Properties

Label 1176.2.c.e.589.6
Level 11761176
Weight 22
Character 1176.589
Analytic conductor 9.3909.390
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1176,2,Mod(589,1176)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1176.589");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1176=23372 1176 = 2^{3} \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1176.c (of order 22, degree 11, 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: 9.390407277709.39040727770
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16+x142x132x124x112x10+16x9+8x8+32x78x6++256 x^{16} + x^{14} - 2 x^{13} - 2 x^{12} - 4 x^{11} - 2 x^{10} + 16 x^{9} + 8 x^{8} + 32 x^{7} - 8 x^{6} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 25 2^{5}
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 589.6
Root 0.8650141.11882i-0.865014 - 1.11882i of defining polynomial
Character χ\chi == 1176.589
Dual form 1176.2.c.e.589.5

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+(1.11882+0.865014i)q21.00000iq3+(0.5035011.93558i)q43.57776iq5+(0.865014+1.11882i)q6+(1.11098+2.60110i)q81.00000q9+(3.09481+4.00286i)q100.941967iq11+(1.935580.503501i)q126.15117iq133.57776q15+(3.492971.94914i)q163.78375q17+(1.118820.865014i)q182.41460iq19+(6.925061.80141i)q20+(0.814815+1.05389i)q22+2.98743q23+(2.601101.11098i)q247.80037q25+(5.32085+6.88203i)q26+1.00000iq27+2.68125iq29+(4.002863.09481i)q30+10.7137q31+(5.594030.840746i)q320.941967q33+(4.233323.27300i)q34+(0.503501+1.93558i)q36+1.70724iq37+(2.08866+2.70149i)q386.15117q39+(9.306113.97483i)q404.56000q413.50672iq43+(1.823260.474281i)q44+3.57776iq45+(3.34238+2.58417i)q466.84583q47+(1.94914+3.49297i)q48+(8.727186.74743i)q50+3.78375iq51+(11.90613.09712i)q52+7.59176iq53+(0.8650141.11882i)q543.37013q552.41460q57+(2.319322.99983i)q58+0.116189iq59+(1.80141+6.92506i)q60+8.15432iq61+(11.9867+9.26752i)q62+(5.53143+5.77955i)q6422.0074q65+(1.053890.814815i)q663.97580iq67+(1.90512+7.32377i)q682.98743iq693.92572q71+(1.110982.60110i)q72+6.22876q73+(1.476781.91008i)q74+7.80037iq75+(4.673651.21575i)q76+(6.882035.32085i)q785.47255q79+(6.97354+12.4970i)q80+1.00000q81+(5.101803.94446i)q82+1.19560iq83+13.5373iq85+(3.03337+3.92338i)q86+2.68125q87+(2.450151.04651i)q881.82102q89+(3.094814.00286i)q90+(1.504175.78242i)q9210.7137iq93+(7.659235.92174i)q948.63884q95+(0.8407465.59403i)q96+12.0241q97+0.941967iq99+O(q100)q+(-1.11882 + 0.865014i) q^{2} -1.00000i q^{3} +(0.503501 - 1.93558i) q^{4} -3.57776i q^{5} +(0.865014 + 1.11882i) q^{6} +(1.11098 + 2.60110i) q^{8} -1.00000 q^{9} +(3.09481 + 4.00286i) q^{10} -0.941967i q^{11} +(-1.93558 - 0.503501i) q^{12} -6.15117i q^{13} -3.57776 q^{15} +(-3.49297 - 1.94914i) q^{16} -3.78375 q^{17} +(1.11882 - 0.865014i) q^{18} -2.41460i q^{19} +(-6.92506 - 1.80141i) q^{20} +(0.814815 + 1.05389i) q^{22} +2.98743 q^{23} +(2.60110 - 1.11098i) q^{24} -7.80037 q^{25} +(5.32085 + 6.88203i) q^{26} +1.00000i q^{27} +2.68125i q^{29} +(4.00286 - 3.09481i) q^{30} +10.7137 q^{31} +(5.59403 - 0.840746i) q^{32} -0.941967 q^{33} +(4.23332 - 3.27300i) q^{34} +(-0.503501 + 1.93558i) q^{36} +1.70724i q^{37} +(2.08866 + 2.70149i) q^{38} -6.15117 q^{39} +(9.30611 - 3.97483i) q^{40} -4.56000 q^{41} -3.50672i q^{43} +(-1.82326 - 0.474281i) q^{44} +3.57776i q^{45} +(-3.34238 + 2.58417i) q^{46} -6.84583 q^{47} +(-1.94914 + 3.49297i) q^{48} +(8.72718 - 6.74743i) q^{50} +3.78375i q^{51} +(-11.9061 - 3.09712i) q^{52} +7.59176i q^{53} +(-0.865014 - 1.11882i) q^{54} -3.37013 q^{55} -2.41460 q^{57} +(-2.31932 - 2.99983i) q^{58} +0.116189i q^{59} +(-1.80141 + 6.92506i) q^{60} +8.15432i q^{61} +(-11.9867 + 9.26752i) q^{62} +(-5.53143 + 5.77955i) q^{64} -22.0074 q^{65} +(1.05389 - 0.814815i) q^{66} -3.97580i q^{67} +(-1.90512 + 7.32377i) q^{68} -2.98743i q^{69} -3.92572 q^{71} +(-1.11098 - 2.60110i) q^{72} +6.22876 q^{73} +(-1.47678 - 1.91008i) q^{74} +7.80037i q^{75} +(-4.67365 - 1.21575i) q^{76} +(6.88203 - 5.32085i) q^{78} -5.47255 q^{79} +(-6.97354 + 12.4970i) q^{80} +1.00000 q^{81} +(5.10180 - 3.94446i) q^{82} +1.19560i q^{83} +13.5373i q^{85} +(3.03337 + 3.92338i) q^{86} +2.68125 q^{87} +(2.45015 - 1.04651i) q^{88} -1.82102 q^{89} +(-3.09481 - 4.00286i) q^{90} +(1.50417 - 5.78242i) q^{92} -10.7137i q^{93} +(7.65923 - 5.92174i) q^{94} -8.63884 q^{95} +(-0.840746 - 5.59403i) q^{96} +12.0241 q^{97} +0.941967i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q2q2+2q48q816q96q10+10q16+2q1820q206q22+8q23+6q2416q256q26+8q30+24q31+8q3212q342q36+24q97+O(q100) 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9} - 6 q^{10} + 10 q^{16} + 2 q^{18} - 20 q^{20} - 6 q^{22} + 8 q^{23} + 6 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{30} + 24 q^{31} + 8 q^{32} - 12 q^{34} - 2 q^{36}+ \cdots - 24 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1176Z)×\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times.

nn 295295 589589 785785 10811081
χ(n)\chi(n) 11 1-1 11 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 −1.11882 + 0.865014i −0.791123 + 0.611657i
33 1.00000i 0.577350i
44 0.503501 1.93558i 0.251750 0.967792i
55 3.57776i 1.60002i −0.599985 0.800012i 0.704827π-0.704827\pi
0.599985 0.800012i 0.295173π-0.295173\pi
66 0.865014 + 1.11882i 0.353141 + 0.456755i
77 0 0
88 1.11098 + 2.60110i 0.392792 + 0.919627i
99 −1.00000 −0.333333
1010 3.09481 + 4.00286i 0.978666 + 1.26581i
1111 0.941967i 0.284014i −0.989866 0.142007i 0.954644π-0.954644\pi
0.989866 0.142007i 0.0453555π-0.0453555\pi
1212 −1.93558 0.503501i −0.558755 0.145348i
1313 6.15117i 1.70603i −0.521889 0.853013i 0.674772π-0.674772\pi
0.521889 0.853013i 0.325228π-0.325228\pi
1414 0 0
1515 −3.57776 −0.923774
1616 −3.49297 1.94914i −0.873243 0.487284i
1717 −3.78375 −0.917694 −0.458847 0.888515i 0.651737π-0.651737\pi
−0.458847 + 0.888515i 0.651737π0.651737\pi
1818 1.11882 0.865014i 0.263708 0.203886i
1919 2.41460i 0.553946i −0.960878 0.276973i 0.910669π-0.910669\pi
0.960878 0.276973i 0.0893313π-0.0893313\pi
2020 −6.92506 1.80141i −1.54849 0.402806i
2121 0 0
2222 0.814815 + 1.05389i 0.173719 + 0.224690i
2323 2.98743 0.622922 0.311461 0.950259i 0.399182π-0.399182\pi
0.311461 + 0.950259i 0.399182π0.399182\pi
2424 2.60110 1.11098i 0.530947 0.226778i
2525 −7.80037 −1.56007
2626 5.32085 + 6.88203i 1.04350 + 1.34968i
2727 1.00000i 0.192450i
2828 0 0
2929 2.68125i 0.497897i 0.968517 + 0.248948i 0.0800849π0.0800849\pi
−0.968517 + 0.248948i 0.919915π0.919915\pi
3030 4.00286 3.09481i 0.730818 0.565033i
3131 10.7137 1.92424 0.962120 0.272625i 0.0878919π-0.0878919\pi
0.962120 + 0.272625i 0.0878919π0.0878919\pi
3232 5.59403 0.840746i 0.988894 0.148624i
3333 −0.941967 −0.163975
3434 4.23332 3.27300i 0.726009 0.561314i
