Properties

Label 368.3.k.b.229.12
Level 368368
Weight 33
Character 368.229
Analytic conductor 10.02710.027
Analytic rank 00
Dimension 176176
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [368,3,Mod(45,368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(368, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("368.45");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 368=2423 368 = 2^{4} \cdot 23
Weight: k k == 3 3
Character orbit: [χ][\chi] == 368.k (of order 44, 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: 10.027273728510.0272737285
Analytic rank: 00
Dimension: 176176
Relative dimension: 8888 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 229.12
Character χ\chi == 368.229
Dual form 368.3.k.b.45.12

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.88889+0.657339i)q2+(0.875057+0.875057i)q3+(3.135812.48328i)q4+(6.272466.27246i)q5+(1.077682.22809i)q6+13.5040q7+(4.29085+6.75194i)q8+7.46855iq9+(7.72485+15.9711i)q10+(9.247509.24750i)q11+(0.571000+4.91702i)q12+(5.063455.06345i)q13+(25.5076+8.87670i)q14+10.9775iq15+(3.6666215.5742i)q16+11.9217iq17+(4.9093714.1073i)q18+(21.628621.6286i)q19+(4.0929635.2455i)q20+(11.8168+11.8168i)q21+(11.3888+23.5463i)q22+(9.25829+21.0543i)q23+(2.153599.66306i)q2453.6875iq25+(6.23590+12.8927i)q26+(14.410914.4109i)q27+(42.346033.5342i)q28+(1.84906+1.84906i)q29+(7.2159520.7353i)q3032.8551q31+(3.31168+31.8282i)q32+16.1842iq33+(7.8366222.5188i)q34+(84.703284.7032i)q35+(18.5465+23.4200i)q36+(23.1273+23.1273i)q37+(55.0712+26.6367i)q38+8.86161iq39+(15.4371+69.2654i)q40+61.1238iq41+(14.552930.0882i)q42+(4.442574.44257i)q43+(6.0342751.9626i)q44+(46.8462+46.8462i)q45+(31.327733.6835i)q46+6.23398q47+(10.4198+16.8368i)q48+133.358q49+(35.2909+101.410i)q50+(10.432210.4322i)q51+(3.3040528.4520i)q52+(6.69376+6.69376i)q53+(36.6935+17.7478i)q54116.009iq55+(57.9435+91.1781i)q56+37.8524q57+(2.277214.70812i)q58+(24.544724.5447i)q59+(27.2603+34.4234i)q60+(35.7487+35.7487i)q61+(62.059721.5970i)q62+100.855iq63+(27.177357.9430i)q6463.5205iq65+(10.638530.5701i)q66+(27.645627.6456i)q67+(29.6050+37.3843i)q68+(26.525210.3222i)q69+(104.316+215.674i)q700.0223440iq71+(50.427232.0464i)q7219.3177iq73+(28.482458.8874i)q74+(46.9796+46.9796i)q75+(121.53314.1133i)q76+(124.878124.878i)q77+(5.8250816.7386i)q7873.1520iq79+(74.6898120.687i)q8041.9962q81+(40.1791115.456i)q82+(26.231826.2318i)q83+(7.71078+66.3995i)q84+(74.7786+74.7786i)q85+(5.47125+11.3118i)q863.23606iq87+(22.7589+102.118i)q8864.1708q89+(119.28157.6935i)q90+(68.376868.3768i)q91+(81.3160+43.0314i)q92+(28.750128.7501i)q93+(11.7753+4.09784i)q94271.328q95+(30.749424.9535i)q96142.243iq97+(251.898+87.6613i)q98+(69.0654+69.0654i)q99+O(q100)q+(-1.88889 + 0.657339i) q^{2} +(-0.875057 + 0.875057i) q^{3} +(3.13581 - 2.48328i) q^{4} +(6.27246 - 6.27246i) q^{5} +(1.07768 - 2.22809i) q^{6} +13.5040 q^{7} +(-4.29085 + 6.75194i) q^{8} +7.46855i q^{9} +(-7.72485 + 15.9711i) q^{10} +(9.24750 - 9.24750i) q^{11} +(-0.571000 + 4.91702i) q^{12} +(5.06345 - 5.06345i) q^{13} +(-25.5076 + 8.87670i) q^{14} +10.9775i q^{15} +(3.66662 - 15.5742i) q^{16} +11.9217i q^{17} +(-4.90937 - 14.1073i) q^{18} +(-21.6286 - 21.6286i) q^{19} +(4.09296 - 35.2455i) q^{20} +(-11.8168 + 11.8168i) q^{21} +(-11.3888 + 23.5463i) q^{22} +(9.25829 + 21.0543i) q^{23} +(-2.15359 - 9.66306i) q^{24} -53.6875i q^{25} +(-6.23590 + 12.8927i) q^{26} +(-14.4109 - 14.4109i) q^{27} +(42.3460 - 33.5342i) q^{28} +(-1.84906 + 1.84906i) q^{29} +(-7.21595 - 20.7353i) q^{30} -32.8551 q^{31} +(3.31168 + 31.8282i) q^{32} +16.1842i q^{33} +(-7.83662 - 22.5188i) q^{34} +(84.7032 - 84.7032i) q^{35} +(18.5465 + 23.4200i) q^{36} +(-23.1273 + 23.1273i) q^{37} +(55.0712 + 26.6367i) q^{38} +8.86161i q^{39} +(15.4371 + 69.2654i) q^{40} +61.1238i q^{41} +(14.5529 - 30.0882i) q^{42} +(4.44257 - 4.44257i) q^{43} +(6.03427 - 51.9626i) q^{44} +(46.8462 + 46.8462i) q^{45} +(-31.3277 - 33.6835i) q^{46} +6.23398 q^{47} +(10.4198 + 16.8368i) q^{48} +133.358 q^{49} +(35.2909 + 101.410i) q^{50} +(-10.4322 - 10.4322i) q^{51} +(3.30405 - 28.4520i) q^{52} +(-6.69376 + 6.69376i) q^{53} +(36.6935 + 17.7478i) q^{54} -116.009i q^{55} +(-57.9435 + 91.1781i) q^{56} +37.8524 q^{57} +(2.27721 - 4.70812i) q^{58} +(-24.5447 - 24.5447i) q^{59} +(27.2603 + 34.4234i) q^{60} +(35.7487 + 35.7487i) q^{61} +(62.0597 - 21.5970i) q^{62} +100.855i q^{63} +(-27.1773 - 57.9430i) q^{64} -63.5205i q^{65} +(-10.6385 - 30.5701i) q^{66} +(-27.6456 - 27.6456i) q^{67} +(29.6050 + 37.3843i) q^{68} +(-26.5252 - 10.3222i) q^{69} +(-104.316 + 215.674i) q^{70} -0.0223440i q^{71} +(-50.4272 - 32.0464i) q^{72} -19.3177i q^{73} +(28.4824 - 58.8874i) q^{74} +(46.9796 + 46.9796i) q^{75} +(-121.533 - 14.1133i) q^{76} +(124.878 - 124.878i) q^{77} +(-5.82508 - 16.7386i) q^{78} -73.1520i q^{79} +(-74.6898 - 120.687i) q^{80} -41.9962 q^{81} +(-40.1791 - 115.456i) q^{82} +(-26.2318 - 26.2318i) q^{83} +(-7.71078 + 66.3995i) q^{84} +(74.7786 + 74.7786i) q^{85} +(-5.47125 + 11.3118i) q^{86} -3.23606i q^{87} +(22.7589 + 102.118i) q^{88} -64.1708 q^{89} +(-119.281 - 57.6935i) q^{90} +(68.3768 - 68.3768i) q^{91} +(81.3160 + 43.0314i) q^{92} +(28.7501 - 28.7501i) q^{93} +(-11.7753 + 4.09784i) q^{94} -271.328 q^{95} +(-30.7494 - 24.9535i) q^{96} -142.243i q^{97} +(-251.898 + 87.6613i) q^{98} +(69.0654 + 69.0654i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 176q4q24q316q464q64q828q124q1380q16+72q18+68q24+96q26+212q27+28q298q31+136q32104q35264q36+240q98+O(q100) 176 q - 4 q^{2} - 4 q^{3} - 16 q^{4} - 64 q^{6} - 4 q^{8} - 28 q^{12} - 4 q^{13} - 80 q^{16} + 72 q^{18} + 68 q^{24} + 96 q^{26} + 212 q^{27} + 28 q^{29} - 8 q^{31} + 136 q^{32} - 104 q^{35} - 264 q^{36}+ \cdots - 240 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/368Z)×\left(\mathbb{Z}/368\mathbb{Z}\right)^\times.

