Properties

Label 637.2.q.h.491.2
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: 12.0.58891012706304.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x125x102x9+15x8+2x730x6+4x5+60x416x380x2+64 x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 491.2
Root 0.7594791.19298i0.759479 - 1.19298i of defining polynomial
Character χ\chi == 637.491
Dual form 637.2.q.h.589.2

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+(1.20027+0.692976i)q2+(1.412892.44719i)q3+(0.0395678+0.0685334i)q4+0.518957iq5+(3.39169+1.95819i)q62.88158iq8+(2.49250+4.31714i)q9+(0.3596250.622889i)q10+(1.406560.812080i)q11+0.223619q12+(1.426413.31140i)q13+(1.269990.733228i)q15+(1.91773+3.32161i)q16+(0.974127+1.68724i)q176.90897iq18+(2.157401.24558i)q19+(0.03556590.0205340i)q20+(1.12550+1.94943i)q22+(4.570297.91598i)q23+(7.05179+4.07135i)q24+4.73068q25+(4.00680+2.98610i)q26+5.60916q27+(2.61498+4.52928i)q29+(1.01622+1.76014i)q30+5.79391iq31+(0.387453+0.223696i)q32+(3.974632.29475i)q332.70019iq34+(0.1972450.341639i)q36+(8.85879+5.11463i)q37+3.45262q38+(6.08826+8.16934i)q39+1.49542q40+(3.64513+2.10452i)q41+(0.498655+0.863697i)q43+0.128529iq44+(2.240411.29350i)q45+(10.9712+6.33421i)q46+4.51725iq47+(5.419089.38612i)q48+(5.67810+3.27825i)q50+5.50532q51+(0.283381+0.0332676i)q528.89651q53+(6.73251+3.88701i)q54+(0.421434+0.729946i)q55+7.03944iq57+(6.277363.62424i)q58+(5.37392+3.10263i)q59+0.116049iq60+(6.73536+11.6660i)q61+(4.015046.95426i)q628.29100q64+(1.718470.740247i)q65+6.36084q66+(7.25094+4.18633i)q67+(0.07708800.133520i)q68+(12.9146+22.3688i)q69+(4.501682.59905i)q71+(12.4402+7.18234i)q72+11.8395iq73+(7.0886312.2779i)q74+(6.6839211.5769i)q75+(0.1707270.0985694i)q76+(1.6464014.0244i)q78+0.982310q79+(1.72377+0.995221i)q80+(0.4476090.775281i)q81+(2.916765.05197i)q828.91851iq83+(0.8756030.505530i)q851.38223iq86+(7.3893412.7987i)q87+(2.340084.05313i)q88+(10.40876.00949i)q89+3.58546q90+0.723345q92+(14.17888.18614i)q93+(3.130355.42193i)q94+(0.6464011.11960i)q951.26423iq96+(3.829812.21114i)q97+8.09643iq99+O(q100)q+(-1.20027 + 0.692976i) q^{2} +(-1.41289 - 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} +0.518957i q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +(-0.359625 - 0.622889i) q^{10} +(1.40656 - 0.812080i) q^{11} +0.223619 q^{12} +(-1.42641 - 3.31140i) q^{13} +(1.26999 - 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(-0.974127 + 1.68724i) q^{17} -6.90897i q^{18} +(-2.15740 - 1.24558i) q^{19} +(-0.0355659 - 0.0205340i) q^{20} +(-1.12550 + 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +(-7.05179 + 4.07135i) q^{24} +4.73068 q^{25} +(4.00680 + 2.98610i) q^{26} +5.60916 q^{27} +(2.61498 + 4.52928i) q^{29} +(-1.01622 + 1.76014i) q^{30} +5.79391i q^{31} +(0.387453 + 0.223696i) q^{32} +(-3.97463 - 2.29475i) q^{33} -2.70019i q^{34} +(-0.197245 - 0.341639i) q^{36} +(-8.85879 + 5.11463i) q^{37} +3.45262 q^{38} +(-6.08826 + 8.16934i) q^{39} +1.49542 q^{40} +(-3.64513 + 2.10452i) q^{41} +(-0.498655 + 0.863697i) q^{43} +0.128529i q^{44} +(-2.24041 - 1.29350i) q^{45} +(10.9712 + 6.33421i) q^{46} +4.51725i q^{47} +(5.41908 - 9.38612i) q^{48} +(-5.67810 + 3.27825i) q^{50} +5.50532 q^{51} +(0.283381 + 0.0332676i) q^{52} -8.89651 q^{53} +(-6.73251 + 3.88701i) q^{54} +(0.421434 + 0.729946i) q^{55} +7.03944i q^{57} +(-6.27736 - 3.62424i) q^{58} +(5.37392 + 3.10263i) q^{59} +0.116049i q^{60} +(-6.73536 + 11.6660i) q^{61} +(-4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(1.71847 - 0.740247i) q^{65} +6.36084 q^{66} +(-7.25094 + 4.18633i) q^{67} +(-0.0770880 - 0.133520i) q^{68} +(-12.9146 + 22.3688i) q^{69} +(-4.50168 - 2.59905i) q^{71} +(12.4402 + 7.18234i) q^{72} +11.8395i q^{73} +(7.08863 - 12.2779i) q^{74} +(-6.68392 - 11.5769i) q^{75} +(0.170727 - 0.0985694i) q^{76} +(1.64640 - 14.0244i) q^{78} +0.982310 q^{79} +(-1.72377 + 0.995221i) q^{80} +(-0.447609 - 0.775281i) q^{81} +(2.91676 - 5.05197i) q^{82} -8.91851i q^{83} +(-0.875603 - 0.505530i) q^{85} -1.38223i q^{86} +(7.38934 - 12.7987i) q^{87} +(-2.34008 - 4.05313i) q^{88} +(10.4087 - 6.00949i) q^{89} +3.58546 q^{90} +0.723345 q^{92} +(14.1788 - 8.18614i) q^{93} +(-3.13035 - 5.42193i) q^{94} +(0.646401 - 1.11960i) q^{95} -1.26423i q^{96} +(-3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+4q4+18q64q912q10+6q11+4q124q13+6q158q16+4q17+12q20+6q2212q2312q2420q25+42q2612q27+8q29+6q97+O(q100) 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29}+ \cdots - 6 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 −1.20027 + 0.692976i −0.848719 + 0.490008i −0.860218 0.509926i 0.829673π-0.829673\pi
0.0114993 + 0.999934i 0.496340π0.496340\pi
33 −1.41289 2.44719i −0.815731 1.41289i −0.908802 0.417228i 0.863002π-0.863002\pi
0.0930713 0.995659i 0.470332π-0.470332\pi
44 −0.0395678 + 0.0685334i −0.0197839 + 0.0342667i
55 0.518957i 0.232085i 0.993244 + 0.116042i 0.0370208π0.0370208\pi
−0.993244 + 0.116042i 0.962979π0.962979\pi
66 3.39169 + 1.95819i 1.38465 + 0.799429i
77 0 0
88 2.88158i 1.01879i
99 −2.49250 + 4.31714i −0.830833 + 1.43905i
1010 −0.359625 0.622889i −0.113723 0.196975i
1111 1.40656 0.812080i 0.424095 0.244851i −0.272733 0.962090i 0.587928π-0.587928\pi
0.696828 + 0.717239i 0.254594π0.254594\pi
1212 0.223619 0.0645533
1313 −1.42641 3.31140i −0.395616 0.918416i
1414 0 0
1515 1.26999 0.733228i 0.327909 0.189319i
1616 1.91773 + 3.32161i 0.479433 + 0.830403i
1717 −0.974127 + 1.68724i −0.236260 + 0.409215i −0.959638 0.281237i 0.909255π-0.909255\pi
0.723378 + 0.690452i 0.242589π0.242589\pi
1818 6.90897i 1.62846i
1919 −2.15740 1.24558i −0.494942 0.285755i 0.231680 0.972792i 0.425578π-0.425578\pi
−0.726622 + 0.687037i 0.758911π0.758911\pi
2020 −0.0355659 0.0205340i −0.00795277 0.00459154i
2121 0 0
2222 −1.12550 + 1.94943i −0.239958 + 0.415620i
2323 −4.57029 7.91598i −0.952971 1.65059i −0.738943 0.673767i 0.764675π-0.764675\pi
−0.214028 0.976828i 0.568658π-0.568658\pi
2424 −7.05179 + 4.07135i −1.43944 + 0.831061i
2525 4.73068 0.946137
2626 4.00680 + 2.98610i 0.785798 + 0.585622i
2727 5.60916 1.07948
2828 0 0
2929 2.61498 + 4.52928i 0.485589 + 0.841065i 0.999863 0.0165608i 0.00527172π-0.00527172\pi
−0.514274 + 0.857626i 0.671938π0.671938\pi
3030 −1.01622 + 1.76014i −0.185535 + 0.321357i
3131 5.79391i 1.04062i 0.853978 + 0.520308i 0.174183π0.174183\pi
−0.853978 + 0.520308i 0.825817π0.825817\pi
3232 0.387453 + 0.223696i 0.0684926 + 0.0395442i
3333 −3.97463 2.29475i −0.691894 0.399465i
3434 2.70019i 0.463078i
3535 0 0
3636 −0.197245 0.341639i −0.0328742 0.0569398i
3737 −8.85879 + 5.11463i −1.45638 + 0.840840i −0.998831 0.0483462i 0.984605π-0.984605\pi
−0.457546 + 0.889186i 0.651272π0.651272\pi
3838 3.45262 0.560089
3939 −6.08826 + 8.16934i −0.974902 + 1.30814i
4040 1.49542 0.236446
4141 −3.64513 + 2.10452i −0.569273 + 0.328670i −0.756859 0.653578i 0.773267π-0.773267\pi
0.187586 + 0.982248i 0.439934π0.439934\pi
4242 0 0
4343 −0.498655 + 0.863697i −0.0760442 + 0.131712i −0.901540 0.432696i 0.857562π-0.857562\pi
0.825496 + 0.564408i 0.190896π0.190896\pi
4444 0.128529i 0.0193764i
4545 −2.24041 1.29350i −0.333980 0.192824i
