Properties

Label 156.4.q.c.49.3
Level 156156
Weight 44
Character 156.49
Analytic conductor 9.2049.204
Analytic rank 00
Dimension 66
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] = [156,4,Mod(49,156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(156, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("156.49"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 156=22313 156 = 2^{2} \cdot 3 \cdot 13
Weight: k k == 4 4
Character orbit: [χ][\chi] == 156.q (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 9.204297960909.20429796090
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x6+)\mathbb{Q}[x]/(x^{6} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6+443x4+53128x2+1862832 x^{6} + 443x^{4} + 53128x^{2} + 1862832 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 49.3
Root 16.5475i-16.5475i of defining polynomial
Character χ\chi == 156.49
Dual form 156.4.q.c.121.1

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+(1.50000+2.59808i)q3+14.8155iq5+(3.28368+1.89583i)q7+(4.50000+7.79423i)q9+(3.38576+1.95477i)q11+(44.465214.8273i)q13+(38.4917+22.2232i)q15+(33.6203+58.2320i)q17+(9.912165.72279i)q19+11.3750iq21+(26.4388+45.7933i)q2394.4977q2527.0000q27+(29.3449+50.8269i)q29+182.725iq31+(10.15735.86431i)q33+(28.0876+48.6492i)q35+(33.9350+19.5924i)q37+(28.1754137.765i)q39+(197.469114.009i)q41+(178.087+308.456i)q43+(115.47566.6695i)q45108.483iq47+(164.312284.596i)q49201.722q51+642.753q53+(28.960850.1616i)q5534.3367iq57+(550.716+317.956i)q59+(9.62421+16.6696i)q61+(29.5531+17.0625i)q63+(219.673658.772i)q65+(421.110243.128i)q67+(79.3163+137.380i)q69+(331.280+191.264i)q711057.00iq73+(141.747245.512i)q7514.8237q77+460.065q79+(40.500070.1481i)q81+268.768iq83+(862.734498.100i)q85+(88.0347+152.481i)q87+(659.691380.873i)q89+(117.899132.987i)q91+(474.733+274.087i)q93+(84.7857146.853i)q95+(613.504354.207i)q9735.1859iq99+O(q100)q+(1.50000 + 2.59808i) q^{3} +14.8155i q^{5} +(3.28368 + 1.89583i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-3.38576 + 1.95477i) q^{11} +(-44.4652 - 14.8273i) q^{13} +(-38.4917 + 22.2232i) q^{15} +(-33.6203 + 58.2320i) q^{17} +(-9.91216 - 5.72279i) q^{19} +11.3750i q^{21} +(26.4388 + 45.7933i) q^{23} -94.4977 q^{25} -27.0000 q^{27} +(29.3449 + 50.8269i) q^{29} +182.725i q^{31} +(-10.1573 - 5.86431i) q^{33} +(-28.0876 + 48.6492i) q^{35} +(-33.9350 + 19.5924i) q^{37} +(-28.1754 - 137.765i) q^{39} +(197.469 - 114.009i) q^{41} +(-178.087 + 308.456i) q^{43} +(-115.475 - 66.6695i) q^{45} -108.483i q^{47} +(-164.312 - 284.596i) q^{49} -201.722 q^{51} +642.753 q^{53} +(-28.9608 - 50.1616i) q^{55} -34.3367i q^{57} +(550.716 + 317.956i) q^{59} +(-9.62421 + 16.6696i) q^{61} +(-29.5531 + 17.0625i) q^{63} +(219.673 - 658.772i) q^{65} +(421.110 - 243.128i) q^{67} +(-79.3163 + 137.380i) q^{69} +(331.280 + 191.264i) q^{71} -1057.00i q^{73} +(-141.747 - 245.512i) q^{75} -14.8237 q^{77} +460.065 q^{79} +(-40.5000 - 70.1481i) q^{81} +268.768i q^{83} +(-862.734 - 498.100i) q^{85} +(-88.0347 + 152.481i) q^{87} +(659.691 - 380.873i) q^{89} +(-117.899 - 132.987i) q^{91} +(-474.733 + 274.087i) q^{93} +(84.7857 - 146.853i) q^{95} +(-613.504 - 354.207i) q^{97} -35.1859i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+9q3+9q727q9120q1177q13+36q15+32q1724q19+104q23166q25162q27+220q29360q3388q35684q3766q39+576q41+873q97+O(q100) 6 q + 9 q^{3} + 9 q^{7} - 27 q^{9} - 120 q^{11} - 77 q^{13} + 36 q^{15} + 32 q^{17} - 24 q^{19} + 104 q^{23} - 166 q^{25} - 162 q^{27} + 220 q^{29} - 360 q^{33} - 88 q^{35} - 684 q^{37} - 66 q^{39} + 576 q^{41}+ \cdots - 873 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/156Z)×\left(\mathbb{Z}/156\mathbb{Z}\right)^\times.

nn 5353 7979 145145
χ(n)\chi(n) 11 11 e(56)e\left(\frac{5}{6}\right)

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 1.50000 + 2.59808i 0.288675 + 0.500000i
44 0 0
55 14.8155i 1.32513i 0.749002 + 0.662567i 0.230533π0.230533\pi
−0.749002 + 0.662567i 0.769467π0.769467\pi
66 0 0
77 3.28368 + 1.89583i 0.177302 + 0.102365i 0.586024 0.810293i 0.300692π-0.300692\pi
−0.408722 + 0.912659i 0.634026π0.634026\pi
88 0 0
99 −4.50000 + 7.79423i −0.166667 + 0.288675i
1010 0 0
1111 −3.38576 + 1.95477i −0.0928041 + 0.0535805i −0.545684 0.837991i 0.683730π-0.683730\pi
0.452880 + 0.891572i 0.350397π0.350397\pi
1212 0 0
1313 −44.4652 14.8273i −0.948648 0.316334i
1414 0 0
1515 −38.4917 + 22.2232i −0.662567 + 0.382533i
1616 0 0
1717 −33.6203 + 58.2320i −0.479654 + 0.830785i −0.999728 0.0233367i 0.992571π-0.992571\pi
0.520074 + 0.854121i 0.325904π0.325904\pi
1818 0 0
1919 −9.91216 5.72279i −0.119685 0.0690999i 0.438963 0.898505i 0.355346π-0.355346\pi
−0.558647 + 0.829405i 0.688679π0.688679\pi
2020 0 0
2121 11.3750i 0.118201i
2222 0 0
2323 26.4388 + 45.7933i 0.239690 + 0.415155i 0.960625 0.277847i 0.0896209π-0.0896209\pi
−0.720935 + 0.693002i 0.756288π0.756288\pi
2424 0 0
2525 −94.4977 −0.755982
2626 0 0
2727 −27.0000 −0.192450
2828 0 0
2929 29.3449 + 50.8269i 0.187904 + 0.325459i 0.944551 0.328364i 0.106497π-0.106497\pi
−0.756647 + 0.653823i 0.773164π0.773164\pi
3030 0 0
3131 182.725i 1.05866i 0.848417 + 0.529329i 0.177556π0.177556\pi
−0.848417 + 0.529329i 0.822444π0.822444\pi
3232 0 0
3333 −10.1573 5.86431i −0.0535805 0.0309347i
3434 0 0
3535 −28.0876 + 48.6492i −0.135648 + 0.234949i
3636 0 0
3737 −33.9350 + 19.5924i −0.150781 + 0.0870533i −0.573492 0.819211i 0.694412π-0.694412\pi
0.422711 + 0.906264i 0.361078π0.361078\pi
3838 0 0
3939 −28.1754 137.765i −0.115684 0.565642i
4040 0 0
