Properties

Label 350.4.c.b.99.1
Level 350350
Weight 44
Character 350.99
Analytic conductor 20.65120.651
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,4,Mod(99,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.99");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 350=2527 350 = 2 \cdot 5^{2} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 350.c (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 20.650668502020.6506685020
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 99.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 350.99
Dual form 350.4.c.b.99.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q2.00000iq28.00000iq34.00000q416.0000q67.00000iq7+8.00000iq837.0000q928.0000q11+32.0000iq1218.0000iq1314.0000q14+16.0000q16+74.0000iq17+74.0000iq1880.0000q1956.0000q21+56.0000iq22+112.000iq23+64.0000q2436.0000q26+80.0000iq27+28.0000iq28190.000q29+72.0000q3132.0000iq32+224.000iq33+148.000q34+148.000q36346.000iq37+160.000iq38144.000q39+162.000q41+112.000iq42+412.000iq43+112.000q44+224.000q46+24.0000iq47128.000iq4849.0000q49+592.000q51+72.0000iq52318.000iq53+160.000q54+56.0000q56+640.000iq57+380.000iq58+200.000q59198.000q61144.000iq62+259.000iq6364.0000q64+448.000q66716.000iq67296.000iq68+896.000q69+392.000q71296.000iq72538.000iq73692.000q74+320.000q76+196.000iq77+288.000iq78240.000q79359.000q81324.000iq82+1072.00iq83+224.000q84+824.000q86+1520.00iq87224.000iq88810.000q89126.000q91448.000iq92576.000iq93+48.0000q94256.000q96+1354.00iq97+98.0000iq98+1036.00q99+O(q100)q-2.00000i q^{2} -8.00000i q^{3} -4.00000 q^{4} -16.0000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -37.0000 q^{9} -28.0000 q^{11} +32.0000i q^{12} -18.0000i q^{13} -14.0000 q^{14} +16.0000 q^{16} +74.0000i q^{17} +74.0000i q^{18} -80.0000 q^{19} -56.0000 q^{21} +56.0000i q^{22} +112.000i q^{23} +64.0000 q^{24} -36.0000 q^{26} +80.0000i q^{27} +28.0000i q^{28} -190.000 q^{29} +72.0000 q^{31} -32.0000i q^{32} +224.000i q^{33} +148.000 q^{34} +148.000 q^{36} -346.000i q^{37} +160.000i q^{38} -144.000 q^{39} +162.000 q^{41} +112.000i q^{42} +412.000i q^{43} +112.000 q^{44} +224.000 q^{46} +24.0000i q^{47} -128.000i q^{48} -49.0000 q^{49} +592.000 q^{51} +72.0000i q^{52} -318.000i q^{53} +160.000 q^{54} +56.0000 q^{56} +640.000i q^{57} +380.000i q^{58} +200.000 q^{59} -198.000 q^{61} -144.000i q^{62} +259.000i q^{63} -64.0000 q^{64} +448.000 q^{66} -716.000i q^{67} -296.000i q^{68} +896.000 q^{69} +392.000 q^{71} -296.000i q^{72} -538.000i q^{73} -692.000 q^{74} +320.000 q^{76} +196.000i q^{77} +288.000i q^{78} -240.000 q^{79} -359.000 q^{81} -324.000i q^{82} +1072.00i q^{83} +224.000 q^{84} +824.000 q^{86} +1520.00i q^{87} -224.000i q^{88} -810.000 q^{89} -126.000 q^{91} -448.000i q^{92} -576.000i q^{93} +48.0000 q^{94} -256.000 q^{96} +1354.00i q^{97} +98.0000i q^{98} +1036.00 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q8q432q674q956q1128q14+32q16160q19112q21+128q2472q26380q29+144q31+296q34+296q36288q39+324q41+224q44++2072q99+O(q100) 2 q - 8 q^{4} - 32 q^{6} - 74 q^{9} - 56 q^{11} - 28 q^{14} + 32 q^{16} - 160 q^{19} - 112 q^{21} + 128 q^{24} - 72 q^{26} - 380 q^{29} + 144 q^{31} + 296 q^{34} + 296 q^{36} - 288 q^{39} + 324 q^{41} + 224 q^{44}+ \cdots + 2072 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/350Z)×\left(\mathbb{Z}/350\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) 11 1-1

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 − 2.00000i − 0.707107i
33 − 8.00000i − 1.53960i −0.638285 0.769800i 0.720356π-0.720356\pi
0.638285 0.769800i 0.279644π-0.279644\pi
44 −4.00000 −0.500000
55 0 0
66 −16.0000 −1.08866
77 − 7.00000i − 0.377964i
88 8.00000i 0.353553i
99 −37.0000 −1.37037
1010 0 0
1111 −28.0000 −0.767483 −0.383742 0.923440i 0.625365π-0.625365\pi
−0.383742 + 0.923440i 0.625365π0.625365\pi
1212 32.0000i 0.769800i
1313 − 18.0000i − 0.384023i −0.981393 0.192012i 0.938499π-0.938499\pi
0.981393 0.192012i 0.0615011π-0.0615011\pi
1414 −14.0000 −0.267261
1515 0 0
1616 16.0000 0.250000
1717 74.0000i 1.05574i 0.849324 + 0.527872i 0.177010π0.177010\pi
−0.849324 + 0.527872i 0.822990π0.822990\pi
1818 74.0000i 0.968998i
1919 −80.0000 −0.965961 −0.482980 0.875631i 0.660446π-0.660446\pi
−0.482980 + 0.875631i 0.660446π0.660446\pi
2020 0 0
2121 −56.0000 −0.581914
2222 56.0000i 0.542693i
2323 112.000i 1.01537i 0.861541 + 0.507687i 0.169499π0.169499\pi
−0.861541 + 0.507687i 0.830501π0.830501\pi
2424 64.0000 0.544331
2525 0 0
2626 −36.0000 −0.271545
2727 80.0000i 0.570222i
2828 28.0000i 0.188982i
2929 −190.000 −1.21662 −0.608312 0.793698i 0.708153π-0.708153\pi
−0.608312 + 0.793698i 0.708153π0.708153\pi
3030 0 0
3131 72.0000 0.417148 0.208574 0.978007i 0.433118π-0.433118\pi
0.208574 + 0.978007i 0.433118π0.433118\pi
3232 − 32.0000i − 0.176777i
3333 224.000i 1.18162i
3434 148.000 0.746523
3535 0 0
3636 148.000 0.685185
3737 − 346.000i − 1.53735i −0.639638 0.768676i 0.720916π-0.720916\pi
0.639638 0.768676i 0.279084π-0.279084\pi
3838 160.000i 0.683038i
3939 −144.000 −0.591242
4040 0 0
4141 162.000 0.617077 0.308538 0.951212i 0.400160π-0.400160\pi
0.308538 + 0.951212i 0.400160π0.400160\pi
4242 112.000i 0.411476i
4343 412.000i 1.46115i 0.682833 + 0.730575i 0.260748π0.260748\pi
−0.682833 + 0.730575i 0.739252π0.739252\pi
4444 112.000 0.383742
