Properties

Label 624.2.bv.g.49.2
Level 624624
Weight 22
Character 624.49
Analytic conductor 4.9834.983
Analytic rank 00
Dimension 88
Inner twists 22

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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] = [624,2,Mod(49,624)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(624, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) 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("624.49"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 624=24313 624 = 2^{4} \cdot 3 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 624.bv (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.982665086134.98266508613
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 8.0.649638144.4
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x814x6+75x4170x2+169 x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 49.2
Root 2.34138+0.500000i-2.34138 + 0.500000i of defining polynomial
Character χ\chi == 624.49
Dual form 624.2.bv.g.433.3

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+(0.500000+0.866025i)q30.475353iq5+(3.945082.27769i)q7+(0.500000+0.866025i)q9+(1.430690.826009i)q11+(2.881392.16739i)q13+(0.4116670.237676i)q15+(3.969736.87577i)q17+(2.25402+1.30136i)q194.55539iq21+(1.906043.30136i)q23+4.77404q251.00000q27+(0.4116670.713029i)q291.79260iq31+(1.43069+0.826009i)q33+(1.08271+1.87530i)q35+(1.62174+0.936315i)q37+(3.31771+1.41167i)q39+(9.26841+5.35112i)q41+(4.945088.56513i)q43+(0.411667+0.237676i)q45+7.29869iq47+(6.87577+11.9092i)q49+7.93945q5110.0063q53+(0.3926450.680082i)q55+2.60272iq57+(1.287440.743302i)q59+(5.8701410.1674i)q61+(3.945082.27769i)q63+(1.030271.36968i)q65+(2.87826+1.66176i)q67+(1.906043.30136i)q69+(1.651300.953379i)q71+6.14686iq73+(2.38702+4.13444i)q757.52558q77+10.7515q79+(0.5000000.866025i)q8114.7628iq83+(3.268411.88702i)q85+(0.4116670.713029i)q87+(6.32548+3.65202i)q89+(16.3040+1.98758i)q91+(1.552430.896298i)q93+(0.6186061.07146i)q95+(3.624232.09245i)q97+1.65202iq99+O(q100)q+(0.500000 + 0.866025i) q^{3} -0.475353i q^{5} +(-3.94508 - 2.27769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.43069 - 0.826009i) q^{11} +(2.88139 - 2.16739i) q^{13} +(0.411667 - 0.237676i) q^{15} +(3.96973 - 6.87577i) q^{17} +(2.25402 + 1.30136i) q^{19} -4.55539i q^{21} +(-1.90604 - 3.30136i) q^{23} +4.77404 q^{25} -1.00000 q^{27} +(-0.411667 - 0.713029i) q^{29} -1.79260i q^{31} +(1.43069 + 0.826009i) q^{33} +(-1.08271 + 1.87530i) q^{35} +(-1.62174 + 0.936315i) q^{37} +(3.31771 + 1.41167i) q^{39} +(-9.26841 + 5.35112i) q^{41} +(4.94508 - 8.56513i) q^{43} +(0.411667 + 0.237676i) q^{45} +7.29869i q^{47} +(6.87577 + 11.9092i) q^{49} +7.93945 q^{51} -10.0063 q^{53} +(-0.392645 - 0.680082i) q^{55} +2.60272i q^{57} +(-1.28744 - 0.743302i) q^{59} +(5.87014 - 10.1674i) q^{61} +(3.94508 - 2.27769i) q^{63} +(-1.03027 - 1.36968i) q^{65} +(-2.87826 + 1.66176i) q^{67} +(1.90604 - 3.30136i) q^{69} +(-1.65130 - 0.953379i) q^{71} +6.14686i q^{73} +(2.38702 + 4.13444i) q^{75} -7.52558 q^{77} +10.7515 q^{79} +(-0.500000 - 0.866025i) q^{81} -14.7628i q^{83} +(-3.26841 - 1.88702i) q^{85} +(0.411667 - 0.713029i) q^{87} +(-6.32548 + 3.65202i) q^{89} +(-16.3040 + 1.98758i) q^{91} +(1.55243 - 0.896298i) q^{93} +(0.618606 - 1.07146i) q^{95} +(-3.62423 - 2.09245i) q^{97} +1.65202i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+4q34q9+6q116q136q15+12q176q19+2q234q258q27+6q29+6q3310q3524q41+8q436q45+18q49+24q51+66q97+O(q100) 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51}+ \cdots - 66 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/624Z)×\left(\mathbb{Z}/624\mathbb{Z}\right)^\times.

nn 7979 145145 209209 469469
χ(n)\chi(n) 11 e(56)e\left(\frac{5}{6}\right) 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 0 0
33 0.500000 + 0.866025i 0.288675 + 0.500000i
44 0 0
55 0.475353i 0.212584i −0.994335 0.106292i 0.966102π-0.966102\pi
0.994335 0.106292i 0.0338979π-0.0338979\pi
66 0 0
77 −3.94508 2.27769i −1.49110 0.860887i −0.491152 0.871074i 0.663424π-0.663424\pi
−0.999948 + 0.0101870i 0.996757π0.996757\pi
88 0 0
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 0 0
1111 1.43069 0.826009i 0.431369 0.249051i −0.268561 0.963263i 0.586548π-0.586548\pi
0.699930 + 0.714212i 0.253215π0.253215\pi
1212 0 0
1313 2.88139 2.16739i 0.799155 0.601125i
1414 0 0
1515 0.411667 0.237676i 0.106292 0.0613678i
1616 0 0
1717 3.96973 6.87577i 0.962800 1.66762i 0.247388 0.968917i 0.420428π-0.420428\pi
0.715412 0.698702i 0.246239π-0.246239\pi
1818 0 0
1919 2.25402 + 1.30136i 0.517109 + 0.298553i 0.735751 0.677252i 0.236829π-0.236829\pi
−0.218642 + 0.975805i 0.570163π0.570163\pi
2020 0 0
2121 4.55539i 0.994067i
2222 0 0
2323 −1.90604 3.30136i −0.397437 0.688381i 0.595972 0.803005i 0.296767π-0.296767\pi
−0.993409 + 0.114624i 0.963434π0.963434\pi
2424 0 0
2525 4.77404 0.954808
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 −0.411667 0.713029i −0.0764447 0.132406i 0.825269 0.564740i 0.191024π-0.191024\pi
−0.901714 + 0.432334i 0.857690π0.857690\pi
3030 0 0
3131 1.79260i 0.321960i −0.986958 0.160980i 0.948535π-0.948535\pi
0.986958 0.160980i 0.0514654π-0.0514654\pi
3232 0 0
3333 1.43069 + 0.826009i 0.249051 + 0.143790i
3434 0 0
3535 −1.08271 + 1.87530i −0.183011 + 0.316984i
3636 0 0
3737 −1.62174 + 0.936315i −0.266613 + 0.153929i −0.627348 0.778739i 0.715859π-0.715859\pi
0.360734 + 0.932669i 0.382526π0.382526\pi
3838 0 0
3939 3.31771 + 1.41167i 0.531259 + 0.226048i
4040 0 0
4141 −9.26841 + 5.35112i −1.44748 + 0.835705i −0.998331 0.0577505i 0.981607π-0.981607\pi