nn 4747 9797 277277
χ(n)\chi(n) 11 1-1 e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.88889 + 0.657339i −0.944445 + 0.328669i
33 −0.875057 + 0.875057i −0.291686 + 0.291686i −0.837746 0.546060i 0.816127π-0.816127\pi
0.546060 + 0.837746i 0.316127π0.316127\pi
44 3.13581 2.48328i 0.783953 0.620820i
55 6.27246 6.27246i 1.25449 1.25449i 0.300806 0.953685i 0.402744π-0.402744\pi
0.953685 0.300806i 0.0972558π-0.0972558\pi
66 1.07768 2.22809i 0.179613 0.371349i
77 13.5040 1.92914 0.964571 0.263824i 0.0849838π-0.0849838\pi
0.964571 + 0.263824i 0.0849838π0.0849838\pi
88 −4.29085 + 6.75194i −0.536356 + 0.843992i
99 7.46855i 0.829839i
1010 −7.72485 + 15.9711i −0.772485 + 1.59711i
1111 9.24750 9.24750i 0.840682 0.840682i −0.148266 0.988948i 0.547369π-0.547369\pi
0.988948 + 0.148266i 0.0473691π0.0473691\pi
1212 −0.571000 + 4.91702i −0.0475834 + 0.409752i
1313 5.06345 5.06345i 0.389496 0.389496i −0.485012 0.874508i 0.661185π-0.661185\pi
0.874508 + 0.485012i 0.161185π0.161185\pi
1414 −25.5076 + 8.87670i −1.82197 + 0.634050i
1515 10.9775i 0.731834i
1616 3.66662 15.5742i 0.229164 0.973388i
1717 11.9217i 0.701278i 0.936511 + 0.350639i 0.114036π0.114036\pi
−0.936511 + 0.350639i 0.885964π0.885964\pi
1818 −4.90937 14.1073i −0.272743 0.783737i
1919 −21.6286 21.6286i −1.13834 1.13834i −0.988747 0.149598i 0.952202π-0.952202\pi
−0.149598 0.988747i 0.547798π-0.547798\pi
2020 4.09296 35.2455i 0.204648 1.76228i
2121 −11.8168 + 11.8168i −0.562703 + 0.562703i
2222 −11.3888 + 23.5463i −0.517671 + 1.07028i
2323 9.25829 + 21.0543i 0.402534 + 0.915405i
2424 −2.15359 9.66306i −0.0897331 0.402627i
2525 53.6875i 2.14750i
2626 −6.23590 + 12.8927i −0.239842 + 0.495873i
2727 −14.4109 14.4109i −0.533738 0.533738i
2828 42.3460 33.5342i 1.51236 1.19765i
2929 −1.84906 + 1.84906i −0.0637606 + 0.0637606i −0.738268 0.674507i 0.764356π-0.764356\pi
0.674507 + 0.738268i 0.264356π0.264356\pi
3030 −7.21595 20.7353i −0.240532 0.691177i
3131 −32.8551 −1.05984 −0.529922 0.848047i 0.677779π-0.677779\pi
−0.529922 + 0.848047i 0.677779π0.677779\pi
3232 3.31168 + 31.8282i 0.103490 + 0.994630i
3333 16.1842i 0.490429i
3434 −7.83662 22.5188i −0.230489 0.662319i
3535 84.7032 84.7032i 2.42009 2.42009i
3636 18.5465 + 23.4200i 0.515181 + 0.650555i
3737 −23.1273 + 23.1273i −0.625062 + 0.625062i −0.946821 0.321760i 0.895726π-0.895726\pi
0.321760 + 0.946821i 0.395726π0.395726\pi
3838 55.0712 + 26.6367i 1.44924 + 0.700965i
3939 8.86161i 0.227221i
4040 15.4371 + 69.2654i 0.385927 + 1.73163i
4141 61.1238i 1.49083i 0.666603 + 0.745413i 0.267748π0.267748\pi
−0.666603 + 0.745413i 0.732252π0.732252\pi
4242 14.5529 30.0882i 0.346499 0.716385i
4343 4.44257 4.44257i 0.103315 0.103315i −0.653560 0.756875i 0.726725π-0.726725\pi
0.756875 + 0.653560i 0.226725π0.226725\pi
4444 6.03427 51.9626i 0.137142 1.18097i
4545 46.8462 + 46.8462i 1.04103 + 1.04103i
4646 −31.3277 33.6835i −0.681037 0.732249i
4747 6.23398 0.132638 0.0663189 0.997798i 0.478875π-0.478875\pi
0.0663189 + 0.997798i 0.478875π0.478875\pi
4848 10.4198 + 16.8368i 0.217079 + 0.350767i
4949 133.358 2.72159
5050 35.2909 + 101.410i 0.705817 + 2.02819i
5151 −10.4322 10.4322i −0.204553 0.204553i
5252 3.30405 28.4520i 0.0635394 0.547154i
5353 −6.69376 + 6.69376i −0.126297 + 0.126297i −0.767430 0.641133i 0.778465π-0.778465\pi
0.641133 + 0.767430i 0.278465π0.278465\pi
5454 36.6935 + 17.7478i 0.679509 + 0.328663i
5555 116.009i 2.10926i
5656 −57.9435 + 91.1781i −1.03471 + 1.62818i
5757 37.8524 0.664077
5858 2.27721 4.70812i 0.0392622 0.0811745i
5959 −24.5447 24.5447i −0.416012 0.416012i 0.467815 0.883826i 0.345041π-0.345041\pi
−0.883826 + 0.467815i 0.845041π0.845041\pi
6060 27.2603 + 34.4234i 0.454338 + 0.573723i
6161 35.7487 + 35.7487i 0.586044 + 0.586044i 0.936558 0.350513i 0.113993π-0.113993\pi
−0.350513 + 0.936558i 0.613993π0.613993\pi
6262 62.0597 21.5970i 1.00096 0.348338i
6363 100.855i 1.60088i
6464 −27.1773 57.9430i −0.424645 0.905360i
6565 63.5205i 0.977239i
6666 −10.6385 30.5701i −0.161189 0.463184i
6767 −27.6456 27.6456i −0.412621 0.412621i 0.470030 0.882651i 0.344243π-0.344243\pi
−0.882651 + 0.470030i 0.844243π0.844243\pi
6868 29.6050 + 37.3843i 0.435368 + 0.549769i
6969 −26.5252 10.3222i −0.384424 0.149597i
7070 −104.316 + 215.674i −1.49023 + 3.08105i
7171 0.0223440i 0.000314704i −1.00000 0.000157352i 0.999950π-0.999950\pi
1.00000 0.000157352i 5.00867e5π-5.00867e-5\pi
7272 −50.4272 32.0464i −0.700378 0.445089i
7373 19.3177i 0.264625i −0.991208 0.132313i 0.957760π-0.957760\pi
0.991208 0.132313i 0.0422403π-0.0422403\pi
7474 28.4824 58.8874i 0.384898 0.795775i
7575 46.9796 + 46.9796i 0.626394 + 0.626394i
7676 −121.533 14.1133i −1.59912 0.185701i
7777 124.878 124.878i 1.62179 1.62179i
7878 −5.82508 16.7386i −0.0746805 0.214597i
7979 73.1520i 0.925975i −0.886365 0.462987i 0.846778π-0.846778\pi
0.886365 0.462987i 0.153222π-0.153222\pi
8080 −74.6898 120.687i −0.933623 1.50859i
8181 −41.9962 −0.518472
8282 −40.1791 115.456i −0.489989 1.40800i
8383 −26.2318 26.2318i −0.316046 0.316046i 0.531201 0.847246i 0.321741π-0.321741\pi
−0.847246 + 0.531201i 0.821741π0.821741\pi
8484 −7.71078 + 66.3995i −0.0917950 + 0.790470i
8585 74.7786 + 74.7786i 0.879748 + 0.879748i
8686 −5.47125 + 11.3118i −0.0636192 + 0.131532i
8787 3.23606i 0.0371961i
8888 22.7589 + 102.118i 0.258624 + 1.16043i
8989 −64.1708 −0.721020 −0.360510 0.932755i 0.617397π-0.617397\pi
−0.360510 + 0.932755i 0.617397π0.617397\pi
9090 −119.281 57.6935i −1.32535 0.641038i
9191 68.3768 68.3768i 0.751393 0.751393i
9292 81.3160 + 43.0314i 0.883870 + 0.467733i
9393 28.7501 28.7501i 0.309141 0.309141i
9494 −11.7753 + 4.09784i −0.125269 + 0.0435940i
9595 −271.328 −2.85609
9696 −30.7494 24.9535i −0.320306 0.259933i
9797 142.243i 1.46642i −0.680002 0.733210i 0.738021π-0.738021\pi
0.680002 0.733210i 0.261979π-0.261979\pi
9898 −251.898 + 87.6613i −2.57039 + 0.894503i
9999 69.0654 + 69.0654i 0.697631 + 0.697631i
100100 −133.321 168.354i −1.33321 1.68354i
101101 75.6336 + 75.6336i 0.748848 + 0.748848i 0.974263 0.225415i 0.0723738π-0.0723738\pi
−0.225415 + 0.974263i 0.572374π0.572374\pi
102102 26.5627 + 12.8478i 0.260419 + 0.125959i
103103 175.282 1.70177 0.850886 0.525351i 0.176066π-0.176066\pi
0.850886 + 0.525351i 0.176066π0.176066\pi
104104 12.4616 + 55.9146i 0.119823 + 0.537640i
105105 148.240i 1.41181i
106106 8.24371 17.0439i 0.0777709 0.160791i
107107 −75.8520 + 75.8520i −0.708898 + 0.708898i −0.966303 0.257406i 0.917132π-0.917132\pi
0.257406 + 0.966303i 0.417132π0.417132\pi
108108 −80.9763 9.40355i −0.749780 0.0870699i
109109 41.9915 + 41.9915i 0.385243 + 0.385243i 0.872987 0.487744i 0.162180π-0.162180\pi
−0.487744 + 0.872987i 0.662180π0.662180\pi
110110 76.2573 + 219.128i 0.693248 + 1.99208i
111111 40.4754i 0.364643i
112112 49.5141 210.314i 0.442090 1.87780i
113113 109.643i 0.970290i 0.874434 + 0.485145i 0.161233π0.161233\pi
−0.874434 + 0.485145i 0.838767π0.838767\pi
114114 −71.4991 + 24.8819i −0.627185 + 0.218262i
115115 190.135 + 73.9901i 1.65334 + 0.643392i
116116 −1.20656 + 10.3900i −0.0104014 + 0.0895691i
117117 37.8166 + 37.8166i 0.323219 + 0.323219i
118118 62.4964 + 30.2280i 0.529630 + 0.256170i
119119 160.991i 1.35287i
120120 −74.1195 47.1028i −0.617662 0.392523i
121121 50.0325i 0.413492i
122122 −91.0244 44.0264i −0.746101 0.360872i
123123 −53.4868 53.4868i −0.434852 0.434852i
124124 −103.027 + 81.5886i −0.830867 + 0.657972i
125125 −179.941 179.941i −1.43953 1.43953i
126126 −66.2961 190.505i −0.526159 1.51194i
127127 −107.647 −0.847616 −0.423808 0.905752i 0.639307π-0.639307\pi
−0.423808 + 0.905752i 0.639307π0.639307\pi
128128 89.4231 + 91.5833i 0.698618 + 0.715495i
129129 7.77499i 0.0602713i
130130 41.7545 + 119.983i 0.321189 + 0.922948i
131131 −152.448 + 152.448i −1.16372 + 1.16372i −0.180068 + 0.983654i 0.557632π0.557632\pi
−0.983654 + 0.180068i 0.942368π0.942368\pi
132132 40.1899 + 50.7505i 0.304469 + 0.384474i
133133 −292.072 292.072i −2.19603 2.19603i
134134 70.3920 + 34.0470i 0.525314 + 0.254082i
135135 −180.784 −1.33914