4545 0 0
4646 224.000 0.717978
4747 24.0000i 0.0744843i 0.999306 + 0.0372421i 0.0118573π0.0118573\pi
−0.999306 + 0.0372421i 0.988143π0.988143\pi
4848 − 128.000i − 0.384900i
4949 −49.0000 −0.142857
5050 0 0
5151 592.000 1.62542
5252 72.0000i 0.192012i
5353 − 318.000i − 0.824163i −0.911147 0.412082i 0.864802π-0.864802\pi
0.911147 0.412082i 0.135198π-0.135198\pi
5454 160.000 0.403208
5555 0 0
5656 56.0000 0.133631
5757 640.000i 1.48719i
5858 380.000i 0.860284i
5959 200.000 0.441318 0.220659 0.975351i 0.429179π-0.429179\pi
0.220659 + 0.975351i 0.429179π0.429179\pi
6060 0 0
6161 −198.000 −0.415595 −0.207798 0.978172i 0.566630π-0.566630\pi
−0.207798 + 0.978172i 0.566630π0.566630\pi
6262 − 144.000i − 0.294968i
6363 259.000i 0.517951i
6464 −64.0000 −0.125000
6565 0 0
6666 448.000 0.835530
6767 − 716.000i − 1.30557i −0.757542 0.652786i 0.773600π-0.773600\pi
0.757542 0.652786i 0.226400π-0.226400\pi
6868 − 296.000i − 0.527872i
6969 896.000 1.56327
7070 0 0
7171 392.000 0.655237 0.327619 0.944810i 0.393754π-0.393754\pi
0.327619 + 0.944810i 0.393754π0.393754\pi
7272 − 296.000i − 0.484499i
7373 − 538.000i − 0.862577i −0.902214 0.431289i 0.858059π-0.858059\pi
0.902214 0.431289i 0.141941π-0.141941\pi
7474 −692.000 −1.08707
7575 0 0
7676 320.000 0.482980
7777 196.000i 0.290081i
7878 288.000i 0.418072i
7979 −240.000 −0.341799 −0.170899 0.985288i 0.554667π-0.554667\pi
−0.170899 + 0.985288i 0.554667π0.554667\pi
8080 0 0
8181 −359.000 −0.492455
8282 − 324.000i − 0.436339i
8383 1072.00i 1.41768i 0.705370 + 0.708839i 0.250781π0.250781\pi
−0.705370 + 0.708839i 0.749219π0.749219\pi
8484 224.000 0.290957
8585 0 0
8686 824.000 1.03319
8787 1520.00i 1.87312i
8888 − 224.000i − 0.271346i
8989 −810.000 −0.964717 −0.482359 0.875974i 0.660220π-0.660220\pi
−0.482359 + 0.875974i 0.660220π0.660220\pi
9090 0 0
9191 −126.000 −0.145147
9292 − 448.000i − 0.507687i
9393 − 576.000i − 0.642241i
9494 48.0000 0.0526683
9595 0 0
9696 −256.000 −0.272166
9797 1354.00i 1.41730i 0.705561 + 0.708649i 0.250695π0.250695\pi
−0.705561 + 0.708649i 0.749305π0.749305\pi
9898 98.0000i 0.101015i
9999 1036.00 1.05174
100100 0 0
101101 −1358.00 −1.33788 −0.668941 0.743316i 0.733252π-0.733252\pi
−0.668941 + 0.743316i 0.733252π0.733252\pi
102102 − 1184.00i − 1.14935i
103103 832.000i 0.795916i 0.917404 + 0.397958i 0.130281π0.130281\pi
−0.917404 + 0.397958i 0.869719π0.869719\pi
104104 144.000 0.135773
105105 0 0
106106 −636.000 −0.582772
107107 444.000i 0.401150i 0.979678 + 0.200575i 0.0642811π0.0642811\pi
−0.979678 + 0.200575i 0.935719π0.935719\pi
108108 − 320.000i − 0.285111i
109109 −1870.00 −1.64324 −0.821622 0.570033i 0.806930π-0.806930\pi
−0.821622 + 0.570033i 0.806930π0.806930\pi
110110 0 0
111111 −2768.00 −2.36691
112112 − 112.000i − 0.0944911i
113113 − 1378.00i − 1.14718i −0.819143 0.573590i 0.805550π-0.805550\pi
0.819143 0.573590i 0.194450π-0.194450\pi
114114 1280.00 1.05161
115115 0 0
116116 760.000 0.608312
117117 666.000i 0.526254i
118118 − 400.000i − 0.312059i
119119 518.000 0.399033
120120 0 0
121121 −547.000 −0.410969
122122 396.000i 0.293870i
123123 − 1296.00i − 0.950052i
124124 −288.000 −0.208574
125125 0 0
126126 518.000 0.366247
127127 1944.00i 1.35828i 0.734007 + 0.679142i 0.237648π0.237648\pi
−0.734007 + 0.679142i 0.762352π0.762352\pi
128128 128.000i 0.0883883i
129129 3296.00 2.24959
130130 0 0
131131 −848.000 −0.565573 −0.282787 0.959183i 0.591259π-0.591259\pi
−0.282787 + 0.959183i 0.591259π0.591259\pi
132132 − 896.000i − 0.590809i
133133 560.000i 0.365099i
134134 −1432.00 −0.923179
135135 0 0
136136 −592.000 −0.373262
137137 − 2966.00i − 1.84965i −0.380389 0.924827i 0.624210π-0.624210\pi
0.380389 0.924827i 0.375790π-0.375790\pi
138138 − 1792.00i − 1.10540i
139139 −2800.00 −1.70858 −0.854291 0.519795i 0.826008π-0.826008\pi
−0.854291 + 0.519795i 0.826008π0.826008\pi
140140 0 0
141141 192.000 0.114676
142142 − 784.000i − 0.463323i
143143 504.000i 0.294731i
144144 −592.000 −0.342593
145145 0 0
146146 −1076.00 −0.609934
147147 392.000i 0.219943i
148148 1384.00i 0.768676i
149149 −510.000 −0.280408 −0.140204 0.990123i 0.544776π-0.544776\pi
−0.140204 + 0.990123i 0.544776π0.544776\pi
150150 0 0
151151 592.000 0.319048 0.159524 0.987194i 0.449004π-0.449004\pi
0.159524 + 0.987194i 0.449004π0.449004\pi
152152 − 640.000i − 0.341519i
153153 − 2738.00i − 1.44676i
154154 392.000 0.205119
155155 0 0
156156 576.000 0.295621
157157 − 2686.00i − 1.36539i −0.730704 0.682695i 0.760808π-0.760808\pi
0.730704 0.682695i 0.239192π-0.239192\pi
158158 480.000i 0.241688i
159159 −2544.00 −1.26888
160160 0 0
161161 784.000 0.383776
162162 718.000i 0.348219i
163163 1012.00i 0.486294i 0.969989 + 0.243147i 0.0781798π0.0781798\pi
−0.969989 + 0.243147i 0.921820π0.921820\pi
164164 −648.000 −0.308538
165165 0 0
166166 2144.00 1.00245
167167 544.000i 0.252072i 0.992026 + 0.126036i 0.0402254π0.0402254\pi
−0.992026 + 0.126036i 0.959775π0.959775\pi
168168 − 448.000i − 0.205738i
169169 1873.00 0.852526
170170 0 0
171171 2960.00 1.32372
172172 − 1648.00i − 0.730575i
173173 − 1858.00i − 0.816538i −0.912862 0.408269i 0.866132π-0.866132\pi
0.912862 0.408269i 0.133868π-0.133868\pi
174174 3040.00 1.32449
175175 0 0
176176 −448.000 −0.191871
177177 − 1600.00i − 0.679454i
178178 1620.00i 0.682158i
