Properties

Label 637.2.q.i.491.1
Level 637637
Weight 22
Character 637.491
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(491,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.q (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: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 12.0.2346760387617129.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x123x11+x10+10x915x810x7+45x620x560x4+80x3++64 x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 491.1
Root 1.21245+0.727987i1.21245 + 0.727987i of defining polynomial
Character χ\chi == 637.491
Dual form 637.2.q.i.589.1

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+(1.99469+1.15163i)q2+(0.7366801.27597i)q3+(1.652522.86225i)q4+0.847292iq5+(2.93889+1.69677i)q6+3.00585iq8+(0.4146040.718115i)q9+(0.9757691.69008i)q10+(1.30198+0.751701i)q114.86951q12+(2.92329+2.11054i)q13+(1.081120.624183i)q15+(0.1565970.271234i)q16+(1.03570+1.79389i)q17+1.90989iq18+(0.0410731+0.0237136i)q19+(2.42516+1.40016i)q20+(1.731372.99882i)q22+(3.909356.77119i)q23+(3.835362.21435i)q24+4.28210q25+(8.261610.843323i)q265.64180q27+(0.6798541.17754i)q29+(1.43766+2.49010i)q30+7.86105iq31+(4.581562.64516i)q32+(1.91829+1.10753i)q334.77099iq34+(1.370282.37340i)q36+(5.804273.35110i)q370.109237q38+(0.5394605.28482i)q392.54683q40+(8.676225.00922i)q41+(4.632838.02430i)q43+4.96880iq44+(0.608453+0.351290i)q45+(15.5959+9.00428i)q460.360014iq47+(0.230724+0.399625i)q48+(8.54144+4.93141i)q50+3.05192q51+(10.87174.87945i)q52+2.71181q53+(11.25366.49729i)q54+(0.6369101.10316i)q550.0698773iq57+(2.71219+1.56588i)q58+(1.42132+0.820598i)q594.12590iq60+(2.260973.91612i)q61+(9.0530515.6803i)q62+12.8114q64+(1.78825+2.47688i)q655.10186q66+(1.769001.02133i)q67+(3.42303+5.92886i)q68+(5.75988+9.97641i)q69+(12.3096+7.10697i)q71+(2.15854+1.24624i)q726.76150iq73+(7.71847+13.3688i)q74+(3.154545.46382i)q75+(0.1357480.0783743i)q76+(5.01012+11.1628i)q78+11.6590q79+(0.2298140.132683i)q80+(2.91240+5.04442i)q81+(11.5376+19.9837i)q82+11.5362iq83+(1.519940.877541i)q85+21.3413iq86+(1.00167+1.73494i)q87+(2.259503.91357i)q88+(15.16528.75561i)q891.61823q9025.8411q92+(10.03045.79108i)q93+(0.414604+0.718115i)q94+(0.0200923+0.0348009i)q95+7.79456iq96+(0.3691250.213115i)q97+1.24663iq99+O(q100)q+(-1.99469 + 1.15163i) q^{2} +(-0.736680 - 1.27597i) q^{3} +(1.65252 - 2.86225i) q^{4} +0.847292i q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} +(0.414604 - 0.718115i) q^{9} +(-0.975769 - 1.69008i) q^{10} +(-1.30198 + 0.751701i) q^{11} -4.86951 q^{12} +(2.92329 + 2.11054i) q^{13} +(1.08112 - 0.624183i) q^{15} +(-0.156597 - 0.271234i) q^{16} +(-1.03570 + 1.79389i) q^{17} +1.90989i q^{18} +(0.0410731 + 0.0237136i) q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(-3.90935 - 6.77119i) q^{23} +(3.83536 - 2.21435i) q^{24} +4.28210 q^{25} +(-8.26161 - 0.843323i) q^{26} -5.64180 q^{27} +(-0.679854 - 1.17754i) q^{29} +(-1.43766 + 2.49010i) q^{30} +7.86105i q^{31} +(-4.58156 - 2.64516i) q^{32} +(1.91829 + 1.10753i) q^{33} -4.77099i q^{34} +(-1.37028 - 2.37340i) q^{36} +(5.80427 - 3.35110i) q^{37} -0.109237 q^{38} +(0.539460 - 5.28482i) q^{39} -2.54683 q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +4.96880i q^{44} +(0.608453 + 0.351290i) q^{45} +(15.5959 + 9.00428i) q^{46} -0.360014i q^{47} +(-0.230724 + 0.399625i) q^{48} +(-8.54144 + 4.93141i) q^{50} +3.05192 q^{51} +(10.8717 - 4.87945i) q^{52} +2.71181 q^{53} +(11.2536 - 6.49729i) q^{54} +(-0.636910 - 1.10316i) q^{55} -0.0698773i q^{57} +(2.71219 + 1.56588i) q^{58} +(1.42132 + 0.820598i) q^{59} -4.12590i q^{60} +(2.26097 - 3.91612i) q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(-1.78825 + 2.47688i) q^{65} -5.10186 q^{66} +(1.76900 - 1.02133i) q^{67} +(3.42303 + 5.92886i) q^{68} +(-5.75988 + 9.97641i) q^{69} +(12.3096 + 7.10697i) q^{71} +(2.15854 + 1.24624i) q^{72} -6.76150i q^{73} +(-7.71847 + 13.3688i) q^{74} +(-3.15454 - 5.46382i) q^{75} +(0.135748 - 0.0783743i) q^{76} +(5.01012 + 11.1628i) q^{78} +11.6590 q^{79} +(0.229814 - 0.132683i) q^{80} +(2.91240 + 5.04442i) q^{81} +(-11.5376 + 19.9837i) q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +21.3413i q^{86} +(-1.00167 + 1.73494i) q^{87} +(-2.25950 - 3.91357i) q^{88} +(15.1652 - 8.75561i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(10.0304 - 5.79108i) q^{93} +(0.414604 + 0.718115i) q^{94} +(-0.0200923 + 0.0348009i) q^{95} +7.79456i q^{96} +(-0.369125 - 0.213115i) q^{97} +1.24663i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+3q3+4q4+9q6q912q1012q112q12+2q1312q158q1617q17+9q19+3q2015q22+3q23+15q24+10q2515q26++3q97+O(q100) 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26}+ \cdots + 3 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.99469 + 1.15163i −1.41046 + 0.814328i −0.995431 0.0954820i 0.969561π-0.969561\pi
−0.415026 + 0.909810i 0.636227π0.636227\pi
33 −0.736680 1.27597i −0.425323 0.736680i 0.571128 0.820861i 0.306506π-0.306506\pi
−0.996451 + 0.0841807i 0.973173π0.973173\pi
44 1.65252 2.86225i 0.826259 1.43112i
55 0.847292i 0.378920i 0.981888 + 0.189460i 0.0606738π0.0606738\pi
−0.981888 + 0.189460i 0.939326π0.939326\pi
66 2.93889 + 1.69677i 1.19980 + 0.692704i
77 0 0
88 3.00585i 1.06273i
99 0.414604 0.718115i 0.138201 0.239372i
1010 −0.975769 1.69008i −0.308565 0.534451i
1111 −1.30198 + 0.751701i −0.392563 + 0.226646i −0.683270 0.730166i 0.739443π-0.739443\pi
0.290707 + 0.956812i 0.406110π0.406110\pi
1212 −4.86951 −1.40571
1313 2.92329 + 2.11054i 0.810774 + 0.585360i
1414 0 0
1515 1.08112 0.624183i 0.279143 0.161163i
1616 −0.156597 0.271234i −0.0391492 0.0678085i
1717 −1.03570 + 1.79389i −0.251194 + 0.435081i −0.963855 0.266428i 0.914157π-0.914157\pi
0.712661 + 0.701509i 0.247490π0.247490\pi
1818 1.90989i 0.450164i
1919 0.0410731 + 0.0237136i 0.00942282 + 0.00544027i 0.504704 0.863292i 0.331602π-0.331602\pi
−0.495281 + 0.868733i 0.664935π0.664935\pi
2020 2.42516 + 1.40016i 0.542282 + 0.313086i
2121 0 0
2222 1.73137 2.99882i 0.369129 0.639350i
2323 −3.90935 6.77119i −0.815156 1.41189i −0.909216 0.416325i 0.863318π-0.863318\pi
0.0940598 0.995567i 0.470016π-0.470016\pi
2424 3.83536 2.21435i 0.782891 0.452002i
2525 4.28210 0.856419
2626 −8.26161 0.843323i −1.62024 0.165389i
2727 −5.64180 −1.08577
2828 0 0
2929 −0.679854 1.17754i −0.126246 0.218664i 0.795973 0.605331i 0.206959π-0.206959\pi
−0.922219 + 0.386668i 0.873626π0.873626\pi
3030 −1.43766 + 2.49010i −0.262480 + 0.454628i
3131 7.86105i 1.41189i 0.708269 + 0.705943i 0.249477π0.249477\pi
−0.708269 + 0.705943i 0.750523π0.750523\pi
3232 −4.58156 2.64516i −0.809912 0.467603i
3333 1.91829 + 1.10753i 0.333932 + 0.192796i
3434 4.77099i 0.818218i
3535 0 0
3636 −1.37028 2.37340i −0.228380 0.395566i
3737 5.80427 3.35110i 0.954216 0.550917i 0.0598278 0.998209i 0.480945π-0.480945\pi
0.894388 + 0.447292i 0.147612π0.147612\pi
3838 −0.109237 −0.0177206
3939 0.539460 5.28482i 0.0863827 0.846248i
4040 −2.54683 −0.402689
4141 8.67622 5.00922i 1.35500 0.782309i 0.366054 0.930594i 0.380709π-0.380709\pi
0.988945 + 0.148285i 0.0473754π0.0473754\pi
4242 0 0
4343 4.63283 8.02430i 0.706500 1.22369i −0.259647 0.965704i 0.583606π-0.583606\pi