3535 0 0
3636 −0.503501 + 1.93558i −0.0839168 + 0.322597i
3737 1.70724i 0.280668i 0.990104 + 0.140334i 0.0448176π0.0448176\pi
−0.990104 + 0.140334i 0.955182π0.955182\pi
3838 2.08866 + 2.70149i 0.338825 + 0.438239i
3939 −6.15117 −0.984975
4040 9.30611 3.97483i 1.47143 0.628476i
4141 −4.56000 −0.712152 −0.356076 0.934457i 0.615886π-0.615886\pi
−0.356076 + 0.934457i 0.615886π0.615886\pi
4242 0 0
4343 3.50672i 0.534770i −0.963590 0.267385i 0.913840π-0.913840\pi
0.963590 0.267385i 0.0861596π-0.0861596\pi
4444 −1.82326 0.474281i −0.274866 0.0715006i
4545 3.57776i 0.533341i
4646 −3.34238 + 2.58417i −0.492808 + 0.381015i
4747 −6.84583 −0.998567 −0.499284 0.866439i 0.666403π-0.666403\pi
−0.499284 + 0.866439i 0.666403π0.666403\pi
4848 −1.94914 + 3.49297i −0.281334 + 0.504167i
4949 0 0
5050 8.72718 6.74743i 1.23421 0.954231i
5151 3.78375i 0.529831i
5252 −11.9061 3.09712i −1.65108 0.429493i
5353 7.59176i 1.04281i 0.853310 + 0.521404i 0.174592π0.174592\pi
−0.853310 + 0.521404i 0.825408π0.825408\pi
5454 −0.865014 1.11882i −0.117714 0.152252i
5555 −3.37013 −0.454429
5656 0 0
5757 −2.41460 −0.319821
5858 −2.31932 2.99983i −0.304542 0.393897i
5959 0.116189i 0.0151266i 0.999971 + 0.00756328i 0.00240749π0.00240749\pi
−0.999971 + 0.00756328i 0.997593π0.997593\pi
6060 −1.80141 + 6.92506i −0.232560 + 0.894021i
6161 8.15432i 1.04405i 0.852929 + 0.522027i 0.174824π0.174824\pi
−0.852929 + 0.522027i 0.825176π0.825176\pi
6262 −11.9867 + 9.26752i −1.52231 + 1.17698i
6363 0 0
6464 −5.53143 + 5.77955i −0.691429 + 0.722444i
6565 −22.0074 −2.72968
6666 1.05389 0.814815i 0.129725 0.100297i
6767 3.97580i 0.485721i −0.970061 0.242861i 0.921914π-0.921914\pi
0.970061 0.242861i 0.0780857π-0.0780857\pi
6868 −1.90512 + 7.32377i −0.231030 + 0.888137i
6969 2.98743i 0.359644i
7070 0 0
7171 −3.92572 −0.465897 −0.232949 0.972489i 0.574837π-0.574837\pi
−0.232949 + 0.972489i 0.574837π0.574837\pi
7272 −1.11098 2.60110i −0.130931 0.306542i
7373 6.22876 0.729022 0.364511 0.931199i 0.381236π-0.381236\pi
0.364511 + 0.931199i 0.381236π0.381236\pi
7474 −1.47678 1.91008i −0.171673 0.222043i
7575 7.80037i 0.900709i
7676 −4.67365 1.21575i −0.536105 0.139456i
7777 0 0
7878 6.88203 5.32085i 0.779236 0.602467i
7979 −5.47255 −0.615710 −0.307855 0.951433i 0.599611π-0.599611\pi
−0.307855 + 0.951433i 0.599611π0.599611\pi
8080 −6.97354 + 12.4970i −0.779666 + 1.39721i
8181 1.00000 0.111111
8282 5.10180 3.94446i 0.563400 0.435593i
8383 1.19560i 0.131234i 0.997845 + 0.0656172i 0.0209016π0.0209016\pi
−0.997845 + 0.0656172i 0.979098π0.979098\pi
8484 0 0
8585 13.5373i 1.46833i
8686 3.03337 + 3.92338i 0.327096 + 0.423069i
8787 2.68125 0.287461
8888 2.45015 1.04651i 0.261187 0.111558i
8989 −1.82102 −0.193028 −0.0965138 0.995332i 0.530769π-0.530769\pi
−0.0965138 + 0.995332i 0.530769π0.530769\pi
9090 −3.09481 4.00286i −0.326222 0.421938i
9191 0 0
9292 1.50417 5.78242i 0.156821 0.602859i
9393 10.7137i 1.11096i
9494 7.65923 5.92174i 0.789989 0.610781i
9595 −8.63884 −0.886327
9696 −0.840746 5.59403i −0.0858082 0.570938i
9797 12.0241 1.22086 0.610431 0.792069i 0.290996π-0.290996\pi
0.610431 + 0.792069i 0.290996π0.290996\pi
9898 0 0
9999 0.941967i 0.0946713i
100100 −3.92749 + 15.0983i −0.392749 + 1.50983i
101101 1.78101i 0.177217i 0.996067 + 0.0886085i 0.0282420π0.0282420\pi
−0.996067 + 0.0886085i 0.971758π0.971758\pi
102102 −3.27300 4.23332i −0.324075 0.419161i
103103 −12.4230 −1.22407 −0.612037 0.790829i 0.709650π-0.709650\pi
−0.612037 + 0.790829i 0.709650π0.709650\pi
104104 15.9998 6.83384i 1.56891 0.670113i
105105 0 0
106106 −6.56698 8.49379i −0.637842 0.824990i
107107 9.71411i 0.939098i −0.882906 0.469549i 0.844417π-0.844417\pi
0.882906 0.469549i 0.155583π-0.155583\pi
108108 1.93558 + 0.503501i 0.186252 + 0.0484494i
109109 14.2775i 1.36753i −0.729700 0.683767i 0.760340π-0.760340\pi
0.729700 0.683767i 0.239660π-0.239660\pi
110110 3.77056 2.91521i 0.359509 0.277955i
111111 1.70724 0.162044
112112 0 0
113113 −13.8775 −1.30549 −0.652743 0.757580i 0.726382π-0.726382\pi
−0.652743 + 0.757580i 0.726382π0.726382\pi
114114 2.70149 2.08866i 0.253018 0.195621i
115115 10.6883i 0.996690i
116116 5.18980 + 1.35001i 0.481860 + 0.125346i
117117 6.15117i 0.568676i
118118 −0.100505 0.129995i −0.00925228 0.0119670i
119119 0 0
120120 −3.97483 9.30611i −0.362851 0.849528i
121121 10.1127 0.919336
122122 −7.05360 9.12318i −0.638603 0.825974i
123123 4.56000i 0.411161i
124124 5.39437 20.7373i 0.484428 1.86227i
125125 10.0191i 0.896131i
126126 0 0
127127 7.77389 0.689822 0.344911 0.938635i 0.387909π-0.387909\pi
0.344911 + 0.938635i 0.387909π0.387909\pi
128128 1.18926 11.2510i 0.105117 0.994460i
129129 −3.50672 −0.308750
130130 24.6222 19.0367i 2.15951 1.66963i
131131 7.04522i 0.615543i 0.951460 + 0.307772i 0.0995833π0.0995833\pi
−0.951460 + 0.307772i 0.900417π0.900417\pi
132132 −0.474281 + 1.82326i −0.0412809 + 0.158694i
133133 0 0
134134 3.43912 + 4.44819i 0.297095 + 0.384265i
135135 3.57776 0.307925
136136 −4.20368 9.84191i −0.360463 0.843937i
137137 −18.1076 −1.54704 −0.773518 0.633775i 0.781505π-0.781505\pi
−0.773518 + 0.633775i 0.781505π0.781505\pi
138138 2.58417 + 3.34238i 0.219979 + 0.284523i
139139 8.32721i 0.706305i −0.935566 0.353152i 0.885110π-0.885110\pi
0.935566 0.353152i 0.114890π-0.114890\pi
140140 0 0
141141 6.84583i 0.576523i
142142 4.39216 3.39580i 0.368582 0.284969i
143143 −5.79420 −0.484535
144144 3.49297 + 1.94914i 0.291081 + 0.162428i
145145 9.59289 0.796646
146146 −6.96884 + 5.38797i −0.576746 + 0.445911i
147147 0 0
148148 3.30450 + 0.859595i 0.271628 + 0.0706582i
149149 20.7056i 1.69627i 0.529782 + 0.848134i 0.322274π0.322274\pi
−0.529782 + 0.848134i 0.677726π0.677726\pi
150150 −6.74743 8.72718i −0.550925 0.712572i
151151 3.95566 0.321907 0.160954 0.986962i 0.448543π-0.448543\pi
0.160954 + 0.986962i 0.448543π0.448543\pi
152152 6.28060 2.68257i 0.509424 0.217585i
153153 3.78375 0.305898
154154 0 0
155155 38.3311i 3.07883i
156156 −3.09712 + 11.9061i −0.247968 + 0.953251i
157157 11.8706i 0.947381i 0.880691 + 0.473690i 0.157078π0.157078\pi
−0.880691 + 0.473690i 0.842922π0.842922\pi
158158 6.12278 4.73383i 0.487102 0.376604i
159159 7.59176 0.602066
160160 −3.00799 20.0141i −0.237802 1.58225i
161161 0 0
162162 −1.11882 + 0.865014i −0.0879025 + 0.0679619i
163163 17.0530i 1.33569i −0.744299 0.667846i 0.767216π-0.767216\pi
0.744299 0.667846i 0.232784π-0.232784\pi
164164 −2.29596 + 8.82626i −0.179285 + 0.689215i
165165 3.37013i 0.262365i
166166 −1.03421 1.33766i −0.0802705 0.103823i
167167 10.4339 0.807396 0.403698 0.914892i 0.367725π-0.367725\pi
0.403698 + 0.914892i 0.367725π0.367725\pi
168168 0 0
169169 −24.8369 −1.91053