4646 10.9712 + 6.33421i 1.61761 + 0.933928i
4747 4.51725i 0.658909i 0.944171 + 0.329455i 0.106865π0.106865\pi
−0.944171 + 0.329455i 0.893135π0.893135\pi
4848 5.41908 9.38612i 0.782177 1.35477i
4949 0 0
5050 −5.67810 + 3.27825i −0.803004 + 0.463615i
5151 5.50532 0.770899
5252 0.283381 + 0.0332676i 0.0392979 + 0.00461339i
5353 −8.89651 −1.22203 −0.611015 0.791619i 0.709238π-0.709238\pi
−0.611015 + 0.791619i 0.709238π0.709238\pi
5454 −6.73251 + 3.88701i −0.916178 + 0.528956i
5555 0.421434 + 0.729946i 0.0568262 + 0.0984259i
5656 0 0
5757 7.03944i 0.932397i
5858 −6.27736 3.62424i −0.824258 0.475886i
5959 5.37392 + 3.10263i 0.699624 + 0.403928i 0.807207 0.590268i 0.200978π-0.200978\pi
−0.107583 + 0.994196i 0.534311π0.534311\pi
6060 0.116049i 0.0149818i
6161 −6.73536 + 11.6660i −0.862375 + 1.49368i 0.00725571 + 0.999974i 0.497690π0.497690\pi
−0.869630 + 0.493703i 0.835643π0.835643\pi
6262 −4.01504 6.95426i −0.509911 0.883191i
6363 0 0
6464 −8.29100 −1.03637
6565 1.71847 0.740247i 0.213150 0.0918164i
6666 6.36084 0.782965
6767 −7.25094 + 4.18633i −0.885843 + 0.511442i −0.872580 0.488470i 0.837555π-0.837555\pi
−0.0132624 + 0.999912i 0.504222π0.504222\pi
6868 −0.0770880 0.133520i −0.00934830 0.0161917i
6969 −12.9146 + 22.3688i −1.55474 + 2.69288i
7070 0 0
7171 −4.50168 2.59905i −0.534251 0.308450i 0.208495 0.978023i 0.433144π-0.433144\pi
−0.742746 + 0.669573i 0.766477π0.766477\pi
7272 12.4402 + 7.18234i 1.46609 + 0.846447i
7373 11.8395i 1.38571i 0.721076 + 0.692856i 0.243648π0.243648\pi
−0.721076 + 0.692856i 0.756352π0.756352\pi
7474 7.08863 12.2779i 0.824037 1.42727i
7575 −6.68392 11.5769i −0.771793 1.33678i
7676 0.170727 0.0985694i 0.0195838 0.0113067i
7777 0 0
7878 1.64640 14.0244i 0.186418 1.58795i
7979 0.982310 0.110518 0.0552592 0.998472i 0.482401π-0.482401\pi
0.0552592 + 0.998472i 0.482401π0.482401\pi
8080 −1.72377 + 0.995221i −0.192724 + 0.111269i
8181 −0.447609 0.775281i −0.0497343 0.0861423i
8282 2.91676 5.05197i 0.322102 0.557897i
8383 8.91851i 0.978934i −0.872022 0.489467i 0.837191π-0.837191\pi
0.872022 0.489467i 0.162809π-0.162809\pi
8484 0 0
8585 −0.875603 0.505530i −0.0949725 0.0548324i
8686 1.38223i 0.149049i
8787 7.38934 12.7987i 0.792220 1.37217i
8888 −2.34008 4.05313i −0.249453 0.432065i
8989 10.4087 6.00949i 1.10332 0.637005i 0.166233 0.986087i 0.446840π-0.446840\pi
0.937092 + 0.349082i 0.113506π0.113506\pi
9090 3.58546 0.377941
9191 0 0
9292 0.723345 0.0754139
9393 14.1788 8.18614i 1.47027 0.848863i
9494 −3.13035 5.42193i −0.322871 0.559229i
9595 0.646401 1.11960i 0.0663194 0.114869i
9696 1.26423i 0.129030i
9797 −3.82981 2.21114i −0.388858 0.224507i 0.292807 0.956172i 0.405411π-0.405411\pi
−0.681665 + 0.731664i 0.738744π0.738744\pi
9898 0 0
9999 8.09643i 0.813722i
100100 −0.187183 + 0.324210i −0.0187183 + 0.0324210i
101101 −9.15132 15.8506i −0.910591 1.57719i −0.813231 0.581940i 0.802294π-0.802294\pi
−0.0973594 0.995249i 0.531040π-0.531040\pi
102102 −6.60787 + 3.81506i −0.654277 + 0.377747i
103103 5.02046 0.494680 0.247340 0.968929i 0.420444π-0.420444\pi
0.247340 + 0.968929i 0.420444π0.420444\pi
104104 −9.54206 + 4.11033i −0.935676 + 0.403051i
105105 0 0
106106 10.6782 6.16507i 1.03716 0.598804i
107107 −3.07228 5.32134i −0.297008 0.514434i 0.678442 0.734654i 0.262656π-0.262656\pi
−0.975450 + 0.220221i 0.929322π0.929322\pi
108108 −0.221942 + 0.384415i −0.0213564 + 0.0369903i
109109 11.8962i 1.13945i −0.821834 0.569727i 0.807049π-0.807049\pi
0.821834 0.569727i 0.192951π-0.192951\pi
110110 −1.01167 0.584088i −0.0964590 0.0556906i
111111 25.0330 + 14.4528i 2.37602 + 1.37180i
112112 0 0
113113 −1.77806 + 3.07969i −0.167266 + 0.289713i −0.937458 0.348099i 0.886827π-0.886827\pi
0.770192 + 0.637812i 0.220161π0.220161\pi
114114 −4.87817 8.44923i −0.456882 0.791343i
115115 4.10805 2.37178i 0.383078 0.221170i
116116 −0.413875 −0.0384274
117117 17.8511 + 2.09563i 1.65033 + 0.193741i
118118 −8.60020 −0.791713
119119 0 0
120120 −2.11286 3.65957i −0.192877 0.334072i
121121 −4.18105 + 7.24180i −0.380096 + 0.658345i
122122 18.6698i 1.69028i
123123 10.3003 + 5.94689i 0.928748 + 0.536213i
124124 −0.397076 0.229252i −0.0356585 0.0205874i
125125 5.04981i 0.451668i
126126 0 0
127127 −0.711749 1.23279i −0.0631575 0.109392i 0.832718 0.553698i 0.186784π-0.186784\pi
−0.895875 + 0.444306i 0.853450π0.853450\pi
128128 9.17653 5.29807i 0.811098 0.468288i
129129 2.81818 0.248127
130130 −1.54966 + 2.07936i −0.135914 + 0.182372i
131131 −8.67374 −0.757828 −0.378914 0.925432i 0.623702π-0.623702\pi
−0.378914 + 0.925432i 0.623702π0.623702\pi
132132 0.314535 0.181597i 0.0273767 0.0158060i
133133 0 0
134134 5.80205 10.0495i 0.501221 0.868141i
135135 2.91091i 0.250531i
136136 4.86191 + 2.80703i 0.416906 + 0.240701i
137137 7.37667 + 4.25892i 0.630231 + 0.363864i 0.780842 0.624729i 0.214791π-0.214791\pi
−0.150611 + 0.988593i 0.548124π0.548124\pi
138138 35.7981i 3.04733i
139139 −2.51922 + 4.36342i −0.213677 + 0.370100i −0.952863 0.303402i 0.901877π-0.901877\pi
0.739185 + 0.673502i 0.235211π0.235211\pi
140140 0 0
141141 11.0546 6.38237i 0.930964 0.537493i
142142 7.20431 0.604572
143143 −4.69546 3.49933i −0.392654 0.292628i
144144 −19.1198 −1.59332
145145 −2.35050 + 1.35706i −0.195198 + 0.112698i
146146 −8.20451 14.2106i −0.679010 1.17608i
147147 0 0
148148 0.809498i 0.0665403i
149149 2.91409 + 1.68245i 0.238732 + 0.137832i 0.614594 0.788844i 0.289320π-0.289320\pi
−0.375862 + 0.926676i 0.622653π0.622653\pi
150150 16.0450 + 9.26360i 1.31007 + 0.756370i
151151 12.6566i 1.02998i 0.857196 + 0.514991i 0.172205π0.172205\pi
−0.857196 + 0.514991i 0.827795π0.827795\pi
152152 −3.58924 + 6.21674i −0.291125 + 0.504244i
153153 −4.85602 8.41087i −0.392586 0.679979i
154154 0 0
155155 −3.00679 −0.241511
156156 −0.318973 0.740492i −0.0255383 0.0592868i
157157 −10.3691 −0.827547 −0.413773 0.910380i 0.635789π-0.635789\pi
−0.413773 + 0.910380i 0.635789π0.635789\pi
158158 −1.17904 + 0.680717i −0.0937992 + 0.0541550i
159159 12.5698 + 21.7715i 0.996847 + 1.72659i
160160 −0.116089 + 0.201071i −0.00917761 + 0.0158961i
161161 0 0
162162 1.07450 + 0.620364i 0.0844209 + 0.0487404i
163163 13.6428 + 7.87669i 1.06859 + 0.616950i 0.927796 0.373089i 0.121701π-0.121701\pi
0.140794 + 0.990039i 0.455035π0.455035\pi
164164 0.333084i 0.0260095i
165165 1.19088 2.06266i 0.0927098 0.160578i
166166 6.18032 + 10.7046i 0.479686 + 0.830840i
167167 14.2016 8.19930i 1.09895 0.634481i 0.163007 0.986625i 0.447881π-0.447881\pi
0.935946 + 0.352144i 0.114547π0.114547\pi
168168 0 0
169169 −8.93069 + 9.44684i −0.686976 + 0.726680i
170170 1.40128 0.107473
171171 10.7547 6.20920i 0.822429 0.474830i
172172 −0.0394614 0.0683491i −0.00300890 0.00521157i
173173 0.150677 0.260981i 0.0114558 0.0198420i −0.860241 0.509888i 0.829687π-0.829687\pi
0.871696 + 0.490046i 0.163020π0.163020\pi
174174 20.4825i 1.55278i
175175 0 0
176176 5.39483 + 3.11470i 0.406650 + 0.234780i
177177 17.5347i 1.31799i
178178 −8.32887 + 14.4260i −0.624275 + 1.08128i
179179 −4.90791 8.50075i −0.366834 0.635376i 0.622234 0.782831i 0.286225π-0.286225\pi