0.966147 0.257991i 0.0830604π-0.0830604\pi
4444 4.96880i 0.749075i
4545 0.608453 + 0.351290i 0.0907028 + 0.0523673i
4646 15.5959 + 9.00428i 2.29948 + 1.32761i
4747 0.360014i 0.0525134i −0.999655 0.0262567i 0.991641π-0.991641\pi
0.999655 0.0262567i 0.00835873π-0.00835873\pi
4848 −0.230724 + 0.399625i −0.0333021 + 0.0576810i
4949 0 0
5050 −8.54144 + 4.93141i −1.20794 + 0.697406i
5151 3.05192 0.427355
5252 10.8717 4.87945i 1.50763 0.676658i
5353 2.71181 0.372496 0.186248 0.982503i 0.440367π-0.440367\pi
0.186248 + 0.982503i 0.440367π0.440367\pi
5454 11.2536 6.49729i 1.53143 0.884169i
5555 −0.636910 1.10316i −0.0858809 0.148750i
5656 0 0
5757 0.0698773i 0.00925548i
5858 2.71219 + 1.56588i 0.356128 + 0.205611i
5959 1.42132 + 0.820598i 0.185040 + 0.106833i 0.589658 0.807653i 0.299262π-0.299262\pi
−0.404619 + 0.914486i 0.632596π0.632596\pi
6060 4.12590i 0.532651i
6161 2.26097 3.91612i 0.289488 0.501407i −0.684200 0.729295i 0.739848π-0.739848\pi
0.973688 + 0.227887i 0.0731817π0.0731817\pi
6262 −9.05305 15.6803i −1.14974 1.99140i
6363 0 0
6464 12.8114 1.60143
6565 −1.78825 + 2.47688i −0.221805 + 0.307219i
6666 −5.10186 −0.627995
6767 1.76900 1.02133i 0.216117 0.124775i −0.388034 0.921645i 0.626846π-0.626846\pi
0.604151 + 0.796870i 0.293512π0.293512\pi
6868 3.42303 + 5.92886i 0.415103 + 0.718980i
6969 −5.75988 + 9.97641i −0.693409 + 1.20102i
7070 0 0
7171 12.3096 + 7.10697i 1.46088 + 0.843442i 0.999052 0.0435255i 0.0138590π-0.0138590\pi
0.461832 + 0.886967i 0.347192π0.347192\pi
7272 2.15854 + 1.24624i 0.254387 + 0.146870i
7373 6.76150i 0.791373i −0.918386 0.395687i 0.870507π-0.870507\pi
0.918386 0.395687i 0.129493π-0.129493\pi
7474 −7.71847 + 13.3688i −0.897253 + 1.55409i
7575 −3.15454 5.46382i −0.364255 0.630907i
7676 0.135748 0.0783743i 0.0155714 0.00899015i
7777 0 0
7878 5.01012 + 11.1628i 0.567284 + 1.26394i
7979 11.6590 1.31175 0.655873 0.754871i 0.272301π-0.272301\pi
0.655873 + 0.754871i 0.272301π0.272301\pi
8080 0.229814 0.132683i 0.0256940 0.0148344i
8181 2.91240 + 5.04442i 0.323600 + 0.560491i
8282 −11.5376 + 19.9837i −1.27411 + 2.20683i
8383 11.5362i 1.26627i 0.774043 + 0.633133i 0.218232π0.218232\pi
−0.774043 + 0.633133i 0.781768π0.781768\pi
8484 0 0
8585 −1.51994 0.877541i −0.164861 0.0951826i
8686 21.3413i 2.30129i
8787 −1.00167 + 1.73494i −0.107390 + 0.186006i
8888 −2.25950 3.91357i −0.240863 0.417188i
8989 15.1652 8.75561i 1.60750 0.928093i 0.617577 0.786510i 0.288114π-0.288114\pi
0.989927 0.141582i 0.0452189π-0.0452189\pi
9090 −1.61823 −0.170576
9191 0 0
9292 −25.8411 −2.69412
9393 10.0304 5.79108i 1.04011 0.600507i
9494 0.414604 + 0.718115i 0.0427631 + 0.0740679i
9595 −0.0200923 + 0.0348009i −0.00206143 + 0.00357050i
9696 7.79456i 0.795529i
9797 −0.369125 0.213115i −0.0374790 0.0216385i 0.481143 0.876642i 0.340222π-0.340222\pi
−0.518622 + 0.855003i 0.673555π0.673555\pi
9898 0 0
9999 1.24663i 0.125291i
100100 7.07624 12.2564i 0.707624 1.22564i
101101 −4.83499 8.37444i −0.481099 0.833288i 0.518666 0.854977i 0.326429π-0.326429\pi
−0.999765 + 0.0216891i 0.993096π0.993096\pi
102102 −6.08763 + 3.51469i −0.602765 + 0.348007i
103103 −9.97823 −0.983185 −0.491592 0.870825i 0.663585π-0.663585\pi
−0.491592 + 0.870825i 0.663585π0.663585\pi
104104 −6.34397 + 8.78695i −0.622078 + 0.861631i
105105 0 0
106106 −5.40922 + 3.12301i −0.525390 + 0.303334i
107107 −4.93111 8.54094i −0.476709 0.825684i 0.522935 0.852373i 0.324837π-0.324837\pi
−0.999644 + 0.0266888i 0.991504π0.991504\pi
108108 −9.32319 + 16.1482i −0.897124 + 1.55386i
109109 11.6055i 1.11161i −0.831314 0.555803i 0.812411π-0.812411\pi
0.831314 0.555803i 0.187589π-0.187589\pi
110110 2.54087 + 1.46697i 0.242263 + 0.139870i
111111 −8.55178 4.93737i −0.811699 0.468635i
112112 0 0
113113 1.73879 3.01167i 0.163572 0.283314i −0.772576 0.634923i 0.781032π-0.781032\pi
0.936147 + 0.351609i 0.114365π0.114365\pi
114114 0.0804731 + 0.139383i 0.00753699 + 0.0130545i
115115 5.73718 3.31236i 0.534994 0.308879i
116116 −4.49388 −0.417247
117117 2.72762 1.22422i 0.252168 0.113179i
118118 −3.78011 −0.347987
119119 0 0
120120 1.87620 + 3.24967i 0.171273 + 0.296653i
121121 −4.36989 + 7.56887i −0.397263 + 0.688079i
122122 10.4152i 0.942951i
123123 −12.7832 7.38039i −1.15262 0.665467i
124124 22.5003 + 12.9905i 2.02058 + 1.16658i
125125 7.86464i 0.703435i
126126 0 0
127127 −7.84992 13.5965i −0.696567 1.20649i −0.969649 0.244499i 0.921376π-0.921376\pi
0.273082 0.961991i 0.411957π-0.411957\pi
128128 −16.3917 + 9.46373i −1.44883 + 0.836483i
129129 −13.6517 −1.20196
130130 0.714541 7.00000i 0.0626694 0.613940i
131131 2.54517 0.222373 0.111186 0.993800i 0.464535π-0.464535\pi
0.111186 + 0.993800i 0.464535π0.464535\pi
132132 6.34003 3.66042i 0.551829 0.318598i
133133 0 0
134134 −2.35240 + 4.07447i −0.203216 + 0.351981i
135135 4.78025i 0.411419i
136136 −5.39215 3.11316i −0.462373 0.266951i
137137 1.61490 + 0.932362i 0.137970 + 0.0796571i 0.567396 0.823445i 0.307951π-0.307951\pi
−0.429426 + 0.903102i 0.641284π0.641284\pi
138138 26.5331i 2.25865i
139139 7.80462 13.5180i 0.661979 1.14658i −0.318116 0.948052i 0.603050π-0.603050\pi
0.980095 0.198530i 0.0636166π-0.0636166\pi
140140 0 0
141141 −0.459366 + 0.265215i −0.0386856 + 0.0223351i
142142 −32.7385 −2.74735
143143 −5.39257 0.550459i −0.450949 0.0460317i
144144 −0.259703 −0.0216419
145145 0.997721 0.576035i 0.0828562 0.0478371i
146146 7.78676 + 13.4871i 0.644437 + 1.11620i
147147 0 0
148148 22.1510i 1.82080i
149149 −5.51106 3.18181i −0.451484 0.260664i 0.256973 0.966419i 0.417275π-0.417275\pi
−0.708457 + 0.705754i 0.750608π0.750608\pi
150150 12.5846 + 7.26574i 1.02753 + 0.593245i
151151 0.664094i 0.0540432i 0.999635 + 0.0270216i 0.00860228π0.00860228\pi
−0.999635 + 0.0270216i 0.991398π0.991398\pi
152152 −0.0712794 + 0.123460i −0.00578152 + 0.0100139i
153153 0.858811 + 1.48750i 0.0694307 + 0.120258i
154154 0 0
155155 −6.66060 −0.534992
156156 −14.2350 10.2773i −1.13971 0.822844i
157157 16.5760 1.32291 0.661453 0.749986i 0.269940π-0.269940\pi
0.661453 + 0.749986i 0.269940π0.269940\pi
158158 −23.2562 + 13.4269i −1.85016 + 1.06819i
159159 −1.99774 3.46019i −0.158431 0.274411i
160160 2.24122 3.88191i 0.177184 0.306892i
161161 0 0
162162 −11.6186 6.70802i −0.912846 0.527032i
163163 −7.83863 4.52563i −0.613969 0.354475i 0.160548 0.987028i 0.448674π-0.448674\pi
−0.774517 + 0.632553i 0.782007π0.782007\pi
164164 33.1113i 2.58556i
165165 −0.938398 + 1.62535i −0.0730542 + 0.126534i
166166 −13.2855 23.0112i −1.03116 1.78601i
167167 2.30156 1.32880i 0.178100 0.102826i −0.408300 0.912848i 0.633878π-0.633878\pi
0.586400 + 0.810022i 0.300545π0.300545\pi
168168 0 0
169169 4.09120 + 12.3395i 0.314708 + 0.949189i
170170 4.04242 0.310039
171171 0.0340582 0.0196635i 0.00260449 0.00150370i
172172 −15.3117 26.5206i −1.16750 2.02218i
173173 −9.79352 + 16.9629i −0.744588 + 1.28966i 0.205799 + 0.978594i 0.434021π0.434021\pi
−0.950387 + 0.311070i 0.899313π0.899313\pi
174174 4.61423i 0.349804i
175175 0 0
176176 0.407774 + 0.235428i 0.0307371 + 0.0177461i
177177 2.41807i 0.181754i
