Properties

Label 1764.4.k.v.361.2
Level 17641764
Weight 44
Character 1764.361
Analytic conductor 104.079104.079
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1764,4,Mod(361,1764)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1764.361");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1764=223272 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1764.k (of order 33, degree 22, 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: 104.079369250104.079369250
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(3,7)\Q(\sqrt{-3}, \sqrt{7})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+7x2+49 x^{4} + 7x^{2} + 49 Copy content Toggle raw display
Coefficient ring: Z[a1,,a25]\Z[a_1, \ldots, a_{25}]
Coefficient ring index: 2232 2^{2}\cdot 3^{2}
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 361.2
Root 1.32288+2.29129i1.32288 + 2.29129i of defining polynomial
Character χ\chi == 1764.361
Dual form 1764.4.k.v.1549.2

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) == q+(7.93725+13.7477i)q5+(7.9372513.7477i)q11+26.0000q13+(39.6863+68.7386i)q17+(34.000058.8897i)q19+(23.8118+41.2432i)q23+(63.5000+109.985i)q25+253.992q29+(106.000+183.597i)q31+(109.000188.794i)q37396.863q41+260.000q43+(206.369+357.441i)q47+(238.118+412.432i)q53+252.000q55+(142.871+247.459i)q59+(161.000+278.860i)q61+(206.369+357.441i)q65+(178.000+308.305i)q67+1127.09q71+(113.000195.722i)q73+(220.000381.051i)q79+253.992q831260.00q85+(103.184+178.720i)q89+(539.733934.845i)q951330.00q97+O(q100)q+(7.93725 + 13.7477i) q^{5} +(7.93725 - 13.7477i) q^{11} +26.0000 q^{13} +(-39.6863 + 68.7386i) q^{17} +(-34.0000 - 58.8897i) q^{19} +(23.8118 + 41.2432i) q^{23} +(-63.5000 + 109.985i) q^{25} +253.992 q^{29} +(-106.000 + 183.597i) q^{31} +(-109.000 - 188.794i) q^{37} -396.863 q^{41} +260.000 q^{43} +(206.369 + 357.441i) q^{47} +(-238.118 + 412.432i) q^{53} +252.000 q^{55} +(-142.871 + 247.459i) q^{59} +(161.000 + 278.860i) q^{61} +(206.369 + 357.441i) q^{65} +(-178.000 + 308.305i) q^{67} +1127.09 q^{71} +(113.000 - 195.722i) q^{73} +(-220.000 - 381.051i) q^{79} +253.992 q^{83} -1260.00 q^{85} +(103.184 + 178.720i) q^{89} +(539.733 - 934.845i) q^{95} -1330.00 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+104q13136q19254q25424q31436q37+1040q43+1008q55+644q61712q67+452q73880q795040q855320q97+O(q100) 4 q + 104 q^{13} - 136 q^{19} - 254 q^{25} - 424 q^{31} - 436 q^{37} + 1040 q^{43} + 1008 q^{55} + 644 q^{61} - 712 q^{67} + 452 q^{73} - 880 q^{79} - 5040 q^{85} - 5320 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1764Z)×\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times.

nn 785785 883883 10811081
χ(n)\chi(n) 11 11 e(23)e\left(\frac{2}{3}\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 0 0
44 0 0
55 7.93725 + 13.7477i 0.709930 + 1.22963i 0.964883 + 0.262681i 0.0846066π0.0846066\pi
−0.254953 + 0.966953i 0.582060π0.582060\pi
66 0 0
77 0 0
88 0 0
99 0 0
1010 0 0
1111 7.93725 13.7477i 0.217561 0.376827i −0.736501 0.676437i 0.763523π-0.763523\pi
0.954062 + 0.299610i 0.0968565π0.0968565\pi
1212 0 0
1313 26.0000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 0 0
1515 0 0
1616 0 0
1717 −39.6863 + 68.7386i −0.566196 + 0.980680i 0.430741 + 0.902476i 0.358252π0.358252\pi
−0.996937 + 0.0782050i 0.975081π0.975081\pi
1818 0 0
1919 −34.0000 58.8897i −0.410533 0.711065i 0.584415 0.811455i 0.301324π-0.301324\pi
−0.994948 + 0.100390i 0.967991π0.967991\pi
2020 0 0
2121 0 0
2222 0 0
2323 23.8118 + 41.2432i 0.215874 + 0.373904i 0.953543 0.301259i 0.0974067π-0.0974067\pi
−0.737669 + 0.675163i 0.764073π0.764073\pi
2424 0 0
2525 −63.5000 + 109.985i −0.508000 + 0.879882i
2626 0 0
2727 0 0
2828 0 0
2929 253.992 1.62638 0.813192 0.581995i 0.197728π-0.197728\pi
0.813192 + 0.581995i 0.197728π0.197728\pi
3030 0 0
3131 −106.000 + 183.597i −0.614134 + 1.06371i 0.376401 + 0.926457i 0.377161π0.377161\pi
−0.990536 + 0.137255i 0.956172π0.956172\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 −109.000 188.794i −0.484311 0.838850i 0.515527 0.856873i 0.327596π-0.327596\pi
−0.999838 + 0.0180229i 0.994263π0.994263\pi
3838 0 0
3939 0 0
4040 0 0
4141 −396.863 −1.51170 −0.755848 0.654747i 0.772775π-0.772775\pi
−0.755848 + 0.654747i 0.772775π0.772775\pi
4242 0 0
4343 260.000 0.922084 0.461042 0.887378i 0.347476π-0.347476\pi
0.461042 + 0.887378i 0.347476π0.347476\pi
4444 0 0
4545 0 0
4646 0 0
4747 206.369 + 357.441i 0.640467 + 1.10932i 0.985329 + 0.170668i 0.0545926π0.0545926\pi
−0.344861 + 0.938654i 0.612074π0.612074\pi
4848 0 0