4141 197.469 114.009i 0.752183 0.434273i −0.0742993 0.997236i 0.523672π-0.523672\pi
0.826482 + 0.562963i 0.190339π0.190339\pi
4242 0 0
4343 −178.087 + 308.456i −0.631582 + 1.09393i 0.355647 + 0.934620i 0.384261π0.384261\pi
−0.987228 + 0.159311i 0.949073π0.949073\pi
4444 0 0
4545 −115.475 66.6695i −0.382533 0.220856i
4646 0 0
4747 108.483i 0.336678i −0.985729 0.168339i 0.946160π-0.946160\pi
0.985729 0.168339i 0.0538403π-0.0538403\pi
4848 0 0
4949 −164.312 284.596i −0.479043 0.829726i
5050 0 0
5151 −201.722 −0.553856
5252 0 0
5353 642.753 1.66583 0.832914 0.553402i 0.186671π-0.186671\pi
0.832914 + 0.553402i 0.186671π0.186671\pi
5454 0 0
5555 −28.9608 50.1616i −0.0710013 0.122978i
5656 0 0
5757 34.3367i 0.0797897i
5858 0 0
5959 550.716 + 317.956i 1.21520 + 0.701599i 0.963888 0.266307i 0.0858033π-0.0858033\pi
0.251316 + 0.967905i 0.419137π0.419137\pi
6060 0 0
6161 −9.62421 + 16.6696i −0.0202009 + 0.0349890i −0.875949 0.482403i 0.839764π-0.839764\pi
0.855748 + 0.517392i 0.173097π0.173097\pi
6262 0 0
6363 −29.5531 + 17.0625i −0.0591007 + 0.0341218i
6464 0 0
6565 219.673 658.772i 0.419186 1.25709i
6666 0 0
6767 421.110 243.128i 0.767862 0.443325i −0.0642496 0.997934i 0.520465π-0.520465\pi
0.832111 + 0.554609i 0.187132π0.187132\pi
6868 0 0
6969 −79.3163 + 137.380i −0.138385 + 0.239690i
7070 0 0
7171 331.280 + 191.264i 0.553742 + 0.319703i 0.750630 0.660723i 0.229750π-0.229750\pi
−0.196888 + 0.980426i 0.563084π0.563084\pi
7272 0 0
7373 1057.00i 1.69469i −0.531043 0.847345i 0.678200π-0.678200\pi
0.531043 0.847345i 0.321800π-0.321800\pi
7474 0 0
7575 −141.747 245.512i −0.218233 0.377991i
7676 0 0
7777 −14.8237 −0.0219391
7878 0 0
7979 460.065 0.655207 0.327603 0.944815i 0.393759π-0.393759\pi
0.327603 + 0.944815i 0.393759π0.393759\pi
8080 0 0
8181 −40.5000 70.1481i −0.0555556 0.0962250i
8282 0 0
8383 268.768i 0.355436i 0.984081 + 0.177718i 0.0568714π0.0568714\pi
−0.984081 + 0.177718i 0.943129π0.943129\pi
8484 0 0
8585 −862.734 498.100i −1.10090 0.635606i
8686 0 0
8787 −88.0347 + 152.481i −0.108486 + 0.187904i
8888 0 0
8989 659.691 380.873i 0.785698 0.453623i −0.0527478 0.998608i 0.516798π-0.516798\pi
0.838446 + 0.544985i 0.183465π0.183465\pi
9090 0 0
9191 −117.899 132.987i −0.135815 0.153195i
9292 0 0
9393 −474.733 + 274.087i −0.529329 + 0.305608i
9494 0 0
9595 84.7857 146.853i 0.0915667 0.158598i
9696 0 0
9797 −613.504 354.207i −0.642185 0.370766i 0.143271 0.989684i 0.454238π-0.454238\pi
−0.785456 + 0.618918i 0.787571π0.787571\pi
9898 0 0
9999 35.1859i 0.0357203i
100100 0 0
101101 −149.067 258.191i −0.146859 0.254366i 0.783206 0.621762i 0.213583π-0.213583\pi
−0.930065 + 0.367396i 0.880250π0.880250\pi
102102 0 0
103103 664.955 0.636116 0.318058 0.948071i 0.396969π-0.396969\pi
0.318058 + 0.948071i 0.396969π0.396969\pi
104104 0 0
105105 −168.526 −0.156633
106106 0 0
107107 1044.66 + 1809.40i 0.943839 + 1.63478i 0.758058 + 0.652187i 0.226148π0.226148\pi
0.185781 + 0.982591i 0.440518π0.440518\pi
108108 0 0
109109 910.270i 0.799890i 0.916539 + 0.399945i 0.130971π0.130971\pi
−0.916539 + 0.399945i 0.869029π0.869029\pi
110110 0 0
111111 −101.805 58.7772i −0.0870533 0.0502602i
112112 0 0
113113 −28.0095 + 48.5138i −0.0233178 + 0.0403876i −0.877449 0.479670i 0.840756π-0.840756\pi
0.854131 + 0.520058i 0.174090π0.174090\pi
114114 0 0
115115 −678.449 + 391.702i −0.550136 + 0.317621i
116116 0 0
117117 315.660 279.849i 0.249426 0.221129i
118118 0 0
119119 −220.796 + 127.477i −0.170087 + 0.0981999i
120120 0 0
121121 −657.858 + 1139.44i −0.494258 + 0.856080i
122122 0 0
123123 592.407 + 342.027i 0.434273 + 0.250728i
124124 0 0
125125 451.905i 0.323357i
126126 0 0
127127 958.890 + 1660.85i 0.669982 + 1.16044i 0.977909 + 0.209033i 0.0670317π0.0670317\pi
−0.307926 + 0.951410i 0.599635π0.599635\pi
128128 0 0
129129 −1068.52 −0.729288
130130 0 0
131131 −308.770 −0.205934 −0.102967 0.994685i 0.532834π-0.532834\pi
−0.102967 + 0.994685i 0.532834π0.532834\pi
132132 0 0
133133 −21.6989 37.5836i −0.0141469 0.0245031i
134134 0 0
135135 400.017i 0.255022i
136136 0 0
137137 −2570.07 1483.83i −1.60275 0.925346i −0.990935 0.134341i 0.957108π-0.957108\pi
−0.611811 0.791004i 0.709559π-0.709559\pi
138138 0 0
139139 −1129.30 + 1956.00i −0.689108 + 1.19357i 0.283019 + 0.959114i 0.408664π0.408664\pi
−0.972127 + 0.234455i 0.924669π0.924669\pi
140140 0 0
141141 281.847 162.724i 0.168339 0.0971905i
142142 0 0
143143 179.532 36.7176i 0.104988 0.0214719i
144144 0 0
145145 −753.023 + 434.758i −0.431277 + 0.248998i
146146 0 0
147147 492.935 853.788i 0.276575 0.479043i
148148 0 0
149149 406.075 + 234.447i 0.223268 + 0.128904i 0.607463 0.794348i 0.292187π-0.292187\pi
−0.384195 + 0.923252i 0.625521π0.625521\pi
150150 0 0
151151 2143.41i 1.15516i −0.816336 0.577578i 0.803998π-0.803998\pi
0.816336 0.577578i 0.196002π-0.196002\pi
152152 0 0
153153 −302.582 524.088i −0.159885 0.276928i
154154 0 0
155155 −2707.15 −1.40286
156156 0 0
157157 701.045 0.356366 0.178183 0.983997i 0.442978π-0.442978\pi
0.178183 + 0.983997i 0.442978π0.442978\pi
158158 0 0
159159 964.129 + 1669.92i 0.480883 + 0.832914i
160160 0 0
161161 200.494i 0.0981437i
162162 0 0
163163 −2655.81 1533.33i −1.27619 0.736808i −0.300044 0.953925i 0.597001π-0.597001\pi
−0.976146 + 0.217117i 0.930335π0.930335\pi
164164 0 0
165165 86.8824 150.485i 0.0409926 0.0710013i
166166 0 0
167167 −2085.46 + 1204.04i −0.966334 + 0.557913i −0.898117 0.439758i 0.855064π-0.855064\pi
−0.0682170 + 0.997671i 0.521731π0.521731\pi
168168 0 0
169169 1757.30 + 1318.60i 0.799865 + 0.600180i
170170 0 0