178178 −20.1665 + 34.9294i −1.51154 + 2.61807i
179179 −1.44666 2.50569i −0.108129 0.187284i 0.806884 0.590711i 0.201152π-0.201152\pi
−0.915012 + 0.403426i 0.867819π0.867819\pi
180180 2.01096 1.16103i 0.149888 0.0865379i
181181 1.36804 0.101686 0.0508429 0.998707i 0.483809π-0.483809\pi
0.0508429 + 0.998707i 0.483809π0.483809\pi
182182 0 0
183183 −6.66245 −0.492503
184184 20.3532 11.7509i 1.50046 0.866289i
185185 2.83936 + 4.91791i 0.208754 + 0.361572i
186186 −13.3384 + 23.1028i −0.978019 + 1.69398i
187187 3.11415i 0.227729i
188188 −1.03045 0.594929i −0.0751531 0.0433897i
189189 0 0
190190 0.0925559i 0.00671471i
191191 0.756625 1.31051i 0.0547475 0.0948254i −0.837353 0.546663i 0.815898π-0.815898\pi
0.892100 + 0.451837i 0.149231π0.149231\pi
192192 −9.43792 16.3470i −0.681123 1.17974i
193193 6.02229 3.47697i 0.433494 0.250278i −0.267340 0.963602i 0.586145π-0.586145\pi
0.700834 + 0.713324i 0.252811π0.252811\pi
194194 0.981719 0.0704834
195195 4.47778 + 0.457080i 0.320661 + 0.0327322i
196196 0 0
197197 −13.4037 + 7.73860i −0.954971 + 0.551353i −0.894622 0.446825i 0.852555π-0.852555\pi
−0.0603494 + 0.998177i 0.519221π0.519221\pi
198198 −1.43566 2.48664i −0.102028 0.176718i
199199 −3.30764 + 5.72901i −0.234473 + 0.406118i −0.959119 0.283002i 0.908670π-0.908670\pi
0.724647 + 0.689121i 0.242003π0.242003\pi
200200 12.8713i 0.910140i
201201 −2.60637 1.50479i −0.183839 0.106140i
202202 19.2886 + 11.1363i 1.35714 + 0.783545i
203203 0 0
204204 5.04336 8.73535i 0.353106 0.611597i
205205 4.24427 + 7.35129i 0.296433 + 0.513436i
206206 19.9035 11.4913i 1.38674 0.800634i
207207 −6.48333 −0.450622
208208 0.114674 1.12340i 0.00795118 0.0778937i
209209 −0.0713021 −0.00493207
210210 0 0
211211 4.04714 + 7.00986i 0.278617 + 0.482578i 0.971041 0.238912i 0.0767907π-0.0767907\pi
−0.692424 + 0.721490i 0.743457π0.743457\pi
212212 4.48132 7.76187i 0.307778 0.533088i
213213 20.9423i 1.43494i
214214 19.6721 + 11.3577i 1.34475 + 0.776394i
215215 6.79892 + 3.92536i 0.463683 + 0.267707i
216216 16.9584i 1.15387i
217217 0 0
218218 13.3653 + 23.1493i 0.905211 + 1.56787i
219219 −8.62745 + 4.98106i −0.582989 + 0.336589i
220220 −4.21002 −0.283840
221221 −6.81373 + 3.05815i −0.458341 + 0.205713i
222222 22.7442 1.52649
223223 −13.9067 + 8.02903i −0.931261 + 0.537664i −0.887210 0.461366i 0.847360π-0.847360\pi
−0.0440506 + 0.999029i 0.514026π0.514026\pi
224224 0 0
225225 1.77537 3.07504i 0.118358 0.205002i
226226 8.00979i 0.532804i
227227 −1.12220 0.647903i −0.0744831 0.0430029i 0.462296 0.886726i 0.347026π-0.347026\pi
−0.536779 + 0.843723i 0.680359π0.680359\pi
228228 −0.200006 0.115474i −0.0132457 0.00764742i
229229 20.8175i 1.37566i 0.725871 + 0.687831i 0.241437π0.241437\pi
−0.725871 + 0.687831i 0.758563π0.758563\pi
230230 −7.62925 + 13.2142i −0.503058 + 0.871322i
231231 0 0
232232 3.53951 2.04354i 0.232380 0.134165i
233233 13.3043 0.871591 0.435796 0.900046i 0.356467π-0.356467\pi
0.435796 + 0.900046i 0.356467π0.356467\pi
234234 −4.03090 + 5.58314i −0.263508 + 0.364981i
235235 0.305037 0.0198984
236236 4.69751 2.71211i 0.305782 0.176543i
237237 −8.58899 14.8766i −0.557915 0.966337i
238238 0 0
239239 13.3652i 0.864525i −0.901748 0.432263i 0.857715π-0.857715\pi
0.901748 0.432263i 0.142285π-0.142285\pi
240240 −0.338599 0.195490i −0.0218565 0.0126188i
241241 −0.722398 0.417076i −0.0465337 0.0268663i 0.476553 0.879146i 0.341886π-0.341886\pi
−0.523086 + 0.852280i 0.675219π0.675219\pi
242242 20.1300i 1.29401i
243243 −4.17170 + 7.22559i −0.267614 + 0.463522i
244244 −7.47259 12.9429i −0.478384 0.828585i
245245 0 0
246246 33.9980 2.16763
247247 0.0700199 + 0.156008i 0.00445526 + 0.00992657i
248248 −23.6291 −1.50045
249249 14.7199 8.49852i 0.932834 0.538572i
250250 −9.05718 15.6875i −0.572827 0.992165i
251251 −13.6360 + 23.6183i −0.860699 + 1.49078i 0.0105555 + 0.999944i 0.496640π0.496640\pi
−0.871255 + 0.490831i 0.836693π0.836693\pi
252252 0 0
253253 10.1798 + 5.87733i 0.640000 + 0.369504i
254254 31.3163 + 18.0804i 1.96496 + 1.13447i
255255 2.58587i 0.161933i
256256 8.98607 15.5643i 0.561630 0.972771i
257257 −3.27594 5.67409i −0.204348 0.353940i 0.745577 0.666419i 0.232174π-0.232174\pi
−0.949925 + 0.312479i 0.898841π0.898841\pi
258258 27.2308 15.7217i 1.69532 0.978791i
259259 0 0
260260 4.13432 + 9.21148i 0.256399 + 0.571272i
261261 −1.12748 −0.0697893
262262 −5.07682 + 2.93110i −0.313647 + 0.181084i
263263 11.2945 + 19.5627i 0.696450 + 1.20629i 0.969689 + 0.244341i 0.0785717π0.0785717\pi
−0.273239 + 0.961946i 0.588095π0.588095\pi
264264 −3.32906 + 5.76610i −0.204889 + 0.354879i
265265 2.29770i 0.141146i
266266 0 0
267267 −22.3437 12.9002i −1.36742 0.789478i
268268 6.75107i 0.412387i
269269 8.00065 13.8575i 0.487808 0.844909i −0.512093 0.858930i 0.671130π-0.671130\pi
0.999902 + 0.0140210i 0.00446317π0.00446317\pi
270270 5.50510 + 9.53511i 0.335030 + 0.580288i
271271 −7.58582 + 4.37967i −0.460806 + 0.266046i −0.712383 0.701791i 0.752384π-0.752384\pi
0.251577 + 0.967837i 0.419051π0.419051\pi
272272 0.648750 0.0393363
273273 0 0
274274 −4.29496 −0.259468
275275 −5.57522 + 3.21886i −0.336199 + 0.194104i
276276 19.0366 + 32.9724i 1.14587 + 1.98471i
277277 −9.95914 + 17.2497i −0.598387 + 1.03644i 0.394673 + 0.918822i 0.370858π0.370858\pi
−0.993059 + 0.117614i 0.962475π0.962475\pi
278278 35.9522i 2.15627i
279279 5.64514 + 3.25922i 0.337965 + 0.195124i
280280 0 0
281281 14.0234i 0.836566i 0.908317 + 0.418283i 0.137368π0.137368\pi
−0.908317 + 0.418283i 0.862632π0.862632\pi
282282 0.610861 1.05804i 0.0363762 0.0630055i
283283 −0.506295 0.876929i −0.0300961 0.0521280i 0.850585 0.525838i 0.176248π-0.176248\pi
−0.880681 + 0.473710i 0.842915π0.842915\pi
284284 40.6838 23.4888i 2.41414 1.39380i
285285 0.0592065 0.00350709
286286 11.3904 5.11227i 0.673530 0.302295i
287287 0 0
288288 −3.79906 + 2.19339i −0.223862 + 0.129247i
289289 6.35465 + 11.0066i 0.373803 + 0.647446i
290290 −1.32676 + 2.29802i −0.0779101 + 0.134944i
291291 0.627989i 0.0368134i
292292 −19.3531 11.1735i −1.13255 0.653879i
293293 0.172543 + 0.0996176i 0.0100801 + 0.00581972i 0.505032 0.863101i 0.331481π-0.331481\pi
−0.494952 + 0.868921i 0.664814π0.664814\pi
294294 0 0
295295 −0.695286 + 1.20427i −0.0404811 + 0.0701153i
296296 10.0729 + 17.4467i 0.585474 + 1.01407i
297297 7.34554 4.24095i 0.426232 0.246085i
298298 14.6571 0.849065
299299 2.86276 28.0450i 0.165558 1.62188i
300300 −20.8517 −1.20387
301301 0 0
302302 −0.764792 1.32466i −0.0440088 0.0762256i
303303 −7.12368 + 12.3386i −0.409245 + 0.708833i
304304 0.0148539i 0.000851930i
305305 3.31809 + 1.91570i 0.189993 + 0.109693i
306306 −3.42612 1.97807i −0.195858 0.113079i
307307 27.2004i 1.55241i −0.630482 0.776204i 0.717143π-0.717143\pi
0.630482 0.776204i 0.282857π-0.282857\pi
308308 0 0
309309 7.35077 + 12.7319i 0.418171 + 0.724293i
310310 13.2858 7.67057i 0.754584 0.435659i
311311 27.1009 1.53675 0.768376 0.639999i 0.221065π-0.221065\pi
0.768376 + 0.639999i 0.221065π0.221065\pi
312312 15.8854 + 1.62153i 0.899331 + 0.0918013i
313313 22.0785 1.24795 0.623975 0.781445i 0.285517π-0.285517\pi
0.623975 + 0.781445i 0.285517π0.285517\pi
