Properties

Label 1710.2.n.i.1673.6
Level 17101710
Weight 22
Character 1710.1673
Analytic conductor 13.65413.654
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1710,2,Mod(647,1710)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1710, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1710.647"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1710=232519 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1710.n (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20,0,0,0,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 13.654418745613.6544187456
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x204x1910x18+56x17+50x16336x15+672x14776x13+626x12++32 x^{20} - 4 x^{19} - 10 x^{18} + 56 x^{17} + 50 x^{16} - 336 x^{15} + 672 x^{14} - 776 x^{13} + 626 x^{12} + \cdots + 32 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 210 2^{10}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 1673.6
Root 3.06999+1.27163i-3.06999 + 1.27163i of defining polynomial
Character χ\chi == 1710.1673
Dual form 1710.2.n.i.647.6

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.707107+0.707107i)q2+1.00000iq4+(2.21129+0.331972i)q5+(1.82552+1.82552i)q7+(0.707107+0.707107i)q8+(1.798361.32888i)q102.09952iq11+(1.642651.64265i)q132.58168q141.00000q16+(3.293533.29353i)q171.00000iq19+(0.3319722.21129i)q20+(1.484591.48459i)q22+(5.124945.12494i)q23+(4.779591.46817i)q252.32305iq26+(1.825521.82552i)q28+9.48773q29+4.22425q31+(0.7071070.707107i)q324.65775iq34+(3.430744.64278i)q35+(1.64265+1.64265i)q37+(0.7071070.707107i)q38+(1.328881.79836i)q40+7.26473iq41+(5.70884+5.70884i)q43+2.09952q44+7.24776q46+(9.108959.10895i)q47+0.334925iq49+(4.41783+2.34153i)q50+(1.642651.64265i)q52+(10.014510.0145i)q53+(0.696982+4.64265i)q552.58168iq56+(6.70884+6.70884i)q585.56868q5913.7834q61+(2.98700+2.98700i)q621.00000iq64+(4.17768+3.08705i)q65+(3.293533.29353i)q68+(5.708840.857046i)q700.853364iq71+(8.559188.55918i)q732.32305q74+1.00000q76+(3.83273+3.83273i)q771.45962iq79+(2.211290.331972i)q80+(5.13694+5.13694i)q82+(6.315626.31562i)q83+(8.37630+6.18958i)q85+8.07352iq86+(1.48459+1.48459i)q88+8.59262q89+5.99738q91+(5.12494+5.12494i)q9212.8820iq94+(0.331972+2.21129i)q95+(11.017611.0176i)q97+(0.236828+0.236828i)q98+O(q100)q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.21129 + 0.331972i) q^{5} +(-1.82552 + 1.82552i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.79836 - 1.32888i) q^{10} -2.09952i q^{11} +(-1.64265 - 1.64265i) q^{13} -2.58168 q^{14} -1.00000 q^{16} +(-3.29353 - 3.29353i) q^{17} -1.00000i q^{19} +(-0.331972 - 2.21129i) q^{20} +(1.48459 - 1.48459i) q^{22} +(5.12494 - 5.12494i) q^{23} +(4.77959 - 1.46817i) q^{25} -2.32305i q^{26} +(-1.82552 - 1.82552i) q^{28} +9.48773 q^{29} +4.22425 q^{31} +(-0.707107 - 0.707107i) q^{32} -4.65775i q^{34} +(3.43074 - 4.64278i) q^{35} +(-1.64265 + 1.64265i) q^{37} +(0.707107 - 0.707107i) q^{38} +(1.32888 - 1.79836i) q^{40} +7.26473i q^{41} +(5.70884 + 5.70884i) q^{43} +2.09952 q^{44} +7.24776 q^{46} +(-9.10895 - 9.10895i) q^{47} +0.334925i q^{49} +(4.41783 + 2.34153i) q^{50} +(1.64265 - 1.64265i) q^{52} +(10.0145 - 10.0145i) q^{53} +(0.696982 + 4.64265i) q^{55} -2.58168i q^{56} +(6.70884 + 6.70884i) q^{58} -5.56868 q^{59} -13.7834 q^{61} +(2.98700 + 2.98700i) q^{62} -1.00000i q^{64} +(4.17768 + 3.08705i) q^{65} +(3.29353 - 3.29353i) q^{68} +(5.70884 - 0.857046i) q^{70} -0.853364i q^{71} +(-8.55918 - 8.55918i) q^{73} -2.32305 q^{74} +1.00000 q^{76} +(3.83273 + 3.83273i) q^{77} -1.45962i q^{79} +(2.21129 - 0.331972i) q^{80} +(-5.13694 + 5.13694i) q^{82} +(6.31562 - 6.31562i) q^{83} +(8.37630 + 6.18958i) q^{85} +8.07352i q^{86} +(1.48459 + 1.48459i) q^{88} +8.59262 q^{89} +5.99738 q^{91} +(5.12494 + 5.12494i) q^{92} -12.8820i q^{94} +(0.331972 + 2.21129i) q^{95} +(11.0176 - 11.0176i) q^{97} +(-0.236828 + 0.236828i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q1012q1320q1616q22+16q3112q378q46+12q52+20q5816q61+20q73+20q7628q828q8516q88+32q9120q97+O(q100) 20 q + 4 q^{10} - 12 q^{13} - 20 q^{16} - 16 q^{22} + 16 q^{31} - 12 q^{37} - 8 q^{46} + 12 q^{52} + 20 q^{58} - 16 q^{61} + 20 q^{73} + 20 q^{76} - 28 q^{82} - 8 q^{85} - 16 q^{88} + 32 q^{91} - 20 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1710Z)×\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times.

nn 191191 10271027 13511351
χ(n)\chi(n) 1-1 e(34)e\left(\frac{3}{4}\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 0.707107 + 0.707107i 0.500000 + 0.500000i
33 0 0
44 1.00000i 0.500000i
55 −2.21129 + 0.331972i −0.988918 + 0.148462i
66 0 0
77 −1.82552 + 1.82552i −0.689983 + 0.689983i −0.962228 0.272245i 0.912234π-0.912234\pi
0.272245 + 0.962228i 0.412234π0.412234\pi
88 −0.707107 + 0.707107i −0.250000 + 0.250000i
99 0 0
1010 −1.79836 1.32888i −0.568690 0.420228i
1111 2.09952i 0.633030i −0.948588 0.316515i 0.897487π-0.897487\pi
0.948588 0.316515i 0.102513π-0.102513\pi
1212 0 0
1313 −1.64265 1.64265i −0.455588 0.455588i 0.441616 0.897204i 0.354405π-0.354405\pi
−0.897204 + 0.441616i 0.854405π0.854405\pi
1414 −2.58168 −0.689983
1515 0 0
1616 −1.00000 −0.250000
1717 −3.29353 3.29353i −0.798798 0.798798i 0.184108 0.982906i 0.441060π-0.441060\pi
−0.982906 + 0.184108i 0.941060π0.941060\pi
1818 0 0
1919 1.00000i 0.229416i
2020 −0.331972 2.21129i −0.0742312 0.494459i
2121 0 0
2222 1.48459 1.48459i 0.316515 0.316515i
2323 5.12494 5.12494i 1.06862 1.06862i 0.0711590 0.997465i 0.477330π-0.477330\pi
0.997465 0.0711590i 0.0226698π-0.0226698\pi
2424 0 0
2525 4.77959 1.46817i 0.955918 0.293634i
2626 2.32305i 0.455588i
2727 0 0
2828 −1.82552 1.82552i −0.344992 0.344992i
2929 9.48773 1.76183 0.880914 0.473277i 0.156929π-0.156929\pi
0.880914 + 0.473277i 0.156929π0.156929\pi
3030 0 0
3131 4.22425 0.758698 0.379349 0.925254i 0.376148π-0.376148\pi
0.379349 + 0.925254i 0.376148π0.376148\pi
3232 −0.707107 0.707107i −0.125000 0.125000i
3333 0 0
3434 4.65775i 0.798798i
3535 3.43074 4.64278i 0.579900 0.784773i