171171 89.2095 51.5051i 0.0398948 0.0230333i
172172 0 0
173173 1601.64 2774.12i 0.703876 1.21915i −0.263220 0.964736i 0.584784π-0.584784\pi
0.967096 0.254413i 0.0818822π-0.0818822\pi
174174 0 0
175175 −310.300 179.152i −0.134037 0.0773863i
176176 0 0
177177 1907.73i 0.810136i
178178 0 0
179179 778.970 + 1349.22i 0.325268 + 0.563381i 0.981567 0.191121i 0.0612121π-0.0612121\pi
−0.656299 + 0.754501i 0.727879π0.727879\pi
180180 0 0
181181 4053.88 1.66476 0.832382 0.554203i 0.186977π-0.186977\pi
0.832382 + 0.554203i 0.186977π0.186977\pi
182182 0 0
183183 −57.7453 −0.0233260
184184 0 0
185185 −290.270 502.763i −0.115357 0.199805i
186186 0 0
187187 262.880i 0.102800i
188188 0 0
189189 −88.6593 51.1875i −0.0341218 0.0197002i
190190 0 0
191191 −1416.11 + 2452.77i −0.536470 + 0.929194i 0.462620 + 0.886556i 0.346909π0.346909\pi
−0.999091 + 0.0426372i 0.986424π0.986424\pi
192192 0 0
193193 466.890 269.559i 0.174132 0.100535i −0.410401 0.911905i 0.634611π-0.634611\pi
0.584533 + 0.811370i 0.301278π0.301278\pi
194194 0 0
195195 2041.05 417.431i 0.749551 0.153297i
196196 0 0
197197 −72.9076 + 42.0932i −0.0263678 + 0.0152234i −0.513126 0.858313i 0.671513π-0.671513\pi
0.486758 + 0.873537i 0.338179π0.338179\pi
198198 0 0
199199 2734.73 4736.69i 0.974171 1.68731i 0.291525 0.956563i 0.405837π-0.405837\pi
0.682646 0.730750i 0.260829π-0.260829\pi
200200 0 0
201201 1263.33 + 729.383i 0.443325 + 0.255954i
202202 0 0
203203 222.532i 0.0769394i
204204 0 0
205205 1689.09 + 2925.59i 0.575470 + 0.996743i
206206 0 0
207207 −475.898 −0.159793
208208 0 0
209209 44.7469 0.0148096
210210 0 0
211211 −29.7642 51.5532i −0.00971116 0.0168202i 0.861129 0.508387i 0.169758π-0.169758\pi
−0.870840 + 0.491566i 0.836425π0.836425\pi
212212 0 0
213213 1147.59i 0.369161i
214214 0 0
215215 −4569.91 2638.44i −1.44961 0.836931i
216216 0 0
217217 −346.416 + 600.010i −0.108370 + 0.187702i
218218 0 0
219219 2746.16 1585.50i 0.847345 0.489215i
220220 0 0
221221 2358.35 2090.80i 0.717828 0.636391i
222222 0 0
223223 4032.25 2328.02i 1.21085 0.699084i 0.247905 0.968784i 0.420258π-0.420258\pi
0.962944 + 0.269700i 0.0869247π0.0869247\pi
224224 0 0
225225 425.240 736.537i 0.125997 0.218233i
226226 0 0
227227 −3194.70 1844.46i −0.934095 0.539300i −0.0459906 0.998942i 0.514644π-0.514644\pi
−0.888104 + 0.459642i 0.847978π0.847978\pi
228228 0 0
229229 3641.69i 1.05087i −0.850833 0.525436i 0.823902π-0.823902\pi
0.850833 0.525436i 0.176098π-0.176098\pi
230230 0 0
231231 −22.2355 38.5130i −0.00633328 0.0109696i
232232 0 0
233233 −4462.98 −1.25485 −0.627424 0.778678i 0.715891π-0.715891\pi
−0.627424 + 0.778678i 0.715891π0.715891\pi
234234 0 0
235235 1607.22 0.446143
236236 0 0
237237 690.097 + 1195.28i 0.189142 + 0.327603i
238238 0 0
239239 643.226i 0.174087i −0.996205 0.0870436i 0.972258π-0.972258\pi
0.996205 0.0870436i 0.0277419π-0.0277419\pi
240240 0 0
241241 −4264.45 2462.08i −1.13982 0.658078i −0.193437 0.981113i 0.561964π-0.561964\pi
−0.946387 + 0.323035i 0.895297π0.895297\pi
242242 0 0
243243 121.500 210.444i 0.0320750 0.0555556i
244244 0 0
245245 4216.42 2434.35i 1.09950 0.634796i
246246 0 0
247247 355.893 + 401.435i 0.0916798 + 0.103412i
248248 0 0
249249 −698.281 + 403.152i −0.177718 + 0.102605i
250250 0 0
251251 1493.42 2586.68i 0.375553 0.650478i −0.614856 0.788639i 0.710786π-0.710786\pi
0.990410 + 0.138162i 0.0441193π0.0441193\pi
252252 0 0
253253 −179.031 103.363i −0.0444884 0.0256854i
254254 0 0
255255 2988.60i 0.733934i
256256 0 0
257257 157.195 + 272.270i 0.0381539 + 0.0660846i 0.884472 0.466594i 0.154519π-0.154519\pi
−0.846318 + 0.532678i 0.821186π0.821186\pi
258258 0 0
259259 −148.576 −0.0356450
260260 0 0
261261 −528.208 −0.125269
262262 0 0
263263 564.595 + 977.908i 0.132374 + 0.229279i 0.924591 0.380960i 0.124407π-0.124407\pi
−0.792217 + 0.610239i 0.791073π0.791073\pi
264264 0 0
265265 9522.68i 2.20745i
266266 0 0
267267 1979.07 + 1142.62i 0.453623 + 0.261899i
268268 0 0
269269 −44.5279 + 77.1246i −0.0100926 + 0.0174809i −0.871028 0.491234i 0.836546π-0.836546\pi
0.860935 + 0.508715i 0.169879π0.169879\pi
270270 0 0
271271 4564.74 2635.45i 1.02320 0.590747i 0.108174 0.994132i 0.465500π-0.465500\pi
0.915030 + 0.403385i 0.132166π0.132166\pi
272272 0 0
273273 168.660 505.791i 0.0373912 0.112131i
274274 0 0
275275 319.947 184.721i 0.0701582 0.0405059i
276276 0 0
277277 −2173.97 + 3765.42i −0.471556 + 0.816760i −0.999470 0.0325382i 0.989641π-0.989641\pi
0.527914 + 0.849298i 0.322974π0.322974\pi
278278 0 0
279279 −1424.20 822.262i −0.305608 0.176443i
280280 0 0
281281 3386.80i 0.719002i 0.933145 + 0.359501i 0.117053π0.117053\pi
−0.933145 + 0.359501i 0.882947π0.882947\pi
282282 0 0
283283 1045.84 + 1811.45i 0.219678 + 0.380494i 0.954710 0.297539i 0.0961659π-0.0961659\pi
−0.735031 + 0.678033i 0.762833π0.762833\pi
284284 0 0
285285 508.714 0.105732
286286 0 0
287287 864.567 0.177818
288288 0 0
289289 195.855 + 339.231i 0.0398647 + 0.0690476i
290290 0 0
291291 2125.24i 0.428123i
292292 0 0
293293 −2041.92 1178.90i −0.407134 0.235059i 0.282424 0.959290i 0.408862π-0.408862\pi
−0.689558 + 0.724231i 0.742195π0.742195\pi
294294 0 0
295295 −4710.66 + 8159.10i −0.929713 + 1.61031i
296296 0 0
297297 91.4155 52.7788i 0.0178602 0.0103116i
298298 0 0
299299 −496.615 2428.22i −0.0960534 0.469658i
300300 0 0
301301 −1169.56 + 675.246i −0.223961 + 0.129304i
302302 0 0
303303 447.201 774.574i 0.0847888 0.146859i
304304 0 0
305305 −246.968 142.587i −0.0463651 0.0267689i
306306 0 0
307307 6738.19i 1.25267i −0.779555 0.626334i 0.784555π-0.784555\pi