4949 0 0
5050 0 0
5151 0 0
5252 0 0
5353 −238.118 + 412.432i −0.617132 + 1.06890i 0.372875 + 0.927882i 0.378372π0.378372\pi
−0.990007 + 0.141022i 0.954961π0.954961\pi
5454 0 0
5555 252.000 0.617812
5656 0 0
5757 0 0
5858 0 0
5959 −142.871 + 247.459i −0.315257 + 0.546041i −0.979492 0.201483i 0.935424π-0.935424\pi
0.664235 + 0.747524i 0.268757π0.268757\pi
6060 0 0
6161 161.000 + 278.860i 0.337933 + 0.585318i 0.984044 0.177926i 0.0569388π-0.0569388\pi
−0.646110 + 0.763244i 0.723605π0.723605\pi
6262 0 0
6363 0 0
6464 0 0
6565 206.369 + 357.441i 0.393798 + 0.682078i
6666 0 0
6767 −178.000 + 308.305i −0.324570 + 0.562171i −0.981425 0.191845i 0.938553π-0.938553\pi
0.656856 + 0.754016i 0.271886π0.271886\pi
6868 0 0
6969 0 0
7070 0 0
7171 1127.09 1.88396 0.941979 0.335673i 0.108964π-0.108964\pi
0.941979 + 0.335673i 0.108964π0.108964\pi
7272 0 0
7373 113.000 195.722i 0.181173 0.313801i −0.761107 0.648626i 0.775344π-0.775344\pi
0.942280 + 0.334825i 0.108677π0.108677\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 −220.000 381.051i −0.313316 0.542679i 0.665762 0.746164i 0.268106π-0.268106\pi
−0.979078 + 0.203485i 0.934773π0.934773\pi
8080 0 0
8181 0 0
8282 0 0
8383 253.992 0.335895 0.167947 0.985796i 0.446286π-0.446286\pi
0.167947 + 0.985796i 0.446286π0.446286\pi
8484 0 0
8585 −1260.00 −1.60784
8686 0 0
8787 0 0
8888 0 0
8989 103.184 + 178.720i 0.122893 + 0.212858i 0.920908 0.389781i 0.127449π-0.127449\pi
−0.798014 + 0.602639i 0.794116π0.794116\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 539.733 934.845i 0.582900 1.00961i
9696 0 0
9797 −1330.00 −1.39218 −0.696088 0.717957i 0.745078π-0.745078\pi
−0.696088 + 0.717957i 0.745078π0.745078\pi
9898 0 0
9999 0 0
100100 0 0
101101 119.059 206.216i 0.117295 0.203161i −0.801400 0.598129i 0.795911π-0.795911\pi
0.918695 + 0.394968i 0.129244π0.129244\pi
102102 0 0
103103 902.000 + 1562.31i 0.862881 + 1.49455i 0.869136 + 0.494573i 0.164675π0.164675\pi
−0.00625573 + 0.999980i 0.501991π0.501991\pi
104104 0 0
105105 0 0
106106 0 0
107107 −87.3098 151.225i −0.0788837 0.136631i 0.823885 0.566757i 0.191802π-0.191802\pi
−0.902769 + 0.430127i 0.858469π0.858469\pi
108108 0 0
109109 227.000 393.176i 0.199474 0.345499i −0.748884 0.662701i 0.769410π-0.769410\pi
0.948358 + 0.317202i 0.102743π0.102743\pi
110110 0 0
111111 0 0
112112 0 0
113113 −1777.94 −1.48013 −0.740066 0.672534i 0.765206π-0.765206\pi
−0.740066 + 0.672534i 0.765206π0.765206\pi
114114 0 0
115115 −378.000 + 654.715i −0.306510 + 0.530891i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 539.500 + 934.441i 0.405334 + 0.702060i
122122 0 0
123123 0 0
124124 0 0
125125 −31.7490 −0.0227177
126126 0 0
127127 −904.000 −0.631630 −0.315815 0.948821i 0.602278π-0.602278\pi
−0.315815 + 0.948821i 0.602278π0.602278\pi
128128 0 0
129129 0 0
130130 0 0
131131 −666.729 1154.81i −0.444675 0.770200i 0.553355 0.832946i 0.313347π-0.313347\pi
−0.998030 + 0.0627463i 0.980014π0.980014\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 −809.600 + 1402.27i −0.504882 + 0.874481i 0.495102 + 0.868835i 0.335131π0.335131\pi
−0.999984 + 0.00564606i 0.998203π0.998203\pi
138138 0 0
139139 −880.000 −0.536983 −0.268491 0.963282i 0.586525π-0.586525\pi
−0.268491 + 0.963282i 0.586525π0.586525\pi
140140 0 0
141141 0 0
142142 0 0
143143 206.369 357.441i 0.120681 0.209026i
144144 0 0
145145 2016.00 + 3491.81i 1.15462 + 1.99986i
146146 0 0
147147 0 0
148148 0 0
149149 −1285.84 2227.13i −0.706978 1.22452i −0.965973 0.258643i 0.916725π-0.916725\pi
0.258995 0.965879i 0.416609π-0.416609\pi
150150 0 0
151151 −1756.00 + 3041.48i −0.946366 + 1.63915i −0.193373 + 0.981125i 0.561943π0.561943\pi
−0.752993 + 0.658029i 0.771391π0.771391\pi
152152 0 0
153153 0 0
154154 0 0
155155 −3365.40 −1.74397
156156 0 0
157157 161.000 278.860i 0.0818420 0.141755i −0.822199 0.569200i 0.807253π-0.807253\pi
0.904041 + 0.427445i 0.140586π0.140586\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −1702.00 2947.95i −0.817858 1.41657i −0.907257 0.420576i 0.861828π-0.861828\pi
0.0893986 0.995996i 0.471505π-0.471505\pi
164164 0 0
165165 0 0
166166 0 0
167167 2762.16 1.27990 0.639948 0.768418i 0.278956π-0.278956\pi
0.639948 + 0.768418i 0.278956π0.278956\pi
168168 0 0
169169 −1521.00 −0.692308
170170 0 0
171171 0 0
172172 0 0
173173 −1754.13 3038.25i −0.770892 1.33522i −0.937075 0.349129i 0.886478π-0.886478\pi
0.166183 0.986095i 0.446856π-0.446856\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 1801.76 3120.73i 0.752344 1.30310i −0.194340 0.980934i 0.562256π-0.562256\pi