3636 0 0
3737 −1.64265 + 1.64265i −0.270050 + 0.270050i −0.829120 0.559071i 0.811158π-0.811158\pi
0.559071 + 0.829120i 0.311158π0.311158\pi
3838 0.707107 0.707107i 0.114708 0.114708i
3939 0 0
4040 1.32888 1.79836i 0.210114 0.284345i
4141 7.26473i 1.13456i 0.823525 + 0.567280i 0.192004π0.192004\pi
−0.823525 + 0.567280i 0.807996π0.807996\pi
4242 0 0
4343 5.70884 + 5.70884i 0.870590 + 0.870590i 0.992537 0.121947i 0.0389137π-0.0389137\pi
−0.121947 + 0.992537i 0.538914π0.538914\pi
4444 2.09952 0.316515
4545 0 0
4646 7.24776 1.06862
4747 −9.10895 9.10895i −1.32868 1.32868i −0.906525 0.422153i 0.861274π-0.861274\pi
−0.422153 0.906525i 0.638726π-0.638726\pi
4848 0 0
4949 0.334925i 0.0478465i
5050 4.41783 + 2.34153i 0.624776 + 0.331142i
5151 0 0
5252 1.64265 1.64265i 0.227794 0.227794i
5353 10.0145 10.0145i 1.37559 1.37559i 0.523675 0.851918i 0.324561π-0.324561\pi
0.851918 0.523675i 0.175439π-0.175439\pi
5454 0 0
5555 0.696982 + 4.64265i 0.0939811 + 0.626014i
5656 2.58168i 0.344992i
5757 0 0
5858 6.70884 + 6.70884i 0.880914 + 0.880914i
5959 −5.56868 −0.724980 −0.362490 0.931988i 0.618073π-0.618073\pi
−0.362490 + 0.931988i 0.618073π0.618073\pi
6060 0 0
6161 −13.7834 −1.76479 −0.882394 0.470512i 0.844069π-0.844069\pi
−0.882394 + 0.470512i 0.844069π0.844069\pi
6262 2.98700 + 2.98700i 0.379349 + 0.379349i
6363 0 0
6464 1.00000i 0.125000i
6565 4.17768 + 3.08705i 0.518177 + 0.382902i
6666 0 0
6767 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
6868 3.29353 3.29353i 0.399399 0.399399i
6969 0 0
7070 5.70884 0.857046i 0.682337 0.102437i
7171 0.853364i 0.101276i −0.998717 0.0506378i 0.983875π-0.983875\pi
0.998717 0.0506378i 0.0161254π-0.0161254\pi
7272 0 0
7373 −8.55918 8.55918i −1.00178 1.00178i −0.999998 0.00177765i 0.999434π-0.999434\pi
−0.00177765 0.999998i 0.500566π-0.500566\pi
7474 −2.32305 −0.270050
7575 0 0
7676 1.00000 0.114708
7777 3.83273 + 3.83273i 0.436780 + 0.436780i
7878 0 0
7979 1.45962i 0.164221i −0.996623 0.0821103i 0.973834π-0.973834\pi
0.996623 0.0821103i 0.0261660π-0.0261660\pi
8080 2.21129 0.331972i 0.247230 0.0371156i
8181 0 0
8282 −5.13694 + 5.13694i −0.567280 + 0.567280i
8383 6.31562 6.31562i 0.693230 0.693230i −0.269712 0.962941i 0.586928π-0.586928\pi
0.962941 + 0.269712i 0.0869284π0.0869284\pi
8484 0 0
8585 8.37630 + 6.18958i 0.908538 + 0.671355i
8686 8.07352i 0.870590i
8787 0 0
8888 1.48459 + 1.48459i 0.158257 + 0.158257i
8989 8.59262 0.910816 0.455408 0.890283i 0.349493π-0.349493\pi
0.455408 + 0.890283i 0.349493π0.349493\pi
9090 0 0
9191 5.99738 0.628697
9292 5.12494 + 5.12494i 0.534312 + 0.534312i
9393 0 0
9494 12.8820i 1.32868i
9595 0.331972 + 2.21129i 0.0340596 + 0.226873i
9696 0 0
9797 11.0176 11.0176i 1.11867 1.11867i 0.126735 0.991937i 0.459550π-0.459550\pi
0.991937 0.126735i 0.0404499π-0.0404499\pi
9898 −0.236828 + 0.236828i −0.0239232 + 0.0239232i
9999 0 0
100100 1.46817 + 4.77959i 0.146817 + 0.477959i
101101 14.5956i 1.45232i −0.687527 0.726159i 0.741304π-0.741304\pi
0.687527 0.726159i 0.258696π-0.258696\pi
102102 0 0
103103 −5.69373 5.69373i −0.561020 0.561020i 0.368577 0.929597i 0.379845π-0.379845\pi
−0.929597 + 0.368577i 0.879845π0.879845\pi
104104 2.32305 0.227794
105105 0 0
106106 14.1626 1.37559
107107 −11.2683 11.2683i −1.08934 1.08934i −0.995596 0.0937480i 0.970115π-0.970115\pi
−0.0937480 0.995596i 0.529885π-0.529885\pi
108108 0 0
109109 9.19081i 0.880320i 0.897919 + 0.440160i 0.145078π0.145078\pi
−0.897919 + 0.440160i 0.854922π0.854922\pi
110110 −2.79001 + 3.77569i −0.266017 + 0.359998i
111111 0 0
112112 1.82552 1.82552i 0.172496 0.172496i
113113 3.32007 3.32007i 0.312326 0.312326i −0.533484 0.845810i 0.679118π-0.679118\pi
0.845810 + 0.533484i 0.179118π0.179118\pi
114114 0 0
115115 −9.63138 + 13.0341i −0.898131 + 1.21543i
116116 9.48773i 0.880914i
117117 0 0
118118 −3.93765 3.93765i −0.362490 0.362490i
119119 12.0248 1.10231
120120 0 0
121121 6.59201 0.599273
122122 −9.74636 9.74636i −0.882394 0.882394i
123123 0 0
124124 4.22425i 0.379349i
125125 −10.0817 + 4.83324i −0.901731 + 0.432298i
126126 0 0
127127 −6.97903 + 6.97903i −0.619289 + 0.619289i −0.945349 0.326060i 0.894279π-0.894279\pi
0.326060 + 0.945349i 0.394279π0.394279\pi
128128 0.707107 0.707107i 0.0625000 0.0625000i
129129 0 0
130130 0.771189 + 5.13694i 0.0676377 + 0.450540i
131131 1.52919i 0.133606i −0.997766 0.0668029i 0.978720π-0.978720\pi
0.997766 0.0668029i 0.0212799π-0.0212799\pi
132132 0 0
133133 1.82552 + 1.82552i 0.158293 + 0.158293i
134134 0 0
135135 0 0
136136 4.65775 0.399399
137137 −8.70549 8.70549i −0.743760 0.743760i 0.229539 0.973299i 0.426278π-0.426278\pi
−0.973299 + 0.229539i 0.926278π0.926278\pi
138138 0 0
139139 11.8451i 1.00469i −0.864668 0.502344i 0.832471π-0.832471\pi
0.864668 0.502344i 0.167529π-0.167529\pi
140140 4.64278 + 3.43074i 0.392387 + 0.289950i
141141 0 0
142142 0.603419 0.603419i 0.0506378 0.0506378i
143143 −3.44877 + 3.44877i −0.288401 + 0.288401i
144144 0 0
145145 −20.9801 + 3.14966i −1.74230 + 0.261565i
146146 12.1045i 1.00178i
147147 0 0
148148 −1.64265 1.64265i −0.135025 0.135025i
149149 −19.3650 −1.58644 −0.793221 0.608934i 0.791598π-0.791598\pi
−0.793221 + 0.608934i 0.791598π0.791598\pi
150150 0 0
151151 2.09187 0.170234 0.0851170 0.996371i 0.472874π-0.472874\pi
0.0851170 + 0.996371i 0.472874π0.472874\pi
152152 0.707107 + 0.707107i 0.0573539 + 0.0573539i
153153 0 0
154154 5.42029i 0.436780i
155155 −9.34104 + 1.40233i −0.750290 + 0.112638i
156156 0 0
157157 0.0362263 0.0362263i 0.00289117 0.00289117i −0.705660 0.708551i 0.749349π-0.749349\pi
0.708551 + 0.705660i 0.249349π0.249349\pi
158158 1.03211 1.03211i 0.0821103 0.0821103i
159159 0 0
160160 1.79836 + 1.32888i 0.142173 + 0.105057i
161161 18.7114i 1.47467i
162162 0 0
163163 14.6211 + 14.6211i 1.14521 + 1.14521i 0.987483 + 0.157727i 0.0504166π0.0504166\pi
0.157727 + 0.987483i 0.449583π0.449583\pi
164164 −7.26473 −0.567280
165165 0 0
166166 8.93164 0.693230
