Properties

Label 684.2.bo.c.289.1
Level 684684
Weight 22
Character 684.289
Analytic conductor 5.4625.462
Analytic rank 00
Dimension 1212
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] = [684,2,Mod(73,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 4])) 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("684.73"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 684=223219 684 = 2^{2} \cdot 3^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 684.bo (of order 99, degree 66, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,0,0,0,0,0,3] 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: 5.461767498265.46176749826
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ9)\Q(\zeta_{9})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x126x113x10+70x915x8426x7+64x6+1659x5+267x4++4161 x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 289.1
Root 1.752270.342020i-1.75227 - 0.342020i of defining polynomial
Character χ\chi == 684.289
Dual form 684.2.bo.c.613.1

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+(0.216181+0.181398i)q5+(0.579936+1.00448i)q7+(0.622469+1.07815i)q11+(0.9770965.54139i)q13+(6.25251+2.27573i)q17+(3.09208+3.07231i)q19+(4.65029+3.90205i)q23+(0.854412+4.84561i)q25+(3.64892+1.32810i)q29+(0.0400606+0.0693870i)q31+(0.05683880.322349i)q35+3.71365q37+(1.116976.33464i)q41+(0.1894070.158931i)q43+(10.89393.96505i)q47+(2.82735+4.89711i)q49+(3.502552.93899i)q53+(0.3301400.120161i)q55+(9.32947+3.39565i)q59+(4.275343.58744i)q61+(0.793965+1.37519i)q65+(3.47734+1.26565i)q67+(7.14016+5.99131i)q71+(0.191208+1.08439i)q731.44397q77+(1.509238.55928i)q79+(5.77114+9.99591i)q83+(1.76449+0.642221i)q85+(0.4185342.37362i)q89+(4.99955+4.19512i)q91+(1.225760.103280i)q95+(13.46384.90042i)q97+O(q100)q+(-0.216181 + 0.181398i) q^{5} +(-0.579936 + 1.00448i) q^{7} +(0.622469 + 1.07815i) q^{11} +(0.977096 - 5.54139i) q^{13} +(6.25251 + 2.27573i) q^{17} +(3.09208 + 3.07231i) q^{19} +(4.65029 + 3.90205i) q^{23} +(-0.854412 + 4.84561i) q^{25} +(-3.64892 + 1.32810i) q^{29} +(-0.0400606 + 0.0693870i) q^{31} +(-0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +(-1.11697 - 6.33464i) q^{41} +(0.189407 - 0.158931i) q^{43} +(10.8939 - 3.96505i) q^{47} +(2.82735 + 4.89711i) q^{49} +(-3.50255 - 2.93899i) q^{53} +(-0.330140 - 0.120161i) q^{55} +(9.32947 + 3.39565i) q^{59} +(-4.27534 - 3.58744i) q^{61} +(0.793965 + 1.37519i) q^{65} +(-3.47734 + 1.26565i) q^{67} +(-7.14016 + 5.99131i) q^{71} +(0.191208 + 1.08439i) q^{73} -1.44397 q^{77} +(-1.50923 - 8.55928i) q^{79} +(-5.77114 + 9.99591i) q^{83} +(-1.76449 + 0.642221i) q^{85} +(0.418534 - 2.37362i) q^{89} +(4.99955 + 4.19512i) q^{91} +(-1.22576 - 0.103280i) q^{95} +(-13.4638 - 4.90042i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+3q73q119q13+3q1712q19+12q2318q2527q29+6q3133q3512q373q41+27q43+15q47+9q49+21q5327q55+48q59++12q97+O(q100) 12 q + 3 q^{7} - 3 q^{11} - 9 q^{13} + 3 q^{17} - 12 q^{19} + 12 q^{23} - 18 q^{25} - 27 q^{29} + 6 q^{31} - 33 q^{35} - 12 q^{37} - 3 q^{41} + 27 q^{43} + 15 q^{47} + 9 q^{49} + 21 q^{53} - 27 q^{55} + 48 q^{59}+ \cdots + 12 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/684Z)×\left(\mathbb{Z}/684\mathbb{Z}\right)^\times.

nn 325325 343343 533533
χ(n)\chi(n) e(19)e\left(\frac{1}{9}\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 0
44 0 0
55 −0.216181 + 0.181398i −0.0966793 + 0.0811235i −0.689846 0.723956i 0.742322π-0.742322\pi
0.593167 + 0.805079i 0.297877π0.297877\pi
66 0 0
77 −0.579936 + 1.00448i −0.219195 + 0.379657i −0.954562 0.298012i 0.903677π-0.903677\pi
0.735367 + 0.677669i 0.237010π0.237010\pi
88 0 0
99 0 0
1010 0 0
1111 0.622469 + 1.07815i 0.187682 + 0.325074i 0.944477 0.328578i 0.106569π-0.106569\pi
−0.756795 + 0.653652i 0.773236π0.773236\pi
1212 0 0
1313 0.977096 5.54139i 0.270998 1.53690i −0.480397 0.877051i 0.659508π-0.659508\pi
0.751395 0.659853i 0.229381π-0.229381\pi
1414 0 0
1515 0 0
1616 0 0
1717 6.25251 + 2.27573i 1.51646 + 0.551945i 0.960260 0.279106i 0.0900381π-0.0900381\pi
0.556196 + 0.831051i 0.312260π0.312260\pi
1818 0 0
1919 3.09208 + 3.07231i 0.709371 + 0.704835i
2020 0 0
2121 0 0
2222 0 0
2323 4.65029 + 3.90205i 0.969652 + 0.813635i 0.982496 0.186283i 0.0596441π-0.0596441\pi
−0.0128443 + 0.999918i 0.504089π0.504089\pi
2424 0 0
2525 −0.854412 + 4.84561i −0.170882 + 0.969122i
2626 0 0
2727 0 0
2828 0 0
2929 −3.64892 + 1.32810i −0.677587 + 0.246621i −0.657811 0.753183i 0.728517π-0.728517\pi
−0.0197756 + 0.999804i 0.506295π0.506295\pi
3030 0 0
3131 −0.0400606 + 0.0693870i −0.00719510 + 0.0124623i −0.869601 0.493756i 0.835624π-0.835624\pi
0.862405 + 0.506218i 0.168957π0.168957\pi
3232 0 0
3333 0 0
3434 0 0
3535 −0.0568388 0.322349i −0.00960751 0.0544869i
3636 0 0
3737 3.71365 0.610521 0.305260 0.952269i 0.401256π-0.401256\pi
0.305260 + 0.952269i 0.401256π0.401256\pi
3838 0 0
3939 0 0
4040 0 0
4141 −1.11697 6.33464i −0.174441 0.989305i −0.938787 0.344498i 0.888049π-0.888049\pi
0.764346 0.644806i 0.223062π-0.223062\pi
4242 0 0
4343 0.189407 0.158931i 0.0288842 0.0242368i −0.628231 0.778027i 0.716221π-0.716221\pi