0.779555 0.626334i 0.215445π-0.215445\pi
308308 0 0
309309 997.433 + 1727.60i 0.183631 + 0.318058i
310310 0 0
311311 −8796.16 −1.60381 −0.801904 0.597453i 0.796179π-0.796179\pi
−0.801904 + 0.597453i 0.796179π0.796179\pi
312312 0 0
313313 −1286.70 −0.232360 −0.116180 0.993228i 0.537065π-0.537065\pi
−0.116180 + 0.993228i 0.537065π0.537065\pi
314314 0 0
315315 −252.789 437.843i −0.0452160 0.0783163i
316316 0 0
317317 10694.6i 1.89486i 0.319960 + 0.947431i 0.396331π0.396331\pi
−0.319960 + 0.947431i 0.603669π0.603669\pi
318318 0 0
319319 −198.710 114.725i −0.0348765 0.0201360i
320320 0 0
321321 −3133.97 + 5428.20i −0.544926 + 0.943839i
322322 0 0
323323 666.499 384.803i 0.114814 0.0662880i
324324 0 0
325325 4201.86 + 1401.14i 0.717160 + 0.239143i
326326 0 0
327327 −2364.95 + 1365.40i −0.399945 + 0.230908i
328328 0 0
329329 205.665 356.223i 0.0344641 0.0596937i
330330 0 0
331331 −3605.97 2081.91i −0.598798 0.345716i 0.169771 0.985484i 0.445697π-0.445697\pi
−0.768568 + 0.639768i 0.779031π0.779031\pi
332332 0 0
333333 352.663i 0.0580355i
334334 0 0
335335 3602.05 + 6238.93i 0.587465 + 1.01752i
336336 0 0
337337 −12074.9 −1.95182 −0.975909 0.218177i 0.929989π-0.929989\pi
−0.975909 + 0.218177i 0.929989π0.929989\pi
338338 0 0
339339 −168.057 −0.0269251
340340 0 0
341341 −357.185 618.663i −0.0567234 0.0982477i
342342 0 0
343343 2546.57i 0.400880i
344344 0 0
345345 −2035.35 1175.11i −0.317621 0.183379i
346346 0 0
347347 −4917.13 + 8516.73i −0.760708 + 1.31758i 0.181778 + 0.983340i 0.441815π0.441815\pi
−0.942486 + 0.334245i 0.891519π0.891519\pi
348348 0 0
349349 6376.59 3681.52i 0.978026 0.564663i 0.0763521 0.997081i 0.475673π-0.475673\pi
0.901673 + 0.432418i 0.142339π0.142339\pi
350350 0 0
351351 1200.56 + 400.337i 0.182567 + 0.0608786i
352352 0 0
353353 4691.43 2708.60i 0.707365 0.408397i −0.102720 0.994710i 0.532755π-0.532755\pi
0.810084 + 0.586313i 0.199421π0.199421\pi
354354 0 0
355355 −2833.67 + 4908.06i −0.423649 + 0.733782i
356356 0 0
357357 −662.389 382.431i −0.0981999 0.0566957i
358358 0 0
359359 660.418i 0.0970907i −0.998821 0.0485453i 0.984541π-0.984541\pi
0.998821 0.0485453i 0.0154585π-0.0154585\pi
360360 0 0
361361 −3364.00 5826.62i −0.490450 0.849485i
362362 0 0
363363 −3947.15 −0.570720
364364 0 0
365365 15659.9 2.24569
366366 0 0
367367 1288.28 + 2231.36i 0.183236 + 0.317374i 0.942981 0.332848i 0.108010π-0.108010\pi
−0.759745 + 0.650221i 0.774676π0.774676\pi
368368 0 0
369369 2052.16i 0.289515i
370370 0 0
371371 2110.59 + 1218.55i 0.295355 + 0.170523i
372372 0 0
373373 −2587.69 + 4482.01i −0.359210 + 0.622171i −0.987829 0.155543i 0.950287π-0.950287\pi
0.628619 + 0.777714i 0.283621π0.283621\pi
374374 0 0
375375 −1174.08 + 677.858i −0.161679 + 0.0933452i
376376 0 0
377377 −551.202 2695.13i −0.0753007 0.368186i
378378 0 0
379379 5345.24 3086.07i 0.724449 0.418261i −0.0919388 0.995765i 0.529306π-0.529306\pi
0.816388 + 0.577504i 0.195973π0.195973\pi
380380 0 0
381381 −2876.67 + 4982.54i −0.386815 + 0.669982i
382382 0 0
383383 −4584.41 2646.81i −0.611625 0.353122i 0.161976 0.986795i 0.448213π-0.448213\pi
−0.773601 + 0.633673i 0.781547π0.781547\pi
384384 0 0
385385 219.619i 0.0290723i
386386 0 0
387387 −1602.78 2776.10i −0.210527 0.364644i
388388 0 0
389389 7481.61 0.975148 0.487574 0.873082i 0.337882π-0.337882\pi
0.487574 + 0.873082i 0.337882π0.337882\pi
390390 0 0
391391 −3555.51 −0.459872
392392 0 0
393393 −463.156 802.209i −0.0594481 0.102967i
394394 0 0
395395 6816.07i 0.868237i
396396 0 0
397397 −827.803 477.932i −0.104650 0.0604200i 0.446761 0.894653i 0.352577π-0.352577\pi
−0.551412 + 0.834233i 0.685911π0.685911\pi
398398 0 0
399399 65.0967 112.751i 0.00816770 0.0141469i
400400 0 0
401401 6919.93 3995.22i 0.861758 0.497536i −0.00284281 0.999996i 0.500905π-0.500905\pi
0.864600 + 0.502460i 0.167572π0.167572\pi
402402 0 0
403403 2709.31 8124.90i 0.334890 1.00429i
404404 0 0
405405 1039.28 600.026i 0.127511 0.0736186i
406406 0 0
407407 76.5973 132.670i 0.00932871 0.0161578i
408408 0 0
409409 −5914.45 3414.71i −0.715039 0.412828i 0.0978850 0.995198i 0.468792π-0.468792\pi
−0.812924 + 0.582370i 0.802126π0.802126\pi
410410 0 0
411411 8902.99i 1.06850i
412412 0 0
413413 1205.58 + 2088.13i 0.143639 + 0.248790i
414414 0 0
415415 −3981.92 −0.471000
416416 0 0
417417 −6775.80 −0.795713
418418 0 0
419419 −1601.07 2773.13i −0.186676 0.323332i 0.757464 0.652877i 0.226438π-0.226438\pi
−0.944140 + 0.329545i 0.893105π0.893105\pi
420420 0 0
421421 3408.00i 0.394527i 0.980351 + 0.197263i 0.0632054π0.0632054\pi
−0.980351 + 0.197263i 0.936795π0.936795\pi
422422 0 0
423423 845.541 + 488.173i 0.0971905 + 0.0561130i
424424 0 0
425425 3177.04 5502.79i 0.362609 0.628058i
426426 0 0
427427 −63.2056 + 36.4918i −0.00716332 + 0.00413574i
428428 0 0
429429 364.694 + 411.362i 0.0410433 + 0.0462955i
430430 0 0
431431 8669.72 5005.46i 0.968922 0.559408i 0.0700148 0.997546i 0.477695π-0.477695\pi
0.898908 + 0.438138i 0.144362π0.144362\pi
432432 0 0
433433 6353.96 11005.4i 0.705201 1.22144i −0.261418 0.965226i 0.584190π-0.584190\pi
0.966619 0.256218i 0.0824765π-0.0824765\pi
434434 0 0
435435 −2259.07 1304.27i −0.248998 0.143759i
436436 0 0
437437 605.214i 0.0662502i
438438 0 0
439439 −1396.56 2418.90i −0.151831 0.262980i 0.780069 0.625693i 0.215184π-0.215184\pi
−0.931901 + 0.362713i 0.881850π0.881850\pi
440440 0 0
441441 2957.61 0.319362
442442 0 0
443443 16148.4 1.73191 0.865953 0.500126i 0.166713π-0.166713\pi
0.865953 + 0.500126i 0.166713π0.166713\pi
444444 0 0
445445 5642.81 + 9773.63i 0.601112 + 1.04116i