167167 −8.05215 8.05215i −0.623094 0.623094i 0.323227 0.946321i 0.395232π-0.395232\pi
−0.946321 + 0.323227i 0.895232π0.895232\pi
168168 0 0
169169 7.60342i 0.584878i
170170 1.54624 + 10.2996i 0.118591 + 0.789946i
171171 0 0
172172 −5.70884 + 5.70884i −0.435295 + 0.435295i
173173 12.5516 12.5516i 0.954278 0.954278i −0.0447212 0.999000i 0.514240π-0.514240\pi
0.999000 + 0.0447212i 0.0142400π0.0142400\pi
174174 0 0
175175 −6.04507 + 11.4054i −0.456965 + 0.862170i
176176 2.09952i 0.158257i
177177 0 0
178178 6.07590 + 6.07590i 0.455408 + 0.455408i
179179 −11.9025 −0.889638 −0.444819 0.895620i 0.646732π-0.646732\pi
−0.444819 + 0.895620i 0.646732π0.646732\pi
180180 0 0
181181 −4.82767 −0.358838 −0.179419 0.983773i 0.557422π-0.557422\pi
−0.179419 + 0.983773i 0.557422π0.557422\pi
182182 4.24079 + 4.24079i 0.314348 + 0.314348i
183183 0 0
184184 7.24776i 0.534312i
185185 3.08705 4.17768i 0.226965 0.307149i
186186 0 0
187187 −6.91484 + 6.91484i −0.505663 + 0.505663i
188188 9.10895 9.10895i 0.664339 0.664339i
189189 0 0
190190 −1.32888 + 1.79836i −0.0964069 + 0.130466i
191191 7.88988i 0.570892i −0.958395 0.285446i 0.907858π-0.907858\pi
0.958395 0.285446i 0.0921417π-0.0921417\pi
192192 0 0
193193 −1.49129 1.49129i −0.107346 0.107346i 0.651394 0.758740i 0.274185π-0.274185\pi
−0.758740 + 0.651394i 0.774185π0.774185\pi
194194 15.5813 1.11867
195195 0 0
196196 −0.334925 −0.0239232
197197 −14.4190 14.4190i −1.02731 1.02731i −0.999616 0.0276953i 0.991183π-0.991183\pi
−0.0276953 0.999616i 0.508817π-0.508817\pi
198198 0 0
199199 2.84447i 0.201639i 0.994905 + 0.100820i 0.0321465π0.0321465\pi
−0.994905 + 0.100820i 0.967853π0.967853\pi
200200 −2.34153 + 4.41783i −0.165571 + 0.312388i
201201 0 0
202202 10.3207 10.3207i 0.726159 0.726159i
203203 −17.3201 + 17.3201i −1.21563 + 1.21563i
204204 0 0
205205 −2.41169 16.0644i −0.168440 1.12199i
206206 8.05215i 0.561020i
207207 0 0
208208 1.64265 + 1.64265i 0.113897 + 0.113897i
209209 −2.09952 −0.145227
210210 0 0
211211 −10.7289 −0.738607 −0.369304 0.929309i 0.620404π-0.620404\pi
−0.369304 + 0.929309i 0.620404π0.620404\pi
212212 10.0145 + 10.0145i 0.687797 + 0.687797i
213213 0 0
214214 15.9357i 1.08934i
215215 −14.5191 10.7287i −0.990192 0.731692i
216216 0 0
217217 −7.71148 + 7.71148i −0.523489 + 0.523489i
218218 −6.49888 + 6.49888i −0.440160 + 0.440160i
219219 0 0
220220 −4.64265 + 0.696982i −0.313007 + 0.0469905i
221221 10.8202i 0.727846i
222222 0 0
223223 13.0260 + 13.0260i 0.872288 + 0.872288i 0.992721 0.120433i 0.0384283π-0.0384283\pi
−0.120433 + 0.992721i 0.538428π0.538428\pi
224224 2.58168 0.172496
225225 0 0
226226 4.69529 0.312326
227227 20.4647 + 20.4647i 1.35829 + 1.35829i 0.876029 + 0.482259i 0.160184π0.160184\pi
0.482259 + 0.876029i 0.339816π0.339816\pi
228228 0 0
229229 1.89472i 0.125206i −0.998038 0.0626032i 0.980060π-0.980060\pi
0.998038 0.0626032i 0.0199403π-0.0199403\pi
230230 −16.0269 + 2.40605i −1.05678 + 0.158650i
231231 0 0
232232 −6.70884 + 6.70884i −0.440457 + 0.440457i
233233 2.12791 2.12791i 0.139404 0.139404i −0.633961 0.773365i 0.718572π-0.718572\pi
0.773365 + 0.633961i 0.218572π0.218572\pi
234234 0 0
235235 23.1664 + 17.1186i 1.51121 + 1.11669i
236236 5.56868i 0.362490i
237237 0 0
238238 8.50284 + 8.50284i 0.551157 + 0.551157i
239239 14.0763 0.910521 0.455260 0.890358i 0.349546π-0.349546\pi
0.455260 + 0.890358i 0.349546π0.349546\pi
240240 0 0
241241 11.1960 0.721200 0.360600 0.932720i 0.382572π-0.382572\pi
0.360600 + 0.932720i 0.382572π0.382572\pi
242242 4.66125 + 4.66125i 0.299637 + 0.299637i
243243 0 0
244244 13.7834i 0.882394i
245245 −0.111186 0.740616i −0.00710340 0.0473162i
246246 0 0
247247 −1.64265 + 1.64265i −0.104519 + 0.104519i
248248 −2.98700 + 2.98700i −0.189675 + 0.189675i
249249 0 0
250250 −10.5464 3.71119i −0.667014 0.234716i
251251 21.3245i 1.34599i 0.739647 + 0.672995i 0.234992π0.234992\pi
−0.739647 + 0.672995i 0.765008π0.765008\pi
252252 0 0
253253 −10.7599 10.7599i −0.676471 0.676471i
254254 −9.86983 −0.619289
255255 0 0
256256 1.00000 0.0625000
257257 19.5098 + 19.5098i 1.21699 + 1.21699i 0.968681 + 0.248309i 0.0798749π0.0798749\pi
0.248309 + 0.968681i 0.420125π0.420125\pi
258258 0 0
259259 5.99738i 0.372659i
260260 −3.08705 + 4.17768i −0.191451 + 0.259089i
261261 0 0
262262 1.08130 1.08130i 0.0668029 0.0668029i
263263 6.06124 6.06124i 0.373752 0.373752i −0.495090 0.868842i 0.664865π-0.664865\pi
0.868842 + 0.495090i 0.164865π0.164865\pi
264264 0 0
265265 −18.8204 + 25.4694i −1.15613 + 1.56457i
266266 2.58168i 0.158293i
267267 0 0
268268 0 0
269269 −9.04067 −0.551219 −0.275610 0.961270i 0.588880π-0.588880\pi
−0.275610 + 0.961270i 0.588880π0.588880\pi
270270 0 0
271271 12.5180 0.760417 0.380209 0.924901i 0.375852π-0.375852\pi
0.380209 + 0.924901i 0.375852π0.375852\pi
272272 3.29353 + 3.29353i 0.199700 + 0.199700i
273273 0 0
274274 12.3114i 0.743760i
275275 −3.08246 10.0349i −0.185879 0.605124i
276276 0 0
277277 9.58199 9.58199i 0.575726 0.575726i −0.357997 0.933723i 0.616540π-0.616540\pi
0.933723 + 0.357997i 0.116540π0.116540\pi
278278 8.37574 8.37574i 0.502344 0.502344i
279279 0 0
280280 0.857046 + 5.70884i 0.0512183 + 0.341168i
281281 4.36612i 0.260461i 0.991484 + 0.130230i 0.0415717π0.0415717\pi
−0.991484 + 0.130230i 0.958428π0.958428\pi
282282 0 0
283283 −18.6452 18.6452i −1.10834 1.10834i −0.993369 0.114972i 0.963322π-0.963322\pi
−0.114972 0.993369i 0.536678π-0.536678\pi
284284 0.853364 0.0506378
285285 0 0
286286 −4.87730 −0.288401
287287 −13.2619 13.2619i −0.782828 0.782828i
288288 0 0
289289 4.69467i 0.276157i
290290 −17.0623 12.6080i −1.00193 0.740369i
291291 0 0
292292 8.55918 8.55918i 0.500888 0.500888i
293293 −17.8949 + 17.8949i −1.04543 + 1.04543i −0.0465116 + 0.998918i 0.514810π0.514810\pi
−0.998918 + 0.0465116i 0.985190π0.985190\pi
294294 0 0
295295 12.3140 1.84865i 0.716946 0.107632i
296296 2.32305i 0.135025i
297297 0 0
298298 −13.6931 13.6931i −0.793221 0.793221i
299299 −16.8369 −0.973705
300300 0 0