0.657115 + 0.753790i 0.271776π0.271776\pi
4444 0 0
4545 0 0
4646 0 0
4747 10.8939 3.96505i 1.58904 0.578362i 0.611893 0.790940i 0.290408π-0.290408\pi
0.977144 + 0.212578i 0.0681859π0.0681859\pi
4848 0 0
4949 2.82735 + 4.89711i 0.403907 + 0.699587i
5050 0 0
5151 0 0
5252 0 0
5353 −3.50255 2.93899i −0.481113 0.403702i 0.369716 0.929145i 0.379455π-0.379455\pi
−0.850829 + 0.525443i 0.823900π0.823900\pi
5454 0 0
5555 −0.330140 0.120161i −0.0445161 0.0162025i
5656 0 0
5757 0 0
5858 0 0
5959 9.32947 + 3.39565i 1.21459 + 0.442076i 0.868295 0.496049i 0.165216π-0.165216\pi
0.346298 + 0.938124i 0.387438π0.387438\pi
6060 0 0
6161 −4.27534 3.58744i −0.547401 0.459324i 0.326659 0.945142i 0.394077π-0.394077\pi
−0.874060 + 0.485818i 0.838522π0.838522\pi
6262 0 0
6363 0 0
6464 0 0
6565 0.793965 + 1.37519i 0.0984792 + 0.170571i
6666 0 0
6767 −3.47734 + 1.26565i −0.424824 + 0.154623i −0.545580 0.838059i 0.683691π-0.683691\pi
0.120756 + 0.992682i 0.461468π0.461468\pi
6868 0 0
6969 0 0
7070 0 0
7171 −7.14016 + 5.99131i −0.847382 + 0.711038i −0.959211 0.282690i 0.908773π-0.908773\pi
0.111830 + 0.993727i 0.464329π0.464329\pi
7272 0 0
7373 0.191208 + 1.08439i 0.0223792 + 0.126919i 0.993951 0.109828i 0.0350300π-0.0350300\pi
−0.971571 + 0.236747i 0.923919π0.923919\pi
7474 0 0
7575 0 0
7676 0 0
7777 −1.44397 −0.164556
7878 0 0
7979 −1.50923 8.55928i −0.169802 0.962994i −0.943974 0.330019i 0.892945π-0.892945\pi
0.774172 0.632975i 0.218166π-0.218166\pi
8080 0 0
8181 0 0
8282 0 0
8383 −5.77114 + 9.99591i −0.633465 + 1.09719i 0.353373 + 0.935483i 0.385035π0.385035\pi
−0.986838 + 0.161711i 0.948299π0.948299\pi
8484 0 0
8585 −1.76449 + 0.642221i −0.191386 + 0.0696587i
8686 0 0
8787 0 0
8888 0 0
8989 0.418534 2.37362i 0.0443645 0.251603i −0.954557 0.298027i 0.903671π-0.903671\pi
0.998922 + 0.0464239i 0.0147825π0.0147825\pi
9090 0 0
9191 4.99955 + 4.19512i 0.524095 + 0.439768i
9292 0 0
9393 0 0
9494 0 0
9595 −1.22576 0.103280i −0.125760 0.0105963i
9696 0 0
9797 −13.4638 4.90042i −1.36704 0.497562i −0.448816 0.893624i 0.648154π-0.648154\pi
−0.918224 + 0.396062i 0.870376π0.870376\pi
9898 0 0
9999 0 0
100100 0 0
101101 2.97288 16.8600i 0.295813 1.67764i −0.368068 0.929799i 0.619981π-0.619981\pi
0.663881 0.747838i 0.268908π-0.268908\pi
102102 0 0
103103 6.64081 + 11.5022i 0.654339 + 1.13335i 0.982059 + 0.188573i 0.0603863π0.0603863\pi
−0.327720 + 0.944775i 0.606280π0.606280\pi
104104 0 0
105105 0 0
106106 0 0
107107 0.494870 0.857140i 0.0478409 0.0828628i −0.841113 0.540859i 0.818099π-0.818099\pi
0.888954 + 0.457996i 0.151433π0.151433\pi
108108 0 0
109109 10.3519 8.68625i 0.991529 0.831991i 0.00574045 0.999984i 0.498173π-0.498173\pi
0.985788 + 0.167992i 0.0537283π0.0537283\pi
110110 0 0
111111 0 0
112112 0 0
113113 −16.5369 −1.55566 −0.777829 0.628476i 0.783679π-0.783679\pi
−0.777829 + 0.628476i 0.783679π0.783679\pi
114114 0 0
115115 −1.71313 −0.159750
116116 0 0
117117 0 0
118118 0 0
119119 −5.91198 + 4.96074i −0.541950 + 0.454750i
120120 0 0
121121 4.72506 8.18405i 0.429551 0.744005i
122122 0 0
123123 0 0
124124 0 0
125125 −1.39979 2.42450i −0.125201 0.216854i
126126 0 0
127127 −0.388935 + 2.20576i −0.0345124 + 0.195729i −0.997189 0.0749239i 0.976129π-0.976129\pi
0.962677 + 0.270653i 0.0872397π0.0872397\pi
128128 0 0
129129 0 0
130130 0 0
131131 −16.5173 6.01181i −1.44313 0.525255i −0.502463 0.864599i 0.667573π-0.667573\pi
−0.940662 + 0.339344i 0.889795π0.889795\pi
132132 0 0
133133 −4.87927 + 1.32418i −0.423087 + 0.114821i
134134 0 0
135135 0 0
136136 0 0
137137 −4.36728 3.66458i −0.373122 0.313086i 0.436873 0.899523i 0.356086π-0.356086\pi
−0.809995 + 0.586437i 0.800530π0.800530\pi
138138 0 0
139139 0.891090 5.05362i 0.0755813 0.428643i −0.923413 0.383808i 0.874613π-0.874613\pi
0.998994 0.0448352i 0.0142763π-0.0142763\pi
140140 0 0
141141 0 0
142142 0 0
143143 6.58265 2.39589i 0.550469 0.200354i
144144 0 0
145145 0.547914 0.949015i 0.0455018 0.0788114i
146146 0 0
147147 0 0
148148 0 0
149149 2.06723 + 11.7238i 0.169354 + 0.960454i 0.944461 + 0.328624i 0.106585π0.106585\pi
−0.775107 + 0.631830i 0.782304π0.782304\pi
150150 0 0
151151 −14.8628 −1.20952 −0.604759 0.796409i 0.706731π-0.706731\pi
−0.604759 + 0.796409i 0.706731π0.706731\pi
152152 0 0
153153 0 0
154154 0 0
155155 −0.00392629 0.0222671i −0.000315367 0.00178854i
156156 0 0
157157 −8.45258 + 7.09255i −0.674589 + 0.566047i −0.914420 0.404767i 0.867353π-0.867353\pi
0.239831 + 0.970815i 0.422908π0.422908\pi
158158 0 0
159159 0 0
160160 0 0
161161 −6.61640 + 2.40817i −0.521446 + 0.189791i
162162 0 0
163163 −1.99237 3.45089i −0.156055 0.270295i 0.777388 0.629021i 0.216544π-0.216544\pi
−0.933443 + 0.358727i 0.883211π0.883211\pi
164164 0 0
165165 0 0
166166 0 0
167167 6.19785 + 5.20061i 0.479604 + 0.402436i 0.850283 0.526325i 0.176431π-0.176431\pi
−0.370679 + 0.928761i 0.620875π0.620875\pi
168168 0 0
169169 −17.5362 6.38267i −1.34894 0.490974i
170170 0 0
171171 0 0
172172 0 0
173173 −6.13327 2.23233i −0.466304 0.169721i 0.0981735 0.995169i 0.468700π-0.468700\pi
−0.564477 + 0.825449i 0.690922π0.690922\pi
