0.139813i 0.955350π0.955350\pi
332332 −3.98335 + 6.34997i −0.218615 + 0.348500i
333333 6.19899 6.91716i 0.339702 0.379058i
334334 19.7816 + 11.9095i 1.08240 + 0.651659i
335335 −19.5119 + 33.7956i −1.06605 + 1.84645i
336336 −4.74491 + 26.5485i −0.258856 + 1.44834i
337337 −28.4780 −1.55129 −0.775647 0.631167i 0.782576π-0.782576\pi
−0.775647 + 0.631167i 0.782576π0.782576\pi
338338 3.86869 2.14003i 0.210429 0.116402i
339339 −16.3032 11.8158i −0.885467 0.641748i
340340 −16.0639 + 25.6079i −0.871189 + 1.38879i
341341 7.70853i 0.417441i
342342 1.37385 18.4421i 0.0742895 0.997237i
343343 4.48757i 0.242306i
344344 2.40929 + 4.75930i 0.129900 + 0.256604i
345345 −2.58930 + 24.9160i −0.139403 + 1.34143i
346346 −3.59365 6.49650i −0.193196 0.349254i
347347 5.79778 0.311241 0.155621 0.987817i 0.450262π-0.450262\pi
0.155621 + 0.987817i 0.450262π0.450262\pi
348348 1.39543 0.562854i 0.0748031 0.0301722i
349349 0.0557583 0.0965762i 0.00298467 0.00516961i −0.864529 0.502583i 0.832383π-0.832383\pi
0.867514 + 0.497413i 0.165717π0.165717\pi
350350 11.7961 19.5932i 0.630528 1.04730i
351351 15.4577 14.0167i 0.825069 0.748157i
352352 13.9111 + 9.83151i 0.741462 + 0.524021i
353353 −31.2249 18.0277i −1.66194 0.959519i −0.971790 0.235849i 0.924213π-0.924213\pi
−0.690146 0.723670i 0.742454π-0.742454\pi
354354 23.8794 10.1445i 1.26917 0.539176i
355355 −25.5171 14.7323i −1.35431 0.781909i
356356 25.2294 13.3582i 1.33716 0.707983i
357357 −19.7656 + 27.2721i −1.04611 + 1.44339i
358358 0.233262 12.7261i 0.0123283 0.672595i
359359 12.7970 22.1650i 0.675399 1.16983i −0.300953 0.953639i 0.597305π-0.597305\pi
0.976352 0.216186i 0.0693619π-0.0693619\pi
360360 18.1588 18.1486i 0.957055 0.956515i
361361 −4.17347 + 18.5360i −0.219656 + 0.975577i
362362 −17.0540 + 9.43374i −0.896341 + 0.495826i
363363 −1.96375 + 2.70953i −0.103070 + 0.142213i
364364 27.6300 14.6292i 1.44821 0.766780i
365365 −1.56208 0.901870i −0.0817633 0.0472060i
366366 14.4831 6.15276i 0.757042 0.321610i
367367 11.6822i 0.609804i 0.952384 + 0.304902i 0.0986238π0.0986238\pi
−0.952384 + 0.304902i 0.901376π0.901376\pi
368368 −10.7473 + 15.8140i −0.560242 + 0.824361i
369369 0.924770 + 0.828756i 0.0481416 + 0.0431433i
370370 −13.2457 0.242787i −0.688614 0.0126219i
371371 41.8986 2.17527
372372 −6.98462 5.46348i −0.362135 0.283268i
373373 13.7257 + 23.7736i 0.710691 + 1.23095i 0.964598 + 0.263724i 0.0849508π0.0849508\pi
−0.253908 + 0.967228i 0.581716π0.581716\pi
374374 10.2977 + 18.6160i 0.532483 + 0.962609i
375375 4.04628 1.80720i 0.208949 0.0933232i
376376 1.92160 34.9143i 0.0990990 1.80057i
377377 −1.51060 0.872144i −0.0777997 0.0449177i
378378 21.5390 18.8235i 1.10785 0.968177i
379379 8.84686i 0.454433i 0.973844 + 0.227216i 0.0729624π0.0729624\pi
−0.973844 + 0.227216i 0.927038π0.927038\pi
380380 −21.1879 + 15.7100i −1.08692 + 0.805905i
381381 8.94353 + 6.48188i 0.458191 + 0.332077i
382382 −17.3273 10.4319i −0.886541 0.533743i
383383 −1.37298 −0.0701560 −0.0350780 0.999385i 0.511168π-0.511168\pi
−0.0350780 + 0.999385i 0.511168π0.511168\pi
384384 18.7678 5.63649i 0.957740 0.287636i
385385 −17.7332 30.7148i −0.903767 1.56537i
386386 0.117786 6.42605i 0.00599515 0.327078i
387387 1.16340 5.53706i 0.0591390 0.281465i
388388 2.68583 + 5.07268i 0.136352 + 0.257526i
389389 32.5422i 1.64995i 0.565166 + 0.824977i 0.308812π0.308812\pi
−0.565166 + 0.824977i 0.691188π0.691188\pi
390390 −29.5408 3.61828i −1.49586 0.183219i
391391 −20.6800 + 11.9396i −1.04583 + 0.603813i
392392 20.5737 10.4150i 1.03913 0.526035i
393393 7.03600 + 15.7535i 0.354919 + 0.794658i
394394 27.3747 + 0.501762i 1.37912 + 0.0252784i
395395 −20.3820 35.3027i −1.02553 1.77627i
396396 −4.99047 17.3650i −0.250780 0.872624i
397397 8.64308 14.9703i 0.433784 0.751335i −0.563412 0.826176i 0.690512π-0.690512\pi
0.997195 + 0.0748408i 0.0238449π0.0238449\pi
398398 −4.34897 7.86195i −0.217994 0.394084i
399399 −24.7249 + 15.8869i −1.23779 + 0.795338i
400400 −16.5729 1.21713i −0.828643 0.0608565i
401401 14.8592i 0.742031i 0.928627 + 0.371015i 0.120990π0.120990\pi
−0.928627 + 0.371015i 0.879010π0.879010\pi
402402 31.3586 + 3.84093i 1.56403 + 0.191568i
403403 10.2797i 0.512070i
404404 0.393693 10.7358i 0.0195870 0.534124i
405405 −27.0678 + 2.97311i −1.34501 + 0.147735i
406406 −2.04857 1.23334i −0.101669 0.0612098i
407407 −4.66172 + 8.07433i −0.231073 + 0.400230i
408408 24.1663 + 3.86355i 1.19641 + 0.191274i
409409 0.0451886 0.0782689i 0.00223443 0.00387015i −0.864906 0.501934i 0.832622π-0.832622\pi
0.867140 + 0.498064i 0.165955π0.165955\pi
410410 0.0324587 1.77085i 0.00160302 0.0874562i
411411 28.3353 12.6555i 1.39768 0.624248i
412412 −14.3466 + 7.59606i −0.706804 + 0.374231i
413413 −35.7070 20.6154i −1.75703 1.01442i
414414 19.3853 5.95778i 0.952736 0.292809i
415415 −9.82067 5.66997i −0.482078 0.278328i
416416 −18.5511 13.1108i −0.909544 0.642812i