301301 −20.8432 −1.20138
302302 1.47917 + 1.47917i 0.0851170 + 0.0851170i
303303 0 0
304304 1.00000i 0.0573539i
305305 30.4791 4.57571i 1.74523 0.262005i
306306 0 0
307307 −12.5089 + 12.5089i −0.713923 + 0.713923i −0.967353 0.253431i 0.918441π-0.918441\pi
0.253431 + 0.967353i 0.418441π0.418441\pi
308308 −3.83273 + 3.83273i −0.218390 + 0.218390i
309309 0 0
310310 −7.59671 5.61351i −0.431464 0.318826i
311311 30.0324i 1.70298i 0.524369 + 0.851491i 0.324301π0.324301\pi
−0.524369 + 0.851491i 0.675699π0.675699\pi
312312 0 0
313313 −2.49454 2.49454i −0.141000 0.141000i 0.633084 0.774083i 0.281789π-0.281789\pi
−0.774083 + 0.633084i 0.781789π0.781789\pi
314314 0.0512317 0.00289117
315315 0 0
316316 1.45962 0.0821103
317317 −14.4465 14.4465i −0.811398 0.811398i 0.173446 0.984843i 0.444510π-0.444510\pi
−0.984843 + 0.173446i 0.944510π0.944510\pi
318318 0 0
319319 19.9197i 1.11529i
320320 0.331972 + 2.21129i 0.0185578 + 0.123615i
321321 0 0
322322 −13.2310 + 13.2310i −0.737333 + 0.737333i
323323 −3.29353 + 3.29353i −0.183257 + 0.183257i
324324 0 0
325325 −10.2629 5.43949i −0.569281 0.301729i
326326 20.6773i 1.14521i
327327 0 0
328328 −5.13694 5.13694i −0.283640 0.283640i
329329 33.2572 1.83353
330330 0 0
331331 17.8028 0.978533 0.489267 0.872134i 0.337265π-0.337265\pi
0.489267 + 0.872134i 0.337265π0.337265\pi
332332 6.31562 + 6.31562i 0.346615 + 0.346615i
333333 0 0
334334 11.3875i 0.623094i
335335 0 0
336336 0 0
337337 8.82883 8.82883i 0.480937 0.480937i −0.424494 0.905431i 0.639548π-0.639548\pi
0.905431 + 0.424494i 0.139548π0.139548\pi
338338 5.37643 5.37643i 0.292439 0.292439i
339339 0 0
340340 −6.18958 + 8.37630i −0.335677 + 0.454269i
341341 8.86891i 0.480279i
342342 0 0
343343 −13.3901 13.3901i −0.722996 0.722996i
344344 −8.07352 −0.435295
345345 0 0
346346 17.7506 0.954278
347347 3.97699 + 3.97699i 0.213496 + 0.213496i 0.805751 0.592255i 0.201762π-0.201762\pi
−0.592255 + 0.805751i 0.701762π0.701762\pi
348348 0 0
349349 16.3895i 0.877308i −0.898656 0.438654i 0.855455π-0.855455\pi
0.898656 0.438654i 0.144545π-0.144545\pi
350350 −12.3394 + 3.79035i −0.659567 + 0.202603i
351351 0 0
352352 −1.48459 + 1.48459i −0.0791287 + 0.0791287i
353353 2.24748 2.24748i 0.119621 0.119621i −0.644762 0.764383i 0.723044π-0.723044\pi
0.764383 + 0.644762i 0.223044π0.223044\pi
354354 0 0
355355 0.283293 + 1.88703i 0.0150356 + 0.100153i
356356 8.59262i 0.455408i
357357 0 0
358358 −8.41637 8.41637i −0.444819 0.444819i
359359 −15.4071 −0.813158 −0.406579 0.913616i 0.633278π-0.633278\pi
−0.406579 + 0.913616i 0.633278π0.633278\pi
360360 0 0
361361 −1.00000 −0.0526316
362362 −3.41368 3.41368i −0.179419 0.179419i
363363 0 0
364364 5.99738i 0.314348i
365365 21.7682 + 16.0854i 1.13940 + 0.841948i
366366 0 0
367367 −7.28985 + 7.28985i −0.380527 + 0.380527i −0.871292 0.490765i 0.836717π-0.836717\pi
0.490765 + 0.871292i 0.336717π0.336717\pi
368368 −5.12494 + 5.12494i −0.267156 + 0.267156i
369369 0 0
370370 5.13694 0.771189i 0.267057 0.0400922i
371371 36.5633i 1.89827i
372372 0 0
373373 −5.96016 5.96016i −0.308605 0.308605i 0.535763 0.844368i 0.320024π-0.320024\pi
−0.844368 + 0.535763i 0.820024π0.820024\pi
374374 −9.77906 −0.505663
375375 0 0
376376 12.8820 0.664339
377377 −15.5850 15.5850i −0.802668 0.802668i
378378 0 0
379379 18.4581i 0.948128i 0.880490 + 0.474064i 0.157213π0.157213\pi
−0.880490 + 0.474064i 0.842787π0.842787\pi
380380 −2.21129 + 0.331972i −0.113437 + 0.0170298i
381381 0 0
382382 5.57899 5.57899i 0.285446 0.285446i
383383 3.44149 3.44149i 0.175852 0.175852i −0.613693 0.789545i 0.710317π-0.710317\pi
0.789545 + 0.613693i 0.210317π0.210317\pi
384384 0 0
385385 −9.74762 7.20291i −0.496785 0.367094i
386386 2.10901i 0.107346i
387387 0 0
388388 11.0176 + 11.0176i 0.559336 + 0.559336i
389389 13.9339 0.706475 0.353238 0.935534i 0.385081π-0.385081\pi
0.353238 + 0.935534i 0.385081π0.385081\pi
390390 0 0
391391 −33.7583 −1.70723
392392 −0.236828 0.236828i −0.0119616 0.0119616i
393393 0 0
394394 20.3916i 1.02731i
395395 0.484554 + 3.22765i 0.0243806 + 0.162401i
396396 0 0
397397 −3.29740 + 3.29740i −0.165492 + 0.165492i −0.784994 0.619503i 0.787334π-0.787334\pi
0.619503 + 0.784994i 0.287334π0.287334\pi
398398 −2.01135 + 2.01135i −0.100820 + 0.100820i
399399 0 0
400400 −4.77959 + 1.46817i −0.238979 + 0.0734086i
401401 17.5402i 0.875918i 0.898995 + 0.437959i 0.144298π0.144298\pi
−0.898995 + 0.437959i 0.855702π0.855702\pi
402402 0 0
403403 −6.93896 6.93896i −0.345654 0.345654i
404404 14.5956 0.726159
405405 0 0
406406 −24.4943 −1.21563
407407 3.44877 + 3.44877i 0.170949 + 0.170949i
408408 0 0
409409 14.2981i 0.706995i −0.935435 0.353498i 0.884992π-0.884992\pi
0.935435 0.353498i 0.115008π-0.115008\pi
410410 9.65394 13.0646i 0.476774 0.645214i
411411 0 0
412412 5.69373 5.69373i 0.280510 0.280510i
413413 10.1658 10.1658i 0.500224 0.500224i
414414 0 0
415415 −11.8690 + 16.0623i −0.582629 + 0.788466i
416416 2.32305i 0.113897i
417417 0 0
418418 −1.48459 1.48459i −0.0726135 0.0726135i
419419 7.08174 0.345966 0.172983 0.984925i 0.444659π-0.444659\pi
0.172983 + 0.984925i 0.444659π0.444659\pi
420420 0 0
421421 6.84570 0.333639 0.166820 0.985987i 0.446650π-0.446650\pi
0.166820 + 0.985987i 0.446650π0.446650\pi
422422 −7.58647 7.58647i −0.369304 0.369304i
423423 0 0
424424 14.1626i 0.687797i
425425 −20.5772 10.9063i −0.998140 0.529031i
426426 0 0
427427 25.1620 25.1620i 1.21767 1.21767i
428428 11.2683 11.2683i 0.544672 0.544672i
429429 0 0
430430 −2.68018 17.8529i −0.129250 0.860942i
431431 18.5138i 0.891780i 0.895088 + 0.445890i 0.147113π0.147113\pi
−0.895088 + 0.445890i 0.852887π0.852887\pi
432432 0 0
433433 4.67392 + 4.67392i 0.224614 + 0.224614i 0.810438 0.585824i 0.199229π-0.199229\pi
−0.585824 + 0.810438i 0.699229π0.699229\pi
434434 −10.9057 −0.523489
435435 0 0
436436 −9.19081 −0.440160
437437 −5.12494 5.12494i −0.245159 0.245159i
438438 0 0
439439 32.4355i 1.54806i −0.633146 0.774032i 0.718237π-0.718237\pi
0.633146 0.774032i 0.281763π-0.281763\pi