174174 0 0
175175 −4.37181 3.66838i −0.330478 0.277304i
176176 0 0
177177 0 0
178178 0 0
179179 −4.91617 8.51506i −0.367452 0.636445i 0.621715 0.783244i 0.286436π-0.286436\pi
−0.989166 + 0.146799i 0.953103π0.953103\pi
180180 0 0
181181 12.9463 4.71208i 0.962293 0.350246i 0.187361 0.982291i 0.440007π-0.440007\pi
0.774932 + 0.632045i 0.217784π0.217784\pi
182182 0 0
183183 0 0
184184 0 0
185185 −0.802823 + 0.673648i −0.0590247 + 0.0495276i
186186 0 0
187187 1.43842 + 8.15771i 0.105188 + 0.596551i
188188 0 0
189189 0 0
190190 0 0
191191 −1.03137 −0.0746275 −0.0373137 0.999304i 0.511880π-0.511880\pi
−0.0373137 + 0.999304i 0.511880π0.511880\pi
192192 0 0
193193 −0.407183 2.30925i −0.0293097 0.166224i 0.966640 0.256140i 0.0824510π-0.0824510\pi
−0.995949 + 0.0899169i 0.971340π0.971340\pi
194194 0 0
195195 0 0
196196 0 0
197197 7.78406 13.4824i 0.554592 0.960581i −0.443344 0.896352i 0.646208π-0.646208\pi
0.997935 0.0642291i 0.0204588π-0.0204588\pi
198198 0 0
199199 12.8701 4.68434i 0.912339 0.332064i 0.157153 0.987574i 0.449769π-0.449769\pi
0.755186 + 0.655510i 0.227546π0.227546\pi
200200 0 0
201201 0 0
202202 0 0
203203 0.782093 4.43547i 0.0548922 0.311309i
204204 0 0
205205 1.39056 + 1.16682i 0.0971207 + 0.0814940i
206206 0 0
207207 0 0
208208 0 0
209209 −1.38768 + 5.24614i −0.0959878 + 0.362883i
210210 0 0
211211 20.2595 + 7.37386i 1.39472 + 0.507638i 0.926608 0.376030i 0.122711π-0.122711\pi
0.468116 + 0.883667i 0.344933π0.344933\pi
212212 0 0
213213 0 0
214214 0 0
215215 −0.0121165 + 0.0687159i −0.000826336 + 0.00468638i
216216 0 0
217217 −0.0464652 0.0804801i −0.00315426 0.00546335i
218218 0 0
219219 0 0
220220 0 0
221221 18.7200 32.4240i 1.25924 2.18107i
222222 0 0
223223 −19.9848 + 16.7693i −1.33828 + 1.12295i −0.356220 + 0.934402i 0.615935π0.615935\pi
−0.982063 + 0.188551i 0.939621π0.939621\pi
224224 0 0
225225 0 0
226226 0 0
227227 −21.7357 −1.44265 −0.721325 0.692596i 0.756467π-0.756467\pi
−0.721325 + 0.692596i 0.756467π0.756467\pi
228228 0 0
229229 −20.1255 −1.32993 −0.664964 0.746875i 0.731553π-0.731553\pi
−0.664964 + 0.746875i 0.731553π0.731553\pi
230230 0 0
231231 0 0
232232 0 0
233233 −16.8667 + 14.1529i −1.10498 + 0.927184i −0.997750 0.0670504i 0.978641π-0.978641\pi
−0.107226 + 0.994235i 0.534197π0.534197\pi
234234 0 0
235235 −1.63581 + 2.83330i −0.106708 + 0.184824i
236236 0 0
237237 0 0
238238 0 0
239239 2.18637 + 3.78691i 0.141425 + 0.244955i 0.928033 0.372497i 0.121498π-0.121498\pi
−0.786609 + 0.617452i 0.788165π0.788165\pi
240240 0 0
241241 −2.60506 + 14.7740i −0.167807 + 0.951679i 0.778317 + 0.627872i 0.216074π0.216074\pi
−0.946123 + 0.323807i 0.895037π0.895037\pi
242242 0 0
243243 0 0
244244 0 0
245245 −1.49954 0.545790i −0.0958024 0.0348692i
246246 0 0
247247 20.0461 14.1325i 1.27550 0.899226i
248248 0 0
249249 0 0
250250 0 0
251251 17.9754 + 15.0832i 1.13460 + 0.952042i 0.999249 0.0387556i 0.0123394π-0.0123394\pi
0.135351 + 0.990798i 0.456784π0.456784\pi
252252 0 0
253253 −1.31233 + 7.44261i −0.0825057 + 0.467913i
254254 0 0
255255 0 0
256256 0 0
257257 0.0996901 0.0362842i 0.00621850 0.00226335i −0.338909 0.940819i 0.610058π-0.610058\pi
0.345128 + 0.938556i 0.387836π0.387836\pi
258258 0 0
259259 −2.15368 + 3.73029i −0.133823 + 0.231789i
260260 0 0
261261 0 0
262262 0 0
263263 2.70397 + 15.3350i 0.166734 + 0.945594i 0.947259 + 0.320469i 0.103841π0.103841\pi
−0.780525 + 0.625124i 0.785048π0.785048\pi
264264 0 0
265265 1.29031 0.0792633
266266 0 0
267267 0 0
268268 0 0
269269 −2.43886 13.8315i −0.148700 0.843321i −0.964321 0.264734i 0.914716π-0.914716\pi
0.815621 0.578586i 0.196395π-0.196395\pi
270270 0 0
271271 8.77391 7.36218i 0.532977 0.447221i −0.336151 0.941808i 0.609125π-0.609125\pi
0.869128 + 0.494587i 0.164681π0.164681\pi
272272 0 0
273273 0 0
274274 0 0
275275 −5.75613 + 2.09506i −0.347108 + 0.126337i
276276 0 0
277277 −12.8642 22.2814i −0.772932 1.33876i −0.935949 0.352135i 0.885456π-0.885456\pi
0.163017 0.986623i 0.447878π-0.447878\pi
278278 0 0
279279 0 0
280280 0 0
281281 20.6252 + 17.3066i 1.23039 + 1.03242i 0.998213 + 0.0597510i 0.0190307π0.0190307\pi
0.232181 + 0.972673i 0.425414π0.425414\pi
282282 0 0
283283 −2.78007 1.01186i −0.165258 0.0601491i 0.258066 0.966127i 0.416915π-0.416915\pi
−0.423324 + 0.905978i 0.639137π0.639137\pi
284284 0 0
285285 0 0
286286 0 0
287287 7.01078 + 2.55172i 0.413834 + 0.150623i
288288 0 0
289289 20.8922 + 17.5306i 1.22895 + 1.03121i
290290 0 0
291291 0 0
292292 0 0
293293 5.01204 + 8.68111i 0.292807 + 0.507156i 0.974472 0.224508i 0.0720775π-0.0720775\pi
−0.681666 + 0.731664i 0.738744π0.738744\pi
294294 0 0
295295 −2.63282 + 0.958268i −0.153289 + 0.0557925i
296296 0 0
297297 0 0
298298 0 0
299299 26.1666 21.9564i 1.51325 1.26977i
300300 0 0
301301 0.0497991 + 0.282425i 0.00287037 + 0.0162787i
302302 0 0
303303 0 0
304304 0 0
305305 1.57500 0.0901844
306306 0 0
307307 −2.87822 16.3232i −0.164269 0.931614i −0.949815 0.312811i 0.898729π-0.898729\pi
0.785547 0.618802i 0.212382π-0.212382\pi
308308 0 0
309309 0 0
310310 0 0