−0.989069 + 0.147455i 0.952892π0.952892\pi
180180 0.177296 0.102362i 0.0132149 0.00762960i
181181 −12.4320 −0.924062 −0.462031 0.886864i 0.652879π-0.652879\pi
−0.462031 + 0.886864i 0.652879π0.652879\pi
182182 0 0
183183 38.0652 2.81386
184184 −22.8105 + 13.1697i −1.68162 + 0.970881i
185185 −2.65427 4.59733i −0.195146 0.338003i
186186 −11.3456 + 19.6512i −0.831900 + 1.44089i
187187 3.16427i 0.231395i
188188 −0.309583 0.178738i −0.0225786 0.0130358i
189189 0 0
190190 1.79176i 0.129988i
191191 6.12346 10.6061i 0.443078 0.767434i −0.554838 0.831958i 0.687220π-0.687220\pi
0.997916 + 0.0645248i 0.0205531π0.0205531\pi
192192 11.7142 + 20.2897i 0.845403 + 1.46428i
193193 −10.0752 + 5.81692i −0.725229 + 0.418711i −0.816674 0.577099i 0.804185π-0.804185\pi
0.0914452 + 0.995810i 0.470851π0.470851\pi
194194 6.12908 0.440042
195195 −4.23953 3.15955i −0.303599 0.226260i
196196 0 0
197197 −1.55984 + 0.900572i −0.111134 + 0.0641631i −0.554537 0.832159i 0.687104π-0.687104\pi
0.443403 + 0.896322i 0.353771π0.353771\pi
198198 −5.61064 9.71791i −0.398731 0.690622i
199199 −3.29657 + 5.70982i −0.233687 + 0.404759i −0.958890 0.283777i 0.908413π-0.908413\pi
0.725203 + 0.688535i 0.241746π0.241746\pi
200200 13.6319i 0.963918i
201201 20.4895 + 11.8296i 1.44522 + 0.834397i
202202 21.9681 + 12.6833i 1.54567 + 0.892394i
203203 0 0
204204 −0.217833 + 0.377298i −0.0152514 + 0.0264162i
205205 −1.09215 1.89166i −0.0762793 0.132120i
206206 −6.02590 + 3.47906i −0.419845 + 0.242397i
207207 45.5658 3.16704
208208 8.26369 11.0884i 0.572984 0.768840i
209209 −4.04603 −0.279870
210210 0 0
211211 −5.35996 9.28373i −0.368995 0.639118i 0.620414 0.784275i 0.286965π-0.286965\pi
−0.989409 + 0.145157i 0.953631π0.953631\pi
212212 0.352015 0.609708i 0.0241765 0.0418749i
213213 14.6886i 1.00645i
214214 7.37513 + 4.25803i 0.504154 + 0.291073i
215215 −0.448221 0.258781i −0.0305684 0.0176487i
216216 16.1633i 1.09977i
217217 0 0
218218 8.24382 + 14.2787i 0.558342 + 0.967076i
219219 28.9736 16.7279i 1.95785 1.13037i
220220 −0.0667009 −0.00449697
221221 6.97662 + 0.819021i 0.469298 + 0.0550933i
222222 −40.0617 −2.68877
223223 11.1612 6.44392i 0.747409 0.431517i −0.0773480 0.997004i 0.524645π-0.524645\pi
0.824757 + 0.565487i 0.191312π0.191312\pi
224224 0 0
225225 −11.7912 + 20.4230i −0.786082 + 1.36153i
226226 4.92862i 0.327847i
227227 0.605486 + 0.349577i 0.0401875 + 0.0232023i 0.519959 0.854191i 0.325947π-0.325947\pi
−0.479772 + 0.877393i 0.659280π0.659280\pi
228228 −0.482437 0.278535i −0.0319502 0.0184464i
229229 18.2868i 1.20843i −0.796822 0.604214i 0.793487π-0.793487\pi
0.796822 0.604214i 0.206513π-0.206513\pi
230230 −3.28718 + 5.69356i −0.216750 + 0.375422i
231231 0 0
232232 13.0515 7.53528i 0.856872 0.494715i
233233 −26.7796 −1.75439 −0.877194 0.480137i 0.840587π-0.840587\pi
−0.877194 + 0.480137i 0.840587π0.840587\pi
234234 −22.8783 + 9.85505i −1.49560 + 0.644245i
235235 −2.34426 −0.152923
236236 −0.425268 + 0.245528i −0.0276826 + 0.0159825i
237237 −1.38789 2.40390i −0.0901533 0.156150i
238238 0 0
239239 16.6177i 1.07491i 0.843293 + 0.537454i 0.180614π0.180614\pi
−0.843293 + 0.537454i 0.819386π0.819386\pi
240240 4.87099 + 2.81227i 0.314421 + 0.181531i
241241 −15.0800 8.70643i −0.971387 0.560830i −0.0717279 0.997424i 0.522851π-0.522851\pi
−0.899659 + 0.436594i 0.856185π0.856185\pi
242242 11.5895i 0.745000i
243243 7.14890 12.3823i 0.458602 0.794322i
244244 −0.533007 0.923194i −0.0341222 0.0591015i
245245 0 0
246246 −16.4842 −1.05099
247247 −1.04725 + 8.92073i −0.0666350 + 0.567612i
248248 16.6956 1.06017
249249 −21.8253 + 12.6008i −1.38312 + 0.798546i
250250 −3.49940 6.06113i −0.221321 0.383340i
251251 3.22491 5.58571i 0.203554 0.352567i −0.746117 0.665815i 0.768084π-0.768084\pi
0.949671 + 0.313249i 0.101417π0.101417\pi
252252 0 0
253253 −12.8568 7.42288i −0.808300 0.466672i
254254 1.70858 + 0.986451i 0.107206 + 0.0618954i
255255 2.85703i 0.178914i
256256 0.948120 1.64219i 0.0592575 0.102637i
257257 1.83578 + 3.17966i 0.114513 + 0.198342i 0.917585 0.397540i 0.130136π-0.130136\pi
−0.803072 + 0.595882i 0.796803π0.796803\pi
258258 −3.38257 + 1.95293i −0.210590 + 0.121584i
259259 0 0
260260 −0.0172645 + 0.147063i −0.00107070 + 0.00912044i
261261 −26.0713 −1.61377
262262 10.4108 6.01070i 0.643183 0.371342i
263263 −9.15964 15.8650i −0.564807 0.978275i −0.997068 0.0765263i 0.975617π-0.975617\pi
0.432260 0.901749i 0.357716π-0.357716\pi
264264 −6.61252 + 11.4532i −0.406973 + 0.704897i
265265 4.61690i 0.283614i
266266 0 0
267267 −29.4128 16.9815i −1.80003 1.03925i
268268 0.662575i 0.0404732i
269269 13.7715 23.8529i 0.839661 1.45434i −0.0505171 0.998723i 0.516087π-0.516087\pi
0.890178 0.455613i 0.150580π-0.150580\pi
270270 −2.01719 3.49388i −0.122762 0.212631i
271271 −5.64582 + 3.25961i −0.342959 + 0.198007i −0.661580 0.749875i 0.730114π-0.730114\pi
0.318621 + 0.947882i 0.396780π0.396780\pi
272272 −7.47246 −0.453084
273273 0 0
274274 −11.8053 −0.713186
275275 6.65401 3.84169i 0.401252 0.231663i
276276 −1.02200 1.77016i −0.0615174 0.106551i
277277 2.72093 4.71279i 0.163485 0.283164i −0.772631 0.634855i 0.781060π-0.781060\pi
0.936116 + 0.351691i 0.114393π0.114393\pi
278278 6.98304i 0.418815i
279279 −25.0131 14.4413i −1.49749 0.864579i
280280 0 0
281281 3.54237i 0.211320i 0.994402 + 0.105660i 0.0336955π0.0336955\pi
−0.994402 + 0.105660i 0.966304π0.966304\pi
282282 −8.84566 + 15.3211i −0.526752 + 0.912360i
283283 7.06956 + 12.2448i 0.420242 + 0.727880i 0.995963 0.0897658i 0.0286119π-0.0286119\pi
−0.575721 + 0.817646i 0.695279π0.695279\pi
284284 0.356243 0.205677i 0.0211391 0.0122047i
285285 −3.65317 −0.216395
286286 8.06077 + 0.946296i 0.476643 + 0.0559556i
287287 0 0
288288 −1.93145 + 1.11512i −0.113812 + 0.0657093i
289289 6.60215 + 11.4353i 0.388362 + 0.672663i
290290 1.88082 3.25768i 0.110446 0.191298i
291291 12.4964i 0.732551i
292292 −0.811403 0.468464i −0.0474838 0.0274148i
293293 7.23071 + 4.17465i 0.422423 + 0.243886i 0.696113 0.717932i 0.254911π-0.254911\pi
−0.273691 + 0.961818i 0.588244π0.588244\pi
294294 0 0
295295 −1.61013 + 2.78883i −0.0937455 + 0.162372i
296296 14.7382 + 25.5274i 0.856642 + 1.48375i
297297 7.88964 4.55508i 0.457803 0.264313i
298298 −4.66359 −0.270155
299299 −19.6938 + 26.4255i −1.13892 + 1.52823i
300300 1.05787 0.0610762
301301 0 0
302302 −8.77074 15.1914i −0.504699 0.874165i
303303 −25.8596 + 44.7901i −1.48559 + 2.57312i
304304 9.55474i 0.548002i
305305 −6.05415 3.49536i −0.346659 0.200144i
306306 11.6571 + 6.73021i 0.666390 + 0.384741i
307307 8.33362i 0.475625i 0.971311 + 0.237813i 0.0764304π0.0764304\pi
−0.971311 + 0.237813i 0.923570π0.923570\pi
308308 0 0
309309 −7.09334 12.2860i −0.403526 0.698927i
310310 3.60896 2.08363i 0.204975 0.118342i
311311 −14.6227 −0.829176 −0.414588 0.910009i 0.636074π-0.636074\pi
−0.414588 + 0.910009i 0.636074π0.636074\pi
312312 23.5406 + 17.5438i 1.33273 + 0.993224i
313313 −17.1328 −0.968404 −0.484202 0.874956i 0.660890π-0.660890\pi
−0.484202 + 0.874956i 0.660890π0.660890\pi
314314 12.4458 7.18556i 0.702355 0.405505i
315315 0 0