314314 −33.0639 + 19.0894i −1.86590 + 1.07728i
315315 0 0
316316 19.2668 33.3711i 1.08384 1.87727i
317317 7.06823i 0.396991i 0.980102 + 0.198496i 0.0636056π0.0636056\pi
−0.980102 + 0.198496i 0.936394π0.936394\pi
318318 7.96973 + 4.60133i 0.446920 + 0.258030i
319319 1.77032 + 1.02209i 0.0991188 + 0.0572263i
320320 10.8550i 0.606813i
321321 −7.26531 + 12.5839i −0.405510 + 0.702364i
322322 0 0
323323 −0.0850789 + 0.0491204i −0.00473392 + 0.00273313i
324324 19.2512 1.06951
325325 12.5178 + 9.03756i 0.694362 + 0.501313i
326326 20.8475 1.15464
327327 −14.8082 + 8.54955i −0.818898 + 0.472791i
328328 15.0569 + 26.0794i 0.831381 + 1.43999i
329329 0 0
330330 4.32276i 0.237960i
331331 −5.70588 3.29429i −0.313623 0.181071i 0.334923 0.942245i 0.391290π-0.391290\pi
−0.648547 + 0.761175i 0.724623π0.724623\pi
332332 33.0195 + 19.0638i 1.81218 + 1.04626i
333333 5.55751i 0.304550i
334334 −3.06059 + 5.30110i −0.167468 + 0.290063i
335335 0.865365 + 1.49886i 0.0472799 + 0.0818912i
336336 0 0
337337 −4.22290 −0.230036 −0.115018 0.993363i 0.536693π-0.536693\pi
−0.115018 + 0.993363i 0.536693π0.536693\pi
338338 −22.3712 19.9018i −1.21683 1.08251i
339339 −5.12373 −0.278283
340340 −5.02347 + 2.90030i −0.272436 + 0.157291i
341341 −5.90916 10.2350i −0.319999 0.554254i
342342 −0.0452902 + 0.0784450i −0.00244902 + 0.00424182i
343343 0 0
344344 24.1198 + 13.9256i 1.30045 + 0.750817i
345345 −8.45293 4.88030i −0.455091 0.262747i
346346 45.1142i 2.42535i
347347 4.54739 7.87631i 0.244117 0.422822i −0.717766 0.696284i 0.754835π-0.754835\pi
0.961883 + 0.273462i 0.0881687π0.0881687\pi
348348 3.31056 + 5.73405i 0.177464 + 0.307378i
349349 −7.98521 + 4.61026i −0.427439 + 0.246782i −0.698255 0.715849i 0.746040π-0.746040\pi
0.270816 + 0.962631i 0.412706π0.412706\pi
350350 0 0
351351 −16.4926 11.9073i −0.880310 0.635564i
352352 7.95349 0.423922
353353 1.86584 1.07724i 0.0993087 0.0573359i −0.449523 0.893269i 0.648406π-0.648406\pi
0.548832 + 0.835933i 0.315073π0.315073\pi
354354 2.78473 + 4.82330i 0.148007 + 0.256356i
355355 −6.02167 + 10.4298i −0.319597 + 0.553559i
356356 57.8752i 3.06738i
357357 0 0
358358 5.77128 + 3.33205i 0.305021 + 0.176104i
359359 8.55756i 0.451651i 0.974168 + 0.225825i 0.0725079π0.0725079\pi
−0.974168 + 0.225825i 0.927492π0.927492\pi
360360 −1.05593 + 1.82892i −0.0556521 + 0.0963923i
361361 −9.49888 16.4525i −0.499941 0.865923i
362362 −2.72881 + 1.57548i −0.143423 + 0.0828055i
363363 12.8769 0.675860
364364 0 0
365365 5.72896 0.299867
366366 13.2895 7.67270i 0.694654 0.401059i
367367 1.14912 + 1.99033i 0.0599833 + 0.103894i 0.894458 0.447153i 0.147562π-0.147562\pi
−0.834474 + 0.551047i 0.814229π0.814229\pi
368368 −1.22438 + 2.12070i −0.0638255 + 0.110549i
369369 8.30736i 0.432464i
370370 −11.3273 6.53979i −0.588876 0.339988i
371371 0 0
372372 38.2795i 1.98470i
373373 −5.88418 + 10.1917i −0.304672 + 0.527707i −0.977188 0.212375i 0.931880π-0.931880\pi
0.672517 + 0.740082i 0.265213π0.265213\pi
374374 3.58636 + 6.21175i 0.185446 + 0.321202i
375375 10.0350 5.79373i 0.518207 0.299187i
376376 1.08215 0.0558074
377377 0.497847 4.87715i 0.0256404 0.251186i
378378 0 0
379379 −6.92034 + 3.99546i −0.355474 + 0.205233i −0.667094 0.744974i 0.732462π-0.732462\pi
0.311619 + 0.950207i 0.399129π0.399129\pi
380380 0.0664059 + 0.115018i 0.00340655 + 0.00590032i
381381 −11.5658 + 20.0325i −0.592532 + 1.02630i
382382 3.48542i 0.178329i
383383 −24.4605 14.1223i −1.24988 0.721616i −0.278791 0.960352i 0.589934π-0.589934\pi
−0.971084 + 0.238736i 0.923267π0.923267\pi
384384 24.1508 + 13.9435i 1.23244 + 0.711551i
385385 0 0
386386 −8.00839 + 13.8709i −0.407616 + 0.706012i
387387 −3.84158 6.65381i −0.195278 0.338232i
388388 −1.21997 + 0.704352i −0.0619347 + 0.0357580i
389389 −7.68086 −0.389435 −0.194717 0.980859i 0.562379π-0.562379\pi
−0.194717 + 0.980859i 0.562379π0.562379\pi
390390 −9.45816 + 4.24503i −0.478933 + 0.214955i
391391 16.1957 0.819050
392392 0 0
393393 −1.87498 3.24756i −0.0945801 0.163818i
394394 17.8241 30.8722i 0.897964 1.55532i
395395 9.87862i 0.497047i
396396 3.56817 + 2.06008i 0.179307 + 0.103523i
397397 6.45433 + 3.72641i 0.323933 + 0.187023i 0.653144 0.757233i 0.273449π-0.273449\pi
−0.329211 + 0.944256i 0.606783π0.606783\pi
398398 15.2368i 0.763750i
399399 0 0
400400 −0.670563 1.16145i −0.0335282 0.0580725i
401401 15.7601 9.09912i 0.787024 0.454389i −0.0518898 0.998653i 0.516524π-0.516524\pi
0.838914 + 0.544264i 0.183191π0.183191\pi
402402 6.93186 0.345730
403403 −16.5911 + 22.9801i −0.826461 + 1.14472i
404404 −31.9596 −1.59005
405405 −4.27409 + 2.46765i −0.212381 + 0.122618i
406406 0 0
407407 −5.03804 + 8.72615i −0.249727 + 0.432539i
408408 9.17361i 0.454161i
409409 −25.3594 14.6413i −1.25394 0.723964i −0.282053 0.959399i 0.591015π-0.591015\pi
−0.971890 + 0.235435i 0.924349π0.924349\pi
410410 −16.9320 9.77568i −0.836211 0.482787i
411411 2.74741i 0.135520i
412412 −16.4892 + 28.5602i −0.812365 + 1.40706i
413413 0 0
414414 12.9322 7.46641i 0.635583 0.366954i
415415 −9.77456 −0.479814
416416 −7.81047 17.4021i −0.382940 0.853210i
417417 −22.9980 −1.12622
418418 0.142225 0.0821139i 0.00695647 0.00401632i
419419 −10.3697 17.9608i −0.506591 0.877441i −0.999971 0.00762733i 0.997572π-0.997572\pi
0.493380 0.869814i 0.335761π-0.335761\pi
420420 0 0
421421 24.8696i 1.21207i 0.795437 + 0.606036i 0.207241π0.207241\pi
−0.795437 + 0.606036i 0.792759π0.792759\pi
422422 −16.1456 9.32165i −0.785954 0.453771i
423423 −0.258531 0.149263i −0.0125702 0.00725742i
424424 8.15130i 0.395862i
425425 −4.43497 + 7.68159i −0.215128 + 0.372612i
426426 24.1178 + 41.7733i 1.16851 + 2.02392i
427427 0 0
428428 −32.5950 −1.57554
429429 3.27023 + 7.28626i 0.157888 + 0.351784i
430430 −18.0823 −0.872006
431431 18.3327 10.5844i 0.883055 0.509832i 0.0113906 0.999935i 0.496374π-0.496374\pi
0.871665 + 0.490103i 0.163041π0.163041\pi
432432 0.883489 + 1.53025i 0.0425069 + 0.0736241i
433433 11.7148 20.2906i 0.562977 0.975105i −0.434258 0.900789i 0.642989π-0.642989\pi
0.997235 0.0743163i 0.0236774π-0.0236774\pi
434434 0 0
435435 −1.47000 0.848707i −0.0704813 0.0406924i
436436 −33.2178 19.1783i −1.59084 0.918474i
437437 0.370819i 0.0177387i
438438 11.4727 19.8713i 0.548187 0.949488i
439439 6.01919 + 10.4256i 0.287280 + 0.497584i 0.973160 0.230131i 0.0739155π-0.0739155\pi
−0.685879 + 0.727715i 0.740582π0.740582\pi
440440 3.31593 1.91445i 0.158081 0.0912680i
441441 0 0
442442 10.0694 13.9470i 0.478952 0.663390i
443443 15.7331 0.747503 0.373752 0.927529i 0.378071π-0.378071\pi
0.373752 + 0.927529i 0.378071π0.378071\pi
444444 −28.2640 + 16.3182i −1.34135 + 0.774427i
445445 7.41855 + 12.8493i 0.351673 + 0.609116i
446446 18.4930 32.0308i 0.875669 1.51670i
447447 9.37592i 0.443466i
448448 0 0
449449 22.5177 + 13.0006i 1.06268 + 0.613536i 0.926171 0.377104i 0.123080π-0.123080\pi
0.136504 + 0.990640i 0.456413π0.456413\pi
450450 8.17832i 0.385530i
451451 −7.53087 + 13.0438i −0.354615 + 0.614211i
452452 −5.74676 9.95369i −0.270305 0.468182i
453453 0.847362 0.489225i 0.0398125 0.0229858i
454454 2.98459 0.140074
455455 0 0
456456 0.210041 0.00983605