417417 −2.68610 + 25.8475i −0.131539 + 1.26576i
418418 2.45684 + 18.3997i 0.120168 + 0.899958i
419419 −6.82563 11.8223i −0.333454 0.577559i 0.649733 0.760163i 0.274881π-0.274881\pi
−0.983187 + 0.182604i 0.941547π0.941547\pi
420420 −40.3989 5.70150i −1.97126 0.278205i
421421 9.05530 + 15.6842i 0.441328 + 0.764403i 0.997788 0.0664712i 0.0211741π-0.0211741\pi
−0.556460 + 0.830874i 0.687841π0.687841\pi
422422 5.23893 + 0.0960266i 0.255027 + 0.00467450i
423423 −24.7523 + 27.6200i −1.20350 + 1.34293i
424424 −13.7500 27.1617i −0.667758 1.31909i
425425 −17.9730 10.3767i −0.871821 0.503346i
426426 −2.90006 + 23.6771i −0.140508 + 1.14716i
427427 −21.6566 12.5035i −1.04804 0.605085i
428428 12.4605 + 0.456943i 0.602303 + 0.0220872i
429429 −12.2914 + 16.9593i −0.593434 + 0.818805i
430430 −7.06152 + 3.90620i −0.340537 + 0.188374i
431431 −6.32209 10.9502i −0.304525 0.527452i 0.672631 0.739978i 0.265164π-0.265164\pi
−0.977155 + 0.212526i 0.931831π0.931831\pi
432432 −19.2713 7.78577i −0.927189 0.374593i
433433 10.3116 + 17.8602i 0.495544 + 0.858307i 0.999987 0.00513780i 0.00163542π-0.00163542\pi
−0.504443 + 0.863445i 0.668302π0.668302\pi
434434 −0.258258 + 14.0898i −0.0123968 + 0.676332i
435435 0.928282 + 2.07841i 0.0445077 + 0.0996519i
436436 18.7880 29.9504i 0.899782 1.43437i
437437 −20.5986 + 3.13569i −0.985364 + 0.150000i
438438 −0.177534 + 1.44944i −0.00848289 + 0.0692572i
439439 −10.6777 + 6.16477i −0.509618 + 0.294228i −0.732677 0.680577i 0.761729π-0.761729\pi
0.223058 + 0.974805i 0.428396π0.428396\pi
440440 −14.0920 + 21.5757i −0.671810 + 1.02858i
441441 −23.9358 5.02920i −1.13980 0.239486i
442442 −13.7326 24.8254i −0.653192 1.18082i
443443 3.25827 0.154805 0.0774026 0.997000i 0.475337π-0.475337\pi
0.0774026 + 0.997000i 0.475337π0.475337\pi
444444 4.01203 + 9.94667i 0.190403 + 0.472048i
445445 21.5935 + 37.4011i 1.02363 + 1.77298i
446446 −7.96180 14.3931i −0.377002 0.681534i
447447 28.0666 12.5354i 1.32750 0.592905i
448448 −25.0975 18.4363i −1.18575 0.871032i
449449 19.0008i 0.896701i −0.893858 0.448351i 0.852012π-0.852012\pi
0.893858 0.448351i 0.147988π-0.147988\pi
450450 12.9081 + 12.0017i 0.608494 + 0.565764i
451451 −1.07947 0.623235i −0.0508305 0.0293470i
452452 20.5472 10.8791i 0.966460 0.511711i
453453 −0.576242 + 5.54499i −0.0270742 + 0.260526i
454454 −3.06025 1.84243i −0.143625 0.0864693i
455455 23.6482 + 40.9598i 1.10864 + 1.92023i
456456 18.4130 + 10.8148i 0.862270 + 0.506449i
457457 7.55453 13.0848i 0.353386 0.612083i −0.633454 0.773780i 0.718363π-0.718363\pi
0.986840 + 0.161697i 0.0516968π0.0516968\pi
458458 33.2880 18.4138i 1.55545 0.860421i
459459 −17.4367 19.2293i −0.813878 0.897546i
460460 −24.5033 15.3710i −1.14247 0.716677i
461461 −7.38699 + 4.26488i −0.344046 + 0.198635i −0.662060 0.749451i 0.730318π-0.730318\pi
0.318014 + 0.948086i 0.396984π0.396984\pi
462462 −17.2731 + 22.9363i −0.803618 + 1.06709i
463463 8.79687 5.07887i 0.408825 0.236035i −0.281460 0.959573i 0.590819π-0.590819\pi
0.690285 + 0.723538i 0.257485π0.257485\pi
464464 −0.127257 + 1.73278i −0.00590778 + 0.0804423i
465465 7.87244 10.8622i 0.365076 0.503722i
466466 −4.06062 + 6.74465i −0.188105 + 0.312440i
467467 −6.04500 −0.279729 −0.139865 0.990171i 0.544667π-0.544667\pi
−0.139865 + 0.990171i 0.544667π0.544667\pi
468468 6.65506 + 23.1572i 0.307630 + 1.07044i
469469 −25.1034 43.4803i −1.15917 2.00773i
470470 52.8898 + 0.969440i 2.43962 + 0.0447169i
471471 −1.77096 3.96516i −0.0816017 0.182705i
472472 −1.64636 + 29.9133i −0.0757797 + 1.37687i
473473 5.67930i 0.261135i
474474 −19.8532 + 26.3624i −0.911889 + 1.21086i
475475 −11.3112 14.1412i −0.518996 0.648843i
476476 −18.1987 34.3716i −0.834136 1.57542i
477477 −6.63961 + 31.6004i −0.304007 + 1.44688i
478478 −0.346009 + 0.191401i −0.0158261 + 0.00875446i
479479 −10.9343 −0.499601 −0.249800 0.968297i 0.580365π-0.580365\pi
−0.249800 + 0.968297i 0.580365π0.580365\pi
480480 9.56168 + 28.0605i 0.436429 + 1.28078i
481481 6.21665 10.7676i 0.283455 0.490958i
482482 0.383061 20.8987i 0.0174480 0.951909i
483483 −26.0957 18.9130i −1.18740 0.860573i
484484 −1.80807 3.41487i −0.0821849 0.155221i
485485 −7.51995 + 4.34165i −0.341463 + 0.197144i
486486 10.7837 + 19.2279i 0.489157 + 0.872196i
487487 31.2745i 1.41718i 0.705619 + 0.708592i 0.250669π0.250669\pi
−0.705619 + 0.708592i 0.749331π0.749331\pi
488488 −0.998530 + 18.1427i −0.0452013 + 0.821281i
489489 29.6236 13.2308i 1.33962 0.598318i
490490 16.8859 + 30.5258i 0.762826 + 1.37902i
491491 −7.16052 −0.323150 −0.161575 0.986860i 0.551657π-0.551657\pi
−0.161575 + 0.986860i 0.551657π0.551657\pi
492492 −1.32979 + 0.536377i −0.0599517 + 0.0241817i
493493 −1.08494 + 1.87918i −0.0488634 + 0.0846338i
494494 −3.27633 24.5370i −0.147409 1.10397i
495495 25.9756 8.50726i 1.16752 0.382373i
496496 9.21878 4.45647i 0.413935 0.200101i
497497 32.8294 18.9541i 1.47260 0.850207i
498498 −1.11614 + 9.11252i −0.0500153 + 0.408342i