446446 0 0
447447 1406.68i 0.148845i
448448 0 0
449449 −12559.3 7251.13i −1.32007 0.762142i −0.336330 0.941744i 0.609186π-0.609186\pi
−0.983739 + 0.179602i 0.942519π0.942519\pi
450450 0 0
451451 −445.722 + 772.013i −0.0465371 + 0.0806046i
452452 0 0
453453 5568.75 3215.12i 0.577578 0.333465i
454454 0 0
455455 1970.26 1746.73i 0.203005 0.179974i
456456 0 0
457457 −10615.6 + 6128.91i −1.08660 + 0.627349i −0.932669 0.360733i 0.882527π-0.882527\pi
−0.153931 + 0.988082i 0.549193π0.549193\pi
458458 0 0
459459 907.747 1572.26i 0.0923094 0.159885i
460460 0 0
461461 4391.44 + 2535.40i 0.443665 + 0.256150i 0.705151 0.709057i 0.250879π-0.250879\pi
−0.261486 + 0.965207i 0.584212π0.584212\pi
462462 0 0
463463 5871.79i 0.589385i 0.955592 + 0.294693i 0.0952173π0.0952173\pi
−0.955592 + 0.294693i 0.904783π0.904783\pi
464464 0 0
465465 −4060.73 7033.39i −0.404972 0.701432i
466466 0 0
467467 4555.36 0.451385 0.225693 0.974199i 0.427535π-0.427535\pi
0.225693 + 0.974199i 0.427535π0.427535\pi
468468 0 0
469469 1843.72 0.181525
470470 0 0
471471 1051.57 + 1821.37i 0.102874 + 0.178183i
472472 0 0
473473 1392.48i 0.135362i
474474 0 0
475475 936.677 + 540.791i 0.0904793 + 0.0522383i
476476 0 0
477477 −2892.39 + 5009.76i −0.277638 + 0.480883i
478478 0 0
479479 −4109.82 + 2372.80i −0.392030 + 0.226339i −0.683039 0.730382i 0.739342π-0.739342\pi
0.291009 + 0.956720i 0.406009π0.406009\pi
480480 0 0
481481 1799.43 368.015i 0.170576 0.0348858i
482482 0 0
483483 −520.899 + 300.741i −0.0490719 + 0.0283317i
484484 0 0
485485 5247.74 9089.35i 0.491314 0.850981i
486486 0 0
487487 13274.6 + 7664.07i 1.23517 + 0.713125i 0.968103 0.250553i 0.0806125π-0.0806125\pi
0.267066 + 0.963678i 0.413946π0.413946\pi
488488 0 0
489489 9199.99i 0.850793i
490490 0 0
491491 9269.93 + 16056.0i 0.852029 + 1.47576i 0.879374 + 0.476131i 0.157961π0.157961\pi
−0.0273459 + 0.999626i 0.508706π0.508706\pi
492492 0 0
493493 −3946.33 −0.360515
494494 0 0
495495 521.294 0.0473342
496496 0 0
497497 725.211 + 1256.10i 0.0654530 + 0.113368i
498498 0 0
499499 10245.7i 0.919156i −0.888137 0.459578i 0.848001π-0.848001\pi
0.888137 0.459578i 0.151999π-0.151999\pi
500500 0 0
501501 −6256.38 3612.12i −0.557913 0.322111i
502502 0 0
503503 4421.17 7657.68i 0.391909 0.678806i −0.600793 0.799405i 0.705148π-0.705148\pi
0.992701 + 0.120599i 0.0384816π0.0384816\pi
504504 0 0
505505 3825.22 2208.49i 0.337070 0.194607i
506506 0 0
507507 −789.855 + 6543.50i −0.0691887 + 0.573190i
508508 0 0
509509 15791.0 9116.96i 1.37510 0.793914i 0.383534 0.923527i 0.374707π-0.374707\pi
0.991565 + 0.129613i 0.0413735π0.0413735\pi
510510 0 0
511511 2003.89 3470.84i 0.173478 0.300472i
512512 0 0
513513 267.628 + 154.515i 0.0230333 + 0.0132983i
514514 0 0
515515 9851.61i 0.842940i
516516 0 0
517517 212.059 + 367.297i 0.0180394 + 0.0312451i
518518 0 0
519519 9609.85 0.812766
520520 0 0
521521 −7109.30 −0.597819 −0.298910 0.954281i 0.596623π-0.596623\pi
−0.298910 + 0.954281i 0.596623π0.596623\pi
522522 0 0
523523 −999.051 1730.41i −0.0835286 0.144676i 0.821235 0.570591i 0.193286π-0.193286\pi
−0.904763 + 0.425915i 0.859952π0.859952\pi
524524 0 0
525525 1074.91i 0.0893581i
526526 0 0
527527 −10640.4 6143.26i −0.879516 0.507789i
528528 0 0
529529 4685.48 8115.49i 0.385098 0.667009i
530530 0 0
531531 −4956.44 + 2861.60i −0.405068 + 0.233866i
532532 0 0
533533 −10470.9 + 2141.49i −0.850932 + 0.174031i
534534 0 0
535535 −26807.1 + 15477.1i −2.16630 + 1.25071i
536536 0 0
537537 −2336.91 + 4047.65i −0.187794 + 0.325268i
538538 0 0
539539 1112.64 + 642.383i 0.0889142 + 0.0513347i
540540 0 0
541541 12689.9i 1.00847i −0.863567 0.504234i 0.831775π-0.831775\pi
0.863567 0.504234i 0.168225π-0.168225\pi
542542 0 0
543543 6080.81 + 10532.3i 0.480576 + 0.832382i
544544 0 0
545545 −13486.1 −1.05996
546546 0 0
547547 −8535.41 −0.667180 −0.333590 0.942718i 0.608260π-0.608260\pi
−0.333590 + 0.942718i 0.608260π0.608260\pi
548548 0 0
549549 −86.6179 150.027i −0.00673363 0.0116630i
550550 0 0
551551 671.739i 0.0519366i
552552 0 0
553553 1510.71 + 872.206i 0.116169 + 0.0670705i
554554 0 0
555555 870.811 1508.29i 0.0666016 0.115357i
556556 0 0
557557 −22101.0 + 12760.0i −1.68124 + 0.970663i −0.720397 + 0.693561i 0.756041π0.756041\pi
−0.960841 + 0.277102i 0.910626π0.910626\pi
558558 0 0
559559 12492.2 11075.0i 0.945197 0.837965i
560560 0 0
561561 682.981 394.319i 0.0514001 0.0296759i
562562 0 0
563563 −2965.67 + 5136.70i −0.222004 + 0.384522i −0.955416 0.295262i 0.904593π-0.904593\pi
0.733412 + 0.679784i 0.237926π0.237926\pi
564564 0 0
565565 −718.754 414.973i −0.0535190 0.0308992i
566566 0 0
567567 307.125i 0.0227479i
568568 0 0
569569 −3205.89 5552.76i −0.236200 0.409111i 0.723421 0.690407i 0.242569π-0.242569\pi
−0.959621 + 0.281297i 0.909235π0.909235\pi
570570 0 0
571571 4364.14 0.319849 0.159924 0.987129i 0.448875π-0.448875\pi
0.159924 + 0.987129i 0.448875π0.448875\pi
572572 0 0
573573 −8496.63 −0.619462
574574 0 0
575575 −2498.40 4327.36i −0.181201 0.313849i
576576 0 0
577577 9544.78i 0.688656i −0.938849 0.344328i 0.888107π-0.888107\pi
0.938849 0.344328i 0.111893π-0.111893\pi
578578 0 0
579579 1400.67 + 808.678i 0.100535 + 0.0580440i
580580 0 0
581581 −509.540 + 882.549i −0.0363843 + 0.0630195i
582582 0 0
583583 −2176.21 + 1256.43i −0.154596 + 0.0892559i
584584 0 0
585585 4146.09 + 4676.65i 0.293025 + 0.330523i
586586 0 0
587587 −12963.5 + 7484.47i −0.911517 + 0.526264i −0.880919 0.473267i 0.843074π-0.843074\pi
−0.0305979 + 0.999532i 0.509741π0.509741\pi
588588 0 0