311311 0.215620 0.373465i 0.0122267 0.0211772i −0.859847 0.510551i 0.829441π-0.829441\pi
0.872074 + 0.489374i 0.162775π0.162775\pi
312312 0 0
313313 13.0841 4.76223i 0.739557 0.269177i 0.0553527 0.998467i 0.482372π-0.482372\pi
0.684205 + 0.729290i 0.260149π0.260149\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.87712 16.3170i 0.161595 0.916452i −0.790911 0.611932i 0.790393π-0.790393\pi
0.952506 0.304521i 0.0984962π-0.0984962\pi
318318 0 0
319319 −3.70322 3.10737i −0.207341 0.173980i
320320 0 0
321321 0 0
322322 0 0
323323 12.3415 + 26.2463i 0.686700 + 1.46039i
324324 0 0
325325 26.0165 + 9.46925i 1.44314 + 0.525259i
326326 0 0
327327 0 0
328328 0 0
329329 −2.33495 + 13.2422i −0.128730 + 0.730064i
330330 0 0
331331 −4.74773 8.22332i −0.260959 0.451994i 0.705538 0.708672i 0.250705π-0.250705\pi
−0.966497 + 0.256678i 0.917372π0.917372\pi
332332 0 0
333333 0 0
334334 0 0
335335 0.522150 0.904390i 0.0285281 0.0494121i
336336 0 0
337337 9.65934 8.10515i 0.526178 0.441515i −0.340601 0.940208i 0.610631π-0.610631\pi
0.866779 + 0.498692i 0.166186π0.166186\pi
338338 0 0
339339 0 0
340340 0 0
341341 −0.0997461 −0.00540155
342342 0 0
343343 −14.6778 −0.792529
344344 0 0
345345 0 0
346346 0 0
347347 −8.36688 + 7.02065i −0.449158 + 0.376888i −0.839123 0.543941i 0.816931π-0.816931\pi
0.389965 + 0.920830i 0.372487π0.372487\pi
348348 0 0
349349 −4.20032 + 7.27517i −0.224838 + 0.389431i −0.956271 0.292483i 0.905519π-0.905519\pi
0.731433 + 0.681913i 0.238852π0.238852\pi
350350 0 0
351351 0 0
352352 0 0
353353 6.69379 + 11.5940i 0.356274 + 0.617086i 0.987335 0.158648i 0.0507135π-0.0507135\pi
−0.631061 + 0.775733i 0.717380π0.717380\pi
354354 0 0
355355 0.456761 2.59042i 0.0242423 0.137485i
356356 0 0
357357 0 0
358358 0 0
359359 −26.6099 9.68521i −1.40442 0.511166i −0.474931 0.880023i 0.657527π-0.657527\pi
−0.929486 + 0.368857i 0.879749π0.879749\pi
360360 0 0
361361 0.121876 + 18.9996i 0.00641452 + 0.999979i
362362 0 0
363363 0 0
364364 0 0
365365 −0.238042 0.199741i −0.0124597 0.0104549i
366366 0 0
367367 0.0720091 0.408384i 0.00375884 0.0213175i −0.982871 0.184297i 0.940999π-0.940999\pi
0.986629 + 0.162979i 0.0521104π0.0521104\pi
368368 0 0
369369 0 0
370370 0 0
371371 4.98342 1.81381i 0.258726 0.0941686i
372372 0 0
373373 2.01032 3.48198i 0.104090 0.180290i −0.809276 0.587429i 0.800140π-0.800140\pi
0.913366 + 0.407139i 0.133474π0.133474\pi
374374 0 0
375375 0 0
376376 0 0
377377 3.79416 + 21.5177i 0.195409 + 1.10822i
378378 0 0
379379 14.1791 0.728332 0.364166 0.931334i 0.381354π-0.381354\pi
0.364166 + 0.931334i 0.381354π0.381354\pi
380380 0 0
381381 0 0
382382 0 0
383383 −1.88738 10.7039i −0.0964407 0.546943i −0.994296 0.106653i 0.965987π-0.965987\pi
0.897856 0.440290i 0.145124π-0.145124\pi
384384 0 0
385385 0.312160 0.261933i 0.0159091 0.0133493i
386386 0 0
387387 0 0
388388 0 0
389389 24.0167 8.74136i 1.21769 0.443205i 0.348328 0.937373i 0.386749π-0.386749\pi
0.869367 + 0.494168i 0.164527π0.164527\pi
390390 0 0
391391 20.1960 + 34.9804i 1.02135 + 1.76904i
392392 0 0
393393 0 0
394394 0 0
395395 1.87890 + 1.57659i 0.0945378 + 0.0793267i
396396 0 0
397397 16.1594 + 5.88155i 0.811018 + 0.295186i 0.714044 0.700101i 0.246862π-0.246862\pi
0.0969735 + 0.995287i 0.469084π0.469084\pi
398398 0 0
399399 0 0
400400 0 0
401401 14.4376 + 5.25485i 0.720979 + 0.262415i 0.676341 0.736588i 0.263564π-0.263564\pi
0.0446377 + 0.999003i 0.485787π0.485787\pi
402402 0 0
403403 0.345357 + 0.289789i 0.0172035 + 0.0144354i
404404 0 0
405405 0 0
406406 0 0
407407 2.31164 + 4.00387i 0.114584 + 0.198465i
408408 0 0
409409 −13.4638 + 4.90042i −0.665741 + 0.242310i −0.652713 0.757605i 0.726369π-0.726369\pi
−0.0130280 + 0.999915i 0.504147π0.504147\pi
410410 0 0
411411 0 0
412412 0 0
413413 −8.82135 + 7.40200i −0.434070 + 0.364228i
414414 0 0
415415 −0.565622 3.20780i −0.0277653 0.157465i
416416 0 0
417417 0 0
418418 0 0
419419 17.2723 0.843805 0.421902 0.906641i 0.361363π-0.361363\pi
0.421902 + 0.906641i 0.361363π0.361363\pi
420420 0 0
421421 −4.83458 27.4183i −0.235623 1.33629i −0.841297 0.540573i 0.818208π-0.818208\pi
0.605674 0.795713i 0.292903π-0.292903\pi
422422 0 0
423423 0 0
424424 0 0
425425 −16.3695 + 28.3528i −0.794038 + 1.37531i
426426 0 0
427427 6.08293 2.21401i 0.294374 0.107143i
428428 0 0
429429 0 0
430430 0 0
431431 6.57872 37.3098i 0.316886 1.79715i −0.244558 0.969635i 0.578643π-0.578643\pi
0.561444 0.827515i 0.310246π-0.310246\pi
432432 0 0
433433 5.76405 + 4.83661i 0.277003 + 0.232433i 0.770696 0.637204i 0.219909π-0.219909\pi
−0.493693 + 0.869636i 0.664353π0.664353\pi
434434 0 0
435435 0 0
436436 0 0
437437 2.39074 + 26.3526i 0.114365 + 1.26061i
438438 0 0
439439 −19.9813 7.27259i −0.953655 0.347102i −0.182111 0.983278i 0.558293π-0.558293\pi
−0.771544 + 0.636176i 0.780515π0.780515\pi
440440 0 0
441441 0 0
442442 0 0
443443 2.59412 14.7120i 0.123250 0.698988i −0.859081 0.511839i 0.828964π-0.828964\pi
0.982332 0.187149i 0.0599246π-0.0599246\pi
444444 0 0
445445 0.340090 + 0.589054i 0.0161218 + 0.0279238i
446446 0 0
447447 0 0
448448 0 0
449449 8.47286 14.6754i 0.399859 0.692576i −0.593849 0.804576i 0.702392π-0.702392\pi