179179 300.000 0.125268 0.0626342 0.998037i 0.480050π-0.480050\pi
0.0626342 + 0.998037i 0.480050π0.480050\pi
180180 0 0
181181 −2358.00 −0.968336 −0.484168 0.874975i 0.660878π-0.660878\pi
−0.484168 + 0.874975i 0.660878π0.660878\pi
182182 252.000i 0.102635i
183183 1584.00i 0.639851i
184184 −896.000 −0.358989
185185 0 0
186186 −1152.00 −0.454133
187187 − 2072.00i − 0.810265i
188188 − 96.0000i − 0.0372421i
189189 560.000 0.215524
190190 0 0
191191 1392.00 0.527338 0.263669 0.964613i 0.415067π-0.415067\pi
0.263669 + 0.964613i 0.415067π0.415067\pi
192192 512.000i 0.192450i
193193 − 1778.00i − 0.663126i −0.943433 0.331563i 0.892424π-0.892424\pi
0.943433 0.331563i 0.107576π-0.107576\pi
194194 2708.00 1.00218
195195 0 0
196196 196.000 0.0714286
197197 1214.00i 0.439055i 0.975606 + 0.219528i 0.0704516π0.0704516\pi
−0.975606 + 0.219528i 0.929548π0.929548\pi
198198 − 2072.00i − 0.743690i
199199 −1040.00 −0.370471 −0.185235 0.982694i 0.559305π-0.559305\pi
−0.185235 + 0.982694i 0.559305π0.559305\pi
200200 0 0
201201 −5728.00 −2.01006
202202 2716.00i 0.946025i
203203 1330.00i 0.459841i
204204 −2368.00 −0.812712
205205 0 0
206206 1664.00 0.562798
207207 − 4144.00i − 1.39144i
208208 − 288.000i − 0.0960058i
209209 2240.00 0.741359
210210 0 0
211211 −3868.00 −1.26201 −0.631005 0.775779i 0.717357π-0.717357\pi
−0.631005 + 0.775779i 0.717357π0.717357\pi
212212 1272.00i 0.412082i
213213 − 3136.00i − 1.00880i
214214 888.000 0.283656
215215 0 0
216216 −640.000 −0.201604
217217 − 504.000i − 0.157667i
218218 3740.00i 1.16195i
219219 −4304.00 −1.32802
220220 0 0
221221 1332.00 0.405430
222222 5536.00i 1.67366i
223223 − 3968.00i − 1.19156i −0.803149 0.595778i 0.796844π-0.796844\pi
0.803149 0.595778i 0.203156π-0.203156\pi
224224 −224.000 −0.0668153
225225 0 0
226226 −2756.00 −0.811179
227227 − 3936.00i − 1.15084i −0.817857 0.575422i 0.804838π-0.804838\pi
0.817857 0.575422i 0.195162π-0.195162\pi
228228 − 2560.00i − 0.743597i
229229 −4810.00 −1.38801 −0.694004 0.719971i 0.744155π-0.744155\pi
−0.694004 + 0.719971i 0.744155π0.744155\pi
230230 0 0
231231 1568.00 0.446610
232232 − 1520.00i − 0.430142i
233233 2182.00i 0.613509i 0.951789 + 0.306754i 0.0992430π0.0992430\pi
−0.951789 + 0.306754i 0.900757π0.900757\pi
234234 1332.00 0.372118
235235 0 0
236236 −800.000 −0.220659
237237 1920.00i 0.526234i
238238 − 1036.00i − 0.282159i
239239 3000.00 0.811941 0.405970 0.913886i 0.366934π-0.366934\pi
0.405970 + 0.913886i 0.366934π0.366934\pi
240240 0 0
241241 2042.00 0.545796 0.272898 0.962043i 0.412018π-0.412018\pi
0.272898 + 0.962043i 0.412018π0.412018\pi
242242 1094.00i 0.290599i
243243 5032.00i 1.32841i
244244 792.000 0.207798
245245 0 0
246246 −2592.00 −0.671788
247247 1440.00i 0.370951i
248248 576.000i 0.147484i
249249 8576.00 2.18266
250250 0 0
251251 −528.000 −0.132777 −0.0663886 0.997794i 0.521148π-0.521148\pi
−0.0663886 + 0.997794i 0.521148π0.521148\pi
252252 − 1036.00i − 0.258976i
253253 − 3136.00i − 0.779283i
254254 3888.00 0.960452
255255 0 0
256256 256.000 0.0625000
257257 5634.00i 1.36747i 0.729731 + 0.683734i 0.239645π0.239645\pi
−0.729731 + 0.683734i 0.760355π0.760355\pi
258258 − 6592.00i − 1.59070i
259259 −2422.00 −0.581065
260260 0 0
261261 7030.00 1.66723
262262 1696.00i 0.399921i
263263 − 168.000i − 0.0393891i −0.999806 0.0196945i 0.993731π-0.993731\pi
0.999806 0.0196945i 0.00626937π-0.00626937\pi
264264 −1792.00 −0.417765
265265 0 0
266266 1120.00 0.258164
267267 6480.00i 1.48528i
268268 2864.00i 0.652786i
269269 1310.00 0.296922 0.148461 0.988918i 0.452568π-0.452568\pi
0.148461 + 0.988918i 0.452568π0.452568\pi
270270 0 0
271271 −2208.00 −0.494932 −0.247466 0.968897i 0.579598π-0.579598\pi
−0.247466 + 0.968897i 0.579598π0.579598\pi
272272 1184.00i 0.263936i
273273 1008.00i 0.223469i
274274 −5932.00 −1.30790
275275 0 0
276276 −3584.00 −0.781636
277277 5294.00i 1.14832i 0.818742 + 0.574162i 0.194672π0.194672\pi
−0.818742 + 0.574162i 0.805328π0.805328\pi
278278 5600.00i 1.20815i
279279 −2664.00 −0.571647
280280 0 0
281281 3242.00 0.688262 0.344131 0.938922i 0.388174π-0.388174\pi
0.344131 + 0.938922i 0.388174π0.388174\pi
282282 − 384.000i − 0.0810882i
283283 1592.00i 0.334398i 0.985923 + 0.167199i 0.0534722π0.0534722\pi
−0.985923 + 0.167199i 0.946528π0.946528\pi
284284 −1568.00 −0.327619
285285 0 0
286286 1008.00 0.208407
287287 − 1134.00i − 0.233233i
288288 1184.00i 0.242250i
289289 −563.000 −0.114594
290290 0 0
291291 10832.0 2.18207
292292 2152.00i 0.431289i
293293 5022.00i 1.00133i 0.865642 + 0.500663i 0.166910π0.166910\pi
−0.865642 + 0.500663i 0.833090π0.833090\pi
294294 784.000 0.155523
295295 0 0
296296 2768.00 0.543536
297297 − 2240.00i − 0.437636i
298298 1020.00i 0.198279i
299299 2016.00 0.389927
300300 0 0
301301 2884.00 0.552262
302302 − 1184.00i − 0.225601i
303303 10864.0i 2.05980i
304304 −1280.00 −0.241490
305305 0 0
306306 −5476.00 −1.02301
307307 − 9536.00i − 1.77280i −0.462924 0.886398i 0.653200π-0.653200\pi
0.462924 0.886398i 0.346800π-0.346800\pi
308308 − 784.000i − 0.145041i
309309 6656.00 1.22539
310310 0 0
311311 −968.000 −0.176496 −0.0882480 0.996099i 0.528127π-0.528127\pi
−0.0882480 + 0.996099i 0.528127π0.528127\pi
312312 − 1152.00i − 0.209036i
313313 − 3058.00i − 0.552231i −0.961124 0.276116i 0.910953π-0.910953\pi
0.961124 0.276116i 0.0890473π-0.0890473\pi