316316 −0.0388678 + 0.0673210i −0.00218649 + 0.00378710i
317317 14.0000i 0.786320i 0.919470 + 0.393160i 0.128618π0.128618\pi
−0.919470 + 0.393160i 0.871382π0.871382\pi
318318 −30.1742 17.4211i −1.69209 0.976926i
319319 7.35627 + 4.24714i 0.411872 + 0.237794i
320320 4.30267i 0.240527i
321321 −8.68157 + 15.0369i −0.484558 + 0.839279i
322322 0 0
323323 4.20317 2.42670i 0.233871 0.135025i
324324 0.0708435 0.00393575
325325 −6.74791 15.6652i −0.374307 0.868947i
326326 −21.8334 −1.20924
327327 −29.1124 + 16.8081i −1.60992 + 0.929487i
328328 6.06434 + 10.5037i 0.334847 + 0.579972i
329329 0 0
330330 3.30100i 0.181714i
331331 5.99286 + 3.45998i 0.329397 + 0.190178i 0.655574 0.755131i 0.272427π-0.272427\pi
−0.326176 + 0.945309i 0.605760π0.605760\pi
332332 0.611216 + 0.352886i 0.0335448 + 0.0193671i
333333 50.9928i 2.79439i
334334 −11.3638 + 19.6827i −0.621801 + 1.07699i
335335 −2.17253 3.76292i −0.118698 0.205591i
336336 0 0
337337 11.1559 0.607703 0.303852 0.952719i 0.401727π-0.401727\pi
0.303852 + 0.952719i 0.401727π0.401727\pi
338338 4.17280 17.5275i 0.226970 0.953371i
339339 10.0488 0.545776
340340 0.0692913 0.0400054i 0.00375785 0.00216960i
341341 4.70512 + 8.14950i 0.254796 + 0.441320i
342342 −8.60566 + 14.9054i −0.465341 + 0.805994i
343343 0 0
344344 2.48881 + 1.43692i 0.134188 + 0.0774734i
345345 −11.6084 6.70213i −0.624977 0.360830i
346346 0.417663i 0.0224537i
347347 2.46255 4.26527i 0.132197 0.228971i −0.792326 0.610097i 0.791130π-0.791130\pi
0.924523 + 0.381126i 0.124464π0.124464\pi
348348 0.584759 + 1.01283i 0.0313464 + 0.0542935i
349349 −1.31926 + 0.761675i −0.0706183 + 0.0407715i −0.534893 0.844920i 0.679648π-0.679648\pi
0.464275 + 0.885691i 0.346315π0.346315\pi
350350 0 0
351351 −8.00098 18.5741i −0.427061 0.991415i
352352 0.726636 0.0387298
353353 −15.5261 + 8.96401i −0.826372 + 0.477106i −0.852609 0.522550i 0.824981π-0.824981\pi
0.0262367 + 0.999656i 0.491648π0.491648\pi
354354 12.1511 + 21.0463i 0.645824 + 1.11860i
355355 1.34879 2.33618i 0.0715865 0.123991i
356356 0.951129i 0.0504097i
357357 0 0
358358 11.7816 + 6.80213i 0.622679 + 0.359504i
359359 20.0014i 1.05563i −0.849359 0.527816i 0.823011π-0.823011\pi
0.849359 0.527816i 0.176989π-0.176989\pi
360360 −3.72733 + 6.45592i −0.196447 + 0.340257i
361361 −6.39707 11.0801i −0.336688 0.583161i
362362 14.9217 8.61507i 0.784269 0.452798i
363363 23.6294 1.24022
364364 0 0
365365 −6.14421 −0.321602
366366 −45.6885 + 26.3783i −2.38818 + 1.37882i
367367 13.7078 + 23.7427i 0.715544 + 1.23936i 0.962749 + 0.270395i 0.0871543π0.0871543\pi
−0.247206 + 0.968963i 0.579512π0.579512\pi
368368 17.5292 30.3615i 0.913772 1.58270i
369369 20.9820i 1.09228i
370370 6.37169 + 3.67870i 0.331248 + 0.191246i
371371 0 0
372372 1.29563i 0.0671752i
373373 7.94643 13.7636i 0.411451 0.712653i −0.583598 0.812043i 0.698356π-0.698356\pi
0.995049 + 0.0993893i 0.0316889π0.0316889\pi
374374 −2.19277 3.79798i −0.113385 0.196389i
375375 12.3578 7.13481i 0.638156 0.368440i
376376 13.0168 0.671292
377377 11.2682 15.1199i 0.580341 0.778712i
378378 0 0
379379 7.60284 4.38950i 0.390532 0.225474i −0.291859 0.956461i 0.594274π-0.594274\pi
0.682390 + 0.730988i 0.260940π0.260940\pi
380380 0.0511533 + 0.0886001i 0.00262411 + 0.00454509i
381381 −2.01124 + 3.48357i −0.103039 + 0.178469i
382382 16.9736i 0.868447i
383383 −6.89562 3.98119i −0.352349 0.203429i 0.313370 0.949631i 0.398542π-0.398542\pi
−0.665720 + 0.746202i 0.731875π0.731875\pi
384384 −25.9308 14.9712i −1.32328 0.763994i
385385 0 0
386386 8.06198 13.9638i 0.410344 0.710736i
387387 −2.48580 4.30553i −0.126360 0.218862i
388388 0.303074 0.174980i 0.0153863 0.00888326i
389389 −32.0434 −1.62467 −0.812333 0.583194i 0.801803π-0.801803\pi
−0.812333 + 0.583194i 0.801803π0.801803\pi
390390 7.27808 + 0.854411i 0.368540 + 0.0432648i
391391 17.8082 0.900598
392392 0 0
393393 12.2550 + 21.2263i 0.618184 + 1.07073i
394394 1.24815 2.16186i 0.0628809 0.108913i
395395 0.509777i 0.0256496i
396396 −0.554876 0.320358i −0.0278836 0.0160986i
397397 −5.57251 3.21729i −0.279676 0.161471i 0.353601 0.935396i 0.384957π-0.384957\pi
−0.633277 + 0.773925i 0.718290π0.718290\pi
398398 9.13777i 0.458035i
399399 0 0
400400 9.07219 + 15.7135i 0.453609 + 0.785675i
401401 −0.462092 + 0.266789i −0.0230758 + 0.0133228i −0.511494 0.859287i 0.670908π-0.670908\pi
0.488418 + 0.872610i 0.337574π0.337574\pi
402402 −32.7906 −1.63545
403403 19.1859 8.26451i 0.955719 0.411685i
404404 1.44839 0.0720601
405405 0.402337 0.232290i 0.0199923 0.0115426i
406406 0 0
407407 −8.30697 + 14.3881i −0.411761 + 0.713191i
408408 15.8640i 0.785387i
409409 34.4269 + 19.8764i 1.70230 + 0.982824i 0.943424 + 0.331590i 0.107585π0.107585\pi
0.758877 + 0.651234i 0.225748π0.225748\pi
410410 2.62176 + 1.51367i 0.129479 + 0.0747550i
411411 24.0695i 1.18726i
412412 −0.198648 + 0.344069i −0.00978670 + 0.0169511i
413413 0 0
414414 −54.6913 + 31.5760i −2.68793 + 1.55188i
415415 4.62832 0.227195
416416 0.188078 1.60209i 0.00922128 0.0785490i
417417 14.2375 0.697213
418418 4.85633 2.80380i 0.237531 0.137139i
419419 11.9088 + 20.6266i 0.581783 + 1.00768i 0.995268 + 0.0971665i 0.0309779π0.0309779\pi
−0.413485 + 0.910511i 0.635689π0.635689\pi
420420 0 0
421421 23.2419i 1.13274i −0.824151 0.566370i 0.808347π-0.808347\pi
0.824151 0.566370i 0.191653π-0.191653\pi
422422 12.8668 + 7.42865i 0.626346 + 0.361621i
423423 −19.5016 11.2593i −0.948200 0.547444i
424424 25.6360i 1.24500i
425425 −4.60828 + 7.98178i −0.223535 + 0.387173i
426426 −10.1789 17.6303i −0.493168 0.854192i
427427 0 0
428428 0.486253 0.0235039
429429 −1.92937 + 16.4348i −0.0931510 + 0.793482i
430430 0.717316 0.0345920
431431 −2.34424 + 1.35345i −0.112918 + 0.0651932i −0.555395 0.831586i 0.687433π-0.687433\pi
0.442477 + 0.896780i 0.354100π0.354100\pi
432432 10.7569 + 18.6314i 0.517540 + 0.896406i
433433 2.90945 5.03932i 0.139819 0.242174i −0.787609 0.616176i 0.788681π-0.788681\pi
0.927428 + 0.374002i 0.122015π0.122015\pi
434434 0 0
435435 6.64198 + 3.83475i 0.318459 + 0.183862i
436436 0.815290 + 0.470708i 0.0390453 + 0.0225428i
437437 22.7706i 1.08927i
438438 −23.1841 + 40.1560i −1.10778 + 1.91873i
439439 −19.0851 33.0563i −0.910882 1.57769i −0.812822 0.582513i 0.802070π-0.802070\pi
−0.0980599 0.995181i 0.531264π-0.531264\pi
440440 2.10340 1.21440i 0.100276 0.0578942i
441441 0 0
442442 −8.94139 + 3.85158i −0.425298 + 0.183201i
443443 −31.6740 −1.50488 −0.752440 0.658661i 0.771123π-0.771123\pi
−0.752440 + 0.658661i 0.771123π0.771123\pi
444444 −1.98100 + 1.14373i −0.0940139 + 0.0542790i
445445 3.11867 + 5.40169i 0.147839 + 0.256065i
446446 −8.93097 + 15.4689i −0.422894 + 0.732473i
447447 9.50845i 0.449734i
448448 0 0
449449 27.1975 + 15.7025i 1.28353 + 0.741045i 0.977491 0.210975i 0.0676638π-0.0676638\pi
0.306036 + 0.952020i 0.400997π0.400997\pi
450450 32.6842i 1.54075i
451451 −3.41807 + 5.92027i −0.160951 + 0.278775i
452452 −0.140708 0.243713i −0.00661834 0.0114633i
453453 30.9732 17.8824i 1.45525 0.840187i
454454 −0.968995 −0.0454772
455455 0 0
456456 20.2847 0.949920