0.993708 + 0.112000i 0.0357258π0.0357258\pi
450450 0 0
451451 6.13441 5.14738i 0.288858 0.242381i
452452 0 0
453453 0 0
454454 0 0
455455 −1.84180 −0.0863447
456456 0 0
457457 −10.2922 −0.481448 −0.240724 0.970594i 0.577385π-0.577385\pi
−0.240724 + 0.970594i 0.577385π0.577385\pi
458458 0 0
459459 0 0
460460 0 0
461461 −4.59397 + 3.85480i −0.213962 + 0.179536i −0.743470 0.668770i 0.766821π-0.766821\pi
0.529507 + 0.848305i 0.322377π0.322377\pi
462462 0 0
463463 −1.69033 + 2.92774i −0.0785563 + 0.136063i −0.902627 0.430423i 0.858364π-0.858364\pi
0.824071 + 0.566487i 0.191698π0.191698\pi
464464 0 0
465465 0 0
466466 0 0
467467 1.03045 + 1.78480i 0.0476837 + 0.0825906i 0.888882 0.458136i 0.151483π-0.151483\pi
−0.841198 + 0.540727i 0.818149π0.818149\pi
468468 0 0
469469 0.745318 4.22691i 0.0344156 0.195180i
470470 0 0
471471 0 0
472472 0 0
473473 0.289251 + 0.105279i 0.0132998 + 0.00484073i
474474 0 0
475475 −17.5291 + 12.3580i −0.804290 + 0.567023i
476476 0 0
477477 0 0
478478 0 0
479479 4.53663 + 3.80668i 0.207284 + 0.173932i 0.740519 0.672035i 0.234580π-0.234580\pi
−0.533235 + 0.845967i 0.679024π0.679024\pi
480480 0 0
481481 3.62860 20.5788i 0.165450 0.938312i
482482 0 0
483483 0 0
484484 0 0
485485 3.79954 1.38292i 0.172528 0.0627952i
486486 0 0
487487 13.3232 23.0764i 0.603731 1.04569i −0.388520 0.921440i 0.627013π-0.627013\pi
0.992251 0.124252i 0.0396532π-0.0396532\pi
488488 0 0
489489 0 0
490490 0 0
491491 −6.15100 34.8841i −0.277591 1.57430i −0.730610 0.682795i 0.760764π-0.760764\pi
0.453019 0.891501i 0.350347π-0.350347\pi
492492 0 0
493493 −25.8373 −1.16365
494494 0 0
495495 0 0
496496 0 0
497497 −1.87730 10.6467i −0.0842086 0.477571i
498498 0 0
499499 −26.5322 + 22.2631i −1.18774 + 0.996634i −0.187846 + 0.982198i 0.560151π0.560151\pi
−0.999896 + 0.0144356i 0.995405π0.995405\pi
500500 0 0
501501 0 0
502502 0 0
503503 29.0173 10.5614i 1.29382 0.470912i 0.398840 0.917020i 0.369413π-0.369413\pi
0.894979 + 0.446109i 0.147190π0.147190\pi
504504 0 0
505505 2.41569 + 4.18410i 0.107497 + 0.186190i
506506 0 0
507507 0 0
508508 0 0
509509 −11.9255 10.0067i −0.528590 0.443540i 0.339024 0.940778i 0.389903π-0.389903\pi
−0.867614 + 0.497238i 0.834348π0.834348\pi
510510 0 0
511511 −1.20014 0.436815i −0.0530910 0.0193235i
512512 0 0
513513 0 0
514514 0 0
515515 −3.52210 1.28194i −0.155202 0.0564890i
516516 0 0
517517 11.0560 + 9.27711i 0.486244 + 0.408007i
518518 0 0
519519 0 0
520520 0 0
521521 11.1132 + 19.2486i 0.486877 + 0.843295i 0.999886 0.0150876i 0.00480270π-0.00480270\pi
−0.513009 + 0.858383i 0.671469π0.671469\pi
522522 0 0
523523 −10.1135 + 3.68103i −0.442234 + 0.160960i −0.553534 0.832827i 0.686721π-0.686721\pi
0.111299 + 0.993787i 0.464499π0.464499\pi
524524 0 0
525525 0 0
526526 0 0
527527 −0.408385 + 0.342676i −0.0177895 + 0.0149272i
528528 0 0
529529 2.40523 + 13.6408i 0.104575 + 0.593077i
530530 0 0
531531 0 0
532532 0 0
533533 −36.1941 −1.56774
534534 0 0
535535 0.0485015 + 0.275066i 0.00209690 + 0.0118921i
536536 0 0
537537 0 0
538538 0 0
539539 −3.51988 + 6.09660i −0.151612 + 0.262599i
540540 0 0
541541 11.5235 4.19422i 0.495435 0.180323i −0.0822049 0.996615i 0.526196π-0.526196\pi
0.577639 + 0.816292i 0.303974π0.303974\pi
542542 0 0
543543 0 0
544544 0 0
545545 −0.662215 + 3.75561i −0.0283662 + 0.160873i
546546 0 0
547547 14.2562 + 11.9624i 0.609552 + 0.511475i 0.894500 0.447068i 0.147532π-0.147532\pi
−0.284948 + 0.958543i 0.591976π0.591976\pi
548548 0 0
549549 0 0
550550 0 0
551551 −15.3630 7.10401i −0.654488 0.302641i
552552 0 0
553553 9.47288 + 3.44785i 0.402828 + 0.146617i
554554 0 0
555555 0 0
556556 0 0
557557 0.706865 4.00883i 0.0299508 0.169860i −0.966163 0.257931i 0.916959π-0.916959\pi
0.996114 + 0.0880715i 0.0280704π0.0280704\pi
558558 0 0
559559 −0.695630 1.20487i −0.0294220 0.0509604i
560560 0 0
561561 0 0
562562 0 0
563563 −12.4377 + 21.5428i −0.524188 + 0.907920i 0.475416 + 0.879761i 0.342298π0.342298\pi
−0.999603 + 0.0281586i 0.991036π0.991036\pi
564564 0 0
565565 3.57496 2.99975i 0.150400 0.126201i
566566 0 0
567567 0 0
568568 0 0
569569 −19.2420 −0.806667 −0.403334 0.915053i 0.632149π-0.632149\pi
−0.403334 + 0.915053i 0.632149π0.632149\pi
570570 0 0
571571 13.5395 0.566612 0.283306 0.959030i 0.408569π-0.408569\pi
0.283306 + 0.959030i 0.408569π0.408569\pi
572572 0 0
573573 0 0
574574 0 0
575575 −22.8811 + 19.1995i −0.954207 + 0.800675i
576576 0 0
577577 −12.8402 + 22.2398i −0.534543 + 0.925855i 0.464643 + 0.885498i 0.346183π0.346183\pi
−0.999185 + 0.0403567i 0.987151π0.987151\pi
578578 0 0
579579 0 0
580580 0 0
581581 −6.69379 11.5940i −0.277705 0.481000i
582582 0 0
583583 0.988438 5.60571i 0.0409369 0.232165i
584584 0 0
585585 0 0
586586 0 0
587587 −17.4378 6.34683i −0.719734 0.261962i −0.0439211 0.999035i 0.513985π-0.513985\pi
−0.675813 + 0.737073i 0.736207π0.736207\pi
588588 0 0
589589 −0.337049 + 0.0914715i −0.0138878 + 0.00376902i
590590 0 0
591591 0 0
592592 0 0
593593 −2.75772 2.31400i −0.113246 0.0950248i 0.584406 0.811461i 0.301327π-0.301327\pi
−0.697652 + 0.716437i 0.745772π0.745772\pi