499499 33.9896i 1.52158i 0.648997 + 0.760791i 0.275189π0.275189\pi
−0.648997 + 0.760791i 0.724811π0.724811\pi
500500 −0.187523 + 5.11364i −0.00838629 + 0.228689i
501501 28.1278 + 2.92308i 1.25666 + 0.130594i
502502 8.85569 4.89868i 0.395249 0.218639i
503503 21.1844 + 36.6924i 0.944565 + 1.63603i 0.756619 + 0.653855i 0.226850π0.226850\pi
0.187946 + 0.982179i 0.439817π0.439817\pi
504504 8.53989 + 31.9073i 0.380397 + 1.42126i
505505 16.2521 0.723208
506506 −17.8129 + 9.85353i −0.791882 + 0.438043i
507507 3.17759 4.38436i 0.141122 0.194716i
508508 −11.2717 + 5.96802i −0.500101 + 0.264788i
509509 −6.44054 3.71845i −0.285472 0.164817i 0.350426 0.936590i 0.386037π-0.386037\pi
−0.635898 + 0.771773i 0.719370π0.719370\pi
510510 −4.50112 + 36.7487i −0.199313 + 1.62726i
511511 2.00973 1.16032i 0.0889051 0.0513294i
512512 −3.71541 + 22.3203i −0.164200 + 0.986427i
513513 −8.06396 21.1654i −0.356032 0.934474i
514514 15.1713 25.1993i 0.669175 1.11149i
515515 −12.2790 21.2679i −0.541079 0.937177i
516516 5.14595 + 4.02525i 0.226538 + 0.177202i
517517 18.6141 32.2405i 0.818645 1.41794i
518518 8.79129 14.6022i 0.386267 0.641585i
519519 −7.36245 5.33598i −0.323176 0.234223i
520520 18.7924 28.7723i 0.824103 1.26175i
521521 1.07049i 0.0468992i 0.999725 + 0.0234496i 0.00746492π0.00746492\pi
−0.999725 + 0.0234496i 0.992535π0.992535\pi
522522 1.25484 1.34961i 0.0549227 0.0590708i
523523 7.38254 4.26231i 0.322816 0.186378i −0.329831 0.944040i 0.606992π-0.606992\pi
0.652647 + 0.757662i 0.273658π0.273658\pi
524524 −19.9091 0.730089i −0.869731 0.0318941i
525525 2.89524 27.8600i 0.126359 1.21591i
526526 −11.1318 + 6.15772i −0.485368 + 0.268489i
527527 12.7880 0.557052
528528 20.5375 + 3.67060i 0.893782 + 0.159742i
529529 0.0754029 + 0.130602i 0.00327839 + 0.00567833i
530530 40.3006 22.2929i 1.75055 0.968344i
531531 21.2069 23.6638i 0.920299 1.02692i
532532 −3.87421 33.7136i −0.167968 1.46167i
533533 1.43954 + 0.831117i 0.0623533 + 0.0359997i
534534 21.0333 27.9293i 0.910200 1.20862i
535535 18.8631i 0.815522i
536536 −19.9488 + 30.5429i −0.861658 + 1.31925i
537537 −6.35721 14.2337i −0.274334 0.614229i
538538 8.42100 13.9872i 0.363055 0.603031i
539539 24.5507 1.05747
540540 10.7021 29.5658i 0.460545 1.27231i
541541 0.207415 + 0.359253i 0.00891746 + 0.0154455i 0.870450 0.492257i 0.163828π-0.163828\pi
−0.861532 + 0.507703i 0.830495π0.830495\pi
542542 −0.00992972 + 0.0164932i −0.000426518 + 0.000708442i
543543 −14.0075 + 19.3273i −0.601121 + 0.829412i
544544 −16.3098 + 23.0775i −0.699279 + 0.989441i
545545 46.3205 + 26.7431i 1.98415 + 1.14555i
546546 23.0346 30.5868i 0.985791 1.30899i
547547 27.9073i 1.19323i 0.802528 + 0.596614i 0.203488π0.203488\pi
−0.802528 + 0.596614i 0.796512π0.796512\pi
548548 −1.31319 + 35.8099i −0.0560967 + 1.52972i
549549 12.8622 14.3523i 0.548944 0.612541i
550550 −15.1570 9.12530i −0.646298 0.389104i
551551 −1.47854 + 1.18265i −0.0629878 + 0.0503826i
552552 −3.69689 + 23.1239i −0.157350 + 0.984218i
553553 52.4457 2.23022
554554 11.7953 + 7.10137i 0.501134 + 0.301708i
555555 −14.8149 + 6.61680i −0.628857 + 0.280868i
556556 −25.4194 15.9456i −1.07802 0.676246i
557557 9.40864 5.43208i 0.398657 0.230165i −0.287247 0.957856i 0.592740π-0.592740\pi
0.685904 + 0.727692i 0.259407π0.259407\pi
558558 −10.5858 2.42757i −0.448132 0.102767i
559559 7.57365i 0.320331i
560560 26.4805 38.9643i 1.11900 1.64654i
561561 21.0974 + 15.2904i 0.890731 + 0.645563i
562562 −16.3352 0.299415i −0.689059 0.0126301i
563563 −6.07143 10.5160i −0.255880 0.443198i 0.709254 0.704953i 0.249032π-0.249032\pi
−0.965134 + 0.261755i 0.915699π0.915699\pi
564564 −16.0199 39.7167i −0.674559 1.67237i
565565 17.5861 + 30.4600i 0.739853 + 1.28146i
566566 31.8510 + 0.583811i 1.33880 + 0.0245394i
567567 14.0996 32.0715i 0.592129 1.34688i
568568 −23.0611 15.0622i −0.967624 0.631996i
569569 −10.8712 6.27649i −0.455745 0.263124i 0.254509 0.967071i 0.418086π-0.418086\pi
−0.710253 + 0.703946i 0.751420π0.751420\pi
570570 −15.3289 + 28.4363i −0.642059 + 1.19106i
571571 27.6064 15.9386i 1.15529 0.667008i 0.205120 0.978737i 0.434241π-0.434241\pi
0.950171 + 0.311729i 0.100908π0.100908\pi
572572 −11.3170 21.3742i −0.473187 0.893700i
573573 −24.6381 2.56042i −1.02927 0.106963i
574574 1.95220 + 1.17533i 0.0814834 + 0.0490572i
575575 9.92913 17.1978i 0.414073 0.717196i
576576 17.8820 16.0073i 0.745085 0.666970i
577577 16.0365 0.667607 0.333803 0.942643i 0.391668π-0.391668\pi
0.333803 + 0.942643i 0.391668π0.391668\pi
578578 −9.84521 + 5.44605i −0.409507 + 0.226526i
579579 −3.21008 7.18731i −0.133406 0.298694i
580580 −2.62666 0.0963228i −0.109066 0.00399959i
581581 12.6350 7.29479i 0.524186 0.302639i
582582 5.61554 + 4.22900i 0.232771 + 0.175298i
583583 32.4122i 1.34238i
584584 −1.41174 0.922066i −0.0584182 0.0381554i
585585 −34.6399 + 11.3449i −1.43218 + 0.469053i
586586 12.9415 + 23.3953i 0.534609 + 0.966452i