136136 −80.4948 51.1543i −0.591873 0.376135i
137137 84.7818 0.618845 0.309423 0.950925i 0.399864π-0.399864\pi
0.309423 + 0.950925i 0.399864π0.399864\pi
138138 56.8884 + 2.06142i 0.412235 + 0.0149378i
139139 −46.6363 46.6363i −0.335513 0.335513i 0.519163 0.854675i 0.326244π-0.326244\pi
−0.854675 + 0.519163i 0.826244π0.826244\pi
140140 55.2714 475.955i 0.394795 3.39968i
141141 −5.45508 + 5.45508i −0.0386885 + 0.0386885i
142142 0.0146876 + 0.0422053i 0.000103434 + 0.000297221i
143143 93.6485i 0.654884i
144144 116.317 + 27.3844i 0.807755 + 0.190169i
145145 23.1963i 0.159974i
146146 12.6982 + 36.4889i 0.0869743 + 0.249924i
147147 −116.696 + 116.696i −0.793848 + 0.793848i
148148 −15.0912 + 129.954i −0.101968 + 0.878070i
149149 30.8347 30.8347i 0.206944 0.206944i −0.596023 0.802967i 0.703253π-0.703253\pi
0.802967 + 0.596023i 0.203253π0.203253\pi
150150 −119.621 57.8577i −0.797471 0.385718i
151151 152.378i 1.00912i 0.863376 + 0.504561i 0.168346π0.168346\pi
−0.863376 + 0.504561i 0.831654π0.831654\pi
152152 238.839 53.2299i 1.57131 0.350196i
153153 −89.0381 −0.581948
154154 −153.794 + 317.968i −0.998661 + 2.06473i
155155 −206.082 + 206.082i −1.32956 + 1.32956i
156156 22.0059 + 27.7883i 0.141063 + 0.178130i
157157 −34.5790 34.5790i −0.220249 0.220249i 0.588355 0.808603i 0.299776π-0.299776\pi
−0.808603 + 0.588355i 0.799776π0.799776\pi
158158 48.0856 + 138.176i 0.304340 + 0.874532i
159159 11.7148i 0.0736783i
160160 220.413 + 178.869i 1.37758 + 1.11793i
161161 125.024 + 284.317i 0.776545 + 1.76595i
162162 79.3263 27.6058i 0.489668 0.170406i
163163 −1.27838 + 1.27838i −0.00784279 + 0.00784279i −0.711017 0.703175i 0.751765π-0.751765\pi
0.703175 + 0.711017i 0.251765π0.251765\pi
164164 151.788 + 191.673i 0.925535 + 1.16874i
165165 101.515 + 101.515i 0.615240 + 0.615240i
166166 66.7921 + 32.3058i 0.402362 + 0.194613i
167167 310.909i 1.86173i −0.365361 0.930866i 0.619055π-0.619055\pi
0.365361 0.930866i 0.380945π-0.380945\pi
168168 −29.0821 130.490i −0.173108 0.776725i
169169 117.723i 0.696586i
170170 −190.403 92.0936i −1.12002 0.541727i
171171 161.534 161.534i 0.944643 0.944643i
172172 2.89891 24.9632i 0.0168541 0.145135i
173173 101.807 101.807i 0.588477 0.588477i −0.348742 0.937219i 0.613391π-0.613391\pi
0.937219 + 0.348742i 0.113391π0.113391\pi
174174 2.12719 + 6.11256i 0.0122252 + 0.0351296i
175175 724.995i 4.14283i
176176 −110.115 177.930i −0.625655 1.01096i
177177 42.9560 0.242689
178178 121.212 42.1819i 0.680964 0.236977i
179179 140.985 140.985i 0.787625 0.787625i −0.193480 0.981104i 0.561977π-0.561977\pi
0.981104 + 0.193480i 0.0619774π0.0619774\pi
180180 263.233 + 30.5685i 1.46241 + 0.169825i
181181 −127.844 + 127.844i −0.706319 + 0.706319i −0.965759 0.259440i 0.916462π-0.916462\pi
0.259440 + 0.965759i 0.416462π0.416462\pi
182182 −84.2095 + 174.103i −0.462689 + 0.956609i
183183 −62.5643 −0.341881
184184 −181.883 27.8294i −0.988496 0.151247i
185185 290.130i 1.56827i
186186 −35.4072 + 73.2043i −0.190361 + 0.393572i
187187 110.246 + 110.246i 0.589552 + 0.589552i
188188 19.5486 15.4807i 0.103982 0.0823443i
189189 −194.605 194.605i −1.02966 1.02966i
190190 512.509 178.355i 2.69742 0.938709i
191191 28.2910i 0.148121i −0.997254 0.0740603i 0.976404π-0.976404\pi
0.997254 0.0740603i 0.0235957π-0.0235957\pi
192192 74.4851 + 26.9218i 0.387943 + 0.140217i
193193 −114.005 −0.590701 −0.295350 0.955389i 0.595436π-0.595436\pi
−0.295350 + 0.955389i 0.595436π0.595436\pi
194194 93.5017 + 268.681i 0.481967 + 1.38495i
195195 55.5841 + 55.5841i 0.285046 + 0.285046i
196196 418.185 331.165i 2.13360 1.68962i
197197 54.3132 + 54.3132i 0.275701 + 0.275701i 0.831390 0.555689i 0.187545π-0.187545\pi
−0.555689 + 0.831390i 0.687545π0.687545\pi
198198 −175.856 85.0576i −0.888164 0.429584i
199199 −219.466 −1.10285 −0.551423 0.834226i 0.685915π-0.685915\pi
−0.551423 + 0.834226i 0.685915π0.685915\pi
200200 362.494 + 230.365i 1.81247 + 1.15182i
201201 48.3829 0.240711
202202 −192.581 93.1467i −0.953369 0.461122i
203203 −24.9696 + 24.9696i −0.123003 + 0.123003i
204204 −58.6194 6.80731i −0.287350 0.0333692i
205205 383.397 + 383.397i 1.87023 + 1.87023i
206206 −331.089 + 115.220i −1.60723 + 0.559320i
207207 −157.245 + 69.1460i −0.759639 + 0.334039i
208208 −60.2934 97.4249i −0.289872 0.468389i
209209 −400.020 −1.91397
210210 −97.4441 280.009i −0.464019 1.33338i
211211 111.383 111.383i 0.527882 0.527882i −0.392059 0.919940i 0.628237π-0.628237\pi
0.919940 + 0.392059i 0.128237π0.128237\pi
212212 −4.36788 + 37.6129i −0.0206032 + 0.177419i
213213 0.0195523 + 0.0195523i 9.17946e−5 + 9.17946e-5i
214214 93.4157 193.137i 0.436522 0.902508i
215215 55.7316i 0.259217i
216216 159.137 35.4666i 0.736743 0.164197i
217217 −443.675 −2.04459
218218 −106.920 51.7147i −0.490459 0.237223i
219219 16.9040 + 16.9040i 0.0771874 + 0.0771874i
220220 −288.083 363.783i −1.30947 1.65356i
221221 60.3651 + 60.3651i 0.273145 + 0.273145i
222222 26.6060 + 76.4535i 0.119847 + 0.344385i
223223 158.502 0.710772 0.355386 0.934720i 0.384349π-0.384349\pi
0.355386 + 0.934720i 0.384349π0.384349\pi
224224 44.7209 + 429.807i 0.199647 + 1.91878i
225225 400.968 1.78208
226226 −72.0725 207.103i −0.318905 0.916386i
227227 186.887 + 186.887i 0.823292 + 0.823292i 0.986579 0.163287i 0.0522095π-0.0522095\pi
−0.163287 + 0.986579i 0.552210π0.552210\pi
228228 118.698 93.9982i 0.520605 0.412273i
229229 −75.6971 + 75.6971i −0.330555 + 0.330555i −0.852797 0.522242i 0.825096π-0.825096\pi
0.522242 + 0.852797i 0.325096π0.325096\pi
230230 −407.780 14.7764i −1.77296 0.0642450i
231231 218.551i 0.946108i
232232 −4.55070 20.4187i −0.0196151 0.0880117i
233233 200.737i 0.861532i 0.902464 + 0.430766i 0.141757π0.141757\pi
−0.902464 + 0.430766i 0.858243π0.858243\pi
234234 −96.2898 46.5731i −0.411495 0.199030i
235235 39.1024 39.1024i 0.166393 0.166393i
236236 −137.919 16.0161i −0.584402 0.0678650i
237237 64.0121 + 64.0121i 0.270093 + 0.270093i
238238 −105.826 304.094i −0.444645 1.27771i
239239 −127.508 −0.533507 −0.266754 0.963765i 0.585951π-0.585951\pi
−0.266754 + 0.963765i 0.585951π0.585951\pi
240240 170.966 + 40.2504i 0.712358 + 0.167710i
241241 228.352i 0.947518i 0.880655 + 0.473759i 0.157103π0.157103\pi
−0.880655 + 0.473759i 0.842897π0.842897\pi
242242 32.8883 + 94.5059i 0.135902 + 0.390520i
243243 166.447 166.447i 0.684968 0.684968i
244244 200.875 + 23.3271i 0.823259 + 0.0956028i
245245 836.481 836.481i 3.41421 3.41421i
246246 136.190 + 65.8718i 0.553617 + 0.267771i
247247 −219.030 −0.886762
248248 140.976 221.836i 0.568453 0.894499i
249249 45.9086 0.184372
250250 458.171 + 221.606i 1.83268 + 0.886426i
251251 −136.585 + 136.585i −0.544162 + 0.544162i −0.924746 0.380584i 0.875723π-0.875723\pi
0.380584 + 0.924746i 0.375723π0.375723\pi
252252 250.452 + 316.263i 0.993857 + 1.25501i
253253 280.316 + 109.084i 1.10797 + 0.431161i
254254 203.334 70.7607i 0.800527 0.278585i
255255 −130.871 −0.513219
256256 −229.112 114.210i −0.894968 0.446131i
257257 −48.2818 −0.187867 −0.0939334 0.995578i 0.529944π-0.529944\pi
−0.0939334 + 0.995578i 0.529944π0.529944\pi
258258 −5.11081 14.6861i −0.0198093 0.0569229i
259259 −312.311 + 312.311i −1.20583 + 1.20583i
260260 −157.739 199.188i −0.606690 0.766109i
261261 −13.8098 13.8098i −0.0529110 0.0529110i
262262 187.747 388.167i 0.716592 1.48155i
263263 220.965 0.840171 0.420086 0.907484i 0.362000π-0.362000\pi
0.420086 + 0.907484i 0.362000π0.362000\pi
264264 −109.275 69.4438i −0.413919 0.263045i
265265 83.9727i 0.316878i
266266 743.682 + 359.701i 2.79580 + 1.35226i
267267 56.1531 56.1531i 0.210311 0.210311i
268268 −155.343 18.0396i −0.579639 0.0673118i
269269 −270.861 + 270.861i −1.00692 + 1.00692i −0.00694234 + 0.999976i 0.502210π0.502210\pi
−0.999976 + 0.00694234i 0.997790π0.997790\pi
270270 341.481 118.836i 1.26474 0.440134i
271271 −247.486 −0.913232 −0.456616 0.889664i 0.650939π-0.650939\pi
−0.456616 + 0.889664i 0.650939π0.650939\pi
272272 185.671 + 43.7125i 0.682616 + 0.160708i
273273 119.667i 0.438341i
274274 −160.144 + 55.7304i −0.584466 + 0.203396i