457457 −26.6700 + 15.3979i −1.24757 + 0.720284i −0.970624 0.240602i 0.922655π-0.922655\pi
−0.276945 + 0.960886i 0.589322π0.589322\pi
458458 −23.9742 41.5245i −1.12024 1.94031i
459459 5.84322 10.1208i 0.272738 0.472396i
460460 21.8949i 1.02086i
461461 29.5278 + 17.0479i 1.37525 + 0.794000i 0.991583 0.129472i 0.0413284π-0.0413284\pi
0.383665 + 0.923472i 0.374662π0.374662\pi
462462 0 0
463463 1.69184i 0.0786263i −0.999227 0.0393131i 0.987483π-0.987483\pi
0.999227 0.0393131i 0.0125170π-0.0125170\pi
464464 −0.212926 + 0.368799i −0.00988485 + 0.0171211i
465465 4.90674 + 8.49871i 0.227544 + 0.394118i
466466 −26.5378 + 15.3216i −1.22934 + 0.709761i
467467 28.3524 1.31199 0.655996 0.754764i 0.272249π-0.272249\pi
0.655996 + 0.754764i 0.272249π0.272249\pi
468468 1.00344 9.83015i 0.0463838 0.454399i
469469 0 0
470470 −0.608453 + 0.351290i −0.0280658 + 0.0162038i
471471 −12.2112 21.1504i −0.562662 0.974559i
472472 −2.46659 + 4.27226i −0.113534 + 0.196647i
473473 13.9300i 0.640503i
474474 34.2647 + 19.7827i 1.57383 + 0.908651i
475475 0.175879 + 0.101544i 0.00806989 + 0.00465915i
476476 0 0
477477 1.12433 1.94739i 0.0514794 0.0891650i
478478 15.3918 + 26.6595i 0.704007 + 1.21938i
479479 5.44077 3.14123i 0.248595 0.143526i −0.370526 0.928822i 0.620822π-0.620822\pi
0.619121 + 0.785296i 0.287489π0.287489\pi
480480 −6.60426 −0.301442
481481 24.0402 + 2.45396i 1.09614 + 0.111891i
482482 1.92128 0.0875117
483483 0 0
484484 14.4427 + 25.0154i 0.656484 + 1.13706i
485485 0.180570 0.312757i 0.00819927 0.0142016i
486486 19.2171i 0.871703i
487487 11.2736 + 6.50879i 0.510854 + 0.294942i 0.733185 0.680030i 0.238033π-0.238033\pi
−0.222331 + 0.974971i 0.571366π0.571366\pi
488488 11.7712 + 6.79613i 0.532859 + 0.307647i
489489 13.3358i 0.603065i
490490 0 0
491491 −6.17616 10.6974i −0.278726 0.482768i 0.692342 0.721569i 0.256579π-0.256579\pi
−0.971068 + 0.238801i 0.923246π0.923246\pi
492492 −42.2490 + 24.3925i −1.90473 + 1.09970i
493493 2.81650 0.126849
494494 −0.319332 0.230550i −0.0143674 0.0103730i
495495 −1.05626 −0.0474754
496496 2.13218 1.23102i 0.0957378 0.0552743i
497497 0 0
498498 −19.5744 + 33.9038i −0.877148 + 1.51926i
499499 9.15340i 0.409763i −0.978787 0.204881i 0.934319π-0.934319\pi
0.978787 0.204881i 0.0656808π-0.0656808\pi
500500 22.5105 + 12.9965i 1.00670 + 0.581220i
501501 −3.39102 1.95781i −0.151500 0.0874684i
502502 62.8149i 2.80357i
503503 11.2519 19.4888i 0.501696 0.868963i −0.498302 0.867003i 0.666043π-0.666043\pi
0.999998 0.00195935i 0.000623680π-0.000623680\pi
504504 0 0
505505 7.09559 4.09664i 0.315750 0.182298i
506506 −27.0741 −1.20359
507507 12.7308 14.3105i 0.565396 0.635551i
508508 −51.8885 −2.30218
509509 −33.4811 + 19.3303i −1.48402 + 0.856800i −0.999835 0.0181646i 0.994218π-0.994218\pi
−0.484187 + 0.874965i 0.660884π0.660884\pi
510510 −2.97797 5.15800i −0.131867 0.228400i
511511 0 0
512512 3.53972i 0.156435i
513513 −0.231727 0.133787i −0.0102310 0.00590686i
514514 13.0690 + 7.54536i 0.576447 + 0.332812i
515515 8.45447i 0.372549i
516516 −22.5596 + 39.0744i −0.993132 + 1.72016i
517517 0.270623 + 0.468732i 0.0119020 + 0.0206148i
518518 0 0
519519 28.8588 1.26676
520520 −7.44511 5.37520i −0.326490 0.235718i
521521 −40.2351 −1.76273 −0.881366 0.472434i 0.843375π-0.843375\pi
−0.881366 + 0.472434i 0.843375π0.843375\pi
522522 2.24897 1.29844i 0.0984348 0.0568313i
523523 −0.366073 0.634057i −0.0160073 0.0277254i 0.857911 0.513799i 0.171762π-0.171762\pi
−0.873918 + 0.486073i 0.838429π0.838429\pi
524524 4.20594 7.28491i 0.183737 0.318243i
525525 0 0
526526 −45.0581 26.0143i −1.96463 1.13428i
527527 −14.1018 8.14169i −0.614285 0.354658i
528528 0.693741i 0.0301912i
529529 −19.0660 + 33.0234i −0.828959 + 1.43580i
530530 −2.64610 4.58319i −0.114939 0.199081i
531531 1.17857 0.680446i 0.0511455 0.0295288i
532532 0 0
533533 35.9353 + 3.66817i 1.55653 + 0.158886i
534534 59.4251 2.57157
535535 7.23667 4.17809i 0.312868 0.180635i
536536 3.06996 + 5.31733i 0.132602 + 0.229674i
537537 −2.13146 + 3.69179i −0.0919791 + 0.159312i
538538 36.8553i 1.58894i
539539 0 0
540540 −13.6823 7.89946i −0.588791 0.339939i
541541 23.6537i 1.01695i 0.861076 + 0.508476i 0.169791π0.169791\pi
−0.861076 + 0.508476i 0.830209π0.830209\pi
542542 10.0876 17.4722i 0.433298 0.750494i
543543 −1.00781 1.74558i −0.0432492 0.0749099i
544544 9.49024 5.47919i 0.406891 0.234918i
545545 9.83325 0.421210
546546 0 0
547547 −12.9472 −0.553582 −0.276791 0.960930i 0.589271π-0.589271\pi
−0.276791 + 0.960930i 0.589271π0.589271\pi
548548 5.33730 3.08149i 0.227998 0.131635i
549549 −1.87481 3.24727i −0.0800151 0.138590i
550550 7.41388 12.8412i 0.316129 0.547552i
551551 0.0644871i 0.00274724i
552552 −29.9876 17.3133i −1.27636 0.736904i
553553 0 0
554554 45.8771i 1.94913i
555555 4.18340 7.24585i 0.177575 0.307569i
556556 −25.7946 44.6775i −1.09393 1.89475i
557557 −5.54845 + 3.20340i −0.235096 + 0.135732i −0.612921 0.790145i 0.710005π-0.710005\pi
0.377825 + 0.925877i 0.376672π0.376672\pi
558558 −15.0137 −0.635581
559559 30.4787 13.6795i 1.28911 0.578582i
560560 0 0
561561 −3.97355 + 2.29413i −0.167764 + 0.0968584i
562562 −16.1498 27.9723i −0.681239 1.17994i
563563 −3.66042 + 6.34004i −0.154268 + 0.267201i −0.932792 0.360414i 0.882635π-0.882635\pi
0.778524 + 0.627615i 0.215969π0.215969\pi
564564 1.75309i 0.0738185i
565565 2.55176 + 1.47326i 0.107354 + 0.0619806i
566566 2.01980 + 1.16613i 0.0848986 + 0.0490162i
567567 0 0
568568 −21.3625 + 37.0009i −0.896349 + 1.55252i
569569 −2.15872 3.73901i −0.0904981 0.156747i 0.817223 0.576322i 0.195513π-0.195513\pi
−0.907721 + 0.419575i 0.862179π0.862179\pi
570570 −0.118098 + 0.0681842i −0.00494660 + 0.00285592i
571571 −34.1695 −1.42995 −0.714974 0.699152i 0.753561π-0.753561\pi
−0.714974 + 0.699152i 0.753561π0.753561\pi
572572 −10.4869 + 14.5252i −0.438478 + 0.607330i
573573 −2.22956 −0.0931413
574574 0 0
575575 −16.7402 28.9949i −0.698115 1.20917i
576576 5.31166 9.20007i 0.221319 0.383336i
577577 6.35656i 0.264627i 0.991208 + 0.132314i 0.0422406π0.0422406\pi
−0.991208 + 0.132314i 0.957759π0.957759\pi
578578 −25.3511 14.6364i −1.05447 0.608796i
579579 −8.87301 5.12283i −0.368750 0.212898i
580580 3.80763i 0.158103i
581581 0 0
582582 −0.723214 1.25264i −0.0299782 0.0519237i
583583 −3.53074 + 2.03847i −0.146228 + 0.0844249i
584584 20.3240 0.841014
585585 1.03727 + 2.31109i 0.0428857 + 0.0955518i
586586 −0.458892 −0.0189566
587587 −27.2036 + 15.7060i −1.12281 + 0.648256i −0.942118 0.335283i 0.891168π-0.891168\pi
−0.180695 + 0.983539i 0.557835π0.557835\pi
588588 0 0
589589 −0.186414 + 0.322878i −0.00768104 + 0.0133040i
590590 3.20286i 0.131860i
591591 19.7484 + 11.4018i 0.812342 + 0.469006i
592592 −1.81786 1.04954i −0.0747136 0.0431359i
593593 0.473013i 0.0194243i 0.999953 + 0.00971215i 0.00309152π0.00309152\pi
−0.999953 + 0.00971215i 0.996908π0.996908\pi
594594 −9.76804 + 16.9187i −0.400787 + 0.694184i
595595 0 0
596596 −18.2143 + 10.5160i −0.746086 + 0.430753i
597597 9.74670 0.398906
598598 26.5872 + 59.2378i 1.08723 + 2.42242i
599599 −9.62695 −0.393347 −0.196673 0.980469i 0.563014π-0.563014\pi
−0.196673 + 0.980469i 0.563014π0.563014\pi