587587 18.9447 + 32.8132i 0.781932 + 1.35435i 0.930815 + 0.365491i 0.119099π0.119099\pi
−0.148883 + 0.988855i 0.547568π0.547568\pi
588588 17.4005 22.2451i 0.717585 0.917374i
589589 10.3928 + 4.06128i 0.428229 + 0.167342i
590590 −45.3140 0.830580i −1.86555 0.0341944i
591591 30.6176 13.6748i 1.25944 0.562505i
592592 −12.3513 0.907092i −0.507635 0.0372813i
593593 −0.224349 + 0.129528i −0.00921292 + 0.00531908i −0.504599 0.863354i 0.668360π-0.668360\pi
0.495386 + 0.868673i 0.335026π0.335026\pi
594594 −14.5616 16.6623i −0.597470 0.683662i
595595 50.9539 29.4182i 2.08890 1.20603i
596596 −1.30073 + 35.4702i −0.0532801 + 1.45292i
597597 −8.90990 6.45750i −0.364658 0.264288i
598598 23.7545 13.1402i 0.971394 0.537343i
599599 5.98755 10.3707i 0.244645 0.423737i −0.717387 0.696675i 0.754662π-0.754662\pi
0.962032 + 0.272938i 0.0879954π0.0879954\pi
600600 −19.0110 + 7.26598i −0.776120 + 0.296632i
601601 12.1188 20.9904i 0.494337 0.856216i −0.505642 0.862743i 0.668744π-0.668744\pi
0.999979 + 0.00652730i 0.00207772π0.00207772\pi
602602 0.190273 10.3807i 0.00775495 0.423087i
603603 36.7715 12.0430i 1.49745 0.490429i
604604 −5.45316 3.42078i −0.221886 0.139190i
605605 5.06234 2.92275i 0.205814 0.118826i
606606 −5.14459 12.1099i −0.208985 0.491932i
607607 8.98311 5.18640i 0.364613 0.210510i −0.306489 0.951874i 0.599154π-0.599154\pi
0.671103 + 0.741365i 0.265821π0.265821\pi
608608 −20.5842 + 13.5754i −0.834798 + 0.550556i
609609 −2.91291 0.302713i −0.118037 0.0122665i
610610 −27.4834 0.503754i −1.11277 0.0203964i
611611 −24.8228 + 42.9944i −1.00422 + 1.73937i
612612 28.8074 8.27886i 1.16447 0.334653i
613613 −17.3644 + 30.0761i −0.701343 + 1.21476i 0.266652 + 0.963793i 0.414083π0.414083\pi
−0.967995 + 0.250969i 0.919251π0.919251\pi
614614 −20.9006 + 34.7157i −0.843481 + 1.40101i
615615 −0.884614 1.98064i −0.0356711 0.0798669i
616616 −14.9745 29.5806i −0.603339 1.19184i
617617 −22.8372 13.1851i −0.919393 0.530812i −0.0359516 0.999354i 0.511446π-0.511446\pi
−0.883441 + 0.468542i 0.844780π0.844780\pi
618618 −11.9605 + 15.8819i −0.481120 + 0.638862i
619619 13.0555 + 7.53759i 0.524745 + 0.302961i 0.738874 0.673844i 0.235358π-0.235358\pi
−0.214129 + 0.976805i 0.568691π0.568691\pi
620620 7.24834 + 13.6898i 0.291100 + 0.549797i
621621 18.3998 16.6846i 0.738358 0.669530i
622622 −2.29311 + 1.26847i −0.0919454 + 0.0508612i
623623 −55.5631 −2.22609
624624 −27.3879 4.89494i −1.09639 0.195955i
625625 −28.5130 −1.14052
626626 0.116004 6.32885i 0.00463646 0.252952i
627627 12.2899 + 19.1268i 0.490810 + 0.763852i
628628 5.01111 + 0.183764i 0.199965 + 0.00733296i
629629 −13.3948 7.73349i −0.534085 0.308354i
630630 −47.7638 + 14.6795i −1.90295 + 0.584844i
631631 20.8654 12.0466i 0.830638 0.479569i −0.0234332 0.999725i 0.507460π-0.507460\pi
0.854071 + 0.520156i 0.174126π0.174126\pi
632632 −17.2113 33.9991i −0.684627 1.35241i
633633 5.85955 2.61706i 0.232896 0.104019i
634634 38.0619 + 0.697653i 1.51163 + 0.0277074i
635635 −9.64731 16.7096i −0.382842 0.663102i
636636 −29.3683 22.9724i −1.16453 0.910914i
637637 −32.7397 −1.29719
638638 −0.954098 + 1.58475i −0.0377731 + 0.0627407i
639639 9.09297 + 27.7640i 0.359712 + 1.09833i
640640 −33.9497 4.37951i −1.34198 0.173115i
641641 31.1331 17.9747i 1.22969 0.709959i 0.262721 0.964872i 0.415380π-0.415380\pi
0.966964 + 0.254913i 0.0820467π0.0820467\pi
642642 14.0555 5.97111i 0.554725 0.235661i
643643 29.5252i 1.16436i 0.813060 + 0.582180i 0.197800π0.197800\pi
−0.813060 + 0.582180i 0.802200π0.802200\pi
644644 32.8890 17.4137i 1.29601 0.686195i
645645 −5.80006 + 8.00277i −0.228377 + 0.315109i
646646 −30.5239 + 4.07574i −1.20095 + 0.160358i
647647 20.2868 0.797555 0.398778 0.917048i 0.369435π-0.369435\pi
0.398778 + 0.917048i 0.369435π0.369435\pi
648648 −25.4182 + 1.38459i −0.998520 + 0.0543918i
649649 −15.9478 + 27.6225i −0.626007 + 1.08428i
650650 20.2127 + 12.1691i 0.792807 + 0.477310i
651651 7.03844 + 15.7589i 0.275858 + 0.617642i
652652 −1.37289 + 37.4379i −0.0537666 + 1.46618i
653653 −41.8593 + 24.1675i −1.63808 + 0.945746i −0.656587 + 0.754250i 0.728001π0.728001\pi
−0.981493 + 0.191496i 0.938666π0.938666\pi
654654 5.26441 42.9804i 0.205855 1.68067i
655655 30.1389i 1.17762i
656656 0.121271 1.65127i 0.00473484 0.0644712i
657657 0.556646 + 1.69963i 0.0217168 + 0.0663091i
658658 −35.1033 + 58.3062i −1.36847 + 2.27301i
659659 9.78463 0.381155 0.190578 0.981672i 0.438964π-0.438964\pi
0.190578 + 0.981672i 0.438964π0.438964\pi
660660 −4.41061 + 31.2520i −0.171683 + 1.21648i
661661 23.8165 41.2514i 0.926355 1.60449i 0.136987 0.990573i 0.456258π-0.456258\pi
0.789367 0.613921i 0.210409π-0.210409\pi
662662 20.9046 34.7223i 0.812481 1.34952i
663663 −28.1345 20.3906i −1.09265 0.791906i
664664 −8.87546 5.79694i −0.344435 0.224965i
665665 50.7532 7.72607i 1.96812 0.299604i
666666 9.62004 + 8.94449i 0.372769 + 0.346592i