−0.449152 + 0.893455i 0.648274π0.648274\pi
4242 0 0
4343 4.94508 8.56513i 0.754118 1.30617i −0.191694 0.981455i 0.561398π-0.561398\pi
0.945812 0.324715i 0.105268π-0.105268\pi
4444 0 0
4545 0.411667 + 0.237676i 0.0613678 + 0.0354307i
4646 0 0
4747 7.29869i 1.06462i 0.846549 + 0.532311i 0.178676π0.178676\pi
−0.846549 + 0.532311i 0.821324π0.821324\pi
4848 0 0
4949 6.87577 + 11.9092i 0.982253 + 1.70131i
5050 0 0
5151 7.93945 1.11175
5252 0 0
5353 −10.0063 −1.37447 −0.687234 0.726436i 0.741175π-0.741175\pi
−0.687234 + 0.726436i 0.741175π0.741175\pi
5454 0 0
5555 −0.392645 0.680082i −0.0529443 0.0917022i
5656 0 0
5757 2.60272i 0.344739i
5858 0 0
5959 −1.28744 0.743302i −0.167610 0.0967696i 0.413848 0.910346i 0.364184π-0.364184\pi
−0.581458 + 0.813576i 0.697518π0.697518\pi
6060 0 0
6161 5.87014 10.1674i 0.751595 1.30180i −0.195455 0.980713i 0.562618π-0.562618\pi
0.947049 0.321088i 0.104048π-0.104048\pi
6262 0 0
6363 3.94508 2.27769i 0.497033 0.286962i
6464 0 0
6565 −1.03027 1.36968i −0.127790 0.169888i
6666 0 0
6767 −2.87826 + 1.66176i −0.351635 + 0.203016i −0.665405 0.746482i 0.731741π-0.731741\pi
0.313770 + 0.949499i 0.398408π0.398408\pi
6868 0 0
6969 1.90604 3.30136i 0.229460 0.397437i
7070 0 0
7171 −1.65130 0.953379i −0.195973 0.113145i 0.398803 0.917037i 0.369426π-0.369426\pi
−0.594776 + 0.803892i 0.702759π0.702759\pi
7272 0 0
7373 6.14686i 0.719435i 0.933061 + 0.359718i 0.117127π0.117127\pi
−0.933061 + 0.359718i 0.882873π0.882873\pi
7474 0 0
7575 2.38702 + 4.13444i 0.275629 + 0.477404i
7676 0 0
7777 −7.52558 −0.857619
7878 0 0
7979 10.7515 1.20964 0.604821 0.796361i 0.293245π-0.293245\pi
0.604821 + 0.796361i 0.293245π0.293245\pi
8080 0 0
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 0 0
8383 14.7628i 1.62043i −0.586135 0.810213i 0.699351π-0.699351\pi
0.586135 0.810213i 0.300649π-0.300649\pi
8484 0 0
8585 −3.26841 1.88702i −0.354509 0.204676i
8686 0 0
8787 0.411667 0.713029i 0.0441354 0.0764447i
8888 0 0
8989 −6.32548 + 3.65202i −0.670500 + 0.387113i −0.796266 0.604947i 0.793194π-0.793194\pi
0.125766 + 0.992060i 0.459861π0.459861\pi
9090 0 0
9191 −16.3040 + 1.98758i −1.70912 + 0.208355i
9292 0 0
9393 1.55243 0.896298i 0.160980 0.0929418i
9494 0 0
9595 0.618606 1.07146i 0.0634676 0.109929i
9696 0 0
9797 −3.62423 2.09245i −0.367985 0.212456i 0.304593 0.952483i 0.401480π-0.401480\pi
−0.672578 + 0.740026i 0.734813π0.734813\pi
9898 0 0
9999 1.65202i 0.166034i
100100 0 0
101101 −2.75965 4.77985i −0.274595 0.475613i 0.695438 0.718587i 0.255211π-0.255211\pi
−0.970033 + 0.242973i 0.921877π0.921877\pi
102102 0 0
103103 11.8902 1.17157 0.585786 0.810466i 0.300786π-0.300786\pi
0.585786 + 0.810466i 0.300786π0.300786\pi
104104 0 0
105105 −2.16541 −0.211323
106106 0 0
107107 2.98412 + 5.16864i 0.288486 + 0.499672i 0.973448 0.228906i 0.0735150π-0.0735150\pi
−0.684963 + 0.728578i 0.740182π0.740182\pi
108108 0 0
109109 9.79260i 0.937961i 0.883209 + 0.468980i 0.155378π0.155378\pi
−0.883209 + 0.468980i 0.844622π0.844622\pi
110110 0 0
111111 −1.62174 0.936315i −0.153929 0.0888711i
112112 0 0
113113 0.969727 1.67962i 0.0912243 0.158005i −0.816802 0.576918i 0.804255π-0.804255\pi
0.908027 + 0.418913i 0.137589π0.137589\pi
114114 0 0
115115 −1.56931 + 0.906042i −0.146339 + 0.0844888i
116116 0 0
117117 0.436315 + 3.57905i 0.0403373 + 0.330884i
118118 0 0
119119 −31.3218 + 18.0836i −2.87126 + 1.65772i
120120 0 0
121121 −4.13542 + 7.16276i −0.375947 + 0.651160i
122122 0 0
123123 −9.26841 5.35112i −0.835705 0.482494i
124124 0 0
125125 4.64611i 0.415561i
126126 0 0
127127 4.43631 + 7.68392i 0.393659 + 0.681838i 0.992929 0.118709i 0.0378756π-0.0378756\pi
−0.599270 + 0.800547i 0.704542π0.704542\pi
128128 0 0
129129 9.89016 0.870780
130130 0 0
131131 3.97750 0.347516 0.173758 0.984788i 0.444409π-0.444409\pi
0.173758 + 0.984788i 0.444409π0.444409\pi
132132 0 0
133133 −5.92820 10.2679i −0.514040 0.890344i
134134 0 0
135135 0.475353i 0.0409118i
136136 0 0
137137 15.1527 + 8.74840i 1.29458 + 0.747426i 0.979462 0.201627i 0.0646227π-0.0646227\pi
0.315118 + 0.949053i 0.397956π0.397956\pi
138138 0 0
139139 −10.1386 + 17.5605i −0.859941 + 1.48946i 0.0120427 + 0.999927i 0.496167π0.496167\pi
−0.871984 + 0.489534i 0.837167π0.837167\pi
140140 0 0
141141 −6.32085 + 3.64934i −0.532311 + 0.307330i
142142 0 0
143143 2.33210 5.48091i 0.195020 0.458337i
144144 0 0
145145 −0.338940 + 0.195687i −0.0281474 + 0.0162509i
146146 0 0
147147 −6.87577 + 11.9092i −0.567104 + 0.982253i
148148 0 0
149149 6.65516 + 3.84236i 0.545212 + 0.314778i 0.747188 0.664612i 0.231403π-0.231403\pi
−0.201977 + 0.979390i 0.564737π0.564737\pi
150150 0 0
151151 1.65202i 0.134439i −0.997738 0.0672196i 0.978587π-0.978587\pi
0.997738 0.0672196i 0.0214128π-0.0214128\pi
152152 0 0
153153 3.96973 + 6.87577i 0.320933 + 0.555873i
154154 0 0
155155 −0.852115 −0.0684436
156156 0 0
157157 −13.4855 −1.07626 −0.538132 0.842861i 0.680870π-0.680870\pi
−0.538132 + 0.842861i 0.680870π0.680870\pi
158158 0 0
159159 −5.00314 8.66569i −0.396775 0.687234i
160160 0 0
161161 17.3655i 1.36859i
162162 0 0
163163 16.4045 + 9.47117i 1.28490 + 0.741839i 0.977741 0.209818i 0.0672870π-0.0672870\pi
0.307163 + 0.951657i 0.400620π0.400620\pi
164164 0 0
165165 0.392645 0.680082i 0.0305674 0.0529443i
166166 0 0
167167 2.42015 1.39728i 0.187277 0.108125i −0.403430 0.915010i 0.632182π-0.632182\pi
0.590707 + 0.806886i 0.298849π0.298849\pi
168168 0 0
169169 3.60487 12.4902i 0.277298 0.960784i
170170 0 0
171171 −2.25402 + 1.30136i −0.172370 + 0.0995176i
172172 0 0
173173 3.47535 6.01949i 0.264226 0.457653i −0.703134 0.711057i 0.748217π-0.748217\pi