275275 −496.475 496.475i −1.80536 1.80536i
276276 −108.811 + 33.5012i −0.394243 + 0.121381i
277277 −151.298 151.298i −0.546201 0.546201i 0.379139 0.925340i 0.376220π-0.376220\pi
−0.925340 + 0.379139i 0.876220π0.876220\pi
278278 118.747 + 57.4349i 0.427146 + 0.206600i
279279 245.380i 0.879499i
280280 208.462 + 935.359i 0.744509 + 3.34057i
281281 136.441 0.485556 0.242778 0.970082i 0.421941π-0.421941\pi
0.242778 + 0.970082i 0.421941π0.421941\pi
282282 6.71821 13.8899i 0.0238235 0.0492549i
283283 142.308 142.308i 0.502856 0.502856i −0.409468 0.912324i 0.634286π-0.634286\pi
0.912324 + 0.409468i 0.134286π0.134286\pi
284284 −0.0554864 0.0700665i −0.000195375 0.000246713i
285285 237.428 237.428i 0.833080 0.833080i
286286 61.5588 + 176.892i 0.215241 + 0.618502i
287287 825.416i 2.87601i
288288 −237.710 + 24.7335i −0.825383 + 0.0858801i
289289 146.872 0.508209
290290 −15.2478 43.8152i −0.0525786 0.151087i
291291 124.470 + 124.470i 0.427734 + 0.427734i
292292 −47.9712 60.5765i −0.164285 0.207454i
293293 68.2180 68.2180i 0.232826 0.232826i −0.581045 0.813871i 0.697356π-0.697356\pi
0.813871 + 0.581045i 0.197356π0.197356\pi
294294 143.717 297.134i 0.488832 1.01066i
295295 −307.911 −1.04377
296296 −56.9184 255.390i −0.192292 0.862803i
297297 −266.530 −0.897407
298298 −37.9745 + 78.5121i −0.127431 + 0.263464i
299299 153.486 + 59.7286i 0.513332 + 0.199761i
300300 263.983 + 30.6556i 0.879942 + 0.102185i
301301 59.9924 59.9924i 0.199310 0.199310i
302302 −100.164 287.824i −0.331668 0.953061i
303303 −132.367 −0.436856
304304 −416.151 + 257.544i −1.36892 + 0.847183i
305305 448.464 1.47038
306306 168.183 58.5282i 0.549618 0.191269i
307307 302.327 302.327i 0.984777 0.984777i −0.0151088 0.999886i 0.504809π-0.504809\pi
0.999886 + 0.0151088i 0.00480945π0.00480945\pi
308308 81.4867 701.702i 0.264567 2.27825i
309309 −153.382 + 153.382i −0.496382 + 0.496382i
310310 253.801 524.733i 0.818713 1.69269i
311311 244.971i 0.787690i 0.919177 + 0.393845i 0.128855π0.128855\pi
−0.919177 + 0.393845i 0.871145π0.871145\pi
312312 −59.8330 38.0238i −0.191772 0.121871i
313313 −516.407 −1.64986 −0.824932 0.565232i 0.808787π-0.808787\pi
−0.824932 + 0.565232i 0.808787π0.808787\pi
314314 88.0461 + 42.5858i 0.280402 + 0.135624i
315315 632.610 + 632.610i 2.00829 + 2.00829i
316316 −181.657 229.391i −0.574864 0.725920i
317317 −235.214 + 235.214i −0.742001 + 0.742001i −0.972963 0.230962i 0.925813π-0.925813\pi
0.230962 + 0.972963i 0.425813π0.425813\pi
318318 7.70062 + 22.1281i 0.0242158 + 0.0695851i
319319 34.1983i 0.107205i
320320 −533.914 192.977i −1.66848 0.603052i
321321 132.750i 0.413550i
322322 −423.049 454.861i −1.31382 1.41261i
323323 257.850 257.850i 0.798297 0.798297i
324324 −131.692 + 104.288i −0.406458 + 0.321878i
325325 −271.844 271.844i −0.836442 0.836442i
326326 1.57438 3.25504i 0.00482940 0.00998477i
327327 −73.4899 −0.224740
328328 −412.704 262.273i −1.25824 0.799613i
329329 84.1836 0.255877
330330 −258.479 125.020i −0.783270 0.378850i
331331 63.9148 + 63.9148i 0.193096 + 0.193096i 0.797033 0.603936i 0.206402π-0.206402\pi
−0.603936 + 0.797033i 0.706402π0.706402\pi
332332 −147.399 17.1170i −0.443972 0.0515573i
333333 −172.727 172.727i −0.518701 0.518701i
334334 204.373 + 587.273i 0.611894 + 1.75830i
335335 −346.812 −1.03526
336336 140.709 + 227.364i 0.418777 + 0.676679i
337337 364.246i 1.08085i −0.841392 0.540425i 0.818263π-0.818263\pi
0.841392 0.540425i 0.181737π-0.181737\pi
338338 −77.3839 222.366i −0.228946 0.657887i
339339 −95.9437 95.9437i −0.283020 0.283020i
340340 420.188 + 48.7952i 1.23585 + 0.143515i
341341 −303.828 + 303.828i −0.890991 + 0.890991i
342342 −198.937 + 411.302i −0.581688 + 1.20264i
343343 1139.17 3.32119
344344 10.9336 + 49.0583i 0.0317836 + 0.142611i
345345 −231.124 + 101.633i −0.669925 + 0.294588i
346346 −125.380 + 259.223i −0.362370 + 0.749199i
347347 −185.323 185.323i −0.534072 0.534072i 0.387709 0.921782i 0.373266π-0.373266\pi
−0.921782 + 0.387709i 0.873266π0.873266\pi
348348 −8.03604 10.1477i −0.0230921 0.0291600i
349349 188.541 188.541i 0.540232 0.540232i −0.383365 0.923597i 0.625235π-0.625235\pi
0.923597 + 0.383365i 0.125235π0.125235\pi
350350 476.567 + 1369.44i 1.36162 + 3.91267i
351351 −145.938 −0.415777
352352 324.956 + 263.706i 0.923170 + 0.749166i
353353 −405.785 −1.14953 −0.574766 0.818317i 0.694907π-0.694907\pi
−0.574766 + 0.818317i 0.694907π0.694907\pi
354354 −81.1391 + 28.2366i −0.229207 + 0.0797645i
355355 −0.140152 0.140152i −0.000394794 0.000394794i
356356 −201.227 + 159.354i −0.565246 + 0.447624i
357357 −140.876 140.876i −0.394611 0.394611i
358358 −173.630 + 358.980i −0.485000 + 1.00274i
359359 −43.5284 −0.121249 −0.0606245 0.998161i 0.519309π-0.519309\pi
−0.0606245 + 0.998161i 0.519309π0.519309\pi
360360 −517.312 + 115.293i −1.43698 + 0.320258i
361361 574.589i 1.59166i
362362 157.446 325.520i 0.434934 0.899225i
363363 43.7813 + 43.7813i 0.120610 + 0.120610i
364364 44.6179 384.215i 0.122577 1.05554i
365365 −121.169 121.169i −0.331970 0.331970i
366366 118.177 41.1259i 0.322888 0.112366i
367367 51.3496i 0.139917i 0.997550 + 0.0699585i 0.0222867π0.0222867\pi
−0.997550 + 0.0699585i 0.977713π0.977713\pi
368368 361.851 66.9922i 0.983290 0.182044i
369369 −456.507 −1.23715
370370 −190.714 548.023i −0.515442 1.48114i
371371 −90.3925 + 90.3925i −0.243646 + 0.243646i
372372 18.7603 161.549i 0.0504309 0.434273i
373373 20.6559 20.6559i 0.0553779 0.0553779i −0.678876 0.734253i 0.737532π-0.737532\pi
0.734253 + 0.678876i 0.237532π0.237532\pi
374374 −280.712 135.774i −0.750567 0.363032i
375375 314.917 0.839778
376376 −26.7490 + 42.0914i −0.0711410 + 0.111945i
377377 18.7252i 0.0496690i
378378 495.509 + 239.666i 1.31087 + 0.634037i
379379 −148.912 + 148.912i −0.392909 + 0.392909i −0.875723 0.482814i 0.839615π-0.839615\pi
0.482814 + 0.875723i 0.339615π0.339615\pi
380380 −850.835 + 673.785i −2.23904 + 1.77312i
381381 94.1974 94.1974i 0.247237 0.247237i
382382 18.5968 + 53.4386i 0.0486827 + 0.139892i
383383 67.6650i 0.176671i −0.996091 0.0883355i 0.971845π-0.971845\pi
0.996091 0.0883355i 0.0281548π-0.0281548\pi
384384 −158.391 1.89028i −0.412476 0.00492261i
385385 1566.59i 4.06905i
386386 215.343 74.9401i 0.557884 0.194145i
387387 33.1795 + 33.1795i 0.0857352 + 0.0857352i
388388 −353.229 446.046i −0.910384 1.14960i
389389 −142.032 + 142.032i −0.365120 + 0.365120i −0.865694 0.500574i 0.833122π-0.833122\pi
0.500574 + 0.865694i 0.333122π0.333122\pi
390390 −141.530 68.4546i −0.362897 0.175525i
391391 −251.004 + 110.375i −0.641954 + 0.282288i
392392 −572.218 + 900.423i −1.45974 + 2.29700i
393393 266.801i 0.678882i
394394 −138.294 66.8895i −0.350999 0.169770i
395395 −458.843 458.843i −1.16163 1.16163i
396396 388.085 + 45.0672i 0.980013 + 0.113806i
397397 128.831 128.831i 0.324510 0.324510i −0.525984 0.850494i 0.676303π-0.676303\pi
0.850494 + 0.525984i 0.176303π0.176303\pi
398398 414.548 144.264i 1.04158 0.362472i
399399 511.159 1.28110
400400 −836.139 196.852i −2.09035 0.492129i
401401 265.047i 0.660965i 0.943812 + 0.330482i 0.107211π0.107211\pi
−0.943812 + 0.330482i 0.892789π0.892789\pi
402402 −91.3900 + 31.8040i −0.227338 + 0.0791144i
403403 −166.360 + 166.360i −0.412805 + 0.412805i
404404 424.992 + 49.3532i 1.05196 + 0.122161i
405405 −263.420 + 263.420i −0.650419 + 0.650419i
406406 30.7514 63.5784i 0.0757423 0.156597i
407407 427.739i 1.05096i
408408 115.200 25.6746i 0.282354 0.0629279i
409409 490.325i 1.19884i −0.800435 0.599420i 0.795398π-0.795398\pi
0.800435 0.599420i 0.204602π-0.204602\pi
410410 −976.216 472.173i −2.38101 1.15164i
411411 −74.1889 + 74.1889i −0.180508 + 0.180508i
412412 549.653 435.276i 1.33411 1.05649i
413413 −331.451 331.451i −0.802545 0.802545i
414414 251.567 233.973i 0.607649 0.565151i
415415 −329.076 −0.792953
416416 177.929 + 144.392i 0.427714 + 0.347096i
417417 81.6187 0.195728
418418 755.594 262.949i 1.80764 0.629064i
419419 205.235 + 205.235i 0.489822 + 0.489822i 0.908250 0.418428i 0.137419π-0.137419\pi
−0.418428 + 0.908250i 0.637419π0.637419\pi