170170 −11.7100 15.1458i −0.898116 1.16163i
171171 2.41460i 0.184649i
172172 −6.78756 1.76564i −0.517547 0.134629i
173173 14.5742i 1.10805i −0.832499 0.554027i 0.813091π-0.813091\pi
0.832499 0.554027i 0.186909π-0.186909\pi
174174 −2.99983 + 2.31932i −0.227417 + 0.175827i
175175 0 0
176176 −1.83602 + 3.29027i −0.138395 + 0.248013i
177177 0.116189 0.00873333
178178 2.03738 1.57521i 0.152708 0.118067i
179179 3.77961i 0.282501i 0.989974 + 0.141251i 0.0451123π0.0451123\pi
−0.989974 + 0.141251i 0.954888π0.954888\pi
180180 6.92506 + 1.80141i 0.516163 + 0.134269i
181181 1.12363i 0.0835189i 0.999128 + 0.0417595i 0.0132963π0.0132963\pi
−0.999128 + 0.0417595i 0.986704π0.986704\pi
182182 0 0
183183 8.15432 0.602784
184184 3.31898 + 7.77060i 0.244679 + 0.572856i
185185 6.10808 0.449075
186186 9.26752 + 11.9867i 0.679527 + 0.878906i
187187 3.56417i 0.260638i
188188 −3.44688 + 13.2507i −0.251390 + 0.966406i
189189 0 0
190190 9.66528 7.47272i 0.701193 0.542128i
191191 14.0300 1.01518 0.507589 0.861600i 0.330537π-0.330537\pi
0.507589 + 0.861600i 0.330537π0.330537\pi
192192 5.77955 + 5.53143i 0.417103 + 0.399197i
193193 0.780195 0.0561597 0.0280798 0.999606i 0.491061π-0.491061\pi
0.0280798 + 0.999606i 0.491061π0.491061\pi
194194 −13.4528 + 10.4010i −0.965852 + 0.746750i
195195 22.0074i 1.57598i
196196 0 0
197197 2.37637i 0.169309i 0.996410 + 0.0846545i 0.0269787π0.0269787\pi
−0.996410 + 0.0846545i 0.973021π0.973021\pi
198198 −0.814815 1.05389i −0.0579064 0.0748966i
199199 −13.5839 −0.962938 −0.481469 0.876463i 0.659897π-0.659897\pi
−0.481469 + 0.876463i 0.659897π0.659897\pi
200200 −8.66608 20.2895i −0.612784 1.43469i
201201 −3.97580 −0.280431
202202 −1.54060 1.99262i −0.108396 0.140200i
203203 0 0
204204 7.32377 + 1.90512i 0.512766 + 0.133385i
205205 16.3146i 1.13946i
206206 13.8991 10.7461i 0.968393 0.748714i
207207 −2.98743 −0.207641
208208 −11.9895 + 21.4859i −0.831320 + 1.48978i
209209 −2.27447 −0.157328
210210 0 0
211211 14.1932i 0.977103i 0.872535 + 0.488551i 0.162474π0.162474\pi
−0.872535 + 0.488551i 0.837526π0.837526\pi
212212 14.6945 + 3.82246i 1.00922 + 0.262528i
213213 3.92572i 0.268986i
214214 8.40284 + 10.8683i 0.574406 + 0.742942i
215215 −12.5462 −0.855645
216216 −2.60110 + 1.11098i −0.176982 + 0.0755928i
217217 0 0
218218 12.3502 + 15.9739i 0.836462 + 1.08189i
219219 6.22876i 0.420901i
220220 −1.69687 + 6.52318i −0.114403 + 0.439793i
221221 23.2745i 1.56561i
222222 −1.91008 + 1.47678i −0.128196 + 0.0991152i
223223 −0.198178 −0.0132710 −0.00663548 0.999978i 0.502112π-0.502112\pi
−0.00663548 + 0.999978i 0.502112π0.502112\pi
224224 0 0
225225 7.80037 0.520025
226226 15.5264 12.0042i 1.03280 0.798510i
227227 25.7560i 1.70949i −0.519050 0.854744i 0.673714π-0.673714\pi
0.519050 0.854744i 0.326286π-0.326286\pi
228228 −1.21575 + 4.67365i −0.0805151 + 0.309520i
229229 16.1617i 1.06800i −0.845485 0.533999i 0.820689π-0.820689\pi
0.845485 0.533999i 0.179311π-0.179311\pi
230230 9.24554 + 11.9583i 0.609633 + 0.788504i
231231 0 0
232232 −6.97421 + 2.97883i −0.457879 + 0.195570i
233233 25.1239 1.64592 0.822959 0.568100i 0.192321π-0.192321\pi
0.822959 + 0.568100i 0.192321π0.192321\pi
234234 −5.32085 6.88203i −0.347835 0.449892i
235235 24.4927i 1.59773i
236236 0.224894 + 0.0585014i 0.0146394 + 0.00380812i
237237 5.47255i 0.355480i
238238 0 0
239239 16.0389 1.03747 0.518736 0.854935i 0.326403π-0.326403\pi
0.518736 + 0.854935i 0.326403π0.326403\pi
240240 12.4970 + 6.97354i 0.806679 + 0.450140i
241241 −13.1691 −0.848293 −0.424147 0.905594i 0.639426π-0.639426\pi
−0.424147 + 0.905594i 0.639426π0.639426\pi
242242 −11.3143 + 8.74763i −0.727308 + 0.562319i
243243 1.00000i 0.0641500i
244244 15.7834 + 4.10570i 1.01043 + 0.262841i
245245 0 0
246246 −3.94446 5.10180i −0.251490 0.325279i
247247 −14.8526 −0.945047
248248 11.9028 + 27.8674i 0.755826 + 1.76958i
249249 1.19560 0.0757683
250250 −8.66662 11.2095i −0.548125 0.708950i
251251 8.64704i 0.545796i −0.962043 0.272898i 0.912018π-0.912018\pi
0.962043 0.272898i 0.0879822π-0.0879822\pi
252252 0 0
253253 2.81406i 0.176918i
254254 −8.69756 + 6.72453i −0.545733 + 0.421934i
255255 13.5373 0.847742
256256 8.40173 + 13.6166i 0.525108 + 0.851035i
257257 −14.4651 −0.902307 −0.451154 0.892446i 0.648987π-0.648987\pi
−0.451154 + 0.892446i 0.648987π0.648987\pi
258258 3.92338 3.03337i 0.244259 0.188849i
259259 0 0
260260 −11.0807 + 42.5972i −0.687199 + 2.64177i
261261 2.68125i 0.165966i
262262 −6.09421 7.88230i −0.376502 0.486970i
263263 19.8967 1.22688 0.613440 0.789741i 0.289785π-0.289785\pi
0.613440 + 0.789741i 0.289785π0.289785\pi
264264 −1.04651 2.45015i −0.0644082 0.150796i
265265 27.1615 1.66852
266266 0 0
267267 1.82102i 0.111444i
268268 −7.69549 2.00182i −0.470077 0.122280i
269269 16.9660i 1.03443i −0.855854 0.517217i 0.826968π-0.826968\pi
0.855854 0.517217i 0.173032π-0.173032\pi
270270 −4.00286 + 3.09481i −0.243606 + 0.188344i
271271 1.07637 0.0653849 0.0326925 0.999465i 0.489592π-0.489592\pi
0.0326925 + 0.999465i 0.489592π0.489592\pi
272272 13.2165 + 7.37504i 0.801370 + 0.447178i
273273 0 0
274274 20.2591 15.6633i 1.22390 0.946256i
275275 7.34769i 0.443083i
276276 −5.78242 1.50417i −0.348061 0.0905406i
277277 4.89143i 0.293898i −0.989144 0.146949i 0.953055π-0.953055\pi
0.989144 0.146949i 0.0469453π-0.0469453\pi
278278 7.20315 + 9.31662i 0.432016 + 0.558774i
279279 −10.7137 −0.641414
280280 0 0
281281 −0.754188 −0.0449911 −0.0224956 0.999747i 0.507161π-0.507161\pi
−0.0224956 + 0.999747i 0.507161π0.507161\pi
282282 −5.92174 7.65923i −0.352635 0.456101i
283283 19.4302i 1.15501i −0.816389 0.577503i 0.804027π-0.804027\pi
0.816389 0.577503i 0.195973π-0.195973\pi
284284 −1.97660 + 7.59856i −0.117290 + 0.450892i
285285 8.63884i 0.511721i
286286 6.48265 5.01206i 0.383327 0.296370i
287287 0 0
288288 −5.59403 + 0.840746i −0.329631 + 0.0495414i
289289 −2.68324 −0.157838
290290 −10.7327 + 8.29798i −0.630245 + 0.487274i
291291 12.0241i 0.704865i
292292 3.13619 12.0563i 0.183531 0.705541i
293293 21.9433i 1.28194i −0.767564 0.640972i 0.778532π-0.778532\pi
0.767564 0.640972i 0.221468π-0.221468\pi
294294 0 0
295295 0.415698 0.0242029
296296 −4.44069 + 1.89671i −0.258110 + 0.110244i
297297 0.941967 0.0546585
298298 −17.9106 23.1658i −1.03753 1.34196i
299299 18.3762i 1.06272i
300300 15.0983 + 3.92749i 0.871699 + 0.226754i
301301 0 0
302302 −4.42566 + 3.42170i −0.254668 + 0.196897i
303303 1.78101 0.102316
304304 −4.70638 + 8.43412i −0.269929 + 0.483730i
305305 29.1742 1.67051
306306 −4.23332 + 3.27300i −0.242003 + 0.187105i
307307 2.18555i 0.124736i −0.998053 0.0623679i 0.980135π-0.980135\pi
0.998053 0.0623679i 0.0198652π-0.0198652\pi
308308 0 0
309309 12.4230i 0.706720i