440440 −3.77569 2.79001i −0.179999 0.133008i
441441 0 0
442442 −7.65105 + 7.65105i −0.363923 + 0.363923i
443443 −2.39842 + 2.39842i −0.113952 + 0.113952i −0.761784 0.647831i 0.775676π-0.775676\pi
0.647831 + 0.761784i 0.275676π0.275676\pi
444444 0 0
445445 −19.0008 + 2.85251i −0.900722 + 0.135222i
446446 18.4216i 0.872288i
447447 0 0
448448 1.82552 + 1.82552i 0.0862479 + 0.0862479i
449449 27.3174 1.28919 0.644595 0.764525i 0.277026π-0.277026\pi
0.644595 + 0.764525i 0.277026π0.277026\pi
450450 0 0
451451 15.2525 0.718211
452452 3.32007 + 3.32007i 0.156163 + 0.156163i
453453 0 0
454454 28.9414i 1.35829i
455455 −13.2619 + 1.99096i −0.621729 + 0.0933378i
456456 0 0
457457 4.28791 4.28791i 0.200580 0.200580i −0.599669 0.800249i 0.704701π-0.704701\pi
0.800249 + 0.599669i 0.204701π0.204701\pi
458458 1.33977 1.33977i 0.0626032 0.0626032i
459459 0 0
460460 −13.0341 9.63138i −0.607716 0.449066i
461461 26.0363i 1.21263i 0.795224 + 0.606316i 0.207353π0.207353\pi
−0.795224 + 0.606316i 0.792647π0.792647\pi
462462 0 0
463463 −7.86306 7.86306i −0.365427 0.365427i 0.500379 0.865806i 0.333194π-0.333194\pi
−0.865806 + 0.500379i 0.833194π0.833194\pi
464464 −9.48773 −0.440457
465465 0 0
466466 3.00932 0.139404
467467 4.57597 + 4.57597i 0.211751 + 0.211751i 0.805011 0.593260i 0.202159π-0.202159\pi
−0.593260 + 0.805011i 0.702159π0.702159\pi
468468 0 0
469469 0 0
470470 4.27647 + 28.4858i 0.197259 + 1.31395i
471471 0 0
472472 3.93765 3.93765i 0.181245 0.181245i
473473 11.9858 11.9858i 0.551109 0.551109i
474474 0 0
475475 −1.46817 4.77959i −0.0673643 0.219303i
476476 12.0248i 0.551157i
477477 0 0
478478 9.95345 + 9.95345i 0.455260 + 0.455260i
479479 23.6217 1.07930 0.539652 0.841888i 0.318556π-0.318556\pi
0.539652 + 0.841888i 0.318556π0.318556\pi
480480 0 0
481481 5.39658 0.246063
482482 7.91680 + 7.91680i 0.360600 + 0.360600i
483483 0 0
484484 6.59201i 0.299637i
485485 −20.7056 + 28.0207i −0.940194 + 1.27236i
486486 0 0
487487 −14.9536 + 14.9536i −0.677612 + 0.677612i −0.959459 0.281847i 0.909053π-0.909053\pi
0.281847 + 0.959459i 0.409053π0.409053\pi
488488 9.74636 9.74636i 0.441197 0.441197i
489489 0 0
490490 0.445074 0.602315i 0.0201064 0.0272098i
491491 37.3226i 1.68435i −0.539207 0.842173i 0.681276π-0.681276\pi
0.539207 0.842173i 0.318724π-0.318724\pi
492492 0 0
493493 −31.2481 31.2481i −1.40734 1.40734i
494494 −2.32305 −0.104519
495495 0 0
496496 −4.22425 −0.189675
497497 1.55784 + 1.55784i 0.0698785 + 0.0698785i
498498 0 0
499499 24.7116i 1.10624i 0.833101 + 0.553121i 0.186563π0.186563\pi
−0.833101 + 0.553121i 0.813437π0.813437\pi
500500 −4.83324 10.0817i −0.216149 0.450865i
501501 0 0
502502 −15.0787 + 15.0787i −0.672995 + 0.672995i
503503 −19.3802 + 19.3802i −0.864120 + 0.864120i −0.991814 0.127693i 0.959243π-0.959243\pi
0.127693 + 0.991814i 0.459243π0.459243\pi
504504 0 0
505505 4.84534 + 32.2751i 0.215615 + 1.43622i
506506 15.2168i 0.676471i
507507 0 0
508508 −6.97903 6.97903i −0.309644 0.309644i
509509 −31.1709 −1.38163 −0.690813 0.723034i 0.742747π-0.742747\pi
−0.690813 + 0.723034i 0.742747π0.742747\pi
510510 0 0
511511 31.2500 1.38242
512512 0.707107 + 0.707107i 0.0312500 + 0.0312500i
513513 0 0
514514 27.5911i 1.21699i
515515 14.4806 + 10.7003i 0.638093 + 0.471513i
516516 0 0
517517 −19.1244 + 19.1244i −0.841092 + 0.841092i
518518 4.24079 4.24079i 0.186330 0.186330i
519519 0 0
520520 −5.13694 + 0.771189i −0.225270 + 0.0338189i
521521 3.18272i 0.139438i −0.997567 0.0697188i 0.977790π-0.977790\pi
0.997567 0.0697188i 0.0222102π-0.0222102\pi
522522 0 0
523523 8.17601 + 8.17601i 0.357512 + 0.357512i 0.862895 0.505383i 0.168649π-0.168649\pi
−0.505383 + 0.862895i 0.668649π0.668649\pi
524524 1.52919 0.0668029
525525 0 0
526526 8.57189 0.373752
527527 −13.9127 13.9127i −0.606047 0.606047i
528528 0 0
529529 29.5300i 1.28391i
530530 −31.3176 + 4.70159i −1.36035 + 0.204224i
531531 0 0
532532 −1.82552 + 1.82552i −0.0791465 + 0.0791465i
533533 11.9334 11.9334i 0.516893 0.516893i
534534 0 0
535535 28.6581 + 21.1766i 1.23900 + 0.915545i
536536 0 0
537537 0 0
538538 −6.39272 6.39272i −0.275610 0.275610i
539539 0.703183 0.0302882
540540 0 0
541541 36.1737 1.55523 0.777614 0.628742i 0.216430π-0.216430\pi
0.777614 + 0.628742i 0.216430π0.216430\pi
542542 8.85160 + 8.85160i 0.380209 + 0.380209i
543543 0 0
544544 4.65775i 0.199700i
545545 −3.05109 20.3235i −0.130694 0.870564i
546546 0 0
547547 −8.84018 + 8.84018i −0.377979 + 0.377979i −0.870372 0.492394i 0.836122π-0.836122\pi
0.492394 + 0.870372i 0.336122π0.336122\pi
548548 8.70549 8.70549i 0.371880 0.371880i
549549 0 0
550550 4.91609 9.27534i 0.209623 0.395502i
551551 9.48773i 0.404191i
552552 0 0
553553 2.66458 + 2.66458i 0.113309 + 0.113309i
554554 13.5510 0.575726
555555 0 0
556556 11.8451 0.502344
557557 −10.8373 10.8373i −0.459190 0.459190i 0.439200 0.898390i 0.355262π-0.355262\pi
−0.898390 + 0.439200i 0.855262π0.855262\pi
558558 0 0
559559 18.7552i 0.793261i
560560 −3.43074 + 4.64278i −0.144975 + 0.196193i
561561 0 0
562562 −3.08731 + 3.08731i −0.130230 + 0.130230i
563563 −3.71984 + 3.71984i −0.156772 + 0.156772i −0.781135 0.624362i 0.785359π-0.785359\pi
0.624362 + 0.781135i 0.285359π0.285359\pi
564564 0 0
565565 −6.23946 + 8.44380i −0.262496 + 0.355233i
566566 26.3683i 1.10834i
567567 0 0
568568 0.603419 + 0.603419i 0.0253189 + 0.0253189i
569569 24.0334 1.00753 0.503767 0.863839i 0.331947π-0.331947\pi
0.503767 + 0.863839i 0.331947π0.331947\pi
570570 0 0
571571 −2.37267 −0.0992930 −0.0496465 0.998767i 0.515809π-0.515809\pi
−0.0496465 + 0.998767i 0.515809π0.515809\pi
572572 −3.44877 3.44877i −0.144200 0.144200i
573573 0 0
574574 18.7552i 0.782828i
575575 16.9708 32.0194i 0.707732 1.33530i
576576 0 0
577577 10.3672 10.3672i 0.431593 0.431593i −0.457577 0.889170i 0.651283π-0.651283\pi
0.889170 + 0.457577i 0.151283π0.151283\pi
578578 −3.31964 + 3.31964i −0.138079 + 0.138079i
579579 0 0
580580 −3.14966 20.9801i −0.130783 0.871152i