0.967361 + 0.253404i 0.0815501π0.0815501\pi
174174 0 0
175175 −18.8340 10.8738i −1.42371 0.821982i
176176 0 0
177177 1.48660i 0.111740i
178178 0 0
179179 −4.97287 8.61326i −0.371689 0.643785i 0.618136 0.786071i 0.287888π-0.287888\pi
−0.989826 + 0.142286i 0.954555π0.954555\pi
180180 0 0
181181 12.9887 0.965446 0.482723 0.875773i 0.339648π-0.339648\pi
0.482723 + 0.875773i 0.339648π0.339648\pi
182182 0 0
183183 11.7403 0.867867
184184 0 0
185185 0.445080 + 0.770901i 0.0327229 + 0.0566777i
186186 0 0
187187 13.1161i 0.959146i
188188 0 0
189189 3.94508 + 2.27769i 0.286962 + 0.165678i
190190 0 0
191191 −5.82333 + 10.0863i −0.421362 + 0.729820i −0.996073 0.0885364i 0.971781π-0.971781\pi
0.574711 + 0.818356i 0.305114π0.305114\pi
192192 0 0
193193 0.538044 0.310640i 0.0387292 0.0223603i −0.480510 0.876989i 0.659549π-0.659549\pi
0.519240 + 0.854629i 0.326215π0.326215\pi
194194 0 0
195195 0.671040 1.57708i 0.0480542 0.112937i
196196 0 0
197197 −1.60770 + 0.928203i −0.114544 + 0.0661317i −0.556177 0.831064i 0.687732π-0.687732\pi
0.441634 + 0.897195i 0.354399π0.354399\pi
198198 0 0
199199 −6.89578 + 11.9438i −0.488829 + 0.846677i −0.999917 0.0128512i 0.995909π-0.995909\pi
0.511088 + 0.859528i 0.329243π0.329243\pi
200200 0 0
201201 −2.87826 1.66176i −0.203016 0.117212i
202202 0 0
203203 3.75061i 0.263241i
204204 0 0
205205 2.54367 + 4.40576i 0.177658 + 0.307712i
206206 0 0
207207 3.81208 0.264958
208208 0 0
209209 4.29974 0.297420
210210 0 0
211211 11.4313 + 19.7997i 0.786966 + 1.36307i 0.927817 + 0.373034i 0.121683π0.121683\pi
−0.140851 + 0.990031i 0.544984π0.544984\pi
212212 0 0
213213 1.90676i 0.130649i
214214 0 0
215215 −4.07146 2.35066i −0.277671 0.160313i
216216 0 0
217217 −4.08298 + 7.07194i −0.277171 + 0.480074i
218218 0 0
219219 −5.32333 + 3.07343i −0.359718 + 0.207683i
220220 0 0
221221 −3.46410 28.4157i −0.233021 1.91145i
222222 0 0
223223 6.39821 3.69401i 0.428456 0.247369i −0.270233 0.962795i 0.587101π-0.587101\pi
0.698689 + 0.715426i 0.253767π0.253767\pi
224224 0 0
225225 −2.38702 + 4.13444i −0.159135 + 0.275629i
226226 0 0
227227 −8.27690 4.77867i −0.549357 0.317172i 0.199505 0.979897i 0.436066π-0.436066\pi
−0.748863 + 0.662725i 0.769400π0.769400\pi
228228 0 0
229229 17.6017i 1.16315i −0.813492 0.581575i 0.802437π-0.802437\pi
0.813492 0.581575i 0.197563π-0.197563\pi
230230 0 0
231231 −3.76279 6.51734i −0.247573 0.428810i
232232 0 0
233233 −19.3391 −1.26695 −0.633473 0.773765i 0.718371π-0.718371\pi
−0.633473 + 0.773765i 0.718371π0.718371\pi
234234 0 0
235235 3.46945 0.226322
236236 0 0
237237 5.37577 + 9.31111i 0.349194 + 0.604821i
238238 0 0
239239 18.6417i 1.20583i 0.797805 + 0.602916i 0.205994π0.205994\pi
−0.797805 + 0.602916i 0.794006π0.794006\pi
240240 0 0
241241 −0.0524342 0.0302729i −0.00337758 0.00195005i 0.498310 0.866999i 0.333954π-0.333954\pi
−0.501688 + 0.865049i 0.667287π0.667287\pi
242242 0 0
243243 0.500000 0.866025i 0.0320750 0.0555556i
244244 0 0
245245 5.66106 3.26841i 0.361672 0.208811i
246246 0 0
247247 9.31529 1.13561i 0.592717 0.0722569i
248248 0 0
249249 12.7850 7.38139i 0.810213 0.467777i
250250 0 0
251251 9.29869 16.1058i 0.586928 1.01659i −0.407704 0.913114i 0.633671π-0.633671\pi
0.994632 0.103475i 0.0329962π-0.0329962\pi
252252 0 0
253253 −5.45391 3.14882i −0.342884 0.197964i
254254 0 0
255255 3.77404i 0.236340i
256256 0 0
257257 14.9531 + 25.8996i 0.932750 + 1.61557i 0.778597 + 0.627524i 0.215932π0.215932\pi
0.154154 + 0.988047i 0.450735π0.450735\pi
258258 0 0
259259 8.53055 0.530063
260260 0 0
261261 0.823335 0.0509631
262262 0 0
263263 −5.03341 8.71813i −0.310373 0.537583i 0.668070 0.744099i 0.267121π-0.267121\pi
−0.978443 + 0.206516i 0.933787π0.933787\pi
264264 0 0
265265 4.75651i 0.292190i
266266 0 0
267267 −6.32548 3.65202i −0.387113 0.223500i
268268 0 0
269269 −14.0668 + 24.3645i −0.857669 + 1.48553i 0.0164768 + 0.999864i 0.494755π0.494755\pi
−0.874146 + 0.485663i 0.838578π0.838578\pi
270270 0 0
271271 22.5593 13.0246i 1.37038 0.791188i 0.379402 0.925232i 0.376130π-0.376130\pi
0.990975 + 0.134044i 0.0427962π0.0427962\pi
272272 0 0
273273 −9.87328 13.1259i −0.597558 0.794413i
274274 0 0
275275 6.83017 3.94340i 0.411875 0.237796i
276276 0 0
277277 −3.92578 + 6.79965i −0.235877 + 0.408551i −0.959527 0.281616i 0.909130π-0.909130\pi
0.723650 + 0.690167i 0.242463π0.242463\pi
278278 0 0
279279 1.55243 + 0.896298i 0.0929418 + 0.0536600i
280280 0 0
281281 1.26064i 0.0752037i −0.999293 0.0376018i 0.988028π-0.988028\pi
0.999293 0.0376018i 0.0119719π-0.0119719\pi
282282 0 0
283283 1.30966 + 2.26840i 0.0778513 + 0.134842i 0.902323 0.431061i 0.141861π-0.141861\pi
−0.824471 + 0.565904i 0.808527π0.808527\pi
284284 0 0
285285 1.23721 0.0732861
286286 0 0
287287 48.7528 2.87779
288288 0 0
289289 −23.0175 39.8674i −1.35397 2.34514i
290290 0 0
291291 4.18490i 0.245323i
292292 0 0
293293 22.0305 + 12.7193i 1.28703 + 0.743070i 0.978124 0.208021i 0.0667023π-0.0667023\pi
0.308910 + 0.951091i 0.400036π0.400036\pi
294294 0 0
295295 −0.353330 + 0.611986i −0.0205717 + 0.0356312i
296296 0 0
297297 −1.43069 + 0.826009i −0.0830170 + 0.0479299i
298298 0 0
299299 −12.6474 5.38139i −0.731417 0.311214i
300300 0 0
301301 −39.0175 + 22.5267i −2.24893 + 1.29842i
302302 0 0
303303 2.75965 4.77985i 0.158538 0.274595i
304304 0 0
305305 −4.83309 2.79039i −0.276742 0.159777i
306306 0 0
307307 15.5100i 0.885203i −0.896718 0.442601i 0.854056π-0.854056\pi
0.896718 0.442601i 0.145944π-0.145944\pi
308308 0 0
309309 5.94508 + 10.2972i 0.338204 + 0.585786i
310310 0 0