420420 368.122 + 464.853i 0.876482 + 1.10679i
421421 −278.850 + 278.850i −0.662352 + 0.662352i −0.955934 0.293582i 0.905153π-0.905153\pi
0.293582 + 0.955934i 0.405153π0.405153\pi
422422 −137.174 + 283.607i −0.325057 + 0.672054i
423423 46.5588i 0.110068i
424424 −16.4740 73.9178i −0.0388537 0.174334i
425425 640.047 1.50599
426426 −0.0497845 0.0240796i −0.000116865 5.65249e-5i
427427 482.750 + 482.750i 1.13056 + 1.13056i
428428 −49.4957 + 426.220i −0.115644 + 0.995840i
429429 81.9477 + 81.9477i 0.191020 + 0.191020i
430430 36.6346 + 105.271i 0.0851966 + 0.244816i
431431 329.470i 0.764431i 0.924073 + 0.382216i 0.124839π0.124839\pi
−0.924073 + 0.382216i 0.875161π0.875161\pi
432432 −277.278 + 171.599i −0.641847 + 0.397220i
433433 561.046i 1.29572i 0.761760 + 0.647859i 0.224335π0.224335\pi
−0.761760 + 0.647859i 0.775665π0.775665\pi
434434 838.054 291.645i 1.93100 0.671993i
435435 −20.2980 20.2980i −0.0466622 0.0466622i
436436 235.954 + 27.4007i 0.541180 + 0.0628457i
437437 255.131 655.618i 0.583824 1.50027i
438438 −43.0416 20.8182i −0.0982684 0.0475301i
439439 534.808i 1.21824i −0.793078 0.609121i 0.791523π-0.791523\pi
0.793078 0.609121i 0.208477π-0.208477\pi
440440 783.286 + 497.777i 1.78020 + 1.13131i
441441 995.990i 2.25848i
442442 −153.703 74.3427i −0.347745 0.168196i
443443 −195.027 195.027i −0.440241 0.440241i 0.451852 0.892093i 0.350764π-0.350764\pi
−0.892093 + 0.451852i 0.850764π0.850764\pi
444444 −100.512 126.923i −0.226378 0.285863i
445445 −402.508 + 402.508i −0.904513 + 0.904513i
446446 −299.393 + 104.190i −0.671285 + 0.233609i
447447 53.9642i 0.120725i
448448 −367.002 782.462i −0.819201 1.74657i
449449 −154.215 −0.343463 −0.171731 0.985144i 0.554936π-0.554936\pi
−0.171731 + 0.985144i 0.554936π0.554936\pi
450450 −757.384 + 263.572i −1.68307 + 0.585715i
451451 565.243 + 565.243i 1.25331 + 1.25331i
452452 272.274 + 343.819i 0.602376 + 0.760662i
453453 −133.339 133.339i −0.294346 0.294346i
454454 −475.858 230.161i −1.04815 0.506963i
455455 857.781i 1.88523i
456456 −162.419 + 255.577i −0.356182 + 0.560476i
457457 378.638 0.828530 0.414265 0.910156i 0.364039π-0.364039\pi
0.414265 + 0.910156i 0.364039π0.364039\pi
458458 93.2248 192.742i 0.203548 0.420834i
459459 171.803 171.803i 0.374299 0.374299i
460460 779.964 240.139i 1.69557 0.522040i
461461 305.291 305.291i 0.662236 0.662236i −0.293671 0.955907i 0.594877π-0.594877\pi
0.955907 + 0.293671i 0.0948770π0.0948770\pi
462462 −143.662 412.819i −0.310957 0.893547i
463463 536.251 1.15821 0.579104 0.815253i 0.303402π-0.303402\pi
0.579104 + 0.815253i 0.303402π0.303402\pi
464464 22.0178 + 35.5774i 0.0474521 + 0.0766754i
465465 360.668i 0.775629i
466466 −131.952 379.170i −0.283159 0.813670i
467467 −326.848 326.848i −0.699888 0.699888i 0.264498 0.964386i 0.414794π-0.414794\pi
−0.964386 + 0.264498i 0.914794π0.914794\pi
468468 212.495 + 24.6765i 0.454049 + 0.0527275i
469469 −373.326 373.326i −0.796004 0.796004i
470470 −48.1566 + 99.5636i −0.102461 + 0.211837i
471471 60.5172 0.128487
472472 271.042 60.4067i 0.574241 0.127980i
473473 82.1653i 0.173711i
474474 −162.990 78.8342i −0.343860 0.166317i
475475 −1161.18 + 1161.18i −2.44459 + 2.44459i
476476 399.786 + 504.837i 0.839886 + 1.06058i
477477 −49.9927 49.9927i −0.104807 0.104807i
478478 240.849 83.8162i 0.503868 0.175348i
479479 462.127i 0.964774i −0.875958 0.482387i 0.839770π-0.839770\pi
0.875958 0.482387i 0.160230π-0.160230\pi
480480 −349.394 + 36.3540i −0.727905 + 0.0757375i
481481 234.208i 0.486918i
482482 −150.105 431.331i −0.311420 0.894878i
483483 −358.197 139.391i −0.741608 0.288594i
484484 −124.245 156.893i −0.256704 0.324158i
485485 −892.212 892.212i −1.83961 1.83961i
486486 −204.988 + 423.813i −0.421787 + 0.872043i
487487 373.680i 0.767310i 0.923476 + 0.383655i 0.125335π0.125335\pi
−0.923476 + 0.383655i 0.874665π0.874665\pi
488488 −394.765 + 87.9808i −0.808945 + 0.180289i
489489 2.23730i 0.00457526i
490490 −1030.17 + 2129.87i −2.10239 + 4.34668i
491491 517.615 + 517.615i 1.05421 + 1.05421i 0.998444 + 0.0557624i 0.0177589π0.0177589\pi
0.0557624 + 0.998444i 0.482241π0.482241\pi
492492 −300.547 34.9017i −0.610869 0.0709385i
493493 −22.0440 22.0440i −0.0447139 0.0447139i
494494 413.724 143.977i 0.837498 0.291451i
495495 866.420 1.75034
496496 −120.467 + 511.693i −0.242878 + 1.03164i
497497 0.301733i 0.000607109i
498498 −86.7163 + 30.1775i −0.174129 + 0.0605974i
499499 269.165 269.165i 0.539409 0.539409i −0.383947 0.923355i 0.625435π-0.625435\pi
0.923355 + 0.383947i 0.125435π0.125435\pi
500500 −1011.10 117.417i −2.02221 0.234833i
501501 272.063 + 272.063i 0.543040 + 0.543040i
502502 168.211 347.776i 0.335081 0.692780i
503503 −83.3763 −0.165758 −0.0828790 0.996560i 0.526412π-0.526412\pi
−0.0828790 + 0.996560i 0.526412π0.526412\pi
504504 −680.968 432.754i −1.35113 0.858640i
505505 948.818 1.87885
506506 −601.191 21.7848i −1.18812 0.0430530i
507507 −103.014 103.014i −0.203184 0.203184i
508508 −337.561 + 267.318i −0.664491 + 0.526217i
509509 376.327 376.327i 0.739346 0.739346i −0.233106 0.972451i 0.574889π-0.574889\pi
0.972451 + 0.233106i 0.0748888π0.0748888\pi
510510 247.201 86.0266i 0.484708 0.168680i
511511 260.865i 0.510500i
512512 507.841 + 65.1252i 0.991877 + 0.127198i
513513 623.374i 1.21515i
514514 91.1989 31.7375i 0.177430 0.0617461i
515515 1099.45 1099.45i 2.13486 2.13486i
516516 19.3075 + 24.3809i 0.0374176 + 0.0472498i
517517 57.6487 57.6487i 0.111506 0.111506i
518518 384.627 795.215i 0.742522 1.53516i
519519 178.173i 0.343300i
520520 428.887 + 272.557i 0.824782 + 0.524148i
521521 −195.384 −0.375017 −0.187508 0.982263i 0.560041π-0.560041\pi
−0.187508 + 0.982263i 0.560041π0.560041\pi
522522 35.1628 + 17.0074i 0.0673618 + 0.0325813i
523523 −530.989 + 530.989i −1.01528 + 1.01528i −0.0153946 + 0.999881i 0.504900π0.504900\pi
−0.999881 + 0.0153946i 0.995100π0.995100\pi
524524 −99.4766 + 856.617i −0.189841 + 1.63477i
525525 634.412 + 634.412i 1.20840 + 1.20840i
526526 −417.379 + 145.249i −0.793496 + 0.276139i
527527 391.690i 0.743245i
528528 252.056 + 59.3413i 0.477378 + 0.112389i
529529 −357.568 + 389.854i −0.675933 + 0.736964i
530530 −55.1985 158.615i −0.104148 0.299274i
531531 183.313 183.313i 0.345223 0.345223i
532532 −1641.18 190.585i −3.08492 0.358243i
533533 309.497 + 309.497i 0.580671 + 0.580671i
534534 −69.1554 + 142.979i −0.129504 + 0.267750i
535535 951.558i 1.77861i
536536 305.284 68.0384i 0.569560 0.126937i
537537 246.739i 0.459477i
538538 333.579 689.674i 0.620036 1.28192i
539539 1233.23 1233.23i 2.28799 2.28799i
540540 −566.904 + 448.937i −1.04982 + 0.831365i
541541 −706.134 + 706.134i −1.30524 + 1.30524i −0.380427 + 0.924811i 0.624223π0.624223\pi
−0.924811 + 0.380427i 0.875777π0.875777\pi
542542 467.474 162.682i 0.862497 0.300151i
543543 223.741i 0.412046i
544544 −379.447 + 39.4810i −0.697513 + 0.0725753i
545545 526.780 0.966569
546546 −78.6618 226.038i −0.144069 0.413989i
547547 −336.508 + 336.508i −0.615188 + 0.615188i −0.944293 0.329105i 0.893253π-0.893253\pi
0.329105 + 0.944293i 0.393253π0.393253\pi
548548 265.860 210.537i 0.485146 0.384192i
549549 −266.991 + 266.991i −0.486322 + 0.486322i
550550 1264.14 + 611.434i 2.29843 + 1.11170i
551551 79.9848 0.145163
552552 183.510 134.806i 0.332447 0.244213i
553553 987.844i 1.78634i
554554 385.238 + 186.331i 0.695376 + 0.336337i
555555 −253.880 253.880i −0.457442 0.457442i
556556 −262.053 30.4315i −0.471319 0.0547330i
557557 −303.865 303.865i −0.545539 0.545539i 0.379608 0.925147i 0.376059π-0.376059\pi
−0.925147 + 0.379608i 0.876059π0.876059\pi
558558 161.298 + 463.496i 0.289065 + 0.830639i
559559 44.9894i 0.0804819i
560560 −1008.61 1629.76i −1.80109 2.91029i
561561 −192.943 −0.343928
562562 −257.722 + 89.6880i −0.458580 + 0.159587i
563563 −487.003 487.003i −0.865015 0.865015i 0.126901 0.991915i 0.459497π-0.459497\pi
−0.991915 + 0.126901i 0.959497π0.959497\pi
564564 −3.55960 + 30.6526i −0.00631135 + 0.0543486i
565565 687.730 + 687.730i 1.21722 + 1.21722i
566566 −175.260 + 362.349i −0.309646 + 0.640193i