0.946684 0.322164i 0.104410π-0.104410\pi
180180 0 0
181181 −502.000 −0.206151 −0.103076 0.994674i 0.532868π-0.532868\pi
−0.103076 + 0.994674i 0.532868π0.532868\pi
182182 0 0
183183 0 0
184184 0 0
185185 1730.32 2997.00i 0.687653 1.19105i
186186 0 0
187187 630.000 + 1091.19i 0.246365 + 0.426716i
188188 0 0
189189 0 0
190190 0 0
191191 1246.15 + 2158.39i 0.472085 + 0.817675i 0.999490 0.0319393i 0.0101683π-0.0101683\pi
−0.527405 + 0.849614i 0.676835π0.676835\pi
192192 0 0
193193 −655.000 + 1134.49i −0.244290 + 0.423122i −0.961932 0.273290i 0.911888π-0.911888\pi
0.717642 + 0.696412i 0.245221π0.245221\pi
194194 0 0
195195 0 0
196196 0 0
197197 −1174.71 −0.424847 −0.212424 0.977178i 0.568136π-0.568136\pi
−0.212424 + 0.977178i 0.568136π0.568136\pi
198198 0 0
199199 −2296.00 + 3976.79i −0.817885 + 1.41662i 0.0893526 + 0.996000i 0.471520π0.471520\pi
−0.907238 + 0.420618i 0.861813π0.861813\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 −3150.00 5455.96i −1.07320 1.85883i
206206 0 0
207207 0 0
208208 0 0
209209 −1079.47 −0.357264
210210 0 0
211211 −1780.00 −0.580759 −0.290380 0.956911i 0.593782π-0.593782\pi
−0.290380 + 0.956911i 0.593782π0.593782\pi
212212 0 0
213213 0 0
214214 0 0
215215 2063.69 + 3574.41i 0.654615 + 1.13383i
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 −1031.84 + 1787.20i −0.314069 + 0.543984i
222222 0 0
223223 4088.00 1.22759 0.613795 0.789465i 0.289642π-0.289642\pi
0.613795 + 0.789465i 0.289642π0.289642\pi
224224 0 0
225225 0 0
226226 0 0
227227 −2428.80 + 4206.80i −0.710155 + 1.23002i 0.254644 + 0.967035i 0.418042π0.418042\pi
−0.964799 + 0.262989i 0.915292π0.915292\pi
228228 0 0
229229 3191.00 + 5526.97i 0.920818 + 1.59490i 0.798153 + 0.602455i 0.205811π0.205811\pi
0.122664 + 0.992448i 0.460856π0.460856\pi
230230 0 0
231231 0 0
232232 0 0
233233 −1095.34 1897.19i −0.307975 0.533428i 0.669944 0.742411i 0.266318π-0.266318\pi
−0.977919 + 0.208983i 0.932985π0.932985\pi
234234 0 0
235235 −3276.00 + 5674.20i −0.909373 + 1.57508i
236236 0 0
237237 0 0
238238 0 0
239239 5349.71 1.44788 0.723941 0.689862i 0.242329π-0.242329\pi
0.723941 + 0.689862i 0.242329π0.242329\pi
240240 0 0
241241 −2107.00 + 3649.43i −0.563169 + 0.975438i 0.434048 + 0.900890i 0.357085π0.357085\pi
−0.997217 + 0.0745482i 0.976249π0.976249\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 −884.000 1531.13i −0.227723 0.394428i
248248 0 0
249249 0 0
250250 0 0
251251 1428.71 0.359279 0.179640 0.983732i 0.442507π-0.442507\pi
0.179640 + 0.983732i 0.442507π0.442507\pi
252252 0 0
253253 756.000 0.187863
254254 0 0
255255 0 0
256256 0 0
257257 420.674 + 728.630i 0.102105 + 0.176851i 0.912552 0.408961i 0.134109π-0.134109\pi
−0.810447 + 0.585812i 0.800776π0.800776\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 −134.933 + 233.711i −0.0316363 + 0.0547957i −0.881410 0.472352i 0.843405π-0.843405\pi
0.849774 + 0.527148i 0.176738π0.176738\pi
264264 0 0
265265 −7560.00 −1.75248
266266 0 0
267267 0 0
268268 0 0
269269 1373.14 2378.36i 0.311235 0.539074i −0.667395 0.744704i 0.732591π-0.732591\pi
0.978630 + 0.205629i 0.0659242π0.0659242\pi
270270 0 0
271271 3122.00 + 5407.46i 0.699808 + 1.21210i 0.968533 + 0.248886i 0.0800645π0.0800645\pi
−0.268725 + 0.963217i 0.586602π0.586602\pi
272272 0 0
273273 0 0
274274 0 0
275275 1008.03 + 1745.96i 0.221042 + 0.382856i
276276 0 0
277277 −4063.00 + 7037.32i −0.881307 + 1.52647i −0.0314180 + 0.999506i 0.510002π0.510002\pi
−0.849889 + 0.526962i 0.823331π0.823331\pi
278278 0 0
279279 0 0
280280 0 0
281281 3079.65 0.653796 0.326898 0.945060i 0.393997π-0.393997\pi
0.326898 + 0.945060i 0.393997π0.393997\pi
282282 0 0
283283 302.000 523.079i 0.0634348 0.109872i −0.832564 0.553929i 0.813128π-0.813128\pi
0.895999 + 0.444057i 0.146461π0.146461\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −693.500 1201.18i −0.141156 0.244490i
290290 0 0
291291 0 0
292292 0 0
293293 −7667.39 −1.52878 −0.764392 0.644752i 0.776961π-0.776961\pi
−0.764392 + 0.644752i 0.776961π0.776961\pi
294294 0 0
295295 −4536.00 −0.895241
296296 0 0
297297 0 0
298298 0 0
299299 619.106 + 1072.32i 0.119745 + 0.207405i
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 −2555.80 + 4426.77i −0.479818 + 0.831069i
306306 0 0
307307 −1636.00 −0.304142 −0.152071 0.988370i 0.548594π-0.548594\pi
−0.152071 + 0.988370i 0.548594π0.548594\pi
308308 0 0
309309 0 0
310310 0 0
311311 −1635.07 + 2832.03i −0.298124 + 0.516366i −0.975707 0.219081i 0.929694π-0.929694\pi
0.677583 + 0.735447i 0.263028π0.263028\pi
312312 0 0