310310 33.1570 + 42.8855i 1.88319 + 2.43573i
311311 27.2685 1.54626 0.773129 0.634249i 0.218691π-0.218691\pi
0.773129 + 0.634249i 0.218691π0.218691\pi
312312 −6.83384 15.9998i −0.386890 0.905810i
313313 −1.36654 −0.0772412 −0.0386206 0.999254i 0.512296π-0.512296\pi
−0.0386206 + 0.999254i 0.512296π0.512296\pi
314314 −10.2683 13.2811i −0.579472 0.749494i
315315 0 0
316316 −2.75543 + 10.5926i −0.155005 + 0.595879i
317317 8.19107i 0.460056i 0.973184 + 0.230028i 0.0738819π0.0738819\pi
−0.973184 + 0.230028i 0.926118π0.926118\pi
318318 −8.49379 + 6.56698i −0.476308 + 0.368258i
319319 2.52565 0.141410
320320 20.6779 + 19.7901i 1.15593 + 1.10630i
321321 −9.71411 −0.542189
322322 0 0
323323 9.13622i 0.508353i
324324 0.503501 1.93558i 0.0279723 0.107532i
325325 47.9814i 2.66153i
326326 14.7511 + 19.0792i 0.816987 + 1.05670i
327327 −14.2775 −0.789546
328328 −5.06608 11.8610i −0.279727 0.654914i
329329 0 0
330330 −2.91521 3.77056i −0.160477 0.207563i
331331 15.4318i 0.848208i 0.905613 + 0.424104i 0.139411π0.139411\pi
−0.905613 + 0.424104i 0.860589π0.860589\pi
332332 2.31419 + 0.601987i 0.127008 + 0.0330383i
333333 1.70724i 0.0935559i
334334 −11.6736 + 9.02543i −0.638749 + 0.493850i
335335 −14.2245 −0.777165
336336 0 0
337337 −0.543923 −0.0296294 −0.0148147 0.999890i 0.504716π-0.504716\pi
−0.0148147 + 0.999890i 0.504716π0.504716\pi
338338 27.7879 21.4842i 1.51146 1.16859i
339339 13.8775i 0.753722i
340340 26.2027 + 6.81607i 1.42104 + 0.369653i
341341 10.0920i 0.546511i
342342 −2.08866 2.70149i −0.112942 0.146080i
343343 0 0
344344 9.12134 3.89591i 0.491790 0.210053i
345345 −10.6883 −0.575439
346346 12.6069 + 16.3058i 0.677749 + 0.876606i
347347 11.4632i 0.615375i −0.951487 0.307688i 0.900445π-0.900445\pi
0.951487 0.307688i 0.0995552π-0.0995552\pi
348348 1.35001 5.18980i 0.0723684 0.278202i
349349 1.23092i 0.0658899i 0.999457 + 0.0329449i 0.0104886π0.0104886\pi
−0.999457 + 0.0329449i 0.989511π0.989511\pi
350350 0 0
351351 6.15117 0.328325
352352 −0.791955 5.26939i −0.0422113 0.280860i
353353 −34.2183 −1.82126 −0.910628 0.413228i 0.864401π-0.864401\pi
−0.910628 + 0.413228i 0.864401π0.864401\pi
354354 −0.129995 + 0.100505i −0.00690913 + 0.00534180i
355355 14.0453i 0.745446i
356356 −0.916884 + 3.52473i −0.0485948 + 0.186811i
357357 0 0
358358 −3.26941 4.22869i −0.172794 0.223493i
359359 33.9072 1.78955 0.894777 0.446513i 0.147334π-0.147334\pi
0.894777 + 0.446513i 0.147334π0.147334\pi
360360 −9.30611 + 3.97483i −0.490475 + 0.209492i
361361 13.1697 0.693144
362362 −0.971958 1.25714i −0.0510850 0.0660737i
363363 10.1127i 0.530779i
364364 0 0
365365 22.2850i 1.16645i
366366 −9.12318 + 7.05360i −0.476876 + 0.368697i
367367 −19.2447 −1.00456 −0.502282 0.864704i 0.667506π-0.667506\pi
−0.502282 + 0.864704i 0.667506π0.667506\pi
368368 −10.4350 5.82291i −0.543963 0.303540i
369369 4.56000 0.237384
370370 −6.83382 + 5.28358i −0.355273 + 0.274680i
371371 0 0
372372 −20.7373 5.39437i −1.07518 0.279685i
373373 14.8337i 0.768061i 0.923320 + 0.384030i 0.125464π0.125464\pi
−0.923320 + 0.384030i 0.874536π0.874536\pi
374374 −3.08306 3.98765i −0.159421 0.206196i
375375 10.0191 0.517382
376376 −7.60560 17.8067i −0.392229 0.918310i
377377 16.4928 0.849425
378378 0 0
379379 11.7500i 0.603555i 0.953378 + 0.301778i 0.0975800π0.0975800\pi
−0.953378 + 0.301778i 0.902420π0.902420\pi
380380 −4.34966 + 16.7212i −0.223133 + 0.857780i
381381 7.77389i 0.398269i
382382 −15.6970 + 12.1362i −0.803130 + 0.620941i
383383 19.0655 0.974200 0.487100 0.873346i 0.338055π-0.338055\pi
0.487100 + 0.873346i 0.338055π0.338055\pi
384384 −11.2510 1.18926i −0.574152 0.0606894i
385385 0 0
386386 −0.872895 + 0.674880i −0.0444292 + 0.0343505i
387387 3.50672i 0.178257i
388388 6.05415 23.2737i 0.307353 1.18154i
389389 2.00331i 0.101572i 0.998710 + 0.0507859i 0.0161726π0.0161726\pi
−0.998710 + 0.0507859i 0.983827π0.983827\pi
390390 −19.0367 24.6222i −0.963962 1.24680i
391391 −11.3037 −0.571652
392392 0 0
393393 7.04522 0.355384
394394 −2.05559 2.65872i −0.103559 0.133944i
395395 19.5795i 0.985150i
396396 1.82326 + 0.474281i 0.0916221 + 0.0238335i
397397 8.48379i 0.425789i −0.977075 0.212895i 0.931711π-0.931711\pi
0.977075 0.212895i 0.0682891π-0.0682891\pi
398398 15.1979 11.7503i 0.761802 0.588988i
399399 0 0
400400 27.2465 + 15.2040i 1.36232 + 0.760199i
401401 −14.0926 −0.703753 −0.351876 0.936046i 0.614456π-0.614456\pi
−0.351876 + 0.936046i 0.614456π0.614456\pi
402402 4.44819 3.43912i 0.221855 0.171528i
403403 65.9019i 3.28281i
404404 3.44729 + 0.896739i 0.171509 + 0.0446144i
405405 3.57776i 0.177780i
406406 0 0
407407 1.60816 0.0797135
408408 −9.84191 + 4.20368i −0.487247 + 0.208113i
409409 30.3577 1.50109 0.750547 0.660817i 0.229790π-0.229790\pi
0.750547 + 0.660817i 0.229790π0.229790\pi
410410 −14.1123 18.2530i −0.696959 0.901452i
411411 18.1076i 0.893181i
412412 −6.25499 + 24.0458i −0.308161 + 1.18465i
413413 0 0
414414 3.34238 2.58417i 0.164269 0.127005i
415415 4.27758 0.209978
416416 −5.17157 34.4098i −0.253557 1.68708i
417417 −8.32721 −0.407785
418418 2.54471 1.96745i 0.124466 0.0962311i
419419 30.8896i 1.50905i 0.656269 + 0.754527i 0.272134π0.272134\pi
−0.656269 + 0.754527i 0.727866π0.727866\pi
420420 0 0
421421 20.0940i 0.979321i 0.871913 + 0.489661i 0.162879π0.162879\pi
−0.871913 + 0.489661i 0.837121π0.837121\pi
422422 −12.2774 15.8796i −0.597652 0.773008i
423423 6.84583 0.332856
424424 −19.7469 + 8.43432i −0.958996 + 0.409607i
425425 29.5146 1.43167
426426 −3.39580 4.39216i −0.164527 0.212801i
427427 0 0
428428 −18.8025 4.89106i −0.908852 0.236418i
429429 5.79420i 0.279747i
430430 14.0369 10.8527i 0.676920 0.523362i
431431 8.01747 0.386188 0.193094 0.981180i 0.438148π-0.438148\pi
0.193094 + 0.981180i 0.438148π0.438148\pi
432432 1.94914 3.49297i 0.0937779 0.168056i
433433 −26.9812 −1.29663 −0.648316 0.761371i 0.724527π-0.724527\pi
−0.648316 + 0.761371i 0.724527π0.724527\pi
434434 0 0
435435 9.59289i 0.459944i
436436 −27.6353 7.18872i −1.32349 0.344277i
437437 7.21343i 0.345065i
438438 5.38797 + 6.96884i 0.257447 + 0.332984i
439439 36.5152 1.74278 0.871388 0.490594i 0.163220π-0.163220\pi
0.871388 + 0.490594i 0.163220π0.163220\pi
440440 −3.74416 8.76605i −0.178496 0.417905i
441441 0 0
442442 −20.1328 26.0399i −0.957617 1.23859i
443443 0.219929i 0.0104491i 0.999986 + 0.00522457i 0.00166304π0.00166304\pi
−0.999986 + 0.00522457i 0.998337π0.998337\pi
444444 0.859595 3.30450i 0.0407946 0.156825i
445445 6.51517i 0.308848i
446446 0.221725 0.171427i 0.0104990 0.00811728i
447447 20.7056 0.979341
448448 0 0
449449 20.6799 0.975946 0.487973 0.872859i 0.337736π-0.337736\pi
0.487973 + 0.872859i 0.337736π0.337736\pi