314314 −5372.00 −0.965476
315315 0 0
316316 960.000 0.170899
317317 − 4986.00i − 0.883412i −0.897160 0.441706i 0.854373π-0.854373\pi
0.897160 0.441706i 0.145627π-0.145627\pi
318318 5088.00i 0.897235i
319319 5320.00 0.933739
320320 0 0
321321 3552.00 0.617612
322322 − 1568.00i − 0.271370i
323323 − 5920.00i − 1.01981i
324324 1436.00 0.246228
325325 0 0
326326 2024.00 0.343862
327327 14960.0i 2.52994i
328328 1296.00i 0.218170i
329329 168.000 0.0281524
330330 0 0
331331 8612.00 1.43009 0.715043 0.699081i 0.246407π-0.246407\pi
0.715043 + 0.699081i 0.246407π0.246407\pi
332332 − 4288.00i − 0.708839i
333333 12802.0i 2.10674i
334334 1088.00 0.178242
335335 0 0
336336 −896.000 −0.145479
337337 − 10206.0i − 1.64972i −0.565336 0.824861i 0.691253π-0.691253\pi
0.565336 0.824861i 0.308747π-0.308747\pi
338338 − 3746.00i − 0.602827i
339339 −11024.0 −1.76620
340340 0 0
341341 −2016.00 −0.320154
342342 − 5920.00i − 0.936014i
343343 343.000i 0.0539949i
344344 −3296.00 −0.516594
345345 0 0
346346 −3716.00 −0.577380
347347 2004.00i 0.310030i 0.987912 + 0.155015i 0.0495426π0.0495426\pi
−0.987912 + 0.155015i 0.950457π0.950457\pi
348348 − 6080.00i − 0.936558i
349349 −1330.00 −0.203992 −0.101996 0.994785i 0.532523π-0.532523\pi
−0.101996 + 0.994785i 0.532523π0.532523\pi
350350 0 0
351351 1440.00 0.218979
352352 896.000i 0.135673i
353353 − 978.000i − 0.147461i −0.997278 0.0737304i 0.976510π-0.976510\pi
0.997278 0.0737304i 0.0234904π-0.0234904\pi
354354 −3200.00 −0.480447
355355 0 0
356356 3240.00 0.482359
357357 − 4144.00i − 0.614352i
358358 − 600.000i − 0.0885782i
359359 9680.00 1.42309 0.711547 0.702638i 0.247995π-0.247995\pi
0.711547 + 0.702638i 0.247995π0.247995\pi
360360 0 0
361361 −459.000 −0.0669194
362362 4716.00i 0.684717i
363363 4376.00i 0.632728i
364364 504.000 0.0725736
365365 0 0
366366 3168.00 0.452443
367367 − 8656.00i − 1.23117i −0.788070 0.615585i 0.788920π-0.788920\pi
0.788070 0.615585i 0.211080π-0.211080\pi
368368 1792.00i 0.253844i
369369 −5994.00 −0.845624
370370 0 0
371371 −2226.00 −0.311504
372372 2304.00i 0.321121i
373373 − 5278.00i − 0.732666i −0.930484 0.366333i 0.880613π-0.880613\pi
0.930484 0.366333i 0.119387π-0.119387\pi
374374 −4144.00 −0.572944
375375 0 0
376376 −192.000 −0.0263342
377377 3420.00i 0.467212i
378378 − 1120.00i − 0.152398i
379379 −6340.00 −0.859272 −0.429636 0.903002i 0.641358π-0.641358\pi
−0.429636 + 0.903002i 0.641358π0.641358\pi
380380 0 0
381381 15552.0 2.09122
382382 − 2784.00i − 0.372884i
383383 6232.00i 0.831437i 0.909493 + 0.415718i 0.136470π0.136470\pi
−0.909493 + 0.415718i 0.863530π0.863530\pi
384384 1024.00 0.136083
385385 0 0
386386 −3556.00 −0.468901
387387 − 15244.0i − 2.00232i
388388 − 5416.00i − 0.708649i
389389 14810.0 1.93033 0.965163 0.261649i 0.0842664π-0.0842664\pi
0.965163 + 0.261649i 0.0842664π0.0842664\pi
390390 0 0
391391 −8288.00 −1.07197
392392 − 392.000i − 0.0505076i
393393 6784.00i 0.870757i
394394 2428.00 0.310459
395395 0 0
396396 −4144.00 −0.525868
397397 5154.00i 0.651566i 0.945445 + 0.325783i 0.105628π0.105628\pi
−0.945445 + 0.325783i 0.894372π0.894372\pi
398398 2080.00i 0.261962i
399399 4480.00 0.562107
400400 0 0
401401 3282.00 0.408716 0.204358 0.978896i 0.434489π-0.434489\pi
0.204358 + 0.978896i 0.434489π0.434489\pi
402402 11456.0i 1.42133i
403403 − 1296.00i − 0.160194i
404404 5432.00 0.668941
405405 0 0
406406 2660.00 0.325157
407407 9688.00i 1.17989i
408408 4736.00i 0.574674i
409409 −5810.00 −0.702411 −0.351205 0.936298i 0.614228π-0.614228\pi
−0.351205 + 0.936298i 0.614228π0.614228\pi
410410 0 0
411411 −23728.0 −2.84773
412412 − 3328.00i − 0.397958i
413413 − 1400.00i − 0.166803i
414414 −8288.00 −0.983896
415415 0 0
416416 −576.000 −0.0678864
417417 22400.0i 2.63053i
418418 − 4480.00i − 0.524220i
419419 −13560.0 −1.58102 −0.790512 0.612446i 0.790186π-0.790186\pi
−0.790512 + 0.612446i 0.790186π0.790186\pi
420420 0 0
421421 −738.000 −0.0854345 −0.0427172 0.999087i 0.513601π-0.513601\pi
−0.0427172 + 0.999087i 0.513601π0.513601\pi
422422 7736.00i 0.892376i
423423 − 888.000i − 0.102071i
424424 2544.00 0.291386
425425 0 0
426426 −6272.00 −0.713332
427427 1386.00i 0.157080i
428428 − 1776.00i − 0.200575i
429429 4032.00 0.453769
430430 0 0
431431 1272.00 0.142158 0.0710790 0.997471i 0.477356π-0.477356\pi
0.0710790 + 0.997471i 0.477356π0.477356\pi
432432 1280.00i 0.142556i
433433 5062.00i 0.561811i 0.959735 + 0.280906i 0.0906348π0.0906348\pi
−0.959735 + 0.280906i 0.909365π0.909365\pi
434434 −1008.00 −0.111487
435435 0 0
436436 7480.00 0.821622
437437 − 8960.00i − 0.980812i
438438 8608.00i 0.939055i
439439 −5640.00 −0.613172 −0.306586 0.951843i 0.599187π-0.599187\pi
−0.306586 + 0.951843i 0.599187π0.599187\pi
440440 0 0
441441 1813.00 0.195767
442442 − 2664.00i − 0.286682i
443443 − 13388.0i − 1.43585i −0.696119 0.717927i 0.745091π-0.745091\pi
0.696119 0.717927i 0.254909π-0.254909\pi
444444 11072.0 1.18345
445445 0 0
446446 −7936.00 −0.842557
447447 4080.00i 0.431717i
448448 448.000i 0.0472456i
449449 3230.00 0.339495 0.169747 0.985488i 0.445705π-0.445705\pi
0.169747 + 0.985488i 0.445705π0.445705\pi
450450 0 0
451451 −4536.00 −0.473596
452452 5512.00i 0.573590i
453453 − 4736.00i − 0.491207i
454454 −7872.00 −0.813769
455455 0 0
456456 −5120.00 −0.525803
457457 − 10646.0i − 1.08971i −0.838529 0.544857i 0.816584π-0.816584\pi