311311 −19.0829 −1.08209 −0.541047 0.840993i 0.681972π-0.681972\pi
−0.541047 + 0.840993i 0.681972π0.681972\pi
312312 0 0
313313 12.3406 0.697535 0.348767 0.937209i 0.386600π-0.386600\pi
0.348767 + 0.937209i 0.386600π0.386600\pi
314314 0 0
315315 −1.08271 1.87530i −0.0610036 0.105661i
316316 0 0
317317 19.5636i 1.09880i −0.835559 0.549401i 0.814856π-0.814856\pi
0.835559 0.549401i 0.185144π-0.185144\pi
318318 0 0
319319 −1.17794 0.680082i −0.0659518 0.0380773i
320320 0 0
321321 −2.98412 + 5.16864i −0.166557 + 0.288486i
322322 0 0
323323 17.8957 10.3321i 0.995745 0.574893i
324324 0 0
325325 13.7559 10.3472i 0.763040 0.573959i
326326 0 0
327327 −8.48064 + 4.89630i −0.468980 + 0.270766i
328328 0 0
329329 16.6242 28.7939i 0.916520 1.58746i
330330 0 0
331331 −22.2820 12.8645i −1.22473 0.707099i −0.258808 0.965929i 0.583330π-0.583330\pi
−0.965923 + 0.258830i 0.916663π0.916663\pi
332332 0 0
333333 1.87263i 0.102619i
334334 0 0
335335 0.789923 + 1.36819i 0.0431581 + 0.0747520i
336336 0 0
337337 4.90141 0.266997 0.133498 0.991049i 0.457379π-0.457379\pi
0.133498 + 0.991049i 0.457379π0.457379\pi
338338 0 0
339339 1.93945 0.105337
340340 0 0
341341 −1.48070 2.56465i −0.0801844 0.138884i
342342 0 0
343343 30.7559i 1.66066i
344344 0 0
345345 −1.56931 0.906042i −0.0844888 0.0487797i
346346 0 0
347347 9.48091 16.4214i 0.508962 0.881548i −0.490984 0.871169i 0.663363π-0.663363\pi
0.999946 0.0103797i 0.00330403π-0.00330403\pi
348348 0 0
349349 10.4045 6.00707i 0.556943 0.321551i −0.194975 0.980808i 0.562462π-0.562462\pi
0.751918 + 0.659257i 0.229129π0.229129\pi
350350 0 0
351351 −2.88139 + 2.16739i −0.153797 + 0.115687i
352352 0 0
353353 12.3074 7.10567i 0.655056 0.378197i −0.135334 0.990800i 0.543211π-0.543211\pi
0.790391 + 0.612603i 0.209878π0.209878\pi
354354 0 0
355355 −0.453191 + 0.784950i −0.0240529 + 0.0416608i
356356 0 0
357357 −31.3218 18.0836i −1.65772 0.957088i
358358 0 0
359359 14.2766i 0.753488i −0.926317 0.376744i 0.877044π-0.877044\pi
0.926317 0.376744i 0.122956π-0.122956\pi
360360 0 0
361361 −6.11292 10.5879i −0.321732 0.557257i
362362 0 0
363363 −8.27084 −0.434106
364364 0 0
365365 2.92192 0.152941
366366 0 0
367367 8.61854 + 14.9278i 0.449884 + 0.779222i 0.998378 0.0569323i 0.0181319π-0.0181319\pi
−0.548494 + 0.836155i 0.684799π0.684799\pi
368368 0 0
369369 10.7022i 0.557137i
370370 0 0
371371 39.4756 + 22.7912i 2.04947 + 1.18326i
372372 0 0
373373 −4.76528 + 8.25370i −0.246737 + 0.427360i −0.962618 0.270861i 0.912692π-0.912692\pi
0.715882 + 0.698221i 0.246025π0.246025\pi
374374 0 0
375375 4.02365 2.32306i 0.207781 0.119962i
376376 0 0
377377 −2.73159 1.16227i −0.140684 0.0598602i
378378 0 0
379379 1.95064 1.12620i 0.100198 0.0578492i −0.449064 0.893500i 0.648242π-0.648242\pi
0.549262 + 0.835651i 0.314909π0.314909\pi
380380 0 0
381381 −4.43631 + 7.68392i −0.227279 + 0.393659i
382382 0 0
383383 32.9004 + 18.9950i 1.68113 + 0.970601i 0.960913 + 0.276852i 0.0892910π0.0892910\pi
0.720217 + 0.693749i 0.244042π0.244042\pi
384384 0 0
385385 3.57730i 0.182316i
386386 0 0
387387 4.94508 + 8.56513i 0.251373 + 0.435390i
388388 0 0
389389 32.0413 1.62456 0.812280 0.583267i 0.198226π-0.198226\pi
0.812280 + 0.583267i 0.198226π0.198226\pi
390390 0 0
391391 −30.2659 −1.53061
392392 0 0
393393 1.98875 + 3.44461i 0.100319 + 0.173758i
394394 0 0
395395 5.11077i 0.257151i
396396 0 0
397397 30.0512 + 17.3501i 1.50823 + 0.870776i 0.999954 + 0.00957973i 0.00304937π0.00304937\pi
0.508273 + 0.861196i 0.330284π0.330284\pi
398398 0 0
399399 5.92820 10.2679i 0.296781 0.514040i
400400 0 0
401401 −24.9439 + 14.4013i −1.24564 + 0.719169i −0.970236 0.242161i 0.922144π-0.922144\pi
−0.275401 + 0.961329i 0.588811π0.588811\pi
402402 0 0
403403 −3.88525 5.16518i −0.193538 0.257296i
404404 0 0
405405 −0.411667 + 0.237676i −0.0204559 + 0.0118102i
406406 0 0
407407 −1.54681 + 2.67915i −0.0766725 + 0.132801i
408408 0 0
409409 25.4140 + 14.6728i 1.25664 + 0.725521i 0.972420 0.233238i 0.0749320π-0.0749320\pi
0.284220 + 0.958759i 0.408265π0.408265\pi
410410 0 0
411411 17.4968i 0.863053i
412412 0 0
413413 3.38603 + 5.86477i 0.166615 + 0.288586i
414414 0 0
415415 −7.01753 −0.344477
416416 0 0
417417 −20.2771 −0.992975
418418 0 0
419419 −11.3709 19.6949i −0.555503 0.962159i −0.997864 0.0653223i 0.979192π-0.979192\pi
0.442361 0.896837i 0.354141π-0.354141\pi
420420 0 0
421421 0.831698i 0.0405345i 0.999795 + 0.0202672i 0.00645170π0.00645170\pi
−0.999795 + 0.0202672i 0.993548π0.993548\pi
422422 0 0
423423 −6.32085 3.64934i −0.307330 0.177437i
424424 0 0
425425 18.9516 32.8252i 0.919289 1.59226i
426426 0 0
427427 −46.3164 + 26.7408i −2.24141 + 1.29408i
428428 0 0
429429 5.91266 0.720800i 0.285466 0.0348005i
430430 0 0
431431 −22.7562 + 13.1383i −1.09613 + 0.632849i −0.935201 0.354118i 0.884781π-0.884781\pi
−0.160925 + 0.986967i 0.551448π0.551448\pi
432432 0 0
433433 −2.73224 + 4.73238i −0.131303 + 0.227423i −0.924179 0.381959i 0.875249π-0.875249\pi
0.792876 + 0.609383i 0.208583π0.208583\pi
434434 0 0
435435 −0.338940 0.195687i −0.0162509 0.00938248i
436436 0 0
437437 9.92180i 0.474624i
438438 0 0
439439 6.65230 + 11.5221i 0.317497 + 0.549920i 0.979965 0.199169i 0.0638244π-0.0638244\pi
−0.662468 + 0.749090i 0.730491π0.730491\pi
440440 0 0
441441 −13.7515 −0.654835
442442 0 0
443443 14.0879 0.669336 0.334668 0.942336i 0.391376π-0.391376\pi
0.334668 + 0.942336i 0.391376π0.391376\pi
444444 0 0
445445 1.73600 + 3.00683i 0.0822941 + 0.142538i
446446 0 0
447447 7.68471i 0.363474i
448448 0 0
449449 −7.89016 4.55539i −0.372360 0.214982i 0.302129 0.953267i 0.402303π-0.402303\pi