313313 2519.00 + 4363.04i 0.454896 + 0.787902i 0.998682 0.0513213i 0.0163433π-0.0163433\pi
−0.543787 + 0.839223i 0.683010π0.683010\pi
314314 0 0
315315 0 0
316316 0 0
317317 4936.97 + 8551.09i 0.874725 + 1.51507i 0.857055 + 0.515225i 0.172292π0.172292\pi
0.0176705 + 0.999844i 0.494375π0.494375\pi
318318 0 0
319319 2016.00 3491.81i 0.353838 0.612865i
320320 0 0
321321 0 0
322322 0 0
323323 5397.33 0.929770
324324 0 0
325325 −1651.00 + 2859.62i −0.281788 + 0.488071i
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 −214.000 370.659i −0.0355363 0.0615506i 0.847710 0.530460i 0.177981π-0.177981\pi
−0.883247 + 0.468909i 0.844647π0.844647\pi
332332 0 0
333333 0 0
334334 0 0
335335 −5651.32 −0.921686
336336 0 0
337337 −9106.00 −1.47192 −0.735958 0.677028i 0.763268π-0.763268\pi
−0.735958 + 0.677028i 0.763268π0.763268\pi
338338 0 0
339339 0 0
340340 0 0
341341 1682.70 + 2914.52i 0.267223 + 0.462845i
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 976.282 1690.97i 0.151036 0.261602i −0.780572 0.625065i 0.785072π-0.785072\pi
0.931609 + 0.363463i 0.118406π0.118406\pi
348348 0 0
349349 −1834.00 −0.281294 −0.140647 0.990060i 0.544918π-0.544918\pi
−0.140647 + 0.990060i 0.544918π0.544918\pi
350350 0 0
351351 0 0
352352 0 0
353353 −5246.52 + 9087.25i −0.791060 + 1.37016i 0.134250 + 0.990947i 0.457137π0.457137\pi
−0.925311 + 0.379209i 0.876196π0.876196\pi
354354 0 0
355355 8946.00 + 15494.9i 1.33748 + 2.31658i
356356 0 0
357357 0 0
358358 0 0
359359 −6691.11 11589.3i −0.983685 1.70379i −0.647639 0.761948i 0.724243π-0.724243\pi
−0.336046 0.941845i 0.609090π-0.609090\pi
360360 0 0
361361 1117.50 1935.57i 0.162925 0.282194i
362362 0 0
363363 0 0
364364 0 0
365365 3587.64 0.514481
366366 0 0
367367 104.000 180.133i 0.0147923 0.0256209i −0.858535 0.512756i 0.828625π-0.828625\pi
0.873327 + 0.487135i 0.161958π0.161958\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 −2887.00 5000.43i −0.400759 0.694135i 0.593058 0.805159i 0.297920π-0.297920\pi
−0.993818 + 0.111024i 0.964587π0.964587\pi
374374 0 0
375375 0 0
376376 0 0
377377 6603.80 0.902156
378378 0 0
379379 −12004.0 −1.62692 −0.813462 0.581618i 0.802420π-0.802420\pi
−0.813462 + 0.581618i 0.802420π0.802420\pi
380380 0 0
381381 0 0
382382 0 0
383383 3524.14 + 6103.99i 0.470170 + 0.814359i 0.999418 0.0341086i 0.0108592π-0.0108592\pi
−0.529248 + 0.848467i 0.677526π0.677526\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 603.231 1044.83i 0.0786248 0.136182i −0.824032 0.566543i 0.808280π-0.808280\pi
0.902657 + 0.430361i 0.141614π0.141614\pi
390390 0 0
391391 −3780.00 −0.488907
392392 0 0
393393 0 0
394394 0 0
395395 3492.39 6049.00i 0.444864 0.770527i
396396 0 0
397397 −1735.00 3005.11i −0.219338 0.379904i 0.735268 0.677777i 0.237056π-0.237056\pi
−0.954606 + 0.297872i 0.903723π0.903723\pi
398398 0 0
399399 0 0
400400 0 0
401401 682.604 + 1182.30i 0.0850065 + 0.147236i 0.905394 0.424572i 0.139576π-0.139576\pi
−0.820387 + 0.571808i 0.806242π0.806242\pi
402402 0 0
403403 −2756.00 + 4773.53i −0.340660 + 0.590041i
404404 0 0
405405 0 0
406406 0 0
407407 −3460.64 −0.421469
408408 0 0
409409 5921.00 10255.5i 0.715830 1.23985i −0.246808 0.969064i 0.579382π-0.579382\pi
0.962638 0.270790i 0.0872849π-0.0872849\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 2016.00 + 3491.81i 0.238462 + 0.413028i
416416 0 0
417417 0 0
418418 0 0
419419 3460.64 0.403493 0.201746 0.979438i 0.435338π-0.435338\pi
0.201746 + 0.979438i 0.435338π0.435338\pi
420420 0 0
421421 15518.0 1.79644 0.898220 0.439547i 0.144861π-0.144861\pi
0.898220 + 0.439547i 0.144861π0.144861\pi
422422 0 0
423423 0 0
424424 0 0
425425 −5040.16 8729.81i −0.575255 0.996371i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 3468.58 6007.76i 0.387646 0.671423i −0.604486 0.796616i 0.706621π-0.706621\pi
0.992132 + 0.125192i 0.0399548π0.0399548\pi
432432 0 0
433433 −4006.00 −0.444610 −0.222305 0.974977i 0.571358π-0.571358\pi
−0.222305 + 0.974977i 0.571358π0.571358\pi
434434 0 0
435435 0 0
436436 0 0
437437 1619.20 2804.54i 0.177247 0.307000i
438438 0 0
439439 3752.00 + 6498.65i 0.407912 + 0.706524i 0.994656 0.103249i 0.0329238π-0.0329238\pi
−0.586744 + 0.809773i 0.699590π0.699590\pi
440440 0 0
441441 0 0
442442 0 0
443443 9135.78 + 15823.6i 0.979806 + 1.69707i 0.663066 + 0.748561i 0.269255π0.269255\pi
0.316740 + 0.948512i 0.397412π0.397412\pi
444444 0 0
445445 −1638.00 + 2837.10i −0.174491 + 0.302228i
446446 0 0
447447 0 0
448448 0 0
449449 −8445.24 −0.887651 −0.443826 0.896113i 0.646379π-0.646379\pi
−0.443826 + 0.896113i 0.646379π0.646379\pi