0.838529 0.544857i 0.183416π-0.183416\pi
458458 9620.00i 0.981470i
459459 −5920.00 −0.602009
460460 0 0
461461 7282.00 0.735698 0.367849 0.929886i 0.380094π-0.380094\pi
0.367849 + 0.929886i 0.380094π0.380094\pi
462462 − 3136.00i − 0.315801i
463463 − 12688.0i − 1.27357i −0.771043 0.636783i 0.780265π-0.780265\pi
0.771043 0.636783i 0.219735π-0.219735\pi
464464 −3040.00 −0.304156
465465 0 0
466466 4364.00 0.433816
467467 − 2816.00i − 0.279034i −0.990220 0.139517i 0.955445π-0.955445\pi
0.990220 0.139517i 0.0445550π-0.0445550\pi
468468 − 2664.00i − 0.263127i
469469 −5012.00 −0.493460
470470 0 0
471471 −21488.0 −2.10215
472472 1600.00i 0.156030i
473473 − 11536.0i − 1.12141i
474474 3840.00 0.372103
475475 0 0
476476 −2072.00 −0.199517
477477 11766.0i 1.12941i
478478 − 6000.00i − 0.574129i
479479 3160.00 0.301428 0.150714 0.988577i 0.451843π-0.451843\pi
0.150714 + 0.988577i 0.451843π0.451843\pi
480480 0 0
481481 −6228.00 −0.590379
482482 − 4084.00i − 0.385936i
483483 − 6272.00i − 0.590861i
484484 2188.00 0.205485
485485 0 0
486486 10064.0 0.939326
487487 − 14176.0i − 1.31905i −0.751684 0.659523i 0.770758π-0.770758\pi
0.751684 0.659523i 0.229242π-0.229242\pi
488488 − 1584.00i − 0.146935i
489489 8096.00 0.748699
490490 0 0
491491 −11268.0 −1.03568 −0.517839 0.855478i 0.673263π-0.673263\pi
−0.517839 + 0.855478i 0.673263π0.673263\pi
492492 5184.00i 0.475026i
493493 − 14060.0i − 1.28444i
494494 2880.00 0.262302
495495 0 0
496496 1152.00 0.104287
497497 − 2744.00i − 0.247656i
498498 − 17152.0i − 1.54337i
499499 4460.00 0.400114 0.200057 0.979784i 0.435887π-0.435887\pi
0.200057 + 0.979784i 0.435887π0.435887\pi
500500 0 0
501501 4352.00 0.388090
502502 1056.00i 0.0938876i
503503 1512.00i 0.134029i 0.997752 + 0.0670147i 0.0213474π0.0213474\pi
−0.997752 + 0.0670147i 0.978653π0.978653\pi
504504 −2072.00 −0.183123
505505 0 0
506506 −6272.00 −0.551036
507507 − 14984.0i − 1.31255i
508508 − 7776.00i − 0.679142i
509509 11790.0 1.02668 0.513342 0.858184i 0.328407π-0.328407\pi
0.513342 + 0.858184i 0.328407π0.328407\pi
510510 0 0
511511 −3766.00 −0.326024
512512 − 512.000i − 0.0441942i
513513 − 6400.00i − 0.550813i
514514 11268.0 0.966946
515515 0 0
516516 −13184.0 −1.12479
517517 − 672.000i − 0.0571654i
518518 4844.00i 0.410875i
519519 −14864.0 −1.25714
520520 0 0
521521 1362.00 0.114530 0.0572652 0.998359i 0.481762π-0.481762\pi
0.0572652 + 0.998359i 0.481762π0.481762\pi
522522 − 14060.0i − 1.17891i
523523 − 6968.00i − 0.582580i −0.956635 0.291290i 0.905916π-0.905916\pi
0.956635 0.291290i 0.0940845π-0.0940845\pi
524524 3392.00 0.282787
525525 0 0
526526 −336.000 −0.0278523
527527 5328.00i 0.440401i
528528 3584.00i 0.295405i
529529 −377.000 −0.0309855
530530 0 0
531531 −7400.00 −0.604770
532532 − 2240.00i − 0.182549i
533533 − 2916.00i − 0.236972i
534534 12960.0 1.05025
535535 0 0
536536 5728.00 0.461589
537537 − 2400.00i − 0.192863i
538538 − 2620.00i − 0.209956i
539539 1372.00 0.109640
540540 0 0
541541 7062.00 0.561218 0.280609 0.959822i 0.409464π-0.409464\pi
0.280609 + 0.959822i 0.409464π0.409464\pi
542542 4416.00i 0.349969i
543543 18864.0i 1.49085i
544544 2368.00 0.186631
545545 0 0
546546 2016.00 0.158016
547547 − 8196.00i − 0.640650i −0.947308 0.320325i 0.896208π-0.896208\pi
0.947308 0.320325i 0.103792π-0.103792\pi
548548 11864.0i 0.924827i
549549 7326.00 0.569519
550550 0 0
551551 15200.0 1.17521
552552 7168.00i 0.552700i
553553 1680.00i 0.129188i
554554 10588.0 0.811987
555555 0 0
556556 11200.0 0.854291
557557 − 7466.00i − 0.567944i −0.958833 0.283972i 0.908348π-0.908348\pi
0.958833 0.283972i 0.0916522π-0.0916522\pi
558558 5328.00i 0.404215i
559559 7416.00 0.561115
560560 0 0
561561 −16576.0 −1.24749
562562 − 6484.00i − 0.486674i
563563 − 24968.0i − 1.86905i −0.355896 0.934526i 0.615824π-0.615824\pi
0.355896 0.934526i 0.384176π-0.384176\pi
564564 −768.000 −0.0573380
565565 0 0
566566 3184.00 0.236455
567567 2513.00i 0.186131i
568568 3136.00i 0.231661i
569569 −14250.0 −1.04990 −0.524948 0.851134i 0.675915π-0.675915\pi
−0.524948 + 0.851134i 0.675915π0.675915\pi
570570 0 0
571571 6372.00 0.467005 0.233503 0.972356i 0.424981π-0.424981\pi
0.233503 + 0.972356i 0.424981π0.424981\pi
572572 − 2016.00i − 0.147366i
573573 − 11136.0i − 0.811890i
574574 −2268.00 −0.164921
575575 0 0
576576 2368.00 0.171296
577577 − 8366.00i − 0.603607i −0.953370 0.301803i 0.902411π-0.902411\pi
0.953370 0.301803i 0.0975886π-0.0975886\pi
578578 1126.00i 0.0810301i
579579 −14224.0 −1.02095
580580 0 0
581581 7504.00 0.535832
582582 − 21664.0i − 1.54296i
583583 8904.00i 0.632532i
584584 4304.00 0.304967
585585 0 0
586586 10044.0 0.708044
587587 20384.0i 1.43328i 0.697441 + 0.716642i 0.254322π0.254322\pi
−0.697441 + 0.716642i 0.745678π0.745678\pi
588588 − 1568.00i − 0.109971i
589589 −5760.00 −0.402948
590590 0 0
591591 9712.00 0.675970
592592 − 5536.00i − 0.384338i
593593 − 9378.00i − 0.649424i −0.945813 0.324712i 0.894733π-0.894733\pi
0.945813 0.324712i 0.105267π-0.105267\pi
594594 −4480.00 −0.309456
595595 0 0
596596 2040.00 0.140204
597597 8320.00i 0.570377i
598598 − 4032.00i − 0.275720i
599599 9000.00 0.613907 0.306953 0.951725i 0.400690π-0.400690\pi
0.306953 + 0.951725i 0.400690π0.400690\pi
600600 0 0
601601 7562.00 0.513245 0.256623 0.966512i 0.417390π-0.417390\pi