−0.674489 + 0.738285i 0.735636π0.735636\pi
450450 0 0
451451 −8.84015 + 15.3116i −0.416266 + 0.720994i
452452 0 0
453453 1.43069 0.826009i 0.0672196 0.0388093i
454454 0 0
455455 0.944802 + 7.75014i 0.0442930 + 0.363332i
456456 0 0
457457 −7.42323 + 4.28580i −0.347244 + 0.200481i −0.663471 0.748202i 0.730917π-0.730917\pi
0.316227 + 0.948684i 0.397584π0.397584\pi
458458 0 0
459459 −3.96973 + 6.87577i −0.185291 + 0.320933i
460460 0 0
461461 34.2647 + 19.7827i 1.59587 + 0.921374i 0.992272 + 0.124083i 0.0395989π0.0395989\pi
0.603595 + 0.797291i 0.293734π0.293734\pi
462462 0 0
463463 11.4836i 0.533688i 0.963740 + 0.266844i 0.0859808π0.0859808\pi
−0.963740 + 0.266844i 0.914019π0.914019\pi
464464 0 0
465465 −0.426058 0.737954i −0.0197580 0.0342218i
466466 0 0
467467 25.9125 1.19909 0.599545 0.800341i 0.295348π-0.295348\pi
0.599545 + 0.800341i 0.295348π0.295348\pi
468468 0 0
469469 15.1399 0.699097
470470 0 0
471471 −6.74277 11.6788i −0.310691 0.538132i
472472 0 0
473473 16.3387i 0.751255i
474474 0 0
475475 10.7608 + 6.21275i 0.493739 + 0.285061i
476476 0 0
477477 5.00314 8.66569i 0.229078 0.396775i
478478 0 0
479479 −29.7135 + 17.1551i −1.35764 + 0.783836i −0.989306 0.145856i 0.953407π-0.953407\pi
−0.368338 + 0.929692i 0.620073π0.620073\pi
480480 0 0
481481 −2.64353 + 6.21284i −0.120535 + 0.283281i
482482 0 0
483483 −15.0390 + 8.68276i −0.684297 + 0.395079i
484484 0 0
485485 −0.994652 + 1.72279i −0.0451648 + 0.0782278i
486486 0 0
487487 −35.2110 20.3291i −1.59556 0.921199i −0.992328 0.123636i 0.960545π-0.960545\pi
−0.603235 0.797563i 0.706122π-0.706122\pi
488488 0 0
489489 18.9423i 0.856602i
490490 0 0
491491 8.44822 + 14.6327i 0.381263 + 0.660367i 0.991243 0.132050i 0.0421560π-0.0421560\pi
−0.609980 + 0.792417i 0.708823π0.708823\pi
492492 0 0
493493 −6.53683 −0.294404
494494 0 0
495495 0.785291 0.0352962
496496 0 0
497497 4.34301 + 7.52231i 0.194811 + 0.337422i
498498 0 0
499499 24.6899i 1.10527i −0.833422 0.552637i 0.813622π-0.813622\pi
0.833422 0.552637i 0.186378π-0.186378\pi
500500 0 0
501501 2.42015 + 1.39728i 0.108125 + 0.0624257i
502502 0 0
503503 −15.7181 + 27.2246i −0.700837 + 1.21388i 0.267337 + 0.963603i 0.413856π0.413856\pi
−0.968173 + 0.250281i 0.919477π0.919477\pi
504504 0 0
505505 −2.27212 + 1.31181i −0.101108 + 0.0583746i
506506 0 0
507507 12.6193 3.12319i 0.560441 0.138706i
508508 0 0
509509 −22.9856 + 13.2707i −1.01882 + 0.588216i −0.913762 0.406251i 0.866836π-0.866836\pi
−0.105058 + 0.994466i 0.533503π0.533503\pi
510510 0 0
511511 14.0007 24.2498i 0.619352 1.07275i
512512 0 0
513513 −2.25402 1.30136i −0.0995176 0.0574565i
514514 0 0
515515 5.65202i 0.249058i
516516 0 0
517517 6.02878 + 10.4422i 0.265145 + 0.459245i
518518 0 0
519519 6.95071 0.305102
520520 0 0
521521 16.0605 0.703625 0.351813 0.936070i 0.385565π-0.385565\pi
0.351813 + 0.936070i 0.385565π0.385565\pi
522522 0 0
523523 0.497514 + 0.861719i 0.0217548 + 0.0376804i 0.876698 0.481041i 0.159741π-0.159741\pi
−0.854943 + 0.518722i 0.826408π0.826408\pi
524524 0 0
525525 21.7476i 0.949143i
526526 0 0
527527 −12.3255 7.11612i −0.536906 0.309983i
528528 0 0
529529 4.23401 7.33352i 0.184087 0.318849i
530530 0 0
531531 1.28744 0.743302i 0.0558700 0.0322565i
532532 0 0
533533 −15.1080 + 35.5069i −0.654400 + 1.53798i
534534 0 0
535535 2.45693 1.41851i 0.106222 0.0613274i
536536 0 0
537537 4.97287 8.61326i 0.214595 0.371689i
538538 0 0
539539 19.6742 + 11.3589i 0.847427 + 0.489262i
540540 0 0
541541 10.8825i 0.467874i 0.972252 + 0.233937i 0.0751610π0.0751610\pi
−0.972252 + 0.233937i 0.924839π0.924839\pi
542542 0 0
543543 6.49437 + 11.2486i 0.278700 + 0.482723i
544544 0 0
545545 4.65494 0.199396
546546 0 0
547547 −18.1985 −0.778111 −0.389056 0.921214i 0.627199π-0.627199\pi
−0.389056 + 0.921214i 0.627199π0.627199\pi
548548 0 0
549549 5.87014 + 10.1674i 0.250532 + 0.433933i
550550 0 0
551551 2.14291i 0.0912911i
552552 0 0
553553 −42.4157 24.4887i −1.80370 1.04137i
554554 0 0
555555 −0.445080 + 0.770901i −0.0188926 + 0.0327229i
556556 0 0
557557 4.84699 2.79841i 0.205373 0.118572i −0.393786 0.919202i 0.628835π-0.628835\pi
0.599159 + 0.800630i 0.295502π0.295502\pi
558558 0 0
559559 −4.31522 35.3974i −0.182514 1.49715i
560560 0 0
561561 11.3589 6.55806i 0.479573 0.276881i
562562 0 0
563563 12.2381 21.1971i 0.515776 0.893351i −0.484056 0.875037i 0.660837π-0.660837\pi
0.999832 0.0183136i 0.00582972π-0.00582972\pi
564564 0 0
565565 −0.798410 0.460962i −0.0335894 0.0193928i
566566 0 0
567567 4.55539i 0.191308i
568568 0 0
569569 −8.93411 15.4743i −0.374537 0.648717i 0.615720 0.787965i 0.288865π-0.288865\pi
−0.990258 + 0.139247i 0.955532π0.955532\pi
570570 0 0
571571 1.74669 0.0730968 0.0365484 0.999332i 0.488364π-0.488364\pi
0.0365484 + 0.999332i 0.488364π0.488364\pi
572572 0 0
573573 −11.6467 −0.486547
574574 0 0
575575 −9.09952 15.7608i −0.379476 0.657272i
576576 0 0
577577 10.6236i 0.442267i −0.975244 0.221133i 0.929024π-0.929024\pi
0.975244 0.221133i 0.0709756π-0.0709756\pi
578578 0 0
579579 0.538044 + 0.310640i 0.0223603 + 0.0129097i
580580 0 0
581581 −33.6251 + 58.2404i −1.39500 + 2.41622i
582582 0 0
583583 −14.3159 + 8.26528i −0.592903 + 0.342313i
584584 0 0
585585 1.70131 0.207403i 0.0703406 0.00857507i
586586 0 0
587587 −38.8023 + 22.4025i −1.60154 + 0.924651i −0.610364 + 0.792121i 0.708977π0.708977\pi
−0.991179 + 0.132530i 0.957690π0.957690\pi
588588 0 0
589589 2.33282 4.04056i 0.0961220 0.166488i
590590 0 0
591591 −1.60770 0.928203i −0.0661317 0.0381812i
592592 0 0
593593 34.9834i 1.43660i −0.695736 0.718298i 0.744921π-0.744921\pi