450450 0 0
451451 −3150.00 + 5455.96i −0.328886 + 0.569648i
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 −5107.00 8845.58i −0.522747 0.905424i −0.999650 0.0264683i 0.991574π-0.991574\pi
0.476903 0.878956i 0.341759π-0.341759\pi
458458 0 0
459459 0 0
460460 0 0
461461 1285.84 0.129907 0.0649537 0.997888i 0.479310π-0.479310\pi
0.0649537 + 0.997888i 0.479310π0.479310\pi
462462 0 0
463463 −1408.00 −0.141329 −0.0706645 0.997500i 0.522512π-0.522512\pi
−0.0706645 + 0.997500i 0.522512π0.522512\pi
464464 0 0
465465 0 0
466466 0 0
467467 −5698.95 9870.87i −0.564702 0.978093i −0.997077 0.0763989i 0.975658π-0.975658\pi
0.432375 0.901694i 0.357676π-0.357676\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 2063.69 3574.41i 0.200610 0.347466i
474474 0 0
475475 8636.00 0.834204
476476 0 0
477477 0 0
478478 0 0
479479 5381.46 9320.96i 0.513330 0.889114i −0.486550 0.873653i 0.661745π-0.661745\pi
0.999880 0.0154612i 0.00492166π-0.00492166\pi
480480 0 0
481481 −2834.00 4908.63i −0.268647 0.465311i
482482 0 0
483483 0 0
484484 0 0
485485 −10556.5 18284.5i −0.988347 1.71187i
486486 0 0
487487 −2356.00 + 4080.71i −0.219221 + 0.379702i −0.954570 0.297987i 0.903685π-0.903685\pi
0.735349 + 0.677688i 0.237018π0.237018\pi
488488 0 0
489489 0 0
490490 0 0
491491 −15795.1 −1.45178 −0.725891 0.687810i 0.758572π-0.758572\pi
−0.725891 + 0.687810i 0.758572π0.758572\pi
492492 0 0
493493 −10080.0 + 17459.1i −0.920853 + 1.59496i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 8270.00 + 14324.1i 0.741916 + 1.28504i 0.951622 + 0.307272i 0.0994160π0.0994160\pi
−0.209706 + 0.977764i 0.567251π0.567251\pi
500500 0 0
501501 0 0
502502 0 0
503503 10921.7 0.968137 0.484068 0.875030i 0.339159π-0.339159\pi
0.484068 + 0.875030i 0.339159π0.339159\pi
504504 0 0
505505 3780.00 0.333085
506506 0 0
507507 0 0
508508 0 0
509509 1087.40 + 1883.44i 0.0946922 + 0.164012i 0.909480 0.415747i 0.136480π-0.136480\pi
−0.814788 + 0.579759i 0.803147π0.803147\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 −14318.8 + 24800.9i −1.22517 + 2.12205i
516516 0 0
517517 6552.00 0.557363
518518 0 0
519519 0 0
520520 0 0
521521 5865.63 10159.6i 0.493240 0.854316i −0.506730 0.862105i 0.669146π-0.669146\pi
0.999970 + 0.00778848i 0.00247917π0.00247917\pi
522522 0 0
523523 −7720.00 13371.4i −0.645453 1.11796i −0.984197 0.177079i 0.943335π-0.943335\pi
0.338743 0.940879i 0.389998π-0.389998\pi
524524 0 0
525525 0 0
526526 0 0
527527 −8413.49 14572.6i −0.695441 1.20454i
528528 0 0
529529 4949.50 8572.79i 0.406797 0.704593i
530530 0 0
531531 0 0
532532 0 0
533533 −10318.4 −0.838538
534534 0 0
535535 1386.00 2400.62i 0.112004 0.193996i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 −9523.00 16494.3i −0.756794 1.31081i −0.944477 0.328577i 0.893431π-0.893431\pi
0.187683 0.982230i 0.439902π-0.439902\pi
542542 0 0
543543 0 0
544544 0 0
545545 7207.03 0.566450
546546 0 0
547547 1892.00 0.147890 0.0739452 0.997262i 0.476441π-0.476441\pi
0.0739452 + 0.997262i 0.476441π0.476441\pi
548548 0 0
549549 0 0
550550 0 0
551551 −8635.73 14957.5i −0.667685 1.15646i
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 11826.5 20484.1i 0.899650 1.55824i 0.0717089 0.997426i 0.477155π-0.477155\pi
0.827941 0.560814i 0.189512π-0.189512\pi
558558 0 0
559559 6760.00 0.511480
560560 0 0
561561 0 0
562562 0 0
563563 −3476.52 + 6021.50i −0.260245 + 0.450757i −0.966307 0.257393i 0.917137π-0.917137\pi
0.706062 + 0.708150i 0.250470π0.250470\pi
564564 0 0
565565 −14112.0 24442.7i −1.05079 1.82002i
566566 0 0
567567 0 0
568568 0 0
569569 5508.45 + 9540.92i 0.405846 + 0.702946i 0.994420 0.105498i 0.0336436π-0.0336436\pi
−0.588573 + 0.808444i 0.700310π0.700310\pi
570570 0 0
571571 −3790.00 + 6564.47i −0.277770 + 0.481111i −0.970830 0.239768i 0.922929π-0.922929\pi
0.693060 + 0.720880i 0.256262π0.256262\pi
572572 0 0
573573 0 0
574574 0 0
575575 −6048.19 −0.438655
576576 0 0
577577 3359.00 5817.96i 0.242352 0.419766i −0.719032 0.694977i 0.755415π-0.755415\pi
0.961384 + 0.275211i 0.0887478π0.0887478\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 3780.00 + 6547.15i 0.268528 + 0.465103i
584584 0 0
585585 0 0
586586 0 0
587587 −24288.0 −1.70779 −0.853895 0.520445i 0.825766π-0.825766\pi
−0.853895 + 0.520445i 0.825766π0.825766\pi
588588 0 0
589589 14416.0 1.00849
590590 0 0
591591 0 0
592592 0 0
593593 10056.5 + 17418.4i 0.696410 + 1.20622i 0.969703 + 0.244286i 0.0785537π0.0785537\pi
−0.273293 + 0.961931i 0.588113π0.588113\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 2992.34 5182.89i 0.204113 0.353535i −0.745737 0.666241i 0.767902π-0.767902\pi