594594 0 0
595595 0.378193 2.14484i 0.0155044 0.0879298i
596596 0 0
597597 0 0
598598 0 0
599599 −12.3328 + 4.48878i −0.503905 + 0.183407i −0.581450 0.813582i 0.697514π-0.697514\pi
0.0775443 + 0.996989i 0.475292π0.475292\pi
600600 0 0
601601 −6.78825 + 11.7576i −0.276898 + 0.479602i −0.970612 0.240649i 0.922640π-0.922640\pi
0.693714 + 0.720251i 0.255973π0.255973\pi
602602 0 0
603603 0 0
604604 0 0
605605 0.463097 + 2.62635i 0.0188276 + 0.106777i
606606 0 0
607607 −18.3633 −0.745343 −0.372672 0.927963i 0.621558π-0.621558\pi
−0.372672 + 0.927963i 0.621558π0.621558\pi
608608 0 0
609609 0 0
610610 0 0
611611 −11.3275 64.2415i −0.458262 2.59893i
612612 0 0
613613 4.42518 3.71316i 0.178731 0.149973i −0.549033 0.835801i 0.685004π-0.685004\pi
0.727764 + 0.685827i 0.240559π0.240559\pi
614614 0 0
615615 0 0
616616 0 0
617617 39.3443 14.3201i 1.58394 0.576507i 0.607885 0.794025i 0.292018π-0.292018\pi
0.976056 + 0.217518i 0.0697961π0.0697961\pi
618618 0 0
619619 −18.0480 31.2601i −0.725412 1.25645i −0.958804 0.284068i 0.908316π-0.908316\pi
0.233392 0.972383i 0.425017π-0.425017\pi
620620 0 0
621621 0 0
622622 0 0
623623 2.14153 + 1.79696i 0.0857986 + 0.0719936i
624624 0 0
625625 −22.3757 8.14410i −0.895029 0.325764i
626626 0 0
627627 0 0
628628 0 0
629629 23.2197 + 8.45126i 0.925828 + 0.336974i
630630 0 0
631631 −29.6886 24.9117i −1.18188 0.991717i −0.999965 0.00840360i 0.997325π-0.997325\pi
−0.181918 0.983314i 0.558231π-0.558231\pi
632632 0 0
633633 0 0
634634 0 0
635635 −0.316039 0.547396i −0.0125416 0.0217227i
636636 0 0
637637 29.8994 10.8825i 1.18466 0.431179i
638638 0 0
639639 0 0
640640 0 0
641641 −5.24003 + 4.39691i −0.206969 + 0.173667i −0.740380 0.672189i 0.765354π-0.765354\pi
0.533411 + 0.845856i 0.320910π0.320910\pi
642642 0 0
643643 −2.89363 16.4106i −0.114114 0.647171i −0.987185 0.159579i 0.948986π-0.948986\pi
0.873072 0.487592i 0.162125π-0.162125\pi
644644 0 0
645645 0 0
646646 0 0
647647 −36.1664 −1.42185 −0.710924 0.703269i 0.751723π-0.751723\pi
−0.710924 + 0.703269i 0.751723π0.751723\pi
648648 0 0
649649 2.14629 + 12.1722i 0.0842494 + 0.477802i
650650 0 0
651651 0 0
652652 0 0
653653 −4.83426 + 8.37319i −0.189179 + 0.327668i −0.944977 0.327137i 0.893916π-0.893916\pi
0.755798 + 0.654805i 0.227249π0.227249\pi
654654 0 0
655655 4.66127 1.69656i 0.182131 0.0662902i
656656 0 0
657657 0 0
658658 0 0
659659 −4.94409 + 28.0393i −0.192594 + 1.09226i 0.723209 + 0.690629i 0.242666π0.242666\pi
−0.915803 + 0.401627i 0.868445π0.868445\pi
660660 0 0
661661 −19.5360 16.3927i −0.759863 0.637601i 0.178228 0.983989i 0.442964π-0.442964\pi
−0.938091 + 0.346388i 0.887408π0.887408\pi
662662 0 0
663663 0 0
664664 0 0
665665 0.814604 1.17135i 0.0315890 0.0454231i
666666 0 0
667667 −22.1508 8.06223i −0.857683 0.312171i
668668 0 0
669669 0 0
670670 0 0
671671 1.20652 6.84252i 0.0465772 0.264153i
672672 0 0
673673 20.3192 + 35.1938i 0.783246 + 1.35662i 0.930041 + 0.367456i 0.119771π0.119771\pi
−0.146795 + 0.989167i 0.546896π0.546896\pi
674674 0 0
675675 0 0
676676 0 0
677677 10.2220 17.7050i 0.392862 0.680457i −0.599964 0.800027i 0.704818π-0.704818\pi
0.992826 + 0.119570i 0.0381517π0.0381517\pi
678678 0 0
679679 12.7305 10.6822i 0.488552 0.409944i
680680 0 0
681681 0 0
682682 0 0
683683 −39.8318 −1.52412 −0.762061 0.647505i 0.775813π-0.775813\pi
−0.762061 + 0.647505i 0.775813π0.775813\pi
684684 0 0
685685 1.60887 0.0614718
686686 0 0
687687 0 0
688688 0 0
689689 −19.7084 + 16.5373i −0.750831 + 0.630022i
690690 0 0
691691 14.0389 24.3160i 0.534064 0.925025i −0.465144 0.885235i 0.653998π-0.653998\pi
0.999208 0.0397906i 0.0126691π-0.0126691\pi
692692 0 0
693693 0 0
694694 0 0
695695 0.724079 + 1.25414i 0.0274659 + 0.0475723i
696696 0 0
697697 7.43206 42.1493i 0.281509 1.59652i
698698 0 0
699699 0 0
700700 0 0
701701 4.02822 + 1.46615i 0.152144 + 0.0553757i 0.416969 0.908921i 0.363092π-0.363092\pi
−0.264826 + 0.964296i 0.585314π0.585314\pi
702702 0 0
703703 11.4829 + 11.4095i 0.433086 + 0.430317i
704704 0 0
705705 0 0
706706 0 0
707707 15.2115 + 12.7639i 0.572087 + 0.480038i
708708 0 0
709709 −0.715927 + 4.06022i −0.0268872 + 0.152485i −0.995296 0.0968845i 0.969112π-0.969112\pi
0.968408 + 0.249369i 0.0802234π0.0802234\pi
710710 0 0
711711 0 0
712712 0 0
713713 −0.457045 + 0.166351i −0.0171165 + 0.00622989i
714714 0 0
715715 −0.988438 + 1.71202i −0.0369655 + 0.0640261i
716716 0 0
717717 0 0
718718 0 0
719719 7.79796 + 44.2244i 0.290815 + 1.64929i 0.683742 + 0.729724i 0.260351π0.260351\pi
−0.392927 + 0.919570i 0.628538π0.628538\pi
720720 0 0
721721 −15.4050 −0.573712
722722 0 0
723723 0 0
724724 0 0
725725 −3.31776 18.8160i −0.123219 0.698807i
726726 0 0
727727 −26.7341 + 22.4326i −0.991514 + 0.831979i −0.985786 0.168005i 0.946268π-0.946268\pi
−0.00572754 + 0.999984i 0.501823π0.501823\pi
728728 0 0
729729 0 0
730730 0 0
731731 1.54595 0.562680i 0.0571791 0.0208115i
732732 0 0
733733 0.524006 + 0.907605i 0.0193546 + 0.0335232i 0.875540 0.483145i 0.160506π-0.160506\pi
−0.856186 + 0.516668i 0.827172π0.827172\pi
734734 0 0
735735 0 0
736736 0 0