667667 −1.79812 1.03814i −0.0696233 0.0401971i
668668 −17.3524 + 27.6620i −0.671386 + 1.07027i
669669 −16.3116 11.8220i −0.630645 0.457063i
670670 −47.2805 28.4652i −1.82660 1.09971i
671671 −9.67251 + 16.7533i −0.373403 + 0.646753i
672672 −37.4159 7.39726i −1.44335 0.285356i
673673 −18.5127 + 32.0650i −0.713614 + 1.23602i 0.249878 + 0.968277i 0.419610π0.419610\pi
−0.963492 + 0.267738i 0.913724π0.913724\pi
674674 0.738075 40.2672i 0.0284296 1.55103i
675675 20.5535 + 6.59856i 0.791106 + 0.253979i
676676 2.92569 + 5.52570i 0.112526 + 0.212527i
677677 11.5974 + 6.69576i 0.445724 + 0.257339i 0.706023 0.708189i 0.250488π-0.250488\pi
−0.260298 + 0.965528i 0.583821π0.583821\pi
678678 17.1298 22.7461i 0.657867 0.873557i
679679 11.1716i 0.428728i
680680 −35.7927 23.3777i −1.37259 0.896494i
681681 −4.35144 0.452206i −0.166747 0.0173286i
682682 10.8997 + 0.199785i 0.417370 + 0.00765017i
683683 −17.3858 −0.665251 −0.332625 0.943059i 0.607934π-0.607934\pi
−0.332625 + 0.943059i 0.607934π0.607934\pi
684684 26.0411 + 2.42057i 0.995708 + 0.0925527i
685685 −54.2099 −2.07125
686686 −6.34532 0.116306i −0.242266 0.00444059i
687687 27.3415 37.7251i 1.04314 1.43930i
688688 −6.79198 + 3.28332i −0.258942 + 0.125176i
689689 43.2234i 1.64668i
690690 −35.1635 4.30696i −1.33865 0.163963i
691691 10.2721 + 5.93061i 0.390770 + 0.225611i 0.682494 0.730892i 0.260895π-0.260895\pi
−0.291724 + 0.956503i 0.594229π0.594229\pi
692692 9.27904 4.91296i 0.352736 0.186763i
693693 −7.23091 + 34.4146i −0.274680 + 1.30730i
694694 −0.150263 + 8.19792i −0.00570392 + 0.311189i
695695 22.6973 39.3129i 0.860957 1.49122i
696696 0.759696 + 1.98770i 0.0287962 + 0.0753435i
697697 1.03391 1.79078i 0.0391620 0.0678306i
698698 0.135111 + 0.0813439i 0.00511404 + 0.00307891i
699699 −0.996643 + 9.59037i −0.0376965 + 0.362741i
700700 27.3986 + 17.1872i 1.03557 + 0.649615i
701701 34.5702 + 19.9591i 1.30570 + 0.753846i 0.981375 0.192101i 0.0615300π-0.0615300\pi
0.324324 + 0.945946i 0.394863π0.394863\pi
702702 19.4187 + 22.2200i 0.732911 + 0.838642i
703703 −8.42995 10.5390i −0.317941 0.397487i
704704 −14.2621 + 19.4151i −0.537522 + 0.731734i
705705 59.1553 26.4206i 2.22792 0.995059i
706706 26.3000 43.6841i 0.989815 1.64407i
707707 −10.4547 + 18.1081i −0.393189 + 0.681024i
708708 13.7252 + 34.0278i 0.515826 + 1.27884i
709709 −11.7027 −0.439505 −0.219753 0.975556i 0.570525π-0.570525\pi
−0.219753 + 0.975556i 0.570525π0.570525\pi
710710 21.4924 35.6987i 0.806597 1.33975i
711711 −8.31100 + 39.5552i −0.311687 + 1.48344i
712712 18.2343 + 36.0200i 0.683359 + 1.34991i
713713 12.2363i 0.458254i
714714 −38.0499 28.6550i −1.42398 1.07239i
715715 31.6860 18.2939i 1.18499 0.684153i
716716 17.9883 + 0.659654i 0.672256 + 0.0246524i
717717 −0.284198 + 0.392130i −0.0106136 + 0.0146443i
718718 31.0092 + 18.6691i 1.15725 + 0.696724i
719719 −19.9654 + 34.5812i −0.744585 + 1.28966i 0.205803 + 0.978593i 0.434019π0.434019\pi
−0.950388 + 0.311066i 0.899314π0.899314\pi
720720 25.1911 + 26.1465i 0.938815 + 0.974423i
721721 31.5956 1.17668
722722 −26.1013 6.38159i −0.971388 0.237498i
723723 −10.4398 23.3744i −0.388259 0.869304i
724724 −12.8971 24.3585i −0.479316 0.905277i
725725 1.80450i 0.0670175i
726726 −3.78031 2.84691i −0.140301 0.105659i
727727 2.26330 1.30672i 0.0839410 0.0484634i −0.457442 0.889239i 0.651234π-0.651234\pi
0.541383 + 0.840776i 0.317901π0.317901\pi
728728 19.9693 + 39.4473i 0.740111 + 1.46201i
729729 21.9544 + 15.7164i 0.813124 + 0.582090i
730730 1.31571 2.18538i 0.0486965 0.0808844i
731731 −9.42159 −0.348470
732732 8.32449 + 20.6382i 0.307682 + 0.762809i
733733 −16.7836 29.0701i −0.619918 1.07373i −0.989500 0.144532i 0.953832π-0.953832\pi
0.369582 0.929198i 0.379501π-0.379501\pi
734734 −16.5183 0.302771i −0.609702 0.0111755i
735735 34.5947 + 25.0727i 1.27605 + 0.924822i
736736 −22.0821 15.6063i −0.813956 0.575256i
737737 −33.6358 + 19.4196i −1.23899 + 0.715331i
738738 −1.19581 + 1.28612i −0.0440183 + 0.0473429i
739739 −15.2623 8.81167i −0.561431 0.324142i 0.192288 0.981338i 0.438409π-0.438409\pi
−0.753720 + 0.657196i 0.771742π0.771742\pi
740740 0.686590 18.7229i 0.0252396 0.688267i
741741 −16.3892 25.5066i −0.602072 0.937010i
742742 −1.08590 + 59.2436i −0.0398647 + 2.17490i
743743 −18.2705 −0.670281 −0.335141 0.942168i 0.608784π-0.608784\pi
−0.335141 + 0.942168i 0.608784π0.608784\pi
744744 7.90626 9.73448i 0.289858 0.356883i
745745 −53.6957 −1.96726
746746 −33.9711 + 18.7917i −1.24377 + 0.688012i
747747 3.49958 + 10.6854i 0.128043 + 0.390960i
748748 −26.5894 + 14.0783i −0.972205 + 0.514753i
749749 −21.0172 12.1343i −0.767954 0.443378i
750750 2.45046 + 5.76818i 0.0894783 + 0.210624i
751751 36.8395 + 21.2693i 1.34429 + 0.776127i 0.987434 0.158032i 0.0505151π-0.0505151\pi
0.356857 + 0.934159i 0.383848π0.383848\pi
752752 49.3182 + 3.62199i 1.79845 + 0.132080i
753753 7.27373 10.0361i 0.265069 0.365736i
754754 1.27234 2.11334i 0.0463359 0.0769635i