581581 23.0586i 0.956633i
582582 0 0
583583 −21.0256 21.0256i −0.870791 0.870791i
584584 12.1045 0.500888
585585 0 0
586586 −25.3072 −1.04543
587587 21.0872 + 21.0872i 0.870360 + 0.870360i 0.992511 0.122152i 0.0389794π-0.0389794\pi
−0.122152 + 0.992511i 0.538979π0.538979\pi
588588 0 0
589589 4.22425i 0.174057i
590590 10.0145 + 7.40009i 0.412289 + 0.304657i
591591 0 0
592592 1.64265 1.64265i 0.0675124 0.0675124i
593593 2.52768 2.52768i 0.103799 0.103799i −0.653300 0.757099i 0.726616π-0.726616\pi
0.757099 + 0.653300i 0.226616π0.226616\pi
594594 0 0
595595 −26.5904 + 3.99191i −1.09010 + 0.163652i
596596 19.3650i 0.793221i
597597 0 0
598598 −11.9055 11.9055i −0.486853 0.486853i
599599 4.86149 0.198635 0.0993175 0.995056i 0.468334π-0.468334\pi
0.0993175 + 0.995056i 0.468334π0.468334\pi
600600 0 0
601601 15.6846 0.639790 0.319895 0.947453i 0.396352π-0.396352\pi
0.319895 + 0.947453i 0.396352π0.396352\pi
602602 −14.7384 14.7384i −0.600692 0.600692i
603603 0 0
604604 2.09187i 0.0851170i
605605 −14.5768 + 2.18836i −0.592632 + 0.0889696i
606606 0 0
607607 2.15135 2.15135i 0.0873208 0.0873208i −0.662097 0.749418i 0.730333π-0.730333\pi
0.749418 + 0.662097i 0.230333π0.230333\pi
608608 −0.707107 + 0.707107i −0.0286770 + 0.0286770i
609609 0 0
610610 24.7875 + 18.3165i 1.00362 + 0.741613i
611611 29.9256i 1.21066i
612612 0 0
613613 −25.6148 25.6148i −1.03457 1.03457i −0.999381 0.0351923i 0.988796π-0.988796\pi
−0.0351923 0.999381i 0.511204π-0.511204\pi
614614 −17.6903 −0.713923
615615 0 0
616616 −5.42029 −0.218390
617617 −4.42755 4.42755i −0.178246 0.178246i 0.612345 0.790591i 0.290226π-0.290226\pi
−0.790591 + 0.612345i 0.790226π0.790226\pi
618618 0 0
619619 26.6804i 1.07238i 0.844098 + 0.536189i 0.180136π0.180136\pi
−0.844098 + 0.536189i 0.819864π0.819864\pi
620620 −1.40233 9.34104i −0.0563191 0.375145i
621621 0 0
622622 −21.2361 + 21.2361i −0.851491 + 0.851491i
623623 −15.6860 + 15.6860i −0.628448 + 0.628448i
624624 0 0
625625 20.6889 14.0345i 0.827558 0.561380i
626626 3.52782i 0.141000i
627627 0 0
628628 0.0362263 + 0.0362263i 0.00144559 + 0.00144559i
629629 10.8202 0.431430
630630 0 0
631631 −44.2590 −1.76192 −0.880962 0.473186i 0.843104π-0.843104\pi
−0.880962 + 0.473186i 0.843104π0.843104\pi
632632 1.03211 + 1.03211i 0.0410551 + 0.0410551i
633633 0 0
634634 20.4305i 0.811398i
635635 13.1158 17.7495i 0.520485 0.704367i
636636 0 0
637637 0.550164 0.550164i 0.0217983 0.0217983i
638638 14.0854 14.0854i 0.557645 0.557645i
639639 0 0
640640 −1.32888 + 1.79836i −0.0525285 + 0.0710863i
641641 9.64240i 0.380852i −0.981702 0.190426i 0.939013π-0.939013\pi
0.981702 0.190426i 0.0609869π-0.0609869\pi
642642 0 0
643643 8.17076 + 8.17076i 0.322223 + 0.322223i 0.849619 0.527396i 0.176832π-0.176832\pi
−0.527396 + 0.849619i 0.676832π0.676832\pi
644644 −18.7114 −0.737333
645645 0 0
646646 −4.65775 −0.183257
647647 6.20608 + 6.20608i 0.243986 + 0.243986i 0.818497 0.574511i 0.194808π-0.194808\pi
−0.574511 + 0.818497i 0.694808π0.694808\pi
648648 0 0
649649 11.6916i 0.458934i
650650 −3.41064 11.1032i −0.133776 0.435505i
651651 0 0
652652 −14.6211 + 14.6211i −0.572605 + 0.572605i
653653 −14.3615 + 14.3615i −0.562008 + 0.562008i −0.929877 0.367870i 0.880087π-0.880087\pi
0.367870 + 0.929877i 0.380087π0.380087\pi
654654 0 0
655655 0.507647 + 3.38147i 0.0198354 + 0.132125i
656656 7.26473i 0.283640i
657657 0 0
658658 23.5164 + 23.5164i 0.916765 + 0.916765i
659659 −49.6826 −1.93536 −0.967680 0.252182i 0.918852π-0.918852\pi
−0.967680 + 0.252182i 0.918852π0.918852\pi
660660 0 0
661661 33.7100 1.31117 0.655584 0.755122i 0.272422π-0.272422\pi
0.655584 + 0.755122i 0.272422π0.272422\pi
662662 12.5885 + 12.5885i 0.489267 + 0.489267i
663663 0 0
664664 8.93164i 0.346615i
665665 −4.64278 3.43074i −0.180039 0.133038i
666666 0 0
667667 48.6241 48.6241i 1.88273 1.88273i
668668 8.05215 8.05215i 0.311547 0.311547i
669669 0 0
670670 0 0
671671 28.9386i 1.11716i
672672 0 0
673673 −7.48868 7.48868i −0.288667 0.288667i 0.547886 0.836553i 0.315433π-0.315433\pi
−0.836553 + 0.547886i 0.815433π0.815433\pi
674674 12.4859 0.480937
675675 0 0
676676 7.60342 0.292439
677677 −34.8468 34.8468i −1.33927 1.33927i −0.896766 0.442504i 0.854090π-0.854090\pi
−0.442504 0.896766i 0.645910π-0.645910\pi
678678 0 0
679679 40.2259i 1.54373i
680680 −10.2996 + 1.54624i −0.394973 + 0.0592957i
681681 0 0
682682 6.27127 6.27127i 0.240139 0.240139i
683683 0.0313944 0.0313944i 0.00120127 0.00120127i −0.706506 0.707707i 0.749730π-0.749730\pi
0.707707 + 0.706506i 0.249730π0.249730\pi
684684 0 0
685685 22.1403 + 16.3604i 0.845938 + 0.625097i
686686 18.9364i 0.722996i
687687 0 0
688688 −5.70884 5.70884i −0.217647 0.217647i
689689 −32.9005 −1.25341
690690 0 0
691691 17.8533 0.679170 0.339585 0.940575i 0.389713π-0.389713\pi
0.339585 + 0.940575i 0.389713π0.389713\pi
692692 12.5516 + 12.5516i 0.477139 + 0.477139i
693693 0 0
694694 5.62431i 0.213496i
695695 3.93224 + 26.1929i 0.149158 + 0.993553i
696696 0 0
697697 23.9266 23.9266i 0.906285 0.906285i
698698 11.5891 11.5891i 0.438654 0.438654i
699699 0 0
700700 −11.4054 6.04507i −0.431085 0.228482i
701701 32.4158i 1.22433i −0.790730 0.612165i 0.790299π-0.790299\pi
0.790730 0.612165i 0.209701π-0.209701\pi
702702 0 0
703703 1.64265 + 1.64265i 0.0619536 + 0.0619536i
704704 −2.09952 −0.0791287
705705 0 0
706706 3.17842 0.119621
707707 26.6446 + 26.6446i 1.00208 + 1.00208i
708708 0 0
709709 5.58539i 0.209764i 0.994485 + 0.104882i 0.0334464π0.0334464\pi
−0.994485 + 0.104882i 0.966554π0.966554\pi
710710 −1.13402 + 1.53465i −0.0425588 + 0.0575945i
711711 0 0
712712 −6.07590 + 6.07590i −0.227704 + 0.227704i
713713 21.6490 21.6490i 0.810763 0.810763i
714714 0 0
715715 6.48134 8.77113i 0.242388 0.328022i
716716 11.9025i 0.444819i
717717 0 0
718718 −10.8945 10.8945i −0.406579 0.406579i
719719 −28.8576 −1.07621 −0.538104 0.842878i 0.680859π-0.680859\pi
−0.538104 + 0.842878i 0.680859π0.680859\pi
720720 0 0
721721 20.7881 0.774189