0.256623 + 0.966512i 0.417390π0.417390\pi
602602 − 5768.00i − 0.390509i
603603 26492.0i 1.78912i
604604 −2368.00 −0.159524
605605 0 0
606606 21728.0 1.45650
607607 − 2976.00i − 0.198999i −0.995038 0.0994993i 0.968276π-0.968276\pi
0.995038 0.0994993i 0.0317241π-0.0317241\pi
608608 2560.00i 0.170759i
609609 10640.0 0.707971
610610 0 0
611611 432.000 0.0286037
612612 10952.0i 0.723380i
613613 − 4278.00i − 0.281871i −0.990019 0.140935i 0.954989π-0.954989\pi
0.990019 0.140935i 0.0450110π-0.0450110\pi
614614 −19072.0 −1.25356
615615 0 0
616616 −1568.00 −0.102559
617617 18794.0i 1.22629i 0.789972 + 0.613143i 0.210095π0.210095\pi
−0.789972 + 0.613143i 0.789905π0.789905\pi
618618 − 13312.0i − 0.866484i
619619 −18040.0 −1.17139 −0.585694 0.810532i 0.699178π-0.699178\pi
−0.585694 + 0.810532i 0.699178π0.699178\pi
620620 0 0
621621 −8960.00 −0.578989
622622 1936.00i 0.124801i
623623 5670.00i 0.364629i
624624 −2304.00 −0.147811
625625 0 0
626626 −6116.00 −0.390486
627627 − 17920.0i − 1.14140i
628628 10744.0i 0.682695i
629629 25604.0 1.62305
630630 0 0
631631 −21688.0 −1.36828 −0.684141 0.729350i 0.739823π-0.739823\pi
−0.684141 + 0.729350i 0.739823π0.739823\pi
632632 − 1920.00i − 0.120844i
633633 30944.0i 1.94299i
634634 −9972.00 −0.624667
635635 0 0
636636 10176.0 0.634441
637637 882.000i 0.0548605i
638638 − 10640.0i − 0.660253i
639639 −14504.0 −0.897918
640640 0 0
641641 −10558.0 −0.650571 −0.325285 0.945616i 0.605460π-0.605460\pi
−0.325285 + 0.945616i 0.605460π0.605460\pi
642642 − 7104.00i − 0.436717i
643643 26152.0i 1.60394i 0.597363 + 0.801971i 0.296215π0.296215\pi
−0.597363 + 0.801971i 0.703785π0.703785\pi
644644 −3136.00 −0.191888
645645 0 0
646646 −11840.0 −0.721112
647647 25584.0i 1.55458i 0.629145 + 0.777288i 0.283405π0.283405\pi
−0.629145 + 0.777288i 0.716595π0.716595\pi
648648 − 2872.00i − 0.174109i
649649 −5600.00 −0.338705
650650 0 0
651651 −4032.00 −0.242744
652652 − 4048.00i − 0.243147i
653653 − 15198.0i − 0.910787i −0.890290 0.455393i 0.849499π-0.849499\pi
0.890290 0.455393i 0.150501π-0.150501\pi
654654 29920.0 1.78894
655655 0 0
656656 2592.00 0.154269
657657 19906.0i 1.18205i
658658 − 336.000i − 0.0199068i
659659 6100.00 0.360580 0.180290 0.983613i 0.442296π-0.442296\pi
0.180290 + 0.983613i 0.442296π0.442296\pi
660660 0 0
661661 −2318.00 −0.136399 −0.0681995 0.997672i 0.521725π-0.521725\pi
−0.0681995 + 0.997672i 0.521725π0.521725\pi
662662 − 17224.0i − 1.01122i
663663 − 10656.0i − 0.624200i
664664 −8576.00 −0.501225
665665 0 0
666666 25604.0 1.48969
667667 − 21280.0i − 1.23533i
668668 − 2176.00i − 0.126036i
669669 −31744.0 −1.83452
670670 0 0
671671 5544.00 0.318962
672672 1792.00i 0.102869i
673673 10222.0i 0.585482i 0.956192 + 0.292741i 0.0945673π0.0945673\pi
−0.956192 + 0.292741i 0.905433π0.905433\pi
674674 −20412.0 −1.16653
675675 0 0
676676 −7492.00 −0.426263
677677 25434.0i 1.44388i 0.691955 + 0.721941i 0.256750π0.256750\pi
−0.691955 + 0.721941i 0.743250π0.743250\pi
678678 22048.0i 1.24889i
679679 9478.00 0.535688
680680 0 0
681681 −31488.0 −1.77184
682682 4032.00i 0.226383i
683683 8532.00i 0.477991i 0.971021 + 0.238996i 0.0768181π0.0768181\pi
−0.971021 + 0.238996i 0.923182π0.923182\pi
684684 −11840.0 −0.661862
685685 0 0
686686 686.000 0.0381802
687687 38480.0i 2.13698i
688688 6592.00i 0.365287i
689689 −5724.00 −0.316498
690690 0 0
691691 20672.0 1.13806 0.569030 0.822317i 0.307319π-0.307319\pi
0.569030 + 0.822317i 0.307319π0.307319\pi
692692 7432.00i 0.408269i
693693 − 7252.00i − 0.397519i
694694 4008.00 0.219224
695695 0 0
696696 −12160.0 −0.662247
697697 11988.0i 0.651475i
698698 2660.00i 0.144244i
699699 17456.0 0.944559
700700 0 0
701701 −21458.0 −1.15614 −0.578072 0.815985i 0.696195π-0.696195\pi
−0.578072 + 0.815985i 0.696195π0.696195\pi
702702 − 2880.00i − 0.154841i
703703 27680.0i 1.48502i
704704 1792.00 0.0959354
705705 0 0
706706 −1956.00 −0.104271
707707 9506.00i 0.505672i
708708 6400.00i 0.339727i
709709 9850.00 0.521755 0.260878 0.965372i 0.415988π-0.415988\pi
0.260878 + 0.965372i 0.415988π0.415988\pi
710710 0 0
711711 8880.00 0.468391
712712 − 6480.00i − 0.341079i
713713 8064.00i 0.423561i
714714 −8288.00 −0.434413
715715 0 0
716716 −1200.00 −0.0626342
717717 − 24000.0i − 1.25006i
718718 − 19360.0i − 1.00628i
719719 18840.0 0.977209 0.488605 0.872505i 0.337506π-0.337506\pi
0.488605 + 0.872505i 0.337506π0.337506\pi
720720 0 0
721721 5824.00 0.300828
722722 918.000i 0.0473191i
723723 − 16336.0i − 0.840308i
724724 9432.00 0.484168
725725 0 0
726726 8752.00 0.447407
727727 37504.0i 1.91327i 0.291291 + 0.956634i 0.405915π0.405915\pi
−0.291291 + 0.956634i 0.594085π0.594085\pi
728728 − 1008.00i − 0.0513173i
729729 30563.0 1.55276
730730 0 0
731731 −30488.0 −1.54260
732732 − 6336.00i − 0.319925i
733733 − 13338.0i − 0.672101i −0.941844 0.336051i 0.890909π-0.890909\pi
0.941844 0.336051i 0.109091π-0.109091\pi
734734 −17312.0 −0.870569
735735 0 0
736736 3584.00 0.179495
737737 20048.0i 1.00200i
738738 11988.0i 0.597946i
739739 −17100.0 −0.851196 −0.425598 0.904912i 0.639936π-0.639936\pi
−0.425598 + 0.904912i 0.639936π0.639936\pi
740740 0 0
741741 11520.0 0.571117
742742 4452.00i 0.220267i
743743 19632.0i 0.969352i 0.874694 + 0.484676i 0.161062π0.161062\pi
−0.874694 + 0.484676i 0.838938π0.838938\pi
744744 4608.00 0.227067