450450 −8.72718 + 6.74743i −0.411403 + 0.318077i
451451 4.29537i 0.202261i
452452 −6.98733 + 26.8611i −0.328656 + 1.26344i
453453 3.95566i 0.185853i
454454 22.2793 + 28.8163i 1.04562 + 1.35242i
455455 0 0
456456 −2.68257 6.28060i −0.125623 0.294116i
457457 −8.58418 −0.401551 −0.200776 0.979637i 0.564346π-0.564346\pi
−0.200776 + 0.979637i 0.564346π0.564346\pi
458458 13.9801 + 18.0820i 0.653249 + 0.844917i
459459 3.78375i 0.176610i
460460 −20.6881 5.38157i −0.964588 0.250917i
461461 13.8203i 0.643676i −0.946795 0.321838i 0.895699π-0.895699\pi
0.946795 0.321838i 0.104301π-0.104301\pi
462462 0 0
463463 28.8694 1.34168 0.670838 0.741604i 0.265935π-0.265935\pi
0.670838 + 0.741604i 0.265935π0.265935\pi
464464 5.22613 9.36555i 0.242617 0.434785i
465465 −38.3311 −1.77756
466466 −28.1090 + 21.7325i −1.30212 + 1.00674i
467467 12.4341i 0.575381i −0.957723 0.287691i 0.907112π-0.907112\pi
0.957723 0.287691i 0.0928875π-0.0928875\pi
468468 11.9061 + 3.09712i 0.550360 + 0.143164i
469469 0 0
470470 −21.1866 27.4029i −0.977264 1.26400i
471471 11.8706 0.546970
472472 −0.302220 + 0.129084i −0.0139108 + 0.00594159i
473473 −3.30322 −0.151882
474474 −4.73383 6.12278i −0.217432 0.281229i
475475 18.8347i 0.864197i
476476 0 0
477477 7.59176i 0.347603i
478478 −17.9446 + 13.8739i −0.820767 + 0.634577i
479479 38.2820 1.74915 0.874575 0.484891i 0.161141π-0.161141\pi
0.874575 + 0.484891i 0.161141π0.161141\pi
480480 −20.0141 + 3.00799i −0.913514 + 0.137295i
481481 10.5015 0.478827
482482 14.7338 11.3914i 0.671104 0.518865i
483483 0 0
484484 5.09175 19.5740i 0.231443 0.889726i
485485 43.0194i 1.95341i
486486 0.865014 + 1.11882i 0.0392378 + 0.0507505i
487487 −1.80458 −0.0817733 −0.0408867 0.999164i 0.513018π-0.513018\pi
−0.0408867 + 0.999164i 0.513018π0.513018\pi
488488 −21.2102 + 9.05930i −0.960140 + 0.410095i
489489 −17.0530 −0.771163
490490 0 0
491491 4.10278i 0.185156i −0.995705 0.0925780i 0.970489π-0.970489\pi
0.995705 0.0925780i 0.0295108π-0.0295108\pi
492492 8.82626 + 2.29596i 0.397918 + 0.103510i
493493 10.1452i 0.456917i
494494 16.6173 12.8477i 0.747648 0.578045i
495495 3.37013 0.151476
496496 −37.4227 20.8825i −1.68033 0.937652i
497497 0 0
498498 −1.33766 + 1.03421i −0.0599420 + 0.0463442i
499499 44.4007i 1.98765i −0.110961 0.993825i 0.535393π-0.535393\pi
0.110961 0.993825i 0.464607π-0.464607\pi
500500 19.3927 + 5.04460i 0.867269 + 0.225601i
501501 10.4339i 0.466150i
502502 7.47981 + 9.67445i 0.333840 + 0.431792i
503503 8.88976 0.396375 0.198187 0.980164i 0.436495π-0.436495\pi
0.198187 + 0.980164i 0.436495π0.436495\pi
504504 0 0
505505 6.37202 0.283551
506506 2.43420 + 3.14842i 0.108213 + 0.139964i
507507 24.8369i 1.10304i
508508 3.91416 15.0470i 0.173663 0.667604i
509509 11.0463i 0.489621i −0.969571 0.244810i 0.921274π-0.921274\pi
0.969571 0.244810i 0.0787257π-0.0787257\pi
510510 −15.1458 + 11.7100i −0.670668 + 0.518527i
511511 0 0
512512 −21.1785 7.96682i −0.935967 0.352087i
513513 2.41460 0.106607
514514 16.1838 12.5125i 0.713836 0.551903i
515515 44.4465i 1.95855i
516516 −1.76564 + 6.78756i −0.0777279 + 0.298806i
517517 6.44855i 0.283607i
518518 0 0
519519 −14.5742 −0.639735
520520 −24.4498 57.2434i −1.07220 2.51029i
521521 −33.9951 −1.48935 −0.744675 0.667427i 0.767396π-0.767396\pi
−0.744675 + 0.667427i 0.767396π0.767396\pi
522522 2.31932 + 2.99983i 0.101514 + 0.131299i
523523 18.2103i 0.796282i 0.917324 + 0.398141i 0.130345π0.130345\pi
−0.917324 + 0.398141i 0.869655π0.869655\pi
524524 13.6366 + 3.54727i 0.595718 + 0.154963i
525525 0 0
526526 −22.2607 + 17.2109i −0.970613 + 0.750430i
527527 −40.5380 −1.76586
528528 3.29027 + 1.83602i 0.143190 + 0.0799026i
529529 −14.0753 −0.611968
530530 −30.3887 + 23.4951i −1.32000 + 1.02056i
531531 0.116189i 0.00504219i
532532 0 0
533533 28.0493i 1.21495i
534534 −1.57521 2.03738i −0.0681658 0.0881663i
535535 −34.7547 −1.50258
536536 10.3414 4.41704i 0.446682 0.190787i
537537 3.77961 0.163102
538538 14.6758 + 18.9818i 0.632720 + 0.818365i
539539 0 0
540540 1.80141 6.92506i 0.0775201 0.298007i
541541 30.1308i 1.29542i −0.761886 0.647712i 0.775726π-0.775726\pi
0.761886 0.647712i 0.224274π-0.224274\pi
542542 −1.20426 + 0.931077i −0.0517275 + 0.0399932i
543543 1.12363 0.0482197
544544 −21.1664 + 3.18117i −0.907502 + 0.136392i
545545 −51.0814 −2.18809
546546 0 0
547547 36.0927i 1.54321i −0.636101 0.771606i 0.719454π-0.719454\pi
0.636101 0.771606i 0.280546π-0.280546\pi
548548 −9.11719 + 35.0488i −0.389467 + 1.49721i
549549 8.15432i 0.348018i
550550 −6.35586 8.22072i −0.271015 0.350533i
551551 6.47415 0.275808
552552 7.77060 3.31898i 0.330739 0.141265i
553553 0 0
554554 4.23116 + 5.47262i 0.179765 + 0.232509i
555555 6.10808i 0.259274i
556556 −16.1180 4.19276i −0.683556 0.177812i
557557 42.4146i 1.79717i −0.438804 0.898583i 0.644598π-0.644598\pi
0.438804 0.898583i 0.355402π-0.355402\pi
558558 11.9867 9.26752i 0.507437 0.392325i
559559 −21.5704 −0.912333
560560 0 0
561561 3.56417 0.150479
562562 0.843798 0.652384i 0.0355935 0.0275191i
563563 11.8537i 0.499574i −0.968301 0.249787i 0.919639π-0.919639\pi
0.968301 0.249787i 0.0803606π-0.0803606\pi
564564 13.2507 + 3.44688i 0.557955 + 0.145140i
565565 49.6504i 2.08881i
566566 16.8074 + 21.7388i 0.706468 + 0.913751i
567567 0 0
568568 −4.36141 10.2112i −0.183001 0.428452i
569569 5.42414 0.227392 0.113696 0.993516i 0.463731π-0.463731\pi
0.113696 + 0.993516i 0.463731π0.463731\pi
570570 −7.47272 9.66528i −0.312998 0.404834i
571571 19.5852i 0.819617i 0.912172 + 0.409809i 0.134404π0.134404\pi
−0.912172 + 0.409809i 0.865596π0.865596\pi
572572 −2.91738 + 11.2152i −0.121982 + 0.468929i
573573 14.0300i 0.586113i
574574 0 0
575575 −23.3031 −0.971804
576576 5.53143 5.77955i 0.230476 0.240815i
577577 6.22349 0.259087 0.129544 0.991574i 0.458649π-0.458649\pi
0.129544 + 0.991574i 0.458649π0.458649\pi
578578 3.00205 2.32104i 0.124869 0.0965426i
579579 0.780195i 0.0324238i
580580 4.83003 18.5678i 0.200556 0.770988i
581581 0 0
582582 10.4010 + 13.4528i 0.431136 + 0.557635i
583583 7.15119 0.296172
584584 6.92005 + 16.2016i 0.286354 + 0.670428i
585585 22.0074 0.909894
586586 18.9813 + 24.5506i 0.784110 + 1.01417i
587587 0.894279i 0.0369108i −0.999830 0.0184554i 0.994125π-0.994125\pi
0.999830 0.0184554i 0.00587487π-0.00587487\pi
588588 0 0
589589 25.8693i 1.06593i
590590 −0.465089 + 0.359584i −0.0191474 + 0.0148039i
591591 2.37637 0.0977506
592592 3.32764 5.96333i 0.136765 0.245091i
593593 −22.6996 −0.932161 −0.466080 0.884742i 0.654334π-0.654334\pi
−0.466080 + 0.884742i 0.654334π0.654334\pi
594594 −1.05389 + 0.814815i −0.0432416 + 0.0334323i
595595 0 0
596596 40.0774 + 10.4253i 1.64163 + 0.427036i
597597 13.5839i 0.555953i
598598 15.8957 + 20.5596i 0.650022 + 0.840743i