600600 16.4234 9.48206i 0.670483 0.387103i
601601 −20.5399 35.5762i −0.837842 1.45118i −0.891696 0.452635i 0.850484π-0.850484\pi
0.0538542 0.998549i 0.482849π-0.482849\pi
602602 0 0
603603 1.69379i 0.0689765i
604604 1.90080 + 1.09743i 0.0773424 + 0.0446537i
605605 −6.41304 3.70257i −0.260727 0.150531i
606606 32.8155i 1.33304i
607607 9.54289 16.5288i 0.387334 0.670882i −0.604756 0.796411i 0.706729π-0.706729\pi
0.992090 + 0.125529i 0.0400627π0.0400627\pi
608608 −0.125453 0.217290i −0.00508777 0.00881228i
609609 0 0
610610 −8.82474 −0.357303
611611 0.759825 1.05242i 0.0307392 0.0425765i
612612 5.67680 0.229471
613613 32.9131 19.0024i 1.32935 0.767500i 0.344149 0.938915i 0.388167π-0.388167\pi
0.985199 + 0.171415i 0.0548340π0.0548340\pi
614614 31.3249 + 54.2563i 1.26417 + 2.18961i
615615 6.25334 10.8311i 0.252159 0.436752i
616616 0 0
617617 7.20117 + 4.15759i 0.289908 + 0.167378i 0.637900 0.770119i 0.279803π-0.279803\pi
−0.347992 + 0.937497i 0.613136π0.613136\pi
618618 −29.3250 16.9308i −1.17962 0.681056i
619619 44.4728i 1.78751i 0.448553 + 0.893756i 0.351940π0.351940\pi
−0.448553 + 0.893756i 0.648060π0.648060\pi
620620 −11.0068 + 19.0643i −0.442042 + 0.765640i
621621 22.0558 + 38.2018i 0.885069 + 1.53298i
622622 −54.0579 + 31.2103i −2.16752 + 1.25142i
623623 0 0
624624 −1.51790 + 0.681266i −0.0607646 + 0.0272725i
625625 14.7468 0.589874
626626 −44.0397 + 25.4263i −1.76018 + 1.01624i
627627 0.0525269 + 0.0909792i 0.00209772 + 0.00363336i
628628 27.3921 47.4445i 1.09306 1.89324i
629629 13.8829i 0.553549i
630630 0 0
631631 −10.1779 5.87622i −0.405177 0.233929i 0.283539 0.958961i 0.408492π-0.408492\pi
−0.688715 + 0.725032i 0.741825π0.741825\pi
632632 35.0453i 1.39403i
633633 5.96290 10.3280i 0.237004 0.410503i
634634 −8.14001 14.0989i −0.323281 0.559939i
635635 11.5202 6.65117i 0.457164 0.263944i
636636 −13.2052 −0.523620
637637 0 0
638638 −4.70831 −0.186404
639639 10.2072 5.89315i 0.403792 0.233129i
640640 −8.01854 13.8885i −0.316961 0.548992i
641641 5.24342 9.08186i 0.207102 0.358712i −0.743698 0.668516i 0.766930π-0.766930\pi
0.950801 + 0.309804i 0.100263π0.100263\pi
642642 33.4679i 1.32087i
643643 −27.0912 15.6411i −1.06837 0.616825i −0.140635 0.990061i 0.544915π-0.544915\pi
−0.927736 + 0.373237i 0.878248π0.878248\pi
644644 0 0
645645 11.5669i 0.455448i
646646 0.113137 0.195959i 0.00445133 0.00770992i
647647 13.4337 + 23.2679i 0.528135 + 0.914757i 0.999462 + 0.0327983i 0.0104419π0.0104419\pi
−0.471327 + 0.881959i 0.656225π0.656225\pi
648648 −15.1627 + 8.75422i −0.595649 + 0.343898i
649649 −2.46738 −0.0968530
650650 −35.3770 3.61119i −1.38760 0.141643i
651651 0 0
652652 −25.9070 + 14.9574i −1.01459 + 0.585776i
653653 2.07081 + 3.58674i 0.0810369 + 0.140360i 0.903696 0.428176i 0.140844π-0.140844\pi
−0.822659 + 0.568536i 0.807510π0.807510\pi
654654 19.6919 34.1073i 0.770014 1.33370i
655655 2.15650i 0.0842615i
656656 −2.71734 1.56886i −0.106094 0.0612536i
657657 −4.85553 2.80334i −0.189432 0.109369i
658658 0 0
659659 −10.7276 + 18.5807i −0.417887 + 0.723801i −0.995727 0.0923492i 0.970562π-0.970562\pi
0.577840 + 0.816150i 0.303896π0.303896\pi
660660 3.10144 + 5.37185i 0.120723 + 0.209099i
661661 −36.7084 + 21.1936i −1.42779 + 0.824335i −0.996946 0.0780909i 0.975118π-0.975118\pi
−0.430844 + 0.902426i 0.641784π0.641784\pi
662662 15.1753 0.589803
663663 8.92164 + 6.44122i 0.346488 + 0.250156i
664664 −34.6762 −1.34570
665665 0 0
666666 6.40021 + 11.0855i 0.248003 + 0.429554i
667667 −5.31558 + 9.20685i −0.205820 + 0.356491i
668668 8.78349i 0.339844i
669669 20.4896 + 11.8297i 0.792173 + 0.457361i
670670 −3.45226 1.99317i −0.133373 0.0770027i
671671 6.79830i 0.262445i
672672 0 0
673673 −14.7928 25.6219i −0.570220 0.987650i −0.996543 0.0830790i 0.973525π-0.973525\pi
0.426323 0.904571i 0.359809π-0.359809\pi
674674 8.42336 4.86323i 0.324456 0.187324i
675675 −24.1588 −0.929871
676676 42.0793 + 8.68114i 1.61844 + 0.333890i
677677 −32.1659 −1.23624 −0.618118 0.786085i 0.712105π-0.712105\pi
−0.618118 + 0.786085i 0.712105π0.712105\pi
678678 10.2202 5.90066i 0.392506 0.226613i
679679 0 0
680680 2.63775 4.56872i 0.101153 0.175202i
681681 1.90919i 0.0731604i
682682 23.5738 + 13.6104i 0.902689 + 0.521168i
683683 7.44986 + 4.30118i 0.285061 + 0.164580i 0.635712 0.771926i 0.280706π-0.280706\pi
−0.350651 + 0.936506i 0.614040π0.614040\pi
684684 0.129977i 0.00496980i
685685 −0.789983 + 1.36829i −0.0301837 + 0.0522797i
686686 0 0
687687 26.5625 15.3359i 1.01342 0.585100i
688688 −2.90195 −0.110636
689689 7.92740 + 5.72340i 0.302010 + 0.218044i
690690 22.4813 0.855847
691691 17.7033 10.2210i 0.673466 0.388826i −0.123923 0.992292i 0.539548π-0.539548\pi
0.797388 + 0.603466i 0.206214π0.206214\pi
692692 32.3680 + 56.0629i 1.23044 + 2.13119i
693693 0 0
694694 20.9477i 0.795164i
695695 11.4537 + 6.61279i 0.434463 + 0.250837i
696696 −5.21498 3.01087i −0.197673 0.114127i
697697 20.7522i 0.786046i
698698 10.6187 18.3921i 0.401922 0.696150i
699699 −9.80099 16.9758i −0.370708 0.642084i
700700 0 0
701701 −25.1373 −0.949422 −0.474711 0.880142i 0.657447π-0.657447\pi
−0.474711 + 0.880142i 0.657447π0.657447\pi
702702 46.6104 + 4.75787i 1.75920 + 0.179574i
703703 0.317866 0.0119885
704704 −16.6803 + 9.63036i −0.628661 + 0.362958i
705705 −0.224715 0.389217i −0.00846324 0.0146588i
706706 −2.48118 + 4.29753i −0.0933804 + 0.161740i
707707 0 0
708708 −6.92112 3.99591i −0.260112 0.150176i
709709 25.5416 + 14.7464i 0.959234 + 0.553814i 0.895937 0.444181i 0.146505π-0.146505\pi
0.0632970 + 0.997995i 0.479838π0.479838\pi
710710 27.7390i 1.04103i
711711 4.83389 8.37254i 0.181285 0.313995i
712712 26.3180 + 45.5841i 0.986309 + 1.70834i
713713 53.2287 30.7316i 1.99343 1.15091i
714714 0 0
715715 0.466399 4.56908i 0.0174423 0.170874i
716716 −9.56254 −0.357369
717717 −17.0536 + 9.84591i −0.636879 + 0.367702i
718718 −9.85518 17.0697i −0.367792 0.637034i
719719 4.16576 7.21531i 0.155357 0.269086i −0.777832 0.628472i 0.783681π-0.783681\pi
0.933189 + 0.359386i 0.117014π0.117014\pi
720720 0.220044i 0.00820055i
721721 0 0
722722 37.8946 + 21.8784i 1.41029 + 0.814231i
723723 1.22901i 0.0457073i
724724 2.26071 3.91567i 0.0840188 0.145525i
725725 −2.91120 5.04235i −0.108119 0.187268i
726726 −25.6853 + 14.8294i −0.953271 + 0.550371i
727727 −9.66141 −0.358322 −0.179161 0.983820i 0.557338π-0.557338\pi
−0.179161 + 0.983820i 0.557338π0.557338\pi
728728 0 0
729729 29.7672 1.10249
730730 −11.4275 + 6.59766i −0.422950 + 0.244190i
731731 9.59645 + 16.6215i 0.354938 + 0.614770i
732732 −11.0098 + 19.0696i −0.406935 + 0.704832i
733733 14.0179i 0.517762i −0.965909 0.258881i 0.916646π-0.916646\pi
0.965909 0.258881i 0.0833538π-0.0833538\pi
734734 −4.58425 2.64672i −0.169208 0.0976921i
735735 0 0
736736 41.3635i 1.52468i
737737 −1.53547 + 2.65951i −0.0565598 + 0.0979644i
738738 9.56704 + 16.5706i 0.352168 + 0.609972i
739739 −33.6145 + 19.4073i −1.23653 + 0.713910i −0.968383 0.249468i 0.919744π-0.919744\pi
−0.268146 + 0.963378i 0.586411π0.586411\pi
740740 18.7683 0.689938
741741 0.147479 0.204271i 0.00541779 0.00750410i
742742 0 0