589589 1045.70 1811.20i 0.0731531 0.126705i
590590 0 0
591591 −218.723 126.280i −0.0152234 0.00878926i
592592 0 0
593593 22985.5i 1.59174i 0.605468 + 0.795869i 0.292986π0.292986\pi
−0.605468 + 0.795869i 0.707014π0.707014\pi
594594 0 0
595595 −1888.63 3271.20i −0.130128 0.225388i
596596 0 0
597597 16408.4 1.12488
598598 0 0
599599 12936.8 0.882446 0.441223 0.897397i 0.354545π-0.354545\pi
0.441223 + 0.897397i 0.354545π0.354545\pi
600600 0 0
601601 13153.7 + 22782.9i 0.892764 + 1.54631i 0.836547 + 0.547894i 0.184570π0.184570\pi
0.0562168 + 0.998419i 0.482096π0.482096\pi
602602 0 0
603603 4376.30i 0.295550i
604604 0 0
605605 −16881.4 9746.46i −1.13442 0.654959i
606606 0 0
607607 −13036.5 + 22579.9i −0.871722 + 1.50987i −0.0115075 + 0.999934i 0.503663π0.503663\pi
−0.860214 + 0.509933i 0.829670π0.829670\pi
608608 0 0
609609 −578.156 + 333.798i −0.0384697 + 0.0222105i
610610 0 0
611611 −1608.51 + 4823.71i −0.106503 + 0.319389i
612612 0 0
613613 13208.8 7626.08i 0.870305 0.502471i 0.00285537 0.999996i 0.499091π-0.499091\pi
0.867450 + 0.497525i 0.165758π0.165758\pi
614614 0 0
615615 −5067.28 + 8776.78i −0.332248 + 0.575470i
616616 0 0
617617 3054.01 + 1763.23i 0.199270 + 0.115049i 0.596315 0.802751i 0.296631π-0.296631\pi
−0.397045 + 0.917799i 0.629964π0.629964\pi
618618 0 0
619619 9081.76i 0.589704i 0.955543 + 0.294852i 0.0952703π0.0952703\pi
−0.955543 + 0.294852i 0.904730π0.904730\pi
620620 0 0
621621 −713.847 1236.42i −0.0461283 0.0798966i
622622 0 0
623623 2888.29 0.185741
624624 0 0
625625 −18507.4 −1.18447
626626 0 0
627627 67.1204 + 116.256i 0.00427517 + 0.00740481i
628628 0 0
629629 2634.81i 0.167022i
630630 0 0
631631 11545.3 + 6665.70i 0.728387 + 0.420534i 0.817832 0.575457i 0.195176π-0.195176\pi
−0.0894450 + 0.995992i 0.528509π0.528509\pi
632632 0 0
633633 89.2927 154.659i 0.00560674 0.00971116i
634634 0 0
635635 −24606.2 + 14206.4i −1.53774 + 0.887817i
636636 0 0
637637 3086.36 + 15090.9i 0.191972 + 0.938656i
638638 0 0
639639 −2981.52 + 1721.38i −0.184581 + 0.106568i
640640 0 0
641641 2246.03 3890.24i 0.138398 0.239712i −0.788493 0.615044i 0.789138π-0.789138\pi
0.926890 + 0.375333i 0.122472π0.122472\pi
642642 0 0
643643 21952.2 + 12674.1i 1.34636 + 0.777323i 0.987732 0.156156i 0.0499102π-0.0499102\pi
0.358631 + 0.933479i 0.383244π0.383244\pi
644644 0 0
645645 15830.6i 0.966404i
646646 0 0
647647 5405.35 + 9362.34i 0.328449 + 0.568890i 0.982204 0.187816i 0.0601409π-0.0601409\pi
−0.653756 + 0.756706i 0.726808π0.726808\pi
648648 0 0
649649 −2486.12 −0.150368
650650 0 0
651651 −2078.50 −0.125135
652652 0 0
653653 −5024.03 8701.87i −0.301080 0.521486i 0.675301 0.737542i 0.264014π-0.264014\pi
−0.976381 + 0.216056i 0.930680π0.930680\pi
654654 0 0
655655 4574.57i 0.272891i
656656 0 0
657657 8238.49 + 4756.49i 0.489215 + 0.282448i
658658 0 0
659659 10461.2 18119.3i 0.618376 1.07106i −0.371406 0.928471i 0.621124π-0.621124\pi
0.989782 0.142589i 0.0455426π-0.0455426\pi
660660 0 0
661661 −14162.0 + 8176.43i −0.833340 + 0.481129i −0.854995 0.518637i 0.826440π-0.826440\pi
0.0216550 + 0.999766i 0.493106π0.493106\pi
662662 0 0
663663 8969.59 + 2990.98i 0.525415 + 0.175204i
664664 0 0
665665 556.818 321.479i 0.0324699 0.0187465i
666666 0 0
667667 −1551.69 + 2687.60i −0.0900773 + 0.156018i
668668 0 0
669669 12096.7 + 6984.06i 0.699084 + 0.403616i
670670 0 0
671671 75.2525i 0.00432949i
672672 0 0
673673 −8681.74 15037.2i −0.497261 0.861281i 0.502734 0.864441i 0.332327π-0.332327\pi
−0.999995 + 0.00316005i 0.998994π0.998994\pi
674674 0 0
675675 2551.44 0.145489
676676 0 0
677677 −15301.1 −0.868639 −0.434320 0.900759i 0.643011π-0.643011\pi
−0.434320 + 0.900759i 0.643011π0.643011\pi
678678 0 0
679679 −1343.03 2326.20i −0.0759071 0.131475i
680680 0 0
681681 11066.8i 0.622730i
682682 0 0
683683 −3082.15 1779.48i −0.172672 0.0996923i 0.411173 0.911557i 0.365119π-0.365119\pi
−0.583845 + 0.811865i 0.698453π0.698453\pi
684684 0 0
685685 21983.7 38076.8i 1.22621 2.12385i
686686 0 0
687687 9461.39 5462.54i 0.525436 0.303361i
688688 0 0
689689 −28580.1 9530.28i −1.58028 0.526959i
690690 0 0
691691 −15496.5 + 8946.91i −0.853132 + 0.492556i −0.861707 0.507407i 0.830604π-0.830604\pi
0.00857407 + 0.999963i 0.497271π0.497271\pi
692692 0 0
693693 66.7065 115.539i 0.00365652 0.00633328i
694694 0 0
695695 −28979.1 16731.1i −1.58164 0.913160i
696696 0 0
697697 15332.0i 0.833202i
698698 0 0
699699 −6694.47 11595.2i −0.362243 0.627424i
700700 0 0
701701 16354.9 0.881194 0.440597 0.897705i 0.354767π-0.354767\pi
0.440597 + 0.897705i 0.354767π0.354767\pi
702702 0 0
703703 448.493 0.0240615
704704 0 0
705705 2410.84 + 4175.69i 0.128791 + 0.223072i
706706 0 0
707707 1130.42i 0.0601329i
708708 0 0
709709 10044.0 + 5798.90i 0.532031 + 0.307168i 0.741843 0.670573i 0.233952π-0.233952\pi
−0.209812 + 0.977742i 0.567285π0.567285\pi
710710 0 0
711711 −2070.29 + 3585.85i −0.109201 + 0.189142i
712712 0 0
713713 −8367.58 + 4831.02i −0.439507 + 0.253749i
714714 0 0
715715 543.987 + 2659.85i 0.0284531 + 0.139123i
716716 0 0
717717 1671.15 964.839i 0.0870436 0.0502546i
718718 0 0
719719 11713.7 20288.7i 0.607577 1.05235i −0.384062 0.923307i 0.625475π-0.625475\pi
0.991639 0.129047i 0.0411917π-0.0411917\pi
720720 0 0
721721 2183.50 + 1260.64i 0.112785 + 0.0651163i
722722 0 0
723723 14772.5i 0.759883i
724724 0 0
725725 −2773.03 4803.02i −0.142052 0.246041i
726726 0 0
727727 17357.7 0.885503 0.442752 0.896644i 0.354002π-0.354002\pi
0.442752 + 0.896644i 0.354002π0.354002\pi
728728 0 0
729729 729.000 0.0370370
730730 0 0