755755 4.86919 8.43369i 0.177208 0.306933i
756756 26.0577 + 30.9435i 0.947711 + 1.12540i
757757 14.5044 25.1223i 0.527171 0.913087i −0.472328 0.881423i 0.656586π-0.656586\pi
0.999499 0.0316637i 0.0100805π-0.0100805\pi
758758 −12.5092 0.229287i −0.454356 0.00832810i
759759 −14.6309 + 20.1873i −0.531067 + 0.732753i
760760 −21.6644 30.3664i −0.785851 1.10151i
761761 −8.77550 + 5.06654i −0.318112 + 0.183662i −0.650551 0.759463i 0.725462π-0.725462\pi
0.332439 + 0.943125i 0.392128π0.392128\pi
762762 −9.39701 + 12.4779i −0.340418 + 0.452028i
763763 −59.5944 + 34.4068i −2.15746 + 1.24561i
764764 15.1995 24.2300i 0.549900 0.876611i
765765 14.1130 + 43.0919i 0.510256 + 1.55799i
766766 0.0355841 1.94136i 0.00128570 0.0701443i
767767 21.2673 36.8360i 0.767917 1.33007i
768768 7.48345 + 26.6833i 0.270036 + 0.962850i
769769 7.21239 12.4922i 0.260086 0.450481i −0.706179 0.708033i 0.749583π-0.749583\pi
0.966264 + 0.257552i 0.0829159π0.0829159\pi
770770 43.8896 24.2783i 1.58167 0.874928i
771771 3.72365 35.8314i 0.134104 1.29044i
772772 9.08323 + 0.333093i 0.326913 + 0.0119883i
773773 −20.1732 + 11.6470i −0.725580 + 0.418914i −0.816803 0.576916i 0.804256π-0.804256\pi
0.0912227 + 0.995831i 0.470922π0.470922\pi
774774 7.79912 + 1.78853i 0.280334 + 0.0642873i
775775 −9.20985 + 5.31731i −0.330827 + 0.191003i
776776 −7.24226 + 3.66623i −0.259982 + 0.131610i
777777 2.15774 20.7632i 0.0774085 0.744877i
778778 −46.0139 0.843408i −1.64968 0.0302377i
779779 1.40899 1.12702i 0.0504821 0.0403796i
780780 5.88178 41.6763i 0.210601 1.49225i
781781 −14.6626 25.3964i −0.524670 0.908755i
782782 −16.3464 29.5505i −0.584545 1.05672i
783783 0.689914 2.14898i 0.0246555 0.0767983i
784784 14.1933 + 29.3607i 0.506903 + 1.04859i
785785 7.58596i 0.270754i
786786 −22.4574 + 9.54045i −0.801029 + 0.340297i
787787 41.3050 23.8474i 1.47236 0.850069i 0.472845 0.881145i 0.343227π-0.343227\pi
0.999517 + 0.0310765i 0.00989354π0.00989354\pi
788788 −1.41896 + 38.6941i −0.0505483 + 1.37842i
789789 −9.14320 + 12.6156i −0.325506 + 0.449126i
790790 50.4454 27.9048i 1.79477 0.992807i
791791 −45.2514 −1.60895
792792 24.6830 6.60635i 0.877074 0.234746i
793793 12.8988 22.3414i 0.458050 0.793366i
794794 20.9436 + 12.6091i 0.743260 + 0.447480i
795795 33.1014 45.6724i 1.17398 1.61983i
796796 11.2293 5.94558i 0.398013 0.210735i
797797 17.5689 10.1434i 0.622323 0.359299i −0.155450 0.987844i 0.549683π-0.549683\pi
0.777773 + 0.628545i 0.216349π0.216349\pi
798798 −21.8229 35.3721i −0.772521 1.25216i
799799 53.4849 + 30.8795i 1.89216 + 1.09244i
800800 2.15052 23.4021i 0.0760323 0.827389i
801801 8.80501 41.9064i 0.311110 1.48069i
802802 −21.0105 0.385111i −0.741906 0.0135987i
803803 −0.897605 1.55470i −0.0316758 0.0548641i
804804 −6.24372 + 44.2408i −0.220199 + 1.56025i
805805 28.1492 + 48.7559i 0.992130 + 1.71842i
806806 −14.5353 0.266424i −0.511984 0.00938439i
807807 2.06686 19.8887i 0.0727568 0.700115i
808808 15.1699 + 0.834915i 0.533675 + 0.0293722i
809809 14.0970i 0.495624i 0.968808 + 0.247812i 0.0797116π0.0797116\pi
−0.968808 + 0.247812i 0.920288π0.920288\pi
810810 −3.50238 38.3503i −0.123061 1.34749i
811811 5.19959 3.00199i 0.182582 0.105414i −0.405923 0.913907i 0.633050π-0.633050\pi
0.588505 + 0.808493i 0.299717π0.299717\pi
812812 1.79701 2.86466i 0.0630627 0.100530i
813813 −0.00243716 + 0.0234520i −8.54749e−5 + 0.000822497i
814814 −11.2961 6.80082i −0.395928 0.238369i
815815 −56.6745 −1.98522
816816 −6.08929 + 34.0705i −0.213168 + 1.19270i
817817 −7.65696 2.99217i −0.267883 0.104683i
818818 0.109499 + 0.0659241i 0.00382855 + 0.00230498i
819819 9.64281 45.8938i 0.336947 1.60366i
820820 2.50310 + 0.0917917i 0.0874121 + 0.00320551i
821821 25.4733i 0.889023i 0.895773 + 0.444511i 0.146623π0.146623\pi
−0.895773 + 0.444511i 0.853377π0.853377\pi
822822 17.1601 + 40.3935i 0.598529 + 1.40888i
823823 −16.0564 9.27019i −0.559692 0.323139i 0.193330 0.981134i 0.438071π-0.438071\pi
−0.753022 + 0.657995i 0.771405π0.771405\pi
824824 −10.3688 20.4826i −0.361215 0.713544i
825825 −21.5521 2.23972i −0.750348 0.0779771i
826826 30.0752 49.9545i 1.04645 1.73814i
827827 −1.50477 2.60634i −0.0523261 0.0906314i 0.838676 0.544631i 0.183330π-0.183330\pi
−0.891002 + 0.453999i 0.849997π0.849997\pi
828828 7.92175 + 27.5648i 0.275300 + 0.957942i
829829 28.3457 0.984487 0.492244 0.870457i 0.336177π-0.336177\pi
0.492244 + 0.870457i 0.336177π0.336177\pi
830830 8.27173 13.7392i 0.287116 0.476896i
831831 16.7720 + 1.74296i 0.581814 + 0.0604628i
832832 19.0192 25.8911i 0.659373 0.897611i
833833 40.7280i 1.41114i
834834 −36.4781 4.46798i −1.26313 0.154713i
835835 −42.7812 24.6998i −1.48051 0.854770i
836836 −26.0804 + 2.99704i −0.902009 + 0.103655i
837837 −13.0010 + 2.81118i −0.449379 + 0.0971686i
838838 16.8934 9.34487i 0.583573 0.322813i
839839 −21.4490 37.1508i −0.740502 1.28259i −0.952267 0.305266i 0.901255π-0.901255\pi