743743 29.7863 17.1971i 1.09275 0.630901i 0.158445 0.987368i 0.449352π-0.449352\pi
0.934308 + 0.356467i 0.116019π0.116019\pi
744744 17.4071 + 30.1500i 0.638175 + 1.10535i
745745 2.69592 4.66948i 0.0987710 0.171076i
746746 27.1057i 0.992410i
747747 8.28434 + 4.78297i 0.303108 + 0.175000i
748748 −8.91346 5.14619i −0.325908 0.188163i
749749 0 0
750750 −13.3445 + 23.1134i −0.487272 + 0.843980i
751751 24.0735 + 41.6965i 0.878454 + 1.52153i 0.853037 + 0.521850i 0.174758π0.174758\pi
0.0254165 + 0.999677i 0.491909π0.491909\pi
752752 −0.0976479 + 0.0563770i −0.00356085 + 0.00205586i
753753 40.1816 1.46430
754754 4.62364 + 10.3017i 0.168383 + 0.375167i
755755 −0.562681 −0.0204781
756756 0 0
757757 3.45319 + 5.98110i 0.125508 + 0.217387i 0.921931 0.387353i 0.126611π-0.126611\pi
−0.796423 + 0.604740i 0.793277π0.793277\pi
758758 9.20262 15.9394i 0.334254 0.578945i
759759 17.3188i 0.628634i
760760 −0.104606 0.0603945i −0.00379447 0.00219074i
761761 −27.6895 15.9865i −1.00374 0.579511i −0.0943888 0.995535i 0.530090π-0.530090\pi
−0.909353 + 0.416025i 0.863423π0.863423\pi
762762 53.2781i 1.93006i
763763 0 0
764764 −2.50067 4.33129i −0.0904712 0.156701i
765765 −1.26035 + 0.727663i −0.0455680 + 0.0263087i
766766 65.0548 2.35053
767767 2.42301 + 5.39860i 0.0874898 + 0.194932i
768768 −26.4795 −0.955495
769769 −12.4665 + 7.19752i −0.449553 + 0.259549i −0.707641 0.706572i 0.750241π-0.750241\pi
0.258089 + 0.966121i 0.416907π0.416907\pi
770770 0 0
771771 −4.82664 + 8.35999i −0.173827 + 0.301078i
772772 22.9830i 0.827177i
773773 −32.2829 18.6385i −1.16114 0.670382i −0.209560 0.977796i 0.567203π-0.567203\pi
−0.951576 + 0.307414i 0.900536π0.900536\pi
774774 15.3255 + 8.84818i 0.550864 + 0.318041i
775775 33.6618i 1.20917i
776776 0.640590 1.10953i 0.0229958 0.0398300i
777777 0 0
778778 15.3209 8.84553i 0.549281 0.317128i
779779 0.475146 0.0170239
780780 8.70789 12.0612i 0.311792 0.431859i
781781 −21.3693 −0.764652
782782 −32.3053 + 18.6515i −1.15524 + 0.666975i
783783 3.83560 + 6.64346i 0.137073 + 0.237418i
784784 0 0
785785 14.0447i 0.501276i
786786 7.47999 + 4.31857i 0.266802 + 0.154038i
787787 −12.4263 7.17430i −0.442948 0.255736i 0.261899 0.965095i 0.415651π-0.415651\pi
−0.704847 + 0.709359i 0.748985π0.748985\pi
788788 51.1527i 1.82224i
789789 16.6409 28.8229i 0.592432 1.02612i
790790 −11.3765 19.7047i −0.404759 0.701064i
791791 0 0
792792 −3.74719 −0.133150
793793 14.8746 6.67605i 0.528213 0.237073i
794794 −17.1658 −0.609192
795795 2.93179 1.69267i 0.103980 0.0600328i
796796 10.9319 + 18.9346i 0.387470 + 0.671118i
797797 −5.54219 + 9.59935i −0.196314 + 0.340026i −0.947331 0.320257i 0.896231π-0.896231\pi
0.751016 + 0.660284i 0.229564π0.229564\pi
798798 0 0
799799 0.645824 + 0.372866i 0.0228476 + 0.0131911i
800800 −19.6187 11.3268i −0.693625 0.400464i
801801 14.5204i 0.513054i
802802 −20.9577 + 36.2998i −0.740042 + 1.28179i
803803 5.08262 + 8.80336i 0.179362 + 0.310664i
804804 −8.61415 + 4.97338i −0.303798 + 0.175398i
805805 0 0
806806 6.62941 64.9450i 0.233511 2.28759i
807807 −23.5757 −0.829904
808808 25.1723 14.5332i 0.885558 0.511277i
809809 21.2768 + 36.8525i 0.748052 + 1.29566i 0.948755 + 0.316013i 0.102344π0.102344\pi
−0.200703 + 0.979652i 0.564323π0.564323\pi
810810 5.68365 9.84438i 0.199703 0.345896i
811811 16.3622i 0.574554i −0.957848 0.287277i 0.907250π-0.907250\pi
0.957848 0.287277i 0.0927500π-0.0927500\pi
812812 0 0
813813 11.1766 + 6.45284i 0.391982 + 0.226311i
814814 23.2079i 0.813437i
815815 3.83453 6.64160i 0.134318 0.232645i
816816 −0.477922 0.827785i −0.0167306 0.0289783i
817817 0.380570 0.219722i 0.0133145 0.00768710i
818818 67.4455 2.35818
819819 0 0
820820 28.0549 0.979721
821821 −2.68944 + 1.55275i −0.0938621 + 0.0541913i −0.546196 0.837657i 0.683925π-0.683925\pi
0.452334 + 0.891848i 0.350591π0.350591\pi
822822 3.16401 + 5.48023i 0.110358 + 0.191145i
823823 24.5082 42.4494i 0.854301 1.47969i −0.0229903 0.999736i 0.507319π-0.507319\pi
0.877292 0.479958i 0.159348π-0.159348\pi
824824 29.9930i 1.04486i
825825 8.21432 + 4.74254i 0.285986 + 0.165114i
826826 0 0
827827 13.0887i 0.455140i −0.973762 0.227570i 0.926922π-0.926922\pi
0.973762 0.227570i 0.0730780π-0.0730780\pi
828828 −10.7138 + 18.5569i −0.372331 + 0.644896i
829829 −24.6282 42.6574i −0.855374 1.48155i −0.876297 0.481771i 0.839994π-0.839994\pi
0.0209227 0.999781i 0.493340π-0.493340\pi
830830 19.4972 11.2567i 0.676757 0.390726i
831831 29.3468 1.01803
832832 37.4514 + 27.0391i 1.29839 + 0.937411i
833833 0 0
834834 45.8739 26.4853i 1.58848 0.917111i
835835 1.12588 + 1.95009i 0.0389629 + 0.0674856i
836836 −0.117828 + 0.204084i −0.00407517 + 0.00705840i
837837 44.3505i 1.53298i
838838 41.3684 + 23.8841i 1.42905 + 0.825062i
839839 −14.9508 8.63182i −0.516157 0.298004i 0.219204 0.975679i 0.429654π-0.429654\pi
−0.735361 + 0.677676i 0.762987π0.762987\pi
840840 0 0
841841 13.5756 23.5136i 0.468124 0.810815i
842842 −28.6407 49.6071i −0.987024 1.70957i
843843 17.8934 10.3308i 0.616282 0.355810i
844844 26.7519 0.920839
845845 −10.4551 + 3.46644i −0.359667 + 0.119249i
846846 0.687585 0.0236397
847847 0 0
848848 −0.424662 0.735535i −0.0145829 0.0252584i
849849 −0.745955 + 1.29203i −0.0256011 + 0.0443424i
850850 20.4298i 0.700738i
851851 −45.3818 26.2012i −1.55567 0.898166i
852852 −59.9419 34.6075i −2.05358 1.18563i
853853 52.4163i 1.79470i 0.441319 + 0.897350i 0.354511π0.354511\pi
−0.441319 + 0.897350i 0.645489π0.645489\pi
854854 0 0
855855 0.0166607 + 0.0288572i 0.000569784 + 0.000986895i
856856 25.6728 14.8222i 0.877477 0.506611i
857857 10.1271 0.345935 0.172967 0.984928i 0.444664π-0.444664\pi
0.172967 + 0.984928i 0.444664π0.444664\pi
858858 −14.9142 10.7677i −0.509162 0.367603i
859859 0.510237 0.0174090 0.00870452 0.999962i 0.497229π-0.497229\pi
0.00870452 + 0.999962i 0.497229π0.497229\pi
860860 22.4707 12.9735i 0.766244 0.442391i
861861 0 0
862862 −24.3787 + 42.2251i −0.830341 + 1.43819i
863863 20.4991i 0.697797i 0.937161 + 0.348898i 0.113444π0.113444\pi
−0.937161 + 0.348898i 0.886556π0.886556\pi
864864 25.8482 + 14.9235i 0.879375 + 0.507707i
865865 −14.3725 8.29797i −0.488680 0.282139i
866866 53.9646i 1.83379i
867867 9.36269 16.2167i 0.317974 0.550747i
868868 0 0
869869 −15.1799 + 8.76412i −0.514943 + 0.297302i
870870 3.90960 0.132548
871871 7.32685 + 0.747905i 0.248261 + 0.0253418i
872872 34.8844 1.18133
873873 −0.306082 + 0.176716i −0.0103593 + 0.00598094i
874874 0.427047 + 0.739668i 0.0144451 + 0.0250196i
875875 0 0
876876 32.9252i 1.11244i
877877 9.77794 + 5.64530i 0.330178 + 0.190628i 0.655920 0.754830i 0.272281π-0.272281\pi
−0.325742 + 0.945459i 0.605614π0.605614\pi
878878 −24.0128 13.8638i −0.810394 0.467881i
879879 0.293545i 0.00990103i
880880 −0.199476 + 0.345503i −0.00672435 + 0.0116469i
881881 −11.2634 19.5088i −0.379474 0.657268i 0.611512 0.791235i 0.290562π-0.290562\pi
−0.990986 + 0.133967i 0.957228π0.957228\pi
882882 0 0
883883 −28.0268 −0.943178 −0.471589 0.881819i 0.656319π-0.656319\pi
−0.471589 + 0.881819i 0.656319π0.656319\pi
884884 −2.50663 + 24.5562i −0.0843071 + 0.825915i
885885 2.04881 0.0688701
886886 −31.3827 + 18.1188i −1.05432 + 0.608713i