457457 27.5640 15.9141i 1.28939 0.744429i 0.310844 0.950461i 0.399388π-0.399388\pi
0.978545 + 0.206032i 0.0660551π0.0660551\pi
458458 12.6723 + 21.9491i 0.592140 + 1.02562i
459459 −5.46403 + 9.46398i −0.255039 + 0.441741i
460460 0.375385i 0.0175024i
461461 −1.01005 0.583153i −0.0470427 0.0271601i 0.476294 0.879286i 0.341980π-0.341980\pi
−0.523337 + 0.852126i 0.675313π0.675313\pi
462462 0 0
463463 20.3441i 0.945469i 0.881205 + 0.472734i 0.156733π0.156733\pi
−0.881205 + 0.472734i 0.843267π0.843267\pi
464464 −10.0297 + 17.3719i −0.465615 + 0.806470i
465465 4.24825 + 7.35819i 0.197008 + 0.341228i
466466 32.1427 18.5576i 1.48898 0.859664i
467467 −1.56939 −0.0726229 −0.0363114 0.999341i 0.511561π-0.511561\pi
−0.0363114 + 0.999341i 0.511561π0.511561\pi
468468 −0.849948 + 1.14048i −0.0392889 + 0.0527185i
469469 0 0
470470 2.81375 1.62452i 0.129788 0.0749334i
471471 14.6504 + 25.3753i 0.675055 + 1.16923i
472472 8.94049 15.4854i 0.411519 0.712773i
473473 1.61979i 0.0744781i
474474 3.33169 + 1.92355i 0.153030 + 0.0883517i
475475 −10.2060 5.89243i −0.468283 0.270363i
476476 0 0
477477 22.1745 38.4074i 1.01530 1.75856i
478478 −11.5157 19.9457i −0.526714 0.912295i
479479 −6.68501 + 3.85959i −0.305446 + 0.176349i −0.644887 0.764278i 0.723095π-0.723095\pi
0.339441 + 0.940627i 0.389762π0.389762\pi
480480 0.656080 0.0299458
481481 29.5729 + 22.0394i 1.34841 + 1.00491i
482482 24.1334 1.09925
483483 0 0
484484 −0.330870 0.573083i −0.0150395 0.0260492i
485485 1.14749 1.98751i 0.0521047 0.0902481i
486486 19.8161i 0.898875i
487487 −0.0659739 0.0380900i −0.00298956 0.00172602i 0.498504 0.866887i 0.333883π-0.333883\pi
−0.501494 + 0.865161i 0.667216π0.667216\pi
488488 33.6165 + 19.4085i 1.52175 + 0.878582i
489489 44.5155i 2.01306i
490490 0 0
491491 0.893574 + 1.54772i 0.0403264 + 0.0698474i 0.885484 0.464670i 0.153827π-0.153827\pi
−0.845158 + 0.534517i 0.820494π0.820494\pi
492492 −0.815121 + 0.470610i −0.0367485 + 0.0212167i
493493 −10.1893 −0.458902
494494 −4.92487 11.4330i −0.221580 0.514395i
495495 −4.20170 −0.188852
496496 −19.2451 + 11.1112i −0.864131 + 0.498906i
497497 0 0
498498 17.4642 30.2488i 0.782589 1.35548i
499499 8.33493i 0.373123i −0.982443 0.186561i 0.940266π-0.940266\pi
0.982443 0.186561i 0.0597343π-0.0597343\pi
500500 −0.346080 0.199810i −0.0154772 0.00893576i
501501 −40.1305 23.1694i −1.79290 1.03513i
502502 8.93914i 0.398973i
503503 0.720238 1.24749i 0.0321138 0.0556228i −0.849522 0.527554i 0.823109π-0.823109\pi
0.881636 + 0.471931i 0.156443π0.156443\pi
504504 0 0
505505 8.22576 4.74914i 0.366041 0.211334i
506506 20.5755 0.914693
507507 35.7363 + 8.50779i 1.58710 + 0.377844i
508508 0.112649 0.00499801
509509 −12.8394 + 7.41282i −0.569096 + 0.328568i −0.756788 0.653660i 0.773233π-0.773233\pi
0.187692 + 0.982228i 0.439899π0.439899\pi
510510 −1.97985 3.42920i −0.0876693 0.151848i
511511 0 0
512512 23.8204i 1.05272i
513513 −12.1012 6.98664i −0.534282 0.308468i
514514 −4.40686 2.54430i −0.194378 0.112224i
515515 2.60540i 0.114808i
516516 −0.111509 + 0.193139i −0.00490891 + 0.00850248i
517517 3.66837 + 6.35380i 0.161335 + 0.279440i
518518 0 0
519519 −0.851561 −0.0373794
520520 −2.13308 4.95192i −0.0935419 0.217156i
521521 0.334388 0.0146498 0.00732489 0.999973i 0.497668π-0.497668\pi
0.00732489 + 0.999973i 0.497668π0.497668\pi
522522 31.2926 18.0668i 1.36964 0.790763i
523523 −16.2533 28.1515i −0.710705 1.23098i −0.964593 0.263744i 0.915043π-0.915043\pi
0.253887 0.967234i 0.418291π-0.418291\pi
524524 0.343201 0.594441i 0.0149928 0.0259683i
525525 0 0
526526 21.9881 + 12.6948i 0.958726 + 0.553521i
527527 −9.77570 5.64400i −0.425836 0.245857i
528528 17.6029i 0.766068i
529529 −30.2751 + 52.4380i −1.31631 + 2.27991i
530530 3.19941 + 5.54153i 0.138973 + 0.240709i
531531 −26.7890 + 15.4666i −1.16254 + 0.671194i
532532 0 0
533533 12.1683 + 9.06855i 0.527070 + 0.392803i
534534 47.0710 2.03696
535535 2.76155 1.59438i 0.119392 0.0689311i
536536 12.0633 + 20.8942i 0.521053 + 0.902491i
537537 −13.8686 + 24.0212i −0.598476 + 1.03659i
538538 38.1732i 1.64576i
539539 0 0
540540 −0.199495 0.115178i −0.00858488 0.00495649i
541541 10.6015i 0.455796i 0.973685 + 0.227898i 0.0731852π0.0731852\pi
−0.973685 + 0.227898i 0.926815π0.926815\pi
542542 4.51767 7.82483i 0.194051 0.336105i
543543 17.5650 + 30.4235i 0.753786 + 1.30560i
544544 −0.754856 + 0.435816i −0.0323642 + 0.0186855i
545545 6.17364 0.264450
546546 0 0
547547 10.2327 0.437519 0.218760 0.975779i 0.429799π-0.429799\pi
0.218760 + 0.975779i 0.429799π0.429799\pi
548548 −0.583756 + 0.337032i −0.0249368 + 0.0143973i
549549 −33.5758 58.1549i −1.43298 2.48199i
550550 −5.32440 + 9.22214i −0.227033 + 0.393233i
551551 13.0286i 0.555038i
552552 64.4574 + 37.2145i 2.74349 + 1.58396i
553553 0 0
554554 7.54216i 0.320436i
555555 −7.50037 + 12.9910i −0.318373 + 0.551438i
556556 −0.199360 0.345301i −0.00845474 0.0146440i
557557 27.7067 15.9965i 1.17397 0.677793i 0.219359 0.975644i 0.429603π-0.429603\pi
0.954612 + 0.297851i 0.0962700π0.0962700\pi
558558 40.0300 1.69460
559559 3.57133 + 0.419257i 0.151051 + 0.0177327i
560560 0 0
561561 7.74359 4.47076i 0.326934 0.188756i
562562 −2.45478 4.25180i −0.103549 0.179351i
563563 −5.39566 + 9.34556i −0.227400 + 0.393868i −0.957037 0.289967i 0.906356π-0.906356\pi
0.729637 + 0.683835i 0.239689π0.239689\pi
564564 1.01014i 0.0425348i
565565 −1.59823 0.922737i −0.0672380 0.0388199i
566566 −16.9708 9.79808i −0.713335 0.411844i
567567 0 0
568568 −7.48937 + 12.9720i −0.314247 + 0.544292i
569569 −12.3007 21.3054i −0.515672 0.893170i −0.999835 0.0181917i 0.994209π-0.994209\pi
0.484163 0.874978i 0.339124π-0.339124\pi
570570 4.38479 2.53156i 0.183659 0.106035i
571571 −16.5724 −0.693534 −0.346767 0.937951i 0.612721π-0.612721\pi
−0.346767 + 0.937951i 0.612721π0.612721\pi
572572 0.425610 0.183335i 0.0177956 0.00766563i
573573 −34.6070 −1.44573
574574 0 0
575575 −21.6206 37.4480i −0.901641 1.56169i
576576 20.6653 35.7934i 0.861054 1.49139i
577577 14.6611i 0.610348i 0.952297 + 0.305174i 0.0987147π0.0987147\pi
−0.952297 + 0.305174i 0.901285π0.901285\pi
578578 −15.8487 9.15027i −0.659221 0.380601i
579579 28.4702 + 16.4373i 1.18318 + 0.683111i
580580 0.214784i 0.00891840i
581581 0 0
582582 −8.65969 14.9990i −0.358956 0.621730i
583583 −12.5135 + 7.22467i −0.518256 + 0.299215i
584584 34.1166 1.41175
585585 −1.08754 + 9.26394i −0.0449644 + 0.383017i
586586 −11.5717 −0.478024
587587 −30.5998 + 17.6668i −1.26299 + 0.729186i −0.973652 0.228041i 0.926768π-0.926768\pi
−0.289336 + 0.957227i 0.593435π0.593435\pi
588588 0 0
589589 7.21676 12.4998i 0.297362 0.515045i
590590 4.46313i 0.183744i
591591 4.40775 + 2.54481i 0.181310 + 0.104680i
592592 −33.9776 19.6170i −1.39647 0.806253i
593593 16.4294i 0.674675i −0.941384 0.337338i 0.890474π-0.890474\pi
0.941384 0.337338i 0.109526π-0.109526\pi
594594 −6.31313 + 10.9347i −0.259031 + 0.448655i
595595 0 0
596596 −0.230608 + 0.133142i −0.00944608 + 0.00545370i
597597 18.6307 0.762504
598598 5.32564 45.3651i 0.217782 1.85512i
599599 12.0819 0.493653 0.246826 0.969060i 0.420612π-0.420612\pi
0.246826 + 0.969060i 0.420612π0.420612\pi