0.695736 0.718298i 0.255079π-0.255079\pi
594594 0 0
595595 8.59610 + 14.8889i 0.352406 + 0.610385i
596596 0 0
597597 −13.7916 −0.564451
598598 0 0
599599 −21.9569 −0.897133 −0.448566 0.893749i 0.648065π-0.648065\pi
−0.448566 + 0.893749i 0.648065π0.648065\pi
600600 0 0
601601 2.88702 + 5.00047i 0.117764 + 0.203973i 0.918881 0.394534i 0.129094π-0.129094\pi
−0.801117 + 0.598507i 0.795761π0.795761\pi
602602 0 0
603603 3.32352i 0.135344i
604604 0 0
605605 3.40483 + 1.96578i 0.138426 + 0.0799204i
606606 0 0
607607 −9.72276 + 16.8403i −0.394635 + 0.683527i −0.993054 0.117656i 0.962462π-0.962462\pi
0.598420 + 0.801183i 0.295795π0.295795\pi
608608 0 0
609609 −3.24812 + 1.87530i −0.131621 + 0.0759911i
610610 0 0
611611 15.8191 + 21.0304i 0.639971 + 0.850799i
612612 0 0
613613 −8.21222 + 4.74133i −0.331689 + 0.191500i −0.656591 0.754247i 0.728002π-0.728002\pi
0.324902 + 0.945748i 0.394669π0.394669\pi
614614 0 0
615615 −2.54367 + 4.40576i −0.102571 + 0.177658i
616616 0 0
617617 −37.6567 21.7411i −1.51600 0.875263i −0.999824 0.0187816i 0.994021π-0.994021\pi
−0.516177 0.856482i 0.672645π-0.672645\pi
618618 0 0
619619 5.40607i 0.217288i 0.994081 + 0.108644i 0.0346509π0.0346509\pi
−0.994081 + 0.108644i 0.965349π0.965349\pi
620620 0 0
621621 1.90604 + 3.30136i 0.0764868 + 0.132479i
622622 0 0
623623 33.2727 1.33304
624624 0 0
625625 21.6617 0.866466
626626 0 0
627627 2.14987 + 3.72369i 0.0858576 + 0.148710i
628628 0 0
629629 14.8677i 0.592812i
630630 0 0
631631 14.4714 + 8.35505i 0.576096 + 0.332609i 0.759581 0.650413i 0.225404π-0.225404\pi
−0.183484 + 0.983023i 0.558738π0.558738\pi
632632 0 0
633633 −11.4313 + 19.7997i −0.454355 + 0.786966i
634634 0 0
635635 3.65257 2.10881i 0.144948 0.0836857i
636636 0 0
637637 45.6236 + 19.4126i 1.80767 + 0.769155i
638638 0 0
639639 1.65130 0.953379i 0.0653245 0.0377151i
640640 0 0
641641 0.0468720 0.0811847i 0.00185133 0.00320660i −0.865098 0.501602i 0.832744π-0.832744\pi
0.866950 + 0.498396i 0.166077π0.166077\pi
642642 0 0
643643 14.8696 + 8.58496i 0.586399 + 0.338558i 0.763672 0.645604i 0.223394π-0.223394\pi
−0.177273 + 0.984162i 0.556728π0.556728\pi
644644 0 0
645645 4.70131i 0.185114i
646646 0 0
647647 16.1224 + 27.9248i 0.633837 + 1.09784i 0.986760 + 0.162185i 0.0518543π0.0518543\pi
−0.352923 + 0.935652i 0.614812π0.614812\pi
648648 0 0
649649 −2.45590 −0.0964023
650650 0 0
651651 −8.16597 −0.320050
652652 0 0
653653 −3.32119 5.75247i −0.129968 0.225111i 0.793696 0.608315i 0.208154π-0.208154\pi
−0.923664 + 0.383203i 0.874821π0.874821\pi
654654 0 0
655655 1.89071i 0.0738763i
656656 0 0
657657 −5.32333 3.07343i −0.207683 0.119906i
658658 0 0
659659 −4.78529 + 8.28837i −0.186408 + 0.322869i −0.944050 0.329802i 0.893018π-0.893018\pi
0.757642 + 0.652671i 0.226351π0.226351\pi
660660 0 0
661661 −25.6891 + 14.8316i −0.999189 + 0.576882i −0.908008 0.418953i 0.862397π-0.862397\pi
−0.0911805 + 0.995834i 0.529064π0.529064\pi
662662 0 0
663663 22.8767 17.2079i 0.888457 0.668298i
664664 0 0
665665 −4.88090 + 2.81799i −0.189273 + 0.109277i
666666 0 0
667667 −1.56931 + 2.71813i −0.0607640 + 0.105246i
668668 0 0
669669 6.39821 + 3.69401i 0.247369 + 0.142819i
670670 0 0
671671 19.3952i 0.748742i
672672 0 0
673673 5.57180 + 9.65064i 0.214777 + 0.372005i 0.953204 0.302329i 0.0977642π-0.0977642\pi
−0.738427 + 0.674334i 0.764431π0.764431\pi
674674 0 0
675675 −4.77404 −0.183753
676676 0 0
677677 −5.44763 −0.209369 −0.104685 0.994505i 0.533383π-0.533383\pi
−0.104685 + 0.994505i 0.533383π0.533383\pi
678678 0 0
679679 9.53192 + 16.5098i 0.365802 + 0.633587i
680680 0 0
681681 9.55734i 0.366238i
682682 0 0
683683 −25.3654 14.6447i −0.970579 0.560364i −0.0711666 0.997464i 0.522672π-0.522672\pi
−0.899413 + 0.437100i 0.856006π0.856006\pi
684684 0 0
685685 4.15857 7.20286i 0.158891 0.275207i
686686 0 0
687687 15.2435 8.80083i 0.581575 0.335773i
688688 0 0
689689 −28.8320 + 21.6875i −1.09841 + 0.826227i
690690 0 0
691691 20.5580 11.8692i 0.782063 0.451524i −0.0550979 0.998481i 0.517547π-0.517547\pi
0.837161 + 0.546957i 0.184214π0.184214\pi
692692 0 0
693693 3.76279 6.51734i 0.142937 0.247573i
694694 0 0
695695 8.34743 + 4.81939i 0.316636 + 0.182810i
696696 0 0
697697 84.9700i 3.21847i
698698 0 0
699699 −9.66955 16.7481i −0.365736 0.633473i
700700 0 0
701701 7.62417 0.287961 0.143980 0.989581i 0.454010π-0.454010\pi
0.143980 + 0.989581i 0.454010π0.454010\pi
702702 0 0
703703 −4.87394 −0.183824
704704 0 0
705705 1.73472 + 3.00463i 0.0653335 + 0.113161i
706706 0 0
707707 25.1425i 0.945582i
708708 0 0
709709 −26.4127 15.2494i −0.991950 0.572702i −0.0860931 0.996287i 0.527438π-0.527438\pi
−0.905857 + 0.423585i 0.860772π0.860772\pi
710710 0 0
711711 −5.37577 + 9.31111i −0.201607 + 0.349194i
712712 0 0
713713 −5.91801 + 3.41676i −0.221631 + 0.127959i
714714 0 0
715715 −2.60537 1.10857i −0.0974352 0.0414582i
716716 0 0
717717 −16.1442 + 9.32085i −0.602916 + 0.348093i
718718 0 0
719719 3.31529 5.74224i 0.123639 0.214150i −0.797561 0.603238i 0.793877π-0.793877\pi
0.921200 + 0.389089i 0.127210π0.127210\pi
720720 0 0
721721 −46.9076 27.0821i −1.74693 1.00859i
722722 0 0
723723 0.0605458i 0.00225172i
724724 0 0
725725 −1.96532 3.40403i −0.0729900 0.126422i
726726 0 0
727727 −17.4607 −0.647583 −0.323792 0.946128i 0.604958π-0.604958\pi
−0.323792 + 0.946128i 0.604958π0.604958\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −39.2612 68.0025i −1.45213 2.51516i
732732 0 0
733733 23.3284i 0.861653i −0.902435 0.430826i 0.858222π-0.858222\pi
0.902435 0.430826i 0.141778π-0.141778\pi
734734 0 0