887887 −10.3118 17.8605i −0.346235 0.599696i 0.639342 0.768922i 0.279207π-0.279207\pi
−0.985577 + 0.169226i 0.945873π0.945873\pi
888888 14.8410 25.7053i 0.498031 0.862615i
889889 0 0
890890 −29.5954 17.0869i −0.992040 0.572754i
891891 −7.58379 4.37850i −0.254066 0.146685i
892892 53.0725i 1.77700i
893893 0.00853722 0.0147869i 0.000285687 0.000494824i
894894 −10.7976 18.7020i −0.361127 0.625490i
895895 2.12305 1.22574i 0.0709658 0.0409721i
896896 0 0
897897 −37.8935 + 17.0074i −1.26523 + 0.567861i
898898 −59.8876 −1.99848
899899 9.25671 5.34437i 0.308729 0.178245i
900900 −5.86767 10.1631i −0.195589 0.338770i
901901 −2.80863 + 4.86468i −0.0935689 + 0.162066i
902902 34.6912i 1.15509i
903903 0 0
904904 9.05263 + 5.22654i 0.301086 + 0.173832i
905905 1.15913i 0.0385308i
906906 −1.12681 + 1.95170i −0.0374359 + 0.0648409i
907907 20.7315 + 35.9081i 0.688379 + 1.19231i 0.972362 + 0.233479i 0.0750109π0.0750109\pi
−0.283982 + 0.958829i 0.591656π0.591656\pi
908908 −3.70892 + 2.14134i −0.123085 + 0.0710630i
909909 −8.01841 −0.265954
910910 0 0
911911 40.8187 1.35239 0.676193 0.736725i 0.263629π-0.263629\pi
0.676193 + 0.736725i 0.263629π0.263629\pi
912912 −0.0189531 + 0.0109426i −0.000627600 + 0.000362345i
913913 −8.67180 15.0200i −0.286995 0.497090i
914914 35.4655 61.4280i 1.17309 2.03186i
915915 5.64504i 0.186619i
916916 59.5849 + 34.4014i 1.96874 + 1.13665i
917917 0 0
918918 26.9170i 0.888393i
919919 24.3839 42.2341i 0.804350 1.39318i −0.112379 0.993665i 0.535847π-0.535847\pi
0.916729 0.399510i 0.130820π-0.130820\pi
920920 9.95645 + 17.2451i 0.328254 + 0.568553i
921921 −34.7068 + 20.0380i −1.14363 + 0.660274i
922922 −78.5317 −2.58630
923923 20.9850 + 46.7557i 0.690730 + 1.53898i
924924 0 0
925925 24.8544 14.3497i 0.817209 0.471816i
926926 1.94837 + 3.37468i 0.0640275 + 0.110899i
927927 −4.13701 + 7.16552i −0.135877 + 0.235346i
928928 7.19330i 0.236132i
929929 −25.4464 14.6915i −0.834868 0.482012i 0.0206482 0.999787i 0.493427π-0.493427\pi
−0.855517 + 0.517775i 0.826760π0.826760\pi
930930 −19.5748 11.3015i −0.641883 0.370591i
931931 0 0
932932 21.9855 38.0801i 0.720160 1.24735i
933933 −19.9647 34.5799i −0.653615 1.13210i
934934 −56.5541 + 32.6515i −1.85051 + 1.06839i
935935 2.63859 0.0862912
936936 3.67980 + 8.19881i 0.120278 + 0.267986i
937937 21.0196 0.686681 0.343340 0.939211i 0.388442π-0.388442\pi
0.343340 + 0.939211i 0.388442π0.388442\pi
938938 0 0
939939 −16.2648 28.1714i −0.530781 0.919340i
940940 0.504079 0.873090i 0.0164412 0.0284770i
941941 24.1033i 0.785744i 0.919593 + 0.392872i 0.128518π0.128518\pi
−0.919593 + 0.392872i 0.871482π0.871482\pi
942942 48.7150 + 28.1256i 1.58722 + 0.916383i
943943 −67.8368 39.1656i −2.20907 1.27541i
944944 0.514013i 0.0167297i
945945 0 0
946946 −16.0423 27.7860i −0.521579 0.903402i
947947 2.89292 1.67023i 0.0940072 0.0542751i −0.452259 0.891886i 0.649382π-0.649382\pi
0.546267 + 0.837611i 0.316049π0.316049\pi
948948 −56.7739 −1.84393
949949 14.2704 19.7658i 0.463238 0.641624i
950950 −0.467765 −0.0151763
951951 9.01883 5.20703i 0.292456 0.168849i
952952 0 0
953953 −2.48562 + 4.30522i −0.0805171 + 0.139460i −0.903472 0.428647i 0.858991π-0.858991\pi
0.822955 + 0.568106i 0.192324π0.192324\pi
954954 5.17925i 0.167685i
955955 1.11039 + 0.641082i 0.0359313 + 0.0207449i
956956 −38.2546 22.0863i −1.23724 0.714322i
957957 3.01183i 0.0973585i
958958 −7.23509 + 12.5315i −0.233755 + 0.404876i
959959 0 0
960960 13.8506 7.99667i 0.447028 0.258091i
961961 −30.7961 −0.993423
962962 −50.7787 + 22.7906i −1.63717 + 0.734798i
963963 −8.17783 −0.263527
964964 −2.38755 + 1.37845i −0.0768978 + 0.0443970i
965965 2.94601 + 5.10264i 0.0948354 + 0.164260i
966966 0 0
967967 47.4943i 1.52731i 0.645623 + 0.763657i 0.276598π0.276598\pi
−0.645623 + 0.763657i 0.723402π0.723402\pi
968968 −22.7509 13.1352i −0.731241 0.422182i
969969 0.125352 + 0.0723720i 0.00402689 + 0.00232492i
970970 0.831803i 0.0267076i
971971 17.2357 29.8532i 0.553121 0.958033i −0.444926 0.895567i 0.646770π-0.646770\pi
0.998047 0.0624662i 0.0198966π-0.0198966\pi
972972 13.7876 + 23.8808i 0.442238 + 0.765978i
973973 0 0
974974 −29.9830 −0.960717
975975 2.31002 22.6301i 0.0739798 0.724743i
976976 −1.41624 −0.0453329
977977 −11.5598 + 6.67406i −0.369831 + 0.213522i −0.673385 0.739292i 0.735160π-0.735160\pi
0.303553 + 0.952814i 0.401827π0.401827\pi
978978 −15.3579 26.6007i −0.491093 0.850597i
979979 −13.1632 + 22.7993i −0.420698 + 0.728670i
980980 0 0
981981 −8.33408 4.81169i −0.266087 0.153625i
982982 24.6390 + 14.2253i 0.786263 + 0.453949i
983983 12.5344i 0.399785i 0.979818 + 0.199893i 0.0640594π0.0640594\pi
−0.979818 + 0.199893i 0.935941π0.935941\pi
984984 22.1843 38.4244i 0.707210 1.22492i
985985 −6.55685 11.3568i −0.208919 0.361858i
986986 −5.61804 + 3.24358i −0.178915 + 0.103297i
987987 0 0
988988 0.562243 + 0.0573923i 0.0178873 + 0.00182589i
989989 −72.4455 −2.30363
990990 2.10691 1.21643i 0.0669620 0.0386605i
991991 5.20596 + 9.01698i 0.165373 + 0.286434i 0.936788 0.349899i 0.113784π-0.113784\pi
−0.771415 + 0.636332i 0.780451π0.780451\pi
992992 20.7938 36.0158i 0.660202 1.14350i
993993 9.70736i 0.308054i
994994 0 0
995995 −4.85414 2.80254i −0.153887 0.0888464i
996996 56.1759i 1.78000i
997997 2.87635 4.98198i 0.0910949 0.157781i −0.816877 0.576812i 0.804297π-0.804297\pi
0.907972 + 0.419031i 0.137630π0.137630\pi
998998 10.5414 + 18.2582i 0.333681 + 0.577953i
999999 −32.7465 + 18.9062i −1.03605 + 0.598167i
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 637.2.q.i.491.1 12
7.2 even 3 637.2.u.g.361.6 12
7.3 odd 6 91.2.k.b.23.1 yes 12
7.4 even 3 637.2.k.i.569.1 12
7.5 odd 6 91.2.u.b.88.6 yes 12
7.6 odd 2 637.2.q.g.491.1 12
13.2 odd 12 8281.2.a.co.1.2 12
13.4 even 6 inner 637.2.q.i.589.1 12
13.11 odd 12 8281.2.a.co.1.11 12
21.5 even 6 819.2.do.e.361.1 12
21.17 even 6 819.2.bm.f.478.6 12
91.4 even 6 637.2.u.g.30.6 12
91.17 odd 6 91.2.u.b.30.6 yes 12
91.24 even 12 1183.2.e.j.170.2 24
91.30 even 6 637.2.k.i.459.6 12
91.41 even 12 8281.2.a.cp.1.2 12
91.54 even 12 1183.2.e.j.508.11 24
91.69 odd 6 637.2.q.g.589.1 12
91.76 even 12 8281.2.a.cp.1.11 12
91.80 even 12 1183.2.e.j.170.11 24
91.82 odd 6 91.2.k.b.4.6 12
91.89 even 12 1183.2.e.j.508.2 24
273.17 even 6 819.2.do.e.667.1 12
273.173 even 6 819.2.bm.f.550.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.k.b.4.6 12 91.82 odd 6
91.2.k.b.23.1 yes 12 7.3 odd 6
91.2.u.b.30.6 yes 12 91.17 odd 6
91.2.u.b.88.6 yes 12 7.5 odd 6
637.2.k.i.459.6 12 91.30 even 6
637.2.k.i.569.1 12 7.4 even 3
637.2.q.g.491.1 12 7.6 odd 2
637.2.q.g.589.1 12 91.69 odd 6
637.2.q.i.491.1 12 1.1 even 1 trivial
637.2.q.i.589.1 12 13.4 even 6 inner
637.2.u.g.30.6 12 91.4 even 6
637.2.u.g.361.6 12 7.2 even 3
819.2.bm.f.478.6 12 21.17 even 6
819.2.bm.f.550.1 12 273.173 even 6
819.2.do.e.361.1 12 21.5 even 6
819.2.do.e.667.1 12 273.17 even 6
1183.2.e.j.170.2 24 91.24 even 12
1183.2.e.j.170.11 24 91.80 even 12
1183.2.e.j.508.2 24 91.89 even 12
1183.2.e.j.508.11 24 91.54 even 12
8281.2.a.co.1.2 12 13.2 odd 12
8281.2.a.co.1.11 12 13.11 odd 12
8281.2.a.cp.1.2 12 91.41 even 12
8281.2.a.cp.1.11 12 91.76 even 12