0.211765 0.977321i 0.432079π-0.432079\pi
840840 9.10882 56.9753i 0.314284 1.96583i
841841 28.8113 0.993494
842842 −22.4118 + 12.3975i −0.772363 + 0.427246i
843843 −18.2703 + 8.16011i −0.629264 + 0.281049i
844844 −0.271559 + 7.40523i −0.00934743 + 0.254899i
845845 −8.19152 + 4.72937i −0.281797 + 0.162695i
846846 −38.4124 35.7150i −1.32065 1.22791i
847847 7.52062i 0.258411i
848848 38.7623 18.7382i 1.33110 0.643471i
849849 35.6242 15.9109i 1.22262 0.546061i
850850 15.1383 25.1445i 0.519239 0.862450i
851851 7.39989 12.8170i 0.253665 0.439361i
852852 −33.4037 4.71427i −1.14439 0.161508i
853853 12.7676 + 22.1141i 0.437155 + 0.757174i 0.997469 0.0711062i 0.0226529π-0.0226529\pi
−0.560314 + 0.828280i 0.689320π0.689320\pi
854854 18.2409 30.2979i 0.624190 1.03677i
855855 −2.21570 + 39.5030i −0.0757752 + 1.35097i
856856 −0.969050 + 17.6071i −0.0331215 + 0.601797i
857857 −17.8659 + 10.3149i −0.610288 + 0.352350i −0.773078 0.634311i 0.781284π-0.781284\pi
0.162790 + 0.986661i 0.447951π0.447951\pi
858858 −23.6616 17.8193i −0.807792 0.608340i
859859 −44.1631 25.4976i −1.50683 0.869967i −0.999969 0.00793693i 0.997474π-0.997474\pi
−0.506858 0.862030i 0.669193π-0.669193\pi
860860 −5.34025 10.0861i −0.182101 0.343932i
861861 2.77588 + 0.288473i 0.0946018 + 0.00983113i
862862 15.6472 8.65549i 0.532944 0.294807i
863863 0.580286 0.0197532 0.00987658 0.999951i 0.496856π-0.496856\pi
0.00987658 + 0.999951i 0.496856π0.496856\pi
864864 11.5084 27.0473i 0.391522 0.920169i
865865 7.94181 + 13.7556i 0.270030 + 0.467705i
866866 −25.5212 + 14.1175i −0.867245 + 0.479731i
867867 −8.08648 + 11.1575i −0.274631 + 0.378929i
868868 −19.9160 0.730342i −0.675991 0.0247894i
869869 40.5713i 1.37629i
870870 −2.96287 + 1.25870i −0.100451 + 0.0426740i
871871 44.8551 25.8971i 1.51986 0.877490i
872872 41.8623 + 27.3420i 1.41764 + 0.925917i
873873 8.42579 + 1.77035i 0.285170 + 0.0599174i
874874 −3.89992 29.2072i −0.131917 0.987948i
875875 4.97976 8.62520i 0.168347 0.291585i
876876 −2.04488 0.288594i −0.0690901 0.00975070i
877877 −23.2433 −0.784870 −0.392435 0.919780i 0.628367π-0.628367\pi
−0.392435 + 0.919780i 0.628367π0.628367\pi
878878 −8.44010 15.2578i −0.284840 0.514925i
879879 26.5138 + 19.2160i 0.894288 + 0.648140i
880880 −30.1423 20.4849i −1.01610 0.690547i
881881 7.48812i 0.252281i 0.992012 + 0.126141i 0.0402590π0.0402590\pi
−0.992012 + 0.126141i 0.959741π0.959741\pi
882882 7.73152 33.7144i 0.260334 1.13522i
883883 −24.9720 + 14.4176i −0.840374 + 0.485190i −0.857391 0.514665i 0.827916π-0.827916\pi
0.0170172 + 0.999855i 0.494583π0.494583\pi
884884 35.4584 18.7741i 1.19260 0.631442i
885885 −50.6821 + 22.6362i −1.70366 + 0.760908i
886886 −0.0844459 + 4.60712i −0.00283701 + 0.154779i
887887 −14.8290 + 25.6846i −0.497909 + 0.862403i −0.999997 0.00241298i 0.999232π-0.999232\pi
0.502088 + 0.864816i 0.332565π0.332565\pi
888888 −14.1683 + 5.41513i −0.475458 + 0.181720i
889889 24.8238 0.832565
890890 −53.4439 + 29.5634i −1.79144 + 0.990968i
891891 −24.8101 10.9073i −0.831168 0.365408i
892892 20.5579 10.8848i 0.688329 0.364449i
893893 33.6605 + 42.0819i 1.12640 + 1.40822i
894894 16.9974 + 40.0103i 0.568477 + 1.33815i
895895 27.2312i 0.910240i
896896 26.7189 35.0094i 0.892616 1.16958i
897897 19.5110 26.9209i 0.651455 0.898861i
898898 26.8666 + 0.492450i 0.896551 + 0.0164333i
899899 0.555953 + 0.962938i 0.0185421 + 0.0321158i
900900 −17.3046 + 17.9407i −0.576820 + 0.598023i
901901 53.7697 1.79133
902902 0.909216 1.51020i 0.0302736 0.0502841i
903903 −5.18561 11.6105i −0.172566 0.386373i
904904 14.8503 + 29.3352i 0.493913 + 0.975675i
905905 36.1100 20.8481i 1.20034 0.693016i
906906 −7.82555 0.958504i −0.259986 0.0318442i
907907 −31.9137 + 18.4254i −1.05968 + 0.611804i −0.925342 0.379132i 0.876222π-0.876222\pi
−0.134333 + 0.990936i 0.542889π0.542889\pi
908908 2.68446 4.27937i 0.0890869 0.142016i
909909 −12.0006 10.7546i −0.398034 0.356708i
910910 −58.5291 + 32.3764i −1.94022 + 1.07327i
911911 5.88938 10.2007i 0.195124 0.337965i −0.751817 0.659372i 0.770822π-0.770822\pi
0.946941 + 0.321407i 0.104156π0.104156\pi
912912 −15.7691 + 25.7553i −0.522167 + 0.852844i
913913 −5.64316 9.77423i −0.186761 0.323480i
914914 18.3059 + 11.0211i 0.605504 + 0.364544i
915915 −30.7391 + 13.7291i −1.01620 + 0.453869i
916916 25.1740 + 47.5457i 0.831771 + 1.57095i
917917 33.5807 + 19.3878i 1.10893 + 0.640243i
918918 27.6416 24.1568i 0.912310 0.797292i
919919 48.5036i 1.59999i 0.600010 + 0.799993i 0.295163π0.295163\pi
−0.600010 + 0.799993i 0.704837π0.704837\pi
920920 22.3693 34.2487i 0.737494 1.12915i
921921 −5.12987 + 49.3631i −0.169035 + 1.62657i
922922 −5.83899 10.5556i −0.192297 0.347629i
923923 19.5534 + 33.8675i 0.643608 + 1.11476i
924924 −31.9837 25.0182i −1.05219 0.823039i
925925 12.8625 0.422917
926926 6.95341 + 12.5702i 0.228503 + 0.413082i
927927 −5.00692 + 23.8298i −0.164449 + 0.782674i