735735 5.66106 + 3.26841i 0.208811 + 0.120557i
736736 0 0
737737 −2.74526 + 4.75493i −0.101123 + 0.175150i
738738 0 0
739739 1.88090 1.08594i 0.0691899 0.0399468i −0.465006 0.885308i 0.653948π-0.653948\pi
0.534196 + 0.845361i 0.320614π0.320614\pi
740740 0 0
741741 5.64111 + 7.49947i 0.207231 + 0.275500i
742742 0 0
743743 40.3332 23.2864i 1.47968 0.854296i 0.479948 0.877297i 0.340656π-0.340656\pi
0.999735 + 0.0230015i 0.00732227π0.00732227\pi
744744 0 0
745745 1.82647 3.16355i 0.0669168 0.115903i
746746 0 0
747747 12.7850 + 7.38139i 0.467777 + 0.270071i
748748 0 0
749749 27.1876i 0.993414i
750750 0 0
751751 21.1998 + 36.7191i 0.773590 + 1.33990i 0.935583 + 0.353106i 0.114874π0.114874\pi
−0.161993 + 0.986792i 0.551792π0.551792\pi
752752 0 0
753753 18.5974 0.677726
754754 0 0
755755 −0.785291 −0.0285797
756756 0 0
757757 0.402625 + 0.697367i 0.0146337 + 0.0253462i 0.873250 0.487273i 0.162008π-0.162008\pi
−0.858616 + 0.512620i 0.828675π0.828675\pi
758758 0 0
759759 6.29763i 0.228589i
760760 0 0
761761 1.04395 + 0.602723i 0.0378430 + 0.0218487i 0.518802 0.854894i 0.326378π-0.326378\pi
−0.480959 + 0.876743i 0.659711π0.659711\pi
762762 0 0
763763 22.3045 38.6326i 0.807478 1.39859i
764764 0 0
765765 3.26841 1.88702i 0.118170 0.0682254i
766766 0 0
767767 −5.32063 + 0.648627i −0.192117 + 0.0234206i
768768 0 0
769769 −13.1878 + 7.61397i −0.475564 + 0.274567i −0.718566 0.695459i 0.755201π-0.755201\pi
0.243002 + 0.970026i 0.421868π0.421868\pi
770770 0 0
771771 −14.9531 + 25.8996i −0.538524 + 0.932750i
772772 0 0
773773 15.7092 + 9.06971i 0.565021 + 0.326215i 0.755158 0.655543i 0.227560π-0.227560\pi
−0.190137 + 0.981757i 0.560893π0.560893\pi
774774 0 0
775775 8.55793i 0.307410i
776776 0 0
777777 4.26528 + 7.38767i 0.153016 + 0.265031i
778778 0 0
779779 −27.8550 −0.998008
780780 0 0
781781 −3.15000 −0.112716
782782 0 0
783783 0.411667 + 0.713029i 0.0147118 + 0.0254816i
784784 0 0
785785 6.41039i 0.228797i
786786 0 0
787787 −15.1991 8.77521i −0.541790 0.312802i 0.204014 0.978968i 0.434601π-0.434601\pi
−0.745804 + 0.666166i 0.767934π0.767934\pi
788788 0 0
789789 5.03341 8.71813i 0.179194 0.310373i
790790 0 0
791791 −7.65130 + 4.41748i −0.272049 + 0.157068i
792792 0 0
793793 −5.12246 42.0191i −0.181904 1.49214i
794794 0 0
795795 −4.11926 + 2.37826i −0.146095 + 0.0843480i
796796 0 0
797797 9.67937 16.7652i 0.342861 0.593852i −0.642102 0.766619i 0.721937π-0.721937\pi
0.984963 + 0.172767i 0.0552708π0.0552708\pi
798798 0 0
799799 50.1841 + 28.9738i 1.77539 + 1.02502i
800800 0 0
801801 7.30404i 0.258075i
802802 0 0
803803 5.07736 + 8.79424i 0.179176 + 0.310342i
804804 0 0
805805 8.25474 0.290941
806806 0 0
807807 −28.1336 −0.990351
808808 0 0
809809 −5.23429 9.06605i −0.184028 0.318745i 0.759221 0.650833i 0.225580π-0.225580\pi
−0.943248 + 0.332088i 0.892247π0.892247\pi
810810 0 0
811811 38.1332i 1.33904i 0.742795 + 0.669518i 0.233500π0.233500\pi
−0.742795 + 0.669518i 0.766500π0.766500\pi
812812 0 0
813813 22.5593 + 13.0246i 0.791188 + 0.456793i
814814 0 0
815815 4.50215 7.79794i 0.157703 0.273150i
816816 0 0
817817 22.2927 12.8707i 0.779921 0.450288i
818818 0 0
819819 6.43069 15.1134i 0.224706 0.528107i
820820 0 0
821821 9.47772 5.47196i 0.330775 0.190973i −0.325410 0.945573i 0.605502π-0.605502\pi
0.656185 + 0.754600i 0.272169π0.272169\pi
822822 0 0
823823 19.7578 34.2215i 0.688714 1.19289i −0.283540 0.958960i 0.591509π-0.591509\pi
0.972254 0.233928i 0.0751578π-0.0751578\pi
824824 0 0
825825 6.83017 + 3.94340i 0.237796 + 0.137292i
826826 0 0
827827 38.3552i 1.33374i −0.745174 0.666870i 0.767633π-0.767633\pi
0.745174 0.666870i 0.232367π-0.232367\pi
828828 0 0
829829 0.548578 + 0.950166i 0.0190529 + 0.0330006i 0.875395 0.483409i 0.160602π-0.160602\pi
−0.856342 + 0.516410i 0.827268π0.827268\pi
830830 0 0
831831 −7.85156 −0.272368
832832 0 0
833833 109.180 3.78285
834834 0 0
835835 −0.664199 1.15043i −0.0229856 0.0398122i
836836 0 0
837837 1.79260i 0.0619612i
838838 0 0
839839 −9.92981 5.73298i −0.342815 0.197924i 0.318701 0.947855i 0.396753π-0.396753\pi
−0.661516 + 0.749931i 0.730087π0.730087\pi
840840 0 0
841841 14.1611 24.5277i 0.488312 0.845782i
842842 0 0
843843 1.09175 0.630322i 0.0376018 0.0217094i
844844 0 0
845845 −5.93725 1.71358i −0.204247 0.0589491i
846846 0 0
847847 32.6291 18.8384i 1.12115 0.647296i
848848 0 0
849849 −1.30966 + 2.26840i −0.0449474 + 0.0778513i
850850 0 0
851851 6.18223 + 3.56931i 0.211924 + 0.122354i
852852 0 0
853853 18.6403i 0.638232i −0.947716 0.319116i 0.896614π-0.896614\pi
0.947716 0.319116i 0.103386π-0.103386\pi
854854 0 0
855855 0.618606 + 1.07146i 0.0211559 + 0.0366430i
856856 0 0
857857 −41.9413 −1.43269 −0.716344 0.697747i 0.754186π-0.754186\pi
−0.716344 + 0.697747i 0.754186π0.754186\pi
858858 0 0
859859 −8.80656 −0.300476 −0.150238 0.988650i 0.548004π-0.548004\pi
−0.150238 + 0.988650i 0.548004π0.548004\pi
860860 0 0
861861 24.3764 + 42.2212i 0.830746 + 1.43889i
862862 0 0
863863 20.0833i 0.683643i 0.939765 + 0.341822i 0.111044π0.111044\pi
−0.939765 + 0.341822i 0.888956π0.888956\pi
864864 0 0
865865 −2.86138 1.65202i −0.0972898 0.0561703i
866866 0 0
867867 23.0175 39.8674i 0.781714 1.35397i
868868 0 0
869869 15.3821 8.88087i 0.521802 0.301263i
870870 0 0
871871 −4.69171 + 11.0265i −0.158972 + 0.373618i
872872 0 0
873873 3.62423 2.09245i 0.122662 0.0708187i
874874 0 0
875875 −10.5824 + 18.3293i −0.357751 + 0.619643i
876876 0 0
877877 −29.0698 16.7835i −0.981617 0.566737i −0.0788594 0.996886i 0.525128π-0.525128\pi
−0.902758 + 0.430149i 0.858461π0.858461\pi
878878 0 0
879879 25.4386i 0.858023i