0.949850 + 0.312706i 0.101236π0.101236\pi
600600 0 0
601601 −8230.00 −0.558584 −0.279292 0.960206i 0.590100π-0.590100\pi
−0.279292 + 0.960206i 0.590100π0.590100\pi
602602 0 0
603603 0 0
604604 0 0
605605 −8564.30 + 14833.8i −0.575518 + 0.996826i
606606 0 0
607607 −4348.00 7530.96i −0.290741 0.503578i 0.683244 0.730190i 0.260569π-0.260569\pi
−0.973985 + 0.226612i 0.927235π0.927235\pi
608608 0 0
609609 0 0
610610 0 0
611611 5365.58 + 9293.46i 0.355267 + 0.615341i
612612 0 0
613613 2897.00 5017.75i 0.190879 0.330612i −0.754663 0.656113i 0.772200π-0.772200\pi
0.945542 + 0.325501i 0.105533π0.105533\pi
614614 0 0
615615 0 0
616616 0 0
617617 13493.3 0.880423 0.440212 0.897894i 0.354903π-0.354903\pi
0.440212 + 0.897894i 0.354903π0.354903\pi
618618 0 0
619619 9668.00 16745.5i 0.627770 1.08733i −0.360228 0.932864i 0.617301π-0.617301\pi
0.987998 0.154466i 0.0493656π-0.0493656\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 7685.50 + 13311.7i 0.491872 + 0.851947i
626626 0 0
627627 0 0
628628 0 0
629629 17303.2 1.09686
630630 0 0
631631 632.000 0.0398725 0.0199362 0.999801i 0.493654π-0.493654\pi
0.0199362 + 0.999801i 0.493654π0.493654\pi
632632 0 0
633633 0 0
634634 0 0
635635 −7175.28 12427.9i −0.448413 0.776674i
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 9445.33 16359.8i 0.582010 1.00807i −0.413231 0.910626i 0.635600π-0.635600\pi
0.995241 0.0974442i 0.0310668π-0.0310668\pi
642642 0 0
643643 28460.0 1.74549 0.872747 0.488173i 0.162336π-0.162336\pi
0.872747 + 0.488173i 0.162336π0.162336\pi
644644 0 0
645645 0 0
646646 0 0
647647 5127.47 8881.03i 0.311563 0.539644i −0.667138 0.744934i 0.732481π-0.732481\pi
0.978701 + 0.205291i 0.0658141π0.0658141\pi
648648 0 0
649649 2268.00 + 3928.29i 0.137175 + 0.237595i
650650 0 0
651651 0 0
652652 0 0
653653 2984.41 + 5169.15i 0.178850 + 0.309777i 0.941487 0.337050i 0.109429π-0.109429\pi
−0.762637 + 0.646827i 0.776096π0.776096\pi
654654 0 0
655655 10584.0 18332.0i 0.631376 1.09357i
656656 0 0
657657 0 0
658658 0 0
659659 8048.38 0.475751 0.237876 0.971296i 0.423549π-0.423549\pi
0.237876 + 0.971296i 0.423549π0.423549\pi
660660 0 0
661661 6089.00 10546.5i 0.358298 0.620589i −0.629379 0.777098i 0.716691π-0.716691\pi
0.987677 + 0.156509i 0.0500240π0.0500240\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 6048.00 + 10475.4i 0.351094 + 0.608112i
668668 0 0
669669 0 0
670670 0 0
671671 5111.59 0.294085
672672 0 0
673673 12902.0 0.738983 0.369491 0.929234i 0.379532π-0.379532\pi
0.369491 + 0.929234i 0.379532π0.379532\pi
674674 0 0
675675 0 0
676676 0 0
677677 7040.34 + 12194.2i 0.399679 + 0.692264i 0.993686 0.112196i 0.0357884π-0.0357884\pi
−0.594008 + 0.804459i 0.702455π0.702455\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 −9977.13 + 17280.9i −0.558952 + 0.968133i 0.438632 + 0.898667i 0.355463π0.355463\pi
−0.997584 + 0.0694666i 0.977870π0.977870\pi
684684 0 0
685685 −25704.0 −1.43372
686686 0 0
687687 0 0
688688 0 0
689689 −6191.06 + 10723.2i −0.342323 + 0.592921i
690690 0 0
691691 −1084.00 1877.54i −0.0596777 0.103365i 0.834643 0.550791i 0.185674π-0.185674\pi
−0.894321 + 0.447426i 0.852341π0.852341\pi
692692 0 0
693693 0 0
694694 0 0
695695 −6984.78 12098.0i −0.381220 0.660293i
696696 0 0
697697 15750.0 27279.8i 0.855916 1.48249i
698698 0 0
699699 0 0
700700 0 0
701701 30987.0 1.66956 0.834782 0.550581i 0.185594π-0.185594\pi
0.834782 + 0.550581i 0.185594π0.185594\pi
702702 0 0
703703 −7412.00 + 12838.0i −0.397651 + 0.688752i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 9647.00 + 16709.1i 0.511002 + 0.885082i 0.999919 + 0.0127514i 0.00405901π0.00405901\pi
−0.488916 + 0.872331i 0.662608π0.662608\pi
710710 0 0
711711 0 0
712712 0 0
713713 −10096.2 −0.530302
714714 0 0
715715 6552.00 0.342701
716716 0 0
717717 0 0
718718 0 0
719719 14160.1 + 24525.9i 0.734466 + 1.27213i 0.954957 + 0.296744i 0.0959007π0.0959007\pi
−0.220491 + 0.975389i 0.570766π0.570766\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 −16128.5 + 27935.4i −0.826203 + 1.43103i
726726 0 0
727727 15860.0 0.809099 0.404549 0.914516i 0.367428π-0.367428\pi
0.404549 + 0.914516i 0.367428π0.367428\pi
728728 0 0
729729 0 0
730730 0 0
731731 −10318.4 + 17872.0i −0.522081 + 0.904270i
732732 0 0
733733 −19249.0 33340.2i −0.969956 1.68001i −0.695664 0.718367i 0.744890π-0.744890\pi
−0.274293 0.961646i 0.588444π-0.588444\pi
734734 0 0
735735 0 0
736736 0 0
737737 2825.66 + 4894.19i 0.141227 + 0.244613i
738738 0 0