599599 −39.0356 −1.59495 −0.797476 0.603351i 0.793832π-0.793832\pi
−0.797476 + 0.603351i 0.793832π0.793832\pi
600600 −20.2895 + 8.66608i −0.828317 + 0.353791i
601601 −0.397117 −0.0161987 −0.00809936 0.999967i 0.502578π-0.502578\pi
−0.00809936 + 0.999967i 0.502578π0.502578\pi
602602 0 0
603603 3.97580i 0.161907i
604604 1.99168 7.65652i 0.0810403 0.311539i
605605 36.1808i 1.47096i
606606 −1.99262 + 1.54060i −0.0809447 + 0.0625825i
607607 21.8315 0.886112 0.443056 0.896494i 0.353894π-0.353894\pi
0.443056 + 0.896494i 0.353894π0.353894\pi
608608 −2.03006 13.5073i −0.0823298 0.547794i
609609 0 0
610610 −32.6406 + 25.2361i −1.32158 + 1.02178i
611611 42.1099i 1.70358i
612612 1.90512 7.32377i 0.0770099 0.296046i
613613 24.9947i 1.00953i 0.863258 + 0.504763i 0.168420π0.168420\pi
−0.863258 + 0.504763i 0.831580π0.831580\pi
614614 1.89053 + 2.44523i 0.0762955 + 0.0986813i
615615 16.3146 0.657867
616616 0 0
617617 −17.0538 −0.686560 −0.343280 0.939233i 0.611538π-0.611538\pi
−0.343280 + 0.939233i 0.611538π0.611538\pi
618618 −10.7461 13.8991i −0.432270 0.559102i
619619 4.98901i 0.200525i 0.994961 + 0.100263i 0.0319683π0.0319683\pi
−0.994961 + 0.100263i 0.968032π0.968032\pi
620620 −74.1931 19.2998i −2.97967 0.775097i
621621 2.98743i 0.119881i
622622 −30.5085 + 23.5877i −1.22328 + 0.945780i
623623 0 0
624624 21.4859 + 11.9895i 0.860123 + 0.479963i
625625 −3.15608 −0.126243
626626 1.52890 1.18207i 0.0611073 0.0472452i
627627 2.27447i 0.0908336i
628628 22.9766 + 5.97688i 0.916868 + 0.238503i
629629 6.45975i 0.257567i
630630 0 0
631631 15.7236 0.625947 0.312973 0.949762i 0.398675π-0.398675\pi
0.312973 + 0.949762i 0.398675π0.398675\pi
632632 −6.07991 14.2346i −0.241846 0.566224i
633633 14.1932 0.564130
634634 −7.08539 9.16431i −0.281397 0.363961i
635635 27.8131i 1.10373i
636636 3.82246 14.6945i 0.151570 0.582675i
637637 0 0
638638 −2.82574 + 2.18473i −0.111872 + 0.0864942i
639639 3.92572 0.155299
640640 −40.2535 4.25490i −1.59116 0.168190i
641641 24.6707 0.974433 0.487216 0.873281i 0.338012π-0.338012\pi
0.487216 + 0.873281i 0.338012π0.338012\pi
642642 10.8683 8.40284i 0.428938 0.331634i
643643 47.6908i 1.88074i −0.340150 0.940371i 0.610478π-0.610478\pi
0.340150 0.940371i 0.389522π-0.389522\pi
644644 0 0
645645 12.5462i 0.494007i
646646 −7.90296 10.2218i −0.310938 0.402170i
647647 −19.2945 −0.758547 −0.379273 0.925285i 0.623826π-0.623826\pi
−0.379273 + 0.925285i 0.623826π0.623826\pi
648648 1.11098 + 2.60110i 0.0436435 + 0.102181i
649649 0.109447 0.00429615
650650 −41.5046 53.6824i −1.62794 2.10560i
651651 0 0
652652 −33.0075 8.58619i −1.29267 0.336261i
653653 41.5457i 1.62581i −0.582396 0.812905i 0.697885π-0.697885\pi
0.582396 0.812905i 0.302115π-0.302115\pi
654654 15.9739 12.3502i 0.624628 0.482932i
655655 25.2061 0.984884
656656 15.9280 + 8.88806i 0.621882 + 0.347020i
657657 −6.22876 −0.243007
658658 0 0
659659 21.7026i 0.845414i −0.906266 0.422707i 0.861080π-0.861080\pi
0.906266 0.422707i 0.138920π-0.138920\pi
660660 6.52318 + 1.69687i 0.253914 + 0.0660504i
661661 14.7670i 0.574368i −0.957875 0.287184i 0.907281π-0.907281\pi
0.957875 0.287184i 0.0927191π-0.0927191\pi
662662 −13.3487 17.2653i −0.518813 0.671037i
663663 23.2745 0.903906
664664 −3.10988 + 1.32829i −0.120687 + 0.0515478i
665665 0 0
666666 1.47678 + 1.91008i 0.0572242 + 0.0740142i
667667 8.01006i 0.310151i
668668 5.25345 20.1956i 0.203262 0.781391i
669669 0.198178i 0.00766200i
670670 15.9146 12.3044i 0.614833 0.475359i
671671 7.68110 0.296526
672672 0 0
673673 3.09088 0.119145 0.0595724 0.998224i 0.481026π-0.481026\pi
0.0595724 + 0.998224i 0.481026π0.481026\pi
674674 0.608550 0.470501i 0.0234405 0.0181230i
675675 7.80037i 0.300236i
676676 −12.5054 + 48.0738i −0.480976 + 1.84899i
677677 38.8018i 1.49128i −0.666351 0.745638i 0.732145π-0.732145\pi
0.666351 0.745638i 0.267855π-0.267855\pi
678678 −12.0042 15.5264i −0.461020 0.596287i
679679 0 0
680680 −35.2120 + 15.0398i −1.35032 + 0.576749i
681681 −25.7560 −0.986973
682682 8.72970 + 11.2911i 0.334277 + 0.432357i
683683 26.0073i 0.995140i −0.867424 0.497570i 0.834226π-0.834226\pi
0.867424 0.497570i 0.165774π-0.165774\pi
684684 4.67365 + 1.21575i 0.178702 + 0.0464854i
685685 64.7846i 2.47529i
686686 0 0
687687 −16.1617 −0.616609
688688 −6.83509 + 12.2489i −0.260585 + 0.466985i
689689 46.6982 1.77906
690690 11.9583 9.24554i 0.455243 0.351972i
691691 9.94014i 0.378141i −0.981964 0.189070i 0.939453π-0.939453\pi
0.981964 0.189070i 0.0605475π-0.0605475\pi
692692 −28.2095 7.33810i −1.07237 0.278953i
693693 0 0
694694 9.91581 + 12.8252i 0.376399 + 0.486837i
695695 −29.7928 −1.13010
696696 2.97883 + 6.97421i 0.112912 + 0.264357i
697697 17.2539 0.653538
698698 −1.06477 1.37718i −0.0403020 0.0521270i
699699 25.1239i 0.950272i
700700 0 0
701701 32.3250i 1.22090i −0.792056 0.610449i 0.790989π-0.790989\pi
0.792056 0.610449i 0.209011π-0.209011\pi
702702 −6.88203 + 5.32085i −0.259745 + 0.200822i
703703 4.12228 0.155475
704704 5.44415 + 5.21043i 0.205184 + 0.196375i
705705 24.4927 0.922450
706706 38.2840 29.5993i 1.44084 1.11398i
707707 0 0
708708 0.0585014 0.224894i 0.00219862 0.00845205i
709709 44.1160i 1.65681i 0.560128 + 0.828406i 0.310752π0.310752\pi
−0.560128 + 0.828406i 0.689248π0.689248\pi
710710 −12.1494 15.7141i −0.455958 0.589739i
711711 5.47255 0.205237
712712 −2.02312 4.73665i −0.0758196 0.177513i
713713 32.0065 1.19865
714714 0 0
715715 20.7303i 0.775268i
716716 7.31575 + 1.90303i 0.273402 + 0.0711198i
717717 16.0389i 0.598984i
718718 −37.9360 + 29.3302i −1.41576 + 1.09459i
719719 −6.45859 −0.240865 −0.120432 0.992722i 0.538428π-0.538428\pi
−0.120432 + 0.992722i 0.538428π0.538428\pi
720720 6.97354 12.4970i 0.259889 0.465737i
721721 0 0
722722 −14.7345 + 11.3920i −0.548362 + 0.423966i
723723 13.1691i 0.489762i
724724 2.17488 + 0.565750i 0.0808290 + 0.0210259i
725725 20.9148i 0.776755i
726726 8.74763 + 11.3143i 0.324655 + 0.419911i
727727 −25.6040 −0.949600 −0.474800 0.880094i 0.657480π-0.657480\pi
−0.474800 + 0.880094i 0.657480π0.657480\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 19.2769 + 24.9329i 0.713469 + 0.922806i
731731 13.2686i 0.490756i
732732 4.10570 15.7834i 0.151751 0.583370i
733733 10.3299i 0.381544i 0.981634 + 0.190772i 0.0610991π0.0610991\pi
−0.981634 + 0.190772i 0.938901π0.938901\pi
734734 21.5313 16.6469i 0.794734 0.614449i
735735 0 0
736736 16.7118 2.51167i 0.616004 0.0925813i
737737 −3.74507 −0.137951
738738 −5.10180 + 3.94446i −0.187800 + 0.145198i
739739 46.3422i 1.70472i 0.522952 + 0.852362i 0.324831π0.324831\pi
−0.522952 + 0.852362i 0.675169π0.675169\pi
740740 3.07542 11.8227i 0.113055 0.434611i
741741 14.8526i 0.545623i