722722 −0.707107 0.707107i −0.0263158 0.0263158i
723723 0 0
724724 4.82767i 0.179419i
725725 45.3475 13.9296i 1.68416 0.517333i
726726 0 0
727727 20.3720 20.3720i 0.755555 0.755555i −0.219955 0.975510i 0.570591π-0.570591\pi
0.975510 + 0.219955i 0.0705910π0.0705910\pi
728728 −4.24079 + 4.24079i −0.157174 + 0.157174i
729729 0 0
730730 4.01836 + 26.7665i 0.148726 + 0.990674i
731731 37.6045i 1.39085i
732732 0 0
733733 −11.7713 11.7713i −0.434784 0.434784i 0.455468 0.890252i 0.349472π-0.349472\pi
−0.890252 + 0.455468i 0.849472π0.849472\pi
734734 −10.3094 −0.380527
735735 0 0
736736 −7.24776 −0.267156
737737 0 0
738738 0 0
739739 30.7303i 1.13043i 0.824943 + 0.565216i 0.191207π0.191207\pi
−0.824943 + 0.565216i 0.808793π0.808793\pi
740740 4.17768 + 3.08705i 0.153575 + 0.113482i
741741 0 0
742742 −25.8542 + 25.8542i −0.949136 + 0.949136i
743743 −33.6074 + 33.6074i −1.23294 + 1.23294i −0.270105 + 0.962831i 0.587058π0.587058\pi
−0.962831 + 0.270105i 0.912942π0.912942\pi
744744 0 0
745745 42.8216 6.42864i 1.56886 0.235527i
746746 8.42894i 0.308605i
747747 0 0
748748 −6.91484 6.91484i −0.252831 0.252831i
749749 41.1410 1.50326
750750 0 0
751751 39.7645 1.45103 0.725513 0.688208i 0.241603π-0.241603\pi
0.725513 + 0.688208i 0.241603π0.241603\pi
752752 9.10895 + 9.10895i 0.332169 + 0.332169i
753753 0 0
754754 22.0405i 0.802668i
755755 −4.62573 + 0.694442i −0.168347 + 0.0252733i
756756 0 0
757757 4.66245 4.66245i 0.169460 0.169460i −0.617282 0.786742i 0.711766π-0.711766\pi
0.786742 + 0.617282i 0.211766π0.211766\pi
758758 −13.0518 + 13.0518i −0.474064 + 0.474064i
759759 0 0
760760 −1.79836 1.32888i −0.0652332 0.0482034i
761761 19.9340i 0.722607i 0.932448 + 0.361303i 0.117668π0.117668\pi
−0.932448 + 0.361303i 0.882332π0.882332\pi
762762 0 0
763763 −16.7780 16.7780i −0.607406 0.607406i
764764 7.88988 0.285446
765765 0 0
766766 4.86700 0.175852
767767 9.14738 + 9.14738i 0.330293 + 0.330293i
768768 0 0
769769 45.7105i 1.64836i −0.566325 0.824182i 0.691635π-0.691635\pi
0.566325 0.824182i 0.308365π-0.308365\pi
770770 −1.79939 11.9858i −0.0648454 0.431939i
771771 0 0
772772 1.49129 1.49129i 0.0536728 0.0536728i
773773 −11.3039 + 11.3039i −0.406574 + 0.406574i −0.880542 0.473968i 0.842821π-0.842821\pi
0.473968 + 0.880542i 0.342821π0.342821\pi
774774 0 0
775775 20.1902 6.20193i 0.725253 0.222780i
776776 15.5813i 0.559336i
777777 0 0
778778 9.85274 + 9.85274i 0.353238 + 0.353238i
779779 7.26473 0.260286
780780 0 0
781781 −1.79166 −0.0641105
782782 −23.8707 23.8707i −0.853615 0.853615i
783783 0 0
784784 0.334925i 0.0119616i
785785 −0.0680806 + 0.0921328i −0.00242990 + 0.00328836i
786786 0 0
787787 −21.8619 + 21.8619i −0.779292 + 0.779292i −0.979710 0.200418i 0.935770π-0.935770\pi
0.200418 + 0.979710i 0.435770π0.435770\pi
788788 14.4190 14.4190i 0.513656 0.513656i
789789 0 0
790790 −1.93966 + 2.62492i −0.0690100 + 0.0933906i
791791 12.1217i 0.430999i
792792 0 0
793793 22.6413 + 22.6413i 0.804017 + 0.804017i
794794 −4.66323 −0.165492
795795 0 0
796796 −2.84447 −0.100820
797797 −13.3091 13.3091i −0.471433 0.471433i 0.430945 0.902378i 0.358180π-0.358180\pi
−0.902378 + 0.430945i 0.858180π0.858180\pi
798798 0 0
799799 60.0012i 2.12269i
800800 −4.41783 2.34153i −0.156194 0.0827854i
801801 0 0
802802 −12.4028 + 12.4028i −0.437959 + 0.437959i
803803 −17.9702 + 17.9702i −0.634154 + 0.634154i
804804 0 0
805805 −6.21166 41.3763i −0.218932 1.45832i
806806 9.81317i 0.345654i
807807 0 0
808808 10.3207 + 10.3207i 0.363080 + 0.363080i
809809 27.0517 0.951089 0.475544 0.879692i 0.342251π-0.342251\pi
0.475544 + 0.879692i 0.342251π0.342251\pi
810810 0 0
811811 21.6005 0.758496 0.379248 0.925295i 0.376183π-0.376183\pi
0.379248 + 0.925295i 0.376183π0.376183\pi
812812 −17.3201 17.3201i −0.607816 0.607816i
813813 0 0
814814 4.87730i 0.170949i
815815 −37.1852 27.4776i −1.30254 0.962498i
816816 0 0
817817 5.70884 5.70884i 0.199727 0.199727i
818818 10.1103 10.1103i 0.353498 0.353498i
819819 0 0
820820 16.0644 2.41169i 0.560994 0.0842198i
821821 3.62159i 0.126394i 0.998001 + 0.0631972i 0.0201297π0.0201297\pi
−0.998001 + 0.0631972i 0.979870π0.979870\pi
822822 0 0
823823 19.7193 + 19.7193i 0.687372 + 0.687372i 0.961650 0.274278i 0.0884390π-0.0884390\pi
−0.274278 + 0.961650i 0.588439π0.588439\pi
824824 8.05215 0.280510
825825 0 0
826826 14.3765 0.500224
827827 20.6069 + 20.6069i 0.716572 + 0.716572i 0.967902 0.251329i 0.0808677π-0.0808677\pi
−0.251329 + 0.967902i 0.580868π0.580868\pi
828828 0 0
829829 38.1819i 1.32611i −0.748570 0.663055i 0.769259π-0.769259\pi
0.748570 0.663055i 0.230741π-0.230741\pi
830830 −19.7504 + 2.96505i −0.685547 + 0.102919i
831831 0 0
832832 −1.64265 + 1.64265i −0.0569486 + 0.0569486i
833833 1.10309 1.10309i 0.0382197 0.0382197i
834834 0 0
835835 20.4787 + 15.1325i 0.708695 + 0.523683i
836836 2.09952i 0.0726135i
837837 0 0
838838 5.00755 + 5.00755i 0.172983 + 0.172983i
839839 48.7158 1.68186 0.840928 0.541147i 0.182010π-0.182010\pi
0.840928 + 0.541147i 0.182010π0.182010\pi
840840 0 0
841841 61.0171 2.10404
842842 4.84064 + 4.84064i 0.166820 + 0.166820i
843843 0 0
844844 10.7289i 0.369304i
845845 2.52412 + 16.8133i 0.0868324 + 0.578397i
846846 0 0
847847 −12.0339 + 12.0339i −0.413489 + 0.413489i
848848 −10.0145 + 10.0145i −0.343898 + 0.343898i
849849 0 0
850850 −6.83838 22.2622i −0.234555 0.763586i
851851 16.8369i 0.577163i
852852 0 0
853853 −11.2720 11.2720i −0.385945 0.385945i 0.487294 0.873238i 0.337984π-0.337984\pi
−0.873238 + 0.487294i 0.837984π0.837984\pi
854854 35.5844 1.21767
855855 0 0
856856 15.9357 0.544672
857857 8.44951 + 8.44951i 0.288630 + 0.288630i 0.836538 0.547908i 0.184576π-0.184576\pi
−0.547908 + 0.836538i 0.684576π0.684576\pi
858858 0 0
859859 48.2324i 1.64567i 0.568282 + 0.822834i 0.307608π0.307608\pi
−0.568282 + 0.822834i 0.692392π0.692392\pi
860860 10.7287 14.5191i 0.365846 0.495096i
861861 0 0
862862 −13.0913 + 13.0913i −0.445890 + 0.445890i
863863 3.19558 3.19558i 0.108779 0.108779i −0.650622 0.759401i 0.725492π-0.725492\pi