739739 13178.0 22825.0i 0.655968 1.13617i −0.325682 0.945479i 0.605594π-0.605594\pi
0.981650 0.190691i 0.0610728π-0.0610728\pi
740740 0 0
741741 0 0
742742 0 0
743743 9000.85 0.444427 0.222213 0.974998i 0.428672π-0.428672\pi
0.222213 + 0.974998i 0.428672π0.428672\pi
744744 0 0
745745 20412.0 35354.6i 1.00381 1.73865i
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 8900.00 + 15415.3i 0.432444 + 0.749015i 0.997083 0.0763227i 0.0243179π-0.0243179\pi
−0.564639 + 0.825338i 0.690985π0.690985\pi
752752 0 0
753753 0 0
754754 0 0
755755 −55751.3 −2.68741
756756 0 0
757757 2882.00 0.138373 0.0691863 0.997604i 0.477960π-0.477960\pi
0.0691863 + 0.997604i 0.477960π0.477960\pi
758758 0 0
759759 0 0
760760 0 0
761761 4198.81 + 7272.55i 0.200009 + 0.346425i 0.948531 0.316684i 0.102570π-0.102570\pi
−0.748522 + 0.663110i 0.769236π0.769236\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 −3714.63 + 6433.94i −0.174873 + 0.302889i
768768 0 0
769769 −40630.0 −1.90527 −0.952637 0.304111i 0.901641π-0.901641\pi
−0.952637 + 0.304111i 0.901641π0.901641\pi
770770 0 0
771771 0 0
772772 0 0
773773 −2262.12 + 3918.10i −0.105256 + 0.182308i −0.913843 0.406068i 0.866899π-0.866899\pi
0.808587 + 0.588377i 0.200233π0.200233\pi
774774 0 0
775775 −13462.0 23316.9i −0.623960 1.08073i
776776 0 0
777777 0 0
778778 0 0
779779 13493.3 + 23371.1i 0.620602 + 1.07491i
780780 0 0
781781 8946.00 15494.9i 0.409876 0.709926i
782782 0 0
783783 0 0
784784 0 0
785785 5111.59 0.232408
786786 0 0
787787 3248.00 5625.70i 0.147114 0.254809i −0.783046 0.621964i 0.786335π-0.786335\pi
0.930160 + 0.367155i 0.119668π0.119668\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 4186.00 + 7250.36i 0.187452 + 0.324676i
794794 0 0
795795 0 0
796796 0 0
797797 2301.80 0.102301 0.0511506 0.998691i 0.483711π-0.483711\pi
0.0511506 + 0.998691i 0.483711π0.483711\pi
798798 0 0
799799 −32760.0 −1.45052
800800 0 0
801801 0 0
802802 0 0
803803 −1793.82 3106.99i −0.0788325 0.136542i
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 3746.38 6488.93i 0.162813 0.282001i −0.773063 0.634329i 0.781277π-0.781277\pi
0.935877 + 0.352328i 0.114610π0.114610\pi
810810 0 0
811811 38864.0 1.68274 0.841368 0.540462i 0.181751π-0.181751\pi
0.841368 + 0.540462i 0.181751π0.181751\pi
812812 0 0
813813 0 0
814814 0 0
815815 27018.4 46797.3i 1.16124 2.01133i
816816 0 0
817817 −8840.00 15311.3i −0.378546 0.655662i
818818 0 0
819819 0 0
820820 0 0
821821 7857.88 + 13610.2i 0.334034 + 0.578564i 0.983299 0.181999i 0.0582566π-0.0582566\pi
−0.649265 + 0.760562i 0.724923π0.724923\pi
822822 0 0
823823 −18208.0 + 31537.2i −0.771192 + 1.33574i 0.165718 + 0.986173i 0.447006π0.447006\pi
−0.936910 + 0.349570i 0.886328π0.886328\pi
824824 0 0
825825 0 0
826826 0 0
827827 24684.9 1.03794 0.518970 0.854792i 0.326316π-0.326316\pi
0.518970 + 0.854792i 0.326316π0.326316\pi
828828 0 0
829829 8651.00 14984.0i 0.362439 0.627762i −0.625923 0.779885i 0.715278π-0.715278\pi
0.988362 + 0.152123i 0.0486109π0.0486109\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 21924.0 + 37973.5i 0.908636 + 1.57380i
836836 0 0
837837 0 0
838838 0 0
839839 29240.8 1.20323 0.601613 0.798788i 0.294525π-0.294525\pi
0.601613 + 0.798788i 0.294525π0.294525\pi
840840 0 0
841841 40123.0 1.64513
842842 0 0
843843 0 0
844844 0 0
845845 −12072.6 20910.3i −0.491490 0.851285i
846846 0 0
847847 0 0
848848 0 0
849849 0 0
850850 0 0
851851 5190.96 8991.01i 0.209100 0.362172i
852852 0 0
853853 −82.0000 −0.00329147 −0.00164574 0.999999i 0.500524π-0.500524\pi
−0.00164574 + 0.999999i 0.500524π0.500524\pi
854854 0 0
855855 0 0
856856 0 0
857857 −5325.90 + 9224.72i −0.212286 + 0.367690i −0.952430 0.304759i 0.901424π-0.901424\pi
0.740144 + 0.672449i 0.234758π0.234758\pi
858858 0 0
859859 −12754.0 22090.6i −0.506590 0.877440i −0.999971 0.00762634i 0.997572π-0.997572\pi
0.493381 0.869813i 0.335761π-0.335761\pi
860860 0 0
861861 0 0
862862 0 0
863863 −17088.9 29598.9i −0.674059 1.16750i −0.976743 0.214414i 0.931216π-0.931216\pi
0.302684 0.953091i 0.402117π-0.402117\pi
864864 0 0
865865 27846.0 48230.7i 1.09456 1.89583i
866866 0 0
867867 0 0
868868 0 0
869869 −6984.78 −0.272661
870870 0 0
871871 −4628.00 + 8015.93i −0.180039 + 0.311836i
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 −5419.00 9385.98i −0.208651 0.361394i 0.742639 0.669692i 0.233574π-0.233574\pi
−0.951290 + 0.308298i 0.900240π0.900240\pi
878878 0 0
879879 0 0
880880 0 0
881881 6175.18 0.236149 0.118074 0.993005i 0.462328π-0.462328\pi
0.118074 + 0.993005i 0.462328π0.462328\pi
882882 0 0