731731 −11974.7 20740.7i −0.605881 1.04942i
732732 0 0
733733 842.308i 0.0424438i −0.999775 0.0212219i 0.993244π-0.993244\pi
0.999775 0.0212219i 0.00675565π-0.00675565\pi
734734 0 0
735735 12649.3 + 7303.05i 0.634796 + 0.366500i
736736 0 0
737737 −950.517 + 1646.34i −0.0475071 + 0.0822848i
738738 0 0
739739 31137.8 17977.4i 1.54996 0.894873i 0.551822 0.833962i 0.313933π-0.313933\pi
0.998143 0.0609105i 0.0194004π-0.0194004\pi
740740 0 0
741741 −509.120 + 1526.79i −0.0252402 + 0.0756923i
742742 0 0
743743 9844.48 5683.72i 0.486082 0.280640i −0.236865 0.971542i 0.576120π-0.576120\pi
0.722948 + 0.690903i 0.242787π0.242787\pi
744744 0 0
745745 −3473.44 + 6016.18i −0.170815 + 0.295860i
746746 0 0
747747 −2094.84 1209.46i −0.102605 0.0592393i
748748 0 0
749749 7921.98i 0.386466i
750750 0 0
751751 −6487.12 11236.0i −0.315204 0.545950i 0.664277 0.747487i 0.268740π-0.268740\pi
−0.979481 + 0.201537i 0.935406π0.935406\pi
752752 0 0
753753 8960.53 0.433652
754754 0 0
755755 31755.7 1.53074
756756 0 0
757757 1209.83 + 2095.49i 0.0580872 + 0.100610i 0.893607 0.448851i 0.148167π-0.148167\pi
−0.835520 + 0.549461i 0.814833π0.814833\pi
758758 0 0
759759 620.180i 0.0296589i
760760 0 0
761761 24443.6 + 14112.5i 1.16436 + 0.672246i 0.952346 0.305020i 0.0986631π-0.0986631\pi
0.212018 + 0.977266i 0.431996π0.431996\pi
762762 0 0
763763 −1725.72 + 2989.03i −0.0818811 + 0.141822i
764764 0 0
765765 7764.60 4482.90i 0.366967 0.211869i
766766 0 0
767767 −19773.2 22303.6i −0.930861 1.04998i
768768 0 0
769769 14068.7 8122.55i 0.659726 0.380893i −0.132447 0.991190i 0.542283π-0.542283\pi
0.792172 + 0.610297i 0.208950π0.208950\pi
770770 0 0
771771 −471.585 + 816.810i −0.0220282 + 0.0381539i
772772 0 0
773773 1680.27 + 970.103i 0.0781824 + 0.0451387i 0.538582 0.842573i 0.318960π-0.318960\pi
−0.460399 + 0.887712i 0.652294π0.652294\pi
774774 0 0
775775 17267.1i 0.800326i
776776 0 0
777777 −222.864 386.011i −0.0102898 0.0178225i
778778 0 0
779779 −2609.79 −0.120033
780780 0 0
781781 −1495.51 −0.0685193
782782 0 0
783783 −792.312 1372.33i −0.0361621 0.0626346i
784784 0 0
785785 10386.3i 0.472233i
786786 0 0
787787 17188.1 + 9923.54i 0.778512 + 0.449474i 0.835903 0.548878i 0.184945π-0.184945\pi
−0.0573908 + 0.998352i 0.518278π0.518278\pi
788788 0 0
789789 −1693.79 + 2933.72i −0.0764263 + 0.132374i
790790 0 0
791791 −183.948 + 106.203i −0.00826858 + 0.00477387i
792792 0 0
793793 675.107 598.517i 0.0302317 0.0268020i
794794 0 0
795795 −24740.6 + 14284.0i −1.10372 + 0.637235i
796796 0 0
797797 −17877.2 + 30964.2i −0.794533 + 1.37617i 0.128601 + 0.991696i 0.458951π0.458951\pi
−0.923135 + 0.384476i 0.874382π0.874382\pi
798798 0 0
799799 6317.18 + 3647.22i 0.279707 + 0.161489i
800800 0 0
801801 6855.71i 0.302415i
802802 0 0
803803 2066.19 + 3578.74i 0.0908023 + 0.157274i
804804 0 0
805805 −2970.41 −0.130054
806806 0 0
807807 −267.168 −0.0116540
808808 0 0
809809 1708.12 + 2958.56i 0.0742329 + 0.128575i 0.900752 0.434333i 0.143016π-0.143016\pi
−0.826520 + 0.562908i 0.809683π0.809683\pi
810810 0 0
811811 26171.6i 1.13318i −0.823999 0.566591i 0.808262π-0.808262\pi
0.823999 0.566591i 0.191738π-0.191738\pi
812812 0 0
813813 13694.2 + 7906.36i 0.590747 + 0.341068i
814814 0 0
815815 22717.0 39347.0i 0.976370 1.69112i
816816 0 0
817817 3530.45 2038.31i 0.151181 0.0872845i
818818 0 0
819819 1567.07 320.495i 0.0668596 0.0136740i
820820 0 0
821821 34547.3 19945.9i 1.46859 0.847889i 0.469206 0.883089i 0.344540π-0.344540\pi
0.999380 + 0.0352001i 0.0112069π0.0112069\pi
822822 0 0
823823 −18207.2 + 31535.8i −0.771157 + 1.33568i 0.165772 + 0.986164i 0.446989π0.446989\pi
−0.936929 + 0.349520i 0.886345π0.886345\pi
824824 0 0
825825 959.840 + 554.164i 0.0405059 + 0.0233861i
826826 0 0
827827 43200.2i 1.81647i 0.418464 + 0.908234i 0.362569π0.362569\pi
−0.418464 + 0.908234i 0.637431π0.637431\pi
828828 0 0
829829 −11372.3 19697.3i −0.476447 0.825231i 0.523188 0.852217i 0.324742π-0.324742\pi
−0.999636 + 0.0269858i 0.991409π0.991409\pi
830830 0 0
831831 −13043.8 −0.544506
832832 0 0
833833 22096.8 0.919098
834834 0 0
835835 −17838.4 30897.0i −0.739310 1.28052i
836836 0 0
837837 4933.57i 0.203739i
838838 0 0
839839 14931.8 + 8620.89i 0.614426 + 0.354739i 0.774696 0.632334i 0.217903π-0.217903\pi
−0.160270 + 0.987073i 0.551236π0.551236\pi
840840 0 0
841841 10472.3 18138.5i 0.429384 0.743715i
842842 0 0
843843 −8799.17 + 5080.20i −0.359501 + 0.207558i
844844 0 0
845845 −19535.6 + 26035.3i −0.795319 + 1.05993i
846846 0 0
847847 −4320.39 + 2494.38i −0.175266 + 0.101190i
848848 0 0
849849 −3137.53 + 5434.36i −0.126831 + 0.219678i
850850 0 0
851851 −1794.40 1036.00i −0.0722812 0.0417316i
852852 0 0
853853 25949.7i 1.04162i −0.853673 0.520809i 0.825630π-0.825630\pi
0.853673 0.520809i 0.174370π-0.174370\pi
854854 0 0
855855 763.072 + 1321.68i 0.0305222 + 0.0528660i
856856 0 0
857857 −43312.3 −1.72640 −0.863198 0.504866i 0.831542π-0.831542\pi
−0.863198 + 0.504866i 0.831542π0.831542\pi
858858 0 0
859859 −30465.4 −1.21009 −0.605045 0.796191i 0.706845π-0.706845\pi
−0.605045 + 0.796191i 0.706845π0.706845\pi
860860 0 0
861861 1296.85 + 2246.21i 0.0513316 + 0.0889090i
862862 0 0
863863 34192.7i 1.34871i −0.738409 0.674354i 0.764422π-0.764422\pi
0.738409 0.674354i 0.235578π-0.235578\pi
864864 0 0
865865 41099.9 + 23729.0i 1.61554 + 0.932730i
866866 0 0
867867 −587.565 + 1017.69i −0.0230159 + 0.0398647i
868868 0 0
869869 −1557.67 + 899.321i −0.0608059 + 0.0351063i
870870 0 0
871871 −22329.6 + 4566.81i −0.868669 + 0.177658i
872872 0 0
873873 5521.54 3187.86i 0.214062 0.123589i