0.759401 + 0.650622i 0.225492π0.225492\pi
864864 0 0
865865 −23.5884 + 31.9219i −0.802029 + 1.08538i
866866 6.60992i 0.224614i
867867 0 0
868868 −7.71148 7.71148i −0.261745 0.261745i
869869 −3.06451 −0.103956
870870 0 0
871871 0 0
872872 −6.49888 6.49888i −0.220080 0.220080i
873873 0 0
874874 7.24776i 0.245159i
875875 9.58111 27.2275i 0.323901 0.920457i
876876 0 0
877877 13.8213 13.8213i 0.466711 0.466711i −0.434136 0.900847i 0.642946π-0.642946\pi
0.900847 + 0.434136i 0.142946π0.142946\pi
878878 22.9354 22.9354i 0.774032 0.774032i
879879 0 0
880880 −0.696982 4.64265i −0.0234953 0.156504i
881881 13.9308i 0.469341i 0.972075 + 0.234670i 0.0754011π0.0754011\pi
−0.972075 + 0.234670i 0.924599π0.924599\pi
882882 0 0
883883 −8.79801 8.79801i −0.296076 0.296076i 0.543398 0.839475i 0.317137π-0.317137\pi
−0.839475 + 0.543398i 0.817137π0.817137\pi
884884 −10.8202 −0.363923
885885 0 0
886886 −3.39188 −0.113952
887887 −19.4915 19.4915i −0.654461 0.654461i 0.299603 0.954064i 0.403146π-0.403146\pi
−0.954064 + 0.299603i 0.903146π0.903146\pi
888888 0 0
889889 25.4808i 0.854597i
890890 −15.4526 11.4185i −0.517972 0.382750i
891891 0 0
892892 −13.0260 + 13.0260i −0.436144 + 0.436144i
893893 −9.10895 + 9.10895i −0.304820 + 0.304820i
894894 0 0
895895 26.3200 3.95131i 0.879779 0.132078i
896896 2.58168i 0.0862479i
897897 0 0
898898 19.3163 + 19.3163i 0.644595 + 0.644595i
899899 40.0786 1.33670
900900 0 0
901901 −65.9659 −2.19764
902902 10.7851 + 10.7851i 0.359105 + 0.359105i
903903 0 0
904904 4.69529i 0.156163i
905905 10.6754 1.60265i 0.354861 0.0532740i
906906 0 0
907907 −12.0103 + 12.0103i −0.398795 + 0.398795i −0.877808 0.479013i 0.840995π-0.840995\pi
0.479013 + 0.877808i 0.340995π0.340995\pi
908908 −20.4647 + 20.4647i −0.679144 + 0.679144i
909909 0 0
910910 −10.7854 7.96979i −0.357534 0.264196i
911911 30.3411i 1.00525i −0.864506 0.502623i 0.832369π-0.832369\pi
0.864506 0.502623i 0.167631π-0.167631\pi
912912 0 0
913913 −13.2598 13.2598i −0.438835 0.438835i
914914 6.06402 0.200580
915915 0 0
916916 1.89472 0.0626032
917917 2.79157 + 2.79157i 0.0921857 + 0.0921857i
918918 0 0
919919 54.6727i 1.80349i 0.432272 + 0.901743i 0.357712π0.357712\pi
−0.432272 + 0.901743i 0.642288π0.642288\pi
920920 −2.40605 16.0269i −0.0793252 0.528391i
921921 0 0
922922 −18.4104 + 18.4104i −0.606316 + 0.606316i
923923 −1.40178 + 1.40178i −0.0461400 + 0.0461400i
924924 0 0
925925 −5.43949 + 10.2629i −0.178849 + 0.337441i
926926 11.1200i 0.365427i
927927 0 0
928928 −6.70884 6.70884i −0.220228 0.220228i
929929 15.0006 0.492153 0.246077 0.969250i 0.420859π-0.420859\pi
0.246077 + 0.969250i 0.420859π0.420859\pi
930930 0 0
931931 0.334925 0.0109767
932932 2.12791 + 2.12791i 0.0697021 + 0.0697021i
933933 0 0
934934 6.47140i 0.211751i
935935 12.9952 17.5862i 0.424987 0.575131i
936936 0 0
937937 −15.4325 + 15.4325i −0.504157 + 0.504157i −0.912727 0.408570i 0.866028π-0.866028\pi
0.408570 + 0.912727i 0.366028π0.366028\pi
938938 0 0
939939 0 0
940940 −17.1186 + 23.1664i −0.558347 + 0.755606i
941941 44.9592i 1.46563i −0.680428 0.732815i 0.738206π-0.738206\pi
0.680428 0.732815i 0.261794π-0.261794\pi
942942 0 0
943943 37.2313 + 37.2313i 1.21242 + 1.21242i
944944 5.56868 0.181245
945945 0 0
946946 16.9505 0.551109
947947 −28.0152 28.0152i −0.910372 0.910372i 0.0859292 0.996301i 0.472614π-0.472614\pi
−0.996301 + 0.0859292i 0.972614π0.972614\pi
948948 0 0
949949 28.1194i 0.912795i
950950 2.34153 4.41783i 0.0759691 0.143333i
951951 0 0
952952 −8.50284 + 8.50284i −0.275579 + 0.275579i
953953 14.5780 14.5780i 0.472227 0.472227i −0.430408 0.902635i 0.641630π-0.641630\pi
0.902635 + 0.430408i 0.141630π0.141630\pi
954954 0 0
955955 2.61922 + 17.4468i 0.0847560 + 0.564565i
956956 14.0763i 0.455260i
957957 0 0
958958 16.7031 + 16.7031i 0.539652 + 0.539652i
959959 31.7841 1.02636
960960 0 0
961961 −13.1557 −0.424377
962962 3.81596 + 3.81596i 0.123031 + 0.123031i
963963 0 0
964964 11.1960i 0.360600i
965965 3.79274 + 2.80261i 0.122093 + 0.0902192i
966966 0 0
967967 −5.38393 + 5.38393i −0.173136 + 0.173136i −0.788356 0.615220i 0.789067π-0.789067\pi
0.615220 + 0.788356i 0.289067π0.289067\pi
968968 −4.66125 + 4.66125i −0.149818 + 0.149818i
969969 0 0
970970 −34.4547 + 5.17255i −1.10627 + 0.166081i
971971 47.0342i 1.50940i −0.656070 0.754700i 0.727782π-0.727782\pi
0.656070 0.754700i 0.272218π-0.272218\pi
972972 0 0
973973 21.6235 + 21.6235i 0.693217 + 0.693217i
974974 −21.1476 −0.677612
975975 0 0
976976 13.7834 0.441197
977977 −26.0939 26.0939i −0.834816 0.834816i 0.153355 0.988171i 0.450992π-0.450992\pi
−0.988171 + 0.153355i 0.950992π0.950992\pi
978978 0 0
979979 18.0404i 0.576574i
980980 0.740616 0.111186i 0.0236581 0.00355170i
981981 0 0
982982 26.3911 26.3911i 0.842173 0.842173i
983983 −7.67835 + 7.67835i −0.244901 + 0.244901i −0.818874 0.573973i 0.805401π-0.805401\pi
0.573973 + 0.818874i 0.305401π0.305401\pi
984984 0 0
985985 36.6713 + 27.0979i 1.16844 + 0.863410i
986986 44.1915i 1.40734i
987987 0 0
988988 −1.64265 1.64265i −0.0522596 0.0522596i
989989 58.5149 1.86067
990990 0 0
991991 −16.9894 −0.539685 −0.269842 0.962904i 0.586972π-0.586972\pi
−0.269842 + 0.962904i 0.586972π0.586972\pi
992992 −2.98700 2.98700i −0.0948373 0.0948373i
993993 0 0
994994 2.20311i 0.0698785i
995995 −0.944285 6.28995i −0.0299359 0.199405i
996996 0 0
997997 3.67554 3.67554i 0.116406 0.116406i −0.646505 0.762910i 0.723770π-0.723770\pi
0.762910 + 0.646505i 0.223770π0.223770\pi
998998 −17.4737 + 17.4737i −0.553121 + 0.553121i
999999 0 0
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 1710.2.n.i.1673.6 yes 20
3.2 odd 2 inner 1710.2.n.i.1673.5 yes 20
5.2 odd 4 inner 1710.2.n.i.647.5 20
15.2 even 4 inner 1710.2.n.i.647.6 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1710.2.n.i.647.5 20 5.2 odd 4 inner
1710.2.n.i.647.6 yes 20 15.2 even 4 inner
1710.2.n.i.1673.5 yes 20 3.2 odd 2 inner
1710.2.n.i.1673.6 yes 20 1.1 even 1 trivial