883883 22100.0 0.842270 0.421135 0.906998i 0.361632π-0.361632\pi
0.421135 + 0.906998i 0.361632π0.361632\pi
884884 0 0
885885 0 0
886886 0 0
887887 10366.1 + 17954.5i 0.392399 + 0.679655i 0.992765 0.120070i 0.0383119π-0.0383119\pi
−0.600366 + 0.799725i 0.704979π0.704979\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 14033.1 24306.0i 0.525866 0.910827i
894894 0 0
895895 57204.0 2.13645
896896 0 0
897897 0 0
898898 0 0
899899 −26923.2 + 46632.3i −0.998819 + 1.73000i
900900 0 0
901901 −18900.0 32735.8i −0.698835 1.21042i
902902 0 0
903903 0 0
904904 0 0
905905 −3984.50 6901.36i −0.146353 0.253491i
906906 0 0
907907 −3406.00 + 5899.37i −0.124691 + 0.215970i −0.921612 0.388113i 0.873127π-0.873127\pi
0.796921 + 0.604083i 0.206460π0.206460\pi
908908 0 0
909909 0 0
910910 0 0
911911 −11636.0 −0.423182 −0.211591 0.977358i 0.567864π-0.567864\pi
−0.211591 + 0.977358i 0.567864π0.567864\pi
912912 0 0
913913 2016.00 3491.81i 0.0730776 0.126574i
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 584.000 + 1011.52i 0.0209623 + 0.0363078i 0.876316 0.481736i 0.159994π-0.159994\pi
−0.855354 + 0.518044i 0.826660π0.826660\pi
920920 0 0
921921 0 0
922922 0 0
923923 29304.3 1.04503
924924 0 0
925925 27686.0 0.984119
926926 0 0
927927 0 0
928928 0 0
929929 −4817.91 8344.87i −0.170151 0.294711i 0.768321 0.640064i 0.221092π-0.221092\pi
−0.938473 + 0.345354i 0.887759π0.887759\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 −10000.9 + 17322.1i −0.349803 + 0.605876i
936936 0 0
937937 −32254.0 −1.12454 −0.562269 0.826954i 0.690071π-0.690071\pi
−0.562269 + 0.826954i 0.690071π0.690071\pi
938938 0 0
939939 0 0
940940 0 0
941941 −2055.75 + 3560.66i −0.0712173 + 0.123352i −0.899435 0.437054i 0.856022π-0.856022\pi
0.828218 + 0.560406i 0.189355π0.189355\pi
942942 0 0
943943 −9450.00 16367.9i −0.326335 0.565230i
944944 0 0
945945 0 0
946946 0 0
947947 3436.83 + 5952.77i 0.117932 + 0.204265i 0.918948 0.394378i 0.129040π-0.129040\pi
−0.801016 + 0.598643i 0.795707π0.795707\pi
948948 0 0
949949 2938.00 5088.77i 0.100497 0.174066i
950950 0 0
951951 0 0
952952 0 0
953953 −33971.4 −1.15471 −0.577357 0.816492i 0.695916π-0.695916\pi
−0.577357 + 0.816492i 0.695916π0.695916\pi
954954 0 0
955955 −19782.0 + 34263.4i −0.670294 + 1.16098i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −7576.50 13122.9i −0.254322 0.440498i
962962 0 0
963963 0 0
964964 0 0
965965 −20795.6 −0.693714
966966 0 0
967967 43952.0 1.46163 0.730817 0.682573i 0.239139π-0.239139\pi
0.730817 + 0.682573i 0.239139π0.239139\pi
968968 0 0
969969 0 0
970970 0 0
971971 −1968.44 3409.44i −0.0650569 0.112682i 0.831662 0.555282i 0.187390π-0.187390\pi
−0.896719 + 0.442600i 0.854056π0.854056\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 6079.94 10530.8i 0.199094 0.344840i −0.749141 0.662410i 0.769534π-0.769534\pi
0.948235 + 0.317570i 0.102867π0.102867\pi
978978 0 0
979979 3276.00 0.106947
980980 0 0
981981 0 0
982982 0 0
983983 19716.1 34149.4i 0.639722 1.10803i −0.345771 0.938319i 0.612383π-0.612383\pi
0.985494 0.169713i 0.0542840π-0.0542840\pi
984984 0 0
985985 −9324.00 16149.6i −0.301612 0.522406i
986986 0 0
987987 0 0
988988 0 0
989989 6191.06 + 10723.2i 0.199054 + 0.344771i
990990 0 0
991991 −5380.00 + 9318.43i −0.172453 + 0.298698i −0.939277 0.343160i 0.888503π-0.888503\pi
0.766824 + 0.641858i 0.221836π0.221836\pi
992992 0 0
993993 0 0
994994 0 0
995995 −72895.7 −2.32256
996996 0 0
997997 4985.00 8634.27i 0.158352 0.274273i −0.775923 0.630828i 0.782715π-0.782715\pi
0.934274 + 0.356555i 0.116049π0.116049\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 1764.4.k.v.361.2 4
3.2 odd 2 inner 1764.4.k.v.361.1 4
7.2 even 3 inner 1764.4.k.v.1549.2 4
7.3 odd 6 1764.4.a.s.1.2 2
7.4 even 3 252.4.a.f.1.1 2
7.5 odd 6 1764.4.k.u.1549.1 4
7.6 odd 2 1764.4.k.u.361.1 4
21.2 odd 6 inner 1764.4.k.v.1549.1 4
21.5 even 6 1764.4.k.u.1549.2 4
21.11 odd 6 252.4.a.f.1.2 yes 2
21.17 even 6 1764.4.a.s.1.1 2
21.20 even 2 1764.4.k.u.361.2 4
28.11 odd 6 1008.4.a.bc.1.1 2
84.11 even 6 1008.4.a.bc.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.4.a.f.1.1 2 7.4 even 3
252.4.a.f.1.2 yes 2 21.11 odd 6
1008.4.a.bc.1.1 2 28.11 odd 6
1008.4.a.bc.1.2 2 84.11 even 6
1764.4.a.s.1.1 2 21.17 even 6
1764.4.a.s.1.2 2 7.3 odd 6
1764.4.k.u.361.1 4 7.6 odd 2
1764.4.k.u.361.2 4 21.20 even 2
1764.4.k.u.1549.1 4 7.5 odd 6
1764.4.k.u.1549.2 4 21.5 even 6
1764.4.k.v.361.1 4 3.2 odd 2 inner
1764.4.k.v.361.2 4 1.1 even 1 trivial
1764.4.k.v.1549.1 4 21.2 odd 6 inner
1764.4.k.v.1549.2 4 7.2 even 3 inner