600600 −33.3598 + 19.2603i −1.36191 + 0.786297i
601601 3.90743 + 6.76787i 0.159387 + 0.276067i 0.934648 0.355574i 0.115715π-0.115715\pi
−0.775261 + 0.631642i 0.782381π0.782381\pi
602602 0 0
603603 41.7377i 1.69969i
604604 −0.867401 0.500794i −0.0352941 0.0203770i
605605 −3.75818 2.16979i −0.152792 0.0882144i
606606 71.6803i 2.91181i
607607 17.7825 30.8001i 0.721768 1.25014i −0.238523 0.971137i 0.576663π-0.576663\pi
0.960291 0.279002i 0.0900035π-0.0900035\pi
608608 −0.557261 0.965205i −0.0225999 0.0391442i
609609 0 0
610610 9.68882 0.392289
611611 14.9584 6.44347i 0.605153 0.260675i
612612 0.768568 0.0310675
613613 −10.3376 + 5.96839i −0.417530 + 0.241061i −0.694020 0.719956i 0.744162π-0.744162\pi
0.276490 + 0.961017i 0.410829π0.410829\pi
614614 −5.77500 10.0026i −0.233060 0.403672i
615615 −3.08618 + 5.34542i −0.124447 + 0.215548i
616616 0 0
617617 −20.4124 11.7851i −0.821772 0.474450i 0.0292550 0.999572i 0.490687π-0.490687\pi
−0.851027 + 0.525122i 0.824020π0.824020\pi
618618 17.0278 + 9.83103i 0.684960 + 0.395462i
619619 28.5571i 1.14781i −0.818923 0.573904i 0.805428π-0.805428\pi
0.818923 0.573904i 0.194572π-0.194572\pi
620620 0.118972 0.206066i 0.00477803 0.00827579i
621621 −25.6355 44.4020i −1.02872 1.78179i
622622 17.5512 10.1332i 0.703738 0.406303i
623623 0 0
624624 −38.8110 4.55623i −1.55368 0.182395i
625625 21.0328 0.841311
626626 20.5640 11.8726i 0.821903 0.474526i
627627 5.71659 + 9.90142i 0.228298 + 0.395425i
628628 0.410283 0.710632i 0.0163721 0.0283573i
629629 19.9292i 0.794628i
630630 0 0
631631 −38.9646 22.4962i −1.55116 0.895561i −0.998048 0.0624526i 0.980108π-0.980108\pi
−0.553109 0.833109i 0.686559π-0.686559\pi
632632 2.83061i 0.112596i
633633 −15.1460 + 26.2337i −0.602001 + 1.04270i
634634 −9.70169 16.8038i −0.385303 0.667365i
635635 0.639763 0.369367i 0.0253882 0.0146579i
636636 −1.98943 −0.0788860
637637 0 0
638638 −11.7727 −0.466085
639639 22.4409 12.9562i 0.887747 0.512541i
640640 2.74947 + 4.76222i 0.108682 + 0.188243i
641641 −1.26650 + 2.19364i −0.0500238 + 0.0866437i −0.889953 0.456052i 0.849263π-0.849263\pi
0.839929 + 0.542696i 0.182596π0.182596\pi
642642 24.0645i 0.949749i
643643 −15.9150 9.18853i −0.627627 0.362360i 0.152206 0.988349i 0.451362π-0.451362\pi
−0.779832 + 0.625988i 0.784696π0.784696\pi
644644 0 0
645645 1.46251i 0.0575863i
646646 −3.36329 + 5.82539i −0.132327 + 0.229197i
647647 −10.4643 18.1248i −0.411396 0.712558i 0.583647 0.812008i 0.301625π-0.301625\pi
−0.995043 + 0.0994494i 0.968292π0.968292\pi
648648 −2.23404 + 1.28982i −0.0877612 + 0.0506690i
649649 10.0783 0.395609
650650 18.9549 + 14.1263i 0.743473 + 0.554079i
651651 0 0
652652 −1.07963 + 0.623326i −0.0422817 + 0.0244113i
653653 24.0580 + 41.6696i 0.941461 + 1.63066i 0.762686 + 0.646769i 0.223880π0.223880\pi
0.178775 + 0.983890i 0.442786π0.442786\pi
654654 23.2952 40.3484i 0.910913 1.57775i
655655 4.50130i 0.175880i
656656 −13.9808 8.07180i −0.545857 0.315151i
657657 −51.1129 29.5100i −1.99410 1.15130i
658658 0 0
659659 1.10819 1.91944i 0.0431690 0.0747708i −0.843634 0.536919i 0.819588π-0.819588\pi
0.886803 + 0.462148i 0.152921π0.152921\pi
660660 0.0942408 + 0.163230i 0.00366832 + 0.00635371i
661661 0.552034 0.318717i 0.0214716 0.0123966i −0.489226 0.872157i 0.662721π-0.662721\pi
0.510697 + 0.859761i 0.329387π0.329387\pi
662662 −9.59073 −0.372754
663663 −7.85287 18.2303i −0.304980 0.708006i
664664 −25.6994 −0.997331
665665 0 0
666666 35.3368 + 61.2052i 1.36927 + 2.37165i
667667 23.9024 41.4002i 0.925506 1.60302i
668668 1.29771i 0.0502100i
669669 −31.5390 18.2091i −1.21937 0.704003i
670670 5.21523 + 3.01102i 0.201482 + 0.116326i
671671 21.8786i 0.844614i
672672 0 0
673673 7.70343 + 13.3427i 0.296945 + 0.514324i 0.975436 0.220285i 0.0706988π-0.0706988\pi
−0.678490 + 0.734609i 0.737365π0.737365\pi
674674 −13.3901 + 7.73081i −0.515769 + 0.297780i
675675 26.5352 1.02134
676676 −0.294057 0.985841i −0.0113099 0.0379170i
677677 11.6812 0.448945 0.224473 0.974480i 0.427934π-0.427934\pi
0.224473 + 0.974480i 0.427934π0.427934\pi
678678 −12.0613 + 6.96358i −0.463210 + 0.267435i
679679 0 0
680680 −1.45673 + 2.52312i −0.0558629 + 0.0967574i
681681 1.97565i 0.0757072i
682682 −11.2948 6.52107i −0.432501 0.249705i
683683 19.8419 + 11.4557i 0.759227 + 0.438340i 0.829018 0.559221i 0.188900π-0.188900\pi
−0.0697909 + 0.997562i 0.522233π0.522233\pi
684684 0.982737i 0.0375759i
685685 −2.21020 + 3.82817i −0.0844473 + 0.146267i
686686 0 0
687687 −44.7514 + 25.8372i −1.70737 + 0.985752i
688688 −3.82515 −0.145833
689689 12.6901 + 29.4599i 0.483454 + 1.12233i
690690 18.5777 0.707239
691691 40.9046 23.6163i 1.55608 0.898405i 0.558458 0.829533i 0.311393π-0.311393\pi
0.997625 0.0688729i 0.0219403π-0.0219403\pi
692692 0.0119239 + 0.0206529i 0.000453280 + 0.000785104i
693693 0 0
694694 6.82596i 0.259110i
695695 −2.26443 1.30737i −0.0858946 0.0495913i
696696 −36.8805 21.2930i −1.39795 0.807109i
697697 8.20026i 0.310607i
698698 1.05565 1.82843i 0.0399568 0.0692071i
699699 37.8365 + 65.5347i 1.43111 + 2.47875i
700700 0 0
701701 12.2098 0.461158 0.230579 0.973054i 0.425938π-0.425938\pi
0.230579 + 0.973054i 0.425938π0.425938\pi
702702 22.4748 + 16.7495i 0.848256 + 0.632169i
703703 25.4827 0.961097
704704 −11.6618 + 6.73295i −0.439521 + 0.253758i
705705 3.31218 + 5.73686i 0.124744 + 0.216063i
706706 12.4237 21.5185i 0.467572 0.809858i
707707 0 0
708708 1.20171 + 0.693808i 0.0451630 + 0.0260749i
709709 −15.4910 8.94374i −0.581777 0.335889i 0.180062 0.983655i 0.442370π-0.442370\pi
−0.761839 + 0.647766i 0.775703π0.775703\pi
710710 3.73873i 0.140312i
711711 −2.44841 + 4.24076i −0.0918224 + 0.159041i
712712 −17.3169 29.9937i −0.648977 1.12406i
713713 45.8644 26.4798i 1.71764 0.991678i
714714 0 0
715715 1.81600 2.43674i 0.0679146 0.0911290i
716716 0.776780 0.0290296
717717 40.6667 23.4789i 1.51872 0.876836i
718718 13.8605 + 24.0070i 0.517268 + 0.895935i
719719 −4.56317 + 7.90364i −0.170178 + 0.294756i −0.938482 0.345329i 0.887767π-0.887767\pi
0.768304 + 0.640085i 0.221101π0.221101\pi
720720 9.92235i 0.369784i
721721 0 0
722722 15.3564 + 8.86604i 0.571507 + 0.329960i
723723 49.2048i 1.82995i
724724 0.491906 0.852006i 0.0182815 0.0316646i
725725 12.3706 + 21.4266i 0.459434 + 0.795763i
726726 −28.3617 + 16.3746i −1.05260 + 0.607719i
727727 −33.6859 −1.24934 −0.624670 0.780889i 0.714767π-0.714767\pi
−0.624670 + 0.780889i 0.714767π0.714767\pi
728728 0 0
729729 −43.0880 −1.59585
730730 7.37471 4.25779i 0.272950 0.157588i
731731 −0.971507 1.68270i −0.0359325 0.0622369i
732732 −1.50616 + 2.60874i −0.0556691 + 0.0964218i
733733 46.4344i 1.71509i 0.514406 + 0.857547i 0.328013π0.328013\pi
−0.514406 + 0.857547i 0.671987π0.671987\pi
734734 −32.9062 18.9984i −1.21459 0.701245i
735735 0 0
736736 4.08942i 0.150738i
737737 −6.79927 + 11.7767i −0.250454 + 0.433799i
738738 14.5400 + 25.1841i 0.535226 + 0.927039i
739739 −1.60237 + 0.925127i −0.0589440 + 0.0340314i −0.529182 0.848508i 0.677501π-0.677501\pi
0.470238 + 0.882539i 0.344168π0.344168\pi
740740 0.420095 0.0154430