880880 0 0
881881 17.6280 + 30.5326i 0.593903 + 1.02867i 0.993701 + 0.112067i 0.0357471π0.0357471\pi
−0.399797 + 0.916604i 0.630920π0.630920\pi
882882 0 0
883883 −7.59185 −0.255486 −0.127743 0.991807i 0.540773π-0.540773\pi
−0.127743 + 0.991807i 0.540773π0.540773\pi
884884 0 0
885885 −0.706661 −0.0237541
886886 0 0
887887 15.9073 + 27.5523i 0.534115 + 0.925115i 0.999206 + 0.0398516i 0.0126885π0.0126885\pi
−0.465090 + 0.885263i 0.653978π0.653978\pi
888888 0 0
889889 40.4182i 1.35558i
890890 0 0
891891 −1.43069 0.826009i −0.0479299 0.0276723i
892892 0 0
893893 −9.49823 + 16.4514i −0.317846 + 0.550526i
894894 0 0
895895 −4.09433 + 2.36386i −0.136858 + 0.0790153i
896896 0 0
897897 −1.66327 13.6437i −0.0555349 0.455548i
898898 0 0
899899 −1.27817 + 0.737954i −0.0426295 + 0.0246121i
900900 0 0
901901 −39.7222 + 68.8009i −1.32334 + 2.29209i
902902 0 0
903903 −39.0175 22.5267i −1.29842 0.749643i
904904 0 0
905905 6.17424i 0.205239i
906906 0 0
907907 −12.4320 21.5328i −0.412796 0.714984i 0.582398 0.812904i 0.302115π-0.302115\pi
−0.995194 + 0.0979194i 0.968781π0.968781\pi
908908 0 0
909909 5.51930 0.183064
910910 0 0
911911 −28.9183 −0.958105 −0.479052 0.877786i 0.659020π-0.659020\pi
−0.479052 + 0.877786i 0.659020π0.659020\pi
912912 0 0
913913 −12.1942 21.1210i −0.403569 0.699002i
914914 0 0
915915 5.58078i 0.184495i
916916 0 0
917917 −15.6915 9.05952i −0.518181 0.299172i
918918 0 0
919919 −9.62560 + 16.6720i −0.317519 + 0.549960i −0.979970 0.199146i 0.936183π-0.936183\pi
0.662451 + 0.749106i 0.269516π0.269516\pi
920920 0 0
921921 13.4321 7.75500i 0.442601 0.255536i
922922 0 0
923923 −6.82439 + 0.831947i −0.224628 + 0.0273839i
924924 0 0
925925 −7.74227 + 4.47000i −0.254564 + 0.146973i
926926 0 0
927927 −5.94508 + 10.2972i −0.195262 + 0.338204i
928928 0 0
929929 13.1348 + 7.58336i 0.430938 + 0.248802i 0.699746 0.714392i 0.253296π-0.253296\pi
−0.268808 + 0.963194i 0.586630π0.586630\pi
930930 0 0
931931 35.7914i 1.17302i
932932 0 0
933933 −9.54146 16.5263i −0.312373 0.541047i
934934 0 0
935935 −6.23478 −0.203899
936936 0 0
937937 49.2136 1.60774 0.803869 0.594807i 0.202771π-0.202771\pi
0.803869 + 0.594807i 0.202771π0.202771\pi
938938 0 0
939939 6.17032 + 10.6873i 0.201361 + 0.348767i
940940 0 0
941941 46.2058i 1.50627i −0.657868 0.753133i 0.728541π-0.728541\pi
0.657868 0.753133i 0.271459π-0.271459\pi
942942 0 0
943943 35.3320 + 20.3989i 1.15057 + 0.664280i
944944 0 0
945945 1.08271 1.87530i 0.0352205 0.0610036i
946946 0 0
947947 −17.6367 + 10.1826i −0.573117 + 0.330889i −0.758393 0.651797i 0.774015π-0.774015\pi
0.185277 + 0.982686i 0.440682π0.440682\pi
948948 0 0
949949 13.3226 + 17.7115i 0.432470 + 0.574940i
950950 0 0
951951 16.9426 9.78181i 0.549401 0.317197i
952952 0 0
953953 15.8233 27.4068i 0.512568 0.887794i −0.487326 0.873220i 0.662028π-0.662028\pi
0.999894 0.0145737i 0.00463912π-0.00463912\pi
954954 0 0
955955 4.79455 + 2.76814i 0.155148 + 0.0895748i
956956 0 0
957957 1.36016i 0.0439678i
958958 0 0
959959 −39.8523 69.0263i −1.28690 2.22897i
960960 0 0
961961 27.7866 0.896342
962962 0 0
963963 −5.96823 −0.192324
964964 0 0
965965 −0.147663 0.255761i −0.00475345 0.00823322i
966966 0 0
967967 16.7482i 0.538585i 0.963058 + 0.269293i 0.0867899π0.0867899\pi
−0.963058 + 0.269293i 0.913210π0.913210\pi
968968 0 0
969969 17.8957 + 10.3321i 0.574893 + 0.331915i
970970 0 0
971971 −2.70131 + 4.67881i −0.0866892 + 0.150150i −0.906110 0.423043i 0.860962π-0.860962\pi
0.819421 + 0.573193i 0.194295π0.194295\pi
972972 0 0
973973 79.9948 46.1850i 2.56452 1.48062i
974974 0 0
975975 15.8389 + 6.73936i 0.507250 + 0.215832i
976976 0 0
977977 −33.3556 + 19.2579i −1.06714 + 0.616114i −0.927399 0.374074i 0.877961π-0.877961\pi
−0.139742 + 0.990188i 0.544627π0.544627\pi
978978 0 0
979979 −6.03320 + 10.4498i −0.192822 + 0.333977i
980980 0 0
981981 −8.48064 4.89630i −0.270766 0.156327i
982982 0 0
983983 32.5378i 1.03779i −0.854837 0.518897i 0.826343π-0.826343\pi
0.854837 0.518897i 0.173657π-0.173657\pi
984984 0 0
985985 0.441224 + 0.764222i 0.0140586 + 0.0243501i
986986 0 0
987987 33.2483 1.05831
988988 0 0
989989 −37.7021 −1.19886
990990 0 0
991991 −0.491235 0.850844i −0.0156046 0.0270280i 0.858118 0.513453i 0.171634π-0.171634\pi
−0.873722 + 0.486425i 0.838301π0.838301\pi
992992 0 0
993993 25.7291i 0.816487i
994994 0 0
995995 5.67754 + 3.27793i 0.179990 + 0.103917i
996996 0 0
997997 25.0536 43.3942i 0.793457 1.37431i −0.130358 0.991467i 0.541613π-0.541613\pi
0.923814 0.382840i 0.125054π-0.125054\pi
998998 0 0
999999 1.62174 0.936315i 0.0513097 0.0296237i
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 624.2.bv.g.49.2 8
3.2 odd 2 1872.2.by.m.1297.3 8
4.3 odd 2 312.2.bf.b.49.2 8
12.11 even 2 936.2.bi.c.361.3 8
13.2 odd 12 8112.2.a.cs.1.2 4
13.4 even 6 inner 624.2.bv.g.433.3 8
13.11 odd 12 8112.2.a.cq.1.3 4
39.17 odd 6 1872.2.by.m.433.2 8
52.3 odd 6 4056.2.c.p.337.4 8
52.11 even 12 4056.2.a.bd.1.3 4
52.15 even 12 4056.2.a.be.1.2 4
52.23 odd 6 4056.2.c.p.337.5 8
52.43 odd 6 312.2.bf.b.121.3 yes 8
156.95 even 6 936.2.bi.c.433.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
312.2.bf.b.49.2 8 4.3 odd 2
312.2.bf.b.121.3 yes 8 52.43 odd 6
624.2.bv.g.49.2 8 1.1 even 1 trivial
624.2.bv.g.433.3 8 13.4 even 6 inner
936.2.bi.c.361.3 8 12.11 even 2
936.2.bi.c.433.2 8 156.95 even 6
1872.2.by.m.433.2 8 39.17 odd 6
1872.2.by.m.1297.3 8 3.2 odd 2
4056.2.a.bd.1.3 4 52.11 even 12
4056.2.a.be.1.2 4 52.15 even 12
4056.2.c.p.337.4 8 52.3 odd 6
4056.2.c.p.337.5 8 52.23 odd 6
8112.2.a.cq.1.3 4 13.11 odd 12
8112.2.a.cs.1.2 4 13.2 odd 12