742742 0 0
743743 −38.1002 −1.39776 −0.698880 0.715239i 0.746318π-0.746318\pi
−0.698880 + 0.715239i 0.746318π0.746318\pi
744744 27.8674 11.9028i 1.02167 0.436376i
745745 74.0796 2.71407
746746 −12.8314 16.5962i −0.469790 0.607631i
747747 1.19560i 0.0437448i
748748 6.89875 + 1.79456i 0.252243 + 0.0656157i
749749 0 0
750750 −11.2095 + 8.66662i −0.409312 + 0.316460i
751751 −7.51999 −0.274408 −0.137204 0.990543i 0.543812π-0.543812\pi
−0.137204 + 0.990543i 0.543812π0.543812\pi
752752 23.9123 + 13.3435i 0.871992 + 0.486586i
753753 −8.64704 −0.315116
754754 −18.4525 + 14.2665i −0.671999 + 0.519557i
755755 14.1524i 0.515059i
756756 0 0
757757 41.2006i 1.49746i −0.662873 0.748731i 0.730663π-0.730663\pi
0.662873 0.748731i 0.269337π-0.269337\pi
758758 −10.1639 13.1461i −0.369169 0.477486i
759759 −2.81406 −0.102144
760760 −9.59761 22.4705i −0.348142 0.815090i
761761 28.6212 1.03752 0.518759 0.854920i 0.326394π-0.326394\pi
0.518759 + 0.854920i 0.326394π0.326394\pi
762762 6.72453 + 8.69756i 0.243604 + 0.315079i
763763 0 0
764764 7.06413 27.1563i 0.255571 0.982481i
765765 13.5373i 0.489444i
766766 −21.3308 + 16.4919i −0.770712 + 0.595877i
767767 0.714700 0.0258063
768768 13.6166 8.40173i 0.491346 0.303171i
769769 −14.6303 −0.527581 −0.263791 0.964580i 0.584973π-0.584973\pi
−0.263791 + 0.964580i 0.584973π0.584973\pi
770770 0 0
771771 14.4651i 0.520947i
772772 0.392829 1.51013i 0.0141382 0.0543509i
773773 42.4716i 1.52760i 0.645455 + 0.763798i 0.276668π0.276668\pi
−0.645455 + 0.763798i 0.723332π0.723332\pi
774774 −3.03337 3.92338i −0.109032 0.141023i
775775 −83.5710 −3.00196
776776 13.3586 + 31.2759i 0.479545 + 1.12274i
777777 0 0
778778 −1.73289 2.24134i −0.0621271 0.0803558i
779779 11.0105i 0.394494i
780780 42.5972 + 11.0807i 1.52522 + 0.396754i
781781 3.69790i 0.132321i
782782 12.6467 9.77785i 0.452247 0.349655i
783783 −2.68125 −0.0958202
784784 0 0
785785 42.4703 1.51583
786786 −7.88230 + 6.09421i −0.281153 + 0.217373i
787787 7.56670i 0.269724i 0.990864 + 0.134862i 0.0430591π0.0430591\pi
−0.990864 + 0.134862i 0.956941π0.956941\pi
788788 4.59966 + 1.19650i 0.163856 + 0.0426236i
789789 19.8967i 0.708340i
790790 −16.9365 21.9058i −0.602575 0.779375i
791791 0 0
792792 −2.45015 + 1.04651i −0.0870623 + 0.0371861i
793793 50.1586 1.78118
794794 7.33860 + 9.49181i 0.260437 + 0.336852i
795795 27.1615i 0.963320i
796796 −6.83951 + 26.2928i −0.242420 + 0.931924i
797797 11.4622i 0.406013i −0.979177 0.203007i 0.934929π-0.934929\pi
0.979177 0.203007i 0.0650713π-0.0650713\pi
798798 0 0
799799 25.9029 0.916379
800800 −43.6355 + 6.55813i −1.54275 + 0.231865i
801801 1.82102 0.0643425
802802 15.7671 12.1903i 0.556755 0.430456i
803803 5.86729i 0.207052i
804804 −2.00182 + 7.69549i −0.0705987 + 0.271399i
805805 0 0
806806 57.0061 + 73.7321i 2.00795 + 2.59710i
807807 −16.9660 −0.597231
808808 −4.63258 + 1.97867i −0.162974 + 0.0696093i
809809 17.0821 0.600573 0.300287 0.953849i 0.402918π-0.402918\pi
0.300287 + 0.953849i 0.402918π0.402918\pi
810810 3.09481 + 4.00286i 0.108741 + 0.140646i
811811 16.6693i 0.585338i 0.956214 + 0.292669i 0.0945434π0.0945434\pi
−0.956214 + 0.292669i 0.905457π0.905457\pi
812812 0 0
813813 1.07637i 0.0377500i
814814 −1.79924 + 1.39108i −0.0630632 + 0.0487574i
815815 −61.0115 −2.13714
816816 7.37504 13.2165i 0.258178 0.462671i
817817 −8.46732 −0.296234
818818 −33.9647 + 26.2599i −1.18755 + 0.918155i
819819 0 0
820820 31.5782 + 8.21440i 1.10276 + 0.286859i
821821 43.0233i 1.50152i 0.660572 + 0.750762i 0.270314π0.270314\pi
−0.660572 + 0.750762i 0.729686π0.729686\pi
822822 −15.6633 20.2591i −0.546321 0.706616i
823823 34.6509 1.20786 0.603928 0.797039i 0.293602π-0.293602\pi
0.603928 + 0.797039i 0.293602π0.293602\pi
824824 −13.8017 32.3135i −0.480806 1.12569i
825825 7.34769 0.255814
826826 0 0
827827 36.5937i 1.27249i 0.771489 + 0.636243i 0.219513π0.219513\pi
−0.771489 + 0.636243i 0.780487π0.780487\pi
828828 −1.50417 + 5.78242i −0.0522736 + 0.200953i
829829 7.55875i 0.262526i 0.991348 + 0.131263i 0.0419033π0.0419033\pi
−0.991348 + 0.131263i 0.958097π0.958097\pi
830830 −4.78583 + 3.70017i −0.166119 + 0.128435i
831831 −4.89143 −0.169682
832832 35.5510 + 34.0248i 1.23251 + 1.17960i
833833 0 0
834834 9.31662 7.20315i 0.322608 0.249425i
835835 37.3298i 1.29185i
836836 −1.14520 + 4.40243i −0.0396075 + 0.152261i
837837 10.7137i 0.370320i
838838 −26.7199 34.5598i −0.923024 1.19385i
839839 −33.3899 −1.15275 −0.576374 0.817186i 0.695533π-0.695533\pi
−0.576374 + 0.817186i 0.695533π0.695533\pi
840840 0 0
841841 21.8109 0.752099
842842 −17.3816 22.4815i −0.599009 0.774763i
843843 0.754188i 0.0259756i
844844 27.4722 + 7.14631i 0.945632 + 0.245986i
845845 88.8603i 3.05689i
846846 −7.65923 + 5.92174i −0.263330 + 0.203594i
847847 0 0
848848 14.7974 26.5178i 0.508144 0.910626i
849849 −19.4302 −0.666843
850850 −33.0215 + 25.5306i −1.13263 + 0.875692i
851851 5.10025i 0.174834i
852852 7.59856 + 1.97660i 0.260322 + 0.0677173i
853853 18.6855i 0.639779i 0.947455 + 0.319889i 0.103646π0.103646\pi
−0.947455 + 0.319889i 0.896354π0.896354\pi
854854 0 0
855855 8.63884 0.295442
856856 25.2674 10.7922i 0.863620 0.368870i
857857 −30.8881 −1.05512 −0.527559 0.849518i 0.676893π-0.676893\pi
−0.527559 + 0.849518i 0.676893π0.676893\pi
858858 −5.01206 6.48265i −0.171109 0.221314i
859859 40.8604i 1.39414i −0.717004 0.697069i 0.754487π-0.754487\pi
0.717004 0.697069i 0.245513π-0.245513\pi
860860 −6.31703 + 24.2843i −0.215409 + 0.828087i
861861 0 0
862862 −8.97007 + 6.93522i −0.305522 + 0.236215i
863863 3.75352 0.127771 0.0638857 0.997957i 0.479651π-0.479651\pi
0.0638857 + 0.997957i 0.479651π0.479651\pi
864864 0.840746 + 5.59403i 0.0286027 + 0.190313i
865865 −52.1429 −1.77291
866866 30.1870 23.3391i 1.02580 0.793095i
867867 2.68324i 0.0911277i
868868 0 0
869869 5.15496i 0.174870i
870870 8.29798 + 10.7327i 0.281328 + 0.363872i
871871 −24.4558 −0.828653
872872 37.1371 15.8620i 1.25762 0.537156i
873873 −12.0241 −0.406954
874874 6.23972 + 8.07051i 0.211062 + 0.272989i
875875 0 0
876876 −12.0563 3.13619i −0.407345 0.105962i
877877 30.0472i 1.01462i −0.861763 0.507311i 0.830639π-0.830639\pi
0.861763 0.507311i 0.169361π-0.169361\pi
878878 −40.8538 + 31.5862i −1.37875 + 1.06598i
879879 −21.9433 −0.740130
880880 11.7718 + 6.56885i 0.396827 + 0.221436i
881881 42.4160 1.42903 0.714516 0.699619i 0.246647π-0.246647\pi
0.714516 + 0.699619i 0.246647π0.246647\pi
882882 0 0
883883 20.3124i 0.683568i 0.939779 + 0.341784i 0.111031π0.111031\pi
−0.939779 + 0.341784i 0.888969π0.888969\pi
884884 45.0497 + 11.7187i 1.51519 + 0.394143i
885885 0.415698i 0.0139735i
886886 −0.190242 0.246060i −0.00639129 0.00826655i