567567 −567.117 −1.00021
568568 0.150865 + 0.0958746i 0.000265608 + 0.000168793i
569569 1119.37 1.96727 0.983633 0.180185i 0.0576696π-0.0576696\pi
0.983633 + 0.180185i 0.0576696π0.0576696\pi
570570 −292.404 + 604.545i −0.512990 + 1.06061i
571571 −150.035 + 150.035i −0.262758 + 0.262758i −0.826174 0.563416i 0.809487π-0.809487\pi
0.563416 + 0.826174i 0.309487π0.309487\pi
572572 −232.556 293.664i −0.406566 0.513399i
573573 24.7563 + 24.7563i 0.0432046 + 0.0432046i
574574 −542.578 1559.12i −0.945258 2.71624i
575575 1130.35 497.054i 1.96583 0.864441i
576576 432.751 202.975i 0.751303 0.352387i
577577 804.212 1.39378 0.696891 0.717177i 0.254566π-0.254566\pi
0.696891 + 0.717177i 0.254566π0.254566\pi
578578 −277.426 + 96.5449i −0.479975 + 0.167033i
579579 99.7610 99.7610i 0.172299 0.172299i
580580 57.6028 + 72.7391i 0.0993152 + 0.125412i
581581 −354.234 354.234i −0.609697 0.609697i
582582 −316.930 153.292i −0.544554 0.263388i
583583 123.801i 0.212352i
584584 130.432 + 82.8890i 0.223342 + 0.141933i
585585 474.406 0.810951
586586 −84.0139 + 173.699i −0.143368 + 0.296414i
587587 437.230 + 437.230i 0.744855 + 0.744855i 0.973508 0.228653i 0.0734322π-0.0734322\pi
−0.228653 + 0.973508i 0.573432π0.573432\pi
588588 −76.1473 + 655.724i −0.129502 + 1.11518i
589589 710.609 + 710.609i 1.20647 + 1.20647i
590590 581.610 202.402i 0.985780 0.343054i
591591 −95.0542 −0.160836
592592 275.390 + 444.988i 0.465186 + 0.751669i
593593 −1084.67 −1.82912 −0.914561 0.404449i 0.867463π-0.867463\pi
−0.914561 + 0.404449i 0.867463π0.867463\pi
594594 503.446 175.200i 0.847552 0.294950i
595595 1009.81 + 1009.81i 1.69716 + 1.69716i
596596 20.1205 173.263i 0.0337593 0.290710i
597597 192.045 192.045i 0.321684 0.321684i
598598 −329.181 11.9282i −0.550469 0.0199469i
599599 266.048i 0.444154i −0.975029 0.222077i 0.928716π-0.928716\pi
0.975029 0.222077i 0.0712836π-0.0712836\pi
600600 −518.785 + 115.621i −0.864642 + 0.192702i
601601 1140.44i 1.89757i −0.315924 0.948784i 0.602315π-0.602315\pi
0.315924 0.948784i 0.397685π-0.397685\pi
602602 −73.8837 + 152.754i −0.122730 + 0.253745i
603603 206.473 206.473i 0.342409 0.342409i
604604 378.396 + 477.827i 0.626484 + 0.791105i
605605 −313.827 313.827i −0.518722 0.518722i
606606 250.027 87.0102i 0.412587 0.143581i
607607 −35.5662 −0.0585934 −0.0292967 0.999571i 0.509327π-0.509327\pi
−0.0292967 + 0.999571i 0.509327π0.509327\pi
608608 616.771 760.024i 1.01443 1.25004i
609609 43.6997i 0.0717565i
610610 −847.100 + 294.793i −1.38869 + 0.483267i
611611 31.5654 31.5654i 0.0516619 0.0516619i
612612 −279.207 + 221.107i −0.456220 + 0.361285i
613613 558.143 558.143i 0.910510 0.910510i −0.0858021 0.996312i 0.527345π-0.527345\pi
0.996312 + 0.0858021i 0.0273453π0.0273453\pi
614614 −372.331 + 769.793i −0.606402 + 1.25373i
615615 −670.988 −1.09104
616616 307.337 + 1379.00i 0.498923 + 2.23864i
617617 838.248 1.35859 0.679293 0.733867i 0.262286π-0.262286\pi
0.679293 + 0.733867i 0.262286π0.262286\pi
618618 188.898 390.546i 0.305660 0.631951i
619619 155.904 155.904i 0.251865 0.251865i −0.569870 0.821735i 0.693006π-0.693006\pi
0.821735 + 0.569870i 0.193006π0.193006\pi
620620 −134.475 + 1158.00i −0.216895 + 1.86774i
621621 169.992 436.832i 0.273738 0.703434i
622622 −161.029 462.724i −0.258889 0.743929i
623623 −866.562 −1.39095
624624 138.012 + 32.4922i 0.221174 + 0.0520708i
625625 −915.157 −1.46425
626626 975.437 339.455i 1.55821 0.542260i
627627 350.040 350.040i 0.558278 0.558278i
628628 −194.303 22.5638i −0.309399 0.0359297i
629629 −275.717 275.717i −0.438342 0.438342i
630630 −1610.77 779.092i −2.55678 1.23665i
631631 −325.044 −0.515126 −0.257563 0.966262i 0.582919π-0.582919\pi
−0.257563 + 0.966262i 0.582919π0.582919\pi
632632 493.918 + 313.884i 0.781515 + 0.496652i
633633 194.933i 0.307951i
634634 289.678 598.909i 0.456906 0.944652i
635635 −675.213 + 675.213i −1.06333 + 1.06333i
636636 −29.0913 36.7355i −0.0457410 0.0577603i
637637 675.250 675.250i 1.06005 1.06005i
638638 −22.4799 64.5968i −0.0352349 0.101249i
639639 0.166877 0.000261154
640640 1135.36 + 13.5497i 1.77399 + 0.0211714i
641641 353.421i 0.551359i −0.961250 0.275680i 0.911097π-0.911097\pi
0.961250 0.275680i 0.0889029π-0.0889029\pi
642642 87.2615 + 250.750i 0.135921 + 0.390576i
643643 −733.825 733.825i −1.14125 1.14125i −0.988221 0.153031i 0.951097π-0.951097\pi
−0.153031 0.988221i 0.548903π-0.548903\pi
644644 1098.09 + 581.096i 1.70511 + 0.902323i
645645 48.7683 + 48.7683i 0.0756098 + 0.0756098i
646646 −317.555 + 656.545i −0.491572 + 1.01632i
647647 158.817i 0.245467i −0.992440 0.122733i 0.960834π-0.960834\pi
0.992440 0.122733i 0.0391660π-0.0391660\pi
648648 180.199 283.556i 0.278085 0.437586i
649649 −453.954 −0.699467
650650 692.176 + 334.789i 1.06489 + 0.515061i
651651 388.241 388.241i 0.596377 0.596377i
652652 −0.834178 + 7.18331i −0.00127941 + 0.0110173i
653653 −669.245 + 669.245i −1.02488 + 1.02488i −0.0251947 + 0.999683i 0.508021π0.508021\pi
−0.999683 + 0.0251947i 0.991979π0.991979\pi
654654 138.814 48.3078i 0.212254 0.0738651i
655655 1912.44i 2.91976i
656656 951.955 + 224.118i 1.45115 + 0.341644i
657657 144.275 0.219596
658658 −159.014 + 55.3371i −0.241662 + 0.0840990i
659659 405.338 + 405.338i 0.615081 + 0.615081i 0.944266 0.329185i 0.106774π-0.106774\pi
−0.329185 + 0.944266i 0.606774π0.606774\pi
660660 570.420 + 66.2412i 0.864272 + 0.100366i
661661 324.045 324.045i 0.490235 0.490235i −0.418145 0.908380i 0.637320π-0.637320\pi
0.908380 + 0.418145i 0.137320π0.137320\pi
662662 −162.742 78.7144i −0.245833 0.118904i
663663 −105.646 −0.159345
664664 289.672 64.5588i 0.436253 0.0972271i
665665 −3664.02 −5.50980
666666 439.803 + 212.723i 0.660365 + 0.319403i
667667 −56.0497 21.8115i −0.0840325 0.0327009i
668668 −772.075 974.952i −1.15580 1.45951i
669669 −138.698 + 138.698i −0.207322 + 0.207322i
670670 655.089 227.973i 0.977745 0.340258i
671671 661.172 0.985354
672672 −415.239 336.973i −0.617915 0.501447i
673673 −488.918 −0.726475 −0.363238 0.931697i 0.618329π-0.618329\pi
−0.363238 + 0.931697i 0.618329π0.618329\pi
674674 239.433 + 688.021i 0.355242 + 1.02080i
675675 −773.685 + 773.685i −1.14620 + 1.14620i
676676 292.339 + 369.157i 0.432455 + 0.546090i
677677 −346.064 + 346.064i −0.511173 + 0.511173i −0.914886 0.403713i 0.867719π-0.867719\pi
0.403713 + 0.914886i 0.367719π0.367719\pi
678678 244.295 + 118.160i 0.360316 + 0.174277i
679679 1920.84i 2.82893i
680680 −825.763 + 184.037i −1.21436 + 0.270642i
681681 −327.074 −0.480285
682682 374.180 773.615i 0.548650 1.13433i
683683 −235.665 235.665i −0.345045 0.345045i 0.513215 0.858260i 0.328454π-0.328454\pi
−0.858260 + 0.513215i 0.828454π0.828454\pi
684684 105.406 907.674i 0.154102 1.32701i
685685 531.790 531.790i 0.776336 0.776336i
686686 −2151.76 + 748.819i −3.13668 + 1.09157i
687687 132.478i 0.192836i
688688 −52.9002 85.4787i −0.0768898 0.124242i
689689 67.7871i 0.0983847i
690690 369.761 343.900i 0.535885 0.498406i
691691 −448.303 + 448.303i −0.648774 + 0.648774i −0.952697 0.303923i 0.901704π-0.901704\pi
0.303923 + 0.952697i 0.401704π0.401704\pi
692692 66.4318 572.060i 0.0959997 0.826677i
693693 932.659 + 932.659i 1.34583 + 1.34583i
694694 471.875 + 228.235i 0.679935 + 0.328869i
695695 −585.048 −0.841795
696696 21.8497 + 13.8854i 0.0313932 + 0.0199503i
697697 −728.702 −1.04548
698698 −232.198 + 480.069i −0.332662 + 0.687778i
699699 −175.656 175.656i −0.251296 0.251296i
700700 −1800.37 2273.45i −2.57195 3.24778i
701701 −601.042 601.042i −0.857406 0.857406i 0.133626 0.991032i 0.457338π-0.457338\pi
−0.991032 + 0.133626i 0.957338π0.957338\pi
702702 275.661 95.9306i 0.392679 0.136653i
703703 1000.42 1.42307
704704 −787.150 284.506i −1.11811 0.404128i
705705 68.4336i 0.0970689i
706706 766.484 266.738i 1.08567 0.377816i
707707 1021.36 + 1021.36i 1.44463 + 1.44463i
708708 134.702 106.672i 0.190257 0.150666i
709709 −431.081 + 431.081i −0.608012 + 0.608012i −0.942426 0.334414i 0.891462π-0.891462\pi
0.334414 + 0.942426i 0.391462π0.391462\pi
710710 0.356858 + 0.172604i 0.000502617 + 0.000243104i