745745 0 0
746746 −10556.0 −0.518073
747747 − 39664.0i − 1.94274i
748748 8288.00i 0.405133i
749749 3108.00 0.151621
750750 0 0
751751 33912.0 1.64776 0.823879 0.566766i 0.191805π-0.191805\pi
0.823879 + 0.566766i 0.191805π0.191805\pi
752752 384.000i 0.0186211i
753753 4224.00i 0.204424i
754754 6840.00 0.330369
755755 0 0
756756 −2240.00 −0.107762
757757 − 31386.0i − 1.50693i −0.657490 0.753463i 0.728382π-0.728382\pi
0.657490 0.753463i 0.271618π-0.271618\pi
758758 12680.0i 0.607597i
759759 −25088.0 −1.19978
760760 0 0
761761 −34558.0 −1.64616 −0.823079 0.567927i 0.807746π-0.807746\pi
−0.823079 + 0.567927i 0.807746π0.807746\pi
762762 − 31104.0i − 1.47871i
763763 13090.0i 0.621088i
764764 −5568.00 −0.263669
765765 0 0
766766 12464.0 0.587915
767767 − 3600.00i − 0.169476i
768768 − 2048.00i − 0.0962250i
769769 −39130.0 −1.83493 −0.917467 0.397812i 0.869769π-0.869769\pi
−0.917467 + 0.397812i 0.869769π0.869769\pi
770770 0 0
771771 45072.0 2.10535
772772 7112.00i 0.331563i
773773 25982.0i 1.20894i 0.796629 + 0.604468i 0.206614π0.206614\pi
−0.796629 + 0.604468i 0.793386π0.793386\pi
774774 −30488.0 −1.41585
775775 0 0
776776 −10832.0 −0.501090
777777 19376.0i 0.894608i
778778 − 29620.0i − 1.36495i
779779 −12960.0 −0.596072
780780 0 0
781781 −10976.0 −0.502884
782782 16576.0i 0.758001i
783783 − 15200.0i − 0.693747i
784784 −784.000 −0.0357143
785785 0 0
786786 13568.0 0.615718
787787 35424.0i 1.60448i 0.596999 + 0.802242i 0.296360π0.296360\pi
−0.596999 + 0.802242i 0.703640π0.703640\pi
788788 − 4856.00i − 0.219528i
789789 −1344.00 −0.0606434
790790 0 0
791791 −9646.00 −0.433593
792792 8288.00i 0.371845i
793793 3564.00i 0.159598i
794794 10308.0 0.460727
795795 0 0
796796 4160.00 0.185235
797797 − 30606.0i − 1.36025i −0.733096 0.680126i 0.761925π-0.761925\pi
0.733096 0.680126i 0.238075π-0.238075\pi
798798 − 8960.00i − 0.397469i
799799 −1776.00 −0.0786362
800800 0 0
801801 29970.0 1.32202
802802 − 6564.00i − 0.289006i
803803 15064.0i 0.662014i
804804 22912.0 1.00503
805805 0 0
806806 −2592.00 −0.113275
807807 − 10480.0i − 0.457142i
808808 − 10864.0i − 0.473013i
809809 −16810.0 −0.730542 −0.365271 0.930901i 0.619024π-0.619024\pi
−0.365271 + 0.930901i 0.619024π0.619024\pi
810810 0 0
811811 −9368.00 −0.405616 −0.202808 0.979218i 0.565007π-0.565007\pi
−0.202808 + 0.979218i 0.565007π0.565007\pi
812812 − 5320.00i − 0.229920i
813813 17664.0i 0.761997i
814814 19376.0 0.834310
815815 0 0
816816 9472.00 0.406356
817817 − 32960.0i − 1.41141i
818818 11620.0i 0.496679i
819819 4662.00 0.198905
820820 0 0
821821 34382.0 1.46156 0.730780 0.682614i 0.239157π-0.239157\pi
0.730780 + 0.682614i 0.239157π0.239157\pi
822822 47456.0i 2.01365i
823823 4472.00i 0.189410i 0.995505 + 0.0947048i 0.0301907π0.0301907\pi
−0.995505 + 0.0947048i 0.969809π0.969809\pi
824824 −6656.00 −0.281399
825825 0 0
826826 −2800.00 −0.117947
827827 − 1716.00i − 0.0721538i −0.999349 0.0360769i 0.988514π-0.988514\pi
0.999349 0.0360769i 0.0114861π-0.0114861\pi
828828 16576.0i 0.695720i
829829 7910.00 0.331394 0.165697 0.986177i 0.447013π-0.447013\pi
0.165697 + 0.986177i 0.447013π0.447013\pi
830830 0 0
831831 42352.0 1.76796
832832 1152.00i 0.0480029i
833833 − 3626.00i − 0.150820i
834834 44800.0 1.86007
835835 0 0
836836 −8960.00 −0.370680
837837 5760.00i 0.237867i
838838 27120.0i 1.11795i
839839 19360.0 0.796641 0.398320 0.917246i 0.369593π-0.369593\pi
0.398320 + 0.917246i 0.369593π0.369593\pi
840840 0 0
841841 11711.0 0.480175
842842 1476.00i 0.0604113i
843843 − 25936.0i − 1.05965i
844844 15472.0 0.631005
845845 0 0
846846 −1776.00 −0.0721751
847847 3829.00i 0.155332i
848848 − 5088.00i − 0.206041i
849849 12736.0 0.514839
850850 0 0
851851 38752.0 1.56099
852852 12544.0i 0.504402i
853853 − 698.000i − 0.0280177i −0.999902 0.0140088i 0.995541π-0.995541\pi
0.999902 0.0140088i 0.00445930π-0.00445930\pi
854854 2772.00 0.111072
855855 0 0
856856 −3552.00 −0.141828
857857 − 23406.0i − 0.932945i −0.884536 0.466472i 0.845525π-0.845525\pi
0.884536 0.466472i 0.154475π-0.154475\pi
858858 − 8064.00i − 0.320863i
859859 −7280.00 −0.289162 −0.144581 0.989493i 0.546183π-0.546183\pi
−0.144581 + 0.989493i 0.546183π0.546183\pi
860860 0 0
861861 −9072.00 −0.359086
862862 − 2544.00i − 0.100521i
863863 − 9808.00i − 0.386869i −0.981113 0.193435i 0.938037π-0.938037\pi
0.981113 0.193435i 0.0619627π-0.0619627\pi
864864 2560.00 0.100802
865865 0 0
866866 10124.0 0.397260
867867 4504.00i 0.176429i
868868 2016.00i 0.0788335i
869869 6720.00 0.262325
870870 0 0
871871 −12888.0 −0.501370
872872 − 14960.0i − 0.580974i
873873 − 50098.0i − 1.94222i
874874 −17920.0 −0.693539
875875 0 0
876876 17216.0 0.664012
877877 − 8066.00i − 0.310570i −0.987870 0.155285i 0.950370π-0.950370\pi
0.987870 0.155285i 0.0496295π-0.0496295\pi
878878 11280.0i 0.433578i
879879 40176.0 1.54164
880880 0 0
881881 25842.0 0.988240 0.494120 0.869394i 0.335490π-0.335490\pi
0.494120 + 0.869394i 0.335490π0.335490\pi
882882 − 3626.00i − 0.138428i
883883 5692.00i 0.216932i 0.994100 + 0.108466i 0.0345939π0.0345939\pi
−0.994100 + 0.108466i 0.965406π0.965406\pi
884884 −5328.00 −0.202715
885885 0 0
886886 −26776.0 −1.01530
887887 − 13536.0i − 0.512395i −0.966624 0.256198i 0.917530π-0.917530\pi
0.966624 0.256198i 0.0824698π-0.0824698\pi
888888 − 22144.0i − 0.836829i