874874 0 0
875875 −856.737 + 1483.91i −0.0331006 + 0.0573319i
876876 0 0
877877 −17808.5 10281.7i −0.685690 0.395884i 0.116305 0.993214i 0.462895π-0.462895\pi
−0.801996 + 0.597330i 0.796228π0.796228\pi
878878 0 0
879879 7073.42i 0.271423i
880880 0 0
881881 8859.76 + 15345.6i 0.338812 + 0.586839i 0.984209 0.177008i 0.0566418π-0.0566418\pi
−0.645398 + 0.763847i 0.723308π0.723308\pi
882882 0 0
883883 35140.1 1.33925 0.669625 0.742699i 0.266455π-0.266455\pi
0.669625 + 0.742699i 0.266455π0.266455\pi
884884 0 0
885885 −28264.0 −1.07354
886886 0 0
887887 −18493.9 32032.4i −0.700072 1.21256i −0.968441 0.249244i 0.919818π-0.919818\pi
0.268368 0.963316i 0.413516π-0.413516\pi
888888 0 0
889889 7271.58i 0.274332i
890890 0 0
891891 274.247 + 158.336i 0.0103116 + 0.00595339i
892892 0 0
893893 −620.825 + 1075.30i −0.0232644 + 0.0402951i
894894 0 0
895895 −19989.3 + 11540.8i −0.746555 + 0.431024i
896896 0 0
897897 5563.78 4932.58i 0.207101 0.183605i
898898 0 0
899899 −9287.34 + 5362.05i −0.344550 + 0.198926i
900900 0 0
901901 −21609.5 + 37428.8i −0.799021 + 1.38394i
902902 0 0
903903 −3508.68 2025.74i −0.129304 0.0746538i
904904 0 0
905905 60060.0i 2.20604i
906906 0 0
907907 1163.43 + 2015.11i 0.0425920 + 0.0737715i 0.886536 0.462661i 0.153105π-0.153105\pi
−0.843944 + 0.536432i 0.819772π0.819772\pi
908908 0 0
909909 2683.20 0.0979057
910910 0 0
911911 34700.9 1.26201 0.631005 0.775779i 0.282643π-0.282643\pi
0.631005 + 0.775779i 0.282643π0.282643\pi
912912 0 0
913913 −525.380 909.985i −0.0190444 0.0329859i
914914 0 0
915915 855.522i 0.0309101i
916916 0 0
917917 −1013.90 585.377i −0.0365126 0.0210805i
918918 0 0
919919 −15829.7 + 27417.9i −0.568199 + 0.984149i 0.428546 + 0.903520i 0.359026π0.359026\pi
−0.996744 + 0.0806286i 0.974307π0.974307\pi
920920 0 0
921921 17506.3 10107.3i 0.626334 0.361614i
922922 0 0
923923 −11894.5 13416.6i −0.424173 0.478453i
924924 0 0
925925 3206.78 1851.44i 0.113987 0.0658107i
926926 0 0
927927 −2992.30 + 5182.81i −0.106019 + 0.183631i
928928 0 0
929929 34177.5 + 19732.4i 1.20703 + 0.696877i 0.962109 0.272667i 0.0879056π-0.0879056\pi
0.244918 + 0.969544i 0.421239π0.421239\pi
930930 0 0
931931 3761.28i 0.132407i
932932 0 0
933933 −13194.2 22853.1i −0.462979 0.801904i
934934 0 0
935935 3894.68 0.136224
936936 0 0
937937 −572.068 −0.0199452 −0.00997260 0.999950i 0.503174π-0.503174\pi
−0.00997260 + 0.999950i 0.503174π0.503174\pi
938938 0 0
939939 −1930.05 3342.94i −0.0670764 0.116180i
940940 0 0
941941 26136.2i 0.905437i 0.891654 + 0.452718i 0.149546π0.149546\pi
−0.891654 + 0.452718i 0.850454π0.850454\pi
942942 0 0
943943 10441.7 + 6028.51i 0.360581 + 0.208182i
944944 0 0
945945 758.366 1313.53i 0.0261054 0.0452160i
946946 0 0
947947 −8465.13 + 4887.34i −0.290475 + 0.167706i −0.638156 0.769907i 0.720303π-0.720303\pi
0.347681 + 0.937613i 0.386969π0.386969\pi
948948 0 0
949949 −15672.4 + 46999.6i −0.536089 + 1.60766i
950950 0 0
951951 −27785.5 + 16042.0i −0.947431 + 0.547000i
952952 0 0
953953 18961.0 32841.4i 0.644498 1.11630i −0.339919 0.940455i 0.610400π-0.610400\pi
0.984417 0.175849i 0.0562670π-0.0562670\pi
954954 0 0
955955 −36338.9 20980.2i −1.23131 0.710895i
956956 0 0
957957 688.350i 0.0232510i
958958 0 0
959959 −5626.20 9744.86i −0.189447 0.328131i
960960 0 0
961961 −3597.42 −0.120755
962962 0 0
963963 −18803.8 −0.629226
964964 0 0
965965 3993.64 + 6917.19i 0.133223 + 0.230749i
966966 0 0
967967 23198.3i 0.771467i 0.922610 + 0.385733i 0.126052π0.126052\pi
−0.922610 + 0.385733i 0.873948π0.873948\pi
968968 0 0
969969 1999.50 + 1154.41i 0.0662880 + 0.0382714i
970970 0 0
971971 17277.8 29926.0i 0.571030 0.989053i −0.425430 0.904991i 0.639877π-0.639877\pi
0.996461 0.0840622i 0.0267894π-0.0267894\pi
972972 0 0
973973 −7416.52 + 4281.93i −0.244360 + 0.141082i
974974 0 0
975975 2662.51 + 13018.5i 0.0874549 + 0.427615i
976976 0 0
977977 26697.5 15413.8i 0.874236 0.504740i 0.00548232 0.999985i 0.498255π-0.498255\pi
0.868754 + 0.495245i 0.164922π0.164922\pi
978978 0 0
979979 −1489.04 + 2579.09i −0.0486107 + 0.0841961i
980980 0 0
981981 −7094.85 4096.21i −0.230908 0.133315i
982982 0 0
983983 35014.7i 1.13611i 0.822990 + 0.568055i 0.192304π0.192304\pi
−0.822990 + 0.568055i 0.807696π0.807696\pi
984984 0 0
985985 −623.630 1080.16i −0.0201731 0.0349408i
986986 0 0
987987 1233.99 0.0397958
988988 0 0
989989 −18833.6 −0.605535
990990 0 0
991991 −21702.4 37589.7i −0.695661 1.20492i −0.969957 0.243275i 0.921778π-0.921778\pi
0.274297 0.961645i 0.411555π-0.411555\pi
992992 0 0
993993 12491.4i 0.399198i
994994 0 0
995995 70176.3 + 40516.3i 2.23592 + 1.29091i
996996 0 0
997997 −11481.0 + 19885.6i −0.364700 + 0.631679i −0.988728 0.149723i 0.952162π-0.952162\pi
0.624028 + 0.781402i 0.285495π0.285495\pi
998998 0 0
999999 916.246 528.995i 0.0290178 0.0167534i
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 156.4.q.c.49.3 6
3.2 odd 2 468.4.t.f.361.1 6
4.3 odd 2 624.4.bv.f.49.3 6
13.2 odd 12 2028.4.a.o.1.6 6
13.3 even 3 2028.4.b.h.337.6 6
13.4 even 6 inner 156.4.q.c.121.1 yes 6
13.10 even 6 2028.4.b.h.337.1 6
13.11 odd 12 2028.4.a.o.1.1 6
39.17 odd 6 468.4.t.f.433.3 6
52.43 odd 6 624.4.bv.f.433.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.4.q.c.49.3 6 1.1 even 1 trivial
156.4.q.c.121.1 yes 6 13.4 even 6 inner
468.4.t.f.361.1 6 3.2 odd 2
468.4.t.f.433.3 6 39.17 odd 6
624.4.bv.f.49.3 6 4.3 odd 2
624.4.bv.f.433.1 6 52.43 odd 6
2028.4.a.o.1.1 6 13.11 odd 12
2028.4.a.o.1.6 6 13.2 odd 12
2028.4.b.h.337.1 6 13.10 even 6
2028.4.b.h.337.6 6 13.3 even 3