737737 −3.52909 2.96126i −0.129996 0.109079i
738738 0 0
739739 −20.8426 7.58607i −0.766706 0.279058i −0.0710882 0.997470i 0.522647π-0.522647\pi
−0.695618 + 0.718412i 0.744869π0.744869\pi
740740 0 0
741741 0 0
742742 0 0
743743 −35.7965 13.0288i −1.31325 0.477982i −0.411957 0.911203i 0.635155π-0.635155\pi
−0.901288 + 0.433221i 0.857377π0.857377\pi
744744 0 0
745745 −2.57357 2.15948i −0.0942884 0.0791174i
746746 0 0
747747 0 0
748748 0 0
749749 0.573986 + 0.994173i 0.0209730 + 0.0363263i
750750 0 0
751751 11.9657 4.35515i 0.436634 0.158922i −0.114345 0.993441i 0.536477π-0.536477\pi
0.550979 + 0.834519i 0.314255π0.314255\pi
752752 0 0
753753 0 0
754754 0 0
755755 3.21306 2.69608i 0.116935 0.0981203i
756756 0 0
757757 7.21125 + 40.8970i 0.262097 + 1.48643i 0.777175 + 0.629284i 0.216652π0.216652\pi
−0.515078 + 0.857143i 0.672237π0.672237\pi
758758 0 0
759759 0 0
760760 0 0
761761 −36.4398 −1.32094 −0.660471 0.750851i 0.729643π-0.729643\pi
−0.660471 + 0.750851i 0.729643π0.729643\pi
762762 0 0
763763 2.72173 + 15.4357i 0.0985333 + 0.558810i
764764 0 0
765765 0 0
766766 0 0
767767 27.9324 48.3803i 1.00858 1.74691i
768768 0 0
769769 −11.0091 + 4.00697i −0.396997 + 0.144495i −0.532801 0.846241i 0.678860π-0.678860\pi
0.135804 + 0.990736i 0.456638π0.456638\pi
770770 0 0
771771 0 0
772772 0 0
773773 −6.22310 + 35.2929i −0.223829 + 1.26940i 0.641081 + 0.767473i 0.278486π0.278486\pi
−0.864911 + 0.501926i 0.832625π0.832625\pi
774774 0 0
775775 −0.301994 0.253403i −0.0108480 0.00910251i
776776 0 0
777777 0 0
778778 0 0
779779 16.0082 23.0189i 0.573553 0.824736i
780780 0 0
781781 −10.9041 3.96875i −0.390178 0.142013i
782782 0 0
783783 0 0
784784 0 0
785785 0.540717 3.06656i 0.0192990 0.109450i
786786 0 0
787787 −1.05573 1.82858i −0.0376328 0.0651819i 0.846596 0.532237i 0.178648π-0.178648\pi
−0.884228 + 0.467055i 0.845315π0.845315\pi
788788 0 0
789789 0 0
790790 0 0
791791 9.59033 16.6109i 0.340993 0.590617i
792792 0 0
793793 −24.0568 + 20.1860i −0.854282 + 0.716827i
794794 0 0
795795 0 0
796796 0 0
797797 −14.9794 −0.530596 −0.265298 0.964166i 0.585470π-0.585470\pi
−0.265298 + 0.964166i 0.585470π0.585470\pi
798798 0 0
799799 77.1376 2.72893
800800 0 0
801801 0 0
802802 0 0
803803 −1.05012 + 0.881152i −0.0370578 + 0.0310952i
804804 0 0
805805 0.993506 1.72080i 0.0350165 0.0606503i
806806 0 0
807807 0 0
808808 0 0
809809 −19.1248 33.1251i −0.672392 1.16462i −0.977224 0.212211i 0.931933π-0.931933\pi
0.304831 0.952406i 0.401400π-0.401400\pi
810810 0 0
811811 5.50463 31.2183i 0.193294 1.09622i −0.721534 0.692379i 0.756563π-0.756563\pi
0.914828 0.403844i 0.132326π-0.132326\pi
812812 0 0
813813 0 0
814814 0 0
815815 1.05670 + 0.384606i 0.0370145 + 0.0134722i
816816 0 0
817817 1.07394 + 0.0904882i 0.0375726 + 0.00316578i
818818 0 0
819819 0 0
820820 0 0
821821 10.7629 + 9.03111i 0.375627 + 0.315188i 0.810983 0.585070i 0.198933π-0.198933\pi
−0.435356 + 0.900258i 0.643378π0.643378\pi
822822 0 0
823823 −3.19150 + 18.0999i −0.111249 + 0.630923i 0.877291 + 0.479960i 0.159349π0.159349\pi
−0.988539 + 0.150963i 0.951762π0.951762\pi
824824 0 0
825825 0 0
826826 0 0
827827 −5.23011 + 1.90360i −0.181869 + 0.0661948i −0.431349 0.902185i 0.641962π-0.641962\pi
0.249481 + 0.968380i 0.419740π0.419740\pi
828828 0 0
829829 21.0061 36.3837i 0.729573 1.26366i −0.227490 0.973780i 0.573052π-0.573052\pi
0.957064 0.289878i 0.0936146π-0.0936146\pi
830830 0 0
831831 0 0
832832 0 0
833833 6.53353 + 37.0535i 0.226373 + 1.28383i
834834 0 0
835835 −2.28324 −0.0790148
836836 0 0
837837 0 0
838838 0 0
839839 −5.46639 31.0014i −0.188721 1.07029i −0.921081 0.389371i 0.872692π-0.872692\pi
0.732360 0.680918i 0.238419π-0.238419\pi
840840 0 0
841841 −10.6645 + 8.94862i −0.367743 + 0.308573i
842842 0 0
843843 0 0
844844 0 0
845845 4.94881 1.80122i 0.170244 0.0619638i
846846 0 0
847847 5.48047 + 9.49246i 0.188311 + 0.326165i
848848 0 0
849849 0 0
850850 0 0
851851 17.2696 + 14.4909i 0.591993 + 0.496741i
852852 0 0
853853 −10.6345 3.87065i −0.364119 0.132529i 0.153480 0.988152i 0.450952π-0.450952\pi
−0.517599 + 0.855623i 0.673174π0.673174\pi
854854 0 0
855855 0 0
856856 0 0
857857 46.2117 + 16.8197i 1.57856 + 0.574550i 0.974891 0.222683i 0.0714814π-0.0714814\pi
0.603672 + 0.797233i 0.293704π0.293704\pi
858858 0 0
859859 19.9118 + 16.7080i 0.679382 + 0.570069i 0.915826 0.401576i 0.131537π-0.131537\pi
−0.236444 + 0.971645i 0.575982π0.575982\pi
860860 0 0
861861 0 0
862862 0 0
863863 −0.199487 0.345522i −0.00679062 0.0117617i 0.862610 0.505869i 0.168828π-0.168828\pi
−0.869401 + 0.494108i 0.835495π0.835495\pi
864864 0 0
865865 1.73084 0.629973i 0.0588502 0.0214197i
866866 0 0
867867 0 0
868868 0 0
869869 8.28873 6.95507i 0.281176 0.235935i
870870 0 0
871871 3.61575 + 20.5059i 0.122515 + 0.694817i
872872 0 0
873873 0 0
874874 0 0
875875 3.24715 0.109774
876876 0 0
877877 1.98754 + 11.2719i 0.0671145 + 0.380625i 0.999801 + 0.0199377i 0.00634679π0.00634679\pi
−0.932687 + 0.360687i 0.882542π0.882542\pi
878878 0 0
879879 0 0
880880 0 0
881881 −8.37742 + 14.5101i −0.282242 + 0.488858i −0.971937 0.235242i 0.924412π-0.924412\pi