741741 23.3104 10.0412i 0.856328 0.368871i
742742 0 0
743743 28.7095 16.5755i 1.05325 0.608094i 0.129693 0.991554i 0.458601π-0.458601\pi
0.923558 + 0.383460i 0.125268π0.125268\pi
744744 −23.5890 40.8574i −0.864816 1.49791i
745745 −0.873120 + 1.51229i −0.0319886 + 0.0554059i
746746 22.0268i 0.806457i
747747 38.5024 + 22.2294i 1.40873 + 0.813331i
748748 −0.216858 0.125203i −0.00792913 0.00457788i
749749 0 0
750750 −9.88850 + 17.1274i −0.361077 + 0.625404i
751751 −10.3871 17.9910i −0.379032 0.656503i 0.611890 0.790943i 0.290410π-0.290410\pi
−0.990922 + 0.134441i 0.957076π0.957076\pi
752752 −15.0046 + 8.66289i −0.547160 + 0.315903i
753753 −18.2257 −0.664182
754754 −3.04717 + 25.9565i −0.110971 + 0.945280i
755755 −6.56824 −0.239043
756756 0 0
757757 −21.8075 37.7717i −0.792607 1.37283i −0.924348 0.381551i 0.875390π-0.875390\pi
0.131741 0.991284i 0.457943π-0.457943\pi
758758 −6.08364 + 10.5372i −0.220968 + 0.382727i
759759 41.9508i 1.52272i
760760 −3.22622 1.86266i −0.117027 0.0675657i
761761 −10.7302 6.19511i −0.388971 0.224573i 0.292743 0.956191i 0.405432π-0.405432\pi
−0.681714 + 0.731619i 0.738765π0.738765\pi
762762 5.57497i 0.201960i
763763 0 0
764764 0.484583 + 0.839323i 0.0175316 + 0.0303656i
765765 4.36488 2.52007i 0.157813 0.0911132i
766766 11.0355 0.398728
767767 2.60862 22.2208i 0.0941917 0.802347i
768768 −5.35835 −0.193353
769769 4.80955 2.77680i 0.173437 0.100134i −0.410769 0.911740i 0.634740π-0.634740\pi
0.584205 + 0.811606i 0.301406π0.301406\pi
770770 0 0
771771 5.18750 8.98501i 0.186823 0.323587i
772772 0.920651i 0.0331349i
773773 −37.9355 21.9021i −1.36445 0.787764i −0.374235 0.927334i 0.622095π-0.622095\pi
−0.990212 + 0.139570i 0.955428π0.955428\pi
774774 5.96726 + 3.44520i 0.214489 + 0.123835i
775775 27.4092i 0.984566i
776776 −6.37159 + 11.0359i −0.228727 + 0.396166i
777777 0 0
778778 38.4608 22.2053i 1.37889 0.796100i
779779 10.4853 0.375677
780780 0.384283 0.165534i 0.0137596 0.00592705i
781781 −8.44253 −0.302098
782782 −21.3746 + 12.3406i −0.764354 + 0.441300i
783783 14.6678 + 25.4054i 0.524185 + 0.907916i
784784 0 0
785785 5.38113i 0.192061i
786786 −29.4187 16.9849i −1.04933 0.605830i
787787 −21.4782 12.4005i −0.765616 0.442029i 0.0656923 0.997840i 0.479074π-0.479074\pi
−0.831309 + 0.555811i 0.812408π0.812408\pi
788788 0.142535i 0.00507758i
789789 −25.8831 + 44.8308i −0.921462 + 1.59602i
790790 −0.353263 0.611870i −0.0125685 0.0217693i
791791 0 0
792792 23.3305 0.829015
793793 48.2381 + 5.66293i 1.71299 + 0.201096i
794794 8.91801 0.316489
795795 −11.2985 + 6.52316i −0.400715 + 0.231353i
796796 −0.260876 0.451850i −0.00924649 0.0160154i
797797 8.23575 14.2647i 0.291725 0.505283i −0.682492 0.730893i 0.739104π-0.739104\pi
0.974218 + 0.225610i 0.0724373π0.0724373\pi
798798 0 0
799799 −7.62168 4.40038i −0.269636 0.155674i
800800 1.83292 + 1.05823i 0.0648034 + 0.0374142i
801801 59.9146i 2.11698i
802802 0.369756 0.640437i 0.0130566 0.0226146i
803803 9.61464 + 16.6530i 0.339293 + 0.587673i
804804 −1.62145 + 0.936144i −0.0571841 + 0.0330152i
805805 0 0
806806 −17.3012 + 23.2150i −0.609408 + 0.817715i
807807 −77.8301 −2.73975
808808 −45.6747 + 26.3703i −1.60683 + 0.927704i
809809 −0.690968 1.19679i −0.0242932 0.0420770i 0.853623 0.520891i 0.174400π-0.174400\pi
−0.877916 + 0.478814i 0.841067π0.841067\pi
810810 −0.321942 + 0.557621i −0.0113119 + 0.0195928i
811811 6.83571i 0.240034i −0.992772 0.120017i 0.961705π-0.961705\pi
0.992772 0.120017i 0.0382950π-0.0382950\pi
812812 0 0
813813 15.9538 + 9.21093i 0.559524 + 0.323041i
814814 23.0261i 0.807066i
815815 −4.08767 + 7.08004i −0.143185 + 0.248003i
816816 10.5577 + 18.2865i 0.369595 + 0.640157i
817817 2.15160 1.24223i 0.0752750 0.0434601i
818818 −55.0954 −1.92637
819819 0 0
820820 0.172856 0.00603640
821821 −9.13009 + 5.27126i −0.318642 + 0.183968i −0.650787 0.759260i 0.725561π-0.725561\pi
0.332145 + 0.943228i 0.392228π0.392228\pi
822822 16.6796 + 28.8899i 0.581767 + 1.00765i
823823 7.41652 12.8458i 0.258524 0.447776i −0.707323 0.706891i 0.750097π-0.750097\pi
0.965847 + 0.259114i 0.0834307π0.0834307\pi
824824 14.4669i 0.503977i
825825 −18.8027 10.8558i −0.654627 0.377949i
826826 0 0
827827 55.6758i 1.93604i 0.250879 + 0.968018i 0.419280π0.419280\pi
−0.250879 + 0.968018i 0.580720π0.580720\pi
828828 −1.80294 + 3.12278i −0.0626564 + 0.108524i
829829 0.0232424 + 0.0402570i 0.000807242 + 0.00139818i 0.866429 0.499301i 0.166410π-0.166410\pi
−0.865622 + 0.500699i 0.833076π0.833076\pi
830830 −5.55524 + 3.20732i −0.192825 + 0.111328i
831831 −15.3775 −0.533438
832832 11.8264 + 27.4548i 0.410006 + 0.951823i
833833 0 0
834834 −17.0888 + 9.86624i −0.591738 + 0.341640i
835835 4.25508 + 7.37002i 0.147253 + 0.255050i
836836 0.160092 0.277288i 0.00553691 0.00959022i
837837 32.4990i 1.12333i
838838 −28.5875 16.5050i −0.987540 0.570157i
839839 −22.1248 12.7738i −0.763833 0.440999i 0.0668370 0.997764i 0.478709π-0.478709\pi
−0.830670 + 0.556765i 0.812043π0.812043\pi
840840 0 0
841841 0.823775 1.42682i 0.0284060 0.0492007i
842842 16.1061 + 27.8965i 0.555052 + 0.961378i
843843 8.66886 5.00497i 0.298572 0.172380i
844844 0.848327 0.0292006
845845 −4.90250 4.63464i −0.168651 0.159437i
846846 31.2096 1.07301
847847 0 0
848848 −17.0611 29.5507i −0.585881 1.01478i
849849 19.9770 34.6012i 0.685609 1.18751i
850850 12.7737i 0.438135i
851851 80.9745 + 46.7507i 2.77577 + 1.60259i
852852 −1.00666 0.581197i −0.0344877 0.0199115i
853853 22.6671i 0.776105i 0.921637 + 0.388053i 0.126852π0.126852\pi
−0.921637 + 0.388053i 0.873148π0.873148\pi
854854 0 0
855855 3.22231 + 5.58120i 0.110201 + 0.190873i
856856 −15.3339 + 8.85303i −0.524102 + 0.302590i
857857 −37.0535 −1.26572 −0.632862 0.774264i 0.718120π-0.718120\pi
−0.632862 + 0.774264i 0.718120π0.718120\pi
858858 −9.07319 21.0633i −0.309754 0.719088i
859859 4.24339 0.144782 0.0723912 0.997376i 0.476937π-0.476937\pi
0.0723912 + 0.997376i 0.476937π0.476937\pi
860860 0.0354702 0.0204788i 0.00120953 0.000698320i
861861 0 0
862862 1.87581 3.24900i 0.0638904 0.110661i
863863 7.50051i 0.255320i 0.991818 + 0.127660i 0.0407467π0.0407467\pi
−0.991818 + 0.127660i 0.959253π0.959253\pi
864864 2.17328 + 1.25475i 0.0739366 + 0.0426873i
865865 0.135438 + 0.0781951i 0.00460503 + 0.00265871i
866866 8.06472i 0.274050i
867867 18.6562 32.3135i 0.633598 1.09742i
868868 0 0
869869 1.38168 0.797714i 0.0468703 0.0270606i
870870 −10.6296 −0.360376
871871 24.2054 + 18.0393i 0.820170 + 0.611238i
872872 −34.2800 −1.16087
873873 19.0916 11.0225i 0.646153 0.373057i
874874 −15.7795 27.3309i −0.533749 0.924481i
875875 0 0
876876 2.64755i 0.0894523i
877877 −24.4996 14.1448i −0.827291 0.477637i 0.0256330 0.999671i 0.491840π-0.491840\pi
−0.852924 + 0.522035i 0.825173π0.825173\pi
878878 45.8145 + 26.4510i 1.54617 + 0.892679i
879879 23.5933i 0.795781i
880880 −1.61640 + 2.79968i −0.0544888 + 0.0943773i
881881 19.7860 + 34.2704i 0.666609 + 1.15460i 0.978846 + 0.204596i 0.0655882π0.0655882\pi
−0.312238 + 0.950004i 0.601079π0.601079\pi
882882 0 0
883883 −28.3609 −0.954419 −0.477209 0.878790i 0.658352π-0.658352\pi