711711 546.339 0.768410
712712 275.347 433.277i 0.386723 0.608535i
713713 −304.182 691.742i −0.426623 0.970186i
714714 358.703 + 173.496i 0.502385 + 0.242992i
715715 −587.406 587.406i −0.821547 0.821547i
716716 91.9967 792.207i 0.128487 1.10643i
717717 111.577 111.577i 0.155616 0.155616i
718718 82.2204 28.6129i 0.114513 0.0398508i
719719 −770.221 −1.07124 −0.535620 0.844459i 0.679922π-0.679922\pi
−0.535620 + 0.844459i 0.679922π0.679922\pi
720720 901.359 557.825i 1.25189 0.774756i
721721 2367.01 3.28296
722722 −377.699 1085.33i −0.523129 1.50323i
723723 −199.821 199.821i −0.276377 0.276377i
724724 −83.4219 + 718.366i −0.115224 + 0.992219i
725725 99.2711 + 99.2711i 0.136926 + 0.136926i
726726 −111.477 53.9189i −0.153550 0.0742684i
727727 453.890 0.624333 0.312166 0.950027i 0.398945π-0.398945\pi
0.312166 + 0.950027i 0.398945π0.398945\pi
728728 168.281 + 755.070i 0.231156 + 1.03718i
729729 86.6644i 0.118881i
730730 308.524 + 149.226i 0.422636 + 0.204419i
731731 52.9631 + 52.9631i 0.0724529 + 0.0724529i
732732 −196.190 + 155.365i −0.268019 + 0.212247i
733733 −300.003 300.003i −0.409281 0.409281i 0.472207 0.881488i 0.343458π-0.343458\pi
−0.881488 + 0.472207i 0.843458π0.843458\pi
734734 −33.7541 96.9937i −0.0459865 0.132144i
735735 1463.94i 1.99175i
736736 −639.460 + 364.399i −0.868831 + 0.495108i
737737 −511.305 −0.693766
738738 862.291 300.080i 1.16842 0.406612i
739739 −675.318 + 675.318i −0.913827 + 0.913827i −0.996571 0.0827442i 0.973632π-0.973632\pi
0.0827442 + 0.996571i 0.473632π0.473632\pi
740740 720.474 + 909.792i 0.973614 + 1.22945i
741741 191.664 191.664i 0.258656 0.258656i
742742 111.323 230.160i 0.150031 0.310189i
743743 1008.64 1.35753 0.678765 0.734356i 0.262516π-0.262516\pi
0.678765 + 0.734356i 0.262516π0.262516\pi
744744 70.7566 + 317.481i 0.0951030 + 0.426722i
745745 386.818i 0.519219i
746746 −25.4389 + 52.5948i −0.0341003 + 0.0705024i
747747 195.913 195.913i 0.262267 0.262267i
748748 619.484 + 71.9389i 0.828187 + 0.0961750i
749749 −1024.31 + 1024.31i −1.36756 + 1.36756i
750750 −594.843 + 207.007i −0.793125 + 0.276009i
751751 180.767i 0.240701i −0.992731 0.120351i 0.961598π-0.961598\pi
0.992731 0.120351i 0.0384019π-0.0384019\pi
752752 22.8577 97.0892i 0.0303958 0.129108i
753753 239.038i 0.317448i
754754 −12.3088 35.3698i −0.0163247 0.0469096i
755755 955.782 + 955.782i 1.26594 + 1.26594i
756756 −1093.50 126.985i −1.44643 0.167970i
757757 977.765 977.765i 1.29163 1.29163i 0.357854 0.933778i 0.383509π-0.383509\pi
0.933778 0.357854i 0.116491π-0.116491\pi
758758 183.393 379.165i 0.241944 0.500218i
759759 −340.747 + 149.838i −0.448942 + 0.197415i
760760 1164.23 1831.99i 1.53188 2.41052i
761761 989.507i 1.30027i −0.759818 0.650136i 0.774712π-0.774712\pi
0.759818 0.650136i 0.225288π-0.225288\pi
762762 −116.009 + 239.848i −0.152243 + 0.314761i
763763 567.053 + 567.053i 0.743189 + 0.743189i
764764 −70.2546 88.7153i −0.0919563 0.116120i
765765 −558.488 + 558.488i −0.730049 + 0.730049i
766766 44.4788 + 127.812i 0.0580664 + 0.166856i
767767 −248.562 −0.324070
768768 300.426 100.546i 0.391179 0.130919i
769769 80.4319i 0.104593i −0.998632 0.0522964i 0.983346π-0.983346\pi
0.998632 0.0522964i 0.0166541π-0.0166541\pi
770770 1029.78 + 2959.11i 1.33737 + 3.84300i
771771 42.2493 42.2493i 0.0547980 0.0547980i
772772 −357.499 + 283.107i −0.463081 + 0.366719i
773773 −178.335 + 178.335i −0.230705 + 0.230705i −0.812987 0.582282i 0.802160π-0.802160\pi
0.582282 + 0.812987i 0.302160π0.302160\pi
774774 −84.4827 40.8623i −0.109151 0.0527937i
775775 1763.91i 2.27601i
776776 960.414 + 610.342i 1.23765 + 0.786523i
777777 546.579i 0.703448i
778778 174.920 361.646i 0.224832 0.464840i
779779 1322.02 1322.02i 1.69707 1.69707i
780780 312.332 + 36.2702i 0.400426 + 0.0465003i
781781 −0.206626 0.206626i −0.000264566 0.000264566i
782782 401.565 373.480i 0.513510 0.477597i
783783 53.2932 0.0680628
784784 488.973 2076.94i 0.623690 2.64916i
785785 −433.791 −0.552600
786786 175.378 + 503.957i 0.223128 + 0.641167i
787787 386.055 + 386.055i 0.490541 + 0.490541i 0.908477 0.417936i 0.137246π-0.137246\pi
−0.417936 + 0.908477i 0.637246π0.637246\pi
788788 305.191 + 35.4410i 0.387298 + 0.0449758i
789789 −193.357 + 193.357i −0.245066 + 0.245066i
790790 1168.32 + 565.088i 1.47888 + 0.715302i
791791 1480.62i 1.87183i
792792 −762.675 + 169.976i −0.962973 + 0.214617i
793793 362.023 0.456524
794794 −158.661 + 328.032i −0.199825 + 0.413139i
795795 −73.4809 73.4809i −0.0924288 0.0924288i
796796 −688.205 + 544.996i −0.864579 + 0.684669i
797797 162.290 + 162.290i 0.203626 + 0.203626i 0.801552 0.597926i 0.204008π-0.204008\pi
−0.597926 + 0.801552i 0.704008π0.704008\pi
798798 −965.523 + 336.005i −1.20993 + 0.421058i
799799 74.3198i 0.0930160i
800800 1708.77 177.796i 2.13597 0.222245i
801801 479.263i 0.598331i
802802 −174.226 500.644i −0.217239 0.624245i
803803 −178.640 178.640i −0.222466 0.222466i
804804 151.720 120.148i 0.188706 0.149438i
805805 2567.57 + 999.162i 3.18953 + 1.24119i
806806 204.881 423.591i 0.254195 0.525548i
807807 474.037i 0.587407i
808808 −835.206 + 186.141i −1.03367 + 0.230373i
809809 1355.76i 1.67584i −0.545791 0.837921i 0.683771π-0.683771\pi
0.545791 0.837921i 0.316229π-0.316229\pi
810810 324.415 670.727i 0.400512 0.828058i
811811 643.692 + 643.692i 0.793702 + 0.793702i 0.982094 0.188392i 0.0603275π-0.0603275\pi
−0.188392 + 0.982094i 0.560327π0.560327\pi
812812 −16.2934 + 140.307i −0.0200658 + 0.172792i
813813 216.564 216.564i 0.266377 0.266377i
814814 −281.170 807.952i −0.345417 0.992570i
815815 16.0371i 0.0196774i
816816 −200.724 + 124.222i −0.245985 + 0.152233i
817817 −192.173 −0.235217
818818 322.310 + 926.171i 0.394022 + 1.13224i
819819 510.675 + 510.675i 0.623535 + 0.623535i
820820 2154.34 + 250.178i 2.62725 + 0.305095i
821821 826.135 + 826.135i 1.00625 + 1.00625i 0.999980 + 0.00627455i 0.00199726π0.00199726\pi
0.00627455 + 0.999980i 0.498003π0.498003\pi
822822 91.3674 188.902i 0.111153 0.229808i
823823 1360.74i 1.65339i 0.562647 + 0.826697i 0.309783π0.309783\pi
−0.562647 + 0.826697i 0.690217π0.690217\pi
824824 −752.110 + 1183.50i −0.912755 + 1.43628i
825825 868.887 1.05320
826826 843.951 + 408.199i 1.02173 + 0.494188i
827827 446.717 446.717i 0.540166 0.540166i −0.383412 0.923578i 0.625251π-0.625251\pi
0.923578 + 0.383412i 0.125251π0.125251\pi
828828 −321.382 + 607.313i −0.388143 + 0.733470i
829829 −233.334 + 233.334i −0.281464 + 0.281464i −0.833693 0.552229i 0.813778π-0.813778\pi
0.552229 + 0.833693i 0.313778π0.313778\pi
830830 621.587 216.314i 0.748901 0.260619i
831831 264.788 0.318638
832832 −431.002 155.781i −0.518032 0.187236i
833833 1589.86i 1.90859i
834834 −154.169 + 53.6512i −0.184855 + 0.0643299i
835835 −1950.16 1950.16i −2.33553 2.33553i
836836 −1254.39 + 993.363i −1.50046 + 1.18823i
837837 473.473 + 473.473i 0.565678 + 0.565678i
838838 −522.576 252.758i −0.623600 0.301620i
839839 −212.932 −0.253793 −0.126896 0.991916i 0.540502π-0.540502\pi
−0.126896 + 0.991916i 0.540502π0.540502\pi
840840 −1000.91 636.076i −1.19156 0.757233i
841841 834.162i 0.991869i
842842 343.419 710.017i 0.407860 0.843250i
843843 −119.394 + 119.394i −0.141630 + 0.141630i
844844 72.6807 625.872i 0.0861146 0.741554i
845845 738.412 + 738.412i 0.873861 + 0.873861i
846846 −30.6049 87.9444i −0.0361760 0.103953i
847847 675.639i 0.797684i
848848 79.7065 + 128.794i 0.0939936 + 0.151879i
849849 249.056i 0.293352i
850850 −1208.98 + 420.728i −1.42233 + 0.494974i
851851 −701.048 272.810i −0.823793 0.320576i
852852 0.109866 + 0.0127584i 0.000128951 + 1.49747e-5i
853853 319.516 + 319.516i 0.374579 + 0.374579i 0.869142 0.494563i 0.164672π-0.164672\pi
−0.494563 + 0.869142i 0.664672π0.664672\pi
854854 −1229.19 594.532i −1.43934 0.696173i
855855 2026.43i 2.37009i
856856 −186.679 837.618i −0.218083 0.978525i
857857 1427.30i 1.66547i 0.553674 + 0.832733i 0.313225π0.313225\pi
−0.553674 + 0.832733i 0.686775π0.686775\pi
858858 −208.658 100.923i −0.243191 0.117626i
859859 −281.675 281.675i −0.327911 0.327911i 0.523881 0.851792i 0.324484π-0.324484\pi