0.689694 + 0.724101i 0.257745π0.257745\pi
882882 0 0
883883 −43.5805 + 15.8620i −1.46660 + 0.533799i −0.947175 0.320718i 0.896076π-0.896076\pi
−0.519425 + 0.854516i 0.673854π0.673854\pi
884884 0 0
885885 0 0
886886 0 0
887887 3.45930 19.6187i 0.116152 0.658730i −0.870022 0.493014i 0.835895π-0.835895\pi
0.986173 0.165717i 0.0529937π-0.0529937\pi
888888 0 0
889889 −1.99008 1.66988i −0.0667452 0.0560059i
890890 0 0
891891 0 0
892892 0 0
893893 45.8666 + 21.2091i 1.53487 + 0.709736i
894894 0 0
895895 2.60740 + 0.949015i 0.0871557 + 0.0317221i
896896 0 0
897897 0 0
898898 0 0
899899 0.0540251 0.306392i 0.00180184 0.0102187i
900900 0 0
901901 −15.2114 26.3469i −0.506766 0.877744i
902902 0 0
903903 0 0
904904 0 0
905905 −1.94399 + 3.36710i −0.0646206 + 0.111926i
906906 0 0
907907 8.40693 7.05425i 0.279147 0.234232i −0.492455 0.870338i 0.663900π-0.663900\pi
0.771602 + 0.636106i 0.219456π0.219456\pi
908908 0 0
909909 0 0
910910 0 0
911911 1.79760 0.0595572 0.0297786 0.999557i 0.490520π-0.490520\pi
0.0297786 + 0.999557i 0.490520π0.490520\pi
912912 0 0
913913 −14.3694 −0.475559
914914 0 0
915915 0 0
916916 0 0
917917 15.6177 13.1048i 0.515743 0.432760i
918918 0 0
919919 −2.62319 + 4.54349i −0.0865309 + 0.149876i −0.906043 0.423187i 0.860911π-0.860911\pi
0.819512 + 0.573063i 0.194245π0.194245\pi
920920 0 0
921921 0 0
922922 0 0
923923 26.2235 + 45.4205i 0.863158 + 1.49503i
924924 0 0
925925 −3.17299 + 17.9949i −0.104327 + 0.591669i
926926 0 0
927927 0 0
928928 0 0
929929 −24.9915 9.09617i −0.819946 0.298436i −0.102220 0.994762i 0.532595π-0.532595\pi
−0.717726 + 0.696326i 0.754817π0.754817\pi
930930 0 0
931931 −6.30304 + 23.8287i −0.206574 + 0.780955i
932932 0 0
933933 0 0
934934 0 0
935935 −1.79075 1.50262i −0.0585638 0.0491408i
936936 0 0
937937 1.97310 11.1900i 0.0644582 0.365561i −0.935468 0.353411i 0.885022π-0.885022\pi
0.999926 0.0121492i 0.00386732π-0.00386732\pi
938938 0 0
939939 0 0
940940 0 0
941941 46.0984 16.7785i 1.50277 0.546962i 0.545991 0.837791i 0.316153π-0.316153\pi
0.956775 + 0.290829i 0.0939309π0.0939309\pi
942942 0 0
943943 19.5239 33.8164i 0.635785 1.10121i
944944 0 0
945945 0 0
946946 0 0
947947 0.862194 + 4.88975i 0.0280175 + 0.158895i 0.995607 0.0936345i 0.0298485π-0.0298485\pi
−0.967589 + 0.252530i 0.918737π0.918737\pi
948948 0 0
949949 6.19587 0.201126
950950 0 0
951951 0 0
952952 0 0
953953 7.05030 + 39.9842i 0.228382 + 1.29522i 0.856114 + 0.516787i 0.172872π0.172872\pi
−0.627732 + 0.778429i 0.716017π0.716017\pi
954954 0 0
955955 0.222964 0.187089i 0.00721493 0.00605405i
956956 0 0
957957 0 0
958958 0 0
959959 6.21374 2.26162i 0.200652 0.0730314i
960960 0 0
961961 15.4968 + 26.8412i 0.499896 + 0.865846i
962962 0 0
963963 0 0
964964 0 0
965965 0.506918 + 0.425355i 0.0163183 + 0.0136927i
966966 0 0
967967 −4.40584 1.60359i −0.141682 0.0515681i 0.270206 0.962803i 0.412908π-0.412908\pi
−0.411888 + 0.911234i 0.635130π0.635130\pi
968968 0 0
969969 0 0
970970 0 0
971971 31.9910 + 11.6438i 1.02664 + 0.373666i 0.799800 0.600266i 0.204939π-0.204939\pi
0.226839 + 0.973932i 0.427161π0.427161\pi
972972 0 0
973973 4.55948 + 3.82586i 0.146170 + 0.122651i
974974 0 0
975975 0 0
976976 0 0
977977 5.37934 + 9.31729i 0.172100 + 0.298086i 0.939154 0.343497i 0.111611π-0.111611\pi
−0.767054 + 0.641583i 0.778278π0.778278\pi
978978 0 0
979979 2.81964 1.02627i 0.0901161 0.0327996i
980980 0 0
981981 0 0
982982 0 0
983983 −46.0661 + 38.6540i −1.46928 + 1.23287i −0.552480 + 0.833526i 0.686318π0.686318\pi
−0.916800 + 0.399346i 0.869237π0.869237\pi
984984 0 0
985985 0.762906 + 4.32665i 0.0243082 + 0.137859i
986986 0 0
987987 0 0
988988 0 0
989989 1.50095 0.0477275
990990 0 0
991991 −6.88681 39.0571i −0.218767 1.24069i −0.874249 0.485478i 0.838646π-0.838646\pi
0.655482 0.755211i 0.272465π-0.272465\pi
992992 0 0
993993 0 0
994994 0 0
995995 −1.93255 + 3.34728i −0.0612660 + 0.106116i
996996 0 0
997997 13.8021 5.02356i 0.437117 0.159098i −0.114082 0.993471i 0.536393π-0.536393\pi
0.551199 + 0.834374i 0.314170π0.314170\pi
998998 0 0
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 684.2.bo.c.289.1 12
3.2 odd 2 76.2.i.a.61.2 yes 12
12.11 even 2 304.2.u.e.289.1 12
19.5 even 9 inner 684.2.bo.c.613.1 12
57.5 odd 18 76.2.i.a.5.2 12
57.23 odd 18 1444.2.e.g.653.3 12
57.29 even 18 1444.2.a.g.1.3 6
57.32 even 18 1444.2.e.h.429.4 12
57.44 odd 18 1444.2.e.g.429.3 12
57.47 odd 18 1444.2.a.h.1.4 6
57.53 even 18 1444.2.e.h.653.4 12
228.47 even 18 5776.2.a.bw.1.3 6
228.119 even 18 304.2.u.e.81.1 12
228.143 odd 18 5776.2.a.by.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.2.i.a.5.2 12 57.5 odd 18
76.2.i.a.61.2 yes 12 3.2 odd 2
304.2.u.e.81.1 12 228.119 even 18
304.2.u.e.289.1 12 12.11 even 2
684.2.bo.c.289.1 12 1.1 even 1 trivial
684.2.bo.c.613.1 12 19.5 even 9 inner
1444.2.a.g.1.3 6 57.29 even 18
1444.2.a.h.1.4 6 57.47 odd 18
1444.2.e.g.429.3 12 57.44 odd 18
1444.2.e.g.653.3 12 57.23 odd 18
1444.2.e.h.429.4 12 57.32 even 18
1444.2.e.h.653.4 12 57.53 even 18
5776.2.a.bw.1.3 6 228.47 even 18
5776.2.a.by.1.4 6 228.143 odd 18