−0.477209 + 0.878790i 0.658352π0.658352\pi
884884 −0.332179 + 0.445724i −0.0111724 + 0.0149913i
885885 9.09974 0.305884
886886 38.0174 21.9494i 1.27722 0.737403i
887887 −21.8593 37.8614i −0.733963 1.27126i −0.955177 0.296036i 0.904335π-0.904335\pi
0.221214 0.975225i 0.428998π-0.428998\pi
888888 41.6469 72.1345i 1.39758 2.42068i
889889 0 0
890890 −7.48649 4.32233i −0.250948 0.144885i
891891 −1.25918 0.726988i −0.0421841 0.0243550i
892892 1.01989i 0.0341483i
893893 5.62659 9.74554i 0.188287 0.326122i
894894 6.58913 + 11.4127i 0.220374 + 0.381698i
895895 4.41152 2.54699i 0.147461 0.0851366i
896896 0 0
897897 92.4934 + 10.8583i 3.08826 + 0.362547i
898898 −43.5257 −1.45247
899899 −26.2422 + 15.1509i −0.875227 + 0.505312i
900900 −0.933105 1.61619i −0.0311035 0.0538728i
901901 8.66632 15.0105i 0.288717 0.500073i
902902 9.47456i 0.315468i
903903 0 0
904904 8.87439 + 5.12363i 0.295158 + 0.170409i
905905 6.45167i 0.214461i
906906 −24.7841 + 42.9274i −0.823397 + 1.42617i
907907 −18.3493 31.7818i −0.609277 1.05530i −0.991360 0.131171i 0.958126π-0.958126\pi
0.382083 0.924128i 0.375207π-0.375207\pi
908908 −0.0479154 + 0.0276640i −0.00159013 + 0.000918062i
909909 91.2387 3.02620
910910 0 0
911911 −35.5211 −1.17686 −0.588432 0.808546i 0.700255π-0.700255\pi
−0.588432 + 0.808546i 0.700255π0.700255\pi
912912 −23.3823 + 13.4998i −0.774265 + 0.447022i
913913 −7.24254 12.5444i −0.239693 0.415161i
914914 −22.0562 + 38.2024i −0.729553 + 1.26362i
915915 19.7542i 0.653054i
916916 1.25326 + 0.723569i 0.0414088 + 0.0239074i
917917 0 0
918918 15.1458i 0.499885i
919919 −10.9667 + 18.9949i −0.361758 + 0.626583i −0.988250 0.152844i 0.951157π-0.951157\pi
0.626492 + 0.779428i 0.284490π0.284490\pi
920920 −6.83449 11.8377i −0.225327 0.390277i
921921 20.3940 11.7745i 0.672005 0.387982i
922922 1.61644 0.0532348
923923 −2.18521 + 18.6142i −0.0719272 + 0.612693i
924924 0 0
925925 −41.9082 + 24.1957i −1.37793 + 0.795549i
926926 −14.0980 24.4184i −0.463287 0.802437i
927927 −12.5135 + 21.6740i −0.410997 + 0.711867i
928928 2.33984i 0.0768090i
929929 13.4383 + 7.75858i 0.440895 + 0.254551i 0.703977 0.710223i 0.251406π-0.251406\pi
−0.263082 + 0.964773i 0.584739π0.584739\pi
930930 −10.1981 5.88788i −0.334409 0.193071i
931931 0 0
932932 1.05961 1.83529i 0.0347086 0.0601171i
933933 20.6602 + 35.7845i 0.676385 + 1.17153i
934934 1.88370 1.08755i 0.0616364 0.0355858i
935935 −1.64212 −0.0537031
936936 6.03874 51.4394i 0.197382 1.68135i
937937 −40.8110 −1.33324 −0.666618 0.745399i 0.732259π-0.732259\pi
−0.666618 + 0.745399i 0.732259π0.732259\pi
938938 0 0
939939 24.2067 + 41.9273i 0.789957 + 1.36825i
940940 0.0927572 0.160660i 0.00302541 0.00524016i
941941 51.5936i 1.68190i −0.541109 0.840952i 0.681996π-0.681996\pi
0.541109 0.840952i 0.318004π-0.318004\pi
942942 −35.1689 20.3048i −1.14586 0.661565i
943943 33.3186 + 19.2365i 1.08500 + 0.626427i
944944 23.8001i 0.774627i
945945 0 0
946946 −1.12248 1.94419i −0.0364949 0.0632110i
947947 −4.31462 + 2.49105i −0.140206 + 0.0809482i −0.568462 0.822709i 0.692461π-0.692461\pi
0.428256 + 0.903657i 0.359128π0.359128\pi
948948 0.219663 0.00713433
949949 39.2054 16.8881i 1.27266 0.548210i
950950 16.3333 0.529921
951951 34.2608 19.7805i 1.11098 0.641426i
952952 0 0
953953 15.1163 26.1822i 0.489664 0.848123i −0.510265 0.860017i 0.670453π-0.670453\pi
0.999929 + 0.0118941i 0.00378608π0.00378608\pi
954954 61.4657i 1.99003i
955955 5.50413 + 3.17781i 0.178110 + 0.102832i
956956 −1.13887 0.657525i −0.0368336 0.0212659i
957957 24.0029i 0.775904i
958958 5.34921 9.26511i 0.172825 0.299342i
959959 0 0
960960 −10.5295 + 6.07919i −0.339837 + 0.196205i
961961 −2.56939 −0.0828835
962962 −50.7682 5.95995i −1.63683 0.192156i
963963 30.6306 0.987058
964964 1.19336 0.688988i 0.0384356 0.0221908i
965965 −3.01873 5.22860i −0.0971764 0.168315i
966966 0 0
967967 29.9990i 0.964703i 0.875978 + 0.482352i 0.160217π0.160217\pi
−0.875978 + 0.482352i 0.839783π0.839783\pi
968968 20.8678 + 12.0481i 0.670718 + 0.387239i
969969 −11.8772 6.85731i −0.381551 0.220288i
970970 3.18073i 0.102127i
971971 22.0620 38.2125i 0.708003 1.22630i −0.257594 0.966253i 0.582930π-0.582930\pi
0.965597 0.260044i 0.0837371π-0.0837371\pi
972972 0.565732 + 0.979876i 0.0181459 + 0.0314295i
973973 0 0
974974 0.105582 0.00338306
975975 −28.8016 + 38.6465i −0.922391 + 1.23768i
976976 −51.6665 −1.65380
977977 −12.9925 + 7.50121i −0.415666 + 0.239985i −0.693221 0.720725i 0.743809π-0.743809\pi
0.277555 + 0.960710i 0.410476π0.410476\pi
978978 30.8482 + 53.4306i 0.986417 + 1.70852i
979979 9.76037 16.9055i 0.311943 0.540301i
980980 0 0
981981 51.3577 + 29.6514i 1.63973 + 0.946696i
982982 −2.14506 1.23845i −0.0684516 0.0395206i
983983 6.01856i 0.191962i 0.995383 + 0.0959812i 0.0305989π0.0305989\pi
−0.995383 + 0.0959812i 0.969401π0.969401\pi
984984 17.1364 29.6812i 0.546290 0.946202i
985985 −0.467358 0.809488i −0.0148913 0.0257924i
986986 12.2299 7.06093i 0.389479 0.224866i
987987 0 0
988988 −0.569930 0.424745i −0.0181319 0.0135129i
989989 9.11600 0.289872
990990 5.04318 2.91168i 0.160283 0.0925392i
991991 −16.9200 29.3063i −0.537482 0.930946i −0.999039 0.0438356i 0.986042π-0.986042\pi
0.461557 0.887111i 0.347291π-0.347291\pi
992992 −1.29607 + 2.24487i −0.0411504 + 0.0712746i
993993 19.5542i 0.620535i
994994 0 0
995995 −2.96315 1.71078i −0.0939382 0.0542353i
996996 1.99435i 0.0631934i
997997 13.1608 22.7951i 0.416805 0.721928i −0.578811 0.815462i 0.696483π-0.696483\pi
0.995616 + 0.0935340i 0.0298164π0.0298164\pi
998998 5.77591 + 10.0042i 0.182833 + 0.316676i
999999 −49.6904 + 28.6888i −1.57213 + 0.907672i
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.h.491.2 12
7.2 even 3 637.2.u.i.361.5 12
7.3 odd 6 637.2.k.h.569.2 12
7.4 even 3 637.2.k.g.569.2 12
7.5 odd 6 637.2.u.h.361.5 12
7.6 odd 2 91.2.q.a.36.2 12
13.2 odd 12 8281.2.a.ch.1.1 6
13.4 even 6 inner 637.2.q.h.589.2 12
13.11 odd 12 8281.2.a.by.1.6 6
21.20 even 2 819.2.ct.a.127.5 12
28.27 even 2 1456.2.cc.c.673.1 12
91.4 even 6 637.2.u.i.30.5 12
91.17 odd 6 637.2.u.h.30.5 12
91.30 even 6 637.2.k.g.459.5 12
91.41 even 12 1183.2.a.p.1.1 6
91.55 odd 6 1183.2.c.i.337.3 12
91.62 odd 6 1183.2.c.i.337.10 12
91.69 odd 6 91.2.q.a.43.2 yes 12
91.76 even 12 1183.2.a.m.1.6 6
91.82 odd 6 637.2.k.h.459.5 12
273.251 even 6 819.2.ct.a.316.5 12
364.251 even 6 1456.2.cc.c.225.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.2 12 7.6 odd 2
91.2.q.a.43.2 yes 12 91.69 odd 6
637.2.k.g.459.5 12 91.30 even 6
637.2.k.g.569.2 12 7.4 even 3
637.2.k.h.459.5 12 91.82 odd 6
637.2.k.h.569.2 12 7.3 odd 6
637.2.q.h.491.2 12 1.1 even 1 trivial
637.2.q.h.589.2 12 13.4 even 6 inner
637.2.u.h.30.5 12 91.17 odd 6
637.2.u.h.361.5 12 7.5 odd 6
637.2.u.i.30.5 12 91.4 even 6
637.2.u.i.361.5 12 7.2 even 3
819.2.ct.a.127.5 12 21.20 even 2
819.2.ct.a.316.5 12 273.251 even 6
1183.2.a.m.1.6 6 91.76 even 12
1183.2.a.p.1.1 6 91.41 even 12
1183.2.c.i.337.3 12 91.55 odd 6
1183.2.c.i.337.10 12 91.62 odd 6
1456.2.cc.c.225.1 12 364.251 even 6
1456.2.cc.c.673.1 12 28.27 even 2
8281.2.a.by.1.6 6 13.11 odd 12
8281.2.a.ch.1.1 6 13.2 odd 12