928928 −2.44681 0.224848i −0.0803205 0.00738100i
929929 13.9413 8.04901i 0.457399 0.264079i −0.253551 0.967322i 0.581599π-0.581599\pi
0.710950 + 0.703243i 0.248265π0.248265\pi
930930 15.1548 + 11.4130i 0.496947 + 0.374246i
931931 −12.9347 + 33.0998i −0.423916 + 1.08480i
932932 −9.43154 5.91643i −0.308940 0.193799i
933933 −1.88348 + 2.59877i −0.0616622 + 0.0850799i
934934 0.156671 8.54748i 0.00512642 0.279682i
935935 −22.7575 39.4172i −0.744251 1.28908i
936936 −32.9162 + 8.80992i −1.07590 + 0.287961i
937937 −2.32881 4.03361i −0.0760788 0.131772i 0.825476 0.564437i 0.190907π-0.190907\pi
−0.901555 + 0.432665i 0.857573π0.857573\pi
938938 62.1307 34.3687i 2.02864 1.12218i
939939 −3.16152 7.07859i −0.103172 0.231001i
940940 −2.74153 + 74.7597i −0.0894188 + 2.43839i
941941 −39.8576 23.0118i −1.29932 0.750163i −0.319034 0.947743i 0.603358π-0.603358\pi
−0.980287 + 0.197580i 0.936692π0.936692\pi
942942 5.65253 2.40133i 0.184170 0.0782397i
943943 1.71353 + 0.989308i 0.0558003 + 0.0322163i
944944 −42.2540 3.10318i −1.37525 0.101000i
945945 −45.3355 + 41.1094i −1.47477 + 1.33729i
946946 −8.03040 0.147193i −0.261091 0.00478565i
947947 −7.16391 12.4083i −0.232796 0.403214i 0.725834 0.687870i 0.241454π-0.241454\pi
−0.958630 + 0.284656i 0.908121π0.908121\pi
948948 −36.7612 28.7552i −1.19395 0.933926i
949949 1.19700 + 2.07327i 0.0388564 + 0.0673013i
950950 20.2885 15.6273i 0.658245 0.507018i
951951 42.5709 19.0135i 1.38046 0.616555i
952952 49.0723 24.8417i 1.59044 0.805124i
953953 26.2384 + 15.1488i 0.849946 + 0.490717i 0.860633 0.509226i 0.170068π-0.170068\pi
−0.0106866 + 0.999943i 0.503402π0.503402\pi
954954 −44.5102 10.2073i −1.44107 0.330472i
955955 37.4734 + 21.6353i 1.21261 + 0.700101i
956956 −0.261668 0.494209i −0.00846295 0.0159838i
957957 −0.234175 + 2.25339i −0.00756979 + 0.0728416i
958958 0.283388 15.4608i 0.00915586 0.499517i
959959 34.8723 60.4007i 1.12609 1.95044i
960960 −39.9248 + 12.7927i −1.28857 + 0.412884i
961961 −12.2236 + 21.1718i −0.394308 + 0.682962i
962962 15.0639 + 9.06926i 0.485681 + 0.292405i
963963 12.4824 13.9286i 0.402241 0.448842i
964964 29.5403 + 1.08328i 0.951429 + 0.0348900i
965965 13.7504i 0.442642i
966966 27.4189 36.4086i 0.882189 1.17143i
967967 49.3216i 1.58608i 0.609172 + 0.793038i 0.291502π0.291502\pi
−0.609172 + 0.793038i 0.708498π0.708498\pi
968968 4.87541 2.46806i 0.156702 0.0793265i
969969 −31.7302 + 20.3881i −1.01932 + 0.654960i
970970 −5.94409 10.7456i −0.190853 0.345019i
971971 −14.3746 + 24.8975i −0.461303 + 0.798999i −0.999026 0.0441217i 0.985951π-0.985951\pi
0.537724 + 0.843121i 0.319284π0.319284\pi
972972 −27.4673 + 14.7495i −0.881014 + 0.473090i
973973 29.2016 + 50.5786i 0.936160 + 1.62148i
974974 −44.2214 0.810554i −1.41695 0.0259718i
975975 28.7409 + 2.98679i 0.920445 + 0.0956537i
976976 −25.6274 1.88211i −0.820314 0.0602448i
977977 −7.76297 + 4.48195i −0.248359 + 0.143390i −0.619013 0.785381i 0.712467π-0.712467\pi
0.370653 + 0.928771i 0.379134π0.379134\pi
978978 17.9403 + 42.2299i 0.573667 + 1.35036i
979979 42.9829i 1.37374i
980980 −43.6004 + 23.0851i −1.39276 + 0.737425i
981981 −16.5062 50.3992i −0.527003 1.60912i
982982 0.185582 10.1248i 0.00592216 0.323095i
983983 −13.1412 22.7612i −0.419139 0.725970i 0.576714 0.816946i 0.304335π-0.304335\pi
−0.995853 + 0.0909759i 0.971001π0.971001\pi
984984 −0.723960 1.89420i −0.0230790 0.0603848i
985985 −58.5762 −1.86639
986986 −2.62899 1.58279i −0.0837241 0.0504062i
987987 −8.61577 + 82.9068i −0.274243 + 2.63895i
988988 34.7796 3.99671i 1.10649 0.127152i
989989 9.01518i 0.286666i
990990 11.3558 + 36.9494i 0.360912 + 1.17433i
991991 17.2201 + 9.94205i 0.547016 + 0.315820i 0.747918 0.663792i 0.231054π-0.231054\pi
−0.200902 + 0.979611i 0.564387π0.564387\pi
992992 6.06241 + 13.1506i 0.192482 + 0.417533i
993993 5.13085 49.3725i 0.162822 1.56679i
994994 25.9498 + 46.9113i 0.823077 + 1.48794i
995995 9.61103 + 16.6468i 0.304690 + 0.527739i
996996 −12.8560 1.81436i −0.407356 0.0574903i
997997 −40.3929 −1.27926 −0.639629 0.768684i 0.720912π-0.720912\pi
−0.639629 + 0.768684i 0.720912π0.720912\pi
998998 −48.0605 0.880921i −1.52133 0.0278851i
999999 15.3180 + 4.91772i 0.484639 + 0.155590i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 684.2.o.a.11.59 yes 232
4.3 odd 2 inner 684.2.o.a.11.19 232
9.5 odd 6 684.2.bi.a.239.97 yes 232
19.7 even 3 684.2.bi.a.83.20 yes 232
36.23 even 6 684.2.bi.a.239.20 yes 232
76.7 odd 6 684.2.bi.a.83.97 yes 232
171.140 odd 6 inner 684.2.o.a.311.19 yes 232
684.311 even 6 inner 684.2.o.a.311.59 yes 232
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.2.o.a.11.19 232 4.3 odd 2 inner
684.2.o.a.11.59 yes 232 1.1 even 1 trivial
684.2.o.a.311.19 yes 232 171.140 odd 6 inner
684.2.o.a.311.59 yes 232 684.311 even 6 inner
684.2.bi.a.83.20 yes 232 19.7 even 3
684.2.bi.a.83.97 yes 232 76.7 odd 6
684.2.bi.a.239.20 yes 232 36.23 even 6
684.2.bi.a.239.97 yes 232 9.5 odd 6