889889 13608.0 0.513383
890890 0 0
891891 10052.0 0.377951
892892 15872.0i 0.595778i
893893 − 1920.00i − 0.0719489i
894894 8160.00 0.305270
895895 0 0
896896 896.000 0.0334077
897897 − 16128.0i − 0.600332i
898898 − 6460.00i − 0.240059i
899899 −13680.0 −0.507512
900900 0 0
901901 23532.0 0.870105
902902 9072.00i 0.334883i
903903 − 23072.0i − 0.850264i
904904 11024.0 0.405589
905905 0 0
906906 −9472.00 −0.347336
907907 17004.0i 0.622501i 0.950328 + 0.311251i 0.100748π0.100748\pi
−0.950328 + 0.311251i 0.899252π0.899252\pi
908908 15744.0i 0.575422i
909909 50246.0 1.83339
910910 0 0
911911 −14568.0 −0.529813 −0.264906 0.964274i 0.585341π-0.585341\pi
−0.264906 + 0.964274i 0.585341π0.585341\pi
912912 10240.0i 0.371799i
913913 − 30016.0i − 1.08804i
914914 −21292.0 −0.770544
915915 0 0
916916 19240.0 0.694004
917917 5936.00i 0.213767i
918918 11840.0i 0.425684i
919919 1400.00 0.0502522 0.0251261 0.999684i 0.492001π-0.492001\pi
0.0251261 + 0.999684i 0.492001π0.492001\pi
920920 0 0
921921 −76288.0 −2.72940
922922 − 14564.0i − 0.520217i
923923 − 7056.00i − 0.251626i
924924 −6272.00 −0.223305
925925 0 0
926926 −25376.0 −0.900548
927927 − 30784.0i − 1.09070i
928928 6080.00i 0.215071i
929929 13830.0 0.488426 0.244213 0.969722i 0.421470π-0.421470\pi
0.244213 + 0.969722i 0.421470π0.421470\pi
930930 0 0
931931 3920.00 0.137994
932932 − 8728.00i − 0.306754i
933933 7744.00i 0.271733i
934934 −5632.00 −0.197307
935935 0 0
936936 −5328.00 −0.186059
937937 − 24166.0i − 0.842549i −0.906933 0.421275i 0.861583π-0.861583\pi
0.906933 0.421275i 0.138417π-0.138417\pi
938938 10024.0i 0.348929i
939939 −24464.0 −0.850216
940940 0 0
941941 −10838.0 −0.375461 −0.187730 0.982221i 0.560113π-0.560113\pi
−0.187730 + 0.982221i 0.560113π0.560113\pi
942942 42976.0i 1.48645i
943943 18144.0i 0.626564i
944944 3200.00 0.110330
945945 0 0
946946 −23072.0 −0.792955
947947 − 40916.0i − 1.40400i −0.712175 0.702002i 0.752290π-0.752290\pi
0.712175 0.702002i 0.247710π-0.247710\pi
948948 − 7680.00i − 0.263117i
949949 −9684.00 −0.331250
950950 0 0
951951 −39888.0 −1.36010
952952 4144.00i 0.141080i
953953 − 56618.0i − 1.92449i −0.272189 0.962244i 0.587747π-0.587747\pi
0.272189 0.962244i 0.412253π-0.412253\pi
954954 23532.0 0.798613
955955 0 0
956956 −12000.0 −0.405970
957957 − 42560.0i − 1.43759i
958958 − 6320.00i − 0.213142i
959959 −20762.0 −0.699103
960960 0 0
961961 −24607.0 −0.825988
962962 12456.0i 0.417461i
963963 − 16428.0i − 0.549725i
964964 −8168.00 −0.272898
965965 0 0
966966 −12544.0 −0.417802
967967 17504.0i 0.582100i 0.956708 + 0.291050i 0.0940046π0.0940046\pi
−0.956708 + 0.291050i 0.905995π0.905995\pi
968968 − 4376.00i − 0.145300i
969969 −47360.0 −1.57010
970970 0 0
971971 23112.0 0.763851 0.381926 0.924193i 0.375261π-0.375261\pi
0.381926 + 0.924193i 0.375261π0.375261\pi
972972 − 20128.0i − 0.664204i
973973 19600.0i 0.645783i
974974 −28352.0 −0.932707
975975 0 0
976976 −3168.00 −0.103899
977977 23874.0i 0.781778i 0.920438 + 0.390889i 0.127832π0.127832\pi
−0.920438 + 0.390889i 0.872168π0.872168\pi
978978 − 16192.0i − 0.529410i
979979 22680.0 0.740404
980980 0 0
981981 69190.0 2.25185
982982 22536.0i 0.732335i
983983 15312.0i 0.496823i 0.968655 + 0.248411i 0.0799085π0.0799085\pi
−0.968655 + 0.248411i 0.920091π0.920091\pi
984984 10368.0 0.335894
985985 0 0
986986 −28120.0 −0.908239
987987 − 1344.00i − 0.0433435i
988988 − 5760.00i − 0.185476i
989989 −46144.0 −1.48361
990990 0 0
991991 −16528.0 −0.529797 −0.264899 0.964276i 0.585339π-0.585339\pi
−0.264899 + 0.964276i 0.585339π0.585339\pi
992992 − 2304.00i − 0.0737420i
993993 − 68896.0i − 2.20176i
994994 −5488.00 −0.175120
995995 0 0
996996 −34304.0 −1.09133
997997 − 28606.0i − 0.908687i −0.890827 0.454344i 0.849874π-0.849874\pi
0.890827 0.454344i 0.150126π-0.150126\pi
998998 − 8920.00i − 0.282924i
999999 27680.0 0.876633
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 350.4.c.b.99.1 2
5.2 odd 4 350.4.a.l.1.1 1
5.3 odd 4 14.4.a.a.1.1 1
5.4 even 2 inner 350.4.c.b.99.2 2
15.8 even 4 126.4.a.h.1.1 1
20.3 even 4 112.4.a.a.1.1 1
35.3 even 12 98.4.c.f.79.1 2
35.13 even 4 98.4.a.a.1.1 1
35.18 odd 12 98.4.c.d.79.1 2
35.23 odd 12 98.4.c.d.67.1 2
35.27 even 4 2450.4.a.bo.1.1 1
35.33 even 12 98.4.c.f.67.1 2
40.3 even 4 448.4.a.o.1.1 1
40.13 odd 4 448.4.a.b.1.1 1
55.43 even 4 1694.4.a.g.1.1 1
60.23 odd 4 1008.4.a.s.1.1 1
65.38 odd 4 2366.4.a.h.1.1 1
105.23 even 12 882.4.g.b.361.1 2
105.38 odd 12 882.4.g.k.667.1 2
105.53 even 12 882.4.g.b.667.1 2
105.68 odd 12 882.4.g.k.361.1 2
105.83 odd 4 882.4.a.i.1.1 1
140.83 odd 4 784.4.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.a.a.1.1 1 5.3 odd 4
98.4.a.a.1.1 1 35.13 even 4
98.4.c.d.67.1 2 35.23 odd 12
98.4.c.d.79.1 2 35.18 odd 12
98.4.c.f.67.1 2 35.33 even 12
98.4.c.f.79.1 2 35.3 even 12
112.4.a.a.1.1 1 20.3 even 4
126.4.a.h.1.1 1 15.8 even 4
350.4.a.l.1.1 1 5.2 odd 4
350.4.c.b.99.1 2 1.1 even 1 trivial
350.4.c.b.99.2 2 5.4 even 2 inner
448.4.a.b.1.1 1 40.13 odd 4
448.4.a.o.1.1 1 40.3 even 4
784.4.a.s.1.1 1 140.83 odd 4
882.4.a.i.1.1 1 105.83 odd 4
882.4.g.b.361.1 2 105.23 even 12
882.4.g.b.667.1 2 105.53 even 12
882.4.g.k.361.1 2 105.68 odd 12
882.4.g.k.667.1 2 105.38 odd 12
1008.4.a.s.1.1 1 60.23 odd 4
1694.4.a.g.1.1 1 55.43 even 4
2366.4.a.h.1.1 1 65.38 odd 4
2450.4.a.bo.1.1 1 35.27 even 4