887887 17.3844 0.583711 0.291855 0.956462i 0.405727π-0.405727\pi
0.291855 + 0.956462i 0.405727π0.405727\pi
888888 1.89671 + 4.44069i 0.0636494 + 0.149020i
889889 0 0
890890 −5.63571 7.28928i −0.188909 0.244337i
891891 0.941967i 0.0315571i
892892 −0.0997827 + 0.383590i −0.00334097 + 0.0128435i
893893 16.5299i 0.553152i
894894 −23.1658 + 17.9106i −0.774779 + 0.599021i
895895 13.5225 0.452008
896896 0 0
897897 −18.3762 −0.613563
898898 −23.1370 + 17.8884i −0.772093 + 0.596945i
899899 28.7262i 0.958073i
900900 3.92749 15.0983i 0.130916 0.503276i
901901 28.7253i 0.956980i
902902 −3.71555 4.80573i −0.123714 0.160013i
903903 0 0
904904 −15.4177 36.0967i −0.512784 1.20056i
905905 4.02009 0.133632
906906 3.42170 + 4.42566i 0.113679 + 0.147033i
907907 21.8203i 0.724533i 0.932075 + 0.362266i 0.117997π0.117997\pi
−0.932075 + 0.362266i 0.882003π0.882003\pi
908908 −49.8530 12.9682i −1.65443 0.430364i
909909 1.78101i 0.0590723i
910910 0 0
911911 11.9139 0.394727 0.197363 0.980330i 0.436762π-0.436762\pi
0.197363 + 0.980330i 0.436762π0.436762\pi
912912 8.43412 + 4.70638i 0.279282 + 0.155844i
913913 1.12622 0.0372724
914914 9.60412 7.42544i 0.317676 0.245612i
915915 29.1742i 0.964469i
916916 −31.2824 8.13745i −1.03360 0.268869i
917917 0 0
918918 3.27300 + 4.23332i 0.108025 + 0.139720i
919919 −37.7665 −1.24580 −0.622900 0.782301i 0.714046π-0.714046\pi
−0.622900 + 0.782301i 0.714046π0.714046\pi
920920 27.8013 11.8745i 0.916583 0.391491i
921921 −2.18555 −0.0720162
922922 11.9548 + 15.4624i 0.393709 + 0.509226i
923923 24.1477i 0.794833i
924924 0 0
925925 13.3171i 0.437863i
926926 −32.2996 + 24.9724i −1.06143 + 0.820645i
927927 12.4230 0.408025
928928 2.25425 + 14.9990i 0.0739995 + 0.492367i
929929 −34.5094 −1.13222 −0.566108 0.824331i 0.691552π-0.691552\pi
−0.566108 + 0.824331i 0.691552π0.691552\pi
930930 42.8855 33.1570i 1.40627 1.08726i
931931 0 0
932932 12.6499 48.6294i 0.414361 1.59291i
933933 27.2685i 0.892732i
934934 10.7557 + 13.9115i 0.351936 + 0.455197i
935935 12.7517 0.417026
936936 −15.9998 + 6.83384i −0.522970 + 0.223371i
937937 2.63475 0.0860735 0.0430367 0.999073i 0.486297π-0.486297\pi
0.0430367 + 0.999073i 0.486297π0.486297\pi
938938 0 0
939939 1.36654i 0.0445952i
940940 47.4078 + 12.3321i 1.54627 + 0.402229i
941941 20.5159i 0.668799i 0.942431 + 0.334399i 0.108533π0.108533\pi
−0.942431 + 0.334399i 0.891467π0.891467\pi
942942 −13.2811 + 10.2683i −0.432721 + 0.334559i
943943 −13.6227 −0.443615
944944 0.226469 0.405846i 0.00737094 0.0132092i
945945 0 0
946946 3.69570 2.85733i 0.120157 0.0928999i
947947 31.4487i 1.02194i 0.859597 + 0.510972i 0.170714π0.170714\pi
−0.859597 + 0.510972i 0.829286π0.829286\pi
948948 10.5926 + 2.75543i 0.344031 + 0.0894923i
949949 38.3142i 1.24373i
950950 −16.2923 21.0726i −0.528592 0.683686i
951951 8.19107 0.265614
952952 0 0
953953 7.69660 0.249317 0.124659 0.992200i 0.460216π-0.460216\pi
0.124659 + 0.992200i 0.460216π0.460216\pi
954954 6.56698 + 8.49379i 0.212614 + 0.274997i
955955 50.1961i 1.62431i
956956 8.07561 31.0447i 0.261184 1.00406i
957957 2.52565i 0.0816428i
958958 −42.8305 + 33.1145i −1.38379 + 1.06988i
959959 0 0
960960 19.7901 20.6779i 0.638724 0.667375i
961961 83.7838 2.70270
962962 −11.7492 + 9.08394i −0.378811 + 0.292878i
963963 9.71411i 0.313033i
964964 −6.63063 + 25.4898i −0.213558 + 0.820972i
965965 2.79135i 0.0898568i
966966 0 0
967967 −58.4850 −1.88075 −0.940375 0.340140i 0.889526π-0.889526\pi
−0.940375 + 0.340140i 0.889526π0.889526\pi
968968 11.2350 + 26.3041i 0.361108 + 0.845447i
969969 9.13622 0.293498
970970 37.2124 + 48.1308i 1.19482 + 1.54539i
971971 46.6300i 1.49643i 0.663457 + 0.748215i 0.269089π0.269089\pi
−0.663457 + 0.748215i 0.730911π0.730911\pi
972972 −1.93558 0.503501i −0.0620839 0.0161498i
973973 0 0
974974 2.01899 1.56099i 0.0646927 0.0500173i
975975 47.9814 1.53663
976976 15.8939 28.4828i 0.508751 0.911713i
977977 −1.50961 −0.0482967 −0.0241484 0.999708i 0.507687π-0.507687\pi
−0.0241484 + 0.999708i 0.507687π0.507687\pi
978978 19.0792 14.7511i 0.610084 0.471687i
979979 1.71534i 0.0548225i
980980 0 0
981981 14.2775i 0.455845i
982982 3.54897 + 4.59026i 0.113252 + 0.146481i
983983 22.1661 0.706988 0.353494 0.935437i 0.384993π-0.384993\pi
0.353494 + 0.935437i 0.384993π0.384993\pi
984984 −11.8610 + 5.06608i −0.378115 + 0.161501i
985985 8.50207 0.270898
986986 8.77574 + 11.3506i 0.279476 + 0.361477i
987987 0 0
988988 −7.47829 + 28.7484i −0.237916 + 0.914609i
989989 10.4761i 0.333120i
990990 −3.77056 + 2.91521i −0.119836 + 0.0926516i
991991 −57.8841 −1.83875 −0.919374 0.393384i 0.871304π-0.871304\pi
−0.919374 + 0.393384i 0.871304π0.871304\pi
992992 59.9328 9.00751i 1.90287 0.285989i
993993 15.4318 0.489713
994994 0 0
995995 48.6000i 1.54072i
996996 0.601987 2.31419i 0.0190747 0.0733279i
997997 50.9825i 1.61463i 0.590118 + 0.807317i 0.299081π0.299081\pi
−0.590118 + 0.807317i 0.700919π0.700919\pi
998998 38.4073 + 49.6763i 1.21576 + 1.57247i
999999 −1.70724 −0.0540145
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 1176.2.c.e.589.6 16
4.3 odd 2 4704.2.c.e.2353.9 16
7.2 even 3 168.2.bc.a.109.15 yes 32
7.4 even 3 168.2.bc.a.37.7 32
7.6 odd 2 1176.2.c.f.589.6 16
8.3 odd 2 4704.2.c.e.2353.8 16
8.5 even 2 inner 1176.2.c.e.589.5 16
21.2 odd 6 504.2.cj.e.109.2 32
21.11 odd 6 504.2.cj.e.37.10 32
28.11 odd 6 672.2.bk.a.625.16 32
28.23 odd 6 672.2.bk.a.529.1 32
28.27 even 2 4704.2.c.f.2353.8 16
56.11 odd 6 672.2.bk.a.625.1 32
56.13 odd 2 1176.2.c.f.589.5 16
56.27 even 2 4704.2.c.f.2353.9 16
56.37 even 6 168.2.bc.a.109.7 yes 32
56.51 odd 6 672.2.bk.a.529.16 32
56.53 even 6 168.2.bc.a.37.15 yes 32
84.11 even 6 2016.2.cr.e.1297.1 32
84.23 even 6 2016.2.cr.e.1873.16 32
168.11 even 6 2016.2.cr.e.1297.16 32
168.53 odd 6 504.2.cj.e.37.2 32
168.107 even 6 2016.2.cr.e.1873.1 32
168.149 odd 6 504.2.cj.e.109.10 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.bc.a.37.7 32 7.4 even 3
168.2.bc.a.37.15 yes 32 56.53 even 6
168.2.bc.a.109.7 yes 32 56.37 even 6
168.2.bc.a.109.15 yes 32 7.2 even 3
504.2.cj.e.37.2 32 168.53 odd 6
504.2.cj.e.37.10 32 21.11 odd 6
504.2.cj.e.109.2 32 21.2 odd 6
504.2.cj.e.109.10 32 168.149 odd 6
672.2.bk.a.529.1 32 28.23 odd 6
672.2.bk.a.529.16 32 56.51 odd 6
672.2.bk.a.625.1 32 56.11 odd 6
672.2.bk.a.625.16 32 28.11 odd 6
1176.2.c.e.589.5 16 8.5 even 2 inner
1176.2.c.e.589.6 16 1.1 even 1 trivial
1176.2.c.f.589.5 16 56.13 odd 2
1176.2.c.f.589.6 16 7.6 odd 2
2016.2.cr.e.1297.1 32 84.11 even 6
2016.2.cr.e.1297.16 32 168.11 even 6
2016.2.cr.e.1873.1 32 168.107 even 6
2016.2.cr.e.1873.16 32 84.23 even 6
4704.2.c.e.2353.8 16 8.3 odd 2
4704.2.c.e.2353.9 16 4.3 odd 2
4704.2.c.f.2353.8 16 28.27 even 2
4704.2.c.f.2353.9 16 56.27 even 2