−0.851792 + 0.523881i 0.824484π0.824484\pi
860860 −138.397 174.764i −0.160927 0.203214i
861861 −722.286 722.286i −0.838892 0.838892i
862862 −216.573 622.333i −0.251245 0.721963i
863863 −1210.34 −1.40248 −0.701240 0.712925i 0.747370π-0.747370\pi
−0.701240 + 0.712925i 0.747370π0.747370\pi
864864 410.949 506.397i 0.475635 0.586108i
865865 1277.15i 1.47648i
866866 −368.797 1059.75i −0.425863 1.22373i
867867 −128.522 + 128.522i −0.148237 + 0.148237i
868868 −1391.28 + 1101.77i −1.60286 + 1.26932i
869869 −676.473 676.473i −0.778450 0.778450i
870870 51.6834 + 24.9981i 0.0594063 + 0.0287334i
871871 −279.964 −0.321428
872872 −463.703 + 103.345i −0.531770 + 0.118515i
873873 1062.35 1.21689
874874 −50.9515 + 1406.10i −0.0582969 + 1.60881i
875875 −2429.92 2429.92i −2.77705 2.77705i
876876 94.9854 + 11.0304i 0.108431 + 0.0125918i
877877 −427.618 + 427.618i −0.487592 + 0.487592i −0.907546 0.419954i 0.862046π-0.862046\pi
0.419954 + 0.907546i 0.362046π0.362046\pi
878878 351.550 + 1010.19i 0.400399 + 1.15056i
879879 119.389i 0.135824i
880880 −1806.75 425.362i −2.05312 0.483366i
881881 609.490i 0.691816i 0.938269 + 0.345908i 0.112429π0.112429\pi
−0.938269 + 0.345908i 0.887571π0.887571\pi
882882 −654.703 1881.31i −0.742293 2.13301i
883883 −737.504 + 737.504i −0.835225 + 0.835225i −0.988226 0.153001i 0.951106π-0.951106\pi
0.153001 + 0.988226i 0.451106π0.451106\pi
884884 339.197 + 39.3900i 0.383707 + 0.0445588i
885885 269.440 269.440i 0.304452 0.304452i
886886 496.583 + 240.186i 0.560478 + 0.271090i
887887 1110.67i 1.25216i −0.779759 0.626080i 0.784658π-0.784658\pi
0.779759 0.626080i 0.215342π-0.215342\pi
888888 273.287 + 173.674i 0.307756 + 0.195578i
889889 −1453.67 −1.63517
890890 495.710 1024.88i 0.556977 1.15155i
891891 −388.360 + 388.360i −0.435870 + 0.435870i
892892 497.033 393.605i 0.557211 0.441262i
893893 −134.832 134.832i −0.150988 0.150988i
894894 −35.4728 101.932i −0.0396787 0.114018i
895895 1768.64i 1.97614i
896896 1207.57 + 1236.74i 1.34773 + 1.38029i
897897 −186.575 + 82.0433i −0.207999 + 0.0914641i
898898 291.295 101.371i 0.324382 0.112886i
899899 60.7510 60.7510i 0.0675762 0.0675762i
900900 1257.36 995.715i 1.39707 1.10635i
901901 −79.8013 79.8013i −0.0885696 0.0885696i
902902 −1439.24 696.125i −1.59561 0.771758i
903903 104.993i 0.116272i
904904 −740.301 470.460i −0.818917 0.520421i
905905 1603.79i 1.77214i
906906 339.512 + 164.214i 0.374737 + 0.181251i
907907 −743.443 + 743.443i −0.819672 + 0.819672i −0.986060 0.166388i 0.946790π-0.946790\pi
0.166388 + 0.986060i 0.446790π0.446790\pi
908908 1050.14 + 121.949i 1.15654 + 0.134306i
909909 −564.874 + 564.874i −0.621423 + 0.621423i
910910 563.853 + 1620.25i 0.619618 + 1.78050i
911911 1154.54i 1.26733i −0.773607 0.633665i 0.781550π-0.781550\pi
0.773607 0.633665i 0.218450π-0.218450\pi
912912 138.791 589.521i 0.152183 0.646405i
913913 −485.157 −0.531388
914914 −715.206 + 248.894i −0.782501 + 0.272313i
915915 −392.432 + 392.432i −0.428887 + 0.428887i
916916 −49.3946 + 425.349i −0.0539242 + 0.464355i
917917 −2058.65 + 2058.65i −2.24499 + 2.24499i
918918 −211.584 + 437.450i −0.230484 + 0.476525i
919919 −1153.62 −1.25530 −0.627649 0.778497i 0.715983π-0.715983\pi
−0.627649 + 0.778497i 0.715983π0.715983\pi
920920 −1315.41 + 966.296i −1.42980 + 1.05032i
921921 529.106i 0.574490i
922922 −375.981 + 777.340i −0.407789 + 0.843102i
923923 −0.113138 0.113138i −0.000122576 0.000122576i
924924 542.724 + 685.334i 0.587363 + 0.741704i
925925 1241.65 + 1241.65i 1.34232 + 1.34232i
926926 −1012.92 + 352.498i −1.09386 + 0.380668i
927927 1309.11i 1.41220i
928928 −64.9756 52.7286i −0.0700168 0.0568196i
929929 841.858 0.906199 0.453099 0.891460i 0.350318π-0.350318\pi
0.453099 + 0.891460i 0.350318π0.350318\pi
930930 237.081 + 681.261i 0.254926 + 0.732539i
931931 −2884.34 2884.34i −3.09811 3.09811i
932932 498.486 + 629.473i 0.534857 + 0.675401i
933933 −214.364 214.364i −0.229758 0.229758i
934934 832.229 + 402.530i 0.891037 + 0.430974i
935935 1383.03 1.47918
936936 −417.601 + 93.0702i −0.446155 + 0.0994340i
937937 1678.33 1.79118 0.895588 0.444884i 0.146755π-0.146755\pi
0.895588 + 0.444884i 0.146755π0.146755\pi
938938 950.573 + 459.770i 1.01340 + 0.490160i
939939 451.886 451.886i 0.481241 0.481241i
940940 25.5154 219.720i 0.0271441 0.233744i
941941 −579.610 579.610i −0.615951 0.615951i 0.328539 0.944490i 0.393444π-0.393444\pi
−0.944490 + 0.328539i 0.893444π0.893444\pi
942942 −114.310 + 39.7803i −0.121349 + 0.0422296i
943943 −1286.92 + 565.902i −1.36471 + 0.600108i
944944 −472.260 + 292.268i −0.500276 + 0.309606i
945945 −2441.30 −2.58339
946946 54.0104 + 155.201i 0.0570935 + 0.164060i
947947 −463.504 + 463.504i −0.489445 + 0.489445i −0.908131 0.418686i 0.862491π-0.862491\pi
0.418686 + 0.908131i 0.362491π0.362491\pi
948948 359.690 + 41.7698i 0.379420 + 0.0440610i
949949 −97.8139 97.8139i −0.103071 0.103071i
950950 1430.06 2956.64i 1.50532 3.11225i
951951 411.652i 0.432862i
952952 −1087.00 690.787i −1.14181 0.725617i
953953 1575.01 1.65268 0.826342 0.563169i 0.190418π-0.190418\pi
0.826342 + 0.563169i 0.190418π0.190418\pi
954954 127.293 + 61.5686i 0.133431 + 0.0645373i
955955 −177.454 177.454i −0.185816 0.185816i
956956 −399.842 + 316.639i −0.418245 + 0.331212i
957957 −29.9254 29.9254i −0.0312701 0.0312701i
958958 303.774 + 872.907i 0.317092 + 0.911176i
959959 1144.89 1.19384
960960 636.070 298.339i 0.662573 0.310770i
961961 118.460 0.123267
962962 −153.954 442.392i −0.160035 0.459867i
963963 −566.505 566.505i −0.588271 0.588271i
964964 567.062 + 716.068i 0.588238 + 0.742809i
965965 −715.093 + 715.093i −0.741029 + 0.741029i
966966 768.221 + 27.8374i 0.795260 + 0.0288171i
967967 28.9033i 0.0298897i −0.999888 0.0149448i 0.995243π-0.995243\pi
0.999888 0.0149448i 0.00475727π-0.00475727\pi
968968 337.816 + 214.682i 0.348984 + 0.221779i
969969 451.266i 0.465703i
970970 2271.78 + 1098.80i 2.34204 + 1.13279i
971971 −944.362 + 944.362i −0.972567 + 0.972567i −0.999634 0.0270668i 0.991383π-0.991383\pi
0.0270668 + 0.999634i 0.491383π0.491383\pi
972972 108.612 935.283i 0.111741 0.962225i
973973 −629.776 629.776i −0.647251 0.647251i
974974 −245.634 705.841i −0.252191 0.724682i
975975 475.757 0.487956
976976 687.835 425.681i 0.704749 0.436148i
977977 527.542i 0.539961i −0.962866 0.269981i 0.912983π-0.912983\pi
0.962866 0.269981i 0.0870173π-0.0870173\pi
978978 1.47067 + 4.22602i 0.00150375 + 0.00432108i
979979 −593.419 + 593.419i −0.606148 + 0.606148i
980980 545.829 4700.27i 0.556968 4.79619i
981981 −313.616 + 313.616i −0.319690 + 0.319690i
982982 −1317.97 637.470i −1.34213 0.649155i
983983 −361.383 −0.367633 −0.183816 0.982961i 0.558845π-0.558845\pi
−0.183816 + 0.982961i 0.558845π0.558845\pi
984984 590.643 131.636i 0.600247 0.133776i
985985 681.354 0.691730
986986 56.1290 + 27.1483i 0.0569259 + 0.0275337i
987987 −73.6654 + 73.6654i −0.0746357 + 0.0746357i
988988 −686.837 + 543.913i −0.695179 + 0.550520i
989989 134.666 + 52.4046i 0.136164 + 0.0529875i
990990 −1636.57 + 569.532i −1.65310 + 0.575284i
991991 193.580 0.195338 0.0976690 0.995219i 0.468861π-0.468861\pi
0.0976690 + 0.995219i 0.468861π0.468861\pi
992992 −108.806 1045.72i −0.109683 1.05415i
993993 −111.858 −0.112647
994994 0.198341 + 0.569941i 0.000199538 + 0.000573381i
995995 −1376.59 + 1376.59i −1.38351 + 1.38351i
996996 143.961 114.004i 0.144539 0.114462i
997997 963.584 + 963.584i 0.966484 + 0.966484i 0.999456 0.0329724i 0.0104973π-0.0104973\pi
−0.0329724 + 0.999456i 0.510497π0.510497\pi
998998 −331.490 + 685.356i −0.332155 + 0.686729i
999999 666.571 0.667238
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 368.3.k.b.229.12 yes 176
16.13 even 4 inner 368.3.k.b.45.11 176
23.22 odd 2 inner 368.3.k.b.229.11 yes 176
368.45 odd 4 inner 368.3.k.b.45.12 yes 176
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
368.3.k.b.45.11 176 16.13 even 4 inner
368.3.k.b.45.12 yes 176 368.45 odd 4 inner
368.3.k.b.229.11 yes 176 23.22 odd 2 inner
368.3.k.b.229.12 yes 176 1.1 even 1 trivial